Step-by-step explanation:
We can not exactly predict the values of mean and median of the data un till and unless we know about the skewness of the data.
Skewness represents the asymmetry or tapering in the distribution of data sample. If skewness is
Negative skew: median > mean:
Positive skew: mean > median :
Although this generalization is not always true.
jonesville and smithville each have a population of size 2600 at time t = 0, where t is measured in years. Suppose jonesville's population grows by 170 people per year. Suppose the population of smithville grows by 7% per year.
1. Which is true? (Circle one)
A. Both towns are growing exponentially.
B. Jonesville is growing linearly and Smithville is growing exponentially.
C. Jo nesville is growing exponentially and Smithville is growing linearly
D. Both towns are growing linearly.
Answer: B. Jonesville is growing linearly and Smithville is growing exponentially.
Step-by-step explanation:
Linear growth :
Population grow by a constant amount after each time period.The rate of change of dependent variable with respect to independent variable is a constant.It is represented by line on graph.Equation for linear growth : [tex]y=mx+c[/tex] , c = initial value and m is the rate of change of y with respect to x.Exponential growth :
Population grow by a constant ratio .It is represented by a curve on graph.Equation for exponential growth : [tex]y=a(1+r)^x[/tex] , a = initial value and r is rate of growth ( in decimal ) and x is time period.Given : Jonesville's population grows by 170 people per year.
i.e .Population grow by a constant amount per year.
⇒ Jonesville is growing linearly.
The population of smithville grows by 7% per year.
i.e. Population grow by a constant ratio.
⇒Smithville is growing exponentially.
Hence, the true statement is "B. Jonesville is growing linearly and Smithville is growing exponentially."
Final answer:
Jonesville is experiencing linear growth with a constant increase of 170 people per year, while Smithville is experiencing exponential growth, with its population growing by 7% yearly. The correct answer is B, signifying two different types of growth for the towns.
Explanation:
The correct answer to the question is B: Jonesville is growing linearly and Smithville is growing exponentially. This can be determined by looking at the type of growth each town is experiencing. Jonesville's population increases by a fixed amount each year (170 people), which is characteristic of linear growth. Conversely, Smithville's population increases by a percentage (7%) of the population each year, which is a key feature of exponential growth as the rate of growth increases with an increasing population base.
Linear growth occurs when a quantity increases by the same fixed amount over equal increments of time. In the case of Jonesville, it grows by 170 people every year, resulting in a straight line if graphed over time. On the other hand, exponential growth refers to an increase that is proportional to the quantity's current value, leading to faster and faster growth as time goes on. For Smithville, a 7% growth rate implies that each year the town will grow by 7% of its population at the end of the previous year, meaning the actual number of people added each year will continue to increase as the population grows.
Determine whether the underlined value is a parameter or a statistic. The average age of men who had walked on the moon was 39 years, 11 months, 15 days.
Is the value a parameter or a statistic?
A. The value is a parameter because the men who had walked on the moon are a population.
B. The value is a parameter because the men who had walked on the moon are a sample.
C. The value is a statistic because the men who had walked on the moon are a sample.
D. The value is a statistic because the men who had walked on the moon are a population.
Answer:
A. The value is a parameter because the men who had walked on the moon are a population.
Correct option the value reported represent the mean for all the individuals in the population of interest and for this reason represent a parameter.
Step-by-step explanation:
For this case we know that the average age of men who had walked on the moon was 39 years, 11 months, 15 days.
So then we need to assume that this value was calculated from the average of all the mean who walked on the moon, so then we have a population represented by a parameter.
And let's analyze one by one the possible options given:
A. The value is a parameter because the men who had walked on the moon are a population.
Correct option the value reported represent the mean for all the individuals in the population of interest and for this reason represent a parameter.
B. The value is a parameter because the men who had walked on the moon are a sample.
The value represent a parameter but the reason is not because represent a sample, is a parameter because represent the population of interest.
C. The value is a statistic because the men who had walked on the moon are a sample.
False the men who had walked on the moon are a population since they know the information about the men who walked on the moon and not represent a sample for this case.
D. The value is a statistic because the men who had walked on the moon are a population.
False the men who had walked on the moon are a population since they know the information about the men who walked on the moon, and if is a population then can't be a statistic.
The average age of men who had walked on the moon represents a parameter because it describes a characteristic of a specific population: all men who have walked on the moon.
Explanation:In the context of statistical study, a parameter refers to a characteristic of a population, while a statistic is a measure that describes a sample. In this case, the group referred to is 'all men who had walked on the moon,' which is a population, not a sample, because it includes every individual of interest that fits a specific criteria. Therefore, the average age of men who walked on the moon is a parameter, not a statistic. So, the correct response is:
A. The value is a parameter because the men who had walked on the moon are a population.
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Billy is walking from the front door of his house to his bus stop, which is 960 feet away from his front door. As Billy walks out his front door, he walks in a straight path toward his bus stop at a constant rate of 7.5 feet per second.
(A) Illustrate the situation with a diagram and define variables to represent the values of the relevant varying quantitities. (Label the variables on your picture.)
(B) Define a function f to determine Billy's distance from his bus stop in terms of the number of seconds he has been walking.
(C) What is the independent quantity and what is the domain of f (the values the independent quantity can take on)?
(D) What is the dependent quantity and what is the range of f (the values the dependent quantity can take on)?
(E) What do each of the following represent: f(0) and f(60.25)?
Answer:
b) 690 - 7.5*t
c) 0 < t < 92s time (t) is independent quantity
d) 0 < s < 690ft distance from bus stop (s) is dependent quantity
e) f(0) = 690 ft away from bus stop , f(60.25) = 238.125 ft away from bus stop
Step-by-step explanation:
Part a - see diagram
part b
initial distance from bus stop s0 = 690 ft
distance covered = 7.5*t
s = s0 - distance covered
s = 690 - 7.5*t = f(t)
part c
s = 0 or s = 690
0 = 690 -7.5*t
t = 92 s
Hence domain : 0 < t < 92s time (t) is independent quantity
part d
s = 0 or s = 690
Hence range : 0 < s < 690ft distance from bus stop (s) is dependent quantity because it depends on time (t)
part e
f(0) is s @t = 0
f(0) = 690 ft away from bus stop
f(60.25) is s @t = 60.25
f(60.25) = 690 - 7.5*60.25 = 238.125 ft away from bus stop.
Determine whether the statement is true or false. You toss a coin and roll a die. The event "tossing tails and rolling a 4 or 6" is a simple event.
Answer: False.
Step-by-step explanation:
The probability for any event = [tex]\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
Definition : A simple event is an event that has only one possible favorable outcomes.
If we toss a coin and roll a die .
The possible outcomes for event "tossing tails and rolling a 4 or 6" = {(T, 4) , (T,6)}
Since this event has 2 possible favorable outcomes , Therefore it is not an simple event.
Hence, the given statement is "false".
The statement 'tossing tails and rolling a 4 or 6' is not a simple event. A simple event only consists of a single outcome, whereas this case includes multiple outcomes: getting tails in the coin toss and either a 4 or 6 in the die roll. As such, the statement is false.
Explanation:The statement 'tossing tails and rolling a 4 or 6' is false. This is because it is not a simple event. In probability theory, a simple event is an event that consists of a single outcome. However, in this case, there are multiple outcomes - getting a tails on the coin toss, and getting either a 4 or 6 on the die roll.
For example, the possible sets are: {Tails, 4} and {Tails, 6}. This indicates that there are multiple outcomes within this event, thus it cannot be considered a simple event.
Hence, the given statement is false because a single outcome in this scenario could only be {Tails, 4} or {Tails, 6}, not both of them combined.
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Suppose you toss a fair coin 10,000 times. Should you expect to get exactly 5000 heads? Why or why not? What does the law of large numbers tell you about the results you are likely to get? a. You shouldn't expect to get exactly 5000 heads, because you cannot predict precisely how many heads will occur. b. You should expect to get exactly 5000 heads, because the proportion of heads should be 50% for such a large number of tosses. c. You should expect to get exactly 5000 heads, because for a fair coin, the proportion of heads is exactly 50%. d. You shouldn't expect to get exactly 5000 heads, because it is not easy to count precisely the number of heads that occurred.
The answer is:
You shouldn't expect to get exactly 5000 heads, because you cannot predict precisely how many heads will occur.
The outcome in tossing a fair coin is based on chance.
However, according to the law of large numbers, the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances.
For example, in the case of a fair coin, where both head and tail have equal probability of occurrence, as the number of tosses becomes sufficiently large (say 1 million tosses), the ratio heads to tails in the outcome will be extremely close to 1:1.
So according to the law, we should expect to approach a point where half of the outcomes are heads and the other half are tails, as the number of tosses become very large.
The answer is (a). You should not expect to get exactly 5000 heads, because you cannot predict precisely how many heads will occur.
The law of large numbers states that as the number of independent trials of a random experiment increases, the observed frequency of each outcome approaches the expected frequency. In other words, the more times you toss a fair coin, the closer the proportion of heads will get to 50%.
However, the law of large numbers does not guarantee that you will get exactly 5000 heads even if you toss a fair coin 10,000 times. It is still possible to get more or fewer than 5000 heads, even though it is unlikely.
For example, if you toss a fair coin 100 times, you might get 55 heads and 45 tails. This is within the normal range of variation, even though it is not exactly 50 heads and 50 tails.
As the number of tosses increases, the probability of getting exactly 50/50 heads and tails decreases. However, the probability of getting close to 50/50 heads and tails increases.
In conclusion, you should not expect to get exactly 5000 heads even if you toss a fair coin 10,000 times. However, you can expect the proportion of heads to be close to 50%.
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Suppose the reaction temperature X (in deg C) in a certainchemical process has uniform distribution with A= -5 and B=5.
a. Compute P(X<0)
b. Compute P(-2.5
c. Compute P(-2
Answer:
Step-by-step explanation:
Given that the reaction temperature X (in deg C) in a certainchemical process has uniform distribution with A= -5 and B=5
Thus the pdf of X would be
[tex]f(x) = 0.1 , -5\leq x\leq 5[/tex]
the cumulative probability
[tex]F(x) = \frac{x-a}{10} ,-5\leq x\leq 5[/tex]
a) P(X<0) = F(0) = [tex]\frac{0-(-5)}{10} =0.5[/tex]
b) P(x<-2.5) = F(-2.5)
= [tex]\frac{0-(-2,5)}{10} =0.25[/tex]
c) P(X>-2) = 1-F(-2)
=1-0.2 = 0.8
With its radar, an aircraft spots another aircraft 8000 feet away at a 12 degree angle of depression Determine the vertical distance and horizontal distance between the two aircraft.
Answer:the vertical distance is 1663.2 feet.
The horizontal distance is 7824.8 feet.
Step-by-step explanation:.
The vertical distance between the two aircrafts is represented by x.
To determine x, we would apply trigonometric ratio
Sin θ = opposite side/hypotenuse
Sine 12 = x/8000
x = 8000Sin12 = 8000 × 0.2079
x = 1663.2 feet
The horizontal distance between the two aircrafts is represented by y.
To determine y, we would apply trigonometric ratio
Cos θ = opposite side/hypotenuse
Cos 12 = y/8000
x = 8000Cos12 = 8000 × 0.9781
x = 7824.8 feet
One tire manufacturer claims that his tires last an average of 42,000 miles with a standard deviation of 7800 miles. A random sample of 100 of his tires is taken. What is the probability that the average of these 100 tires will last greater than 41,000 miles?
Answer:
89.97% probability that the average of these 100 tires will last greater than 41,000 miles.
Step-by-step explanation:
The solve this problem, it is important to know the Normal Probability distribution and the Central Limit Theorem.
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]\mu = 42000, \sigma = 7800, n = 100, s = \frac{7800}{\sqrt{100}} = 780[/tex]
What is the probability that the average of these 100 tires will last greater than 41,000 miles?
This is 1 subtracted by the pvalue of Z when X = 41000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem, we use s instead of [tex]\sigma[/tex].
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{41000 - 42000}{780}[/tex]
[tex]Z = -1.28[/tex]
[tex]Z = -1.28[/tex] has a pvalue of 0.1003.
So there is a 1-0.1003 = 0.8997 = 89.97% probability that the average of these 100 tires will last greater than 41,000 miles.
A wire 6 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures?
Give the length of wire used for each:
For the square:
For the circle:
(for both, include units)
Where should the wire be cut to maximize the total area? Again, give the length of wire used for each:For the square:For the circle:(for both, include units)
Answer:
Used wire in circle x = 2.64 m
Used in square L - x = 3.36 m
Total wire used 6 m
Step-by-step explanation:
We have a wire of 6 meters long.
We will cut it a distance x from one end, to get two pieces
x and 6 - x
We are going to use the piece x to get the circle then
So Perimetr of a circle is 2π*r (r is the radius of the circle) then:
x = 2*π*r ⇒ r = x/2*π
And area would be A(c) = π* (x/2*π)² ⇒ A(c) = x²/4π
From 6 - x we will get a square, and as the perimeter is 4 times the side
we have
( 6 - x )/ 4 is the side of the square
And the area is A(s) = [( 6 - x ) /4]²
Total area as function of x is
A(t) = A(c) + A(s)
A(x) = x²/4π + [ ( 6 - x ) / 4 ]²
A(x) = x²/4π + (36 + x² - 12x) /16
A(x) = 1 / 16π [ 4x² + 36π + πx² - 12π x ]
Taking drivatives on both sides of the equation we get:
A´(x) = 1/ 16π [8x +2πx - 12π]
A´(x) = 0 ⇒ 1/ 16π [8x +2πx - 12π] = 0
[8x +2πx - 12π] = 0
8x + 6.28x - 37.68 = 0
14.28x - 37.68 = 0 ⇒ x = 37.68 /14.28
x = 2.64 m length of wire used in the circle
Then the length L for the side of the square is
(6 - x )/4 ⇒ ( 6 - 2.64 )/ 4 ⇒ 3.36 / 4
L = 0.84 m total length of wire used in the square is
3.36 m
And total length of wire used is 6 m
The function is a quadratic function and "a" coefficient is positive then is open upward parabola there is not a maximun
Answer:
Wire used in circle , x = 2.64 m
Wire used in square, L - x = 3.36 m
Total used wire is 6 m
Step-by-step explanation:
We have a wire of 6 metres long.
We will cut it a distance x metre from one end, to get two pieces x metre and 6 - x metres.
We are going to use the piece of x metre to get the circle
So, Perimeter of the circle is [tex]2\pi r[/tex] (r is the radius of the circle) then
[tex]x = 2\pi r[/tex] ⇒ [tex]r = \frac{x}{2} \pi[/tex]
And area would be [tex]A(c) =\pi (\frac{x}{2} \pi )^{2}[/tex]⇒[tex]A(c) = \frac{x^{2} }{4\pi }[/tex]
From [tex]6 - x[/tex] we will get the square, and as the perimeter is 4 times the side
we have
[tex]\frac{6 - x}{4}[/tex] is the side of the square
and the area is [tex]A(s) = (\frac{6 - x}{4}) ^{2}[/tex]
Total area of the function of x is
[tex]A(t) = A(c) + A(s)[/tex]
[tex]A(x) = \frac{x^{2} }{4\pi } +(\frac{6 - x}{4} )^{2}\\A(x) = \frac{x^{2} }{4\pi } + \frac{36+x^{2} -12x}{16} \\A(x) = \frac{1}{16\pi } (4x^{2} +36\pi +\pi x^{2} -12\pi x)[/tex]
Taking derivative on the both side of the equation we get :
[tex]A^{'} = \frac{1}{16\pi } (8x+2\pi x-12\pi )\\[/tex]
[tex]A^{'} = 0[/tex]
[tex]\frac{1}{16\pi } (8x+2\pi x-12\pi ) = 0\\(8x+2\pi x-12\pi ) = 0\\8x + 6.28x-37.68=0\\14.28x-37.68=0\\x=2.64 m[/tex]
length of wire used in the circle is x = 2.64 m
Then the length L of the wire used in the square is
[tex]\frac{6 - x}{4}[/tex] ⇒[tex]\frac{6 - 2.64}{4}[/tex] ⇒ [tex]\frac{3.36}{4}[/tex]
L = 0.84 m
Total length of the wire used in the square is 4L = 3.36 m
And total length of the wire used is 6 m
The function is a quadratic function and "a" coefficient is positive then is open upward parabola there is not a maximum.
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and the level of measurement for the educationeducation of the respondents in a survey classified as Institutional comma Autodidactic comma or OtherInstitutional, Autodidactic, or Other. Explain your choice.
The Question is understood as asking for [the Level of] Education of the respondents in a survey classified as [with values] Institutional, Autodidactic, or Other.
Answer:
The level of measurement is the Nominal Scale.
Step-by-step explanation:
The variable studied here is Education (of the respondents), and it is measured using three categories: Institutional, Autodidactic or Other.
As can be seen, the variable Education is measured using those categories that act as labels. These labels are simply names and they have neither relation in order to the other categories ---that is, no value is higher or lower than other--- and nor numerical meaning at all, as it is with other levels of measurement like Ordinal, Interval or Ratio.
For instance, having an Institutional value is not saying that it represents a higher value than having Autodidactic value or Other value. Moreover, if we substituted Institutional, Audidactic and Other by 0, 1, or 2, these values have no numerical value but are a way to classify the different possible values for the Education variable.
In other words, they represent only a way to classify values for the Education variable. No more than this.
As a result, the level of measurement for the variable Education is the Nominal Scale.
As part of the National Health and Nutrition Examination Survey, subjects were asked how long they slept the preceding night, and the following times (hours) were reported: 8, 7, 5, 7, 4, 7, 6, 7, 8, 8, 8, 6
The standard deviation is 1.3 hours.
What is the variance?
Final answer:
The variance for the given data is 1.69 hours squared.
Explanation:
To find the variance, we need to square the standard deviation. The standard deviation is given as 1.3 hours, so when we square it, we get 1.69 hours squared. Therefore, the variance for the given data is 1.69 hours squared.
How many possible birth orders with respect to gender are possible in a family with six children
Answer:
There are 64 possible birth orders in a family with six children.
Step-by-step explanation:
Let's start from 1 children.
You can have M or F. So two possible birth orders.
With two children, you can have M-M, M-F, F-M, F-F. So 2^2 = 4 possible birth orders.
For three children.
M-M-M, M-M-F, M-F-M, M-F-F, F-M-M, F-M-F, F-F-M, F-F-F. So 2^3 = 8 possible birth orders.
Generalizing:
For n children, you can have [tex]2^{n}[/tex] birth orders.
In this problem, we have that:
The family has 6 chilren.
So there are [tex]2^{6} = 64[/tex] possible birth orders.
The volume of a cube is 7.14 cubic meters. What is the cross-sectional area that is parallel to one of its faces?
A = ________
Answer:
A = 3.706 square meters
Step-by-step explanation:
the length of a cube has equal side.
therefore, the volume of a cube is given by S³
V = S³ = 7.14
where S is the length of a side
the surface area of a cube is = 6S²
where the area a aside is calculated, then it is multiply by 6.
if S³ = 7.14
S = ∛(7.14) = 1.925 m
What is the cross-sectional area that is parallel to one of its faces?
this is saying we should calculate for the cross-sectional area of one face. All faces in a cube is equal and parallel to each other.
the crossectional area of one side of a cube is = S² = 1.925² = 3.706 square meters
A = 3.706 square meters
Determine if the statement is true or false:
1. If two matrices are equivalent, then one can be transformed into the other with a sequence of elementary row operations.
2.Different sequences of row operations can lead to different echelon forms for the same matrix.
3.Different sequences of row operations can lead to different reduced echelon forms for the same matrix.
4.If a linear system has four equations and seven variables, then it must have infinitely many solutions.
Answer:
Step-by-step explanation:
given are four statements and we have to find whether true or false.
.1 If two matrices are equivalent, then one can be transformed into the other with a sequence of elementary row operations.
True
2.Different sequences of row operations can lead to different echelon forms for the same matrix.
True in whatever way we do the reduced form would be equivalent matrices
3.Different sequences of row operations can lead to different reduced echelon forms for the same matrix.
False the resulting matrices would be equivalent.
4.If a linear system has four equations and seven variables, then it must have infinitely many solutions.
True, because variables are more than equations. So parametric solutions infinite only is possible
Statements 1 and 2 are true, and statements 3 and 4 are false. While equivalent matrices can be transformed into each other and different row operations can yield different echelon forms, the reduced echelon form is unique, and a linear system with more variables than equations does not necessarily have infinitely many solutions.
Explanation:1. The statement is true. If two matrices are equivalent, one can indeed be transformed into the other through a sequence of elementary row operations. These operations include swapping two rows, multiplying a row by a non-zero scalar, or adding a multiple of one row to another row.
2. The statement is true. Different sequences of row operations can yield different echelon forms of the same matrix as the operations can redistribute information about the system of equations in different ways.
3. The statement is false. Regardless of the sequence of row operations performed, the reduced echelon form of a matrix is unique. This is because the reduced echelon form is a canonical form, meaning there's only one possible reduced echelon form for a given matrix.
4. The statement is false. Even though a linear system has more variables than equations, this does not guarantee that it will have infinitely many solutions. It could have no solutions or, under certain conditions, even a unique solution. Further analysis is required in these cases.
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Please help!!! I suck at math and this just makes my brain stop working
Answer:
We have 4.25 quarts of gasoline.
4 quarts = 1 gallon
.25 quarts = one sixteenth of a gallon.
1 / 16 = 0.0625 gallons
So, we have 1.0625 gallons of gasoline
We need 2.4 fluid ounces for every gallon of gasoline.
So, we need 1.0625 times 2.4 ounces per gallon which equals
2.55 fluid ounces.
Step-by-step explanation:
Answer:you should add 2.52 fluid ounce of oil
Step-by-step explanation:
You have to mix the oil and gas together in a specific ratio of 2.4 fluid ounce for every gallon of gasoline.
Since you have 4.2 quarts of gas, the first step is to 4.2 quarts of gas to gallons.
1 US liquid quart = 0.25 US liquid gallon.
Therefore, 4.2 quarts of gas would be
0.25 × 4.2 = 1.05 gallon of gasoline.
Therefore,
Since you use 2.4 fluid ounce of oil for every gallon of gasoline, then the amount of oil that you would add to 1.05 gallon of gasoline would be
2.4 × 1.05 = 2.52
What is the correct negation of "There is someone in Spain who speaks at least 10 languages"?1) "Everyone in Spain speaks at least 10 languages."2) "Everyone outside of Spain speaks at least 10 languages."3) "There is someone in Spain who speaks at most 9 languages."4) "Everyone in Spain speaks at most 9 languages."5) "Everyone outside of Spain speaks at most 9 languages."6) "There is someone outside of Spain who speaks at most 9 languages."7) "There is someone outside of Spain who speaks at least 10 languages."
Answer:
4) "Everyone in Spain speaks at most 9 languages."
Step-by-step explanation:
A negation is a statement that contradicts the original statement. Since the original statement regards people in Spain, options 2, 5, 6 and 7 can be ruled out as they refer to speakers outside of Spain.
Evaluating the remaining statements.
1) "Everyone in Spain speaks at least 10 languages."
If that is true, then someone in Spain speaks at least 10 languages, it doesn't negate the original statement.
3) "There is someone in Spain who speaks at most 9 languages."
It only refers to one specific individual, it doesn't negate the original statement.
4) "Everyone in Spain speaks at most 9 languages."
This means that nobody in Spain speaks more than 9 languages, contradicting the original statement.
The answer is statement 4.
Suppose Q is the midpoint of line segment PR, PQ = x + 10, and QR = 4x - 2
What is the value of PR?
A. 4
B. 8
C. 14
D. 28
answer and step by step in the attachment
The value of PR is 28.
PQ = x + 10
QR = 4x - 2
To solve the question, we'll equate both equations which will be:
PQ = QR.
x + 10 = 4x - 2
Collect like terms
4x - x = 10 + 2.
3x = 12
x = 12/3
x = 4
Therefore,
PQ = x + 10 = 4 + 10 = 14
QR = 4x - 2 = 4(4) - 2 = 16 - 2 = 14
Therefore, PR = 14 + 14 = 28
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If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage c for a child of age a, pharmacists use the equation c = 0.0417D(a + 1). Suppose the dosage for an adult is 200 mg.
(a) Find the slope of the graph of c. (Round your answer to two decimal places.)
(b) What is the dosage for a newborn? (Round your answer to two decimal places.)
Answer:
a) The slope of the graph of c is 8.34.
b) The dosage for a newborn is 8.34mg.
Step-by-step explanation:
A first order function in the following format
[tex]c(a) = ba + d[/tex]
Has slope b.
The appropriate dosage c is a function of the age a.
In this problem, we have that:
[tex]c(a) = 0.0417D(a + 1)[/tex]
Suppose the dosage for an adult is 200 mg. This means that [tex]D = 200[/tex]
So
[tex]c(a) = 0.0417*200(a + 1)[/tex]
[tex]c(a) = 8.34a + 8.34[/tex]
(a) Find the slope of the graph of c.
The slope of the graph of c is 8.34.
(b) What is the dosage for a newborn? (Round your answer to two decimal places.)
A newborn has age a = 0. So this is c(0).
[tex]c(a) = 8.34a + 8.34[/tex]
[tex]c(0) = 8.34*0 + 8.34 = 8.34[/tex]
The dosage for a newborn is 8.34mg.
how do I solve these three
Answer:
below
Step-by-step explanation:
2(x+5)=3x+1
2x+10=3x+1
10-1=3x-2x
9=x
x=9
3y-4=6-2y
3y+2y=6+4
5y=10
y=10/5
y=2
3(n+2)= 9(6-n)
3n+6=54-9n
3n+9n=54-6
12n=48
n=48/12
n=4
Answer:
Step-by-step explanation:
1) 2(x + 5) = 3x + 1
Multiplying each term inside the parenthesis by 2, it becomes
2x + 10 = 3x + 1
Subtracting 2x and - 1 from both sides of the equation
2x - 2x + 10 - 1 = 3x - 2x + 1 - 1
3x - 2x = 10 - 1
x = 9
2) 3y - 4 = 6 - 2y
Adding 4 and 2y to the left hand side and the right hand side of the equation, it becomes
3y + 2y - 4 + 4 = 6 + 4 + 2y - 2y
5y = 10
Dividing the both sides of the equation by 5, it becomes
5y/5 = 10/5
y = 10/2 = 5
3) 3(n + 2) = 9(6 - n)
3n + 6 = 54 - 9n
Subtracting 6 from both sides and adding 9n to both sides of the equation, it becomes
3n + 9n + 6 - 6 = 54 - 6 - 9n + 9n
12n = 48
Dividing both sides of the equation by 12, it becomes
12n/12 = 48/12
n = 4
A 10-lb block sits on a plane that is inclined at 60◦above the horizontal. The heightof the plane decreases from left to right. The gravitational force acting on the blockis~F.Make an illustration and work with 2-D vectors to answer the following:
What is a unit vector that points down the plane (parallel to the plane)?
Answer:
It is shown in the pic.
Step-by-step explanation:
We can call this unit vector u, that points down the plane (parallel to the plane) and v is an unit vector that points in a direction that is normal to the plane.
Drug x, a drug that claims to treat male pattern scalp hair loss, was administered for 12 months to over 1800 men aged 18 to 41 with mild to moderate amounts of ongoing hair loss. Whether they were receiving drug x or a placebo ( a pill containing no medication), all men were given a medicated shampoo. In general, men who took drug x maintained or increased the number of visible scalp hairs; while scalp hairs counts in men who took the placebo continued to decrease. This concluded that drug x is effective in maintaining or increasing the amount of scalp hair in men.a. Which statement in this example can be referred to as descriptive statistics?b. Which statement in this example can be referred to as inferential statistics?
The following statement
'In general, men who took drug x maintained or increased the number of visible scalp hairs; while scalp hairs counts in men who took the placebo continued to decrease'
can be referred as descriptive statistics, since we are saying that the msot of the men who took the drug gain scalp hairs while the contrary happened from those men who took placebo.
On the other hand, the statement
'drug x is effective in maintaining or increasing the amount of scalp hair in men'
Is a deduction you make, so it can be referred as inferential statistics
In a class of 125 students, 27 are computer science majors, 51 are mechanical engineering majors, 12 are civil engineers and the rest are general engineering majors. Assume students only have one major.
Suppose six students from the class are chosen at random what is the probability none are mechanical engineering majors?
I tried 74/125 * 73/124 * 72/123 * 71/122 * 70/121 * 69/120 * 68/119 but had incorrect answer
Answer:
There is a 3.95% probability that none are mechanical engineering majors.
Step-by-step explanation:
[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
There are 125 students.
51 of them are mechanical engineering majors and 125-51 = 74 are not mechanical engineering majors.
Suppose six students from the class are chosen at random what is the probability none are mechanical engineering majors?
The total number of students is 125. So total number of 6 student groups is
[tex]C_{125,6} = \frac{125!}{6!119!}[/tex]
The total number of non mechanical engineering students is 74. So the total number of 6 non mechanical engineering students is.
[tex]C_{74,6} = \frac{74!}{6!68!}[/tex]
The probability is:
[tex]\frac{C_{74,6}}{C_{125,6}} = 74/125 * 73/124 * 72/123 * 71/122 * 70/121 * 69/120 = 0.0395[/tex]
The 68/119 ends up simplified in this exercise, this is your mistake.
There is a 3.95% probability that none are mechanical engineering majors.
Construct the cumulative frequency distribution for the given data. Daily Low (degrees°F) Frequency 35-39 11 40-44 22 45-49 44 50-54 13 55-59 66 60-64 88 65-69 11 Construct the cumulative frequency distribution.
The cumulative frequency distribution of a data set is found by adding the frequency of each category to the sum of the frequencies of all previous categories. Using this method, the cumulative frequency distribution for the given data set is as follows: 35-39: 11, 40-44: 33, 45-49: 77, 50-54: 90, 55-59: 156, 60-64: 244, 65-69: 255.
Explanation:To construct the cumulative frequency distribution for the given data, we need to take into account the sum of all frequencies to the current one in addition to its own frequency. Let's look at how this works using the provided data:
35-39: 11 (there are no previous categories, so the cumulative frequency is 11)40-44: 22 + 11 = 3345-49: 44 + 33 = 7750-54: 13 + 77 = 9055-59: 66 + 90 = 15660-64: 88 + 156 = 24465-69: 11 + 244 = 255Therefore, the cumulative frequency distribution for the given data set is:
35-39: 1140-44: 3345-49: 7750-54: 9055-59: 15660-64: 24465-69: 255Learn more about Cumulative Frequency Distribution here:https://brainly.com/question/31839381
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A cumulative frequency distribution adds each frequency to the cumulative total of the previous ones. The sequence of cumulative frequencies for the given temperature data is 11, 33, 77, 90, 156, 244, and 255 respectively.
To construct a cumulative frequency distribution, we add up the frequencies as we go down the list of daily low temperatures. We will begin with the first frequency and add each subsequent frequency to the cumulative total of the previous frequencies. Here is how it would look for the data provided:
35-39: 11 (11)
40-44: 22 (11 + 22 = 33)
45-49: 44 (33 + 44 = 77)
50-54: 13 (77 + 13 = 90)
55-59: 66 (90 + 66 = 156)
60-64: 88 (156 + 88 = 244)
65-69: 11 (244 + 11 = 255)
The numbers in brackets represent the cumulative frequencies. Remember, to calculate Heating Degree Days (HDD) and Cooling Degree Days (CDD), you sum the number of days when the average temperature is below or above 65°F, respectively, multiplied by the difference from 65°F.
What is the additive inverse of the complex number -8 + 3i?
-8-3i
-8+3i
8-3i
8+3i
Answer:
cc
Step-by-step explanation:
The additive inverse of the complex number -8 + 3i is 8 - 3i.
What are complex Numbers?The complex number is basically the combination of a real number and an imaginary number.
The additive inverse of a complex number is the number that, when added to the original number, results in zero.
Or it is the negative of the original number.
To find the additive inverse of the complex number -8 + 3i
we need to negate both the real and imaginary parts. So:
Additive inverse = -( -8 + 3i)
= 8 - 3i
Therefore, the additive inverse of the complex number -8 + 3i is 8 - 3i.
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Membership in Mensa requires an IQ score above 131.5. Nine candidates take an IQ test, and they have a mean IQ score of 133. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15 (this should be used as the baseline for the questions below.) (a) If one person is randomly selected from the general population, what is the probability of getting someone with an IQ of at least 133?
Answer:
a) [tex]P(X\geq 133)=P(\frac{X-\mu}{\sigma}\geq \frac{133-\mu}{\sigma})=P(Z\geq \frac{133-100}{15})=P(Z\geq 2.2)[/tex]
And we can find this probability using the complement rule:
[tex]P(Z\geq 2.2)=1- P(z<2.2)=1-0.986=0.0139 [/tex]
b) [tex]P(\bar X\geq 133)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}\geq \frac{133-\mu}{\sigma_{\bar x}})=P(Z\geq \frac{133-100}{5})=P(Z\geq 6.6)[/tex]
And we can find this probability using the complement rule:
[tex]P(Z\geq 6.6)=1- P(z<6.6)=1-0.999999=2.06x10^{-11} [/tex]
c) No. The mean can be lower than 131.5 if we find the probability:
[tex]P(\bar X\leq 133)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}\leq \frac{131.5-\mu}{\sigma_{\bar x}})=P(Z\leq \frac{131.5-100}{5})=P(Z\leq 6.3)[/tex]
[tex]P(Z\leq 6.3) \approx 1 [/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
A. If 1 person is randomly selected from thegeneral population, find the probability of getting someone with anIQ score of at least 133.
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(100,15)[/tex]
Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]
We are interested on this probability
[tex]P(X\geq 133)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X\geq 133)=P(\frac{X-\mu}{\sigma}\geq \frac{133-\mu}{\sigma})=P(Z\geq \frac{133-100}{15})=P(Z\geq 2.2)[/tex]
And we can find this probability using the complement rule:
[tex]P(Z\geq 2.2)=1- P(z<2.2)=1-0.986=0.0139 [/tex]
And the probability is calculated from the normal standard table or with excel.
B. If 9 people are randomly selected,find the probability that their mean IQ score is at least 133.
For this case since the distribution for the random variable X is normal then the distribution for the sample mean is also normal and given by:
[tex] \bar X = \sim N(\mu= 100 ,\sigma_{\bar x}= \frac{15}{\sqrt{9}}=5)[/tex]
The new z score is defined as
[tex]z=\frac{x-\mu}{\sigma_{\bar x}}[/tex]
If we apply this formula to our probability we got this:
[tex]P(\bar X\geq 133)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}\geq \frac{133-\mu}{\sigma_{\bar x}})=P(Z\geq \frac{133-100}{5})=P(Z\geq 6.6)[/tex]
And we can find this probability using the complement rule:
[tex]P(Z\geq 6.6)=1- P(z<6.6)=1-0.999999=2.06x10^{-11} [/tex]
And the probability is calculated from the normal standard table or with excel.
C. Although the results are available,the individual IQ test scores have been lost. Can it be concluded that all 9 candidates have IQ scores above 131.5 so that they allare eligible for Mensa membership?
No. The mean can be lower than 131.5 if we find the probability:
[tex]P(\bar X\leq 133)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}\leq \frac{131.5-\mu}{\sigma_{\bar x}})=P(Z\leq \frac{131.5-100}{5})=P(Z\leq 6.3)[/tex]
[tex]P(Z\leq 6.3) \approx 1 [/tex]
Answer:
0.0139
Step-by-step explanation:
We have to find P(X≥133)
IQ scores normally distributed with mean=100 and standard deviation=sd=15
[tex]P(X\geq 133)=P(\frac{x-mean}{sd} \geq \frac{133-100}{15}[/tex]
[tex]P(Z\geq 2.2)=P(0<Z<infinity)-P(0<z<2.2)[/tex]
[tex]P(Z\geq 2.2)=0.5-0.4861[/tex]
[tex]P(Z\geq 2.2)=0.0139[/tex]
P(X≥133)=0.0139.
So, if one person is selected at random the probability of getting someone with at least 133 IQ score is 1.39%
Suppose that the average and standard deviation of the fine for speeding on a particular highway are 111.12 and 13.04, respectively. Calculate an interval that is symmetric around the mean such that it contains approximately 68% of fines. Assume that the fine amount has a normal distribution. 1) (124.16, 98.08) 2) (111.12, 13.04) 3) (98.08, 124.16) 4) (85.04, 137.2) 5) (137.2, 85.04)
Answer:
3) (98.08, 124.16)
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 111.12
Standard deviation = 13.04
Calculate an interval that is symmetric around the mean such that it contains approximately 68% of fines.
68% of the fines are within 1 standard deviation of the mean speed. So
From 111.12 - 13.04 = 98.08 to 111.12 + 13.04 = 124.16
The interval notation in the smallest value before the highest value.
So the correct answer is:
3) (98.08, 124.16)
A researcher is interested in studying the perceived life satisfaction among younger adults and hypothesizes that life satisfaction among younger adults is different than the general public. She did a pilot study and gave a life satisfaction test (known to have high reliability and validity) to nine younger adults (between 20 and 30). Scores on the measure range from 0 to 5 with 5 indicative of high life satisfaction, and 0 indicative of no life satisfaction.
The data are presented below. Assume that life satisfaction for general public is 2.5, conduct the appropriate test and answer the questions. 4, 3, 3, 4, 5, 2, 2, 2, 2.
What would be the null hypothesis of this study?
A.H0: Mean= 3
B.H0: Mean = 2.5
C.H0: Mean < 5
D.H0: Mean >2.5
E.None of the above
Answer:
Option B) [tex]H_0: \text{Mean} = 2.5[/tex]
Step-by-step explanation:
We are given the following in the question:
A researcher is interested in studying the perceived life satisfaction among younger adults.
The hypothesis is conducted to check that life satisfaction among younger adults is different than the general public.
Life satisfaction for general public = 2.5
Data:
4, 3, 3, 4, 5, 2, 2, 2, 2
We have to design the null hypothesis.
The researcher claims that life satisfaction is different for younger adult and general public.
But the null hypothesis always state equality between the population and the sample.
Thus, the null hypothesis will be
Option B) [tex]H_0: \text{Mean} = 2.5[/tex]
For each of the following hypothetical populations, give a plausible sample of size 4:a. All distances that might result when you throw a football b. Page lengths of books published 5 years from now c. All possible earthquake-strength measurements (Richter scale) that might be recorded in California during the next year d. All possible yields (in grams) from a certain chemical reaction carried out in a laboratory
Answer:
Yes a
Step-by-step explanation:
I took the test
Find the domain of each function. (Enter your answers using interval notation.)(a) f(x)=8/(1+e^x) .(b) f(x)=5/(1−e^x)
Final answer:
The domain of f(x) = 8/(1 + eˣ) is all real numbers, or (-∞, ∞). For f(x) = 5/(1 - eˣ), the domain is all real numbers except x = 0, which in interval notation is (-∞, 0) ∪ (0, ∞).
Explanation:
Finding the Domain of Functions
To find the domain of a function, we look for all possible values of x for which the function is defined. The exponential function eˣ is defined for all real numbers, so we mainly need to be concerned with the denominators in these functions not being equal to zero.
For the function f(x) = 8/(1 + eˣ), since 1 + eˣ is always greater than zero for all real x (because the exponential function eˣ is always positive), the function is defined for all real numbers. Therefore, the domain is all real numbers, or in interval notation, (-∞, ∞).For the function f(x) = 5/(1 - eˣ), we must exclude any value of x that makes the denominator zero. The denominator 1 - eˣ equals zero when eˣ = 1. This occurs when x = 0. Therefore, the domain of this function is all real numbers except x = 0, or in interval notation, (-∞, 0) ∪ (0, ∞).Your city is represented in a coordinate plane where each unit represents 1 kilometer. The library is at (−2, −2), the post office is at (2, 2), and your house is at (−3, 2). You ride your bike from your house to the library, then the post office, and then back home. What is the minimum distance that you can ride your bike? Round your answer to the nearest tenth.
By using the distance formula, we calculate the distances between the house, library, and post office, finding the total minimum distance to be approximately 14.8 kilometers.
Explanation:This question requires the use of the distance formula in mathematics, which is derived from the Pythagorean theorem. The formula is √[(x₂ - x₁)² + (y₂ - y₁)²]. To find the total minimum distance you ride your bike, you calculate the distance from your house to the library, then the library to the post office, and finally, the post office back to your house.
First, calculate the distance from your house at (-3, 2) to the library at (-2, -2): √[(-2 - (-3))² + (-2 - 2)²] = √[1² + -4²] = √[1 + 16] = √17 ≈ 4.1 kilometers.
Second, calculate the distance from the library at (-2, -2) to the post office at (2, 2): √[(2 - (-2))² + (2 - (-2))²] = √[4² + 4²] = √[16 + 16] = √32 ≈ 5.7 kilometers.
Finally, calculate the distance from the post office at (2, 2) back to your house at (-3, 2): √[(-3 - 2)² + (2 - 2)²] = √[-5² + 0²] = √[25 + 0] = √25 = 5 kilometers.
Adding these distances together, 4.1 km + 5.7 km + 5 km = 14.8 kilometers.
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