A top-fuel dragster ran a 1/4-mile (1320 ft) race. It had traveled 1305.48 feet after 3.58 seconds and it traveled the entire 1320 feet in 3.61 seconds. What was its speed, approximately, in feet per second at the end of the race? In miles per hour?

Answer: B. Jonesville is growing linearly and Smithville is growing exponentially.

Step-by-step explanation:

Linear growth :

Exponential growth :

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.

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.

For more information :

https://brainly.com/question/4351903?referrer=searchResults

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.

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

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.

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

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.

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.

https://brainly.com/question/31469353

#SPJ3

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.

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.

https://brainly.com/question/32189796

#SPJ3

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.

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.

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:

Therefore, the cumulative frequency distribution for the given data set is:

https://brainly.com/question/31839381

#SPJ6

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.

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]

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.

Answer:

Yes a

Step-by-step explanation:

I took the test

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.

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.

https://brainly.com/question/34354095

#SPJ3

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%

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%.

For such more question on heads

https://brainly.com/question/31590485

#SPJ3

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

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

Read related link on:

https://brainly.com/question/14117256

Answer:

cc

Step-by-step explanation:

The additive inverse of the complex number -8 + 3i is 8 - 3i.

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.

To learn more on Complex Numbers click:

https://brainly.com/question/10251853

#SPJ7

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.

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

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.

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.

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

Answer:

Option A.

Step-by-step explanation:

Let M be the milk per gallon.

C be the cookies per dozen.

B be the bundle (one gallon of milk and a dozen cookies ).

Milk can be sold by itself for a profit of $1.50 per gallon. Cookies can likewise be sold at a profit of $2.50 per dozen and bundle is sold for a profit of $3.00 per bundle.

[tex]Profit= 1.5M + 2.5C + 3B[/tex]

We need to maximize the profits. So, our objective function is

Therefore, the correct option is A.

Answer:

[tex] \\ P(49<x<61) = 0.8413 - 0.1587 = 0.6826 [/tex] or 68.26%.

Step-by-step explanation:

The daily demand for milk containers has a Normal (or Gaussian) distribution, and we can use values from the cumulative distribution function and z-scores to solve the question.

We know from the question that the mean of the distribution is:

[tex] \\ \mu = 55 [/tex]

And a standard deviation of:

[tex] \\ \sigma = 6 [/tex]

The z-scores permit calculates the probabilities for any case whose values have a Normal o Gaussian distribution. Then, for this, we need to calculate the z-scores for 49 containers and 61 containers to establish the corresponding probabilities, as well as the differences between these two values to determine the probability between them.

These z-scores are given by:

[tex] \\ z = \frac{x-\mu}{\sigma} [/tex]

Thus,

The z-scores for 49 and 61 containers are:

[tex] \\ z_{49} = \frac{49 - 55}{6} = \frac{-6}{6} = -1 [/tex] [1]

[tex] \\ z_{61} = \frac{61 - 55}{6} = \frac{6}{6} = 1 [/tex] [2]

Well, this is a special case when in both cases the values are one standard deviation from the mean, but in one case ([tex] \\ z_{49} = -1 [/tex]) the values are smaller than the mean and in the other case ([tex] \\ z_{61} = 1 [/tex]) the values are greater than the mean.

In other words, the cumulative probability for ([tex] \\ z_{61} = 1 [/tex]), obtained from any Table of the Normal Distribution available on the Web, is: 0.8413 (or 84.13%) and the cumulative probability for ([tex] \\ z_{49} = -1 [/tex]) is: 1 - 0.8413 = 0.1587 (or 15.87%), because of the symmetry of the Normal Distribution.

Then, the probability of expecting to sell between 49 and 61 containers in a day is the difference of both obtained probabilities:

[tex] \\ P(49<x<61) = 0.8413 - 0.1587 = 0.6826 [/tex] or 68.26%.

See the graph below.

Final answer:

Approximately 68% of the time, the number of milk containers sold in a day at the supermarket is expected to be between 49 and 61 containers, following the Empirical Rule for normal distribution.

Explanation:

The question asks us about the probability of daily sales being between certain values when they follow a bell-shaped distribution, specifically between 49 and 61 containers. Since we know the distribution is approximately normal with a mean of 55 containers and a standard deviation of six containers, we can use the Empirical Rule or the Standard Normal Distribution to find the probability.

In the context of a normal distribution, we know that:

About 68% of the data falls within one standard deviation of the mean. (Mean ± 1SD)

About 95% falls within two standard deviations. (Mean ± 2SD)

For this supermarket, one standard deviation from the mean (55 ± 6) gives us a range from 49 to 61 containers. Therefore, approximately 68% of the time, we can expect the number of milk containers sold to be between 49 and 61 containers in a day, based on the Empirical Rule.

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.

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)

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.

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.

https://brainly.com/question/34212393

#SPJ12

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