Answer:
[tex]p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}[/tex], for [tex]r_{1} = 0[/tex]
Step-by-step explanation:
The general form of quintic-order polynomial is:
[tex]p_{5}(t) = a\cdot x^{5} + b\cdot x^{4} + c\cdot x^{3} + d\cdot x^{2} + e \cdot x + f[/tex]
According to the statement of the problem, the polynomial has the following roots:
[tex]p_{5} (t) = (x - r_{1})\cdot (x-3)^{2}\cdot x^{2} \cdot (x+1)[/tex]
Then, some algebraic handling is done to expand the polynomial:
[tex]p_{5} (t) = (x - r_{1}) \cdot (x^{3}-6\cdot x^{2}+9\cdot x) \cdot (x+1)\\p_{5} (t) = (x - r_{1}) \cdot (x^{4}-5\cdot x^{3} + 3 \cdot x^{2} + 9 \cdot x)[/tex]
[tex]p_{5} (t) = x^{5} - (5+r_{1})\cdot x^{4} + (3 + 5\cdot r_{1})\cdot x^{3} +(9-3\cdot r_{1})\cdot x^{2} - 9 \cdot r_{1}\cdot x[/tex]
If [tex]r_{1} = 0[/tex], then:
[tex]p_{5} (t) = x^{5} - 5\cdot x^{4} + 3\cdot x^{3} +9\cdot x^{2}[/tex]
The polynomial P(x) given has a degree of 5, leading coefficient of 1, roots at 3, 0 (both with multiplicity 2), and -1 (with multiplicity 1). It can be written as P(x) = (x - 3)^2 * x^2 * (x + 1), according to the Fundamental Theorem of Algebra.
Explanation:A polynomial P(x) of degree 5 with a leading coefficient of 1 and roots at x = 3, x = 0 with multiplicity 2, and x = -1 with multiplicity 1 can be expressed as:
P ( x ) = (x - 3)^2 * x^2 * (x + 1)
This polynomial function is derived based on the fundamental theorem of algebra that states each polynomial equation of degree 'n' has 'n' roots or zeros, considering multiplicity. Here, the factors (x-3)^2, x^2 and (x+1) correspond to the roots 3, 0 and -1 with their respective multiplicities. Multiplicity refers to the number of times a number occurs as a root in the polynomial function.
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Brinley is making headbands for her friends.Each headband needs 16 and a half inches of elastic and she has 132 inches of elastic.Use the guess,check,and revise strategy to solve the equation 16 and a half h = 132 to find h, the headbands Brinely can make.
Answer:
8 headbands can be made.
Step-by-step explanation:
dividing both sides by 16.5, the material needed for one, leaves the equation as h=8, because 132 divided by 16.5 equals 8
Brinley can make 8 hands from the elastic she has.
What is the unitary method?
The unitary method is a method in which you find the value of a unit and then the value of a required number of units. Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value.
Given here, A headband needs 16 and a half inches of elastic and Brinley has 132 inches of elastic
Therefore the number of headbands that she could make is
= 132/16.5
=8 Headbands.
Hence, Brinley can make 8 hands from the elastic she has.
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You shuffle a standard 52 card deck of cards, so that any order of the cards is equally likely, than draw 4 cards. How many different ways are there to make that draw, where you care about the order
Answer:
270725 different ways
Step-by-step explanation:
The problem tells us that the order of the letters does not matter. Therefore, in the combination the order is NOT important and is signed as follows:
C (n, r) = n! / r! (n - r)!
We have to n = 52 and r = 4
C (52, 4) = 52! / 4! * (52-4)! = 52! / (4! * 48!) = 270725
Which means that there are 270725 different ways in total to make that raffle
The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Approximate the following probabilities: _________.a. More than 25 chips are defective. b. Between 20 and 30 chips are defective.
Answer:
a) The approximate probability that more than 25 chips are defective is 0.1075.
b) The approximate probability of having between 20 and 30 defecitve chips is 0.44.
Step-by-step explanation:
Lets call X the total amount of defective chips. X has Binomial distribution with parameters n=1000, p =0.02. Using the Central Limit Theorem, we can compute approximate probabilities for X using a normal variable with equal mean and standard deviation.
The mean of X is np = 1000*0.2 = 20, and the standard deviation is √np(1-p) = √(20*0.98) = 4.427
We will work with a random variable Y with parameters μ=20, σ=4.427. We will take the standarization of Y, W, given by
[tex] W = \frac{Y-\mu}{\sigma} = \frac{Y-20}{4.427} [/tex]
The values of the cummmulative distribution function of the standard normal random variable W, which we will denote [tex] \phi [/tex] , can be found in the attached file. Now we can compute both probabilities. In order to avoid trouble with integer values, we will correct Y from continuity.
a)
[tex]P(X > 25) = P(X > 25.5) \approx P(Y>25.5) = P(\frac{Y-20}{4.427} > \frac{25.5-20}{4.427}) =\\P(W > 1.2423) = 1-\phi(1.2423) = 1-0.8925 = 0.1075[/tex]
Hence the approximate probability that more than 25 chips are defective is 0.1075.
b)
[tex]P(20<X<30) = P(20.5 < X < 29.5) \approx P(20.5<Y>29.5) = \\P(\frac{20.5-20}{4.427} < \frac{Y-20}{4.427} < \frac{29.5-20}{4.427}) = P(0.1129 < W < 2.14) = \phi(2.14)-\phi(0.1129) = \\0.9838-0.5438 = 0.44[/tex]
As a result, the approximate probability of having between 20 and 30 defecitve chips is 0.44.
Final answer:
To approximate the probabilities of defective chips where 2% are defective from a lot of 1000, the binomial distribution is used, with more complex probability calculations often requiring statistical software. Both (a) more than 25 defective and (b) between 20 and 30 defective scenarios can be estimated using normal approximation due to the large sample size and small defect probability.
Explanation:
To approximate the probability of defective chips in the scenario where 2% of the semiconductor chips produced are defective, we can use the binomial distribution as an approximation because the sample size is large (n=1000) and the probability of a defect (p=0.02) is small.
For part (a), more than 25 chips are defective, we are looking for P(X>25). The calculation for this is more complex and typically done using statistical software or a calculator with binomial capabilities.
For part (b), between 20 and 30 chips are defective, we need to find the probability that X is between 20 and 30 inclusively, or P(20 ≤ X ≤ 30). This requires calculating the cumulative probability for 20 through 30 and then subtracting the lower end from the higher end.
In real-world applications, as the number of trials is large and the probability of success is small, the binomial distribution can be approximated by a normal distribution. The mean (μ) of the distribution is np and the variance (σ2) is np(1-p), which would give us μ = 20 and σ2 = 19.6 for this example. We can then use the standard normal table or a calculator to find the probabilities for parts (a) and (b).
What is the answer for number 10? please explain step by step
hope it helps you!!!!!
Statistics!! Please help, 10 points and brainliest!
1. You are comparing the heights of contemporary males and eighteenth-century males. The sample mean for a sample of 30 contemporary males is 70.1 inches with a sample standard deviation of 2.52 inches. The sample mean for eighteenth-century males was 65.2 inches with a sample standard deviation of 3.51 inches. Is there sufficient data to conclude that contemporary males are taller than eighteenth-century males?
A. The p-value is less than 0.00001. There is insufficient data to reject the null hypothesis.
B. The p-value is greater than 0.00001. There is sufficient data to reject the null hypothesis.
C. The p-value is greater than 0.00001. There is insufficient data to reject the null hypothesis.
D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.
Answer:
[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]
[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]
And the best conclusion for this case would be:
D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.
Step-by-step explanation:
Data given and notation
[tex]\bar X=70.1[/tex] represent the sample mean
[tex]\sigma=2.52[/tex] represent the population standard deviation
[tex]n=30[/tex] sample size
[tex]\mu_o =65.2[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 65.2, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 65.2[/tex]
Alternative hypothesis:[tex]\mu > 65.2[/tex]
If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=30-1=29[/tex]
Since is a one side right tailed test the p value would be:
[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]
And the best conclusion for this case would be:
D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.
The correct option is D. The p-value is less than [tex]0.00001.[/tex] There is sufficient data to reject the null hypothesis.
Hypotheses:
Null hypothesis [tex](\(H_0\)): \(\mu_1 = \mu_2\)[/tex] (the mean height of contemporary males is equal to the mean height of eighteenth-century males)
Alternative hypothesis [tex](\(H_1\)): \(\mu_1 > \mu_2\)[/tex] (the mean height of contemporary males is greater than the mean height of eighteenth-century males)
Given Data:
Sample mean for contemporary males [tex](\(\bar{x}_1\)) = 70.1 inches[/tex]
Sample standard deviation for contemporary males [tex](\(s_1\)) = 2.52 inches[/tex]
Sample size for contemporary males [tex](\(n_1\)) = 30[/tex]
Sample mean for eighteenth-century males [tex](\(\bar{x}_2\)) = 65.2 inches[/tex]
Sample standard deviation for eighteenth-century males [tex](\(s_2\)) = 3.51\ inches[/tex]
Sample size for eighteenth-century males [tex](\(n_2\)) = 30[/tex]
Test Statistic:
We use a two-sample t-test for the difference of means:
[tex]\[t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\][/tex]
Substituting the given values:
[tex]\[t = \frac{70.1 - 65.2}{\sqrt{\frac{2.52^2}{30} + \frac{3.51^2}{30}}}\][/tex]
First, calculate the variances and their respective terms:
[tex]\[s_1^2 = 2.52^2 = 6.3504, \quad s_2^2 = 3.51^2 = 12.3201\][/tex]
[tex]\[\frac{s_1^2}{n_1} = \frac{6.3504}{30} = 0.21168, \quad \frac{s_2^2}{n_2} = \frac{12.3201}{30} = 0.41067\][/tex]
[tex]\[\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{0.21168 + 0.41067} = \sqrt{0.62235} = 0.7889\][/tex]
Now calculate the t-value:
[tex]\[t = \frac{70.1 - 65.2}{0.7889} = \frac{4.9}{0.7889} = 6.21\][/tex]
Degrees of Freedom:
Since the sample sizes are the same, we can use the following approximation for degrees of freedom [tex]df[/tex]
[tex]\[df = n_1 + n_2 - 2 = 30 + 30 - 2 = 58\][/tex]
P-value:
Using a t-distribution table or a calculator for a one-tailed test with [tex]58[/tex] degrees of freedom, we find that a t-value of [tex]6.21[/tex] corresponds to a p-value much less than [tex]0.00001.[/tex]
The prices (in dollars) of 50 randomly chosen types of shoes at 4 different stores are shown in the box plots. At which store would a person MOST LIKELY pay $60 for a pair of shoes?
Answer:
C
Step-by-step explanation:
I think you missed attaching the picture, so hope my photo fits your questions well!
We must consider the median of the data sets, it may represent the center of the dispersion measure. Then we see answer C is the most suitable one, this is because it's median is approximately to $60.
An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer travel if they swim from one corner to the opposite?
The swimmer will travel a distance of 55.92 meters when swimming from one corner to the opposite corner of an Olympic-size swimming pool.
Given, the length and width of the pool form the two sides of the right-angled triangle, and the distance the swimmer will travel is the hypotenuse.
Using the Pythagorean theorem, we can calculate the distance as follows:
Distance² = Length² + Width²
Distance² = 50² + 25²
Distance² = 2500 + 625
Distance² = 3125
Distance = √3125
Distance = 55.90 meters
Therefore, a swimmer will travel approximately 55.92 meters.
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Final answer:
To determine the distance a swimmer travels across an Olympic-sized pool from corner to opposite, the Pythagorean theorem is used, giving approximately 55.90 meters as the distance.
Explanation:
The student's question entails calculating distances and speeds in different swimming and water current scenarios, which is a classic physics problem involving kinematics and geometry. However, since it involves calculations and applying formulae, particularly the Pythagorean theorem, and rate, time, and distance relationships, it falls under the subject of Mathematics.
To Calculate the Distance Swum Across an Olympic-sized Pool
For an Olympic-sized pool that is 50 meters in length and 25 meters in width, a swimmer traveling from one corner to the opposite would traverse a diagonal. To calculate this diagonal distance, we use the Pythagorean theorem:
Diagonal2 = Length2 + Width2
Diagonal = √(Length2 + Width2)
Substitute the given values:
Diagonal = √(502 + 252) = √(2500 + 625)
Diagonal = √(3125) meters
The swimmer will travel approximately √(3125) meters, which is about 55.90 meters.
Show that the curve y = 4 x 3 + 7 x − 5 y=4x3+7x-5 has no tangent line with slope 2 2. y = 4 x 3 + 7 x − 5 ⇒ m = y ' = y=4x3+7x-5⇒m=y′= Preview , but x 2 x2 0 0 for all x x, so m ≥ m≥ for all x x.
Answer:
There is no such point where the given curve has a tangent line with slope 2.
Step-by-step explanation:
We have been given a curve [tex]y=4x^3+7x-5[/tex]. We are asked to show that the given curve has no tangent line with slope 2.
First of all, we will find the derivative of given curve as shown below:
[tex]y'=\frac{d}{dx}(4x^3)+\frac{d}{dx}(7x)-\frac{d}{dx}(5)[/tex]
[tex]y'=4\cdot 3x^{3-1}+7x^{1-1}-0[/tex]
[tex]y'=12x^{2}+7x^{0}[/tex]
[tex]y'=12x^{2}+7(1)[/tex]
[tex]y'=12x^{2}+7[/tex]
We know that derivative represents slope of tangent line, so we will equate derivative of the given curve with 2 and solve for the point (x), where the slope of tangent line will be equal to 2 as:
[tex]12x^2+7=2[/tex]
[tex]12x^2+7-7=2-7[/tex]
[tex]12x^2=-5[/tex]
[tex]x^2=-\frac{5}{12}[/tex]
We know that square of any real number could never be negative, therefore, there is no such point where the given curve has a tangent line with slope 2.
Final answer:
The proof involves finding the derivative of the given curve y = 4x³ + 7x - 5, setting it equal to the desired slope (2), and showing that the resulting equation has no real solutions, proving that no tangent line with slope 2 exists for this curve.
Explanation:
The question is about proving that the curve y = 4x³ + 7x - 5 does not have any tangent line with slope 2. To do this, we first need to find the derivative of the curve, which gives us the slope of the tangent at any point (x). The derivative of y with respect to x is given by y' = 12x² + 7. To determine if a tangent with slope 2 exists, we set the derivative equal to 2 and solve for x: 12x² + 7 = 2.
Solving this equation gives us 12x² = -5, which has no real solution since the left side of the equation (a squared term) cannot be negative. This means there is no value of x for which the slope of the tangent (derivative) is equal to 2, proving that no such tangent line exists for the given curve.
What is the center of the circle described by the equation
x^2+4x+y^2-6y=12
(4, -6)
(-4, 6)
(-2, 3)
(2, -3)
Answer:
The center of the circle is (-2 , 3) ⇒ 3rd answer
Step-by-step explanation:
The equation of a circle is (x - h)² + (y - k)² = r², where
(h , k) are the coordinates of its centerr is the radius of it∵ The equation of the circle is x² + 4x + y² - 6y = 12
- Lets make a completing square for x² + 4x
∵ x² = (x)(x)
∵ 4x ÷ 2 = 2x
- That means the second term of the bracket (x + ...)² is 2
∴ The bracket is (x + 2)
∵ (x + 2)² = x² + 4x + 4
∴ We must add 4 and subtract 4 in the equation of the circle
∴ (x² + 4x + 4) - 4 + y² - 6y = 12
Lets make a completing square for y² - 6y
∵ y² = (y)(y)
∵ -6y ÷ 2 = -3y
- That means the second term of the bracket (y + ....) is -3
∴ The bracket is (y - 3)
∵ (y - 3)² = y² - 6y + 9
∴ We must add 9 and subtract 9 in the equation of the circle
∴ (x² + 4x + 4) - 4 + (y² - 6y + 9) - 9= 12
Now lets simplify the equation
∵ (x + 2)² + (y - 3)² - 13 = 12
- Add 13 to both sides
∴ (x + 2)² + (y - 3)² = 25
- Compare it with the form of the equation of the circle to
find h and k
∵ (x - h)² + (y - k)² = r²
∴ h = -2 and k = 3
The center of the circle is (-2 , 3)
If the median of a negatively skewed distribution is 31, which value could be the mean of the distribution?
A. 33
B. 36
C. 31
D. 28
Answer:
D. 28
Step-by-step explanation:
If a distribution is negatively skewed, the mean of the distribution is always less than the median.
If the median of a negatively skewed distribution is 31, then from the given options, the only value that is less than 31 is 28.
Therefore the mean could be 28.
The correct answer is D
Add a party there were four large submarine sandwiches all the same size during the party 2/3 of the chicken sandwich three force of a turn a sandwich 712s of the roast beef sandwich and 5/6 of the veggie sandwich or eat it which sandwich had the least amount
Answer:
Veggie
Step-by-step explanation:
I corrected your question for a better situation.
At a party there were four large submarine sandwiches all the same size . During the party 2/3 of the chicken sandwich three over 4 of the tuna sandwich 7/12 of the roast beef sandwich and 5/6 of the veggie sandwich were eating which sandwich had the least amount left
Here is my answer:
Chicken sandwich left: 1 - 2/3 =1/3 Tuna sandwich left = 1 - 3/4 = 1/4 Roast sandwich left = 1 -7/12 = 5/12 Veggie sandwich left = 1 - 5/6 = 1/6So the sandwich had the least amount is Veggie
How many times will the string literal "Hi" appear in the lblMsg control? Dim intCount As Integer Do While intCount > 4 lblMsg.Text = lblMsg.Text & "Hi" & ControlChars.NewLine intCount += 1
Answer:
0
Step-by-step explanation:
In my opinion, the string won't display because, the intCount was not initialized before you started outputting the "Hi" string. So in order fro you to get the string to appear, the control point or value has to be initialized to maybe 0. then you can start looping from there. And if you are looping from the top or using greater than (>), The loop works best buy subtracting the control value else, you can end up with infinity loop.
Write a quadratic function in vertex form whose graph has the vertex (5,−2) and passes through the point (7,0).
The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].
Solution:
The equation of a quadratic in vertex form is [tex]y=a(x-h)^{2}+k[/tex].
where (h, k) are the coordinates of the vertex and "a" is a multiplier.
Here (h, k) = (5, –2)
Substitute this in the vertex form.
[tex]y=a(x-5)^{2}+(-2)[/tex]
[tex]y=a(x-5)^{2}-2[/tex] – – – – (1)
Passes through the point (7, 0).
Here x = 7 and y = 0.
Substitute this in equation (1), we get
[tex]0=a(7-5)^{2}-2[/tex]
[tex]0=4a-2[/tex]
Add 2 on both sides.
2 = 4a
Divide 2 on both sides, we get
[tex]$a=\frac{1}{2}[/tex]
Substitute the value of a in equation (1),
[tex]$y=\frac{1}{2} (x-5)^{2}-2[/tex]
The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].
Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds. If the track is 1800 m long, what is the speed of each toy train?
Answer:
Step-by-step explanation:
Given that Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds
Circular track is 1800 m.
Let speed be x and y respectively
When in same direction relative speed = x-y and when in opposite directions =x+y
30(x+y) = 1800
x+y= 60
120(x-y) = 1800
x-y = 15
Solving x = 37.5 m/hr and y = 12.5 per hour.
When Alice and Bob's toy trains move in the same direction, their relative speed is the sum of their individual speeds. When they move in opposite directions, their relative speed is the difference between their individual speeds. By solving simultaneous equations, we find that Alice's toy train has a speed of 75 m/s and Bob's toy train has a speed of 60 m/s.
Explanation:Let's assume the speed of Alice's toy train is x m/s and the speed of Bob's toy train is y m/s.
When the trains move in the same direction, they meet every 120 seconds. Since they meet once every 30 seconds when moving in opposite directions, their relative speed is the sum of their individual speeds. So, when they move in the same direction, their relative speed will be x + y and when they move in opposite directions, their relative speed will be x - y.
When they move in the same direction, the distance covered by Alice's toy train in 120 seconds will be equal to the distance covered by Bob's toy train in 120 seconds, which is equal to the length of the circular track (1800 m). So, the equation can be written as:
x × 120 = y × 120 = 1800Simplifying the equation, we get:
x + y = 1800/120 = 15Similarly, when they move in opposite directions, the distance covered by Alice's toy train in 30 seconds will be equal to the distance covered by Bob's toy train in 30 seconds:
x × 30 = y × 30 = 1800Simplifying the equation, we get:
x - y = 1800/30 = 60Solving the equations simultaneously, we find that x = 75 m/s and y = -60 m/s. Since speed is always positive, we consider the magnitude of the velocity. Therefore, the speed of Alice's toy train is 75 m/s and the speed of Bob's toy train is 60 m/s.
A school is putting on a play. On the first night of the play, twice as many adults attended the lay as students. Students tickets cost $3 and adults tickets cost $5. The total amount of money earned from tickets sales was $1,131. Write a system of equations that represent this situation.
Answer:
x+2x+$3+$5=$1131
Step-by-step explanation:
Take students to be x then the adults be 2x and the dollars being played and the total money.Then you will take the $3+$8 and subtract from $1131 dollars then you'll get x
Answer: The system of equations that represent this situation is
x = 2y
5x + 3y = 1131
Step-by-step explanation:
Let x represent the number of adult tickets sold on the first night of the play.
Let y represent the number of student tickets sold on the first night of the play.
On the first night of the play, twice as many adults attended the play as students. This means that
x = 2y
Students tickets cost $3 and adults tickets cost $5. The total amount of money earned from tickets sales was $1,131. This means that
5x + 3y = 1131- - - - - - - - - 1
Which set of ordered pairs represents a function? A {(22, 5), (23, 10), (22, 7), (23, 5)} B {(22, 5), (26, 10), (23, 7), (23, 5)} C {(22, 10), (23, 10), (24, 7), (25, 5)} D {(24, 10), (23, 6), (22, 7), (24, 5)}
Answer:
C
Step-by-step explanation:
A function is a special kind of relation in which each valid input gives exactly one output.
C {(22, 10), (23, 10), (24, 7), (25, 5)}
So C is the correct option.
A farmer has 90 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wide, what are the dimensions
Answer:
W = 15 ft. and L = 30 ft.
Step-by-step explanation:
Perimeter = 90 ft.
Twice as long as it is wide: L=2W
P = 2(L + W) = 2(2W + W) = 6W
90 = 6W
W = 15 ft. and L = 30 ft.
Answer:
The dimensions are: Width= 15ft
Length=30ft
Step-by-step explanation:
Perimeter of fence=90feet
He wants to make a rectangle with dimensions length and with.
The rectangle length is twice as long as the width= L= 2W
Perimeter of a rectangle = 2(L + W)
90= 2(2W +W)
90= 6W
90/6=W=15ft
L=2W= 2× 15=30ft
John Worker had $31,000 in taxable income. What was his tax?
Final answer:
To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax. If the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.
Explanation:
To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax.
From the given information, we don't have the specific tax rate for $31,000. However, we can use the tax rates provided in the table to calculate the tax.
For example, if the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.
The power P required to do a fixed amount of work varies inversely as the time t. If a power of 15 J/h is required to do a fixed amount of work in 2 hours, what is the power required to do the same work in 1 hour?
Answer: the power required to do the same work in 1 hour is 30 j/h
Step-by-step explanation:
If two variables vary inversely, an increase in one of the variables causes a decrease in the other variable and vice versa.
The power P required to do a fixed amount of work varies inversely as the time t. If we introduce a constant of variation, k, the expression would be
P = k/t
If a power of 15 J/h is required to do a fixed amount of work in 2 hours, it means that
15 = k/2
k = 15 × 2 = 30
The equation becomes
P = 30/t
Therefore, the power required to do the same work in 1 hour is
P = 30/1 = 30 j/h
Before polling the students in Scion School of Business, a researcher divides all the current students into groups based on their class standing, such as freshman, sophomores, and so on. Then, she randomly draws a sample of 50 students from each of these groups to create a representative sample of the entire student body in the school. Which of the following sampling methods is the researcher practicing? 1. stratified random sampling 2. simple random sampling 3. cluster sampling 4. systematic random sampling 5. snowball sampling
Answer:
Correct option: 3. Cluster Sampling.
Step-by-step explanation:
Cluster sampling method is the type of sampling where first the entire population is divided into groups and then a random sample of fixed size is selected from each group.
In this case also, the researcher first divides the population of students in Scion School of Business into groups according to their class standing.
Then he selects 50 students from each of these groups to create a representative sample of the entire student body.
Thus, the sampling method used is Cluster Sampling.
Employees at Driscoll's Electronics as a base salary plus a 20% Commission on their total sales for the year. Suppose. The base salary is $40,000.
a. Write an equation to represent the total earnings of an employee. Remember to define your variable(s).
b. Stewart wants to make $65,000 this year. How much?must he make in sales?to achieve this salary? Write and solve an equation to answer this question.
c. Describe the equation 52,000 + 0.3s = 82,000 in terms of the problem situation.
Answer:
Step-by-step explanation:
Let x represent the total sales made in a year.
Employees at Driscoll's Electronics as a base salary plus a 20% Commission on their total sales for the year. If the base salary is $40,000, it means that if the employee makes a total sales of $x in a year, the total equation to represent earnings would be
0.2x + 40000
b) if Stewart wants to make $65,000 this year, it means that
0.2x + 40000 = 65000
0.2x = 65000 - 40000
0.2x = 25000
x = 25000/0.2
x = 125000
c) 52,000 + 0.3s = 82,000
The base salary is $52000
The percentage of commission from sales is 30%
Calculate the area of the sector
Answer:
Step-by-step explanation:
1/2 3
Answer: Area of sector = 11.8 square meters
Step-by-step explanation:
The formula for determining the area of a sector is expressed as
Area of sector = θ/360 × πr²
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 3 m
θ = 150 degrees
Therefore,
Area of sector = 150/360 × 3.14 × 3²
Area of sector = 11.8 square meters rounded up to the nearest tenth.
Which of the following are ordered pairs for the equation y = 2x - 3?
(0,-3) (1,-1) (2,1)
(-3,0) (-2,2) (-1,4)
(0,-3) (2,-2) (4,-1)
(-3,0) (-1,1) (1,2)
Answer:
A.
Step-by-step explanation:
The problem states that -3 is our y-intercept, so (0,-3) must be one of the answer choices. Next, just graph the equation to find the other two coordinate pairs are (1,-1) and (2,1).
Solve -1 4/5 x = 9.
5
-5
-
Answer:
C) -5
Step-by-step explanation:
-1 4/5 x= 9.
Change the left side to an improper fraction
(5*1+4)/5 = 9/5
-9/5 x =9
Multiply each side by -5/9 to isolate x
-5/9 * 9/5x = 9 * (-5/9)
x = -5
Answer:
x=-5
Step-by-step explanation:
-1 4/5x=9
-9/5x=9
-9x=9*5
-9x=45
x=45/(-9)
x=-5
Ms.Lopez has created a floor plan of a dollhouse. The area of the entire dollhouse is 576 square inches
Answer:
(a)Area of the bedroom=96 square inches
(b)Area of the living room =144 square inches
(c)Area of the dollhouse that is not of the bedroom or living room =336 square inches.
Step-by-step explanation:
The area of the bedroom is 1/6 the area of the entire dollhouse
The area of the living room is 3/2 times the area of the bedroom.
The area of the entire dollhouse is 576 square inches
Let the area of bedroom=b
Let the area of living room=l
(a) The area of the bedroom is 1/6 the area of the entire dollhouse
[tex]b=\frac{1}{6}X576=96[/tex] square inches
(b)The area, in square inches, of the living room
The area of the living room is 3/2 times the area of the bedroom
l= [tex]\frac{3}{2}X96=144[/tex] square inches
(c)The total area of the house =576 square inches
Area of the bedroom=96 square inches
Area of the living room =144 square inches
Area of the dollhouse that is not of the bedroom or living room
=576-(96+144)=576-240=336 square inches.
The area of the living room is 3/2 times the area of the bedroom
This is gotten by subtracting the area of the bedroom and living room from the total area of the house.
Out of 30 states, the three most common insects are Monarch butterflies, honeybees, and ladybugs. The number of Of states that have monarch butterflies as their official insect is one more than the number of states that have ladybugs as their official insect. The number of states that have honeybees as their official insect is three times the number of states with ladybugs as their state insect minus one. How many states have each kind of insect as their state insect?
There are 7 states with Monarch butterflies, 17 states with honeybees, and 6 states with ladybugs as their official insect.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us consider M, H, and L to represent the number of states with Monarch butterflies, honeybees, and ladybugs as their official insect, respectively.
We know that M + H + L = 30, since there are 30 states in total.
From the problem statement, we also know that:
M = L + 1 (1)
H = 3L - 1 (2)
We can use equations (1) and (2) to solve for M, H, and L:
M + H + L = 30
Substituting equation (1) and (2) into this equation:
(L + 1) + (3L - 1) + L = 30
5L = 30
L = 6
So there are 6 states with ladybugs as their official insect. Using equation (1) and (2), we can then find:
M = L + 1 = 7
H = 3L - 1 = 17
Hence, there are 7 states with Monarch butterflies, 17 states with honeybees, and 6 states with ladybugs as their official insect.
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Final answer:
To solve this problem, assign variables to represent the number of states that have each kind of insect. Use the given information to set up equations and solve simultaneously to find the values of 'm', 'h', and 'l'.
Explanation:
To solve this problem, let's assign variables to represent the number of states that have each kind of insect as their state insect. Let 'm' represent the number of states with Monarch butterflies, 'h' represent the number of states with honeybees, and 'l' represent the number of states with ladybugs as their official insect.
According to the problem, we have the following information:
'm' = 'l' + 1 (The number of states with Monarch butterflies is one more than the number of states with ladybugs)
'h' = 3('l') - 1 (The number of states with honeybees is three times the number of states with ladybugs minus one)
We also know that the total number of states is 30. So we can set up the following equation:
m + h + l = 30
Now, we can solve these equations simultaneously to find the values of 'm', 'h', and 'l'.
Using the first equation, we substitute 'l + 1' for 'm' in the second equation:
h = 3('l') - 1
h = 3(l + 1) - 1
h = 3l + 3 - 1
h = 3l + 2
Now, we substitute 'l + 1' for 'm' and '3l + 2' for 'h' in the third equation:
(l + 1) + (3l + 2) + l = 30
Simplifying the equation:
5l + 3 = 30
5l = 27
l = 5.4
Since 'l' represents the number of states with ladybugs, we can't have a fraction of a state. Therefore, we round 'l' down to the nearest whole number:
l = 5
Substituting this value back into the equations, we find that 'm' = 6 and 'h' = 14.
Therefore, there are 6 states with Monarch butterflies as their official insect, 14 states with honeybees, and 5 states with ladybugs.
Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag.
The domestic version of Boeing's 747 has a capacity for 568 passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity.
a) (171.651, 216.214)
b) (181.514, 208.313)
c) (174.412, 217.218)
d) (179.20, 212.716)
Answer:
The correct option is
d) (179.20, 212.716)
Step-by-step explanation:
We have out of a random sample of 1000, 345 carried more than a bag
Therefore in the question our X = 345 passengers carry more than a piece of luggage
n = 1000
Therefore the probability of a passenger carrying more than one luggage = 345/1000 = 0.345
The confidence interval estimator of p is given by
[tex]p'+/-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }[/tex] where p' = 0.345 = probability of desired outcome
n = 1000 = Population size
z at 95 % = Confidence interval estimate, the value is sought from the distribution table as z value is 1.96 at 95 % confidence level
We have [tex]0.345+/-1.96\sqrt{\frac{0.345*(0.655)}{1000} }[/tex] which gives
0.3745 or 0.3155
Which gives the range of confidential interval estimate as
212.695 to 179.224 which is equivalent to
d) (179.20, 212.716).
To determine the interval estimate of the number of passengers carrying more than one piece of luggage on the plane, we use the formula for the confidence interval for a proportion. The interval estimate is (0.3132, 0.3768), so we can expect the number to be between 313 and 377 passengers.
Explanation:To determine the interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane, we can use the formula for the confidence interval for a proportion. First, we calculate the sample proportion of passengers carrying more than one bag, which is 345/1000 = 0.345. Then, we find the standard error using SE = sqrt(p(1-p)/n), where p is the sample proportion and n is the sample size. Substituting the values, we get SE = sqrt(0.345(1-0.345)/1000) = 0.0162.
Next, we find the margin of error by multiplying the standard error by the critical value for the desired level of confidence. Since the problem does not specify a level of confidence, we will use a 95% confidence level, which corresponds to a critical value of 1.96. The margin of error is therefore 1.96 * 0.0162 = 0.0318.
Finally, we construct the confidence interval by subtracting and adding the margin of error from the sample proportion. The interval estimate is given by (0.345 - 0.0318, 0.345 + 0.0318), which simplifies to (0.3132, 0.3768). Therefore, we can expect the number of passengers carrying more than one piece of luggage on the plane to be between 313 and 377.
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Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16".
a. Not binomial: there are more than two outcomes for each trial.
b. Procedure results in a binomial distribution.
c. Not binomial: the trials are not independent.
d. Not binomial: there are too many trials.
Answer:
Correct option is b. Procedure results in a binomial distribution.
Step-by-step explanation:
Consider that X is Binomial random variable. The properties that are satisfied by X are:
There are n independent trials.Each trial has only two outcomes: Success & Failure.Each trial has the same probability of success.Suppose a roulette wheel is spun and the number of times the ball lands on '16' is observed.
If the random variable X is defined as the number of times the ball lands on '16', then the random variable X follows a Binomial distribution.
Because,
Each spin is independent of each otherSuccess: The ball lands on '16'Failure: The ball does not lands on '16'The probability of the ball landing on '16' is [tex]\frac{1}{37}[/tex] for each trial.Thus, the correct option is b. Procedure results in a binomial distribution.
Find the probability of winning second prize (that is, picking five of the six winning numbers) with a 6/44 lottery, as played in Connecticut, Missouri, Oregon, and Virginia. (Round the answer to five decimal places.)
Answer:
The answer to the question is
The probability of winning second prize (that is, picking five of the six winning numbers) with a 6/44 lottery, as played in Connecticut, Missouri, Oregon, and Virginia is 3.49905×10⁻⁵≡ 0.00003 to five decimal places.
Step-by-step explanation:
The probability of winning the second prize or picking five of the six winning numbers) with a 6/44 lottery is given by
Number of 5 sets of numbers in 44 = ₄₄C₅ = 1086008 ways
Number of 5 set of winning numbers in 44 = 1
Number of ways of picking the last number to make it 6 numbers is given by
44 - 5 lucky numbers - The 1 winning number = 38
Therefore, there are 38 ways from 1086008 of selecting the 5 second place winning numbers
Therefore the probability of picking the 5 second place winning numbers is [tex]\frac{38}{1086008}[/tex] = 3.49905×10⁻⁵
What is the rate of change in the y-values with respect to the x-values?
Answer:
The answer to your question is the last option
Step-by-step explanation:
Process
1.- To calculate the rate of change, calculate slope
Formula
m = (y2 - y1) / (x2 - x1)
x1 = 1 y1 = 1200
x2 = 2 y2 = 2400
2.- Substitution
m = (2400 - 1200) / (2 - 1)
3.- Simplification
m = 1200 / 1
4.- Result
m = 1200 meters / minute
Answer:
(d) 1200 Meters per minute
Step-by-step explanation: