What is the value of expression below when w = 4?

3w^2 - 3w + 8

Therefore, the probability that a senior boy does both wrestling and football is approximately 0.063 or 6.3%.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. The probability of an event can be determined by calculating the ratio of the number of favorable outcomes to the total number of possible outcomes.

Here,

Let A be the event that a senior boy wrestles, and B be the event that a senior boy plays football. Then, we want to find P(A and B), the probability that a senior boy does both wrestling and football. We know that there are 143 senior boys in total, 104 of whom do not do either wrestling or football. Therefore, the number of boys who do at least one of the two sports is:

N(A or B) = N(A) + N(B) - N(A and B)

= 21 + 27 - N(A and B) (since we don't know N(A and B))

= 48 - N(A and B)

We also know that N(A or B) = 143 - 104 = 39.

Therefore, we can solve for N(A and B):

N(A and B) = 48 - N(A or B)

= 48 - 39

= 9

So there are 9 senior boys who do both wrestling and football.

Finally, we can find the probability that a senior boy does both sports by dividing N(A and B) by the total number of senior boys:

P(A and B) = N(A and B) / N(total)

= 9 / 143

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Answer:

In mathematics, a function is a rule that assigns one unique output value for each input value. A linear function is a function that has a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will form a straight line.

For example, the function f(x) = 2x + 1 is a linear function because its graph is a straight line. As x increases by 1, the output of the function increases by 2.

On the other hand, a nonlinear function is a function that does not have a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will not form a straight line.

For example, the function f(x) = x^2 is a nonlinear function because its graph is a curve. As x increases, the output of the function increases at an increasing rate.

In general, nonlinear functions can take many different forms and can have complex behaviors, whereas linear functions have a simple, predictable behavior.

Note that the actual area under the above given curve  between x =2 and x = 6 is 12,870 (Option A)

To derive the actual arae under the curve, we have to tke the limit as the number of rectangles approaches infinity, which means we need to evaluate:

Limn → ∞ RN

Replacing the given formula for Rn, we get:

Limn →∞ [ 193955n⁴ + 863n³ - 38080n² - 204815n⁴

This will given us:

Limn → ∞  [ 193955n + + 863/n - 38080/n² - 2048/n⁴/15]

Note: As n approaches infinity, the second and 3rd terms will become relative negligible when palced side by side with the 1st term and the fouth term nears zero.

Thus:

Limn → ∞ (193055 / 15) = 12870.33

So Option A is the correct answer when approximated.

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On studing about the nature of system of linear equation the correct option is B.

How to determine the nature of system of linear equations of two variables?

Consider the following two linear equations:

\(a_1x + b_1y + c_1 = 0a_2x + b_2y + c_2 = 0\)

(1) If  \(\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\) them the system of equations have unique solution.

(2) If  \(\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}\) them the system of equations have infinitely many solutions.

(3) If  \(\frac{a_1}{a_2}= \frac{b_1}{b_2}\ne \frac{c_1}{c_2}\) them the system of equations have no solution.

Now, consider the given equation.

2x+3y = -17

y = x - 4

Rearrange the above equation as follows:

2x+3y +17 = 0

x - y - 4 = 0

Now, on comparing,

\(a_1=2, a_2=1, b_1=3, b_2=-1, c_1=17, c_2=-4\)

Now, take ratio as follows:

\(\frac{a_1}{a_2}=\frac{2}{1}\\\frac{b_1}{b_2}=\frac{3}{-1}\\\frac{c_1}{c_2}=\frac{17}{-4}\)

It satisfies the first condition hence, there is one solution for the system of equations.

Hence, the correct option is B.

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Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Answer:

12.

Step-by-step explanation:

There are 3 * 4 = 12 possible outcomes

for example

Walk / Red

Walk/Green

Walk/Blue

Walk/Orange

- and there are  4 similar outcomes for Run and Stop.

Answer:

$52

$57.6

Step-by-step explanation:

$20 off $72 is equal to 72-20=$52

20% of $72 is $14.4 which will then lead to 72-14.4=$57.6

Answer:

If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s .

Step-by-step explanation:

To find the margin of error, we can use the formula: E = z√((p(1-p))/n)

where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.

From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.

Plugging in the values, we get:

E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385

So the margin of error is 0.0385.

To find the confidence interval, we can use the formula:

p ± E

where p is the sample proportion and E is the margin of error.

Plugging in the values, we get:

0.696 ± 0.0385

So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].

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The volume of the sand pit is V = 694.6 feet²

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangle be represented as V

Now , the length of the sand pit = 30.2 feet

The width of the sand pit = 9.2 feet

The depth of the sand pit = 30 inches = 2.5 feet

Now , the volume of the rectangular pit = L x W x H

On simplifying the equation , we get

The volume of the rectangular pit V = 30.2 x 9.2 x 2.5

The volume of the rectangular pit V = 694.6 feet²

Hence , the volume of the rectangular sand pit is 694.6 feet²

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Since f(x) varies directly with x, we can write

where k is the constant of proportionality. We know that when x=5, f(5)=70, then we have

then, k is given as

Then, the equation which model the problem is

Now, we can substitute x=9 into this result. It yields,

Therefore, the answer is 126

y=kx

20=k(12)

k= 20/12 = 5/3

y= (5/3)x

y = 5x/3  or

3y=5x

Answer: 120 beads

Step-by-step explanation:

480 divided by four is equal to 120. Joe has 120 while Anna has 360. Mr Taylor gave each person 120 beads.

(so many typos in question so I do not know the names.)

Answer: 120

Step-by-step explanation:

480/4 is equal to 120. Joe has 120 while Anna has 360. Mr Taylor gave each person 120 beads.

Answer: y=5

Step-by-step explanation:

114+7y+y+26=180

8y+140=180

    -140   -140

8y=40

8     8

y=5

Answer:

horizontal shrink by a factor of 8

Step-by-step explanation:

The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

Answer:

--------------------------

Opposite sides of a parallelogram are parallel and congruent.

Set opposite sides equal and solve for unknowns:

A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

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Answer:

a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.

b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Step-by-step explanation:

For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

One out of four cars needs to have oil added.

This means that \(p = \frac{1}{4} = 0.25\)

a. One out of the next four cars needs oil.

This is P(X = 1) when n = 4. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219\)

0.4219 = 42.19% probability that one out of the next four cars needs oil.

b. Two out of the next eight cars needs oil.

This is P(X = 2) when n = 8. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115\)

0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c.Three out of the next 12 cars need oil.

This is P(X = 3) when n = 12. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581\)

0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.

We're given:

\(\dfrac{3240\hspace{4}feet}{hour}\)

We also know that:

\(\dfrac{hour}{60\hspace{4}minutes}\)

Multiply the two to cancel out the hour:

\(\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}\)

Simplify:

\(=\dfrac{54\hspace{4}feet}{minute}\)

\(\dfrac{54\hspace{4}feet}{minute}\)

Answer:

0.6568 = 65.68% probability that she would be correct.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

45000, 45500, 44500, 46000 and 44000 units. This rate of sales is considered average for the product over the last twenty years or so.

This means that:

\(\mu = \frac{45000 + 45500 + 44500 + 46000 + 44000}{5} = 45000\)

Standard deviation of 1500 units.

This means that \(\sigma = 1500\)

What is the likelihood that she would be correct if she predicts sales between 43000 and 46000?

This is the pvalue of Z when X = 46000 subtracted by the pvalue of Z when X = 43000. So

X = 46000

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{46000 - 45000}{1500}\)

\(Z = 0.67\)

\(Z = 0.67\) has a pvalue of 0.7486

X = 43000

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{43000 - 45000}{1500}\)

\(Z = -1.33\)

\(Z = -1.33\) has a pvalue of 0.0918

0.7486 - 0.0918 = 0.6568

0.6568 = 65.68% probability that she would be correct.

Answer:

10times

Step-by-step explanation:

there is a 50/50 chance of both 20 divided by 2 is 10

After tossing 20 times a coin probability of getting heads is equals to 10.

" Probability of any event is defined as the ratio of total number of favourable outcomes to the total number of outcomes."

Formula used

\(Probability =\frac{Number of favourable outcomes}{Total number of oucomes}\)

According to the question,

Number of times coin tossed = 20

When we toss a coin there only two outcomes Head and Tail.

As per the formula,

Probability of head = 1 / 2

Probability of tail = 1 / 2

Therefore,

Probability of getting head when Karla tossed coin 20 times is equals to 20 / 2 = 10 times.

Hence, after tossing a coin 20 times  probability of getting heads is equals to 10 times.

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Answer:

2(x-8)

Step-by-step explanation:

Let the number be x

2[x+(-8)]

2(x-8)

Answer:

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation is 9.5 for a population.

This means that \(\sigma = 9.5\)

Sample of 60:

This means that \(n = 60\)

What is the standard deviation of the distribution of sample means for samples of size 60?

\(s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264\)

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Based on the information, the hedgehogs have made the better offer

The Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:

PV = S(t) * e^(-rt)

The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:

PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt

= 736,918.63

Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:

PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt

= 753,472.49

Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.

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The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

The binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

To determine which binomial is a factor of the trinomial x² - 13x + 30, we need to factorize the trinomial completely.

In this case, we need to find two binomials in the form (x - a)(x - b) that satisfy the equation:

(x - a)(x - b) = x² - 13x + 30

So, (x - 3)(x - 10) = x² - 13x + 30.

Therefore, the binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

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