Mr. Jackson had $110 to purchase school supplies for his class. He bought 32 boxes of colored pencils and 32 dry erase markers. Each box of colored pencils cost $2.40, and each dry erase marker cost $0.79. How much money did Mr. Jackson have left after these purchases?

Answer:

(A)The sample comes from a population of tires with 60,000 miles where 5% of tires are worn out.

Step-by-step explanation:

The tire manufacturer has a 60,000 mile warranty for tread life. To verify the authenticity of its claim, it picks a sample of 250 tires (out of the population of tires) that have been used for 60,000 miles.  

Given the hypothesis:

[tex]H_0[/tex]: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.  

[tex]H_a[/tex]: The proportion of tires that are worn out after 60,000 miles is less than 0.05.

It is assumed that 5% of the tires in the sample are worn out and the hypothesis is formulated to prove or disprove this assumption.

Answer: 0.25

Step-by-step explanation:

I did the quiz

Answer:

0.25

Step-by-step explanation:

Hope this helps, have a nice day

Answer:

She should guarantee a weight of 4.18 pounds.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 8.6, \sigma = 1.9[/tex]

What weight should she guarantee so that she will have to give her customer's money back only 1% of the time?

She should guarantee the 1st percentile of weights, which is X when Z has a pvalue of 0.01. So it is X when Z = -2.327.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.327 = \frac{X - 8.6}{1.9}[/tex]

[tex]X - 8.6 = -2.327*1.9[/tex]

[tex]X = 4.18[/tex]

She should guarantee a weight of 4.18 pounds.

The turkey farmer should guarantee that her 6-week poults will weigh at least  4.2 pounds to ensure that she will have to give money back only 1% of the time.

Given:

- Mean weight [tex](\( \mu \))[/tex] of poults: 8. 6 pounds

- Standard deviation [tex](\( \sigma \))[/tex] of poults: 1.9 pounds

1. Use the z-score corresponding to the 1st percentile of the normal distribution, which is approximately [tex]\( z_{0.01} \approx -2.3263 \)[/tex].

2. Calculate the guaranteed weight X:

  [tex]\[ X = \mu + z_{0.01} \cdot \sigma \] \[ X = 8.6 + (-2.3263) \cdot 1.9 \] \[ X \approx 4.2 \text{ pounds} \][/tex]

Therefore, the turkey farmer should guarantee that her 6-week poults will weigh at least 4.2 pounds to ensure that she will have to give her customers' money back only 1% of the time. This ensures that 99% of the poults will weigh at least 4.2 pounds.

Answer:

d) 300 times for the first game and 30 times for the second

Step-by-step explanation:

We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.

As the coin is flipped more than one time and calculated the proportion, we have to use the sampling distribution of the sampling proportions.

The mean and standard deviation of this sampling distribution is:

[tex]\mu_p=p\\\\ \sigma_p=\sqrt{\dfrac{p(1-p)}{N}}[/tex]

We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.

The probability of getting a proportion within this interval can be calculated as:

[tex]P(0.45<x<0.55)=P(z_L<z<z_H)[/tex]

referring the z values to the z-score of the standard normal distirbution.

We can calculate this values of z as:

[tex]z_H=\dfrac{p_H-\mu_p}{\sigma_p}=\dfrac{(p_H-p)}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_H-p)>0\\\\\\z_L=\dfrac{p_L-\mu_p}{\sigma_p}=\dfrac{p_L-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_L-p)<0[/tex]

If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.

With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.

For the second game, we win if we get a proportion over 80%.

The probability of winning is:

[tex]P(p>0.8)=P(z>z^*)[/tex]

The z value is calculated as before:

[tex]z^*=\dfrac{p^*-\mu_p}{\sigma_p}=\dfrac{p^*-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p^*-p)>0[/tex]

As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).

If our chances of winnings depend on P(z>z*), they become lower as z* increases.

Then, we can conclude that our chances of winning decrease with the increase of the number of trials.

We prefer the option of 30 trials for this game.

Final answer:

For the first game where 45% to 55% heads are needed, flipping the coin 300 times is beneficial due to the law of large numbers. For the second game requiring over 80% heads, flipping only 30 times is better to have a higher chance of deviation from the theoretical probability. So the correct option is d.

Explanation:

In determining whether you would rather flip a coin 30 times or 300 times for each game, one must consider the law of large numbers, which implies that as the number of trials increases, the experimental probabilities tend to get closer to the theoretical probabilities. In this case, a fair coin has a 50% chance of landing on heads on any given flip.

For the first game, where you win if you land between 45% and 55% heads, it's advantageous to flip the coin more times. This is because, with a larger number of flips (like 300), the results are more likely to converge to the expected probability, making it more probable you'll land within that range. Hence, you should choose 300 flips for the first game.

For the second game, where you win if you land more than 80% heads, you would prefer fewer flips, such as 30. It's less likely for a fair coin to consistently land on heads as the number of flips increases, so reducing the number of flips increases the chance of a more significant deviation from the expected probability.

The correct answer, therefore, would be option d: 300 times for the first game and 30 times for the second game.

Step-by-step explanation:

[tex]hi \: your \: answer \: is \: d \\ w = {x}^{2} - 2yz \\ w - {x }^{2} = - 2yz \\ 2yz = {x }^{2} - w \\ divide \: both \: sides \: by \: 2z \\ y = \frac{ {x}^{2} - w }{2z} [/tex]

Answer:

Answer B

[tex]y = \frac{w - {x}^{2} }{2z} [/tex]

Step-by-step explanation:

[tex]w = {x}^{2} - 2yz \\ w - {x}^{2} = 2yz \\ \frac{w - {x}^{2} }{2z} = \frac{2zy}{2z} \\ \\ y = \frac{w - {x}^{2} }{2z} [/tex]

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Answer:

an exterior angle is the correct answer.....

Answer:

A

Step-by-step explanation:

We have been given that Ben has a square garden that has sides measuring X feet, Ben wants to increase every side of his garden by 11 feet in order to plant more vegetables. So each side of garden would be [tex]X+11[/tex].

We are also told that after Ben increased his garden it will have a perimeter of 104 feet.

We know that perimeter of square is 4 times the side length. So perimeter of garden after enlargement would be [tex]4(X+11)[/tex].

Now we will equate perimeter of new garden with 104 as:

[tex]4(X+11)=104[/tex]

Therefore, the equation [tex]4(X+11)=104[/tex] can be used to solve for X.

[tex]\frac{4(X+11)}{4}=\frac{104}{4}[/tex]

[tex]X+11=26[/tex]

[tex]X+11-11=26-11[/tex]

[tex]X=15[/tex]

Therefore, the value of X is 15 feet.

Answer:

what is the question?

Step-by-step explanation:

Answer:

By the Empirical Rule, 68% of light bulbs last between 1345 hours and 1455 hours

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 = 1400 hours

Standard deviation = 55 hours

Using the empirical rule, what percentage of light bulbs last between 1345 hours and 1455 hours?

1345 = 1400 - 1*55

So 1345 is one standard deviation below the mean.

1455 = 1400 + 1*55

So 1455 is one standard deviation above the mean.

By the Empirical Rule, 68% of light bulbs last between 1345 hours and 1455 hours

Answer:

1225000

Step-by-step explanation:

The hydrostatic force against one side of the submerged equilateral triangle can be obtained by integrating the product of the fluid pressure and the area of an infinitesimally small strip on the triangle from base to top, yielding a result of 49,000 Newton.

To express the hydrostatic force against one side of the equilateral triangular plate as an integral, we need to start with the equation for the pressure at any point in a fluid: P = ρgh. This is the product of the water density (ρ), gravitational acceleration (g), and height inside the fluid (h).

Next, we multiply this by the area of an infinitesimally small horizontal strip on our triangular plate, and then integrate to account for the entire side of the triangle, from the base to the top. In this problem, the area of the strip depends on the height, and for an equilateral triangle with a side length of 10m, it can be expressed as 10-2y.

Therefore, the hydrostatic force F becomes the integral ∫(0 to 10) ρg(10 - y)dy, where ρ is the weight density of water 1000 kg/m3, g stands for the acceleration due to gravity 9.8 m/s2, and y is the height varying from 0 to 10 m. Evaluating this integral, we get F = 49,000 Newton.

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Answer:

B=16

Step-by-step explanation:

If 75% is 12, 100% would be 16. B = 16!

Answer:16

Step-by-step explanation:

12/3=4 4=25%of b 4+12=16

Answer:

12m^3

Step-by-step explanation:

Basically, you are looking for the volume of the Oil. In order to do that you simply need to use the rectangular prism volume formula: lwh

lwh=V

(5)(2)(1.2)=V

10(1.2)=V

12=V

Given one to one f(6)=3, f'(6)=5, find tangent line to y=f⁻¹(x) at (3,6)

OK, we know

f⁻¹(3)=6

The inverse function is the reflection in y=x.  So slopes, i.e. the derivative will be the reciprocal.  We know the derivative of f at 6 is 5, so the derivative of f⁻¹  at y=6 is 1/5, which corresponds to x=3.

f⁻¹ ' (3) = 1/5

That slope through (3,6) is the tangent line we seek:

y - 6 = (1/5) (x-3)

That's the tangent line.

y = x/5 + 27/5

First, find the inverse function.

Note that an inverse is a reflection; y = x

The derivative given will be the reciprocal and when f is at 6, it equals 5. So, when it is at y = 6 it is at x = 1/5 and corresponds to 3.

f^-1(3) = 1/5

The point (3, 6) is the point in which the slope goes through. We can write all this information in slope-intercept form.

y = 1/5x + 27/5

Best of Luck1

I suppose "below the sphere" means "inside" it, or below the upper half of it. The integral is

[tex]\displaystyle\iiint_Fz\,\mathrm dV[/tex]

where

[tex]F=\{(x,y,z)\mid0\le x\le2,x\le y\le2,0\le z\le\sqrt{8-x^2-y^2}\}[/tex]

Evaluating the integral in Cartesian coordinates is straightforward enough to not require changing coordinates:

[tex]\displaystyle\int_0^2\int_x^2\int_0^{\sqrt{8-x^2-y^2}}z\,\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

[tex]=\displaystyle\frac12\int_0^2\int_x^2(8-x^2-y^2)\,\mathrm dy\,\mathrm dx[/tex]

[tex]=\displaystyle\frac12\int_0^2\left(16-8x-2x^2+\frac{4x^3-8}3\right)\,\mathrm dx=\boxed{\frac{16}3}[/tex]

The problem involves calculating a triple integral of a function over a specified region. The function is transformed into spherical coordinates considering the given boundaries. Afterwards, we solve the triple integral by integrating with respect to the spherical coordinates.

The given function in the question you're asking about belongs to triple integration, a concept in calculus that extends the idea of one-dimensional integration to three dimensions. In the context of the problem, your function, f(x, y, z) = z, is defined over the region F below the sphere x2 + y2 + z2 = 8 and above the triangular region in the xy-plane bounded by x = 0, y = 2, and y = x.

Firstly, let's convert the coordinates to spherical coordinates. This is appropriate especially when dealing with volumes of spheres or parts of spheres. If we translate these conditions into spherical coordinates, where:

The triple integral thus becomes:

∫02π∫0π/4∫02 ρcosϕ * ρ2sinϕ dρ dϕ dθ.

Note that ρ2sinϕ in the equation above is the Jacobian determinant that arises from the transformation to spherical coordinates. Proceed to solve the triple integral above by integrating with respect to ρ, then ϕ, and finally θ.

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Answer:

156

Step-by-step explanation:

Total number of games played by Ronique's team is ≤ 279(round off).

" At least represents the minimum quantity of the number . it can be more than the given condition."

According to the question,

Number of games  team won each year for the past 7 years are

31, 24, 32, 22, 34, 28, 38.

Total number of games won by team = 31 + 24 + 32+22 + 34 + 28 + 38

                                                              = 209

Team won at least  75% of the seasons they played

'x' represents the total number of seasons they played

Therefore,

75% of x ≤ 209

⇒[tex]\frac{75}{100} (x)\leq 209[/tex]

⇒ [tex]x \leq \frac{(209)(100)}{75}[/tex]

⇒ [tex]x\leq 278.666..[/tex]

⇒[tex]x\leq 279 (round off)[/tex]

Hence, total number of games played by Ronique's team is ≤ 279(round off).

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Answer:

y = 3/5x + (-3)

Step-by-step explanation:

because slope intercept form is y = mx + b

and m = 3/5

and b = -3

so you plug them in to the formula and there's your answer

The equation in slope-intercept form for the line with a slope of 3/5 and a y-intercept of -3 is y = (3/5)x - 3.

We have,

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Slope (m) = 3/5

Y-intercept (b) = -3

Plug in the values of the slope and y-intercept into the equation.

y = (3/5)x - 3

Therefore,

The equation in slope-intercept form for the line with a slope of 3/5 and a y-intercept of -3 is y = (3/5)x - 3.

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Step-by-step explanation:

x/ 3 = 2 / 9

Cross multiply

9x = 6

x = 6 / 9

x = 2 / 3

Answer:

There are 154 children, 77 adults and 86 students in attendance

Step-by-step explanation:

Given

Seat capacity = 317

Total tickets = $2296

Charges is as follows;

Children = $5.00

Students = $7.00

Adults = $12.00

Required

Number of children, students and adults

Let A, C and S represent adults, children and students respectively.

So,

From sales of tickets, we have the following:

12A + 5C + 7S = 2296 --- Equation 1

From attendance, we have

A + C + S = 317 --- Equation 2

Given that, there are half as many adults as there are children.

So, A = ½C

Substitute ½C for A in equation 1 and 2

12A + 5C + 7S = 2296 becomes

12 * ½C + 5C + 7S = 2296

6C + 5C + 7S = 2296

11C + 7S = 2296 ---- Equation 3

A + C + S = 317

½C + C + S = 317

Multiply through by 2

2(½C + C + S) = 2 * 317

C +2C + 2S = 634

3C + 2S = 634 ----- Equation 4

We'll solve equations 3 and 4, simultaneously.

First, write out the two equations.

11C + 7S = 2296 ---- (3)

3C + 2S = 634 ------ (4)

Using elimination method to eliminate S.

Multiply (3) by 2 and multiply (4) by 7.

2 (11C + 7S = 2296 )

22C + 14S = 4592 ---- Equation 5

7 (3C + 2S = 634 )

21C + 14S = 4438 ------ Equation 6

Subtract (6) from (5)

22C + 14S = 4592

21C + 14S = 4438

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

22C - 21C + 14S - 14S = 4592 - 4438

C = 154

Recall that A = ½C

So, A = ½ * 154

A = 77

Recall equation 2

A + C + S = 317

Make S the subject of formula

S = 317 - A - C

Substituton 77 for A and 154 for C

So,

S = 317 - 77 - 154

S = 86

Hence, there are 154 children, 77 adults and 86 students in attendance

There are five successful outcomes for choosing an even number between 0 and 9, which are 0, 2, 4, 6, and 8.

Hernando is choosing a random number between 0 and 9. The even numbers in this range are 0, 2, 4, 6, and 8. To determine the number of successful outcomes for choosing an even number, we simply count the even numbers listed.

There are five even numbers between 0 and 9 which are: 0, 2, 4, 6, and 8. Therefore, there are five successful outcomes for choosing an even number.

Answer:

The mean of the sampling distribution = $1350

Step-by-step explanation:

Given -

Population mean [tex]\boldsymbol{(\nu)}[/tex] = $1350

Standard deviation = $150

Sample size ( n ) = 25

The mean of the sampling distribution = population mean

[tex]\boldsymbol{(\nu)_{M}} = \boldsymbol{(\nu)}[/tex]

The mean of the sampling distribution = $1350

Given:

A rhino runs at a speed of about 28 miles per hour.

We need to determine the speed in feet per second.

Converting miles to feet:

The miles can be converted to feet by multiplying 5280 with 28 miles per hour.

Thus, we have;

[tex]28\times 5280=147840[/tex]

Thus, the speed of the rhino in feet per hour is 147840

Converting hours to seconds:

The hours can be converted into seconds by dividing 147840 by 3600 (Because an hour has 60 seconds in a minute and 60 minutes in an hour)

Thus, we get;

[tex]Speed=\frac{147840}{3600}[/tex]

[tex]Speed = 41.066667[/tex]

Rounding off to the nearest whole number, we get;

[tex]Speed =41[/tex]

Therefore, the speed of the rhino is 41 feet per second.

Hence, Option B is the correct answer.

Answer:

80 yards

Step-by-step explanation:

There are 3 feet in a yard, therefore you take 240 feet divided by 3 to get how many yards there are, and in your case it is 80 yards.

Answer:

Depending on the exact measurements of the sides, the way to find perimeter would be to add up all the measurements along the sides. If this shape were only two sides, which is impossible, the perimeter would be 10 + 19, or 29.

Step-by-step explanation:

Answer:

you have to stretch the shape out and then add them

Step-by-step explanation:

so 10+19+10+19=58

Answer:

[tex]a = \frac{w + 4 - 3b}{6} [/tex]

Step-by-step explanation:

[tex]w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b}{6} = \frac{6a}{6} \\ a = \frac{w + 4 - 3b}{6} [/tex]

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Answer:

a = 1/7, b = 0.2, c = 3/9

Step-by-step explanation:

[tex]0.2=\frac{2}{10} = \frac{1}{5}[/tex]

[tex]\frac{1}{7}[/tex]

[tex]\frac{3}{9}=\frac{1}{3}[/tex]

[tex]\frac{1}{5} > \frac{1}{7}[/tex] placing it farther along the number line, making 0.2 the red label (b)

[tex]\frac{1}{7}[/tex] is the smallest fraction that you are given, so it will be closest to 0, making it the blue label (a)

[tex]\frac{1}{3} > \frac{1}{4}[/tex] so [tex]\frac{3}{9}[/tex] is the green label (c)

Answer: the t-test statistic is - 1.77

Step-by-step explanation:

For the null hypothesis,

H 0: μ = 2600

For the alternative hypothesis,

H a: μ ≠ 2600

This is a two tailed test

Since no population standard deviation is given, the distribution is a student's t.

Since n = 50,

Degrees of freedom, df = n - 1 = 50 - 1 = 49

t = (x - µ)/(s/√n)

Where

x = sample mean = $2450

µ = population mean = $2600

s = samples standard deviation = $600

Therefore,

t = (2450 - 2600)/(600/√50) = - 1.77

The t-test statistic calculated for the given data comparing the mean Pell grant award at San Jose State University to the national average for 2007-2008 is approximately -1.77.

The t-test statistic is calculated using the formula: t = (sample mean - population mean) / (standard deviation / sqrt(sample size)). In this case, the sample mean is the mean Pell grant award for the 50 students from San Jose State University ($2,450), the population mean is the average Pell grant award according to the National Postsecondary Student Aid Study for 2007-2008 ($2,600), the standard deviation is $600, and the sample size is 50. Substitute these values into the formula to get: t = ($2,450 - $2,600) / ($600 / sqrt(50)) = -$150 / ($600 / 7.071) = -$150 / 84.85 = -1.77. So the t-test statistic is approximately -1.77, comparing the mean Pell grant award at San Jose State University to the national average for 2007-2008.

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Answer:

The time it will take to paint 60 banners is 12 hours.

Step-by-step explanation:

The question is:

Several students from one school painted 15 banners in 3 hours. How many hours will it take for students to paint 60 banners

Solution:

The Unitary method is a mathematical procedure to determine the value of 1 unit from n unit values.

It is provided that the time it takes to paint 15 banners is, t = 3 hours.

Then the time it should have taken to paint 1 banner is, [tex]\frac{3}{15}=\frac{1}{5}\ hours[/tex].

Compute the time it will take to paint 60 banners as follows:

Time = [tex]60\times \frac{1}{5}=12[/tex]

Thus, the time it will take to paint 60 banners is 12 hours.

Answer:

The grammar has start symbol S, terminals are 1,3,5,7 an  9 ; and the variables are S, A, B, C and D

Step-by-step explanation:

CHECK THE ATTACHMENT FOR EXPLANATION