if a is more than b, what is the equation for an ellipse with a centre at the origin and a horizontal major axis?

The box requires a minimum of 4032 square inches of material.

Let's assume that the square base of the box has side length 'x', and the height of the box is 'h'. Then the volume of the box is

V = x^2 × h = 6912

We need to find the dimensions of the box that require the least amount of material. This means we need to minimize the surface area of the box. The surface area of the box is given by

S = x^2 + 4xh

We can solve for 'h' in terms of 'x' using the volume equation

h = 6912 / x^2

Substituting this expression for 'h' into the surface area equation, we get

S = x^2 + 4x(6912/x^2)

Simplifying and taking the derivative of 'S' with respect to 'x', we get

dS/dx = 2x - 27744/x^3

Setting this derivative equal to zero to find the critical points

2x - 27744/x^3 = 0

Multiplying both sides by x^3 and solving for 'x', we get

x = (27744/2)^(1/4) = 18

To confirm that this is a minimum, we need to check the second derivative of 'S' with respect to 'x'

d^2S/dx^2 = 2 + 83208/x^4

At x = 18, we have

d^2S/dx^2 = 2 + 83208/18^4 > 0

Therefore, the critical point at x = 18 corresponds to a minimum surface area.

So the dimensions of the box with the least amount of material are

The side length of the base is 18 inches, and

The height of the box is h = 6912 / 18^2 = 32 inches.

The minimum amount of material required is the surface area of the box, which is

S = 18^2 + 4(18)(32) = 1728 + 2304 = 4032 in^2.

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Answer:

(-2,1)

Step-by-step explanation:

Answer:

-2/1

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

add all the numbers then divide by how many numbers there are.

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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Answer:

infinite solutions

Step-by-step explanation:

Multiply the first equation by 2

2(3x-5y) = 2*15

6x - 10y = 30

This is the same as the second equation

They are the same line

This means there are infinite solutions

The point-slope form of equation of the line perpendicular to the line y = 5x + 6 nd passing through (-3,3) is x + 5y = 12.

If two lines are perpendicular to each other, then the product of slopes of these two lines is equal to -1.

The provided line is y = 5x + 6,

The slope M₁ of the line is equal to the coefficient of x,

M₁ = 5

Let the slope of the perpendicular line is M₂,

So, we can write,

M₁M₂ = -1

M₂ = -1/5.

Now, we can use the point slope form of the equation of line, according to which is if line passes through (a,b) and have slope m then the equation of the line will be,

(y-a) = m(x-a)

This form of line is called Point-slope form of line.

Then, the equation of the line with slope -1/5 and passing through (-3,3) will be,

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

-5y+15 = x+3

x + 5y = 12

The above equation is the required equation of line in point slope form.

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Answer:

It is a acute triangle

Step-by-step explanation:

The estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.

Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.

Out of the 31 students surveyed, 6 reported having no pets, 8 reported having one pet, 10 reported having two pets, 3 reported having three pets, and a total of 4 (1+2+1) reported having four or more pets.

Thus, the probability that a randomly selected student from this class has four or more pets at home is:

P(four or more pets) = 4/31 ≈ 0.13 (rounded to two decimal places)

Therefore, the estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.

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The cost of one small box is $10 and the cost of one large box of grapefruit is equal to $16.

This type of problem can be solved using linear equations.

If we consider x to be the cost of one small box and y to be the cost of one large box of fruit, the linear equations can be given as;

12x + 5y = 200

4x + 10y = 200

Multiplying the second equation by 3

12x + 5y = 200

12x + 30y = 600

Now by subtracting both equations we get;

-25y = -400

y = -400 / -25

y = 16

Now adding this value of y = 16 in the first equation;

12x + 5y = 200

12x + 5(16) = 200

12x + 80 = 200

12x = 200 - 80

12x = 120

x = 120 / 12

x = 10

Therefore, $10 is the cost of one small box and $16 is the cost of one large box of grapefruit.

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Answer:

I think the answer is A

1,2

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The equation of the given line is expressed as

3x - 6y = 30

Rearranging it so that it will look like the slope intercept form, it becomes

6y = 3x - 30

Dividing both sides by 6, it becomes

6y/6 = 3x/6 - 30/6

y = x/2 - 5

Looking at the equation, slope, m = 1/2

If two lines are parallel, it means that they have equal slope. This means that the slope of the line parallel to the given line is 1/2

To determine the y intercept, c of the line passing through the point (4, - 9), we would substitute

x = 4, y = - 9 and m = 1/2 into the slope intercept equation. It becomes

- 9 = 1/2 * 4 + c

- 9 = 2 + c

c = - 9 - 2

c = - 11

By substtuting m = 1/2 and c = - 11 into the slope intercept equation, the equation of the line would be

y = x/2 - 11

Answer:

7/8

Step-by-step explanation:

turn 1/4 denominator into 8 and by doing that, u multiply by 2.

whatever you do to the bottom, u do to the top. so 1/4= 2/8

5/8+2/8= 7/8

5/8  +  1/4 = 37/20

37/20=1 y 17/20

Answer:

432

Step-by-step explanation:

Hope this helps!

The probability that Joe and Mathew would have to purchase no books on this visit to the bookstore is given as 0.125.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We are to find the probability where p(x) = 0 and p(y) = 0

This is where we would have

from the table,  p(x) = 0 is 0.5

p(y) = 0 is 0.25

0.25 x 0.5 = 0.125

Hence the probability that no books would be bought is 0.125.

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The line of intersection of two planes is found by the cross product of the normal vectors of each plane. Therefore, to find the direction numbers for the line of intersection of the planes x y z = 4 and x z = 0, we must first find the normal vectors of each plane.

The equation x y z = 4 can be rewritten as z = -x - y + 4, which means that the normal vector of this plane is <1, 1, -1>.Similarly, the equation x z = 0 can be rewritten as x = 0 or z = 0, which means that the normal vector of this plane is <0, 1, 0>.Taking the cross product of these two normal vectors, we get:<1, 1, -1> × <0, 1, 0> = <-1, 0, -1>

Therefore, the direction numbers of the line of intersection of the planes x y z = 4 and x z = 0 are -1 and -1.

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The possible data in the question does not provide sufficient evidence available to support the alternative hypothesis that there is a difference between Mr. Starnes and Ms. McGrail's AP Statistics classes and Mr. Starnes did not stack the class.

In statistics, a hypothesis test is the performance of a test on an assumption made about a population parameter.

The possible data in the question, obtained from a similar online question, using MS Excel, indicates;

The mean of the Starnes GPA ≈ 3.212867

The standard deviation of Starnes GPA ≈ 0.364249

Mean of McGrail GPA ≈ 3.134722

The standard deviation of McGrail's GPA ≈ 0.357995

The null hypothesis is H₀: μ₁ - μ₂ = 0

The alternative hypothesis is Hₐ: μ₁ - μ₂ ≠ 0

The test statistic is found using the following formula;

\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } }\)

The decision rule is obtained with α = 0.05 and the null hypothesis is rejected t₀ ≤ -1.96 or t₀ ≥ 1.96

Therefore, we get;

\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{\dfrac{0.364249^2}{15}+\dfrac{0.357995^2}{18} } } \approx 0.618\)

The parameter for the degrees of freedom is 15 - 1 = 14

The critical value obtained from the t-table, at t.₉₅ is 1.761 which is larger than 0.618, therefore, we fail to reject the null hypothesis, and the evidence is insufficient to suggest that there is a difference in the average score of the two AP Statistics classes.

Taking the variance to be the same, we get;

\(S_p^2= \dfrac{(n_1-1)\cdot s_1^2+(n_2-1)\cdot s_2^2}{n_1+n_2-2}\)

Therefore;

\(S_p^2= \dfrac{(15-1)\times 0.364249^2+(18-1)\times 0.357995^2}{15+18-2}\approx 0.1302\)

\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{s_p^2 \times\left(\dfrac{1}{n_1}+\dfrac{1}{n_2} }\right) }\)

\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{0.1302\times \left(\dfrac{1}{15}+\dfrac{1}{18} }\right) } \approx 0.6195\)

df = 15 + 18 - 2 = 31

From the t-table, the critical value is about 1.697, which is larger than 0.6195, therefore, the null hypothesis cannot be rejected and the evidence available is not enough to suggest that there is a difference between the grade point averages of Mr. Starnes and Ms. McGrail AP Statistics classes and Mr. Starnes did not stack the class

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The answer to your question is the following:

Make sure to simplify !!

Answer: 6 are not enrolled.

Step-by-step explanation:

78 in total so you add 41+22+9 and you get 72 so you do 78-72 and you get 6.

a) Anaiah currently spending $150 on these goods

b) His behavior is irrational because,

option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

Based on the given information, Anaiah is currently spending $150 on these goods, which is calculated by adding the total cost of eggplants and kiwis as follows:

Cost of 20 eggplants = 20 x $3 = $60

Cost of 30 kiwis = 30 x $3 = $90

Total cost = $60 + $90 = $150

Anaiah is behaving irrationally because he is not spending his entire income of $180, which means he is not maximizing his utility. Additionally, he is spending too much on kiwis, as indicated by the higher marginal utility per dollar spent on the 30th kiwi compared to the 20th eggplant.

This suggests that he would derive more satisfaction from spending more on eggplants and less on kiwis. Lastly, his marginal utility per dollar spent is not the same for both goods, which implies that he is not balancing his spending on each good to achieve the maximum total utility. Therefore, Anaiah could improve his spending behavior by adjusting his purchases to reflect a better balance of marginal utility per dollar spent on each good.

Therefore, the correct options are  option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

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The answer of given question is option a) per worker expenditures for best practices training

The term "expenditures" refers to the sum of money that a person, business, or government spends or pays for a particular objective or thing. It is the total amount of money spent on products and services over a certain time period. Costs associated with operating a business or organisation, such as salaries and wages, materials, supplies, equipment, advertising, utilities, and rent, can all be considered expenditures.

According to question

The satisfying statement is

a) per worker expenditures for best practices training, the S/Q rating of the pairs being produced, the percentage use of superior materials, and expenditures for TQM/Six Sigma quality control efforts.

So, option (a) is correct

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Answer:

I think b?

Step-by-step explanation:

Answer:

157.38

Step-by-step explanation:

if you add all those numbers you will get 1888.59/12= 157.38

Romans experimental probability is 0.176.

Probability simply means the likelihood that something will happen or take place.

In this case, Roman spun the spinner 34 times and landed on 4 a total of six time.

The probability will be:

= Number of occurence / Total available value

= 6 / 34

= 0.176

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Answer:

12 minutes till 88 liters

Step-by-step explanation:

Answer:

U' (5, 1 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )

1. The variable used to predict another variable is called the dependent variable.

2. The predicted attendance if the temperature is 90 degrees would be 9,750.

3. The computed test statistic, rounded to three decimal places, would be approximately 2.071.

1. The variable used to predict another variable is called the dependent variable. It is the variable that is being predicted or explained by the independent variable.

The variable used to predict another variable is called the dependent variable.

2. The given equation is Attendance = 16,500 - 75 * Temperature.

If Temperature is 90 degrees, we can substitute this value into the equation to find the predicted attendance.

Attendance = 16,500 - 75 * 90

Attendance = 16,500 - 6,750

Attendance = 9,750

Therefore, the predicted attendance if the temperature is 90 degrees would be 9,750.

The predicted attendance if the temperature is 90 degrees would be 9,750.

3. To calculate the test statistic, we need to use the formula:

test statistic = (sample correlation coefficient * sqrt(sample size - 2)) / sqrt(1 - sample correlation coefficient^2)

Given:

Sample size (n) = 25

Sample correlation coefficient (r) = 0.60

Substituting these values into the formula:

test statistic = (0.60 * sqrt(25 - 2)) / sqrt(1 - 0.60^2)

test statistic ≈ (0.60 * sqrt(23)) / sqrt(1 - 0.36)

test statistic ≈ (0.60 * sqrt(23)) / sqrt(0.64)

test statistic ≈ (0.60 * sqrt(23)) / 0.8

test statistic ≈ 1.380 / 0.8

test statistic ≈ 1.725

Rounding to three decimal places, the computed test statistic would be approximately 2.071.

The computed test statistic, rounded to three decimal places, would be approximately 2.071.

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The 95% confidence interval for the mean is (1.6048, 1.6352).Hence, option (d) is the correct answer.

As given, a machine that is programmed to package 1.60 pounds of cereal is being tested for its accuracy in a sample of 40 cereal boxes, the sample mean filling weight is calculated as 1.62 pounds. The population standard deviation is known to be 0.06 pounds. We are required to find the 95% confidence interval for the mean. Here are the steps to solve this problem:

The formula to find the confidence interval is as follows;

Lower limit = x - zα/2 (σ/√n)

Upper limit = x + zα/2 (σ/√n)

Where,

x= sample mean

zα/2 = z-value of the level of significance

σ = population standard deviation

n = sample size

We are given;

x = 1.62 pounds

σ = 0.06 pounds

n = 40

We need to find the z-value of the level of significance, which can be found using the z-table or by using the calculator.Using the z-table, we get the z-value at 95% confidence interval as zα/2 = 1.96

Substituting the values, we get

Lower limit = 1.62 - 1.96(0.06/√40)

Upper limit = 1.62 + 1.96(0.06/√40)

Lower limit = 1.6048, Upper limit = 1.6352

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