Please help me answer the following question :)

Answer:

The equation of the ellipse is:

(x^2)/16 + (y^2)/4 = 1

Step-by-step explanation:

An ellipse is a set of points on a plane, the sum of whose distances from two fixed points (called foci) is constant. The distance between the foci of an ellipse is denoted by 2c, and the distance between the center of the ellipse and one of its vertices is denoted by a.

In this problem, the foci are located at (2,0) and (-2,0), so the distance between the foci is 2c = 4, which means that c = 2. The major vertices of the ellipse are located at (4,0) and (-4,0), so the distance between the center and one of the vertices is a = 4.

The formula for the equation of an ellipse centered at the origin is:

(x^2)/(a^2) + (y^2)/(b^2) = 1

where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex. Since the center of this ellipse is at the origin and the major axis lies on the x-axis, we know that b = a, so we can substitute a for b in the equation:

(x^2)/(a^2) + (y^2)/(a^2) = 1

To find a, we use the fact that c^2 = a^2 - b^2:

a^2 - b^2 = c^2

a^2 - a^2 = 4

b^2 = 4

b = 2

Now we can substitute a = 4 and b = 2 into the equation:

(x^2)/(16) + (y^2)/(4) = 1

This is the equation of the ellipse.

Number of people = number of cups of coffee + 1 = 5 + 1 = 6

Therefore, there were 5 friends with Dylan at the cafe.

Let's start by subtracting the change Dylan received from the amount he paid to find out the total cost of everything he bought:

Total cost =

We know that Dylan bought himself a cup of tea, which costs less than a cup of coffee. So, the £5.39 must have been spent on buying coffee for his friends.

Let's assume that each cup of coffee costs £1. We can use this assumption to find out how many cups of coffee Dylan bought for his friends:

Number of cups of coffee = total cost ÷ cost per cup of coffee = £5.39 ÷ £1 = 5.39

Since we can't buy a fraction of a cup of coffee, we can round this number down to the nearest whole number. Therefore, Dylan bought 5 cups of coffee for his friends.

However, we need to remember that Dylan himself also bought a drink, which wasn't a cup of coffee. So, the total number of people at the cafe was:

Number of people =[tex]number of cups of coffee + 1 = 5 + 1 = 6[/tex]

Therefore, there were 5 friends with Dylan at the cafe.

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Answer:

= 75 cubic units

Step-by-step explanation:

Volume = height * width * length

Then:

volume = 4 1/2 * 3 1/3 * 5

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2

3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3

Then:

volume = 9/2 * 10/3 * 5/1

volume = (9*10*5) / (2*3*1)

volume = 450 / 6

Volume = 75 cubic units

Answer:

Median: 19

Mean: 18

Step-by-step explanation:

Numbers: 19, 20, 40, 3, 17, 5, 22

Number in order from least to greatest: 3, 5, 17, 19, 20, 22, 40

The median is the number in the middle of a data set.

The median is: 19

The mean is the average of a set of data.

The mean is: [tex]\frac{3 + 5 + 17 + 19 + 20 + 22 + 40}{7}[/tex] = 18

So, Median is 19

      Mean is 18

Answer:

because he is wittery hitting da gwity

The study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study, resulting in a Type I Error (false positive) of 1.67, meaning an overestimation of the true relative risk of the association by 67%.

In this case, the study has a measurement bias due to the small sample size and the likely difference between the population of city x and the sample used in the study. As a result, we can expect the relative risk to be overestimated. This is known as a Type I Error (false positive) and can be calculated using the formula:

Type I Error = (4.0 – 1.5) / 1.5 = 1.67

In other words, the study overestimated the true relative risk by 67%. This is an example of an inflated relative risk due to a lack of representativeness of the sample population.

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The equation for the cost of ticket 13.50 = 1.5m is and the price for a matinee movie ticket is $9.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's use "m" to represent the price of a ticket to a matinee movie.

From the given information, we know that the cost of a ticket to an evening movie is 1.5 times more than a ticket for a matinee movie.

This means that -

Cost of an evening movie ticket = 1.5 × Cost of a matinee movie ticket

We also know that the cost of a ticket to an evening movie is $13.50.

Substituting this value into the equation above, we get -

$13.50 = 1.5m

To solve for "m", we can divide both sides of the equation by 1.5 -

$13.50 / 1.5 = m

m = $9

Therefore, the price of a ticket to a matinee movie is $9.

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The inequality in the expression [tex]41-x < 17[/tex] is the less than inequality

The solution to the inequality is [tex]x > 24[/tex]

The inequality is given as:

[tex]41-x < 17[/tex]

Subtract 41 from both sides of the inequality

[tex]41 - 41 -x < 17 - 41[/tex]

Evaluate the difference

[tex]-x < -24[/tex]

Multiply both sides by -1

[tex]-1 \times -x < -24 \times -1[/tex]

Evaluate the product

[tex]x > 24[/tex]

The amount of plastic wrap used to wrap the container is 3.06π square inches.

What is cylinder ?

A cylinder is a multi object used in geometry that has a round base, a curving surface rising from it, and another circular shape at the top or lid. One way to visualize a cylinder is as a stack of infinitely thin circular discs stacked one on top of the other. The height and radius of a cylinder, which measure the distance from the base to the top and the edge of the circular base, respectively, determine the shape of the object.

The plastic wrap covers the entire surface area of the cylinder. The formula for the surface area of a cylinder is:

Surface area of cylinder = 2πr² + 2πrh

where r is the radius of the circular base of the cylinder, and h is the height of the cylinder.

We can use the given diameter of the circular base, which is 1.8 inches, to find the radius r:

r = d/2 = 1.8/2 = 0.9 inches

We are also given the height of the rectangle, which is 0.8 inches.

Now we can substitute the values of r and h into the formula for the surface area of the cylinder:

Surface area of cylinder = 2π(0.9)² + 2π(0.9)(0.8)

Surface area of cylinder = 2π(0.81) + 2π(0.72)

Surface area of cylinder = 1.62π + 1.44π

Surface area of cylinder = 3.06π square inches

Therefore, the amount of plastic wrap used to wrap the container is 3.06π square inches.

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Answer:

4%

Step-by-step explanation:

The formula for simple interest is I = Prt, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.

In this case, we know that:

P = £500 (the principal amount)

I = £40 (the interest earned)

t = 2 years (the time the money was invested)

We can rearrange the formula to solve for r:

r = I / Pt

Substituting the given values, we get:

r = 40 / (500 x 2)

r = 0.04 or 4%

Therefore, the simple interest rate per annum is 4%.

You should invite at least 23 guests to your party to have at least a 2/3 chance of having a guest with the same birthday as yours.

For your party, you need to invite at least 23 randomly chosen guests in order to have a probability of 2/3 or higher of having a guest with the same birthday as yours. This is known as the birthday paradox and it is based on the probability of two people having the same birthday. To calculate the number of guests needed for the probability of having at least one match, you can use the following formula:

P(at least one match) = 1 - (365/365)^n

where n is the number of guests you invite.
So, to solve for n, you would rearrange the equation to:

n = ln(1-P) / ln(365/365)

When P = 2/3, this equation gives us n = 23.

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The standard deviation of demand over the lead time is 23.72.

The demand over lead time is normally distributed with a mean of 80. The reorder point for a 95% service level is 119. To calculate the standard deviation of demand over the lead time, we need to use the following formula:

z = (x - μ) / σ, where z is the number of standard deviations from the mean, x is the reorder point for a 95% service level, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

To solve for σ, we need to first find the z-score for a 95% service level, which can be obtained from the standard normal distribution table.

The z-score for a 95% service level is 1.645.

Substituting the given values in the formula, we get:

1.645 = (119 - 80) / σ

Solving for σ, we get:σ = (119 - 80) / 1.645

σ = 23.72

Therefore, the standard deviation of demand over the lead time is 23.72.

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Answer:

  x = 10

Step-by-step explanation:

You want to find the value of x, where a chord of segment lengths 9 and x crosses a chord of segment lengths 6 and 15.

The product of the segment lengths is the same for intersecting chords:

  9x = 6·15

  x = 90/9 . . . . divide by 9

  x = 10

Answer:

238.64

Step-by-step explanation:

center to edge is a radius

2pi(radius) = circumference, so 6.28(38) = circumference = 238.64

The measure of angle m∠KSP is 14⁰.

A special property of a parallelogram is that opposite angles are equal in measure. This means that if you take any two angles of a parallelogram that are opposite each other, they will have the same degree measure.

The measure of angle m∠KSP is calculated as follows;

The measure of angle P and R = ¹/₂[ 360 - (76 x 2)] (sum of angles in quadrilateral )

The measure of angle P and R = 104

The measure of QPK = 180 - (76 x 2) (sum of angles in a triangle )

The measure of QPK =  28⁰

Angle P consists of QPK plus KPS

KPS = 104 - QPK

KPS = 104 - 28

KPS = 76

The measure of angle m∠KSP is calculated as;

KSP = 180 - (90 + 76) ( sum of angles in a triangle)

KSP = 14⁰

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Answer:

38

Step-by-step explanation:

We know that Q and P are supplementary because they are parallelograms.

So,

180 - < Q = < P                               Use substitution

180 - 76 = < P                                 Solve

180 - 76 = 104

104 = < P

Since we know that < QPK and < KPS are congruent and are apart of < P we can multiply < P by 1/2 to find either < QPK or < KPS.

So,

1/2(104)                                           Simplify using distributive property

52

If a shape is a triangle, then it’s interior angles all add up to 180.

< KPS + < PKS + < KSP = 180        Use substitutions

52 + 90 + < KSP = 180                  Move variables to one side

< KSP = 180 - 52 - 90                    Simplify  
< KSP = 38

And there’s your answer: 38

around 85 degrees. I did it with a protractor.

We don't have enough information to determine the exact side length of either square A or square C, so we cannot directly calculate their areas. However, we can use the relationship between the areas of the squares to make some conclusions.

Since the area of square B is 64 square units, we know that its side length is √64 = 8 units.

Similarly, since the area of square C is 100 square units, we know that its side length is √100 = 10 units.

Square A is composed of square B and four identical triangles. We know the area of square B is 64 square units, so we need to determine the area of the four triangles to find the area of square A.

Each triangle has a base of 8 units (which is also the length of one side of square B) and a height of half the length of one side of square A. Let's call this length x.

The area of one triangle is (1/2) * 8 * x = 4x square units.

The total area of the four triangles is 4 times the area of one triangle, which is 16x square units.

Therefore, the area of square A is 64 + 16x square units.

We still don't know the exact value of x, but we can make some observations. Since square A is larger than square B, we know that x > 4. And since the triangles make up exactly half of square A (the other half being square B), we know that the area of square A is twice the area of the four triangles. Therefore:

64 + 16x = 2(16x)

64 + 16x = 32x

64 = 16x

x = 4

So the length of each side of square A is 8 + 2x = 16 units, and its area is 64 + 16x = 128 square units.

The length of CA is just the length of one side of square C, which is 10 units.

By answering the presented question, we may conclude that If the two graphs are identical, F(x) may polynomials be a valid factorization of G(x), but more study is required to establish this.

A polynomial is a mathematical statement composed of variables and coefficients that be combined using only addition, subtraction, multiplication, and non-negative integer exponents. The phrase 2x3 + 5x2 - 3x + 1 is a polynomial, for example, where x is the variable and the coefficients of the various components are 2, 5, -3, and 1. Polynomials may include one or more variables, but each term must have the same variable (s). The degree of a polynomial is the highest exponent of its variable (s). In the above example, the degree of the polynomial is 3. Polynomials are used in many areas of mathematics, including algebra, calculus, and numerical analysis.

If you believe that one polynomial function is not the right factorization of another, you may use your graphing calculator to confirm this by graphing both functions and comparing their graphs.

Then, in your calculator, insert the polynomial function that you believe is the right factorization. Let us refer to this function as G. (x).

Graph the function G(x) on your calculator by hitting the "graph" button or the equivalent button.

Examine the two graphs. If the two graphs disagree, F(x) does not represent the right factorization of G. (x). If the two graphs are identical, F(x) may still be a valid factorization of G(x), but more study is required to establish this.

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Answer:

  k = 2/5

Step-by-step explanation:

Given a diagram with triangles ONM and OAB such that M is the midpoint of OB, A lies on AN with AN = 2·OA, and P is the point of intersection of NM and AB, you want the ratio AP/AB.

Please refer to the attached diagram.

Point C is located at the midpoint of AN, which makes OA≅AC≅CN, or AN is 2/3 of ON. Segments AD and CE are parallel to AN, so divide OM into thirds. The length DM is 2 of those thirds, and the length MB is equal to OM, so is 3 of those thirds. That is, the ratio DM/DB is (2/3)/(2/3+3/3) = 2/5.

Triangle BAD is similar to triangle BPM, so the ratio AP/AB is also 2/5.

The 99% confidence interval for the true average number of alcoholic drinks all UF female students have in a one week period is option (d)  (3.35, 4.75)

To construct a confidence interval for the true average number of alcoholic drinks all UF female students have in a one week period, we can use the following formula

Confidence interval = sample mean ± (critical value) x (standard error)

Where the standard error is calculated as

Standard error = standard deviation / square root of sample size

We are given

Sample size (n) = 170

Sample mean (X) = 4.05

Standard deviation (s) = 4.66

Confidence level = 99%

To find the critical value, we need to look up the t-value with 169 degrees of freedom (since we are using a t-distribution because the sample size is less than 30) and a 99% confidence level. Using a t-distribution table or a calculator, we find the t-value to be approximately 2.62.

Substituting the values into the formula, we get:

Standard error = 4.66 / √170 ≈ 0.357

Confidence interval = 4.05 ± (2.62) x (0.357) ≈ (3.35, 4.75)

Therefore, the correct option is (d) (3.35, 4.75)

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The time period required is 31.91 months(Approx)

The monthly payments based on the given information would be $129.88

Putting into a financial calculator;

PV=-1245

PMT=50

I/Y=(19/12)=1.58333333%

Solving for N;we get N=31.91

Hence time period required=31.91 months(Approx)

b.Putting into a financial calculator;

PV=-2456.80

N=(2*12)=24

I/Y=(23.99/12)=1.99916667%

Solving for PMT;we get PMT=129.88

Hence monthly payments=$129.88(Approx)

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A.

by simply putting the suggested solution into the equation and see if it stays true. if yes, it is a solution.

(5 + 2i)² - 10(5 + 2i) = -29

25 + 20i - 4 - 50 - 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution.

B. for a parabola the 2 solutions are usually symmetrical around the center line.

so, I suspect 5 - 2i to be a solution too.

(5 - 2i)² - 10(5 - 2i) = -29

25 - 20i - 4 - 50 + 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution too.

C.

nowhere.

with 2 complex solutions there are no real number solutions left. and that means there is no intersection with the x-axis.

every quadratic equation must have 2 and only 2 solutions. a solution is normally an intersection with the x-axis (the x- value when y = 0).

Answer: A. (x,y)----->(x,-y)

because their x coordinates are all -6. But their y coordinates are 6 and -6.

In the percentage , the total number of students in sixth grade is 250.

What is percentage?

Percentage is Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Here we know that total number of students is 100%.

Students purchased their  lunch = 24%

Students brought their lunch from home = 190

Then percentage of students brought their lunch from home is

=> (100%-24%) = 190

=> 76% = 190

Then Total number of students in sixth grade is,

76%   = 190

100% = x

=> x = [tex]\frac{190\times100\%}{76\%}[/tex] =  250.

Hence the total number of students in sixth grade is 250.

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Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .

The amount of money earned or charged on a principal sum of money over time is referred to as interest in mathematics. In financial transactions like loans, investments, and savings accounts, it is frequently utilized.  Simple interest is calculated for the full time period as a fixed percentage of the principal amount. For instance, after a year, you would owe $50 in interest if you borrowed $1,000 at a simple interest rate of 5% per year.

given

We can use the following formula for simple interest to determine the interest rate given the principal, period, and simple interest:

I = P * r * t

where r is the interest rate expressed as a decimal, P is the principal, I is the simple interest, and t is the amount of time in years.

This formula can be changed to account for the interest rate:

r = I / (P * t)

In this instance, the principal, period, and simple interest are all provided. These values can be plugged in to find the interest rate:

r = I / (P * t)

r = 600 / (4000 * 5)

r = 0.03

Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .

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Answer:

26.4

Step-by-step explanation:

You can add Y together because they have the same variable making it 10y

The equation is now 10y - 84 = 180

Add 84 to 180 since on the left side it was -84 (Imagine it crossed a magic bridge and become the opposite of what it is)

The equation is now 10y = 264

Divide the equation by 10 because 10 crossed a "magic bridge" to the other side and became division instead of multiplication

The equation is now solved = 26.4

We can cross check this by adding it to the first equation

3(26.4) + 7(26.4) - 84

which gives us 180

Hope this helps

Answer: y=26.4

Step-by-step explanation:

First we need to simplify 3y+7y .... that would be 10y.

Now we have 10y-84=180. We can add 84 to both sides of the equation

So now we have 10y= 180+84 = 10y= 264

Divide both sides by 10= y= 26.4

Now we can check this answer by inputting 26.4 to all the y values in the equation.

(3*26.4) +(7*26.4) - 84=180

79.2 + 184.8 -84=180

180=180    so we know 26.4 is the correct answer

Answer:

The exchange rate at the post office is £1= 1.17 euros

How many euros will you get for £280?

Step-by-step explanation:

280 * 1.17 = 327.6

Answer:

Step-by-step explanation:

The mean is found by adding the numbers and dividing by how many numbers there are.

              [tex]Mean=\frac{-2+3+0-15+5-20-4}{7} =\frac{-33}{7} =-4\frac{5}{7}[/tex]

If f ( x ) = f ( g ( x ) ) , where f ( 5 ) = 7 , f ' ( 5 ) = 5 , f ' ( 0 ) = 3 , g ( 0 ) = 5 , and g ' ( 0 ) = 3 ,f'(0) = 15

We start by using the chain rule to find the derivative of f(x) with respect to x:

f'(x) = f'(g(x)) * g'(x)

Next, we evaluate this equation at x = 0, and use the given values to solve for f'(0):

f'(0) = f'(g(0)) * g'(0)

f'(0) = f'(5) * 3 (since g(0) = 5 and g'(0) = 3)

Now, we need to find f'(5) using the given information. We can start by using the definition of the derivative:

f'(5) = lim h->0 [f(5+h) - f(5)] / h

We know that f(5) = 7, so we can simplify this expression:

f'(5) = lim h->0 [f(5+h) - 7] / h

Using the fact that f(x) = f(g(x)), we can substitute g(x) for x:

f'(5) = lim h->0 [f(g(5+h)) - 7] / h

Now, we can use the mean value theorem to approximate f(g(5+h)):

f'(5) = lim h->0 [f'(g(c)) * g'(5+h)] / 1

where 5 < c < 5 + h. Since f'(5) = 5 and g'(5) = 3, we can simplify this expression:

f'(5) = lim h->0 [5 * 3] / 1 = 15

Therefore, we have found that f'(0) = f'(5) * 3 = 5 * 3 = 15.

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