In 2010, Mr. Kelly visited the White House and met President Obama. While walking along the grounds, he excitedly realized that the walking path formed an ellipse. He paced it off and calculated that it was 1060 feet long and 890 feet wide. Unfortunately, the Secret Service didn’t take kindly to someone measuring the grounds so he was tackled and hauled off the premises.

A. Write an equation of the ellipse

B. The area of an ellipse is A=3.14ab. What is the area of the ellipse at the White House?

The account balances for the first 6 months are approximately $100.34, $100.68, $101.02, $101.36, $101.71, and $102.06, respectively.

The monthly balance of the account is given by [tex]A =e^{0.041t/12}[/tex]  where t is measured in months.

To find the account balances for the first 6 months, we can simply plug in the values of t = 1, 2, 3, 4, 5, and 6 into the formula:

When t = 1,

[tex]A = e^{(0.041/12)}[/tex]

A ≈ $100.34

When t = 2,

[tex]A = e^{(0.041/6)}[/tex]

A ≈ $100.68

When t = 3,

[tex]A = e^{(0.041/4)}[/tex]

A ≈ $101.02

When t = 4,

[tex]A = e^{(0.041/3)}[/tex]

A ≈ $101.36

When t = 5,

[tex]A = e^{(0.041/2.4)}[/tex]

A ≈ $101.71

When t = 6,

[tex]A = e^{(0.041/2)}[/tex]

A ≈ $102.06

Therefore, the account balances for the first 6 months are approximately $100.34, $100.68, $101.02, $101.36, $101.71, and $102.06, respectively.

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The value of angle XWZ is 117.5°

Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.

The sum of angles on a straight line is 180°. This means that if there angles A, B, C lie on a straight line, therefore ;

A+B + C = 180°

angle XWY is 90° and angle VWZ Iis 62.5°

therefore to find angle XWZ

ZWY= 90- 62.5

= 27.5°

Therefore angle XWZ = 90+ 27.5°

= 117.5°

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Answer:

Therefore

a=12

<B=66°

<C=24°

Step-by-step explanation:

Hyp²=opp²+adj²

x²=5²+11²

x²=25+121

x²=126

[tex] \sqrt{ {x}^{2} } = \sqrt{146} [/tex]

x=12

sinß=opp/hyp

sinß=11/12

[tex] \beta = { \sin( \frac{11}{12} ) }^{ - 1} [/tex]

ß=66°

<A+<B+<C=180°

90+66+<C=180

<C+156=180

<C=180-156

<C=24°

The radius of convergence, R, of the series (-1)nx^n-1 can be found using the ratio test the interval of convergence is (-1, 1) in interval notation. .

We have
lim |(-1)^(n+1)x^(n) / (-1)^nx^(n-1)| as n approaches infinity
= lim |x|

Since the limit exists only when |x| < 1, the radius of convergence is R = 1.
To find the interval of convergence, we need to check the endpoints x = -1 and x = 1.
When x = -1, the series becomes (-1)^n(-1)^n-1 = (-1)^2n-1 which diverges.

When x = 1, the series becomes (-1)^n1^n-1 = (-1)^(n-1) which also diverges.
Therefore, the interval of convergence is (-1, 1) in interval notation.

Note that the endpoints are not included in the interval of convergence because the series diverges at those points.

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The radius of convergence is R = 1 and the interval of convergence is (-1, 1).

To find the radius of convergence, we can use the ratio test:
lim┬(n→∞)⁡|(-1)^(n+1)x^n|/|(-1)^(n)x^(n-1)| = lim┬(n→∞)⁡|x|/1 = |x|
The series converges if |x| < 1 and diverges if |x| > 1. So the radius of convergence is R = 1.
To find the interval of convergence, we need to test the endpoints x = -1 and x = 1. When x = -1, the series becomes (-1)^n(-1)^n = 1, which is a divergent series. When x = 1, the series becomes (-1)^n, which is an oscillating series that does not converge.
Therefore, the interval of convergence is (-1, 1), where -1 is excluded and 1 is included, since the series converges for -1 < x < 1 and diverges for x ≤ -1 and x ≥ 1.
In summary, the radius of convergence is R = 1 and the interval of convergence is (-1, 1).

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The center and the radius is (h, k) = (-1, 1) and r = √3

Given is a circle equation x² + y² + 2x - 2y - 1 = 0, firstly we will change it in (x-h)² + (y-k)² = r² form and then find the center and the radius,

So,

x² + y² + 2x - 2y - 1 = 0

Add 2 to both side,

x² + y² + 2x - 2y - 1 +2 = 0 + 2

x² + y² + 2x - 2y + 1 + 1 = 2+1

(x+1)² + (y-1)² = 3

(x+1)² + (y-1)² = (√3)²..............(i)

In the standard form of equation of a circle (x-h)² + (y-k)² = r²,

(h, k) is the center and r is the radius,

So, comparing the equation (i) with the standard form of equation of a circle.

We get,

(h, k) = (-1, 1)

and r = √3

Hence the center and the radius is (h, k) = (-1, 1) and r = √3

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The largest area that can be enclosed with 100 meters of fencing is 1250 square meters.

To find the largest area that can be enclosed with 100 meters of fencing, we need to determine the dimensions of the rectangular area that would maximize the area.

Let's assume the length of the rectangle is L and the width is W. We are given that the total amount of fencing available is 100 meters, which means the perimeter of the rectangle should equal 100 meters:

2L + W = 100

To express the area of the rectangle in terms of L and W, we can use the formula:

Area = L * W

We want to maximize the area, so we can rewrite the equation in terms of a single variable using the perimeter equation:

W = 100 - 2L

Substituting this expression for W in the area equation:

Area = L * (100 - 2L)

Expanding and rearranging:

Area = 100L - 2L²

To find the maximum area, we can take the derivative of the area equation with respect to L and set it to zero:

d(Area)/dL = 100 - 4L = 0

Solving for L:

4L = 100

L = 25

Substituting this value back into the perimeter equation to find W:

W = 100 - 2L

= 100 - 2(25) = 50

Therefore, the dimensions of the rectangle that would maximize the area are L = 25 meters and W = 50 meters. To find the maximum area, we can substitute these values back into the area equation:

Area = L * W = 25 * 50 = 1250 square meters

Thus, the largest area that can be enclosed with 100 meters of fencing is 1250 square meters.

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Answer:

3x^3 + 7x^2 - 5x - 10

Step-by-step explanation:

In order to find the sum, we need to add all of the like terms together between the two polynomials.

[tex](x^3+12x^2-5x+4)+(2x^3-5x^2-14)[/tex]

Lets begin with x^3 terms. There is a 1 in front of the x, so 2 + 1 = 3

[tex]3x^3[/tex]

Now x^2 terms. 12 - 5 = 7

[tex]3x^3+7x^2[/tex]

We can keep x terms the same since there is no x terms in the second polynomial.

[tex]3x^3+7x^2-5x[/tex]

Finally integers. -14 + 4 = -10

[tex]3x^3+7x^2-5x-10[/tex]

Answer: 9

Step-by-step explanation: it just is

Answer:

9

Step-by-step explanation:

How do u not know what the sum of 4 and 5 is? I'm not trying to be mean I'm just wondering

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools.

To determine if there is sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools, we can use a two-sample z-test for the difference in proportions.

The null hypothesis is that there is no difference between the proportions of students with ear infections at the two schools, while the alternative hypothesis is that there is a difference.

Let p1 be the proportion of students with ear infections at the first school and p2 be the proportion at the second school. The test statistic is given by:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat is the pooled proportion, n1 and n2 are the sample sizes from the first and second schools, respectively.

The pooled proportion is given by:

p_hat = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of students with ear infections in each school.

Using the given data, we have:

n1 = 40, n2 = 30

x1 = 11, x2 = 12

p1 = x1/n1 = 11/40 = 0.275

p2 = x2/n2 = 12/30 = 0.4

p_hat = (x1 + x2) / (n1 + n2) = (11 + 12) / (40 + 30) = 0.355

The test statistic is:

z = (0.275 - 0.4) / sqrt(0.355 * 0.645 * (1/40 + 1/30)) = -1.197

Using a standard normal table or calculator, the p-value for a two-tailed test with a test statistic of -1.197 is approximately 0.231.

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Any weight between 13 and 19 pounds, however, would be considered healthy.

The absolute value inequality can be explained as follows: the absolute value of the difference between the weight of the dog and the healthy weight of 16 pounds represents the distance between the dog's weight and the healthy weight. The inequality states that this distance should be greater than 3 pounds, which means that any weight that is more than 3 pounds away from the healthy weight of 16 pounds is considered unhealthy.

For example, if the dog weighs 12 pounds, then the absolute value of the difference between the weight and the healthy weight is 4 pounds, which is greater than 3 pounds. Therefore, 12 pounds is an unhealthy weight for the breed. Similarly, if the dog weighs 20 pounds, then the absolute value of the difference between the weight and the healthy weight is 4 pounds, which is also greater than 3 pounds. Therefore, 20 pounds is also an unhealthy weight for the breed. Any weight between 13 and 19 pounds, however, would be considered healthy.

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Answer:

  ≈ 0.14159265359

Step-by-step explanation:

You want the value of f(x) = |x| when x = 3-π.

The function value is ...

  f(3-π) = |3-π| ≈ |-0.14159265359| = 0.14159265359

The absolute value function changes the sign from negative to positive. Pi is irrational, so the actual value is irrational. It is rounded up to the value shown.

<95141404393>

Answer:

The correct answer is: Age and height are positively correlated.

Positive correlation means that as one variable increases, the other variable also increases. In this case, as a child ages, they also get taller. There are many factors that contribute to a child's height, including genetics, nutrition, and health. However, age is one of the most important factors.

Here are some additional details about the relationship between age and height:

The correlation between age and height is positive and strong. This means that there is a strong relationship between the two variables.

The correlation between age and height is linear. This means that the relationship between the two variables is straight.

The correlation between age and height is not perfect. This means that there are some children who are taller or shorter than expected for their age.

Overall, the relationship between age and height is positive and strong. This means that as a child ages, they also get taller.

Step-by-step explanation:

Answer:

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

Distributive Property is:

Use same rule to find the product:

Let's calculate the profit made by the owner on each branch at the end of the season. The owner buys a wooden branch for $2. After marking up the price by 75%, the selling price becomes:

$2 + ($2 * 0.75) = $2 + $1.50 = $3.50

However, at the end of the season, the owner sells the branches for 30% off. So the selling price after the discount is:

$3.50 - ($3.50 * 0.30) = $3.50 - $1.05 = $2.45

To calculate the profit made on each branch, we subtract the original cost from the selling price:

$2.45 - $2 = $0.45

Therefore, the owner makes a profit of $0.45 on each branch at the end of the season.

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The concurrency of the median of the triangle is P ( -1 , 0 )

Given data ,

Let the triangle be represented as ΔABC

Now , the coordinates of the triangle are A(-4,4) B(2,0) and C(-1,-4)

On simplifying , we get

Midpoint of AB:

x-coordinate: (x₁ + x₂) / 2 = (-4 + 2) / 2 = -1

y-coordinate: (y₁ + y₂) / 2 = (4 + 0) / 2 = 4/2 = 2

Midpoint of BC:

x-coordinate: (x₂ + x₃) / 2 = (2 + (-1)) / 2 = 1/2 = 0.5

y-coordinate: (y₂ + y₃) / 2 = (0 + (-4)) / 2 = -4/2 = -2

Midpoint of AC:

x-coordinate: (x₁ + x₃) / 2 = (-4 + (-1)) / 2 = -5/2 = -2.5

y-coordinate: (y₁ + y₃) / 2 = (4 + (-4)) / 2 = 0

Now, we have the midpoints of the sides of the triangle:

Midpoint of AB: (-1, 2)

Midpoint of BC: (0.5, -2)

Midpoint of AC: (-2.5, 0)

The point of concurrency of the medians is the centroid of the triangle, which can be found by taking the average of the midpoints.

x-coordinate: (-1 + 0.5 - 2.5) / 3 = -3 / 3 = -1

y-coordinate: (2 - 2 - 0) / 3 = 0

Hence , the coordinates of point P, the point of concurrency of the medians, are P(-1, 0)

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The exact value of tan(tetha) is 4/3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The hypotenuse is the side facing the right angle and the opposite is the side facing the acute angle and the adjascent is the third side.

The opposite side = √ 5²-3²

= √ 25 -9

= √16

= 4

Therefore ;

Tan(tetha) = 4/3

the exact value of tan(tetha) is 4/3

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Answer:

y=-5/11x+3/11 (B)

Step-by-step explanation:

m= -5/11

b=3/11

substitute: y=-5/11x+3/11

The radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.

We are given the surface area (A) of the zorb and asked to find its radius (r) using the formula r = √(A / 4π). Let's follow these steps to solve for the radius:
1. Write down the given information:
  A (surface area) = 49.29 sq m
2. Write down the formula for the radius of a sphere:
 r = (√A / 4π)
3. Plug in the given surface area (A) into the formula:
  r = √(49.29 / 4π)
4. Calculate the value inside the square root:
  49.29 / 4π ≈ 3.923
5. Take the square root of the calculated value:
  r = √(3.923) ≈ 1.98
So, the radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.

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1. Lines that have different slopes and intersect at one point have one solution.

2. Lines that have the same slope and different y-intercepts (they do not intersect) have no solution.

3. Lines that have the same slope and the same y-intercepts have infinitely many solutions.

Slope is:

S=rise/run

S=Y/X

The Original price of the bracelet, before tax, is $12.

Let's assume that the original price of the bracelet is x dollars.

The sales tax is 6%, which means that the tax paid is 6/100 * x = 0.06x dollars.

We know that Casey paid $0.72 in sales tax, so we can set up the equation:

0.06x = 0.72

Solving for x, we get:

x = 0.72/0.06

x = 12

Therefore, the original price of the bracelet, before tax, is $12.

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Answer:

we cannot solve this as there is no picture shown, try linking in the picture please

The series of transformations that correctly maps rectangle ABCE to LMNO is: Translate rectangle ABCD right 9 units, then dilate the result by a scale factor of 3 centered at the origin.

Based on the diagram, translation is by adding 9 to the x-coordinates of all the points in the rectangle.

Also,the dilation us by multiplying the coordinates of all the points in the translated rectangle A'B'C'D' by a factor of 3.

Hence, the series of transformations that correctly maps rectangle ABCE to LMNO is to teanslate rectangle ABCD right 9 units, then dilate the result by a scale factor of 3 centered at the origin.

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The volume of the composite solid consisting of a cube and a square-based pyramid will be 26,099.2 cm³.

The volume of the cube is given by;

V_cube = s³ = 28³

V = 21,952 cm³.

The volume of the pyramid is given by V_pyramid = (1/3)Bh,

where;  B = area of the base and h = height .

The base of the pyramid is a square with sides equal to the base of the cube therefore we have

B = s² = 28² = 784 cm².

Thus, V_pyramid = (1/3)(784)(16)

V  = 4,147.2 cm³.

The total volume of the composite solid is the sum of the volumes of the cube and the pyramid then we get;

V_total = V_cube + V_pyramid = 21,952 + 4,147.2

V_total = 26,099.2 cm³.

Therefore, the volume of the solid is; 26,099.2 cm³.

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The number of ways to choose five articles to read is given as follows:

21 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The combination formula is used in the context of this problem as the order in which the articles are read does not matter.

Five articles are chosen from a set of seven, hence the number of ways to choose the articles is given as follows:

[tex]C_{7,5} = \frac{7!}{5!2!} = 21[/tex]

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So the points on the ellipse that are farthest away from the point (1,0) are: (1/15)(2 + sqrt(394)), ±sqrt(4 - 4(1/15)(2 + sqrt(394))^2 )and (1/15)(2 - sqrt(394)), ±sqrt(4 - 4(1/15)(2 - sqrt(394))^2).

We want to find the points on the ellipse that are farthest away from the point (1,0). The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So, we need to maximize the distance d, subject to the constraint that the point (x, y) lies on the ellipse 4x^2 + y^2 = 4.

Using Lagrange multipliers, we set up the following system of equations:

f(x, y) = (x - 1)^2 + y^2 = λg(x, y) = λ(4x^2 + y^2 - 4)

Taking the partial derivatives with respect to x, y, and λ, we get:

fx = 2(x - 1) = 8λx

fy = 2y = 2λy

g(x, y) = 4x^2 + y^2 - 4 = 0

From the second equation, we can see that y = 0 or λ = 1. If y = 0, then the first equation simplifies to:

(x - 1)^2 = λ(4x^2 - 4)

Solving for λ and substituting into the equation for g(x,y), we get:

4x^2 - (x - 1)^2 - 4 = 0

Simplifying, we get:

15x^2 - 2x - 11 = 0

Using the quadratic formula, we get:

x = (1/15)(2 ± sqrt(394))

Substituting into the equation for the ellipse, we get the corresponding y-values:

y = ±sqrt(4 - 4x^2)

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Answer and Explanation: The conditions when the net force and the net torque are zero are called static equilibrium.

This means that there is evidence to suggest that the mean amount of codeine in the painkiller is not exactly 5 mg.

(a) The null hypothesis is that the mean amount of codeine in the painkiller is exactly 5 mg. The alternate hypothesis is that the mean amount of codeine in the painkiller is not exactly 5 mg.
(b) The picture of the distribution of the test statistics (under H0) would be a normal distribution with a mean of 5 mg and a standard deviation of 0.75 mg/sqrt(100) = 0.075 mg. The critical values for a two-tailed test at a significance level of 0.05 are -1.96 and +1.96. The region(s) of rejection are the values outside of this range. This can be represented in a graph as shaded areas on both sides of the distribution curve.
(c) The calculated value of the test statistic is (4.7 - 5) / (0.75 / sqrt(100)) = -2.67.
(d) Since the calculated value of the test statistic (-2.67) falls within the region of rejection, we reject the null hypothesis. This means that there is evidence to suggest that the mean amount of codeine in the painkiller is not exactly 5 mg.

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