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The equation of the ellipse with the foci is x²/36 + y²/(27) = 1.

The distance between the foci of an ellipse is calculated using the following formula;

c² = a² - b²

Where;

For this question, a = 6 and c = 3, the value of b is calculated as;

c² = a² - b²

3² = 6² - b²

9 = 36 - b²

b² = 27

b = √27

b = 3√3

The equation of the ellipse is calculated as;

x²/a² + y²/b² = 1

x²/36 + y²/(27) = 1

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Answer:

it can be simplify as follows:

The most accurate for a Zero-Based Budget is You put every dollar of your take-home pay into a budget category each month. Option A

Zero-based budgeting (ZBB) is simply defined as a method of budgeting having that all expenses must be checked for each new period.

The process of zero-based budgeting is one that begins from a zero account

Note that the budgets are carried out when it is needed for the upcoming period, regardless of whether the budget is less or greater than the previous one.

It is important to note the following;

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Selena can serve the pizza at around 6:40 P.M.

The regression line should have the equation y = -1.7x + 300, where y is the temperature, x is the time in minutes since the pizza was taken out of the oven, -1.7 is the slope of the line, and 300 is the y-intercept.

Set y (the temperature) to 130°F, and solve for x (the time).

130 = -1.7x + 300

-170 = -1.7x

x ≈ 100

According to the regression model, the pizza will reach 130°F after about 100 minutes after it was taken out of the oven. Therefore, Selena can serve the pizza at around:

= 5 + 1:40

= 6:40 P.M.

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The surface area of the triangular prism is 108 km².

Given is a triangular prism we need to find the surface area of the prism,

SA = perimeter × length

= (3 + 4 + 5) × 9

= 12 × 9

= 108

Hence, the surface area of the triangular prism is 108 km².

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The requried lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.

To calculate the present value of Peter's annuity,

[tex]PV = PMT * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

In this case, PMT = 87325, r = 0.107/12 = 0.008917, and n = 21*12 = 252.

Substitute the value in the formula given above:

[tex]PV = 87325 * (1 - (1 + 0.008917)^{-252} / 0.008917[/tex]

PV = 8747531.78

Thus, the lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.

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The angle that is marked as Q has a value of 30°

The cosine rule, also known as the law of cosines, is a mathematical formula used to calculate the length of a side or the measure of an angle of a triangle.

Cosine rule  useful in solving triangles when you know the lengths of two sides and the measure of the angle between them, or when you know the lengths of three sides.

By the use of the cosine rule, we have that;

7^2 = 12^2 + 14^2 - 2(12 * 14)Cos Q

49 = 144 + 196 -336CosQ

49- 340 =  -336CosQ

-291=  -336CosQ

Q = Cos-1 (-291/-336)

Q = 30

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Answer: Discover how a 3D solid shape can be made up from a 2D net. Understand how nets are formed with examples of common 3D polygons and prisms.

Step-by-step explanation:

The function of g(x) is 3 ([tex]2^x[/tex]) + 3.

We have,

f(x) = 3 ([tex]2^x[/tex]) -3

Now, the function f(x) have shifted by -3 unit to move 6 unit up.

This means that we have the shifting of

= -3 + 6

= +3 unit

Also, g(x) crosses the y-axis at about 5 or 6 when x=0.

Then, the function of g(x) is

= 3 ([tex]2^x[/tex]) + 3

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A conversion of 300 degrees to radians is equal to 5.24 radians.

In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = rθ

Where:

Next, we would convert degrees to radians;

300 = rads × 180/π

Radians = 300π/180 = 5.24 radians.

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The radius of the sphere that has a volume of 33.51032164 cubic meters is approximately 2 meters.

The radius of a sphere is the distance from the center of the sphere to any point around the circumference. The radius is half of the length of the diameter of a sphere.

The volume of  a sphere = 4/3 * π * r³

Given that:

Volume ≈ 33.5 cubic meters

Use the formula to find the radius of the sphere:

33.5 = 4/3 * π * r³

33.5 = 4π/3 * r³

3 * 33.5 = 4π * r³

100.5/4π = r³

r³ = 7.998

r = ∛7.998

r ≈ 2 meters.

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Alma need to use 6 cups of blue paint and 4 cups of red paint with the 2 cups of white paint.

Here, Alma makes 5 cups of her favorite shade of purple paint by mixing

3 cups of blue paint,

1 1/2 cups of red paint,

and 1/2 a cup of white paint.

Alma has 2 cups of white paint.

The ratio of blue to the white paint is:

3 : (1/2)

so, for 2 cups of white paint,

3 : (1/2) = x : 2

x = 6 cups of blue paint

The ratio of red to the white paint is,

3: (1 1/2)

3 : (3/2)

So, for 2 cups of white paint,

3 : (3/2) = y : 2

y = 4 cups of red paint

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There are 190 pages would be in a book with 19 chapters.

We have to given that;

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.

Now, We get;

For 19 chapters at x - axis,

The value of pages at y - axis is, 190

Thus, There are 190 pages would be in a book with 19 chapters.

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The function that represents the fox population is P(t) = 6100 x [tex]1.06^{t}[/tex]

The fox population in 2008 is 9722.

The equation that would represent the population of the foxes is an exponential equation.

The form of the exponential equation would be

Future population = present population x [tex](1 + r)^{t}[/tex]

Where:

P(t) = 6100 x [tex](1 + 0.06)^{t}[/tex]

P(t) = 6100 x [tex]1.06^{t}[/tex]

Fox population in 2008 = 6100 x [tex]1.06^{8}[/tex] = 9722

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No, the pairs of vectors 3i - 8j, 8i - 3j are not orthogonal.

The dot product will help us to determine if the pair of vectors are orthogonal or not.

If the dot product is equal to zero, then the pair of vectors are orthogonal.

The dot product of the vectors is calculated as follows;

(3i - 8j).(8i - 3j)

= (3i x 8i) - (3i x 3j) - (8j x 8i) + (8j x 3j)

= (24) - (0) - (0) + (24)

= 24 + 24

= 48

So the pairs of vectors are not orthogonal.

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Salton City has a lower altitude because -60.96 meters is less than -38.1 meters.

Option C is the correct answer.

We have,

The altitude of Bombay Beach is -60.96 meters.

The altitude of Salton City is -38.1 meters.

Altitude is the height of a location above sea level, and a negative value indicates that the location is below sea level.

Therefore, we can see that Salton City has a higher altitude than Bombay Beach because -38.1 meters is a higher altitude than -60.96 meters.

Thus,

Salton City has a lower altitude because -60.96 meters is less than -38.1 meters.

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There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.

We have,

Based on a sample of 217 subjects, 53 of them developed nausea.

To test this claim, a hypothesis test is conducted using a significance level of 0.01.

The null hypothesis, denoted as H0, assumes that the true proportion of users who develop nausea is less than or equal to 20%, while the alternative hypothesis, denoted as Ha, assumes that the true proportion is greater than 20%.

If the test statistic, calculated from the sample data, falls in the rejection region, which is determined based on the significance level and the degrees of freedom, then the null hypothesis is rejected, and it can be concluded that there is sufficient evidence to support the alternative hypothesis.

In this case,

If the test statistic falls in the rejection region, it means that the evidence suggests that more than 20% of users of the pain drug develop nausea, and the claim that less than or equal to 20% of users develop nausea is not supported by the data.

Thus,

There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.

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Answer:

a) Utilizando la fórmula para el tamaño de muestra, tenemos:

n = (Z * σ / E)^2

donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 95% (Z = 1.96), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 2).

Sustituyendo los valores, obtenemos:

n = (1.96 * 9 / 2)^2 ≈ 77

Por lo tanto, se debe tomar una muestra de al menos 77 familias.

b) De manera similar, tenemos:

n = (Z * σ / E)^2

donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 99% (Z = 2.58), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 1.5).

Sustituyendo los valores, obtenemos:

n = (2.58 * 9 / 1.5)^2 ≈ 261

Por lo tanto, se debe tomar una muestra de al menos 261 familias.

Step-by-step explanation:

Answer:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the ending amount, P is the principal (starting amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

We know P = $5700, A = $6100, n = 1 (since the interest is compounded annually), and t = 12. We can solve for r:

$6100 = $5700(1 + r/1)^(1*12)

$6100/$5700 = (1 + r)^12

1.0702 = (1 + r)^12

log(1.0702) = log[(1 + r)^12]

0.0291 = 12log(1 + r)

0.00243 = log(1 + r)

10^(0.00243) = 1 + r

r = 0.0059 or 0.59%

Therefore, the interest rate of the savings account is 0.59%.

Answer: In decimal form, 14.85

Answer in fraction form: 297/20

Step-by-step explanation:

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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Answer:

The answer is 50% or 1/2

Step-by-step explanation:

There are four outcomes on that chart: 1,2,3,3

There are two threes which means 2/4=.5 or 1/2

Answer:

1/2 chance of landing on a 3.

Step-by-step explanation:

Out of the 4 sections on the spinner, 2 of them have the number 3. This means that there is a 2/4 chance that the spinner lands on a three. This fraction can be simplified into 1/2.

The firm set 14.49% as the required rate of return for the project.

We will first calculate the Project's discount rate which can we calculated using the formula that:

= Rf rate + Beta*risk premium

= 3.0% + 1.29*7.2%

= 3.0% + 0.09288

= 0.12288

= 12.29%

The required rate of return for the project will be:

= Project's discount rate + Adjustment rate

= 12.29% + 2.2%

= 14.49%

Thus, the firm set 14.49% as the required rate of return for the project.

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The approximate height of the pole in centimeters is 17,500 centimeters.

We have,

Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.

We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.

25 = L/7

where L is the total length of the pole.

We can solve for L by multiplying both sides of the equation by 7:

L = 7 x 25

  = 175 meters

Now we need to convert this length to centimeters.

Since 1 meter is equal to 100 centimeters,

175 meters x 100

= 17,500 centimeters

Therefore,

The approximate height of the pole in centimeters is 17,500 centimeters.

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The complete question.

The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.

The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.

Take a look at the quadratic function:

f(x) = 2x^2 + 8x + 7

In this situation, a = 2 and b = 8, yielding:

f(x) = 2(x^2 + 4x) + 7

It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:

f(x) = 2(x^2 + 4x + 16 - 16) + 7

The expression inside the parenthesis can now be written as a perfect square:

f(x) = 2((x + 2)^2 - 16) + 7

Finally, the phrase is simplified by spreading the 2:

f(x) = 2(x + 2)^2 - 32 + 7

f(x) = 2(x + 2)^2 - 25

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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7

Answer:

The correlation coefficient of a data set can be significantly altered by removing an influential point from the data set.

Step-by-step explanation:

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The evaluated form of the factorial expression 5! / 3! 2! is 10.

Let's evaluate the factorial expression as follows:

The factorial function (!) says to multiply all whole numbers from our chosen number down to 1.

Therefore,

5! / 3! 2!

Hence,

5! = 5 × 4 × 3 × 2 × 1 = 120

3! = 3 × 2 × 1 = 6

2! = 2 × 1 = 2

Hence,

5! / 3! 2! = 120 / 6 × 2

120 / 6 × 2 = 120 / 12 = 10

Therefore,

5! / 3! 2! = 10

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Some solutions for the given system of inequalities are:

(5, 12)

(6, 12)

(7, 13)

And so on.

Here we have the following system of inequalities:

x > 4

y  ≥ 12

We want to see which ordered pair, of the form (x, y), is a solution for the system.

A solution is a pair that makes both inequalities true.

So, x must be larger than 4.

y can be equal to 12, or larger than 12.

Then some solutions are:

(5, 12)

(6, 12)

(7, 13)

And so on.

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