The area, a, of an ellipse can be determined using the formula a = Ï€xy, where x and y are half the lengths of the largest and smallest diameters of the ellipse. which is an equivalent equation solved for y? y = a · Ï€x y = a (Ï€x) y = a â€" Ï€x y = a ÷ (Ï€x)

The equation of the line parallel to the line shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3) and the equation of the line perpendicular to the line shown in the graph passing through the point (-2, 3) is y = (-3/2)x.

What is slope?

The slope of a line passing through two points [tex](x_1, y_1) \: and \: (x_2, y_2)[/tex] is given by slope = [tex]\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Given line passes through (0,-6) and (9,0)

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope.

The slope of the line passing through (0,-6) and (9,0) can be found using the slope formula

slope = (change in y) / (change in x)

= (0 - (-6)) / (9 - 0)

= 6 / 9

= 2/3

Therefore, any line parallel to this line will also have a slope of 2/3.

We can now use the point-slope form of a line to find the equation of the line passing through (-2,3) with a slope of 2/3:

y - y1 = m(x - x1) (point-slope form)

where m is the slope, and (x1,y1) is a point on the line.

Substituting the values, we get:

y - 3 = (2/3)(x - (-2))

y - 3 = (2/3)(x + 2)

y - 3 = (2/3)x + (4/3)

y = (2/3)x + (4/3) + 3

y = (2/3)x + (13/3)

Therefore, the equation of the line parallel to the line passing through (0,-6) and (9,0) shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3).

Using the points (0,-6) and (9,0), we can find the slope of the original line:

slope = (0 - (-6)) / (9 - 0) = 6/9 = 2/3

The slope of any line perpendicular to this line will be the negative reciprocal of this slope. So, the slope of the perpendicular line will be:

perpendicular slope = -1 / (2/3) = -3/2

Now we have the slope of the perpendicular line, and we also have a point it passes through: (-2, 3). We can use the point-slope form of a line to write the equation of the perpendicular line: y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is the point it passes through. Plugging in the values we have, we get:

y - 3 = (-3/2)(x - (-2))

Simplifying:

y - 3 = (-3/2)x - 3

y = (-3/2)x + 0

So the equation of the line perpendicular to the line passing through (0,-6) and (9,0), and passing through (-2, 3), is y = (-3/2)x.

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The fire stations should be located in District 1 and District 4.

This will ensure that all districts can be reached within an 8-minute response time, while minimizing the number of stations needed.

To minimize the number of fire stations needed while ensuring an 8-minute response time, follow these steps:
1. Analyze the table and find districts with response times of 8 minutes or less to all other districts.
2. Identify any districts that are not covered by these districts and repeat step 1 for them.
3. Combine the results to determine the optimal locations for fire stations.
From the table:
1. District 1 has a response time of 8 minutes or less to districts 2, 3, 5, and 6.

However, it doesn't cover districts 4 and 7.
2. District 4 has a response time of 8 minutes or less to districts 1, 2, 3, 5, 6, and 7.

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we can found it by using algebra.This checks out, so we can conclude that Simone has:
4 $100 bills
5 $50 bills
2 $20 bills
9 $10 bills

And the total amount of money she has is indeed $780.Let's start by using algebra to represent the information given in the problem. Let:

x = 20 (Simone has 20 bills in total)
h = x/5 (One fifth of the bills are hundreds)
f = x/4 (One fourth of the bills are fifties)
t = x/10 (One tenth of the bills are twenties)
n = x - h - f - t (The rest of the bills are tens)
We also know that the total amount of money Simone has is $780. We can use this information to write an equation:
100h + 50f + 20t + 10n = 780

Now we can substitute the values we found for h, f, t, and n in terms of x:

100(x/5) + 50(x/4) + 20(x/10) + 10(x - x/5 - x/4 - x/10) = 780

We can see that the number of bills must be a whole number, and therefore x must be a multiple of 20. Let's try assuming that Simone has 20 bills of each denomination, which would give us:

h = x/5 = 4 (4 hundreds)
f = x/4 = 5 (5 fifties)
t = x/10 = 2 (2 twenties)
n = x - h - f - t = 9 (9 tens)
Using these values in the algebraic  equation we derived earlier, we get:
100(4) + 50(5) + 20(2) + 10(9) = 780.

Simone has 20 bills. One fifth of the bills are hundreds, 1/4 of them are fifties, 1/10 of them are $20s. The rest of the bills are tens.

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A system of linear equations with more equations than unknowns is called overdetermined system. This system always be consistent. Because it may result in contradictions or inconsistencies.

An overdetermined system of linear equations cannot always be consistent, due to contradictions or inconsistencies. Since there are more equations than unknowns, there are likely to be restrictions and dependencies among the equations, and not all of them may be satisfied simultaneously.

However, in certain cases, an overdetermined system can still be consistent if the equations are compatible and do not contradict each other. In such cases, the system may have a unique solution or a set of solutions that satisfy all of the equations.

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The sample size is needed to achieve a margin of error of .05 for a 90% confidence interval for a proportion of interest to be near 0.25 is equals to the 203.

From the above problem we have,

Mardin of error, E = 0.05

confidence interval, α = 90%

proportion of interest, p = 0.25

We have to determine the sample size.

Using the formula for minimum sample size is written as n = (Z² × p(1 -p)]/E² --(1)

Using the Z-distribution table and the z-score value for 90% is equals to 1.645.

Plug all known values in above equation,

=> n = [(1.645)² × 0.25 ( 1 - 0.25)]/(0.05)²

=> n = (1.645)² × 0.25 ×0.75/(0.05)²

=> n = 0.5074/0.0025

=> n = 202.96 ~ 203

Hence, required sample value is 203

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As per the number of gym machines, the type of data is b. quantitative discrete data.

A discrete quantitative variable has a distinct quantitative meaning but can only take particular integer values rather than any value within a period. The number of needle sticks, the number of births, and the number of hospitalisations are a few examples of discrete numeric factors.

Similarly to that, the information given in the question refers to the quantity of gym equipment, which qualifies as quantitative data because it is a numerical assessment. Furthermore, rather than representing a continuous range of values, the data is discrete, which means that it reflects a limited collection of whole integers such as 10, 12, 15, 20, and 22. These numbers are the total number of gym machines that are available.

Complete Question:

the data are the number of machines in a gym. you sample five gyms. one gym has 12 machines, one gym has 15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 machines. what type of data is this?

a. Qualitative data

b. Quantitative discrete data

c. Discreet data

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Answer: 12

Step-by-step explanation: Finding area of triangles. To find a triangle's area, use the formula area = 1/2 * base * height. Choose a side to use for the base, and find the height of the triangle from that base. Then, plug in the measurements you have for the base and height into the formula.

No , because 7 t shirts will cost 56 $ in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have $50 to buy T-shirts.

You can buy 3 T-shirts for $24.

                 You can buy 1 T-shirts for = 24/3 = 8

then 3 + 3 = 6 = 24 + 24 = 48 + 8 =  $56

so, you don't buy 7 t - shirts because you have only $56 .

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Answer:

44

Step-by-step explanation:

come on now.

the perimeter is

2×length + 2×width = 110

width = 4×length

so, we use the second equation in the first :

2×length + 2×(4×length) = 110

2×length + 8×length = 110

10×length = 110

length = 110/10 = 11

width = 4×length = 4×11 = 44

The actual height of the town's bell is 15 feet.

To find the actual height of the town's bell using the given scale and the height of the miniature replica, follow these steps:
1. Identify the scale:

The scale provided is 1 inch to 3 feet, which means that 1 inch on the replica represents 3 feet in reality.
2. Determine the height of the miniature replica:

The replica is 5 inches tall.
3. Apply the scale to find the actual height:

Since 1 inch represents 3 feet, we can multiply the height of the replica (5 inches) by the scale factor (3 feet) to find the actual height of the bell.

Actual height = Replica height × Scale factor.

Actual height = 5 inches × 3 feet/inch
4. Calculate the result:

Multiplying 5 inches by 3 feet/inch will give us the actual height of the bell in feet.
Actual height = 15 feet.

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Answer: 216

Step-by-step explanation:

Brainliest pls:)

Then answer and explanation is in the doc below.

Answer:

x ≈ 8.0

Step-by-step explanation:

Using the tangent of the angle is equal to the opposite over the adjacent

tan(37º) = 6/x

x = 6/tan(37º)

x=7.96226892972

Answer:

15.625 inches^3

Step-by-step explanation:

The volume of a cube is a simple calculation:

V=a^3

"a" is any edge of the cube.

Therefore, it would be (2.5^3), which would be 15.625 inches^3

The particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

What is differential equation?

Differential equations are used to model a wide range of phenomena in science, engineering, and mathematics, including physics, chemistry, biology, economics, and engineering.

Integration is a mathematical concept and technique used to find the integral of a function. The integral of a function is a measure of the area under the curve of the function, between two specified points on the x-axis.

To find the particular solution to the differential equation

[tex]\frac{dy}{da} = (a+1)(y+1)[/tex]

with the initial condition y(4) = 3, we can use separation of variables:

[tex]\frac{dy}{y+1} = (a+1) da[/tex]

Integrating both sides:

[tex]\int \frac{dy}{y+1} = \int (a+1) da\ln |y+1| = \frac{1}{2}a^2 + a + C_1, \text{ where } C_1 \text{ is an arbitrary constant of integration}[/tex]

Solving for y, we get:

[tex]y+1 = Ce^{\frac{1}{2}a^2 + a}[/tex]

where C is another arbitrary constant of integration. We can solve for C using the initial condition y(4) = 3:

[tex]3+1 = Ce^{\frac{1}{2}(4^2) + 4}C = 4e^{10}[/tex]

Substituting back, we get:

[tex]y+1 = 4e^{\frac{1}{2}a^2 + a + 10}y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

Therefore, the particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

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Answer:

3,266.53

Step-by-step explanation:

ok so 3 divided by 75.16 so then the answer would be 0.039914848 so then we then have to round to the nearest whatever so i just used a calculator so I think the answer is 3,266.53

The general solution of the given higher-order differential equation is y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2)).

To find the general solution of the given higher-order differential equation, first, let's rewrite the equation in a more standard form:
16y'''' + 16y'' + 4y = 0
Now, we'll solve this fourth-order linear homogeneous differential equation using the characteristic equation method.
1. Write the characteristic equation:
16r^4 + 16r^2 + 4 = 0
2. Divide the equation by 4 to simplify:
4r^4 + 4r^2 + 1 = 0
3. Apply a substitution: let t = r^2, then the equation becomes:
4t^2 + 4t + 1 = 0
4. Solve the quadratic equation for t using the quadratic formula:
t = (-B ± √(B^2 - 4AC)) / 2A
t = (-4 ± √(4^2 - 4(4)(1))) / (2 * 4)
t = (-4 ± √(16 - 16)) / 8
t = -4/8 = -1/2
5. Substitute back r^2 for t:
r^2 = -1/2
6. Solve for r:
r = ±√(-1/2)
r = ±(1/√2)i
7. Since the roots are complex conjugates, the general solution can be written as:
y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2))
where A and B are arbitrary constants determined by the initial conditions of the problem.

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Answer:

The answer to your problem is, 4.51 or in option terms A. 4

Step-by-step explanation:

A=π [tex]R^{2}[/tex]

d = 2 r

We would need to solve for D

d = 2 [tex]\sqrt{\frac{A}{tt} } = 2 x \sqrt{\frac{16}{tt} }-around- 4.51352-or-4.51[/tex]

Thus the answer to your problem is, 4.51 or A. 4

Answer:

(n - 3) (n + 7)

Step-by-step explanation:

n² + 4n - 21

Consider the form x² + bx + c. Find a pair of integers whose product is

c and whose sum is b. In this case, whose product is −21 and whose sum is 4.

-3, 7

Write the factored form using these integers.

(n - 3) (n + 7)

So, the answer is (n - 3) (n + 7)

Answer:

D. 20 in by 30 in by 10 in

Step-by-step explanation:

The rest of them would equal 600 in³ but answer choice D when multiplied together equaled 6,000 in³.

Answer:

x=2

Step-by-step explanation:

Answer: 6x-12= -72

Step-by-step explanation: 12 is a bigger number than 6 and a negative times a positive is always a negative. 6x12 is already 72 but we have to keep the negative so it becomes -72.

Or if its another equation involving x then it's going to be 2. ;)

The story based on the distance-time graph is given below:

Once upon a time, there was a daring bird named Ziggy. Ziggy loved to soar high in the sky, feeling the wind rush beneath her wings.

One day, as she flew higher and higher, she spotted a berry bush on the ground below. Without thinking twice, she dove down to snatch a berry.

But as she got closer, she realized the bush was a trap set by a mischievous fox. Ziggy narrowly escaped the trap and soared back into the sky, but not before losing some altitude.

Determined to keep flying, Ziggy flapped her wings with all her might, gradually ascending back up to her previous height. And as she flew onward, she couldn't help but wonder what other surprises lay ahead.

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According to the given information we can conclude that Richard paid $123.90 for the car rental.

To solve this problem, we need to calculate the total cost of the car rental based on the daily rate and the mileage charge.

First, we can calculate the cost of the rental for two days by multiplying the daily rate by the number of days:

2 days x $34.95 per day = $69.90

Next, we need to calculate the cost of the mileage charge. To do this, we can multiply the number of miles driven by the mileage rate:

300 miles x $0.18 per mile = $54.00

Finally, we can find the total cost of the car rental by adding the cost of the rental and the cost of the mileage charge:

$69.90 + $54.00 = $123.90

Therefore, Richard paid $123.90 for the car rental.

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Step-by-step explanation:

6.3    goes to  2.52

6.3 : 2.52   = 2.5 :1  = 5 : 2

Answer:

Step-by-step explanation:

3 divided by 3/4 can be changes to multiplication

We can solve the equation like 3*4/3

3 divided by 3/4 is 4

Answer:

3 one

Step-by-step explanation:

Answer: the answer is B-130

Explanation: it is farther closest to 50 than the other options.

Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

Probability that is established using logic is known as theoretical probability.

Experimental probability is calculated based on the outcomes of numerous iterations of an experiment.

A probability is a number that falls between (and includes) 0 and 1.

If the likelihood of a situation E is represented by P(E), then:

Given:

Total marbles in  bag = 12

theoretical probability P(E) = favourable outcome / total outcome

P(red marble) = 5/12

Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

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Answer:

A

Step-by-step explanation:

Given:

r (radius) = 2 in

h (height) = 8 in

Find:

A (surface area) - ?

.

First, we have to find the lateral area of the cylinder:

[tex]a(lateral) = 2\pi \times r \times h = 2 \times π\times 2 \times 8 = 32\pi \: {in}^{2} [/tex]

Now, let's find the area of both bases (since a cylinder has 2 identical bases, we have to multiply the area of one base by 2):

[tex]a(2 \: bases) = 2 \times \pi {r}^{2} = 2 \times π\times {2}^{2} = 8\pi \: {in}^{2} [/tex]

In order to find the surface area, we have to add both lateral and bases' areas together:

[tex]a(surface) =32\pi + 8\pi = 40\pi \: {in}^{2} [/tex]

110,664,000 possible selections for Head Girl, Deputy Head Girl, Head Boy, and Deputy Head Boy from a group of 101 girls and 105 boys.

How to calculate different possible selections could be made?​

To find the number of possible selections that can be made, we need to multiply the number of choices available for each position.

For the Head Girl position, there are 101 girls to choose from. After one girl is selected for Head Girl, there are 100 girls remaining to choose from for the Deputy Head Girl position. So there are a total of 101 x 100 = 10,100 possible combinations of girls that can be chosen for these two positions.

Similarly, there are 105 boys to choose from for Head Boy, and 104 boys remaining to choose from for Deputy Head Boy. So there are a total of 105 x 104 = 10,920 possible combinations of boys that can be chosen for these two positions.

To find the total number of possible selections, we multiply the number of combinations for the girls by the number of combinations for the boys:

10,100 x 10,920 = 110,664,000

Therefore, there are 110,664,000 different possible selections that could be made.

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