there are between 24 and 40 students in a class. The ratio is 4:7, how many students are there

The equation of the ellipse with focus at (-2,0) and vertices at (±7, 0) is given as follows:

x²/49 + y²/45 = 1.

The equation of an ellipse of center (h,k) is given by the equation presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

The center of the ellipse is given by the mean of the coordinates of the vertices, as follows:

Hence:

x²/a² + y²/b² = 1.

The vertices are at x + a and x - a, hence the parameter a is given as follows:

a = 7.

Considering the focus at (-2,0), the parameter c is given as follows:

c = -2.

We need the parameter c to obtain parameter b as follows:

c² = a² - b²

b² = a² - c²

b² = 49 - 4

b² = 45.

Hence the equation is given as follows:

x²/49 + y²/45 = 1.

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9% of the volume of the original volume is removed.

Given that the dimensions of solid box is 15 cm by 10 cm by 8 cm.

So the volume of solid box = 15*10*8 cubic cm = 1200 cubic centimeter

The volume of the cube with side 3 cm = 3*3*3 = 27 cubic centimeter

For each corner one cube so the number of cube is 4

So total volume removed = 4*27 = 108 cubic centimeters

The percent of volume is removed = (108/1200)*100% = 9%

Hence the percentage of volume removed is 9%.

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Answer:

Step-by-step explanation:

Just subtract all the numbers from 38.75

U is a subspace of R3.  A basis for U is  {(1, -2, 3)}  and dim(U) = 1.

a) To show that U is a subspace of R3, we must verify the three conditions:

1. U is non-empty, since the vector (0,0,0) ∈ U, since 0 + 2(0) - 3(0) = 0.
2. U is closed under addition, since for any two vectors (x1, y1, z1) and (x2, y2, z2) ∈ U, their sum (x1+x2, y1+y2, z1+z2) also satisfies the equation x1+x2 + 2(y1+y2) - 3(z1+z2) = 0, so it is also in U.
3. U is closed under scalar multiplication, since for any scalar c and any vector (x, y, z) ∈ U, the vector c(x,y,z) = (cx, cy, cz) also satisfies the equation cx + 2cy - 3cz = 0, so it is also in U.

Therefore, U is a subspace of R3.

b) To find a basis for U, we must find a linearly independent set of vectors which span U. One such set is the vector (1, -2, 3), since it satisfies the equation x + 2y - 3z = 0. Therefore, {(1, -2, 3)} is a basis for U.

c) The dimension of U is the number of vectors in its basis, which is 1. Therefore, dim(U) = 1.

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Complete question :

The manager of Pia’s Taco Casa makes a deposit into the restaurant’s checking account at the end of the day. She has 2 fifty-dollar bills, 16 twenty-dollar bills, 4 ten-dollar bills, 1 five-dollar bill, 24 quarters, 12 dimes, and 3 nickels. She wants to receive 20 one-dollar bills to use as change the next day. How much is the total deposit

Answer:

$452.35

Step-by-step explanation:

1 Nickel = 25 cents = $0.25

1 dime = 10 cent = $0.10

1 quarter = 5 cent = $0.05

Notes deposited :

2 fifty-dollar bills = $50 * 2 = $100

16 twenty-dollar bills = $20 * 16 = $320

4 ten-dollar bills = $10 * 4 = $40

1 five-dollar bill = $5 * 1 = $5

24 quarters = 24 * $0.25 = $6

12 dimes = 12 * $0.1 = $1.2

3 nickels = 3 * $0.05 = $0.15

Total deposit :

$(100+320+40+5+6+1.2+0.15) =$472.35

Amount to withdraw:

20 $1 bill = $1 * 20 = $20

Net deposit :

Deposit - withdraw

$472.35 - $20

= $452.35

Answer:

48 minutes

Answer:

48

The number of cookies in the jar initially was 42

To find out how many cookies were in the jar initially, we can use algebra to represent the problem. Let x be the number of cookies in the jar initially. After Latoya took half of the cookies, Mark took 1/3 of the remaining cookies, Kandi took 1/4 of the remaining cookies, and Shannon took 1 cookie, there are 2 cookies left in the jar.

We can use this information to set up the equation:

x/2 - (x/2)/3 - (x/2)/4 - 1 - 2 = 0.

By solving this equation, we get x = 42. This means there were 42 cookies in the jar initially. To find out how many cookies were there before Latoya came, we just add the 2/3 of a cookie that was left over to the 2 whole cookies we know of.

So, 42+2/3 = 42.67 which means 42 cookies were there before Latoya came.

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Answer:

Step-by-step explanation:

Grove City = 45,032

Franklin = 41,064

Franklin < Grove City

5 thousands > 1 thousand

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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Answer:

Step-by-step explanation:

Step 1, find BJ

Step 2, find BP

Step 3, find PQ

Step 4, find the elevation of peak P

The ending values in vector `x` after executing the given code snippet would be `7 3 0 8 8`.

The given code snippet appears to be incorrect and incomplete. There are a few issues:

1. The loop condition is not properly defined. Instead of `i < x.size() - 1`, it should be `i < x.size() - 1` to ensure that `i` does not exceed the valid index range of the vector `x`.

2. The increment expression `i` is missing in the loop statement, causing an infinite loop since `i` never changes.

Assuming the correct loop condition is `i < x.size() - 1` and the missing increment expression is `i++`, let's correct the code:

cpp

#include <iostream>

#include <vector>

int main() {

   std::vector<int> x = {4, 7, 3, 0, 8};

   int i;

   for (i = 0; i < x.size() - 1; i++) {

       x.at(i) = x.at(i + 1);

   }

   // Printing the modified vector x

   for (int element : x) {

       std::cout << element << " ";

   }

   std::cout << std::endl;

  return 0;

}

Now, running this corrected code will give the following output:

7 3 0 8 8

After executing the loop, the vector `x` will have the ending values `7, 3, 0, 8, 8`. The last element `x.at(4)` is assigned the value of `x.at(4 + 1)`, which is `8`.

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Answer:

180

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Because 20x9=180

Please MARK BRAINLEST!!

The equation of the line that is tangent to circle a from point c( 1,3) is y = (-5/2)x + 11/2.

To find the equation of the line tangent to Circle A from point C (1, 3), we can use the properties of tangents to circles.

First, let's determine the slope of the line connecting the center of Circle A (6, 5) and point C (1, 3). The slope can be calculated as

(y₂ - y₁) / (x₂ - x₁)

= (3 - 5) / (1 - 6)

= 2/5.

The line tangent to the circle will be perpendicular to the line connecting the center of the circle and point C. The slope of the tangent line will be the negative reciprocal of the slope we calculated, which is -5/2.

Using the slope-intercept form of a line, y = mx + b, we can substitute the coordinates of point C (1, 3) and the slope -5/2 to solve for the y-intercept b.

3 = (-5/2)(1) + b

3 = -5/2 + b

b = 3 + 5/2

b = 11/2

Therefore, the equation of the tangent line is y = (-5/2)x + 11/2.

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It would take Kit 1.25 hours to build the wall when working alone.

If Jamie can build the wall in 6 hours working alone, then Jamie's work rate is 1/6 of the wall per hour.

If Kit takes x hours to build the wall working alone, then Kit's work rate is 1/x of the wall per hour.

When Jamie and Kit work together, their combined work rate is 1/4.5 of the wall per hour.

According to the work rate formula, when two people work together, their combined work rate is the sum of their individual work rates. Therefore, we can write the equation: \(1/6+1/x = 1/4.5\)

To solve for x, we need to find a common denominator. The least common multiple (LCM) of 6 and 4.5 is 18, so we can rewrite the equation:\(3/18+2/18=1/4.5\)

Simplifying the equation:\(5/18 = 1/4.5\)

To isolate x, we take the reciprocal of both sides: \(18/5 = 4.5/x\)

Cross-multiplying: \(18x = 22.5\)

Dividing both sides by 18:\(x= 22.5/18\)

Simplifying: x = 1.25

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Answer:

936 dollars

Step-by-step explanation:

I've got the area of the parallelogram and the area is 360 feet.area of parallelogram is equal to based x height then I took the money x the feet then I got 936 dollars hope it helps.

Correlation is a statistical measure that describes the strength and direction of a relationship between two variables. It indicates how much one variable tends to change in response to changes in the other variable.

The sample correlation coefficient between X and Y can be calculated using the following formula: r =\([nΣxy - (Σx)(Σy)] / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]\)

where n is the sample size, Σxy is the sum of the products of the corresponding x and y values, Σx and Σy are the sums of the x and y values, Σx^2 and Σy^2 are the sums of the squared x and y values, respectively.

Using the given information, we can calculate the necessary values as follows:

n = 45

Σx = 153.7

Σy = 231.2

Σxy = 712.5

Σx^2 = 718

Σy^2 = 1775.2

Substituting these values into the formula, we get:

r = [nΣxy - (Σx)(Σy)] / [√(nΣx^2 - (Σx)^2) √(nΣy^2 - (Σy)^2)]

r = [45(712.5) - (153.7)(231.2)] / [√(45(718) - (153.7)^2) √(45(1775.2) - (231.2)^2)]

r = 0.804

Therefore, the sample correlation coefficient between X and Y is 0.804. This indicates a strong positive linear relationship between the two variables.

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Answer:

0.15cm^2

Step-by-step explanation:

- find area of rectangle (length x height)

- find area circle (pi x radius^2)

- to find area of shaded region, substract area rectangle and area of circle

- to find nearest hundredth, which is equal to 1/100, round up to nearest 0.01

Answer:

129

Step-by-step explanation:

Answer:

I think the answer is 129. I'm not sure and if I'm wrong I apologize.

Step-by-step explanation:

3+18=21

21+108=129

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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For the acute angle θ with sinθ=3/5, the exact values of cos θ, tan θ, cot θ, sec θ, csc θ are 4/5, 3/4, 4/3, 5/4, and 5/3 respectively.

Given that sin θ = 3/5, we need to find the values of cos θ, tan θ, cot θ, sec θ, csc θ. We can solve this problem using the Pythagorean theorem. To do this, we draw a right-angled triangle.

The hypotenuse of the right-angled triangle is 5. This is because sin θ = 3/5. The adjacent side is the value we need to find, which is cos θ. Using the Pythagorean theorem, we find the opposite side to be 4

Opposite side = √(5² - 3²) = √16 = 4cos θ = 4/5To find the values of tan θ, cot θ, sec θ, and csc θ, we can use the following formulas.

tan θ = sin θ/cos θcot θ = 1/tan θsec θ = 1/cos θcsc θ = 1/sin θSubstituting the values of sin θ and cos θ

we found earlier, we get;tan θ = sin θ/cos θ = (3/5) / (4/5) = 3/4cot θ = 1/tan θ = 4/3sec θ = 1/cos θ = 5/4csc θ = 1/sin θ = 5/3

Hence, the exact values of cos θ, tan θ, cot θ, sec θ, csc θ are 4/5, 3/4, 4/3, 5/4, and 5/3 respectively.

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Answer:

4+1+4+g=36

g=27

dg=32

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

DE : EF : FG = 4 : 1 : 4

DG = 36

DG = DE + EF + FG

-> 4x + x + 4x = 36

9x = 36

x = 4

so EG = EF + FG

= x + 4x

= 5x

= 20

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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Answer:

789x86=8u

Step-by-step explanation:

Answer: ? the measure of what

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hi ,  Butteryfly   :P

given  m= -2

Point P1( -1, -4)    in the form (x1,y1)

use the point-slope formula, below, and plug in our knows.

y - y1 = m(x -x1)

y-(-4) = -2(x-(-1)

note the careful detail of the negatives

y+4 = -2(x+1)

y+4 = -2x -2

y = -2x -2 -4

y = -2x -6

now use Desmos or your favorite free on-line graphing tool.  i'm litterally copy and pasting our line equation into Desmos for the graph attached.

The gas station serves 16 vehicles per hour, and 72 vehicles arrive in 4 hours. The vehicles will spend 4.50 hours at the gas station.



To find the total time the vehicles will spend at the gas station, we need to calculate the total number of vehicles that arrive and then divide it by the rate at which the gas station serves vehicles.

Given:

Arrival rate: 18 vehicles per hour

Service rate: 16 vehicles per hour

Time: 4 hours

First, let's calculate the total number of vehicles that arrive during the 4-hour period:

Total number of vehicles = Arrival rate * Time

                      = 18 vehicles/hour * 4 hours

                      = 72 vehicles

Since the gas station can serve 16 vehicles per hour, we can determine the time it takes to serve all the vehicles:

Time to serve all vehicles = Total number of vehicles / Service rate

                         = 72 vehicles / 16 vehicles/hour

                         = 4.5 hours

Therefore, the vehicles will spend 4.5 hours at the gas station. Rounded to 2 decimal places, the answer is 4.50 hours.

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The linear regression equation that represents the correlation between homework grade (x) and test grade (y) is y = 0.6x + 18.5. Using this equation, the estimated homework grade for a student with a test grade of 32 is 38.

To find the linear regression equation, we need to calculate the slope and the y-intercept using the given data:

1: Calculate the mean of the homework grades (x) and test grades (y) from the table.

  Mean of x: (50 + 70 + 80 + 90) / 4 = 72.5

  Mean of y: (60 + 85 + 95 + 100) / 4 = 85

2: Calculate the differences between each homework grade (x) and the mean of x, and each test grade (y) and the mean of y.

  Difference for x: (50 - 72.5), (70 - 72.5), (80 - 72.5), (90 - 72.5) = -22.5, -2.5, 7.5, 17.5

  Difference for y: (60 - 85), (85 - 85), (95 - 85), (100 - 85) = -25, 0, 10, 15

3: Calculate the sum of the product of the differences for x and y, as well as the sum of the squared differences for x.

  Sum of (x - mean of x) * (y - mean of y): (-22.5 * -25) + (-2.5 * 0) + (7.5 * 10) + (17.5 * 15) = 162.5

  Sum of (x - mean of x)^2: (-22.5)^2 + (-2.5)^2 + (7.5)^2 + (17.5)^2 = 1050

4: Calculate the slope (b) using the formula:

  b = Sum of (x - mean of x) * (y - mean of y) / Sum of (x - mean of x)^2

  b = 162.5 / 1050 ≈ 0.155

5: Calculate the y-intercept (a) using the formula:

  a = mean of y - (b * mean of x)

  a = 85 - (0.155 * 72.5) ≈ 85 - 11.24 ≈ 73.76

6: Write the linear regression equation by rounding the coefficients to the nearest tenth:

  y = 0.2x + 73.8

7: Substitute the given test grade (y = 32) into the equation to estimate the homework grade (x):

  32 = 0.2x + 73.8

  0.2x = 32 - 73.8

  0.2x = -41.8

  x ≈ -209 (rounded to the nearest integer)

Therefore, the estimated homework grade for a student with a test grade of 32 is 38.

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Answer:

n = -10

Step-by-step explanation:

4 - n = 14

Subtract 14 from both sides.

4 - 14 - n = 0

Add n to both sides.

-10 = n

So, n = -10

After answering the provided question, we can conclude that the average (arithmetic mean) of 2x and 2y is 48.

The mean of a dataset is the sum of all values divided by the total number of values; this is also known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the total number of values in the dataset by the sum of those values yields this result. Calculations can be performed using both raw data and data that has been combined into frequency tables. The average of a number is referred to as its average. It is simple to calculate: Divide the total number of digits by the number of digits. the total divided by the count.

The average (arithmetic mean) of 2x and 2y is 48.

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Answer:3048.7804878

Step-by-step explanation:

I took the same test p.s. you may need to round.