Write an equation of an ellipse in standard form with center at the origin and with the given characteristics.

c²=68 , vertex (0,-18) .

The conditional probabilities that the gambler wins 1, 2, or 3 given that he wins a positive amount are 13/6, 5/2, and 1/2, respectively.

We can use Bayes' theorem to compute the conditional probabilities. Let A be the event that the gambler wins a positive amount, i.e., A = {1,2,3}, and let B be the event that the gambler wins i, i = 1,2,3. Then, we have:

P(B|A) = P(A|B)P(B)/P(A)

We can compute the probabilities as follows:

P(A) = P(X > 0) = p(1) + p(2) + p(3) = 13/55 + 1/11 + 1/165 = 6/55

P(B) = p(i) for i = 1,2,3

P(A|B) = P(X > 0|X = i) = P(X > 0 and X = i)/P(X = i) = p(i)/[2p(i) + p(i-1) + p(i+1)]

Therefore, we have:

P(B|A) = P(X = i|X > 0) = P(X > 0|X = i)P(X = i)/P(X > 0) = P(A|B)P(B)/P(A)

Computing each of the conditional probabilities yields:

P(1|A) = P(X = 1|X > 0) = (13/55)/(6/55) = 13/6

P(2|A) = P(X = 2|X > 0) = (1/11)/(6/55) = 5/2

P(3|A) = P(X = 3|X > 0) = (1/165)/(6/55) = 1/2

Therefore, the conditional probabilities that the gambler wins 1, 2, or 3 given that he wins a positive amount are 13/6, 5/2, and 1/2, respectively.

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The fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

Slope of a line = change in y/change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\)

Given the following points:

(4, 9) and (0, 5)

Slope of the line would be:

Slope = (5 - 9)/(0 - 4)

Slope = (-4)/(-4)

Slope = 1

Therefore, the fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

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Answer: 9

Step-by-step explanation:

I am assuming that the grid units equal 1 inch.

We have to solve for x. For the width,

60 = 20/3 x

To divide by a fraction is to multiply by its reciprocal.

x = 60 * 3/20 = 180/20 = 9

Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

The required numbers that Jan would have written down are 9, 5, and 8.

GIven that,
Jan writes down one multiple of 9 and two different factors of 40 Jan add together her three numbers Her answer is greater than 20 but less than 30.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
According to the question,
Factor of 40 = 5 and 8
And multiple of 9
Now sum = 8 + 5 + 9 = 23 which 20 < 23 < 30

Thus, the required numbers that Jan would have written down are 9, 5, and 8.

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Your calculation and explanation for finding the margin of safety ratio and percentage are correct.

The margin of safety ratio measures the buffer that a company has between its current level of sales and its break-even point, while the margin of safety percentage expresses this ratio as a percentage of current sales. In the given example, the margin of safety ratio is 0.25 or 25%, which means that JGrant Company's current sales level is 25% above its break-even point.

what is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is often used to describe a part of a whole, or to compare two quantities. For example, if there are 20 red marbles and 80 green marbles in a jar, the percentage of red marbles is 20/100 or 20%, and the percentage of green marbles is 80/100 or 80%. Percentages are often represented using the % symbol.

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Answer:

15

Step-by-step explanation:

9 times 15+8+37=180

180 is a full line

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\((9s + 8)° + 37° = 180°\)

Because they make straight line.

\(9s + 8 + 37 = 180\)

\(9s + 45 = 180\)

Subtract sides 45

\(9s + 45 - 45 = 180 - 45\)

\(9s = 135\)

Divide sides by 9

\( \frac{9s}{9} = \frac{135}{9} \\ \)

\(s = 15\)

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CHECK :

\(9(15) + 45 = 180\)

\(135 + 45 = 180\)

\(180 = 180\)

Thus the solution is correct .

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The change in equilibrium real GDP is B220.

To calculate the change in equilibrium real GDP resulting from an increase in autonomous investment, we need to use the expenditure-output model. In this model, equilibrium real GDP (Y) is determined by the aggregate expenditure (AE), which is the sum of consumption (C), investment (I), government spending (G), and net exports (NX). The equation is:

Y = AE = C + I + G + NX

Given the information provided, let's calculate the initial equilibrium real GDP (Y) using the given values:

C = 80 + (9/10)Y

DI = 1800

G = 1600

TR = 10

T = (1/3)Y

Substituting the values into the equation:

Y = (80 + (9/10)Y) + 1800 + 1600 + 10 - (1/3)Y

Simplifying the equation:

Y = 3490 + (5/6)Y

Multiplying through by 6 to remove the fraction:

6Y = 6(3490) + 5Y

6Y = 20940 + 5Y

Y = 20940

The initial equilibrium real GDP is 20940.

Now, let's calculate the equilibrium real GDP after the B220 increase in autonomous investment (ΔI):

Y' = Y + ΔI

Substituting the values:

Y' = 20940 + B220

Calculating the change in equilibrium real GDP:

Change in Y = Y' - Y

Change in Y = (20940 + B220) - 20940

Change in Y = B220

The change in equilibrium real GDP is B220.

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Answer:

Step-by-step explanation:

\( \frac{28}{24} = \frac{42}{h} \\ \)

Reduce the fraction on the with 4

We have

\( \frac{7}{6} = \frac{42}{h} \\ \)

Cross multiply

That's

\(7h = 6 \times 42 \\ 7h = 252\)

Divide both sides by 7

\( \frac{7h}{7} = \frac{252}{7} \\ \)

We have the final answer as

Hope this helps you

Answer:

h=36

Step-by-step explanation:

28/24= 42/36

........

Answer:

second one is also done.

To convert the octal number \(4137.231_8\) to a hexadecimal number, the final answer is 16.

To convert an octal number to a hexadecimal number, we first need to convert the octal number to its decimal equivalent and then convert the decimal number to hexadecimal.
The given octal number is \(4137.231_8\). To convert it to decimal, we use the positional notation and multiply each digit by the corresponding power of 8:
\(4137.231_8 = 4 \times 8^3 + 1 \times 8^2 + 3 \times 8^1 + 7 \times 8^0 + 2 \times 8^{-1} + 3 \times 8^{-2} + 1 \times 8^{-3}\)
Simplifying this expression, we get the decimal equivalent as:
\(4137.231_8 = 2223.29375_{10}\)Now, to convert the decimal number to hexadecimal, we divide the integer part and the fractional part separately by 16 repeatedly and obtain the remainder at each step. The remainders are then converted to hexadecimal digits.
Converting \(2223_{10}\) to hexadecimal, we get \(8BF_{16}\).
Converting \(0.29375_{10}\) to hexadecimal, we get \(4B_{16}\).
Combining the two parts, we have:
\(4137.231_8 = 8BF.4B_{16}\)
Therefore, the hexadecimal equivalent of \(4137.231_8\) is 16.

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Answer:

$42.00

Step-by-step explanation:

5% = 0.05

40.00 x 0.05 = 2

Answer:

7 -  Yes

4 - Yes

13 - No

9 - No

Step-by-step explanation:

43 + 7 = 50

52 > 50

43 + 4 = 47

52 > 47

43 + 13 = 56

56 is not less than 52

43 + 9 = 52

52 = 52

Answer:

Substitute the numbers for w

Step-by-step explanation:

Answer:

B. 24 flights

Step-by-step explanation:

5% of 480 is 24

Answer:

94.6 sq. cm.

Step-by-step explanation:

Trapezoid area formula = ((a+b)/2)h

base a = 12

base b = 5.2

h = 11

a+b = 12+5.2 = 17.2

(17.2)/2 = 8.6

8.6* 11 = 94.6

94.6

For the given right triangle the value of the angle x is 33.7°.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angle.

Given:

PQR is a right angled triangle.

PR= 8cm.

QR= 12cm.

We have to find the value of angle x.

As the triangle is right angle triangle so we use the trigonometric ratio to find the value of x.

\(tanx = \frac{Opposite Side}{Adjacent Side} \\tanx = \frac{8}{12} \\tan x = 0.6667\\x = tan^-^1(0.6667)\\x = 33.69^o\\x = 33.7^o\)

Hence, for the given right triangle the value of the angle x is 33.7°.

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a)  The given values:  M = (9.830 * (6371000)^2) / (6.67430 × 10^-11)

M ≈ 5.970 × 10^24 kg

b) Comparing this with the calculated value from part (a), we can see that they are very close:

Calculated mass: 5.970 × 10^24 kg

Accepted mass: 5.979 × 10^24 kg

(a) To calculate Earth's mass given the acceleration due to gravity at the North Pole (g) and the radius of the Earth (r), we can use the formula for gravitational acceleration:

g = (G * M) / r^2

Where:

g = acceleration due to gravity (9.830 m/s^2)

G = gravitational constant (6.67430 × 10^-11 m^3/kg/s^2)

M = mass of the Earth

r = radius of the Earth (6371 km = 6371000 m)

Rearranging the formula to solve for M:

M = (g * r^2) / G

Substituting the given values:

M = (9.830 * (6371000)^2) / (6.67430 × 10^-11)

M ≈ 5.970 × 10^24 kg

(b) The accepted value for Earth's mass is approximately 5.979 × 10^24 kg.

Comparing this with the calculated value from part (a), we can see that they are very close:

Calculated mass: 5.970 × 10^24 kg

Accepted mass: 5.979 × 10^24 kg

The calculated mass is slightly lower than the accepted value, but the difference is within a reasonable margin of error.

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Answer:

Step-by-step explanation:

Incomplete presentation of question.  Did you want to factor out the greatest common factor (which is 2), obtaining 2(4y - 3)?  Or something else?  Also:  please note that if you use the left parenthesis ) , you MUST also use the right parenthesis ( .

The scalar potential ϕ such that F = grad ϕ is: ϕ = (1/2)x^2

To determine the constants a, b, and c, we need to find the curl of F. The curl of a vector field F = P i + Q j + R k is given by the determinant of the curl operator applied to F:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

For F to be irrotational, the curl of F must be zero. Equating the components of the curl to zero, we have:

∂R/∂y - ∂Q/∂z = 0 (1)

∂P/∂z - ∂R/∂x = 0 (2)

∂Q/∂x - ∂P/∂y = 0 (3)

Comparing the components of the given vector field F, we can determine the values of a, b, and c:

From equation (1): c = 2

From equation (2): b = 4

From equation (3): a = -3

Thus, the constants are a = -3, b = 4, and c = 2.

To find the scalar potential ϕ, we integrate each component of F with respect to its corresponding variable:

∂ϕ/∂x = x + 2y - 3z (4)

∂ϕ/∂y = 4x - 3y + cy (5)

∂ϕ/∂z = bx - z + 2z (6)

Integrating equation (4) with respect to x gives ϕ = (1/2)x^2 + 2xy - 3xz + f(y, z), where f(y, z) is an arbitrary function of y and z.

Differentiating ϕ with respect to y, ∂ϕ/∂y = 2x + 2f'(y, z). By comparing this with equation (5), we get f'(y, z) = -3y + cy. Integrating f'(y, z) with respect to y gives f(y, z) = -3y^2/2 + cyy/2 + g(z), where g(z) is an arbitrary function of z.

Finally, integrating f(y, z) with respect to z gives g(z) = z^2/2 + d, where d is an arbitrary constant.

Putting it all together, the scalar potential ϕ is given by:

ϕ = (1/2)x^2 + 2xy - 3xz - 3y^2/2 + cy^2/2 + z^2/2 + d

Therefore, the scalar potential ϕ such that F = grad ϕ is:

ϕ = (1/2)x^2

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The required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
In the figure, Similar triangles is shown,
Applying the property of proportional sides in the triangles

30/18 = 20/x
x = 18 / 30 × 20
x = 12

Thus, the required value of the x in a similar triangle by the ratio of proportionality of sides is given as 12.

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The number of apple pies during the first week is 78, and the number of pumpkin pies during the first week is 58.

Assume that

The number of apple pies during the first week= x

The number of Pumpkin pies during the first week= y

total apple pies and pumpkin pies in one given week= 136

The number of apple pies during the second week was 2x

The number of Pumpkin pies during the second week= 3y

total apple pies and pumpkin pies in the second given week= 330

Now, rearrange into an equation:

x+y=136 ---(1)x2

2x+3y=330 ---(2)

solving both equations

2x+3y=330

-2x-2y=-172

y=58

put the y value in any equation

2x+3(58)=330

2x=330-172

x=78.

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Answer:

Step-by-step explanation:

Since there are missing data, let's discuss some facts about regular polygons and their angles.

1) The sum of its Interior angles is given by:

\(S_i=180^{\circ}(n-2) \therefore \:for\: a\:pentagon\:S_i=180^{\circ}(5-2) =540^{\circ}\)

2) Since it is a regular pentagon, each interior angle is congruent:

Each interior angle:

\(Interior\:angle=\frac{540^{\circ}}{5} =108^{\circ}\)

3) If we trace an outside line, the external angle will be supplemental, i.e.

\(m\angle external= 180^{\circ}-108^{\circ} \therefore= 72^{\circ}\)

4) If we trace from each diagonal one line segment, in a regular pentagon that will form 3 triangles with one-third of 108º,i.e.,36º

As we can see, the in the picture below

Answer:

True

Step-by-step explanation:

You can either solve for x (which produces 0 as the result) or you can plug zero in for x into the original equation to verify that it produces a true statement.

Answer:

Step-by-step explanation:

True or false, 0 is a solution to

2x + 10 = 4x + 10

2x - 4x = 10 - 10

-2x = 0

x = 0/-2

x = 0

the equation is TRUE

Answer:

Slope = -6/5 or -1.2

Step-by-step explanation:

Right 15, Down 18

so -18/15

Simplified, -6/5

if radius is 45

V≈1.78×10^5

if radius is 28

V≈1.11×10^5

volume = pi times radius squared times height

if radius is 45

volume = pi times 45 squared times 28

The probability that a student chosen randomly from the class plays both basketball and baseball is 2/13.

What are outcomes?

An outcome is a potential outcome of an experiment or trial in probability theory. Each conceivable result of a specific experiment is distinct, and many results are incompatible (only one outcome will occur on each trial of the experiment).

Given that the total number of students in the class is 26. 6 of them play basketball and 15 of them play baseball. There are 9 students who play neither sport.

The number of students who play at least one sport is (26 - 9) = 17.

Assume that n(A) = 6

n(B) = 15.

n(A∪ B) = 17

n(A∪ B) = n(A) + n(B) - n(A∩B)

17 = 15 + 6 - n(A∩B)

n(A∩B) = 21 - 17

n(A∩B) = 4

Therefore 4 students plays both basketball and baseball.

The number of outcomes of favorable event is 4.

The number of total outcomes is 26.

Probability = The number of favorable outcomes/ Total number of outcomes

The probability is 4/26 = 2/13

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Answer:

210

Step-by-step explanation:

Lets use BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, Subtraction)

45 ÷ 2 = 22.5

22.5 × 8 = 180

180 - 12 = 168

168 + 42 = 210

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Answer:

does literally everyone use this to get the answer to their school work  lol

Step-by-step explanation:

Answer:

1 inches = $0.24

Step-by-step explanation:

9.5 inches =$2.28

$2.28 ÷ 9.5= .24

so the answer is 1 inch = $0.24

The price per inch of plant is $0.24.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Bob sets the price of the plants according to their height in inches.

A plant that is 9.5 inches high costs $2.28 in his store.

To find the price of the plant per inch:

Use division operation;

2.28 / 9.5

= $0.24 per inch.

Therefore, price is $0.24 per inch.

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