Below, the two-way table is given for a class of students. Juniors Seniors Free Freshmen Sophomore Male 4 6 2 2. Female 3 4 6 3 Total If a student is selected at random, find the probability the student is a junior given that it's male. Round to the nearest whole percent.​

Answer:

E(X) = 38.9346

Var(X) = 25.588

E(Y) = 38.25

Var(Y) = 26.1875

Step-by-step explanation:

Given - Four buses carrying 153 high school students arrive to Montreal. The buses carry, respectively, 36, 46, 32, and 39 students. One of the students is randomly selected.One of the 4 bus drivers is also randomly selected.

To find - Compute the expectations and variances of X and Y.

Proof -

Let us assume that,

X be The number of students that were on the bus carrying this randomly selected student.

Y denote the number of students on his bus.

Now,

E(X) =  \(\frac{36(36) + 46(46) + 32(32) + 39(39)}{153}\)

       = \(\frac{5957}{153}\)

       = 38.9346

⇒E(X) = 38.9346

Now,

E(Y) = \(\frac{36 + 46 + 32 + 39}{4}\)

      =  \(\frac{153}{4}\)

      = 38.25

⇒E(Y) = 38.25

Now,

Var(X) = \(\frac{36(36 - 38.9346)^{2} + 46(46 - 38.9346)^{2} + 32(32 - 38.9346)^{2} + 39(39 - 38.9346)^{2}}{153}\)

          = \(\frac{310.0276 + 2296.3144 + 1308.5091 + 0.1668}{153}\)

          = \(\frac{3915.0179}{153}\)

          = 25.588

⇒Var(X) = 25.588

Now,

Var(Y) = E(Y²) - [E(Y)]²

          = \(\frac{36^{2} + 46^{2} + 32^{2} + 39^{2} }{4} - (38.25)^{2}\)

          = \(\frac{5957}{4} - 1463.0625\)

          = 1489.25 - 1463.0625

          = 26.1875

⇒Var(Y) = 26.1875

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Given: The function below

To Determine: The range and the graph of h9x)

Solution

Please note the ddomain is the input of the function. Let us use the values of x (domain) to get the range as shown below

Hence, the range is {7, 5, -1, -9}

Let use the domain, the set of x-values to plot a graph against the corresponding y- values

The table of values showing x-values and corresponding y-values is

The graph of the domain and the range values is as shown below

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

We have,

We can simplify the given expression as follows:

(X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y)

= (5X - 5Y) ÷ 8 - 1 ÷ (4X + 4Y)

[distributing the factors]

= (5X - 5Y) /8 - 1/(4X + 4Y)

[finding a common denominator]

= ((5X - 5Y)(4X + 4Y) - 1)/(4X + 4Y)

= (20X² + 20XY - 20XY - 20Y² - 1) / (4X + 4Y)

= (20X² - 20Y² - 1) / (4X + 4Y)

Therefore,

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

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Susan invested $7000 in the fund that paid a 9% profit, and the remaining (10,000 - 7000) = $3000 in the stock that suffered a 3% loss.

Let's assume that Susan invested x dollars in the fund that paid a 9% profit, and the remaining (10,000 - x) dollars in the stock that suffered a 3% loss.

The net profit from the investment in the fund would be 9% of x, or 0.09x dollars.

The net loss from the investment in the stock would be 3% of (10,000 - x), or 0.03(10,000 - x) dollars.

Given that her overall net profit was $540, we can write the equation:

0.09x - 0.03(10,000 - x) = 540

Now let's solve for x:

0.09x - 0.03(10,000 - x) = 540

0.09x - 300 + 0.03x = 540

0.12x = 540 + 300

0.12x = 840

x = 840 / 0.12

x = 7000

So, Susan invested $7000 in the fund that paid a 9% profit, and the remaining (10,000 - 7000) = $3000 in the stock that suffered a 3% loss.

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Answer: A

Step-by-step explanation:  Milligram to Centigram

Hope it helped u,

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Answer:

I think it is kilogram to gram

Step-by-step explanation:

Answer:

Hola senor

Step-by-step explanation:

When the function f is transformed to g, the equation is g(x) = 2x + 14 - 1

The equation of function f is given as

f(x) = 2x - 1

The transformation is given as

Horizontal shift of 7 units left.

The above transformation rule can be represented as

Horizontal shift of 7 units left.: (x, y) = (x + 7, y)

When the above rule is applied, we have the following equation

g(x) = f(x + 7)

So, we have

g(x) = 2(x + 7) - 1

Open the brackets

g(x) = 2x + 14 - 1

Hence, the equation of function g is g(x) = 2x + 14 - 1

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Answer: umm i dont know...

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Because the two lines are parallel, the angle of y would be 109 degrees. Since a straight line = 180 degrees, just subtract 71 from it to get y.

Next to find the x value :

We know that since angle y is 109 degrees, this angle must equal to 71.

     71 = 4x - 25

     71 + 25 = 4x

     96 = 4x

Divide both sides by 4

      24 = x

We can check to see if it works :

     (4(24) - 25) = (96 - 25) = 71, so this is correct

Hope this helps! Best of luck <3

The equation models the height, H, for n bounces, will be H = 920 (0.56)ⁿ.

Consider the function:

y = a (1 ± r) ˣ

Where n is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

Some students performed an experiment in which they dropped a rubber ball from a height of 920 centimeters.

They noticed that after each bounce, it reached 56% of its previous height.

Then the equation models the height, H, for n bounces will be

H = 920 (0.56)ⁿ

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The value of g, for a  30-sided regular polygon has an angle measure represented as 6g° is calculated to be 28

The problem is solved using the formula for number of angles for n sided polygon

The formula is (n - 2)180

where n = number of sides

for 30-sided polygon the angles is solved as below

= (n - 2)180

= ( 30 - 2 ) * 180

= 28 * 180

= 5040

this is represented as 6g

each angle is measured 5040 / 30 = 168

6g = 168

g = 28

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Answer: 28

Step-by-step explanation: 168 is the whole polygon, so 6 times 28 is 168 therefore its correct, btw i also did the test

Answer:

A. 1/2

Step-by-step explanation:

So 15/24 = 0.625

therefore you need to convert all the fractions into decimals and determine which decimal is less than 0.625

a) 0.5 ------ding ding ding correct answer :)

b) 0.875

c) 0.79

d) 0.75

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The sampling distribution has a mean value of 171.3 feet; two standard deviations from the mean are 295.3 feet in a positive direction and 47.3 feet in a negative direction.

To calculate these values, the formula for standard deviation is used, which is:

Standard Deviation = (X-mean)/standard error

Therefore, to calculate two standard deviations from the mean in the positive direction, we use:

295.3 ft = (X-171.3)/48

To calculate two standard deviations from the mean in the negative direction, we use:

47.3 ft = (X-171.3)/48

Therefore, the mean of the sampling distribution is 171.3 ft, and two standard deviations from the mean in the positive direction is 295.3 ft, and two standard deviations in the negative direction is 47.3 ft.

Complete Question:

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 171.3 ft and standard deviation 48 ft.

You intend to measure a random sample of n =28 trees. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes of the mean, and two standard deviations from the mean in the positive and negative direction. Be accurate to two decimal places.

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9514 1404 393

Answer:

Step-by-step explanation:

x > 2 and x < 10

The expression x > 2 graphs as an open circle at x=2 and shading of the number line to the right of that.

The expression x < 10 graphs as an open circle at x=10 and shading to the left of that. The conjunction 'and' means that the only values of interest are those where the shading overlaps, between (and not including) 2 and 10.

__

x > 2 or x > 10

The graph of x > 2 is described above.

The expression x > 10 graphs as an open circle at x=10 and shading to the right of that. The conjunction 'or' means that any shaded value is of interest. Since all values to the right of x=2 are shaded, that is what the graph of this conjunction looks like.

hey there ..

plz show the graph also ..

The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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Answer:

18%

Step-by-step explanation:

Divide 64/303.

Divide 9/303.

Subtract the answers and you'll get 18%.

The percentage of the sample population with brown eyes and black hair is larger than the percentage of the sample population with blue eyes and black hair by 18.25%

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given here, according to the survey, the population with Brown eyes & black hair and Blue eyes and black hair  is 64 and 9 respectively

Also, the marginal total is equal to 303

therefore, the percentages of the two groups are

Brown eyes & black hair =64/303 × 100

                                         = 21.12%

similarly we can calculate  Blue eyes and black hair = 9/303 × 100

                                                                                      = 2.97%

Hence the difference is  21.22% - 2.97% =  18.25% (approx)

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Answer:

see below

Step-by-step explanation:

The first step is to read the problem

Then you need to make a plan

Implement the plan

Then evaluate the answer to see if it makes sense

Answer:

c

Step-by-step explanation:

Answer:

A. Yes, the points have no pattern.

Step-by-step explanation:

just did it on edge and got 100%

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Darren needs approximately 49 feet of tape.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

P = 2(L + W)

P = 2(10 + 8)

P = 2(18)

P = 36 feet.

In Mathematics and Geometry, the perimeter of a semicircle can be calculated by using this mathematical equation:

P = 2(π × radius)

P = 2(3.14 × 8/4)

P = 2(6.28)

P = 12.56 feet.

Approximate length of tape = 12.56 feet + 36 feet

Approximate length of tape = 48.56 ≈ 49 feet.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

i think it is 60 because 30 divided by 3-4 equals 2Step-by-step explanation:

Answer: Choice A

Step-by-step explanation:

it increases

Answer:

The Point C shows the location of 5-2i in the complex plane: 5 points to the right of the origin and 2 points down from the origin.

Step-by-step explanation:

We have the complex number 5-2i and we have to show the location of the point that represents that number in the complex plane

In the complex plane the real numbers are located in the horizontal axis, increasing to the right. The positives real numbers are at the right of the origin and the negatives to the left.

The complex numbers are located in the vertical axis, with the positives over the origin and the negatives below the origin.

This complex number 5-2i is the sum of a real part (5) and a imaginary part (-2i), so the point will be 5 units rigth on the horizontal axis (for the real part) and 2 units down in the vertical axis (for the imaginary part).

Answer:

c. point c

Step-by-step explanation:

The solution that can be used to fill in location A is 45%.

In this case, Rena is trying to make a 45% solution. The alligation diagram shows two solutions with concentrations of 20% and 45%. The concentration at location A represents the concentration of the final mixture.

To determine the concentration at location A, we can visually observe the positioning of the concentrations on the diagram. The closer a concentration is to location A, the more it contributes to the final mixture.

In this case, the concentration of 45% is closer to location A than the concentration of 20%.

This means that more of the 45% solution should be used in the mixture to achieve a 45% concentration.

Therefore, the solution that can be used to fill in location A is 45%.

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Answer:

The ordered pair is: \((\frac{7\sqrt{3}}{2},\frac{5\sqrt{3}}{2})\)

Step-by-step explanation:

We are given the following plane curve:

\(x = 7 \cos{t}\)

\(y = 5 \cos{t}\)

Ordered pair for a value of t:

We find (x,y) for these values of t. So, when \(t = \frac{\pi}{6}\)

\(x = 7 \cos{\frac{\pi}{6}} = 7\frac{\sqrt{3}}{2} = \frac{7\sqrt{3}}{2}\)

\(y = 5 \cos{\frac{\pi}{6}} = 5\frac{\sqrt{3}}{2} = \frac{5\sqrt{3}}{2}\)

The ordered pair is: \((\frac{7\sqrt{3}}{2},\frac{5\sqrt{3}}{2})\)

Answer:

see explanation

Step-by-step explanation:

calculate slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

consider the middle dotted line

with

(x₁, y₁ ) = (- 5, - 3) and (x₂, y₂ ) = (6, 8) ← 2 points on the line

m = \(\frac{8-(-3)}{6-(-5)}\) = \(\frac{8+3}{6+5}\) = \(\frac{11}{11}\) = 1

consider the line of reflection ( the solid line )

with

(x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 1, 4) ← 2 points on the line

m = \(\frac{4-3}{-1-0}\) = \(\frac{1}{-1}\) = - 1

Answer:

e

Step-by-step explanation:

5(4x +3)=-4(5-2x)

5×4x +5×3=-4 ×5 -4 × -2x

20x +15=-20+8x