If a student thinks of a number from 1 to 75, what is the probability that the number will be 20, 30, or 40?If a student thinks of a number from 1 to 75, what is the probability that the number will be 20, 30, or 40?

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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Answer:

Step-by-step explanation:

Volume of a cube:

V = a3

Surface area of a cube:

the area of each face (a x a) times 6 faces

S = 6a2

Face diagonal of a cube:

By the pythagorean theorem we know that

f2 = a2 + a2

Then f2 = 2a2

solving for f we get

f = a√2

Diagonal of the solid cube:

Again, by the pythagorean theorem we know that

d2 = a2 + f2

substituting f into this equation we get

d2 = a2 + (a√2)2 = a2 + 2a2 = 3a2

solving for d we get

d = a√3

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

Answer:

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The slope of a line perpendicular to the line whose equation is x - 2y = -8 is -2.

In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90° (right angles).

From the information provided above, the slope for the equation of line m is given  by:

x - 2y = -8

2y = x + 8

y = x/2 + 4

slope (m) of line m = 1/2

In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

Slope, m₂ of perpendicular line = -2

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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The width of the garden is 4 feet.

What is Rectangle ?

A rectangle is a quadrilateral with four right angles, opposite sides that are parallel, and equal in length. It is a type of parallelogram where the adjacent sides are equal in length, but the opposite sides are not necessarily equal.

Let's start by using the formula for the perimeter of a rectangle:

Perimeter = 2(length + width)

We know that the perimeter is 34 feet, so we can plug in that value and simplify:

34 = 2(l + w)

17 = l + w

We also know that the length is 5 more than 2 times the width, so we can write an equation for that:

l = 2w + 5

We can substitute this expression for l into the first equation:

17 = (2w + 5) + w

Simplifying, we get:

17 = 3w + 5

12 = 3w

w = 4

Therefore, the width of the garden is 4 feet.

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To find the equation of the time they spent we need to use the:

Where m is the slope and (x1,y1) is a point of the table.

We can find the slope with:

Using the first two points on the table we have:

Now plugging the values of the slope and the first point into the equation we have that:

Therefore the equation that represents the time they spent is:

where x is the number of people they survey and y is the time it takes.

(a) An appropriate sample space S for this experiment is the set of all possible sequences of four children, where each child can be either a boy (b) or a girl (g). So, the sample space S is:

S = {bbbb, bbbg, bbgb, bgbb, gbbb, bggg, bgbg, gbgg, ggbb, gbgb, bggg, gbgg, gggg, gggb, gggg}

There are 2^4 = 16 possible outcomes in the sample space.

(b) The event E that there are three boys and a girl in the family can be represented by the set of all sequences in the sample space S that have three b's and one g. So, the event E is:

E = {bbbg, bbgb, bgbb, gbbb}

There are 4 possible outcomes in the event E.

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

a) 9 cm2

b) 12 cm2

c) 18 cm2

d) 27 cm2

Answer:

\(\frac{107}{14}\) or \(7\frac{9}{14}\)

Step-by-step explanation:

\(5 \frac{1}{2} +2\frac{1}{7}\)

\(5 \frac{1}{2} +2\frac{1}{7} =\frac{11}{2} +\frac{15}{7}\)

\(\frac{11}{2} +\frac{15}{7}\)

\(\frac{11}{2} +\frac{15}{7}=\frac{77+30}{14} =\frac{107}{14}\)

\(\frac{107}{14} =7\frac{9}{14}\)

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The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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Answer: x=70°

Step-by-step explanation:

These are supplementary angles, meaning they add up to 180°

45+(2x-5)=180°

45+2x-5=180

40+2x=180

2x=140

x=70°

A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

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Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

Answer:

m<P=130°

m<Q=130°

m<R=50°

Step-by-step explanation:

m<P=130

m<Q=130

m<R=50

Answer:

21 servings

Step-by-step explanation:

4/7 = 12/x

cross multiply and you get

4x = 7(12)

4x = 84

x = 21

Answer:162

Step-by-step explanation:

162

Answer:

1/4 ft

Step-by-step explanation:

A = l x w

5/24 = 10/12 x w

Solve for w

5/24 divided by 10/12 = w

Take inverse of 10/12 and multiply

5/24 times 12/10

1/4

Answer:

7/8X-8=216      

x=256

7/8x-8=216

     +8  +8

7/8x=224

7/8    7/8

x=256

Step-by-step explanation:

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

Answer:

            4  to  1

Step-by-step explanation:

                                                Tablespoon of cocoa   to Tablespoon of sugar

                                                                          8             :                2

                                                                          \(\frac{8}{2}\)              :                \(\frac{2}{2}\)

                                                                          4             to                1

When recipe is doubled:                             ( 8 x 2)         to        (2 x 2)

                                                                         16             :              4

                                                                         \(\frac{16}{4}\)             :               \(\frac{4}{4}\)

                                                                          4           to              1

It can be observed that the ratio remains the same

Answer: 45

Step-by-step explanation:

\(f(-5)=2(-5)^{2} -5\)

\(f(-5)= 2(25) -5\)

\(f(-5) = 50-5\)

\(f(-5) = 45\)

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

Answer:

Explanation:

Here, we want to get the volume enclosed by the tent

Mathematically, that would be the product of the area of the triangular base and the height of the tent

We have the area of the traingular base as:

Finally,we muliply this by the height of the tent

We have this as:

Answer:

9

Step-by-step explanation:

9x8=72 72+18=90

Answer:

C.    AA

Step-by-step explanation:

Since m<Y = 27°, then m<W = 27°.

We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).

Answer: C.   AA