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For the following sample of scores, find the mean, median, mode, range and ss, variance, and standard deviation. What is the shape of this distribution? What is the best way to report average in this distribution?

x f

18 1

17 2

16 4

15 5

14 4

13 2

--- ---

2 1

Answer:

1/7

Step-by-step explanation:

The probability of picking an even number is 3/7.

Without putting the first card back, the probability of picking an even number again is 2/6.

\(3/7 \times 2/6\)

\(= 6/42\)

\(=1/7\)

Answer:

x = 16.5

Step-by-step-explanation:

The height of the larger triangle is 11, and the height of smaller triangle is 2. Which means that the larger triangle height is 5.5 times greater than the smaller triangle's height.

If the base of the smaller triangle is 3, that means that base of the whole/larger triangle is 16.5 because 3 * 5.5 = 16.5

Yes, you would distribute the exponent to both the denominator and numerator. For example, if you had an expression like (2/3)^4, you would distribute the exponent to end up with (2^4)/(3^4).

For example, if you have an expression like (2/3)^4, the exponent of 4 should be distributed to both the numerator and denominator, resulting in (2^4)/(3^4). This is equivalent to multiplying the numerator and denominator by the same amount, 4 times. This is the same as writing (2*2*2*2)/(3*3*3*3), or simply

16/81.

1. Start with the expression

(2/3)^4

2. Distribute the exponent of 4 to the numerator and denominator, resulting in

(2^4)/(3^4)

3. This is equivalent to multiplying the numerator and denominator by 4, so (2^4)/(3^4)

= (2*2*2*2)/(3*3*3*3)

4. Simplify the expression to 16/81

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Answer:

18

Step-by-step explanation:

Mode is the value that appears most often in a set of data values. So, in this case, the answer is 18.

Answer:

1) 11

2) 15

Step-by-step explanation:

The bars on the sides of the numbers represent the absolute value/magnitude of the number, so you will need to remove the negative symbol if it is present in front of the number (if it is already a positive number, leave it as it is).

Example:

\(|-3+2| = |-1|\)

\(= 1\)

Hope this helps :)

Answer:

uhhh

Step-by-step explanation:

sorry but i really need the points

Answer:

x=4

Step-by-step explanation:

x=4 because when you have 3x+2=14 Subtract 2 from both sides. Then 3x+2−2=14−23x=12. Divide both sides by 3.3x3=123

The value of x in the figure having 3 angles on a line as shown in the image attached below is 28.

The angle is formed by two rays and a common point.

To calculate the value of x using the diagram attached below:

∠AOC+∠COD+∠BOD = 180° because the sum of all the angles on a line is 180°

On substituting the values from the figure,

∠AOC=3x-7

∠COD=55

∠BOD=x+20

∠AOC+∠COD+∠BOD =3x-7+55+x+20

3x-7+55+x+20=180

4x+68=180

4x=112

x=28

Thus, the value of x is 28 for the figure attached below.

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Answer:

A

Step-by-step explanation:

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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Using the t-distribution, it is found that the desired measures are given as follows:

At the null hypothesis, it is tested if the mean GPA of the students is of 3.3, that is:

\(H_0: \mu = 3.3\)

At the alternative hypothesis, it is tested if the mean GPA is different than 3.3, hence:

\(H_1: \mu \neq 3.3\).

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

The values of the parameters are given as follows:

\(\overline{x} = 3.33, \mu = 3.3, s = 0.08, n = 55\)

Hence, the test statistic is:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{3.33 - 3.3}{\frac{0.08}{\sqrt{55}}}\)

t = 2.78.

We are testing if the mean is different of a value, hence we have a two-tailed test. Using a t-distribution calculator, with 55 - 1 = 54 df and t = 2.78, the p-value is of 0.01.

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Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Answer:

71. 19  72. 100  73. 9  74.1  75. 90  76. 4

Step-by-step explanation:

#71.

Start with 2b-a

Plug in the given numbers where the variables are.

Now the equation is 2(12) - 5

Solve 2(12) - 5

2(12) = 24      24 - 5 = 19

#72.

Start with d(ab-c)

Plug in the given numbers where the variables are.

Now the equation is 2((5×12) - 10)

Solve in the parenthesis first.

5×12= 60    60-10=50    2(50)= 100

#73.

Start with 3+ \(\frac{b}{d}\)

Plug in the given numbers where the variables are.

Now the equation is 3+ \(\frac{12}{2}\)

Solve.

\(\frac{12}{2}\) = 6    3+6 = 9

#74.

Start with \(\frac{4a}{b+4d}\)

Plug in the given numbers where the variables are.

Now the equation is \(\frac{4(5)}{12+(4x2)}\)

Solve.

4(5)= 20    

(4×2)= 8    12+8= 20

Now the fraction is  \(\frac{20}{20}\) = 1

#75.

Start with 2a² - c

Plug in the given numbers where the variables are.

Now the equation is 2(5)² - 10

Solve 2(5) = 10      10² = 100  100-10= 90

#76.

Start with b - c + d

Plug in the given numbers where the variables are.

Now the equation is 12 - 10 + 2

Solve.

12 - 10 = 2     2 + 2 = 4

Answer:

24% of 100 is 24 meaning you subtract 24 to 100. Giving you $76 as the final price.

Step-by-step explanation:

Answer:

Open circle at -1 and shading to the left

Step-by-step explanation:

Given the question :

Which number line shows the solution to the inequality −2(3x − 1) < 8? Group of answer choices Open circle at 2 and shading to the right Open circle at 2 and shading to the left Open circle at -1 and shading to the right Open circle at -1 and shading to the left.

−2(3x − 1) < 8

Open the bracket and simplify :

-2(3x - 1) < 8

-6x + 2 < 8

-6x < 8 - 2

-6x < 6

Divide both sides by - 6

-6x/-6 < 6/-6

x > - 1

Or - 1 < x

Since - 1 is less than x, from - 1 we draw to the left

Answer:

An explicit representation for the nth term of the sequence:

\(f_n=-\frac{1}{2}\cdot \:4^{n-1}\)

It means, option (B) should be true.

Step-by-step explanation:

Given the geometric sequence

\(-\frac{1}{2},\:-2,\:-8,\:-32,...\)

A geometric sequence has a constant ratio, denoted by 'r', and is defined by

\(f_n=f_1\cdot r^{n-1}\)

Determining the common ratios of all the adjacent terms

\(\frac{-2}{-\frac{1}{2}}=4,\:\quad \frac{-8}{-2}=4,\:\quad \frac{-32}{-8}=4\)

As the ratio is the same, so

r = 4

Given that f₁ = -1/2

substituting r = 4, and f₁ = -1/2 in the nth term

\(f_n=f_1\cdot r^{n-1}\)

\(f_n=-\frac{1}{2}\cdot \:4^{n-1}\)

Thus, an explicit representation for the nth term of the sequence:

\(f_n=-\frac{1}{2}\cdot \:4^{n-1}\)

It means, option (B) should be true.

Answer:

73 hot dogs

58 hamburgers

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The mean and the standard deviation, from the frequency table, are given as follows:

The frequency table gives the number of times that each observation appears.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:

Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:

Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.

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The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

Here, we have,

we know that,

The sum of the angles in a triangle add to 180

x+2x+6x = 180

Combine like terms

9x= 180

Divide by 9

9x/9 = 180/9

x = 20.

Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

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complete question:

The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)

Answer:

236 ft^3

Step-by-step explanation:

Base radius = 5 ft

Height = 3 ft

Volume =   πr^2h

              =  π × 5^2 × 3

              =  75π

               =  235.61944901923 feet^3

Nearest Cubic Foot = 236 ft^3

Nearest Cubic Foot:

Hence Answer is:

236 ft^3

Hope this helps!

Answer :

X = 2

Y = -1

Z = -2

4-3-2 = -1

6-3-2 = 1

4-4-2 = -2

In the diagram, the correct option is

angle DAB = angle DCB

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a geometric postulate used in proving the congruence of triangles.

According to CPCTC, if two triangles are proven to be congruent (having all corresponding angles and sides congruent), then their corresponding parts, including angles and sides, are also congruent.

The two triangles in the figure are congruent by the SAS congruence theorem and hence applying the CPCTC we have that

angle DAB = angle DCB

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Answer:

I think x equals 4410

Step-by-step explanation:

63 x70 I think

9514 1404 393

Answer:

  x = 47

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  x° +63° +70° = 180°

  x = 47 . . . . . . . . . . . divide by °, subtract 133

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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A function is a relationship between inputs where each input is related to exactly one output.

The value of \(h^{-1}(x)\) is (x -5)/5

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

h(x) = 5x + 2

To find \(h^{-1}(x)\).

Step 1: Keep h(x) = y.

Step 2: Replace y with x and x with y.

Step 3: Solve for y.

Step 4: Change y = \(h^{-1}(x)\)

Now,

y = 5x + 2

x = 5y + 2

x - 2 = 5y

(x - 2) / 5 = y

y = (x - 2) / 5

\(h^{-1}(x)\) = (x -2) / 5

Thus,

The value of \(h^{-1}(x)\) is (x -5)/5

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