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Area: Mastery Test
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12 units
The area of the triangular section is 4 square units. The area of the entire figure is
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Answer:

4 , 12 divided by 3 equals 4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The mean is the average of all ages meaning that the ages are close to 11.6 but don't necessarily have to be 11.6.

Answer:

26.5

Step-by-step explanation:

I rounded it up. Basically use pythagorean theorem.

Answer:

The population growth rate is of 1.86%.

Step-by-step explanation:

Population growth rate:

Immigration plus births subtracted by emigration and deaths.

In this question, we have that:

Birth: 14.3 per 1000

Death: 11.8 per 1000

Immigrations: 21.6 per 1000

Emigrations: 5.5 per 1000

Rate:

[tex]\frac{14.3 + 21.6 - 11.8 - 5.5}{1000} = \frac{18.6}{1000} = 0.0186[/tex]

As a percentage:

Multiply by 100%. So

0.0186*100% = 1.86%

The population growth rate is of 1.86%.

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Since [tex]\frac{1}{6} and \frac{1}{6}[/tex] have the same denominators, we add them first. We then add [tex]\frac{1}{3}[/tex] to the result.

Answer:

b

Step-by-step explanation:

There are four solid and dotted sections and eight sections in total so the probability is 4/8 or 1/2

Answer:

For the restaurant that charges 95 cents, the z-score is -4.29.

For the restaurant that charges $1, the z-score is -3.57.

For the restaurant that charges $1.35, the z-score is 1.43

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average cost of a glass of iced tea is $1.25 with a standard deviation of 7c.

This means that [tex]\mu = 1.25, \sigma = 0.07[/tex]

Restaurant that charges 95 cents:

The z-score is found when X = 0.95. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.95 - 1.25}{0.07}[/tex]

[tex]Z = -4.29[/tex]

For the restaurant that charges 95 cents, the z-score is -4.29.

Restaurant that charges $1:.

X = 1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1 - 1.25}{0.07}[/tex]

[tex]Z = -3.57[/tex]

For the restaurant that charges $1, the z-score is -3.57.

Restaurant that charges $1.35:

X = 1.35

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.35 - 1.25}{0.07}[/tex]

[tex]Z = 1.43[/tex]

For the restaurant that charges $1.35, the z-score is 1.43

Answer:

Answer:[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex]by using Pythagoras law:h²=p²+b²

9²=x²+7²

x²=81-49

x=√32units

Answer:

V>_8

Step-by-step explanation:

20+2.5v >_ 40

The number of visits Nolan can make to earn his first free movie ticket is 8.

The inequality that represents the information in the question is: 20 + 2.5x ≥ 40.

Where x represents the number of visits to the movie theater.

In order to determine the value of x, take the following steps combine similar terms

2.5x  ≥40 - 20

Add similar terms

2.5x  ≥ 20

Divide both sides by 2.5

x  ≥ 8

To learn more about inequality, please check: https://brainly.com/question/5031619

Answer:

B, neither

Step-by-step explanation:

21 is not a perfect square or perfect cube.

Answer:

4.6

Step-by-step explanation:

Answer:

There are 220 boys in the course.

Step-by-step explanation:

If we group the five boys and four girls together, there would be 44 (396/9) groups of nine people. Since there are five boys in every group, you would do 44*5 which is 220.

Answer:

220 boys

Step-by-step explanation:

boys:girls

5:4

396 total

(5x44)+(4x44)=396

220+176=396

220 boys

Answer:

3 ; 4/3

Step-by-step explanation:

x + 4(1/x) = 13/3

x + 4/x = 13/3

x^2 -13/3x + 4 = 0

3x^2 - 13x + 12 = 0

Δ = 169 - 144 = 25

x1 = (13 + 5)/6 = 3

x2 = (13-5)/6 = 4/3

Answer:

4/3 or 3

Step-by-step explanation:

Let, the number be x.

According to the question,

x+4×1/x=13/3

or, x+4/x=13/3

or, x^2+4/x=13/3

or, 3(x^2+4)=13x

or, 3x^2+12=13x

or, 3x^2-13x+12=0

or, 3x^2-(4+9)x+12=0

or, 3x^2-4x-9x+12=0

or, x(3x-4)-3(3x-4)=0

or, (3x-4)(x-3)=0

Either, Or,

3x-4=0 x-3=0

or, 3x=4 .•. x=3

.•. x=4/3

So, the possible numbers are 4/3 or 3.

Answer:

16.44 would be your right answer

Step-by-step explanation:

Answer:

46.44 cm 3

Step-by-step explanation:

Answer:

9.8

Step-by-step explanation:

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {5}^{2} + {b}^{2} = {11}^{2} [/tex]

[tex] {b}^{2} = {11}^{2} - {5}^{2} [/tex]

[tex] {b}^{2} = 121 - 25[/tex]

[tex] {b}^{2} = 96[/tex]

[tex] \sqrt{b} = \sqrt{96} [/tex]

[tex]b = 9.78[/tex]

Answer:

use a calculator

Step-by-step explanation:

also if this is easier change 1/2 and 1/3 to 0.5 and 0.3 where it would be 8.5 x 3.3

Answer: 96 cubic units

Step-by-step explanation: I checked on Khan and that’s what they’re saying is the correct answer.

Answer:

The volume of the cone is 96 cubic unit.

Step-by-step explanation:

volume of squared based pyramid = (1/3) × (Base Area) × (Height).

                      96 [tex]unit^{3}[/tex]                        = (1/3)× 30×(Height)

                                            9.6 unit    = Height

volume of cone  = (1/3) × (Base Area) × (Height).

                             = (1/3) × 30 ×      9.6 unit    

                             = 96[tex]unit^{3}[/tex]  

Click here to know more about the  volume of squared based pyramid .

https://brainly.com/question/9266950

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9514 1404 393

Answer:

  40 square units

Step-by-step explanation:

The area can be considered as that of two trapezoids, a rectangle, and a triangle. The total area is the sum of the areas of these.

Draw two horizontal lines, one beginning at the left-most point, and another 2 units below that. Draw a vertical line segment extending the vertical line at the top down to the first horizontal line. Now the figure is divided as described above.

The upper left trapezoid has bases of 3 and 5, and a height of 4. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(3 +5)(4) = 16

The trapezoid between the two horizontal lines has bases of 8 and 7, and a height of 2. Its area is ...

  A = (1/2)(8 +7)(2) = 15

The rectangle at upper right has a base of 2 and a height of 3. Its area is ...

  A = bh

  A = 2(3) = 6

The triangle at the bottom has a base of 3 and a height of 2. Its area is ...

  A = 1/2bh

  A = 1/2(3)(2) = 3

Then the total area of all of these pieces is ...

  Area = 16 +15 +6 +3 = 40 . . . . square units

Answer:

the answer is 40 square units

Area of the composite figure, which is not drawn to scale is,

⇒ 488 cm²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

To find the area of the composite figure, which is not drawn to scale.

Now, The figure is made by a rectangle and a triangle.

We know that;

Area of rectangle = Lenght x Width

Hence, We get;

Area of rectangle = Lenght x Width

Area of rectangle = 22 x 17

Area of rectangle = 374 cm²

And, Area of triangle = 1/2 × Height × Base

⇒ Area of triangle = 1/2 × (22 - 10) × 19

⇒ Area of triangle = 1/2 × 12 × 19

⇒ Area of triangle = 114 cm²

Thus, Area of the composite figure, which is not drawn to scale is,

⇒ 374 + 114 cm²

⇒ 488 cm²

Learn more about the triangle visit;

brainly.com/question/1058720

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Answer:

Top one, least to greatest:

[tex]-\sqrt{54}[/tex], [tex]-\frac{3}{9}[/tex], [tex]\frac{9}{5}[/tex], [tex]\pi[/tex], 6.6, [tex]\sqrt{75}[/tex]

Bottom one, greatest to least

9.6, [tex]\sqrt{34}[/tex], [tex]\frac{9}{9}[/tex], -4.2, [tex]-7\frac{2}{5}[/tex], [tex]-\sqrt{85}[/tex]

Answer:

Hope I helped and the answers are bellow

Step-by-step explanation:

Part A

-_/- 54 = - 7.38

-3/9 = - 0.3333

9/5 = 1.80

Pi= 3.14

Then 6.6

And finally _/- 75 = 8.66

Part B

9.6

_/- 34 = 5.83

9/9 = 1

-4.2

-7 2/5 = -7.40

-_/- 85 = - 9.21

p-value is a measure of the probability that an observed difference could have occurred just by random chance.

Answer:

the answer is 40.

Step-by-step explanation:

[tex]t \: = \: \frac{600}{9 + 6} = 40[/tex]

9514 1404 393

Answer:

  $131,600

Step-by-step explanation:

If the listing price is P, then the net is the difference between that and all of the various costs.

  P -(5%×P) -94,000 -16000 = 15,000

  0.95P = 125,000

  P ≈ 131,600 . . . . . . divide by 0.95

The minimum listing price must be $131,600.

Answer:

The answer is 8

Answer:

16 inches

Step-by-step explanation:

First, do 56/7. You do this to see how much more feet it is than the scale. The answer is 8.

Because the answer is 8, you would multiply 2 inches by 8 to be proportional to 56 feet.

Answer:

The sample size 'n' = 72,030

Step-by-step explanation:

Step(i):-

Given that the Estimate Error = 0.013

Given that the standard deviation of the Population = 1.5

The estimated error is determined by

[tex]E = \frac{Z_{0.98} S.D }{\sqrt{n} }[/tex]

Step(ii):-

Given that the Level of significance = 0.98 or 0.02

Z₀.₀₂ =   2.326

The estimated error is determined by

        [tex]E = \frac{Z_{0.98} S.D }{\sqrt{n} }[/tex]

   [tex]0.013 = \frac{2.326 X 1.5 }{\sqrt{n} }[/tex]

      [tex]\sqrt{n} = \frac{3.489}{0.013} = 268.38[/tex]

Squaring on both sides, we get

    n =  72,030

Final answer:-

The sample size 'n' = 72,030

This one takes time to type all the math work.

Let me see.

There are two triangles here.

They both have the same area.

A = (1/2)(base)(height) times 2

A = (1/2)(42)(56) times 2

A = 1,176 times 2

A = 2,352 inches^2.

We also have three rectangles. We need to find the area of each rectangle individually.

Area of bottom rectangle = 42 times 72 or 3,024 inches^2.

Area of back rectangle = 56 times 72 or 4,032 inches^2.

Area of slanted rectangle = 70 times 72 0r 5,040 inches^2.

We now add all the areas together to find the total area of the entire figure.

Total Area = 2,352 inches^2 + 3,040 inches^2 + 4,032 inches^2 + 5,040 inches^2

Total area = 14,448 inches^2

Done!

Did you understand what was done here?

Answer:

a. We fail to reject the null hypothesis

b. p > 0.01

c. The test result is not statistically significant

d. There not is enough statistical evidence to suggest that regular exercise improves academic achievement

Step-by-step explanation:

No. Physical Exercise (X₂); 3.75, 2.74, 3.42, 1.67, 3, 3.25, 2.65

Physical Exercise (X₁); 4.00, 2.67, 3.65, 2.11, 3.21, 3.60, 2.80

GPAs Pair number; 1, 2, 3, 4, 5, 6, 7

The null hypothesis, H₀; μ₁ ≤ μ₂

The alternative hypothesis, Hₐ; μ₁ > μ₂

From the data, we have;

[tex]\overline d[/tex] ≈ 0.222857

Where;

d = X₁ - X₂

[tex]\overline d = \dfrac{1}{n} \times \sum_{i = 1}^{n} d_i[/tex]

Similarly, we have;

[tex]s_d^2=\dfrac{\sum \left (d-\overline d \right )^{2} }{n - 1}[/tex]

From which we get;

[tex]s_d[/tex] ≈ 0.160905

The critical-t at n - 1 = 7 - 1 = 6 degrees of freedom for α = 1% = 0.01, is given as follows;

[tex]t_{\alpha /2}[/tex] = [tex]t_{(0.005, \, 6)}[/tex] = 3.707

The test statistic, t = [tex]\overline d[/tex]/([tex]s_d[/tex]/√n)

∴ t = 0.222857/(0.160905/√7) ≈ 3.664

The test statistic , t ≈ 3.664

Therefore, given that the test statistic is smaller than the critical-t,

b. The p-value estimate is p > 0.01

c. The test result is not statistically significant

d. The test result can be reported in a literature as that there is not enough statistical evidence to reject the null hypothesis, therefore, there not is enough statistical evidence to suggest that regular exercise improves academic achievement

Answer:

The answer is A. 8, 9, 10

Answer:

A. 8, 9, 10.

Step-by-step explanation:

Consecutive numbers counting numbers which are 1 greater than the other, therefore:

x + (x + 1) + (x + 2) = 27

(x + x + x) + (1 + 2) = 27

3x + 3 = 27

–3 –3

3x = 24

÷3 ÷3

x = 8.

x = 8 → [ x + (x + 1) + (x + 2) ] =

(8) + (8 + 1) + (8 + 2) = 8 + 9 + 10

Answer:

Where is the picture of the figure

Step-by-step explanation: