Find the surface area of each figure. Round your answers to the nearest hundredth. DO
NOT leave in terms of pi.

EXPLANATION

Let's see the facts:

Heights of 8th grade boys ---------------> Normally distributed

Mean= 50 inches

Standard deviation= 4 inches

d) Probability that boy shorter than 56 inches:

x=56

P(x<56)

We know that z-score=

Replacing terms:

P-value from Z-table =

P(x<56) = 0.93319

Answer: The probability that an 8th grade boy will be shorter than 56 inches is 0.93319*100= 93.3%.

c) Percentage of 8th grade boys that are between 56 and and 60 inches tall is:

P-value from Z-table =

P(x<60) = 0.93319

P-value from Z-table =

P(x<60) = 0.99379

Then, subtracting both probabilities.

P(56

Answer: the percentage of 8th grade boys that are between 56 and 60 inches tall is 0.0606*100 = 6.06%.

a) We have that,

According to the Empirical Rule, we can assevere that 50+- 3σ = 50+- 3*4 ---->

50 + 12 = 62 inches

50 - 12 = 38 inches

About 99.7% of 8th grade boys height will fall between 38 inches and 62 inches.

Answer: Approximately 99.7% of the heights fall between 38 inches and 62 inches.

b) According to the Empirical Rule, we can assevere that around 68% of the data will fall within one standard deviation of the mean. As we already know, the standard deviation σ is a natural yardstick for any measurements that follow a normal distribution.

So, 50 +- σ = 50 +- 4 ---->

50 + σ = 50 + 4 = 54

50 - σ = 50 - 4 = 46

Answer: About 68% of 8th grade boys height will fall between 46 inches and 54 inches.

ANSWER:

B. Similar - SAS

EXPLANATION:

Given:

Recall that the SAS Similarity Rule states that if two sides of one triangle are proportional to two corresponding sides of another triangle and the included angle in both triangles are congruent, then the two triangles are said to be similar.

Looking at triangles ABC and DEF, we can see that, we can see that;

Since the two corresponding sides of both triangles are in equal proportion and the included angle in both triangles are congruent, then triangles ABC and DEF are similar by the SAS Similarity Rule

Solution:

Scott paid;

$13.24 for 3.41-pound bag of shrimp

This means,

$18.99 for 4.96-pound bag of shrimp

This means,

Therefore, the bag that is a better buy based on the unit price is the 4.96-pound because of the unit price which is lesser than the unit price for the 3.41-pound bag.

Thus, the 4.96-pound is a better buy.

Is his answer reasonable: No, Emtiaz's answer is not reasonable because he assumed that the rate of descent was proportional.

The average rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Next, we would determine the rate at which the skydiver falls per seconds:

Rate = time/distance

Rate = 100/0.8

Rate = 125

Also, an equation which models the height (h) of the skydiver at a 0.8 seconds is given by:

h = 125t

At 3.1 seconds, we have:

Rate = time/distance

Rate = 500/3.1

Rate = 161.3

At 1.5 seconds, we have:

Rate = time/distance

Rate = 187.5/1.5

Rate = 125

Therefore, the average rate of change at each time interval is not equal and as such Emtiaz's answer is not reasonable because the rate increases as the time increases.

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The actual distance between the golf vein and the farthest gold dust strike is; 79 miles.

It follows from the task content that the actual distance between both locations is to be determined.

It follows from the distance formula in coordinates geometry that;

D = √{(x2 - x1)² + (y2 - y1)²}

Therefore, the distance between the gold vein and the farthest gold dust strike is;

D = √{(-9 -(-9))² + (71 - (-8))²}

D = √79²

D = 79.

Ultimately, the distance on the graph is 79 units and since each unit on the.graoh represents 1 mile, the actual distance between the gold vein and the farthest gold dust strike is; 79 miles.

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Answer:

Step-by-step explanation:

The results do not apply to any population because this was a convenience sample.

The confidence interval (0.53, 0.72) applies only to the population of those students who drive to the college. The correct answer is D.

The confidence interval is a statistical measure used to estimate an unknown population parameter, such as the proportion of students who support the building of a multi-level parking structure.

In this case, the students conducting the survey set up a table near the student parking lot and asked students who passed by to complete the survey. Therefore, the sample used for the survey consists only of students who use the student parking lot.

Since the survey was conducted exclusively among students who use the parking lot, the results and the subsequent confidence interval can only be generalized to that specific population.

The confidence interval (0.53, 0.72) represents the estimated range of proportions of students who support the parking structure within the population of students who drive to the college. It cannot be extended to the entire student body, students who do not use the parking lot, or any other population beyond those who drive to the college.

The correct answer is D.

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Lisa's car gets 31 miles per gallon.

Thus in 22 gallons she can drive,

22x31=682 miles.

Lisa can drive 682 miles.

The system of inequalities is 1.25x + 2y >= 375 and x + y <= 500, while the smallest number of chocolate covered almonds is 400

We make use of the following representations:

x = chocolate bars

y = chocolate covered almond

Using the above as a guide, and the given parameters;

We have:

1.25x + 2y >= 375 -- the amount raised

x + y <= 500 --- number of bars sold

From the question, we have

x = 100

Substitute x = 100 in x + y <= 500

100 + y <= 500

Evaluate

y <= 400

So, the least amount to sell is 400

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Given: Mitchell's dog is 1/3 as old as Katie's cat. The sum of their ages is 12 years.

Required: To find out how old is Mitchell's dog.

Explanation: Let Mitchell's dog be x years old. Then Katie's cat is 3x. Now according to the question-

Hence Mitchell's dog is 3 years old.

Final Answer: Mitchell's dog is 3 years old.

Claim - The vertical pillars represent a state that has ratified the new government.

Evidence - The evidence is given in the document itself and is reflected in the cartoon. See the image attached.

Reasoning - The Massachusetts Centinel, August 2, 1789, "The Federal Pillars," via Library of Congress. The Massachusetts Centinel published a series of cartoons illustrating the Constitution's ratification. Each vertical pillar indicates a state that has approved the new administration.

The Constitution became the formal structure of the government of the United States of America on June 21, 1788, when New Hampshire became the ninth of 13 states to ratify it.

The Constitution has been revised 27 times, the most recently in 1992, despite the fact that over 11,000 modifications have been suggested since 1789. Article V of the Constitution specifies two procedures for proposing revisions to the document.

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As per the graph, the line passes through coordinates - (1,0) and (0,3)

Since the line passes through both these coordinates, these are the solutions of the equation.

For Option b, 6x + 2y = 6,

If (1,0) is the solution of 6x + 2y = 6, then

⇒ 6(1) + 2(0) = 6

⇒ 6 + 0 = 6

⇒ 6 = 6

If (0,3) is the solution of 6x + 2y = 6, then

⇒ 6(0) + 2(3) = 6

⇒ 0 + 6 = 6

⇒ 6 = 6

Since, these two are solutions of this equation, hence the equation of the given line is: 6x + 2y = 6

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The given parallelogram is a rhombus when x = 9 units

The parallelogram is a four sided plane with opposite sides parallel. So the opposite angles are equal. A parallelogram that has all angles are right angles is called rectangle.

The rhombus is a four sided plane with all of whose sides have the same length.

The sides are given,

9x-8 and 5x+28

In rhombus all the sides are equal

Then the equation will be

9x-8 = 5x+28

Rearrange the terms and solve it

9x-5x = 28+8

4x = 36

x = 36/4

x = 9

Hence, the given parallelogram is a rhombus when x = 9 units

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7+14m

Explanation

Step 1

Let

m represents Marbel's age

Then,

the product of 14 and Mabel's age=

now, Seven more than the product of 14 and Mabel's age

then

Solution:

Given:

The dinner bill = $21.00

The tip = 15% of the bill

Hence,

Therefore, the tip will be $3.15

Answer:

These points are mine :)))

Step-by-step explanation:

He spent $14.44 more on groceries this week than last week

From the question, the given parameters are

Amount spent last week = $58.34

Amount spent this week = $72.78

The additional amount that was spent at the grocery store this week is calculated by subtracting the amount spent this week from the amount spent last week

This is represented as

Additional amount = Amount spent this week - Amount spent last week

Substitute the known values in the above equation

So, we have

Additional amount = 72.78 - 58.34

Evaluate the difference

Additional amount = 14.44

Hence, an additional of $14.44 was this week

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The solution of the equation for t is t = i/pr

The equation is given as

i = prt

Divide both sides of the equation by p

So, we have the following equation

i/p = prt/p

Divide both sides of the equation by r

So, we have the following equation

i/pr = prt/pr

Evaluate the quotients

i/pr = t

Rewrite as

t = i/pr

By the above computation, we changed the subject of the formula in i = prt from i to t.

This implies that solving for t is a concept of subject of formula

Hence, the solution is t = i/pr

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Given the parallelogram in the attached image.

Recall that two adjacent angles in a parallelogram add up to 180 degrees.

So;

Given;

Answer:

You have completed about 55%

Answer: I would say you have completed about 55% on the test.

Part D: There are more than 200,000 people in this city is the correct option

The population of the city in which Devon lives <=240000

Data interpretation: The process of examining data through some predetermined processes in order to give it some meaning and reach a pertinent conclusion is known as data interpretation. It entails using the outcomes of the data analysis to draw conclusions about the relationships that were looked at.

Part a:

According to this part, more than 300,000 people live in this city, which may be possible but we cannot be sure about it.

Part b:

According to this part more than 250,000 people live in the city, which may or may not be possible as we are sure only about 240,000 people

Part c:

According to this part, more than 245,000 people live in this city, which is again a may or may not be possible situation given the fact

Part d:

According to this part, more than 200,000 people live in the city. We are sure about this because it is estimated that 240,000 people live in the city. Hence this is the correct option

Although a part of your question is missing, you might refer to this full question: Devon lives in a city with an estimated population of 240,000 people. Which statement about this population is true?

A) There are more than 300,000 people in this city.

B) There are more than 250,000 people in this city.

C) There are more than 245,000 people in this city.

D) There are more than 200,000 people in this city

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In order to find the solution to this equation graphically, let's use each side of the equation as a function, and then graph both functions in the same coordinate plane:

Graphing y1 in red and y2 in blue, we have:

The intersection point between the graphs is located at (-0.26, 0.77), therefore the solution to the equation is:

STEP - BY - STEP EXPLANATION

Whatto find?

• 90% confidence interval for the population proportion.

• 95% confidence interval for the ppulation proportion.

Given:

n= 800

p=0.66

q=1- p= 1- 0.66 =0.34

a) Given a 90% confidence interval,

α =1- 0.90= 0.10

b)

Given 95% confidence interal.

1- 0.95 =0.

ANSWER

a) (0.6276, 0.6324)

Step 1:

Write the equation

Step 2:

Express the equation in exponential form

Final answer

x = 4

Multiply the numbers and combine exponents with the same base.

Answer:

• The factoring pattern: Difference of two squares (Option A)

• The factored form: (a+9)(a-9).

Explanation:

Given the expression:

81 is the square of 9, thus, the expression above can be written in the form below.

The expression is a difference of two squares.

By the factoring pattern of the difference of two squares:

Thus, we have that:

• The factoring pattern: Difference of two squares (Option A)

• The factored form: (a+9)(a-9).

You have to translate the triangle ABC using the translation rule:

(x,y) → (x-1,y+2)

This rule indicates that the triangle will be translated 1 unit left and 2 units up. To determine the coordinates of each vertex after the translation, you have to subtract 1 to the x-coordinate of each point and add 2 to the y-coordinate.

Original → Translation

A(6,1) → A'(6-1,1+2) = A'(5,3)

B(1,7) → B'(1-1,7+2) = B'(0,9)

C(-3,-2) → C'(-3-1,-2+2) = C'(-4,0)

The coordinates of the vertices of triangle A'B'C' will be

A'(5,3)

B'(0,9)

C'(-4,0)

The correct option is C.

x³ is N²/15. The index form of a number is that digit written as an exponential expression or an unmarried number presented to another number.

A number's index form is that number written as an exponential expression or as a single number raised to another number. The exponent, or index, of an exponential expression indicates how many times the base must be multiplied by itself to evaluate the expression.

This fact can be used to write a number in index form. An index number is a number that has been multiplied by a power. The power, also known as the index, indicates how many times the number must be multiplied by itself. For example, 25 means multiplying 2 by itself five times

= 222222 = 32. There are several important index number rules:

ya × yb = y.

Therefore,

[tex]$x^3=\frac{N^2}{15}[/tex]

For [tex]$x^3=f(a)$[/tex] the solutions are

[tex]$x=\sqrt[3]{f(a)}, \sqrt[3]{f(a)} \frac{-1-\sqrt{3} i}{2}, \sqrt[3]{f(a)} \frac{-1+\sqrt{3} i}{2}$$$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2},[/tex][tex]$x=\sqrt[3]{\frac{N^2}{15}} \frac{-1-\sqrt{3} i}{2}$$[/tex]

Simplify

[tex]$\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2}: \quad-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}-\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x^3=\frac{N^2}{15}[/tex]

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Given:

Here the system of eqution is given as

Required:

Solve using the substitution method

Explanaton:

First put

in

we get

now isolate x

now put the value of x first equation

Final answer:

Solution of given system of equation by using elimination is

The height of the ball at a horizontal distance of R meters from Kaori is H(R)=4H.

Kaori taking a free throw is a guarantee. H(d) simulates the basketball's height (in meters) at d meters of horizontal separation from Kaori.

It is said that H(R) = 4H.

In this case, H(R) displays the height of a basketball instead of H(d). Therefore, it is evident that a basketball's height is 4H since H(R)=4H at d = R.

The horizontal distance from Kaori is R because d is the horizontal distance from Kaori.

Thus the height of the ball is 4H meters at a horizontal distance of R meters from Kaori, according to the expression H(R)=4H.

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We must write the ratio 7 to 15 and reduce it to the lowest term if possible.

The ratio is:

Because 15 is not divisible by 7, we conclude that the ratio is already in its lowest form.