57
Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
Refer to Exhibit 18-2. The test statistic based on the number of students who preferred to get out early equals
Group of answer choices
1.825
0.67
0.82
3.65

Answer:

The simplified expression is sec^2a

Step-by-step explanation:

We can start by using the trigonometric identities:

cot^2 a + 1 = csc^2 a

tan^2 a + 1 = sec^2 a

Using these identities, we can rewrite the expression as:

(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)

= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))

= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)

Now we can use the identity:

sin^2 a + cos^2 a = 1

to rewrite the expression further:

= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)

= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)

= sin^2 a / sin^2 a (1 - cos^2 a)

= 1 / (1 - cos^2 a)

= sec^2 a

Therefore, the simplified expression is sec^2 a.

Answer:

Volume = length x width x height

Step-by-step explanation:

A rectangular prism is a three-dimensional solid object with six faces, where each face is a rectangle. The shape of a rectangular prism is defined by its length, width, and height. The volume of a rectangular prism is the amount of space it occupies and can be calculated by multiplying its length, width, and height. The formula for the volume of a rectangular prism is:

Volume = length x width x height

Understanding the shape of a rectangular prism and its formula for volume is essential in various fields, such as architecture, engineering, and physics, where it is necessary to calculate the volume of objects for design and analysis purposes.

If you multiply that is how u get volume

A quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0) is equals to the f(x) = (1/3)( x² + 10x + 16).

A quadratic function is a polynomial function with one or more variables, the highest degree of the variable is two. It is also called the polynomial of degree 2. The form of quadratic function is

f(x) = ax² + bx + c ----(1)

is determined by three points and must be a≠ 0. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs (-8,0), (-5,-3), and (-2,0) and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point ( -8,0), x = -8, y = f(x) = 0 in equation (1),

=> 0 = a(-8)² + b(-8) + c

=> 64a - 8b + c = 0 --(2)

Similarly, for second point ( -5,-3) , f(x) = -3, x = -5

=> - 3 = a(-5)² + (-5)b + c

=> 25a - 5b + c = -3 --(3)

Continue for third point (-2,0)

=> 0 = a(-2)² + b(-2) + c

=> 4a -2b + c = 0 --(4)

So, we have three equations and three values to determine.

Subtract equation (4) from (2)

=> 64 a - 8b + c - 4a + 2b -c = 0

=> 60a - 6b = 0

=> 10a - b = 0 --(5)

subtract equation (4) from (3)

=> 21a - 3b = -3 --(6)

from equation (4) and (5),

=> 3( 10a - b) - 21a + 3b = -(- 3)

=> 30a - 3b - 21a + 3b = 3

=> 9a = 3

=> a = 1/3

from (5) , b = 10a = 10/3

from (4), c = 2b - 4a = 20/3 - 4/3 = 16/3

So, f(x)= (1/3)( x² + 10x + 16)

Hence, required values are 1/3, 10/3, and 16/3.

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The height of the monster on the 40-inch TV screen will be 8 inches, which is larger than its height on Hunter's tablet.

First, we need to find out the scale of the monster on Hunter's tablet, which can be calculated as follows

Screen aspect ratio = 8/6 = 4/3

Height of monster on tablet = 5 inches

Width of monster on tablet = (4/3) x 5 = 6.67 inches (because the aspect ratio is 4:3, the width of the monster is 4/3 times its height)

Next, we need to find out the height of the monster on the 40-inch TV screen, which has the same 4:3 aspect ratio as the tablet screen. We can do this by using a proportion

Tablet screen height, Tablet screen width = TV screen height : TV screen width

Substituting the values we know, we get,

6 inches : 8 inches = TV screen height : 10.67 inches (because 40 inches is 4/3 times the width of the TV screen)

Solving for TV screen height, we get,

TV screen height = (6/8) x 10.67 = 8 inches

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ANSWER:
x=y/5
STEPS:
1. Divide each term in 5x=y

2. Simplify

----------------------
I hope this helped!! Much love <333

the probability of Jacinta selecting a green marble is 5/11. The total number of marbles in the bag is:

2 (blue) + 4 (red) + 5 (green) = 11

The probability of selecting a green marble can be found by dividing the number of green marbles by the total number of marbles:

P(selecting a green marble) = number of green marbles / total number of marbles

= 5 / 11

Therefore, the probability of Jacinta selecting a green marble is 5/11. Answer: 5/11.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Cindy will take 0.25 hours or 15 minutes to travel a distance of 2 miles at a constant speed of 8 miles per hour.

The formula for time is: time = distance / speed where "distance" is the distance traveled by an object, and "speed" is the rate at which the object is moving.This formula can be used to calculate the time taken by an object to travel a certain distance at a constant speed, or to calculate the speed or distance if the other two variables are known.

The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel.This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.

In the given question,

We can use the formula:

time = distance / speed

where "distance" is the distance traveled and "speed" is the speed at which Cindy is riding her bike.

Substituting the given values, we get:

time = 2 miles / 8 miles per hour

Simplifying, we get:time = 0.25 hours.

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Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

By answering the presented question, we may conclude that So, the Pythagorean theorem length of MN is expressed in terms of a and b.

Its Pythagorean theorem is just a fundamental mathematical principle that explains the connection between the sides of a triangle that is right. It asserts that the sum of the squares of both the widths of the other two sides is a square of both the width of the hypotenuse (the side facing the perfect angle) the side opposite the right angle). The mathematical mathematics is as follows: c2 = a2 + b2 At which "c" indicates the length of the right triangle and "a" and "b" reflect the extents of the additional two sides, started referring to as the legs.

Because M is the midpoint of OE and N is the midpoint of AB, we can draw a line segment connecting M and N that is parallel to OB and AE and perpendicular to AB.

the Pythagorean theorem

[tex]OE² = OX² + XE²OE²[/tex]

[tex](a + b/2)² + (2a - b/√3)²OE² = 7a²/4 + 3ab/2 + b²/4AN²[/tex]

[tex]AE² + EN²AN² = (2a√3)² + (b/2)²AN²[/tex]

[tex]12a² + b²/4MN² = AN² + AM²MN² \\\\ 12a² + b²/4 + (7a²/4 + 3ab/2 + b²/4)MN²\\\\19a²/2 + 3ab/2 + b²/2MN = √(19a²/2 + 3ab/2 + b²/2)[/tex]

So, the length of MN is expressed in terms of a and b.

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The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:

P(x > 52) = 1 - P(x ≤ 52)

P(x ≤ 52) = (52 - 58) / 6 = -1

P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.

Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.

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10/73 is the value of x in inequality.

What does the word "inequality" mean?

In mathematics, inequalities describe the connection between two values that are not equal. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal.

                    However different inequalities are used to compare the values to determine if they are less than or higher than. The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

the inequality  12≥ 73x + 2

                    = 12 - 2  ≥  73x

                     = 10 ≥ 73x

                   = 10/73 ≥ x

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In linear equation, 54 hours time will Rosmaria spend running if she trains for 12 week.

What is a linear equation in math?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Rosmaria runs 1.5 hours.

In the first week, Rosmaria ran 3 hours.

Rosmaria spend running if she trains for 12 weeks = 12 * 1.5 * 3

                                                             = 54

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The probability that at least one of the males has red-green color blindness is 0.6057.

Number of males in a group, n = 7

Probability of red-green color blindness, p = 0.06

Probability of non-red-green color blindness, q = 0.94

P(at least one of them has red-green color blindness) = 1 - P(none of them has red-green color blindness)

Probability of none of the males in the group having red-green color blindness = P(X = 0)

Now, let us apply the Binomial Probability formula, which is:

P(X = x) = (nCx)pxq^n−x where n = 7, x = 0, p = 0.06, q = 0.94

P(X = 0) = (7C0)(0.06)0.94^(1 - 0.06)7-0

= 0.3943

Now, using the given formula:

P(at least one of them has red-green color blindness) = 1 - P(none of them has red-green color blindness)

P(at least one of them has red-green color blindness) = 1 - 0.3943

P(at least one of them has red-green color blindness) = 0.6057

Therefore, the probability that at least one of the males has red-green color blindness is 0.6057.

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Given, X has a uniform distribution on the interval (-1,1]. We are to determine the incorrect statement among the following:

Statement 5: The variance of a uniform distribution is (b-a)^2/12. Here, a=-1 and b=1. Hence, Var(X) = (1-(-1))^2/12 = 1/3. This statement is correct .Therefore, the incorrect statement is P(X ≤ 0.5) = 0.5.

Statement 1: f(x) = 0.5 for -1 < x ≤ 1Statement 2: P(X ≤ 0.5) = 0.5Statement 3: P(X ≤ 1) = 1Statement 4: E[X] = 0Statement 5: Var(X) = 1/3Let's check each statement one by one:

Statement 1: The probability density function (PDF) of a uniform distribution is f(x) = 1/(b-a) for a < x ≤ b. Here, a=-1 and b=1. Hence, f(x) = 1/(1-(-1)) = 0.5 for -1 < x ≤ 1. This statement is correct.

Statement 2: The cumulative distribution function (CDF) of a uniform distribution is F(x) = (x-a)/(b-a) for a < x ≤ b. Here, a=-1 and b=1. Hence, [tex]P(X ≤ 0.5) = F(0.5) = (0.5-(-1))/(1-(-1)) = 0.75[/tex], which is not equal to 0.5. Therefore, this statement is incorrect.

Statement 3: P(X ≤ 1) = F(1) = (1-(-1))/(1-(-1)) = 1. This statement is correct.

Statement 4: The expected value of a uniform distribution is (a+b)/2. Here, a=-1 and b=1. Hence,[tex]E[X] = (-1+1)/2 = 0.[/tex] This statement is correct.

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Answer:

142 sq cm

Step-by-step explanation:

A= 2(lh + wh + lw)

2(7*3+5*3+7*5)

2(21+15+35)

2(71)

A= 142 sq cm

Answer:

$31.45

Step-by-step explanation:

If something was reduced by 15 percent its the same as .85x or 85% of the original price. 37*.85 = $31.45

Answer:

Step-by-step explanation:

The probability of landing on a number greater than 4 on the first spin is 2/3, because 2 out of the 3 numbers (5, 4, 6) are greater than 4.

If the first spin lands on a number greater than 4, then there are two numbers left (4 and 5) for the second spin. The probability of landing on a number less than 6 on the second spin is 2/2 or simply 1, because both 4 and 5 are less than 6.

Therefore, the probability of landing on a number greater than 4 on the first spin and a number less than 6 on the second spin is:

(2/3) x (1) = 2/3 or approximately 0.67.

The equation of the quadratic function represented by the given table is  y = -x² + 4x - 7.

A quadratic function is a function of the form:\sf(x) = ax^2 + bx + c\swhere a, b, and c are constants and x is the parameter. The graph of a quadratic function is a parabola, which is an Inverted curve. Whether the parabola opens up (if a > 0) or down (if a 0) depends on the sign of the coefficient a.

The width of the parabola is also determined by the coefficient a. The parabola is narrow if |a| is greater than 1. (i.e. it has a small width relative to its height). The parabola is wide if |a| is greater than 1.

The standard form of the quadratic equation is given as:

y = ax² + bx + c

Substitute the value of x and y from the table:

3 = a(2)² + b(2) + c

4a + 2b + c = 3........(1)

For point (4, -1):

-1 = a(4)² + b(4) + c

16a + 4b + c = -1..........(2)

For (6, -13):

-13 = a(6)² + b(6) + c

36a + 6b + c = -13..........(3)

From 1 we have:

c = 3 - 4a - 2b

Substitute the value of c in equation 2 and 3:

16a + 4b + 3 - 4a - 2b = - 1

12a + 2b = - 4........(4)

36a + 6b + 3 - 4a - 2b = -13

32a + 4b = -16.......(5)

Multiply equation 4 with 2 and subtract with equation 5:

32a + 4b = -16

-(24a + 4b = - 8)

a = -1

Substitute the value of a in equation 5:

32(-1) + 4b = -16

-32 + 4b = -16

b = 4

Substitute the value of a and b in equation 1:

16a + 4b + c = -1

16(-1) + 4(4) + c = -1

-16 + 8 + c = -1

-8 + c = -1

c = 7

Using the algebraic techniques we have:

a = -1

b = 4

c = 7

Hence, the equation of the quadratic function represented by the given table is y = -x² + 4x - 7.

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Answer:

Step-by-step explanation:

If the width to length ratio is 2 to 3, then for every 2 inches in the width, there are 3 inches in the length.

a. For 2 inches in the width, there are 3 inches in the length.

b. For 4 inches in the width, there are 6 inches in the length.

c. For 6 inches in the width, there are 9 inches in the length.

d. For 8 inches in the width, there are 12 inches in the length.

The length of the rectangle is 12 inches.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Width to length ratio = 2 to 3

Now,

Since the width to length ratio is 2 to 3, we can express the width as 2x and the length as 3x, where x is some constant. Then, we can use the given information to solve for x.

a. For every 2 inches in the width, there are 3 inches in the length.

This means that:

2x = 2 inches

3x = 3 inches

Solving for x, we get:

x = 1 inch

Then, we can find the length by multiplying x by the length factor:

3x = 3 inches

Therefore, the length of the rectangle is 3 inches.

b. For every 4 inches in the width, there are 6 inches in the length.

This means that:

2x = 4 inches

3x = 6 inches

Solving for x, we get:

x = 2 inches

Then, we can find the length by multiplying x by the length factor:

3x = 6 inches

Therefore, the length of the rectangle is 6 inches.

c. For every 6 inches in the width, there are 9 inches in the length.

This means that:

2x = 6 inches

3x = 9 inches

Solving for x, we get:

x = 3 inches

Then, we can find the length by multiplying x by the length factor:

3x = 9 inches

Therefore, the length of the rectangle is 9 inches.

d. For every 8 inches in the width, there are 12 inches in the length.

This means that:

2x = 8 inches

3x = 12 inches

Solving for x, we get:

x = 4 inches

Then, we can find the length by multiplying x by the length factor:

3x = 12 inches

Therefore, by the given ratio the answer will be 12 inches.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1200[1+(0.05)(3)]\implies A=1200(1.15) \implies A = 1380[/tex]

The value of m∠B is 212 - 24x.

The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.

As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.

To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.

Thus,

m∠A + m∠B + m∠C + m∠D = 360

Substituting the given values, we get:

(16x)° + m∠B + (8x+20)° + 128° = 360

Simplifying and solving for m∠B, we get:

m∠B = 360 - (16x)° - (8x+20)° - 128°

m∠B = 212 - 24x

Therefore, the value of m∠B is 212 - 24x.

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Answer:

(3, 4)

Step-by-step explanation:

We are given the following system of equations:

x + y = 7

x + 2y = 11

We want to solve to find the values of x and y.

There are three ways to solve a system of equations: substitution, graphing, and elimination.

Any one of these methods will work, however let's do elimination for this.

To eliminate, we can add or subtract the equations together to clear the variables.
It is helpful to rewrite this system as:

x + 2y = 11

x + y = 7

We can subtract x + y = 7 from x+2y=11:

x + 2y = 11

-(x+y = 7)

This is equivalent to:
x + 2y = 11

-x - y = - 7

_________

0 + y = 4

So, y = 4

Now, we need to find x.

We can plug in 4 for y in either x + y = 7 or x + 2y = 11.

Taking x + y =7 for instance:

x + 4 = 7

Subtract 4 from both sides.

x = 3

So, x = 3 and y =4

As a point, this is (3, 4).

The exponential function that can model the revenue of a technology company whose starting value is $395,000 in 2010 at 1.2% annual growth is b) S(t)=395*(1.012)^(t).

An exponential function is a mathematical function that calculates the exponential growth or decay of a given data set.

An exponential function is defined by the formula f(x) = ab^x.

There are two kinds of exponential functions:

Starting value of the revenue in thousands of dollars = $395,000

Time measured in years after 2010 = t

Annual growth rate = 1.2%

Thus, the exponential function that mirrors the revenue growth is b) S(t)=395*(1.012)^(t).

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a) R(t)=395*e^((0.012t))

b) S(t)=395*(1.012)^(t)

The value of  y = 2.34 and x = 2.31

Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.

Here two similar triangles are given below, ΔABC ≈ ΔCEF

For similar triangle we can write,

⇒ CE/CF = AE/BF

⇒ 3.9/5 = y/3    ⇒ y = (3×3.9)/5

So, y = 2.34

Similarly,

⇒ CF/CB = EF/AB

⇒ 5/8 = x/3.7    ⇒ x = (5×3.7)/8

⇒ x = 18.5/8 = 2.31

Therefore, The value of  y = 2.34 and x = 2.31

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According to the question the value of triangles y = 2.34 and x = 2.31

Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.

Here two similar triangles are given below, ΔABC ≈ ΔCEF
For similar triangle we can write,
⇒ CE/CF = AE/BF
⇒ 3.9/5 = y/3    ⇒ y = (3×3.9)/5
So, y = 2.34
Similarly,
⇒ CF/CB = EF/AB
⇒ 5/8 = x/3.7    ⇒ x = (5×3.7)/8
⇒ x = 18.5/8 = 2.31
Therefore, The value of  y = 2.34 and x = 2.31

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By answering the presented question, we may conclude that In general, expressions it is often most convenient to choose numbers that are powers of ten. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Tavon may have chosen to multiply both sides of the equation by 10 because he wanted to remove the decimal point and work with integers. Then he can use his knowledge of integer multiplication and division to solve the equations more easily.

Tavon may have used a different number and removed the decimal point. For example, you could multiply both sides by 100 or 1000 instead of 10. However, you should carefully choose a number that is manageable and does not overcomplicate the problem. Multiplying by larger numbers complicates the calculations, and multiplying by smaller ones does not eliminate the decimal point entirely. In general, it is often most convenient to choose numbers that are powers of ten. 

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Answer: 4

Step-by-step explanation:

4. shift the boundary line up 1

Step-by-step explanation:

The equation that represents how much will be in the account after 7 years is:

M = 7,600(1+0.06)^7

Here's the explanation:

The formula for calculating the future value (M) of a present value (P) invested at an annual interest rate (r) for a certain number of years (t) is M = P(1+r)^t.

In this case, the present value (P) is 7,600 dollars, the annual interest rate (r) is 6% or 0.06, and the number of years (t) is 7.

Substituting these values into the formula, we get M = 7,600(1+0.06)^7. This represents how much will be in the account after 7 years if no money is added or removed from the account.

Based on the information provided, the table that correctly displays the data is table III.

Note: The question is incomplete; below I attach the missing information:

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Answer:

Step-by-step explanation:

The given line is y = 5x + 2. We know that any line perpendicular to this line will have a slope that is negative reciprocal of 5. The negative reciprocal of 5 is -1/5.

Line A is perpendicular to y = 5x + 2, so it has a slope of -1/5. We also know that the y-intercept of line A is 3. Therefore, the equation of line A can be written as:

y = (-1/5)x + 3

or in the form y = mx + c, where m = -1/5 and c = 3.

The value of x is 8/3 or 2.67 cm (rounded to two decimal places).

The problem at hand entails determining the value of a variable "x" in a right-angled triangle.

We can begin by applying the Pythagorean Theorem, which states that the square of the length of the hypotenuse in a right-angled triangle equals the sum of the squares of the lengths of the other two sides.

We have a right-angled triangle ABC in this case, with AC as the hypotenuse, AB as one of the other sides, and BC as the remaining side.

We know that AB equals 5 cm and BC equals x cm. We must locate AC.

The Pythagorean Theorem yields:

[tex]AC^2 = AB^2 + BC^2[/tex]

[tex]AC^2 = 5^2 + x^2[/tex]

[tex]AC^2 = 25 + x^2[/tex]

Also, we know that AC = 2x + 1. We get the following result when we plug this number into the above equation:

[tex](2x + 1)^2 = 25 + x^2[/tex]

[tex]4x^2 + 4x+ 1 = 25 + x^2[/tex]

[tex]3x^2 + 4x - 24 = 0[/tex]

The above quadratic equation can be factored as follows:

[tex](3x - 8)(x + 3) = 0[/tex]

As a result, either[tex]3x - 8 = 0 or x + 3 = 0.[/tex]

We get the following when we solve for x:

3x - 8 = 0

3x = 8

x = 8/3

or

x + 3 = 0

x = -3

We reject the second solution because length cannot be negative.

As a result, the value of x is 8/3 or 2.67 cm (rounded to two decimal places).

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