the population of weights for men attending a local health club is normally distributed with a mean of 166-lbs and a standard deviation of 26-lbs. an elevator in the health club is limited to 33 occupants, but it will be overloaded if the total weight is in excess of 5940-lbs. assume that there are 33 men in the elevator. what is the average weight beyond which the elevator would be considered overloaded? average weight

Since quadrilateral H'I'J'K' is a translation of quadrilateral HIJK, the translation rule include the following: (x, y)  → (x - 8, y + 10).

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of quadrilateral HIJK horizontally left by 8 units and vertically up by 10 units, the coordinate J of quadrilateral H'I'J'K' include the following:

(x, y)                               →                  (x - 8, y + 10)

J (8, -2)                        →                  (8 - 8, -2 + 10) = J' (0, 8).

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Answer:

f(x + 1) + 2

Step-by-step explanation:

All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.

P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.

There are 64 degrees of freedom for the test for independence in this contingency table.

To find the degrees of freedom for a test for independence in a contingency table, you can use the following formula:
Degrees of freedom (df) = (number of rows - 1) * (number of columns - 1).
In your case, the contingency table has nine rows and nine columns. Using the formula:
df = (9 - 1) * (9 - 1)
df = 8 * 8
df = 64.

In a contingency table, the degrees of freedom (df) for the test of independence are calculated as:

df = (number of rows - 1) x (number of columns - 1)

In this case, the contingency table has nine rows and nine columns, so the degrees of freedom are:

df = (9-1) x (9-1) = 64

This means that there are 64 degrees of freedom for the test of independence.

Degrees of freedom are important because they determine the critical values for the test statistic, which in turn affects the decision to reject or fail to reject the null hypothesis.

In general, as the degrees of freedom increase, the critical values decrease, making it easier to reject the null hypothesis.

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There are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.

To determine the degrees of freedom for the test for independence in a contingency table with nine rows and columns, we use the formula df = (r-1)(c-1), where r is the number of rows and c is the number of columns.

Substituting in the values, we get:df = (9-1)(9-1)df = 8 x 8df = 64A contingency table is a table that shows the frequency distribution of two or more categorical variables.

A test for independence is a statistical test that checks whether the variables are related or not.

Therefore, there are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.

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Answer:

To find the values of f(g(x)) for the given values of x, we need to first evaluate g(x) for each value of x, and then plug the result into f(x).

Using the given functions:

g(x) = 2x - 5

f(x) = √(x+1)

Therefore, we have:

f(g(x)) = √(g(x) + 1) = √(2x - 5 + 1) = √(2x - 4) = 2√(x - 2)

So, we can complete the table as follows:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

Therefore, the completed table is:

x f(g(x))

4 2

10 4

20 6

34 8

52 10

The bank's claim is exaggerated and not entirely accurate.

The bank's claim that virtually all of its customers are served in less than 11 minutes is misleading, as it implies that almost all customers are served in 11 minutes or less. However, based on the given information that service times follow an exponential distribution with a mean of 4.5 minutes, we can calculate the probability that a customer will be served in less than 11 minutes using the cumulative distribution function of the exponential distribution:

P(X < 11) = 1 - [tex]e^{(-11/4.5)[/tex] = 0.956

This means that approximately 95.6% of customers will be served in less than 11 minutes, not "virtually all." Therefore, the bank's claim is exaggerated and not entirely accurate.

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Step-by-step explanation:

Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3

Step-by-step explanation:

Volume of a sphere is given by the formula

4/3 pi r^3       diameter = 6.3 cm  so radius, r = 3.15 cm

4/3 * pi * (3.15)^3 = 130.9 cm^3

After solving equation , the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).

A mathematical assertion that demonstrates the equality of two expressions is called an equation The equals symbol (=) is used to denote the separation of two phrases. Numerous mathematical ideas and relationships, including linear functions, quadratic functions, and trigonometric functions, can be represented by equations.

Let's use the letter 'h' to indicate how many hours the plumber put in.

The plumber costs $35 to come to Jerald's residence and $50 for every hour they work. If Jerald is charged a total of $190 by the plumber, the following equation can be written:

$50h + $35 = $190

To solve for 'h,' we obtain:

$50h = $190 - $35

$50h = $155

h = 155 / 50

h = 3.1

Consequently, the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).

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If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.

As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.

However, the formula for calculating the variance is:

Variance = (sum of the squared differences from the mean) / (number of observations)

The first error Cara may have made is in calculating the sum of the squared differences from the mean.

The correct steps to find the variance are:

Find the mean:

Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78

Calculate the differences from the mean for each observation:

87 - 78 = 9

46 - 78 = -32

90 - 78 = 12

78 - 78 = 0

89 - 78 = 11

Square each difference:

[tex]9^2 = 81[/tex]

[tex](-32)^2 = 1024[/tex]

[tex]12^2 = 144[/tex]

[tex]0^2 = 0[/tex]

[tex]11^2 = 121[/tex]

Find the sum of the squared differences:

81 + 1024 + 144 + 0 + 121 = 1370

Divide the sum of squared differences by the number of observations:

Variance = 1370 / 5 = 274.

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the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

How to solve the question?

Let x be the number of coupons sent to existing members. Then the number of coupons sent to potential members is 3x, as they provided 3 times as many coupons to potential members than to existing members.

According to the problem, the total number of coupons sent is 200. Therefore, we can write the following equation:

x + 3x = 200

Simplifying this equation, we get:

4x = 200

Dividing both sides by 4, we get:

x = 50

Therefore, the number of coupons sent to existing members is 50, and the number of coupons sent to potential members is 3 times as many, or 150.

In conclusion, the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

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The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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In both cases, the subject term (S) and the predicate term (P) are distributed, which means that the proposition makes a claim about the entire class of S and the entire class of P.

Traditional categorical logic, a proposition with both of its terms (subject and predicate) distributed is called a universal proposition.

Stronger claim than a particular proposition.

A universal proposition is a statement that applies to all members of a category or class.

Asserts that the subject term is either entirely included or entirely excluded from the predicate term.

There are two types of universal propositions:

Universal affirmative proposition (A): All S are P.

Universal negative proposition (E): No S are P.

"All mammals are warm-blooded" is a universal affirmative proposition (A) because it claims that the subject term (mammals) is entirely included in the predicate term (warm-blooded).

It distributes both terms and claims the most knowledge.

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The probability that a student who did not complete the homework passed the test is 0.25.

Answer:

Step-by-step explanation:

1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3

The point of tangency is (-3, -2).

To find the point of  tangency , we really want to find the convergence point between the line and the circle. We can begin by tracking down the situation of the circle with focus (- 1,2).

A circle's equation for its center (a,b) and radius (r) is as follows:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

Plugging in the values for the center and solving for r, we get:

[tex](x + 1)^2 + (y - 2)^2 = r^2[/tex]

Now we need to find the intersection point between this circle and the line 2x+3y=-22. We can do this by substituting y = (-2/3)x - (22/3) into the equation of the circle:

[tex](x + 1)^2 + ((-2/3)x - (16/3))^2 = r^2[/tex]

Expanding and simplifying, we get:

[tex]10x^2 + 24x + 44 = 9r^2[/tex]

Next, we can make use of the fact that the line intersects the circle at a tangent. This indicates that the distance between the intersection point and the center of the circle is the same as its radius. The distance between the center of the circle and the line can be determined using the distance formula:

distance = [tex]|2x + 3y - (-22)\sqrt{2^2 + 3^2}| = |2x + 3y + 22| \sqrt(13)[/tex]

Setting this equal to the radius r, we get:

[tex]|2x + 3y + 22| \sqrt{13} = \sqrt{10x^2 + 24x + 44} / 3[/tex]

Squaring both sides and simplifying, we get:

[tex]36(2x + 3y + 22)^2 = 13(10x^2 + 24x + 44)[/tex]

Expanding and simplifying, we get:

[tex]26x^2 + 36xy + 45y^2 + 52x + 132y + 240 = 0[/tex]

Now we can use the quadratic formula to solve for x:

x = (-18y - 13 ± [tex]\sqrt{169 - 720y^2[/tex])) / 13

Substituting this into the equation for the line, we get:

2(-18y - 13 ± [tex]\sqrt{169 - 720y^2))[/tex] / 13 + 3y = -22

Simplifying, we get:

y = -2

Substituting y = -2 into the equation for x, we get:

x = -3

Therefore, the point of tangency is (-3, -2).

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The compound interest investment earns more interest than the simple interest investment, and the difference becomes more significant over time.

After 10 years, the difference is relatively small, but after 20 years, the compound interest investment has earned over $3,700 more than the simple interest investment.

To calculate the amount after 10 and 20 years, we can use the following formulas:

Simple Interest: A = P * (1 + r * t)

Compound Interest: A = P * (1 + r/n)^(n*t)

Where:

Using these formulas and the information given in the table, we can calculate the amount after 10 years and 20 years for each type of investment.

For simple interest, the interest is not compounded, so we just add the interest to the principal:

Amount after 10 years: A = $50,000 * (1 + 0.0275 * 10) = $68,750

Amount after 20 years: A = $50,000 * (1 + 0.0275 * 20) = $87,500

For compound interest, we need to use the formula above with n=12 (since the interest is compounded monthly):

Amount after 10 years: A = $50,000 * (1 + 0.0275/12)^(12*10) = $68,704.23

Amount after 20 years: A = $50,000 * (1 + 0.0275/12)^(12*20) = $91,262.47

To compare the two investments, we can look at the difference between the amounts after 10 and 20 years:

Difference after 10 years: $68,750 - $68,704.23 = $45.77

Difference after 20 years: $87,500 - $91,262.47 = $3,762.47

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Based on the given scenario, Steve who manages the property is a real estate agent.

The correct answer choice is option A

A real estate agent is a person who serves as n intermediary between tenant and landlord, buyers and sellers of properties. They collect rent, make little repairs and screen interested people. The real estate agent receives their reward based on commission, that is, a particular percentage of the property.

Therefore, Jordan is the tenant, Dave is the landlord and Steve is the real estate agent.

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Answer: I'll have to say it's C or D but I think it's D

Hope it helped :D

Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.

1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).

Step 1: Set up the equation using the given information.

One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:

Reciprocal of the original number + 1 = $\frac{7}{3}$

Step 2: Solve for the reciprocal of the original number.

Reciprocal of the original number = $\frac{7}{3}$ - 1

Step 3: Simplify the equation.

Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$

Reciprocal of the original number = $\frac{4}{3}$

Step 4: Find the original number.

Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:

Original number = $\frac{1}{(\frac{4}{3})}$

Step 5: Simplify the expression.

Original number = $\frac{1}{1} \times \frac{3}{4}$

Original number = $\frac{3}{4}$

The original number expressed as a common fraction is $\frac{3}{4}$.

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The resistance of each bulb that is connected in series with a 110 V line is 24.55 Ω with a 13.75 V Voltage difference across each bulb. The power dissipated in each bulb is 7.7 W, if 0.56 A current flows through them.

The voltage across 8 identical bulbs is 110 V

Since they are connected in a series and identical, the Voltage difference across each bulb is [tex]\frac{110}{8}[/tex] V which is 13.75 V

According to the question,

The current flowing through the bulb = 0.56 A

So according to Ohm's Law,

V = IR

13.75 = 0.56 * R

R = 24.55 Ω

The power dissipated in each bulb can be calculated as

P = VI

P = 13.75 * 0.56 = 7.7 W

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In summary, the voltage across each bulb is 13.75V, the resistance of each bulb is 24.55Ω, and the power dissipated in each bulb is 7.7W.

When eight identical lights are connected in series across a 110-V line, the voltage across each bulb will be 110/8 = 13.75 V.
To find the resistance of each bulb, we can use Ohm's law, which states that resistance is equal to voltage divided by current (R = V/I). Therefore, the resistance of each bulb is 13.75/0.56 = 24.55 ohms.
To find the power dissipated in each bulb, we can use the formula P = VI, where P is power, V is voltage, and I is current. Therefore, the power dissipated in each bulb is 13.75 x 0.56 = 7.7 watts.
To find the voltage across each bulb, divide the total voltage by the number of bulbs:

Voltage across each bulb = Total Voltage / Number of Bulbs = 110V / 8 = 13.75V per bulb

Next, use Ohm's Law to find the resistance of each bulb:

Resistance (R) = Voltage (V) / Current (I) = 13.75V / 0.56A = 24.55Ω per bulb

Finally, find the power dissipated in each bulb using the formula:

Power (P) = Voltage (V) x Current (I) = 13.75V x 0.56A = 7.7W per bulb

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Answer: y=1/2x-3

Step-by-step explanation:

I'm assuming you're trying to find it in slope intercept form!

y=mx+b

y=1/2x-3

easy

The equation when solved for b gives ± 7√a/3. Option C

Algebraic expressions are defined as expressions that are composed of terms, variables, constants, coefficients and factors.

They are also composed of arithmetic operations, such as;

From the information given, we have;

9ab² = 49

To determine the value of b, take the following steps

Divide both sides by 9a

b² = 49/9a

Now, find the square root of both sides, we have;

b = [tex]\sqrt{\frac{49}{9a} }[/tex]

b = ± 7√a/3

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Answer:

In its simplest form, the ratios of the length of sides in a 45 45 90 special right angle triangles should be 1 : 1 : 2 1:1:\sqrt{2} 1:1:2on:

And because this is a 30-60-90 triangle, and we were told that the shortest side is 8, the hypotenuse must be 16 and the missing side must be 8 * 3 , or 8 3 . Our final answer is 8√3

Duri can make 72 cupcakes on his own and Habib can make 36 cupcakes on her own, assuming they have enough of all the other ingredients.

To determine how many cupcakes each person can make on their own, we need to check if they have enough of all the other ingredients required to make 12 cupcakes.

Terrance has 1 cup of flour and 6 eggs, which is not enough to make 12 cupcakes.

Duri has 12 cups of flour and 1000 grams of butter, which is more than enough to make 12 cupcakes. However, the recipe requires 3/4 cup of sugar, 2 eggs, and 3/4 cup of milk, which we do not know if Duri has enough of.

Habib has 3 cups of milk and 6 cups of sugar, which is enough to make 12 cupcakes.

Anika has 1 cup of sugar and 4 cups of milk, which is not enough to make 12 cupcakes.

Therefore, only Duri and Habib have enough ingredients to make 12 cupcakes on their own.

To determine how many cupcakes they can make, we need to calculate how much of each ingredient is required for one cupcake and then divide the available ingredients by that amount.

For one cupcake, we need:

1/6 cups of flour

1/16 cup of sugar

1/6 eggs

1/16 cups of milk

125/12 grams of butter

Duri has 12 cups of flour and 1000 grams of butter, which is enough to make 72 cupcakes. Habib has 6 cups of sugar and 3 cups of milk, which is enough to make 36 cupcakes.

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Answer:

9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.

[tex] \frac{3x + 2}{x + 5} - \frac{2x - 3}{x + 5} [/tex]

[tex] = \frac{3x + 2 - (2x - 3)}{x + 5} [/tex]

[tex] = \frac{3x + 2 - 2x + 3}{x + 5} [/tex]

[tex] \frac{x + 5}{x + 5} = 1[/tex]

10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.

[tex] \frac{4x}{x - 2} + \frac{x - 4}{x - 5} [/tex]

[tex] = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} [/tex]

Answer: 64 sqaure centimetres.

Step-by-step explanation:

- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.

Top and Bottom

4 x 4 = 16

16 x 2 = 32

Both faces are the same so once we find the area of one, we can just double it.

North, South, East and West Side

4 x 2 = 8

8 x 4 = 32

All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.

To find the overall surface area add all the areas you have.

32 + 32 = 64

or

16 +_16 + 8 + 8 + 8 + 8 = 64

If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the

correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot

diagram is correct.

A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize

the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-

effect relationship.

The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.

A scatter plot diagram is a graphical representation that displays the relationship between two variables.

The x-axis represents the input variable, while the y-axis represents the output variable.

By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.

If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect

the key characteristic (output variable).

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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).

The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
 To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:

A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.

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Answer:

The correct answer is:

10√2

Explanation:

In a right triangle, the hypotenuse is the side opposite the right angle and is also the longest side. The other two sides are called the legs.

In this problem, the hypotenuse of the resulting triangles is given as 20 inches. Since the quilt squares are cut on the diagonal to form triangular quilt pieces, the hypotenuse of each triangle is formed by the diagonal cut of a square.

Let's denote the side length of each square as "s" inches.

According to the Pythagorean Theorem, which relates the sides of a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

In this case, the hypotenuse is 20 inches, so we have:

20^2 = s^2 + s^2 (since the two legs of the right triangle are the sides of the square)

400 = 2s^2

Dividing both sides by 2, we get:

200 = s^2

Taking the square root of both sides, we get:

s = √200

Since we are looking for the side length of each piece in simplified radical form, we can further simplify √200 as follows:

√200 = √(100 x 2) = 10√2

So, the side length of each quilt piece is 10√

The side length of each piece of the triangular pieces of quilt cut from squares will be 10√2 inches.

This is a simple mathematics problem that can be solved using the Pythagoras theorem. This theorem states that in a right-angled triangle, the square root of the sum of the two perpendicular sides (p,b) is equal to the longest side, called the hypotenuse (h).

[tex]h = \sqrt{p^2 + b^2}[/tex]

Since the triangle pieces have been cut from a square, they will be right-angled triangles, and the two perpendicular sides will be equal, i.e., p = b.

20 = √2p²  (since p and b are equal, b can be taken as p)

On squaring both sides,

400 = 2p²

p² = 400/2

p² = 200

p = √200

p = 10√2 = b

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If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.

Explain month

A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.

According to the given information

If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:

$2299.99 * (1 + 0.020825)²⁴ = $3,637.16

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The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.

Let us consider the score that Tim needs to get on his fourth quiz be x.

Score he needs to get in order to have a mean quiz score of 90,

Set up an equation using the formula for the mean ,

(mean score) = (sum of scores) / (number of scores)

If Tim wants his mean quiz score to be 90, then we have,

⇒ 90 = (86 + 92 + 94 + x) / 4

Multiplying both sides by 4, we get,

⇒360 = 86 + 92 + 94 + x

Simplifying this equation, we get,

⇒ x = 360 - 272

⇒ x = 88

Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.

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