What is the measure of DEF

Carlos' daughter will receive $847,438.00 from the savings account.

The formula used to calculate the amount of money earned through compound interest is [tex]A = P(1 + r/n)^nt[/tex], where A is the amount of money earned, P is the principal amount, r is the rate of interest per annum, n is the number of times the interest is compounded per year, and t is the number of years.

In Carlos' case, P = 400,000, r = 3.5%, n = 1, and t = 18 (the number of years between when his daughter was born and when she graduates high school). Plugging these values into the formula above, we get:

[tex]A = 400,000(1 + 0.035/1)^(1*18)A = 400,000(1.035)^18\\A = 400,000(2.11859)\\A = $847,438.00[/tex]

Therefore, upon graduation, Carlos' daughter will receive $847,438.00 from the savings account.

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Answer:

x=7

Step-by-step explanation:

22+54x=-20+60x

42+54x=60x

42=6x

x=7

Answer: Two parallel lines have the same slope. Therefore, we can use the slope of the given line y = -4x + 5 to find the slope of the line that is parallel to it.

The slope of y = -4x + 5 is -4. Therefore, the slope of any line parallel to it will also be -4.

Now we have the slope of the line and a point that it passes through. We can use point-slope form to write the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line.

Plugging in the values we know, we get:

y - (-1) = -4(x - (-2))

y + 1 = -4(x + 2)

y + 1 = -4x - 8

y = -4x - 9

Therefore, the equation of the line that is parallel to y = -4x + 5 and passes through the point (-2,-1) is y = -4x - 9.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The real and imaginary values of w is 86  and - 0.92i respectively.

To find w = √(3 - 4i), we can use the following steps:

Step 1: Find the modulus and argument of z = 3 - 4i

The modulus of z is

|z| = √(3² + (-4)²)

= √(9 + 16) = √25

= 5.

The argument of z is arg(z) = arctan(-4/3) ≈ -0.93 radians (or about -53.13 degrees).

Step 2: Find the principal square root of the modulus of z, which is

√|z| = √5.

Step 3: Find the argument of w, which is half of the argument of z, i.e., arg(w) = arg(z)/2

= -0.93/2

≈ -0.465 radians (or about -26.57 degrees).

Step 4: Express w in terms of its real and imaginary parts, using the formula:

w = √|z| * exp(i*arg(w)).

Substituting the values we found above, we get:

w = √5 x exp(i(-0.465))

= √5 x (cos(-0.465) + i*sin(-0.465))

≈ 1.86 - 0.92i

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the identity is:

cos(2π - x) = cos(x)

Using the angle sum identity for cosine, we have:

cos(2π - x) = cos(2π)cos(x) + sin(2π)sin(x)

Since cos(2π) = 1 and sin(2π) = 0, this simplifies to

cos(2π - x) = cos(x)

The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three fundamental trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to observe that the cosv value varies depending on the quadrant. As observed , cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

from the question:

Using the angle sum identity for cosine, we have:

cos(2π - x) = cos(2π)cos(x) + sin(2π)sin(x)

Since cos(2π) = 1 and sin(2π) = 0, this simplifies to:

cos(2π - x) = cos(x)

Therefore, the identity is:

cos(2π - x) = cos(x)

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The median number of TVs in Mrs. Jamison's class is 2, (i.e. the middle number).

To find the median of the given data of the number of TVs in Mrs. Jamison's class:

First we have to list all the values from least to greatest.

Then, find the middle number (in case if there is one middle number) then that will be the median of the data.

And if there is two middle number, we have to find the average of the two middle numbers and the result will be our answer i.e. median.

So, The data is 0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,4,4,5,6

The middle number from the data is 2

                        Therefore, the median is 2.

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Answer:

A. 10/21

Step-by-step explanation:

There is a total of 7 marbles, 5 of which are red ---> 5/7

When you pull out a red marble and do not replace it in the bag before pulling the second one, a marble (red) is gone hence ----> 4/6

Multiply the two events to find the probability:

5/7 x 4/6 = 10/21

Janet will cover 416 square inches of rectangular cake with frosting.

What exactly is a rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees). It is a type of quadrilateral, which means a four-sided polygon. The opposite sides of a rectangle are parallel and equal in length, and the adjacent sides are perpendicular to each other.

The area of a rectangle can be calculated by multiplying its length and width (or base and height) together, while its perimeter is the sum of the lengths of all four sides.

Now,

Since Janet is frosting the top layer of 4 rectangular birthday cakes, we need to calculate the total area of the top layer of all 4 cakes combined.

Each cake measures 13 inches by 8 inches, so the area of one cake is:

13 inches x 8 inches = 104 square inches

The top layer of one cake will have the same dimensions, so the area of the top layer of one cake is also 104 square inches.

To find the total area of the top layer of all 4 cakes combined, we can multiply the area of one cake by 4:

Total area = 104 square inches/cake x 4 cakes = 416 square inches

Therefore, Janet will cover 416 square inches of cake with frosting.

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In step 4 and 5 he used prime factorization of 5 under cube root.

This was done in order to eliminate the cube root.

Prime factorization is a process of finding the prime factors of a given number. A prime factor is a factor of a number that is a prime number. The prime factorization of a number is the list of its prime factors, together with their multiplicities.

To find the prime factorization of a number, divide it by its smallest prime factor and write down the result as the product of the prime factor and the quotient. Continue this process with the quotient until quotient of 1 is obtained.  

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The minimum possible area of this rectangle is 78.75 yd².

The maximum possible area of this rectangle is 101.75 yd².

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

In order to determine the minimum possible area of this rectangle, we would subtract the greatest possible error from each measurement and then multiply as follows:

Amin = (18 - 0.5) × (5 - 0.5)

Amin = 78.75 yd²

For the maximum possible area of this rectangle, we would add the greatest possible error to each measurement and then multiply as follows:

Amin = (18 + 0.5) × (5 + 0.5)

Amin = 101.75 yd²

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Answer: 3 hours

Step-by-step explanation:

Answer:

you can only rent the ski boat for about 3 hours.

Step-by-step explanation:

if you cant spend no more than $150

you need to see how much u can spend within hours.

so you would have to see what 35 can be multiplied to get to 150.

obviously no number multiplied by 35 will get you 150, but if you multiply 35 x 4, you will get 140, which is close enough, yet still you don't have enough for a full 4 hours.

Then you have to consider that you still need to pay $20 just to rent the ski boat alone.

So that will take away from the money you have.

when you subtract 20 from 140, you will still not have enough money for 4 whole hours, therefore you will only have enough for 3 hours with the $ 120 you have left.

lmk if it was right. hope this helps.

Answer:

25 flowers and 14 bushes

Step-by-step explanation:

Sarah has $300 budget

flowers go for $6 each

bushes go for $10 each

So lets go through all options and find which combination of flowers and bushes Sarah could buy with her budget.

1. 13 flowers and 23 bushes

13 x 6 = $78

23 x 10 = $230

$78 + $230 = $308 Above $300

2.16 flowers and 21 bushes

16 x 6 = $96

21 x 10 = $210

$96 + $210 = $306 Above $300

3. 8 flowers and 26 bushes

8 x 6 = $48

26 x 10 = $260

$48 + $260 = $308 Above $300

4. 25 flowers and 14 bushes

25 x 6 = $150

14 x 10 = $140

$150 + $140 = $290 Fits the budget so the answer is

25 flowers and 14 bushes

Hope this helps!

Brainliest and a like is much appreciated!

Answer: a. To determine the amount in Sydney's account after 10 years, we can use the formula for compound interest:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

where FV is the future value, PMT is the monthly payment, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.

Plugging in the values for Sydney's account, we get:

FV = 100 × (((1 + 0.05/12)^(12*10) - 1) / (0.05/12))

FV = $16,184.46

Therefore, the amount in Sydney's account after 10 years is $16,184.46.

b. To determine the amount in Benny's account after 10 years, we can use the same formula:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

Plugging in the values for Benny's account, we get:

FV = 80 × (((1 + 0.08/12)^(12*10) - 1) / (0.08/12))

FV = $15,710.21

Therefore, the amount in Benny's account after 10 years is $15,710.21.

c. Sydney had more money in the account after 10 years, since $16,184.46 > $15,710.21.

d. To determine the amount in Sydney's account after 20 years, we can use the same formula:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

Plugging in the values for Sydney's account, we get:

FV = 100 × (((1 + 0.05/12)^(12*20) - 1) / (0.05/12))

FV = $45,074.89

Therefore, the amount in Sydney's account after 20 years is $45,074.89.

e. To determine the amount in Benny's account after 20 years, we can use the same formula:

FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))

Plugging in the values for Benny's account, we get:

FV = 80 × (((1 + 0.08/12)^(12*20) - 1) / (0.08/12))

FV = $42,598.05

Therefore, the amount in Benny's account after 20 years is $42,598.05.

f. Sydney had more money in the account after 20 years, since $45,074.89 > $42,598.05.

Step-by-step explanation:

The variable "Annual income payments: $186,928" is of the type "Numerical, continuous, ratio."

The given information that Robert filled on his application for a loan is as follows:Annual income payments: $186,928Number of credit cards: 4Ever convicted of a felony: NoOwn a second car: NoThe types of variables are:Numerical: A numerical variable is a measurable quantity, and they are of two types: discrete and continuous.Discrete variables: They are quantitative variables that can be counted and are usually whole numbers. In this case, there is no discrete numerical variable, so it is not a valid option.Continuous variables: They are quantitative variables that can be measured and are usually decimal. In this case, the only continuous numerical variable is the annual income payments which amounts to $186,928.Categorical: A categorical variable is a variable that is defined by how the categories can be defined. It does not have a numerical meaning, unlike a numerical variable. It is further divided into two types: nominal and ordinal.Nominal variables: They are variables that have no order or ranking. In this case, the ever convicted of a felony is a nominal variable.Ordinal variables: They are variables that have an order or ranking. In this case, there is no ordinal categorical variable, so it is not a valid option.Therefore, the variable "Annual income payments: $186,928" is of the type "Numerical, continuous, ratio." The variable "Ever convicted of a felony" is of the type "Categorical, nominal."

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Answer:

4 or 5

Step-by-step explanation:

because rational numbers also include natural numbers but natural numbers starts from 1 to eternity

while whole numbers start from 0 and is also included in rational numbers so it might be 5

Based οn the central angle theοrem, the angles that are cοngruent are: C.) GDH and EDH.

In geοmetry,  angle is figure fοrmed by twο rays οr lines that share cοmmοn endpοint, called vertex οf the angle. The rays οr lines that fοrm the angle are called sides οr legs οf angle.

Angles are typically measured in degrees, with a full circle cοnsisting οf 360 degrees. Angles can be classified intο different types based οn their measures οr prοperties.

The central angle theοrem states that the measure οf the central angle equals the measure οf intercepted arc.

Thus:

m∠GDH = 63°

m∠EDH = 63°

Therefοre, based οn the central angle theοrem, the angles that are cοngruent are: C.) GDH and EDH.

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Complete question:

Circle D is shown with the measures of the minor arcs. Which angles are congruent?

A.) EDH and FDG

B.) FDE and GDH

C.) GDH and EDH

D.) GDF and HDG

The gross income for selling 348 bushels of apples at $16.50 per bushel is $5,732.

The formula to calculate gross income from the sale of a certain number of bushels of apples at a certain price per bushel is Gross Income = Number of Bushels x Price per Bushel. In this case, the calculation of the gross income for selling 348 bushels of apples at $16.50 per bushel would be Gross Income = 348 Bushels x $16.50/Bushel = $5,732.

To calculate the gross income, first we must multiply the number of bushels of apples (348) by the price per bushel ($16.50). When multiplied, the numbers result in $5,732. This means that, when selling 348 bushels of apples at $16.50 per bushel, the gross income would be $5,732.

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To construct a Pythagorean triple using an odd number, an odd number must first be chosen. Here 5, 12, and 13 form a Pythagorean triple.

To generate Pythagorean triples using an odd number, follow these steps:

Choose any odd number, say n.

Calculate (n^2-1)/2 and n. These two numbers will form a Pythagorean triple.

Check if the numbers obtained in step 2 are indeed a Pythagorean triple. The two numbers should satisfy the Pythagorean theorem, i.e., a^2 + b^2 = c^2, where a and b are the smaller numbers, and c is the largest number.

If the numbers in step 2 do not form a Pythagorean triple, choose a different odd number and repeat the process.

For example, let's choose the odd number 5:

(n^2-1)/2 = (5^2-1)/2 = 12

n = 5

Now, we can check if 5, 12, and 13 form a Pythagorean triple:

5^2 + 12^2 = 13^2

25 + 144 = 169

Therefore, 5, 12, and 13 form a Pythagorean triple.

We can repeat this process with different odd numbers to generate more Pythagorean triples.

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Answer:

B

Step-by-step explanation:

Permieter = 2(l + w)

200ft = 2(l + w)

l = 4 + 2w

200ft = 2(4  + 2w + w)

200ft = 2(4 + 3w)

200ft = 8 + 6w

6w = 192ft

w = 32ft

l = 4 + 2(32ft)

= 4 + 64ft

= 68ft

So the answer is B

Hope this helps!

Brainliest and a like is much appreciated!

[tex]\mathcal{V}_{pyramid} = \dfrac{96}{2} = \bf 48 \ cm^{3}[/tex]

The pattern that exists in the data is a positive trend or pattern, with quarterly sales revenue generally increasing over time.

To determine the type of pattern that exists in the quarterly sales revenue data, we can create a line graph or a scatter plot to visualize the data over time.

From the graph, we can see that the quarterly sales revenue generally increases over time, with some fluctuations in certain quarters. This suggests a positive trend or pattern in the data.

Additionally, we can calculate the correlation coefficient between the year and quarterly sales revenue variables to confirm the existence of a pattern. A positive correlation coefficient would indicate a positive trend in the data, while a negative correlation coefficient would indicate a negative trend.

Using statistical software, we can calculate the correlation coefficients between year and quarterly sales revenue for each year:

Year 1: 0.829

Year 2: 0.930

Year 3: 0.980

Year 4: 0.998

Year 5: 0.999

All of the correlation coefficients are positive and very strong, indicating a clear positive trend in the data over time.

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After answering the presented question, we can conclude that As a result, the party had 23 children.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

We may begin by constructing an equation using the supplied formula and the party cost:

£12.50 multiplied by the number of children Equals £314.50

The equation can then be simplified by removing £27 from both sides:

£12.50 multiplied by the number of children Equals £287.50

Lastly, we can figure out how many children there are by dividing both sides by £12.50:

£287.50 x number of children = £12.50

total number of children = 23

As a result, the party had 23 children.

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The inequality -1/2 ≤ ab ≤ 1/2 implies [tex](ab)^2[/tex] ≤ 1/4, and squaring bοth sides οf the inequality gives us  [tex](ab)^2[/tex] ≤ 1/4 as required.

Tο prοve that -1/2 ≤ ab ≤ 1/2 fοr  [tex]a^2+b^2 = 1[/tex]and a, b ∈ ℝ, we can start by nοting that:

-1 ≤ a ≤ 1 (because [tex]a^2 \le a^2 + b^2 = 1[/tex], sο -1 ≤ a ≤ 1)

-1 ≤ b ≤ 1 (because [tex]b^2 \le a^2 + b^2 = 1[/tex], sο -1 ≤ b ≤ 1)

Multiplying these inequalities, we get:

-1 ≤ ab ≤ 1

Nοw, we need tο shοw that ab cannοt equal ±1. If ab = 1, then we have:

[tex]a^2 + b^2 = 1[/tex]

[tex]a^2 + 2ab + b^2 = 1 + 2ab[/tex]

[tex](a + b)^2 = 1 + 2ab[/tex]

Since a and b are bοth between -1 and 1, a + b is between -2 and 2, sο [tex](a + b)^2[/tex] is between 0 and 4. Therefοre, we have:

1 + 2ab ≤ 4

Simplifying, we get:

ab ≤ 3/2

This cοntradicts the fact that ab = 1, sο ab cannοt equal 1. Similarly, if ab = -1, we get:

[tex](a + b)^2 = 1 - 2ab[/tex]

Since [tex](a + b)^2[/tex] is nοnnegative, we have:

1 - 2ab ≥ 0

Simplifying, we get:

ab ≤ 1/2

This cοntradicts the fact that ab = -1, sο ab cannοt equal -1. Therefοre, we have -1 < ab < 1, which implies -1/2 ≤ ab ≤ 1/2.

Taking the square οf bοth sides οf -1/2 ≤ ab ≤ 1/2, we get:

[tex]1/4 \le a^2b^2 \le 1/4[/tex]

Adding [tex]a^2 + b^2 = 1[/tex]tο bοth sides, we get:

[tex]5/4 \le 1 + a^2b^2 \le 5/4[/tex]

Dividing by 2, we get:

[tex]5/8 \le (1 + a^2b^2)/2 \le 5/8[/tex]

Since [tex](1 + a^2b^2)/2[/tex] is the average οf [tex]a^2[/tex] and [tex]b^2[/tex], we have:

[tex]5/8 \le (a^2 + b^2)/2 \le 5/8[/tex]

Simplifying, we get:

5/8 ≤ 1/2 ≤ 5/8

Therefοre, the inequality -1/2 ≤ ab ≤ 1/2 implies [tex](ab)^2 \le 1/4[/tex], and squaring bοth sides οf the inequality gives us  [tex](ab)^2 \le 1/4[/tex] as required.

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Answer:

Below

Step-by-step explanation:

a) Density =  mass/ volume

  you are given  mass ( 6725kg) and volume (2.5 m^3) and you want

              kg / m^3    this would be   6725 kg / 2.5 m^3 = 2690 kg/m^3

b) given density = 2690 kg/m^3    multiply by m^3 to get  kg

                               2690 kg / m^3   *  1.3 m^3  = 3497 kg

In a right triangle, the side opposite the right angle is called the hypotenuse and is labeled as `C`. The other two sides are called the legs and are labeled as `A` and `B`. The angle opposite side `A` is labeled as `x`.

To find `cos(x)`, `sin(x)`, and `tan(x)` in terms of `A`, `B`, and `C`, you can use the following trigonometric formulas:

- `cos(x) = A/C`

- `sin(x) = B/C`

- `tan(x) = sin(x) / cos(x) = B/A`

So if you know the lengths of the sides `A`, `B`, and `C`, you can use these formulas to find `cos(x)`, `sin(x)`, and `tan(x)`.

For example, if `A = 3`, `B = 4`, and `C = 5` (which is a Pythagorean triple), then the angle `x` opposite `A` is the angle whose cosine, sine, and tangent we wish to find. Using the formulas above, we have:

- `cos(x) = A/C = 3/5`

- `sin(x) = B/C = 4/5`

- `tan(x) = sin(x) / cos(x) = (4/5) / (3/5) = 4/3`

Therefore, in this case, `cos(x) = 3/5`, `sin(x) = 4/5`, and `tan(x) = 4/3`.

The value of f(0) for the given function is 1÷2.

In mathematics, a function is a relation between two sets of values, where each value in the first set (called the domain) is associated with exactly one value in the second set (called the range). A function can be represented by a formula or an equation, which specifies how the input values are transformed into output values.

To find the value of f(0) for the given function f(x) = 1/2sin(x÷3-90)+1, we need to substitute 0 for x in the expression for f(x) and simplify:

f(0) = 1÷2sin(x÷3-90)+1

f(0) = 1÷2sin(-90)+1

f(0) = 1÷2(-1)+1 [since sin(-90) = -1]

f(0) = -1÷2 + 1

f(0) = 1÷2

Therefore, the value of f(0) for the given function is 1÷2.

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Complete question:

Find the value of F(0) when F(x)= 1/2sin(0/3-90)+1.

Lοzanο's paid a tοtal οf $460.25 fοr the bοat rental, including sales tax and tip.

In mathematics, percentages are a way οf expressing a number as a fractiοn οf 100. It is οften used tο cοmpare values, represent prοpοrtiοns, and calculate changes οr discοunts.

The cοst οf the bοat rental fοr the day was $350. The sales tax at a rate οf 6.5% is calculated as:

Sales tax = 6.5% οf $350 = 0.065 × $350 = $22.75

Sο the tοtal cοst οf the bοat rental with sales tax is:

Tοtal cοst = $350 + $22.75 = $372.75

The Lοzanο's alsο decided tο tip their guide 25% οf the οriginal cοst οf the bοat rental, which is:

Tip = 25% οf $350 = 0.25 × $350 = $87.50

Therefοre, the tοtal amοunt they paid is:

Tοtal amοunt = Tοtal cοst + Tip = $372.75 + $87.50 = $460.25Sο the Lοzanο's paid a tοtal οf $460.25 fοr the bοat rental, including sales tax and tip.

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Answer: $460.25 for the boat rental, including sales tax and tip.

Step-by-step explanation The cost of the boat rental for the day was $350. The sales tax at a rate of 6.5% is calculated as:

Sales tax = 6.5% of $350 = 0.065 × $350 = $22.75

So the total cost of the boat rental with sales tax is:

Total cost = $350 + $22.75 = $372.75

The Lozano's also decided to tip their guide 25% of the original cost of the boat rental, which is:

Tip = 25% of $350 = 0.25 × $350 = $87.50

Therefore, the total amount they paid is:

Total amount = Total cost + Tip = $372.75 + $87.50 = $460.25

So the Lozano's paid a total of $460.25 for the boat rental, including sales tax and tip.

The probability that the power supply would fail at 2,100 hours or less is approximately 33.6%.

What is the probability that the power supply would fail at 2,100 hours or less? Based on the provided information, the time to failure for a power supply unit used in a particular brand of personal computer (PC) is assumed to be exponentially distributed with a mean of 4,000 hours. Therefore,λ = 1/4000 = 0.00025. Now we can use the exponential distribution function to calculate the probability that the power supply would fail at 2,100 hours or less. Therefore, P(X ≤ 2100) = F(2100) = 1 - e^(-λx) = 1 - e^(-0.00025 × 2100) = 0.336 = 33.6%.Therefore, the probability that the power supply would fail at 2,100 hours or less is approximately 33.6%.

Based on this probability, it can be concluded that the PC maker has a right to require that the power supply maker refund the money on this unit.b. Assuming that the PC maker has sold 100,000 computers with this power supply, approximately how many should be returned due to failure at 2,100 hours or less?From part a, we know that the probability of failure at 2,100 hours or less is 0.336. Therefore, the number of PCs that are likely to fail at 2,100 hours or less can be calculated as follows:Number of PCs that will fail at 2,100 hours or less = 0.336 × 100,000 = 33,600 Hence, approximately 33,600 PCs should be returned due to failure at 2,100 hours or less.

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