The table represents a linear relationship between the number of hours a computer repair takes and the total cost of the repair. What is the
slope of the line?
Hours, x
3
5
7
Total Cost, y
320
470
620

Answer:  The continuous interest rate at which the money was invested is approximately 15.4%.

Step-by-step explanation: We can use the formula for continuous compounding to find the value of r:

A = Pe^(rt)

Where A is the final value, P is the initial investment, e is the base of the natural logarithm, r is the continuous interest rate, and t is the time.

Plugging in the given values, we get:

$100,000 = $25,000e^(r*18)

Dividing both sides by $25,000 and taking the natural logarithm of both sides, we get:

ln(4) = 18r

Solving for r, we get:

r = ln(4)/18 ≈ 0.154

Multiplying by 100 to convert to a percentage and rounding to one decimal point, we get:

r ≈ 15.4%

Therefore, the continuous interest rate at which the money was invested is approximately 15.4%.

17(4+15)

= 17*19

=323

Answer:- 323

Rectangular prism and triangular prism is discussed below.

Rectangular prism

Rectangular prism

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There is an estimate that 340 of the school's 425 students have at least one sibling.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

To estimate the number of students in the school who have at least one sibling, we can use the proportion from the sample.

The proportion of students with at least one sibling can be calculated as:

= 96/120

= 0.8

Expected number of students with at least one sibling in the school:

= Proportion x Total number of students

= 0.8 x 425

= 340

Therefore, it would expect 340 of the 425 students at the school to have at least one sibling.

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Answer:

Radius: 14

Step-by-step explanation:

We know

Circumference of circle = 2 · r · π

Circumference = 28π

Find radius!

Let's solve

28π = 2 · r · π

14π = r · π

r = 14

So, the radius is 14

Answer:

The radius is 14.

Step-by-step explanation:

Since the circumference is 28pi, we can find the diameter.

C = pi•d

C = 28pi

28pi = pi•d

divide both sides by pi.

d = 28

The diameter is 28.

So, cut it in half to find the radius. 28/2 is 14. The radius is 14.

Answer:

Step-by-step explanation:

The type of transformation shown with polygons ABCD and A'B'C'D' would be C. Horizontal translation.

The image displays the preimage of a polygon ABCD, alongside a second figure to its right, titled A' B' C' D'. Each point sustains the same positioning within both images.

This suggests that the second image was established by shifting the preimage from left to right. In contrast, the other transformations cited - reflection across the x-axis, 90° clockwise rotation, and vertical translation - would lead to a different placement and orientation of each point in the subsequent portrait.

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Answer:

The type of transformation shown with polygons ABCD and A'B'C'D' would be C. Horizontal translation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

That is rounded to the nearest cent.

if you want to round to the nearest dollar it is $35

Answer:

Step-by-step explanation:

did you figure it out?  i need help too

The solution is: the value of x is : x = 98.5.

Formula

<x = 1/2 (arc 1 + arc2)

This is the basic angle formula for the way two chords intersect.

Givens

arc1 = 96

arc2 = 101

Solution

<x = 1/2 (arc1 + arc2)                 Substitute values

<x = 1/2(96 + 101)

<x = 1/2(197)

<x = 98.5

Answer

x = 98.5

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Answer: 25.461 cm

Step-by-step explanation:

The circumference of a circle can be found using the formula C = πd, where d is the diameter and π (pi) is a constant value of approximately 3.14159.

Substituting d = 8.1 cm into the formula, we get:

C = πd

C = 3.14159 x 8.1 cm

C = 25.461 cm (rounded to 3 significant figures)

Therefore, the circumference of the circle with diameter 8.1 cm is approximately 25.461 cm.

Answer:1: $124.25 2: 20,222.50Rs, 3: 33.90 euro, 4:0.94 pounds

Step-by-step explanation:

Answer: The length of the field is 100 feet and the width is 60 feet.

Step-by-step explanation:

a. The perimeter of a rectangle is the sum of the lengths of all its sides. For a soccer field, the perimeter is the sum of the lengths of two adjacent sides, which are equal in length, and the sum of the lengths of the other two adjacent sides, which are also equal in length. Therefore, we can write the equation:

2l + 2w = 320

b. According to the problem, the length of the field is 20 less than twice the width. In equation form, this is:

l = 2w - 20

c. To solve the system of equations, we can substitute the expression for l from equation b into equation a, and then solve for w:

2(2w - 20) + 2w = 320

Simplifying:

4w - 40 + 2w = 320

6w - 40 = 320

6w = 360

w = 60

Now that we know the width is 60 feet, we can substitute this value into equation b to find the length:

l = 2w - 20

l = 2(60) - 20

l = 100

Therefore, the length of the field is 100 feet and the width is 60 feet.

Answer:

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The unused length of the ribbon is 3 inches.

Given that, Luann has a piece of ribbon that is 1 yard long she cuts off 33 inches to tie a gift box,

We need to find the unused length of the ribbon,

Since, 1 yard = 36 inches

Therefore, Luann has 36 inches long ribbon, in which she used 33 inches,

So, the left length = 36 - 33 = 3 inches.

Hence, the unused length of the ribbon is 3 inches.

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The indefinite integral will be ∫x⁵e^(x⁶ - 4) dx = (1/6)e^(x⁶ - 4) + C

Lets say u = x⁶ - 4 and du/dx = 6x⁵

it then becomes ∫x⁵e^(x⁶ - 4) dx = ∫e^(x⁶ - 4 * 1/6)du

e^(x⁶ - 4) = ∫(1/6)e^(x⁶ - 4)du = (1/6) ∫e^(x⁶ - 4) du = (1/6)e^(x⁶ - 4) + C

= ∫x⁵e^(x⁶ - 4) dx = (1/6)e^(x⁶ - 4) + C

An indefinite integral that when you differentiate it will give you the main  or first function.

The above answer is based on the question below as seen in the photo;

Find the indefinite integral (Use C for the constant of integration)

∫x⁵e^(x⁶ - 4) dx

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The population is normally distributed is 90 %.

Given that

C = 0.90,

x = 13.7,

s = 3.0,

n = 10

Use the following formula is necessary:

CI = x t*(s /[tex]\sqrt{n}[/tex])

Where CI stands for confidence interval, x represents sample mean, s represents sample standard deviation, n represents sample size, and t represents the desired level of confidence and the t-value from the t-distribution with n-1 degrees of freedom.

According to the information given, we have:

Since alpha + C equals 1, C = 0.90,

which means that alpha is 0.10. x = 13.7 s = 3.0 n = 10

The t-distribution must be used in place of the z-distribution because n is small (n 30).

Which has a degree of freedom of n-1 = 9 and a confidence level of 90%. About 1.833 is the t-value.

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The probability of disposing more than seven pineapple pies cumulatively throughout four hours due to greater than one hour exhibiting a dispersion of over two pies is 0.1618.

The likelihood of selling more than 2 pineapple pies in at least one hour can be computed through the application of the complement rule:

P(at least two hours with a minimum of two pies dispersed) = 1 - P(less than two hours meeting the criterion of having more than two pies sold)

P(X < 2) = P(X = 0) + P(X = 1) = (e^(-4)*4^0)/0! + (e^(-4)*4^1)/1!

= 0.0183 + 0.0732 = 0.0915

Consequently, the probability of vending more than two pineapple pies during a given hour is 1 - 0.0915 = 0.9085.

Finally, we can calculate the probability of trading beyond seven pineapple pies total with Poisson distribution parameters λ = 4:

P(X > 7) = 1 - P(X <= 7) = 1  -[P(X=0) + P(X=1) + ... + P(X=7)]

= 1 - [e^(-4)(4^0)/0! + e^(-4)(4^1)/1! + ... + e^(-4)*(4^7)/7!]

= 1 - (0.0183 + 0.0732 + 0.1465 + 0.1954 + 0.1954 + 0.1563 + 0.1042 + 0.0595)

= 0.1472

Therefore, the likelihood of disposing more than seven pineapple pies cumulatively throughout four hours due to greater than one hour exhibiting a dispersion of over two pies is 0.1472/0.9085 = 0.1618.

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12 or 128

by the way question is not complete

the answer is 128 , if repetition is allowed

and answer is 12 , if repetition is not allowed

To calculate the percent change in population, we first need to find the difference between the two population numbers, then divide that difference by the original population, and finally, multiply by 100 to get the percentage change.

The difference in population is:

50,000 - 48,000 = 2,000

To find the percent change, we divide the difference by the original population:

2,000 / 50,000 = 0.04

Finally, we multiply by 100 to get the percentage change:

0.04 x 100 = 4%

Therefore, the percent change in the town's population from 2000 to 2010 is a decrease of 4%.

Step-by-step explanation:

To find the percent change, we need to calculate the difference between the initial population and final population, and then divide it by the initial population.

Change in population = Final population - Initial population

= 48,000 - 50,000

= -2,000

Since the change is negative, it means that there was a decrease in the population.

Percent change = (Change in population / Initial population) x 100%

= (-2,000 / 50,000) x 100%

= -0.04 x 100%

= -4%

Therefore, the percent change in the town's population is -4%.

There total of 126 ways in which nine people can sit on chairs in the room when four of these people be chosen to stand up.

The problem is asking how many ways we can choose 4 people out of 9 to stand up. This is a combination problem since the order in which the people are chosen is irrelevant. We can utilize the combination formula, which is,

n choose k = n!/(k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, we have n=9 people and k=4 people to choose. Putting all the values in formula,

9 choose 4 = 9!/(4!(9-4)!)

9 choose 4 = 362880/(24 x 120)

9 choose 4 = 126.

Therefore, there are 126 ways to choose 4 people out of 9 to stand up.

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The range of equation represented by the graph is [1, ∞}.

The set of all potential values that a function could output or produce is known as its range. To put it another way, it is the collection of all values that the function "hits" or "reaches" when given various input values.

It's crucial to remember that not every function has a range that encompasses all potential values. For instance, the set [-1, 1] is the range of the function g(x) = sin(x), which only returns values between -1 and 1.

The range of the function are all the output values of the of the function or the y-coordinates of the graph.

For the given graph we see that the y-coordinates corresponding to the graph are from: 1 to ∞.

Hence, the range of equation represented by the graph is [1, ∞}.

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The domain and the range of the graphed function are given as follows:

From the graph of the function, the domain and range are obtained as follows:

The graph is given by the image presented at the end of the answer.

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Answer:

$14,636.97

Step-by-step explanation:

FV = PV x (1 + r/n)^(nt)

where r is the annual interest rate (as a decimal), n is the number of compounding periods per year, t is the number of years the money is invested, and PV is the present value.

In this case, r = 0.04 (4% as a decimal), n = 2 (since it is compounded semiannually), t = 4, and PV = $12500. Substituting these values into the formula, we get:

FV = $12500 x (1 + 0.04/2)^(2x4)

FV = $12500 x (1.02)^8

FV = $14,636.97

Therefore, the future value of the investment after four years is $14,636.97.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$12500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 12500\left(1+\frac{0.04}{2}\right)^{2\cdot 4} \implies A \approx 14645.74[/tex]

Answer:

mark me brilliant

Step-by-step explanation:

First, we need to determine the amount of time each sales representative can spend on selling each week.

A 40-hour work week is equivalent to 2,400 minutes (40 hours x 60 minutes/hour).

If 50% of each rep's time is consumed by non-selling tasks and travel time, then they have 1,200 minutes (2,400 minutes x 50%) available for selling each week.

Each sales call takes 32 minutes, so a rep can make 75 sales calls per week (1,200 minutes available for selling ÷ 32 minutes per sales call).

It takes 10 visits per year to acquire and service each account, which means a sales rep needs to visit each of the 688 potential adopters 10 times per year, or 6,880 visits in total per year.

Each sales rep can make 75 visits per week, which means they can make 3,900 visits per year (75 visits per week x 52 weeks in a year).

Therefore, Shannon will need to hire 1.76 sales reps (6,880 total visits needed ÷ 3,900 visits per year per sales rep).

Rounding up to the nearest 1/10 of a rep, Shannon should hire 1.8 sales reps.

The probability that Janie wins the game is approximately 0.0955.

The probability distribution of a binomial random variable is known as the binomial distribution. The sample space of a random experiment serves as the domain of a random variable, which is a real-valued function. To further comprehend this, let's look at an illustration.

We can approach this problem using the binomial distribution. Let X be the number of heads in the remaining tosses until one player wins the game, and let p be the probability that the coin lands tails (since if it lands tails, Janie earns a point). Since the first 33 tosses have already been made, there are 50 - 33 = 17 tosses remaining until one player wins.

Since 17 of the first 33 tosses were heads, there were 33 - 17 = 16 tails. Therefore, the probability of getting a tail is p = 1/2.

Let Y be the total number of tosses until one player wins. Since each toss is independent and has a probability of 1/2 of resulting in a head, Y follows a geometric distribution with parameter p = 1/2.

The game ends when one player reaches 18 points, which means there must be at least 35 tosses. Therefore, the probability that Janie wins the game is:

P(Janie wins) = P(Y = 35) + P(Y = 37) + P(Y = 39) + ... + P(Y = 67)

We can use the formula for the geometric distribution to calculate each of these probabilities:

[tex]P(Y = k) = (1 - p)^{(k-1)} * p[/tex]

where k is the number of tosses until one player wins. Plugging in p = 1/2, we get:

[tex]P(Y = k) = (1/2)^{(k-1)} * (1/2)[/tex]

Now we can substitute this into the expression for P(Janie wins):

P(Janie wins) = (1/2)³⁴ + (1/2)³⁶ + (1/2)³⁸ + ... + (1/2)⁶⁶

This is a finite geometric series with first term (1/2)³⁴ and common ratio 1/4 (since each successive term is multiplied by (1/2)²). Therefore, we can use the formula for the sum of a finite geometric series to simplify the expression:

P(Janie wins) = [(1/2)³⁴ * (1 - (1/4)¹⁷)] / (1 - 1/4)

= [(1/2)³⁴ * (1 - (1/2)³⁴)] / (3/4)

= 0.0955

Therefore, the probability that Janie wins the game is approximately 0.0955.

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The first method to find GCF for numbers 34 and 85 is to list all factors for both numbers and pick the highest common one:

All factors of 34: 1, 2, 17, 34

All factors of 85: 1, 5, 17, 85

So the Greatest Common Factor for 34 and 85 is 17

The second method to find GCF for numbers 34 and 85 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 34: 2, 17

All Prime Factors of 85: 5, 17

As we can see there is only one Prime Factor common to both numbers. It is 17. So 17 is the Greatest Common Factor of 34 and 85