The tip of a pendulum swings through an arc whose length is 8 centimeters. If the radius of the pendulum is 26 centimeters, then what radian angle did the tip rotate through? Round your answer to the nearest hundredth

Answer:

\(y=4x-6\)

Step-by-step explanation:

The slope is \(\frac{-2-2}{1-2}=4\).

\(y-2=4(x-2) \\ \\ y-2=4x-8 \\ \\ y=4x-6\)

Based on the information given, the amount that he'll be expected to save in 30 years will be $83.

From the question given, since Buzz had $47 and had been saving for 17 years, the amount saved per year will be:

= $47/17

= $2.7647

Therefore, the amount that'll be saved in 30 years will be:

= 30 × $2.7647

= $82.941

= $83

The amount saved will be $83.

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Step-by-step explanation:

loss % = 25%

loss = $1200 × 25 ÷100

= $30000 ÷100

= $300

selling price = cost price + loss

= $1200 + $300

= $1500

Answer:

81 = 3⁴

√81

= √3⁴

=√(3²)(3²)

=√(3²)²

=3²

=3x3

=9

---------------------------------------------------------------------

√625

=√5⁴

=√(5²)(5²)

=√(5²)²

=5x5

=25

1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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Answer:

[ -2, ∞ ), [ -1, ∞ )

Step-by-step explanation:

Domain: all x values

[ -2, ∞ )

Range: all y values

[ -1, ∞ )

The height of the tree is approximately 156.7 feet.

What is Trigonometry?

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

The height of the tree can be calculated using trigonometry.

Let's call the height of the tree "h".

Then, using the right triangle formed by the height of the tree, the distance from the base of the tree to where Jerome is standing, and the angle between the ground and the top of the tree, we can set up the following equation:

tan(33°) = h / 90

Solving for h, we get:

h = 90 * tan(33°)

Using a calculator to find the value of tan(33°), we get:

h = 90 * 1.730

h ≈ 156.7 feet

So, The height of the tree is approximately 156.7 feet.

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Neither AB nor BA can be computed.

The statement that is true for the matrices A and B is: Neither AB nor BA can be computed.

In order to multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. For matrix A, it is a 2x2 matrix, and for matrix B, it is a 3x3 matrix.

Since the number of columns in A (2) is not equal to the number of rows in B (3), the product AB cannot be computed.

Similarly, since the number of columns in B (3) is not equal to the number of rows in A (2), the product BA also cannot be computed.

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Answer:

D

Step-by-step explanation:

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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The volume will be 9 times increased if she triples the dimension of the square. So, yes, he is right because 3 is 2 times in the formula.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Given

Clare sketches a rectangular prism with a height of 11 and a square base and labels the edges of the base 8.

The side of the square is 8.

The height of the prism is 11.

Volume = Area of square × height.

The volume of the original prism will be.

\(\rm V_1 = 8 * 8 * 11\\\\V_1 = 704\)

If she triples the side of the square.

Then dimensions will be

The side of the square is 24.

The height of the prism is 11.

The volume of the modified prism will be.

\(\rm V_2 = 24 * 24* 11\\\\V_2 = 9*704\\\\V_2 = 9 \ Times \ of \ V_1\)

Thus, the volume will be 9 times bigger. So, yes, he is right because 3 is 2 times in the formula.

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The coordinates of the image of the point (-9, 3) under the same translation is (-8, 1).

Given,

The points whose image is there = (0, 9)

The points under translation = (1, 7)

We have to find the image of the point (-9, 3) under the same translation:

Now, we have to find the transformation of given points:

Point: (0, 9)

Translation: (1, 7)

x coordinate:

1 - 0 = 1

x coordinate is increased by 1.

y coordinate:

7 - 9 = -2

y coordinate is increased by -2

Apply the same transformation to the point given:

Point : (-9, 3)

x coordinate:

1 + (-9) = 1 - 9 = -8

y coordinate:

-2 + 3 = 3 - 2 = 1

Therefore, the coordinates of the image of the point (-9, 3) under the same translation is (-8, 1).

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The word "and" in probability implies that we use the Multiplication rule.

The correct option is Option D.

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

The relationship between two events is explained by the probability multiplication rule.

Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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Answer:

x = 2

Step-by-step explanation:

3x - 1 = 5

First, add 1 onto both sides. (When doing these type of questions you must do the inverse!)

3x = 6

Divide by 3 on both sides to get x.

x = 2

Hope this helps and I hope you have a good day!

Answer: 2

Step-by-step explanation: move constant to the right, calculate, divide both sides

the answer might be 18.64 but im actually kinda du.mb so its probably not right.

Answer:

is 10 points alot? the other guy don't think so

Answer:

0

Step-by-step explanation:

First, we plug in the -3 into the equation:

18 - 2(-3)^2

0

The value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

Given equation: 2x³ + 12x² = 0

Solving this equation by factoring as follows:

2x³ + 12x² = 0

= 2x²(x+6) = 0

So, x + 6 = 0 or 2x² = 0

x = -6 or x = 0

Therefore, the value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

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The triangles in this problem, regarding their similarity, are classified as follows:

a. Similar.

b. Similar.

c. Not Similar.

d. Not Similar.

Similar triangles are triangles that share these two features listed as follows:

For item a, it is found that the triangles are similar, as when a triangle is bisected, the triangle is similar with the bisected triangle.

For item b, the triangles are similar, as equilateral triangles have the same angle measures of 60º. The triangles have different side lengths, hence it underwent a dilation.

For item c, the triangles are not similar, as the ratios of the side lengths are different.

For item d, the triangles are not similar, as they have different angle measures.

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Marisa can expect to make a profit with her company as per the given information. The profit she earns from the 49 pairs will cover the cost of repairing the one pair that needs repair.

Based on the profit analysis, Marisa can expect to make a profit with her company. The calculation and expiation are provided as follows:
Profit Calculation:

Marisa wants to make a profit of $5.00 on each pair of earrings. This means that for every pair sold, she will earn $5.00.
Cost of Repair:

Marisa has improved the quality control, resulting in only 1 pair in 50 need to be returned for repair. The cost of repairing each pair is $60.
Profit Analysis:

Let's analyze the profit situation.
  - For every 50 pairs sold, one pair will need repair, costing Marisa $60.
  - However, for the remaining 49 pairs, she will earn $5.00 profit on each, totaling $245.00 ($5.00 x 49).
  - So, the total profit from the 49 pairs will offset the cost of the one pair that needs repair.
Based on the profit analysis, Marisa can expect to make a profit with her company. The profit she earns from the 49 pairs will cover the cost of repairing the one pair that needs repair. Therefore, her company can be considered profitable.

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Answer:

5

Step-by-step explanation:

21-6=15/3=5

Answer:

5 tickets

Step-by-step explanation:

21-6=16 16 divided by 3= 5.333 so about 5 tickets

Answer:

I think its $1000

Step-by-step explanation:

if she earned $12 the 1012-12=1000

Answer:

I really don't know much but this is what I know

If she has $12 dollars in interest and a year later she has $1012 making it so she earned EXACTLY $1,000 in the time being.

Answer: 1517.54

Step-by-step explanation:

So we can divide solving this question into two parts: the 2% compound interest and the 5% compound interest.

We know that the compound interest equations is A = P(1+r/n)^nt where:

A is final amount

P is principal (initial) amount

r is interest rate

n is number times interest compounded

t is number of time periods

Given this, in the 2% compound we know:

A = ?

P = 1200

r = 2%

n = 1 (because it didn't say how many times compounded so we assume 1)

t = 2

This becomes:

A = 1200 (1 + (0.02/1))^ 1 * 2

A = 1248.48

Because we switching to 5% from 2%, we can assume that the final amount from the 2% will be the initial amount in the 5%. Thus:

A = ?

P = 1248.48

r = 5%

n = 1

t = 4 (because there were 6 years in total and we used 2 years for 2%)

This becomes:

A = 1248.48 (1 + (0.05/1))^ 1 * 4

A = 1517.54

No, a linear model is not appropriate for the given data because; the residual plot is is such that the residuals (actual value - predicted) are large thereby indicating the inappropriateness of a linear model.

It follows from the task content that it is requited to be determined if a linear model is appropriate for the given data.

As evident in the scatter plot and the line of best fit; it follows that the data points are far off the predicted values by the line of best fit.

Additionally, the residual plot indicates the inappropriateness of a linear model for the given data as points on the residual plot are far off the horizontal axis.

Conclusively, a linear model is not appropriate for the given data.

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Answer: The answer is 3

Step-by-step explanation:

The constant of proportionality of the relationship shown in the graph is 3 and this can be determined by using the two-point slope form of the line.

Given :

The graph of a straight line is given.

The following steps can be used in order to determine the constant of proportionality of the relationship shown in the graph:

Step 1 - The two-point slope form of the line can be used in order to determine the constant of proportionality of the relationship shown in the graph.

Step 2 - The two-point slope form of the line is given below:

y - y1 / x - x1 = y2 - y1 / x2 - x1

where (x1, y1)  and (x2, y2)  points on the line.

Step 3 - So, substitute (1,3) and (2,6) in the above equation.

y - 3 / x - 1 = 6 - 3 / 2 - 1

Step 4 - Simplify the above equation.

(y - 3) = 3(x - 1)

y - 3 = 3x - 3

y = 3x

So, the constant of proportionality of the relationship shown in the graph is 3. Therefore, the correct option is B).

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~"Gamer"~

If Alex can pay $1,500 per month, it will take approximately 17.2 years to pay off the loan. If Alex can pay $2,000 per month, it will take approximately 11.8 years to pay off the loan.

To calculate the time it takes to pay off a loan, we can use the formula for the number of periods (n) in an annuity:

n = -log(1 - (r * P) / A) / log(1 + r)

where:

r = monthly interest rate

P = loan amount

A = monthly payment

Given:

Loan amount (P) = $180,000

Annual interest rate = 8%

Monthly interest rate (r) = Annual interest rate / 12 = 8% / 12 = 0.0066667 (rounded to five decimal places)

a. If Alex can pay $1,500 per month:

Monthly payment (A) = $1,500

Using the formula, we can calculate the number of periods (n):

n = -log(1 - (0.0066667 * 180000) / 1500) / log(1 + 0.0066667)

Calculating this equation will give us the number of periods (n) in months. To convert it to years, we divide by 12.

n = -log(1 - 0.08) / log(1.0066667)

n ≈ 205.875

Number of years = 205.875 / 12 ≈ 17.15625

Therefore, if Alex can pay $1,500 per month, it will take approximately 17.2 years to pay off the loan.

b. If Alex can pay $2,000 per month:

Monthly payment (A) = $2,000

Using the same formula:

n = -log(1 - (0.0066667 * 180000) / 2000) / log(1 + 0.0066667)

n ≈ 141.625

Number of years = 141.625 / 12 ≈ 11.80208

Therefore, if Alex can pay $2,000 per month, it will take approximately 11.8 years to pay off the loan.

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(Annuity number of periods) Alex Karev has taken out a $180,000 loan with an annual rate of 8 percent compounded monthly to pay off hospital bills from his wife Izzy's illness. If the most Alex can afford to pay is $1,500 per month, how long will it take to pay off the loan? How long will it take for him to pay off the loan if he can pay $2,000 per month? Use five decimal places for the monthly percentage rate in your calculations. years. (Round a. If Alex can pay $1,500 per month, the number of years it takes for him to pay off the loan is to one decimal place.)

Answer:

a) 272 used at least one prescription​ medication.

b) The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

Step-by-step explanation:

Question a:

86.6% out of 3149, so:

0.866*3149 = 2727.

272 used at least one prescription​ medication.

Question b:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

For this problem, we have that:

\(n = 3149, \pi = 0.866\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a p-value of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).  

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 - 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.856\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 + 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.876\)

For the percentage:

0.856*100% = 85.6%

0.876*100% = 87.6%.

The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

The number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

Suppose that we have:

Then, we get:

\(CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\)

where \(Z_{\alpha/2}\) is the critical value of Z at specified level of significance and is obtainable from its critical value table(available online or in some books)

For this case, we have:

Part (a):

The number of subjects used at least one prescription​ medication is:

\(\dfrac{3149}{100} \times 86.6 \approx 2727\)

Thus, the sample proportion we get is:

\(\hat{p} = \dfrac{2727}{3149} \approx 0.8659\)

For level of significance 0.10, we get: \(Z_{\alpha/2} = 1.645\)

Thus, the confidence interval needed is:

\(CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\CI \approx 0.8659\pm 1.645 \times \sqrt{\dfrac{0.8659(1-0.8659)}{3149}}\\\\\\CI \approx 0.8659 \pm 0.0099\)

Thus, CI is [0.8659 - 0.0099, 0.8659 + 0.0099] = [0.8560, 0.8758]

Thus, the number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

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Answer:

C.    Student C, who is paid $290 for 20 hours of work

Step-by-step explanation:

What we know:

    - Student A ( 164.50 = 14 hours )

    - Student B ( 162.00 = 12 hours

    - Student C ( 14.50h = p )

What we need to figure out:

    - How much each person makes per hour ( Pt.1 )

    - Who will make the most in 20 hours ( Pt.2 )

How to execute:

    - Divide for A & B

    - Convert for C

    - Multiply for all

Step 1: Divide the total pay by the hours for A & B

Student A:   164.50 ÷ 14 = 11.75 per hour ( Found PT.1 )

Student B:    162.00 ÷ 12 = 13.50 per hour ( Found PT.1 )

Step 2: Convert C so that it looks like A & B

Student C:    14.5(h) = p  --->   p ÷ h =   14.5 per hour ( Found PT.1 )

Step 3: Multiply the hourly rate by the 20 hours

Student A:   11.75 × 20 = 235 for 20 hours      ( Found PT.2 )

Student B:   13.50 × 20 = 270 for 20 hours     ( Found PT.2 )

Student C:   14.50 × 20 = 290 for 20 hours     ( Found PT.2 )

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I saw the comment about not being able to mark the other person brainliest because no one else answered. I'm here to fix that. Also, the answer is C.