AC is the perpendicular bisector of G . Determine the length of the following sides.

A. GH

B. CH

The first option with 2-year term and higher monthly payments is better since it results in less total paid in the end.

An individual borrower can receive a personal loan to utilise for personal, family, or household needs. The majority of personal loans are unsecured, which means they are not secured by property like a house or a car. Instead, the approval of a personal loan is determined by the borrower's creditworthiness and capacity to pay back the loan. The lender decides the loan amount, interest rate, and repayment conditions for a personal loan based on the borrower's credit score, income, and employment history, among other things. Personal loans are frequently used to pay for unforeseen bills, finance home improvements, and consolidate debt.

For the given plans of payment of 2 years and 5 years we have:

Option 1: 24 monthly payments of $354.56 = $8,534.56 total paid.

Option 2: 60 monthly payments of $154.66 = $9,279.60 total paid.

Comparing the total payment for the various years we have see that the plan with 2 years payment is better option.

Hence, the first option with 2-year term and higher monthly payments is better since it results in less total paid in the end.

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Answer: Part A is (-9, 13) Part B is (9, 13)

Step-by-step explanation:

(a) The simplified and correct expression is (6×7)-(5 +4) = 16

(b) The simplified and correct expression is (-2x²) + (24÷12)-4 = 2

a. 6×7-5 +4= 16

In this calculation, we need to use brackets to ensure the correct order of operations, which is typically remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division [from left to right], Addition and Subtraction [from left to right]).

Without brackets, the calculation would be evaluated as follows:

6×7-5 +4 = 42-5 +4 (applying multiplication first)

= 37 +4 (applying subtraction)

= 41 (applying addition)

However, the desired result is 16. To achieve this, we can use brackets to group the addition and subtraction operations together, like this:

(6×7)-(5 +4) = 42 - 9 (applying addition within the brackets first)

= 33 (applying subtraction)

b. -2x²+24÷12-4=2

Similarly, in this calculation, we need to use brackets to ensure the correct order of operations.

Without brackets, the calculation would be evaluated as follows:

-2x²+24÷12-4 = -2x²+2-4 (applying division first)

= -2x²-2 (applying addition and subtraction)

However, the desired result is 2. To achieve this, we can use brackets to group the division and subtraction operations together, like this:

-2x²+(24÷12)-4 = -2x²+2-4 (applying division within the brackets first)

= -2x²-2 (applying addition and subtraction)

By adding brackets to each calculation to ensure the desired order of operations, we arrive at the correct results of 16 and 2, respectively.

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Answer:

9

Step-by-step explanation:

Based on the Pythagorean theorem, A equals the square root of C squared minus B squared. By plugging in these numbers, you get 9.

The probability of a simple event is the likelihood or chance of that event occurring. The formula is P(A) = Number of favorable outcomes / Total number of possible outcomes.

It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The formula for the probability of a simple event is:

P(A) = Number of favorable outcomes / Total number of possible outcomes

For example, if we toss a fair coin, the probability of getting heads is:

P(Heads) = 1 (number of favorable outcomes) / 2 (total number of possible outcomes)

So, the probability of getting heads is 0.5 or 50%.

A simple event is an event that has only one possible outcome. For instance, rolling a specific number on a dice, drawing a specific card from a deck of cards, or picking a specific colored ball from a bag of balls are all examples of simple events.

In summary, the probability of a simple event is the ratio of the number of ways the event can happen to the total number of possible outcomes.

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Part A

According to the equation, the values of a is a = 2009 + f(a) and b is b = 800 + f(b).

Part B

Approximately it takes 8 years from 2009 for the population of wild tigers in Nepal to reach 800.

To find these values, we need to set the equation for the population of wild tigers equal to 800 and solve for x. The equation becomes 800 = 121(2)ˣ.

Taking the logarithm of both sides, we get

=> log(800) = log(121) + x log(2).

Solving for x, we get

=> x = (log(800) - log(121))/log(2).

Moving on to the second part of the problem, we are asked to determine approximately how many years from 2009 it will take for the population of wild tigers in Nepal to reach 800. Using the equation we derived in Part A, we can plug in values of a and use trial and error to find the answer. However, this can be time-consuming.

Instead, we can use a calculator to get an approximate answer. Plugging in the values for log(800) and log(121) into the equation we derived in Part A, we get x = 7.75.

Therefore, it will take approximately 8 years from 2009 for the population of wild tigers in Nepal to reach 800.

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The GDP of the hypothetical country in this case is R363 billion.

To calculate GDP, we use the following formula:

GDP = C + G + I + NX

where:

C = consumer spending

G = government spending

I = business investment

NX = net exports (exports - imports)

Now, let's plug in the given values into the formula and calculate the GDP:

GDP = R220 billion (C) + R50 billion (G) + R100 billion (I) + (R25 billion - R32 billion) (NX)

GDP = R220 billion + R50 billion + R100 billion - R7 billion

GDP = R363 billion

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The total surface area of the prism is  177.2 m².

The total surface area of the prism is calculated by applying the formula for total surface area of prism.

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 4 m (3 m) + (3.8 m + 4 m + 4 m) x 14 m

S.A = 177.2 m²

Thus, the surface area of the prism is calculated using the formula for surface of right prism.

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The probability that the landing uppermost of the first die is 6 given the conditions as required is; 1/36.

It follows from the task content that; the probability that the number landing uppermost on the first die is a 6 if it is known that the sum of the numbers landing uppermost is 7 is to be determined.

This implies that the first die gives 6 and the second die gives 1 so that the required probability is;

P = (1/6) × (1/6)

P = 1 / 36.

Ultimately, the required probability as described is; 1/36.

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Answer:

1.8

Step-by-step explanation:

5x+3(8-1)=30

5x+24-3=30

5x+21=30

5x=9

x=9/5 or 1 4/5 or 1.8

Answer:

Step-by-step explanation:

Social media usage is one of the most popular online activities and in 2021, 82 percent of the population in the United States had a social networking profile, representing a two percent increase from the 80 percent usage reach in the previous year.

Social media usage is one of the most popular online activities, and in 2021, 82 percent of the population in the United States had a social networking profile, marking a two percent rise over the previous year's usage reach of 80 percent.

Brainlist?

Answer:

32

Step-by-step explanation:

512 / 4 = 128

128 / 4 = 32

32 / 4 = 8

8 / 4 = 2

I hope this helps you .

Answer:

[tex]3.37 \times 9 \\ = 30.33[/tex]

hope it helps

The null hypothesis represents the default assumption or the status quo, while the alternative hypothesis represents the alternative possibility or the hypothesis that is being tested.

These two hypotheses are mutually exclusive, meaning that if one is true, the other must be false.

The null and alternative hypotheses divide all possibilities into two non-overlapping sets.

In statistical hypothesis testing, the null and alternative hypotheses divide all possibilities into two non-overlapping sets.

These two hypotheses represent different explanations or theories about the data, and they are used to make inferences about the population from the sample data.

The null hypothesis represents the default assumption or the status quo. It states that there is no significant difference or relationship between two variables, or that the observed data is due to random chance alone. The alternative hypothesis, on the other hand, represents an alternative explanation or theory about the data.

It states that there is a significant difference or relationship between two variables, or that the observed data is not due to random chance alone.

The null and alternative hypotheses are mutually exclusive, meaning that if one hypothesis is true, the other hypothesis must be false.

They are also exhaustive, meaning that they cover all possible explanations for the observed data.

By dividing all possibilities into two non-overlapping sets, the null and alternative hypotheses allow us to make a decision about which hypothesis is more likely to be true based on the evidence provided by the sample data.

In order to test the null and alternative hypotheses, we use statistical methods to calculate the probability of obtaining the observed data if the null hypothesis were true.

This probability is called the p-value, and it represents the likelihood of obtaining the observed data or a more extreme result if there were no true effect or relationship in the population.

If the p-value is small enough, we reject the null hypothesis in favor of the alternative hypothesis.

The null and alternative hypotheses divide all possibilities into two non-overlapping sets and provide a framework for making inferences about the population based on sample data.

By testing the null hypothesis and calculating the p-value, we can make decisions about which hypothesis is more likely to be true based on the evidence provided by the sample data.

In statistical hypothesis testing, we use evidence from the data to decide whether to reject the null hypothesis in favor of the alternative hypothesis or not.

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For a hypothesis testing by considering two samples related to rate of people who exercise and who do not exercise, the observed t-value < standard so, null hypothesis does not rejected and there is no evidence to support the claim.

We have a researcher who was interested in making a comparison of resting pulse rate of people who exercise regularly and who do not exercise regularly. There is two independent samples. In 1ˢᵗ sample, sample size, n₁= 16

Sample mean, [tex]\bar X_1[/tex] = 72.3

Standard deviations, s₁ = 10.3

In case of second sample, sample size, n₂ = 12

Sample mean, [tex] \bar X_2[/tex] = 69.0

Standard deviations, s₂ = 8.9

Level of significance = 2.5% = 0.25

Consider the null and alternative hypothesis for the test hypothesis are defined as [tex]H_0 : μ_1 =μ_2[/tex]

[tex]H_a : μ_1 >μ_2[/tex]

The test statistic : using t-test formula

[tex]t = \frac{ \bar X_1 - \bar X_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}}}[/tex]

[tex]= \frac{72.3- 69}{ \sqrt{ \frac {10.3^2}{16} + \frac{8.9^2}{12}}}[/tex]

= 0.91

Degree of freedom, df = n1 + n2 - 2

= 16 + 12 -2 = 26

Using the t-distribution table, the critical value for t(0.025, df = 26) is equals to the 2.06. Now, the observed t-value = 0.91 is less than 2.06 ( standard t value), so, we do not reject H₀ . Hence, no evidence to support the researcher claim.

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Answer: The 8 oz steak is a better buy as it has a lower unit price at $1.06 per ounce compared to $1.14 per ounce for the 14 oz steak.

Step-by-step explanation: To determine which is a better buy, we can calculate the unit price of each steak.

The unit price is the price per ounce of steak.

For the 8 oz steak:

Unit price = price ÷ quantity = $8.50 ÷ 8 = $1.06 per ounce

For the 14 oz steak:

Unit price = price ÷ quantity = $16.00 ÷ 14 = $1.14 per ounce

Therefore, the 8 oz steak is a better buy as it has a lower unit price at $1.06 per ounce compared to $1.14 per ounce for the 14 oz steak.

The value of the functions are;

f(-4) = 1/16

f(-3) = 1/8

f(-2) = 1/4

f(-1) = 1/2

f(0) = 1

It is important to note that functions are described as equations or expressions that shows the relationship between two variables.

From the information given, we have that;

The function, f(x) = 2ˣ

To determine the value of f(x) for -4, we have to substitute the value

f(x) = 2⁻⁴

find the value

f(-4) = 1/2⁴ = 1/16

For the value of f(-3)

f(-3) =2⁻³

find the value

f(-3) = 1/2³ = 1/8

For the value of -2

f(-2) = 2⁻²

f(-2) = 1/2² = 1/4

For the value of -1

f(-1) = 2⁻¹

f(-1) = 1/2¹ = 1/2

For the value of 0

f(0) = 2⁰

f(0) = 1

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The system of equations that models this scenario is:

Let p be the number of bags of popcorn.

Let s be the number of sodas Dave buys.

Since Dave needs to buy at least one of each item for all six kids, we have:

p + s = 6 -----(1)

Given:

The cost of a bag of popcorn is $2.50.

The cost of a soda is $4.00.

The total cost of Dave's purchase can be expressed as:

2.50p + 4.00s = C -----(2) where the C is the total cost of Dave's purchase.

Since Dave can spend at most $40, we have:

2.50p + 4.00s ≤ 40 -----(3).

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The image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

What is meant by vertices?

Vertices (singular: vertex) are the points where two or more edges meet in a geometric shape or object. They are also known as corners and are a defining feature of many shapes, including polygons, polyhedra, and graphs.

What is meant by a triangle?

A triangle is a geometric shape with three sides and three angles. It is a fundamental shape in geometry and has many practical applications in mathematics, science, and engineering.

According to the given information

In this case, the line of reflection is x = -2. The distance from N's x-coordinate to the line of reflection is |-5 - (-2)| = 3. So the x-coordinate of N' is -2 + 3 = 1. The y-coordinate of N' remains the same as N's y-coordinate, so N' = (1, 2).

The distance from M's x-coordinate to the line of reflection is |-2 - (-2)| = 0. So the x-coordinate of M' is -2 + 0 = -2. The y-coordinate of M' remains the same as M's y-coordinate, so M' = (-2, 1).

The distance from O's x-coordinate to the line of reflection is |-3 - (-2)| = 1. So the x-coordinate of O' is -2 + 1 = -1. The y-coordinate of O' remains the same as O's y-coordinate, so O' = (-1, 3).

So the image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

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The minimum number of cuts John needs to make to cut a 5-inch piece of paper using scissors with blades that are 4 and 3/8 inches long is either one or two

To determine the minimum number of cuts John needs to make to cut a 5-inch piece of paper using scissors with blades that are 4 and 3/8 inches long:

Subtract the length of the blades from the desired length of the paper:

5 - 4 3/8 = 1/8 inch

Therefore, the minimum number of cuts John needs to make are 4 and 3/8 inches long is either one or two, depending on whether he chooses to fold the paper or not.

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--The complete Question is, John needs to cut a piece of paper using a pair of scissors. He measures the scissors to the nearest 1/8 inch and finds that the length of the blades is 4 and 3/8 inches. If John wants to cut a piece of paper that is exactly 5 inches long, what is the minimum number of cuts he needs to make? --

Answer:

The words "per" and "each" are associated with quantity and division. They are used to express the ratio or rate of one thing in relation to another. For example, "The cost is $10 per pound" or "Each student receives one book."

Answer:

The words per and each are associated with Division.

Step-by-step explanation:

Think of the words "percent". We can divide the word into two easier terms, "per" and "cent". Per means for each. Dividing also means for each.

I'm trying my best without an answer key to help me see what you want to be answered, let me know if there is something specific you would like to know. :)

-a friendly 8th grader :D

At 4:00 PM, the distance between Andy and Bill is minimal, about 6.04 miles apart.

Pythagorean theorem is used to find the distance between Andy and Bill at any point in time.

Suppose 3 t hours have passed.

12:00 am.

At that point, Andy moved a remove of 4 miles south from point A, and Charge moved a remove of 5 miles west of point B.

The separation between Andy and Charge is given by

[tex]D(t) = sqrt[(9 - 5t)^2 + (4t)^2][/tex]

To find the time when the distance between Andy and Bill is minimal, we need to find the value of t that minimizes D(t).

To do this, find the derivative of D(t) with respect to t, set it to zero, and solve for t.

dD/dt = (1/2)[2(9 - 5t)(-5) + 2(4t)*(4)]

= -45 + 16t

Setting dD/dt = 0 gives: -45 + 16t = 0

Solving for t gives: t = 45/16 ≈ 2.81 hours

Therefore, the time at which the distance between Andy and Bill is minimal is 3.

48 hours (rounded to the nearest minute).

Note that at this point Andy has traveled a remove of 42.81 = 11.24 miles south of point A, and Charge has traveled a remove of 52.81 = 14.05 miles west of point B.

The separations between them are:

[tex]D(2.81) = sqrt[(9 - 52.81)^2 + (42.81)^2] ≈ 6.04 miles[/tex]

therefore, At 4:00 PM, the distance between Andy and Bill is minimal, about 6.04 miles apart.

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The surface area of the triangular prism is 312 ft².

In order to calculate the surface area of a prism, we  twice the perimeter of base of the prism to twice the area of the base of the prism

To calculate the surface area of the triangular prism in the question, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the surface area is 312 ft².

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The equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

To find the equation of a circle in general form, we need to complete the square for both x and y terms.

x^2 + y^2 - 2x - 6y - 26 = 0

First, we will complete the square for x terms:

x^2 - 2x + y^2 - 6y - 26 = 0

(x - 1)^2 - 1 + y^2 - 6y - 26 = 0

(x - 1)^2 + y^2 = 27

Now, we will complete the square for y terms:

(x - 1)^2 + (y - 3)^2 = 36

Therefore, the equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

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Answer:

x2+y2−2x−6y−26=0

Step-by-step explanation:

Just took the test.

The equation that represents the cost of the rental truck is y = 0.42x + 71. The Option C is correct.

Let x be the number of miles driven

Let y be the cost of the rental truck.

We can set up a system of equations to represent the given information:

For Bob:

y = mx + b

112.96 = 138m + b

For Carl:

y = mx + b

142.78 = 209m + b

Solving for b in both equations, we get:

b = 112.96 - 138m

b = 142.78 - 209m

Setting the two expressions for b equal to each other, we get:

112.96 - 138m = 142.78 - 209m

209m - 138m  = 142.78 - 112.96

71 m = 29.82

m = 0.42

Substituting m into equation for b:

b = 71.

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Answer:

  see attached

Step-by-step explanation:

You want a clock face with an angle of 240° between the hour and minute hands.

There are 22 possible locations for the minute hand such that the long arc between the hour and minute hands is 240°. The two of these that do not involve fractions of a second are 4:00 and 8:00.

The next occurrence will be 21 minutes 49 1/11 seconds later. And the one after that will be 43 minutes 38 2/11 seconds later, or 1 hour 5 minutes and 27 3/11 seconds after the first occurrence of the pair.

A clock face illustrating 8:00 is attached. You may need to scale it to your desired radius.

You can set your compass to 2" and draw the clock face circle. The points for 12 and 8 can be located by using the 10:00 position as the center of arcs with the same radius. Where those arcs intersect the original circle are the locations of 12 and 8.

Results from the Simple Interest:

1. The amount Tucker will receive in interest after 5 years = $1,165.50.

2 The simple interest rate Wilson would need to make his $9,000 grow to $85,000 in 16 years =  53%.

3. The number of years it will take for $7,000 to double in an account with 2.8% simple interest = ≈36 years.

4. The ending balance after 6 years = $25,472.

Using Simple interest formula: S.I. = P × R × T

Simple interest (SI) formular = Interest (I) = Principal (P) * Rate (R) * Time(T)

Given:

P= $7,400

R = 3.15% or 0.0315

T = 5 years

Plugging in the values:

Interest = ($7,400 * 0.0315 * 5)

Interest = $1,165.50

2) Using SI  formular: I = P* R * T

Given:

P = $9,000

I = $85,000 - $9,000 = $76,000 (as the total cost is the principal plus interest)

T = 16 years

Plugging in the values:

$76,000 = $9,000 * Rate * 16

R = $76,000 / ($9,000 * 16)

To convert  to percentage, we multiply by 100:

Rate = 0.531 * 100

Rate = 53.1%.

3) Using SI  formular: I = P* R * T

Given:

P = $7,000

R = 2.8%

I = P

T = ?

Plugging in the values and solving for Time (T):

$7,000 = $7,000 * 0.028 * T

T = $7,000 / ($7,000 * 0.028) = 35.7

T  ≈36 years

4. Using SI  formular: I = P* R * T

Given:

P = $20,000

R = 4.56%

T = 6 years

Plugging in the values:

P = $20,000

R = 4.56% or 0.0456

T = 6 years

Ending Balance (EB) = P + (Pl *  R * T)

EB = $20,000 + ($20,000 * 0.0456 * 6)

EB = $20,000 + $5,472

EB = $25,472

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Answer:

The answer for x is 27

Step-by-step explanation:

2x/3-1x/9+5=20

2x/3-x/9=20-5

6x-x/9=15

5x/9=15

multiply both sides by 9

5x/9×9=15×9

5x=15×9

divide both sides by 5

5x/5=15×9/5

x=3×9

x=27

Answer:

Step-by-step explanation:

The value of k given the absolute value functions is (a) k = -5

Given that

graph = f(x)

table = g(x)

Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.

Also, from the given table, we have g(0) = -4.

Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.

But we also know that g(0) = -4. Thus, we have:

1 + k = -4

Solving for k, we get:

k = -5

Therefore, the value of k is -5.

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