a new car is purchased for 15500 dollars. the value of the car depreciates at 7.5% per year. what will the value of the car be, to the nearest tenth, after 6 years.

The measure of the angle ∠MAR will be equal to 26°. The correct option is A.

In geometry, an angle bisector is a line that divides an angle into two equal angles. A bisector is something that divides a shape or object into two equal parts. An angle bisector is a ray that divides an angle into two equal parts of the same measurement.

Given that Ray AT bisects ∠MAR. If m∠MAT = (8x − 3)° and m∠RAT = (2x + 9)°,

The two angles ∠MAT and ∠RAT will be equal. Then calculate the value of x.

8x - 3 = 2x + 9

8x - 2x = 9 + 3

6x = 12

x = 2

The angle ∠MAR is calculated as,

∠MAR = 2 x ∠RAT

∠MAR = 2 x ( 2x + 9)

∠MAR = 2 x ( 2 x 2 + 9 )

∠MAR = 2 x ( 13 )

∠MAR  = 26°

Option A is correct for the angle ∠MAR.

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Answer:

A all the way

Step-by-step explanation:

Answer:

a=1/2b, 2a=b

Step-by-step explanation:

Since angle a is 1/2 the size of angle b, a=1/2b and b=2a. In order to get a numeral answer, you need the number of one of the angles.

Answer:

Taylor would need 4 hours to read the whole novel.

Step-by-step explanation:

Proportions

According to the conditions of the problem, Taylor reads 1/6 of a novel in 2/3 of an hour.

To read the entire novel he would need six times that time.

Thus, to read the whole novel, Taylor would need 6*2/3 = 12/3= 4 hours

Taylor would need 4 hours

They will need 4 buses.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

For the class field trip,

the fourth grades at Jefferson Elementary School need to take buses.

Each bus fits 55 students,

and there are 200 students in fourth grade.

The number of buses,

= 200/55

= 3.63

≈ 4.

Therefore, the need is for 4 buses.

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Spinning a spinner with four equal sized sections and assigning a novel to each section.

Spinning a spinner with four equal-sized sections and assigning a novel to each section is the correct option to stimulate randomly choosing a novel. The spinner can be designed with each section representing one of the four novels

The spinner is spun to randomly select one of the novels. Since each section is equal-sized, each novel has an equal probability of being selected.

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The complete question Members of a book club have 4 different novels to choose from each time they meet. Which of the following could be used to stimulate randomly choosing a novel?

(a) Placing 6 marbles in a bag (3 red and 3 blue) and drawing one ball from the bag

(b) spinning a spinner with four equal sized sections and assigning a novel to each section

(c)Tossing a fair coin, where each of the outcomes represents a novel

(d) Rolling a number cube labeled 1-6, where each book is represented by 2 numbers

day 1  4 cm

day 2  8 cm

day 3  12 cm

day 4  16 cm

day 5  20 cm

day 6  24 cm

day 7  28 cm

????

The length of the curve defined by from the point (-3, 2136) and (3, 2238), by use of distance formula is approximately 102.17 units.

The formula for the distance between two points (x1, y1) and (x2, y2) is given by:

\(d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)\)

In this case, we have:

x1 = -3, y1 = 2136

x2 = 3, y2 = 2238

Substituting these values into the formula, we get:

\(d = \sqrt{((3 - (-3))^2 + (2238 - 2136)^2)\)

\(= \sqrt{(6^2 + 102^2)\)

= \(\sqrt{(10440)\)

≈ 102.17

Therefore, the length of the curve defined by the points (-3, 2136) and (3, 2238) is approximately 102.17 units.

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_____The given question is incorrect, the correct question is given below:

To find the length of the curve defined by from the point (-3,2136) to the point (3,2238), you'd have to compute by using distance formula.

a. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. The tennis ball is initially at a height of 126 feet above the ground.

a. The x-coordinate of the vertex is 2. To find the y-coordinate, we substitute this value back into the equation:

h(2) = -14(2)² + 56(2) + 126

h(2) = -14(4) + 112 + 126

h(2) = -56 + 112 + 126

h(2) = 182

Therefore, the vertex of the equation is (2, 182). In this context, the vertex represents the highest point reached by the tennis ball during its trajectory. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. In order to find the y-intercept, we set t equal to zero and evaluate h(t):

h(0) = -14(0)² + 56(0) + 126

h(0) = 126

The y-intercept is 126. In this context, the y-intercept represents the initial height of the ball when it is thrown. Therefore, the tennis ball is initially at a height of 126 feet above the ground.

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Answer:

x = 8

y = 11

Step-by-step explanation:

Replace the y in first equation with 2x - 5 since it's equal to it

3x - 4(2x - 5) = -20 multiply 4 with inside the parenthesis

3x - 8x + 20 = -20 add like terms

-5x + 20 = -20 subtract 20 from both sides

-5x = -40 divide both sides by -5

x = 8 now use this to find y

y = 2x - 5

y = 2*8 - 5

y = 11

Answer:

This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.

Step-by-step explanation:

x < 3 or x > 5

This means, x is less than 3, but greater than 5.

Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.

Answer:

Step-by-step explanation:

Let's assume the length of the shorter side of the rectangular garden is x, then the length of the longer side will be 2x.

The distance between the centres of the adjacent sides of the garden is the hypotenuse of a right-angled triangle whose other two sides are x and 2x/2 = x.

Therefore, by the Pythagorean theorem:

(√(x^2 + x^2))^2 = (20)^2

2x^2 = 400

x^2 = 200

x = √(200) ≈ 14.14

So the length of the shorter side is approximately 14.14 meters, and the length of the longer side is approximately 28.28 meters.

The perimeter of the garden is:

2(shorter side + longer side) = 2(14.14 + 28.28) = 84.84 meters

The area of the garden is:

shorter side × longer side = 14.14 × 28.28 = 400 square meters

Answer:

B) -3

Step-by-step explanation:

Use distributive property.

∴ 3(x-1) = 3x - 3

Hence, it is verified that choice B) -3 is the correct answer.

Answer:

a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

b) Wider

Step-by-step explanation:

Question a:

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 \(1 - \frac{\alpha}{2}\).

In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.

This means that \(n = 3900, \pi = \frac{1911}{3900} = 0.49\)

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:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 - 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.4768\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.49 + 1.645\sqrt{\frac{0.49*0.51}{3900}} = 0.5032\)

The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.

Question b:

The margin of error is:

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

The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.

Answer:

C. 1/(4^10)

Step-by-step explanation:

Answer:-4/5

Step-by-step explanation:

The value of x is -15

Functions are simply defined as expressions or rules showing the relationship between two variables.

These variables are listed as;

From the information given, we have that;

g(x) =x  -1, if g(x) = -16

Now, we have to equate the two functions, we get;

x - 1 = -16

collect the like terms, we get;

x =-16 + 1

add the values, we have;

x = -15

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The complete question:

Given g(x) =x  -1, if g(x) = -16, find x.

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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For given  regression model, the number 59.89 in the table tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

In this question we have been given a summary of regression model.

We need to explain the meaning of the number 59.89 in the table.

For given regression model, to view the results of the model, we can use the summary() function in R programming.

In given summary consider the 'Coefficients' table.

The first row gives the estimates of the y-intercept, and the second row gives the regression coefficient of the model.

The 'Estimate' column is the estimated effect, also called the regression coefficient or r² value.

The number 59.89 in the table is coefficient for IsSandwich.

This number tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Therefore, the meaning of the number 59.89 in the table: for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

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The complete question is as shown in the following image

Answer:

A) (2,6)

Step-by-step explanation:

Answer:

The correct answer is "The term number, n"

Answer:

the term number, n

Step-by-step explanation:

PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)

\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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Answer:

  8) a. Use center G and the same radius

  9) b. WX ≅ JK

Step-by-step explanation:

8) You want to know the next step in constructing a perpendicular bisector.

9) You want to know how WX relates to JK.

A perpendicular bisector of GH is the set of points equidistant from G and H. The arc shown is a set of points at some distance from H. We want to find two points on that arc that are the same distance from G, so the next step is ...

  a) Using G as a center, draw an arc with the same radius as the first arc

All of the points on the arc are the same distance from W as J is from K. Point X is a point on the arc, so WX will have the same length as JK.

  b) WX is congruent to JK

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{28.28 \: }}}}}\)

Step-by-step explanation:

Given, diameter of a circle = 6

pi ( π ) = 22 / 7

Finding the radius of the circle

We know that the radius of a circle is just half of the diameter. So, 6 / 2 = 3

Finding the area of circle having radius of 3

\( \boxed{ \sf{area \: of \: circle = \pi \: {r}^{2} }}\)

plug the values

⇒\( \sf{area \: of \: circle = \frac{22}{7} \times {3}^{2} }\)

Evaluate the power

⇒\( \sf{area \: of \: circle = \frac{22}{7} \times 9}\)

Calculate

⇒\( \sf{area \:of \: circle = 28.28 \: }\)

Hope I helped!

Best regards! :D

Answer:

The mean of the sample distribution of the sample mean is the same as the population mean, which is 40 dollars. The standard deviation of the sample distribution of the sample mean (also called the standard error) is given by:

standard error = standard deviation / sqrt(sample size) = 8 / sqrt(49) = 8 / 7

To find the probability that the sample mean would be less than 37.4 dollars, we need to standardize the sample mean using the standard error and then look up the probability from a standard normal distribution table. The z-score for a sample mean of 37.4 dollars is:

z = (37.4 - 40) / (8 / 7) = -1.225

Looking up this z-score in a standard normal distribution table, we find that the probability of getting a sample mean less than 37.4 dollars is 0.1103 (rounded to four decimal places). Therefore, the probability that the sample mean would be less than 37.4 dollars is 0.1103.

give thanks, your welcome <3

Step-by-step explanation:

The baker made a batch of chocolate chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is B. Likely.

Generally,  Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

A probability of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform decision-making in a wide range of fields, including statistics, finance, and engineering.

A probability of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.

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Answer:

Step-by-step explanation: