Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y = 10,000 – 250x and the value of the car after x months is represented by y = 8,000 – 50x. Which statement describes when Melinda’s loan will be equal to the value of the car?

After 10 months, the loan and value of the car will both be equal to $7,500.
After 12 months, the loan and value of the car will both be equal to $7,000.
After 14 months, the loan and value of the car will both be equal to $6,500.
After 16 months, the loan and value of the car will both be equal to $6,000.

Answer:

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

1999:

20 out of 100 in the bottom third, so:

[tex]p_1 = \frac{20}{100} = 0.2[/tex]

[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]

2001:

10 out of 100 in the bottom third, so:

[tex]p_2 = \frac{10}{100} = 0.1[/tex]

[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]

Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:

[tex]H_0: p_1 - p_2 = 0[/tex]

At the alternative hypothesis, we test if the proportion has been reduced, that is, the subtraction of the proportion in 1999 by the proportion in 2001 is positive. So:

[tex]H_1: p_1 - p_2 > 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.1 - 0}{0.05}[/tex]

[tex]z = 2[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of at least 0.1, which is the p-value of z = 2.

Looking at the z-table, the p-value of z = 2 is 0.9772.

1 - 0.9772 = 0.0228.

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Answer:

31 = 16²-15²

Step-by-step explanation:

16² = 256

15² = 225

256 - 225 = 31

Answer:

Protein smoothie =14

Berry Smoothie= 29

Step-by-step explanation:

Let number of protein smoothie be X

Let number of berry smoothie be Y

1. X+Y=43

Y=43-X

2. 10X+6Y=314

5X+3Y= 157

5x+3(43-x)=157 (substitute)

5x+129-3x=157

2x=157-129

x=14

X+Y=43

Y=43-14

Y=29

Brainliest please~

The approximate area of the shaded region is 2794 m². The correct option is the first option 2794 square meters

From the question, we are to determine the approximate area of the shaded region

The area of the shaded region = Area of the triangle - Area of the circle

Area of triangle = 1/2 × base × height

Area of the triangle = 1/2 × 90 × 90

Area of the triangle = 4050 m²

Area of a circle = πr²

Where r is the radius

In the diagram,

Diameter = 40 m

∴ Radius = 40/2 = 20 m

Thus,

Area of the circle = π × 20²

Area of the circle = 3.14 × 400

Area of the circle = 1256 m²

Therefore,

The area of the shaded region = 4050 m² - 1256 m²

The area of the shaded region = 2794 m²

Hence,

The darkened area covers about 2794 m²  

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Answer:

see above is the answer handwriting is bad sorry for that

Answer: I think the correct answer is 40 but I am not sure.

Step-by-step explanation:

Answer: 40

The angle measure of BCD is m∠BCD = 140°.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given that a quadrilateral ABCD.

To find the angle measure of BCD,

first, we find the other interior angle with supplementary angles.

m∠DAB = 180 - 25 = 155°

m∠ABC = 180 - 146 = 34°

m∠ADC = 180 - 149 = 31°

And the total sum of the interior angles of a quadrilateral is 360°

So, m∠BCD = 360 - (34 + 31 + 155)

m∠BCD = 140°

Therefore, m∠BCD = 140°.

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Answer:

[tex]4x^2+4x+5[/tex]

Step-by-step explanation:

[tex]f(x)=5x^2-3\\g(x)=x^2-4x-8[/tex]

Set up an expression.

[tex]5x^2-3-(x^2-4x-8)[/tex]

Distribute the negative (-1)

[tex]5x^2-3-x^2+4x+8[/tex]

Solve / Simplify

[tex]4x^2+4x+5[/tex]

I'm late, but I hope this helps!

Answer:

x=4

Step-by-step explanation:

log5(x+1)=1, (x+1)=5, x=4

Answer:

x= -6

Step-by-step explanation:

i got it wrong and the answer is -6

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

⅝ - 5/9 = 5/72

Answer:

1020m = 1.02km

Step-by-step explanation:

Speed of sound is about 340m/s.

it takes 3s for the sound to reach the ear of the spectator, thus the sound-source is 340 * 3m ( 1020m ) away.

Answer:

Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.

4+z/y = 36/18

Step-by-step explanation:

a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:

16/4 = 18/y

Note that the arrangement depends on which of the triangles sides cones first.

Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.

b) Same rule in (a) applies to the sum as well. Hence;

4+z/y = 16+20/18

4+z/y = 36/18

Answer:

0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.

Step-by-step explanation:

The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

Desired outcomes:

Two cases:

6 redwoods(6! ways) then the 6 pine trees(6! ways)

6 pine trees(6! ways) then the 6 redwoods(6! ways)

So

[tex]D = 2*6!*6![/tex]

Total outcomes:

12 trees, so:

[tex]D = 12![/tex]

What is the probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other?

[tex]p = \frac{D}{T} = \frac{2*6!*6!}{12!} = 0.0022[/tex]

0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.

Answer:it’s 3

Step-by-step explanation:

Source trust me bro

Answer:

Enrollment at walnut junior = 142

Enrollment at walnut high = 710

Step-by-step explanation:

Let :

Enrollment at walnut junior = x

Enrollment at walnut high = 5x

Total enrollment in both schools = 852

Mathematically ;

x + 5x = 852

6x = 852

x = 142

5x = 142 * 5 = 710

Hence,

Enrollment at walnut junior = 142

Enrollment at walnut high = 710

Answer:

please tell me the complete question

Answer:

Option B.)

Step-by-step explanation:

Just took the test and got 100% :]

The system of logarithmic equation is graphed and the point of intersection of the equation is log₃ ( 5x ) = log₅ ( 2x + 8 ) is A ( 1.0 , 1.4 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the solution to the logarithmic equation be represented as A

Now , the value of A is

log₃ ( 5x ) = log₅ ( 2x + 8 )

On simplifying , we get

log₃ ( 5x ) = log₁₀ ( 5x ) / log₁₀ ( 3 )

log₅ ( 2x + 8 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )

Substituting the logarithmic quantities , we get

log₁₀ ( 5x ) / log₁₀ ( 3 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )

On cross multiplying , we get

log₁₀ ( 5x ) / log₁₀ ( 2x + 8 ) = log₁₀ ( 3 ) / log₁₀ ( 5 )

( 5x ) / ( 2x + 8 ) = 3/5

On cross multiplying , we get

25x = 6x + 24

Subtracting 6x on both sides , we get

19x = 24

Divide by 19 on both sides , we get

x = 1.26

Therefore , the approximate values of the function on graphing is A ( 1.0 , 1.4 )

Hence , the solution of function from graphing is A ( 1.0 , 1.4 )

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Answer:

N80

Step-by-step explanation:

One ruler is N60 and one pencil is N20.

9514 1404 393

Answer:

  C)

Step-by-step explanation:

The table that has a constant ratio between y and x values is the one that represents a proportional relationship.

A) 2/4 ≠ 4/16

B) 1/1 ≠ 4/16

C) 6/8 = 12/16 = 18/24 = 30/40, a proportional relationship

Answer:

X + 2y = 1

3x + y = 13

Step-by-step explanation:

A and b are the coefficients of X and y

I wasn't sure about my answer so used Gauthmath

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.

tan(54) = 16/BC

BC = 16/tan(54)

BC = 11.62 units

Hope this helps!

Answer:

The key difference between simple interest and compound interest is that in simple interest, the interest is calculated based on the principal amount of the loan.

The formula is principal multiplied by time by rate divided by 100.

Compound interest on the other hand, has to do with the principal amount and accumulated interest on previous periods.

The difference affects the effectiveness of each because in SI, interest is calculated once, while in CI, there's accumulated interest.

The answer is always your welcome

Answer:

always

Step-by-step explanatia;won:

9514 1404 393

Answer:

  (b)  3x -2

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  P = (x) +(x +2) +(x -4)

  P = (x +x +x) +(+2 -4)

  P = 3x -2

Answer:

81/25

Step-by-step explanation:

change 3.24 into faction

324 over 100 because there are two decimal points .

simplfy into the smallest fraction

the answer is 81 over 25

Answer:

This the right order:

4^2+2^2 = 20

5^2= 25

6^2-6 = 30

Answer:

-4,-6

Step-by-step explanation:

x = y-2

2y = 4x+16

2y = 4(y-2) + 16

2y = 4y -8 + 16

-2y = 8

y = -4

x = -6

Option C

Because in Side Angle Side there should be 2 sides and a angle stuffed between them.

In this If CD ≅ RS then √QRS is not ≅ and We cannot use SAS

Therefore the wrong statement is Option c

Answered by Gauthmath must click thanks and mark brainliest

Because in Side Angle Side there should be 2 sides and a angle stuffed between them.

In this If CD ≅ RS then √QRS is not ≅ . Option C is correct

To determine a congruency statement that would not result in Triangle BCD being congruent to Triangle QRS, we need to find a condition that does not satisfy the congruence criteria. The congruence of two triangles can be determined by considering their corresponding angles and sides.

Here are the possible congruency statements:

Angle-Angle-Side (AAS): If we have two angles of one triangle congruent to two angles of the other triangle, and the included side between these angles congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Angle-Side-Angle (ASA): If we have two angles of one triangle congruent to two angles of the other triangle, and a side adjacent to one of these angles congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Side-Angle-Side (SAS): If we have two sides of one triangle congruent to two sides of the other triangle, and the included angle between these sides congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Side-Side-Side (SSS): If we have all three sides of one triangle congruent to the corresponding sides of the other triangle, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.

Based on these congruency statements, there is no option that would not result in Triangle BCD being congruent to Triangle QRS. All four statements have the potential to establish congruence between the two triangles.

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Answer:

Television = 820

DVD Player = 410

Step-by-step explanation: Imagine the television  as 2, and the DVD player as 1. If you’re were to draw it out with boxes, you’d see that the tv  has two boxes and the DVD player has 1 box. All are exactly the same amount, and there are a total of three boxes. So divided 1230 by 3 and you get 410. Using the idea of the boxes, the DVD player get’s one 410, and the tv gets two 410s, or 820.

Answer:

(a) sin 60° = √ 3/ 2 OR 0.8660

(b) tan 34° = 0.6745

(c) cos 124°​ = − 0.5591