Joel is going to start a business. To cover his start-up costs he takes out two loans. Loan 1: Joel made an initial payment of $2,000 and will make monthly payments of $300 per month. Loan 2: Joel made an initial payment of $1,000 and will make monthly payments of $200 per month. How many months will it take Joel to pay off these two loans if they are $21,500 in total?​

Answer:

Step-by-step explanation:

Hi there!

According to the question;

radius (r) = 7

We know,

Circumference (c) = 2πr

                              = 2π * 7

                              = 14π

Therefore the circumference of p is 14π.

Hope it helps!

Answer:

C.

Step-by-step explanation:

Take note of the domain of possible solutions:

• √(2x + 1) is defined for 2x + 1 ≥ 0, or x ≥ -1/2

• √(x + 1) is defined for x + 1 ≥ 0, or x ≥ -1

So any solutions to this equation must fall in the interval x ≥ -1/2, or [-1/2, ∞).

To solve, move one of the root expressions to the right side, then square both sides:

√(2x + 1) = 2 + √(x + 1))

[√(2x + 1)]² = [2 + √(x + 1))]²

2x + 1 = 4 + 4 √(x + 1) + (x + 1)

Simplify this to

x - 4 = 4 √(x + 1)

and now square both sides again and solve for x :

[x - 4]² = [4 √(x + 1)]²

x ² - 8x + 16 = 16 (x + 1)

x ² - 8x + 16 = 16x + 16

x ² - 24x = 0

x (x - 24) = 0

x = 0   or   x - 24 = 0

x = 0   or   x = 24

Both of these solutions are greater than -1/2; however, if x = 0, we get

√(2×0 + 1) - √(0 + 1) = √1 - √1 = 1 - 1 = 0 ≠ 2

so the only solution is x = 24.

Answer:

• √(2x + 1) is defined for 2x + 1 ≥ 0, or x ≥ -1/2

• √(x + 1) is defined for x + 1 ≥ 0, or x ≥ -1

So any solutions to this equation must fall in the interval x ≥ -1/2, or [-1/2, ∞).

To solve, move one of the root expressions to the right side, then square both sides:

√(2x + 1) = 2 + √(x + 1))

[√(2x + 1)]² = [2 + √(x + 1))]²

2x + 1 = 4 + 4 √(x + 1) + (x + 1)

Simplify this to

x - 4 = 4 √(x + 1)

and now square both sides again and solve for x :

[x - 4]² = [4 √(x + 1)]²

x ² - 8x + 16 = 16 (x + 1)

x ² - 8x + 16 = 16x + 16

x ² - 24x = 0

x (x - 24) = 0

x = 0   or   x - 24 = 0

x = 0   or   x = 24

Both of these solutions are greater than -1/2; however, if x = 0, we get

√(2×0 + 1) - √(0 + 1) = √1 - √1 = 1 - 1 = 0 ≠ 2

so the only solution is x = 24.

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Answer:e. The sampling distribution of the difference in sample proportion is approximately normal.

Step-by-step explanation:

(200) (0.06) >= 10

(200) (0.94) >=10

(197)(0.086) >=10

(197)(0.914) >= 10

We test the sample proportions of it is normal :

Deer population 1:

Sample size, n1 = 200

Proportion, p1 = 0.06

q = 1 - p = 1 - 0.06 = 0.94

n1 * p = 200 * 0.06 = 12

n1 * q = 200 * 0.94 = 188

Deer population 2:

Sample size, n2 = 197

Proportion, p = 0.086

q = 1 - p = 1 - 0.086 = 0.914

n2 * p = 197 * 0.086 = 16.94

n2 * q = 197 * 0.914 = 180.06

Since for samples and proportions ;

n*p and nq ≥ 10 ;

We cm conclude that the sampling distribution of the difference in sample mean is appropriately normal.

The sampling distribution of the difference in sample proportions is approximately normal because samples and proportions are greater than or equal to 10.

Given :

For dear population 1, the sample size is 200 and proportion is 0.06.

\(\rm q_1 = 1-p_1=1-0.06=0.94\)

\(\rm n_1p_1=200\times 0.06=12\\\)

\(\rm n_1q_1=200\times 0.94 = 188\)

Now, for dear population 2, the sample size is 197 and the proportion is 0.086.

\(\rm q_2 = 1-p_2=1-0.086=0.914\)

\(\rm n_2p_2=197\times 0.086=16.94\)

\(\rm n_2q_2=197\times 0.914 = 180.06\)

Therefore, from the above calculations, it can be concluded that the sampling distribution of the difference in sample proportions is approximately normal because samples and proportions are greater than or equal to 10.

So, the correct option is e).

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Answer:

12 -16. 19

4. 8. 22

3. -9. -4

Step-by-step explanation:

13-1 = 12

-10-6= -16

12 - -7 = 12+7=19

6-2 = 4

Keep subtracting

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

Step-by-step explanation:

30

Answer:

3.45

Step-by-step explanation:

so the first step is to make 15% a fraction

this gives you 15/100 of 23

multiply 15 by 23 and get 345

divede 345 to get 3.45

The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.

For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.

In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Answer:

9.) A= 23mm².

P= 20mm.

T= PARALLELOGRAM.

Step-by-step explanation:

9.) A=(5+5) × 1/2 × 4.6

= (10) × 1/2 × 4.6

= 5mm× 4.6 mm

= 23mm².

P=(5+5+5+5)

= 20mm.

T= PARALLELOGRAM.

Answer:

E) A hypothesis test with a null hypothesis that the dropout rate is less than or equal to the highest dropout rate

Step-by-step explanation:

The hypothesis test is the type of test that helped a scientist to determine the relationship between two variables-one constant independent variable and an dependent variable. For the dropout rates in the different schools, it would be better to use the hypothesis test for the evaluation.

Answer:

Number is yellow box=3

Step-by-step explanation:

We know this because the way we get that number is subtracting the two numbers above it, which is 8 and 5, which give us 3.

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We have that Total votes cast in the election is the vote cast for Margie and Rachel summed up

\(Total\ vote=\sum Rachel +\sum Margie\)

It is important to note that an election comprise of two or more candidates facing off against each other to decide who a group of people want for a position

From the Question we are told that

There is suppose to be a table of votes cast

Generally the Total votes cast in the election is the vote cast for Margie and Rachel summed up

Therefore

\(Total\ vote=\sum Rachel +\sum Margie\)

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The length of line having mid point B ⇒  7x - 2.

Given that,

B is the mid point of AC

And also given that

length of segment AB = 2x+5

And length of segment BC = 5x - 7

A straight path established by linking a group of points in a plane is known as a line. It is a one-dimensional form with only a length and no width or height. A line can extend indefinitely in both ends in opposite directions. To indicate a line, we can use upper case characters.

Now since B is the mid point of AC,

So, The line AC is sum of the line segment AB and line segment BC.

Therefore,

AC = AB+BC

     = (2x+5)+(5x - 7)

     = 7x - 2

Hence,

The length of AC is 7x - 2

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Answer:   b

Step-by-step explanation:

x= 5+√35 and 5-√35

Answer:

\(P_4= 0.2\)

Step-by-step explanation:

From the question we are told that

Consider all seven-digit numbers

Created from the digits 0-9

Generally number of digits that starts with 6 is mathematically  given as

The total amount of digits from 0-9(0,1,2,3,4,5,6,7,8,9 = 10

The total amount of even digits within 0-9 (0,2,4,6,8) = 5

The total amount of 3-digit numbers giving the first and last digits to be even = 5 * 10 * 5 = 250

The total 3-digit numbers giving the first digit is 4 and last digit is even = 1 * 10 * 5 = 50

Probability the number starts with 4

      \(P_4 = \frac{50}{250}\)

      \(P_4= 0.2\)

Answer:

x is 12

Step-by-step explanation:

Answer:

0.2(2 tenths) times 0.3(3 tenths) = 0.06

Step-by-step explanation:

2 times 3 equals 6.

The 6 would have a 0 before it because you are using multiplication. If you were using addition, it would be 0.5(5 tenths) since you are adding tenths.

Answer: x = ( -3)

Step-by-step explanation:

7 ( x+3 ) = 7x + 21

7x = -21

7x ÷ 7 = -21÷7

X = ( -3)

The value of x in the similar triangle is 6 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:

Hence,

5 / 40 = x / 48

48 × 5 = 40x

240 = 40x

divide both sides by 40

x = 240 / 40

x = 6

Therefore,

x = 6

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Step-by-step explanation:

Rectangle: A quadrilateral with four right angles; a rectangle is a type of parallelogram. Square: A quadrilateral with four congruent sides and four right angles; a square is both a rhombus and a rectangle. Trapezoid: A quadrilateral with exactly one pair of parallel sides (the parallel sides are called bases)

Answer:

512 cubic inches

Step-by-step explanation:

\( \sqrt[3]{64} = 4\)

\( {8}^{3} = 512\)

Answer: $12 for one ticket.

Step-by-step explanation:

simply divide 48 by 4, that's how you find the price for one ticket.

Answer:

true

Step-by-step explanation:

Answer:

Step-by-step explanation:

According to the question, the equation is:

Let's see

Answer: 8

Step-by-step explanation:

"Of" is the same as multiplication so,

2/5 × 20/1 = ?  

20/1 is the same as 20. (20÷1 = 20/1)

In fraction multiplication, we multiply the numerators and then we multiply the denominators and get ↓↓↓↓

Below is a fraction.↓↓↓

2 x 20            40

______    =  ____

5 x 1                 5

Since 40 divided by 5 equals 8 then,

40/5 = 8

Therefore :

2/5 of 20 is 8.

So:

Kara drew 8 of the 20 pictures in art class.

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Answer: 33.3333333...%

Step-by-step explanation: 200/600=1/3

                                            1/3 =33.3333333...%

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D

To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.

From the given table, we can see that there are 22 students with gray eyes and red hair.

The total number of students with gray eyes is the marginal total for gray eyes, which is 35.

To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:

Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes

Relative frequency = 22 / 35

Simplifying the fraction, we have:

Relative frequency = 0.6286

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.

Therefore, the correct answer is option OD) 0.63.

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