Categorize these samples as representative or not representative of the given populations.

Final answer:

After rearranging the formula and solving for the interest rate, the required rate is found to be approximately 4.7%.

Explanation:

The subject of this question is finding the required annual interest rate that will grow a principal amount of $5,200 to $6,500 when compounded quarterly over five years. To solve this, we shall use the compound interest formula:

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

Where:A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

We are given:

A = $6,500

P = $5,200

n = 4 (since interest is compounded quarterly)

t = 5 years

We need to solve for r. First, we rearrange the formula to isolate r:

(1 + r/n) = (A/P)[tex]^({1/(nt))}[/tex]

Then we can insert our known values and solve for r:

(1 + r/4) = ($6,500/$5,200)^(1/(4*5))
Calculate the right-hand side:

(1 + r/4) = (1.25)[tex]^({1/20)}[/tex]
Find the 20th root of 1.25:

(1 + r/4) ≈ 1.01168
Subtract 1 from both sides:

r/4 ≈ 0.01168
Multiply both sides by 4:

r ≈ 0.04672

Convert the decimal to a percentage:
r ≈ 4.672%
Round to the nearest tenth of a percent:

r ≈ 4.7%
Therefore, the required annual interest rate to the tenth of a percent for $5200 to grow to $6500 with interest compounded quarterly for five years is approximately 4.7%.

Final answer:

Sally pays 70% of the price of a new van for a used van, which is calculated by dividing the price of the used van by the price of the new van and multiplying by 100.

Explanation:

To determine what percent of the price of a new van Sally pays for a used van, we use the formula for percentage: (Part / Whole) × 100. In this case, the price of the used van ($14,000) is the part, and the price of the new van ($20,000) is the whole. Hence, the calculation will be ($14,000 / $20,000) × 100.

Therefore, Sally pays 70% of the price of a new van for a used van.

The atom consists of a tiny nucleus surrounded by moving electrons. The nucleus contains protons, which have a positive charge equal in magnitude to the electron's negative charge.

Answer:

-18^x-45x on edge

Step-by-step explanation:

sorry if this is late just letting people know in the future

For a better understanding of the explanation provided here please go through the diagram in the attachment given below.

As we can see from the diagram of the congruent triangles ABC and FGH, the vertices A,B,C of [tex] \Delta ABC [/tex] correspond to the vertices F,G,H of [tex] \Delta FGH [/tex], so the corresponding sides must correspond too. Thus, AB corresponds to FG, BC corresponds to GH and CA corresponds to GF.

Now, we know that BC=10.4. Therefore, it's corresponding side GH must be 10.4 too because they are corresponding sides of a congruent triangle.

Thus, GH=10.4 is the correct answer.

All statements are true. Ratio of corresponding angles, areas, perimeters, and altitudes is 2:1. No false statement exists.

To determine which statement regarding the two triangles is NOT true, let's analyze each option step by step.

Given:

- Two triangles are similar.

- The ratio of the lengths of each pair of corresponding sides is 2:1.

Let's denote the lengths of corresponding sides in the first triangle as [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], and in the second triangle as [tex]\( 2a \)[/tex], [tex]\( 2b \)[/tex], and [tex]\( 2c \),[/tex] respectively.

A. Their corresponding angles have a ratio of 2:1.

- This statement is true because corresponding angles in similar triangles are congruent, so their ratios would indeed be 2:1.

B. Their areas have a ratio of 4:1.

- The area of a triangle is proportional to the square of the length of its sides. So if the ratio of the lengths of corresponding sides is 2:1, the ratio of their areas would be [tex]\( (2:1)^2 = 4:1 \)[/tex]. Hence, this statement is also true.

C. Their perimeters have a ratio of 2:1.

- The perimeters of triangles are directly proportional to the lengths of their sides. Since the ratio of the lengths of corresponding sides is 2:1, the ratio of their perimeters would indeed be 2:1. So, this statement is also true.

D. Their altitudes have a ratio of 2:1.

- The ratio of the altitudes of two similar triangles is equal to the ratio of their corresponding sides. So, if the ratio of corresponding sides is 2:1, the ratio of their altitudes would also be 2:1. Therefore, this statement is true.

Since all the statements are true, the correct answer is NONE.

Step-by-step explanation: Well you see here 9x10 isnt 9 its 90 and 3x10 isnt -4 its 30

Answer:

x + 230 ≤ 500

Step-by-step explanation:

Given,

The time for which Tom used the phone = 230 minutes,

Let he further used the mobile for x minutes,

So, the total time for which he used the phone = ( x + 230 ) minutes,

According to the question,

For the extra minutes more than 500 minutes, the mobile phone carrier charges an extra fee,

Thus, if he wants to use the phone, without going over the 500-minute limit,

Then, the total time used by him ≤ 500 minutes,

⇒ x + 230 ≤ 500

Which is the required inequality.

The total volume of pool is:

                      1040 cubic ft.

We know that the total volume of the pool is the sum of the volume of two rectangular prism.

Hence, the volume of first rectangular prism is:

                       20×10×4=800 cubic ft.

Volume of second rectangular prism is:

                      6×4×10=240 cubic ft.

Hence, total volume of pool is:

                 800+240=1040 cubic ft.

Final answer:

The first step of rationalizing the denominator of 7√11 is to multiply both the numerator and denominator by the conjugate of the denominator.

Explanation:

The first step of rationalizing the denominator of 7√11 is to multiply both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of √11 is -√11. Therefore, we multiply both the numerator and denominator by -√11 to get:

7√11 * -√11 = -77

√11 * -√11 = -11

So, the rationalized denominator is -11. The denominator becomes -11, and the simplified expression is:

-77 / -11 = 7

Final answer:

A triangle with two perpendicular sides could be scalene or isosceles if the non-perpendicular sides are unequal or equal, respectively. It cannot be equilateral because equilateral triangles have no right angles.

Explanation:

If a triangle has two sides that are perpendicular to each other, it could potentially be a scalene or isosceles triangle, but it cannot be equilateral. When two sides of a triangle are perpendicular, they form a right angle. Thus, if a triangle has a right angle, it is a right triangle by definition. According to Theorem 2, if two angles of a triangle are equal, the opposite sides are equal, and the triangle is isosceles.

In our case, this theorem would apply if the two non-perpendicular sides are of equal length, resulting in an isosceles right triangle. On the other hand, Theorem 3 states that in a triangle with unequal angles, the side opposite the greater of the angles is greater than the side opposite the smaller. Therefore, if the sides forming the right angle are of different lengths, the triangle would be scalene.