7th grade math! Proportionality and similar shapes
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The numerical expression for 'subtract 50 from the sum of 6 and 4 to the tenth power' is written as[tex](6 + 4^{10}) - 50,[/tex] following the order of operations.

To write the statement "subtract 50 from the sum of 6 and 4 to the tenth power" as a numerical expression, you would first calculate 4 to the tenth power, then add 6 to this result, and finally subtract 50 from the total sum.

The expression would look like this:

[tex](6 + 4^{10) - 50[/tex]

It's important to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here, you calculate the exponent before adding 6 and then subtract 50 from the result.

A square is a quadrilateral defined by its properties of equal sides and right angles.

A square is a quadrilateral with four equal sides and four right angles.

Its properties include:

All sides are equal in length

All angles are right angles

The diagonals are equal in length and bisect each other at right angles

The equation can be framed as follows:

Before tax cost *(1+tax rate) = Final cost

Given tax rate = 10% = 0.1

Final cost = $825

Before tax cost *(1+0.1) = 825

Before tax cost * 1.1 = 825

Before tax cost = 825/1.1

Before tax cost = $750

Price of the couch before taxes = $750

Answer:

7988.16

Step-by-step explanation:

This is a matter of plugging in numbers.

P = 7000 (starting value)

l = 0.045 (rate)

t = 3 (number of years)

A(t) = 7000(1 + 0.045)^3

A(t) = 7000(1.045)^3

After three years, William will have 7988.16

The amount in William's account after 3 years with compound interest will be $7,988.16. Hence the correct option is B.

The compounded interest formula is:

A(t) = P(1 + i)^t

where P is the principal amount ($7000), i is the interest rate (4.5% or 0.045), and t is the time in years (3).

Calculate the total amount:

A(3) = 7000(1 + 0.045)^3

A(3) = 7000(1.045)^3

A(3) = 7000 * 1.144976125

A(3) = $7,988.16

Answer:

One step equations

3 + x = 5 ___x = 2

Y + 14 = 20____x = 6

Equations with Fractions

4/5q = 32___q = 40

3/4x = 6___x = 8

Equation with decimals

3.2x – 2.7 = 1.2x___x = 1.35

Equation with distributive Property

7x + 3 (x + 1) = 10x + 3

Infinitely Many solutions

Real World Problem

Monica knows that she should spend no more than  1/3 of her income on her rent. She really wants to move into a cool condo downtown and has found a great place where the rent is $2,300 per month. Based on that, how much should Monica earn each month to afford the rent on her cool new place?

Hope This Helps!

Final answer:

Nicole ran 0.5 miles. The expression for Nicole's running distance, starting from your 4 miles run, is (4 / 2^3) or 4 / 8, which simplifies to 0.5 miles.

Explanation:

Expression for Nicole's Running Distance

The expression to find out how far Nicole ran is based on a sequence of halving distances starting from the original distance you ran. You ran 4 miles. Rob ran half as far as you, so Rob ran 4 miles / 2 = 2 miles. Tim ran half as far as Rob, therefore Tim ran 2 miles / 2 = 1 mile. Finally, Nicole ran half as far as Tim. Hence, Nicole ran 1 mile / 2, which is equal to 0.5 miles.

In a form of an expression, the distance Nicole ran can be represented as:

(4 / 2) / 2) / 2

Or simplified to:

(4 / 2^3)

Or,

4 / 8 = 0.5 miles

Traci's coin-flipping experiment is more likely to yield results farthest from the theoretical probability of 1/2 if she conducts the experiment with only a few flips, due to the law of large numbers.

Traci wants to investigate the probability of landing on heads using a coin-flipping experiment. To find the result furthest from the theoretical probability, Traci should plan an experiment with fewer flips. The law of large numbers implies that as the number of trials increases, the experimental probability will converge closer to the theoretical probability. Hence, if Traci flips the coin only a few times, there's a greater chance that the experimental results will diverge significantly from the expected outcome of 50% heads and 50% tails. On the other hand, flipping the coin many times, such as in Pearson's experiment with 24,000 flips, is likely to yield a result very close to the theoretical probability. This is because individual variations have less impact on the overall outcome as the sample size increases.

The cross-section of the rectangular pyramid, obtained by slicing it parallel to the longer sides of the base and through the top vertex, forms a 9-12-15 right triangle. The area of the cross-section is 54 square inches (Option C).

The rectangular pyramid has a base with sides of 5 inches and 12 inches, and diagonals measuring 13 inches. The height of the pyramid is 9 inches.

The cross-section obtained by slicing the pyramid parallel to the longer sides of the base and passing through the top vertex will form a right triangle with legs of 9 inches and 12 inches, and a hypotenuse of 13 inches (as given by the diagonals).

This right triangle is a 3-4-5 right triangle scaled up by a factor of 3, making it a 9-12-15 right triangle. The area of a right triangle is given by [tex]\(\frac{1}{2} \times \text{base} \times \text{height}\).[/tex]

So, the area of the cross-section is [tex]\(\frac{1}{2} \times 12 \times 9 = 54\)[/tex] square inches.

Therefore, the correct answer is (C) 54 square inches.

Learn more about area of the cross-section here:

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87.40 hop this helps

3*0.1 + 4*0.01 + 8*0.001 ? 1.2

Multiply:

0.3 + 0.04 + 0.008 ? 1.2

0.348 < 1.2

One and two tenths is larger

Time required to cut a [tex]25[/tex] foot log into [tex]5[/tex] sections is equal to [tex]12[/tex] minutes as per given condition.

" Time is defined as the duration required to complete something. It is a measurable period with some definite or indefinite action."

According to the question,

Time required to cut a log [tex]=3[/tex] minutes

Length of a given log [tex]=25[/tex] foot

Length of each section to be cut [tex]= 5[/tex] foot

Number of section cut from given log [tex]= \frac{25}{5}[/tex]

                                                               [tex]=5[/tex] logs

As shown in the diagram,

Number of log Bob has to cut to get [tex]5[/tex] logs [tex]= 4[/tex]

Time required to get [tex]5[/tex] logs [tex]= 3\times 4[/tex]

                                              [tex]= 12[/tex] minutes

Hence, time required to cut a [tex]25[/tex] foot log into [tex]5[/tex] sections is equal to [tex]12[/tex] minutes as per given condition.

Learn more about time here

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Answer:

Option d

Volume of the prism is, 2184 cubic inches

Step-by-step explanation:

Since this figure represents the rectangular prism;

from this figure; we have

Length of rectangular Prism [tex](l)[/tex] = 13 in

Width of rectangular Prism (w)= 14 in

and height of rectangular Prism (h) = 12 in

Now, we  can determine the volume of a rectangular prism by either multiplying the area of the base times the height or by multiplying the length, width and height.

i.e, [tex]V = A \cdot l[/tex] cubic unit where A is the area of the rectangular prism and [tex]l[/tex] is the length respectively or

[tex]V = l\cdot w \cdot h[/tex]

⇒ [tex]V = 13 \cdot 14 \cdot 12[/tex] cubic inches

Simplify we get,

[tex]V = 2184[/tex] cubic inches

Therefore, the volume of the prism is,  2184 cubic inches

Answer:

17.4 inches

Step-by-step explanation:

The mean is the average of all the numbers listed in the set. In order to find the mean you must add up all the numbers in the set and divide it by the number of numbers in the set.

Answer: C

Step-by-step explanation:

If you add up all of the numbers, then divide by how many numbers there are, you find the mean.

In this Question, you add 11,15,19,17,23,20,17,13,18, and 21. You get 174 as the answer. You divide by 10 and get 17.4. C is the answer.

The sales price is 35%.

Who needs a kite that big? Anyways, to get the area of the kite you would multiply it's dimensions together:

9.2 x 8 = 73.6 feet