a plumber has 6 1/3 feet of piping she needs 75 inches of piping does she have enough

The annual interest rate is 7.5%.

What is Simple interest?

Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.

The formula for simple interest is:

I = P × r × t

where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.

In this case, we know I = $562.50, P = $1500, and t = 5 years.

we ca substitute values into the formula,

562.50 = 1500× r ×5

Simplifying, we get:

r = 562.50 / (1500 ×5)

r = 0.075

r = 7.5%

Therefore, the annual interest rate is 7.5%.

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To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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In order to simply construct a histogram, we require additional data and the range is excessive here.

The lowest and highest valleys for this set of data are 191 and 646, respectively. Therefore, the range is excessive here. However, the total number of data, in this case, is only 2468, or ten numbers. Therefore, only N is 10 is provided. That indicates that the question contains 10 data. Therefore, we are unable to create a histogram for this data.

In the given number of data, which is too little and too close to causing a disaster. He still possesses him. Therefore, in order to simply construct a histogram, we require additional data. But with these 10 pieces of data, this is impossible. Additionally, the range is extremely wide, allowing us to construct a histogram for this question.

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Complete Question:

Listed below are blood platelet counts (1000 cells/ uL ) randomly selected from adults in the United States. Why does it not make sense to construct a histogram for this data set?

191 286 263 193 193 215 162 646 250 386

Complete Question: Which of the following is an example of the difference of two​ squares?

A x² − 9

B x³ − 9

C (x + 9)²

D (x − 9)²

Answer:

A. \( x^2 - 9 \).

Step-by-step explanation:

An easy way to spot an expression that is a difference of two squares is to note that the first term and the second term in the expression are both perfect squares. Both terms usually have the negative sign between them.

Thus, difference of two squares takes the following form: \( a^2 - b^2 = (a + b)(a - b) \).

a² and b² are perfect squares. Expanding \( (a + b)(a - b) \) will give us \( a^2 - b^2 \).

Therefore, an example of the difference of two squares, from the given options, is \( x^2 - 9 \).

\( x^2 - 9 \) can be factorised as \( x^2 - 3^2 = (x + 3)(x - 3) \).

Answer:

Step-by-step explanation:

-15-9 = -24

I would think about it as adding 15 and 9, but just make the answer negative.

The total area is 376 square feet. The rectangle portion has an area of 120 square feet. That leaves 376-120 = 256 square feet for the square portion.

So we can say the following:

\(\text{x}^2 = 376 - 120\\\\\text{x}^2 = 256\\\\\text{x} = \sqrt{256}\\\\\text{x} = 16\\\\\)

Or a slight variation is this

\(\text{x}^2 = 376 - 120\\\\\text{x} = \sqrt{376 - 120}\\\\\text{x} = \sqrt{256}\\\\\text{x} = 16\\\\\)

The side length of the square portion is 16 feet.

Composing f(x)=2x-8 and g(x)=1/2x+4 results in the identity function, f(g(x)) = x.

To compose the two functions, we substitute g(x) into f(x) in place of x:

f(g(x)) = 2(g(x)) - 8

= 2(1/2x + 4) - 8

= x + 8 - 8

= x

Therefore, composing the two functions results in the identity function, f(g(x)) = x.

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Answer:

m∡x = 95°

m∡y = 147°

m∡z = 128°

Step-by-step explanation:

m∡z = 180-52 = 128

measure of third angle in left triangle = 180-(45+50) = 85°

m∡x = 180-85 = 95°

measure of top angle in right triangle = 180-(95+52) = 33°

m∡y = 180-33 = 147°

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

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

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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The solution is, f(x) = 7 is a even function.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

Solution:

Given that we have to find the even function

A function is even if and only if f(–x) = f(x)

Steps to follow:

Replace x with -x and compare the result to f(x).

If f(-x) = f(x), the function is even.

If f(-x) = - f(x), the function is odd.

If f(-x) ≠ f(x) and f(-x) ≠ -f(x), the function is neither even nor odd.

now,

Option 4

f(x) = 7

f(-x) = 7

Thus f(-x) = f(x)

Thus it is a even function.

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Answer:

5<n+12=2?

is

5<n=2?

Step-by-step explanation:

+12-12=0

left with 5<n=2

An equation is formed of two equal expressions. The solution of "The quotient of 5 less than a number and 12 is 2" is 29.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given statement can be converted to an equation as shown below,

Solving the equation,

(x-5)/12=2

x - 5 = 2 × 12

x - 5 = 24

x = 24 + 5

x = 29

Hence, the solution of "The quotient of 5 less than a number and 12 is 2" is 29.

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Answer:

y = 700x - 8

Step-by-step explanation:

Answer:

6(7+4) is correct.

Step-by-step explanation:

answer each problem one by one. for the first one, 8(5+3), 8 times 5 is 40. you need 42, not 40. for the second one, 6(7+4), 6 times 7 is 42. 6 times 4 is 24. this problem simplified is 42+24. so that one is correct. but still, study every problem to understand. 4(10+6) is the third problem. 4 times 10 is 40. not correct. 14 times 3 is 42. that is correct so let's see where this problem leads to. 14 times 2 is 28. not correct. therefore, 6(7+4) is correct.

The required, example of being "underwater" on a car is option B, owing $8600 on a car that's worth $8200.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

Here,
Being "underwater" on a car means owning more on a car than it is currently worth.

Based on the given options, the example of being "underwater" on a car is option B, owing $8600 on a car that's worth $8200.

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Answer:

Step-by-step explanation:

If we are looking for the ratio of the area of the inner square to the area of the outer square, that means that we need the areas of each of these squares, and we need to find the areas without any numbers. But that's ok; the answer they want is not a number answer. The answer will have a's and b's in it instead of numbers.

First the area of the inner square. Here we go:

Look at the triangle in the lower left corner of this coordinate plane. It is a right triangle. The height of it is b. That's because the height is a "y" thing and the y-coordinates of each of those sets of coordinates is b and 0. The height is then b - 0 = b.

The length of the base is a - b. That's because the length is an "x" thing and the x-coordinates of each of those sets of coordinates is (a - b) and 0. The length is then a - b - 0 = a - b.

Now we need the length of the hypotenuse which also serves as one of the sides of the inner square. Using Pythagorean's Theorem, we can find the length of the hypotenuse, which I will label as "?":

\(?^2=b^2+(a-b)^2\) and

\(?^2=b^2+a^2-2ab+b^2\) and

\(?^2=a^2-2ab+2b^2\) so

?, the length of the hypotenuse, is

\(?=\sqrt{a^2-2ab+2b^2}\) and now we can use that to find the area of the inner square. The formula for a square's area is

\(A=s^2\) so

\(A=(\sqrt{a^_2}-2ab+2b^2})^2\) which gives us finally:

\(A=a^2-2ab+2b^2\) **

Now for the outer square. Those blue triangles you see are all congruent. We can use the side lengths for the triangles we found above to find the length of a side of the outer square. One side of the outer square is made up of one base length of these triangles and one height. We found the base length to be (a - b) and the height to be b; therefore, the length of one side of the outer square is b + (a - b) which is just "a". That's is, just a length of "a". The area is found by multiplying this side length by itself, so the area of the outer square is

A = a²

The ratio of the area of the inner to the outer is:

\(\frac{A_i}{A_o}:\frac{a^2-2ab+2b^2}{a^2}\) and that does not reduce.

Answer:

A

Step-by-step explanation:

Edmentum

The numeric values for this problem are given as follows:

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

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The solution is:

If my parents are going to pay the 5%, then, they will pay: $2979.

I will need to save $62.06 each month to accomplish my goal.

Here,

I'm going to a 4-year college that will cost $14895/year.

It means that I will need to pay: 14895*4 = $59.580

If my parents are going to pay the 5%, then, they will pay: $2979.

Now, if I want to save my total contribution for all four years, and I have four years to accomplish  the goal, then:

Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.

Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.

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complete question:

You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.

How much do you need to pay for each year of attending?

If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?

The equivalent speed in still water to achieve the actual speed is 27.172 km/h

Given data ,

The boat's velocity vector in still water will have two components: one along the north direction (opposite to the current) with magnitude "v" km/h, and one along the northwest direction (due to the current) with magnitude 4 km/h.

Since the boat is moving in a direction that is 45 degrees between north and northwest, we can use trigonometry to find the component of velocity in the northwest direction. By using the cosine of 45 degrees, we get:

Component of velocity in northwest direction = 4 km/h x cos(45 degrees) = 4 km/h x 0.707 = 2.828 km/h

Now , adding the components of velocity in the north and northwest directions should result in a speed of 30 km/h, which is the real speed needed to go through still water.

v + 2.828 = 30

v = 27.172 km/h

Hence , the equivalent speed of the boat in still water to achieve an actual speed of 30 km/h is approximately 27.172 km/h

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The perimeter of the smaller figure among the two figures with similarity ratio of 4:3 is 18cm.

A ratio is a number that allows one quantity to be expressed as a fraction of another quantity. Two numbers in a ratio can only be compared if they have the same units. Use ratios to compare two things.  

The similarity of two similar shapes is the ratio of each pair of corresponding sides. Simply put, when two figures are found to be similar, all pairs of corresponding sides have the same proportions. 

According to the information:

Perimeter of larger figure= 24cm

Let, perimeter of smaller figure be "x"

So,

4:3 = 24/x

4/3 = 24/x

⇒x = (24 x 3)/4

⇒x = 72/4

⇒x = 18

Thus the perimeter of smaller figure is 18cm.

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Given:

The geometric sequence 3,6,12,24.

Required:

Find the 6th term of the geometric sequence.

Explanation:

The given sequence is 3,6,12,24.

The nth term of the sequence is given by the formula:

Where a = first term and r = common ratio

From the given sequence

a = 3, r = 6/3 = 2

Then 6th term is:

Final answer:

The first option is the correct answer.

The angle of sinθ between the horizontal vector (1, 0) and the slant vector (15/17, -8/17) is sin⁻¹(8/17), which is approximately 29.11 degrees.

To find the angle of sinθ between a horizontal vector and a slant vector, we can use the dot product formula:

a · b = |a| |b| cos(θ)

where a and b are vectors, |a| and |b| are their magnitudes, and theta is the angle between them.

In this case, the horizontal vector is (1, 0) and the slant vector is (15/17, -8/17).

The magnitude of the horizontal vector is 1, and the magnitude of the slant vector is:

|b| = sqrt((15/17)² + (-8/17)²) = sqrt(225/289 + 64/289) = sqrt(289/289) = 1

The dot product of the two vectors is:

a · b = (1)(15/17) + (0)(-8/17) = 15/17

So we have:

15/17 = (1)(1) cos(θ)

cos(θ) = 15/17

To find sin(θ), we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

sin²(θ) = 1 - cos²(θ) = 1 - (15/17)² = 64/289

Taking the square root of both sides, we get:

sin(theta) = sqrt(64/289) = 8/17

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Answer:

The answer is 243 patches.

Step-by-step explanation:

Area of a rectangular piece of fabric = 15 × 9 = 135 cm²

Area of 27 pieces of fabric = 135 × 27 = 3645 cm²

Number of patches can be cut from = 3645 ÷ 15 = 243

Answer:

5,000

Step-by-step explanation:

=10÷2[500÷5{6+4}

=10÷2[500÷5×10]

=10÷2[100×10]

=10÷2×1000

=5×1000

=5000

Answer:

£1,616.2

Step-by-step explanation:

1,496 - 149 = 1347

1347 + 269.20 = 1616.2

Answer:

B. -3d + 47.25

Step-by-step explanation:

Each of them has $15.75

Each spent $d

Amount each still has = 15.75 - d

Therefore, total amount the 3 of them has = 3(15.75 - d) = 3*15.75 - 3*d

= 47.25 - 3d

Which is also am equivalent of -3d + 47.25

Answer:

y = -12x - 43

Step-by-step explanation:

"slope-intercept form" looks like y = mx + b.

We are given m = -12 and a point on the line which is (4, -5).

Substituting 4 for x, -5 for y and -12 for m, we get:

-5 = -12(4) + b.  Then b = -43, and the desired equation is y = -12x - 43.

Two ways we use rate out of class

Two ways we use percentages outside of class

Interest rates: Interest rates are used in financial transactions such as loans, mortgages, and investments. Understanding interest rates is important to make informed decisions about borrowing money or investing in stocks and bonds.

Exchange rates: Exchange rates are used when converting one currency into another. They affect international trade, travel, and investment. Understanding exchange rates is important for businesses and individuals who deal with international transactions.

Discounts and sales: Percentages are commonly used in advertising to promote discounts and sales. Understanding percentages is important to evaluate whether a discount or sale is a good deal or not.

Tax rates: Tax rates are expressed as a percentage of income or value of goods and services. Understanding tax rates is important for individuals and businesses to calculate their tax obligations and make informed financial decisions.

Understanding rates and percentages is important because they are used in many real-world situations. Knowing how to calculate and interpret rates and percentages can help individuals make informed decisions related to personal finance, investments, and business transactions. It also helps individuals understand and evaluate advertisements and government policies that involve rates and percentages.

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