Which of the following is equal to the fraction below?
(4/5)^6


A. 6(4/5)

B. 4^6/5

C. 4^6/5^6

D. 24/30

If a and b are positive integers such that a^3b = x and a^b = y then x/y² is solved to be y

The problem is solved by simplifying and substitution

Simplifying the expression a^3b = x and a^b = y will result to

a^(b3) = x and a^b = y

y^3 = x

substituting y^3 = x into the equation x/y²

= x / y²

= y³ / y²

apply power rule

= y³ ⁻ ²

= y

hence the solution of the equation x/y² while considering that a^3b = x and a^b = y will result to a solution of y

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Answer:

The expression below, 4x=20 when x=5.

Step-by-step explanation:

4(5)=20

Answer:

Part 1

[tex]\boxed{r = 8.9 \;cm}[/tex]

Part 2

[tex]\boxed{SA=995.4\;cm^2}[/tex]

Step-by-step explanation:

If r is the radius of a sphere

Volume of a sphere:
[tex]V = \dfrac{4}{3}\pi r^2[/tex]

Surface Area
[tex]SA = 4\pi r^2[/tex]

Part 1
We are given volume = 3,000 cm³

Setting this to volume to the equation for volume gives
[tex]3000 = \dfrac{4}{3} \pi r^3\\\\[/tex]

Multiplying both sides by 3/4 yields

[tex]\dfrac{3}{4}\cdot 3000 = \pi r^3\\\\2250 = \pi r^3\\\\r^3 = \dfrac{2250}{\pi}\\\\r^3 \approx 716.1972\\\\\\r = \sqrt[3]{716.1972} \\\\r = 8.947\\\\\\\textrm{Rounded to the nearest tenth:}\\\\\boxed{r = 8.9 \;cm}\\\\\text{(Answer\;Part 1)}\\[/tex]

Part 2

Using r = 8.9 cm we can compute the surface area SA using the formula for surface area

[tex]SA = 4\pi r^2\\\\SA = 4\pi (8.9)^2\\\\SA = 995.38\;cm^2\\\\\textrm{Rounded to the nearest tenth:}\\\\\boxed{SA=995.4\;cm^2}\\\\\textrm{(Answer Part 2)}[/tex]

The area of a triangle with the base of 7 cm and the height of 12 cm is 42 square cm.

In the given question we have to find the area of a triangle with the base of 7 cm and the height of 12 cm.

The entire area bounded by a triangle's three sides is referred to as the triangle's area. In essence, it equals half of the base times height, or A = 1/2bh. So, in order to calculate the area of a triangular polygon, we need to know its base (b) and height (h).

Area of Triangle = 1/2 ×b×h

Area of Triangle = 1/2 ×7×12

Area of Triangle = 7×6

Area of Triangle = 42 square cm

Hence, the area of a triangle with the base of 7 cm and the height of 12 cm is 42 square cm.

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The zero of the polynomial 3x² - 8x + 5​ is x=1 and x= 5/3

A Polynomial is an expression of two or more than two algebraic terms having different exponential powers on the same variable in different terms. An example of a polynomial can be  4x∧3+5x∧2+2x+1=0

The zeroes of polynomials are all the values for the variable that gives the solution of the equation as zero. There are three types of roots real and distinct, equal roots, and non-real roots.

Polynomial is in the form a[tex]x^{2}[/tex]+bx+c=0

where a=3,  b=8 , c=5

b∧2-4ac= 64-4 x 3 x 5 = 4

since b∧2-4ac>0 gives real and distinct roots

now, 3x² - 8x + 5​

=(3x^2-3x)+(-5x+5)

=3x(x-1)-5(x-1)

=(3x-5)(x-1)

∴x-1=0

x=1

and 3x-5=0

x=5/3

Therefore the roots of the equation are 1, 0 and 5/3

The correct question is Which of the following is a zero of the polynomial 3x² - 8x + 5? 0 or 112

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The 10 examples of substitutes good and services are :

Similar products that a client may employ for the same purpose are substitute goods. If the product they prefer is offered, your customers might buy it, but they might also look at alternatives if the price, the product's availability, or its quality changes. The demand for an item is frequently affected by these changes as well.

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The number of books Sophia and her brother read is 32 and 8 respectively.

Given that,

The total number of books = 40 books

The number of books Sophia read = 4[The number of books Sophia's brother read]

Assuming that the number of books Sophia's brother read = a

So, the number of books Sophia read = 4a

Thus,

a + 4a = 40

Solving the equation further, we get:

5a = 40

a = 8

The number of books Sophia's brother read = 8 books

Hence, the number of books Sophia read = 32 books

Therefore, The number of books Sophia and her brother read is 32 and 8 respectively.

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The seconds will take to print the sport rep is 10 seconds.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given

Periodical Express is a newspaper printing company. They printed 450 copies of The Informer in just 15 seconds.

They next need to print 300 copies of the Sport Report.

If they print at the same rate

Let the number of seconds be x .

so ,

for 450 copies it takes 15 seconds .

than for 300 copies it takes x seconds

than x = 300 * 15 / 450

x = 10

Hence the seconds will take to print the sport rep is 10 seconds.

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The equation [tex]7x-2x^{2} =0[/tex] is said to be a quadratic equation as the highest degree is 2.

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no other term which is raised to a higher power than 2.

The given equation is [tex]7x-2x^{2} =0[/tex].

As we know that, a quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

On comparing equation [tex]7x-2x^{2} =0[/tex] with standard form of quadratic equation [tex]ax^{2} +bx+c=0[/tex], we get, a = -2, b = 7,c = 0.

Thus, the equation [tex]7x-2x^{2} =0[/tex] is a quadratic equation.

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Therefore , the solution of the given problem of fraction comes out to be  20  bald eagles are there.

Any quantity of equal portions, or fractions, can be used to represent a whole. In standard English, the quantity of a specific size is stated as a fraction. 8, 3/4. Wholes also include fractions. In mathematics, numbers are represented as the numerator to denominator ratio. These are each integers in simple fractions. There is a fraction in the fraction or denominator of a difficult fraction. Because numerators and numerator and denominator of real fractions differ from one another. A fraction is a total that represents a portion of a whole. By dividing the whole to smaller components, you can assess it. For instance, 12 is employed to denote half of a number.

Here,

You'd get 18 osprey if: a. 2:3 b. 2/3 = 12/x; 

cross multiplying 2x would give you 36 x.

c. You'd have 20 bald eagles if you took the ratio of 2/3 to x/30 and multiplied it by three.

=>2/3 =x/30

=>x = 2*30/3

=> x =20

Therefore , the solution of the given problem of fraction comes out to be  20  bald eagles are there.

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Answer:

5, 0, Undefined.

Step-by-step explanation:

Answer:

1) 5

2) 0

3) Undefined

Slope is a measure of steepness of a line. In Algebra 1, It is how much the y-value changes when the x-value increases by 1.

y-intercept is the y-value of the line when it intersects with the y-axis, or the y-value of the line when the x-value of the line is 0.

This form is the most common form for expressing linear equations for graphing and is used when the slope and y-intercept is known.

Form

y = mx + b

Lets break it down. y and x stay as a variable when graphing is it only substituted for a constant when solving for x-intercept, etc.

m is the slope.

b is the y-intercept.

Q1

y = mx + b

y = 5x

Because 5 is the m value, the slope is 5.

Q2

y = mx + b

y = 3

Think about it. What cancels out any real value? Multiplying it by 0. If there is no coefficient behind the x, it means the slope is 0.

y = 0x + 3 = y = 3

Because 0 is the m value, the slope is 0.

When y is equal to a constant after solving, it is a horizontal line with the y-intercept of the constant it is equal to (in this case 3).

Q3

y = mx + b

x = 5

The slope is undefined.

When x is equal to a constant after solving, it is a straight vertical line with the x-intercept of the constant it is equal to (in this case 5). The slope is always undefined.

The equation of the line in slope intercept form is y = 1 / 2x - 9 / 2.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the slope of the line is 1 / 2 and the line passes through (5, -2).

Hence,

y = 1 / 2 x + b

let's find the y-intercept using (5, -2)

Therefore,

-2 = 1 / 2 (5) + b

b = -2 - 5 / 2

b =  -4 - 5/ 2

b = -9 / 2

Therefore, the equation of the line is y = 1 / 2x - 9 / 2

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The future value of Joshua's account in 2 years, given the deposits and the interest, is $ 2, 108.21

The fact that the amount that Joshua Levine deposits is a constant amount of $ 250, makes it an annuity. It is ordinary because it is deposited at the end of the period.

To find the value of this annuity, first find the periodic interest :

= 6 % / 4 quarters per year

= 1 . 5 %

Then find the number of periods :

= 2 years x 4

= 8 quarters

The future value is:

= Annuity x Future value interest factor, 8 periods, 1. 5%

= 250 x 8.4328391063537

= $ 2, 108.21

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The tennis ball's initial height is 19 feet.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, a tennis ball is dropped from a certain height.

Its height in feet is given by h = -16t²+19 where t represents the time in seconds after launch.

Initial height is 0

-16t²+19 =0

16t²=19

t²=19/16

t=√(19/16)

t=√1.1875

t=1.089 seconds

So, the initial height is 19

Therefore, the tennis ball's initial height is 19 feet.

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Answer:

true

Step-by-step explanation:

i think

False, while co-authoring in Excel enables collaboration and real-time editing, it may not support all advanced features and functionalities available in a single-user environment.

In a co-authoring environment, where multiple users collaborate on an Excel document simultaneously, not all Excel features are supported. While many basic features and functions can be used in a co-authoring setting, certain advanced features may not be fully compatible or functional.

Co-authoring in Excel typically supports common features such as data entry, formatting, basic calculations, and simple formulas. However, features that involve complex dependencies, extensive macros, advanced charts, or specialized add-ins may not function as expected or may be disabled in a co-authoring scenario.

It's important to note that the specific features supported in a co-authoring environment can vary depending on the version of Excel being used, the collaboration platform, and any restrictions or limitations set by the administrator or hosting service.

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Answer:

|5 -4|

| |

|9 -3|

Step-by-step explanation:

The measure of angle x is 57.5 degrees. The measure of angle y is 122.5 degrees. The correct option is C.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

The measures of two supplementary angles total 180 degrees.

The measure of angle y is 65 degrees less than the measure of angle x.

Let the measure of angle y is m∠y.

And the angle measure of x is m∠x.

So,

m∠x + m∠y = 180°   {equation 1}

And according to the question,

m∠y = m∠x - 65°        {equation 2}

Substituting the value from equation 2 to equation 1,

2m∠x = 180 + 65

m∠x = 245/2

m∠x = 122.5°

And m∠y = 122.5 - 65

m∠y = 57.5°

Therefore, the angle measures are m∠x = 122.5° and m∠y = 57.5°.

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We can start solving the problem by using algebra. Let x be the total length of the movie in minutes. Then we know that:

1/3 of the movie is x/3 minutes.

1/5 of the movie is x/5 minutes.

We are told that Joshua watched 1/3 of the movie in the morning and had 1/5 of the movie left to watch at night. Therefore, we can set up the equation:

x/3 + y = x/5, where y is the length of the movie that Joshua watched at night.

We can then solve for y by isolating it on one side:

y = x/5 - x/3

We know that 1/3 + 1/5 = 8/15.

We can simplify by multiplying both sides of the equation by 15:

y = (8/15)*x = 8x/15

We can conclude that Joshua watched 8/15 or approximately 53.33% of the movie at night.

Answer: I don't get it, there aren't  any numbers

Step-by-step explanation:

The statement that is correct based on the data will be B. The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela. This was Illustrated as:

1/8 = 3/24 = 4/32

The correct option is B.

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Answer:

the person above me is incorrect I took the test and redid it and the correct answer is D

The given statement justifies the additive property of equality.

When the same quantity is added to both sides of an equation, the equation remains true, which is known as the addition property of equality. One of the basic characteristics of equality in mathematics, it is also highly significant.

Equations are solved using the addition condition of equality.

The additive property of equality states that:

If a=b and c=d, then.

a+c = b+d.

The given statement also depicts the additive property.

Hence, the prove statement depicts the additive property of equality.

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Answer: In math, the number 2 is called a "natural number" or "integer." It is the first positive even number and the second positive number in the set of natural numbers (1, 2, 3, 4, ...). The number two is also a base of the binary numeral system, which is used in computer science.

Step-by-step explanation:

Answer: To solve a 3-step equation, you can follow these steps:

Simplify both sides of the equation, if necessary, by combining like terms.

Isolate the variable on one side of the equation.

Use inverse operations to solve for the variable.

Check your solution by substituting it back into the original equation.

Example:

Solve for x: 2x + 5 = 11

Subtract 5 from both sides of the equation: 2x = 6

Divide both sides of the equation by 2: x = 3

Check your solution by substituting x = 3 back into the original equation: 2(3) + 5 = 11

The solution is x = 3.

It's important to note that a 3-step equation is not a specific term, it just means an equation that can be solved in 3 steps. It can be a linear equation or quadratic equation or any other type of equation.

Step-by-step explanation:

Based on the box plot concept and the available options, the box plot that correctly represents the data is option A.

Box plot is a term that is used to describe the box and whisker plot which shows the five-number summary of a set of data.

Generally, this five-number summary is the minimum, first quartile, median, third quartile, and maximum.

Make a box plot of the data.

Let's make a box plot for the same dataset from above.

Step 1: Scale and label an axis that fits the five-number summary.

Recall that Q1 = 54, the median is 58, and Q3 = 62

Also, the min is 52 and the max is 64.

Therefore, when we draw the box from Q1 to Q3 and from Q1 to the min, and from Q3 to the max, we have option A as the answer.

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The percent equivalent to 66 over 165 is 40%.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

We have to calculate the percent of the numbers 66 over 165.

First divide 66 with 165. The multiply with 100 to get the required percentage.

(66 / 165) × 100 = 0.4 × 100 = 40%

Hence the required percentage is 40%.

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The probability that a randomly selected point within the circle falls in the red shaded area is the fraction 7/11.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

total possible outcome is the area of the circle

the required outcome is the area of the square

area of the circle = (22/7)(4)²

area of the circle = (22/7)(16)

area of the circle = 352/7

area of the square = (4√2)²

area of the square = (4√2)(4√2)

area of the square = 16 × 2

area of the square = 32

probability a randomly selected point within the circle falls in the red shaded area is calculated as follows;

32/(352/7)

changing division to multiplication

32 × 7/352

32 is a factor of 352 and can cancel out

1 × 7/11

7/11

Therefore, the probability a randomly selected point within the circle falls in the red shaded area is 7/11.

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The weekly pay of Howard as an assistant pharmacist in Rockville recruitment is $984.66

The payment for the recruitment agency job = $51,200

The agency fees = 40% of the first three week's pay

Howard's weekly salary can be found using the formula,

                W = A / N

where W is the weekly salary

           A is the annual salary

           N is the number of weeks

Let us substitute the known values in the above equation, we get

              W = 51,200 / 52 [ Total no. of weeks in one year will be 52 weeks]

                   = $984.66

Thus, his weekly pay for Howard as the recruitment agency job is $984.66

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The full question is

The Rockville Employment Agency just placed Howard Jacobson in a job as a junior pharmacist. The job pays $51.2k. The agency fee is equal to 40% of the first three weeks' pay. What is Howard's weekly salary to the nearest cent?

To solve inequalities in 9th grade:  simplify the algebraic expressions by combining like terms and isolating the target variable, then applying the mathematic operators.

Inequalities is taught in 9th grade. To solve the inequality:

-  First, simplify the expression: open the parentheses of algebraic expression, combine the terms like, and isolate the target variable.

- Use mathematic operators such as: addition, subtraction, multiplication, and division. All mathematic operations must be done on both sides. Addition and subtraction do not change the inequality. Multiplication and division with positive numbers will not change the inequality.

Multiplication and division with negative numbers will change the sign of the inequality.

Example:

Solve the inequality: 3(x + 2)  <  7x - 18

Step 1: Open the parentheses.

3(x + 2)  <  7x - 18

⇔ 3x + 6 < 7x - 18

Step 2: Subtract both sides with 7x and 6, this operation does not change the inequality sign

3x + 6 - 7x -6 < 7x - 18 - 7x - 6

-4x < -24

Step 3: Divide both sides with (-4). Since we divide with negative numbers, flip the inequality sign.

-4x/(-4) > -24/(-4)

x > 6

Hence, the solution is x > 6

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Answer:

First, we need to simplify the expression by combining like terms. We have -4 + 3x^2-3 and -1. We can combine the like terms -4 and -1 to get -5.

Now, the expression can be rewritten as -5 + 3x^2-3. Next, we need to use the order of operations to evaluate the expression. The first step is to simplify any terms within parentheses, so we simplify 3x^2-3 to 3x^2-3 = 3x^2-3.

Now, the expression can be rewritten as -5 + 3x^2-3. The next step is to perform any multiplication or division, so we multiply 3 with x^2 to get 3x^2.

The expression is now -5 + 3x^2. The last step is to perform any addition or subtraction, so we add -5 and 3x^2 to get 3x^2-5.

Therefore, the answer to the expression is 3x^2-5.