Which expression is equivalent to square root a^7

Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

9514 1404 393

Answer:

  8 employees, $24,000 in monthly profit

Step-by-step explanation:

We are given ...

Then for x=8 and y=24, the interpretation is ...

  for 8 employees, the monthly profit is $24,000

Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Answer:

5AB + 40 = +2

Step-by-step explanation:

IN FIRST BLANK (5AB)

SECOND BLANK (40)

Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

Answer:

116,031 about

Step-by-step explanation:

Answer:

20,211

Step-by-step explanation:

Use the correct order of operations, and do one step at a time.

12 x 12/12 x 12 x 12 x 12 - 777 + 21 x 12 x 12/12 =

= 144/12 x 12 x 12 x 12 - 777 + 252 x 12/12

= 12 x 12 x 12 x 12 - 777 + 3024/12

= 144 x 12 x 12 - 777 + 252

= 1728 x 12 - 777 + 252

= 20,736 - 777 + 252

= 19,959 + 252

= 20,211

9514 1404 393

Answer:

  x = 14°

Step-by-step explanation:

There are two ways you can go at this.

1) an exterior angle is equal to the sum of the remote interior angles

  124° = (2x) +(180° -6x)

  -56° = -4x

  x = 14°

__

2) sum of exterior angles is 360°

  124° +6x +(180° -2x) = 360°

  4x = 56°

  x = 14°

The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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Answer: If a person needs roughly 2,100 to 2,400 calories per day, and they eat a treat that has 1,100 calories, they should consume 1,000 to 1,300 fewer calories for the rest of the day. This is because the body will only be able to process so many calories at once, and any excess calories will be stored as fat.

It is important to note that this is just a general guideline. The number of additional calories that a person should consume after eating ice cream will vary depending on their individual metabolism and activity level. If you are unsure how many calories you should be consuming, it is always best to speak with a registered dietitian.

Here are some tips for eating ice cream without sabotaging your weight loss goals:

* Choose lower-calorie options. There are many ice cream brands that offer lower-calorie options, such as light ice cream and frozen yogurt.

* Eat smaller portions. Instead of eating a whole pint of ice cream, try eating a half-cup or a single-serve container.

* Add healthy toppings. Instead of piling on the toppings, try adding healthy options like fruit, nuts, or granola.

* Enjoy your ice cream! Don't feel guilty about eating ice cream every once in a while. Just be sure to make it part of a balanced diet.

a) The terminal point is 0.896 radius length.

b) The value returned is -0.896.

We have,

The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)

a. Since the circle's radius is 3 units long, we divide the x-coordinate by 3:

x-coordinate of terminal point: -2.69

Number of radius lengths to the right: -2.69 / 3 ≈ -0.896

However, since the angle is measured from the 3-o'clock direction, we consider it to be in the clockwise direction.

Thus, the number of radius lengths to the right is

Number of radius lengths to the right: -(-0.896) = 0.896

Therefore, the terminal point is 0.896 radius length.

b. Using Trigonometry

cos(h) = x-coordinate of terminal point / radius length

cos(h) = -2.69 / 3 ≈ -0.896

c. As, θ = h. From the given information, we have:

θ ≈ -0.896 radians

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Answer:

303.75

Step-by-step explanation:

135/20=6.75

6.75•45= 303.75

The next step of the valid proof is that AE = CE because of the perpendicular bisector theorem.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from the endpoints of the line segment on which it is drawn.

In this case, Julia is using this figure to prove that triangle ABC is an isosceles triangle. After the steps given, the next step will be to indicate that AE = CE because of the perpendicular bisector theorem.

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Answer:

AC = BC  because of the perpendicular bisector theorem

Step-by-step explanation:

I got it right on the test

Answer:

C

Step-by-step explanation:

The answer is C because a rational number is a number that doesn't go forever, and an integer is a positive or negative whole number. For example, 3.5 is rational but not an integer. So, the correct answer is C, and I hope it helps!

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

laverne because he had less times so if u subtract 23 by 31 and 37 by 46 laverne has more

Answer: Marcus is the better hitter

===========================================================

Explanation:

We'll need to compute batting averages for each player.

To compute the batting average, we divide the number of hits over the number of at bats.

For Marcus, his batting average is 37/46 = 0.804 approximately.

Laverne on the other hand has a batting average of roughly 23/31 = 0.742

We see that Marcus has the better batting average because 0.804 is larger than 0.742; it's similar to saying how 804 is larger than 742.

Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

11. Angle KEF = 40°, Angle KEJ = 50°

12. Angle HEF = 115°, Angle KED = 140°

13. Angle JEF = 90°, Angle KEF = 90°

14.   Angle DEF = 180°

The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.

11.  Acute angles: Those angles are less than 90 degree angles.

     Angle KEF = 40°

     Angle KEJ = 50°

     Angle KEH = 75°

     Angle JEH = 25°

     Angle HED = 65°

12. Obtuse angles: Those angles are more than 90 degree angles.

     Angle HEF = 115°

     Angle KED = 140°

13. Right angle: Those angles are 90 degree angle.

     Angle JEF = 90°

     Angle KEF = 90°

14. Straight angle: Those angles make 180 degree angle.

     Angle DEF = 180°

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Answer:

The value of the test statistic is \(t = -1.61\)

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Our test statistic is:

\(t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the expected mean, \(\sigma\) is the standard deviation and n is the size of the sample.

A publisher reports that 52% of their readers own a laptop.

This means that \(\mu = 0.52\)

Sample of 180:

Means that \(n = 180\)

By the Central Limit Theorem:

\(\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.52*0.48}{180}} = 0.0372\)

A random sample of 180 found that 46% of the readers owned a laptop.

This means that \(X = 0.46\)

Find the value of the test statistic.

\(t = \frac{X - \mu}{s}\)

\(t = \frac{0.46 - 0.52}{0.0372}\)

\(t = -1.61\)

The value of the test statistic is \(t = -1.61\)

Step-by-step explanation:

24-11=13

The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.

According to the problem, two equations can be set up:

If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:

A + n = 7(B - n)

If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:

A - n = 2(B + n)

We can rearrange these equations to make them easier to solve:

8n = 7B - A

3n = A - 2B

Setting these equal to each other, since they are both equal to 24n, gives:

21B - 3A = 8A - 16B

37B = 11A

A / B = 37 / 11

= 3. 36

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Answer:

b 150

Step-by-step explanation:

Answer:

But where are the rectangles??

Answer:

The answer is 2x + 1

Step-by-step explanation:

Divide : x+4/4+x

Any expression by itself eqauls 1 : x + 1 + x

Collect the like terms : x + 1 + x

Collect the like terms : 2x + 1

Final answer: 2x + 1

Step-by-step explanation:

Greetings !

Firstly, find the class-midpoints (X) to solve for the mean.

Thus, mid points of each classes are

\(5.15.25.35.45\)

Solve, for p using mean grouped data formula

\( \frac{5(3) + 15(4) + 25(p) + 35(3) + 45(2)}{3 + 4 + p + 3 + 2} = 24\)

multiply each values add them and solve for p.

\( \frac{15 + 60 + 25p + 105 + 90}{12 + p} = 24\)

make a cross multiplication

\(270 + 25p = 24(12 + p) \\ 270 + 25p = 288 + 24p\)

subtract 270 from both sides

\(270 + 25p - 270 = 288 + 24p - 270 \\ 25p = 24p + 18\)

subtract 24p from both sides

\(25p - 24p = 24p + 18 - 24p \\ p = 18\)

Also refer the attached image for further details

Hope it helps!

Answer:

There were 3 associates and 5 partners in the case.

Since a law firm is going to designate associates and partners to a big new case, and the daily rate charged to the client for each associate (A) is $ 500 and the daily rate for each partner (P) is $ 1000, and the law firm assigned a total of 8 lawyers to the case and was able to charge the client $ 6500 per day for these lawyers' services, to determine the equation that represents the total number of lawyers on the case, and to effectively determine these numbers, the following calculations must be made:

A + P = 8

500A + 1000P = 6500

1000 x 8 = 8000

8000 - 6500 = 1500

1500/500 = 3

3 x 500 + 5 x 1000 = 6500

Therefore, there were 3 associates and 5 partners in the case.

The function that satisfies the given conditions is f(x) = x+2x²+1, the correct option is 1.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

x →-∞, f(x) → ∞

x →∞, f(x) → -∞

Now,

Let's consider the end behavior of this function.

As x gets larger and larger (approaches infinity), the terms involving x² and x become much larger than the constant term 1. In other words, the function grows without bound as x approaches infinity. This is consistent with the given end behavior description: "as x approaches infinity, f(x) approaches infinity".

Now let's consider the end behavior as x approaches negative infinity. In this case, the dominant term in the function is -2x², since x² becomes very large as x approaches negative infinity. As a result, the function becomes very negative (large negative values) as x approaches negative infinity. This is consistent with the given end behavior description: "as x approaches negative infinity, f(x) approaches negative infinity".

Functions 2) and 3) do not satisfy the given conditions. Function 2) does not grow without bound as x approaches infinity or negative infinity, and function 3) does not approach infinity as x approaches infinity.

Therefore, the function will be f(x) = x+2x²+1.

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Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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Let x be the length of each of the equal sides of the isosceles triangle. Then the length of the base is x - 4. The perimeter of the triangle is the sum of the lengths of the three sides, which is:

x + x + (x - 4) = 3x - 4

We know that the perimeter is 32, so we can set 3x - 4 equal to 32 and solve for x:

3x - 4 = 32

Adding 4 to both sides gives:

3x = 36

Dividing by 3 gives:

x = 12

Therefore, one of the equal sides of the triangle is 12 inches long, and the length of the base is 12 - 4 = 8 inches.

So the three sides of the triangle are 12 inches, 12 inches, and 8 inches.

The correct equation to solve the problem is (C) 3x - 4 = 32.

Answer:

The expected number of boys a family might have is 2.5.

Step-by-step explanation:

Let X denote the number of boys in a family with 5 children.

The probability of a boy is, p = 0.50.

The child can either be a by or a girl independently.

The random variable X follows a binomial distribution with parameters n = 5 and p = 0.50.

The probability mass function is:

\(p_{X}(x)={5\choose x}(0.50)^{x}(1-0.50)^{5-x};\ x=0,1,2...5\)

Compute the expected number of boys a family might have as follows:

\(E(X)=\sum x\cdot p_{X}(x)\)

x                                      p (x)                                           x · p (x)

0       \(p(0)={5\choose 0}(0.50)^{0}(1-0.50)^{5-0}=0.03125\)          \(0\times 0.03125=0\)

1        \(p(1)={5\choose 1}(0.50)^{1}(1-0.50)^{5-1}=0.15625\)          \(1\times 0.15625=0.15625\)

2       \(p(2)={5\choose 2}(0.50)^{2}(1-0.50)^{5-2}=0.3125\)           \(2\times 0.3125=0.625\)

3       \(p(3)={5\choose 3}(0.50)^{3}(1-0.50)^{5-3}=0.3125\)           \(3\times 0.3125=0.9375\)

4       \(p(4)={5\choose 4}(0.50)^{4}(1-0.50)^{5-4}=0.15625\)         \(4\times 0.15625=0.625\)

5       \(p(5)={5\choose 5}(0.50)^{5}(1-0.50)^{5-5}=0.03125\)         \(5\times 0.03125=0.15625\)

Then,

\(E(X)=\sum x\cdot p_{X}(x)\)

         \(=0+0.15625+0.625+0.9375+0.625+0.15625\\\\=2.5\)

Thus, the expected number of boys a family might have is 2.5.