Write the radical expression [tex]\frac{8}{7\sqrt x^15}[/tex] in exponential form.

The value of the expression is found to be 1 0 when the value of x is equal to 2.

The expression provided to us is 5.x³/x² for x = 2.

Now, in order to evaluate this expression, we will follow the simple,

5.x³/x² = 5x.

First as we can see, x³ can be divided by x²and then we will get x as the outcome of the simple division operation,

So, we will get,

5x

Now, we have to put the value of x equal to 2 so that we get to know about the exact value of the expression,

x = 2,

= 5(2)

= 10

So, the value of the expression is found to be 10 when the value of x was 2.

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Complete question - Evaluate the expression 5.x³/x² for x equals to 2.

A relative frequency distribution for quantitative data identifies the proportion of observations that occur in each bin.

Relative frequency distribution is a type of frequency distribution that shows the proportion or percentage of observations that fall into each bin or class interval. It is calculated by dividing the frequency of each bin by the total number of observations. This allows us to compare the relative frequencies of different bins, and see how the data is distributed across the range of values.

For example, if we have 100 observations and 20 of them fall into the first bin, the relative frequency of the first bin would be 20/100 = 0.2 or 20%. This means that 20% of the observations fall into the first bin.

In summary, a relative frequency distribution for quantitative data identifies the proportion of observations that occur in each bin, allowing us to compare the relative frequencies of different bins and see how the data is distributed across the range of values.

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Answer:

[tex]\frac{9(7-\sqrt{2}) }{47}[/tex]

Step-by-step explanation:

The factor that represents the area of the yard that can be mowed is (225 - x²).

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The total area of the lawn is given by the formula -

Area of square lawn = (side length of square lawn)²

= (15 yards)²

= 225 square yards

The shed is also a square, with side length x yards.

So, the area of the shed is -

Area of square shed = (side length of square shed)²

= x²

To find the area of the yard that can be mowed, we need to subtract the area of the shed from the total area of the lawn -

Area of yard that can be mowed = Area of square lawn - Area of square shed

= 225 - x²

Therefore, the value is obtained as (225 - x²).

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Answer:

The perimeter of the new space used for the playground is 108 feet.

The perimeter of the space used for the new playground is 150 feet.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

The current space is rectangular and has a length of 24 feet and a width of 26 feet.

and, the new space is 36 feet long.

let the width of new space is x.

Since, the two space are similar then the scale factor will be

= 36/24 = 1.5

So, the width of new space = 1.5 x 26 = 39 feet

Thus, the Perimeter of new space

= 2(l +w)

= 2 (36+ 39)

= 150 feet

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Answer:

50% smaller

Step-by-step explanation:

Answer: $640

Step-by-step explanation:

100%-65%=35%

$224/35%=6.4

6.4*100%=$640

To check the solution

$640*65%=$416

$224+$416=$640

The extra income earned in monthly compounding is $142.04.

Compounding is defined as calculating interest on both the amount borrowed plus previous interest.

Given is that $10,000 is deposited into a savings account which is compounded monthly followed by compounded annually.

Annual compounding for 30 years -

Total money after annual compounding for 30 years -

T{A} = 10000 + (10000 x 0.023/1)^(30 x 1)

T{A} = $19,781.95

Monthly compounding for 30 years -

Total money after annual compounding for 30 years -

T{A} = 10000 + (10000 x 0.023/1)^(30 x 1)

T{A} = $19,923.99

Extra interest earned -

E = 19,923.99 - 19,781.95 = $142.04

Therefore, the extra income earned in monthly compounding is $142.04.

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The value of the mean excluding the outlier is 130. 5

An outlier can be defined as a data point that differs significantly or greatly from other observations.

It occurs as a result of;

From the information given, we have that;

121, 89, 410, 203, 55, 230, 182, 148, 135, 233, 11, 219, 108, 192

Since, the outlier is 410

The mean is given as;

= 121 + 89+ 203+ 55 + 230+182 + 148 + 135 + 233+ 11+ 219 + 108 + 192/13

Add the values

= 1696/13

= 130. 5

Hence, the value is 130. 5

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Answer:

8

Step-by-step explanation:

To evaluate the expression for j = -2, we simply substitute -2 for j and simplify:

10l(-2)l - 12 = 10 * |-2| - 12 (Note that the absolute value of -2 is 2)

= 10 * 2 - 12

= 20 - 12

= 8

Therefore, the value of the expression 10lj| − 12 when j = -2 is 8.

Linda can choose any combination of three events that adds up to more than a kilometer but less than 1.5 kilometers

In order to find the best combination of events for Linda to sign up for to run a total of more than a kilometer but less than 1.5 kilometers, we must first determine the total distances of the individual events.

Depending on the events offered, Linda can choose three events that add up to more than a kilometer but less than 1.5 kilometers.

If Linda has the option of running the 100m, 200m, and 800m, she can satisfy her requirement of running more than a kilometer but less than 1.5 kilometers by choosing the 100m, 200m, and 800m.

This would add up to 1100m, which is slightly over a kilometer but below 1.5 kilometers.

Another option for Linda is to run the 100m, 400m, and 600m, which would add up to 1100m, once again satisfying her requirement.

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The correlation coefficient -0.32 which is negative and close to zero, we conclude that there is an inverse and weak correlation between the acceptance rate at the top 100 u.s. mba programs and the percent of students in those programs who are employed upon graduation

The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables. Its values can range from -1 to 1.

Now, since the correlation coefficient between the acceptance rate at the top 100 u.s. mba programs and the percent of students in those programs who are employed upon graduation is -0.32.

Since the correlation coefficient is negative and close to zero, we conclude that there is an inverse and weak correlation between the acceptance rate at the top 100 u.s. mba programs and the percent of students in those programs who are employed upon graduation

So, there is an inverse and weak correlation between them.

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The equation of line passes through the points (0, -3) and (4, -1) will be;

⇒ y = 1/2x - 3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, -3) and (4, -1)

Now,

Since, The equation of line passes through the points (0, -3) and (4, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-3)) / (4 - 0)

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - (-3) = 1/2 (x - 0)

⇒ y + 3 = 1/2x

⇒ y = 1/2x - 3

Therefore, The equation of line passes through the points ((0, -3) and

(4, -1) will be;

⇒ y = 1/2x - 3

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On 1 slice of pizza there will be 1/24th of the cheese and the constant of proportionality is 1/3.

Define Proportion.

The word "proportion" generally denotes a portion, share, or sum when contrasted to a total. When two ratios are equal, they are in proportion, as stated by the definition of proportion. Two ratios or fractions are equal when an equation is applied, or when a statement to that effect is made.

Two sets of supplied numbers are said to grow or fall in the same ratio in terms of proportion if they are directly proportionate to one another. For proportionality, use the symbols ":" or "=".

Given, 50lbs of cheese is used for 150 large pizzas.

For 1 pizza cheese used will be= 50/150

=1/3

So, the constant of proportionality here is 1/3.

Now, in 1 pizza there are 8 slices.

Cheese for each slice= 1/3 × 1/8

= 1/24.

Therefore, on 1 slice of pizza there will be 1/24th of the cheese.

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This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.

Given that they have three quadrants or more, triangles are considered polygons. It has a straightforward geometric shape. The letters ABC form a right-angled triangle when put together. Euclidean geometry creates a new rectangle of square when the borders are incompatible. Given that they have three sides and three corners, triangles are categorised as polygons.

Here,

No, it is not possible to form a triangle with side lengths 8, 9, and 17.

To see why, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Symbolically, for sides a, b, and c, this can be written as:

a + b > c

a + c > b

b + c > a

Let's check if these inequalities are satisfied for the sides of 8, 9, and 17:

8 + 9 > 17 (true)

8 + 17 > 9 (true)

9 + 17 > 8 (true)

All three inequalities are true, which means that the given side lengths satisfy the triangle inequality and a triangle can be formed.

In this case, we see that 8 + 9 = 17, which is exactly the length of the third side.

This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.

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We know that a statistical technique that allows a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is known as the Factor analysis.

Factor analysis is most likely a statistical procedure that identifies clusters of related items also known as factors which are on a test; used to identify different dimensions of performance that underlie one's total score.

We can say that factor analysis is more like a technique which is used in mathematics for reducing a larger number into a smaller number.

In other words, its a method for reducing a large variable into a smaller variable factor also this technique takes out the maximum ordinary variance from all of the variables and then puts them in the common score.

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The length of EF= 15 cm.

As, the question states that the triangles are similar; their ratios are also equal.

AC/DF = AB/DE - CB/EF

Plug in the values

12/10 = AB/DE = 18/EF

If we isolate EF,

EF = 180/12

EF= 15cm

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Answer:

If r = 2 units and h = 13 units, what is the surface area of the cylinder shown above?

Step-by-step explanation:

You're welcome.

The probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

The tree diagram makes it easier to arrange and see all of the potential possibilities. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end. To determine when to multiply and when to add, use tree diagrams.

Let A be an event: the first ticket extracted was the 5.

Let B be an event: the second ticket is 2.

The probability for the following is given as:

P (B/ A) = 2/7

Hence. the probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

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The length of the line segment AB is 38.6 m. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle falls under the umbrella of the branch of mathematics known as trigonometry.

We are given a right angled triangle, with angle ACB = 90° and angle CAB = 75°.

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos θ = 10/x

Here, θ = 75°

So,

⇒cos 75° = 10/x

⇒x = 10/cos 75°

⇒x = 38.6

Hence, the length of the line segment AB is 38.6 m.

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The solutions are x=3.69 and x=-4.2

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

2x²+x-31=0

Solve this with the quadratic formula

x=-b±√b²-4ac/2a

a=2,b=1,c=-31

x=-1±√1+248/4

x=-1±√249/4

x=-1+√249/4

x=-1 + 15.77/4 =14.77/4

x=3.6925

and x=-1-√249/4

x=-1 -15.77/4 =-4.1925

Hence, the solutions are x=3.69 and x=-4.2

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The area of the shaded part in the circle will be 10840.99 ft².

The circumference = 2 * pi * r = 221.056

Use this fact to find r

2*pi*r =  221.056

Divide by pi

2*r =  221.056 / 3.141

2*r =  70.378      

Divide by 2

r = 35.19

Now that you have the radius of the inner circle, use it to find the area.

Area = pi * r^2

Area = 3888.37

Now we need the radius of the outer circle

r = 35.19 + 33.3

r = 68.49

Find the area of the other circle

Area = pi * 68.49^2

Area = 14729.36

Finally the area of the shaded region is the area of the large circle - the area of the small circle

Area of the shaded area = 14729.36- 3888.37

Area of the shaded area = 10840.99 to the nearest hundredth.

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Answer:

There are 1.91 cups in a pound

A quadratic equation can be solved by factoring if its coefficients are rational numbers and its discriminant, which is the expression under the square root in the quadratic formula, is a perfect square.

To determine if a quadratic equation can be solved by factoring, you must first ensure that its coefficients are rational numbers, meaning that they can be expressed as a ratio of two integers. Once you have confirmed this, you can calculate the discriminant of the quadratic equation, which is the expression b²-4ac, where a, b, and c are the coefficients of the quadratic equation in standard form.

If the discriminant is a perfect square, then the quadratic equation can be solved by factoring. If the discriminant is not a perfect square, then the quadratic equation cannot be solved by factoring using rational numbers, but may still be solvable using other methods, such as completing the square or the quadratic formula.

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Answer: We can use the formula for the price elasticity of demand to solve this problem:

Price elasticity of demand = percent change in quantity demanded / percent change in price

We are given that the price of chicken breast rises from $3.00 to $3.60 per pound, which is a 20% increase:

percent change in price = (3.60 - 3.00) / 3.00 = 0.20 = 20%

We are also given that the demand for chicken breast falls by 25%, which is a 25% decrease:

percent change in quantity demanded = -25%

Using these values in the formula, we get:

Price elasticity of demand = (-25%) / (20%) = -1.25

Since we are interested in the absolute value of the price elasticity of demand, we have:

|Price elasticity of demand| = |-1.25| = 1.25

A price elasticity of demand greater than 1 is considered elastic, and a price elasticity of demand less than 1 is considered inelastic. Therefore, the answer is (d) 1.25; elastic.

Step-by-step explanation:

The binomial probability distribution is a discrete ​probability distribution that describes probabilities for experiments in which there are two mutually exclusive​ outcomes.

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

In binomial probability distribution, the number of ‘Success’ in a sequence of n experiments, where each time a question is asked for yes-no, then the boolean-valued outcome is represented either with success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 − p). A single success/failure test is also called a Bernoulli trial or Bernoulli experiment, and a series of outcomes is called a Bernoulli process.

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3x + 8 = 3x + x, which has one solution at x = 8 for the equation..

In arithmetic, a solution to the equation expresses can be substituted for the variable to provide a piece of real number information.

The equation is given as 3x+8=3x+ ____.

If 3x + 8 = 3x + 9 has no solution for the equation.

If 3x + 8 = 3x + 8 has infinite solutions for the equation.

If 3x + 8 = 3x + x is equal to 3x + 8 = 4x, which has one solution at x=8 for the equation.

Therefore, 3x + 8 = 3x + x, which has one solution at x = 8 for the equation.

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The question seems incomplete, the complete question would be as:

3x+8=3x+ ____

What value could you write in after 3x that would make the equation true for:

Group of answer choices

no values of x

[ Choose ]

all values of x

[ Choose ]

just one value of x

[ Choose ]

The inequality for solving the problem is d * cost per day + 275 * $0.10 ≤ $140

To solve this problem, we need to write an inequality that represents the total cost of renting the car and driving the planned miles. The total cost is the sum of the daily rental fee (d times the cost per day) and the cost of driving the planned miles (275 times $0.10 per mile). We can write the inequality as follows:

d * cost per day + 275 * $0.10 ≤ $140

Next, we need to solve for d, the number of days Salma can afford to rent the car. To do this, we can rearrange the inequality to isolate d on one side:

d * cost per day ≤ $140 - 275 * $0.10

d ≤ ($140 - 275 * $0.10) / cost per day

Now we can plug in the given cost per day for the car rental and solve for d. For example, if the cost per day is $30, we would have:

d ≤ ($140 - 275 * $0.10) / $30

d ≤ ($140 - $27.50) / $30

d ≤ $112.50 / $30

d ≤ 3.75

Since Salma cannot rent the car for a fraction of a day, we need to round down to the nearest whole number. Therefore, Salma can afford to rent the car for at most 3 days while staying within her budget.

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x, which can be simplified to x < 5

and

-6x – 5 < 10 – x, which can be simplified to -5x < 15, and then x > -3

Therefore, the correct options are:

x < 5

A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

What is the function?

A function is a mathematical relationship between two variables, where each input value (independent variable) corresponds to exactly one output value (dependent variable). It is often represented using a formula or equation.

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

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