Given the algebraic expression (125x^7/3) ^-1/3 create an equivalent expression

The necessary explanation is that segment BP is congruent to segment BP, which is the common side of both triangles.

Two figures or items are congruent in geometry if they have about the same size, or if one has the same shape and size as its mirror counterpart.

As seen in the illustration, segment BP and segment BP are congruent since segment BP is the common side of both triangles BPS and BPY.

As a result, the necessary explanation seems to be that segment BP is congruent to segment BP and that segment BP is the identical side of both triangles.

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The population variance of the capacities is 30.76

the capacities (in ampere-hours) of 10 batteries are 140, 136, 150, 144, 148, 152, 138, 141, 143, 151.

The number of observations n = 10

mean = (x₁ + x₂ + x₃.....x₁₀)/10

mean = (140 + 136 + 150 + 144 + 148 + 152 + 138+ 141 + 143 + 151)/10

mean = 1443/10 = 144.3

variance = ∑(x - mean)²/(n - 1)

variance = ((140 - 144.3)² + (136 - 144.3)² + (150 - 144.3)² + (144- 144.3)² + (148 - 144.3)² + (152 - 144.3)² + (138 - 144.3)² + (141-144.3)² + (143 - 144.3)² + (151 - 144.3)²)/(10 - 1)

variance = 276.9/9 = 30.76

Therefore, the population variance of the capacities is 30.76

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The solution to f(x) = g(x) is

x = 0

x = 1

What do you mean by a solution?

We can substitute a value, or values, for a variable (such as x), making the equation true and thus finding a solution. All values of x in the domain, such that f(x) = g, are the solutions if two functions, f, and g, both map to the same co-domain.

as in: x + 2 = 7.

5 + 2 = 7 is what we get when we substitute 5 for x.

Given that 5 + 2 = 7, x = 5 is a solution.

Solution Explained:

A set of values in the table that tell us what the values of each function f(x) and g(x) are for a given value for the variable "x" is already giving us a hint.

We can infer from the table that f(x) decreases when x>0 and moves in the opposite way when x0.

G(x) follows a distinct path; it grows as x increases and shrinks as x lowers.

As a result, there is not much room for equality between the two functions.

You can thus utilize the points shown in the table to begin your test.

f(0)= 0,25 ^ 0=1 since a number raised to 0 is always 0.

g(0)=-0.75 * 0 + 1 = 1

f(1)=0.25^1=0.25 since a number raised to 1 is always equals to itself

g(1)=-0.75*1+1=0.25

So f(x)=g(x), when x=1 and when x=0

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Answer:

-4x^2 - 6x

Step-by-step explanation:

2x(-2x-3)

Use the distributive property to multiply 2x by -2x - 3.

-4x^2 - 6x

Answer:

b = 20

Step-by-step explanation:

the variables a and b are proportional , so the equation relating them is

a = kb ← k is the constant of proportion

to find k use the condition a = 12 , b = 3

12 = 3k ( divide both sides by 3 )

4 = k

a = 4b ← equation of proportion

when b = 5 , then

a = 4 × 5 = 20

The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.

GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.

The given expression is,

16a⁴b + 8ab³

Simplify the expression, by factor method,

8 x 2 x a x a x a x a x b  + 8 x a x b x b x b

The common term is 8ab,

8ab(2a³ + b²)

The required expression is 8ab(2a³ + b²).

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The probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times is 0.37

Given:

P = 0.65

1-P = 1-0.65 = 0.35

n = 25

x = 15

The number of favorable outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.

Favorable Results/Total Results = x/n, where Probability(Event)

using binomial distribution:

P(X = x )  = ⁿCₓ (P)ˣ (1-P)ⁿ⁻ˣ

∴ Heads obtained 15 or fewer times

P(X ≤ 15)

we use exceed formula:

P(X≤15) = BINOM DIST(15,25,0.65,FALSE)

= 0.3696920

≈ 0.37

Hence we get the required answer.

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The integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi times the sum of the residues of the poles of f (z) inside the circle.

The poles of f (z) inside the circle are z = 0 and z = −1/2.

The residue at z = 0 is f (0) = 0.

The residue at z = −1/2 is f (−1/2) = −7/16.

Therefore, the integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi (−7/16) = −7πi/8.

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The value of g is g = w² - 14w + 49, according to the question.

What do you mean by formula?

A truth or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more values. When you are aware of the value of one quantity, you can use the formula to determine the value of the other. It facilitates speedy question resolution. Formulas are used in algebra, geometry, and other subjects to speed up and simplify the process of arriving at the result.

According to the given question,

We have :

w = 7 - √g

Firstly isolate the g,

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides,,

w (-7) = -√g + 7 (-7)

w - 7 = -√g

Now, multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g

-1w + 7 = √g

To get rid of the square root, you must square both sides,

Note: -1w is the same as -w.

Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²

g = (-w + 7)²

g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or                                            g = (-w + 7)²    )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²

(-w)(7) = -7w

(7)(-w) = -7w

(7)(7) = 49

g = w² - 7w - 7w + 49

Then, simplify (combine all like terms):

g =w² - 7w - 7w + 49

g = w² - 14w + 49

Therefore, the value of g = w² - 14w + 49 .

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Examining the function  -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0

Where a parabolic curve opens up or down in this case depends on the sign on the coefficient of the x².

The coefficient of  x² is a and in this function is -9

A negative coefficient leads to opening downwards while a positive coefficient will result to opening upwards

The y intercept

-9x² + 7x = 0

x(-9x + 7) = 0

x = 0

-9x + 7 = 0

-9x = -7

x = 7/9

the y intercept is 0 ad 7/9

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The cost of the book after the discount and coupon is $7.32

From the question, we have the following parameters that can be used in our computation:

Amount  = $15.40

Coupon = $5 offer

Discount = 20% off

This means that

Total amount = Amount  * (1 - Discount) - Coupon

So, we have

Total amount = 15.40 * (1 - 20%) - 5

Evaluate

Total amount = 7.32

Hence, the total amount = 7.32

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The probability that the mean blood pressure will be less than 125 is 0.9938

The mean of the pressure readings = 123

The standard deviation = 9.6

Total population = 144

The value is less than 125

The equation of the z-score is

z-score = (Observed value - Mean ) / (Standard deviation /[tex]\sqrt{N}[/tex])

Substitute the values in the equation

z-score = (125 - 123) / (9.6/[tex]\sqrt{144}[/tex])

= 2 / (9.6/12)

= 2 / 0.8

= 2.5

Using the statistical table

The probability of that their mean blood pressure less than 125

P(z < 2.5) = 0.9938

Therefore, the probability is 0.9938

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Answer:

Below

Step-by-step explanation:

shaded area is 3 out of 4     or   3/4    which is .75   which represents 75%

The solution of x in the equation is 79/3

From the question, we have the following parameters that can be used in our computation:

y = 69

5x + 15 = y + 2x - 5

Substitute y = 69 in the equation 5x + 15 = y + 2x - 5

So, we have

5x + 15 = 69 + 2x - 5

Collect the like terms

This gives

5x - 2x =69 - 5 + 15

Evaluate the like terms

This gives

3x = 79

Divide both sides by 3

x = 79/3

Hence, the solution is 79/3

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The probability, which is calculated using the hypergeometric distribution, is 0.845, or 84.5%.

Given,

The answer to this question involves using the hypergeometric distribution because the patients are randomly selected from the sample without replenishment.

Hypergeometric distribution:

The probability of x successes is given by:

P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]

The parameters are:

x is the number of successes.

N is the size of the population = 56074

n is the size of the sample = 40

k is the total number of desired outcomes = 235

The number of unique combinations of x objects from a set of n elements is provided by the following formula:

Cₙ,ₓ = n! / x! (n - x)!

The probability that none left against medical advice is P(X = 0), so:

P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]

P(X = 0) = h(0, 56074, 40, 235) = (C₂₃₅, ₀ × C₅₆₀₇₄₋₄₀, ₄₀₋₀) / C₅₆₀₇₄, ₄₀

= (C₂₃₅, ₀ × C₅₅₈₃₉, ₄₀) /  C₅₆₀₇₄, ₄₀

= 0.845

The probability is 0.845 = 84.5%.

Therefore,

The probability that none of them left the treatment center against medical advice is 0.845 = 84.5%

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The required coupon rate of Samantha's bond is 4%.

The coupon rate is the annual income an investor can expect to receive while holding a particular bond. It is fixed when the bond is issued and is calculated by dividing the sum of the annual coupon payments by the par value. At the time it is purchased, a bond's yield to maturity and its coupon rate are the same.c

We have,

principal amount = $600

Amount after five year = $720

Interest of five year = $(720 - 600) = $120

Then,

Interest of one year = $120/5 = $24

Now,

Coupon rate = ($24/600)×100 = 4%

Thus, required coupon rate is 4%.

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If John and Sam insist on sitting next to each other, there are 48 different ways we can make a round table seat six people.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

Here,

There is no head of the tabel so the first person is just a place marker so there are really only 5 people whose positions matter.

But John and sam are tied together so thet are the equaivalent of one person.

so that is only 4 people.

4!*2 (because it could be john, sam or sam, john)

2*3*4*2 = 48 permutations

In 48 ways we can make seat 6 people at a round table if john and sam insist on sitting next to each other.

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The percent change for the expression for the given rational number is 28%.

As the stated question-

Original quantity = 175

New quantity = 126

Difference = Original quantity - New quantity

Difference = 175 - 126

Difference = 49

Percentage change = Difference/Original quantity x 100 %

Percentage change =49/175 x 100%

Percentage change = 28%

Thus, percent change for the expression for the given rational number is 28%.

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The type of pair of angles that are∠2 and angle∠11 is an alternate interior angles.

When a transversal intersects two coplanar lines, alternate interior angles are formed. They are on the inside of the parallel lines, but on the outside of the transversal.

Angles with the same size that occur on opposite sides of the transversal line are known as alternate angles. The following alternate angles are equal: By drawing a Z shape, we can frequently identify interior alternate angles: Alternate angles are classified into two types: alternate interior angles and alternate exterior angles.

To understand alternate interior angles, imagine a set of parallel lines and then a line intersecting them. The intersecting line is known as a transversal, and all of the angles formed by the parallel lines are known as interior angles.

Both angles are interior angles that lie alternately to each other on the transversal line r. Therefore, they are alternate interior angle.

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Answer: Slade should use 1/3 cup of milk

Step-by-step explanation:

2/3 divided by 1/2 = 1/3

In other words, if you have 2 of something and you give someone half, you would give them 1.

a) The expression that shows how many miles Mrs. Ardoin has gone after x hours is of: s(t) = 15t.

b) Mrs. Thomason has been kayaking for x + 1/3 hours.

c) The expression that shows how many miles Mrs. Thomason has gone after Mrs. Ardoin has been riding for x hours: s(t) = 9t + 3.

d) They will meet after half an hour.

The linear functions for the position are defined as follows:

s(t) = vt + s(0).

In which the variables are given as follows:

Mrs. Ardoin is boating at a constant speed of 15 miles per hour, hence his equation is of:

s(t) = 15t.

Mrs. Thomason has been kayaking for a third of an hour more than Mrs. Ardoin, at a rate of 9 miles per hour, hence his initial position is of:

s(0) = 1/3 x 9 = 3 miles.

Thus the equation is of:

s(t) = 9t + 3.

They will meet when:

15t = 9t + 3

6t = 3

t = 0.5.

Hence after half an hour.

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x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like coordinates.

Given,

In response to our inquiry:

Add "-9y²" to each side of the equation.

4x² + 9y² + -9y² + -1z² = 36 + -9y²

9y² + -9y² = 0 when equivalent phrases are combined.

4x² + 0 + -1z² = 36 + -9y²

4x² + -1z² = 36 + -9y²

Add "z²" to both sides of the equation.

4x² + -1z² + z² = 36 + -9y² + z²

Therefore,

x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like dimensions.

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Answer: $83.35

Step-by-step explanation:

Find 15% of 72.48 = 10.87

10.87 + 72.48 = 83.35

The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

What is integration?

It is defined as the mathematical approach to calculating the smaller parts or components.

It is given that:

A barn is 100 feet long and 40 feet wide.

Find the first derivative of the given function:

After solving the above integration:

= 20(e - 1/e)

The roofing = 100(20(e - 1/e))

= 4701 square feet

Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

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2x3 mixed factorial design is the correct classification of this design.

In the given question, we have to find which is the correct classification of this design.

Three subgroups can be identified within this clinical grouping, though there are no clear divisions between them. The first category includes instances that closely resemble anorexia nervosa or bulimia nervosa but fall short of the diagnostic criteria's cutoff point.

Cases where the characteristics of AN and BN occur in various combinations from those seen in the prototypic illnesses make up the second and largest class.

Those who suffer from binge eating disorder make up the third grouping.

So, 2x3 mixed factorial design is the correct classification of this design.

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The right question is given below:

Answer:

1.8 inches

Step-by-step explanation:

You are writing an article for your school newspaper about the Oakland Athletics.  Season tickets go on sale next week and you have been assigned to write an article to help fans determine whether they should buy season tickets or single-game tickets based on their expected attendance at the games this season.

Buying a season ticket allows you to attend all 81 home games for a single price.  Without a season ticket you have to pay for every single game that you attend.

Image result for Oakland Athletics Tickets Box Office

The table shows different ticket price options.

In this task you will answer six questions about the ticket price options and recommend which is best for fans. Be sure to show all your work for each item.

1. A season has 81 home games. If you purchase a season ticket in the bleacher section , what is the cost per game, in dollars for this ticket?

.2. Complete the table based on the single game ticket for seats in the Left field reserve section.

Step-by-step explanation:

The key role for CPS is to minimize stigma and be an ambassador for recovery. Describe a situation where you had to confront stigma

The slope of a line parallel to the line having equation 10x+12y=-120 is -5/6.

What is the slope of a line parallel to another line?

Parallel lines are coplanar and they never intersect.

Slope is a measure of the angle of a line from the horizontal.

Since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.

According to the given question:

Given equation of line is 10x+12y=-120

Converting this to slope-intercept form we get

y = -5/6 x + 10

Clearly slope of this line is -5/6

Any line parallel to this line will have the same slope

Therefore the slope of a line parallel to the given line is -5/6

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Answer:

one way is that they both have four sides.

another way is that they both have straight lines.

and the other way is that they both have 4 corners.

Step-by-step explanation:

Answer:

According to the web: "A square has four equal sides. In a rectangle, the opposite sides are equal. The diagonals of a square bisect each other at 90°. The diagonals of a rectangle bisect each other at different angles."

Step-by-step explanation:

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The average rate of change of f(x), represented by the table of values, over the interval [-2, 3] is: D. 0.5.

An average rate of change is sometimes referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes with respect to another quantity, over a given interval.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [-2, 3]:

a = -2; f(a) = 2.5

b = 3; f(b) = 5

Substituting the given parameters into the formula, we have the following;

Average rate of change = (5 - 2.5)/(3 - (-2))

Average rate of change = 2.5/5

Average rate of change = 0.5.

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