Your parents limit your
phone use to 18 hours every week. You need
to split that between hours spent on the phone
with your friends and hours spent using the
internet. Your parents count one hour on line
as 1/2 hour of phone time since some of your
time is spent doing homework. An algebraic
model is x + 1/2y
18 where x is hours spent
on the phone and y is the hours spent on line.
2
=

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 amount of time it would take for the balloon's diameter to decrease to 8 feet is 56 minutes.

What is an example of diameter?

If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.

In how long would the diameter have decreased to 8 feet?

A circle's diameter is determined by drawing a line across its center, touching both ends of its circumference.

Minutes are calculated as diameter/decline.

56 minutes from 14/0.25

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Using the conversion factor, we can say that each sheet of paper is 0.0012mm thick.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

So, 500 sheets of A4 paper make up a conventional ream. Each paper measures 297mm in length by 210mm broad, and one ream contains 3742.2cm of paper.

to change cm to mm

3742.2cm = 37422 mm

Sheet 1's surface

(297mm) X 210mm) = 62370mm²

1st volume sheet:

37422mm : 500 = 74.844mm

One sheet's thickness is:

74.844mm : 62370mm = 0.0012mm

Therefore, each sheet of paper is 0.0012mm thick.

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Correct question:
A ream of A4 paper contains 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm find the thickness of each sheet of paper answer in millimeters​

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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By graphing the system of equations, we will see that the solution is x = 3 and y = -2

Here we have te following system of equations:

y = -x + 1

y = (1/3)*x - 3

To solve the system we can graph bot equation in the same coordinate axis and try to identify the intersection points between the graphs.

Below you can see the graph

We can see that the interception point is (3, - 2), then the solution to the system of equations is x = 3 and y = -2.

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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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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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The expression in terms of x that represents the total amount that Zoe paid is 1.2x

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A tax of 5% is applied to the bill.

Zoe decides to leave a tip of 15% on the entire bill (including the tax).

let the bill cost $x.

So, the price after tax and tip

= x+ 5% of x+ 15% of x

= x + 0.05x + 0.15x

= x + 0.20x

= 1.2x

Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x

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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:

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:

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The number of different ways the prizes can be awarded is 161700

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

The number of different ways the prizes can be awarded is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 100 and r = 3

Substitute the known values in the above equation

Total = ¹⁰⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 100!/97!3!

Evaluate

Total = 161700

Hence, the number of ways is 161700

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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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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 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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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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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.

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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Answer:

D

Step-by-step explanation:

A simpler way to see it, of course, is that the mentioned line segments lie on the same line, so they must have the same slope.

answer : x≤-6

steps:

3x+2≥4x+8

-x≥6

x≤-6

Answer:

x≤−6

View graph below

Step-by-step explanation:

x≤−6

Solution Steps

3x+2≥4x+8

Subtract 4x from both sides.

3x+2−4x≥8

Combine 3x and −4x to get −x.

−x+2≥8

Subtract 2 from both sides.

−x≥8−2

Subtract 2 from 8 to get 6.

−x≥6

Divide both sides by −1. Since −1 is negative, the inequality direction is changed.

x≤−6

X could be from -6 to -infinity.

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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Answer:

B

Step-by-step explanation:

Its the second one, Answer B

The amount of sales Terry must make is $1667

How to determine the amount in sales?

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

Commission = 18% of sales

Commission = $300

These parameters mean that

Commission = 18% of sales

Substitute the known values in the above equation, so, we have the following representation

18% of sales = 300

Divide both sides by 18%

Sales = 1667

Hence, the amount is $1667

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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 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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The dimensions of the rectangle should be 150 feet by 400 feet in order to enclose the maximum possible area.

To explain this step by step:

Step 1: We know that the perimeter of a rectangle is equal to 2*length + 2*width.

Step 2: Since we have 600 feet of rope, we can plug this number into the equation: 2*length + 2*width = 600

Step 3: To solve for the length and width, we can divide both sides by 2: length + width = 300

Step 4: We can then separate the equation into two equations: length = 300 - width and width = 300 - length

Step 5: Since we want to find the maximum possible area, we should set width equal to the larger number, 300, and set length equal to the smaller number, 300 - width.

Step 6: Plugging this into the equation, we get: width = 300 and length = 300 - width = 300 - 300 = 0.

Step 7: Therefore, the maximum possible area that can be enclosed with 600 feet of rope is 150 feet by 400 feet dimensions.

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Answer: 25 days

Step-by-step explanation:

We know that it takes 55 days with 15 workers, so we need to find how many days it takes with 1 worker by taking 55 timed 15 = 825 days for 1 worker.

Then we take 825 divided by 33 and get 25 days for 33 workers.

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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

Answer:

1.8 inches

Step-by-step explanation:

Option C, which states that the sample variance is constant as the number of sample values rises when the samples are independent and regularly distributed

Each sampling distribution's variability declines as the sample size go up, becoming more and more leptokurtic. The sample distribution's range is less than the original population's range.

The margin of error & sample size has an inverse relationship, meaning that as sample size rises, sampling error falls. It is because the findings would be more accurate the more evidence you had.

The distribution's dispersion is gauged by the standard error. The dispersion decreases as the sample size increases and the distribution's mean moves closer to the population mean.

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The printed price of the desk on the furniture store is $173. It can be solved by the concept of cost price and selling price.

What is cost price and selling price?

Cost price is the price of the object at which it is purchaged and selling price is the price of the object at which it is sold. If cost price is more than the selling price then the seller will earn a loss. If the cost price is less than then the selling price then the seller will earn a profit.

The cost price of the furniture = $144

Now, 20% of cost price is,

[tex]=\$ 144\times\frac{20}{100}\\=\$28.8[/tex]

Now, price of furniture on the store = Cost price + 20% of cost price

                                                           = $144 + $28.8

                                                           = $172.8$

Round off the price                           = $173

Hence, the printed price of the desk on the furniture store is $173.

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