Simplify by expressing fractional exponents instead of radicals 8 sqrd x^2 y^4

The simplified form of the given fraction is, 2/3.

What is greatest common factor?

The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.

Consider, the given fraction [tex]\frac{48}{72}[/tex]

The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

So, from above the greatest common factor of 48 and 72 is 24.

Therefore,

[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]

Therefore, the simplified form of the given fraction is, 2/3.

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The re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.

ROP = (Daily usage x Lead period) + Safeguard stock

For the given question;

Lead time = 6 days

Safety stock = 2 days x 600 bars = 1200 bars

ROP = (600 x 6) + 1200 = 4800 bars.

Thus, the re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.

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A block exerts a force of 9 N on the ground.

Calculate the pressure the block exerts on the ground, in N/m², when it is

a) 225N/m^2

b) 600N/m^2

Define pressure.

Force applied per unit area is the definition of pressure. P=FA, where F is the force acting perpendicular to the surface area A, is the formula used to calculate pressure mathematically. Having only magnitude and no directional vector properties, pressure is a scalar quantity. The pascal (Pa), or one newton per square meter (N/m 2), is the industry standard for measuring pressure.

Solution Explained:

Given, Force = 9N

For each part of the question we will use the formula

Pressure = Force / Area           (Since, Force = Pressure X Area)

a) Here, Area = 0.04m^2

So using the formula, we have

P = 9/0.04 = 225N/m^2

b) Here, Area = 0.015m^2

So using the formula, we have

P = 9/0.015 = 600N/m^2

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Answer:

Yes

Step-by-step explanation:

3:12 both have a common factor of 3 you divide both sides by 3 to get 1:4

An equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

-3,-1,1,3 is a sequence.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

We know that nth term of arithmetic sequence is aₙ=a+(n-1)d

-3,-1,1,3

First term a=-3

Common difference d=-1-(-3)=-1+3=2

We need to find the 10th term

a₁₀=-3+(10-1)(2)

a₁₀=-3+9(2)

a₁₀=-3+18

a₁₀=15

Hence,  an equation for the nth term of the arithmetic sequence is aₙ=a+(n-1)d and a₁₀ of sequence -3,-1,1,3 is 15.

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I hate to leave you without an answer, but there isn't enough information to be able to answer your problem.

The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

Given,

The width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm.

Z = X - 951/10 ≈ N(0.1)

P(942 ≤ X ≤ 959)

P(942 - 951/10 ≤ X - 951/10 ≤ 959- 951/10)

P( -0.9 ≤ Z ≤ 0.8)

P(Z ≤ 0.8) - P(Z ≤ -0.9)

∅(0.8) - (1 - ∅(0.9))

∅(0.8) + ∅(0.9) - 1

0.788 + 0.859 - 1

0.647

The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.

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Answer: [tex]h=\frac{S}{2πrh}[/tex]

Step-by-step explanation:

= Solve S = 2πrh:

= [tex]h=\frac{S}{2πrh}[/tex]

The nth term of the given sequence is 6n

The given sequence is 6, 12, 22, 36,....

The formula to find the nth term is

T(n) = a + (n-1)d       ... (1)

Where n is the number of terms

a is first term

d is common difference

Here

n = n. a = 6,

d = 12 - 6 = 6

Substitute the values in equation (1)

T(n) = 6 + (n-1)6

⇒ T(n) = 6 + 6n - 6

⇒ T(n) = 6n

Hence the nth term of the given sequence is 6n

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The Cathy's Clothmart job had a profit comprises of pairings of the form (x,y), where the two integers are paired because of some relation.

In this instance, the relation is effectively "in month x it truly had a profit y" The ordered pairs are then, in a really significant sense, (April, 3000), (May, 4000), and (June, 5000). The ordered pairs can be written as follows if the month's number is used to identify them: (4,3000), (5,4000), They generally believed that both kinds of ordered pairings are generally correct.

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May, 4,000

The only correct pair is may and 4,000 because the other options don't have the proper profit to represent the corresponding months.

Answer:

[tex] \frac{3}{4 - x} [/tex]

The probability 11.1% of domestic airfares within the United States are $250 or less.

The formula for the z score is -

z = (x - μ)/σ

In which,

Substitute the value in formula.

P(x ≤ 250) = (250 - 385)/100

P(x ≤ 250) = -1.22

Select the p value from negative z score table;

P(x ≤ 250) = 0.111

P(x ≤ 250) = 11.1%

Thus, 11.1% of domestic flights within the United States are $250 or less.

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The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

By the similar triangle, then the value of r is calculated as,

r/30 = 20/40

r = 15 cm

Then the volume of the frustum is calculated as,

V = 1/3 × (30/2)² × 40 - 1/3 × (15/2)² × 20

V = 1/3 × [9000 - 1125]

V = 1/3 × 7875

V = 2625 cm³

The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.

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Answer: 70%

Step-by-step explanation:

Percentage is always out of 100. And 10x10 =100 so you do the same to 7 multiply it by ten then your answer is 70 which is 70%.

The percentage increase in the number of pieces she saws on that day is 40%.

Here it is given that a seamstress sews 55 pieces per day.

But on a certain day, 77 pieces were sewn.

We have to find the percentage increase in the number of pieces she sews on that day.

So first we have to find the increase in the number of pieces she sews.

Increase in the number = 77 - 55

                                       = 22

The original number per day = 55

Formula to find the percentage increase in the number.

Percentage increase = Increase in number/ original number × 100

Now putting the values in the equation:

Percentage increase = 22 / 55 × 100

                                   = 2/5 × 100

                                   = 40%

Therefore there is a 40% increase in the number of pieces.

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Answer:

Step-by-step explanation:

author link

adioabiola

Ace

12K answers

42.2M people helped

Answer:

1,008 calories

Step-by-step explanation:

504 calories in eight ounces

How many calories are there in one pound

1 pound = 16 ounces

504 calories = 8 ounces

x calories = 1 pound

Recall, 1 pound = 16 ounces

504 calories : 8 ounces = x calories : 16 ounces

504 / 8 = x / 16

Cross Multiply

504 * 16 = 8 * x

8,064 = 8x

Divide both sides by 8

x = 8,064 / 8

= 1,008

x = 1,008 calories

Therefore, there are 1,008 calories in one pound

Answer:

There are 2 zeros. You know they are zeros because they are the only two points that intercept the x-axis. There is one touch zero and one bounce zero, meaning there are both even and odd multiplicities in the graph.

Using the concept of the sine function, the bracket made an angle of 51.37° with the wall.

The sine of an angle is represented by the trigonometric function sin x, where x is the angle under consideration. The ratio between a right-angled triangle's perpendicular and the hypotenuse is known as the sine function. In other words, the hypotenuse is the ratio of the side opposite to the angle being discussed, and its value changes as the angle do. The sine function is used in physics to depict sound and light waves.

Use the trigonometric function sinθ = perpendicular/ hypotenuse

From the given figure, in accordance with ∠x

Perpendicular = 2.5 ft

Hypotenuse = 3.2 ft

So, sinx = 2.5/ 3.2

sinx =  0.78125

x = sin⁻¹(0.78125)

x = 51.37°

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Given,

The probability of head ups of a firefly = 0.1 = 10%

The average flashes per minute is 6.

1 firefly 6 flashes per minute = 0.1 flash per second

Then,

1000 × 0.1 = 100 flashes per second

100 × 10 = 1000 flashes per 10 seconds

There will be 1000 flashes per 10 seconds.

Each flash = 0.1 lumen

40 lumens = 4 flash

70/100 = 0.7

0.7 x 4 = 2.8 = 3 fireflies.

There is 3 fireflies required to produce 40 lumens

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Answer:

answer for 17 is 5+5+8which is 200 cm

Answer:

1 - 9p

2 - 4y

Step-by-step explanation:

1: 3p+2p+4p Since there all common terms you can just add them together! So it would be 9p!

2: 3y + (-y) + 2y

Lets make this easier to understand.

3y -1y + 2y (I added the one because the y technically is a 1.)

Since they are all like terms because they all have y it is pretty easy to solve now! So it would be 4y!

(WILL DO MORE LATER)

The equivalent ratios table is:

Toss     Dollars  

5             2

30           12

45           18

See the diagram in the attachment that shows the plotted points.

Equivalent ratios are ratios that have the same value when they are compared together.

For example, 4/6 = 2/3, therefore, the equivalent ratios are 2:3 and 4:6.

Create an equation that models equivalent ratios that can be used to complete the table if:

x = toss

y = dollars

Therefore, given that 30 toss equals $12,

Constant of proportionality, k = y/x = 12/30

k = 2/5.

Plug in the value of k into y = kx:

y = 2/5x.

Therefore:

2 dollars (y = 2), will give:

2 = 2/5(x)

x = 10/2

x = 5 toss

45 tosses (x = 45) will need:

y = 2/5(45)

y = 18 dollars

The equivalent ratios table would be:

Toss | Dollars  

5           2

30        12

45         18

The graph below shows the points, (5, 2), (30, 12), and (45, 18), where y = dollars, and x = toss.

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Answer:

Step-by-step explanation: I am guessing that it is 180

The function that will standardize a multivariate normal sample is

Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))

According to a multivariate normal distribution with mean vector m and variance-covariance matrix M, then this random vector, X , will have the joint density function as shown:

Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))

where, |M| denotes the determinant of the variance-covariance matrix M and M^(-1) is just the inverse of the variance-covariance matrix M.

Hence, the function that will standardize a multivariate normal sample is

Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))

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It will take 33.33 years for the account to reach $5500

What is simple interest?

Simple interest is defined as the direct crediting of cash flows related to an investment or deposit.

We know,

Victoria deposited  into a savings account $5000

Annual simple interest rate of 0.3%.

Formula of Simple Interest

                        A = P(1 + rt)

                       5500 = 5000(1 + 0.003t)

                       5500 = 5000 + 15t

                        15t = 500

                         [tex]t = \frac{500}{15} = 33.33[/tex]

It will take 33.33 years for the account to reach $5500

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Answer:

$2.46

Step-by-step explanation:

7.38/3 = 2.46

2.46 x 3 = 7.38

Answer: 9,000 mL

Step-by-step explanation:

If you multiply 2,000 by 4, you would get 8,000 & if you multiply .5 by 2,000, you get 1,000. If you add both the totals, you would end up with a final answer of 9,000 mL.

The greatest number among the given numbers is= 57

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