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2 years ago

6

Use the identity below to complete the tasks: a3 − b3 = (a − b)(a2 + ab + b2) When using the identity for the sum of two cubes t

o factor 125q6 − r6s3. What is a? What is b?

2 answers:

saveliy_v [14]2 years ago

8 0

Answer:

a= $5q^ {2}$

b= $r^{2}s$

Step-by-step explanation:

Here $125q^{6}$ is like the $a^{3}$ in the general formula.

So we can write $125q^{6}$ as:

$(5q^ {2} )^{3}$

We can also write $r^{6} s^{3}$ as:

$(r^{2}s)^{2}$

Therefore:

a³= $(5q^ {2} )^{3}$

b²= $(r^{2}s)^{2}$

RUDIKE [14]2 years ago

7 0

Answer:

a = 5q²

b = r²s

Step-by-step explanation:

The given identity is $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$

we have to use this identity to factor of two cubes given as $[tex]125q^{6}-r^{6}s^{3}=(5q^{2})^{3}-(r^{2}s)^{3}$ [/tex]

As this expression is in the form of a³- b³

Here a is 5q² and b is r²s.

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The number of days (X) after mailout it takes a utility company to receive payment for a customer’s bill is a normal random vari

Monica [59]

Answer:

The latest 2.5% of bills will be received in 20 more days after mail-out.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 31 days

Standard Deviation, σ = 6 days

We are given that the distribution of The number of days (X) is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

$P(X \leq x) = 0.025$

We have to find the value of x such that the probability is 0.025

$P(X \leq x) = 0.025$

$P( X \leq x) = P( z \leq \displaystyle\frac{x - 31}{6})=0.025$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.960) = 0.025$

$\displaystyle\frac{x - 31}{6} = -1.960\\x = 19.24 \approx 20$

Hence, the latest 2.5% of bills will be received in 20 more days after mail-out.

4 0

2 years ago

What value of x would make KM ∥ JN?

stepan [7]

Answer:

x = 10

Step-by-step explanation:

By the converse of the side-splitter theorem, if $\dfrac{JK}{KL}= \dfrac{NM}{ML}$ , then KM ∥ JN.

Substitute the expressions into the proportion:

$\dfrac{x-5}{x}= \dfrac{x-3}{x+4}$

Cross-multiply:

(x – 5)(x+4) = x(x – 3).

Distribute:

$x(x) + x(4) - 5(x) - 5(4) = x(x) + x(-3).$

Multiply and simplify:

$x^2 +4x- 5x - 20 = x^2-3x\\-x-20=-3x\\$Collect like terms$\\-x+3x=20\\2x=20\\$Divide both sides by 2\\x=10$

Solve for x: x = 10

Therefore, the value of x that would make KM parallel to JN is 10.

4 0

2 years ago

the time taken by a student to the university has been shown to be normally distributed with mean of 16 minutes and standard dev

Naya [18.7K]

Answer:

a) 2.84% probability that he is late for his first lecture.

b) 5.112 days

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 16, \sigma = 2.1$

a. Find the probability that he is late for his first lecture.

This is the probability that he takes more than 20 minutes to walk, which is 1 subtracted by the pvalue of Z when X = 20. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20 - 16}{2.1}$

$Z = 1.905$

$Z = 1.905$ has a pvalue of 0.9716

1 - 0.9716 = 0.0284

2.84% probability that he is late for his first lecture.

b. Find the number of days per year he is likely to be late for his first lecture.

Each day, 2.84% probability that he is late for his first lecture.

Out of 180

0.0284*180 = 5.112 days

4 0

2 years ago

Using the midpoint method, find the cross-price elasticity of demand for FedEx and UPS overnight shipping if the price of FedEx

IrinaK [193]

Answer:

Cross price elasticity using midpoint method = 0.56

Step-by-step explanation:

Using the mid-point method

Cross-price Elasticity of Demand = <u>% change in Quantity demanded of UPS</u>

% change of price of FedEx

%change in Quantity demanded of UPS

using Mid-point method = <u> Q2-Q1 </u> × 100

(Q1+Q2)÷ 2

= <u>1.3-1.2 </u> × 100

(1.2+1.3)÷2

= <u>0.1 </u> × 100

1.25

= 8%

% change in price of FedEx

using midpoint method =<u> P2-P1 </u>× 100

(P1+P2)÷ 2

=<u> 75-65 </u>× 100

(65+75)÷2

=<u> 10 </u> × 100

70

= 14.28%

Cross-price Elasticity of Demand = 8% ÷ 14.28%

using midpoint method = 0.56

6 0

2 years ago

Ruth has 12 feet of ribbon.

Shkiper50 [21]

Answer:

See I don't know the answer but I did another one like this if it doesn't help you can report it no problem

Step-by-step explanation:

There are 2 different ways you can solve this problem and you'll get the same answer.

To help you visualize what you have to do, it might be easiest to translate your problem to a unit that easier to use.

Since you only have a ribbon 5 feet long, but you must cut it into 6 pieces, you know it won't even be 1 foot long.

One way to solve the problem would be to translate your 5-foot ribbon into a ribbon divided into inches.

1 foot = 12 inches

To find out how many inches long your ribbon is, you'll need to multiply the number of feet by 12.

Once you know that, then you can more easily divide it by 6. This will tell you how many inches each ribbon is.

Careful! the answer is to be put into feet so once you know how many inches long the ribbon is, you must then divide by 12 to get the correct answer in feet. Don't forget to round to the nearest tenth.

Another way to solve the problem is to simply divide the 5 feet by the number 6 and then round your number to the nearest tenth. It may be harder to visualize the answer this way, but you will get the same answer as if you translated your ribbon into inches and then divided by 12.

Good luck! I hope this helps!

6 0

2 years ago