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3 years ago

Expand the expression (x-5)^3

Mathematics

2 answers:

matrenka [14]3 years ago

5 0

X^3 - 15x^2 + 75x - 125

lbvjy [14]3 years ago

4 0

Answer:

$x^3$ -15 $x^{2}$ +25x-125

Step-by-step explanation:

This is a quadratic equation, so we need to open the equation first. There are three (x-5), and then we multiply them together, and then combine like terms to get the answer.

(x-5)(x-5)(x-5)=

[x(x-5)-5(x-5)](x-5)=

( $x^{2}$ -5x-5x+25)(x-5)=

( $x^{2}$ -10x+25)(x-5)=

x( $x^{2}$ -10x+25)-5( $x^{2}$ -10x+25)

$x^3$ - $10x^2$ +25x- $5x^2$ -125=

$x^3$ -15 $x^{2}$ +25x-125

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HELP PLEASE:

sattari [20]

Answer:

Its 40 for the first and 20for the other one

Step-by-step explanation:

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3 0

3 years ago

Read 2 more answers

Find the prime factorizations foor the following numbers 36 and 84

Varvara68 [4.7K]

Answer:

36 = 2² * 3²
84 = 2² * 3 * 7

Explanation:

Pf of 36 = 2 * 2 * 3 * 3 which then becomes 2 (to the power of 2) times 3 (to the power of 2)

Pf of 84 = 2 * 2 * 3 * 7 which then becomes 2 (to the power of 2) * 3 * 7

If this helps it would be greatly appreciated if you thanked me.

6 0

3 years ago

Consider testing H^0: u=20 against H^a: u<20 where u is the mean number of latex gloves used per week by all hospital employe

iragen [17]

Answer:

Part a: P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=46-1=45$

Since is a one sided test the p value would be:

$p_v =P(t_{(45)}$

Part b: Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can conclude that the true mean is not lower than 20 at 1% of signficance.

a. There is insufficient evidence to reject h^0

Step-by-step explanation:

Data given and notation

$\bar X=19.1$ represent the sample mean

$s=11.8$ represent the sample standard deviation

$n=46$ sample size

$\mu_o =20$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is lower than 20, the system of hypothesis would be:

Null hypothesis: $\mu \geq 20$

Alternative hypothesis: $\mu < 20$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{19.1-20}{\frac{11.8}{\sqrt{46}}}=-0.517$

Part a: P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=46-1=45$

Since is a one sided test the p value would be:

$p_v =P(t_{(45)}$

Part b: Conclusion

a. There is insufficient evidence to reject h^0

5 0

3 years ago

A certain natural number is not divisible by 7. Can it be divisible by 14, explain why or why not

Elanso [62]

For a number to be divisible by 14 it needs to be both divisible by 7 and 2 which are factors of 14. Every time you have a number (x) to check if it is divisible by some larger number you find the factor of that larger number and check is the x divisible by both.

Answer: it cannot be divisible by 14.

3 0

3 years ago

Please help 2 questions

inna [77]

Answer:

1) 2002

2) 92

Step-by-step explanation:

First, you need to find the area of the triangular base. The height of the triangle is 7, and the base is 26, meaning that the area is 7*26/2=91. Multiplying this by the length of the prism, you get 2002 cubic meters.

First, you need to find the area of the trapezoidal base. The two bases of the trapezoid have lengths 12 and 11, while the height is 8, meaning that the area is 8*(12+11)/2=92 cubic centimeters.

Hope this helps!

8 0

3 years ago