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3 years ago

A rectangular shelf with an area equal to x^2-16x+60 square units could have which possible dimensions for length and width

Mathematics

1 answer:

kenny6666 [7]3 years ago

8 0

Answer:

Step-by-step explanation:

x²-16x+60

=x²-6x-10x+60

=x(x-6)-10(x-6)

=(x-6)(x-10)

so dimensions are x-6 and x-10.

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Factor completely:<br>64 - y^3

madam [21]

From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is $4^{3}$ , and $y^{3}$ .

There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.

That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are $a^{3}$ and $b^{3}$ . The difference of those two cubes is:
$a^{3} - b^{3} = (a - b)( a^{2} + ab + b^{2})$

In our problem, a = 4 (since $a^{3}$ = 64) and b = y (since $b^{3} = y^{3}$ . Plug these values into the rule to find the factor of $64 - y^3$ :
$64 - y^3 \\
= (4 - y)( 4^{2} + 4y + y^{2}) \\
= (4 - y)( 16 + 4y + y^{2})$

-----

Answer: $(4 - y)( 16 + 4y + y^{2})$

8 0

2 years ago

Suppose a large shipment of microwave ovens contained 12% defectives. If a sample of size 474 is selected, what is the probabili

melisa1 [442]

Answer:

$P(\hat p>0.14)$

And using the z score given by:

$z = \frac{\hat p -\mu_p}{\sigma_p}$

Where:

$\mu_{\hat p} = 0.12$

$\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149$

If we find the z score for $\hat p =0.14$ we got:

$z = \frac{0.14-0.12}{0.0149}= 1.340$

So we want to find this probability:

$P(z>1.340)$

And using the complement rule and the normal standard distribution and excel we got:

$P(Z>1.340) = 1-P(Z$

Step-by-step explanation:

For this case we have the proportion of interest given $p =0.12$ . And we have a sample size selected n = 474

The distribution of $\hat p$ is given by:

$\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}})$

We want to find this probability:

$P(\hat p>0.14)$

And using the z score given by:

$z = \frac{\hat p -\mu_p}{\sigma_p}$

Where:

$\mu_{\hat p} = 0.12$

$\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149$

If we find the z score for $\hat p =0.14$ we got:

$z = \frac{0.14-0.12}{0.0149}= 1.340$

So we want to find this probability:

$P(z>1.340)$

And using the complement rule and the normal standard distribution and excel we got:

$P(Z>1.340) = 1-P(Z$

4 0

3 years ago

How well does the idea of the melting pot reflect U.S. immigration around 1900?

Minchanka [31]

Answer:

The melting pot theory of ethnic relations, which sees American identity as centered upon the acculturation or assimilation and the intermarriage of white immigrant groups, has been analyzed by the emerging academic field of whiteness studies. This discipline examines the "social construction of whiteness" and highlights the changing ways in which whiteness has been normative to American national identity from the 17th to the 20th century.

Step-by-step explanation:

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3 years ago

What is the answer to this too?

Radda [10]

The answer to this is 5%

4 0

2 years ago

The graph of y=f(x) is shown on the grid.<br> Use the graph to workout and estimate for f(2.5)

Wewaii [24]

Check the picture below.

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1 year ago