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3 years ago

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A rectangular prism has a volume of 160 cm. The height of the prism is 5 cm. The length is twice the width. What are the dimensi

ons of the base?

1 answer:

Westkost [7]3 years ago

5 0

The answer to your question is 8*5*4.
8*5=40
40*4=160 8 is twice of 4. the length is twice the width.

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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

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3 years ago

What is the domain and range of -4.92x² + 17.96x + 575

klio [65]

The domain of the function is D ∈ R or (-∞, ∞) and the range of the function is R ∈ (591.39, ∞)

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = -4.92x² + 17.96x + 575

The above function is a quadratic function and we know,

The quadratic function domain is all real numbers.

The domain of the function is all real numbers or

D ∈ R or (-∞, ∞)

The range:

From the graph of a function:

The maximum value of the graph:

f(1.825) = 591.39

So the range of the function:

R ∈ (591.39, ∞)

Thus, the domain of the function is D ∈ R or (-∞, ∞) and the range of the function is R ∈ (591.39, ∞)

Learn more about the function here:

brainly.com/question/5245372

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1 year ago

Find the value of x in the figure<br><br> A: 205°.<br> B: 65°.<br> C: 115°.<br> D: 155°.

Lemur [1.5K]

The answer is [B]: 65°

Connexus??

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2 years ago

Read 2 more answers

Solve for h. <br>what is h equal to?

Amanda [17]

Answer:

the last one

Step-by-step explanation:

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2 years ago

An average computer mouse inspector can inspect 50 mice per hour. The 48 computer mice inspectors at a particular factory can on

Ronch [10]

Answer: C. Yes, because -2.77 falls in the critical region .

Step-by-step explanation:

Let $\mu$ be the population mean .

As per given , we have

$H_0:\mu=50\\\\ H_a: \mu$

Since the alternative hypothesis is left-tailed and population standard deviation is not given , so we need to perform a left-tailed t-test.

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

Also, it is given that ,

n= 48

$\overline{x}=46$

s= 10

$t=\dfrac{46-50}{\dfrac{10}{\sqrt{48}}}=\dfrac{-4}{\dfrac{10}{6.93}}\\\\=\dfrac{-4}{1.443}\approx-2.77$

Degree of freedom = df = n-1= 47

Using t-distribution , we have

Critical value = $t_{\alpha,df}=t_{0.025,47}=2.0117$

Since, the absolute t-value (|-2.77|=2.77) is greater than the critical value.

So , we reject the null hypothesis.

i.e. -2.77 falls in the critical region.

[Critical region is the region of values that associates with the rejection of the null hypothesis at a given probability level.]

Conclusion : We have sufficient evidence to support the claim that these inspectors are slower than average.

Hence, the correct answer is C. Yes, because -2.77 falls in the critical region

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3 years ago