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2 years ago

If a 35 ft rope is cut into two sections with one section 6 times as long as the other section, how long is the shorter piece?

Mathematics

2 answers:

astra-53 [7]2 years ago

5 0

Hi there, let x be 6x. Now, let's make an equation. x+6x=7x=35 ft. 35 ft ÷ 7 = 5 ft. So, the answer is 5 ft.

Yuliya22 [10]2 years ago

4 0

The smallest piece is 5ft, 5x6+5=35

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In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police

Lyrx [107]

Answer:

Option 3 - 4 miles

Step-by-step explanation:

Given : In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles.

To find : How far apart are the police station and the fire station?

Solution :

Let the distance between police station and fire station be 'x'.

The distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station.

i.e. $2x-3$

The distance between the library and the police station is 5 miles.

i.e. $2x-3=5$

$2x=5+3$

$2x=8$

$x=4$

Therefore, The police and fire stations is 4 miles apart.

So, Option 3 is correct.

3 0

3 years ago

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Tanya [424]

Answer:

Step-by-step explanation:

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2 years ago

Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

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2 years ago

An automotive manufacturer has developed a new type of tire that the research team believes to increase fuel efficiency. The man

Stolb23 [73]

Answer:

One tailed

To conclude if there is an increase in the mean gas mileage due to new type of tire.

Step-by-step explanation:

We are given the following in the question:

The manufacture wants to compare increase in the mean gas mileage.

Population mean = 32 miles per gallon

Thus, the manufacture could carry a hypothesis test to compare mean.

A one tailed test (z-test or t-test) based on the information can be used to compare the increase in mean.

Thus,

The automotive manufacturer should perform a one tailed hypothesis test to conclude if there is an increase in the mean gas mileage due to new type of tire.

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3 years ago

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asambeis [7]

A = {0, 1, 2, 3}

C = {0, a, 2, b}

A ∩ C = {0, 2} → E)

A set of the same elements from the set A and the set C.

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2 years ago