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3 years ago

#11 (Angles with Equations) In the figure below, 2POR is 180°.

Mathematics

1 answer:

lina2011 [118]3 years ago

4 0

Answer:

Step-by-step explanation:

The three angles form a straight line, so they add to 180.

x + x + 70 = 180

Combine like terms

2x+70 =180

Subtract 70 from each side

2x+70-70 =180-70

2x= 110

Divide by 2

x = 55

SQT = x

So SQT = 55

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From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for

vagabundo [1.1K]

Answer:

b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

Step-by-step explanation:

A confidence interval at the level of x% for a proportion being between a and b means that we are x% sure that the true proportion of the population is between a and b.

In this problem, we have that:

95% C.I is (0.5, 0.66)

Interpretation: 95% confident that the true proportion is between 0.5 and 0.66.

The correct answer is:

b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

6 0

3 years ago

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

5 0

3 years ago

Can someone help with a really simple median question? tbh i really don't know it :(

Goryan [66]

I believe the answer is the second answer

4 0

3 years ago

Read 2 more answers

The area of the scale model of a playground is 6 square yards. The scale model is enlarged by a scale factor of 3 to create the

REY [17]

Answer:

B: 54 square feet

Step-by-step explanation:

There are 3 feet in 1 yard. The scale model is 6 square yards.

Multiply 6 by 3 to get the amount of square yards.

There are 18 square yards in the actual playground.

Since there are 3 feet in a yard, multiply 18 by 3.

This gives you your answer:

54 square feet

6 0

3 years ago

Read 2 more answers

Theorem: the sum of any two even integers equals 4k for some integer k. "proof: suppose m and n are any two even integers. by de

icang [17]

Remark

The proof is only true if m and n are equal. Make it more general.

m = 2k

n = 2v

m + n = 2k + 2v = 2(k + v).

k and v can be equal but many times they are not. From that simple equation you cannot do anything for sure but divide by 2.

There are 4 combinations

m is divisible by 4 and n is not. The result will not be divisible by 4.

m is not divisible by 4 but n is. The result will not be divisible by 4.

But are divisible by 4 then the sum will be as well. Here's the really odd result

If both are even and not divisible by 4 then their sum is divisible by 4

3 0

3 years ago