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2 years ago

6

In a random sample of 75 individuals, it was found that 52 of them prefer coffee to tea. What is the margin of error for the tru

e proportion of all individuals who prefer coffee?

1 answer:

Ugo [173]2 years ago

4 0

0.106 is the answer

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The volume of a sphere whose diameter is 18 centimeters is 246 324 648 972 π cubic centimeters. If its diameter were reduced by

Dmitry [639]

1/4, since the radius is also halved if the diameter is halved, meaning (radius/2)^2 is radius^2 * 1/4.

5 0

1 year ago

Read 2 more answers

What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

GalinKa [24]

Options

A. UV = 14 ft and m∠TUV = 45°

B. TU = 26 ft

C. m∠STU = 37° and m∠VTU = 37°

D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°

E. m∠UST = 98° and m ∠TUV = 45°

Answer:

A. UV = 14 ft and m∠TUV = 45°

D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°

Step-by-step explanation:

Given

See attachment for triangle

Required

What proves that: ΔSTU ≅ ΔVTU using SAS

To prove their similarity, we must check the corresponding sides and angles of both triangles

First:

$\angle UST$ must equal $\angle UVT$

So:

$\angle UST = \angle UVT = 98$

Next:

UV must equal US.

So:

$UV = US = 14$

Also:

ST must equal VT

So:

$ST = VT = 20$

Lastly

$\angle TUV$ must equal $\angle TUS$

So:

$\angle TUV = \angle TUS = 45$

Hence: Options A and D are correct

4 0

2 years ago

The volume of the sphere is StartFraction 500 Over 3 EndFractionπ cubic units. A sphere has a radius of x units. What is the val

Tpy6a [65]

Answer:

(b) Radius of the sphere = 5 units.

Step-by-step explanation:

Here, given:

The volume of the sphere = $(\frac{500}{3})\pi$ cubic units ... (1)

Also, radius of the sphere = x units

Now, VOLUME OF SPHERE = $(\frac{4}{3}) \pi r^3$

So, volume of a sphere with radius x = $(\frac{4}{3}) \pi (x)^3$

But volume of sphere is given by (1).

$\implies (\frac{500}{3})\pi = (\frac{4}{3}) \pi (x)^3\\\implies (\frac{500}{3}) = (\frac{4}{3}) (x)^3\\\implies x^3 = (\frac{500}{3}) \times (\frac{3}{4}) = 125\\\implies x^ 3 = 125 = (5)^3\\\implies x = 5$

Hence, radius of the sphere = 5 units.

4 0

2 years ago

Read 2 more answers

What is the y-intercept of the function f(x)=4 - 5x? (Hint: use the commutative property)

Tom [10]

Answer:

Therefore the y-intercept of the function is 4.

Step-by-step explanation:

Intercepts:

The line which intersect on x-axis and y-axis are called intercepts.

y-intercept: The line or function which intersect at y-axis. So when the line intersect at y-axis, X coordinate is zero.

So in the given Function Put x = 0 we will get the y-intercept

$f(x)= 4-5x$

Put x =0

$f(0)= 4-5\times 0$

$f(0)= 4-0=4$

Therefore the y-intercept of the function is 4.

7 0

1 year ago

1. Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 during

dolphi86 [110]

9514 1404 393

Answer:

$3891.10

Step-by-step explanation:

This question is a bit unusual in that the interest is compounded annually, but payments and withdrawals are made monthly. The effective monthly rate is ...

1.05^(1/12) -1 = 0.407412378% = i

We assume that payments to the annuity are made at the end of the month, and that withdrawals are made at the beginning of the month. (The last payment and the first withdrawal are made on the same day.)

The amount of money required in the fund is ...

A = $4000(1 -(1.00407^-360))/(1 -1.00407^-1) = $757,712.88

The amount of money needed each month to be put into the fund is P, where ...

$757,712.88 = P(1 -1.00407)^(-12(60-28))/(1 -1.00407^-1) = 194.7297P

P = $757,712.88/194.7297 = $3891.10

Yejin needs to save $3891.10 each month to meet her retirement goal.

_____

<em>Sanity check</em>

Yejin wants payments for 30 years from the fund to which she has contributed for 32 years. The similarity of the time periods means that Yejin's monthly contribution will need to be very similar to the amount she plans to withdraw.

The only ways to reduce the required contribution are to earn a higher interest on deposits, or to adjust the relative time periods (retire later).

3 0

1 year ago