To the nearest square centimeter, what is the area of the shaded sector in the circle shown below?

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

Arlecino [84]

Answer:

x = - 2

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= x² - 2x + 6x + 4

= x² + 4x + 4

Equating to zero

x² + 4x + 4 = 0 ← left side is a perfect square

(x + 2)² = 0, thus

x + 2 = 0 ( subtract 2 from both sides )

x = - 2

6 0

3 years 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

3 years ago

A study finds that the number of gallons of water used each month per household in a

Mashcka [7]

Answer:

0.5793 = 57.93% probability that the household uses 480 gallons of water or less per month

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 470 gallons and standard deviation of 50 gallons.

This means that $\mu = 470, \sigma = 50$

What is the probability that the household uses 480 gallons of water or less per month?

This is the pvalue of Z when X = 480. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{480 - 470}{50}$

$Z = 0.2$

$Z = 0.2$ has a pvalue of 0.5793

0.5793 = 57.93% probability that the household uses 480 gallons of water or less per month

3 0

3 years ago

@pinkfloyd @taskmasters PLEASE HELP IM STUCK ONE QUESTION??/

Hitman42 [59]

Answer: ||, |||, |

Step-by-step explanation:

Given that Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively.We prove that corresponding angles are congruent as follows: Statements Reasons

segment UV is parallel to segment WZ Given Points S, Q, R, and T all lie on the same line. GivenII.) m∠SQT = 180° Definition of a Straight AngleIII.) m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate I.) m∠SQV + m∠VQT = 180° Substitution Property of Equalitym∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem

m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality

m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT

m∠SQV = m∠ZRS Subtraction Property of Equality

∠SQV ≅ ∠ZRS Definition of Congruency Therefore, the most logical order of statements and reasons I, II, and III to complete the proof is ||, |||, |. I hope this helped.

6 0

3 years ago

URGENT. I DO NOT UNDERSTAND: PLEASES LEAVE AN EXPLANATION

Mandarinka [93]

Answer:

Step-by-step explanation:

To find out area of a triangle you must use this formula; Area=1/2bh

In other words, Area equals half times base times height. Since we know that the base is 5/6, fill that in. You can do the rest on your own, (:

7 0

4 years ago