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1 month ago

What values of b satisfy 4(3b + 2)2 = 64?

1 answer:

8 0

Starting with the equation 4(3b + 2)² = 64, if we divide both sides by 4 we obtain (3b + 2)² = 16. By taking the square root of both sides, we derive two cases: (3b + 2) = 4 and (3b + 2) = -4. Solving each equation for b yields: 3b = 2 or 3b = -6, leading to b values of 2/3 and -2. Ultimately, the results specify that b = 2/3 and b = -2.

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A mortgage firm estimates the true mean current debt of local homeowners, using the current outstanding balance of a random samp

Svet_ta [12734]

Answer:

Option B.

Step-by-step explanation:

As known,

Margin of error = Z * standard error

The margin of error can only be reduced by lowering either the Z value or the standard error, as both are directly proportional to the margin of error.

The Z-value can be diminished by utilizing lower confidence intervals. Standard error can be minimized by augmenting the sample size (as indicated in option B)

The correct choice is option B because it involves a sample size of 50 instead of 35, which subsequently lowers the standard error and consequently the margin of error.

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14 days ago

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean ti

lawyer [12517]

a) Null hypothesis: the mean time of telephone surveys is less than or equal to 15 minutes. Alternative hypothesis: the mean exceeds 15 minutes. b) The computed test statistic is 2.15. c) The p-value found is 0.0158. d) NO, there is significant evidence to support that the mean survey time is fewer than 15 minutes, thus the premium rate is not warranted. Explanation: Data from Microsoft Excel includes: 17, 11, 12, 23, 20, 23, 15, 16, 23, 22, 18, 23, 25, 14, 12, 12, 20, 18, 12, 19, 11, 20, 21, 11, 18, 14, 13, 13, 19, 16, 10, 22, 18, 23. a) The null and alternative hypotheses stem from the assumption that Fowle Marketing Research Inc. bases its charges on the premise that the mean time of a telephone survey is 15 minutes or less.

4 0

23 days ago

g European roulette. The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A bal

Leona [12618]

Answer:

The total expected value and standard deviation of your winnings are -$0.081 and $3, respectively.

Step-by-step explanation:

In European roulette, a wheel with 37 slots is spun: 18 are red, 18 are black, and 1 is green.

Bettors can wager on either red or black. Winning on their chosen color means they double their bet, while losing means they forfeit their stake.

Define the probability for the ball landing in a red slot = $\frac{18}{37}$

The probability of it landing in a black slot = $\frac{18}{37}$

The probability for landing in the green slot = $\frac{1}{37}$

Since bets are only placed on red or black,

The winning probability = $\frac{18}{37}$

and losing probability = $\frac{18}{37}+\frac{1}{37}$

= $\frac{19}{37}$

If a gambler wins, they receive $3, and if they lose, it amounts to -$3.

The expected value of the total winnings is hence;

E(X) = $\sum X \times P(X)$

= $\$3 \times \frac{18}{37} + (-\$3 \times \frac{19}{37})$

= $\$3 \times (-\frac{1}{37})$ = -$0.081

Furthermore, the standard deviation of the total winnings is given by;

S.D.(X) = $\sqrt{(\sum X^{2} \times P(X))-(\sum X \times P(X))^{2} }$

<pTherefore, $E(X^{2})=\sum X^{2} \times P(X)$

= $\$3^{2} \times \frac{18}{37} + (-\$3^{2} \times \frac{19}{37})$

= $\$9 \times (\frac{18}{37}+\frac{19}{37})$ = $9

Thus, S.D.(X) = $\sqrt{\$9-(-\$0.081)^{2} }$

= $\sqrt{8.993}$ = $2.99 ≈ $3

Consequently, the anticipated value and standard deviation of your total winnings are -$0.081 and $3, respectively.

6 0

1 month ago

A 120-liter solution that is 5% salt is mixed with an

lawyer [12517]

First, combine the solution and salt: 120 liters + 80 liters = 200 liters. The percentages average out: 5% + 15% = 20%. Therefore, the ratio is 20:200, leading to a concentration calculation of 20/200 = 0.10. Ultimately, the final concentration is 10% salt.

4 0

1 month ago

Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters

zzz [12365]

Answer:

" Vertical angles are equal " ⇒ 2nd answer

Step-by-step explanation:

* Refer to the attached illustration

- Three lines intersect at point D.

- We have to identify the missing justification in step 3.

∵ Line FA intersects line EC at point D.

- When two lines cross, the angles created are referred to as

vertical angles.

- By the vertical angles theorem, vertical angles are equal.

Thus, ∠ADC and ∠FDE are vertical angles.

Since vertical angles are equal

∴ ∠EDF ≅ ∠ADC

Thus, m∠EDF ≅ m∠ADC

Given that m∠EDF = 120°.

∵ m∠ADC is the sum of m∠ADB and m∠BDC.

Therefore, m∠ADB + m∠BDC = 120°.

∵ m∠ADB = (3x)° ⇒ given.

∵ m∠BDC = (2x)° ⇒ given.

Thus, 3x + 2x = 120 ⇒ combine like terms.

Thus, 5x = 120 ⇒ divide both sides by 5.

Thus, x = 24.

Column (1) Column (2)

m∠EDF = 120° given

m∠ADB = 3 x given

m∠BDC = 2 x given

∠EDF and ∠ADC are vertical angles definition of vertical angles

∠EDF is equal to ∠ADC vertical angles are equal

equal

m∠ADC = m∠ADB + m∠BDC angle addition principle.

m∠EDF = m∠ADC definition of equality.

m∠EDF = m∠ADB + m∠BDC substitution.

120° = 3 x + 2 x substitution.

120 = 5 x addition.

x = 24 division.

∴ The missing justification is " vertical angles are equal "

- From the reasoning above, ∠ADC and ∠FDE are vertical angles and therefore they are equal according to the vertical angle theorem.

6 0

1 month ago

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