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3 years ago

Which number line shows the solution to the inequality −2(3x − 1) < 8?

Mathematics

1 answer:

Liula [17]3 years ago

4 0

Answer:

x∈ (-1, ∞)

Step-by-step explanation:

Solution of the inequality:

−2(3x − 1) < 8 ⇒ Divide both sides by -2, this will change inequality

sign to opposite

3x - 1 > -4 ⇒ add 1 to both sides
3x > -3 ⇒ divide both sides by 3
x > -1 ⇒ answer
x∈ (-1, ∞) ⇒ answer as set

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In Nebraska, the mean rain-fed corn yield of harvested fields are normally

NikAS [45]

Answer: 169.2 per acre are produced if a field is in the top 25%.

Step-by-step explanation:

Given: The mean rain-fed corn yield of harvested fields are normally distributed, produce 147.2 bushels per acre with a standard deviation of 33 bushels per acre.

Let X denote the mean rain-fed corn yield of harvested fields.

Let x denotes the number of bushels per acre are produced if a field is in the top 25%.

Top 25% on a density curve means , (100-25%)i.e. 75% area lies below x.

I.e.

$P(X$ .

Z-score for p-value of 0.75 (one tailed)=0.67 [By z-table]

Then, $\dfrac{x-147.2}{33}=0.6744$

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3 years ago

Is (1, 13) a solution to this system of equations? y = 8x + 5 y = 13 Yes or No

yawa3891 [41]

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2 years ago

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Spencer borrowed $50 from his cousin, who charged him 6% simple interest each year. If Spencer pays his cousin back 3 years late

Orlov [11]

Given:

Principal = $50

Rate of simple interest = 6%

Time = 3 years

To find:

The amount after 3 years.

Solution:

Formula for simple interest:

$I=\dfrac{P\times r\times t}{100}$

Where, P is principal, r is the rate of interest in percentage and t is the number of years.

Putting $P=50,\ r=6,\ t=3$ in the above formula, we get

$I=\dfrac{50\times 6\times 3}{100}$

$I=\dfrac{900}{100}$

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Formula for amount is:

$A=P+I$

Where, P is principal and I is the simple interest.

Putting $P=50,\ I=9$ , we get

$A=50+9$

$A=59$

Therefore, the correct option is B.

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2 years ago