Write the Two statements that form each biconditional.

What is the solution to the inequality? 10x + 18 < -2

padilas [110]

Let's solve your inequality step-by-step.

10x+18<−2

Step 1: Subtract 18 from both sides.

10x+18−18<−2−18

10x<−20

Step 2: Divide both sides by 10.

10x/10<−20/10

x<−2

Answer:

x<−2

4 0

3 years ago

Round 1.49882 nearest to the nearest given place thousandths

I am Lyosha [343]

Okie doke. So, we are rounding this number to the nearest thousandths place, which is three digits behind the decimal. The rules for rounding are if the number is 5 or more in the digit behind it, the number goes up. If it is 4 or less, the number goes back. In other words, we depend on the digit right of the digit we are rounding to in order to see what we do. The number we are rounding is 1.49882. The 8 is in the thousandths place and the 8 is to the right of that, which is the ten thousandths place. Because 8 is greater than 5, the number rounds up. So the number rounded to the nearest thousandth is 1.500.

7 0

4 years ago

A pair of $36 jeans were on sale at Jim's Jeans for 1/3 off. The same pair of jeans were $42 at David's Denims. The jeans were o

nikklg [1K]

Complete question :

A pair of $36 jeans were on sale at Jim's Jeans for 1/3 off. The same pair of jeans were $42 at David's Denims. The jeans were on sale for 2/3 off.

A.) which store had the better buy

B.) how much will you pay at the store that has the better buy

Answer:

A.)David's denim has the better buy

B.) $14

Step-by-step explanation:

Jim's Jean store :

Cost of Jean = $36

Discount = 1/3 off

Discounted cost = $36 - (1/3 * $36)

Discounted cost = $36 - $12 = $24

David's Denim:

Cost of Jean = $42

Discount = 2/3 off

Discounted cost = $42 - (2/3 * $42)

Discounted cost = $42 - $28 = $14

David's denim has the better buy with a discounted price lower than the discounted price at Jim's store.

Cost at store with the better buy is $14

8 0

3 years ago

A professor pays 25 cents for each blackboard error made in lecture to the student who pointsout the error. In a career ofnyears

marta [7]

Answer:

(a) The probability that Y₂₀ exceeds 1000 is 3.91 × 10⁻⁶.

(b) n = 28.09

Step-by-step explanation:

The random variable Yₙ is defined as the total numbers of dollars paid in n years.

It is provided that Yₙ can be approximated by a Gaussian distribution, also known as Normal distribution.

The mean and standard deviation of Yₙ are:

$\mu_{Y_{n}}=40n\\\sigma_{Y_{n}}=\sqrt{100n}$

(a)

For n = 20 the mean and standard deviation of Y₂₀ are:

$\mu_{Y_{n}}=40n=40\times20=800\\\sigma_{Y_{n}}=\sqrt{100n}=\sqrt{100\times20}=44.72\\$

Compute the probability that Y₂₀ exceeds 1000 as follows:

$P(Y_{n}>1000)=P(\frac{Y_{n}-\mu_{Y_{n}}}{\sigma_{Y_{n}}}>\frac{1000-800}{44.72})\\=P(Z> 4.47)\\=1-P(Z$

**Use a z table for probability.

Thus, the probability that Y₂₀ exceeds 1000 is 3.91 × 10⁻⁶.

(b)

It is provided that P (Yₙ > 1000) > 0.99.

$P(Y_{n}>1000)=0.99\\1-P(Y_{n}$

The value of z for which P (Z < z) = 0.01 is 2.33.

Compute the value of n as follows:

$z=\frac{Y_{n}-\mu_{Y_{n}}}{\sigma_{Y_{n}}}\\2.33=\frac{1000-40n}{\sqrt{100n}}\\2.33=\frac{100}{\sqrt{n}}-4\sqrt{n} \\2.33=\frac{100-4n}{\sqrt{n}} \\5.4289=\frac{(100-4n)^{2}}{n}\\5.4289=\frac{10000+16n^{2}-800n}{n}\\5.4289n=10000+16n^{2}-800n\\16n^{2}-805.4289n+10000=0$