Order the side lengths from least to greatest

A submarine at a depth of -2 2/3 feet descended 5 1/2 feet. How many feet must the submarine rise to reach the surface? Explain

vladimir2022 [97]

Original position of the submarine below the Surface = -2 2/3= -8/3

Submarine at a depth of -2 2/3 feet descended by 5 1/2 feet.

So new position of the Submarine = $\frac{-8}{3}-\frac{11}{2}\\\\ = \frac {-16 - 33}{2}\\\\ = \frac{-49}{6}$

To Reach the surface submarine must rise = 0-(-49/6)

As seen from the equation the two negative sign [(-)(-)] will change into a positive sign.

At the surface the position of the submarine = +49/6 feet

5 0

3 years ago

According to the U.S. Census Bureau, 42% of men who worked at home were college graduates. In a sample of $14 women who worked a

Lady bird [3.3K]

Answer:

Step-by-step explanation:

1) The point estimate, p for the proportion of college graduates among women who work at home is

p = x/n

Where

x = number of success = 158

n = number of samples = 514

p = 158/514 = 0.307

2) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

Probability of success, p = 42/100 = 0.42

Probability of failure = 1 - p = 1 - 0.42 = 0.58

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.8 = 0.2

α/2 = 0.2/2 = 0.1

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.1 = 0.9

The z score corresponding to the area on the z table is 1.282. Thus, the z score for a confidence level of 80% is 1.282

Margin of error = 1.282 × √(0.42 × 0.58)/514

Margin of error = 0.028

Therefore, the 80% confidence interval is

0.307 ± 0.028

The lower limit of the confidence interval is

0.307 - 0.028 = 0.279

The upper limit of the confidence interval is

0.307 + 0.028 = 0.335

Therefore, an 80% confidence interval for the proportion of women who work at home is between 0.279 and 0.335

3 0

3 years ago

At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those c

grandymaker [24]

Answer:

a.)

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b.)

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c.)

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

Step-by-step explanation:

We are given the following information

40% of the customers use regular gas (A2)

P(A₁) = 0.40

35% use plus gas (A2)

P(A₂) = 0.35

25% use premium (A3)

P(A₃) = 0.25

Of those customers using regular gas, only 20% fill their tanks (event B).

P(B | A₁) = 0.20

Of those customers using plus, 40% fill their tanks

P(B | A₂) = 0.40

Whereas of those using premium, 50% fill their tanks.

P(B | A₃) = 0.5

a) What is the probability that the next customer will request plus gas and fill their tank?

We are asked to find P(A₂ ∩ B) = ?

Recall that Multiplicative law of probability is given by

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b) What is the probability that the next customer fills the tank?

We are asked to find P(B) = ?

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P( A₂ ∩ B ) is already calculated, we need to calculate

P( A₁ ∩ B ) and P( A₃ ∩ B )

So,

P( A₁ ∩ B ) = P(B | A₁) × P(A₁)

P( A₁ ∩ B ) = 0.20 × 0.40

P( A₁ ∩ B ) = 0.08

P( A₃ ∩ B ) = P(B | A₃) × P(A₃)

P( A₃ ∩ B ) = 0.50 × 0.25

P( A₃ ∩ B ) = 0.125

Finally,

P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c) If the next customer fills the tank, what is the probability that the regular gas is requested? Plus? Premium

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

5 0

4 years ago

PLEASE answer as soon as you can! First correct answer will get BRAINLIEST!!! :)

stiv31 [10]

Answer:

X^2 + 2(30x) + 900

Step-by-step explanation:

You multiply the sides of each square and add them to get the total of the whole square. For the top left square, you multiply x and x. For the top right, you multiply 30 and x. For the bottom left, you multiply 30 and x as well. And for the bottom right, you multiple 30 and 300. Add these together and you get X^2 + 2(30x) + 900.

3 0

3 years ago

Which value of x makes the equation 8x + 38 = 2(11x + 5) true?

dangina [55]

8x+38=2(11x+5)
divide 2 from both sides
4x+19=11x+5
minus 4x from both sides
19=7x+5
minus 5 from both sides
14=7x
divide by 7
2=x

so x would be 2

3 0

2 years ago

Order the side lengths from least to greatest​

Order the side lengths from least to greatest