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3 years ago

3/a x - 4 = 20. x equals -2

Mathematics

1 answer:

Taya2010 [7]3 years ago

3 0

Answer:

$\Large \boxed{a=\frac{-1}{4} }$

Step-by-step explanation:

$\displaystyle \frac{3}{a} \cdot x - 4 = 20$

Let x = -2.

$\displaystyle \frac{3}{a} \cdot (-2) - 4 = 20$

Solving for a.

$\displaystyle \frac{-6}{a}- 4 = 20$

Adding 4 to both sides.

$\displaystyle \frac{-6}{a} = 24$

Multiplying both sides by a, then dividing both sides by 24.

$\displaystyle \frac{-6}{24} = a$

Simplifying.

$\displaystyle \frac{-1}{4} = a$

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SHOW YOU WORK AND EXPLAIN PLS I WILL MARK YOU BRAINLIEST PLEASE.

KatRina [158]

Answer:

a) 1.8 $cm^2$

b) 3.6 $feet^2$

Step-by-step explanation:

Conversion and calculation of areas

The area of a rectangle is A=wh, where w is the width and h is the height. There are 3 feet in one yard

We are told Kalie put 6 stickers, each one of 1/2 centimeters (0.5 cm) wide by 3/5 (0.6 cm) centimeter long. The area of one sticker is

A=(0.5)(0.6)=0.3 $cm^2$

Assuming there is no overlapping, the 6 stickers have a total area

6*0.3 $cm^2$ =1.8 $cm^2$

Each of Elana's wrapping papers measures 2/5 yards long and 1/4 yard wide. Converting them to feet we have

long=2/5*3=1.2 feet

wide=1/4*3=0.75 feet

Area of each paper=1.2 feet*0.75 feet=0.9 $feet^2$

Area of the entire board, assuming no overlapping and no space left uncovered=4*0.9 $feet^2$

Area of board=3.6 $feet^2$

7 0

3 years ago

The height of a wooden pole, h, is equal to 20 feet. A taut wire is stretched from a point on the ground to the top of the pole.

kykrilka [37]

ANSWER

D. 25 feet

EXPLANATION

The height of the wall,h, the taut wire and the distance from the base of the pole to the point on the ground, formed a right triangle.

According to the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.

Let the hypotenuse ( the length of the ) taught wire be,l.

Then

${l}^{2} = {h}^{2} + {b}^{2}$

${l}^{2} = {20}^{2} + {15}^{2}$

${l}^{2} = 400 + 225$

${l}^{2} = 625$

$l= \sqrt{625} = 25ft$

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3 years ago

Let X denote the length of human pregnancies from conception to birth, where X has a normal distribution with mean of 264 days a

Kaylis [27]

Answer:

Step-by-step explanation:

Hello!

X: length of human pregnancies from conception to birth.

X~N(μ;σ²)

μ= 264 day

σ= 16 day

If the variable of interest has a normal distribution, it's the sample mean, that it is also a variable on its own, has a normal distribution with parameters:

X[bar] ~N(μ;σ²/n)

When calculating a probability of a value of "X" happening it corresponds to use the standard normal: Z= (X[bar]-μ)/σ

When calculating the probability of the sample mean taking a given value, the variance is divided by the sample size. The standard normal distribution to use is Z= (X[bar]-μ)/(σ/√n)

a. You need to calculate the probability that the sample mean will be less than 260 for a random sample of 15 women.

P(X[bar]<260)= P(Z<(260-264)/(16/√15))= P(Z<-0.97)= 0.16602

b. P(X[bar]>b)= 0.05

You need to find the value of X[bar] that has above it 5% of the distribution and 95% below.

P(X[bar]≤b)= 0.95

P(Z≤(b-μ)/(σ/√n))= 0.95

The value of Z that accumulates 0.95 of probability is Z= 1.648

Now we reverse the standardization to reach the value of pregnancy length:

1.648= (b-264)/(16/√15)

1.648*(16/√15)= b-264

b= [1.648*(16/√15)]+264

b= 270.81 days

c. Now the sample taken is of 7 women and you need to calculate the probability of the sample mean of the length of pregnancy lies between 1800 and 1900 days.

Symbolically:

P(1800≤X[bar]≤1900) = P(X[bar]≤1900) - P(X[bar]≤1800)

P(Z≤(1900-264)/(16/√7)) - P(Z≤(1800-264)/(16/√7))

P(Z≤270.53) - P(Z≤253.99)= 1 - 1 = 0

d. P(X[bar]>270)= 0.1151

P(Z>(270-264)/(16/√n))= 0.1151

P(Z≤(270-264)/(16/√n))= 1 - 0.1151

P(Z≤6/(16/√n))= 0.8849

With the information of the cumulated probability you can reach the value of Z and clear the sample size needed:

P(Z≤1.200)= 0.8849

$Z= \frac{X[bar]-Mu}{Sigma/\sqrt{n} }$