An exterior angle of a triangle measures 125° and one of the remote interior angles measures 35°. The triangle must be:

A USA Today/CNN/Gallup survey of 369 working parents found 200 who said they spend too little time with their children because o

KengaRu [80]

Answer: a. 0.542

b. 0.051

c. $(0.491,\ 0.593)$

Step-by-step explanation:

Let p be the population proportion of parents spend too little time with their children because of work commitments

As per given , we have

n= 369

$\hat{p}=\dfrac{200}{369}=0.542005420054\approx0.542$

Since the sample proportion is the best estimate for the population proportion.

So , the point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments = 0.542

z-value for 95% confidence interval : $z_{\alpha/2}=1.96$

Margin of error : $E=z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$E=(1.96)\sqrt{\dfrac{0.542(1-0.542)}{369}}\\\\=0.0508364564574\approx0.051$

The margin of error = 0.051

Confidence interval : $\hat{p}\pm E$

$0.542\pm0.051\\\\=(0.542-0.051,\ 0.542+0.051)\\\\=(0.491,\ 0.593)$

95% confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments : $(0.491,\ 0.593)$

6 0

4 years ago

Use logarithms to solve the equation for t. (Round your answer to two decimal places.)

mezya [45]

9514 1404 393

Answer:

2.56

Step-by-step explanation:

Multiply by (1+6e^(-.7t))/1000:

2000/1000 = 1 +6e^(-0.07t)

1 = 6e^(-0.07t) . . . . . . . . . subtract 1

e^(0.07t) = 6 . . . . . . . . . . multiply by e^(0.07t)

0.07t = ln(6) . . . . . . . . . take the natural log

t = ln(6)/0.07 . . . . . . . divide by the coefficient of t

t ≈ 2.55966 ≈ 2.56

7 0

3 years ago

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2984 and standard deviation

DedPeter [7]

Answer:

a. The distribution of X is normal.

b. The probability that the customer consumes less than 2863 calories is 0.4213

c. 42.01% of of the customers consume over 3107 calories

d. The fewest number of calories a person must consume to receive the Piggy award is 4131,41 calories.

Step-by-step explanation:

Let X be the calorie of a randomly chosen customer consumes.

a. The distribution of X is normal.

b. The probability that the customer consumes less than 2863 calories =P(x<2863)=P(z<z*) where z* is the z-statistic of X=2863 calorie.

z* can be calculated using the formula

(1) z*= $\frac{X-M}{s}$ where

X =2863

M is the mean calories consumed by customers at the Chinese buffet (2984)

s is the standard deviation (610)

Then z*= $\frac{2863-2984}{610}$ ≈−0.1984

And P(z<z*)=0.4213

c. The proportion of the customers consume over 3107 calories is

1 - the proportion of the customers consume less than 3107 calories.

= 1- P(z<z*) where z* is the z-statistic of X=3107 calorie.

From above formula (1) we get:

z*= $\frac{3107-2984}{610}$ ≈ 0.5799 and 1-0.5799=0.4201

Thus, 42.01% of of the customers consume over 3107 calories

d. The Piggy award will given out to the 3% of customers, and let z* be the z-score of the the fewest number of calories a person must consume to receive the Piggy award, then

P(z>z*)=0.03 (3%) or P(z<z*)=0.97 gives z*= 1.881

From (1), we have the equation 1.881= $\frac{X-2984}{610}$

We get X= (1.881×610)+2984 =4131,41

The fewest number of calories a person must consume to receive the Piggy award is 4131,41 calories.

7 0

3 years ago

Help! I need to classify each of these numbers

Firdavs [7]

Answer:

1 no 2 no 3 no 4 yes 5 yes

Step-by-step explanation:

A is no, b is no, c is no, d is yes and e is yes.

An integer is a whole number. D and E and -9 and 60 so that is correct.

Hope this helps u plz hit the crown :D

6 0

3 years ago

Read 2 more answers

Solve for y -2(x + 3 y) =18

LUCKY_DIMON [66]

Answer:

y= -3y - 1/3x

Step-by-step explanation:

-2(x + 3y) = 18 Distribute the -2 to the x + 3y

-2x - 6y = 18

+2x +2x Add the 2x to both sides

-6y = 18 + 2x Divide both sides by -6

y= -3y - 1/3x

3 0

3 years ago