Patrycja goes shopping in a supermarket.

Jack is 3 times a as old as lacy. 8 years ago the sum of their ages was 25. how old are they now?

OlgaM077 [116]

Let x = age of jack

Let y = age of Lacy

x=3y (Jack age is 3 times that of Lacy)

(x+y)-8 = 25

Substituting value of x:

(3y+y) -8 = 25

4y - 8 = 25

4y = 33

y = 33/4 = 8.25 or 8 years 3 months (age of Lacy)

x = 3(8.25) = 24.75 or 24 years 9 months (age of Jack)

Checking:

Substituting in equation ( x + y ) -8 = 25

24.75 + 8.25 - 8 = 25

25 = 25

3 0

3 years ago

A paper reported that in a representative sample of 282 American teens age 16 to 17, there were 71 who indicated that they had s

elena-s [515]

Answer:

$z=\frac{0.252 -0.25}{\sqrt{\frac{0.25(1-0.25)}{282}}}=0.0776$

$p_v =P(z>0.0776)=0.4691$

Since the p value is higher than the significance level so then we can conclude that we have enough evidence to FAIL to reject the null hypothesis and there is no evidence in order to say that the true proportion of teens more than a quarter of Americans age 16 to 17 have sent a text message while driving is higher than 0.25

Step-by-step explanation:

Information provided

n=282 represent the sample selected

X=71 represent the teens indicated that they had sent a text message while driving

$\hat p=\frac{71}{282}=0.252$ estimated proportion of teens indicated that they had sent a text message while driving

$p_o=0.25$ is the value that we want to test

$\alpha=0.01$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to check if more than a quarter of Americans age 16 to 17 have sent a text message while driving, and the hypothesis are:

Null hypothesis: $p\leq 0.7$

Alternative hypothesis: $p > 0.25$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.252 -0.25}{\sqrt{\frac{0.25(1-0.25)}{282}}}=0.0776$

Decision

The p value for this case is:

$p_v =P(z>0.0776)=0.4691$

Since the p value is higher than the significance level so then we can conclude that we have enough evidence to FAIL to reject the null hypothesis and there is no evidence in order to say that the true proportion of teens more than a quarter of Americans age 16 to 17 have sent a text message while driving is higher than 0.25

8 0

3 years ago

If the area of a trapezoid is 164 ft squared and the bases are 20 ft and 12.8 ft, what is the height of the trapezoid?

jenyasd209 [6]

Answer:

10

Step-by-step explanation:

3 0

3 years ago

Help!...............

Ket [755]

Y=3x+3
They did 1/3 instead of 3/1