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The ratio of the units digit to the tens digit in a two-digit number is one-half. the tens digit is two more than the units digi

vodomira [7]

Let the first digit of the 2-digit number be x and the second digit be y.
Then the ratio (x/y) equals (1/2). Write a formula for y in terms of x.

The tens digit is 2 more than the units digit. Using the letters x and y, write out the proper equation.

Now solve your two equations simultaneously for x and y.

5 0

3 years ago

Ignoring those who said they weren't sure, there were 297 men asked, and 183 said yes, they had driven a car when they probably

USPshnik [31]

Answer:

$z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998$

$p_v =2*P(z>3.998)=0.0000639$

With the most common significance levels used $\alpha= 0.1, 0.05, 0.01$ we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5

Step-by-step explanation:

Information given

n=297 represent the random sample of male taken

X=183 represent the men who said yes, they had driven a car when they probably had too much alcohol

$\hat p=\frac{183}{297}=0.616$ estimated proportion of men who said yes, they had driven a car when they probably had too much alcohol

$p_o=0.5$ is the value that we want to test

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Hypothesis to test

We need to conduct a hypothesis in order to test the claim that the majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, and the system of hypothesis are:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p > 0.5$

The statistic is given by:

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

After replace we got:

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998$

Decision

We have a right tailed test so then the p value would be:

$p_v =2*P(z>3.998)=0.0000639$

With the most common significance levels used $\alpha= 0.1, 0.05, 0.01$ we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5

7 0

2 years ago

Asap I will fail it’s due soon

Elan Coil [88]

Answer:

See explanation

Step-by-step explanation:

1. From the graph of absolute value function:

a. The domain is $x\in (-\infty, \infty)$

b. The range is $y\in [0,\infty)$

c. The graph is increasing for all $x>0$

d. The graph is decreasing for all $x$

2. From the graph of quadratic function:

a. The domain is $x\in (-\infty, \infty)$

b. The range is $y\in (-\infty,0]$

c. The graph is increasing for all $x$

d. The graph is decreasing for all $x>0$

4 0

2 years ago

Sam had monkeys and lions in his zoo, He counted legs one day to discover that he could see 76 feet on the ground. He knew that

cricket20 [7]

If he counts 76 feet, that means there’s 38 animals in total, because animals have 2 feet. 76/2=38

Hope that helps..!

5 0

3 years ago

Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins $2$ years younger than

vagabundo [1.1K]

Let the youngest sister be n years
Lana will be 2n years, as her youngest sister is half her age
The age of the twins separately will be 2n-2 as they are 2 years younger than Lana
So, the equation looks like this:
n + 2n + 2(2n-2) = 45
Now solve for n:
3n + 4n - 4 = 45
7n - 4 = 45
7n = 49
n = 7
So the youngest sister is 7, Lana is 14 and the twins are 12. 14 + 12 + 12 + 7 =45

8 0

3 years ago

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