Solve the system of equations graphically.

How many ten-digit numbers have at least two equal digits?

hammer [34]

Answer:

8,996,734,079 numbers

Step-by-step explanation:

First let's find the number of ten-digit numbers.

The maximum ten-digit number is 9,999,999,999 and the minimum is 1,000,000,000. So the number of ten-digit numbers is:

$N(total) = 9999999999 - 1000000000 = 8,999,999,999$

Now, to find the number of ten-digit numbers with at least two equal digits, we can find the number of ten-digit numbers with all digits different, and then subtract this amount from the total ten-digit numbers.

To find the number of ten-digit numbers with all digits different, we can use the following logic:

The first digit can have 9 different values (0 not included), the second can also have 9 (one digit used), then the third can have 8 (two digits used), the fourth can have 7, and so on. So we have that:

$N(different) = 9*9! = 3,265,920$

Then the number of ten-digit numbers with at least two equal digits is:

$N(two\ equal) = N(total)-N(different) = 8999999999 - 3265920$

$N(two\ equal) = 8,996,734,079$

3 0

3 years ago

The University of Arkansas recently approved out of state tuition discounts for high school students from any state. The student

Fudgin [204]

Answer:

$z=\frac{0.872 -0.9}{\sqrt{\frac{0.9(1-0.9)}{180}}}=-1.252$

$p_v =P(z$

So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% the proportion of students who came from Arkansas or a bordering state is not significantly lower than 0.9

b. Fail to reject H0; conclude that the new policy increases the percentage of students from states that don’t border Arkansas

Step-by-step explanation:

Data given and notation n

n=180 represent the random sample taken

X=157 represent the students who came from Arkansas or a bordering state

$\hat p=\frac{157}{180}=0.872$ estimated proportion of students who came from Arkansas or a bordering state

$p_o=0.9$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is higher or not than 0.9.:

Null hypothesis: $p\geq 0.9$

Alternative hypothesis: $p < 0.9$

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

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

$z=\frac{0.872 -0.9}{\sqrt{\frac{0.9(1-0.9)}{180}}}=-1.252$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.1$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(z$

So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% the proportion of students who came from Arkansas or a bordering state is not significantly lower than 0.9

b. Fail to reject H0; conclude that the new policy increases the percentage of students from states that don’t border Arkansas

4 0

3 years ago

Directions: Use the drawing tool(s) to form the correct answer on the provided number line.

snow_tiger [21]

5 cus that’s where they meet

4 0

3 years ago

How do find the volume of l blocks

kow [346]

For number 1)

you must first split the figure, so subtract the 8 mm from 12 mm to find the width.... = 4mm

so you use the numbers 10 x 2 x 4 = 80 mm

and 2 x 8 x 3 = 48 mm

80 mm + 48 mm = volume of the figure

5 0

3 years ago

Can someone help me with this one I would appreciate it very much!!

jekas [21]

Answer:

12.5 pounds

Step-by-step explanation:

16 ounces = 1 pound

200 ounces = 1 × 200/16 = 12.5 pounds

6 0

3 years ago