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How many 4 digit numbers can be created from the digits 7.3.1,8,3 and 4

Sloan [31]

1,2,9,6 there's your answer

8 0

3 years ago

I am stuck, please help

ASHA 777 [7]

Answer:

2323

Step-by-step explanation:

Mental math means to find a way to do this problem in your head without using paper, pencil or a calculator.

The question says there are 23 classes and each class is to collect 101 items.

The equation would be 23 x 101.

To do this in your head real quick, make the numbers easier to multiply.

Make the 101 items 100. That means you are telling each class to collect 1 less item or 23 less items total.

You can do this in your head real quick. 23 classes collecting 100 items is 2300 items.

You had each class collect 100 items instead of 101. That mean you didn't collect 23 items. So if you add those back in, you will get

2323 items.

3 0

2 years ago

Translate the sentence into an equation.

zavuch27 [327]

Answer:
2*(b-6)=8

Explication:
1.divide both sides by 2
b - 6 = 4

2. move the constant to the right and change the sign
b= 4 + 6

3. Calculate
b= 10

7 0

3 years ago

Determine which of the indicated column vectors are eigenvectors of the given matrix

gladu [14]

]Eigenvectors are found by the equation $(A-\lambda I) \vec{v} = 0$$ implying that $\det(A-\lambda I) = 0$ . We then can write:

$A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]$

And:

$\det(A-\lambda I) = (4-\lambda)(1-\lambda) - 10 = 0$

Gives us the characteristic polynomial:

$\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6$

So, solving for each eigenvector subspace:

$\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]$

Gives us the system of equations:

$4x + 2y = -x \newline 5x + y = - y$

Producing the subspace along the line $y = -\frac{5}{2} x$

We can see then that 3 is the answer.

7 0

3 years ago

company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26

podryga [215]

Answer:

$t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435$

$p_v =P(t_{(49)}$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

Step-by-step explanation:

Data given and notation

$\bar X=25.02$ represent the sample mean

$s=4.83$ represent the sample standard deviation

$n=50$ sample size

$\mu_o =26$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is at least 26 mpg, the system of hypothesis would be:

Null hypothesis: $\mu \geq 26$

Alternative hypothesis: $\mu < 26$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=50-1=49$

Since is a one sided test the p value would be:

$p_v =P(t_{(49)}$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

3 0

3 years ago