All categories

4 years ago

Solve the problem.

Mathematics

1 answer:

Lorico [155]4 years ago

5 0

Answer:

Step-by-step explanation:

You must use a combination:

$_nC_k=\dfrac{n!}{k!(n-k)!}$

We have <em>n = 16</em>, <em>k = 3</em>.

Substitute:

$_{16}C_3=\dfrac{16!}{3!(16-3)!}=\dfrac{13!\cdot14\cdot15\cdot16}{2\cdot3\cdot13!}\qquad\text{cancel}\ 13!\\\\=\dfrac{14\cdot15\cdot16}{2\cdot3}=\dfrac{7\cdot5\cdot16}{1}=560$

You might be interested in

Please help me due today and giving 23 points

vladimir2022 [97]

Answer:

The answer is b. 4*3 2/5.

Step-by-step explanation:

It states 4 times the amount Ruby mixed. Ruby mixed it 3 2/5 solution. So you would right out 4 x 3 2/5.

5 0

2 years ago

Read 2 more answers

Need help with 9(c) plzzz

MAVERICK [17]

Since we are given the values for both rows only in the second column, we can use this to solve for the rest of the missing values. Simply divide 3 by 2.49 and multiply that resultant by and multiply that by any missing value for cookies to find the missing cost. In order to solve for the cookies when cost is given, divide 2.49 by 3 and multiply that resultant. I will solve for the first, third, and fourth columns.

3/29=1.2
For column 1, 1.2*1=1.20
For column 3, 1.2*20=24.10
For column 4, 1.2*100=12.00

5 0

3 years ago

An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample

valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

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

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

3 0

3 years ago

) find a vector parallel to the line of intersection of the planes 5x − y − 6z = 0 and x + y + z = 1.

snow_tiger [21]

The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.

Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>

We calculate the cross product as a determinant of (i,j,k) and the normal products

i j k
5 -1 -6
1 1 1

=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>

Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0

Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.

5 0

3 years ago

How to solve -12+7x=x

lord [1]

Answer:

x=2

Step-by-step explanation:

So if the equation is -12+7x=x, you need to subtract 7x, because you want to know the value of x. So the equation now looks like this: -12=-6x

you divide-6 to both sides because we want to iscolate the x

The answer is x=2

Hope it helps!

3 0

4 years ago