How do you write 72 in inches

How many proper subsets does the set T = {i, c, j, e} have?

Gala2k [10]

Number of proper subsets = 2^number of elements- 1
= 2^n - 1
No of elements = 4
2^4-1 = 16-1 = 15

5 0

2 years ago

A rectangle has an area of 36 inches squared. Write an equation to show how the length (l) varies inversely the width (w).

Anastaziya [24]

Start with the first sentence, and the definition of the area of a rectangle:
l * w = 36

Rewrite the equation to get
l = 36 / w
or
w = 36 / l
Either one shows the inverse relationship between w and l.

Assuming the last part wants you to write an equation for an x-y graph, the equation would be
y = 36 / x

8 0

2 years ago

Solve x

d1i1m1o1n [39]

Step-by-step explanation:

$x^{2} - 4x - 7 = 0$

First, let's move the $7$ to the right-hand side so we can determine what constant we'll need on the left-hand side to complete the square:

$x^{2} - 4x = 7$

From here, since the coefficient of the $x$ term is $-4$ , we know the square will be $(x - 2)$ (since $-2$ it's half of $-4$ ).

To complete this square, we will need to add $(-2)^{2}$ to both sides of the equation:

$x^{2} - 4x + (-2)^2 = 7 + ^{-2}$

$x^{2} - 4x + 4 = 7 + 4$

$(x - 2)^{2} = 11$

Now we can take the square root of both sides to figure out the solutions to $x$ :

$x - 2 = \pm \sqrt{11}$

$x = 2 \pm \sqrt{11}$

7 0

3 years ago

The average amount of time that students use computers at a university computer center is 36 minutes with a standard deviation o

frosja888 [35]

Answer:

2119 students use the computer for more than 40 minutes. This number is higher than the threshold estabilished of 2000, so yes, the computer center should purchase the new computers.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 36, \sigma = 5$

The first step to solve this question is finding the proportion of students which use the computer more than 40 minutes, which is 1 subtracted by the pvalue of Z when X = 40. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40 - 36}{5}$

$Z = 0.8$

$Z = 0.8$ has a pvalue of 0.7881.

1 - 0.7881 = 0.2119

So 21.19% of the students use the computer for longer than 40 minutes.

Out of 10000

0.2119*10000 = 2119

2119 students use the computer for more than 40 minutes. This number is higher than the threshold estabilished of 2000, so yes, the computer center should purchase the new computers.

8 0

2 years ago

Answer as many as you can please (write in slope-intercept form)

RoseWind [281]

Answer: See below

Step-by-step explanation:

For the first one, we are already given our slope. All we need to do is find the y-intercept, b.

y=-2x+b

6=-2(-3)+b

6=6+b

b=0

The slope-intercept form is y=-2x.