A={1,2,3} set-builder notation

Simplify ((7+sin^2 theta+cos^2 theta)/(4sin^2 theta + 4cos^2 theta))

tino4ka555 [31]

Answer:

2

Step-by-step explanation:

$\frac{7+sin^{2}\theta+cos^{2}\theta}{4sin^{2}\theta+4cos^{2}\theta}} = \frac{7+(sin^{2}\theta+cos^{2}\theta)}{4(sin^{2}\theta+cos^{2}\theta)}} =\frac{7+(1)}{4(1)}}=\frac{8}{4} =2$

$(sin^{2}\theta +cos^{2}\theta=1)\\$

7 0

3 years ago

What is 6/11 - 9/2

Vedmedyk [2.9K]

Answer:

3 and 21/22

Step-by-step explanation:

You convert the fractions so they have the same number as the denominator and then subtract them.

6 0

3 years ago

A process is producing a particular part where the thickness of the part is following a normal distribution with a µ = 50 mm and

Hitman42 [59]

Answer:

0.13% probability that this selected sample has an average thickness greater than 53

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem, we have that:

$\mu = 50, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1$

What is the probability that this selected sample has an average thickness greater than 53?

This is 1 subtracted by the pvalue of Z when X = 53. So

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

By the Central Limit Theorem

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

$Z = \frac{53 - 50}{1}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

1 - 0.9987 = 0.0013

0.13% probability that this selected sample has an average thickness greater than 53

5 0

3 years ago

4. (08.01, 08.02, 08.03 HC)

Dvinal [7]

Answer:

Lets assume a polynomial

Here GCF is 5z

all terms are divisible by 5z. so greatest common factor is 5z

One form of polynomial is

We factor the polynomial further

Other form of polynomial is

and are the two forms of polynomial

First form is created by taking out GCF 5z

<h2>SEcond form is created by factoring x^2 + 5x + 6</h2><h2></h2><h2></h2><h2></h2><h2>hope this help u !!!</h2><h2></h2>

8 0

3 years ago

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one sam

xeze [42]

X = advance
y= same day

x+y=70

30x+15y=1650

--------------------------
30x+15y=1650
- x+y=70 (x15) -> 15x+15y=1050
--------------------------
30x+15y=1650
-15x+15y=1050
--------------------------
15x=600
x=600/15
x=40

so now u can insert the price of x AKA the price of the advanced ticket to find our the price of the same day ticket.

x+y=70
so
40+ y=70
y=70-40
y=30

x = advance =40
y= same day =30

8 0

3 years ago