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3 years ago

Helpppp 2x-1>5 and 3x-5<19

Mathematics

1 answer:

maria [59]3 years ago

6 0

Answer:

3 < x < 8

Step-by-step explanation:

Solve each part separately

2x - 1 > 5 ( add 1 to both sides )

2x > 6 ( divide both sides by 2 )

x > 3 , that is

3 < x

and

3x - 5 < 19 ( add 5 to both sides )

3x < 24 ( divide both sides by 3 )

x < 8

Then putting the two together

3 < x < 8

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Mrs. Daly's reading classes were surveyed about their reading preferences. The data is summarized in the table below.

andriy [413]

Answer:

Required probability is 0.19

Step-by-step explanation:

The two-way table for the given data is,

Fiction Non-Fiction Total

9th grade 35 8 43

10th grade 52 12 64

Total 87 20 107

It is required to find the probability of the students who prefer to read non-fiction novels, given that they are in 9th grade.

That is, to find the conditional probability $P(Non-fiction| 9th\ grade)$ .

Now, $P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

So, we get,

$P(Non-fiction| 9th\ grade)=\dfrac{(Non-fiction\bigcap 9th\ grade)}{P(9th\ grade)}\\\\P(Non-fiction| 9th\ grade)=\dfrac{8}{43}\\\\P(Non-fiction| 9th\ grade)=0.19$

<h3>Thus, the required probability is 0.19.</h3>

5 0

3 years ago

PLZ HELP its Triangle Properties and where using the 45º-45º-90º Triangle Theorem and the 30º-60º-90º Triangle Theorem.

den301095 [7]

Answer:

The answer to your questions is below

Step-by-step explanation:

4.-

In a 45°-45°-90° triangle, the length of the legs are "x" and the length of the hypotenuse is x $\sqrt{2}$

Then, in this problem, the length of the leg is 7 then the length of the hypotenuse will be 7 $\sqrt{2}$

5.- In a 30°-60°-90° triangle, the length of the hypotenuse is 2x, the length of the longer leg is x $\sqrt{3}$ and the length of the shorter leg is x.

In this problem we have the length of the hypotenuse = 20 and find x.

2x = 20

x = 20/2

x = 10

longer leg = x $x\sqrt{3} = 10\sqrt{3}$

6.- nonzero

7.- hypotenuse = 20 cm

Find x

2x = 20

x = 20/2

x = 10

Shoter leg = x = 10 cm

4 0

3 years ago

Read 2 more answers

Prove the following DeMorgan's laws: if LaTeX: XX, LaTeX: AA and LaTeX: BB are sets and LaTeX: \{A_i: i\in I\} {Ai:i∈I} is a fam

MariettaO [177]

$X-(A\cup B)=(X-A)\cap(X-B)$

I'll assume the usual definition of set difference, $X-A=\{x\in X,x\not\in A\}$ .

Let $x\in X-(A\cup B)$ . Then $x\in X$ and $x\not\in(A\cup B)$ . If $x\not\in(A\cup B)$ , then $x\not\in A$ and $x\not\in B$ . This means $x\in X,x\not\in A$ and $x\in X,x\not\in B$ , so it follows that $x\in(X-A)\cap(X-B)$ . Hence $X-(A\cup B)\subset(X-A)\cap(X-B)$ .

Now let $x\in(X-A)\cap(X-B)$ . Then $x\in X-A$ and $x\in X-B$ . By definition of set difference, $x\in X,x\not\in A$ and $x\in X,x\not\in B$ . Since $x\not A,x\not\in B$ , we have $x\not\in(A\cup B)$ , and so $x\in X-(A\cup B)$ . Hence $(X-A)\cap(X-B)\subset X-(A\cup B)$ .

The two sets are subsets of one another, so they must be equal.

$X-\left(\bigcup\limits_{i\in I}A_i\right)=\bigcap\limits_{i\in I}(X-A_i)$

The proof of this is the same as above, you just have to indicate that membership, of lack thereof, holds for all indices $i\in I$ .

Proof of one direction for example:

Let $x\in X-\left(\bigcup\limits_{i\in I}A_i\right)$ . Then $x\in X$ and $x\not\in\bigcup\limits_{i\in I}A_i$ , which in turn means $x\not\in A_i$ for all $i\in I$ . This means $x\in X,x\not\in A_{i_1}$ , and $x\in X,x\not\in A_{i_2}$ , and so on, where $\{i_1,i_2,\ldots\}\subset I$ , for all $i\in I$ . This means $x\in X-A_{i_1}$ , and $x\in X-A_{i_2}$ , and so on, so $x\in\bigcap\limits_{i\in I}(X-A_i)$ . Hence $X-\left(\bigcup\limits_{i\in I}A_i\right)\subset\bigcap\limits_{i\in I}(X-A_i)$ .

4 0

3 years ago

A pizza chain plans to locate a new pizza franchise on the CCSU campus if the results of a survey show that more than 10% of CCS

kari74 [83]

Answer:

a) Null and alternative hypothesis:

$H_0: \pi=0.1\\\\H_a:\pi>0.1$

b) A Type I error is made when a true null hypothesis is rejected. In this case, it would mean a conclusion that the proportion is significantly bigger than 10%, when in fact it is not.

c) The consequences would be that they would be more optimistic than they should about the result of the investment, expecting a proportion of students that is bigger than the true population proportion.

d) A Type II error is made when a false null hypothesis is failed to be rejected. This would mean that, although the proportion is significantly bigger than 10%, there is no enough evidence and it is concluded erroneously that the proportion is not significantly bigger than 10%

e) The consequences would be that the investment may not be made, even when the results would have been more positive than expected from the conclusion of the hypothesis test.

Step-by-step explanation:

a) The hypothesis should be carried to test if the proportion of students that would eat there at least once a week is significantly higher than 10%.

Then, the alternative or spectulative hypothesis will state this claim: that the population proportion is significantly bigger than 10%.

On the contrary, the null hypothesis will state that this proportion is not significantly higher than 10%.

This can be written as:

$H_0: \pi=0.1\\\\H_a:\pi>0.1$

7 0

3 years ago

What is the coordinate of the center of the circle?

Zanzabum

I think it would be (1,-2)

5 0

3 years ago