All categories

3 years ago

Which of the following is a rational number?

Mathematics

1 answer:

Klio2033 [76]3 years ago

5 0

Answer:

√25

Step-by-step explanation:

√25 = √(5²) = 5 . . . . a rational number

The other roots are not the roots of perfect squares, so are irrational.

You might be interested in

While her husband spent 2½ hours picking out new speakers, a statistician decided to determine whether the percent of men who en

AVprozaik [17]

Answer:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

$z=\frac{0.34848-0.34782}{\sqrt{0.34831(1-0.34831)(\frac{1}{66}+\frac{1}{23})}}=0.0057$

$p_v =P(Z>0.0057)=0.4977$

The p value is a very high value and using the significance level $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the percent of men who enjoy shopping for electronic equipment is NOT significantly higher than the percent of women who enjoy shopping for electronic equipment.

Step-by-step explanation:

1) Data given and notation

$X_{M}=23$ represent the number of men that said they enjoyed the activity of Saturday afternoon shopping

$X_{W}=8$ represent the number of women that said they enjoyed the activity of Saturday afternoon shopping

$n_{M}=66$ sample of male selected

$n_{W}=23$ sample of demale selected

$p_{M}=\frac{23}{66}=0.34848$ represent the proportion of men that said they enjoyed the activity of Saturday afternoon shopping

$p_{W}=\frac{8}{23}=0.34782$ represent the proportion of women with red/green color blindness

z would represent the statistic (variable of interest)

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

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment , the system of hypothesis would be:

Null hypothesis: $p_{M} \leq p_{W}$

Alternative hypothesis: $p_{M} > p_{W}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

Where $\hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{23+8}{66+23}=0.34831$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.34848-0.34782}{\sqrt{0.34831(1-0.34831)(\frac{1}{66}+\frac{1}{23})}}=0.0057$

4) Statistical decision

Using the significance level provided $\alpha=0.05$ , the next step would be calculate the p value for this test.

Since is a one side right tail test the p value would be:

$p_v =P(Z>0.0057)=0.4977$

So the p value is a very high value and using the significance level $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the percent of men who enjoy shopping for electronic equipment is NOT significantly higher than the percent of women who enjoy shopping for electronic equipment.

4 0

3 years ago

What is the range of the function f(x) = 3x2 + 6x - 8?

V125BC [204]

Answer:

{y | y ≥ -11 }

Step-by-step explanation:

To answer a question like this, it is often helpful to graph the function or to rewrite it to vertex form.

f(x) = 3x^2 +6x -8

f(x) = 3(x^2 +2x) -8 . . . . factor the leading coefficient from x terms

f(x) = 3(x^2 +2x +1) -8 -3(1) . . . . complete the square*

f(x) = 3(x +1)^2 -11

The form of this equation tells you that the graph is a parabola that opens upward. Its vertex is (-1, -11), so the minimum value is -11. The range is the vertical extent of the function values, so goes upward from -11:

y ≥ -11

_____

* Vertex form is ...

f(x) = a(x -h)^2 +k

where "a" is the vertical scale factor and (h, k) is the vertex. When "a" is positive, the parabola opens upward; when it is negative, the parabola opens downward.

The square is completed by adding the square of half the x-coefficient inside parentheses, and subtracting the equivalent amount outside parentheses. Here, we had 2x inside parentheses, so we added (2/2)^2 = 1 inside and -3(1) outside, because "a" was 3.

_____

Brainly provides tools for properly rendering math symbols. 2-11 is not the same as ≥-11.

7 0

4 years ago

Given f(x)= 17- x2, what is the average rate of change in f(x) over the interval [1, 5)?

makvit [3.9K]

-6 because it is yeah so

7 0

3 years ago

Evaluate 2A - 3B for A = 6 and B = -3.

Rasek [7]

2 (6) - 3 (-3) , 12 - -9 , 12 + 9 , 21

6 0

3 years ago

Read 2 more answers

Eli and Samantha work at a dry cleaners ironing shirts. Eli can iron 20 shirts per hour, and Samantha can iron 35 shirts per hou

MrRa [10]

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> the number of hours Eli worked

y ----> the number of hours Samantha worked

we know that

Eli and they ironed 400 shirts between them

----> equation A

Samantha worked 2 more hours than Eli

----> equation B

solve the system by substitution

substitute equation B in equation A

solve for x

Find the value of y

substitute the value of x in equation B

therefore

The number of hours Eli worked was 6 and the number of hours Samantha worked was 8

5 0

3 years ago