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4 years ago

What is the equation !!! Math 3. 10 points HELP NEEDED!!!

Mathematics

1 answer:

Ira Lisetskai [31]4 years ago

7 0

ANSWER

${f}^{ - 1} (x) = {x}^{2} - 3$

EXPLANATION

Given

$f(x) = \sqrt{x + 3}$

Let

$y= \sqrt{x + 3}$

Interchange x and y.

$x= \sqrt{y + 3}$

Square both sides

${x}^{2} = y + 3$

Solve for y

$y = {x}^{2} - 3$

Therefore the inverse of f(x) is

${f}^{ - 1} (x) = {x}^{2} - 3$

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(Please answer before 5:15 P.M tonight)

taurus [48]

The scale factor of dilation from ABC to $A^{1} B^{1} C^{1}$ is 0.333.

Step-by-step explanation:

Step 1:

First, we plot the coordinates of both triangles.

The coordinates of the triangle $A^{1} B^{1} C^{1}$ are as follows;

$A^{1}$ = (2, 3), $B^{1}$ = (2, 1), and $C^{1}$ = (3, 1).

The coordinates of triangle ABC are;

A = (4, 9), B = (4, 3), and C = (7, 3).

Step 2;

Next, we need to find the distances between at least two coordinates for both triangles.

The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.

The distance of $A^{1} B^{1} = 3-1=2$ , the distance of $B^{1} C^{1} = 3-2=1$ .

The distance of AB $=9-3=6,$ the distance of BC $= 7-4=3.$

Step 3;

To calculate the scale factor, we divide the measurement after scaling by the same measurement before scaling.

In this case, it is the length of the AB.

So The scale factor for AB = $\frac{2}{6} = \frac{1}{3} = 0.333.$

The scale factor for BC = $\frac{1}{3} = 0.333.$

7 0

3 years ago

If x is equal to -6 which equality is true

Papessa [141]

Answer:

-5 - 3x > 10

Step-by-step explanation:

x = -6

Plug in the x value for each inequality:

-5 - 3(-6) > 10

-5 + 18 > 10

13 > 10

True

-3 - 5(-6) < -14

-3 + 30 < -14

27 < -14

False

1 - 2(-6) > 13

1 + 12 > 13

13 > 13

False

2 - (-6) < -3

2 + 6 < -3

8 < -3

False

Only one of these is true; that is the answer.

8 0

3 years ago

A genetic experiment involving peas yielded one sample of offspring consisting of 420 green peas and 174 yellow peas. Use a 0.01

slavikrds [6]

Answer:

a) $z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

b) For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

$z_{crit}= \pm 2.58$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

Step-by-step explanation:

Data given and notation

n=420+174=594 represent the random sample taken

X=174 represent the number of yellow peas

$\hat p=\frac{174}{594}=0.293$ estimated proportion of yellow peas

$p_o=0.23$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of yellow peas is 0.23:

Null hypothesis: $p=0.23$

Alternative hypothesis: $p \neq 0.23$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

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

Since is a bilateral test the p value would be:

$p_v =2*P(z>3.649)=0.00026$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) Critical value

For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

$z_{crit}= \pm 2.58$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

5 0

4 years ago

A cube has side length a. The side lengths are decreased to 20% of their original size. Write an expression in simplest form for

Tanya [424]

Here is the expression:
(0.8a)^3. Hope it help!

5 0

3 years ago

Find the distance between the point (3, 5) and a line with the equation 5 x - 3 y + 10 = 0

timama [110]

The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.