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3 years ago

4. Find x if PQ = RS, PQ = 9x - 7, and RS = 29.

Mathematics

1 answer:

Gnoma [55]3 years ago

4 0

Answer:

x=4

Step-by-step explanation:

Because we know that PQ = RS, we can use the transitive property to replace PQ in the first equation with 29:

9x-7=29

1) Add 7 to both sides:

9x=36

2) divide by 9 on both sides:

x=4

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An article reported on the results of an experiment in which half of the individuals in a group of 60 postmenopausal overweight

slavikrds [6]

Answer:

Step-by-step explanation:

From the given information:

Let's first compute the null and alternative hypothesis

Null hypothesis:

$\mathbf{H_o: \mu_1-\mu_2=1}$

Alternative hypothesis:

$H_a :\mu_1 -\mu_2 > 1$

The number of samples is half in a group of 60

i.e

$n_1=n_2 = 30$

the sample mean for sample 1 $\overline x_1$ = 5.7

the standard deviation for sample 1 $s_1$ = 3.1

the sample mean for sample 2 $\overline x_2$ = 3.9

the standard deviation for sample 2 $s_2$ = 2.7

degree of freedom for this test can be computed by using the formula:

$df = \dfrac{\begin {pmatrix} \dfrac{s_1^2}{n_1} + \dfrac{s^2_2}{n_2} \end {pmatrix}^2 } {\dfrac{ (\dfrac{s_1^2}{n_1}^2)}{ n_1-1} + \dfrac{ (\dfrac{s_2^2}{n_2}^2)}{ n_2-1} }$

$df = \dfrac{\begin {pmatrix} \dfrac{3.1^2}{30} + \dfrac{2.7^2}{30} \end {pmatrix}^2 } {\dfrac{ \begin {pmatrix} \dfrac{3.1^2}{30} \end {pmatrix}^2}{ 30-1} + \dfrac{ \begin {pmatrix} \dfrac{2.7^2}{30} \end {pmatrix}^2}{ 30-1} }}$

df = 114.68

The test statistics can be computed as follows:

$t = \dfrac{ \overline x_1 -\overline x_2- (\mu_1 -\mu_2)}{\sqrt{ \dfrac{s_1^2}{n_1} +\dfrac{s_2^2}{n_2} }}$

$t = \dfrac{ 5.7-3.9- (1)}{\sqrt{ \dfrac{3.1^2}{30} +\dfrac{2.7^2}{30} }}$

t = 1.07

Using the level of significance of 0.1, the P-value for the test statistics at the df of 114.68 is:

P-value = 0.143

Decision rule: To reject the null hypothesis if the level of significance is greater than the p-value.

Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance at 0.1.

Thus, it appears that the true average weight loss for the vegan diet does not exceeds that for the control diet by more than 1 kg.

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3 years ago

Henry counted units to find the distance between two points. For which pair of points could he have done this? Select all that a

zimovet [89]

Answer: point

(5, 3) and (9, 3) (2, 3) and (7, 3)

Step-by-step explanation:

When all the coordinate are plotted on a graph, point (5, 3) and (9, 3) , & point (2, 3) and (7, 3) are found to be in a straight line. So Henry will count some units to find the distance between two points of the coordinate given above.

6 0

3 years ago

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Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three

RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

$f(x)=x^{2}$

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

$g(x)=-5x^{2}+100x-450$

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

$g(x)=-5x^{2}+100x-450$

Complete the square

$g(x)=-5(x^{2}-20x)-450$

$g(x)=-5(x^{2}-20x+100)-450+500$

$g(x)=-5(x^{2}-20x+100)+50$

$g(x)=-5(x-10)^{2}+50$

The vertex is the point (10,50)

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

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3 years ago

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Multiply and divide Decimals

Tanzania [10]

Answer:

$57

Step-by-step explanation:

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2 years ago

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Consider multiplying 26.2 by 16.43 what would a mathematician say the answer is

IgorC [24]

In mathematics multiplying decimals is just like multiplying a whole number and ignoring the decimals., then just put the decimals in the answer – it is how many decimals does the two numbers combined.

First step:

Line the numbers on the right and do not a line the decimal points

26.2

× 16.43

Second Step:

Multiply the numbers starting on the right, just like multiplying a whole number and ignore the decimals.

26.2

× 16.43

786

1048

1572

+ 262

430466

Third step: add the products

26.2

× 16.43

786

1048

1572

+ 262

430.466 is the mathematician’s answer.

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3 years ago