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4 years ago

Write the equations after translating the graph of y = |x|: one unit up,

Mathematics

1 answer:

Tatiana [17]4 years ago

5 0

Answer:

$g(x) = |x| + 1$

Step-by-step explanation:

Given

$y = |x|$

Required

Translate 1 unit up

Start by replacing y with f(x)

$f(x) = |x|$

To translate an the graph of an absolute function upward, you make use of the formula;

$g(x) = f(x) + k$

Where k is the number of units

In this case; $k = 1$

Hence;

$g(x) = f(x) + k$

Substitute $k = 1$

$g(x) = f(x) + 1$

Substitute $f(x) = |x|$

$g(x) = |x| + 1$

<em>Hence, the resulting equation is </em> $g(x) = |x| + 1$ <em></em>

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5:60::3:x, what is the value of x?

lora16 [44]

Step-by-step explanation:

we know that product of means is equal to product of extremes so extremes are 5 and x and means are 60 and 3....

5×x=60×3

5x=180

X=180/5

X=36 Answer

4 0

3 years ago

This week, we are covering relationships that can be approximated by linear equations. For instance, y = 453x + 3768 represents

lana [24]

Answer:

See explanation below.

Step-by-step explanation:

We assume that the data is given by :

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

Where X represent the cost for scholarships in thousands of dollars and y represent the cost of life for an academic semester (The data comes from the web)

We can find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

We have an inverse linear relationship since the slope is negative between the variables of interest.

8 0

4 years ago

One of the values in this data set is 138.In this box Plot, what does this value mean ?

lesya [120]

Answer:

The value is the interquartile range which is 138.

Step-by-step explanation

Internet

8 0

3 years ago

2) In a random survey of 500 women, 315 said they would rather be poor and thin than rich and fat; in a random survey of 400 men

Anton [14]

Answer:

Since the calculated value of Z= 0.242887 is less than Z (0.05) = 1.645 and falls in the critical region we reject the null hypothesis and conclude that there is not sufficient evidence to show that the proportion of women who would rather be poor and thin than rich and fat is greater than the proportion of men who would rather be poor and thin than rich and fat.

Step-by-step explanation:

Here

p1= proportion of women who would rather be poor and thin than rich and fat

p1= 315/500= 0.63

p2= proportion of men who would rather be poor and thin than rich and fat

p2= 220/400= 0.55

1) Formulate the hypothesis as

H0: p1>p2 against the claim Ha: p1 ≤ p2

2) Choose the significance level ∝0.05

3) The test Statistic under H0 , is

Z= p1^ - p2^ / sqrt( pc^qc^( 1/n1 + 1/n2))

pc^= an estimate of the common proportion

pc ^ = n1p1^ + n2p2^/ n1+n2

4) The critical region is Z≤ Z (0.05) = 1.645

5) Calculations

pc^ = 315+ 220/ 500+400= 535/900

pc^= 0.5944

and qc^= 1-0.5944= 0.4055

Thus

Z = 0.63-0.55/ sqrt ( 0.5944*0.4055( 1/500+ 1/400))

Z= 0.08/ sqrt (0.24108 (900/2000))

Z= 0.08/√0.10849

Z= 0.242887

Conclusion :

6 0

3 years ago

Look at pic 10 pts will mark brainilest

Gnoma [55]

Answer:

x/4 = 14

Bottom right one

Step-by-step explanation:

x/4 = 14

Bottom right one

There were 4 total and each payed 13.

7 0

3 years ago

Read 2 more answers