All categories

3 years ago

Please check my answers for me.

1 answer:

3 0

QUESTION 1

The given equation is

$2.5(10 - x) + 10 = 72 - 1.5(5x + 12)$
Clear the decimal by multiplying through by 10 to get,

$25(10 - x) + 100 = 720 - 15(5x + 12)$

Expand the bracket using the distributive property to get;

$250 - 25x + 100 = 720 - 75x - 180$

Group similar terms to get,

$- 25x + 75x = 720 - 250 - 100 - 180$

$50x = 720 - 530$

$50x = 190$

Divide through by 50 to get,

$x = \frac{190}{50}$

$x = \frac{19}{5}$

QUESTION 2

We want to solve the inequality,

$16x \: > \: 12(2x - 6) - 24$

We expand the bracket using the distributive property to obtain,

$16x \: > \: 24x - 72 - 24$

Group similar terms to get,

$16x - 24x \: > \: - 72 - 24$

Simplify to get,

$- 8x \: > \: - 96$

We divide both sides of the inequality by -8 and reverse the sign to obtain,

$x \: < \: \frac{ - 96}{ - 8}$

$x \: < \: 12$

QUESTION 3

Step 1.

Given:4(-6x – 3)+24x= -72x + 132

Step 2.

Distributive property:
-24x – 12 + 24x = -72x + 132

Step 3.

Combine like terms:
–12 = -72x + 132

Step 4.

Addition property of equality:

-144 = -72x

Step 5.

Division property of equality:

2=x

All the properties stated are correct.

You might be interested in

Refer to the figure below to complete the following item. Given: Quadrilateral ROSE is trapezoid with median If MN = 24 and ES =

STatiana [176]

18 is you answer. Hope this helps.

4 0

3 years ago

Read 2 more answers

The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and

kykrilka [37]

Answer:

The calculated χ² = 17.0281 falls in the critical region χ² ≥ 9.49 so we reject the null hypothesis that the quality of management and the reputation of the company are independent and conclude quality of management and the reputation of the company are dependent

The p-value is 0 .001909. The result is significant at p < 0.05

Part b:

40 > 8.5

35> 7.5

25> 4

Step-by-step explanation:

1) Let the null and alternative hypothesis as

H0: the quality of management and the reputation of the company are independent

against the claim

Ha: the quality of management and the reputation of the company are dependent

2) The significance level alpha is set at 0.05

3) The test statistic under H0 is

χ²= ∑ (o - e)²/ e where O is the observed and e is the expected frequency

which has an approximate chi square distribution with ( 3-1) (3-1)= 4 d.f

4) Computations:

Under H0 ,

Observed Expected E χ²= ∑(O-e)²/e

40 35.00 0.71

25 24.50 0.01

5 10.50 2.88

35 40.00 0.62

35 28.0 1.75

10 12.00 0.33

25 25.00 0.00

10 17.50 3.21

15 7.50 7.50

∑ 17.0281

Column Totals 100 70 30 200 (Grand Total)

5) The critical region is χ² ≥ χ² (0.05)2 = 9.49

6) Conclusion:

7) The p-value is 0 .001909. The result is significant at p < 0.05

The p- values tells that the variables are dependent.

Part b:

If we take the excellent row total = 70 and compare it with the excellent column total= 100

If we take the good row total = 70 and compare it with the good column total= 80

If we take the fair row total = 50 and compare it with the fair column total= 30

The two attributes are said to be associated if

Thus we see that ( where (A)(B) are row and columns totals and AB are the cell contents)

AB> (A)(B)/N

40 > 1700/200

40 > 8.5

35> 1500/200

35> 7.5

25> 800/200

25> 4

and so on.

Hence they are positively associated

8 0

3 years ago

i think of a number, multiply it by 2 subract 6 and then divide by 4. If the answer is 8 what is the original number

ivanzaharov [21]

Answer:

Step-by-step explanation:

8 x 4 = 32

32 + 6 = 38

38 / 2 = 19

6 0

3 years ago

What is y+3=4(x-1) in Slope intercept form ?

mina [271]

Y+3=4(x-1)
Y+3=4x-4
-3 -3
Y=4x-7

3 0

3 years ago

Gelneren [198K]

Answer:

General equation of line : $y = mx+c$ --1

Where m is the slope or unit rate

Table 1)

p d

1 3

2 6

4 12

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

First find the slope

First calculate the slope of given points

$m = \frac{y_2-y_1}{x_2-x_1}$ ---A

$(x_1,y_1)=(1,3)$

$(x_2,y_2)=(2,6)$

Substitute values in A

$m = \frac{6-3}{2-1}$

$m = 3$

Thus the unit rate is 3 dollars per pound.

So, It matches the box 1 (Refer the attached figure)

Equation 1 : $p=3d$

$\frac{p}{3}=d$

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

$m = \frac{1}{3}$

Thus the unit rate is $\frac{1}{3}$ dollars per pound

So, It matches the box 2 (Refer the attached figure)

Equation 2 : $\frac{1}{3}d=3p$

$d=9p$

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

$m =9$

Thus the unit rate is 9 dollars per pound

So, It matches the box 3 (Refer the attached figure)

Table 2)

p d

1/9 1

1 9

2 18

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

$(x_1,y_1)=(\frac{1}{9},1)$

$(x_2,y_2)=(1,9)$

Substitute values in A

$m = \frac{9-1}{1-\frac{1}{9}}$

$m = \frac{8}{frac{8}{9}}$

$m = 9$

Thus the unit rate is 9 dollars per pound

So, It matches the box 3 (Refer the attached figure)

3 0

4 years ago

Read 2 more answers