Explain how multiplying with 6 is like multiplying with 3.

Jordan went to the store to buy a bicycle that was advertised for $50. When he arrived, he learned that the model he wanted was

Alika [10]

50 + 0.15(50) = 50 + 7.50 = 57.50 <==

3 0

3 years ago

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John leaves his home. He travels 5 blocks south and three blocks west. As the crow flies, how far is John from his home?

riadik2000 [5.3K]

Answer:

5.83 blocks away from his home

Step-by-step explanation:

If he travels 5 blocks south and 3 blocks west, the distance from his house considered along with the distances travelled gives a right angled triangle whose opposite side and adjacent sides are the distances travelled north and west.

The distance from his house after moving 3 blocks west is the hypotenuse side. As such, the distance may be computed using Pythagoras' theorem. Let the distance from his house be G

G^2 = 5^2 + 3^2

G^2 = 25 + 9

= 34

G = √34

=5.83

John is 5.83 blocks away from his home

3 0

3 years ago

Several years ago, 38% of parents who had children in grades K-12 were satisfied with the quality of education the students r

Colt1911 [192]

Answer:

$0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995$

$0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564$

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

For this case we are interesting in the parameter of the true proportion of people satisfied with the quality of education the students receive

The confidence level is given 95%, the significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values are:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The estimated proportion of people satisfied with the quality of education the students receive is given by:

$\hat p =\frac{499}{1165}= 0.428$

The confidence interval for the proportion if interest is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And replacing the info given we got:

$0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995$

$0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564$

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

8 0

3 years ago

What is the solution to the equation -5 =8m +12 /4

Dima020 [189]

m = -1

-5 = 8m + 12/4
-5 - 12/4 = 8m
4(-5) - (12/4) = 4(8m)

*to remove the denominator, multiply each figure by 4.

-20 -12 = 32m
-32 = 32m
-32/32 = 32m/32
-1 = m

m = -1

To check:

-5 = 8m + 12/4
-5 = 8(-1) + 3
-5 = -8 + 3
-5 = -5

3 0

3 years ago

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What is the value of x and the measure of MNQ

serg [7]

Answer:

3x - 13 +58 = 90, so 3x +45 = 90

Then 3x = 90 - 45 = 45 and x= 45/3 = 15.

m∠MNQ = 3x-13 = 3(15) - 13

= 45-13

= 32

6 0

3 years ago