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4 years ago

-6x - 29 + 7x = 8 and -8x + 6x - 13 = 33

2 answers:

7 0

-6x - 29 + 7x = 8
Combine like terms on the left
x - 29 = 8
add 29 to both sides
x = 8 + 29
x = 37

-8x + 6x - 13 = 33
Combine like terms on the left
-2x - 13 = 33
add 13 to both sides
-2x = 46
divide both sides by -2
x = -23

Mumz [18]4 years ago

5 0

First equation:
-6x-29+7x=8
Combine like terms
-6+7=1
1x-29=8
Add 29 to both sides
1x=37
Divide both sides by 1
x=37

Second equation:
-8x+6x-13=33
Combine like terms
-8+6=-2
-2x-13=33
Add 13 on both sides
-2x=46
Divide both sides by -2
x=-23

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3 years ago

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guajiro [1.7K]

Answer:

1) x= 15

2) x= 34

3) x= 40

Step-by-step explanation:

1) 4x°= 45° +15° (vert. opp angles)

4x°= 60° (simplify)

x°= 60° ÷4 (÷4 on both sides)

x°= 15°

Thus, x= 15.

2) (x+12)° +100° +x°= 180° (adj. angles on a str. line)

2x° +12°= 180° -100°

2x°= 80° -12°

2x°= 68°

x°= 68° ÷2

x°= 34°

x= 34

3) 3x°= 120° (vert. opp. angles)

x°= 120° ÷3

x°= 40°

x= 40

Abbreviations:

1. vert. opp. angles

- vertically opposite angles

- This means that when 2 straight lines intersect, the angles facing opposite each other are equal.

2. adj. angles on a str. line

- adjacent angles on a straight line

- the sum of the angles that lie on a straight line is 180°

4 0

3 years ago

Sweets are sold loose or pre packed in 120 G bags. The 120 G bags are 1.49 pounds each By calculating the price per gram determi

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Complete question :

Sweets are sold loose, or pre-packed in 120g bags.The 120g bags are £1.49 each.The loose sweets are £0.89 for 100g.

By calculating the price per gram, determine which is better value.

Answer:

100 g bag

Step-by-step explanation:

For the 120g bag:

Price per gram :

Price / Numbe of gram

1.49 / 120 = 0.0124 gram per bag

For the 100 g bag :

0.89 / 100

= $0.0089per gram

Since $0.0089 is < $0.0124

Then the 100g bag is of better value

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3 years ago

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Answer:

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Step-by-step explanation:

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4 years ago

Suppose Brianna decided that the error margin of her 95% confidence interval was too large and wanted an error margin of .05 whi

svetoff [14.1K]

Answer:

$n=\frac{0.26 (1-0.26)}{(\frac{0.05}{1.96})^2} =295.65 \approx =296$ (b)

Rounded up would be n =296

Step-by-step explanation:

Assuming this previous info: She randomly interested in the p selects 100 engineering majors, and 26 of them said they earned an A in Calc 1.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The margin of error for the proportion interval is given by this formula:

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

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.96$

Thes estimated proportion is $\hat p = \frac{26}{100}=0.26$

And replacing we got:

$n=\frac{0.26 (1-0.26)}{(\frac{0.05}{1.96})^2} =295.65 \approx =296$ (b)

3 0

3 years ago