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3 years ago

Please HELP??????????

Mathematics

1 answer:

Anton [14]3 years ago

7 0

Answer:

Answer is option c)1/5

Step-by-step explanation:

$the \: formula \: states \: that \\ \sqrt[x]{a } \: can \: also \: be \: written \: as \: {a}^{ \frac{1}{x} }$

so the answer is 1/5

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There are 212 students in the 8th grade class. The number of girls is 49 less than twice the number of boys. How many girls and

Anna71 [15]

Answer:

girls = 125

boys = 87

Step-by-step explanation:

Total number of students in the 8th grade class = 212

Let g represent girls and b represent boys

Number of girls, g = 2b -49

Note that boys and girls in the class give a total of 212

So,

g + b = 212 ....eq 1

Slot in the value of g in the equation

2b - 49 + b = 212

2b + b - 49 = 212

3b - 49 = 212

Add 49 to both sides

3b - 49 + 49 = 212 + 49

3b = 261

Divide both sides by the coefficient of b which is 3

b = 87

Now that we've found the number of boys, let's find that of girls

We will slot in the value of b in eq 1

g + 87 = 212

Subtract 87 from both sides

g + 87 - 87 = 212 - 87

g = 125

So the number of boys is 87 and the number of girls is 125

8 0

3 years ago

Solve each compound inequality

PilotLPTM [1.2K]

5 - 5b < 1 - 4b
5 < 1 + b
4 < b
1 - 4b < 6 - 5b
1 + b < 6
b < 5

4 < b < 5
(The second less than sign is less than or equal to)

6 0

3 years ago

In a study of the effect of cooling rate on the hardness of welded joints, 50 welds cooled at a rate of 10°C/s had an average Ro

Studentka2010 [4]

Answer:

a) The 95% confidence interval would be given by $-1.887 \leq \mu_1 -\mu_2 \leq 2.687$

b) No contradict the result obtained since the confidence interval contains the value 0, so we don't have enough evidence to conclude that we have a significant effect in the colling rate and the hardness.

Step-by-step explanation:

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".

$\bar X_1 =91.1$ represent the sample mean 1

$\bar X_2 =90.7$ represent the sample mean 2

n1=50 represent the sample 1 size

n2=40 represent the sample 2 size

$s_1 =6.55$ sample standard deviation for sample 1

$s_2 =4.32$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Part a

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =91.1-90.7=0.4$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n_1 +n_2 -1=50+40-2=88$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,88)".And we see that $t_{\alpha/2}=1.987$

The standard error is given by the following formula:

$SE=\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}$

And replacing we have:

$SE=\sqrt{\frac{6.55^2}{50}+\frac{4.32^2}{40}}=1.325$

Now we have everything in order to replace into formula (1):

$0.4-1.987\sqrt{\frac{6.55^2}{50}+\frac{4.32^2}{40}}=-1.887$

$0.4+1.987\sqrt{\frac{6.55^2}{50}+\frac{4.32^2}{40}}=2.687$

So on this case the 95% confidence interval would be given by $-1.887 \leq \mu_1 -\mu_2 \leq 2.687$

Part b

No contradict the result obtained since the confidence interval contains the value 0, so we don't have enough evidence to conclude that we have a significant effect in the colling rate and the hardness.

3 0

3 years ago

joe need to cut a piece of sheet metal into 5 pieces. it takes him 2 minutes to make each cut. how many cuts will joe make?

Travka [436]

If he starts with one piece and ends up with 5 pieces, then he makes 4 cuts.

It takes him 8 minutes to do the actual cutting, although he may take breaks
between cuts.

4 0

3 years ago

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What value of x is in the solution set of 3(x – 4) = 5x + 2?

yan [13]

Answer:

-5?

Step-by-step explanation:

3(x - 4) = 5x - 2

3x - 12 = 5x - 2

3x - 5x = -2 + 12

-2x = 10

x = -5

4 0

4 years ago

Read 2 more answers