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3 years ago

(3a ^3)^x = 27a^9 what’s the value of x?

Mathematics

1 answer:

uysha [10]3 years ago

3 0

Answer:

Step-by-step explanation:

$(3a^3)^x=27a^9\\\\(3a^3)^x=3^3a^{3\cdot3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(3a^3)^x=3^3(a^3)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\(3a^3)^x=(3a^3)^3\iff x=3$

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Pls help 10 points !! :))

Julli [10]

Answer:

The second one

Step-by-step explanation:

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3 years ago

A rhinoceros weight when rounded to the nearest thousand was 4,000 pounds. Which of these is the least the rhinoceros could have

Rudik [331]

Answer:

B- 3,500.

Step-by-step explanation:

This is because 3,500 is the lowest number that can be rounded to 4,000.

3,999 and 4,001 can also be rounded but.. (let me show you an image to help).

3,500 < 3,999 < 4,001.

That goes from smallest to largest numbers that round to 4,000.

Hope that helps. x

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3 years ago

A bank is trying to determine which model of safe to install. The bank manager believes that each model is equally resistant to

alexandr402 [8]

Answer:

So on this case the 95% confidence interval would be given by (-1.152;5.152).

$-1.152 < \mu_{safe1}-\mu_{safe2}$

Should we conclude that the average time it takes experts to crack the safes does not differ by model at the 5% significance level?

A) Yes, the 95% confidence interval for ?D contains 0.

Step-by-step explanation:

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

Let put some notation

x=value for Safe 1 , y = value for Safe 2

x: 103, 90, 64, 120, 104, 92, 145, 106, 76

y: 101, 94, 58, 112, 103, 90, 140, 110, 74

The first step is calculate the difference $d_i=x_i-y_i$ and we obtain this:

d: 2, -4, 6, 8, 1, 2, 5, -4, 2

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{18}{9}=2$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =4.093$

The next step is calculate the degrees of freedom given by:

$df=n-1=9-1=8$

Now we need to calculate the critical value on the t distribution with 8 degrees of freedom. The value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , so we need a quantile that accumulates on each tail of the t distribution 0.025 of the area.

We can use the following excel code to find it:"=T.INV(0.025;8)" or "=T.INV(1-0.025;8)". And we got $t_{\alpha/2}=\pm 2.31$

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

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

$2-2.31\frac{4.093}{\sqrt{9}}=-1.152$

$2+2.31\frac{4.093}{\sqrt{9}}=5.152$

So on this case the 95% confidence interval would be given by (-1.152;5.152).

$-1.152 < \mu_{safe1}-\mu_{safe2}$

Should we conclude that the average time it takes experts to crack the safes does not differ by model at the 5% significance level?

A) Yes, the 95% confidence interval for D contains 0.

5 0

3 years ago

Kayla works as a hairdresser. She earned $248.50 in tips in five days. If she earned the same amount each day, about how much di

Svetlanka [38]

She would earn $49.70 per day because $248.50 divided by the number of days (5) would equal $49.70 per day. You can check your work by working backwards. If she earned $49.70 each day for 5 days, she would have $248.50.

7 0

3 years ago

Read 2 more answers

Marie stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the to

Lesechka [4]

Answer:

y= 4+x

Step-by-step explanation:

she has 4 gallons already in the tank

she puts in x more

therefore the total amount in the tank is 4+x

3 0

3 years ago