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RoseWind [281]
1 year ago
11

Find the quotient 3^15/3^3

Mathematics
1 answer:
Sati [7]1 year ago
6 0

There is a property called "Quotient of powers property", which states that:

\frac{a^m}{a^n}=a^{(m-n)}

Where "a" is the common base and "m" and "n" are exponents.

For this case, you have:

\frac{3^{(15)}}{3^3}

Then, in order to find the quotient, you must apply the Quotient of powers property. You need to write the common base (in this case is 3) and then subtract the exponents.

So, you get that the quotient is:

\frac{3^{(15)}}{3^3}=3^{(15-3)}=3^{(12)}

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The swimming pool at Spring Valley High School is a rectangle with a width of 75 meters and a length of 35 meters. Around the pe
stealth61 [152]
Same as before

total=(2w+75)(2w+35)=4w²+220w+2625

pool=75 times 35=2625

minus pool from total
4w²+220w+2625-2625=4w²+220w
4 0
3 years ago
Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body b
sesenic [268]

Answer:

\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001

s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095

-The sample is too small to make judgments about skewness or symmetry.

H0:\mu_{1}=\mu_{2}

H1:\mu_{1} \neq \mu_{2}

t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013

p_v =2*P(t_{(14)}

So the p value is a very high value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a we don't have a significant difference between the two means.

Step-by-step explanation:

First we need to find the difference defined as:

(Operator 1 minus Operator 2)

d1=1.326-1.323=0.003      d2=1.337-1.322=0.015

d3=1.079-1.073=0.006     d4=1.229-1.233=-0.004

d5=0.936-0.934=0.002   d6=1.009-1.019=-0.01

d7=1.179-1.184=-0.005      d8=1.289-1.304=-0.015

Now we can calculate the mean of differences given by:

\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001

And for the sample deviation we can use the following formula:

s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095

Describe the distribution of these differences using words. (which one is correct)

We can plot the distribution of the differences with the folowing code in R

differences<-c(0.003,0.015,0.006,-0.004,0.002,-0.01,-0.005,-0.015)

hist(differences)

And we got the image attached. And we can see that the distribution is right skewed but we don't have anough info to provide a conclusion with just 8 differnences.

-The sample is too small to make judgments about skewness or symmetry.

Use a significance test to examine the null hypothesis that the two operators have the same mean. Give the test statistic. (Round your answer to three decimal places.)

\bar X_{1}=1.173 represent the mean for the operator 1

\bar X_{2}=1.174 represent the mean for the operator 2

s_{1}=0.1506 represent the sample standard deviation for the operator 1

s_{2}=0.1495 represent the sample standard deviation for the operator 2

n_{1}=8 sample size for the operator 1

n_{2}=8 sample size for the operator 2

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0:\mu_{1}=\mu_{2}

H1:\mu_{1} \neq \mu_{2}

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) like this:

t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013

Statistical decision

For this case we don't have a significance level provided \alpha, but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:

df=n_{1}+n_{2}-2=8+8-2=14

Since is a bilateral test the p value would be:

p_v =2*P(t_{(14)}

So the p value is a very high value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a we don't have a significant difference between the two means.

8 0
3 years ago
George said if 2 and 4 are factors of a number, then 8 is a factor of the whole number. is he correct explain
Mamont248 [21]
He is correct and incorrect. 2 and 4 can create factors but they can also be factors of other numbers. So 8 can be a factor of bigger whole numbers and can also have it own smaller factors.
8 0
3 years ago
Side a of the triangle is a utility pole. Henry would like to know how long the guy wire, c, should be.
jasenka [17]

We know that the pole is perpendicular to the ground

And that the length of the pole is 20 feet tall, and the base is 15 feet

Now, the guy wire is a wire that provides support to the pole by connecting the top of the pole to the ground

So this represents a right angled triangle (refer image), and the hypotenuse is the length of the guy wire

Using Pythagoras theorem, we can find out the length of the hypotenuse

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ Hypotenuse² = 20² + 15²

⇒ Hypotenuse² = 400+225

⇒ Hypotenuse² = 625

⇒ Hypotenuse = √625

⇒ Hypotenuse = 25

Hence, the correct option is B  25 ft.

6 0
3 years ago
2/5 of 1 meter=____cm<br> Plz help thx
Crazy boy [7]

Answer:

40 cm

Explanation:

2/5 = 0.4

1 meter = 100 cm

so,

100 x 0.4= 40 cm

4 0
3 years ago
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