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Mumz [18]
3 years ago
12

20 POINTS! Please look at the attached image!

Mathematics
2 answers:
Ira Lisetskai [31]3 years ago
8 0

Answer:

a) 5^4 / 5^2, 5^2

b) 7^3 /  7^3, 7^0=1

c) 8^7/8^4, 8^3

Step-by-step explanation:

A quotient of two powers is basically the powers before its simplified. So for a 5 x 5 x 5 x 5 is 5 being multiplied by itself 4 times divided by 5 x 5 which is 5 being multiplied by itself 2 times. So this leads us to the conclusion that 5^4/5^2 for the quotient of two powers. Then using the rules of powers when dividing powers you subtract so in this case 4-2 is 2. So the answer is 5^2 for single power. The other problems are basically the same as well, just different numbers.

b) (7 x 7 x 7)/ (7 x 7 x 7)= 7^3/7^3=7^0=1

c)(8 x 8 x 8 x 8 x 8 x 8 x 8)/(8 x 8 x 8 x 8)= 8^7/8^4= 8^3

horrorfan [7]3 years ago
8 0

Answer:

a) 5⁴/5² = 5²

b) 7³/7³ = 7⁰

c) 8⁷/8⁴ = 8³

Step-by-step explanation:

Quotient is a fraction.

a) 5×5×5×5 = 5⁴

5×5 = 5²

5⁴/5² = 5^(4-2) = 5²

b) 7×7×7 = 7³

7³/7³ = 7⁰ = 1

c) 8×8×8×8×8×8×8 = 8⁷

8×8×8×8 = 8⁴

8⁷/8⁴ = 8^(7-4) = 8³

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A counselor at a community college claims that the mean GPA for students who have transferred to State University is more than 3
Lena [83]

Answer:

t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3  

If we compare the p value and the significance level for example \alpha=1-0.99=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

Data given and notation  

\bar X=3.25 represent the sample mean

s=0.3 represent the sample standard deviation

n=36 sample size  

\mu_o =3.1 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is more than 3.1, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3.1  

Alternative hypothesis:\mu > 3.1  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3  

P-value  

The first step is calculate the degrees of freedom, on this case:  

df=n-1=36-1=35  

Since is a one right tailed test the p value would be:  

p_v =P(t_{(35)}>3)=0.00247  

Conclusion  

If we compare the p value and the significance level for example \alpha=1-0.99=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

5 0
3 years ago
Glenn needs to cut pieces of a lanyard that are each 1 meter long to make lanyard key chains. If he has 3 pieces of lanyard that
Novosadov [1.4K]

Answer:

30

Step-by-step explanation:

3 pieces each 1 dekameter long

1 dekameter = 10 meters

Convert dekameters to meters

3 pieces each 10 meters long

Multiply

Glenn has 30 meters of lanyard

Divide

He can cut 30 1-meter pieces

Hope this helps :)

3 0
3 years ago
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of
Zolol [24]

Answer:

probability of lasting longer = 1.7%

Step-by-step explanation:

We are given:

x' = 14 years

μ = 12.3 years

s = 0.8 years

Thus, let's use the formula for the Z-score value which is;

z = (x' - μ)/s

Thus;

z = (14 - 12.3)/0.8

z = 2.125

From the z-distribution table attached, the p-value is ;

P(x' > 2.125) = 1 - 0.983 = 0.017 = 1.7%

Thus,probability of lasting longer = 1.7%

5 0
3 years ago
Harry cycles 8 kilometres in 30 minutes.<br> Calculate his average speed, in km/h
Lerok [7]
8 km / 0.5 hr
= 16 km/h
4 0
2 years ago
Read 2 more answers
Can somebody help me please?
madreJ [45]
Factor
(x+7)(x-2)

Proof
7-2=5
7*-2=-14

Zeros
x+7=0
x=-7

x-2=0
x=2

Final answer: C

3 0
3 years ago
Read 2 more answers
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