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UkoKoshka [18]
3 years ago
10

Simplify the following expression as much as possible 4^10 divided by 4^10 . 7^0

Mathematics
2 answers:
nikklg [1K]3 years ago
8 0

Answer:

  • 1

Step-by-step explanation:

<u>Simplify</u>

  • 4^10 divided by 4^10 . 7^0
  • 4^10/(4^10*7^0) =
  • 4^10/4^10 =
  • 1
Svetllana [295]3 years ago
6 0

Answer:

<h2>1</h2>

Step-by-step explanation:

<u>   4¹⁰    </u>

4¹⁰ * 7⁰

<u>   4¹⁰    </u>

4¹⁰ * 1

= 1

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A sample of 100 workers located in Atlanta has an average daily work time of 6.5 hours with a standard deviation of 0.5 hours. A
Readme [11.4K]

Answer:

t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398  

df = n_1 +n_2 -2= 100+110-2= 208

Since is a bilateral test the p value would be:

p_v =2*P(t_{208}

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

\bar X_{1}=6.5 represent the sample mean for Atlanta

\bar X_{2}=6.7 represent the sample mean for Chicago

s_{1}=0.5 represent the sample deviation for Atlanta

s_{2}=0.7 represent the sample standard deviation for Chicago

n_{1}=100 sample size for the group Atlanta

n_{2}=110 sample size for the group Chicago

t would represent the statistic (variable of interest)

\alpha=0.01 significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the meanfor atlanta is different from the mean of Chicago, the system of hypothesis would be:

Null hypothesis:\mu_{1}=\mu_{2}

Alternative hypothesis:\mu_{1} \neq \mu_{2}

Since we don't know the population deviations for each group, 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 value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398  

What is the p-value for this hypothesis test?

The degrees of freedom are given by:

df = n_1 +n_2 -2= 100+110-2= 208

Since is a bilateral test the p value would be:

p_v =2*P(t_{208}

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

3 0
3 years ago
Read 2 more answers
Find the area of the shape.
vesna_86 [32]

Answer:

what was the answer?? I am also needing to know!

8 0
2 years ago
Adult tickets for the movie theater cost $9. Child tickets cost $5.25. Write an expression for the total cost of a group of adul
sammy [17]

Answer:

Step-by-step explanation:

9a + 5.25c

5 0
2 years ago
Let a be a real number and n a positive integer . show that x-a is a factor of x^n- a^n
nikklg [1K]

Answer:

steps below

Step-by-step explanation:

x-a=0

x=a   plug in xⁿ - aⁿ

xⁿ - aⁿ = aⁿ - aⁿ = 0

(x-a) must be a factor of xⁿ - aⁿ

6 0
3 years ago
Pls help i really really need help on this. We just learned this but i can't remember it.
bulgar [2K]

Answer:

114 cm²

Step-by-step explanation:

Area of shaded region

= area of circle -area of square

\boxed{area \: of \: circle = \pi {r}^{2} }

Given that radius= 10cm, r= 10cm.

\boxed{area \: of \: square = side \:  \times side}

Let the length of a side of the square be x cm.

Applying Pythagoras Theorem,

10² +10²= x²

100 +100= x²

x²= 200

x =   \sqrt{200}

Area of square

= x²

= 200cm²

Area of shaded region

= 3.14(10²) -200

= 3.14(100) -200

= 314 -200

= 114 cm²

8 0
2 years ago
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