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Simora [160]
3 years ago
13

Evaluate: 100(1 - 0.02)10. Round to the nearest tenth.

Mathematics
1 answer:
WARRIOR [948]3 years ago
4 0
100(1-0.02)^10

Simplify what's in the parentheses

100(0.98)^10

Do the exponents first.

(0.98)^10 = 0.817073

You multiply 0.81707... by 100, move the decimal to the right.

81.707... Round to the nearest tenth.

Answer: 81.7



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4.One attorney claims that more than 25% of all the lawyers in Boston advertise for their business. A sample of 200 lawyers in B
AleksAgata [21]

Answer:

z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123  

p_v =P(Z>2.123)=0.0169  

The p value obtained was a very low value and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .  

Step-by-step explanation:

1) Data given and notation  

n=200 represent the random sample taken

X=63 represent the lawyers had used some form of advertising for their business

\hat p=\frac{63}{200}=0.315 estimated proportion of lawyers had used some form of advertising for their business

p_o=0.25 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that more than 25% of all the lawyers in Boston advertise for their business:  

Null hypothesis:p\leq 0.25  

Alternative hypothesis:p > 0.25  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

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

z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

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

p_v =P(Z>2.123)=0.0169  

The p value obtained was a very low value and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .  

8 0
3 years ago
Sum of 2 and 5 is divided by the difference of 9 and 4 in expression form ​
Goshia [24]

Answer:

(2 + 5) / (9 - 4)

Step-by-step explanation:

"sum of 2 and 5" = (2 + 5)

"difference of 9 and 4" = (9 - 4)

"sum of 2 and 5 is divided by the difference of 9 and 4"

= (2 + 5) / (9 - 4)

5 0
3 years ago
The functions f(x) and g(x) are described below: f(x) = 7x + 9 g(x) = 7x −4 The graph of g(x) is obtained by shifting down the g
Slav-nsk [51]
Correct Answer:
Option A

Solution:

f(x) = 7x + 9
g(x) = 7x - 4

We can re-write g(x) as:

g(x) = 7x + 9 - 13

Since 7x+9 is equal to f(x), we can write:

g(x) = f(x) - 13

This relation shows that g(x) is obtained by shifting f(x) 13 units vertically down. So the correct answer is option A.
6 0
3 years ago
Two sides of a triangle measure 14 inches and 8 inches. which cannot be the length of the remaining side?
horrorfan [7]
1. The "triangle inequality" states that any of the sides of the triangle, is larger than the difference of the other 2 sides (the larger minus the smaller), and it is smaller than the sum of them.

2. So the third side of this triangle must be larger than 14-8=6 (in) and smaller than 14+8=22 (in)

3. So let a denote the remaining side, then   6 < a < 22, which means a can be any number in between 6 and 22 inches.
3 0
3 years ago
How do I solve proportions? Here’s my questions: <br><br> 1. x/8=5/16<br> 2. 5/12=15/x
Flura [38]

Proportions are very simple once you get the hang of them! What you do is cross multiple. :)

1. x/8=5/16

You first start by multiplying x and 16

Then multiply 5 and 8

So now you have 16x=40

Finally divide 16 from each side

You get: x+0.4!

2. 5/12=15/x

Remember to cross-multiply!

Now we have 5x=180

Next divide 5 from each side

You get: x=36!

7 0
2 years ago
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