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Tpy6a [65]
2 years ago
8

If a«b a = 18 when b = 3, then find a when b = 5 I need help asap

Mathematics
1 answer:
vovangra [49]2 years ago
6 0

Answer:

a = 30

Step-by-step explanation:

Given the following data;

a = 18

b = 3

This is a direct proportion question.

Therefore, a is directly proportional to b.

Mathematically, a = kb

First of all we would find the constant, k;

k = a/b

k = 18/3

k = 6

Now to find the value of a when b = 5

a = kb

a = 6*5

a = 30

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The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, al
Valentin [98]

Answer:

a) p_v =P(t_{(9)}

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best​ Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation  

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: \mu_y- \mu_x \geq 0

Alternative hypothesis: \mu_y -\mu_x

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

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7

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} =11.451

The 4 step is calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679

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

df=n-1=10-1=9

Now we can calculate the p value, since we have a left tailed test the p value is given by:

p_v =P(t_{(9)}

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best​ Actors at 1% of significance.

Part b

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".  

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

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

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that t_{\alpha/2}=3.25  

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

-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469  

-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069  

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0
3 years ago
What is an equiangular triangle?
Sergio [31]
<span>An equiangular triangle is a triangle where all three interior angles are equal in measure.</span>
6 0
3 years ago
Read 2 more answers
The area of a 12-cm-wide rectangle is 288 cm^2 what is its length?
densk [106]

Answer:

24cm

Step-by-step explanation:

The area of the rectangle is length × breadth. You already know the area and the breadth, so you can find the length.

288cm² = length × 12cm

length = 288cm² ÷ 12cm

           = 24cm

3 0
3 years ago
What is the solution set for this inequality?
Natali5045456 [20]

Answer:

x < 56

Step-by-step explanation:

- x + 40 > -16

-x + 40 - 40 > -16 -40

-x > -56

-x / -1 > -56 / -1

x < 56

4 0
3 years ago
The original price of a camera is $150. If a discount of 30% is given, what is the amount of this discount ?
shtirl [24]

Question

The original price of a camera is $150. If a discount of 30% is given, what is the amount of this discount ?


150 : 100 * 30 =

45$ is your answer

---------------------


4 0
3 years ago
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