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zysi [14]
3 years ago
6

Find the variation constant and an equation of variation where y varies directly as x and y=16 when x=2

Mathematics
1 answer:
Jlenok [28]3 years ago
5 0

Answer:

variation constant = k = 8

equation of variation : y = 8x

Step-by-step explanation:

Any relationship of variation can be written as y = kx

where k is the variation constant.

_______________________________________

Let the equationof relation between y and x be y =kx here as well

given

y = 16 when x = 2

substituting this value in the equation y = kx

16 = k*2

=> k = 16/2 = 8

Thus,

variation constant = k = 8

equation of variation : y = 8x

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For the figures shown, HJKL ~ QRST, and the scale factor of HJKL to QRST is 9/7.
ch4aika [34]
Hey there! :)

JK ≈ RS

Scale Factor = 9/7

JK = 56

<u>56</u> · <u>9</u> = <u>504</u>  =  72
 1    7 =   7

Your answer ⇒ B.72

Hope this helps :)
4 0
3 years ago
A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random
Yuliya22 [10]

Answer:

b) independent samples t-test

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

Our notation on this case :  

n_1 =5 represent the sample size for group 1  

n_2 =5 represent the sample size for group 2  

We can calculate the mean and deviation for eaach group with the following formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

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

\bar X_1 =5.92 represent the sample mean for the group 1  

\bar X_2 =5.74 represent the sample mean for the group 2  

s_1=1.88 represent the sample standard deviation for group 1  

s_2=1.81 represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:  

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}  

And now we can calculate the statistic:  

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

The degrees of freedom are given by:  

df=5+5-2=8

And now we can calculate the p value using the altenative hypothesis:  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

7 0
3 years ago
What is the estimated sum?
lyudmila [28]

Answer:

B

Step-by-step explanation:

521,370 would round to 521,400

26,839 would round to 27,800

and adding them would be

548,200

7 0
3 years ago
Joe drove 345 miles on 25 gallons of gas What was his average miles per gallon?
hichkok12 [17]

Answer:

13.8 miles a gallon

Step-by-step explanation:

I think this because 345 divided by 25 equals 13.8 which would mean 13.8 miles for every gallon

7 0
3 years ago
Read 2 more answers
1. Which of the following is a true statement?
san4es73 [151]

Answer:

<u><em>C. To square a number, multiply the number by itself.</em></u>

4 0
2 years ago
Read 2 more answers
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