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STatiana [176]
3 years ago
12

7. Using k as the constant of proportionality, write an equation that expresses: Z varies jointly as x and y. If Z = 24 when x =

3 and y = 4, find Z when x = 5 and y = 6. (show steps)
Mathematics
1 answer:
VARVARA [1.3K]3 years ago
6 0

Answer:

60

Step-by-step explanation:

"z varies jointly as x and y" can be expressed algebraically as z = kxy, where k is the constant of proportionality.

Given:  z = 24 when x = 3 and y = 4, then 24 = k(3)(4), or 24 = 12k.

The const. of prop. must then be k = 2.

So now we have the specific relationship z = 2xy.

If x = 5 and y = 6, then z = 2(5)(6) = 60.


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Read 2 more answers
An independent-measures research study was used to compare two treatment conditions with n= 12 participants in each treatment. T
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Answer:

(a) The data indicate a significant difference between the two treatments.

(b) The data do not indicate a significant difference between the two treatments.

(c) The data indicate a significant difference between the two treatments.

Step-by-step explanation:

Null hypothesis: There is no difference between the two treatments.

Alternate hypothesis: There is a significant difference between the two treatments.

Data given:

M1 = 55

M2 = 52

s1^2 = 8

s2^2 = 4

n1 = 12

n2 = 12

Pooled variance = [(n1-1)s1^2 + (n2-1)s2^2] ÷ (n1+n2-2) = [(12-1)8 + (12-1)4] ÷ (12+12-2) = 132 ÷ 22 = 6

Test statistic (t) = (M1 - M2) ÷ sqrt [pooled variance (1/n1 + 1/n2)] = (55 - 52) ÷ sqrt[6(1/6 + 1/6)] = 3 ÷ 1.414 = 2.122

Degree of freedom = n1+n2-2 = 12+12-2 = 22

(a) For a two-tailed test with a 0.05 (5%) significance level and 23 degrees of freedom, the critical values are -2.069 and 2.069.

Conclusion:

Reject the null hypothesis because the test statistic 2.122 falls outside the region bounded by the critical values.

(b) For a two-tailed test with a 0.01 (1%) significance level and 23 degrees of freedom, the critical values are -2.807 and 2.807.

Conclusion:

Fail to reject the null hypothesis because the test statistic 2.122 falls within the region bounded by the critical values.

(c) For a one-tailed test with 0.05 (5%) significance level and 23 degrees of freedom, the critical value is 1.714.

Conclusion:

Reject the null hypothesis because the test statistic 2.122 is greater than the critical value 1.714.

6 0
3 years ago
Louis wants to carpet the rectangular floor of his basement. The basement has an area of 864 square feet. The width of the basem
Over [174]
29.3938769134 ft

Take the radical of 864 to get an answer based on the limited info provided.
7 0
3 years ago
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