Find the equation of the line parallel to y=5x+1 that contains the point (4,8)
1 answer:
The equation of a parallel line will have the same x-term, but a different constant (y-intercept). The required value can be found by putting the given point values in to the equation to see what it needs to be.
... y = 5x + ___
... 8 = 5·4 + ___
... 8 - 20 = -12 = ___
Your equation is ...
... y = 5x -12
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Answer:
1) z = -6.32
2) p-value = 0.001 × 10^(-2)
3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court
Step-by-step explanation:
We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.
Thus:
Sample proportion; p^ = 400/1000 = 0.4
Sample size: n = 1000
We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.
Thus, the hypothesis is defined as;
Null hypothesis:H0: p ≥ 0.5
Alternative hypothesis: Ha < 0.5
Formula for the test statistic is;
z = (p^ - p)/√(p(1 - p)/n)
Plugging in the relevant values;
z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)
z = -6.32
From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;
We have:
p-value = 0.00001 = 0.001 × 10^(-2)
The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court
Answer:
Chan's Bonus amount was $2400.
Step-by-step explanation:
Let the Total amount receive from bonus be 'x'.
Given:
Chan pays 30% in taxes;
So we can say;
Amount paid in taxes will be equal to 30% of total amount receive
framing in equation form we get;
Amount paid in taxes =
Now Given:
Chan pays 30% in Charity;
So we can say;
Amount paid in charity will be equal to 30% of total amount receive.
framing in equation form we get;
Amount paid in Charity =
Also Given:
Chan pays 30% in old debts;
So we can say;
Amount paid in Old debts will be equal 30% of total amount receive
framing in equation form we get;
Amount paid in Old debts =
Money left with him = $600
Now we can say that Total Amount Receive in bonus will be equal to Amount paid in taxes plus Amount paid in charity plus Amount paid in old debts plus amount left.
framing in equation form we get;
Hence Chan's Bonus amount was $2400.