Answer:
4 is the answer
Step-by-step explanation:
The equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.
We are aware that any straight line's equation can be expressed as
y = mx + c,
where m denotes the slope and c denotes a constant.
Also, two perpendicular lines' slopes are the negative reciprocals of one another.
Here, the equation of the given straight line is
3x+8y=4
i.e. 8y = 4 -3x
i.e. y = (4/8) - (3/8)x
Now the negative reciprocal of - 3/8 is 8/3.
Then we can write the equation of the perpendicular line is
y = (8/3)x + c ...(1)
Since (1) passes through the point (8, -9), so we can put x = 8 and y = -9 in (1) to get the value of c.
So, -9 = (8/3)*8 + c
i.e. -9 = 64/3 + c
i.e. c = -9 -64/3 = - (27 + 64)/3 = - 91/3
(1) can be written as
y = (8/3)x - (91/3)
i.e. 3y = 8x - 91
i.e. 8x - 3y = 91
Therefore the equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.
Learn more about perpendicular lines here -
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Answer:
There is enough statistical evidence to support the claim that the survey is not accurate.
Step-by-step explanation:
We have to perform a test of hypothesis on the proportion.
The claim is that the proportion of families that own stock differs from 48.8%.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample. of size n=250, has a proportion of p=0.568.
The standard error of the proportion is
The z-statistic can now be calculated:
The P-value for this two-tailed test is then:
As the P-value is smaller than the significance level, the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the survey is not accurate.
Answer:
Lindsay owns 12 books
Step-by-step explanation:
1/3x:Lindsay
x:Destiny
1/4x: Henry
1/3x+1/4x+x=57
4/12x+3/12x+x=57
7/12x+x=57
19/12x=57
x=57*12/19
x=36
1/3x=36/3
1/3x=12
In this case you can say in one hour Austin earns $7.50.