Answer:
4) x = -3 or 8
Step-by-step explanation:
We factories each algebraic expression
4) x² -5x - 24 = 0
x² - 8x + 3x - 24 = 0
(x² - 8x) + (3x - 24) = 0
x(x - 8) + 3(x - 8) = 0
(x + 3)(x - 8) = 0
x + 3 = 0, x = -3
x - 8 = 0, x = 8
x = -3 or 8
Answer:
1004.8 in³
Step-by-step explanation:
d = 2r => r = d/2 = 16in/2 = 8 inches
V = Ab×h
= π·r²×h
= 3.14·(8in)²×5in
= 1004
Answer:
The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.
Step-by-step explanation:
We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.
Let us find the sample score that corresponds to z-score of bottom 4%.
From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.
Upon substituting these values in z-score formula we will get our sample scores (x) as:
Therefore, the bolts with diameters less than 5.57 millimeters should be rejected.
Now let us find sample score corresponding to z-score of 1.75 as upper limit.
Therefore, the bolts with diameters greater than 5.85 millimeters should be rejected.
Answer:
The value of y given the values of x and z in the question is -734.85
Step-by-step explanation:
This is a joint variation question.
First, we are made to know that y varies jointly as x and z.
The equation for this can be written as;
y = k * x * z
Where k is the constant of proportionality.
Let’s calculate k first.
117 = k * (-3) * (-11)
33k = 117
K = 117/33 = 3.55
Now, we proceed to get what y is when x = -9 and z = 23
Let’s plug these values into the initial equation written.
y = k * x * z
We use the value of k calculated above;
y = 3.55 * (-9) * (23) = -734.85
The best way to compare fractions would be to make them have like
denominators. We first , in this case, need to convert from decimal to
fraction.
Converting decimals to fractions first requires an
understanding of the decimal places that fall after the decimal. One
place after the decimal is the tenths place. If you have a decimal that
ends at one place after the decimal (or in the tenths place) it can be
written as the number after the decimal in the top of the fraction and
ten (tenths place) in the denominator. ex. .5 ends one place after
the decimal and can be written as 5/10...(read as five tenths).
If a decimal ends at two places after the decimal...(ex. .75)...it
ends in the hundredths place, can be written as that number in the
numerator and 100 in the denominator....(ex 75/100) and is read as
seventy-five hundredths.
one place after the decimal is tenths (over 10), two places is
hundredths (over 100), three places is thousandths (over 1000) , four
places ten-thousandths (over 10000) and so on.
Because each decimal in your problem has a different amount of
decimal places, it makes for different denominators. But, We can add a
zero to the end of a decimal without changing it's value; if we add a
zero to the end of .5 and make it .50 , we then can write it as 50/100
and would now have like denominators.
if .5 = .50 = 50/100 and .75 = 75/100
we now have the question what fractions can fall between 50/100 and 75/100.
That would be fractions such as 51/100, 52/100, 53/100.......74/100.
