Answer:
Step-by-step explanation: 7
Subtract 5 on both sides to get 4x = x + 21
then, subtract x from 4x and x is 1, so 3x = 21 then divide by 3 on both sides
Answer:
Correct option: B
Step-by-step explanation:
The professor can perform a One-mean <em>t</em>-test to determine whether the average score of the students in his class is more than the average score of all the students attending university.
A <em>t</em>-test will be used instead of the <em>z</em>-test because the population standard deviation is not provided instead it is estimated by the sample standard deviation.
The hypothesis for this test can be defined as follows:
<em>H₀</em>: The average score of the students in his class is not more then the entire university, i.e. <em>μ ≤ 35</em>.
<em>Hₐ</em>: The average score of the students in his class is more then the entire university, i.e. <em>μ > 35</em>.
Given:
The test statistic is:
Thus, the correct option is (B).
Answer:
f(w) = 3w + 2,000,000/w
Step-by-step explanation:
We know that the area of a rectangle is the product of its length and width:
A = LW
Filling in the given values lets us write an expression for the length of the field.
1,000,000 = Lw
L = 1,000,000/w
Since there are 3 fences of length w and two of length L, the total perimeter fence length is the sum ...
f(w) = 3w + 2(1,000,000)/w
Combining the constants, we have a function for the perimeter fence length in terms of the width of the field:
f(w) = 3w +2,000,000/w
Answer:
x = 5, x = 1
Step-by-step explanation:
The quadratic equation 0 = 4(x - 3)2 - 16.
Using binomial theorem, (a - b)2 = a2 - 2ab + b2 to expand (x - 3)2.
0 = 4(x2 - 6x + 9 ) - 16.
Using distributive property to multiply 4 by x2 - 6x + 9.
0 = 4x2 - 24x + 36 - 16.
Subtract 16 from 36 to get 20.
0 = 4x2 - 24x + 20.
4x2 - 24x + 20 = 0.
Divide both sides by 4.
x2 - 6x + 5 = 0.
To solve the equation, factor and rewrite as x2 + ax + bx + 5
a + b = -6, ab = 1(5) = 5.
a = -5, b = -1.
Rewriting x2 - 6x + 5 as
(x2 - 5x) + (-x + 5)
Factor x in the first and -1 in the second group.
x(x - 5) - (x - 5)
Factor out common term
(x - 5)(x - 1)
By solving the above, we get
x = 5, x = 1
