Answer:
29*sqrt(5)
Step-by-step explanation:
Start with sqrt (45). You must reduce it to it's prime factors.
45: 9 * 5 9 is not prime so reduce it.
45: 3 * 3 * 5
When you write √45, you should replace it with √(3*3*5)
The rule is
Rule: when you have a pair of equal prime factors under a root sign, you can take one out and throw one away.
Rule 2: If there are an odd number of equal primes one of them will be left underneath the root sign.
√45 = 3√5
11sqrt(45) - 4 sqrt(5) Substitute for 45
11*3*sqrt(5) - 4sqrt(5) Take out sqrt(5) using the distributive property.
(11*3 - 4)*sqrt(5) Combine 11 * 3
(33- 4) * sqrt(5) Do the subtraction
29 * sqrt(5) Answer
Complete question :
There is a competition at the local movie theater for free movie tickets. You must guess all four employees' ages given a few clues. The first clue is when their ages are added together the sum is 106. Kirk is 2 times the quantity of ten years less than the manager's age, Brian is 12 years younger than twice the manager's age, ,and Matt is 6 years older than ½ the manager's age. What are all four of their ages? Be sure to show set up equation work and answer
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following clue :
Let manager's age = m
Kirk's age = k
Brian's age = b
Matt's age = a
Sum of their ages = 106
k = 2(m - 10) = 2m - 20
b = 2m - 12
a = 0.5m + 6
k + b + a + m = 106
Express all their ages in terms of m
2m - 20 + 2m - 12 + 0.5m + 6 + m = 106
5.5m - 20 - 12 + 6 = 106
5.5m - 26 = 106
5.5m = 106 + 26
5.5m = 132
m = 132 / 5.5
m = 24
Manager's age = 24 years
kirk = 2(24 - 10) = 2(14) = 28 years
Brian = 2(24) - 12 = 48 - 12 = 36 years
Matt = 0.5(24) + 6 = 12 + 6 = 18 years
Answer:
x = 4
Step-by-step explanation:
Area of a parallelogram = base times height
Given area = 40
Given height = 4
Given = x + 6
Thus,
40 = 4 * (6 + x )
Step 1 distribute the 4
4 * 6 = 24
4 * x = 4x
we now have 40 = 24 + 4x
step 2 subtract 24 from each side
40 - 24 = 16
24 - 24 cancels out
now we have 16 = 4x
step 3 divide each side by 4
4x / 4 = x
16 / 4 = 4
we're left with x = 4
To check our work, we can plug in the value of x and find the area of the parallelogram then. If it equals 40 the x = 4 is true.
(x + 6) * 4
* substitute 4 for x *
(4 + 6) * 4
4 + 6 = 10
10 * 4 = 40
40 = 40
Hence x = 4
Answer:
345678
Step-by-step explanation:
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Complete question is;
Suppose we are testing the null hypothesis H0: μ = 20 and the alternative Ha: μ ≠ 20, for a normal population with σ = 5. A random sample of 25 observations are drawn from the population, and we find the sample mean of these observations is x¯ = 17.6. The P-value is closest to:
a. 0.0668.
b. 0.0082.
c. 0.0164.
d. 0.1336
Answer:
Option D
Step-by-step explanation:
We are given;
Null hypothesis; H0: μ = 20
Alternative hypothesis; Ha: μ ≠ 20
Population Standard deviation; σ = 5
Sample size; n = 25
Sample mean; x¯ = 17.6
Let's find the z-score from the formula;
z = (x¯ - μ)/(σ/√n)
z = (17.6 - 20)/(5/√5)
z = - 1.073
From online p-value from z-score calculator attached, using z = -1.073; two tailed hypothesis; significance value of 0.05,we have;
The P-Value is 0.283271.
Looking at the given options, the closest to the p-value is option D
