Answer: x^2+2x-8<0
Step-by-step explanation:
A. x^2 - 2x - 8 < 0
(x - 4)(x + 2) < 0
B. x^2 + 2x - 8 < 0
(x + 4)(x - 2) < 0
C. x^2 - 2x - 8 > 0
(x - 4)(x - 2) > 0
D. x^2 + 2x - 8 > 0
(x + 4)(x - 2) > 0
When you test a point in the interval between -4 and 2, for example 0, it is negative.
Answer:
Step-by-step explanation:
A dime is worth 10 cents. Converting to dollars, it becomes 10/100 = $0.1
A quarter is worth 25 cents. Converting to dollars, it becomes 25/100 = $0.25
Let x represent the number of dimes that Jayden has.
Let y represent the number of quarters that Jayden has.
Jayden has some dimes and some quarters. He has at most 25 coins. It means that
x + y ≤ 25
The coins worth at least $4.60 combined. It means that
0.1x + 0.25y ≥ 4.6 - - - - - - - - - - 1
If Jayden has 7 dimes, then
7 + y ≤ 25
y ≤ 25 - 7
y ≤ 18
Substituting x = 7 into equation 1, it becomes
0.1 × 7 + 0.25y ≥ 4.6
0.7 + 0.25y ≥ 4.6
0.25y ≥ 4.6 - 0.7
0.25y ≥ 3.9
y ≥ 3.9/0.25
y ≥ 15.6
All possible values for the number of quarters that he could have would be
15.6 ≤ y ≤ 18
Answer: Yes Rozonda's definition is valid
Step-by-step explanation:
Answer:
Step-by-step explanation:
Move the decimal point in the divisor and dividend.
Turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the dividend (the number you’re dividing) the same number of places to the right.
Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend.
Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place.
Line up each digit in the quotient just over the last digit in the dividend used in that cycle.
Answer:
a) 0.0228
b) 94.6
Step-by-step explanation:
The formula for calculating a z-score when you are given a random.number of samples is z = (x-μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation
n = random number of samples
Given a normal distribution with u = 75 and o = 40, if you select a sample of n = 16,
a) what is the probability that the sample mean is above 95? (4 d.p.) b)
= x = 95
Hence:
z = 95 - 75/40/√16
= 20/40/4
= 20/10
= 2
Probability value from Z-Table:
P(x<95) = 0.97725
P(x>95) = 1 - P(x<95) = 0.02275
The probability that the sample mean is above 95 to 4 decimal places = 0.0228
b) What is the value, of which there is 97.5% chance that a sample mean is less than that value?
97.5% chance = z score for the confidence interval = 1.96
Hence:
z = (x-μ)/σ/√n
1.96 = x - 75/40/√16
1.96 = x - 75/ 40/4
1.96 = x - 75/10
Cross Multiply
1.96 × 10 = x - 75
19.6 = x - 75
x = 19.6 + 75
x = 94.6
The value, of which there is 97.5% chance that a sample mean is less than that value is 94.6
