Answer:
Step-by-step explanation:
4) Given that 3x<15
Divide by +3 without affecting inequality
x<5
Hence answer is (-∞,5)
5) -6x<18
Add 6x to both sides
0<6x+18
Subtract 18
-18<6x
Divide by +6
-3<x
Hence answer is (-3,∞)
6) 2x+6>x-7
Subtract x-6 from both the sides
x >-13
So answer is (-13,∞)
7) -4x+8≥14
Add 4x-14 to both the sides
-6≥4x
x≥-3/2
Hence answer is [-3/2,∞)
T(2)=d you multiply <em>t</em> times 2 to get <em>d</em>
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 17
For the alternative hypothesis,
µ < 17
This is a left tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 80,
Degrees of freedom, df = n - 1 = 80 - 1 = 79
t = (x - µ)/(s/√n)
Where
x = sample mean = 15.6
µ = population mean = 17
s = samples standard deviation = 4.5
t = (15.6 - 17)/(4.5/√80) = - 2.78
We would determine the p value using the t test calculator. It becomes
p = 0.0034
Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.
The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
Can you give specs of it?
Answer: the coin bank has 30 nickels and 10 dimes.
Step-by-step explanation:
The worth of a dime is 10 cents. Converting to dollars, it becomes
10/100 = $0.1
The worth of a nickel is 5 cents. Converting to dollars, it becomes
5/100 = $0.05
Let x represent the number of nickels in the coin bank.
Let y represent the number of dimes in the coin bank.
A coin bank contains only nickels and dimes. The total value of the coins in the bank is $2.50. This means that
0.05x + 0.1y = 2.50 - - - - - - - - - - - 1
The number of nickels is 3 times the number of dimes. This means that
x = 3y
Substituting x = 3y into equation 1, it becomes
0.05 × 3y + 0.1y = 2.50
0.15y + 0.1y = 2.5
0.25y = 2.5
y = 2.5/0.25 = 10
x = 3y = 3 × 10
x = 30
