Answer:
Step 1
Write and solve the inequality:
2,500 + 40a ≥ 4,000, or 40a ≥ 1,500
a ≥ 37.5
Step 2
If the shelter places 30 cats and 10 dogs,
or 40 animals, that will be enough to meet
its goal, because a = 40 is a solution to the
inequality a ≥ 37.5.
Answer:
Step-by-step explanation:
Since the amount of soft drink dispensed into a cup is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = amount in ounce of soft drink dispensed into cup.
µ = mean amount
σ = standard deviation
From the information given,
µ = 7.6oz
σ = 0.4 oz
a) The probability that the machine will overflow an 8-ounce cup is expressed as
P(x > 8) = 1 - P(x ≤ 8)
For x = 8,
z = (8 - 7.6)/0.4 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
P(x ≤ 8) = 1 - 0.84 = 0.16
b) P(x< 8) = 0.84
c) when the machine has just been loaded with 848 cups, the number of cups expected to overflow when served is
0.16 × 848 = 136 cups
<h3>
Answer: t = 7</h3>
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Explanation:
If we replace every copy of x with t, then we go from this
F(x) = 3x+5
to this
F(t) = 3t + 5
All we've done really is change the letter. We still are dealing with a variable. We're told that F(t) is equal to 26, which would allow us to replace the "F(t)" with "26" in the second equation above.
So we now have the equation 26 = 3t+5 which is the same as 3t+5 = 26
Let's solve for t
3t+5 = 26
3t = 26-5 .... subtract 5 from both sides
3t = 21
t = 21/3 .... divide both sides by 3
t = 7 is the answer
Now note that...
F(t) = 3t + 5
F(7) = 3*7 + 5 .... replace t with 7
F(7) = 21 + 5
F(7) = 26
This means we got F(t) = 26 when t = 7
It's the same as saying x = 7 leads to F(x) = 26.
This helps confirm we have the correct answer.
The ratio is 132:89.
If you'd like a ratio simplified, just divide like you would a fraction.
Unfortunately, 89 is a prime number, so your ratio stays the way it is.
Therefore your ratio is 132:89
