Answer:
Let's solve for x.
5x−4y=−23−5x+9y
Step 1: Add 5x to both sides.
5x−4y+5x=−5x+9y−23+5x
10x−4y=9y−23
Step 2: Add 4y to both sides.
10x−4y+4y=9y−23+4y
10x=13y−23
Step 3: Divide both sides by 10.
10x
10
=
13y−23
10
x=
13
10
y+
−23
10
Answer:
x=
13
10
y+
−23
10
Step-by-step explanation:
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Answer:
The confidence interval at at 99% level of confidence is <em>93.7 ≤ μ ≤ 96.9</em>.<em> </em>
Step-by-step explanation:
Step 1:
We must first determine the z-value at a confidence level of 99%.
Therefore,
99% = 100%(1 - 0.01)
Thus,
α = 0.01
Therefore, the z-value will be
z_(α/2) = z_(0.01/2) = z_0.005 = 2.58
(The z-value is read-off from the z table from the standard normal probabilities.)
Step 2:
We can now write the confidence interval:
X - z_(α/2) [s/√(n)] ≤ μ ≤ X + z_(α/2) [s/√(n)]
95.3 - 2.58(6.5/√(104)) ≤ μ ≤ 95.3 + 2.58(6.5/√(104))
<em>93.7 ≤ μ ≤ 96.9</em>
Therefore, confidence interval is <em>93.7 ≤ μ ≤ 96.9 </em>which means that we are 99% confident that the true mean population lies is at least 93.7 and at most 96.9.
Cory brings five 1-gallon jugs of juice.
5 jugs * 1 gallon per jug = 5 gallons of juice total
Knowing that the cups Cory is using to serve can hold 8 fluid ounces, we are asked to figure out how many cups Cory can serve.
1 gallon = 128 fluid ounces
5 gallons = x fluid ounces
Let's set up a proportional equation.
1/128 = 5/x
Now, we can use cross products to simplify and solve.
1 * x = 128 * 5
x = 640 fluid ounces.
Therefore, Cory has a total of 640 fluid ounces.
To find out how many cups he can serve, we need to divide the total amount of juice he has (640 oz) by the amount of juice in each cup (8 oz).
640 / 8 = 80
Thus, Cory can serve 80 cups of juice at parent night.
