Answer:
x=-5
Step-by-step explanation:
Multiply both sides by 3:
Subtract 2x from both sides:
Divide both sides by 4:
Hope this helps!
Can someone solve my homework questions please ?
1 answer:
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She has 10lbs of 25% syrup... so, in the 10lbs, 25% of that is syrup, the rest, namely the 75% remaining is water or other substances.
let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.
how much is 25% of 10lbs? well, (25/100) * 10, or 2.5.
the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs? well, (0/100) * x, or 0.00x, which is just 0.
how much is 10% of "y" lbs? well (10/100) * y, or 0.10y.
whatever "x" and "y" are, we know that 10 + x = y.
we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus
let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.
how much is 25% of 10lbs? well, (25/100) * 10, or 2.5.
the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs? well, (0/100) * x, or 0.00x, which is just 0.
how much is 10% of "y" lbs? well (10/100) * y, or 0.10y.
whatever "x" and "y" are, we know that 10 + x = y.
we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus
Answer:
the probability that we hit the bullseye at least 100 times is 0.0113
Step-by-step explanation:
Given the data in the question;
Binomial distribution
We find the probability of hitting the dart on the disk
⇒ Area of small disk / Area of bigger disk
⇒ πR₁² / πR₂²
given that; disk-shaped board of radius R² = 5, disk-shaped bullseye with radius R₁ = 1
so we substitute
⇒ π(1)² / π(5)² = π/π25 = 1/25 = 0.04
Since we have to hit the disk 2000 times, we represent the number of times the smaller disk ( BULLSEYE ) will be hit by X.
so
X ~ Bin( 2000, 0.04 )
n = 2000
p = 0.04
np = 2000 × 0.04 = 80
Using central limit theorem;
X ~ N( np, np( 1 - p ) )
we substitute
X ~ N( 80, 80( 1 - 0.04 ) )
X ~ N( 80, 80( 0.96 ) )
X ~ N( 80, 76.8 )
So, the probability that we hit the bullseye at least 100 times, P( X ≥ 100 ) will be;
we covert to standard normal variable
⇒ P( X ≥ )
⇒ P( X ≥ 2.28217 )
From standard normal distribution table
P( X ≥ 2.28217 ) = 0.0113
Therefore, the probability that we hit the bullseye at least 100 times is 0.0113
Answer:
a.) depth of the lake = (volume of the lake) / area of lake
= 173,693,585,360,000 / 624,305,840,400 = 278.22 feet
b.) 11 inches = 0.9167 feet
Water gained in cubic feet gained by the lake
= 624,305,840,400 0.9167
= 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year
= 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
= 0.0033
= 0.33%
Step-by-step explanation:
i) acres to square feet : 1 acre = 43560 square feet
therefore 14,332,090 acres = 624,305,840,400 square feet
ii) 1 mile = 5280 feet
1 cubic mile = 5280 5280
5280 = 147,197,952,000 cubic feet
therefore 1180 cubic miles = 173,693,585,360,000 cubic feet
a.) depth of the lake = (volume of the lake) / area of lake
= 173,693,585,360,000 / 624,305,840,400 = 278.22 feet
b.) 11 inches = 0.9167 feet
Water gained in cubic feet gained by the lake
= 624,305,840,400 0.9167 = 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year
= 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
= 0.0033
= 0.33%