Step-by-step explanation:
If x is the kilograms of 30% chocolate, and y is the kilograms of 50% chocolate, then:
x + y = 200
0.30x + 0.50y = 0.46(200)
Solving the system of equations with substitution:
0.30x + 0.50(200 − x) = 0.46(200)
0.30x + 100 − 0.50x = 92
8 = 0.20x
x = 40
y = 200 − x
y = 160
The distributor needs 40 kg of 30% chocolate and 160 kg of 50% chocolate.
To obtain 200 kilograms of a 46% fat-content chocolate, the candy distributor needs to mix 40 kilograms of a 30% fat-content chocolate and 160 kilograms of a 50% fat-content chocolate.
This problem can be solved using a basic mixture problem method. Let's name the amount of the 30% fat-content chocolate as 'x' and the amount of the 50% fat-content chocolate as 'y'. The total weight of the resulting chocolate is provided in the problem, 200 kilograms, therefore we know that x + y = 200.
The total fat in the chocolates should be 46% of 200kg, or 92kg. This gives us another equation based on the fat content, 0.3x + 0.5y = 92.
Solving these two equations linearly, we find the values of x and y. The amount of 30% fat content chocolate (x) is 40 kilograms and the amount of 50% fat-content chocolate (y) is 160 kilograms.
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А.
current value
B.
present value
С. .
future value
Answer:
b. present money
Step-by-step explanation:
the concept that States an amount of money today is worth more than that sum amount in the future. future money is not worth much then the amount received today.
Answer:
I think 1 is the right answer
Step-by-step explanation:
Answer: height of kite is 147.042 feets
Step-by-step explanation:
The diagram of the kite is shown in the attached photo
Triangle ABC is formed and it is a right angle triangle.
The kite string made an angle of 33 degrees with the ground. The string used was 90 yards We will convert the 90 yards to feets.
I yard = 3 feets
90 yards would become
90×3 = 270 feets
This 270 feets form the hypotenuse of the triangle.
To determine the height of the kite h, we will use trigonometric ratio
Sin# = opposite / hypotenuse
Where
# = 33 degrees
Hypotenuse = 270 feets
Opposite = h feets
Sin 33 = h/270
h = 270sin33
h = 270 × 0.5446 = 147.042 feets
Answer:
Step-by-step explanation:
M(x)=-4(x+3)-2
t(x)=-8x^2(x^2-6+1
H(x)=3x(x-2)-4
Answer:
a) 0.25249
b) 0.66575
Step-by-step explanation:
We solve this question using z score formula
= z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 23.2 gallons
σ is the population standard deviation = 2.7 gallons
a) Find the probability that a randomly selected American drinks more than 25 gallons of bottled water in a year.
For x = 25 gallons
z = 25 - 23.2/2.7
z = 0.66667
Probability value from Z-Table:
P(x<25) = 0.74751
P(x>25) = 1 - P(x<25)
1 - 0.74751
= 0.25249
The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is 0.25249
2) What is the probability that the selected person drinks between 22 and 30 gallons
For x = 22 gallons
z = 22 - 23.2/2.7
z = -0.44444
Probability value from Z-Table:
P(x = 22) = 0.32836
For x = 30 gallons
z = 30 - 23.2/2.7
z =2.51852
Probability value from Z-Table:
P(x = 30) = 0.99411
The probability that the selected person drinks between 22 and 30 gallons is
P(x = 30) - P(x = 22)
= 0.99411 - 0.32836
= 0.66575
The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is approximately 0.2514, while the probability that they will drink between 22 and 30 gallons is approximately 0.6643.
This is a statistics question about probability distribution, specifically, normal distribution. You need to find the z-scores and use the standard normal distribution table to find the probabilities.
The average or mean (μ) consumption is 23.2 gallons and standard deviation (σ) is 2.7 gallons.
First, we use the z-score formula: z = (X - μ) / σ
To find out the probability that a selected American drinks more than 25 gallons annually, we substitute X = 25, μ = 23.2 and σ = 2.7 into the z-score formula to get z = (25 - 23.2) / 2.7 ≈ 0.67. Z value of 0.67 corresponds to the probability of 0.7486 in standard normal distribution table, but this is the opposite of what we want. We need to subtract this probability from 1 to find the probability that a person drinks more than 25 gallons annually. So 1 - 0.7486 = 0.2514.
Second, to find the probability an individual drinks between 22 and 30 gallons, we calculate two z-scores: For X = 22, z = (22 - 23.2) / 2.7 ≈ -0.44 with corresponding probability 0.3300, and for X = 30, z = (30 - 23.2) / 2.7 ≈ 2.52 with corresponding probability 0.9943. We find the probability of someone drinking between these quantities by subtracting the smaller probability from the larger, 0.9943 - 0.3300 = 0.6643.
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