You are making a 2 ingredient trail mix with almonds and raisins. There is a 5:7 ratio of almonds to raisins. How many ounces of almonds would be in a 3-pound bag of this trail mix? (There are 16 ounces in 1 pound.) *
Answers
Answer:
There would be 20 ounces of almonds in the bag
Step-by-step explanation:
System of Equations
To solve the problem, we'll set up these two variables:
x = ounces of almonds
y = ounces of raisins
The ratio of almonds to raisins in the trail mix is 5:7, thus:
Cross-multiplying:
7x=5y [1]
A 3-pound bag of this trail mix contains 3*16=48 ounces that include almonds and raisins, thus:
x + y = 48 [2]
Multiplying [2] by 5:
5x + 5y = 240
Substituting from [1]:
5x + 7x = 240
12x = 240
x = 240/12
x = 20
There would be 20 ounces of almonds in the bag
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Answer:
$100,522
Step-by-step explanation:
Answer:
Total Interest $100,522
Step-by-step explanation:
Answers
Answer:
The density curve is symmetric and bell‑shaped.
The normal distribution is a continuous distribution.
Approximately 32% of values fall more than one standard deviation from the mean.
Step-by-step explanation:
Lets take a look at each statement.
The density curve is symmetric and bell‑shaped.
True.
The normal distribution is a continuous distribution.
True, the value of the measure can be a decimal number, like 10.5, for example.
The normal distribution is a discrete distribution.
False. Either the distribution is continuous, or it is discrete. In this case, it is continuous.
The density curve is a flat line extending from the minimum value to the maximum value.
False. This statements describes the uniform probability distribution.
Approximately 32% of values fall more than one standard deviation from the mean.
True. 68% are within 1 standard deviation of the mean and 32% are more than one standard deviation from the mean.
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Answers
Answer:
The posterior probability that the lathe tool is properly adjusted is 94.7%
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
In your problem we have that:
-A is the probability that the part chosen is found to be acceptable.
The problem states that the probability its lathe tool is properly adjusted is 0.8. When it happens, there is a 0.9 probability that the parts produced pass inspection. There is also a 0.2 probability of the lathe is out of adjustment, when it happens the probability of a good part being produced is only 0.2.
So, P(A) = P1 + P2 = 0.8*0.9 + 0.2*0.2 = 0.72 + 0.04 = 0.76
Where P1 is the probability of a good part being produced when lathe tool is properly adjusted and P2 is the probability of a good part being produced when lathe tool is not properly adjusted.
- P(B) is the the probability its lathe tool is properly adjusted. The problem states that P(B) = 0.8
P(A/B) is the probability of A happening given that B has happened. We have that A is the probability that the part chosen is found to be acceptable and B is the probability its lathe tool is properly adjusted. The problem states that when the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. So P(A/B) = 0.9
So, probability of B happening, knowing that A has happened, where B is the lathe tool is properly adjusted and A is that the part randomly chosen is inspected and found to be acceptable is:
The posterior probability that the lathe tool is properly adjusted is 94.7%
Answers
The perimeter of the given figure is 29.7 ft while the area is 63.25 ft².
What is area?
The area is the amοunt οf space within the perimeter οf a 2D shape. It is measured in squareunits, such as cm², m², etc.
Yοu can think οf area as the area inside a given shape οr space. It refers tο hοw much space is taken up. The larger the shape, the larger the area and perimeter οf the shape will be. Nοt tο be cοnfused with vοlume, area οnly refers tο space taken up by a flat οr 2Dοbject.
The perimeter is sum of all sides
Here,
sum of all sides = 1/2 × 2πr + 6 + 8
= 1/2 × (2×3.14×5) + 6 + 8
= 29.7 ft
Area = 1/2 × πr² + 1/2 × 8 × 6
= 1/2 × (3.14×5×5) + 1/2 × 8 × 6
= 63.25 ft²
Thus, the perimeter of the given figure is 29.7 ft while the area is 63.25 ft².
Learn more about perimeter
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Answers
The average electric guitars sold each year in Wyoming is 13,057.
What is Multiplication?
Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
on average the number of electric guitars sold in Texas each year is $91,399, which is seven times the average number of guitars sold each year in Wyoming.
Average number of guitars sold each year in Texas = 91,399
This number is seven times the average number of guitars sold each year in Wyoming.
Let x be the average number of guitars sold in Wyoming each year.
7x = 91,399
Dividing both sides of the equation by 7,
x = 91399 / 7
x = 13,057
Hence 13,057 electric guitars are sold each year in Wyoming.
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x = 91399/7
x = 13057 <===
Answers
Answer:
28π cm²
Step-by-step explanation:
Circumference Formula: C = 2πr
Simply plug in r into the formula:
C = 2π(14)
C = 28π or 87.9646
Answer:
28π cm
Step-by-step explanation:
The circumference of a circle has the formula 2πr.
2 × π × r
Where r is the radius.
2 × π × 14
28 × π
= 28π
The circumference is 28π and the unit is centimeters.