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3 years ago

What was the average grade earned?

Mathematics

1 answer:

Anettt [7]3 years ago

5 0

A 3 I guess or a B. idk....

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For a certain candy, 20% of the pieces are yellow, 5% are red, 5% are blue, 10% are green, and the rest are brown. a)

artcher [175]

Answer:

A) i) the probability it is brown = 60%. (ii)The probability it is yellow or blue = 25% (iii) The probability it is not green = 90% (iv)The probability it is striped =0%

B) i)The probability they are all brown = 21.6%. (ii) Probability the third one is the first one that is red = 4.51% (iii) Probability none are yellow = 51.2% (iv) Probability at least one is green = 27.1%

Step-by-step explanation:

A) The probability that it is brown is the percentage of brown we have. However, Brown is not listed, so we subtract what we are given from 100%. Thus;

100 - (20 + 5 + 5 + 10) = 100 - (40) = 60%.

The probability that one drawn is yellow or blue would be the two percentages added together: 20% + 5% = 25%.

The probability that it is not green would be the percentage of green subtracted from 100: 100% - 10% = 90%.

Since there are no striped candies listed, the probability is 0%.

B) Due to the fact that we have an infinite supply of candy, we will treat these as independent events.

Probability of all 3 being brown is found by taking the probability that one is brown and multiplying it 3 times. Thus;

The percentage of brown candy is 60% from earlier. Thus probability of all 3 being brown is;

0.6 x 0.6 x 0.6 = 0.216 = 21.6%

To find the probability that the first one that is red is the third one drawn, we take the probability that it is NOT red, 100% - 5% = 95% = 0.95

Now, for the first two and the probability that it is red = 5% = 0.05

Thus for the last being first one to be red = 0.95 x 0.95 x 0.05 = 0.0451 = 4.51%.

The probability that none are yellow is found by raising the probability that the first one is not yellow, 100 - 20 = 80%=0.80, to the third power:

0.80³ = 0.512 = 51.2%.

The probability that at least one is green is; 1 - (probability of no green).

We first find the probability that all three are NOT green:

0.90³ = 0.729

1 - 0.729 = 0.271 = 27.1%.

3 0

4 years ago

Sofia has 25 coins in nickels and dimes in her pocket for a total of $1.65. How many of each type of coin does she have? First c

Serga [27]

Answer:

Step-by-step explanation:

Let n represent nickels & d dimes

given: n + d = 25 #1 (number of coins)

given: .05n + .10d = 1.65 #2 (amount in dollars)

n = 25 - d #3 (rewrite of #1)

.05(25 -d) + .10d = 1.65 (substitute #3 in #2)

1.25 - .05d + .10d = 1.65 (multiply out the left side)

.05d = .40 (collection of like terms)

d = 8 (divided both sides by.05)

n + 8 = 25 (substitute answer for d in #1)

n = 17 (subtract both sides by 8)

There are 8 dimes and 17 nickels.

Check:

17(.05) + 8(.10) = 1.65 (answers in #2)

.85 + .80 = 1.65 (multiply out the left side)

1.65 = 1.65 ✔️ QED

6 0

4 years ago

1) IF DE = 9, find BC

swat32

Answer:

1. BC = 18

2. m<ABC = 80°

3. x = 5

Step-by-step explanation:

1. If DE = 9, therefore:

$BC = 2 \times 9 = 18$ (based on the midsegment theorem, DE is half the length of the third side, BC)

2. m<ADE = 80°, then,

m<ABC = 80°

This is because m<ADC and m<ABC are corresponding angles. Corresponding angles are congruent.

3. DE = 2x + 7 , and BC = 7x - 1, find BC

Thus:

$BC = 2 \times DE$ (midsegment theorem)

$7x - 1 = 2 \times (2x + 7)$ (substitution)

Solve for x

$7x - 1 = 4x + 14$

Collect like terms

$7x - 4x = 1 + 14$

$3x = 15$

Divide both sides by 3

x = 5

5 0

3 years ago

Angela shared a cab with her fiends. When they arrived at their destination, they evenly divided the$j fare among the 3 of them.

Pani-rosa [81]

(48 / j) +5 is the answer

8 0

3 years ago

Read 2 more answers

Find the inverse of each function for problems 1–6. State the domain and range of both the function and its inverse. Restrict th

JulsSmile [24]

Answer:

Function:

$f(x)=-x^2$

Domain: (-∞,∞)

Range: (-∞,0]

Inverse Function:

$f^{-1}(x)=\sqrt{-x} ,and\\f^{-1}(x)=-\sqrt{-x}$

Domain: (-∞,0]

Range: (-∞,∞)

Function:

$f(x)=5x-1$

Domain: (-∞,∞)

Range: (-∞,∞)

Inverse Function:

$f^{-1}(x)=\frac{1}{5}x+\frac{1}{5}$

Domain: (-∞,∞)

Range: (-∞,∞)

Function:

$f(x)=-x+3$

Domain: (-∞,∞)

Range: (-∞,∞)

Inverse Function:

$f^{-1}(x)=-x+3$

Domain: (-∞,∞)

Range: (-∞,∞)

Function:

$f(x)=x^{2}+7$

Domain: (-∞,∞)

Range: [7,∞)

Inverse Function:

$f^{-1}(x)=\sqrt{x-7}, and\\f^{-1}(x)=-\sqrt{x-7}$

Domain: [7,∞)

Range: (-∞,∞)

Function:

$f(x)=14x-4$

Domain: (-∞,∞)

Range: (-∞,∞)

Inverse Function:

$f^{-1}(x)=\frac{1}{14}x+\frac{2}{7}$

Domain: (-∞,∞)

Range: (-∞,∞)

Function:

$f(x)=-3x+8$

Domain: (-∞,∞)

Range: (-∞,∞)

Inverse Function:

$f^{-1}(x)=-\frac{1}{3}x+\frac{8}{3}$

Domain: (-∞,∞)

Range: (-∞,∞)

Step-by-step explanation:

To find inverse of a function f(x), there are 4 steps we need to follow:

1. Replace f(x) with y

2. Interchange the y and x

3. Solve for the "new" y

4. Replace the "new" y with the notation for inverse function, $f^{-1}(x)$

Note: The domain of the original function f(x) is the range of the inverse and the range of the original function is the domain of the inverse function.

Let's calculate each of these.

$f(x)=-x^2$

Domain: There is no restriction on values of x we can put on it. Hence domain is (-∞,∞)

Range: No matter what we put into x, the y values will always be negative. And if we put 0, y value would be 0. So range is (-∞,0]

Finding the inverse:

$f(x)=-x^2\\y=-x^2\\x=-y^2\\y^2=-x\\y=+-\sqrt{-x} \\y=\sqrt{-x}, -\sqrt{-x}$

$f^{-1}(x)=\sqrt{-x} ,and\\f^{-1}(x)=-\sqrt{-x}$

Domain: this is the range of the original so domain is (-∞,0]

Range: this is the domain of the original so range is (-∞,∞)

$f(x)=5x-1$

Domain: There is no restriction on values of x we can put on it. Hence domain is (-∞,∞)

Range: All sorts of y values will occur, so the range is (-∞,∞)

Finding the inverse:

$f(x)=5x-1\\y=5x-1\\x=5y-1\\5y=x+1\\y=\frac{1}{5}x+\frac{1}{5}$

$f^{-1}(x)=\frac{1}{5}x+\frac{1}{5}$

Domain: this is the range of the original so domain is (-∞,∞)

Range: this is the domain of the original so range is (-∞,∞)

$f(x)=-x+3$

Domain: There is no restriction on values of x we can put on it. Hence domain is (-∞,∞)

Range: All sorts of y values will occur, so the range is (-∞,∞)

Finding the inverse:

$f(x)=-x+3\\y=-x+3\\x=-y+3\\y=-x+3$

$f^{-1}(x)=-x+3$

Domain: this is the range of the original so domain is (-∞,∞)

Range: this is the domain of the original so range is (-∞,∞)

$f(x)=x^{2}+7$

Domain: There is no restriction on values of x we can put on it. Hence domain is (-∞,∞)

Range: no matter what we put into x, it will always be a positive number greater than 7. Only when we put in 0, y will be 7. So 7 is the lowest number and it can go to infinity. Hence the range is [7,∞)

Finding the inverse:

$f(x)=x^2+7\\y=x^2+7\\x=y^2+7\\y^2=x-7\\y=+-\sqrt{x-7}$

$f^{-1}(x)=\sqrt{x-7}, and\\f^{-1}(x)=-\sqrt{x-7}$

Domain: this is the range of the original so domain is [7,∞)

Range: this is the domain of the original so range is (-∞,∞)

$f(x)=14x-4$

Domain: There is no restriction on values of x we can put on it. Hence domain is (-∞,∞)

Range: no matter what we put into x, we can get any y value from negative infinity to positive infinity. So range is (-∞,∞)

Finding the inverse:

$f(x)=14x-4\\y=14x-4\\x=14y-4\\14y=x+4\\y=\frac{1}{14}x+\frac{2}{7}$

$f^{-1}(x)=\frac{1}{14}x+\frac{2}{7}$

Domain: this is the range of the original so domain is (-∞,∞)

Range: this is the domain of the original so range is (-∞,∞)

$f(x)=-3x+8$

Domain: There is no restriction on values of x we can put on it. Hence domain is (-∞,∞)

Range: no matter what we put into x, we can get any y value from negative infinity to positive infinity. So range is (-∞,∞)

Finding the inverse:

$f(x)=-3x+8\\y=-3x+8\\x=-3y+8\\3y=-x+8\\y=-\frac{1}{3}x+\frac{8}{3}$

$f^{-1}(x)=-\frac{1}{3}x+\frac{8}{3}$

Domain: this is the range of the original so domain is (-∞,∞)

Range: this is the domain of the original so range is (-∞,∞)

8 0

4 years ago