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scZoUnD [109]
3 years ago
11

A sandwich shop is ordering apples and grapes to make chicken salad.Apples cost $2.19 per pound and grapes cost $2.60 per pound.

If they ordered a total of 20 pounds of apples and grapes and pair $35.80. How many pounds of grapes did they order?
Mathematics
1 answer:
andrew11 [14]3 years ago
8 0

Answer:

Grapes=19.51

Step-by-step explanation:

Apples=$2.19 per pound

Grapes=$2.60 per pound

Apples+Grapes=20 pounds

A+G=20

A=20-G

Equation is

PaA+PgG=35.80

2.19A+2.60G=35.80

2.19(20-G)+2.60G=35.80

43.8-2.19G+2.60G=35.80

43.8-0.41G=35.80

-0.41G=35.80-43.8

-0.41G=-8

Divide both sides by 0.41

G=19.51 pounds

Recall

A=20-G

A=20-19.51

A=0.49 pounds

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If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct.
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Answer:

Probability = 0.190

Step-by-step explanation:

Given:

Number of questions, 'n' = 20

Each question has four choices.

Let event of choosing correct answer be success and its probability be represented by 'p'.

Therefore, event of choosing wrong answer is failure and its probability be represented by 'q'.

Now, probability of success is choosing one correct answer out of 4 options. So, p=\frac{1}{4}=0.25

Now, 'p' and 'q' are complements of each other. Therefore,

q=1-p=1-0.25=0.75

Now, we need 4 successes. Therefore, x=4

Using Bernoulli's theorem to find 'x' successes from 'n' questions, we get:

P(x)=_{x}^{n}\textrm{C}p^xq^{n-x}

Plug in 4 for 'x', 20 for 'n', 0.25 for 'p' and 0.75 for 'q'. Solve.

P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{20-4}\\P(4)=_{4}^{20}\textrm{C}(0.25)^4(0.75)^{16}\\P(4)=4845\times (0.25)^4\times (0.65)^{16}\\\\P(4)=0.1896\approx0.190

Therefore, the probability of getting 4 correct answers out of 20 questions is 0.190.

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Answer:

B and D

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D: The Eagles have more players.

Step-by-step explanation:

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Find a cubic function with the given zeros.
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Answer:

The correct option is D) f(x) = x^3 + 2x^2 - 2x - 4 .

Step-by-step explanation:

Consider the provided cubic function.

We need to find the equation having zeros: Square root of two, negative Square root of two, and -2.

A "zero" of a given function is an input value that produces an output of 0.

Substitute the value of zeros in the provided options to check.

Substitute x=-2 in f(x) = x^3 + 2x^2 - 2x + 4 .

f(x) = x^3 + 2x^2 - 2x + 4\\f(x) = (-2)^3 + 2(-2)^2 - 2(-2) + 4\\f(x) =-8 + 2(4)+4 + 4\\f(x) =8

Therefore, the option is incorrect.

Substitute x=-2 in f(x) = x^3 + 2x^2 + 2x - 4 .

f(x) = x^3 + 2x^2 + 2x - 4\\f(x) = (-2)^3 + 2(-2)^2 + 2(-2) - 4\\f(x) =-8+2(4)-4-4\\f(x) =-8

Therefore, the option is incorrect.

Substitute x=-2 in f(x) = x^3 - 2x^2 - 2x - 4 .

f(x) = x^3 - 2x^2 - 2x - 4\\f(x) = (-2)^3 - 2(-2)^2 - 2(-2) - 4\\f(x) =-8-8+4-4\\f(x) =-16

Therefore, the option is incorrect.

Substitute x=-2 in f(x) = x^3 + 2x^2 - 2x - 4 .

f(x) = x^3 + 2x^2 - 2x - 4\\f(x) = (-2)^3+2(-2)^2 - 2(-2) - 4\\f(x) =-8+8+4-4\\f(x) =0

Now check for other roots as well.

Substitute x=√2 in f(x) = x^3 + 2x^2 - 2x - 4 .

f(x) = x^3 + 2x^2 - 2x - 4\\f(x) = (\sqrt{2})^3+2(\sqrt{2})^2 - 2(\sqrt{2}) - 4\\f(x) =2\sqrt{2}+4-2\sqrt{2}-4\\f(x) =0

Substitute x=-√2 in f(x) = x^3 + 2x^2 - 2x - 4 .

f(x) = x^3 + 2x^2 - 2x - 4\\f(x) = (-\sqrt{2})^3+2(-\sqrt{2})^2 - 2(-\sqrt{2}) - 4\\f(x) =-2\sqrt{2}+4+2\sqrt{2}-4\\f(x) =0

Therefore, the option is correct.

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Answer:

A suitable estimate of all families who own their home is 42%.

Step-by-step explanation:

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This means that the sample proportion is of 42%. So that an estimate for the percentage of all families who own their home is of 42%., and that the first option is correct.

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