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3 years ago

Mark u as branliest but answer right plz

Mathematics

1 answer:

yanalaym [24]3 years ago

8 0

Answer:

Step-by-step explanation:

55+4x

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Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 12 young adul

ddd [48]

Answer:

a) 0.194 = 19.4% probability that more than 7 preferred McDonald's

b) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

c) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they prefer McDonalds, or they prefer burger king. The probability of an adult prefering McDonalds is independent from other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

50% of all young adults prefer McDonald's to Burger King when asked to state a preference.

This means that $p = 0.5$

12 young adults were randomly selected

This means that $n = 12$

(a) What is the probability that more than 7 preferred McDonald's?

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.121$

$P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.054$

$P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.016$

$P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.003$

$P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.000$

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.121 + 0.054 + 0.016 + 0.003 + 0.000 = 0.194$

0.194 = 19.4% probability that more than 7 preferred McDonald's

(b) What is the probability that between 3 and 7 (inclusive) preferred McDonald's?

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.054$

$P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.121$

$P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.193$

$P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.226$

$P(X = 7) = C_{12,7}.(0.5)^{7}.(0.5)^{5} = 0.193$

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.054 + 0.121 + 0.193 + 0.226 + 0.193 = 0.787$

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

(c) What is the probability that between 3 and 7 (inclusive) preferred Burger King?

Since $p = 1-p = 0.5$ , this is the same as b) above.

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

7 0

3 years ago

HELLPP. ITS URGENT.50 PTS

ICE Princess25 [194]

Answer:

4x² - 13x + 8 = 0
4x² - 11x + 5 = 0
16x² - 41x + 1 = 0
x² + 5x + 4 = 0
x² - 66x + 64 = 0

Step-by-step explanation:

Given

α and β are roots of 4x²-5x-1=0

Then the sum and product of the roots are:

α+b = -(-5)/4 = 5/4
αβ = -1/4

(i) Roots are α + 1 and β + 1, then we have:

(x - (α + 1))(x - (β + 1)) = 0
(x - α - 1)(x - β - 1) = 0
x² - (α+β+2)x + α+β+ αβ + 1 = 0
x² - (5/4+2)x +5/4 - 1/4 + 1 = 0
x² - 13/4x + 2= 0
4x² - 13x + 8 = 0

(ii) Roots are 2 - α and 2 - β, then we have:

(x + α - 2)(x + β - 2) = 0
x² + (a + β - 4)x - 2(α + β) + αβ + 4 = 0
x² + (5/4 - 4)x - 2(5/4) - 1/4 + 4 = 0
x² - 11/4x - 10/4 - 1/4 + 16/4 = 0
x² - 11/4x + 5/4x = 0
4x² - 11x + 5 = 0

(iii) Roots are α² and β², then:

(x - α²)(x-β²) = 0
x² -(α²+β²)x + (αβ)² = 0
x² - ((α+β)² - 2αβ)x + (-1/4)² = 0
x² - ((5/4)² -2(-1/4))x + 1/16 = 0
x² - ( 25/16 + 1/2)x + 1/16 = 0
x² - 33/16x + 1/16 = 0
16x² - 33x + 1 = 0

(iv) Roots are 1/α and 1/β, then:

(x - 1/α)(x - 1/β) = 0
x² - (1/α+1/β)x + 1/αβ = 0
x² - ((α+β)/αβ)x + 1/αβ = 0
x² - (5/4)/(-1/4)x - 1/(-1/4) = 0
x² + 5x + 4 = 0

(v) Roots are 2/α² and 2/β², then:

(x - 2/α²)(x - 2/β²) = 0
x² - (2/α² + 2/β²)x + 4/(αβ)² = 0
x² - 2((α+β)² - 2αβ)/(αβ)²)x + 4/(αβ)² = 0
x² - 2((5/4)² - 2(-1/4))/(-1/4)²x + 4/(-1/4)² = 0
x² - 2(25/16 + 8/16)/(1/16)x + 4(16) = 0
x² - 2(33)x + 64 = 0
x² - 66x + 64 = 0

3 0

3 years ago

Read 2 more answers

A used-droid dealership buys a droid for $2900 and then sells it for $4300. What is the percent increase?

Anna71 [15]

The percent increase is 48.28

Step-by-step explanation:

Given,

Purchase price of used-droid = $2900

Selling price of used=droid = $4300

Profit = Selling price - purchase price

Profit = 4300-2900 = $1400

Percent increase = $\frac{Profit}{Purchase\ price}*100$

$Percent\ increase=\frac{1400}{2900}*100\\\\Percent\ increase=\frac{140000}{2900}\\\\Percent\ increase=48.275\%$

Rounding off to nearest hundredth;

Percent increase = 48.28%

The percent increase is 48.28

Keywords: percentage, subtraction

Learn more about percentages at:

#LearnwithBrainly

8 0

3 years ago

Jean bought a $1,980 snow thrower on the installment plan. The installment agreement included a 10% down payment and 18 monthly

enyata [817]

Answer:

Jean paid $2,286 for the snow thrower, with a finance charge of $306.

Step-by-step explanation:

Given that Jean bought a $ 1,980 snow thrower through an initial payment of 10% of the initial value, and 18 monthly payments of $ 116, to determine the final price paid by Jean, the following calculation is required:

(1,980 x 0.1) + (18 x 116) = X

198 + 2,088 = X

2,286 = X

Therefore, the final price paid for Jean was $ 2,286.

In turn, the finance charge arises from the difference between the final price and the list price, that is:

2,286 - 1,980 = X

306 = X

Thus, the finance charge is $ 306.

8 0

2 years ago

Convert 50 miles per hour to feet per second ( 1 mile = 5280 feet and 1 hour = 3600 seconds )

wolverine [178]

Answer:

73.3

Step-by-step explanation:

50mi/h * 5280ft/mi * 1h/3600s = 220/3 = 73.3 ft/s

6 0

3 years ago

Read 2 more answers