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2 years ago

Can anybody help me with these three problems thank you

Mathematics

1 answer:

Amiraneli [1.4K]2 years ago

8 0

Answer:

1) 1/7

2) 1/3

3) 1/4

Step-by-step explanation:

1) Since there are 7 days in a week it can be expressed as the fraction 1/7

2) Since there are 3 feet in a yard it can be expressed as the fraction 1/3

3) Since there are 4 quarts in a gallon it can be expressed as the fraction 1/4

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An ice cream shop chose 25 customers at random and asked each to name a

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Suppose a random sample of 200 Americans is asked to disclose whether they can order a meal in a foreign language. Describe the

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Answer:

The distribution of sample proportion Americans who can order a meal in a foreign language is,

$\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})$

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

The sample size of Americans selected to disclose whether they can order a meal in a foreign language is, n = 200.

The sample selected is quite large.

The Central limit theorem can be applied to approximate the distribution of sample proportion.

The distribution of sample proportion is,

$\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})$

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2 years ago

PICKING BRAINIEST which equation could be used to solve for the length of XY?

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The answer is in my attachment

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2 years ago

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Use the intersect method to solve the equation. 14x^3-53x^2+41x-4=-4x^3-x^2+1x+4

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Answer:

x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

Step-by-step explanation:

Solve for x over the real numbers:

14 x^3 - 53 x^2 + 41 x - 4 = -4 x^3 - x^2 + x + 4

Subtract -4 x^3 - x^2 + x + 4 from both sides:

18 x^3 - 52 x^2 + 40 x - 8 = 0

Factor constant terms from the left hand side:

2 (9 x^3 - 26 x^2 + 20 x - 4) = 0

Divide both sides by 2:

9 x^3 - 26 x^2 + 20 x - 4 = 0

Eliminate the quadratic term by substituting y = x - 26/27:

-4 + 20 (y + 26/27) - 26 (y + 26/27)^2 + 9 (y + 26/27)^3 = 0

Expand out terms of the left hand side:

9 y^3 - (136 y)/27 - 1780/2187 = 0

Divide both sides by 9:

y^3 - (136 y)/243 - 1780/19683 = 0

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

-1780/19683 - 136/243 (z + λ/z) + (z + λ/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 136/243) - (1780 z^3)/19683 + z^2 (3 λ^2 - (136 λ)/243) + λ^3 = 0

Substitute λ = 136/729 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 - (1780 u)/19683 + 2515456/387420489 = 0

Find the positive solution to the quadratic equation:

u = (2 (445 + 27 i sqrt(591)))/19683

Substitute back for u = z^3:

z^3 = (2 (445 + 27 i sqrt(591)))/19683

Taking cube roots gives 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) times the third roots of unity:

z = 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = -1/27 (-2)^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = 1/27 (-1)^(2/3) 2^(1/3) (445 + 27 i sqrt(591))^(1/3)

Substitute each value of z into y = z + 136/(729 z):

y = (68 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 1/27 (2 (27 i sqrt(591) + 445))^(1/3) or y = (68 (-2)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) - 1/27 (-2)^(1/3) (27 i sqrt(591) + 445)^(1/3) or y = 1/27 (-1)^(2/3) (2 (27 i sqrt(591) + 445))^(1/3) - (68 (-1)^(1/3) 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3))

Bring each solution to a common denominator and simplify:

y = (2^(1/3) ((27 i sqrt(591) + 445)^(2/3) + 68 2^(1/3)))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = 1/27 2^(1/3) (-1/(445 + 27 i sqrt(591)))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3))

Substitute back for x = y + 26/27:

Answer: x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

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2 years ago

Ming bought 40 pencils and Catherine bought 24. If each package of pencils sold at the store contain the same number of pencils,

sleet_krkn [62]

Answer:

8 pencils.

Step-by-step explanation:

This is a common, GCF question and the question becomes, what number is the GCF of 40 and 24.

40= 2x2x2x5

24=2x2x2x3

Both share 2x2x2, which is 8 so the largest number of pencils in each pack is 8.

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