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2 years ago

Choose the mixed number that is equivalent to this decimal 3.242424...

Mathematics

1 answer:

Vinvika [58]2 years ago

7 0

Answer:

3.24 = 3 6/25

Step-by-step explanation:

- Rewrite the decimal number as a fraction with 1 in the denominator.

- Multiply to remove 2 decimal places. Here, you multiply top and bottom by 100

- Find the Greatest Common Factor (GCF) of 324 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 4

- You should end up with that answer..

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A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates w

sveta [45]

Answer:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

$(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318$

And the 95% confidence interval would be given (-0.1412;-0.0318).

We are confident at 95% that the difference between the two proportions is between $-0.1412 \leq p_A -p_B \leq -0.0318$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion for business

$\hat p_A =\frac{75}{400}=0.1875$ represent the estimated proportion for Business

$n_A=400$ is the sample size required for Business

$p_B$ represent the real population proportion for non Business

$\hat p_B =\frac{137}{500}=0.274$ represent the estimated proportion for non Business

$n_B=500$ is the sample size required for non Business

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

$(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318$

And the 95% confidence interval would be given (-0.1412;-0.0318).

We are confident at 95% that the difference between the two proportions is between $-0.1412 \leq p_A -p_B \leq -0.0318$

7 0

1 year ago

Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas

Anarel [89]

5x + 3y= 8.50
3x + 2y= 5.25

Lydia is the first equation. She bought 5 pounds of apples which is x and bought 3 pounds of bananas which is y. Basically, remember each banana and apple weighs a price per pound. We don't know the price so we just put an x. This is the same for the second equation

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1 year ago

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Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at lea

lbvjy [14]

Answer:

(0, 33) : Yes

(4.8, 30.5) : Yes

Step-by-step explanation:

height of at least 24 ft : y >= 24

horizontal distance of no more than 10 ft. : 0 <= x <= 10

The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.:

y >= 3x and y <= 33

So Constraints:

24 <= y <= 33

y >= 3x

0 <= x <= 10

Now check to see if those coordinate points meet all the constraints

(0, 33) : Yes

(4.8, 30.5) : Yes

(9, 26) : No (because 26 is less than (3 * 9) = 27)

(4, 36) : No (because 36 > 33, must be 24 <= y <= 33)

(2, 22): No (because 22 <24, must be 24 <= y <= 33)

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1 year ago

Find: (4x2y3 + 2xy2 – 2y) – (–7x2y3 + 6xy2 – 2y)

const2013 [10]

Answer:

The coefficients are

11,-4 and 0

Step-by-step explanation:

We are given two algebraic expressions. We are subtracting the second from the first.

First one is

$4x^2y^3+2xy^2-2y$

Second expression is

$-7x^2y^3+6xy^2-2y$

The given expression

= $4x^2y^3+2xy^2-2y-(-7x^2y^3+6xy^2-2y)\\=4x^2y^3+2xy^2-2y+7x^2y^3-6xy^2+2y\\=11x^2y^3-4xy^2+0y$

The coefficients are

11,-4 and 0

7 0

1 year ago

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In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014,

DochEvi [55]

Answer:

The mean of C is 170 households

The standard deviation of C, is approximately 5 households

Step-by-step explanation:

The given parameters are;

The percentage of households in the United States that had a computer in 2014 = 85%

The size of the randomly selected sample in 2014, n = 200

The random variable representing the number of households that had a computer = C

Therefore, we have;

The probability of a household having a computer P = 85/100 = 0.85

Let

Therefore;

The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;

μₓ = 200 × 0.85 = 170

The mean of C = μₓ = 170

The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5

Therefore;

The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05

The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)

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1 year ago

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