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SVETLANKA909090 [29]
2 years ago
7

A construction crew can dig a pit at a rate of

Mathematics
1 answer:
makvit [3.9K]2 years ago
3 0
The answer would be F
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2<br> Solve for k.<br> -8k+ 6 = –10k + 10<br> k
Sever21 [200]

Answer:

k=2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit
Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 159, \sigma = 13, n = 60, s = \frac{13}{\sqrt{60}} = 1.68

What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?

This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So

X = 160

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{160 - 159}{1.68}

Z = 0.6

Z = 0.6 has a pvalue of 0.7257

X = 150

Z = \frac{X - \mu}{s}

Z = \frac{158 - 159}{1.68}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

7 0
3 years ago
A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of
Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0
3 years ago
Sammy usually takes a 18 minute shower in the morning. If a 4 minute shower uses an average of 20-40 gallons of water, what is t
mylen [45]
D 180 gallons of water
5 0
3 years ago
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What is the area of the composite figure
lara [203]

Answer:

Area of composite figure = 216 cm²

Hence, option A is correct.

Step-by-step explanation:

The composite figure consists of two figures.

1) Rectangle

2) Right-angled Triangle

We need to determine the area of the composite figure, so we need to find the area of an individual figure.

Determining the area of the rectangle:

Given

Length l = 14 cm

Width w = 12 cm

Using the formula to determine the area of the rectangle:

A = wl

substituting  l = 14 and w = 12

A = (12)(14)

A = 168 cm²

Determining the area of the right-triangle:

Given

Base b = 8 cm

Height h = 12 cm

Using the formula to determine the area of the right-triangle:

A = 1/2 × b × h

A = 1/2 × 8 × 12

A = 4 × 12

A = 48 cm²

Thus, the area of the figure is:

Area of composite figure = Rectangle Area +  Right-triangle Area

                                            = 168 cm² +  48 cm²

                                            = 216 cm²

Therefore,

Area of composite figure = 216 cm²

Hence, option A is correct.

4 0
3 years ago
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