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3 years ago

I need the answers pls!!!!please

Mathematics

1 answer:

Igoryamba3 years ago

6 0

Answer:

$(4x - 3)(5x - 8) = 20x^2 -47x + 24$

Step-by-step explanation:

Given

$(4x - 3)(5x - 8)$

Required

Identify and correct error

The error is when the inner and outer terms are multiplied. i.e.

$4x * -8 = -32x$ not 32x

$-3 * 5x = -15x$ not 15x

So, the expression is:

$(4x - 3)(5x - 8) = 20x^2 - 32x -15x + 24$

$(4x - 3)(5x - 8) = 20x^2 -47x + 24$

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Johnny and Cage are working together to mold figurines for a craft fair. They already have 8 figurines which were left from the

alukav5142 [94]

Answer:

See Explanation

Step-by-step explanation:

Given

$Initial = 8$

$Increment = 3$ (every hour)

Required

Explain why it is linear

First, we need to determine the equation that represents the scenario

Let x be the number of hours worked and y be the number of figurines at x hours.

The equation is determined as follows:

$y = Initial\ Figurines + Increment * x$

This gives:

$y = 8 + 3 * x$

$y = 8 + 3x$

Reorder

$y = 3x + 8$

A linear equation is of the form

$y = mx + b$

By comparison,

$y = mx + b$ is equivalent to $y = 3x + 8$

<em>Hence, we can conclude that the situation is linear</em>

8 0

3 years ago

Read 2 more answers

Ball bearings are manufactured with a mean diameter of 5 millimeters(mm). Because of variability in the manufacturing process, t

dexar [7]

Answer:

a) 0.0668 of ball bearings have a diameter more than 5.03 mm

b) 0.0124 of ball bearings will be discarded

c) The plant manager should expect to discard 372 balls.

d) 57,710 ball bearings should be manufactured.

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

$\mu = 5, \sigma = 0.02$

(a) What proportion of ball bearings has a diameter more than 5.03 mm?

This is 1 subtracted by the pvalue of Z when X = 5.03. So

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

$Z = \frac{5.03 - 5}{0.02}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 of ball bearings have a diameter more than 5.03 mm

(b) Any ball bearings that have a diameter less than 4.95 mm or greater than 5.05 mm are discarded. What proportion of ball bearings will be discarded?

Lower than 4.95 or greater than 5.05. Both these proportions are the same, so we find one of them, and multiply by 2.

Less than 4.95:

pvalue of Z when X = 4.95. So

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

$Z = \frac{4.95 - 5}{0.02}$

$Z = -2.5$

$Z = -2.5$ has a pvalue of 0.0062

2*0.0062 = 0.0124

0.0124 of ball bearings will be discarded.

(c) Using the results of part (b), if 30,000 ball bearings are manufactured in a day, how many should the plant manager expect to discard?

0.0124 of 30,000. So

0.0124*30000 = 372

The plant manager should expect to discard 372 balls.

(d) If an order comes in for 50,000 ball bearings, how many bearings should the plant manager manufacture if the order states that all ball bearings must be between 4.97 mm and 5.03 mm?

Proportion of bearings between 4.97 mm and 5.03 mm:

pvalue of Z when X = 5.03 subtracted by the pvalue of Z when X = 4.97. So

X = 5.03

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

$Z = \frac{5.03 - 5}{0.02}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 4.97

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

$Z = \frac{4.97 - 5}{0.02}$