A student attempted to generate an equivalent expression using the distributive property, as shown below:

The two lines shown intersect at the point (a,b). Find ab. Each unit square in the grid represents a distance of 1.

Ket [755]

Answer:

(9/5, 8/5)

Step-by-step explanation:

First you want to find the equations of the lines. One line is y = 2x - 2 and the other line is y = 1/3x + 1. Then you want to find the x and y that both work in the two equations.

y = 2x - 2

y = 1/3x + 1

Then you do 2x - 2 = 1/3x + 1

Then you do some maths and you get 9/5, and 8/5

6 0

3 years ago

Sick-leave time used by employees of a firm in a course of one month has approximately normal distribution, with a mean of 200 h

Usimov [2.4K]

Answer:

a)0.62% probability that total sick leave for next month will be less than 150 hours.

b) 225.6 hours should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

In this problem, we have that:

$\mu = 200, \sigma = \sqrt{400} = 20$

a.Find the probability that total sick leave for next month will be less than 150 hours.

This probability is the pvalue of Z when X = 150. So:

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

$Z = \frac{150 - 200}{20}$

$Z = -2.5$

$Z = -2.5$ has a pvalue of 0.0062.

So there is a 0.62% probability that total sick leave for next month will be less than 150 hours.

b.In planning schedules for next month, how much time should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.

This is the value of X when Z has a pvalue of 0.90. So $Z = 1.28$

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

$1.28 = \frac{X - 200}{20}$

$X - 200 = 20*1.28$

$X = 225.6$

225.6 hours should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.

6 0

3 years ago

The numbers a,b,c,d are four consecutive terms of an arithmetic sequence and a+b+c+d=12

likoan [24]

The smallest possible product of these four numbers is 59.0625

<h3>How to find the smallest possible product of these four numbers?</h3>

The equation is given as:

a + b + c + d = 12

The numbers are consecutive numbers.

So, we have:

a + a + 1 + a + 2 + a + 3 = 12

Evaluate the like terms

4a = 6

Divide by 4

a = 1.5

The smallest possible product of these four numbers is represented as:

Product = a * (a + 1) * (a + 2) * (a + 3)

This gives

Product = 1.5 * (1.5 + 1) * (1.5 + 2) * (1.5 + 3)

Evaluate

Product = 59.0625

Hence, the smallest possible product of these four numbers is 59.0625

Read more about consecutive numbers at:

brainly.com/question/10853762

#SPJ1

6 0

1 year ago

Identify the volume of the composite figure rounded to the nearest tenth.

Verdich [7]

Answer:

(c) 115.2 ft³

Step-by-step explanation:

The volume of a composite figure can be found by decomposing it into figures whose volumes are easy to compute. Here, the figure can be nicely represented as a cube and a square pyramid.

__

The volume of the cube on the left is given by ...

V = s³

V = (4.2 ft)³ = 74.088 ft³

__

<h3>Pyramid</h3>

The volume of the pyramid on the right is given by ...

V = 1/3Bh . . . . . where B is the area of the square base

V = 1/3(s²)h = (4.2 ft)²(7 ft) = 41.16 ft³

__

<h3>Total</h3>

The volume of the composite figure is the sum of these volumes:

cube volume + pyramid volume = 74.088 ft³ +41.16 ft³ = 115.248 ft³

The volume of the composite figure is about 115.2 ft³.

6 0

2 years ago

Sam takes out a $167,000 mortgage for 20 years. He makes monthly payments and at the end calculates

cupoosta [38]

Answer:

The Annual rate of interest for the mortgage is 1.8%

Step-by-step explanation:

Given as :

The mortgage principal = p = $167,000

The time period of mortgage = t = 20 years

The Amount paid towards mortgage in 20 years = A = $240,141

Let the Annual percentage rate on interest = r % compounded annually

Now, <u>From Compound Interest method</u>

Amount = Principal × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, $240,141 = $167,000 × $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

or, $\dfrac{240,141}{167,000}$ = $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or , 1.437 = $(1+\dfrac{\textrm r}{100})^{\textrm 20}$

Or, $(1.437)^{\frac{1}{20}}$ = $(1+\dfrac{r}{100})$

or, 1.018 = $(1+\dfrac{r}{100})$

Or, $\dfrac{r}{100}$ = 1.018 - 1

Or, $\dfrac{r}{100}$ = 0.018

∴ r = 0.018 × 100

i.e r = 1.8

So, The rate of interest applied = r = 1.8 %

Hence, The Annual rate of interest for the mortgage is 1.8% Answer

8 0

3 years ago