To explain that the expression 20m−60n+20 can be written as 20(m−3n), John first factors 20m as 20 ⋅ m and 60n as 20 ⋅ 3n, and leaves 20 unchanged. Then, he factors 20 from each term of the expression 20m−60n+20 and puts the remaining factors together within a pair of brackets.


• Explain why John’s reasoning is incorrect.


• Factor 20m−60n+20


• Explain how you found the answer.

Answer:

see solution

Step-by-step explanation:

equation: y = 1 - 3x

when x is -2:
y = 1 -3 * -2  = y = 1+6 = y = 7
coordinates = (x,y) = (-2,7)

when x is -1:
y = 1-3*-1 = y = 1+3 = y = 4
coordinates = (x,y) = (-1,4)

when x is 0:
y = 1 - 3 * 0 = y = 1-0 = y =1
coordinates = (x,y) = (0,1)

when x is 1
y = 1-3*1 = y = 1-3 = y = -2
coordinates = (x,y) = (1,-2)

When x is 2
y = 1-3*2 = y = 1-6 = y = -5
coordinates = (x,y) = (2,-5)

when x is 3
y = 1-3*3 = y = 1-9 = y = -8
coordinates = (x,y) = (3,-8)

Plot these points on the graph and join up the dots to see the line.

bye

The hypotheses for [tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)

Given:

Nationwide scores as  n1=1000, [tex]x_{1}[/tex]` = 21.4 ,σ1 = 3

Carolina scores as n2=500,  [tex]x_{2}[/tex]` = 21.2 ,σ2 = 3

So from here we can say

µ represents population mean.

[tex]u_{1}[/tex] represent population mean for nationwide scores.

[tex]u_{2}[/tex] represents population mean for Carolina scores.

[tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)

Given Question is incomplete, Complete Question here,

a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?

use α=0.01 and [tex]\µ_{1}[/tex] for the nationwide mean act score.

State the hypotheses and identify the claim.

To know more about mean and standard deviation here

https://brainly.com/question/28108712

#SPJ4

What is your question dude???????

The two positive numbers that satisfy the given requirements are √17 and 34

Given the sum of the first number squared and the second number

is 51.

Let's assume first number is x.

second number is y.

Square of first number is [tex]x^2[/tex].

sum of the first number squared and the second number = [tex]x^2 + y[/tex].

[tex]x^2 + y = 51[/tex]

subtract [tex]x^2[/tex] from both side of equal sign.

[tex]x^2 + y- x^2 = 51 - x^2[/tex]

[tex]y = 51 - x^2[/tex]

Product of both numbers p  = x*y.

[tex]p = x*(51 - x^2)[/tex]

[tex]p = 51*x - x^3.[/tex]

Given the product is a maximum.

so derivative of p with respect to x  will be = 0.

derivative of p with respect to x is  [tex]51-3*x^2[/tex]

[tex]51-3*x^2 = 0[/tex]

[tex]3*x^2=51[/tex]

[tex]x^2 = 17[/tex]

x = √17.

put value of x in [tex]y = 51 - x^2[/tex]

[tex]y = 51 - (\sqrt17)^2[/tex] = 51 - 17 = 34

So the value of x and y is √17 and 34 respectively.

To know more about maximum product , here

https://brainly.com/question/10589960

#SPJ4

The change in rate of length of shadow is 2.692 ft/sec.

Given,

Height of tall person =7 ft

Height of tall lamp post = 20 ft

Rate at which tall person walks = 5 ft/sec

Let,

Distance between tall person and lamp post be x ft

the length of shadow be y ft

From similar triangles,

[tex]\frac{x+y}{20}=\frac{y}{7}\\\\7(x+y)=20y\\\\7x+7y=20y\\\\13y=7x\\\\y=\frac{7x}{13}[/tex]

Differentiating on both sides with respect to time 't'

[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}[/tex]

here, [tex]\frac{dx}{dt}[/tex] is nothing but the change in distance between tall person and lamppost it means rate at which tall person walks=5 ft/sec

[tex]\frac{dy}{dt}=\frac{7}{13}*5\\\\\frac{dy}{dt}=\frac{35}{13}=2.692\ ft/sec[/tex]

Thus, the change in rate of length of shadow is 2.692 ft/sec.

To learn more about calculus refer here

https://brainly.com/question/18722670

#SPJ4

The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.

When two rays are linked at their ends, they create an angle in geometry.

The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.

Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

learn more about angles click here:

https://brainly.com/question/25716982

#SPJ4

Answer:

x=36

Step-by-step explanation:

It will take 3 years for the value of the computer of initial value $1000 to reach $512.

Given, Timothy purchased a computer for $1,000.

The value of the computer depreciates by 20% every year.

we have to find the number of years value of computer will take to reach $512.

Let, the function representing this situation be,

V(t) = AB^t

where, A is the initial value of the computer and B is the depreciating rate.

So, V(t) = (1000)(1 - 20/100)^t

V(t) = (1000)(0.8)^t

Now, the value will be, 512

512 = 1000(0.8)^t

0.512 = (0.8)^t

t = 3

So, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

Hence, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

Learn more about Exponential Functions here https://brainly.com/question/12472697

#SPJ4

When the population standard deviation is much greater than 5.

What is the standard deviation?

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Here, we have

The circumstance is a score that is 5 points above the mean considered a central value.

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

To learn more about the standard deviation from the given link

https://brainly.com/question/475676

#SPJ4

The equation representing the situation is written as

the number of customers Olaf had originally is 80

From the given information the following is deduced

Olaf has 11 more than triple the amount of customers as when he started selling newspapers

let the amount be x

3x + 11 = ?

He now has 71 customers

3x + 11 = 71

solving the equation

3x = 71 - 11

3x = 60

x = 20

Olaf had 80 customers

Learn more about linear equations at

https://brainly.com/question/29216888

#SPJ1

The best guess for the mean score for all the Georgia students would be 1050 number here.

Given that:

The mean score for a random sample of Georgia students is 1050.

Assuming,

1) X-bar = 42; µ = 44; standard deviation (sigma) = 10; N = 64. Calculate the standard error.

1) The standard error is computed as:

[tex]\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{64}} = 1.25[/tex]

2) You know that X-bar = 42, mu = 44, sigma-sub-X = 10, and N = 64, Calculate z-obtained.

2) The Z-value is computed as:

[tex]Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{N}}} = \frac{42- 44}{\frac{10}{\sqrt{64}}} = -1.6[/tex]

3) The mean score on most IQ tests is 100 with a standard deviation of 15. If Sally has a score of 110 on an IQ test, what is her z-score.

3) The Z -score here is computed as:

[tex]Z = \frac{X -\mu}{\sigma} = \frac{110-100}{15} = 0.6667[/tex]

The best point estimate for the population mean score is equal to the sample mean which is 1050 in this case. Therefore the best guess for the mean score for all the Georgia students would be 1050 here.

To learn more about the population mean visit: https://brainly.com/question/19538277

#SPJ4

Answer:

Step-by-step explanation:

Answer 3700

Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.

A Gram-positive bacterium called S. epidermidis is a component of the flora of humans. Anaerobic bacteria are what it is. It promotes the growth of pathogens that are present in medical equipment. These may enter the bloodstream. Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling s. epidermidis.

Molds produce a class of antibiotics known as penicillium. Actinomycetes produce the antibody known as novobiocin, which has antibacterial characteristics. Gentamicin is one of the antibodies that can treat infections and aid in halting bacterial development.

Hence the answer is Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.

To learn more about observations click here https://brainly.com/question/24343193

#SPJ4

The probability that a randomly chosen mango of this type won't be deemed to be large in size is 26.43%.

For the stated question;

The formula for the z-score is;

z = (x - μ)/σ

x < 425 gram

mean  μ = 400,

standard deviation σ = 40:

Thus,

z = (425 - 400)/40

z = 0.625

P(X < 425) = 1 - P(z = 0.625)

P(X < 425) = 1 - 0.7357

P(X < 425) = 0.2643

Thus, there is a 26.43% chance that a randomly chosen mango of this sort will not be regarded as being huge in size.

To know more about the z-distribution, here

https://brainly.com/question/27275125

#SPJ4

Answer:0.8413

Step-by-step explanation:

0.8413

The mean is μ=400, and the standard deviation is σ=25.

Open Excel.  Click on an empty cell.  Type =NORMDIST(425,400,25,1) and press ENTER.

The probability, rounded to four decimal places, is P(X<425)≈0.8413.

Answer:

rhe general pattern in data is........

Step-by-step explanation:

.....

There isn't a ton of information regarding exactly what you are looking for to answer this question. However, if you are trying to simply convert the following word phrase to an expression, here you go:

Hence, the final expression would be written as:

[tex](3x+4) < 4(x+1)[/tex]

Hope this helps!

the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Now the simplest way to write an equation is to multiply all the factors.

The zeroes of the equation are 1,2,3,4,5,6,7.

The factors can be written as (x-1)* (x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-7).

So the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]

Hence, the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]

Learn more about equations, by the following link

brainly.com/question/2972832

#SPJ4

If multiplying 2 negative integers then it's a positive

If multiplying 2 positive integers it's positive

Answer: I hope this is helpful

Step-by-step explanation:

The proceeding pattern is summarized in the following rule for multiplying integers. Rule for Multiplying Two Integers: TO MULTIPLY INTEGERS WITH THE SAME SIGN, multiply the absolute value of the factors. The product is positive.

98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

mean x = 16

standard deviation σ = 2.4

sample size n = 65

z score for 98% = 2.576

Interval = x±z*s/

= 16±2.576*2.4/

= 16±2.576*0.39629

= 16±1.0208

Interval = (21.0208,18.9792)

Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

Learn more about the confidence interval here:

brainly.com/question/24131141

#SPJ4

The regression equation is y = 0.9x+ 7.5

given that

xi:  2   6    9    13    20

Yi : 7   18   9    26   23  

from the given data we have:

∑x = 2+6+9+13+20 = 50

∑y = 7+18+9+26+23 = 83

Also, we need to calculate:

∑xy = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001

∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] + [tex]6^{2}[/tex] + [tex]9^{2}[/tex] + [tex]13^{2}[/tex] + [tex]20^{2}[/tex] = 690

∑[tex]y^{2}[/tex]= [tex]7^{2}[/tex] +  [tex]18^{2}[/tex] + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] + [tex]23^{2}[/tex] = 1659

the slope b is calculated:

b = ∑xy - ∑x × ∑y/n ÷ ∑[tex]x^{2}[/tex] - (∑x)^2 /n

now we need to substitute above values in the equation:

b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5

b= 0.9

the y-intercept (a) is :

a = y - bx

where

y = ∑y/n = 83/5 = 16.6

x = ∑x/n = 50/5 = 10

now substitute these values

a = 16.5 - 0.9 × 10

a = 7.5

the regression equation:

y = bx + a

now ,

y = 0.9x+ 7.5

To learn more about  y-intercept :

https://brainly.com/question/14180189

The numerical side length of length AD is 44 units

From the question, we have the following lengths that can be used in our computation:

AD= 4x + 8

CD = 5x - 1

Also, from the complete question (added at the end of the solution), we understand that

The lengths AD and CD are congruent

These parameters and statements above mean that

AD = CD

Substitute the known values in the above equation, so, we have the following representation

4x + 8 = 5x - 1

Collect the like terms

5x - 4x = 1 + 8

Evaluate the like terms

x = 9

Substitute x = 9 in AD= 4x + 8

AD= 4 x 9 + 8

Evaluate

AD= 44

Hence, the length is 44 units

Read more about numerical lengths at

https://brainly.com/question/19131183

#SPJ1

Complete question

Given that lengths AD and CD are congruent.

Find AD

CD = 5x-1 and AD = 4x+8

The summary of the percent of times each and every category appears for the entire sample is called the frequency distribution , the correct option is (d) .

In the question ,

it is asked about what is The summary of the percent of times each and every category appears for the entire sample is called ,

it is called frequency distribution ,

Frequency distribution : it lists all categories of data and number of occurrences for each data category and

it  is also the summary of percent of times each and every category appears for entire sample .

Therefore , the correct option is (d) .

The given question is incomplete , the complete question is

The summary of the percent of times each and every category appears for the entire sample is called the ,

(a) mode

(b) categorical percentage rate

(c) percentage distribution

(d) frequency distribution

Learn more about Frequency Distribution here

https://brainly.com/question/10946549

#SPJ4

Answer:

by dividing by 100

Step-by-step explanation:

630 ÷ 100 = 6.3

The p-value is greater than the significance level, so we do not reject the null hypothesis for the significance level is 0.01 (1%)

What is significance level?

"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.

The p-value for ACT is 0.0286

The significance level is 0.01 (1%)

Hence, the p-value is greater than the significance level, so we do not reject the null hypothesis. We conclude that there is insufficient evidence to conclude that there is any linear relationship at a 1% level of significance between GPA and ACT scores.

Learn more about the significance level, by the following link.

https://brainly.com/question/4599596

#SPJ4

Answer:

Commutative Property of Multiplication

Step-by-step explanation:

Hope it helps!

To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

The equation of the line is written in the slope-intercept form, which is:

y = mx + b, where m represents the slope and b represents the y-intercept.

Finding the distance from the known endpoint to the midpoint and then applying the same transformation to the midpoint is the quickest way to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, so the new x-coordinate is 2-2 = 0.

To know more about slope intercept visit the link:

https://brainly.com/question/24954643?referrer=searchResults

#SPJ4

The expected value of distribution A is 1 and distribution B is 3. The standard deviation for both distributions is the same which is 1.225. In conclusion, distribution B is better than distribution A.

Events with countable or finite outcomes are counted in a discrete probability distribution. This includes the probability values for the discrete random variable. The expected value for this type of distribution is calculated by E(X)=μ=ΣxP(x). And the standard deviation is calculated by σ=√(E(X²)-(E(X))²).

a) Expected value for the distributions A and B is calculated as follows,

The expected value for distribution A,

[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.50)+(1\times0.20)+(2\times0.15)+(3\times0.10)+(4\times0.05)\\&=1\end{aligned}[/tex]

The expected value for distribution B,

[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.05)+(1\times0.10)+(2\times0.15)+(3\times0.20)+(4\times0.50)\\&=3\end{aligned}[/tex]

b) The standard deviation for the distributions A and B is calculated as follows,

First, find E(X²) for distribution A and B to substitute in the standard deviation formula.

The  E(X²) for distribution A is,

[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.50)+(1^2\times0.20)+(2^2\times0.15)+(3^2\times0.10)+(4^2\times0.05)\\&=2.5\end{aligned}[/tex]

The  E(X²) for distribution B is,

[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.05)+(1^2\times0.10)+(2^2\times0.15)+(3^2\times0.20)+(4^2\times0.50)\\&=10.5\end{aligned}[/tex]

Then, the standard deviation for distribution A is,

[tex]\begin{aligned}\sigma_A&=\sqrt{2.5-1^2}\\&=1.225\end{aligned}[/tex]

The standard deviation for distribution B is,

[tex]\begin{aligned}\sigma_B&=\sqrt{10.5-3^2}\\&=1.225\end{aligned}[/tex]

Distribution A and B have the same standard deviation.

c) The standard deviation values are the same for both distributions.  But the expected value of distribution A is lesser than the expected value of distribution B. So distribution B looks better than distribution A.

To know more about discrete probability distribution:

https://brainly.com/question/17145091

#SPJ4

Carrying out the operations on the polynomials shows that

A + B - polynomial

A - B - polynomial

A * B - polynomial

The given polynomials are  

A = 3x²( x − 1 )

B = -3x³ + 4x² − 2x + 1

A + B

= 3x²( x − 1 ) + (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² - 3x³ + 4x² − 2x + 1

= x² − 2x + 1

This is a polynomial

A - B

= 3x²( x − 1 ) - (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² + 3x³ - 4x² + 2x - 1

= 6x³ - 7x² + 2x - 1

This is a polynomial

A * B

= 3x²( x − 1 ) * (-3x³ + 4x² − 2x + 1)

= (3x³ - 3x²) * (-3x³ + 4x² − 2x + 1)

= -9x^6 + 12x^5 - 6x⁴ + 3x³ + 9x^5 - 12x⁴ + 6x³- 3x²

= -9x^6 + 21x^5 - 18x⁴ + 9x³- 3x²

This is a polynomial

Learn more about polynomial at:

https://brainly.com/question/1496352

#SPJ1

The coefficient of determination is 0.588 and the percentage of the total variation is 58.8%.

The coefficient of determination (r^2) refers to a measurement used to explain how much variability of one variable can be caused by its relationship to another related variable. It is the fit of goodness and measures how well a statistical model fits the observed data and is a number between 0 and 1. When the value of linear correlation coefficient r is known, the coefficient of determination can be computed simply by squaring r.

Hence if r = 0.767, then the coefficient of determination = r^2 = 0.588

As percentage of the total variation is same as the coefficient of determination (given in percentage) and is given by the R² value = 58.8%. Hence, about 58.8% of variation is explained by the linear relationship between the two variables.

Note: The question is incomplete. The complete question probably is: Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.767.

Learn more about Coefficient of determination:

https://brainly.com/question/24297732

#SPJ4

Answer:

H

Step-by-step explanation: