4. Find the positive square root, then the negative square root of each of the following numbers:
16
0.36
25
0.64
1.21
0.25
1.44
2 500.​

(1, 0) is the solution of the line y = 3x - 3

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

The given line is

y = 3x - 3

To test whether (1, 0) is a solution of the line y = 3x - 3

Putting x = 1

y = 3[tex]\times[/tex] 1 - 3 =

y = 3 - 3

y = 0

(1, 0) is the solution of the line y = 3x - 3

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An identification and interpretation of the slope in this scenario is: The slope is −0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c          .......equation 1.

Where:

From the information provided, we have the following equation:

y = 3.9 - 0.1x

Rewriting the equation in slope-intercept form, we have:

y = -0.1x + 3.9         .......equation 2.

Comparing equation 1 and equation 2, we have:

Slope, m = -0.1

y-intercept, c = 3.9, which also represents the initial value.

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[tex](\frac{4}{5}, \frac{44}{5})[/tex] is the maximum value of extreme values for the given polynomial.

What is extreme value?

According to the Extreme Value Theorem, if a function is continuous on the interval [a, b], it must have a maximum and a minimum on that range.

Consider, the given function

f(x) = 5x^2 - 8x + 12         ..(1)

Since, if y = f(x) is a function, then the value of x where f'(x) is zero is called extreme value.

Differentiate equation (1) with respect to x.

10x - 8 = 0

10x = 8

x = 8/10

x = 4/5

Plug x = 4/5 in equation (1),

[tex]f(\frac{4}{5}) = 5(\frac{4}{5})^2 -8(\frac{4}{5})+12\\ = \frac{16}{5} -\frac{32}{5} + 12\\ = \frac{44}{5}[/tex]

Therefore, [tex](\frac{4}{5}, \frac{44}{5})[/tex] is the maximum value of extreme values for the given polynomial.

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Answer:

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is the maximum value of extreme values for the given polynomial.

What is extreme value?

According to the Extreme Value Theorem, if a function is continuous on the interval [a, b], it must have a maximum and a minimum on that range.

Consider, the given function

f(x) = 5x^2 - 8x + 12         ..(1)

Since, if y = f(x) is a function, then the value of x where f'(x) is zero is called extreme value.

Differentiate equation (1) with respect to x.

10x - 8 = 0

10x = 8

x = 8/10

x = 4/5

Plug x = 4/5 in equation (1),

Therefore,  is the maximum value of extreme values for the given polynomial.

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Be wise think wise. YES PLEASE BRAINILESTor sum

Step-by-step explanation:

To hypothesize that autism is a quantitative trait normally distributed in the population.

Hypothesis that autism is a quantitative trait normally distributed in the population is actually showing the assumption that we can calculate the level of autism in the population in numbers as well as it is present in everyone at some level just like weight.

There are two types of data:

• Quantitative: Any information that can be counted is referred to as quantitative data and is given a numerical value. You can find out “how many,” “how much,” or “how often” using quantitative variables.

• Qualitative: Qualitative information is descriptive in character and communicated verbally as opposed to numerically.

Hence, here they are assuming that we can measure the level of autism in the population.

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Seventy percent of the time, the length of time to find a parking space takes more than 4 minutes.

For a normally distributed set of data, given the mean and standard deviation, the probability of having the data less than a value can be determined by solving the z-score and using the z-table.

If the probability is 70%, then, using the z-table, the z-score would be -0.52485.

at p = 1 - 0.70 = 0.30   z = -0.52485

Using the formula for finding the z-score, solve for the data value, x.

z-score = (x – μ) / σ

where x = individual data value

μ = mean = 5

σ = standard deviation = 2

z-score = (x – μ) / σ

-0.52485 = (x - 5) / 2

x - 5 = -1.0497

x = 3.9503

Round off to the nearest whole number.

x = 4

Hence, 70% of the time, it takes more than 4 minutes to find a parking space.

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The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.

What is distribution?

Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.

Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.

Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.

So we need to use the mean of non-normal distribution.

Hence the answer will be the mean of the original non-normal distribution.

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Answer:

14, or f(-3)= 14

Step-by-step explanation:

Input the -3, so you will get f(-3)= -1/3(-3) + 13.
Do -1/3 x -3, which will get you 1.
Do 1 + 13, which will get you 14.
So, the answer will be 14, or f(-3)= 14.

Answer:3 and multiplication

Step-by-step explanation: 3 times 9 equals 27.

The value of x in the algebraic expression is option A  96.

Given,

The algebraic expression; 15 = x/6 - 1

We have to solve the expression and find the value of x.

Here,

15 = x/6 - 1

First solve the right hand side

x/6 - 1 = (x - 6) / 6

Now,

15 =  (x - 6) / 6

Multiply both sides with 6.

15 × 6 = (x - 6) × 6 / 6

90 = x - 6

Now add 6 to both sides

90 + 6 = x - 6 + 6

x = 96

That is,

The value of x in the algebraic expression is option A  96.

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Answer:

The domain is the time, in minutes from 0 to however long it takes to drain the cooler.

The range is from 12 quarts water to empty.

Step-by-step explanation:

I don't see a graph, but will use the given information to identify a domain and range for the information provided.

The domain is the range of values that are possible for the x axis.  In this case, the x axis it time, in minutes.  If we set x as the time, in minutes, that the water has been draining, time = 0, is the start of the process.  

The y axis, the range, starts at 12 quarts at time = 0.  It then decreases with time until the cooler is empty.  The range of the function is thus 12 quarts to 0 quarts:  Full to empty.

If we knew the actual rate that the cooler drains (e.g., quarts/minute), we could estabish an upper limit to the domain.  If a graph were shown of the data, this rate could be calculated and an upper end to the domain could be set.  If the rate were 2 quarts/minute, the upper end of the domain would be (12 quarts/2 quarts/minute) = 6 minutes.  The domain would be 0 - 6 minutes.

The final thickness of the sheet is  = 0.0669 cm

brasses are copper zinc alloys. In general, they have good strength and corrosion resistance, although their structure and properties are a function of zinc content , Alloys containing up to approximately 35% zinc are single phase alloys, consisting of a solid solution of zinc and alpha copper

% cold reduction = (initial thickness - final thickness )  × 100

                                                  initial thickness

        0.30%       =            (0.0955cm - final thickness ) ×  100            

                                                     0.0955cm

             final thickness    =     0.0669cm

Brass in an alloy of copper and zinc, bonze is an alloy containing 80% of cropper. A fuses mass of brass and bronze is found to contain 74% . Brass, alloy of copper and zinc, of historical and enduring importance because of its hardness and workability

Hence the final thickness of sheet is 0.0669 cm

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The account balance after 18 years is $8951.6.

Given the principle is (P) = $4000

The rate of interest (r) = 4.5%

Time (t) = 18 years

It is given that, the compound interest compounded quarterly.

So the amount after 18 years is given by,

[tex]A=P\left(1+\frac{r}{400}\right)^{4t}=4000\left(1+\frac{4.5}{400}\right)^{4\times18}\approx8951.6[/tex]

So the amount after 18 years is $8951.6 approximately.

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Amar owes $2,000 on his credit card with a minimum percentage of 4% or $60, whichever is higher.

The Minimum Payment due is $ 80 as it is higher from the minimum payment of $60.

Given :

Credit Card amount = $2000

Minimum Percentage = 4%

By using the below formula we can find the minimum balance

Minimum Balance = Credit Card Amount * Minimum Percentage

Minimum Balance = $2000 * 4%

            = $80

So According to the question Amar owes $2000 on his credit card with a minimum percentage of 4% or a minimum payment of $60, whichever is higher.

So the minimum percentage of 4% or minimum balance is higher than $60.

So that’s why the minimum payment due is $80.

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Answer:  for the first question it is 4

Step-by-step explanation:

5x -3x= 15-7

2x=8

2x/2x      8/2

x=4

Answer:

[tex]10x + 17 - 5x = 27 \\ 10x - 5x = 27 - 17 \\ 5x = 10 \\ x = \frac{10}{5} \\ x = 2 [/tex]

The exponential growth from the exponential function shows it will take approximately 15.09 years for his salary to reach $45000

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. This could also be an exponential growth or exponential decay which depends on the situation.

The exponential function is an important mathematical function which is of the form f(x) = ax

Data;

The exponential function to represent this will be

45000 = 31000(1 + 0.025)ˣ

x = 15.09 years

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Determine the probability that actual weight is within 0.45 g of the prescribed weight we need to integrate with 2.55 to 3.45

we have to integrate  with : 2.55 to 3.45

p(3-0.45<X<3+0.45)

P( 2.55<X<3.45)

= [2.7-24.47-24.3+48.609/3]

=0.6325

What is probability:

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

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The question was incomplete. Check below the complete question.

The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf. f(x) = k 1 ? (x ? 3)2 2 ? x ? 4 0 otherwise.

We conclude that the mean commute time in the U.S. is less than half an hour.

We are given that a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time.

In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.

Let  = mean commute time in the U.S..

So, Null Hypothesis, :  [tex]H_0:[/tex] μ ≥  30 minutes    {means that the mean commute time in the U.S. is more than or equal to half an hour}

Alternate Hypothesis,  :   [tex]H_A[/tex]: μ  < 30 minutes     {means that the mean commute time in the U.S. is less than half an hour}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

                          T.S. =  (X -μ)/[tex]{\frac{s}{\sqrt{n} } }[/tex]   ~ [tex]t_n_-_1[/tex]

where,  X = sample mean commute time = 27.6 minutes

           s = sample standard deviation = 19.6 minutes

           n = sample of people from the 2000 U.S. Census = 500

So, the test statistics  =   (27.6 - 30)/[tex]\frac{19.6}{\sqrt{500} }[/tex] ~ [tex]t_4_9_9[/tex]

                                      =  -2.738

The value of t test statistic is -2.738.

Also, P-value of test statistics is given by the following formula;

          P-value = P( [tex]t_4_9_9[/tex]   < -1.645)

Since, we know that at large sample size, the t distribution follows like normal distribution, that means;

             P( [tex]t_4_9_9[/tex]  < -1.645)  =  P(Z < -1.645) = 1 - P(Z ≤ 1.645)

                                        =  1 - 0.95002 = 0.04998

Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.

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Triangles with the provided side lengths of 3.5, 3.5, and 9 cannot be formed.

According to the Properties of triangle, the length of the third side of a triangle must be greater than the sum of any two of a triangle's sides.

Given the side lengths are 3.5, 3.5 and 9;

Sum of two sides = 3.5 + 3.5 = 7 cannot exceed 9

Thus, it is clear that a triangle cannot be formed using the specified side lengths of 3.5, 3.5, and 9.

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Answer:

y = 2x - 12

Step-by-step explanation:

(y-4)/(-4-4) = (x-8)/(4-8)

(y-4)/-8 = (x-8)/-4

y-4 = 2x - 16

y = 2x - 16 + 4

y = 2x - 12

We are evaluating a project that costs $786,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 65,000 units per year. Price per unit is $48, variable cost per unit is $25, and fixed costs are $725,000 per year. The tax rate is 22 percent, and we require a return of 10 percent on this project

The tax rate for 10% is IRR = 78%.

The Initial evaluating cost is $786000 and the

Depreciation expense per year will be  = $786,000 / 8 = $98,250.

and the contribution margin per unit = $48 - $25 = $23

total units sold  Projected per year = 65,000

fixed costs  will be per year = $725,000

At Present the tax rate = 22%

Net cost fixed per year  = -$786,000

Net Cost Fixed year 1-8 = {[($23 x 65,000) - $98,250 - $725,000] x 0.78} + $98,250 = $622,215

Net Per Variable  = $2,533,471.10

Hence the answer is, The tax rate for 10% is IRR = 78%.

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Answer:

0.0401907 = 0.040 (to 3dp)

Answer 13:1 The ratio stays the same in this problem is says so it will always be that. 169/13=13 13/13=1 That means there's 13 wins for every 1 loss.

Step-by-step explanation:

The age of Flo based on the ratio is 21 years.

From the information illustrated, the ages of Michael, Flo, Ella and Arlo add up to 60 years and the ratio of Michael's age to Flo's age to 3:7:6:4.

In this case, Flo is represented as 7 and the total ratio is (3+7+6+4) = 20

Therefore the age will be:

= 7/20 × Total age

= 7/20 × 60.

= 21

Flo is 21 years

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Answer:

Step-by-step explanation:

Ok:

1. The first one seems to be a quarter which is 25 cents

2. The next two are dimes which are 10 cents each

3. Caculate

25+10+10= 45 cents in total!

4. Answer: 45 cents

Answer:

0.60 gal to 0.12 gal can be rewritten as:

[tex]\frac{0.60}{0.12} =\frac{0.6}{0.6(0.2)} =\frac{1}{0.2}[/tex]

[tex]\frac{1}{0.2}*1=\frac{1}{0.2}*\frac{10}{10} =\frac{10}{2} =5[/tex]

The probability that exactly 2 people are left handed if 11% people are left handed and 5 are selected at random is 100.

Probability is a method with the help of which we chose a particular object on random from many given objects.

P(E) = no of favorable outcomes/total number of outcomes

Let there are 100 people

11% are left handed = 11% of 100 = 11

5 are selected randomly.

No of favorable outcomes = 5

Total no of outcomes = 11

Hence, the probability that people selected are left handed is 5/11

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From the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.

As given in the question,

Number of people selected at random 'n' = 5

Percent of people are left handed = 11%

Probability of success 'p' = 0.11

Probability of failure 'q' = 1- p

                                       = 1-0.11

                                       = 0.89

Exact number of left handed people 'x' = 2

Probability of people that are exactly left handed

= ⁿCₓ (p)ˣ(q)ⁿ⁻ˣ

=⁵C₂(0.11)²(0.89)⁵⁻²

= (5!/ (5-2)!2!) × (0.0121) × (0.704969)

= 10 × (0.0121) × (0.704969)

= 0.0853

Therefore, from the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.

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Answer:

3

Step-by-step explanation:

The interest that the savings earned in a year in terms of hours of work is B. 20 hours.

Interest is the additional earning obtained from an investment.

It is computed as the principal multiplied by the annual percentage rate (APR) and the period.

Earnings per hour = $10

Investment = $4,000

APR = 5%

Period of investment = 1 year

Interest earned = $200 ($4,000 x 5% x 1)

Interest earned expressed as hours = 20 hours ($200/$10)

Thus, the investor, who earns $10 per hour, earns 20 hours in interest by investing $4,000 at 5% in a year.

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