The graph shows a scatter plot for a set of data. Scatter plot with x-axis labeled year and y-axis labeled megawatts. The 18 points plotted are 1982 and 76.2, 1983 and 50.6, 1984 and 46.4, 1985 and 35.5, 1986 and 31.1, 1987 and 26.1, 1988 and 21, 1989 and 15.6, 1990 and 14.9, 1991 and 13.8, 1992 and 13, 1993 and 13, 1994 and 10, 1995 and 10, 1996 and 7, 1997 and 6.9, 1998 and 6.6, and 1999 and 6.
What type of correlation exists? Is the model linear or non-linear?
The graph shows a negative correlation, and it is a linear model.
The graph shows a positive correlation, and it is a linear model.
The graph shows a negative correlation, and it is a non-linear model.
The graph shows a positive correlation, and it is a non-linear model.

Emma would need to invest about $320 to increase her value by $480 over the course of 8 years.

We may use the compound interest formula to determine how much Emma would need to invest:

[tex]\mathrm{A = P(1 + r/n)^{(nt)}}[/tex]

Where:

A is equal to the final sum, in this case $480.

P is the principal sum, which represents the initial investment that we're looking for.

r = the yearly interest rate (0.055 in decimal form, or 5.5%)

n = the number of times the interest is compounded annually (in this case, n = 1 because it is compounded annually).

t = the number of years, in this instance 8 years.

Let's substitute the known values into the formula and solve for P:

[tex]\mathrm{480 = P(1 + 0.055/1)^{(1\times8)}}[/tex]

Simplifying:

[tex]480 = \mathrm P(1.055)^8[/tex]

Dividing both sides by (1.055)⁸:

[tex]\mathrm {P = \frac{480 }{ (1.055)^8}}[/tex]

P ≈ $480 / 1.50

P ≈ $320

Hence the amount to be invested is $320.

Learn more about compound interest click;

https://brainly.com/question/14295570

#SPJ12

The probability that Shelia is diagnosed as having gestational diabetes is 0.003.

In the given question,

A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested.

Mean 129 mg/dl and standard deviation 9 mg/dl.

I have to find the probability that Shelia is diagnosed as having gestational diabetes

Z value corresponding to the mean result of 140 mg/dl is

(140-129)/4 = 2.75

Thus, the probability that Shelia is diagnosed as having gestational diabetes = P(Z > 2.75) = 0.003

To learn more about probability link is here

brainly.com/question/29657446

#SPJ4

The right question is:

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean 129 mg/dl and standard deviation 9 mg/dl. Let LL denote a patient's glucose level.

If the mean result from the four tests is compared to the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes?

The equations out of the following that are true would be:

The remaining two I am not certain if they are true or not. The way they were laid out made little to no sense. If you could maybe evaluate further on the other options, perhaps I can double check them for you and see if there are any other remainder options that are true. However, I know for certain that A and B are true.

The value of the side c which is the hypotenuse of the given right angle triangle using Pythagoras theorem is; c = √148

Pythagoras Theorem is simply the way that we can find the missing length of a right angled triangle. The right angle triangle has three sides, namely the hypotenuse (which is the longest side), Opposite (which does not touch the hypotenuse) and then the adjacent side (which is between the opposite side and the hypotenuse).

The formula is literally;

c² = a² + b²

where;

c is hypotenuse and a and b are opposite and adjacent sides. Thus;

c² = 2² + 12²

c² = 4 + 144

c² = 148

c = √148

Read more about Pythagoras Theorem at; https://brainly.com/question/654982

#SPJ1

Police must investigate 50 cars to find the​ car.

What is permutation and combination?

A combination could be a choice of things from a collection that has distinct members, such the order of choice doesn't matter.

Main body:

there are 2 possible position for the first letter.

there is 1 possible position for the second letter.

there are 5 possible position for the first number.

there are 4 possible position for the second number.

there is 3 possible position for the third number.

there are 2 possible position for the second number.

there is 1 possible position for the third number.

the total possibilities are 2 * 1 * 5 * 4* 3 * 2 * 1 = 50

Or we can solve by saying:

There are 2 letters T and V that can be in the first two positions in any order that is 2!, and there are 5 numbers (1,4 , 6 , 0 and 3) that can be in the last 5 positions in any order that is 5!.

Therefore possible arrangement

2! * 5! = 2 * 1 * 5 * 4 * 3 * 2 * 1 = 50

To know more about permutation and combination , visit:

brainly.com/question/28065038

#SPJ4

Each of the three angles of the triangles whose sum of angles is 180 degree measures 75°, 65°, and 40°

An easy geometric instrument like a protractor is used to measure angles. A protractor is employed more frequently than a compass. Angle measurement is important for determining the precise angle. In geometry, there are several sorts of angles that we face in our daily lives, and we may measure angles using these tools.

Basic geometric instruments like a protractor and a compass are used to measure angles. These instruments aid in determining an angle's precise measurement. A protractor aids in producing an accurate angle measurement, while a compass aids in creating the angle. Angles can be measured in three different ways: in degrees, radians, and revolutions.

Here, we have

Let the largest angle be x degrees, the median y, and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

z = 65 - 25 = 40 degrees.

and x = 180 - 65 - 40 = 75 degrees.

To learn more about measurement of angles, visit:

brainly.com/question/28879387

#SPJ4

Given that the pay was $44,000 last year and $53,000 this year, the compensation will have increased by 20.45%.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal parts are considered to make up the whole.

Here,

Salary of staff last year=$44,000

Salary of staff this year=$53,000

The percent increase,

=(53000-44000)/44000*100

=20.45%

The percent increase in the salary will be 20.45% as the salary last year was $44,000 and the salary this year is $53,000.

To know more about percent,

https://brainly.com/question/16797504

#SPJ4

Answer:

The answer is third one, 6 and 7/20.

Step-by-step explanation:

First, rewrite the decimal number as a fraction with 1 as the denominator.

[tex]\frac{6.35}{1}[/tex]

Then, multiply to remove 2 decimal places.

[tex]\frac{6.35}{1} *\frac{100}{100} = \frac{635}{100}[/tex]

Next, find the GCF(Greatest common factor) of 635 and 100, which is 5.

Divide both the numerator (top) and denominator (bottom) by the GCF (5)

Simply the improper fraction.

There you go!

The dimensions of the rectangle that will maximize the area of the window are length, L = 3.41 feet and width, w = 3.41 feet

Given: Perimeter (P) = 19 feet

Perimeter of window = Perimeter of rectangle + Perimeter of semicircle

P = 2(2r + L) + πr

where r = radius of the semicircle and   L = length of the rectangle

width(w) of the rectangle = 2r

Note: the diameter of the semicircle is the width of the rectangle

19 =  2(2r + L) + πr

19 = 4r + 2L + πr

2L = 19-4r-πr

L = 19/2 -2r- πr/2

Find the area (A) of the window:

A = Area of Rectangle + Area of Semicircle

A = 2rL + 1/2πr²

Put L into A = 2rL + 1/2πr²:

A = 2r(19/2 -2r- πr/2) + 1/2πr²

A = 19r - 4r² - πr² + 1/2πr²

A = 19r - 4r² - 1/2πr²

To maximize the area, differentiate both sides and set A' = 0

A = 19r - 4r² - 1/2πr²

A'  = 19 - 8r - πr

0  = 19 - 8r - πr

8r + πr = 19

r(8 + π) = 19

r = 25/(8 + π)

width(w) = 2r

w = 2[19/(8 + π)]

w = 38/(8 + π)

w = 3.41 feet

put r = 19/(8 + π) into L = 25/2 -2r- πr/2:

L = 19/2 -2(19/(8 + π))- π(19/(8 + π))/2

L = 19/2 - 38/(8 + π) - 19π/2(8 + π)

L = [19(8 + π) - 19(2)- 19π] / [2(8 + π)]

L = 38/(8 + π)

L =  3.41 feet

Therefore, the dimensions of the rectangle are length of 3.41 feet and width of 3.41 feet

Learn more about most economical dimensions on:

brainly.com/question/27404871

#SPJ1

The number of files sorted in the first one and a half hours of sorting is 945.

Here, we are given that a group of clerks must sort 1775 files.

Each clerk sorts at a constant rate of 30 files per hour.

Let the number of clerks who start working initially be x.

Thus, they will sort 30x files in the first hour.

After the first hour, let the number of clerks who stop working be a

Thus, the number of files sorted in the second hour will be 30(x - a)

Similarly, the number of files sorted in the third hour will be 30(x - 2a)x

In the last 10 minutes, the number of files sorted will be 5(x - 3a)

Thus, we can form the following equation-

30x + 30(x - a) + 30(x - 2a) + 5(x - 3a) = 1775

30x + 30x - 30a + 30x - 60a + 5x - 15a = 1775

95x - 105a = 1775

19x - 21a = 355

x = (355 + 21a)/ 19

since x and a both have to be integers, (355 + 21a) must be divisible by 19.

This is the case when a = 3

⇒ x = (355 + 21*3)/ 19

x = 418/ 9

x = 22

Now, the number of files sorted in first one and a half hours will be-

30x + 15(x - a)

= 30*22 + 15(22 - 3)

= 660 + 15*19

= 660 + 285

= 945

Thus, the number of files sorted in the first one and a half hours of sorting is 945.

Learn more about remainders here-

https://brainly.com/question/25289437

#SPJ4

Answer: 4 hours

Step-by-step explanation:

322.58 - 200.14 = 122.44

122.44 divided by 30.61 = 4

Assuming the person's weight and magnitude, we can estimate their weight to be 491N.

A mathematical object's magnitude or size defines whether it is greater or smaller than other items of its kind.

In formal terms, an object's size can be thought of as the outward manifestation of an ordering—of the class of objects to which it belongs.

So, the person's weight will be:

The scale calculates the floor's usual upward force on the passenger.

The most force is produced when going up (when starting an upward trip or ending a downward trip).

The normal force is lowest when there is a downward acceleration.

Regarding any such situation

∑F y​ =ma y changes to +391Nmg = ma for halting and +591Nmg=+ma for starting. (Where a represents the size of the acceleration.)

Add these two simultaneous equations to eliminate a and determine mg:

+591N−mg+391N−mg=0

OR

982N–2mg=0

Fg​ = mg = 982N/2​ = 491N

Therefore, assuming the person's weight and magnitude, we can estimate their weight to be 491N.

Know more about magnitude here:

brainly.com/question/24468862

#SPJ4

Complete question:

A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.

The probability that you win the game is 50%.

The game is symmetrical for you and your opponent. Thus, your probability of winning is as good as your opponent's, so, you have a 50% of winning.

Symmetry goes into play in probability theory in this way: if different outcomes are equivalent, they would have the same probability.

A symmetrical distribution happens when the values of variables come at regular frequencies and usually the mean, median, and mode all happen at the same point.

In general, if there are N symmetrical outcomes, the probability of any given one of them happening is taken to be 1/N.

Learn more about probability at: https://brainly.com/question/11234923

#SPJ4

If a certain unit of a commodity is produced with a marginal cost of [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex], the cost of producing the first 126 units is 289.4

How to differentiate a function?

Differentiation is a way of showing rate of change of a function at a given time.

The given function  [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex],

Differentiate with respect to x

[tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]

input the value 100 for the value of x,

This implies that [tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]

[tex]\frac{dc}{da}[/tex]=1800+4+[tex]\frac{15}{4}[/tex] x[tex]\frac{1}{\sqrt[4]{100^{3} } }[/tex]

[tex]\frac{dc}{da}=1800+4+\frac{15}{4}x\frac{1}{3.16}[/tex]

Simplifying further

[tex]\frac{da}{da} =1804+4.75[/tex]

[tex]\frac{dc}{da} =1808.75\\[/tex]

To produce the first 16 units,

[tex]\frac{1808.75}{100} }[/tex] x [tex]\frac{16}{1}[/tex]

The cost of producing the first 16 units is 289.4

Learn more about cost of production on brainly.com/question/16677716

#SPJ1

The given series [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] is convergence and the sum of the series is 33/28.

In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.

The given series is [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex].

Firstly we check the convergence of the given series.

When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.

We can write the series as:

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex]

As |0.3|<1 and |0.2|<1

Then [tex]\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n[/tex] is convergent.

So [tex]\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex] is also convergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right[/tex]

Series [tex]\sum_{n=1}^{\infty}(x)^{n-1}[/tex] converges to 1/x-1 for |x|<1.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 10/7 - 1/4

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 33/28

Hence, the sum of the given series is 33/28.

To learn more about the convergence of series link is here

brainly.com/question/15415793

#SPJ4

The right question is:

Determine whether the series is convergent or divergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex]

If is is convergent, find the sum. (If the quantity diverges, enter diverges.)

The number form that includes only rational numbers are

(-2/3, 0, 0.321, √49, 101/3}

A rational number is one that has the form p/q, where p and q are both integers and q is not zero

Rational function means that the equation will be a fraction

examining the numbers

(-2/3, 0, 0.321, √49, 101/3}

-2/3 is already a fraction

0 = 0/1 hence can be written as a fraction

√49 = 7 = 7/1

101/3 already a fraction

Learn more on  rational function at:

https://brainly.com/question/29183045

#SPJ1

It will take Lian's dog 12.5 weeks to finish the remaining food

Fractions are numbers written as a quotient, in which a numerator is divided by a denominator

Given that:

Lian's dog eats 1/20 of a bag of dog food each week

Lian currently has of a bag 5/8 remaining

Since Lian's dog eats 1/20 in one week and 5/8 is remaining.

In order to find the number of weeks it will take the dog to finish the remaining food. We can say:

Number of weeks = remaining food / food for one week

Number of weeks = (5/8) / (1/20) = 12.5 weeks

Therefore,  it will take Lian's dog 12.5 weeks to finish the remaining food

Learn more about fractions on:

brainly.com/question/29356621

#SPJ1

Complete Question

Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.

How many weeks will it take Lian's dog to finish this remaining food?

Answer: Y = 8

Step-by-step explanation: If x = to 0 then 0+y=8 therefore y=8

Hope this helps

Answer:

y = 8

Step-by-step explanation:

Given information,

→ x + y = 8

→ x = 0

Now the value of y will be,

→ x + y = 8

→ 0 + y = 8

→ y = 8 - 0

→ [ y = 8 ]

Hence, the value of y is 8.

The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

Traditional IT and project finance methods offer a key business risk and, if not modified, jeopardize the future of technology-based enterprises.

This excerpt from the whitepaper Changing the Finance Method by Keanen Wold, Levi Geinert, Shaun Norris, Charles Betz, Beth Dumke, Sam Guckenheimer, and Troy Magennis discusses that contradiction over how traditional financing methods handle ethical concerns and also what Agile and DevOps teams require to execute successfully.

Balancing the high-risk investment in innovation (research and development department) with regular business-as-usual responsibilities has always been difficult for organizations. Too much risk might, in the case of an unexpected failure, result in a business's dissolution; too little innovation could ultimately cause the company to be overtaken and lose market share to rivals and new upstarts.

To learn more about IT model funding, visit:

brainly.com/question/14797433

#SPJ4

Answer:i am pretty sure it is c

Step-by-step explanation:

this is because it says Which graph best shows how many days each project has lasted? and c is the only one that is talking about days

Answer:

The answer is A) [tex]y=4x[/tex]

Step-by-step explanation:

This is because y directly corresponds to x, if x is 1, then y = 4, if x is 2, then y = 8 and so on.

Answer:

200

Step-by-step explanation:

To find that out, you divide 1,000 by 5.

1,000 ÷ 5 = 200

Could you please mark me as Brainliest? Thank you!

Answer: 200

Step-by-step explanation: 1000 divided by 5 = 200

The students weren't assigned the treatments (new menu item) at random.

In an experiment, randomization refers to assigning volunteers randomly to the treatment. For example, we may define randomization as setting people to therapy at random.  

The results are fair because randomization eliminates bias. To make the results of the experiment precise, it ensures that the groups created for experimenting are as similar to one another as possible.

In the given example, the menu items are not randomly assigned. Because the students were given a choice to choose a menu item instead of selecting the new menu item randomly.  If randomly assigned all the new menu items will have an equal probability of being chosen.

Therefore, option b is the correct option.

The complete question is -

Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment?

a) There was no replication because students did not eat both menu items.

b) The treatments (new menu item) were not randomly assigned to the students.

c) An item that is currently on the menu should have been used as a control.

d) Students should not have been randomly selected.

e) There were no problems, and the study was a well-designed experiment.

To know more about random sampling:

https://brainly.com/question/26377187

#SPJ4

Answer:

144 if u multiply u will get ur answer because it is asking for the least number if 144 is to high that its got to be 1 which it can't that's if u divide it answer - 144

Answer:

45, odd

Step-by-step explanation:

54-9=45

Answer:

32−4x=12,

25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and

x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)

Step-by-step explanation:

hope this help

The result of hypothesis test on the given data null hypothesis is accepted and alternate hypothesis is rejected.

Hypothesis testing is a type of measurable deduction that utilizes information from an example to make determinations about a populace boundary or a populace probability distribution. Initial, a conditional supposition that is made about the boundary or dispersion. This supposition that is known as the invalid speculation and is meant by H0.

We have,

mean(X) = 162, n = 20 , standard deviation(σ) = 45,

Let us consider Null hypothesis H₀: μ=145

And alternate hypothesis Hₐ : μ[tex]\neq[/tex] 145

So, Z = X -  μ/σ/√n

Z = 162 - 145/45/√20 = 1.68

Now Level of significance(α)= 0.05

From the Z table,

Z = 1.96

So,  1.68 < 1.96

Thus, Null hypothesis is accepted and alternate hypothesis is rejected.

To know more about hypothesis test visit:

brainly.com/question/17099835

#SPJ4

a. The transformed equation is given as follows: h(x) = |x - 2| - 3.

b. The graph of the two functions is shown by the image presented at the end of the answer.

The translations are movements to the triangle in each of these directions:

The parent function in this problem is given as follows:

f(x) = |x|.

The first translation was a vertical translation three units down, hence we have that:

g(x) = f(x) - 3 = |x| - 3.

The second translation was a horizontal translation two units right, hence the have that the definition of the transformed equation h(x) is given as follows:

h(x) = g(x - 2) = |x - 2| - 3.

The graph of the functions is given by the image shown at the end of the answer, and the translations are verified on every point of the function, but especially the vertices.

More can be learned about translations at https://brainly.com/question/29211183

#SPJ1

Answer:

28

Step-by-step explanation:

substitute the given values into the expression

x(2 - 4y² )

= - 2(2 - 4(- 2)² )

= - 2(2 - 4(4))

= - 2(2 - 16)

= - 2(- 14)

= 28