(a) It takes the Earth 365 days to complete a full orbit around the sun. It takes Jupiter approximately 4,332 days, 14 h, and 9 min to complete a full orbit around the sun. How many years does it take Jupiter to complete a full orbit around the sun?

Answer:

a testable proposition that explains an observed phenomenon or answers a question

Step-by-step explanation:

Basically an hypothesis is a theory given as a solution to a question proposed by a problem in from of you, but that it needs testing before it can be taken as truth or not

A hypothesis is an educated guess or a testable prediction drawn from observations. It is a tentative statement about reality that can be verified through experiments. If a hypothesis explains a large body of experimental data, it may evolve into a theory.

A hypothesis is a testable prediction about how the world will behave if our idea is correct. Observations and questioning may lead a scientist to form a hypothesis. In essence, a hypothesis is an educated guess or a tentative statement about reality that can be tested to determine its validity.

An example of a hypothesis is 'if I study all night, I will get a passing grade on the test'. The hypothesis, the educated guess in this scenario, then undergoes a process of testing through experimentation, calculation, and comparison with the experiments of others.

If a hypothesis is capable of explaining a large body of experimental data, it can reach the status of a theory. A theory in scientific terms is a well-substantiated, comprehensive, testable explanation of particular aspects of nature. However, theories can be modified if new data becomes available. This process of questioning, observing, hypothesizing, testing, and eventually forming a theory is known as the scientific method.

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Firstly we calculate the height(h)...,

by using trigonometry ratios

;tan 45° = h/5

;where.. h = 5 tan 45°

;h = 5

Then we calculate the side x...using the height h and the angle of 30°

by also using trigonometry ratios

; sin 30° = 5/x

;where.. x = 5/(sin 30°)

Hence...., x = 10

Answer: x = 10

Your first two tests add up to:

85 + 89 = 174

To average 87 for 3 tests, the tests need to add up to : 87 x 3 = 261

To average 91, the 3 tests need to equal: 91 x 3 = 273

So to average 87, the third test needs to be: 261 - 174 = 87

To average 91, the third test needs to be: 273 - 174 = 99

Your score needs to be between 87 and 99

If the [tex]f(x)[/tex] and [tex]t(x)[/tex] are even function then [tex]fo\ t\ (x)[/tex] is an even function, if [tex]f(x)[/tex] and [tex]t(x)[/tex] are odd function then the function [tex]fo\ t\ (x)[/tex] is an odd function and if [tex]f(x)[/tex] is even and [tex]t(x)[/tex] is odd then the function [tex]fo\ t\ (x)[/tex] is an even function.

Further explanation:

An even functrion satisfies the property as shown below:

[tex]\boxed{f(-x)=f(x)}[/tex]

An odd functrion satisfies the property as shown below:

[tex]\boxed{f(-x)=-f(x)}[/tex]

Consider the given composite function as follows:

[tex]\boxed{fo\ t\ (x)=f\left(t(x))\right}[/tex]

If both the function [tex]f(x)[/tex] and [tex]t(x)[/tex] are even function.

[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(t(x))\right\\&=fo\ t\ (x)\end{aligned}[/tex]

From the above calculation it is concluded that,

[tex]\boxed{fo\ t\ (-x)=fo\ t\ (x)}[/tex]

This implies that the composite function [tex]fo\ t\ (x)[/tex] is an even function.

If both the function [tex]f(x)[/tex] and [tex]t(x)[/tex] are odd function.

[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(-t(x))\right\\&=-fo\ t\ (x)\end{aligned}[/tex]

From the above calculation it is concluded that,

[tex]\boxed{fo\ t\ (-x)=-fo\ t\ (x)}[/tex]

This implies that the composite function [tex]fo\ t\ (x)[/tex] is an odd function.

If the function [tex]f(x)[/tex] is even and [tex]t(x)[/tex] is odd.

[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(-t(x))\right\\&=fo\ t\ (x)\end{aligned}[/tex]

From the above calculation it is concluded that,

[tex]\boxed{fo\ t\ (-x)=fo\ t\ (x)}[/tex]

This implies that the composite function [tex]fo\ t\ (x)[/tex] is an even function.

Answer:

A triangle with three sides that are each equal in length to those of another triangle, for example, are congruent. This statement can be abbreviated as SSS. Two triangles that feature two equal sides and one equal angle between them, SAS, are also congruent.

Step-by-step explanation:

Answer:

The mammoth died 17.190 years ago.

Step-by-step explanation:

Given information:

For every 5700 years, the elephant's bones losses a half-life of C-14. And supposing that the living mammoth bones had the same percentage of C-14.

If the mammoth when living has 40%, then:

Answer:

[tex]\large \boxed{\text{17 190 yr ago}}[/tex]

Step-by-step explanation

The amount of C-14 has declined from 40 % to 5 % of the original, that is, to ⅛ of the original amount.

The half-life of C-14 (5730 yr) is the time it takes for half of the isotope to decay.

We can make a table of the amount remaining after each successive half-life.

[tex]\begin{array}{ccc}\textbf{Number of} && \textbf{Fraction} \\\textbf{half-lives} & \textbf{Years} & \textbf{remaining} \\0 &0 & 1 \\1 &5730 &\frac{1}{2 } \\\\2 &11460 &\frac{1}{4 } \\\\3 &17190 &\frac{1}{8} \\\\4 & 22920& \frac{1}{16} \\\end{array}\\\text{We see that the fraction of C-14 is reduced to $\frac{1}{8}$ after three half-lives.}\\\text{The mammoth died $\large \boxed{\textbf{17 190 yr ago}}$}[/tex]

Answer:

  8x + 3(20 - x) = 5(20)

Step-by-step explanation:

If x represents the number of pounds of $8 chocolates, then (20-x) is the number of pounds of $3 chocolates. The cost of the mix attributable to the $8 chocolates will be 8x, and the cost associated with the $3 chocolates will be 3(20-x). The sum of these costs is the cost of the 20 pounds of mix: $5×20.

In equation form, this is ...

  8x + 3(20-x) = 5(20)

_____

The solution is x=8, so 8 lb of $8 chocolates should be mixed with 12 lb of $3 chocolates to make a mix worth $5 per pound.

Final answer:

The correct equation to determine the pounds of each type of chocolate for the mixture is 8x + 3(20 - x) = 5(20), where x represents the pounds of the $8 chocolate.

Explanation:

To solve for how many pounds of each type of chocolate should be used in the mixture, let's designate x as the number of pounds of the $8 chocolate and 20-x as the number of pounds of the $3 chocolate. The total cost of the $8 chocolate will be 8x dollars, and the total cost of the $3 chocolate will be 3(20-x) dollars. The total sales price for the 20-pound mixture must be $5 per pound, which equals $100 (since 20 pounds × $5 per pound = $100). Therefore, the correct equation that represents the situation is 8x + 3(20 - x) = 5(20).

Let's break down this equation:

The $8 chocolate: 8x dollars

The $3 chocolate: 3(20 - x) dollars

Total cost: 8x + 3(20 - x)

The mixture sells for: $5 × 20

The equation balances the cost of both chocolates with the selling price of the mixture.

let's firstly convert both fractions with the same denominator, by simply multiplying one by the denominator of the other, let's proceed,

[tex]\bf \cfrac{1}{5}\cdot \cfrac{3}{3}\implies \cfrac{3}{15}~\hspace{7em}\cfrac{1}{3}\cdot \cfrac{5}{5}\implies \cfrac{5}{15} \\\\[-0.35em] ~\dotfill\\\\ \boxed{\cfrac{3}{15}}\rule[0.35em]{10em}{0.25pt}~~\cfrac{4}{15}~~\rule[0.35em]{10em}{0.25pt}\boxed{\cfrac{5}{15}}[/tex]

well, low and behold, 4/15 doesn't simplify further and is right between those two, and its denominator is not 4.

Answer:

B. 63.8 mph

Step-by-step explanation:

IN order to solve this problem we just have to keep in mind that the miles per hour is calulcated by the number of revolutions that the tire is doing multiplied by the circumference of the tire, so the circumference of the tire is given by the first set of number in the tire the first one would be:

[tex]first:\frac{215}{60} \\Second: \frac{235}{70}[/tex]

So we just have to multiply it by the first one and then divide it by the second:

[tex]\frac{215}{60}*60=215\\215*\frac{235}{70}=63.8[/tex]

SO when the speedometer is on 60 mph, he will actually be going at 63.8 mph.

Answer:

C

Step-by-step explanation:

First, when fractions get raised to an exponent, both the numerator and the denominator get raised to the power.

When exponents get raised to a power, the powers multiply.

E.g. [tex](x^2)^3=(x^2)(x^2)(x^2)=(x*x)(x*x)(x*x)=x^6[/tex]

In this case,

[tex](\frac{4^3}{5^-^2})^5=\frac{4^(^3^*^5^)}{5^(^-^2^*^5^)}=\frac{4^1^5}{5^-^1^0}\\[/tex]

Note that [tex]x^-^n=\frac{1}{x^n}[/tex]

So, 1/5^(-10) = 5^10

So, our answer is C

Answer:

Answered below

Step-by-step explanation:

Sheet 1: Question 3

Vertically opposite angles are equal so you will equate the angles given,

∠LPN = ∠OPM

7 + 13x = -20 + 16x

27 = 3x

x = 9

Sheet 1: Question 4

Vertically opposite angles are equal so you will equate the angles given,

∠ABD = ∠EBC

2x + 20 = 3x + 15

-x = -5

x = 5

Sheet 1: Question 5

Step 1: Find the value of x

Vertically opposite angles are equal so you will equate the angles given,

∠SOP = ∠ROQ

5x = 4x + 10

x = 10

Step 2: Find angles

Angle SOP = 5x = 5(10) = 50°

Angle ROQ = 50° (because it is vertically opposite to angle SOP)

Angle SOR = 180 - 50 (because all angles on a straight line are equal to 180°)

Angle SOR = 130°

Angle POQ = 130° (because it is vertically opposite to angle SOR)

Sheet 1: Question 6

Angle 1 = 72° (because vertically opposite angles)

∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)

∠4 + 72 + 41 = 180

∠4 = 67°

∠3 = 41° (because vertically opposite angles)

∠2 = 67° (because vertically opposite angles)

Sheet 2: Question 3

Step 1: Find the value of x

Sum of complementary angles is equal to 90°

Angle A + Angle B = 90°

7x + 4 + 4x + 9 = 90°

11x = 90 - 13

11x = 77

x = 7

Step 2: Find angle A and angle B using x

Angle A: 7x + 4

7(7) + 4

Angle A = 53°

Angle B: 4x + 9

4(7) + 9

Angle B = 37°

Sheet 3: Question 3

Step 1: Find the value of x

Sum of supplementary angles is equal to 180°.

Angle A + Angle B = 180°

3x - 7 + 2x + 2 = 180°

5x = 185

x = 37

Step 2: Find angle A and angle B using x

Angle A: 3x - 7

3(37)-7

Angle A = 104°

Angle B: 2x + 2

2(37) + 2

Angle B = 76°

Sheet 3: Question 4

Sum of supplementary angles is equal to 180°.

Step 1: Find x

1/4(36x-8) + 1/2(6x-20) = 180°

Take LCM

[36x - 8 + 2(6x - 20)]/4 = 180°

36x - 8 +12x - 40 = 180 x 4

48x - 48 = 720

48x = 768

x = 16

Step 2: Find both angles with the help of x

Angle 1: 1/4(36x-8)

1/4[36(16)-8] = 568/4

Angle 1 = 142°

Angle 2: 1/2(6x-20)

1/2[6(16)-20] = 76/2

Angle 2 = 38°

Sheet 4: Question 1

All angles on a straight line are equal to 180°

Angle z + 138° = 180°

Angle z = 180 - 138

Angle z = 42°

Sheet 4: Question 2

Linear pair 1: 5 and 7 (because both angles are on a straight line and are equal to 180°)

Linear pair 2: 6 and 8 (because both angles are on a straight line and are equal to 180°)

Sheet 4: Question 3

Step 1: Find the value of x

All angles on a straight line are equal to 180° or linear pairs are equal to 180°

Angle LMO + Angle OMN = 180°

7x + 20 + 10 + 5x = 180°

12x = 180 - 30

x = 150/12

x = 12.5

Step 2: Find angles using the value of x

Angle LMO: 7x + 20

7(12.5) + 20

Angle LMO = 107.5°

Angle OMN: 10 + 5x

10 + 5(12.5)

Angle OMN = 72.5°

Sheet 4: Question 4

Linear pairs are equal to 180°.

Angle 1 + Angle 2 = 180°

1/3(27x-6) + 1/2(6x-20) = 180°

Take LCM = 6

[2(27x-6) + 3(6x-20)]/6 = 180

54x - 12 + 18x - 60 = 1080

72x - 72 = 1080

72x = 1152

x = 16

!!

Answer:

Step-by-step explanation:

Easy. its [tex]x^{2} \int\limits^a_b {x} \, dx \\ \\ \left \{ {{y=2} \atop {x=2}} \right. \\ \neq \frac{x}{y} \beta \al\left \{ {{y=2} \atop {x=2}} \right. pha \neq \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \geq \\ \left \{ {{y=2} \atop {x=2}} \right. \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]

The inequality that represents the graph is:

                        [tex]y\geq x+3[/tex]

By looking at the graph we observe that the graph is a solid line which passes through the point (-1,0) and (1,2).This means that the inequality is a inequality with a equality sign(i.e. not strict)

This means that the equation of line is:

[tex]y-2=\dfrac{2-0}{1-(-1)}\times (x-(-1))\\\\y-2=\dfrac{2}{2}\times (x+1)\\\\y-2=x+1\\\\y=x+1+2\\\\y=x+3[/tex]

The shaded region is away from the origin.

This means that the inequality does not pass the zero test.

Hence, the inequality is:

               [tex]y\geq x+3[/tex]

Answer:

C

Step-by-step explanation:

Credit Score is a numerical expression which analyzes a person's credit level by looking at this financial conditions. Will he/she be worthy of loan or not.

payment history comprises 35% of a person's credit score. This is a huge factor. If you consistently make your payments on time, your credit score increases.

length of credit history tells how secure you will be to lenders. Usually 7 years+ is a great length of credit history. This pretty much affects credit score.

marital status doesn't affect credit score. Lenders assess a person based on their financial condition and past activity, NOT whether or not he/she is married or not. That's personal agenda.

debt ratio is the ratio of total debt to total assets. If this is high, it means a person owes money to banks/individuals and is more likely to be not given credit. It affects credit score highly.

THus, the correct answer is C

Answer:

C

Step-by-step explanation:

Explanation:

5(y+3)-11=-y-6 Given

5(y+3)=-y+5 . . . . addition property of equality (11 is added)

5y+15=y+5 . . . . . distributive property (5 is distributed)

5y=-y-10 . . . . . . . addition property of equality (-15 is added)

6y=-10 . . . . . . . . . addition property of equality (y is added)

y=-5/3 Division Property of Equality/Reduce

Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials. More about this later.

If you are given, say, the polynomial equation y = x2 + 5x + 6, you can factor the polynomial as y = (x + 3)(x + 2). Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that x = –2 and x = –3 are the two zeroes of y.

You can, however, also work backwards from the zeroes to find the originating polynomial. For instance, if you are given that x = –2 and x = –3 are the zeroes of a quadratic, then you know that x + 2 = 0, so x + 2 is a factor, and x + 3 = 0, so x + 3 is a factor. Therefore, you know that the quadratic must be of the form y = a(x + 3)(x + 2).

(The extra number "a" in that last sentence is in there because, when you are working backwards from the zeroes, you don't know toward which quadratic you're working. For any non-zero value of "a", your quadratic will still have the same zeroes. But the issue of the value of "a" is just a technical consideration; as long as you see the relationship between the zeroes and the factors, that's all you really need to know for this lesson.)

Anyway, the above is a long-winded way of saying that, if x – n is a factor, then x = n is a zero, and if x = n is a zero, then x – n is a factor. And this is the fact you use when you do synthetic division.

Let's look again at the quadratic from above: y = x2 + 5x + 6. From the Rational Roots Test, you know that ± 1, 2, 3, and 6 are possible zeroes of the quadratic. (And, from the factoring above, you know that the zeroes are, in fact, –3 and –2.) How would you use synthetic division to check the potential zeroes? Well, think about how long polynomial divison works. If we guess that x = 1 is a zero, then this means that x – 1 is a factor of the quadratic. And if it's a factor, then it will divide out evenly; that is, if we divide x2 + 5x + 6 by x – 1, we would get a zero remainder. Let's check:

As expected (since we know that x – 1 is not a factor), we got a non-zero remainder. What does this look like in synthetic division? Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

First, write the coefficients ONLY inside an upside-down division symbol:

Answer:

  3

Step-by-step explanation:

A 6-inch piece of string can be cut into 12 pieces that are 1/2 inch each. If Lee needs 15 pieces, she needs 3 more.

___

Each inch is divided into 2 pieces. That's what 1/2 inch means. 6×2 = 12.

Answer:

  Domain of set B: {2, 4, -4, 0}

Step-by-step explanation:

The domain of the function whose ordered pairs are listed in set B is the set of first numbers of those pairs: {2, 4, -4, 0}.

_____

Comment on the question

A "set" does not have a domain. A "function" has a domain. To make any sense of this question, we have to interpret the question to mean the function described by the ordered pairs in the set.

Answer:

The answer is 54.5

Step-by-step explanation:

The median of a set of observations is the value in the middle in case there is an uneven number of observations or the average between the two values in the middle.

First we arrange the times from less time to longer times.

50 - 52 - 57 - 230 .

The values in the middle are  52 - 57

And the average between this two values is 54.5. Thus that is the median legth of time.

Answer:

The median length of time required to review an application is 54.5 minutes.

Step-by-step explanation:

The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57.

Arranging in ascending order we get

50,52,57,230

Median length of time = [tex]\frac{52+57}{2}=54.5[/tex]

Hence, the median length of time required to review an application is 54.5 minutes.

Answer:

Option C 41%

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The number of people who own at most three t-shirts costing more than $19 each is equal to the number of people who own one t-shirt costing more than $19 each, plus the number of people who own two t-shirt costing more than $19 each, plus the number of people who own three t-shirt costing more than $19 each

Observing the graph

The number of people who own one t-shirt costing more than $19 each is 5

The number of people who own two t-shirt costing more than $19 each is 17

The number of people who own tree t-shirt costing more than $19 each is 23

The number of people who own at most three t-shirts costing more than $19 each is

[tex](5+17+23)=45\ people[/tex]

To find out the percentage divided the number of people who own at most three t-shirts costing more than $19 by one hundred eleven people (total people that shopped in a store) and then multiply by 100

[tex](45/111)100= 40.54\%[/tex]

Round to the nearest whole number

[tex]40.54\%=41\%[/tex]

The question involves the application of statistical principles to determine the percentage of people who own at most three expensive t-shirts. Assuming 59% is the correct answer, this means 66 out of the 111 people surveyed own three or fewer such t-shirts. The examples in the question references demonstrate the principles of economics, but aren't directly related to the question.

The question is about determining the percentage of people who own at most three t-shirts costing more than $19 each from a sample of 111 people. Given that the possible percentages provided are 21% and 59%, the process involves the application of statistical principles, particularly dealing with percentages in relation to a specific sample size. This example fits into a branch of mathematics known as statistics, which deals with data analysis, collection, interpretation, presentation, and organization.

Let's assume from the reference that 59% is the correct answer, this conveys that of the 111 people surveyed, approximately 66 people own three or fewer such t-shirts. This is obtained by calculating 59% of 111, which equals about 65.49 and rounds to 66.

In the references provided, there are examples of how the cost of t-shirts affects purchasing decisions. This is related to the principles of economics which involve opportunity cost and budget constraints, but is not directly tied to answering the initial question.

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Answer:

5r + 2p + 6

Step-by-step explanation:

4r+r = 5r

9-3 = 6

Answer:

Step-by-step explanation:

note : an equation is : y - b = m(x - a)    ... the point is : A ( a , b) and slope : m

in this exercice :  m= - 8     and  a= - 3    and b= -6

an equation is : y+6 = -8(x+3)

you can write :   y+6 = - 8x -24

8x+y = - 30 .....answer : C

Answer:

C. 8x + y = -30

Step-by-step explanation:

-6 = -8[-3] + b

24

-30 = b

y = -8x - 30

+8x +8x

___________

8x + y = -30 >> Standard Linear Equation

* This is the fastest way to do it.

I am joyous to assist you anytime.

Answer:

(a) What is the research objectives?

B. To determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar.

(b) What is the population?

C. Adults in the country aged 18 years or older.

(c) What is the sample?

D. The 1019 adults in the country that were surveyed.

D. The 1019 adults in the country that were surveyed. The research objective is to determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar. The population is adults in the country aged 18 years or older. The sample is the 1019 adults in the country that were surveyed.

The research objective of the survey conducted by the news service is B. To determine the number of adults in the country who believe the federal government wastes 51 cents or more of every dollar.

The population in this study is C. Adults in the country aged 18 years or older.

The sample in this study is D. The 1019 adults in the country that were surveyed.

Answer:

Step-by-step explanation:

Given that an advertiser wishes to estimate the proportion of adults in Utah who already own a gym membership.

Confidence level wanted = 90%

Critical value Z for 90% = 1.645

p is not known hence for maximum std error we know p =0.5

Let us take p =0.5

Margin of error = [tex]1.645*\sqrt{\frac{pq}{n} } =\\1.645*0.5(\frac{1}{\sqrt{n} } ) 0.10\\n=67.65\\n~68[/tex]

Sample size can be 68

Answer:

For solar: [tex]S(x)=6240+75x[/tex]

For traditional: [tex]T(y)=850+320y[/tex]

Step-by-step explanation:

Cost to install solar water heater = $6240

The average annual cost to run the solar water heater is about = $75

Total cost to run x years : [tex]S(x)=6240+75x[/tex]

A traditional gas water heater costs about = $850

The average annual cost to run = $320

Total cost to run y years : [tex]T(y)=850+320y[/tex]

1. The total cost of a solar water heater, including installation and annual running costs, can be calculated as $6240 + ($75 * years).

2. The total cost of a traditional gas water heater, including installation and annual running costs, can be calculated as $850 + ($320 * years).

Given that,

Solar water heater:

Installation cost: $6240 (after rebates)

Annual running cost: $75

Traditional gas water heater:

Installation cost: $850

Annual running cost: $320

Let's create the total cost functions for each water heater as a function of the number of years.

For the solar water heater, the total cost (TC) can be calculated as:

TC_solar(years) = installation cost + (annual running cost * years)

Given the installation cost of $6240 and annual running cost of $75,

The total cost function for the solar water heater becomes:

TC_solar(years) = $6240 + ($75 * years)

For the traditional gas water heater, the total cost (TC) can be calculated as:

TC_gas(years) = installation cost + (annual running cost * years)

Given the installation cost of $850 and annual running cost of $320,

So, The total cost function for the gas water heater becomes:

TC_gas(years) = $850 + ($320 * years)

These equations allow you to determine the total cost of each water heater based on the number of years they are used.

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Answer:

The value of the car in very nice condition will be $35500.

Step-by-step explanation:

Let the value of car in a very nice condition be = x

The value $62125 is [tex]1\frac{3}{4}[/tex] or [tex]\frac{7}{4}[/tex] or 1.75 times of x.

Now, we can calculate for x:

[tex]1.75x=62125[/tex]

[tex]x=\frac{62125}{1.75}[/tex]

x = 35500

Hence, the value of the car in very nice condition will be $35500.

The value of the car in very nice condition is $35,500. This is determined by dividing the value of the car in excellent condition by 1.75.

To determine the value of the car in very nice condition, you need to use the information that a car in excellent condition is worth 1 3/4 times (or 1.75 times) as much as a car in very nice condition.

Given the value of the car in excellent condition is $62,125, you can set up the equation:

Substitute the known value:

To find the Value in Very Nice Condition, divide both sides by 1.75:

Hence, the value of the car in very nice condition is $35,500.

Answer:

B

Step-by-step explanation:

Giving away money because individuals loan dollars to other entitles at a a cost

Answer:

  D.  lending money

Step-by-step explanation:

It depends on the institution. A "for profit" financial institution has the purpose of making money for its investors. To do that, it offers a variety of money-oriented services, some involving payments to customers (interest) and some involving charging customers for the service (fees or interest).

A service offered in the latter category is "lending money."

__

A "not for profit" financial institution has the purpose of providing financial services to its members. Again, some of these services may involve payments to customers, and others may involve collecting interest or fees from customers. These institutions, too, offer the service of "lending money."

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Among the services a financial institution may offer that do not involve lending money are ...

Answer:

See explanation

Step-by-step explanation:

7.8 9.1 9.5 10.0 10.2 10.5 11.1 11.5 11.7 11.8

12.2 12.2 12.5 13.1 13.5 13.7 13.7 14.0 14.4 14.5

14.6 15.2 15.5 16.0 16.0 16.1 16.5 17.2 17.8 18.2

19.0 19.1 19.3 19.8 20.0 20.2 20.3 20.5 20.9 21.1

21.4 21.8 22.0 22.0 22.4 22.5 22.5 22.8 22.8 23.1

23.1 23.2 23.7 23.8 23.8 23.8 23.8 24.0 24.1 24.1

24.5 24.5 24.9 25.1 25.2 25.5 26.1 26.4 26.5 26.7

27.1 29.5

A. The five-number summary is

B. The interquartile range is

[tex]Q_3-Q_1=23.8-14.2=9.6[/tex]

C. See attached diagram

D. The distribution is not symmetric, the left half shows more data than the right part

Answer:

the 3 yard line

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]A=\frac{1}{2} r^{2} \theta\\\frac{dA}{d\theta} =r \\\\when r=2\\rate of change at r=2 is  2[/tex]

We want to find the rate of change of a given function of two variables when we fix one of the two, and then we want to evaluate it at r = 2.

We will get that the rate of change is:

[tex]\frac{dA(r, \theta)}{d\theta} = 12*r^2[/tex]

And when r = 2, the rate is 48.

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We define the rate of change of a function with respect to some variable as the differentiation of the function with respect to that variable.

Here we have the function:

[tex]A(r, \theta) = 12*r^2*\theta[/tex]

We need to differentiate it with respect to θ, we will get:

[tex]\frac{dA(r, \theta)}{d\theta} = 1*12*r^2*\theta^0 = 12*r^2[/tex]

Where I used the general rule to derive functions with exponents:

[tex]f(x) = x^n\\\\\frac{df(x)}{dx} = n*x^{n -1}[/tex]

Now that we know the rate of change, we want to evaluate it in r = 2, we will get:

[tex]\frac{dA(2, \theta)}{d\theta} = 12*2^2 = 48[/tex]

Notice that this does not depend on the value of θ.

If you want to learn more, you can read:

https://brainly.com/question/18904995