what's the value of the function f(x)= 2x+5 if x=3

Answers

Answer 1

Answer:

f(x) = 2(3) + 5

= 6 + 5 = 11

y = 11

x = 3

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.


Related Questions

Kala drove 819 miles in 13 hours.
At the same rate, how long would it take her to drive 441 miles?

Answers

Answer:

[tex]{ \tt{ \frac{819}{13} = \frac{441}{h} }} \\ { \tt{h = \frac{(441 \times 13)}{819} }} \\ h = 7 \: hours[/tex]

What is the probability that in a sample of 400 registered voters to at least 290 voted in their most recent local

Answers

Answer:

The probability that in a sample of 400 registered voters at least 290 voted in their most recent local elections is:

= 72.5%

Step-by-step explanation:

Sample of registered voters = 400

Sample of voters that actually voted = 290

Probability = 290/400 * 100

= 72.5%

b) This result above gives the statistic that for every 100 registered voters, 72.5 voters voted.  Probability measures the chance of an event occurring given other events.  Therefore, one can conclude that the voting was at least 72.5%.  Inversely, 27.5% of the registered voters did not participate or cast their ballots in the local elections.

Consider the probability that no less than 37 out of 295 cell phone calls will be disconnected. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.

a. Area to the right of 36.5
b. Area to the right of 37.5
c. Area to the left of 36.5
d. Area to the left of 37.5
e. Area between 36.5 and 37.5

Answers

Answer:  Choice A) Area to the right of 36.5

==========================================================

Explanation:

The phrasing "no less than" means the same as "at least".

Saying "at least 37" means 37 is the lowest we can go.

If x is the number of disconnected calls, then [tex]x \ge 37[/tex] and we want to find the probability of this happening (the max being 295).

We could use the binomial distribution to find the answer, but that would require adding 295-37+1 = 259 different values which could get tedious. So we could use the normal approximation to make things relatively straight forward.

Assuming this binomial meets the requirements of the normal approximation, then we'd look under the normal curve for the area to the right of 36.5; which is why the answer is choice A.

Why 36.5 and not 37? This has to do with the continuity correction factor when translating from a discrete distribution (binomial) to a continuous one (normal).

If we used 37, then we'd be missing out on the edge case. So we go a bit beyond 37 to capture 36.5 instead. It's like a fail safe to ensure we do account for that endpoint of 37. It's like adding a buffer or padding.

------------

Side notes:

Choice B would be the answer if we wanted to excluded 37 from the group, ie if we wanted to calculate [tex]P(x > 37)[/tex] instead of [tex]P(x \ge 37)[/tex]. So we're moving in the opposite direction of choice A to avoid that edge case. We go with "right" instead of "left" since this is what the inequality sign says.

which equation has the steepest graph ?

Answers

Answer:

Step-by-step explanation:

A.

[tex] \green{\huge{\red{\boxed{\green{\mathfrak{QUESTION}}}}}} [/tex]

which equation has the steepest graph ?

[tex] \red{ \bold{ \textit{STANDARD \: EQUATION}}}[/tex]

[tex]y = mx + c[/tex]

[tex]WHERE \\ m = SLOPE \\ c = Y - INTERCEPT[/tex]

[tex] \huge\green{\boxed{\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}}}[/tex]

[tex] \blue{A.T.Q}[/tex]

PART A:-

[tex]y = mx + c \sim y= -14x+1 [/tex]

[tex] \orange{SO}[/tex]

m= (-14)

which is equal to the slope of the equation .

PART B:-

[tex]y = mx + c \sim y= ¾x-9 [/tex]

[tex] \orange{SO}[/tex]

m= (¾)

PART C:-

[tex]y = mx + c \sim y= 10x-5[/tex]

[tex] \orange{SO}[/tex]

m= (10)

PART D:-

[tex]y = mx + c \sim y= 2x+8[/tex]

[tex] \orange{SO}[/tex]

m= (2)

SO MAXIMUM SLOPE IS :-( -14 )

Negative shows Slope is in negative direction.

[tex] \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star[/tex]

PLEASE HELP
The function in the table is quadratic
True
False

Answers

Answer:

True

Step-by-step explanation:

Each f(x) value increases by 5 so therefore this function would be linear

Hope you understand :)

Solve the following system of equations

Answers

Answer:

Given Two equations :-

[tex]3x {}^{2} - 2 {y}^{2} = 57 .\: .\: .\: . \:(i) \\ - 2 {x}^{2} + 3 {y}^{2} = -23.\: .\: .\: . \:(ii)[/tex]

multiplying eq.(i) by 2 eq.(ii) by 3.

[tex](3x {}^{2} - 2 {y}^{2} = 57 ) \times 2 .\: .\: .\: . \:(i) \\ ( - 2 {x}^{2} + 3{y}^{2} = - 23) \times 3.\: .\: .\: . \:(ii)[/tex]

[tex]6x {}^{2} - 4 {y}^{2} =114 .\: .\: .\: . \:(i) \\ - 6 {x}^{2} + 9 {y}^{2} = - 69.\: .\: .\: . \:(ii)[/tex]

[tex]0 + 5 {y}^{2} = 45 \\ 5y {}^{2} = 45 [/tex]

diving both sides by 5

[tex] {y}^{2} = 9[/tex]

taking Square root

[tex]y = + - 3[/tex]

placing this value of y² in eq. (i)

3x²- 2×9 = 57

3x² - 18 = 57

adding 18 to both sides

3x² = 57 + 18

3x²= 75

diving both sides by 3

x² = 25

x = ± 5

So, the values of x are +5 and -5 and the values of y are +3 and -3

Least to greatest 22,755 20,564 2,3805

Answers

Least to greatest: 20,564 22,755 2,3805

Write 2 1/4 as a decimal ​

Answers

1/4=.25
2=2.
2+.25
2.25=answer

Hey there!

2 1/4

= 2 * 4 + 1 / 4

= 8 + 1 / 4

= 9 / 4


= 9 ÷ 4

= 2.25


Therefore, your answer is: 2.25


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

-10 degrees Celsius is what Fahrenheit

Answers

Answer:

Step-by-step explanation:

i think if its -10 degrees i think the fahrenheit would be 50 degrees

prove the identity of
[tex] 4 sin^{2}x + 7sin^{2} = 4 + 3cos^{2} [/tex]

Answers

Answer:

7sin

2

x+3cos

2

x=4

4sin

2

x+3sin

2

x+3cos

2

x=4

4sin

2

x+3=4

4sin

2

x=1

sin

2

x=

4

1

sinx=

2

1

or sinx=−

2

1

Step-by-step explanation:

TAKING THE POSITIVE ROOT x=

6

π

tan(

6

π

)=

3

1

A sprinkler releases water st a rate of 150 liters per hour. If the sprinkler operated for 80 minutes how many liters of water will be released

Answers

200 liters for 80 minutes of run time

The amount of water released from the sprinkler for 80 minutes is 200 L

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of water from the sprinkler for 80 minutes be = A

Now , the value of A is given by the equation

A sprinkler releases water st a rate of 150 liters per hour

So , 60 minutes = 150 Liters of water

80 minutes = 1/60 hours

80 minutes = 1.333 hours

The amount of water released for 1.333 hours A = 150 x 1.333

On simplifying the equation , we get

The amount of water released for 1.333 hours A = 200 L

Therefore , the value of A is 200 L

To learn more about equations click :

https://brainly.com/question/19297665

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1,620 to the nearest ten ? Please don't answer if you know your wrong !

Answers

Answer:

I will say 2,000 yes so that is what I am putting

A random sample of size 36 is to be taken from a population that is normally distributed with mean 72 and standard deviation 6. The sample mean of the observations in our sample is to be computed. The sampling distribution of the sample mean is

Answers

Answer:

The sampling distribution of the sample mean is approximately normal with mean 72 and standard deviation 1.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Normally distributed with mean 72 and standard deviation 6.

This means that [tex]\mu = 72, \sigma = 6[/tex]

A random sample of size 36

This means that [tex]n = 36, s = \frac{6}{\sqrt{36}} = 1[/tex]

The sampling distribution of the sample mean is

By the Central Limit Theorem, it is approximately normal with mean 72 and standard deviation 1.

Please help ASAP. No links

Answers

Hello my dear friend of USA !!!

DB/AD = BE/EC

=> 6/4 = x+1/x

=> 6x = 4x + 4

=> 2x = 4

=> x = 2

So x = 2

I am from INDIA.

Lots of love ❤️!!!

Have a great day ahead!

Answer:

x = 2

Step-by-step explanation:

[tex]\frac{6}{4} = \frac{x+1}{x}[/tex]

6x = 4x + 4

2x = 4

x = 2

Pls could someone help me with this​

Answers

Answer:

- Bar Gaps should be the same

Y-axis up in units of 5 would help out

Step-by-step explanation:

For which pair of functions is the vertex of k(x) 6 units below the vertex of
f(x)?
A. Ax) = x2 and k(x) = x2 + 6
B. f(x) = x2 and k(x) = (x+6)2
C. Ax) = x and k(x) = (x – 6)2
D. f(x) = x2 and k(x) = x2 - 6

Answers

Using translation concepts, the vertex of k(x) is 6 units below the vertex of f(x) = x² for:

D. f(x) = x² and k(x) = x² - 6.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

We want to shift the vertex 6 units down, hence the transformation is y -> y - 6, so the correct pair is:

D. f(x) = x² and k(x) = x² - 6.

More can be learned about translation concepts at https://brainly.com/question/4521517

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una fuerza constante F de magnitud igual a 3lb se aplica al bloque que se muestra en la figura. F tiene la misma dirección que el vector a= 3i + 4j. determine el trabajo realizado en la dirección de movimiento si el bloque se mueve de P1 (3, 1) a P2 (9, 3). Suponga que la distancia se mide en pies.

Answers

Uh is that Spanish? Bc I can’t speak Spanish

An economic instructor at UCF is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 11 students who took the course last semester follow:

# of observation(s) n = 30
# of independent variable(s) = 1
SSR = 1,297 SSE= 920

Required:
Find the F test statistic.

Answers

Answer:

[tex]F = 39.47[/tex]

Step-by-step explanation:

Given

[tex]n = 30[/tex] --- observations

[tex]p = 1[/tex] -- variables

[tex]SSR = 1,297[/tex]

[tex]SSE= 920[/tex]

Required

The F statistic

This is calculated using:

[tex]F = \frac{SSR}{p} \div \frac{SSE}{n - p -1}[/tex]

[tex]F = \frac{1297}{1} \div \frac{920}{30 - 1 -1}[/tex]

[tex]F = \frac{1297}{1} \div \frac{920}{28}[/tex]

[tex]F = 1297 \div \frac{920}{28}[/tex]

Rewrite as:

[tex]F = 1297 * \frac{28}{920}[/tex]

[tex]F = \frac{1297 *28}{920}[/tex]

[tex]F = \frac{36316}{920}[/tex]

[tex]F = 39.47[/tex]

Give two examples of addition of two mixed numbers with different denominators
SHOW ALL STEPS

Answers

Answer:

First Example: 3 1/2 + 4 3/4, Second Example: 6 3/8 + 7 9/15

Extra Example: 8 4/20 + 3 5/10

Step-by-step explanation:

First Example:

1/2 + 3/4

1/2 is equal to 2/4 so it is now compatible to be added to 3/4.

2/4 + 3/4

= 5/4

Now for the mixed numbers since its 3 and 4, 3 + 4 = 7.

Final answer is 7 5/4.

Second Example:

3/8 + 9/15

9/15 can be reduced to 3/5

Now the equation is 3/8 + 3/5

= 15/40 + 24/40 is an equivalent equation

15/40 + 24/40  

= 39/40

Now for the mixed numbers since its 6 and 7, 6 + 7 = 13

Final answer is 13 39/40.

I am going to include one last example just in case you need one:

Third Example:

4/20 + 5/10

We can reduce these to

1/5 + 1/2

= 2/10 + 5/10 is the equivalent equation

2/10 + 5/10

= 7/10

Now for the mixed numbers since its 8 and 3, 8 + 3 = 11.

Final answer is 11 7/10.

I Hope this helps!

NEED ANSWER QUICK

Timmy and Tommy are two boys whose ages add up to 23. Timmy is 5
years older than Tommy. How old are they?

Answers

Let’s assume that age of Timmy is x yrs.
Then we can conclude that age of Tommy is =
(23 -x) yrs.

Now we know that Timmy is 5 years older than Tommy, therefore,
x = 5 + (23-x)
x = 5 + 23 - x
x + x = 28
2x = 28
x = 28/2
x = 14 Answer. (Age of Timmy)

So, the age of Tommy is 23 - x = 23 - 14 = 9 yrs.

Answer:

Tommy's age is 9 years old.

Timmy's age is 14 years old.

Step-by-step explanation:

Take Tommy's age to be x and Timmy's age to be x+5

x+x+5=23

2x+5=23

2x=23-5=18

x=18÷2=9

x+5=9+5=14

2. The prices, in dollars per unit, of the three commodities X, Y and Z are x, y and z,
respectively
Person A purchases 4 units of Z and sells 3 units of X and 3 units of Y.
Person B purchases 3 units of Y and sells 2 units of X and 1 unit of Z.
Person C purchases 1 unit of X and sells 4 units of Y and 6 units of Z.
In the process, A, B and C earn $40, $50, and $130, respectively.

a) Find the prices of the commodities X, Y, and Z by solving a system of linear
equations (note that selling the units is positive earning and buying the units is
negative earning).​

Answers

Answer:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

Step-by-step explanation:

for person A, we know that earns $40, then we can write the equation:

-4*z + 3*x + 3*y = $40

For person B, we know that earns $50, then:

1*z + 2*x - 3*y = $50

For person C, we know that earns $130, then:

6*z - 1*x + 4*y = $130

Then we have a system of equations:

-4*z + 3*x + 3*y = $40

1*z + 2*x - 3*y = $50

6*z - 1*x + 4*y = $130

To solve the system, we need to isolate one of the variables in one of the equations.

Let's isolate z in the second equation:

z = $50 - 2*x + 3*y

now we can replace this in the other two equations:

-4*z + 3*x + 3*y = $40

6*z - 1*x + 4*y = $130

So we get:

-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40

6*($50 - 2*x + 3*y) - 1*x + 4*y = $130

Now we need to simplify both of these, so we get:

-$200 + 11x - 9y = $40

$350 - 13*x + 28*y = $130

Now again, we need to isolate one of the variables in one of the equations.

Let's isolate x in the first one:

-$200 + 11x - 9y = $40

11x - 9y = $40 + $200 = $240

11x = $240 + 9y

x = ($240 + 9y)/11

Now we can replace this in the other equation:

$350 - 13*x + 28*y = $130

$350 - 13*($240 + 9y)/11 + 28*y = $130

Now we can solve this for y.

- 13*($240 + 9y)/11 + 28*y  = $130 - $350 = -$220

-13*$240  - (13/11)*9y + 28y = - $220

y*(28 - (9*13/1) ) = -$220 + (13/11)*$240

y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66

We know that:

x = ($240 + 9y)/11

Replacing the value of y, we get:

x = ($240 + 9*$3.66)/11  = $24.81

And the equation of z is:

z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36

Then:

Price of X is $24.81

Price of Y is $3.66

Price of Z is $11.36

Question is in picture below

Answers

Answer:

The obove picture the rule is SSA

The answer is D. sas (side angle side)

If a procedure meets all of the conditions of a binomial distribution except the number of trials is not​ fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by ​
P(x) = p(1−p)x−1​
where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor​ (with group O and type Rh negative​ blood) is 0.15. Find the probability that the first subject to be a universal blood donor is the fifth person selected.

Answers

Answer:

0.0783

Step-by-step explanation:

The probability of getting the first success on xtg trial ; this is a geometric distribution :

P(x) = p(1−p)^x−1

The probability of being a universal donor , p = 0.15

The probability of obtaining someone who is a universal donor on 5th trial will be :

P(5) = 0.15(1 - 0.15)^(5 - 1)

P(5) = 0.15(0.85)^4

P(5) = 0.15(0.52200625)

P(5) = 0.0783009375

P(5) = 0.0783

Solve the inequality. |X+19|<7

Answers

Answer:

x<-12

Step-by-step explanation: hope this helps!

What is 70% less than 55?

Answers

Answer:

100-70=30 so

55*0.3=16.5

Hope This Helps!!!

Answer:

Answer :

70% less than 55 is

16.5

Necesito ayuda con esto

Answers

Answer:

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Step-by-step explanation:

Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:

[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]

[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]

[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

in a school project you need to provide a blueprint of the schools rectangular playground .the blueprint dimensions of the playground are 23/147 yd x 3/14 yd after reducing them by the factor of 2/147 what are the original dimensions if the playground in yards

Answers

Answer:

L = 0.16 yd, W = 0.22 yd

Step-by-step explanation:

Dimensions of play ground 23/147 yd x 3/14 yd

reducing factor 2/147

Let the original length is L.

[tex]L - \frac{2L}{147} = \frac{23}{147}\\\\L\frac{143}{147} = \frac{23}{147}\\\\L=\frac{23}{143} yd[/tex]

L = 0.16 yd

Let the width is W.

[tex]W - \frac{2W}{147} = \frac{3}{14}\\\\W\frac{143}{147} = \frac{3}{14}\\\\W=0.22 yd[/tex]

The probability that a 38-year-old white male will live another year is .99813. What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy

Answers

Answer:

The insurance company should charge $1,873.5.

Step-by-step explanation:

Expected earnings:

1 - 0.99813 = 0.00187 probability of the company losing $1 million(if the client dies).

0.99813 probability of the company earning x(price of the insurance).

What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy?

Break even means that the earnings are 0, so:

[tex]0.99813x - 0.00187(1000000) = 0[/tex]

[tex]0.99813x = 0.00187(1000000)[/tex]

[tex]x = \frac{0.00187(1000000)}{0.99813}[/tex]

[tex]x = 1873.5[/tex]

The insurance company should charge $1,873.5.

Sticky buns sell for $1.25 each,or $10.89 per dozen. how much does each bun cost if purchased by the dozen? How much do you save on 12 sticky buns?

Answers

Answer:

If you buy per dozen, each buns costs about 91 cents.

You will save $4.11 if you buy per dozen.

Step-by-step explanation:

1.25 * 12= $15

10.89/12= .9075 = .91 cents

15-10.89= $4.11

Which of the following is equivalent to (2a + a)(3b + 1)?

Tip: Simplify the expression on the left first, and then use the distributive property.

2a + 3ab + a
3a + 3b + 1
3a(3b + 3)
9ab + 3a

Answers

Answer:

9ab+3a

Step-by-step explanation:

(2a+a)(3b+1)=(3a)(3b+1)

3a(3b+1)

=(3a×3b)+3a×1

=9ab+3a

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However, the lab score is worth 21% of your total grade, each major test is worth 25%, and the final exam is worth 29%. Compute the weighted average for the following scores: 60 on the lab, 81 on the first major test, 69 on the second major test, and 79 on the final exam. Enter your answer as a whole number. g An increase in the interest rate: has no effect on investment. may be caused by a drop in investment demand. increases planned investment because people who make money from interest have more money to invest. reduces planned investment because the interest rate is the cost of borrowing to finance investment projects. what is the name given to the male cell in the flower Which of the following vocabulary words are pronouns that directly refer to selves? Select all that apply.ourselvesyourselvesshelveshalvesthemselves Describe telephase (IN YOUR OWN WORDS)-Thank you! Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. 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Hourly wage rates are $30 for Lisa, $15 for David, and $18 for Sarah.Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.) Two years ago, Kuley invested $20,900. She has earned and will earn compound interest of 7.8 percent per year. In 3 years from today, Nabax can make an investment and earn simple interest of 5.3 percent per year. If Nabax wants to have as much in 7 years from today as Kuley will have in 7 years from today, then how much should Nabax invest in 3 years from today How do people with damage to the ventromedial cortex in the frontal lobe respond on a gambling card task? 8. One of the finest examples of training coordination is when the fire department jointly trains with other agencies. On the local level, fire departments that fight fires together should: How do I find the area for this shape DIRECTIONS: Write TRUE if the statement is correct, and FALSE if it is wrong.Once the statement is False, underline the word or words that make thestatement incorrect.6. You may also send feedback in the form of smilesand head nods while listening.7. Any distortions or inconsistencies that occur duringan attempt to communicate can be seen as feedback.8. Facial expressions, tone of voice, gestures and bodylanguage are considered as message.9. The use of complicated jargon, inappropriatebody language, inattention, disinterest, andcultural differences cannot be considered"noise" in the context of interpersonal communication.___10. in this personal communication can be used to form context and maintain relationships.if you answer this... I give you a Brainlest Development is merely the economic progress how? What action taken by the U.S. government during World War II violated the constitutional rights of some citizens? pahelp po ako.1. Which of the following terms refers to energy in motion?A. kinetic energy C. potential energyB. light energy D. thermal energy2. Which of the following is a type of energy gained due to its position?A. kinetic energy C. gravitational potential energyB. light energy D. thermal energy3. How do you get the total mechanical energy of an object in a closed system?A. Get the sum of the initial and final kinetic energy.B. Get the sum of the initial and final potential energy.C. Get the sum of the kinetic energy and the potential energy.D. Get the difference between the kinetic energy and the potential energy.4. Which of the following is the best set up to observe the conservation of mechanical energy?A. A cart rolling down a wooden ramp.B. A wooden block falling in a vacuum.C. A volleyball falling from a tall building.D. a paper plane being launched from a tower.5. A big rock was dropped from the third floor of a building. What happens to the kinetic energy of the ball as it falls?A. The rocks kinetic energy increases.B. The rocks kinetic energy decreases.C. The rocks kinetic energy remains the same.D. The rocks kinetic energy cannot be identified.6. A heavy metallic ball was rolled up on a frictionless ramp. What happens to the gravitational potential energy of the ball as it rolls up the ramp?A. The balls gravitational potential energy increases.B. The balls gravitational potential energy decreases.C. The balls gravitational potential energy remains the same.D. The balls gravitational potential energy cannot be identified.7. A 2kg ball is elevated up a building, how much is its potential energy 10m from the ground?A. 5J C. 98JB. 20J D. 196JFor items 8 to 10, refer to the illustration below. A ball is dropped at point W and travels along a frictionless path to reach point Z.8. At which point does the ball has greatest gravitational potential energy?A. W C. YB. X D. Z9. At which point does the ball has greatest kinetic energy?A. W C. YB. X D. Z10. What happens to the total mechanical energy of the ball as it travels from point W to point Z?A. The total mechanical energy increases.B. The total mechanical energy decreases.C. The total mechanical energy remains the same.D. The total mechanical energy cannot be determined.For items 11 to 12, refer to the illustration below. A pendulum swings back and forth from its highest position to its lowest position and vice versa.11. As a pendulum swings from its highest to lowest position, what happens to its gravitational potential energy and kinetic energy?A. Both its GPE and KE increases.B. Both its GPE and KE decreases.C. Its GPE decreases but KE increases.D. Its GPE increases but KE decreases.12. What happens to the total mechanical energy of the bob as it swings back and forth if only force acting on it is the gravitational force?A. The total mechanical energy increases.B. The total mechanical energy decreases.C. The total mechanical energy remains the same.D. The total mechanical energy cannot be determined.Four ball of masses 0.5 kg, 1 kg, 2 kg, and 5 kg were dropped simultaneously on top of a building with the height of 20 m. Ignoring the air resistance, the four balls reach the ground at the same time.13. Which of the following balls has the greatest gravitational potential energy on top of the building?A. The ball with the mass of 5 kg.B. The ball with the mass of 2 kg.C. The ball with the mass of 0.5 kg.D. All the balls have the same potential energy.14. Which of the following balls has the least kinetic energy on top of the building?A. The ball with the mass of 5kg.B. The ball with the mass of 1kg.C. The ball with the mass of 0.5kg.D. All the balls have the same kinetic energy.15. Which of the following balls has the greatest total mechanical energy?A. The ball with the mass of 2kg.B. The ball with the mass of 1kg.C. The ball with the mass of 0.5kg.D. All the balls have the same total mechanical energy A triangle has vertices on a coordinate grid at D(6,-1)D(6,1), E(-4,-1)E(4,1), and F(-4,-6).F(4,6). What is the length, in units, of DE ?