You are playing right field for the baseball team. Your team is up by one run in the botton of the last inning of the game when a ground ball slips through the infield and comes straight toward you. As you pick up the ball 65m from home plate, you see a runner rounding third base and heading for home with the tying run. ou throw the ball at an angle of 30 degrees above the horizontal with just the right speed so that the ball is caught by the catcher, standing on home plate, at the same height as you threw it. As you release the ball, the runner is 20 meters from home plate and running full speed at 8.0 m/s. Will the ball arrive in time for your team's catcher?

Answers

Answer 1

Answer:

The correct response is "No". The further explanation is given below.

Explanation:

The given values are:

Angle

[tex]\theta = 30^{\circ}[/tex]

Distance

d = 20 m

Speed

s = 8.0 m/s

Now,

⇒  [tex]y(t) = \frac{1}{2}\times a\times t^2 + v0\times t\times (sin \theta)[/tex]

    [tex]0 = -4.9t^2 + v0\times t\times (sin 30)[/tex]

    [tex]x = v0\times (cos \theta)\times t[/tex]

    [tex]65 = v0\times (cos 30)\times t[/tex]

    [tex]v0\times t = \frac{65}{Cos30}[/tex]

    [tex]0 = -4.9t^2 + 65\times \frac{sin30}{cos30}[/tex]

    [tex]t = 2.767 \ sec[/tex]

So,

⇒  [tex]d = r\times t[/tex]

    [tex]20 = 8\times t[/tex]

      [tex]t=2.5 \ sec[/tex]

Therefore, 2.5 < 2.767, so it won't get there.


Related Questions

A spaceship left earth to collect samples from mars? Which statement is true about the strength of the earths gravity on moving spacecrafts

Answers

Answer:

The first one

Explanation:

ANSWER QUICK ! WILL GIVE BRAINLIEST
(EDGE2020 PHYSICS)

Substance X transfers thermal energy to substance Y through conduction. What is an accurate conclusion about the condition of both substances before conduction occurred?

Their molecules had the same amount of energy.
The substances were the same temperature.
Substance X’s molecules were faster than substance Y’s.
Substance X was cooler than substance Y.

Answers

Answer:

Substance X transfers thermal energy to substance Y through conduction. What is an accurate conclusion about the condition of both substances before conduction occurred? Substance X's molecules were faster than substance Y's.

Explanation:

An accurate conclusion about the condition of both substances before conduction occurred is substance X’s molecules were faster than substance Y’s.

What is thermal energy?

Thermal energy is the energy released in the form of heat. It manifests itself by releasing heat. It results from the atoms' movement or vibration, so it displays the system's internal energy. We define thermal energy as part of the internal energy of a system.

It is an extensive quantity, it depends on the size of the system, or on the amount of substance it contains. The SI unit of thermal energy is the joule (J). It is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the potential energy of the system. Thermal energy is often classified into various types on the basis of how this internal energy, in the form of heat, is transferred from one body to another.

The correct answer is option C.

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Mina finds out that a company is pumping water from an aquifer near her home. What can Mina conclude about the water being pumped? The water being pumped is under a lot of pressure and comes from a confined aquifer. The water being pumped is under a lot of pressure and comes from an unconfined aquifer. The water being pumped is at atmospheric pressure and comes from a confined aquifer. The water being pumped is at atmospheric pressure and comes from an unconfined aquifer.

Answers

Answer:

The water being pumped is at atmospheric pressure and comes from an unconfined aquifer.

Answer:

The water being pumped is at atmospheric pressure and comes from an unconfined aquifer.

Explanation:

Explain why the driver's reaction time affects the thinking distance.

Answers

Answer:

The thinking distance depends on the reaction time of the driver which could can affected by alcohol, distractions and tiredness. A faster speed increases both thinking  distance, increasing the total stopping distance.

I hope this is helpful. Would appreciate if you add me as brainliest.

A faster pace extends both the thinking distance and the total stopping distance.

Given that,
To justify, the driver's reaction time affects the thinking distance.

What is reaction time?

The reaction time of an organism is a measure of how quickly it responds to a signal. The time interval between the presentation of the stimulus and the appearance of the appropriate voluntary response in the subject is defined as the RT.

The thinking distance is determined by the driver's reaction time, which can be influenced by drinking, distractions, and fatigue. A higher speed increases both thinking distance and total stopping distance.

Thus, A faster pace extends both the thinking distance and the total stopping distance.

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please help quick, i’m timed!
Question 2 (5 points)

What is the speed of sound in water if the wavelength is 2.5 m and the frequency
592 Hz?

What would happen to the frequency if the wavelength increased to 5 m?

Answers

Explanation:

v=592×2.5

v=1480m/s

ii) v=1480m/s, wavelength= 5m, f=?

f=1480/5

f=296Hz

A moving car of mass 500 kg collides with a stationary truck of
mass 1500 kg, and the two vehicles lock together on impact.
The combined velocity of the car and truck after the collision is
20 m/s. What is the velocity of the car before the collision?

Answers

Answer:

We are given:

m1 = 500 kg             m2 = 1500 kg

v1(initial) = x m/s       v2(initial) = 0 m/s

v1(final) = 20 m/s      v2(final) = 20m/s

According the the law of conservation of momentum:

m1v1(initial) + m2v2(initial) = m1v1(final) + m2v2(final)

Plugging the values in this formula:

(500*x) + (1500 * 0) = (500 * 20) + (1500 * 20)

500x = 20(1500 + 500)

500x = 20(2000)

x = 20 * 4

x = 80 m/s

Therefore, the car was initially moving at a velocity of 80 m/s

(15 points) How does change in a roller coasters motion depend on the sum of the forces and the mass of the ride?

Answers

The sum of the forces divided by the mass is equal to the acceleration of the roller coaster. Acceleration causes a change in the motion.

Does voltage remain the same throughout a series circuit

Answers

It depends on the circuit. Sometimes it becomes a bit weaker, sometimes it stays the same.

Answer:

In a series circuit, the current that flows through each of the components is the same, and the voltage across the circuit is the sum of the individual voltage drops across each component.

A man runs 800m due north in 110 seconds followed by 400m due suoth in 90 seconds calculate his average speed and his average velocity​

Answers

Answer:

Average speed is  6m/s

Average velocity is 5.859m/s

Explanation:

Average speed, s = d/t

d is distant

t is time

speed north is 800m and 110s

speed due south is 400m and 90s  

Average speed = (800+400) / (110+90)

                          = 1200/200

                          =6m/s

Average velocity V = (v + u)/2

v = final velocity

u = initial velocity

V = (7.273 + 4.444)/2 = 11.717/2

V = 5.859m/s

Which would be harder to move: a kilogram of feathers or a kilogram of bricks? Explain your answer.

Answers

Answer:

The kilogram (kg) is the SI unit for mass. Not weight.

So when you say « heavier » and mention kg, I would assume you’re talking about mass.

The mass of 1 kg of feathers and 1 kg ok bricks are identical.

And if you want an answer to your question comparing the weight on Earth of those 2 items, in vacuum of one kilogram of feathers would have exactly the same weight as one kilogram of bricks.

Explanation:

Hope this helps! <3

If you were unfortunate enough to be 5.5 mm away from such a lightning bolt, how large a magnetic field would you experience

Answers

The question is incomplete. Here is the complete question.

Lightning bolts can carry currents up to approximately 20kA. We can model such a current as the equivalent of a very long, straight wire.

(a) If you were unfortunate enough to be 5.5m away from such a lightning bolt, how large a magnetic field would you experience?

(b) How does this field compare to one you would experience by being 5.5cm from a long, straight household current of 5A?

Answer: (a) B = 7.27 x 10⁻⁴ T

              (b) Approximately 40 times higher than a household one.

Explanation: Using Biot-Savart Law, the magnetic field in a straight, long wire is given by

[tex]B=\frac{\mu_{0}I}{2.\pi.r}[/tex]

where:

[tex]\mu_{0}[/tex] (permeability of free space) = [tex]4.\pi.10^{-7}[/tex]T.m/A

(a) If lightning bolt is compared to a long and straight wire, then magnetic field is

[tex]B=\frac{4.\pi.10^{-7}.10.10^{3}}{2.\pi.5.5}[/tex]

B = 7.27 x 10⁻⁴ T

The magnitude of magnetic field in a lightning bolt is 7.27 x 10⁻⁴ T

(b) Magnetic field in a household wire will be

[tex]B=\frac{4.\pi.10^{-7}.5}{2.\pi.5.5.10^{-2}}[/tex]

B = 1.82 x 10⁻⁵ T

Comparing fields:

[tex]\frac{7.27.10^{-4}}{1.82.10^{-5}}[/tex] ≈ 40

The filed for a lightning bolt is approximately 40 times higher than for a household wire.

A beam of light strikes one face of a window pane with an angle of incidence of 30.0°. The index of refraction of the glass is 1.52. The beam travels through the glass and emerges from a parallel face on the opposite side. Ignore reflections.

Required:
a. Find the angle of refraction for the ray inside the glass.
b. Show that the rays in air on either side of the glass (the incident and emerging rays) are parallel to each other.

Answers

(a) The angle of refraction for the ray inside the glass will be 19.26°.

(b)  It  is proved that the rays in the air on either side of the glass are parallel to each other

What will be the angle of refraction for the ray inside the glass?

When a ray of light passes through a different medium some part of the light gets reflected and some part gets refracted by changing its angle in the different medium this angle is called the angle of refraction and the phenomenon is called refraction of light.

It is given that,

The angle of incidence = 30.0°

Index of reflection of glass = 1.52

(a) For finding the angle of the refraction for the ray inside the glass we will use Snell's Law

[tex]\dfrac{Sini}{Sinr} =\mu[/tex]

Put the value into the formula

[tex]Sinr=\dfrac{Sini}{\mu} =\dfrac{Sin30}{1.52}[/tex]

[tex]r=Sin^{-1}(0.329)[/tex]

[tex]r=19.26^o[/tex]

(b) Now for proof of  [tex]Sin\ i =Sin\ e[/tex]

The incident ray and emerging ray are equal then the ray will be parallel.

We need to prove that the rays in the air on either side of the glass are parallel to each other.

Using the formula for emerging ray

[tex]\dfrac{Sin\ e}{Sin\ r} = \mu[/tex]

[tex]Sin\ e=\mu Sin \ r=1.52\times Sin19.26[/tex]

By putting the values in the formula

[tex]e=Sin^{-1}(1.52\times0.3289)[/tex]

[tex]e=30^o[/tex]

Since the incident angle and the emerging angle are equal

[tex]Sin \ i=Sin \ e[/tex]

Thus incident and emerging rays) are parallel to each other.

(a) So the angle of refraction for the ray inside the glass will be 19.26°.

(b)  It  is proved that the rays in the air on either side of the glass are parallel to each other

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the volume of a cube is measured in grams, true or false

Answers

Answer: false

Explanation: They are measured by cubic ______. ______ is feet, meters, inches, any way to measure

A ball tossed vertically upward rises, reaches its highest point, and then falls back to its
starting point. While the ball is rising, what is happening to its speed.
O it is increasing by 10 m/s^2
O it is increasing, but not at a constant rate
it is decreasing by 10 m/s^2
it is decreasing, but not at a constant rate
O it moves with constant speed

Answers

Answer:

Third Option: It is decreasing by 10m/s^2

Explanation:

When a ball is thrown in the air, it's fastest velocity occurs just as it leaves its source (e.g. the hand that throws it), and just before it hits the starting point. This is because this is when it has the most kinetic energy which translated into speed. As it rises, it starts to lose kinetic energy as it transforms into gravitational potential energy as the ball is fighting against the force of gravity as it moves further away from the Earth's surface. This means it begins to slow down until its speed is 0, its highest point, before falling and gaining kinetic energy again. Because of this, we can eliminate options 1, 2 and 5 as we know the ball's velocity decreases as it rises.

As the ball rises it's velocity decreases at a constant rate, as the amount of kinetic energy it has is proportional to its height. Therefore, the best option is option 3, as it states it is decreasing and gives a constant deceleration rate.

Hope this helped!

How to call the police?

Answers

Answer:

dail 911

tell problem and location

plz mark brainliest

Which of the vectors below is the sum of vectors à and b, shown here?

Answers

Answer:

B

Explanation:

Answer:

B

Explanation:

Just took the quiz

PLEASEE HELPPP!!! GIVING 15 PT

Answers

Answer:

between point c and point D

Which describes how the spring constant affects the potential energy of an object for a given displacement from an equilibrium position?
A the higher the spring constant, the greater the gravitational potential energy.
B The lower the spring constant, the greater the gravitational potential energy.
C The higher the spring constant, the greater the elastic potential energy.
D The lower the spring constant, the greater the elastic potential energy

Answers

Answer:

Based on the answer choices provided, the correct answer is:

C, The higher the spring constant, the greater the elastic potential energy.

Explanation:

The spring constant is best defined as the measure of a spring's resistance to force (in regards to factors such as stretching and compression).

Thus, the higher the spring constant, the stiffer the string - this equates to greater elastic potential energy (think of stretching a rubber band or using it as a slingshot).

Hope this helps!

Answer:

C.) The higher the spring constant, the greater the elastic potential energy.

Explanation:

A mass of 0.4 kg is dropped from rest in a medium offering a resistance of 0.2|v|, where is measured in meters per second. Acceleration due to gravity is 9.8 m/s^2.

Required:
a. If the mass is dropped from a height of 25 m, find its velocity when it hits the ground.
b. If the mass is to attain a velocity of no more than 8 m/s, find the maximum height fromwhich it can be dropped.
c. Suppose that the resistive force isk|v|, wherevis measured in m/s, andkis constant.If the mass is dropped from a height of 25 m and must hit the ground with a velocity of no more than 8 m/s, determine the coefficient of resistance that is required.

Answers

Answer:

A.) 22.12 m/s

B.) 3.27 m

C.) 0.57

Explanation:

Given that a mass of 0.4 kg is dropped from rest in a medium offering a resistance of 0.2|v|, where is measured in meters per second. Acceleration due to gravity is 9.8 m/s^2.

a. If the mass is dropped from a height of 25 m, its initial velocity U will be equal to zero. when it hits the ground, the final velocity V will be:

V^2 = U^2 + 2gH

Substitute g and the height into the formula

V^2 = 2 × 9.8 × 25

V^2 = 490

V = 22.12 m/s

b. If the mass is to attain a velocity of no more than 8 m/s, the maximum height from which it can be dropped will be calculated by using the same formula.

V^2 = U^2 + 2gH

Where V = 8 m/s and U = 0

8^2 = 0 + 2 × 9.8 × H

64 = 19.6H

H = 64/19.6

H = 3.27 m

c. Suppose that the resistive force is k|v|, where v is measured in m/s, and k is constant. If the mass is dropped from a height of 25 m and must hit the ground with a velocity of no more than 8 m/s, determine the coefficient of resistance that is required.

The energy at 25m heigh will be:

E = mgh

E = 0.4 × 9.8 × 25

E = 98 J

1/2mv^2 = 98

1/2 × 0.4 × ( 8 - v )^2 = 98

0.2( 8 - v )^2 = 98

( 8-v)^2 = 98/0.2

( 8 - v )^2 = 490

8 - v = 22.12

v = 22.14 - 8

v = 14.14

Coefficient of resistance required will be 8/ 14.14 = 0.57

What are the bumps on a gear called?

Answers

Answer:

Teeth

Explanation:

The main parts of geards are the base and the teeth.  When two wheels are combined and joined by a belt, the larger wheel will rotate more slowly than the smaller wheel, but it will rotate with a greater force. A big wheel with twice the circumference of a small wheel will rotate with twice the force and half the speed of the small wheel.

Gears are connected together in various ways to transmit motion and force. Two connected gears of different sizes will cause one of the gears to turn faster or slower than the other. One gear will also move the force in a different direction than the other.

Gear ratio is the number of teeth on the following gear divided by the number of teeth on the driving gear (the gear inputting the motion).

A low gear ratio = more speed = less force

A high gear ratio = less speed = more force

Please give me brainliest if this helps!

Answer:

Teeth

Explanation:

A car in front of the school goes from rest to 27 m/s in 3.0 seconds. What is its acceleration (assuming
it is constant)?

Answers

The answer is 13.5 because 27÷3.0=13.5

Many biological systems are well-described by the laws of statistical physics. A simple yet often powerful approach is to think of a system as having only two states. For example, an ion channel may be open or closed. In this problem, consider a simple model of membrane channels for ions: The system is described by a Boltzmann distribution with only two states, with energies ε1 (open) and ε2 (closed). Assume the "open" state is the state of higher energy, so that ε1 > ε2.

If the probability of finding an ion channel open is popen and the probability of finding the ion channel closed is pclosed, which of the expressions below best represents the relative probability of open to closed, R = popen/pclosed? Use the notation z1 = e-ε1/kBT and z2 = e-ε2/kBT

a. z1-z2
b. z2-z1
c. z1/z2
d. z2/z1
e. Something else

Answers

Answer:

z1/z2

Explanation:

we have no quantum effects therefore we can make use of Maxwell Boltzmann distribution in the description of this system.

using the boltzman distribution the probability of finding a particle in energy state

[tex]P_{ei} = \frac{gie^{-ei/kol} }{z}[/tex]

we have

gi to be degeneration of the ith state

ei to be energy of ith state

[tex]z=e^{-ei/kbt}[/tex] summation

[tex]P_{ope} = \frac{e^{-ei/kBt} }{z} = \frac{Z_{1} }{Z}[/tex]

We have R to be equal to

[tex]\frac{P_{ope} }{P_{Close} } = \frac{Z1}{Z2}[/tex]

How far away are the Stars?

Answers

Answer:

25,300,000,000,000 miles away

A car traveled at a constant velocity of 70 mph from noon to 2:00 pm. At 3:00 pm the velocity of the car was 80 mph; and finally at 4:30 pm the velocity of the car was 40 mph.
Which statement accurately describes the acceleration of the car?

Answers

Answer:

Not sure which statements were give to you for this question, but the vehicle's acceleration from noon to 2:00 PM was zero, the vehicle had a positive acceleration between 2:00 pm and 3:00 pm, and the vehicle had a negative acceleration at 4:30 PM.

Explanation:

From 12:00 PM to 2:00 PM, the vehicle traveled at a constant velocity of 70 MPH, meaning there wasn't any change to the speed. The velocity remained the same. An hour later, the velocity of the vehicle increased to 80 MPH, and finally at 4:30 PM, the velocity of the car decreased and was at 40 MPH.

At the bifurcation of the femoral artery the pressure is 100 mm Hg. The venous pressure after either the left or right femoral artery is 10 mm Hg. The resistance in the right femoral artery is 1.67 times the resistance through the left femoral artery. The total flow rate just upstream of the bifurcation is 800 mL/min. How does the flow divide into the left and right femoral arteries

Answers

Answer:

The values are [tex]I_L  =  500.37 \ mL / minutes [/tex]

and [tex]I_r  = 299.63 \ mL / minutes [/tex]  

Explanation:

From the question we are told that  

   The pressure at the bifurcation of the femoral artery is  [tex]P = 100\ mm\ Hg[/tex]

   The pressure at the left or right femoral artery is  [tex]P_r = P_l  =  10 \  mm \  Hg[/tex]

   The resistance in the  left femoral artery is  [tex]R_L[/tex]

   The resistance in the  right  femoral artery is  [tex]R_r =  1.67 R_L[/tex]

   The total  flow rate is  [tex]I = 800 mL/minute[/tex]

The diagram illustrating this question is shown on the first uploaded image

Generally this flow of blood through the artery can be compared to the a circuit as shown on the first uploaded image

Generally the rate at which blood flows through the  left femoral artery is mathematically represented as

      [tex]I_L  =  I * \frac{R_r }{R_L + R_r}[/tex]

=>      [tex]I_L  =  800 * \frac{1.67 R_L }{R_L + 1.67 R_L}[/tex]

=>    [tex]I_L  =  800 * \frac{1.67 R_L }{2.67 R_L}[/tex]

=>    [tex]I_L  =  500.37 \ mL / minutes [/tex]

Generally the rate at which blood flows through the  right  femoral artery is mathematically represented as

      [tex]I_r  =  I * \frac{R_L }{R_L + R_r}[/tex]

=>      [tex]I_r  =  800 * \frac{R_L }{R_L + 1.67 R_L}[/tex]

=>    [tex]I_r  =  800 * \frac{ R_L }{2.67 R_L}[/tex]

=>    [tex]I_r  = 299.63 \ mL / minutes [/tex]    

Tension is actually a force that tends to

Answers

Answer:

Pull towards itself.

Explanation:

That's what I know.

Tension is a force that tends to pull or stretch an object. A flexible material, like a rope, cable, or string, is used to transmit the force.

A force known as tension has a tendency to pull or stretch an object. When a flexible medium, like a rope, cable, or string, is under strain and supporting an imposed load or weight, it transmits force via the flexible medium.

A rope or cable that is under tension receives equal and opposing forces pulling it in different directions at either end. For instance, the tension in a rope will be the same along its whole length if both ends are pulled with equal effort.

When you use a pulley system to hoist a weight, suspend an object from a rope, or support the weight of traffic on a bridge, tension can be present.

Therefore, Tension is a force that tends to pull or stretch an object.

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What is the HORIZONTAL component of a vector with a magnitude of 125 m/s and an angle of 25 degrees?

Answers

Answer:

113.29 m/s

Explanation:

I think its this answer choice, hope I'm not too late answering.

The world record for the 100-meter dash is 9.76 s. What is the runner's average speed?

Answers

Answer:

mine is 9.75 so take that as you will

Explanation:

PLEASE ANSWER QUICK (7th grade science measurment of volume)
Estimate the water volume in the graduated cylinder to the nearest 0.1 mL.

(Remember to read from the bottom of the curved meniscus.)


Answers

Answer : The volume of water in graduated cylinder is 15.5 mL.

Explanation :

As we know that for the measurement of the volume of liquid in graduated cylinder are shown by placing the graduated cylinder on the flat surface and then view the height of the liquid in the graduated cylinder with the naked eyes directly level with the liquid.

The liquid will tend to curve downward that means this curve is known as the meniscus.

In the case of colored liquid, we are always read the upper meniscus of the liquid for the measurement.

In the case of colorless liquid, we are always read the lower meniscus of the liquid for the measurement.

In the given image, there are 5 larger and 5 smaller division between the 15 and 20 and the solution is colored. The value of larger division is 1 mL and smaller division is 0.5 mL.

So, we will read the upper meniscus of the liquid for the measurement.

Hence, the volume of water in graduated cylinder is 15.5 mL.

what are day and night are produced by?

Answers

Answer:

Day and night are due to the Earth rotating on its axis, not its orbiting around the sun. The term 'one day' is determined by the time the Earth takes to rotate once on its axis and includes both day time and night time.

Explanation:

Answer:

Day and night are due to the Earth rotating on its axis, not its orbiting around the sun. The term 'one day' is determined by the time the Earth takes to rotate once on its axis and includes both day time and night time.

note:

your welcome and please answer my question its called part 1 math work if you could do that i will give you 40 points

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The shadiest plots were A and D.What is another possible explanation of the student's data?A) The plots were not all the same size. B) The plots were shady but did not have damp soil. C) Juan and Melissa did not count the worms accurately. D) The earthworms moved when the students started counting. Solve for x9 (x +2) < 3(3-5) Consider a system consisting of two Einstein solids, A and B, each containing N= 10 oscillators, and sharing a total of q= 20 units of energy. Assume that the two solids areweakly coupled and the total energy is fixed.Required:a. How many different macrostates are available to solid A or B?b. How many different microstates are available to the combined system of A & B?c. Starting with the exact form for the multiplicity of an Einstein solid, calculate the probability of finding all the energy in solid A, assuming that the system is in thermal equilibrium. d. Calculate the probability of finding exactly half the energy in solid A. Fill in the blank.There are ____ essential minerals. Tobin is solving the equation 3 (x minus 1.25) = 11.25. His work is shown below.3 (x minus 1.25) = 11.25. 3 x minus 3.75 = 11.25. 3 x minus 3.75 + 3.75 = 11.25 + 3.75. 3 x = 15. 3 x times 3 = 45 times 3. x = 135. PLEASE HELP "The universe God is creating is being set up precisely to support life." How do we see this in Genesis 1? How did the union hope to damage confederate trade and transportation during the civil war? Which sentence uses commas correctly?There is no point complaining about Joan's giggling and snorting, Alison's sarcasm, or Lynnette's obsession with puppies and horses.There is no point complaining about Joan's giggling and snorting Alison's sarcasm, or Lynnette's obsession with puppies and horses.There is no point complaining about Joan's giggling, and snorting, Alison's sarcasm, or Lynnette's obsession with puppies, and horses.There is no point complaining about Joan's giggling and snorting, Alison's sarcasm or Lynnette's obsession with puppies, and horses. Maria and John decide to shop for furnishings for the new house. They choose items that amount to $5600.00. The store has 2 fixed installment simple interest loan options for purchasing:Option 1: 20% down payment and financing at 5% simple interest per year for 3 years. Option 2: no down payment and financing at 5.25% simple interest for 4 years.Answer each of the following questions separately, showing all your work to reach each answer.A. Which option will result in smaller finance charge (interest)? What will that finance charge/interest be?B. Which option will result in the smaller monthly payment on this fixed installment loan? What will that monthly payment be? C. They decide to defer any purchases and invest a $5600 bonus that Maria will be getting from work in a savings account. The APR is 21.6% compounded monthly. How much interest will they earn in 4 years? D. They decide to defer any purchases and loan the $5600 bonus to a needy relative at 1.5% simple interest per year. How long will the term of the loan need to be if they want to earn $500 in interest (assuming the loan is not paid off early). The sum of three consecutive number is 54 Find the first two number.