in △abc, b=51∘, b=35, and a=36. what are the two possible values for angle a to the nearest tenth of a degree?

Answers

Answer 1

The two possible values for angle A to the nearest tenth of a degree are 59.1° and 120.9°.

In △ABC, you are given B = 51°, b = 35, and a = 36. To find the two possible values for angle A to the nearest tenth of a degree, you can use the Law of Sines.


the Law of Sines formula: (a/sin(A)) = (b/sin(B))

Plug in the given values: (36/sin(A)) = (35/sin(51°))

Solve for sin(A): sin(A) = (36 * sin(51°))/35


Calculate sin(A): sin(A) ≈ 0.857

Find the two possible values for angle A:
  a. A = arcsin(0.857) ≈ 59.1°
  b. A = 180° - arcsin(0.857) ≈ 120.9°

So, the two possible values for angle A to the nearest tenth of a degree are 59.1° and 120.9°.

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Related Questions

To divide 20 miles by 5 hours, what conversion should be made to make the calculation correct?Convert miles to hour and then divide the two numbers.Change hours to miles and then divide the two numbers.Divide the two numbers as given--units do not have to be the same when dividing.None of these choices are correct.

Answers

To find

To divide 20 miles by 5 hours, what conversion should be made to make the calculation correct?

Explanation

20 miles refer to the distance travelled

5 hours refers to the time taken

So dividing distance by time would give us speed

Since both are different physicals quantity so their units need not be same.

Conclusion

The correct statement is

Divide the two numbers as given--units do not have to be the same when dividing.

Two factors that greatly affect air resistance on falling objects are frontal area and:_________

Answers

The correct answer is "velocity." Frontal area and velocity are two factors that greatly affect air resistance on falling objects. Air resistance, is the force exerted by air molecules on an object as it moves through the air.

Frontal area refers to the cross-sectional area of the object that is directly facing the direction of motion. Objects with larger frontal areas experience more air resistance because they encounter a greater number of air molecules. However, velocity is another crucial factor.

As the velocity of the falling object increases, the air resistance it encounters also increases. This is because at higher velocities, the object pushes more air molecules aside per unit of time, leading to a greater resistance force. Therefore, both frontal area and velocity play significant roles in determining the magnitude of air resistance experienced by falling objects.

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name five example of derived qualities​

Answers

Answer:

velocity, power, energy, force and density

Explanation:

Hurricanes increase the amount of dead plant material found in bodies of water. this most likely results in-

Answers

Hurricanes are powerful tropical cyclones that form over warm ocean waters. They are characterized by strong winds, heavy rainfall, and storm surges, and can cause significant damage and loss of life.

The increase in dead plant material in bodies of water due to hurricanes is likely to result in a higher nutrient content in the water, which can lead to increased algae growth and decreased oxygen levels. This can also have negative effects on the aquatic ecosystem and the organisms that rely on it. Additionally, the buildup of dead plant material can increase the risk of flooding and water pollution.

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What information is included in the general
profile for a serial killer/ criminal?

How do the 4 different types of serial killers
differ from each other?

Describe the typical childhood of a serial
criminal. What types of childhood trauma is
typically found in the background of serial
criminal?

What types of behavioral changes occur from pre-crime to crime spree to post-crime? Are there any warning signs that begin to committheir crimes?

Answers

A serial killer is one that goes on from one place to another killing people everywhere.

Who is a serial killer?

The information about a serial killer that is documented are;

demographic information, such as age, sex, race, occupation, education level, etc.Behavior patterns include things like the modus operandi (MO), signatures, and criteria for choosing victims, among others.Psychopathy, emotional stability, intellect, and personality disorders are examples of personal traits.criminal history, including prior infractions, arrest records, and sentence.Information on a person's relationships, relationships, and other events are included in their social history.

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A race car traveling at 10 meters per second accelerates at a rate of 1.5 meters per second squared while travelling a distance of 600 meters. The final speed of the race car is approximately

Answers

Answer: 44m/s

Explanation:

For Valentine’s Day Sally received a helium-filled balloon at a party. On returning home she accidently left the balloon in the car. Later she went to get the balloon and found it was partially deflated. After being in the house for an hour she noticed it was fully inflated again. Explain why this happened.

Answers

Answer:

The helium molecules move closer together when it's cold causing the balloon to deflate

Explanation:

The possible reason behind it is: the temperature of outside was low, so the Helium gas inside the balloon compressed and  it was partially deflated at the car. When she returned to the house, temperature of the gas of the balloon rises again and  it was fully inflated again.

What is Charles' law of gas?

The experimental gas law known as Charles' law, commonly referred to as the law of volumes, illustrates how gases tend to expand when heated. Charles's law can now be expressed as follows:

The Kelvin temperature and the volume will be directly proportional when the pressure on a sample of a dry gas is kept constant.

This direct proportional relationship can be expressed as follows:

V∝T.

Hence, as the temperature is low outside the house, the balloon was partially deflated at the car and the temperature rises again when it was inside the house, so  it was fully inflated again inside the house.

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a 675-n marine in basic training climbs a 11.5-m vertical rope at a constant speed in 7.50 s. what is his power output?

Answers

The power output of the marine during the vertical climb of 11.5 m at a constant speed in 7.50 s is 1024.4 W. 

Power is the rate of doing work or the rate of transfer of energy in a unit time. Power is given by the expression:

P = W/t

where, P is power measured in watts (W), W is work done measured in joules (J), t is time taken measured in seconds (s).

The formula for work done is given by the expression:

W = F × d

where, F is the force applied measured in newtons (N), d is the distance traveled measured in meters (m)

The power of the marine in basic training during the climb is given by the expression:

P = W/t

P = F × d/t

From the question, the force (F) acting on the marine is equal to his weight (W). The weight (W) of the marine is given by the expression:

W = mg

where, m is the mass of the marine measured in kilograms (kg), g is the acceleration due to gravity which is 9.8 m/s²

On substituting the values given:

W = mg

W = 675 N (given)g = 9.8 m/s²

Hence, W = 675 × 9.8 = 6615 J

The distance (d) traveled by the marine is given as 11.5 m. The time (t) taken to travel the distance is given as 7.50 s.

Substituting the values given:

P = F × d/t

P = W/t

P = (mg × d)/t

P = (6615 × 11.5)/7.50P = 1024.4 W

Therefore, the power output of the marine during the vertical climb of 11.5 m at a constant speed in 7.50 s is 1024.4 W.

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Có mấy cách đo đại lượng vật lí

Answers

Answer:

please write in english

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Answers

formula for net force: force= mass x acceleration


If
you weigh 140 pounds, what is your weight in kilograms

Answers

If you’re 140lb pounds in weight then the kilograms will be (63.503) in kilograms

A particle is projected horizontally at 10 m/ from the top of a tower 20 m high. Calculat the horizontal distance travelled by the particle when it hits the level ground. [g = 10 m/s] ​

Answers

25.1 m is the horizontal distance travelled by the particle when it hits the level ground

v²-u²=2gs

s=v²-u²/2g

s=100/19.6

s=5.1 m

total height=20+5.1=25.1 m

Distance, which is independent of direction, is the length between two points or things. Distance solely considers the overall magnitude and disregards the start and finish places because it is a scalar attribute. Distance can only have a positive or zero value because it is a scalar attribute; it cannot be negative.

The meter (m) is the most widely used unit of measurement for distance, however kilometers (km) can also be used to describe longer distances and centimeters (cm) or millimeters can be used to express shorter distances (mm). The distance traveled is frequently represented by the letter D when computing distance.

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Select an item that is common in our society that you believe is elastic and, using two determinants of elasticity (pages 133-134), briefly explain why you believe this product is elastic.
Select an item that is common in our society that you believe is inelastic and, using two determinants of elasticity (pages 133-134), briefly explain why you believe this product is inelastic. Expectations are a minimum of one paragraph (4 to 5 sentences) for each question in the initial post.

Answers

There are no immediate substitutes for gasoline as public transportation is often limited and walking, biking, or taking a cab is not always feasible. Therefore, people may continue to purchase gasoline despite an increase in price.

One item that is common in our society that I believe is elastic is fast food. Elasticity is the degree to which changes in price affect demand for a good or service.

Fast food is elastic because it has many substitutes such as restaurants, home-cooked meals, and even other fast-food chains. Fast food is also highly responsive to price changes, which means that a small change in price can cause a large change in demand.

For example, a $1 price increase for a burger meal at a fast-food chain might cause many people to switch to a competitor with a cheaper price. Thus, fast food is an elastic product in our society.One item that is common in our society that I believe is inelastic is gasoline.

Gasoline is an inelastic product because it has few substitutes and people need it for transportation. If the price of gasoline increases, people may continue to purchase it even if it means spending more money because there are few alternative options.

Additionally, there are no immediate substitutes for gasoline as public transportation is often limited and walking, biking, or taking a cab is not always feasible.

Therefore, people may continue to purchase gasoline despite an increase in price.

For example, if the price of gasoline increases by $1, a consumer will still purchase gasoline because they require it to get to work or school. Thus, gasoline is an inelastic product in our society.

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One item in our society that I believe is elastic is the price of gasoline  because of  various alternatives to gasoline and the proportion of income spent. An item in our society that I believe is inelastic is medical treatment because of the necessity of medical treatment and lack of substitutes.


Firstly, the availability of substitutes contributes to the elasticity of gasoline. In our society, there are various alternatives to gasoline, such as electric vehicles or public transportation. When the price of gasoline increases, consumers have the option to switch to these substitutes, reducing their demand for gasoline. Conversely, when the price of gasoline decreases, consumers may choose to drive more or purchase larger vehicles, increasing their demand for gasoline. This flexibility in consumer choices demonstrates the elasticity of gasoline.

Secondly, the proportion of income spent on the product also influences the elasticity of gasoline. For many individuals, the cost of gasoline represents a significant portion of their overall budget. When the price of gasoline rises, consumers may have to make adjustments to their spending habits or seek alternative means of transportation to cope with the higher expenses. Conversely, when the price of gasoline decreases, consumers may have more disposable income to spend on other goods and services. This sensitivity to price changes further supports the elasticity of gasoline.

On the other hand, an item in our society that I believe is inelastic is medical treatment. Two determinants of elasticity that contribute to this belief are the necessity of the product and the lack of substitutes.

Firstly, the necessity of medical treatment makes it an inelastic product. When individuals require medical treatment, they often have no choice but to seek the necessary healthcare services regardless of the price. This is especially true for life-saving procedures or medications. The demand for medical treatment is driven by the urgency and importance of preserving one's health, which leads to a less responsive consumer behavior to price changes.

Secondly, the lack of substitutes also contributes to the inelasticity of medical treatment. In many cases, there are limited alternatives or substitutes available for specific medical treatments. For example, if a person requires a specific surgery or medication to treat a condition, they cannot easily switch to a different treatment option to lower their expenses. The lack of viable substitutes reduces consumer choice and makes the demand for medical treatment less responsive to changes in price.

In summary, the price of gasoline is elastic due to the availability of substitutes and the proportion of income spent on the product. On the other hand, medical treatment is inelastic due to its necessity and the lack of substitutes. These determinants of elasticity highlight the different levels of responsiveness to price changes in these two common items in our society.

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The Earth's _____
is what gives us day and night

1. Orbit
2. Rotation
3.Revolution

Answers

Answer:

rotation

Explanation:

............................

Answer: 2nd option, Rotation

I hope this helps, and Stay Safe! :)

Did you know that I’m up in 355 mL can of diet pepper will float in a lake that’s a fact however it’s also a fact that I don’t pay 355 mL can of regular pepper will sink in the same lake based on these two facts, which type of soda is the least dense

Answers

Yes, I'm aware of the fact that a 355 mL can of diet pepper will float in a lake, while a 355 mL can of regular pepper will sink. Based on this observation, we can conclude that diet soda is less dense than regular soda.

Density is defined as the amount of mass per unit volume of a substance. In this case, the density of diet soda is lower than regular soda because the former contains artificial sweeteners that have lower mass than the sugar used in regular soda.

As a result, a can of diet soda displaces less water than the same volume of regular soda, causing it to float while the regular soda sinks.

It's worth noting that the density of soda can also be affected by other factors, such as temperature and pressure. Additionally, density is not the only factor that determines whether an object will float or sink in a fluid. The shape and size of the object, as well as the properties of the fluid, also play a role.

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A bullet is fired through a board 10 cm thick in such a way that the bullet's line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 400 m/s and it emerges from the other side of the board with a speed of 300 m/s, what is the total time the bullet is in contact with the board? Label your answer. To write an exponent in your answer, please type it like this: 10^3.

Answers

The total time the bullet is in contact with the board is 8 x 10^-5 seconds

How to calculate?

V1 = 400ms − the initial velocity of the bullet;

V2 = 300 ms− final velocity of the bullet;

d = 10cm = 0.1m − thickness of the board;

a − acceleration inside the board.

t − total time that the bullet is in contact with the board

To find the total time that the bullet is in contact with the board we can use formula :

t =  V1 -V2 / a

where a has been found to be 1.25 x 10^6 m/s²

Substituting the values, we have that total time that the bullet is in contact with the board = 8 x 10^-5 seconds

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The lamps in circuit drawn below are all identical, Each of the cells have a potential difference of 1.5 volts What is the potential difference across the 3 cells that are joined in series

Answers

Answer:

4.5V

Explanation:

In a arrangement of cells, the cells could be joined end to end(series) or to a common junction (parallel).

When cells are joined in series, the total emf of the cell is the sum of the individual emf of all the cells.

Hence;

Total emf = 1.5V + 1.5V + 1.5 V = 4.5 Volts

how long do you need to make an whose fundimental freqency is a c sharp? the pipe is closed on one end and the seed of sound in air is 340 m/s

Answers

According to the given statement we need a closed pipe with a length of 0.92 meters to produce a C sharp note with a frequency of 277 Hz.

To determine the length of a pipe that produces a C sharp note, we need to consider the frequency of the note and the speed of sound in air. C sharp has a frequency of 277 Hz, which means that the sound wave vibrates 277 times per second.
The formula to calculate the length of a closed pipe that produces a specific frequency is L = (4/3) x wavelength, where wavelength = 2 x length of the pipe. We can rearrange the formula to calculate the length of the pipe:
Length of pipe = wavelength/2 = (3/4) x wavelength
The wavelength of a sound wave can be calculated by dividing the speed of sound by the frequency of the note:
Wavelength = Speed of sound/frequency = 340 m/s / 277 Hz = 1.23 m
Therefore, the length of the pipe needed to produce a C sharp note with a frequency of 277 Hz is:
Length of pipe = (3/4) x 1.23 m = 0.92 m
In summary, we need a closed pipe with a length of 0.92 meters to produce a C sharp note with a frequency of 277 Hz.

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When you blow across the top of an open tube or pluck a tightly bound string, the lowest frequency produced is the fundamental (1st harmonic). The wavelength of the wave produced is ___________ the length of the tube or string.

Answers

When you blow across the top of an open tube or pluck a tightly bound string, the lowest frequency produced is the fundamental (1st harmonic). The wavelength of the wave produced is _twice_ the length of the tube or string.


Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.
1. When you blow across an open tube or pluck a tightly bound string, a standing wave is created.
2. The fundamental frequency (1st harmonic) is the lowest frequency that can be produced by the system.
3. For an open tube or a tightly bound string, the fundamental frequency has a wavelength that is twice the length of the tube or string.
4. This occurs because the wave must travel down the tube/string and then reflect back, creating a complete wavelength that is double the original length.

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1. If you add air to a flat tire through a single small entry hole, why does the air spread out to fill the tire?

Answers

Answer:

The tire fills up just like anything else that holds air when u pump a ball or tire up it fills all the way up cause it is a small confined space and after filling it with air the atoms of the air fill the tire up

Explanation:

Mention 3 scientists that has worked in the field of electricity

Answers

Answer:

Benjamin Franklin, Michael Faraday, and Thomas Edison made important contributions to our understanding of and harnessing of electricity.

2/4 points (graded) you stand on a spherical asteroid of uniform density whose mass is kg and whose radius is 10 km. these are typical values for small asteroids. (a) how fast do you have to throw a rock straight up so that it never comes back to the asteroid and ends up traveling at a speed of 3 m/s when it is very far away?

Answers

To throw a rock so that it never comes back to the asteroid and ends up traveling at a speed of 3 m/s when it is very far away, you need to throw it with a speed of at least 7.14 m/s.

To throw a rock so that it never comes back to the asteroid and ends up traveling at a speed of 3 m/s when it is very far away, you need to calculate the escape velocity of the asteroid.

Escape velocity (ve) is equal to the square root of 2GM/R, where G is the Gravitational constant (6.674 x 10-11 m3/kg s2), M is the mass of the asteroid (kg), and R is the radius of the asteroid (10 km).

So, to calculate the escape velocity,

you need to use the equation:

ve = sqrt (2GM/R) = sqrt (2 x 6.674 x 10-11 x kg/10,000 m) = 7.14 m/s.

Therefore, to throw a rock so that it never comes back to the asteroid and ends up traveling at a speed of 3 m/s when it is very far away, you need to throw it with a speed of at least 7.14 m/s.

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A 0.50-kilogram ball is thrown upward with an initial kinetic energy of 25 joules. Approximately how high will the ball rise

Answers

The height will the ball rise when a 0.50-kilogram ball is thrown upward is 5.1 meters.

Given,

Mass = 0.5 kg

Kinetic energy = 25 joules

Potential energy = mgh = 25

                              = 0.5 × 9.8 × h = 25

                               = 5.1 meters

In general, the work done by a force on an object between two points does depend on the path taken by the object between the two points. For the special case of conservative forces, we have seen that the work does not depend on the path.

Therefore, we can define, for conservative forces, an associated potential energy that, for a given object, depends only on its location. In particular, when a conservative force acts on an object as it moves between two points, we define the define the change in potential  energy associated with that force as minus the work done by that force between those two  points.

kinetic energy of the ball was equal to the work done by the gravitational force. By our definition, the change in gravitational potential energy is equal to minus the work done by the gravitational force.

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which of these can help determine air pressure? select the two correct answers.a. wind speed of the air
b. moisture in the air
c. temperature of the air
d. cloud patterns in the air

Answers

The two factors that can help determine air pressure are the temperature of the air and the cloud patterns in the air that are in options c and d, because wind speed and moisture content of the air are not direct measures of air pressure.

What is the air pressure?

It depends upon the temperature, as when the temperature increases, air molecules gain energy and move faster, leading to a decrease in air pressure, and as the temperature decreases, there is an increase in air pressure. Some clouds are present at low air pressure, while others are at high air pressure.

Hence, the two factors that can help determine air pressure are the temperature of the air and the cloud patterns in the air that are in options c and d, because wind speed and moisture content of the air are not direct measures of air pressure.

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which particles act together to make atoms behave as solids

Answers

Question

Which particles act together to make atoms behave as solids

Answer:

Electrons. Mutually repel elections of other atoms when they get close

Explanation:

A demonstration of the behavior of particles as solids, liquids and gases. Crystals, on the other hand, aren't at all haphazard. Particles are held together by forces of attraction. Protons (+) and Electrons (-) Which subatomic particles act together to make atoms behave as a solids because they are found buzzing around the nucleus.

which statement best explains the genetic variation that results from sexual reproduction

a. each chromosome contains many copies of the same gene

b. offspring receive genes that are exactly the same as one parent’s genes

c. each chromosome contains many different genes

s. offspring receive a mix of genes from two different parents

Answers

Answer:

S. offspring recieve a mix of genes from two different parents

Offspring acquire genes that are exactly the same as one parent’s genes. Option B is correct.

Given that,
To choose the statement best explains the genetic variation that results from sexual reproduction.

What is sexual reproduction?

Sexual reproduction is the process of creating new organisms by combining the genetic details of two individuals of different genders. The genetic details in most animals is carried on chromosomes in the nucleus of reproductive cells called gametes, which unite to form a diploid zygote.

Here,
The solution is due to the fact that each parent has two distinct sets of genes. Furthermore, each parent only passes on half of their DNA to their offspring. And that the half that is passed on is arbitrary. All of this ensures that each child is born with a distinct set of genes.

Thus, Offspring acquire genes that are exactly the same as one parent’s genes. Option B is correct.

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world class speed skaters can skate a 3,000 meter course in about 4 minutes. what is their average speed for this course?

Answers

Answer: 12.5 m/s.

v = d/t

(60 s/1 min)*(4 min) = 240 s

v = 3000 m/240 s  

v = 12.5 m/s  

Which of the following is an example of a transverse wave?
A. longitudinal waves traveling through the ground
B. sound waves traveling through the air
C.light waves traveling from the sun
D.All of these

Answers

Answer:

all of these

Explanation:

D. all of these is the correct answer

What engineering problem was presented in the study?
A. The lightbulbs were too bright.
B. The lightbulbs were too dim.
C: The lightbulbs were exploding after several minutes of use.
D. The lightbulbs were burning out after only a few hours of use.

Answers

Answer:

The lightbulbs were exploding after several mins of use

Explanation:

Answer:

the lightbulbs were exploding after several minutes of use

Explanation:

a p e x :))

2. Speed limits on curves help to reduce the effect of ........force on a vehicle
A. enertia
b. centrifugal
c. gravity

Answers

Answer:

enertia

Explanation:

enertia

The correct answer is (B) Centrifugal Force

The centrifugal force on a vehicle on the curves is outwards or can say away from the curve and pulls the out of the track.

the centrifugal force is given by \(F=\frac{mv^{2} }{r}\), which is directly proportional to speed v.

Speed limits on the curves help in reducing the centrifugal force by reducing the speed.

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3 Mariana wants to put 6 feet of border across the top of a wall. 4 She has 3 9 feet of border. What fraction of the project can she complete? Enter your answer in the boxes. Which of the following accurately describes the period known as the Middle Ages or Medievalperiod?A. Europe between the rise of the Roman Empire and its fallB. World history between the fall of Constantinople and the RenaissanceC. Western Europe between the rise of Christianity and the rise of IslamD. World history between the fall of the Roman Empire and the Renaissance Do the most energetic forms of waves have high amplitudes and long wavelengths I have a late assignment Please help!! Taking notes on a customer complaint is a form a communication. please select the best answer from the choices provided t f if we know that t.05= 1.812 when df = 10, then it is correct to say what is a benefit of following the recommended daily allowances for carbohydrates? How could you describe the universe milliseconds after the Big Bang? A)cool and thinB)two dimensionalC)hot and denseD)flat and freezing Which formula should be used to correctly calculate the monthly mortgage payment? m = p startfraction left-bracket r (1 minus r) superscript n baseline right-bracket over (1 r) superscript n baseline endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction r over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over (n r) endfraction 12. Uche bought two books at A125 each. She wasgiven A1,000 note. What will be - her balanceamount?A. N75 B. N100 C. N250D. N750 E. 1000 Which statement is true about problem-focused coping? A) Problem-focused copying does not make any attempt to remove the stressful situation I am not to familiar with diameter and radius, please help with 2. two charges create 8.00 N of electric force on each other. if you increase their distance to twice its original value, how much electric force do they exert on each other Jerome wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 7 1/2 m by 3 1/4 m. Find the area the grass seed needs to cover. PepsiCo divested its group of fast-food restaurant businesses (KFC, Pizza Hut, and Taco Belly to Yum! Brands in order to allow PepsiCo to focus on its core soft drink and snack-food businesses. A useful guide to determine whether or when to divest a business subsidiary is to ask. a. "Can't we derive a parenting advantage with these businesses?" b. "Do we need to do the math to achieve 1-1 = 3 outcomes from these diversified businesses?" c. "If we were not in this business today, would we want to get into it now?" d. "Have we missed the opportunity to milk these cash cows?" e. "Will these three businesses pass the cost-of-exit' test? To find the number in a square, multiply the numbers in the two circles connected to it. Fill in the missing numbers. When Mrs. Harris was at the grocery store, she selected several peaches to purchase. She weighed them on a scale in the produce department and the scale read 1.75 pounds. When she checked out, the electronic scale read 2.0 pounds. What was the percentage of error between the two scales? im tired and want to go to bed so plz help CAN SOMEONE HELP ME OUT PLEASE AND THANK YOU Use the Method of Integrating Factor to find the general solution of the differential equation x + ( +7 + ) v = = y' for t > 0. of the physical features listed, which is associated with the greatest earthquake hazard? view available hint(s)for part b select show physical labels. of the physical features listed, which is associated with the greatest earthquake hazard? great lakes great plains appalachian mountains colorado plateau sierra nevada