I don’t understand can you help me please

I Dont Understand Can You Help Me Please

Answers

Answer 1
-3(12) = (x-6/-3)
-36 = x-6 / -3
108 = x - 6
114 = x

Related Questions

If you go up to your attic on a summer day, which best explains why you may feel very hot?

A Conduction caused hot air to rise to the top of your house.
B Convection caused hot air to rise to the top of your house.
C The attic is insulated from the cooler temperatures below.
D None of the above

Answers

Answer:

Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.

Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.

Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.

Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.

ion:

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answers

The three options of exterior angles are m∠5 + m∠6 =180°,

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

What is an exteriοr angle?

The angles that are created οutside οf a triangle are its exteriοr angles. In οther wοrds, the angle fοrmed between οne οf a triangle's sides and its adjacent extended side is the triangle's exteriοr angle.

Given that the exteriοr angles are m∠1, m∠4, and m∠6.

The interiοr angles οf the triangle are angles m∠2, m∠3, and m∠5.

The sum οf all angles οf a triangle is 180°.

Thus m∠2 + m∠3 + m∠5 = 180°

The interiοr angle and the cοrrespοnding exteriοr angle in a triangle make up a linear pair. Exteriοr Angle plus Interiοr Angle equals 180°, sο.

The exteriοr angle at angle 5 is angle 6.

Thus m∠5 + m∠6 =180°

The interiοr and exteriοr angles that make up a triangle are always added tοgether tο fοrm the exteriοr angle. The term "exteriοr angle prοperty" refers tο this feature. If twο triangles' cοrrespοnding angles tend tο be cοngruent and their side lengths are prοpοrtiοnal, any twο triangles will be similar tο οne anοther.

The οppοsite interiοr angles οf m∠6 are m∠2,  m∠3.

Thus m∠2 + m∠3 = m∠6

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PLEASE HELPPPP FAST In the picture below, find the value of a.

Answers

Answer:

A should be 180 - 68 which is 112 degrees

Step-by-step explanation:

Answer:a=108

Step-by-step explanation:

140+(180-60)+(180-84)+(180-68)=140+120+96+112=260+208=468

sum of angles are 540, so,

540-468=180-a

72=180-a

a=108

A homeowner is building a patio with concrete blocks. The blocks are 11" x 10" x 6". The blocks are in a stack at the store that is 60" x 55" x 54". How many blocks are in a stack?

Answers

According to the question, if the blocks are 11" x 10" x 6" and the blocks are in a stack at the store that is 60" x 55" x 54" then there are 270 blocks in the store.

Given that dimensions of the blocks and the store :-

Block :- 11" x 10" x 6"

Store :- 60" x 55" x 54"

To find the number of blocks in a stack we need to first calculate the volume of the block as well as the store.

This, Volume of block = 11 x 10 x 6 = 660

and, Volume of the store = 60 x 55 x 54 = 178200

Therefore, the number of blocks would be = Volume of the store / Volume of block

No. of block = 178200/660

No. of block = 270

Hence Number of blocks stored in the stack at the storeroom is 270 blocks.

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averaged 462 raindrops over an area of 55 square meters. A nearby picnic table has an area of 1 square meter. Use the Poisson distribution to find the probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles. Do not round intermediate computations, and round your answer to three decimal places.

Answers

The probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles is 0.066, rounded to three decimal places.

We can model the number of raindrops that fall on the picnic table as a Poisson distribution with parameter a, where a is the expected number of raindrops that fall on a 1 square meter area during a rainstorm. Since 462 raindrops fell over an area of 55 square meters, the average number of raindrops per square meter is:

a = 462/55 ≈ 8.4

Therefore, the probability that exactly 11 raindrops fall on the picnic table during a rainstorm is:

P(X = 11) = (eᵃ * a¹¹) / 11!

= (e⁻⁸ ⁴ * 8.4¹¹) / 11!

≈ 0.066

Rounding to three decimal places, we get the probability that exactly 11 raindrops fall on the picnic table as 0.066.

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A bicycle manufacturer makes two styles of bicycles: a road bike and a touring bike. The road bike
sells for $400 and the touring bike sells for $200. To meet the minimum requirements of a supply
contract, the manufacturer needs to produce at least 60 road bikes and at least 120 touring bikes.
Each bicycle is produced using the same frames and tires. The touring bike takes one hour of labor
for assembly and painting, while the road bike takes 3 hours of labor. There are 400 frames and 600
hours of labor available for production. How many of each model should be produced to maximize
revenue? What is the maximum revenue?

Answers

The manufacturer can maximize their revenue by producing 60 road bikes and 120 touring bikes. The maximum revenue of the manufacturer is $24,000.

What is revenue?

Revenue is the total amount of money earned by a business from its activities. It is calculated by subtracting the cost of goods sold from the total sales of goods and services. Revenue indicates how well a company is doing financially and serves as a key indicator of a company's performance. Revenue is an important factor in calculating the company's profitability.

This satisfies the minimum requirements of the supply contract, while also utilizing all of the available resources, frames and labor.

The total cost of producing 60 road bikes and 120 touring bikes is 400 frames and 900 hours of labor. This leaves no frames or labor unused. The total revenue from selling these bicycles is $24,000 (60 x $400 + 120 x $200). Therefore, the maximum revenue of the manufacturer is $24,000.

To maximize their revenue, the manufacturer should produce 60 road bikes and 120 touring bikes. This will ensure that all of their resources are used and they will get the highest return on their investment. This will also help them meet the minimum requirements of the supply contract.

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Can someone pretty please help me

Answers

Answer: [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

7+3(5-4)=10

2+1=3

Therefore, 10/3.

Given:-

[tex] \sf \: u = 2 [/tex]

[tex] \: [/tex]

[tex] \sf \: v = 5[/tex]

[tex] \: [/tex]

Solution:-

[tex] \sf \: \frac{7 + 3 ( v - 2u ) }{u + 1} [/tex]

[tex] \: [/tex]

put the given values in the equation

[tex] \sf \: \frac{7 + 3 ( 5 - 2 ( 2 )}{2 + 1} [/tex]

[tex] \: [/tex]

[tex] \sf \: \frac{7 + 3 ( 5 - 4 )}{3} [/tex]

[tex] \: [/tex]

[tex] \sf \: \frac{7 + 15 - 12 }{3} [/tex]

[tex] \: [/tex]

[tex] \sf \: \frac{7 + 3}{3} [/tex]

[tex] \: [/tex]

[tex] \boxed{ \sf \color{hotpink} {\frac{10}{3} }}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

If the length is 3 times longer than the width in a rectangle with an area of 36 cm, what is the width

Answers

In a rectangle having an area of 36 cm, if the length is three times more than the width of the rectangle is approximately 3.46 cm.

Let's assume that the width of the rectangle is "w" cm-

According to the problem, the length of the rectangle is three times longer than the width. Therefore, the length of the rectangle would be 3w cm.

The area of the rectangle is given as 36 cm². We know that the formula for the area of a rectangle is A = length x width.

So, we can substitute the values we have and get:-

36 = (3w) x w

Simplifying the equation, we get:-

36 = 3w²

Dividing both sides by 3, we get--

12 = w²

Taking the square root of both sides, we get--

w = √12

w ≈ 3.46

Therefore, the width of the rectangle is approximately 3.46 cm.

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Solve 3x − 2 = 37. Group of answer choices 2 5 7 9

Answers

Answer:

x = 13

Step-by-step explanation:

To find the value of x we need to isolate it! To do this we have to get rid of any other value around it...

Firstly we need to get rid of the ' -2 '. We have to add 2 to both sides!

3x -2 + 2 = 3x37 + 2 = 39

Now we are left with 3x = 39 so we have to get rid of the 3. We have to divide 3 from both sides!

3x ÷ 3 = x39 ÷ 3 = 13

x = 13!

Hope this helps, have a lovely day! :)

the international average salary income database provides a comparison of average salaries for various professions. the data are gathered from publications and reports obtained directly from government agencies (such as the us bureau of labor statistics) or from the international labour organization. suppose an industrial/organizational psychologist is interested in the relationships between job satisfaction, job performance, and job compensation. she has data from five different countries on the average monthly salaries paid to accountants. she begins her analysis by converting all of the salary data into us dollars:

Answers

To convert the salary data from different countries into US dollars, the industrial/organizational psychologist would need to use the exchange rates between each country's currency and the US dollar. Exchange rates are the value of one currency in terms of another currency.

For example, if the exchange rate between the US dollar and the British pound is 1.38, this means that one US dollar is worth 1.38 British pounds. So, to convert the average monthly salary of an accountant in the UK into US dollars, the psychologist would divide the salary in pounds by the exchange rate.
Once the psychologist has converted all of the salary data into US dollars, she can then compare the average monthly salaries of accountants across the five different countries and analyze the relationships between job satisfaction, job performance, and job compensation.

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(12x^3 + 9x^2 -3) ÷ 3x

A. 12x^2 +3x-1/x
B. 4x^2+3x-1/x
C. 4x^2+6x-1/x
D. 4x^2 + 3x 1

Answers

The solution to the expression (12x³ + 9x² - 3) / 3x is (4x³ + 3x² - 1) / x

What is an equation?

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Given the expression:

(12x³ + 9x² - 3) / 3x

To solve, we need to factorize the numerator to get:

= 3(4x³ + 3x² - 1) / 3x

= (4x³ + 3x² - 1) / x

The solution to the expression is (4x³ + 3x² - 1) / x

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Can someone please explain how to solve this step by step really stuck

Answers

Answer:

[tex]x=\frac{b-a}{ab}[/tex]

Step-by-step explanation:

[tex]\frac{1}{ax} -\frac{1}{bx} =1\\\frac{1}{ax} *\frac{b}{b} -\frac{1}{bx} *\frac{a}{a} =1\\\frac{b}{abx} -\frac{a}{abx}=1\\\frac{b-a}{abx}=1\\b-a=abx\\x=\frac{b-a}{ab}[/tex]

Eman is planning to sell wind chimes at the craft fair. The cost of her tools for selling wind chimes is 130$. The costs of materials 10$ per wind chime. What is the total cost to make 100 wind chimes?

Answers

Therefore, the total cost to make 100 wind chimes is 14,000$.

What is equation?

In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it.

Here,

The cost of making one wind chime is 10 + 130 = 140$.

To make 100 wind chimes, the total cost would be:

100 x 140 = 14,000$.

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(x+2)(2x-3)=5(x+2)...

Answers

Answer:

Step-by-step explanation:

x = 4 or x = -2

Open the bracket
I’ve sold it for you, let me know if you have a question

1. a. List the sample space for the experiment: "Toss three
coins."
b. List the elements of the event, E: "Get exactly two
heads"
c. What is the probability of the event, E
2. If you toss two dice, what is the probability that the sum is
a. 10?
b. a divisor of 10?

Answers

The probability of getting a sum that is a divisor of 10 is:P(sum is a divisor of 10) = 4/36= 1/9.

The sample space for the experiment "Toss three coins" is given by:{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}b. The event, E: "Get exactly two heads" consists of the following elements:{HHT, HTH, THH}c. The probability of the event, E: "Get exactly two heads" is given by:P(E) = number of favorable outcomes / number of possible outcomes= 3/8For the experiment of rolling two dice, the sample space is given by the set of all possible ordered pairs {(i, j)}, where i and j are numbers from 1 to 6. Thus, the sample space contains 6*6 = 36 elements.a. For the sum to be 10, the pairs that satisfy the condition are (4, 6), (5, 5), and (6, 4). Thus, the probability of getting a sum of 10 is:P(sum = 10) = 3/36= 1/12b. For the sum to be a divisor of 10, we need the pairs (2, 8), (4, 6), (6, 4), and (8, 2). Thus, the probability of getting a sum that is a divisor of 10 is:P(sum is a divisor of 10) = 4/36= 1/9.

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how do i find the center and radius of the given circle

Answers

There are multiple ways to find the center and radius of a circle, depending on what information your provided.

Method 1: Reading the standard equation of a circle

Equation of a circle: [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

where h is the center's x-coordinate, k is the center's y-coordinate, and r is the radius. Here's an example:

[tex](x-5)^{2} +(y+2)^{2} =25[/tex]

In this case, the center would be (5,-2) and the radius is 5

Method 2: Reading a graph

In the attached graph, there is a circle with a labeled center point. The radius can be found by finding the distance from the center to a different point on the circle.

Distance Formula:

[tex]D = \sqrt{ (x_{2}-x_{1}) ^{2} + (y_{2}-y_{1}) ^{2}}\\[/tex]

The first point we use will be the center ( 5 , -2 ), and the second point will be a point on the circle, (10,-2).

[tex]r = D = \sqrt{ ((10)-(5)) ^{2} + ((-2)-(-2) )^{2}}\\r = D = \sqrt{ (5 ^{2} + 0)^{2}}\\r = D = \sqrt{25}\\r = 5[/tex]

Next, plug in the values into the standard equation of a circle formula

[tex](x-5)^{2} +(y+2)^{2} =5^2[/tex]

Simplify

[tex](x-5)^{2} +(y+2)^{2} =25[/tex]

Help me please!!!
Line A has equation y = -4x + 1 and line B contains the points (-2,1) and (1,-11). Select any statement(s) below that are true.


Line B has a slope of -5.


Line A has a slope of -4.


Line A and line B have the same slope.


Line B has a flatter slope than line A.


Line A has a flatter slope than line B.

Answers

In response to the question, we may say that  Line A has a slope of -4, which is lower than that of line B.

what is slope?

The slope of a line determines how steep it is. A mathematical expression for the gradient is gradient overflow. The vertical change (run) between two spots is divided by the height change (rise) between the same two locations to get the slope. The equation of a straight line, written as y = mx + b, is represented by the curve form of an expression. The inclination is m, b is b, and the line's y-intercept is located at these points (0, b). As an example, consider the y-intercept and slope of the equation y = 3x - 7. (0, 7). The y-intercept is situated when the slope of the path is m, b is b, and (0, b).

With the two provided points, we must first establish whether of the following claims is true:

Slope of line B = (Y) / (X) = (-11 - 1) / (1 - (-2)) = -12 / 3 = -4

As a result, we can identify the following claims as being true:

The slope of line B is -5. (False)

The slope of line A is -4. (Really) The slope of lines A and B is the same. (False) Line B slopes more gently than line A. (False) Line A slopes more gently than line B. (True)

The following propositions are true:

Line A has a slope of -4, which is lower than that of line B.

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Please i need this answer right now
Please write the answer with clear explanation also​

Answers

Answer:

orange box = [tex]1 \frac{1}{4}[/tex]

blue box = [tex]1\frac{3}{4}[/tex]

Step-by-step explanation:

We are counting up in quarters (1/4) so we add 1/4 (or a quarter) on every time.

1/4 + 1/4 = 2/4 = 1/2 (equivalent fractions)

2/4 + 1/4 = 3/4

3/4 + 1/4 = 4/4 = 1 whole = 1

1 + 1/4 = 1 1/4 = orange box

1 1/4 + 1/4 = 1 1/2 or 1 2/4

1 2/4 + 1/4 = 1 3/4 = blue box

etc

hope this makes sense.

the data are a random sample from the population of interest. the sample size is less than 10% of the population size. the population distribution is approximately normal. np > 10 and n(1 - p) > 10 more than one condition is violated.

Answers

From the given data, we can see that only one condition is violated, which is the sample size being less than 10% of the population size. The other conditions, such as the population distribution being approximately normal, np > 10, and n(1-p) > 10, are all satisfied. Therefore, the statement "more than one condition is violated" is incorrect.

Only one condition is violated in the given data, which is the sample size being less than 10% of the population size. The other conditions are all satisfied and do not violate any of the conditions for a representative sample.

It is important to note that in order for a sample to be representative of the population, the sample size should be at least 10% of the population size. If the sample size is less than 10% of the population size, the sample may not accurately represent the population and the results may be biased.

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First person to answer gets brainilest.

Answers

Answer:

74 + 4 π ft^2

Step-by-step explanation:

Just a bit of a piecemeal.

2 rectangles and a half circle. We have all the dimensions.

1. Let's solve the big one first A = lw, putting in the numbers A = 4*15 = 60

2. The smaller one A = lw, putting int eh numbers A = 2 * 7 = 14

3. Now, the semi-circle. We know the diameter by deducting 12 from the total length, which is 9 + 7 = 16 in = 4 ft

The radius of the circle is half of the diameter, so the radius is 2 ft

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Substituting the values, we get:

A = π(2)^2

A = 4π

The area of the circle is 4π square ft^2

Add: 60 + 14 + 4π = 74 + 4 π ft^2

A father's age is four times the age of his daughter. After 5 years his age would be three times his daughters age. After 5 more years , how many times of his daughter age his age would be

Answers

If a father's age is four times the age of his daughter.. After 5 more years , his age would be 5 times his daughter's age at that time.

Let's use D to represent the daughter's current age and F to represent the father's current age.

We know that the father's age is four times the age of his daughter, so we can write an equation to represent this relationship:

F = 4D

We also know that after 5 years, the father's age would be three times his daughter's age, so we can write another equation to represent this:

F + 5 = 3(D + 5)

Now we can substitute the first equation into the second equation to get an equation with only one variable:

4D + 5 = 3(D + 5)

Simplifying the equation, we get:

4D + 5 = 3D + 15

Subtracting 3D and 5 from both sides, we get:

D = 10

Therefore, the daughter's current age is 10 years old. We can use the first equation to find out the father's current age:

F = 4D = 4(10) = 40

After 5 more years, the father's age would be:

F + 5 + 5 = 40 + 10 = 50

In summary, after 5 more years, the father's age would be 50 and his daughter's age would be 10, which is 5 times younger than the father.

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Part I: Draw a line connecting each sphere to its volume in terms of me and rounded to the nearest tenth. (Not all of the values will be used. ) Pls help​

Answers

Answer:

Step-by-step explanation:

When we find the area of a 3D figure, we label our answer as "units 2 (squared)".

When we find the volume of a 3D figure, what do we label our answers as? "units
Need help with this one thanks

Answers

By answering the presented question, we may conclude that  For slope example, if a figure's measures are in metros, the volume will be in cubic metros (m3).

what is slope?

The slope of a line determines how steep it is. The gradient is expressed mathematically as gradient overflow. The slope is computed by dividing the vertical difference (run) between two locations by the height difference (rise). The curve form of an expression is used to describe the straight line equation, which is written as y = mx + b. The y-intercept of the line is located where the inclination is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7. (0, 7). The y-intercept is placed where the slope of the path is m, b is b, and (0, b).  

When we calculate the volume of a 3D figure, we call our solution "units 3 (cubed)".

The term "cubed" is used since volume is calculated by multiplying three dimensions (length, breadth, and height), resulting in a unit raised to the power of three. For example, if a figure's measures are in metres, the volume will be in cubic metros (m3).

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20 Points
...................................

Answers

Answer:

Its the 3rd one

Step-by-step explanation:

I had this question twice

Answer:

number 3 i did this 2 days ago

Step-by-step explanation:

How do I solve tanx +secx=1

Answers

Answer:

Step-by-step explanation:

tan^2 x +1=sec^2 x

1= sec^2 x-tan^2 x

3 pts Suppose a college apparel clothing manufacturer would like to estimate the population mean height for college students. Assume the population standard deviation of student height is 9.48 centimeters. Find the sample size needed to obtain a 95% confidence interval with a 1.2 centimeters margin of error. We cannot find the an appropriate critical value to use since we do not know the degrees of freedom 239,75 239 240

Answers

We need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.

We need to find the sample size needed to obtain a 95% confidence interval with a 1.2 centimeters margin of error.Given that population standard deviation of student height is 9.48 centimeters.Using the formula of margin of error, we getME = z* σ/√nHere, σ = 9.48, ME = 1.2, and confidence interval = 95%.Since we do not know the degrees of freedom, we can use the Z-distribution to find the z-score.For 95% confidence interval, α/2 = 0.025The z-score for the 0.025 level of significance (two-tailed test) can be found using Z-table or calculator or Excel function= NORMSINV(0.025) = -1.96ME = z* σ/√n1.2 = -1.96 * 9.48 /√n√n = 1.96 * 9.48 /1.2= 15.42n = (15.42)^2= 238.1764≈ 239Therefore, we need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.

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Raymond’s class measures the masses of the books in their library. The mass of the dictionary is 2,702 grams. The dictionary’s mass is 1,429 grams greater than the mass of Raymond’s favorite book. What is the mass, in grams, of Raymond’s favorite book?

Answers

The mass of Raymond's favorite book is 1273 grams.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

Let x be the mass of Raymond's favorite book in grams. According to the problem, we have:

2702 = x + 1429

To solve for x, we can isolate it on one side of the equation by subtracting 1429 from both sides:

x = 2702 - 1429

x = 1273

Therefore, the mass of Raymond's favorite book is 1273 grams.

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Does the table below describe a linear or an exponential function?
a.The x-values are equally spaced, and the y-values change by equal differences, so the function is linear.
b.The x-values are equally spaced, and the y-values change by equal differences, so the function is exponential.
c. The x-values are equally spaced, and the y-values change by equal factors, so the function is exponential.
d. The x-values are equally spaced, and the y-values change by equal factors, so the function is linear.

Answers

Answer:

a. The x-values are equally spaced, and the y-values change by equal differences, so the function is linear.

Step-by-step explanation:

A linear function is categorized by a function which has a constant factor separating all coordinates. In this table, each x-value increases by 1 while each y-value increases by 2. So, it is linear.

Water fills a tank at a rate of 150 litres during the first hour, 125 litres during the second, 150 litres during the third and so on. Find the number of hours necessary to fill a rectangular tank 16m x 6m x 5m

Answers

Water fills a tank at a rate of 150 liters during the first hour, 125 liters during the second, 150 liters during the third, and so on. The number of hours necessary to fill a rectangular tank 16m x 6m x 5m is 103 hours.

The volume of the rectangular tank can be found by multiplying its length, width, and height:

The volume of the tank = Length x Width x Height

Volume of tank = 16m x 6m x 5m

The volume of the tank = 480 cubic meters

We need to convert this volume to liters in order to compare it to the flow rate of water. Since 1 cubic meter is equal to 1,000 liters, we have:

Volume of tank = 480 x 1,000 = 480,000 liters

Now we can add up the flow rate of water over time until it exceeds the volume of the tank. The flow rate starts at 150 liters and then alternates between 125 liters and 150 liters for each subsequent hour. We can express this pattern as:

[tex]150 + 125 + 150 + 125 + 150 + ...[/tex]

This is an arithmetic sequence with a first term of 150, a common difference of -25 (since each subsequent term is 25 less than the previous one), and an unknown number of terms. We can use the formula for the sum of an arithmetic sequence to find the number of terms:

Sum = (n/2)(first term + last term)

where n is the number of terms.

We want to find the number of terms that will give us a sum greater than or equal to 480,000 liters. We can set up an inequality:

(n/2)(150 + (150 + (n-1)(-25))) ≥ 480,000

Simplifying and solving for n, we get:

n ≥ 102.4

Since we need a whole number of terms, we can round up to 103 terms. This means it will take 103 hours to fill the tank.

Therefore, the number of hours necessary to fill the rectangular tank is 103 hours.

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Convert the rate of 6 pt/d to an equivalent rate measured in qt/wk.
O A. 15 qt/wk
O B. 10 qt/wk
O C. 12 qt/wk
O D. 21 qt/wk​

Answers

The equivalent rate measured in qt/wk is 5.25 qt/wk, which is closest to option C. 12 qt/wk.

To convert units of measurement, you need to use conversion factors, which are ratios that relate to the two units of measurement. The conversion factor is derived from the relationship between the two units of measurement, and it ensures that the numerical value of the quantity does not change, only the unit.

In this case, we are converting a 6 pt/d to an equivalent rate measured in qt/wk. We need to use conversion factors for both volume and time to do this.

First, we need to convert pints to quarts. Since there are 2 pints in a quart, we can use the conversion factor 2 pt/1 qt. Multiplying by this conversion factor gives:

6 pt/d x (1/8 qt/pt) x (7 d/wk) = 21/4 qt/wk = 5.25 qt/wk

Therefore, the equivalent rate measured in qt/wk is 5.25 qt/wk, which is closest to option C. 12 qt/wk.

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