Which table has a constant of proportionality between y and x of 1/4?

Which Table Has A Constant Of Proportionality Between Y And X Of 1/4?

Answers

Answer 1

Answer: Choice B

Pick any row to find that y/x is equal to 1/4

For example, in the second row we can immediately see that y/x = 1/4 since x = 4 and y = 1 pair up together. The other two rows involve a bit more work, but you should find the result simplifies to 1/4 as well.


Related Questions

Question 3 (Essay Worth 10 points)
(4.04 MC)

Part A: A graph passes through the points (0, 4), (1, 8), and (2, 10). Does this graph represent a linear function or a non-linear function? Explain your answer in words.

Part B: Write one example of a linear function and one example of a non-linear function. (Use x and y as the variables)

Answers

A graph passes through the points (0, 4), (1, 8), and (2, 10) is a non linear function and  y = 3x - 2 is a example of linear function and y= 2× is a example of non linear function

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

For points (0, 4), (1, 8),

m=8-4/1=4

For points (1, 8) and  (2, 10).

m=2/2=1

The slope of line is changing at same rate, so the line is not linear function.

A linear function is a function that represents a straight line on the coordinate plane.

For example, y = 3x - 2

y= 2× is a non linear function

Hence, A graph passes through the points (0, 4), (1, 8), and (2, 10) is a non linear function and  y = 3x - 2 is a example of linear function and y= 2× is a example of non linear function

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PART A : The Slope of the line PR is not constant and hence it is non-linear.

Part B : An example of a linear equation is an equation of a line

y = mx + b.

What is slope?

The slope is defined by the rate of change of the y-axis with respect to the x-axis.

We know slope(m) = (y₂ - y₁)/(x₂ - x₁) and the slope of a linear function is constant.

Given, A graph passes through the points (0, 4), (1, 8), and (2, 10).

Let P(0, 4), Q(1, 8), and R(2, 10).

The slope of the line segment PQ is,

= (8 - 4)/(1 - 0).

= 4/1.

= 4.

The slope of the line segment QR is,

= (10 - 8)/(2 - 1).

= 2/1.

= 2.

So, the Slope of the line PR is not constant and hence it is non-linear.

An example of a linear equation is an equation of a line y = mx + b.

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Consider a three-year bond with face value and coupon rate paid quarterly. Suppose the bond price is traded at a price of . Answer the following questions:
a. (1 mark) What is the current yield on this bond?
b. (1 mark) What is the capital gain on this bond if held till maturity?
c. (1 mark) What is the rate of return on this bond?
d. (2 mark) Define what it means by yield to maturity and explain why it is better than the conventional rate of return.
e. (2 marks) Compute both the per-period and annual yield to maturity on this bond.
f. (2 marks) Assume you bought this bond from this investor at the end of year 2, how much would you pay for that bond if the market interest rate is 5%?

Answers

a. Current yield: Coupon payment / Bond price * 100%

b. Capital gain on a bond: Face value - Purchase price

c. Rate of return on a bond: Total return / Initial investment * 100%

d. Yield to maturity (YTM): Total anticipated return on a bond if held until maturity

e. Per-period yield to maturity: Coupon payments over a specific period / Bond price

f. Bond price at the end of year 2 with 5% market interest rate can be calculated using the bond pricing formula.

a. The current yield on a bond is calculated by dividing the annual coupon payment by the bond price.

Since the coupon rate is paid quarterly, we need to multiply the coupon rate by 4 to get the annual coupon payment.

Therefore, the current yield can be calculated as follows: current yield = (Annual coupon payment / Bond price) * 100%.

b. The capital gain on a bond if held till maturity is the difference between the bond's face value and its purchase price.

It represents the profit or loss made by the bondholder upon maturity.

c. The rate of return on a bond takes into account both the coupon payments and any capital gains or losses.

It is calculated by dividing the total return (coupon payments plus capital gain/loss) by the initial investment and expressing it as a percentage.

d. Yield to maturity (YTM) is the total return anticipated on a bond if held until it matures.

It considers the bond's coupon payments, the purchase price, and the final face value.

YTM takes into account the time value of money, as it considers the present value of all future cash flows.

It is considered better than the conventional rate of return because it provides a more accurate representation of the bond's performance and allows for better comparisons between different bonds.

e. To compute the per-period yield to maturity on this bond, we divide the total coupon payments over the three-year period by the bond price.

The annual yield to maturity is then calculated by compounding the per-period yield to maturity.

The exact calculations cannot be performed without the specific values of the bond's face value, coupon rate, and bond price.

f. Without the specific values for the bond's face value, coupon rate, and bond price, it is not possible to calculate the exact amount to be paid for the bond at the end of year 2 when the market interest rate is 5%.

However, it can be determined using the bond pricing formula, which discounts the future cash flows (coupon payments and face value) by the prevailing market interest rate to calculate the present value of the bond.

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a. Current yield: Coupon payment / Bond price * 100%

b. Capital gain on a bond: Face value - Purchase price

c. Rate of return on a bond: Total return / Initial investment * 100%

d. Yield to maturity (YTM): Total anticipated return on a bond if held until maturity

e. Per-period yield to maturity: Coupon payments over a specific period / Bond price

f. Bond price at the end of year 2 with 5% market interest rate can be calculated using the bond pricing formula.

a. The current yield on a bond is calculated by dividing the annual coupon payment by the bond price.Since the coupon rate is paid quarterly, we need to multiply the coupon rate by 4 to get the annual coupon payment.Therefore, the current yield can be calculated as follows: current yield = (Annual coupon payment / Bond price) * 100%.

b. The capital gain on a bond if held till maturity is the difference between the bond's face value and its purchase price.It represents the profit or loss made by the bondholder upon maturity.

c. The rate of return on a bond takes into account both the coupon payments and any capital gains or losses.It is calculated by dividing the total return (coupon payments plus capital gain/loss) by the initial investment and expressing it as a percentage.

d. Yield to maturity (YTM) is the total return anticipated on a bond if held until it matures.It considers the bond's coupon payments, the purchase price, and the final face value.YTM takes into account the time value of money, as it considers the present value of all future cash flows.It is considered better than the conventional rate of return because it provides a more accurate representation of the bond's performance and allows for better comparisons between different bonds.

e. To compute the per-period yield to maturity on this bond, we divide the total coupon payments over the three-year period by the bond price.The annual yield to maturity is then calculated by compounding the per-period yield to maturity.The exact calculations cannot be performed without the specific values of the bond's face value, coupon rate, and bond price.

f. Without the specific values for the bond's face value, coupon rate, and bond price, it is not possible to calculate the exact amount to be paid for the bond at the end of year 2 when the market interest rate is 5%.However, it can be determined using the bond pricing formula, which discounts the future cash flows (coupon payments and face value) by the prevailing market interest rate to calculate the present value of the bond.

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Does the average Washington State University student drive more or less than 300 miles from Pullman to home? In a sample of 226 students, the sample mean mileage was 285 miles with a sample standard deviation of 50 miles. Plotting the data, we see that the sample is approximately normal. (a) (4 points) Determine if a one-sided or two-sided confidence interval is appropriate for this situation. Explain your reasoning. (b) (10 points) Compute a 95% confidence interval for. Write your solution in interval notation. Interpret the meaning of the interval in the context of the situation. (c) (4 points) Compared the the confidence interval calculated above, if the confidence level is decreased to 90%, the new confidence interval is If the confidence level is increased to 99%, the new confidence interval is __. A. wider, wider B. narrower, narrower C. wider, narrower D. narrower

Answers

A two-sided confidence interval is appropriate because the research question is about whether the average mileage is significantly different from 300 miles.

(a) To determine if a one-sided or two-sided confidence interval is appropriate for this situation, we need to consider the research question and the nature of the hypothesis being tested. If the research question is specifically focused on whether the average mileage is less than or greater than 300 miles, then a one-sided confidence interval would be appropriate. On the other hand, if the research question is broader and seeks to determine whether the average mileage is significantly different from 300 miles (i.e., it could be less or greater), then a two-sided confidence interval would be appropriate.

(b) To compute a 95% confidence interval, we can use the formula:

CI =X ± (Z * (σ/√n))

Where X is the sample mean, Z is the z-value corresponding to the desired confidence level (in this case, 95% corresponds to Z = 1.96 for a large enough sample), σ is the population standard deviation (unknown, so we use the sample standard deviation), and n is the sample size.

Plugging in the given values:

CI = 285 ± (1.96 * (50/√226))

Simplifying the expression:

CI = 285 ± (1.96 * 3.322)

CI = [278.15, 291.85]

Interpretation: The 95% confidence interval for the average mileage from Pullman to home is [278.15, 291.85]. This means that we are 95% confident that the true average mileage of all Washington State University students falls within this interval. It suggests that based on the sample data, the average mileage is likely to be between 278.15 and 291.85 miles.

(c) If the confidence level is decreased to 90%, the new confidence interval will be narrower since a smaller confidence level requires less certainty, resulting in a narrower interval. Conversely, if the confidence level is increased to 99%, the new confidence interval will be wider as a higher confidence level demands greater certainty, leading to a wider interval to capture a larger range of potential values. Therefore, the answer is D. narrower for a confidence level of 90% and A. wider for a confidence level of 99%.

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If someone answers this I'll give brainliests because I have been trying for so long
question: what is the rate of change for y= -3x​

Answers

Answer:

Rate of change, or slope, is 0.

Step-by-step explanation:

Normally, we would say that the number with the -3x if there was one, would be called B but seeming as there is no number, I can only assume that the rate of change is 0. So the point would be (0,0).

Answer:

\( \frac{y}{x} = m = \tan( \theta) \\ \boxed{y = \tan( \theta) x} \\ \boxed{y = mx}\)

where, m and tan∅ is the slope of the line

Here, the rate of change for line y = -3x is the slope of the given line

Comparing the above equation with y = -3x, we get

\( \tan( \theta) = - 3 \\ m = - 3 \\ \boxed{\frac{y}{x} = - 3}\)

Therefore, -3 is the rate of change for y = -3x

-3 is the right answer.

PLEASE PLEASE HELP!!!!WILL MARK BRAINLIEST

PLEASE PLEASE HELP!!!!WILL MARK BRAINLIEST

Answers

Ok so it's lemon juice to sugar. I seen one that is 1:1 (1 juice to 1 sugar) do the 2nd lowest juice to sugar after this and keep going till the last ratio.

Find the midpoint M of the line segment joining the points A = (-2, 8) and B = (-8, -4).

Answers

Answer:

M (- 5, 2 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

Here (x₁, y₁ ) = A (- 2, 8 ) and (x₂, y₂ ) = B (- 8, - 4 ) , then

midpoint = ( \(\frac{-2-8}{2}\) , \(\frac{8-4}{2}\) ) = ( \(\frac{-10}{2}\) , \(\frac{4}{2}\) ) = (- 5, 2 )

Caroline wants to buy 100 g of spice mix from a British or French website.

The conversion rate is €1 = £0.85

What is the price, including delivery costs, that Caroline would pay for the spice mix from the cheaper website? Give your answer in pounds (£).

British website: £0.90 for 25 g Free delivery.
French website: €1.20 for 50 g €0.80 delivery per order.​

Answers

The website which is cheaper for Caroline to buy the spice mix is French website.

Given data ,

Let's calculate the total cost for Caroline from both websites and determine which one is cheaper.

British website:

Price for 100 g = (£0.90 / 25 g) * 100 g = £3.60

Since the British website offers free delivery, the total cost remains £3.60.

French website:

Price for 100 g = (€1.20 / 50 g) * 100 g = €2.40

Delivery cost = €0.80

On simplifying the equation , we get

To convert the price and delivery cost to pounds, we'll use the conversion rate: €1 = £0.85.

Price in pounds = €2.40 * £0.85 = £2.04

Delivery cost in pounds = €0.80 * £0.85 = £0.68

Total cost = Price in pounds + Delivery cost = £2.04 + £0.68 = £2.72

Comparing the total costs:

British website: £3.60

French website: £2.72

Hence , Caroline would pay £2.72 for the spice mix from the cheaper website, which is the French website.

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if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen?

Answers

There are 69300 possible ways of selecting six bottles randomly with two bottles of each variety.

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. In the given question, we have to select 6 bottles randomly with two bottles of each variety,

= ¹⁰C₂× ⁸C₂ × ¹¹C₂

¹⁰C₂= [1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10] / [(1 × 2)(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8)]

= 90/2

= 45

Similarly,  ⁸C₂  = 28

In the same way ¹¹C₂= 55

= ¹⁰C₂× ⁸C₂× ¹¹C₂

= 45 × 28 × 55

= 69300

Therefore, there are 69300 possible ways of selecting 6 bottles with two bottles of each variety.

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how to find square root

Answers

Finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

Finding the square root of a number involves determining the value that, when multiplied by itself, gives the original number. Here are a few methods to find the square root:

Prime Factorization: This method involves breaking down the number into its prime factors. Pair the factors in groups of two, and take one factor from each pair. Multiply these selected factors to find the square root. For example, to find the square root of 36, the prime factors are 2 * 2 * 3 * 3. Taking one factor from each pair (2 * 3), we get 6, which is the square root of 36.

Estimation: Approximate the square root using estimation techniques. Find the perfect square closest to the number you want to find the square root of and estimate the value in between. Refine the estimate using successive approximations if needed. For example, to find the square root of 23, we know that the square root of 25 is 5. Therefore, the square root of 23 will be slightly less than 5.

Using a Calculator: Most calculators have a square root function. Simply input the number and use the square root function to obtain the result.

It's important to note that finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

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what is 4.29 as a mixed number

Answers

We use the decimal system, which means every place you "move" in a decimal number, we multiply or divide by ten. We have the unit on the left side of the dot, and the tenth 1 place to right of the dot, the hundredth 2 places to the right of the dot. In math terms, let's use the famous number pi as an example.

\(3.14159265359\ldots=3+\frac{1}{10}+\frac{4}{100}+\frac{1}{1000}+\frac{5}{10000}+\frac{9}{100000}+\cdots\)

A mixed number is a combination of the unit and the fractional parts of a number. For our number 4.29, we have 4 units and 29 hundredths, which means we can rewrite as:

\(4.29=\frac{429}{100}=4\frac{29}{100}\)

LAST ONE PLEASE ANSWER IT

LAST ONE PLEASE ANSWER IT

Answers

Answer:

B.

Step-by-step explanation:

The product of means that you're multiplying, which means that you need to use parentheses. That narrows it down to B or D. Since the question asks you to provide a number first (x) and then 11, that means that 11 will be subtracted from the number.

A block of glass has a volume of 29cm cubed and a density of 2.694g/cm cubed
Work out the mass of the block of glass
Give your answer correct to 2 decimal places

A block of glass has a volume of 29cm cubed and a density of 2.694g/cm cubedWork out the mass of the

Answers

Answer:

Step-by-step explanation:

mass=density* volume

78.12

Ted and Carl share a 16-ounce bucket of clay. By the end of the week, Ted has used 5/8 of the bucket, and Carl has used 1/4 of the bucket of clay. How many ounces are left in the bucket?

Answers

Answer:2 ounce of clay are left in the bucket

Step-by-step explanation:

Total amount of clay to share = 16 ounce

amount used by Ted = 5/ 8 x 16=10 ounce

Amount used by Carl = 1/4 x 16= 4 ounce

Amount of clay  remaining= Total clay - amount used by Ted and Carl

= 16-(10+4)

=16-14

=2 ounce of clay left in the bucket

This is for a Geometry-H class

This is for a Geometry-H class

Answers

Applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees

How to Apply the Linear Angles Theorem?

Based on the linear angles theorem, we have the following equation which we will use to find the value of y:

3y + 11 + 10y = 180

Add like terms

13y + 11 = 180

Subtract 11 from both sides

13y + 11 - 11 = 180 - 11

13y = 169

13y/13 = 169/13

y = 13

Plug in the value of y

3y + 11 = 3(13) + 11 = 50 degrees

10y = 10(13) = 130 degrees.

Therefore, applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees.

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i need help on 9,10,11 please

i need help on 9,10,11 please

Answers

9) The True Distance is 209 ft

10) The True Distance is; 66.5 ft

11) The True Height is; 57 ft

How to Interpret the Scale of a Map?

We are given that the scale of the map is 1 in : 38 ft

This means that 1 inch represents 38 ft

9) Now, we want to find the true distance of 5.5 inches from the map. Thus;

True distance = (5.5 * 38)/1

True Distance = 209 ft

10) Now, we want to find the true distance of 1.75 inches from the map. Thus;

True distance = (1.75 * 38)/1

True Distance = 66.5 ft

11) We are given the scale is 1 in : 85 ft.

Thus, the true height of 1.5 inches is;

True height = (1.5 * 38)/1

True Height = 57 ft

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The opinions of all 450 students at a high school on whether they support Candidate A for student body president are shown below. Hide and shuffle all of the values. Take a random sample of 25 values from the population. Based on that sample, find the sample proportion and use that value to create a 95% confidence interval for the true proportion of the population who support Candidate A, rounding to the nearest thousandth.
Sample Yes: 19 Sample No: 6 Samples: 25

Answers

Answer:

Step-by-step explanation:

Les opinions des 450 élèves d'un lycée quant à savoir s'ils soutiennent le candidat A à la présidence du corps étudiant sont présentées ci-dessous. Masquez et mélangez toutes les valeurs. Prenez un échantillon aléatoire de 25 valeurs de la population. Sur la base de cet échantillon, trouvez la proportion de l'échantillon et utilisez cette valeur pour créer un intervalle de confiance à 95 % pour la véritable proportion de la population qui soutient le candidat A, en arrondissant au millième le plus proche.

Échantillon Oui : 19 Échantillon N° : 6 Échantillons : 25

Edgar has a fountain that holds 5 quarts of water. He only wants to fill it 3/4 full. How many​ 1-pint containers does it take to fill the​ fountain? How could he fill it with pint and cup​ containers? Explain.

Answers

Answer:

Step-by-step explanation:

1 quart =  2 pints  =  4 cups

1 pint = 2 cups

1/2 pint =  1  cup    .....so.....

First question

5 quarts  =  10 pints

10 * (3/4)  =  7.5 pint   contianers   will fill it  3/4  full  

7.5   pints   =    7  pints   +  1 cup

help i need this for rn :( 100 points

Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −3x2 + 24x + 3 and y = −4x2 + 25x + 15, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point?

3.25 seconds
3.50 seconds
3.75 seconds
4.00 seconds

Answers

Answer:

Step-by-step explanation:

When the balloons collide, they have the same x and y:

-3x^2 + 24x + 3 = y = -4x^2 + 25x + 15

Rearranging like terms together:

(4x^2 - 3x^2) + (24x - 25x) + (3 - 15) = 0

x^2 - x - 12 = 0

(x - 4)(x +3) = 0

x = 4 or -3

As x represents time, it cannot be negative.

The time when the balloons collide is at 4.00 seconds.

The collision means that y is equal

y=-3x²+24x+3y=-4x²+25x+15

So

-3x²+24x+3=-4x²+25x+15-3x²+4x²+24x-25x=15-3x²-x=12x²-x-12=0(x-4)(x+3)=0x=4,-3

As it's time so must be positive

x=4s

Find matrix M such that M × [3 -2 , 6 -8 ] = [-2 16]

Answers

The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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A train traveling at 37 M.P.H. had its speed increased by 22 ft. per sec.
If 88 ft./sec. = 60 M.P.H., then the train is now traveling at M.P.H.

Answers

Answer:

52 mph

Step-by-step explanation:

If 88 ft/sec = 60 mph

The 22 ft/ sec is 60/4 = 15 mph

This is so because 88/22 is 4

So we simply proceed to add this to the previous speed in mph

That gives a total of 15 + 37 = 52 mph

Every summer, Kendra plants a vegetable garden in her yard. Last year, she planted 6 rows of tomatoes and 8 rows of peppers. Kendra wants to keep the same ratio this year, but she only plans to plant 3 rows of tomatoes. How many rows of peppers will Kendra plant this year?

Answers

Answer:

4

Step-by-step explanation:

Let Kendra should plant x rows of peppers this year.

Since, there is a relation of direct proportion between the rows of tomatoes and peppers.

\( \therefore \: \frac{6}{8} = \frac{3}{x} \\ \\6 x = 8 \times 3 \\ \\ 6x = 24 \\ \\ x = \frac{24}{6} \\ \\ x = 4 \\ \\ \)

Hence, Kendra should plant 4 rows of peppers this year.

Answer:

Step-by-step explanation:

Complete the Square
x2 + 10x +

Answers

Answer:

( + 10)

Hope this helps you out

7. Find the corresponding angle.

(look at the picture)

7. Find the corresponding angle.(look at the picture)

Answers

Answer:

angle SXV

Step-by-step explanation:

how o slimplf a fracion

Answers

Divide the numerator by the denominator.

The numerator is the top number on a fraction.The denominator is the bottom number on a fraction.The line that separates them means division!

When a letter like a, b, x or y pops up in a mathematical expression, it's called a variable, but really it's a placeholder that represents a number of unknown value. You can perform all the same mathematical operations on a variable that you'd perform on a known number. That fact comes in handy if the variable pops up in a fraction, where you'll need tools like multiplication, division and canceling of common factors to simplify the fraction.

Combine like terms in both the numerator and the denominator of the fraction. When you first start handling fractions with variable, this may be done for you. But later on, you might encounter "messier" fractions like the following:

(a + a) / (2_a_ - a)

When you combine like terms, you end up with a much more civilized fraction:

2_a_/a

Factor the variable out of both numerator and denominator of the fraction if you can. If the variable is a factor in both places, you can then cancel it. Consider the simplified fraction just given:

2_a_/a

As a quick aside, any time you see a variable by itself, it's understood to have a coefficient of 1. So this could also be written as:

2_a_/1_a_

Which makes it more obvious that when you cancel the common factor a from both the numerator and denominator of the fraction, you're left with the following:

2/1

Which, in turn, simplifies to the whole number 2.

What if you have a fraction like 3_a_/2? You can't factor a out of both the numerator and the denominator of the fraction, but because it's in the numerator, you can treat it as a whole number. To make sense of this, first write the fraction out thusly:

3_a_/2(1)

You can insert the 1 in the denominator thanks to the multiplicative identity property, which states that when you multiply any number by 1, the result will be the original number you started with. So you haven't changed the value of the fraction at all; you've just written it a little differently.

Next, separate the factors thusly:

a/1 × 3/2

And simplify a/1 to a. This gives you:

a × 3/2

Which can be simply written as the mixed number:

a (3/2)

What if you end up with a messy fraction like the following?

(b2 - 9) / (b + 3)

At first glance there's no easy way to factor b out of both numerator and denominator. Yes, b is present in both places, but you'd have to factor it out of the entire term in both places, which would give you the even messier b(b - 9/b) in the numerator and b(1 + 3/b) in the denominator. That's a dead end.

But if you've been paying attention in your other lessons, you might notice that the numerator can actually be rewritten as (b2 - 32), also known as "the difference of squares," because you're subtracting one squared number from another squared number. And there's a special formula that you can memorize to factor the difference of squares. Using that formula, you can rewrite the numerator as follows:

(b - 3)(b + 3)

Now, take a look at that in the context of the entire fraction:

(b - 3)(b + 3) / (b + 3)

Thanks to that standard formula you either memorized or looked up, you now have the identical factor (b + 3) in both the numerator and the denominator of your fraction. Once you cancel that factor, you're left with the following fraction:

(b - 3) / 1

Which simplifies to just:

(b - 3)

My sister needs help

My sister needs help

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the answer to your question is the first one! it's a positive! good luck, wishing you the best on your assignment xoxo!

The measure of an angle is twenty-nine times the measure of its supplementary angle. What is the measure of each angle?

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Answer:

Let's call the measure of the angle x.According to the problem, its supplementary angle measures 180 - x.We are told that x is 29 times the measure of its supplementary angle, so we can set up the equation:x = 29(180 - x)Now we can solve for x:x = 5220 - 29x30x = 5220x = 174So the measure of the angle is 174 degrees, and its supplementary angle measures 6 degrees (180 - 174).

use double integrals to find the area inside the curve r = 3 + sin(θ).

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The area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

Double integration is an important tool in calculus that allow us to calculate the area of irregular shapes in the Cartesian coordinate system. In particular, they are useful when we are dealing with shapes that are defined in polar coordinates.

To find the area inside this curve, we can use a double integral in polar coordinates. The general form of a double integral over a region R in the xy-plane is given by:

∬R f(x,y) dA

where dA represents the infinitesimal area element, and f(x,y) is the function that we want to integrate over the region R.

In polar coordinates, we can express dA as r dr dθ, where r is the distance from the origin to a point in the region R, and θ is the angle that this point makes with the positive x-axis. Using this expression, we can write the double integral in polar coordinates as:

∬R f(x,y) dA = ∫θ₁θ₂ ∫r₁r₂ f(r,θ) r dr dθ

where r₁ and r₂ are the minimum and maximum values of r over the region R, and θ₁ and θ₂ are the minimum and maximum values of θ.

To find the area inside the curve r = 3 + sin(θ), we can set f(r,θ) = 1, since we are interested in calculating the area and not some other function. The limits of integration can be determined by finding the values of r and θ that define the region enclosed by the curve.

To do this, we first note that the curve r = 3 + sin(θ) represents a cardioid, which is a type of curve that is symmetric about the x-axis. Therefore, we only need to consider the region in the first quadrant, where 0 ≤ θ ≤ π/2.

To find the limits of integration for r, we note that the curve intersects the x-axis when r = 0. Therefore, the minimum value of r is 0. The maximum value of r can be found by setting θ = π/2 and solving for r:

r = 3 + sin(π/2) = 4

Therefore, the limits of integration for r are r₁ = 0 and r₂ = 4.

The limits of integration for θ are simply θ₁ = 0 and θ₂ = π/2, since we are only considering the region in the first quadrant.

Putting it all together, we have:

Area = ∬R 1 dA

        = ∫\(0^{\pi /2}\) ∫0⁴ 1 r dr dθ

Evaluating this integral gives us:

Area = π(3² - 2²)/2 = (5π)/2

Therefore, the area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

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use double integrals to find the area inside the curve r = 3 + sin().

Using double integrals, the area inside the curve r = 3 + sin(θ) is 0 units².

For the area inside the curve r = 3 + sin(θ), we can use a double integral in polar coordinates. The area can be expressed as:

A = ∬R r dr dθ

where R represents the region enclosed by the curve.

In this case, the curve r = 3 + sin(θ) represents a cardioid shape. To determine the limits of integration for r and θ, we need to find the bounds where the curve intersects.

To find the bounds for θ, we set the expression inside sin(θ) equal to zero:

3 + sin(θ) = 0

sin(θ) = -3

However, sin(θ) cannot be less than -1 or greater than 1. Therefore, there are no solutions for θ in this case.

Since there are no intersections, the region R is empty, and the area inside the curve r = 3 + sin(θ) is zero.

Hence, the area inside the curve r = 3 + sin(θ) is 0 units².

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Find p(3,4 or 5)!!!! HELPPPPPPPP

Find p(3,4 or 5)!!!! HELPPPPPPPP

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Answer:

triangle) 1/2

Step-by-step explanation:

let me know if this is incorrect

Triangle should be the answer

Identify the center and shape of the distribution:
Center =
Shape =

Identify the center and shape of the distribution:Center = Shape =

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The center and shape of the distribution are respectively:

9.6

Skewed left

What is the center and shape of the distribution?

The center of a distribution is a found using a statistics such as mean, median, or mode, and then provides a single value that is representative of the data. The spread is one that describes how close the data values are to each other using the range or standard deviation. The shape is one that describes how the data looks on a graph.

From the bar graph, we see that the center of the distribution is at 9.6.

Similarly, we also see that it is skewed left because it is longer on the left side of its peak than on its right.

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Which of the following means a study used a bivariate correlational design?
a. presence of measured variables
b. use of correlational stats
c. inclusion of quantitative variables
d. depiction of bar graph

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among the given options, the use of correlational statistics OPTION B is the most reliable indicator that a study employed a bivariate correlational design.

A bivariate correlational design is characterized by the examination of the relationship between two quantitative variables. In this context, the use of correlational statistics is a key indicator of this design. Correlational statistics, such as correlation coefficients (e.g., Pearson's r), are employed to assess the strength and direction of the relationship between the variables under investigation.

The presence of measured variables, inclusion of quantitative variables, or depiction of a bar graph are not definitive indicators of a bivariate correlational design. Measured variables can be present in various study designs, including experimental ones. Similarly, quantitative variables can be utilized in different types of studies, such as experimental, quasi-experimental, or observational designs. The depiction of a bar graph, which is commonly used to illustrate categorical data, does not inherently imply the use of a bivariate correlational design.

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