Select all the correct answers.
Which equations have a greater unit rate than the rate represented in the table?
——
X Y
——
3 2

6 4

9 6
——

y=5/7x

y=3/5x

y=1/3x

y=7/9x

y=7/11x

Answer:

The area of this circle is 50.27

Step-by-step explanation:

The area of this circle is 50.3 units² or 16π

The incircle is defined as the largest circle that can be made in a triangle and is tangent to each side of the triangle.

The area of the circle is the product of the pie and the square of the radius.

The area of the circle = πr²

We are given that radius of the circle as r = 4.

Then we know that

Area = πr²

Substitute the values r = 4

π = 3.14

Area = 3.14(4)²

Area = 3.14 × 16

Area = 50.3

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The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

X=6

Y= - 1

Step-by-step explanation:

X-y =7

X+y =5 cross - y and y

_______

X+x =7 +5

2x= 12

X= 12/2

X= 6

Replace X in first equation:

X - y =7

6 - y =7

6 - 7 =y

y = - 1

Hope this helps you.. Good Luck!

The result for the evaluation of the given definite integral is 24, under the condition that the given definite integral is  \(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx\)  .
The provided definite integral  \(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx\)can be split into two integrals by using integration by parts

\(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx = \int\limits^2_0 {(4-x^{2} )} \, dx - \int\limits^4_2 {(x^{2} -4)} \, dx\)

Hence, the first integral \(\int\limits^2_0 {(4-x^{2} )} \, dx\) is

\(\int\limits^2_0 {(4-x^{2} )} \, dx\) \(= [4x - (1/3)x^{3} ]\)
= [8/3]

Then, the second integral \(\int\limits^4_2 {(x^{2} -4)} \, dx\) is

\(\int\limits^4_2 {(x^{2} -4)} \, dx\)  = [-x³/3 + 4x]
= [-64/3]

Now,
I = [8/3] - [-64/3]
= [72/3]
= 24.
The result for the evaluation of the given definite integral is 24, under  the condition that the given definite integral is \(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx\)

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Answer:

The answer is below

Step-by-step explanation:

Triangles are polygons with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angled triangles.  

Trigonometric identities are equations that uses trigonometric functions to show the relationship between the angles in a right angle triangle and the sides of the right angled triangle.

If θ be an acute angle in a right angled triangle, hyp. is the hypotenuse side of the angle, opp. is the opposite side to the angle and adj. is the adjacent side to the angle, then:

sinθ = opp. / hyp.v;  cosθ = adj. / hyp. ; tanθ = opp. / adj.

The volume of the remaining piece of ice cube is 6911.5 cubic cm

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

Radius, r = 20/2  = 10 cm

Height, h = 33 cm

The volume of the remaining piece is calculated is

V = 2/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 2/3 * 22/7 * 10² * 33

Evaluate

V = 6911.5

Hence, the volume of the remaining piece is 6911.5 cubic cm

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Answer:

125

An exponent is the number written as a superscript above a number. This is used commonly in mathematics to signify multiplication, or the amount to multiply the number by.

If we look at \(5^{3}\) (Five to the power of 3), we can use this expression to solve for the answer.

Therefore, the answer to \(5^{3}\) is 125.

Answer:

45

Step-by-step explanation:

In square, the diagonals bisect each other at 90,

∠DEC = 90°

ED = EC

So, ΔECD is isosceles triangle.

Angles opposite to equal sides are equal.

∠EDC = ∠ECD = 45

Answer:

45°

Step-by-step explanation:

Two diagonals of a square intersect at right angle, I.e., 90°

BD and AC are two such diagonals of the square ABCD.

Since, they intersect at 90°:

∠DEC = 90°

We're given the value of ∠ECD and that is 45°

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

Sum of all angles in a triangle = 180°

=> ∠DEC + ∠ECD + ∠EDC = 180°

=> 90 + 45 + ∠EDC = 180°

=> 135 + ∠EDC = 180

=> ∠EDC = 180 - 135

=> ∠EDC = 45

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

Hence, we know the value of ∠EDC and that is 45°

Answer:

Step-by-step explanation:

What is thirty six times thirty eight divided by three

36 * 38 : 3 =

1368 : 3 =

456

we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = \(\frac{x}{100} *1 pound\)

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so \(\frac{x}{100} * y = 31/2\)

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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Answer:

linear

Step-by-step explanation:

hey there,

< Linear equations are constant. They are not like parabolas so they are not curved but instead are straight, which allows them to be constant. >

Hope this helped! Ask me any more questions if you still don't understand!

Answer: The answer is a Linear Function

Step-by-step explanation:

Answer:

Your answer is 97.

Step-by-step explanation:

I can give an explanation if needed.

Answer:

lil boi

Step-by-step explanation:

To determine the probability of a boy reading horror stories, multiply the percentages of girls and boys. The percentage of girls reading horror stories is 39%, while boys read 41%. The probability of a boy reading horror stories is 20.09%.

To find the probability of a boy reading horror stories, we need to consider the percentages given.

First, we know that 59% of the respondents are girls, so the percentage of boys is 100% - 59% = 41%.

Next, we are told that 61% of the girls read horror stories. Therefore, the percentage of girls who do not read horror stories is 100% - 61% = 39%.

Similarly, 49% of the boys read horror stories, so the percentage of boys who do not read horror stories is 100% - 49% = 51%.

To find the probability of a boy and reading horror stories, we need to multiply the probabilities together:

P(boy and reads horror stories) = P(boy) * P(boy reads horror stories)

P(boy and reads horror stories) = 41% * 49%

Therefore, the probability of a boy reading horror stories is 20.09%.

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7x+2y=1 is the formula used to represent linear equations in two variables.

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Answer:

6√27 + √243

6√9 x 3 + √81 x 3  

6 x 3 √3 + 9√3

18√3 + 9√3

27√3

Answer:

Look below for answer! Have a great day and please mark me brainliest!

Step-by-step explanation:

Bedroom 1: 22x15=330

330x7.25=2392.5

Bedroom 2: 15x12=180

180x7.25=1305

Bedroom 3: 13x12=156

156x7.25=1131

2392.5+1305+1131= 4828.5

Bedroom 1:  22x15=330

330x6.75=2227.5

Bedroom 2: 15x12=180

180x6.75=1215

Bedroom 3: 13x12=156

156x6.75=1053

2227.5+1215+1053+100= 4595.5

Therefore, 6.75 per square foot plus a $100 fixed installation fee would be the cheapest.

Answer:

Step-by-step explanation:

4x = 9 * 5

4x = 45

x = 45/4

x=11,25

P(x) = 2 + (1/4)(x - 4) - (1/32)(x - 4)^2 + (1/256)(x - 4)^3

The estimate is approximately 0.0007635 units away from the true value of √2.

Since √2 is closer to 4 than √3, the polynomial will provide a better approximation for √2.

a) To find the Taylor polynomial of degree 3 based at 4 for √x, we need to compute the function's derivatives at x = 4.

The function f(x) = √x can be written as f(x) = x^(1/2).

First, let's find the derivatives:

f'(x) = (1/2)x^(-1/2) = 1 / (2√x)

f''(x) = (-1/4)x^(-3/2) = -1 / (4x√x)

f'''(x) = (3/8)x^(-5/2) = 3 / (8x^2√x)

Now, let's evaluate the derivatives at x = 4:

f(4) = √4 = 2

f'(4) = 1 / (2√4) = 1 / (2 * 2) = 1/4

f''(4) = -1 / (4 * 4√4) = -1 / (4 * 4 * 2) = -1/32

f'''(4) = 3 / (8 * 4^2√4) = 3 / (8 * 4^2 * 2) = 3/256

Using these values, we can construct the Taylor polynomial of degree 3 based at 4:

P(x) = f(4) + f'(4)(x - 4) + (1/2!)f''(4)(x - 4)^2 + (1/3!)f'''(4)(x - 4)^3

Substituting the values:

P(x) = 2 + (1/4)(x - 4) - (1/32)(x - 4)^2 + (1/256)(x - 4)^3

b) To estimate √2 using the Taylor polynomial obtained in part (a), we substitute x = 2 into the polynomial:

P(2) = 2 + (1/4)(2 - 4) - (1/32)(2 - 4)^2 + (1/256)(2 - 4)^3

Simplifying:

P(2) = 2 - (1/2) - (1/32)(-2)^2 + (1/256)(-2)^3

P(2) = 2 - 1/2 - 1/32 * 4 + 1/256 * (-8)

P(2) = 2 - 1/2 - 1/8 - 1/32

P(2) = 2 - 1/2 - 1/8 - 1/32

P(2) = 15/8 - 1/32

P(2) = 191/128

The estimate for √2 using the Taylor polynomial is 191/128.

The true value of √2 is approximately 1.4142135.

To evaluate how close the estimate is to the true value, we can calculate the difference between them:

True value - Estimate = 1.4142135 - (191/128) ≈ 0.0007635

The estimate is approximately 0.0007635 units away from the true value of √2.

c) We would expect the polynomial to give a better estimate for √2 than for √3. This is because the Taylor polynomial is centered around x = 4, and √2 is closer to 4 than √3. As we construct the Taylor polynomial around a specific point, it becomes more accurate for values closer to that point. Since √2 is closer to 4 than √3, the polynomial will provide a better approximation for √2.

When constructing the Taylor polynomial, we consider the derivatives of the function at the chosen point. As the degree of the polynomial increases, the accuracy of the approximation improves in a small neighborhood around the chosen point. Since √2 is closer to 4 than √3, the derivatives of the function at x = 4 will have a greater influence on the polynomial approximation for √2.

Therefore, we can expect the polynomial to give a better estimate for √2 compared to √3.

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Answer:30,000

Step-by-step explanation: 7,500

                                              x     4

                                            -————

Multiply

The total amount of money Levi spent on renting movie and buying candy is $5.75

Total = Amount Levi rented movie + A package of candy

= $3.20 + $2.55

= $5.75

Therefore, the total money spent by Levi is $5.75

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25463 grams radioactive kind of americium will be left after 2160 years.

We know that Half Life Formula will be,

\(N=I(\frac{1}{2})^{\frac{t}{T}}\)

where N is the quantity left after time 't'; 'T' is the half life of the substance and 'I' is the initial quantity of the substance.

Given that the initial quantity of the substance (I) = 814816 grams

Half life of the radioactive kind of americium is (T) = 432 years

The time elapsed (t) = 2160 years

Now we have to find the quantity left that is the value of N for the given values.

N = \(814816\times(\frac{1}{2})^{\frac{2160}{432}}=814816\times(\frac{1}{2})^5\) = 814816/32 = 25463 grams.

Hence 25463 grams radioactive kind of americium will be left after 2160 years.

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Answer

Explanation

Given:

To determine whether the relation defines y as a function of x, we get the domain first.

Based on the given relation, when we plug in x=0, the value would be undefined. So the function domain is x<0 or x>0.

Hence, the interval notation is:

We can use vertical line test to determine if it is a function as shown in the graph below:

As we can see, there's only one point of intersection so the relation defines y as a function of x. Therefore, the answer is:

Function; domain

(a)The two descriptive statistics that can be cited are as follows: A. Of those investment managers surveyed, 44% were bullish or very bullish on the stock market.

B. Of those investment managers surveyed, 23% selected health care as the sector most likely to lead the market in the next 12 months.

(b)Inference about the population of all investment managers concerning the average return expected on equities over the next 12 months:By looking at the descriptive statistic given, we can say that the average expected return over the next 12 months for equities was 11.3%. Therefore, the inference about the population of all investment managers concerning the average return expected on equities over the next 12 months would be that most investment managers expect a return of about 11.3% on equities over the next 12 months.

(c)Inference about the length of time it will take for technology and telecom stocks to resume sustainable growth:By looking at the descriptive statistic given, we can say that the managers' average response when asked to estimate how long it would take for technology and telecom stocks to resume sustainable growth was 2.3 years. Therefore, the inference about the length of time it will take for technology and telecom stocks to resume sustainable growth would be that investment managers believe it will take about 2.3 years for technology and telecom stocks to resume sustainable growth.

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The orthogonal projection of \(\vec{V}\) =[−7−9] onto the line L through [26] and the origin is given by the vector [-69/10 -207/10].

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To find the orthogonal projection of a vector  \(\vec{V}\)  onto a line L, we need to follow these steps:

Find a vector \(\vec{n}\)  that is orthogonal to the line L.

Find the projection of  \(\vec{v}\) onto \(\vec{n}\) . This projection will be a scalar.

The orthogonal projection of \(\vec{v}\)  onto L is the vector that is obtained by multiplying the scalar projection of \(\vec{v}\)  onto \(\vec{n}\)  by the unit vector in the direction of L.

Let's apply these steps to the problem at hand:

Step 1: Find a vector \(\vec{n}\) that is orthogonal to the line L.

The line L passes through [2 6] and the origin, so we can find the direction vector of the line by subtracting the two points:

\(\vec{d}\) = [2 6]−[0 0]=[2 6].

To find a vector that is orthogonal to \(\vec{d}\), we can take the cross product of  \(\vec{d}\)with the vector [0 0 1]:

\(\vec{n}\) = \(\vec{d}\)  × [0 0 1] = [−6 2 0].

Step 2: Find the projection of  \(\vec{v}\)onto \(\vec{n}\)  .

The projection of  \(\vec{v}\) onto  \(\vec{n}\) is given by the formula:

proj n v = ( \(\vec{v}\) ·  \(\vec{n}\) ) / || \(\vec{n}\) ||² *  \(\vec{n}\)

where · denotes the dot product and ||  \(\vec{n}\) || is the magnitude of  \(\vec{n}\) .

Substituting the values we have:

proj n v = ([-7 -9] · [-6 2 0]) / ||[-6 2 0]||² * [-6 2 0]

= (-54 + (-18)) / (36 + 4) × [-6 2 0]

= -72/40 × [-6 2 0]

= [-27 9 0]/5

Step 3: The orthogonal projection \(\vec{v}\) onto L is given by:

proj L v = (proj n v · \(\vec{d}\)  / || \(\vec{d}\)  ||²) × \(\vec{d}\)  / || \(\vec{d}\)  ||

where || \(\vec{d}\) || is the magnitude of  \(\vec{d}\)  .

Substituting the values we have:

proj L v = ([−27 9 0]/5 · [2 6]/(2² + 6²)) * [2 6]/(2² + 6²)

= -207/40 * [2 6]

= [-69/10 -207/10]

Therefore, the orthogonal projection of  \(\vec{v}\) =[−7−9] onto the line L through [26] and the origin is given by the vector [-69/10 -207/10].

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Answer: To apply l'Hospital's Rule, we need to take the derivative of the numerator and denominator separately with respect to θ.

Taking the derivative of the numerator:

d/dθ [1 - sin(θ)] = -cos(θ)

Taking the derivative of the denominator:

d/dθ [1 + cos(6θ)] = -6 sin(6θ)

Now we can apply l'Hospital's Rule by taking the limit of the ratio of the derivatives:

lim θ→π/2 (-cos(θ)) / (-6 sin(6θ))

When θ approaches π/2, cos(θ) approaches 0 and sin(6θ) approaches 1. Therefore, the limit simplifies to:

= 0 / (-6)

= 0

Hence, the limit of (1 - sin(θ)) / (1 + cos(6θ)) as θ approaches π/2 is 0.

The 4 properties of the rhombus are:

A quadrilateral in Euclidean geometry is a rhombus. It's a parallelogram with all sides equal and diagonals intersecting at 90 degrees. In addition, opposing sides are parallel, and opposing angles are equal. This is a fundamental property of the rhombus. A rhombus is shaped like a diamond. As a result, it's also known as a diamond.

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Answer:

791.28

Step-by-step explanation:

1. 3.14*9²=254.34

2. 3.14*9*19=536.94

3. 536.94+254.34=791.28