Jacob kept track of the number of hours that he spent playing soccer each week for several weeks he spent 3, 6, 7, 8, and 11 hours. What is the range of the data set?

The surface area of a cylinder can be calculated using the formula:

Surface area = 2πr² + 2πrh

where r is the radius of the base and h is the height of the cylinder.

Let's assume that the radius of the base of the smaller cylinder is r, then the radius of the base of the larger cylinder is 4/3 r, since the height is increased by 5 inches or 1/3 of the original height.

So, the surface area of the smaller cylinder is:

Surface area = 2πr² + 2πrh

And the surface area of the larger cylinder is:

Surface area = 2π(4/3 r)² + 2π(4/3 r)(15)

Simplifying these expressions, we get:

Surface area of smaller cylinder = 2πr² + 30πr

Surface area of larger cylinder = 2π(16/9 r²) + 40πr

Now we can find the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder:

Ratio = Surface area of larger cylinder / Surface area of smaller cylinder

= (2π(16/9 r²) + 40πr) / (2πr² + 30πr)

Simplifying this expression, we get:

Ratio = (32/9 r + 40) / (2r + 30)

= (32/9 r + 40) / 2(r + 15)

Since the cylinders are similar, the ratio of their surface areas is proportional to the square of the ratio of their heights:

Ratio = (20/15)²

= 1.7778

So the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is approximately 1.7778, or 1.78 to two decimal places.

Answer:

16:9

Step-by-step explanation:

I took the test

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

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If data shows that overweight children do not suffer from diabetes as predicted in the model that links child obesity and diabetes (i.e., data shows a lower than 80% probability), then the next step would be to review the model's assumptions and revise the model as necessary.

This may involve analyzing additional data or changing the model's structure or parameters, to better reflect the observed relationships between child obesity and diabetes. It is important to ensure that the model is based on accurate and reliable data, as this will help to ensure that the model's predictions are useful and informative.

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Answer: 19

Step-by-step explanation:

4x in this equation is equal to 4(4), which equal sixteen, adding the three will then get you 19

Answer: 19

Step-by-step explanation:

Insert 4 into the x in the equation.

3+ 4 × 4

Multiply.

4 × 4 = 16

Add.

3 + 16= 19

Hope this helps!

Answer:

it is the second option

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

The expression is:

● -9x - 8

Replace x by -6 to evaluate the expression when x = -6

● -9 ×(-6) - 8

● 54-8

● 46

Answer:

\(\huge\boxed{46}\)

Step-by-step explanation:

-9x - 8, when x = -6

Substitute in -6 for x in the expression

-9x - 8

-9(-6) - 8

Multiply -9 * -6

54 - 8

Subtract

\(\huge\boxed{46}\)

Hope this helps :)

Answer:

x³ + x²y - 2xy² - xy + y²

Step-by-step explanation:

Given

(x - y)(x² + 2xy - y)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x² + 2xy - y) - y(x² + 2xy - y) ← distribute both parenthesis

= x³ + 2x²y - xy - x²y - 2xy² + y² ← collect like terms

= x³ + x²y - 2xy² - xy + y²

Answer:

as below

Step-by-step explanation:

(x-y)(\(x^{2}\)+2xy-y)

\(x^{3}\)+2\(x^{2}\)y-xy-\(x^{2}\)y-2x\(y^{2}\)+\(y^{2}\)

\(x^{3}\)+\(x^{2}\)y-xy-2x\(y^{2}\)+\(y^{2}\)

Given:

The expression is:

\(2x^3+mx^2+nx+c\)

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

\(m+n=-6\)

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

\(P(x)=2x^3+mx^2+nx+c\)

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

\(P(2)=P(-1)\)              ...(i)

Substituting \(x=-1\) in the given polynomial.

\(P(-1)=2(-1)^3+m(-1)^2+n(-1)+c\)

\(P(-1)=-2+m-n+c\)

Substituting \(x=2\) in the given polynomial.

\(P(2)=2(2)^3+m(2)^2+n(2)+c\)

\(P(2)=2(8)+m(4)+2n+c\)

\(P(2)=16+4m+2n+c\)

Now, substitute the values of P(2) and P(-1) in (i), we get

\(16+4m+2n+c=-2+m-n+c\)

\(16+4m+2n+c+2-m+n-c=0\)

\(18+3m+3n=0\)

\(3m+3n=-18\)

Divide both sides by 3.

\(\dfrac{3m+3n}{3}=\dfrac{-18}{3}\)

\(m+n=-6\)

Hence proved.

Answer:

P(-5) = 109

Step-by-step explanation:

     If the polynomial p(x) is divided by the linear polynomial (x-a), the remainder is p(a).

   Dividend = divisor * quotient + remainder.

   p(x) = (x-a) * q(x) + p(a)

Here, q(x) is the quotient and p(a) is the remainder.

      P(x) = 4x² - x + 4

     P(-5) = 4*(-5)² - 1*(-5) + 4

              = 4*25 + 5 + 4

              = 100 + 5 + 4

              = 109

Answer:

3

Step-by-step explanation:

she will need 84 apples total so you do 84/32 and u get aroubd 2.6. You then round up to three because you can't have half a bag

The three lines do not have a common point of intersection.

Given the equation is \(−3x1−4x2=7, 3x1−5x2=−52\) and \(−2x1+4x2=38.\)

To find out if the three lines have a common point of intersection, we can use the Gaussian elimination method.

We will form an augmented matrix of the given system of equations.  

\(\[\begin{bmatrix}-3&-4&|&7\\ 3&-5&|&-52\\ -2&4&|&38\end{bmatrix}\]\)

Now we perform some row operations to get the matrix into its reduced row echelon form:

\(\[\begin{bmatrix}-3&-4&|&7\\ 3&-5&|&-52\\ -2&4&|&38\end{bmatrix}\to\begin{bmatrix}1&-\frac{4}{3}&|&-\frac{7}{3}\\ 3&-5&|&-52\\ -2&4&|&38\end{bmatrix}\to\begin{bmatrix}1&-\frac{4}{3}&|&-\frac{7}{3}\\ 0&-1&|&-19\\ 0&2&|&4\end{bmatrix}\to\begin{bmatrix}1&0&|&-5\\ 0&-1&|&-19\\ 0&2&|&4\end{bmatrix}\to\begin{bmatrix}1&0&|&-5\\ 0&1&|&19\\ 0&0&|&42\end{bmatrix}\]\)

The last row of the matrix is inconsistent, which means that the system of equations has no solution.

Therefore, the three lines do not have a common point of intersection. This is how we arrived at our response without actually having computed the answer or graphed the lines.

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Answer:

a diagonal?

Step-by-step explanation:

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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The value of y is 7.

We have the structure

            25

    a                  b

2            y                9

So, (2+y) = a

and, y +9 = b

Then, a+ b= 25

2 +y + y + 9= 25

2y + 11 = 25

2y = 14

y= 7

Thus, the value of y is 7.

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Answer:

Y=23x-43

Step-by-step explanation:

Distribute 23 to (x) and (-2) = 23x-46

The bring the -3 the other side

Y=23x-43

Answer:

v=3,m=2

Step-by-step explanation:

You can find the complete solution in given attachment

I hope it helped you

There is only one group of participants will receive treatment e as the first treatment.

What is lain square design?

A block with a Latin square design has v Latin characters arranged in a

v x v array (a table with v rows and v columns). Latin square designs are

frequently employed in studies in which individuals are assigned to treatments over a predetermined time period, where it is assumed that time has a significant impact on the experimental response.

The Latin Square Design's name comes from the fact that the treatments can be represented by a square written in Latin letters. Latin letters in the Latin square shape represent the treatment factor levels. The number of treatment levels must match the number of rows and columns.

Hence, There is only one group of participants will receive treatment e as the first treatment.

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Answer:

The measures of <2 and <8 are 124 degrees

Step-by-step explanation:

<2 is congruent to <4 by the Vertical Angles Theorem, and <4 is congruent to <8 by the corresponding angles theorem. <2 is congruent to <8 by the Transitive Property so we get <2 is congruent to <8, and it follows that m<2 equals m<8 by the definition of congruence. We can substitute <2 and <8 with 11x+3 and 13x-19 respectively, so we get 11x+3=13x-19. Solve for x, and we get that x=11, and plug in 11 for x into 11x+3, 11(11)+3=121+3=124.

The measure of angle ∠2 is 124.

The measure of angle ∠8 is 124.

The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.

Corresponding angles are always equal.

We can also have alternate angles which are always equal.

We can also have alternate interior and exterior angles which are equal.

The angles on the same side make upto 180 degrees

We have,

∠2 and ∠8 are alternate exterior angles.

This means,

∠2 = ∠8

We can write it as,

11x + 3 = 13x - 19

3 + 19 = 13x  - 11x

22 = 2x

x = 11

Now,

∠2 = 11x + 3 = 11 x 11 + 3 = 121 + 3 = 124

∠8 = 13x - 19 = 143 - 19 = 124

Thus,

The measures of ∠2 and ∠8 are 124.

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The calculated price is -1558. However, since prices cannot be negative in most real-world scenarios, we need to consider the valid range of prices. None of the options are correct.

To find the price at which sales are equal to Q=10, we need to substitute Q=10 into the inverse demand function P=342-190 and solve for P.

Let's start by substituting Q=10 into the inverse demand function:

P = 342 - 190 * Q

P = 342 - 190 * 10

P = 342 - 1900

P = -1558

The calculated price is -1558. However, since prices cannot be negative in most real-world scenarios, we need to consider the valid range of prices.

Given the options provided (a, 18; b, 36; c, 152; d, 171), we can see that none of them match the calculated price of -1558.

Therefore, none of the options are correct.

It is important to note that the calculated price of -1558 may not be realistic or feasible in the context of the problem. It is possible that there may be some error or inconsistency in the information provided.

If you have any additional information or if there are any constraints or limitations mentioned in the problem, please provide them, and I will be happy to assist you further.

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4 divided by 34 is equal to 0 remainder of 4/34, which can be simplified to 2/17 as a fraction.

So,

4 ÷ 34 = 0 remainder 4/34 = 2/17

What is the fraction?

A fraction is a mathematical representation of a part of a whole, where the whole is divided into equal parts. A fraction consists of two numbers, one written above the other and separated by a horizontal line, which is called the fraction bar or the vinculum.

To divide 4 by 34, we write it as a fraction with a numerator of 4 and a denominator of 1, i.e., 4/1.

To perform the division, we start by dividing the first digit of the dividend (4) by the divisor (34). Since 4 is less than 34, the quotient is 0, and the remainder is 4. We then bring down the next digit (0) to form the new dividend, which is now 40.

Next, we divide 34 into 40. The quotient is 1, and the remainder is 6. We bring down the next digit (0) and divide 34 into 60. The quotient is 1, and the remainder is 26.

Finally, we bring down the last digit (0) and divide 34 into 260. The quotient is 7, and the remainder is 2.

Therefore, 4 divided by 34 is equal to 0 remainder of 4/34, which can be simplified to 2/17 as a fraction.

So,

4 ÷ 34 = 0 remainder 4/34 = 2/17

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The quadrilateral whose vertices are A(2, 3); B(4, -2);C(-1,-4); D(-3, 1) is a square.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

Given A(2, 3); B(4, -2);C(-1,-4); D(-3, 1)

Length of AB = \(\sqrt{(4-2)^2+(-2-3)^2}\) = √29 units

Length of BC = \(\sqrt{(-1-4)^2+(-4--2)^2}\) = √29 units

Adjacent sides are equal.

So the quadrilateral must be square or rhombus.

Now, find the length of diagonals.

If the diagonals are equal, then it is square. If they are not equal, then it is rhombus.

AC = \(\sqrt{(-1-2)^2+ (-4-3)^2}\) = √58 units

BD = \(\sqrt{(-3-4)^2+(1--2)^2}\) = √58 units

Diagonals are equal.

So it is a square.

Hence the quadrilateral is a square.

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Answer:

1). AC=8.25cm

2). DB=7cm & EC=14cm

3). See Explanation

Step-by-step explanation:

According To the Question,

Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.

1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 2.5 / 3 = 3.75 / EC

On Solving we get,  

⇒ EC * 2.5 = 3.75 * 3  

⇒ EC * 2.5 = 11.25  

⇒ EC = 11.25 / 2.5  

⇒ EC = 4.5 cm

Thus,  

AC = AE + EC

⇒ AC = 3.75 + 4.50

⇒ AC = 8.25 cm  

Hence the measure of AC is 8.5 cm.

2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 4 / (x-4) = 8 / (3x-19)

on solving we get,

⇒ 3x-19 = 2(x-4)

⇒ 3x-19 = 2x-8

⇒x=11

Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm

And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm

3). If AD=2cm , BD= 4cm , show that BC = 3 DE

Thus, AB = AD + DB = 2+4 = 6cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD/AB = DE / BC

⇒ 2 / 6 = DE / BC

on solving we get

⇒ BC = 3 DE Hence, Proved

The correct expression for f • g in the function f (x) = 2 x, g (x) = 3 x is 3 • 2 .3 x. Thus, Option C is the answer.

Given functions are f(x) = 2x, g(x) = 3x. The domain and target set for functions f and g are the set R.

We have to find the expression for f . g which is equal to f(g(x))

Now f(x) = 2x, so we replace x with g(x) in f(x) and simplify it,

f(g(x)) = 2g(x)f(g(x)) = 2(3x) f(g(x)) = 6x.

Therefore, the correct expression for f . g is 6x.

So, the correct option is (c) 3 • 2 .3 x.

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According to the formula of area of rectangle, the length of each piece is 1.49 inches.

The formula to calculate the area of the rectangle is written as,

A = l x b

where l refers the length and b refers the breadth of the rectangle.

Here we have know that Allie is creating an art project using pieces of paper that are each 8. 06 inches long.

Here we also know that she tapes 5. 4 pieces together end-to-end.

Here the value 8.06 refers the total area of the paper and the value 5.4 refers the breadth of the paper.

Then according to the formula, the length is calculated as,

=> l = 8.06/5.4

=> 1.49

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Answer:

The following are the choices for this problem:A. x+4 B. x+3 C. x-5 D. 4x+3

Factoring 4x^4-21x^3-46x^2+219x+180,  this will give us then the short answer of x+4.

The factor theorem states that if x-n is a factor of function f(x) = 4x^4-21^3-46^2+219x+180 then f(x) = 0.

So let us evaluate f(-4) which gives 4(256) - 21(-64) -46(16) +219(-4) + 180 = 936

Since the function f(-4) does not equate to zero, we could say that x+ 4 is not a factor.

So using x+3: f(-3) = 4(81) - 21(-27) -46(9) +219(-3) + 180 = 0, so x+3 is a factor.

Step-by-step explanation:

hope this helps if do mark brainllest

Answer:

9ms^-2

Step-by-step explanation:

a = dV/dt

a = 54ms^-1/6s

a = 9ms^-2

An illustration of "Cluster sampling" is the practice of selecting a random sample of the city's gas stations, and then surveying every station's patrons.

As per the given question.

Thus, an implementation of "Cluster sampling" is the practice of randomizing sample of the city's gas stations, and thereafter surveying every station's patrons.

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Answer:

The amount invested at 8% was $11,000

The amount invested at 9% was $19,000

Step-by-step explanation:

Let the variable x represent the amount in $ invested at 8% and let y be the amount in $  invested at 9%

Total amount invested:
x + y = 30000   [1]

8% = 8/100 = 0.08

9% = 9/100 = 0.09

Interest at 8% on $x = 0.08x

Interest at 9% on $x = 0.09x

Total Interest :

0.08x + 0.09y = 2590  [2]

Using equations [1] and [2] we can solve for x and y

We have

x + y = 30000   [1]
0.08x + 0.09y = 2590  [2]

Multiply equation 1 by 0.08 to get
0.08x + 0.08y = 0.08(30,000)

0.08x + 0.08y = 2,400  [3]

Subtract [3] from [2] :

0.08x + 0.09y = 2590  
-
0.08x + 0.08y = 2400  
----------------------------------
       0x + 0.01y = 190

Divide both sides by 0.01
0.01y/0.01 = 190/0.01

y = = 19,000

Use [1] to get value of x

x + y = 30,000

x + 19,000 = 30,000

x = 30,000 - 19,000

x = 11,000

Answer:

-x -2

Step-by-step explanation:

1- Apply the Distributive Property

2- Calculate the product or quotient

3- Determine the sign

4- Reorder and gather like terms

   Collect coefficients of like terms

   Calculate the sum or difference