The graph of
y = x3 is transformed as shown in the graph below. Which equation represents the transformed
function?
5
4
3
2
1
3
-1
1
2
5
X
-2
y=x²-4
y =(x-4)

Answer:

12x-48=144

Step-by-step explanation:

X= 16

Answer:

x=16

Step-by-step explanation:

12(x - 4) = 144

Multiply 12*x and 12*-4

12x-48=144

Add 48 to get x on only one side

12x=192

Divide 12x/12 and 192/12

x=16

The differentiable function the value of f(4) is(d: 7.9541).

To find the value of f(4), integrate the given derivative of f(x). Let's integrate √(x²) + 2cos(x)/3 with respect to x.

∫√(x²) + 2cos(x)/3 dx

The integral of √(x²) simplified as follows:

∫√(x²) dx = ∫|x| dx = (1/2)(x |x|) + C

integrate 2cos(x)/3:

∫2cos(x)/3 dx = (2/3) ∫cos(x) dx = (2/3) sin(x) + C

∫(√(x²) + 2cos(x)/3) dx = (1/2)(x |x|) + (2/3) sin(x) + C

that f(1) = 2. So, this information to find the constant C.

f(1) = (1/2)(1 |1|) + (2/3) sin(1) + C

2 = (1/2)(1) + (2/3) sin(1) + C

2 = 1/2 + (2/3) sin(1) + C

C = 2 - 1/2 - (2/3) sin(1)

the constant C, f(4):

f(4) = (1/2)(4 |4|) + (2/3) sin(4) + C

f(4) = 2(4) + (2/3) sin(4) + (2 - 1/2 - (2/3) sin(1))

f(4) = 8 + (2/3) sin(4) + (2 - 1/2 - (2/3) sin(1))

To determine the exact value of f(4), the values of sin(4) and sin(1). sin(4) = -0.7568 and sin(1) =0.8415.

Substituting these values,

f(4) = 8 + (2/3)(-0.7568) + (2 - 1/2 - (2/3)(0.8415))

f(4) =8 - 1.511 + 1.666 - 0.5609

f(4) = 8 - 0.0459

f(4) = 7.9541

To know more about function here

https://brainly.com/question/30721594

#SPJ4

Complete question:

let f be a differentiable function such that f(1)=2 and f′(x)=√x2 2cosx 3. what is the value of f(4) ?

a. 10.790

b. 8.790

c. 12.996

d. 7.9541.

e. -6.79

a) The Pearson correlation coefficient for the original set of scores is -0.2.

b) The Pearson correlation coefficient for the modified set of scores is -0.2.

c) The Pearson correlation coefficient for the modified set of scores is -0.6071.

To compute the Pearson correlation coefficient, we need to calculate the covariance and the standard deviations of the X and Y variables. Let's calculate each step:

X: 4, 6, 3, 9, 6, 2

Y: 5, 5, 2, 4, 5, 3

a. Compute the Pearson correlation:

Step 1: Calculate the means of X (\(\bar{x}\)) and Y (\(\bar{y}\)):

\(\bar{x}\) = (4 + 6 + 3 + 9 + 6 + 2) / 6 = 5

\(\bar{y}\) = (5 + 5 + 2 + 4 + 5 + 3) / 6 = 4.6667

Step 2: Calculate the deviations from the mean for X (dx) and Y (dy):

dx = X - \(\bar{x}\): (-1, 1, -2, 4, 1, -3)

dy = Y - \(\bar{y}\): (0.3333, 0.3333, -2.6667, -0.6667, 0.3333, -1.6667)

Step 3: Calculate the covariance (cov) and the standard deviations (σx and σy):

cov = (dx * dy) / (n - 1)

   = (-1 * 0.3333 + 1 * 0.3333 + -2 * -2.6667 + 4 * -0.6667 + 1 * 0.3333 + -3 * -1.6667) / (6 - 1)

   = -1.2

σx = √((dx * dx) / (n - 1))

   = √(((-1)² + 1² + (-2)² + 4² + 1² + (-3)²) / (6 - 1))

   = √(30 / 5)

   = √(6)

σy = √((dy * dy) / (n - 1))

   = √((0.3333²+0.3333²+(-2.6667)²+(-0.6667)²+0.3333² + (-1.6667)²)/(6- 1))

   = √(6)

Step 4: Calculate the Pearson correlation coefficient (r):

r = cov / (σx * σy)

 = -1.2 / (√(6) * √(6))

 = -1.2 / 6

 = -0.2

Therefore, the Pearson correlation coefficient for the original set of scores is -0.2.

b. Adding two points to each X value and computing the correlation for the modified scores:

Modified X: 6, 8, 5, 11, 8, 4

To compute the correlation, we follow the same steps as in part a:

Step 1: Calculate the means of the modified X (\(\bar{x}\)) and Y (\(\bar{y}\)):

\(\bar{x}\)= (6 + 8 + 5 + 11 + 8 + 4) / 6 = 7

\(\bar{y}\) = (5 + 5 + 2 + 4 + 5 + 3) / 6 = 4.6667

Step 2: Calculate the deviations from the mean for the modified X (dx) and Y (dy):

dx = Modified X - \(\bar{x}\): (-1, 1, -2, 4, 1, -3)

dy = Y - \(\bar{y}\): (0.3333, 0.3333, -2.6667, -0.6667, 0.3333, -1.6667)

Step 3: Calculate the covariance (cov) and the standard deviations (σx and σy):

cov = (dx * dy) / (n - 1)

   = (-1 * 0.3333 + 1 * 0.3333 + -2 * -2.6667 + 4 * -0.6667 + 1 * 0.3333 + -3 * -1.6667) / (6 - 1)

   = -1.2

σx = √((dx * dx) / (n - 1))

   = √(((-1)² + 1² + (-2)² + 4² + 1² + (-3)²) / (6 - 1))

   = √(30 / 5)

   = √(6)

σy = √((dy * dy) / (n - 1))

   = √((0.3333² + 0.3333² + (-2.6667)² + (-0.6667)² + 0.3333² + (-1.6667)²) / (6 - 1))

   = √(6)

Step 4: Calculate the Pearson correlation coefficient (r):

r = cov / (σx * σy)

 = -1.2 / (√(6) * √(6))

 = -1.2 / 6

 = -0.2

Adding a constant to every score does not affect the value of the correlation. The correlation remains the same at -0.2.

c. To compute the correlation coefficient after multiplying each of the original X values by 2, let's follow the steps:

Modified X: 8, 12, 6, 18, 12, 4

Step 1: Calculate the means of the modified X (\(\bar{x}\)) and Y (\(\bar{y}\)):

\(\bar{x}\) = (8 + 12 + 6 + 18 + 12 + 4) / 6 = 10

\(\bar{y}\) = (5 + 5 + 2 + 4 + 5 + 3) / 6 = 4.6667

Step 2: Calculate the deviations from the mean for the modified X (dx) and Y (dy):

dx = Modified X - \(\bar{x}\): (-2, 2, -4, 8, 2, -6)

dy = Y - \(\bar{y}\): (0.3333, 0.3333, -2.6667, -0.6667, 0.3333, -1.6667)

Step 3: Calculate the covariance (cov) and the standard deviations (σx and σy):

cov = (dx * dy) / (n - 1)

   = (-2 * 0.3333 + 2 * 0.3333 + -4 * -2.6667 + 8 * -0.6667 + 2 * 0.3333 + -6 * -1.6667) / (6 - 1)

   = -3.4667

σx = √((dx * dx) / (n - 1))

   = √(((-2)² + 2² + (-4)² + 8² + 2² + (-6)²) / (6 - 1))

   = √(100 / 5)

   = √(20)

   ≈ 4.4721

σy = √((dy * dy) / (n - 1))

= √((0.3333² + 0.3333²+(-2.6667)²+(-0.6667)²+0.3333² + (-1.6667)²)/(6 - 1))

=√(6)

Step 4: Calculate the Pearson correlation coefficient (r):

r = cov / (σx * σy)

= -3.4667 / (4.4721 * √(6))

≈ -0.6071

Multiplying each score by a constant affects the value of the correlation coefficient. In this case, multiplying each original X value by 2 resulted in a correlation coefficient of approximately -0.6071. It shows a stronger negative correlation compared to the original correlation coefficient of -0.2. The correlation coefficient became closer to -1, indicating a stronger linear relationship between the modified X and Y variables.

Learn more about Pearson correlation here

https://brainly.com/question/30916205

#SPJ4

The solution to each of the arithmetic sequence are:

1) a₁₀ = 56

2) a₁₀ = 87

3) missing term is 13

4) missing term is 14

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is nth term

d is common difference

1) a = 2

d = 6

a₁₀ = 2 + (10 - 1)6

a₁₀ = 2 + 54

a₁₀ = 56

2) a = 15

d = 8

a₁₀ = 15 + (10 - 1)8

a₁₀ = 87

3) The missing term will be gotten by finding the common difference.

d = (22 - 4)/2

d = 18/2

d = 9

missing term = 4 + 9 = 13

4) The missing term will be gotten by finding the common difference.

d = (53 - 25)/2

d = 28/2

d = 14

missing term = 4 + 9 = 14

Read more about Arithmetic Sequence at: https://brainly.com/question/6561461

#SPJ1

Using composite functions, the expression that models the distance that she runs is:

D. 5.5 - 0.1t.

The composite function of f(x) and g(x) is given by:

(f ∘ g)(x) = f(g(x)).

In this problem, we have that:

Hence the distance as a function of the temperature is given as follows:

(D ∘ S)(t) = D(S(t)) = 0.5(11 - 0.2t) = 5.5 - 0.1t.

Which means that option D is correct.

More can be learned about composite functions at https://brainly.com/question/10687170

#SPJ1

The addition equation to represent Jackson's net change in money is x + (-y) = 4.63

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Jackson receives 4.63 as his change at the grocery store. He places it into a charity donation jar at the register.

WE need to Write an addition equation to represent Jackson's net change in money.

Given that :

The change received = 4.63

The Net change in money :

Let initial amount before purchase is represented by  x

The Cost of item purchased = y (negative as it is incurred)

The Net change in money:

Initial amount + cost of item purchased = change received

x + (-y) = 4.63

Therefore, an addition equation to represent Jackson's net change in money is x + (-y) = 4.63

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ1

Answer:

2πr + 4a = 8

Step-by-step explanation:

Answer:

0.6915692913385827

Step-by-step explanation:

use pi days arc calc

The calculated length of the segment AD is 14

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

B is the midpoint of AC

BD = 9 and BC = 5

Using the above as a guide, we have the following:

AB = BC = 5

CD = BD - BC

So, we have

CD = 9 - 5

Evaluate

CD = 4

So, we have

AD = AB + BC + CD

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

AD = 5 + 5 + 4

Evaluate

AD = 14

Hence, the length of the segment AD is 14

Read more about line segments at

https://brainly.com/question/24778489

#SPJ1

Answer:

12 bowls

Step-by-step explanation:

If marry had nine pounds of salad, and each salad bowl holds 3/4 pounds each, then the equation is 9 divided by 3/4, which equals twelve.

Answer:

The answer to your problem is:

Step-by-step explanation:

As the mean is 17 the total value if you for example have 5 numbers will be 5*17 = 85.

you can conclude  1, 3 or 4:

For example the numbers could be 2, 8, 24, 25 and 26.

you could have a mode if you include  2 16's instead of the 8 and 24 but you cant say that's not probable.

The median is not 17 nor is it a typical value.

Which would basically conclude to option B.

Thus the answer to your problem is:

The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

Know more about NPV here:

https://brainly.com/question/32720837

#SPJ11



Answer:

38

Step-by-step explanation:

all you have to do is add 22 and 16

Answer:

It would take him 12 hours to drive 696 miles

Step-by-step explanation:

hope this helps!!

Answer:

-3 to the power of x

-2 to the power of x

-1 to the power of x

0 to the power of x

1 to the power of x

2 to the power of x

3 to the power of x

Step-by-step explanation:

Answer:

Both conclusions are correct

Step-by-step explanation:

Ivan: The product of an even number of negative fractions is always positive.

When even numbers of same negative fractions are multiplied together, the product is positive.

For instance: -1 × -1

Since the total numbers to be multiplied are even (two -1), the product becomes +1

Ivan's conclusion is correct.

Polina: The product of an odd number of negative fractions is always negative.

When odd numbers of same negative fractions are multiplied together, the product is negative.

For instance: -1 × -1 × -1 × -1 ×-1

Since the total numbers to be multiplied are odd (five -1), the product becomes -1

(-1 × -1) × (-1 × -1) ×-1

= +1 × +1 × -1

The multiplication of same sign gives positive value while the multiplication of two different signs gives a negative value

= +1 × -1

= -1

Polina's conclusion is correct

Both are correct.

Answer:

both of them

Step-by-step explanation:

The van contains 12 students and the bus contain 33 students.

The given information is:

The senior class at the high school rented and filled 14 vans and 11 buses with 531 students.

For this, we have to convert it into an equation:

14v+11b=531---------(1)

A High school b rented and filled 7 vans and 7 buses with 315 students.

For this, we have to convert it into an equation:

7v+7b=315----------(2)

To, find the number of students in the van and bus we have to solve two equations :

14v+11b=531

7v+7b=315*2

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

14v+11b=531

14v+14b=630

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

        -3b=-99

           b=33

The total number of students on the bus is 33 members.

Now substitute the b value in any equation, and substitute in equation(2) we get the v value:

7v+7(33)=315

7v+231=315

7v=84

v=12

The total number of students in the van is 12 members.

To learn more about Quadratic equations:

https://brainly.com/question/24334139

#SPJ4

A. Slope = Rise / Run = 1/1 = 1

B.  $25

C.  $75

Answer:

Step-by-step explanation:

The angles (2x- 10) and (4x+ 16) are consecutive interior angles and therefore are corresponding

Corresponding angles sum to 180

Surface area = 400 unit square

Surface area = 1100 unit square

Surface area = 1100 unit square

Surface area = 2400 unit square

The first figure is a cuboid;

Surface area of a cuboid = 2lw+2lh+2hw

L = 9

W = 11

h = 4

Surface area = 2( 9 × 11) + 2(9 × 4) + 2( 4× 11)

Surface area = 2(99) + 2(36) + 2(44)

Surface area = 198 + 72 + 88

Surface area = 400 unit square

Surface area of a triangular prism = Area of top + area of base

Area of the top = 1/ 2 b × h

Area = 1/2 × 4 × 8

Area = 16 unit square

Area of base = length × width

Area = 4× 4

Area = 16 unit square

Surface area = 16 + 16

Surface area = 1100 unit square

Surface area of a cylinder = 2πrh + 2πr² = 2 ( 3. 412 × 7. 5 × 15) + 2 ( 3. 141× 7. 5 × 7.5)

Surface area = 706. 95 + 353. 48

Surface area = 1100 unit square

Surface area of a cone =πr(r+ √h² + r2)

Surface area = \(3. 142 * 15 ( 15 + \sqrt{10^2 +34^2 }\)

Surface area = \(47. 13 * 50. 44\)

Surface area = 2400 unit square

Learn more about surface area here:

https://brainly.com/question/76387

#SPJ1

The x value of a point where a vertical line intersects a function represents the input for that output y value. If we can draw any horizontal line that intersects a graph more than once, then the graph does not represent a function because that y value has more than one input.

Answer:

always negative

Step-by-step explanation:

for example -3*2 = -6

The product of a positive integer and a negative integer is always negative.

The reason is that you do inverse operation. Meaning the inverse of a positive is negative.

Answer:

so what is the question ??

The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

The perimeter of a rectangle is P = 2(L + W) where

Given that P = 16 m,

P = 2(L + W)

16 = 2(L + W)

16/2 = L + W

L + W = 8

So, W = 8 - L

The area of the rectangle, A = LW where

Since W = 8 - L, substituting W into the equation for A, we have

A = LW

A = L(8 - L)

A = 8L - L²

So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

Learn more about area of a rectangle here:

https://brainly.com/question/8294080

#SPJ11

Answer: 1.5 inches

Step-by-step explanation:

Answer:

y<-7x+2

Explanation:

The slope-intercept form of a line is: y=mx+b

• When slope, m = -7

• y-intercept, b = 2

We have:

Since the boundary line is dashed, the inequality sign has to be < or >.

However, since the area below the line is shaded, we can now conclude that the inequality sign is: <

The inequality that matches this description is:

Answer:

The amount of force needed to move an object is related to the object's mass. ... The greater the object's mass, the greater the force needed to move it, stop it or change its speed or direction. 3. An object with a small mass is easier to stop or cause a change in motion than an object with a large mass.

Step-by-step explanation:

Answer:

3

Step-by-step explanation: