The degree of the polynomial function f(x) is 4. The roots of the equation f(x) =0 are -2,-1,1 and 3. Which graph could be the graph of f(x)?

Answer: y = ax2 + bx + c

looks like a slightly trick question...

y = ax2 + bx + c is the standard form...

y = a(x - h)2 +k is the graphing form

Step-by-step explanation:

Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).

Then the total differential is

[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]

[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]

The length of the confidence interval is the margin of error, which is the ratio of the standard deviation and the square root of sample size. Hence, to reduce the length of confidence interval by half, Quadruple the sample size.

Recall :

Evaluating an hypothetical scenario :

Let standard deviation, σ = 2

Sample size = 50

Margin of Error = 2/√50 = 0.554

Using Quadruple of the sample size : (50 × 4) = 200 samples

(0.227 ÷ 0.554) = 0.5

Therefore, increasing the sample size, reduces the margin of error. Hence, using quadruple the sample size, will reduce the margin of error by half.

Learn more : https://brainly.com/question/13403969

Answer:

a

Step-by-step explanation:

Answer:

60

step by step explanitation

Answer:

((c)).g(x) = 3 × 2^x +2..

Answer:

Your dollar target for food service is $22,680

Step-by-step explanation:

It is given in the question that total sales are = $54,000

your food service is 42% of your total sales = 42% × $54,000

=  × 54,000

= 0.42 × 54,000

= $22,680

Answer:

The bias is they only picked men to test the new medication on to see if it was ready for the general public to use.

Step-by-step explanation:

Answer:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = - 5x + 750

Next we divide both sides by 2:

2y/2 = - 5x/2 + 750/2

y = - 2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x (-2.5x+375)

A = - 2.5x² + 375x

This is a quadratic equation, with values a = - 2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation

x = - b/2a

x = - 375/2 (-2.5) = - 375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = - 2.5x² + 375x

A = - 2.5 (75) ² + 375 (75) = - 2.5 (5625) + 28125 = - 14062.5 + 28125 = 14062.5

Step-by-step explanation:

Answer:

x = 42

Step-by-step explanation:

24+8 = 32

[tex]\frac{x}{24}[/tex] = [tex]\frac{x+14}{32}[/tex]

32x = 24(x+14)

32x = 24x+336

8x = 336

x = 42

Answer:

a-648²

b-4.2²

Step-by-step explanation:

least 108*48 = 648²

Answer:

6x + 24

Step-by-step explanation:

6 * (4 + x) = 6 * 4 + 6 * x = 6x + 24

Answer:

The cotton is $9 per yard and the wool is $11 per yard

Step-by-step explanation:

Create a system of equations where c is the cost per yard for the cotton and w is the cost per yard for the wool.

50c + 80w = 1330

75c + 20w = 895

Solve by elimination by multiplying the bottom equation by -4:

50c + 80w = 1330

-300c - 80w = -3580

Add these together and solve for c:

-250c = -2250

c = 9

Plug in 9 as c into one of the equations, and solve for w:

50c + 80w = 1330

50(9) + 80w = 1330

450 + 80w = 1330

80w = 880

w = 11

The cotton is $9 per yard and the wool is $11 per yard.

Answer:

1/64

Step-by-step explanation:

25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.

picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.

picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.

so,

1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625

9514 1404 393

Answer:

  $144

Step-by-step explanation:

Multiplication is used to simplify repeated addition. To find the total cost, add up the costs of each of the tickets.

  6 child tickets will cost $10 +10 +10 +10 +10 +10 = 6×$10 = $60

  6 adult tickets will cost $14 +14 +14 +14 +14 +14 = 6×$14 = $84

Then the total cost of all of these tickets will be ...

  $60 +84 = $144 . . . . cost of zoo tickets in all

Answer:

Step-by-step explanation:

Semicircle:

Shaded area of semicircle = area of outer semicircle - area of inner semicircle

Outer semicircle:

d = 40 m  r = 40/2 = 20m

Area of outer semicircle = πr²

                                        = 3.14*20*20

                                        =    1256 m²

Inner semicircle:

d = 30 m  r = 30/2 = 15 m

Area of outer semicircle = πr²

                                        = 3.14*15*15

                                        =  706.5 m²

Shaded area of semicircle = 1256 - 706.5 = 549.5 m²

Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²

Rectangle on both sides:

Length = 50 m

width = 30 m

Area of shaded rectangles on both sides = 2* (length *width)

                                                                      = 2* 50 * 30

                                                                       = 3000 m²

Shaded area = 1099 + 3000 = 4099 m²

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the amount invested at 9%. Then the difference in interest amounts is ...

  (9%)x -(5%)(26876 -x) = 720.78 . . . . . assuming a 1-year investment

  0.14x -1343.80 = 720.78 . . . . . . . . . simplify

  0.14x = 2064.58 . . . . . . . . . . . . . . add 1343.80

  x = 14,747 . . . . . . . . . . . . . . . . divide by 0.14

$14,747 is invested at 9%; $12,129 is invested at 5%.

9514 1404 393

Answer:

  A.  96

Step-by-step explanation:

The surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular lateral faces.

  A = 2(1/2)bh + PH

where b is the base of the triangle, h is its height, P is the perimeter of the triangle, and H is the height of the prism.

  A = (3 cm)(4 cm) +(3 +4 +5 cm)(7 cm) = 12 cm² +84 cm²

  A = 96 cm²

The surface area of the triangular prism is 96 square cm.

Answer:

true

mark me brainist if it comes out to be true

Answer:

The answer is TRUE.

Step-by-step explanation:

Answer:

R = 0.862

Strong positive relationship

Step-by-step explanation:

Given the data:

Test Chemistry Student Score,

x Grade, y

1 2 3 4 5 6 7 8 9 10 11 12

Score,x = 65 50 55 65 55 70 65 70 55 70 50 55

Grade, y = 85 74 76 90 85 87 94 98 81 91 76 74

Using technology :

The CORREL function in excel, calculators will give accurate value of the correlation Coefficient between two variables, x and y. The correlation Coefficient obtained using technology is : 0.862

The correlation Coefficient value ranges between (-1 and 1) with values closer to either - 1 or 1 reflecting stronger relationship. A value of 0 means there is no relationship between the variables. Negative values indicate negative relationships while positive indicates positive association between the variables.

Therefore. With a correlation Coefficient of 0.862, the correlation Coefficient can be interpreted as meaning that ; there is a strong positive relationship between score and grade.

We know

Sum of two interior angles=exterior angle

[tex]\\ \sf\longmapsto 20°+120°=<y[/tex]

[tex]\\ \sf\longmapsto <y=20°+120°[/tex]

[tex]\\ \sf\longmapsto <y=140°[/tex]

Hope it helps

Answer:

24 men will take 3 days to dig a 72 meter trench.

Step-by-step explanation:

If 16 workers dig an 80-meter long trench in five days, how long will it take 24 workers to dig a 72-meter long trench?

If 16 workers take 5 days to dig an 80 meter long trench,

24 workers will definitely take lesser time to dig a 72 meter long trench as both the length of the trench and the number of workers is more

Lets write these values down in order: Number of Workers, Length of Trench, Number of Days:

16 80 5

24 72 ?

Lets represent the ? as x:

We know that Ratio of Trench length to men = 80/16 : 72/24 or 5 : 3

Which means that the first set (16 men) will take 5 days to dig a trench of 80 meters.

And therefore from the above ratio (5: 3), 24 men will take 3 days to dig a 72 meter trench.

HOPE IT WILL DEFINITELY HELP YOU

a=2,5937

b=2,7048

c=2,7181

d=2,7183

e=2,7183

Answer:

V: x = 1; H: y = 4

Step-by-step explanation:

Point A is at x = 1 and y = 4

A vertical line at x=1 and a horizontal line at y = 4

Answer : 19.6cm

I hope this helps you! Have a good day!

Answer:

31.5

Step-by-step explanation:

Angle Z+ Angle X+ Angle Y=180

As the triangle is isosceles, Z=X, hence Z=63/2=31.5