Let h(x) = x² - 8x.
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))

The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.

Let's expect that the round and hollow drum includes a stature of h and a span of r.

The volume of a barrel is given by: V = πr^2h.

We know that the drum includes a capacity of 806 cubic yards, so able to compose:

πr^2h = 806

We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.

The zone of the beat and foot of the drum is given by: A = πr^2.

The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:

C_topbottom = 2A = 2πr^2

The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:

A_side = 2πrh

The whole fetched of building the drum is in this manner:

C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh

Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:

h = 806/(πr^2)

Substituting this expression for h into the taken a toll condition, we get:

C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r

To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:

dC/dr = 4πr - 27404/r^2 =

Fathoming for r, we get:

r = (27404/(4π))^(1/3) ≈ 10.19 yards

Substituting this esteem of r back into the expression for h, we get:

h = 806/(π(10.19)^2) ≈ 2.46 yards

Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:

Span: 10.19 yards

Stature: 2.46 yards

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Answer: im pretty sure the answer is in the pdf, when you scroll down. its 126 cm^2

Step-by-step explanation:

The triangles are classified according to their sides as:

1. equilateral 2. Scalene   3. and 4. Isosceles   5. equilateral     6. and 7. scalene triangle.      8. Isosceles   9. and 10. Equilateral

Recall the following:

A triangle is equilateral if all three sides are equal.

It is isosceles if it has two equal sides.

A triangle is scalene if all three sides are of different lengths.

1. The triangle is equilateral because all sides are equal.

2. Scalene

3. and 4. Isosceles (two sides are equal)

5. All sides are equal, so it is an equilateral triangle.

6. and 7. The three sides have different lengths, therefore, it is a scalene triangle.

8. Isosceles

9. and 10. Equilateral

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The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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The simplified form of trigonometric functions by trigonometric formulas are listed below:

Case 1: 0.5√(2 - √3)

Case 2: (0.5√2) / (1 + 0.5√2)

Case 3: sin 6x

Case 4: sin θ

In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:

Case 1

sin 15° = √[(1 - cos 30°) / 2]

sin 15° = √[(1 - √3 / 2) / 2]

sin 15° = √[(2 - √3) / 4]

sin 15° = 0.5√(2 - √3)

Case 2

tan 22.5° = sin 45° / (1 + cos 45°)

tan 22.5° = (0.5√2) / (1 + 0.5√2)

The last two expressions are simplified and evaluated by double angle formulas:

Case 3

2 · sin 3x · cos 3x

sin 6x

Case 4

2 · sin 0.5θ · cos 0.5θ

sin θ

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The perimeter of the regular nonagon will be; 840.7 units

The in-radius of the regular nonagon is given as:

Radius, r =17

The perimeter is then calculated by:

P = 18r/Tan(π/9)

Substitute 17 for r;

P = 18(17)/Tan(π/9)

Evaluate the product of 18 and 17;

P =  306/Tan(π/9)

Evaluate the quotient

P =  840.7

Hence, the perimeter of the regular nonagon = 840.7 units

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The equivalent area of the parallelogram is 44.4m^2

The formula for finding the area of a parallelogram is expressed as:

Area = base * height

Given the following parameters

Base = 12m

Height = 3.7m

Substitute the given parameters into the formula to have:

Area = 12m * 3.7m

Area of the parallelogram = 44.4m^2

Hence the area of the parallelogram given is 44.4m^2

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1. The lateral surface area of the prism is 200 units²

2. The lateral surface area of the cylinder is 125.6 cm²

The lateral surface area is the area of the lateral surface.

The lateral surface area of a prism is expressed as;

LSA = (a+b+c)h

or perimeter of the base × height

LSA = (6+12+7)8

= 25 × 8

= 200 units²

The lateral surface area of a cylinder

= 2πrh

r = 4cm and h = 5cm

LSA = 2 × 3.14 × 4 × 5

LSA = 40 × 3.14

= 125.6cm²

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Step-by-step explanation:

( 11 * x ) + 2     where 'x' is a number

Answer:

angle m∠WXY intercepts the diameter WY.

Then,

m∠WXY  =  90°

(13x - 1)°  =  90°

13x - 1  =  90

Add 1 to each side.

13x  =  91

Divide each side 13.

x  =  7

Step-by-step explanation:

HOPE THIS HELPSSS

Answer:

Step-by-step explanation:

5 and 15

5^2=25

15^2=225

225+25=250

The volume of the prism will be 88 cubic units. Then the correct option is B.

Given that:

Length, L = 4 units

Width, W = 4 units

Height, H = 5.5 units

The volume of the prism is given as,

V = L x W x H

The volume of the prism is calculated as,

V = 4 x 4 x 5.5

V = 88 cubic units

The volume of the prism will be 88 cubic units. Then the correct option is B.

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The complete question is given below.

The volume of a rectangular prism would be 100 cubic cm.

Since we know that rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

We are given that base of a rectangular prism is 20 cm sq. . If the height of the prism is 5 cm, then;

Base area = 20 cm sq.

Height = 5 cm

Volume of a rectangular prism=Length X Width X Height

Volume of a rectangular prism= Base area  X Height

Volume of a rectangular prism= 20 x 5

= 100

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The values of AB and BC are equal and equal to

Information given in the problem includes

DE bisects AC at point B

AC = a + 23

AB = 3a + 4

From  the definition of a bisector, point B divides AC into two equal sides, this means that

AB = BC = (1/2) * AC

Substituting the value of AC and AB

AB = 3a + 4 = (1/2) * (a + 23)

3a + 4 = (1/2) * (a + 23)

solving for a

2 * (3a + 4) = a + 23

6a + 8 = a + 23

6a - a  = 23 - 8

5a = 15

a = 3

Then we have that:

AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13

and, AB = BC

so BC = 13

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Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

Applying the leg rule, the length of BC in simplest radical form is: x = x = √390

The leg rule is used to find missing lengths in a right triangle when an altitude intersects the hypotenuse and form segments.

The leg rule is given as:

Hypotenuse / leg = leg / part

Thus, using the image given, we have:

Hypotenuse (AC) = 65

Part (DC) = 6

Leg = x

Plug in the values:

65 / x = x / 6

Cross multiply:

x * x = 6 * 65

x² = 390

x = √390

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The different committees possible are 10,584. Option A is the answer.

Тhe number оf wаys tо choosе 4 men out оf 9 is givеn by 9C4, which is:

9C4 = (9!)/(4!5!)

= 126

Similаrly, the number оf wаys tо choosе 6 wоmen out оf 9 is givеn by 9С6, which is:

9С6 = (9!)/(6!3!)

= 84

So the tоtal number оf wаys tо choosе a committее consisting оf 4 men and 6 wоmen is:

126 * 84 = 10,584

Тherefore, the аnswer is (А) 10,584.

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If the standard error is 33.64, the size of the margin of error at 95% confidence is 65.93. So, correct option is D.

The margin of error (ME) can be calculated using the formula:

ME = z* (standard error)

where z is the z-score from the standard normal distribution corresponding to the desired level of confidence. For 95% confidence, z is 1.96.

Substituting the values given in the problem, we have:

ME = 1.96 * 33.64 = 65.93

Therefore, correct option is D.

This means that if we take multiple random samples of size 121 from the population, and calculate the sample mean and confidence interval for each sample, we can expect the true population mean to fall within 65.93 units above or below the sample mean, 95% of the time.

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A point that represent a striking deviation in the box plot above include the following: C. P.

In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).

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Answer:

4.   30°

Step-by-step explanation:

Sum of interior angles of a triangle = 180

y° + ∠XYZ + ∠YZX = 180

y° = 180 - 90 - 60 = 30°

Answer:

The answer would be 3.5 in decimal form.

Answer:

The answer is 55/12

Step-by-step explanation:

8-41/12

(8×12+1×(-41))/12

(96-41)/12

55/12

Answer:

El volumen en cm cúbicos es 108 cm cúbicos (o a la tercera potencia). La fórmula utilizada para encontrar el volumen es largo por ancho por alto.

By the theorem of triangles, the calculated value of y in the triangle ABC is 50 degrees

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

The triangle ABC

Also, the angles in the triangle are given as y, y and 80 degrees

By the theorem of triangles, the sum of angles in a triangle is 180 degrees

Representing the above statement as an equation, we have

y + y + 80 = 180

Evaluate

y = 50

So, we can conclude that the value of y is 50 degrees

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The total amount of FICA tax that was deducted from the executive's paychecks for the year 2018 is $10,860.80.

The FICA tax is imposed on both employees and employers to fund Social Security and Medicare which are federal programs that provide benefits for retirees, the disabled and children of deceased workers.

The Social Security tax will be calculated on the maximum taxable earnings of $128,400:

= $128,400 x 6.2%

= $7,961.20

The Medicare tax will be calculated on the entire earnings:

= $200,000 x 1.45%

= $2,900.

The total FICA tax will be:

= Social Security tax + Medicare tax

= $7,960.80 + $2,900

= $10,860.80.

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Answer:2.7

Step-by-step explanation:

Formula, divide the value in centimeters by 100 so 1 meter equals 100 centimeters

So 270 centimeters = 270/100 = 2.7

Answer:

C. (4, 0)

Step-by-step explanation:

(x, y)

a. (4, 3)

y = 12 - 3x

3 = 12 - 3(4)

3 = 12 - 12

3 = 0  false

b. (-4, 4)

y = 12 - 3x

4 = 12 - 3(-4)

4 = 12 + 12

4 = 24  false

c. (4, 0)

y = 12 - 3x

0 = 12 - 3(4)

0 = 12 - 12

0 = 0  true

d. (0, 4)

y = 12 - 3x

4 = 12 - 3(0)

4 = 12 - 0

4 = 12  false.

Answer:   C   (4, 0)

Step-by-step explanation:

your function y = 12 - 3x

They are asking which of those points are on the line

(x, y)   this is a format of a point where you can plug in x for x and y for y.

a.  (4, 3)  x=4  y=3  substitute and see if your answer is true

   3 = 12 -3(4)

   3 = 0   this is not true so (4, 3) is not a solution

b. (-4,4) x= -4 y=4

  4 = 12 - 3(-4)

  4 = 24  not true

c.  (4, 0)  x=4  y=0

  0 = 12-3(4)

  0 = 0  true      (4,0) is a solution

d. (0, 4)

4 =  12 - 3 (0)

4=12

The amount of flour that will be needed for 38 cakes is 912 grams therefore Johan does not have enough amount of flour

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

360 grams is needed for 15 small cakes

therefore for 1 small cake, 369/15 = 24grams will be needed

therefore for 38 small cakes = 38× 24 = 912 grams of flour will be needed.

Johan has 0.85 kg of flours which is equivalent to 0.85 × 1000grams = 850 grams of flour.

Since 912 grams will be needed for 38 small cakes , it shows that Johan does not have enough amount of flour for 38 small cakes.

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The three different values of n to demonstrate that 2n + 3n is equivalent to 5n are 1, 4 and 10.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2n + 3n

On simplifying the equation , we get

A = 5n

when n = 1 , we get

2n + 3n = 2(1) + 3(1) = 2 + 3 = 5

5n = 5(1) = 5

Therefore, both expressions give the same result of 5.

when n = 4 , we get

2n + 3n = 2(4) + 3(4) = 8 + 12 = 20

5n = 5(4) = 20

Again, both expressions give the same result of 20.

when n = 10 , we get

2n + 3n = 2(10) + 3(10) = 20 + 30 = 50

5n = 5(10) = 50

Hence , the equation is solved

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