Given circle with radius of 5cm.
Find out
(a) diameter
(b) perimeter
(c) area

The average rate of change of f(x) = -3x² + 1 over each of the given intervals are; -18, 6 nd 38

We are given the function;

f(x) = -3x² + 1

(a) From 2 to 4;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(4) = -3(4)² + 1

f(4) = -47  (4, -47)

Slope = (-47 - (-11))/(4 - 2)

Slope = -36/2

Slope = -18

(B) From -2 to 0;

f(-2) = -3(-2)² + 1

f(2) = -12 + 1

f(2) = -11  (-2, -11)

f(4) = -3(0)² + 1

f(4) = 1  (0, 1)

Slope = (1 - (-11))/(0 - (-2))

Slope = 12/2

Slope = 6

(C) From 2 to 5;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(5) = -3(5)² + 1

f(5) = -74  (0, -74)

Slope = ((-74) - 2)/(0 - 2)

Slope = -76/-2

Slope = 38

Read more about average rate of change at; https://brainly.com/question/8728504

#SPJ1

Answer:

y = 47

Step-by-step explanation:

All of the angles in a triangle must add up to 180. The angle marked 3y can help us find the missing angle of the triangle: 180-3y
Then you can make an equation to help solve for y:
50 + (2y-3) + (180-3y) = 180
Combine like terms:
227-y=180
y = 47

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y=47 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \:(2y - 3) + 50 = 3y[/tex]

[tex]\qquad \tt \rightarrow \:2y - 3 + 50 - 3y = 0[/tex]

[tex]\qquad \tt \rightarrow \:2y - 3y + 47 = 0[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 47[/tex]

[tex]\qquad \tt \rightarrow \:y = 47 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

B

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f(x)= 9280 - 20x [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y - 29 = 0[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y = 29[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{20 x+ y}{320} = 29[/tex]

[tex]\qquad \tt \rightarrow \: 20x + y = 29 \sdot320[/tex]

[tex]\qquad \tt \rightarrow \: y = 9280 - 20x[/tex]

[tex]\qquad \tt \rightarrow \: f(x) = 9280 - 20x[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

See attached images for work.

[tex] \huge\underline{\underline{\boxed{\color{blueviolet}{ANSWER}}}}[/tex]

★ 15 trucks can carry 26,850 kg weight

★ We've to find the weight carried by one truck

[tex]\huge \pink {\overline{ \quad \quad \quad \quad \quad \quad \quad\quad \quad}}[/tex]

[tex] \sf{Number \: of \: trucks = 15 }[/tex]

[tex] \sf{Weight \: carried \: by \: one \: truck = \frac{26,850Kg}{15} }[/tex]

[tex] \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 1790Kg[/tex]

Therefore , the weight carried by one truck is 1790 kg

Answer:

X = 92 degrees

Step-by-step explanation:

the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88

180-88= 92 so X = 92

The option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have a table given that shows the survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose.

The probability of a person that is a student:

P(student) = (75+15)/110 = 0.83

The probability:

P(student|pirate) = 75/80 = 0.93

The probability of both events is different.

Thus, the option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

Answer:

$46,819 is the average unemployed salary

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

Here, we can use an angle rule.

We see that angles [tex](8x+50)[/tex]° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.

This means we can use the rule:

Corresponding angles are equal.

This means that:

[tex]8x + 50 = 130[/tex]

We can now use this equation we have formed to solve for [tex]x[/tex]:

[tex]8x + 50 = 130\\8x = 80\\x = 10[/tex]

Therefore, our final answer is [tex]x=10[/tex].

A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,

Vertical Shift by 4 units,

f(x)+4

Vertical stretch by a factor of 3

g(x) = 3(f(x) + 4)

g(x) = -3x + 12

Hence, the function g(x) can be written as g(x) = -3x + 12.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

#Step1

It will result -2x-2y=-8

#2

#3

add

Find x

The Volume and Surface Area of Prism is 294 in² and 114.33 in³.

A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.

Surface rea of rectangular prism,

= 2( lb +bh +lh)

= 2 ( 7*7 + 7*7+ 7*7)

= 2 ( 49+49+49)

= 2*3*49

= 294 in²

Now, Volume,

= bhl/3

= 7*7*7/3

= 114.33 in³

Learn more about volume and surface area here:

https://brainly.com/question/23302816

#SPJ1

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]

      [tex]=142506[/tex]

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]

where;

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]

[tex]\mathbf{^nC_r = 142506}[/tex]

Learn more about combination here:

https://brainly.com/question/11732255

#SPJ11

The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter

As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.

The general form of the cosine function representing the displacement of the rider is:

f(t) = a cos(bt+c) + d, where:

amplitude = |a| which is the distance that travels above and below the midpoint

period = 2 π/|b| which is the time period i.e. time required to complete one cycle

-c/b is the phase shift.

d = vertical displacement of the function

Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.

So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.

The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.

The rider starts from the bottom position, so there will be no phase shift, so c=0

Given that the center of the wheel is 19 m above the ground, so d=19m

Therefore the equation will be

height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter

Learn more about Sinusoidal function

here: https://brainly.com/question/2410297

#SPJ10

Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:

Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:

[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].

0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The numbers should be 2, 2, 5, 9 and 12.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Let us take numbers 2, 2, 5, 9 and 12.

mean = 30/5

mean= 6

range = 10.

Learn more about mean, mode and median here:

https://brainly.com/question/15323584

#SPJ1

Answer:

B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Answer:

A=30

B=35

C=44

Step-by-step explanation:

Answer:

f(1) = 2

f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

the point of coordinates (1 , 2) is on the graph

Then

f(1) = 2

…………………………

We notice that :

f(2) = 4

f(3) = 8

f(4) = 16

16/8 = 8/4 = 4/2 = 2/1 = 2

________________________

This means the common ratio

of the geo sequence = 2

Hence ,

f(n) = 2 × f(n - 1)

Answer: f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

The statements that are true about circle Q are:

The measure of the central angle is 45°.  The measure of the entire circle is 360°.  This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8

To find the area of the shaded sector, this will be:

A = πr² = π(6²) = 36π

1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units.  This is not 4 square units.

The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.

Learn more about circle on:

https://brainly.com/question/24375372

#SPJ1

Answer:

1,3,4

Step-by-step explanation:

Answer:

Yes, the relation is proportional because the ratios are equivalent between each pair of values

Step-by-step explanation:

 Proportional relationships are relationships with equal ratios.

Entries in the respective columns are:

        column 1 (Minutes)              column 2 (Blocks)                 Ratios

                   6                                           3                                    1/2                

                   14                                          7                                    1/2

                   20                                         10                                  1/2

  As the ratio of Blocks and Minutes is same for every row,

   the given table represent a proportional relationship.

  hence, option c is correct.

   Yes, because the ratios are equivalent between each pair of values.

 learn more about proportional relationships at

 brainly.com/question/3181194

#SPJ10

Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)

x = 90°

2x = 180°

Step-by-step explanation:

angle VTS= angle TSR (alternate angle)

now in ∆TRS,

2x + x + x = 360° (angle sum property of ∆)

4x = 360°

x = 90°

Answer:

C

Step-by-step explanation:

= The square root of (5^2+2^2)= The square root of 29 ---> C

The choice trigonometric ratio is tangent and the distance is 3. 98 meters.

The given angle is 86

The opposite side is given as 57 meters

The distance is in the adjacent

Thus, trigonometric ratio to use is the tangent

Tangent = opposite/ adjacent

We have,

tan 86 = 57/x

14. 300 = 57/x

x = 57/ 14. 300

x = 3.i 98 meters

Thus, the choice trigonometric ratio is tangent and the distance is 3. 98 meters.

Learn more about tangent here:

https://brainly.com/question/8120556

#SPJ1

Answer:

y = (- 2/3)x - 3

Step-by-step explanation:

y = mx + c

y = (- 2/3)x + c

- 1 = (- 2/3)(-3) + c

-1 = 2 + c

c = - 3

Therefore,

y = (-2/3)x - 3

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

y = y coordinate              → given: - 1

m = slope                        → given: - 2/3

x = x coordinate              → given: - 3

b = y intercept                 → need to find

y = -2/3x + b → -1 = -2/3(-3) + b

-1 = 2 + b

subtract 2 from both sides

-1 - 2 = 2 - 2 + b

-3 = b

y = -2/3x - 3

The graph of the function has an axis of symmetry at x = 3 will be D. f(x) = x² - 6x - 1. On a coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).

It should be noted that the axis of symettry is the line that divides an object into two equal halves.

Here, the graph of the function has an axis of symmetry at x = 3 is option D. On the coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).

Learn more about graph on:

brainly.com/question/14669826

#SPJ1

Answer: D.  f(x) = x² - 6x - 1

Right on Edge 2023 :)

The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

The figure is divided into two parts one is a rectangle and the second is a semicircle.

Area of figure = Area of rectangle + Area of a semicircle

Area of figure = L × B + (πr²/2)

A = 10 cm × 15 cm + (3.14 ×(5)^2/2)

A= 189.25 cm²

Hence the area of the shape will be 189.25 cm²

To learn more about the area, refer to the link;

https://brainly.com/question/11952845

#SPJ1

Answer:

[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]

Step-by-step explanation:

= (5z + 6)(2z + 1)(2x - 1)

= (5z + 6)[(2z)² - (1)²]

= (5z + 6)(4z² - 1)

Distributing

= 5z (4z² - 1) + 6(4z² - 1)

= 20z³ - 5z + 24z² - 6

Arrange

= 20z³ + 24z² - 5z - 6

[tex]\rule[225]{225}{2}[/tex]