Evaluate the function below it’s a given output value of 8

f(x)=40/5x-1

The value of angle k is 129⁰.

The value of angle b is 64.5⁰.

The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.

k + 113 + 118 = 360 (sum of angles in a circle)

k + 231 = 360

k = 360 - 231

k = 129⁰

The value of angle b is calculated by applying the principle of intersecting chord theorem.

b = ¹/₂ arc k

b = ¹/₂ x 129

b = 64.5⁰

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The volume of C.a .cylinder is twice the volume of a cone.

The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.

The cylinder's volume  can be expressed as π r² h,  along with the surface area  which can be expressed as 2π r h + 2π r² and this can be used to get the values.

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Answer:8.52%

Step-by-step explanation:

There are 14 utensils in the drawer, and then there will be one less in the bowl after each successive utensil is removed. There are then 3 possibilities for the same kind being removed on all pulls:

P(3 spoons) = (6/14)*(5/13)*(4/12)

P(3 forks) = (5/14)*(4/13)*(3/12)

P(3 knives) = (3/14)*(2/13)*(1/12)

Add all of these outcomes together and you'd get about 8.52%

Step-by-step explanation:

a probability is airways the ratio

desired cases / totally possible cases

2 questions, each with a true or false answer option.

that gives us

2 × 2 = 4 answer options in total (the totally possible cases).

but only one of the four combinations is completely right.

so, the probability is

1/4

the 4 possibilities are

true true

false false

true false

false true

formally we can get to the result that way :

the first question has 2 options.

the probabilty to get it right is therefore

1/2

the same for the second question

1/2

but both have to be right for the desired result (question 1 AND question 2 have to be right), so, we need to combine both individual probabilities :

1/2 × 1/2 = 1/4

Note that the probability of both questions being right by guessing is 0.25 or 1/4.

P (both correct) = P(correct on Q1 ) x p(correct on Q2)
=   0.5 x 0.5
= 0.25 or 1/4

Note that probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are.

Statistics is the study of occurrences guided by probability.

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The value of arc LN in the intersecting chords is 100⁰.

The value of arc LN is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

arc LN = 2 x m∠LMN

From the diagram, we have, m∠LMN = 50⁰

The value of arc LN is calculated as follows;

arc LN = 2 x 50⁰

arc LN = 100⁰

Thus, the value of arc LN is based on intersecting chord theorem.

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The values of x and y are given as follows:

The dimensions are obtained applying the proportions in the context in the problem.

The conversion rate between feet and inches is given as follows:

1 feet = 12 inches.

Hence the dimensions of the picture are given as follows:

The height of the entire frame is of 8 ft, while y is half the height outside the picture, thus the value of y is obtained as follows:

y = 0.5(8 - 2) = 3 ft.

The value of x is given as follows:

x = 0.5(12 - 4.5)

x = 3.75 ft.

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The amount of dry ingredients used in the cake recipe is approximately 7 cups.

We have,

3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.

Now, first convert all quantity in same unit.

3 ½ cups of flour

= 3 cups + 0.5 cups

= 3 cups and 8 ounces.

and, 2 ⅔ cups of sugar

= 2 cups + 0.67 cups,

= 2 cups and 10.72 ounces.

and, 1 ¾ cups of cocoa

=1 cup + 0.75 cups

= 1 cup and 12 ounces.

So, the total amount

= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

= 7 cups

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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Answer:

13 years

Step-by-step explanation:

The box and whisker plot that has the greatest interquartile range from the options given is option 3.

In order to calculate the interquartile range of a dataset, we can determine or find the difference between the values at the edges of the rectangular box in a box and whisker plot that displays the data set.

This also implies that we subtract the first quartile from the third quartile.

From the options given, we see that in option 3, the box and whisker plot has the largest interquartile range. This is because: Q3 - Q1 is approximately 9.

9 is higher than the interquartile ranges of the other datasets, therefore, option 3 is the right option.

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Answer:

    [tex]\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1[/tex]

Step-by-step explanation:

Slope intercept form of a line equation is

y = mx + b

where

m = slope

b = y-intercept

A perpendicular line to y = mx + b will have a slope of -1/m

Let's first find the equation for line z in slope-intercept form
Slope m for a line  = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line

Slope of line z is
[tex]m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}[/tex]

So line z will have an equation of the form
[tex]y = -\dfrac{3}{5}x + b[/tex]

We know that a line perpendicular to this line will have a slope of
[tex]- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}[/tex]

So the equation of the perpendicular line is
[tex]y = \dfrac{5}{3}x + b[/tex]

Only one of the 4 choices, name choice A has this slope of 5/3

Therefore the correct answer choice is A

There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:

The perpendicular line passes through (3, 6). This means when x = 3, y =6

Substitute these values of x, y into the equation for the perpendicular line and solve for b

[tex]y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1[/tex]

This corresponds to Choice A

Answer: The spinner is probably because 5 was spun approximately 200 times

Step-by-step explanation:

The length of arc on equator is 69.08 miles.

We have

Radius of Earth = 3960 miles

Angle = 1 degree

So, the length of arc on equator is

= θ/360 x 2πr

= 1/360 x 2 (3.14) (3960)

= 69.08 miles

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Answer:

A. To convert pounds to kilograms, we need to multiply by 0.453592. Therefore, the fish from region A weighs about 130 kg (286 x 0.453592), rounded to the nearest whole number.

B. Similarly, the fish from region B weighs about 279 kg (614 x 0.453592), rounded to the nearest whole number.

Answer:

[tex]\textsf{1)}\quad y = \dfrac{4}{3}x-\dfrac{13}{3}[/tex]

[tex]\textsf{2)} \quad y = \dfrac{3}{2}x-6[/tex]

Step-by-step explanation:

To find the equation of a line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1), we first need to find the slope of the line joining (1, 2) and (-2, -2).

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{-2-1}=\dfrac{-4}{-3}=\dfrac{4}{3}[/tex]

Parallel lines have the same slope, so the slope of the parallel line is m = 4/3.

Substitute the found slope and point (4, 1) into the point-slope formula:

[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - 1 &= \dfrac{4}{3}(x - 4)\\\\y - 1 &= \dfrac{4}{3}x-\dfrac{16}{3}\\\\y &= \dfrac{4}{3}x-\dfrac{13}{3}\end{aligned}[/tex]

Therefore, the equation of the line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1) is:

[tex]\boxed{y = \dfrac{4}{3}x-\dfrac{13}{3}}[/tex]

[tex]\hrulefill[/tex]

To find the equation of a line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3), we first need to find the slope of the line joining (2, -3) and (-1, -1).

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-(-3)}{-1-2}=\dfrac{2}{-3}=-\dfrac{2}{3}[/tex]

The slopes of perpendicular lines are negative reciprocals, so the slope of the parallel line is m = 3/2.

Substitute the found slope and point (2, -3) into the point-slope formula:

[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - (-3) &= \dfrac{3}{2}(x - 2)\\\\y+3&= \dfrac{3}{2}x-3\\\\y &= \dfrac{3}{2}x-6\end{aligned}[/tex]

Therefore, the equation of the line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3):

[tex]\boxed{y = \dfrac{3}{2}x-6}[/tex]

Answer:

(−3,−π/6)

Step-by-step explanation:

Note that the point is on the circle whose radius is labeled 3, so r=3 or r=−3. Of the choices available, only an angle of −π6, drawn from the negative x axis plots at the point A. So θ=−π6, and r must be negative, as the angle is measured from the negative x axis. Thus, the polar coordinates are (−3,−π6).

This query is about identifying the polar coordinates of a specific point on a graph. However, without an accompanying graphical representation, a definitive answer cannot be provided based on the options given. Polar coordinates represent a point using the distance from a reference point and an angle from a reference direction.

The question is about polar coordinates, a way of expressing the location of a point in two-dimensional space. Without seeing the actual point A on a graph, it is not possible to definitively determine its polar coordinates from the provided choices. However, it is very crucial to know that polar coordinates represent a point in the plane using the distance from a reference point and an angle from a reference direction. The distance, represented as r, should always be non-negative whereas the angle θ can range from 0 to 2π, or in negative, -π to π. An understanding of these may help you determine the coordinates of the point A in your problem.

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The area of the front cover a face perpendicular to the thickness is 72 in².

Given:

A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.

The volume of the dictionary will be 216in².

Volume = W×L×H

Surface = volume/ height

= 216/3

= 72 in²

Hence, the area of the front cover of a face perpendicular to the thickness is 72 in².

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Answer:

satiscal

Step-by-step explanation:

The probability that Bashir chooses a card that is either a face card or a spade is 11/26.

To find the probability that the card Bashir chooses is either a face card or a spade, we need to add the probabilities of the two events occurring and then subtract the probability of their intersection (choosing a face card that is also a spade).

First, we need to find the probability of choosing a face card. There are 12 face cards in a deck (4 jacks, 4 queens, and 4 kings), and a total of 52 cards, so the probability of choosing a face card is

P(F) = 12/52 = 3/13

Next, we need to find the probability of choosing a spade. There are 13 spades in a deck (from 2 to ace), and a total of 52 cards, so the probability of choosing a spade is

P(S) = 13/52 = 1/4

To find the probability of choosing either a face card or a spade, we can use the formula

P(F or S) = P(F) + P(S) - P(F and S)

We need to find the probability of choosing a face card that is also a spade (their intersection). There are only 3 face cards that are spades (jack of spades, queen of spades, king of spades), so the probability of choosing a face card that is also a spade is

P(F and S) = 3/52

Now we can plug in the values to get

P(F or S) = P(F) + P(S) - P(F and S)

P(F or S) = 3/13 + 1/4 - 3/52

P(F or S) = 12/52 + 13/52 - 3/52

P(F or S) = 22/52

P(F or S) = 11/26

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The constant of proportionality is equal to 3/10.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/10 = 6/20 = 9/30

Constant of proportionality, k = 3/10.

Therefore, the required linear equation is given by;

y = kx

y = 3/10(x)

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Answer:

Theoretical Probability

Step-by-step explanation:

Total number of possible outcomes

The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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The range of the monthly sales goals is; 37,000.

We are given the stem plot :

Stem  Leaf

1          2, 5, 5, 8

2          4, 4, 6

3          4, 6

4          7, 8, 9

The largest number is 49 and the smallest is 12. Since is in thousands, the numbers become 49,000 and 12,000.

Range = highest value - the lowest value

Range = 49,000 - 12,000 = 37,000

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The amount of paint needed to paint all the surfaces of the 11 poles is; 1260 ft².

It follows from the task content that the amount of paint required to paint all the surfaces of the 11 poles is required to be determined.

First, since the surface area of a cylindrical pole is; A = 2πr (r + h).

where height,h = 22 and radius, r = diameter / 2 = 1.6 / 2 = 0.8 feet.

Therefore, A = 2 × 3.14 × 0.8 (22 + 0.8)

A = 114.5472 ft²

Therefore, for all 11 poles; the total area is; 11 × 114.5472 = 1260 ft² to the nearest whole number.

Ultimately, the quantity of paint needed is such that it is sufficient for an area of; 1260 ft².

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1. <C= 90 degree

AC =  13.25 unit

<B= 60 degree

2.  <C= 90 degree

AC =  13.

<B= 60 degree

1. Using Sine law

sin C/4 = sin 30/2 = sin B/ AC

so, sin C/4 = 1/4

sin C = 1

C= 90 degree

and, <B= 180 - 30- 90= 60 degree

So, sin 30/2 = sin 60/ AC

1/4 AC = √3/2

AC = 2√3

2. Using Sine law

sin 30/ 7.65 = sin B / 15.3

1/15.3 = sin B/15.3

sin B= 1

B = 90 degree

and, <C= 180 - 90 - 30 = 60

So, 1/15.3 = sin 60/ C

C = 13.25

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Answer:

1265 kg of protein

Step-by-step explanation:

If 55kg is eaten in one day then in 23 days there will be x kgs.

To find 'x':

55 x 23 = 1265

The number of ways to choose the starting 11 players with all seniors playing is 4845.

We have,

Since the coach wants all seniors to play, we must choose the remaining

(11 - 7 = 4) players from the remaining (6 + 6 + 8 = 20) players who are not seniors.

The number of ways to choose 4 players from 20 players is given by the combination formula:

[tex]^{20}C_4[/tex]

= 20! / (4! * 16!)

= 4845

Therefore,

The number of ways to choose the starting 11 players with all seniors playing is 4845.

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The number of blue cars and the number of red cars are 3 and 5 respectively

Let b and r represent the number of blue cars and  the number of red cars respectively.

There are a total of 8 cars, we have:

b + r = 8

There are 135 clowns in total. Blue cars hold 20 clowns and red cars only hold 15, we have:

20b + 15r = 135.

Thus, we have a system of equations with two variables:

b + r = 8   ---- (1)

20b + 15r = 135  ---- (2)

We can use elimination to solve for b and r.

Let's use elimination. Multiplying the first equation by 20 and second equation by 1:

20 * (b + r = 8)                  = 20b + 20r = 160  (subtract)

1 * (20b + 15r = 135)         = 20b + 15r = 135

                                      ...............................................

                                                      5r = 25

                                      ...............................................

r = 25/5

r = 5

Using (1):

b + r = 8

b + 5 = 8

b = 8 - 5

b = 3

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The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos²θ sinθ

y = 4 sin²θ cosθ

We have,

We can use the following conversions from polar to Cartesian coordinates:

x = r cosθ

y = r sinθ

To convert the polar equation r = 4 sin(θ)cos(θ) into Cartesian coordinates, we substitute r with its equivalent value 4 sin(θ)cos(θ) and use the above conversions:

x = (4 sinθ cosθ) cosθ

y = (4 sinθ cosθ) sinθ

Simplifying these expressions, we get:

x = 4 cos^2θ sinθ

y = 4 sin^2θ cosθ

The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos^2θ sinθ

y = 4 sin^2θ cosθ

or, in standard form:

x = 4xy

This is the Cartesian equation in terms of x and y, obtained by replacing sinθ and cosθ with x and y, respectively.

Thus,

The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos²θ sinθ

y = 4 sin²θ cosθ

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