given the following table with selected values of f(x) and g(x) evaluate f(g(1))

keeping in mind that a solution to a system of equations is where their graph intersect, Check the picture below.

The probability that numbers 5 and 6 will both be picked is 1/15.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

If a bowl contains 6 balls, marked with the numerals 1 through 6, and two balls are picked out at random, then there are 15 possible outcomes.

6C2 = 15

Since there is only one chance where 5 & 6 will both be picked from 15 total possible outcomes, then the probability is 1/15.

p = 1 / 15

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The functions f(x) = ∛x - 1 and g(x) = x³ + 1 are inverse functions.

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

Distinct Functions

The functions are represented as

f(x)=\sqrt[3]{x-1} and g(x)=x^3+1

Rewrite the functions properly

So, we have the following representations

f(x) = ∛x - 1 and g(x) = x³ + 1

Using the function compositions, the following equation must be true

f(g(x)) = x

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

f(g(x)) = ∛x³ + 1 - 1

Evaluate the like terms

f(g(x)) = ∛x³

So, we have

f(g(x)) = x

Hence, the functions are inverse functions

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Answer: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

An engineer erects a 75-foot cellular telephone tower. Find the angle of elevation to the top of the tower at a point on level ground 50 feet from its base.

The upper bound of the value of A is 10.71

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

The equation of A is then given as

A = f/g

The number of decimal places implies that:

f = 2.75 + 1 = 3.75

g = 0.3 + 0.05 = 0.35

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

A = 3.75/0.35

Evaluate the quotient

A = 10.71

Hence, the upper bound is 10.71

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Using the concept of rotational symmetry, the angle of rotation about the center that results in an image that matches the original figure is; Option A:  90

Rotational symmetry is defined as a process that requires the rotation of a given object about a reference point to produce its image which has the same characteristics. This tells us that its dimensions, measure of internal angles and size do not change except its orientation. The orientation depicts the way in which the object is positioned.

The sum of an angle formed at a point is 360 degrees. Thus turning a given object about a point implies its rotation with respect to a measured  angle.

Thus in the diagram given in the question, the pattern shown divides the angle at the centered point into four equal parts.

Thus;

Angle of rotation = 360/4 = 90 degrees

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The volume comparison of the given data is written below:

In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.

Given, The height of the cone and cylinder is twice the radius, while the radius of a sphere is the same.

The volume of the cone =   πr²h

Since, h = 2r

The volume of the cone =   πr² * 2r = 2/3 πr³

The volume of the Cylinder = πr²h

Since, h = 2r

The volume of the Cylinder = πr² * 2r = 2πr³

The volume of the sphere = 4 πr³

Thus, the volume of 3 cones = 2πr³

that is also equal to The volume of one Cylinder.

Thus, the volume of 2 cones = 4/3πr³

that is also equal to The 1/3 volume of the Cylinder.

Thus, the volume of 1 sphere = 4πr³

that is also equal to The volume of 2 cylinders.

Thus, the volume of 1 cone = 2/3πr³

that is also equal to The 1/6 volume of the cone.

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The ball reaches a height of approximately 1.60256 feet on the fifth bounce.

We can use the formula for the height of the nth bounce, h(n) = h(1) * (0.83)^(n-1), where h(n) is the height of the nth bounce, h(1) is the height of the first bounce, and 0.83 is the bounce coefficient (the percentage of the previous height that the ball reaches on each subsequent bounce).

Given that the first bounce reaches a height of 5.2 feet, we can plug in h(1) = 5.2 into the formula and solve for h(5), the height of the fifth bounce.

h(5) = 5.2 * (0.83)^4

h(5) = 5.2 * 0.30769

h(5) = 1.60256

The height is 1.60256 feet.

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The equation that can be used to solve for the price of each ticket is $296 = 16t - 92. The cost of each ticket is $24.25.

Theequqtion represents the total cost of the tickets

Total amount paid by Mrs. Perkey = total cost of the tickets - total amount saved

$296 = (16 x t) - (16 x $5.75)

$296 = 16t - 92

$296  + 92 = 16t

$388 = 16t

t = $388 / 16

t = $24.25

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Answer:

[tex]a) \frac{d}{dx} (3e {}^{x} ) \\ [/tex]

Recall the property

[tex]\frac{d}{dx} [c \times f(x)] = c \times f'(x) \\[/tex]

[tex] = 3 \frac{d}{dx} e {}^{x} = 3e {}^{x} \\ [/tex]

[tex]b.) \: \: \frac{d}{dx} (x {}^{2} e {}^{x} ) \\ [/tex]

[tex] = x {}^{2} \times e {}^{x} +e {}^{x} \times 2x \\[/tex]

[tex] = e {}^{x} (x {}^{2} \times 2x) \\ [/tex]

[tex]c.) \: \: \frac{d}{dx}( \frac{e {}^{x} }{x {}^{3} } ) \\ [/tex]

[tex] = \frac{x {}^{3} \times e {}^{x} - e {}^{x} \times {3x}^{2} }{ {x}^{6} } \\ [/tex]

[tex]= \frac{x {}^{2} {e}^{x} (x - 3) }{ {x}^{6} } \\ [/tex]

[tex]= \frac{ {e}^{x} (x - 3) }{ {x}^{4} } \\ [/tex]

The inequality that represents the number of songs, Sarah can buy is 0.75n ≤ 20.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Let the number of songs be n.

Since Sarah’s favorite online music store has all songs on sale for $0.75 each and sbe has to $20 spend on songs.

The inequality that represents the number of songs, Sarah can buy is:

(0.75 × n) ≤ 20

0.75n ≤ 20.

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The given can be simplified as [tex]\frac{6a^{2} -1}{a^{2} }[/tex].

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is [tex]\frac{4a^{2} -1}{a^{2} } - \frac{4 - 2a}{a-2}[/tex]

It can be simplified as follows,

[tex]\frac{4a^{2} -1}{a^{2} } - \frac{4 - 2a}{a-2}[/tex]

⇒ [tex]\frac{4a^{2} -1}{a^{2} } - \frac{2(2 - a)}{a-2}[/tex]

⇒ [tex]\frac{4a^{2} -1}{a^{2} } + 2[/tex]

⇒ [tex]\frac{6a^{2} -1}{a^{2} }[/tex]

Hence, the simplification of the given expression is obtained as [tex]\frac{6a^{2} -1}{a^{2} }[/tex].

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Answer:

The first graph (topmost graph)

Step-by-step explanation:

Correlation coefficient of -1: Negative correlation

As variable x (horizontal axis) increases, variable y (vertical axis) should decrease.

Hence, gradient of the graph is negative, sloping downwards as x increases.

Graph 2 is eliminated (positive correlation approximately 1)

Graph 4 is also wrong as there is simply no correlation. (Points are random with no fixed pattern or trend)

Graphs 1 and 3 show negative correlation.

However, for graph 3, several points are not accurate, leading to a straight line not being drawn accurately. (Slightly off) . Correlation of this graph is negative but not closest to -1.

Hence, the first graph is the closest to -1 in terms of correlation coefficient.

Therefore ,we can state after answering the given question that the exponents value is 0.

Exponentiation is a mathematical expression represented by the letter bn that involves numeric values: a base amount, b, and a multiplier, or power, n. It is also referred to as "b raised here to nth power." Exponents demonstrate the number of times that a number has indeed been increased by itself. For example, 2-3 (expressed as 23) means: 2 x Two x 4 = 8. 2 + 3 does not equal 6, nor does 23. Remember that an integer whose power is one is equal to itself. Exponents can be used as a way to express large numbers as powers. Exponent, then, seems to be the quantity that conveys how many time a quantity can be expressed.

Here,

Given  : x⁻² /y⁴

=> here x= 0

So,

=> 0/y⁴

=> 0

hence,

the total is 0.

Therefore ,we can state after answering the given question that the exponent value is 0.

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The complete question is "How do you simplify and write  x⁻² /y⁴ with positive exponents?"

The ratio of dramas to movies, given the number of drama, comedy, and action movies, is 1 : 5.

The ratio of dramas to movies can be found when we first find the number of movies in total :

= Drama movies + Comedy movies + Action movies

= 3 + 8 + 4

= 15 movies

The ratio of dramas to movies would be:

Number of drama movies : Number of total movies

3 movies : 15 movies

In the simplest terms :

3 / 3 : 15 /3

1 : 5

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Full question is:

There are 3 drama movies 8 comedy movies and 4 action movies what's the ratio of dramas to movies ?

Answer:

The answer is -1

Step-by-step explanation:

2^(2x+1) = 2^2x × 2^1 = 2^2x × 2

after this we can make appointments

2^x = t

and then solve it :)

The best deal for buying onions include the following: A. 2 onions for $1.04.

In Business management, price can be defined as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

Based on the information provided, we can calculate each of the price of the onions as follows;

2 for $1.04 = 1/2 × 1.04

2 for $1.04 = $0.52

4 for $2.52 = 1/4 × 2.52

4 for $2.52 = $0.63

8 for $4.32 = 1/8 × 4.32

8 for $4.32 = $0.54

16 for $9.12 = 1/16 × 9.12

16 for $9.12 = $0.57

Therefore, the best deal would be buying 2 onions for $1.04 because it offers the cheapest price.

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If the length of the leg of the isosceles triangle is 17 cm and the base is 16 cm then the length of altitude to the base is  15cm .

An Isosceles triangle is defined as a triangle in which any two side are of  equal length .

The Length of the leg is = 17cm ,

the base of the triangle is = 16cm ;

let the length of the altitude to the base be = x cm ,

The altitude to the base of the triangle divides it into two right angle triangle.

So , in one of the right angle triangles, Base = 16/2 = 8 cm

the Hypotenuse of triangle = length of the leg = 17 cm

By Applying Pythagoras theorem,

we get ,

17² = 8² + x²   ,

289 = 64 + x² ,

x² = 289 - 64

x² = 225 ,

taking Square root(√) on both the sides ,

we get , x = 15 .

Therefore , the length of the altitude to the base is = 15 cm .

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To find the altitude of an isoceles triangle with a base length of 16 cm and a leg length of 17 cm, use the Pythagorean Theorem. Calculate 17² + 16² = c², then solve for c² to get c = √545 = 23.3 cm.

The altitude of the triangle can be found using the Pythagorean Theorem.

a² + b² = c²

17² + 16² = c²

289 + 256 = c²

545 = c²

c = 23.3 cm

(or)

17² + 16² = c² => 289 + 256 = c²

=> 545 = c²

=> c = √545 = 23.3 cm

The altitude of an isoceles triangle can be found by using the Pythagorean Theorem. The formula for the theorem is a² + b² = c², where a and b are the two sides and c is the hypotenuse, which is the altitude. In this situation, a is the leg length of 17 cm and b is the base length of 16 cm. Substituting these values into the equation gives 17² + 16² = c². Solving for c² gives c = √545 = 23.3 cm, which is the length of the altitude.

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$56.4 is the cost of the 6 pairs of shoes.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that shoe store was having a back to school sale where you could buy 5 pairs of shoes for $47.40.

If a large family decided to buy 6 pairs of shoes then the cost of these 6 pair of shoes we have to find.

Let x be the cost of 6 pair of shoes.

5/47=6/x

Apply cross multiplication

5x=282

Divide both sides by 5

x=56.4

Hence, $56.4 is the cost of the 6 pairs of shoes.

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Answer:

y = 4x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, - 1 ) and (x₂, y₂ ) = (3, 7 )

m = [tex]\frac{7-(-1)}{3-1}[/tex] = [tex]\frac{7+1}{2}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then

y = 4x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 7 ) , then

7 = 4(3) + c = 12 + c ( subtract 12 from both sides )

- 5 = c

y = 4x - 5 ← equation of line

Answer:

52%

Step-by-step explanation:

13/25 x 100 = 52%

Answer:

52%

Step-by-step explanation:

13/25 = .52

To change a decimal to a percent, multiply the decimal by 100%

.52 x 1005 = 52%

This makes sense because half of 25 is 12.5 which would be 50% and 13 is just a little more than 12.5

Answer:

☐ 3 pints

☐ 1 gallon

Step-by-step explanation:

4cups = 32 fluid ounces = 2 pints = 1 quart = 0.25 gallons

30 fl oz is less than 4 cups

2 pints is exactly 4 cups but we are looking for numbers greater than 4 cups

3 pints is more than 4 cups  so this is a correct choice

1 quart is exactly 4 cups but we are looking for numbers greater than 4 cups

1 gallon is 16 cups so a valid choice

From the table, we conclude that on Wednesday and Sunday the low temperature farthest from 0°C

The investigator must summarize the facts in tabular form after gathering them in order to study their prominent features. The presentation of data is the name given to such a configuration.

Any acquired data may be arranged in a frequency distribution table and then displayed using pictograms or bar graphs. The lengths of the equally wide bars that make up a bar graph are controlled by the frequency and scale you select.

Observing the data is represented in a table form where rows represent the number of days in a week and two columns represent the high and low temperatures of Anchorage, Alaska.

On Wednesday and Sunday, the low temperature was - 13°C and it is the farthest from 0°C.

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Answer:

[tex]x=57[/tex]

Step-by-step explanation:

By the converse of the alternate interior angles theorem, [tex]x=57[/tex].

Answer: 1000 thousands

Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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The number of volunteers needed for the 5k races is 50 and the number of volunteers needed for the 10k races is 65.

The system of equations that represent the question is:

7a + 9b = 935 equation 1

7a + 7b = 805 equation 2

Where:

The elimination method would be used to determine the values of a and b.

Subtract equation 2 from equation 1

2b = 130

b = 130 / 2

b = 65

Substitute for b in equation 1 :

7a + 9(65) = 935

7a + 585 = 935

7a = 935 - 585

7a = 350

a = 350 /7

a = 50

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Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.