Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x)= 1= ² + 4
X-4

The function value for f(g(4)) include the following: f(g(4)) = 6.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

By critically observing the table of values of the function f and g shown in the image attached above, we can reasonably infer and logically deduce the following function values:

g(4) = 1

f(g(4)) = f(1)

f(1) = 6.

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The price of coffee in 2009 would have been approximately $5.15.

To find the price of coffee in 2009, we need to use the index number for that year. According to the table, the index number for 2009 is 103.0.

We can set up a proportion to solve for the price in 2009:

Price in 2015 / Index in 2015 = Price in 2009 / Index in 2009

Let's denote the price in 2009 as x:

$4.48 / 89.8 = x / 103.0

Now we can solve for x:

x = ($4.48 / 89.8) * 103.0

x ≈ $5.15

Therefore, the price of coffee in 2009 would have been approximately $5.15.

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Answer:

D. 2

Step-by-step explanation:

y=mx+b

m is the slope in this case, and by your equation, we can easily see that the answer should be D, with a slope of 2.

Answer:

d.2

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

y=2x+6

m=2

b=6

slope=2

Answer:

-5

Step-by-step explanation:

Using the Law of Cosines with angle 103° and adjacent sides 9 and 6, the remaining side is approximately 12.26 units long.

To find the remaining sides of the triangle, we can use the Law of Cosines. Let's assume that the angle of 103 degrees is opposite side c, and the adjacent sides are a = 9 and b = 6.

The Law of Cosines states:

[tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C)

Plugging in the known values:

[tex]c^2 = 9^2 + 6^2[/tex] - 2 * 9 * 6 * cos(103°)

Simplifying the equation:

[tex]c^2[/tex] = 81 + 36 - 108 * cos(103°)

Now we need to evaluate cos(103°).

Using a scientific calculator or trigonometric table, we find that cos(103°) ≈ -0.3090.

Substituting the value of cos(103°) back into the equation:

[tex]c^2[/tex] = 81 + 36 - 108 * (-0.3090)

Simplifying further:

[tex]c^2[/tex] = 117 + 33.2724

[tex]c^2[/tex]≈ 150.2724

Taking the square root of both sides:

c ≈ √150.2724

c ≈ 12.26

Therefore, the remaining side (opposite the angle of 103 degrees) is approximately 12.26 units long.

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The area of the circle with a radius of 5 cm is approximately 78.53975 square centimeters.

To calculate the area of a circle, we need to use the formula A = πr², where A represents the area and r represents the radius of the circle. In this case, the given radius is 5 cm.

Plugging the value of the radius into the formula, we get:

A = π(5 cm)²

Simplifying the equation further, we have:

A = π(25 cm²)

Using the value of π (pi) as approximately 3.14159, we can calculate the area:

A ≈ 3.14159 × 25 cm²

A ≈ 78.53975 cm²

It's important to note that the area of a circle is always expressed in square units, as it represents the amount of space enclosed by the circle.

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Answer:

35/12

Step-by-step explanation:

9 2/3 = 29 / 3

6 3/4 = 27 / 4

We have to find the common denominator. In this case, it is 12

29/3 x 4/4 = 116/12

27/4 x 3/3 = 81/12

Now we can subtract both fractions.

116/12 - 81/12 = 35/12

So, the answer is 35/12

Answer:

35/12 or 2 11/12

Step-by-step explanation:

9 2/3 = 29/3

6 3/4 = 27/4

29/3 - 27/4 = 35/12

The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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The options that apply are:

A. A list of all questions from the lessons

B. Description of what you need to know or apply

C. Concepts tested

D. Reference column.

The options that are typically included in a table for each unit are:

- A list of all questions from the lessons: This helps in organizing and categorizing the questions based on the specific unit or topic.

- Description of what you need to know or apply: This provides an overview or summary of the key concepts, knowledge, or skills that are covered in the unit.

- Concepts tested: This section highlights the specific concepts or skills that will be tested or assessed in relation to the unit. It helps students understand the focus areas and what they need to prioritize in their learning.

- Reference column: This column may include additional information such as page numbers, section titles, or references to specific resources or materials that are relevant to the unit. It serves as a guide for further exploration or reference.

A brief quiz, on the other hand, is not typically included in a table for each unit. Quizzes are usually separate assessments that are administered to evaluate understanding and mastery of the unit's content.

So, the options that apply are:

- A list of all questions from the lessons

- Description of what you need to know or apply

- Concepts tested

- Reference column

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Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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Answer:

Step-by-step explanation:

To find the value of an investment compounded continuously, we can use the formula:

A = P * e^(rt)

Where:

A is the final amount

P is the principal amount (initial investment)

e is the mathematical constant approximately equal to 2.71828

r is the annual interest rate (as a decimal)

t is the time period in years

In this case, P = $10,000, r = 0.0315 (3.15% expressed as a decimal), and t = 13.

Plugging in the values into the formula, we get:

A = $10,000 * e^(0.0315 * 13)

Calculating the exponential part:

A = $10,000 * e^(0.4095)

Using a calculator or a math software, we can evaluate e^(0.4095) to get approximately 1.506.

A = $10,000 * 1.506

A ≈ $15,060.

The matrix[tex]A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.[/tex]

To find the inverse of a matrix, we can use the formula:[tex]A^(-1) = (1/det(A)) * adj(A)[/tex]

Where A^(-1) represents the inverse of matrix A, det(A) is the determinant of A, and adj(A) denotes the adjugate of A.

Given the matrix A with 2 rows and 2 columns:

A = | 4  4 |

      | 2  1 |

To find A^(-1), we need to calculate the determinant of A and the adjugate of A.

The determinant of A (det(A)) is calculated as:

det(A) = 4 * 1 - 2 * 4 = -4

The adjugate of A (adj(A)) is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements:

adj(A) = |  1  -4 |

             | -2   4 |

Finally, we can find A^(-1) using the formula mentioned earlier:[tex]A^(-1) = (1/det(A)) * adj(A)A^(-1) = (1/-4) * | 1 -4 |[/tex]

                       | -2   4 |

Simplifying the expression:

A^(-1) = | -0.25  1 |

              |  0.5  -1 |

Therefore, the matrix A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.

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Answer:

Ok, Here is your answer

Step-by-step explanation:

To find the percentage of players who played well on the baseball team, we need to divide the number of players who played well by the total number of players and then multiply by 100.

Number of players who played well = 6

Total number of players = 11

Percentage of players who played well = (6/11) x 100%

= 54.55%

Therefore, the answer is 54.55%. Hence, option D, 54.55%, is the correct answer.

Answer: There will be a total of 18 books per box.

Step-by-step explanation:

Here,

Total number of boxes = 7

Total number of books = 126

Let n be the total number of books per boxes.

Now,

n = 126 / 7 = 18

Therefore, the total number of books per boxes is 18.

Answer:

5.4 ft²

Step-by-step explanation:

To find the surface area of the cone-shaped megaphone, use the surface area of a cone formula.

[tex]\boxed{\begin{minipage}{7cm}\underline{Surface area of a cone}\\\\$S.A.=\pi r^2+\pi rl$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\ \phantom{ww}$\bullet$ $l$ is the slant height of the cone.\\\end{minipage}}[/tex]

The radius of a circle is half its diameter.

Therefore, if the diameter of the cone's circular base is 1.2 ft, then its radius is r = 0.6 ft.

Given values:

Substitute the values into the formula and solve:

[tex]\begin{aligned}\textsf{Surface area}&=3.14 \cdot0.6^2+3.14 \cdot 0.6 \cdot 2.25\\&=3.14 \cdot 0.36+3.14 \cdot 0.6 \cdot 2.25\\&=1.1304+1.884 \cdot 2.25\\&=1.1304+4.239\\&=5.3694\\&=5.4\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the surface area of the cone-shaped megaphone is 5.4 ft² (rounded to the nearest tenth).

Answer:

Step-by-step explanation:

x-6y=4

To solve these equations, we can use the elimination method. We want to eliminate one of the variables, either x or y, by multiplying one of the equations by a constant so that the coefficients of one variable will be the same in both equations but with opposite signs. For example, we can multiply the first equation by 4 to get:

-20x - 24y = -128

Then we can add this equation to the second equation to eliminate y:

-20x - 24y + 4x - 6y = -128 + 4

Simplifying this equation gives:

-16x - 30y = -124

Now we can isolate one variable in terms of the other:

-16x - 30y = -124

-16x = 30y - 124

x = (30/(-16))y + (-124/(-16))

x = (-15/8)y + 31/2

We can substitute this expression for x into either of the original equations to solve for y. For example, substituting into the first equation gives:

-5((-15/8)y + 31/2) - 6y = -32

Multiplying by -8 to clear the fractions gives:

75y - 248 - 48y = 256

Simplifying and solving for y gives:

27y = 504

y = 18.67

Then we can substitute this value of y back into our expression for x to find:

x = (-15/8)(18.67) + 31/2

x = -12.25

Therefore, the solution to the system of equations is:

x = -12.25

y = 18.67

Answer:

$2,400

Step-by-step explanation:

This is a very simple problem. Simply type the following into a calculator: 0.15*16000, and you should get 2400.

We have to turn the percentage into a decimal less than one because 15% represents 15/100.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

268.8

Step-by-step explanation:

Let the sides of the base triangle be:

a = 8.8 cm

b = 5.7 cm

c = 6.8 cm

Let h be the length

h = 10.8 cm

The surface area is given by:

[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}[/tex]

Where

[tex]s = \frac{a + b + c}{2} \\\\= \frac{8.8 + 5.7 + 6.8}{2} \\\\=\frac{21.3}{2} \\\\= 10.65[/tex]

[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}\\\\= (8.8 + 5.7 + 6.8)*10.8 + 2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\= 21.3*10.8 +2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\=230.04 + 2\sqrt{ 10.65(1.85)(4.95)(3.85)}\\\\=230.04 + 2\sqrt{ 375.48}\\\\= 230.04 + 2*19.38\\\\=230.04 +38.76\\\\=268.8[/tex]

Answer:

Step-by-step explanation:

Sure, I can help you with that.

The scale of the map is 300 miles / 25 inches = 12 miles / inch.

Therefore, 35 inches on the map would be 35 * 12 = 420 miles.

Here's the calculation:

Code snippet

scale = actual distance / distance on map

12 miles / inch = 300 miles / 25 inches

35 inches * 12 miles / inch = 420 miles

Use code with caution. Learn more

I hope this helps! Let me know if you have other questions.

(i) The probability that none of the 11 patients will have the mild side effect can be calculated using the binomial distribution.

In this case, the probability of an individual patient having the side effect is 6% or 0.06, and the probability of not having the side effect is 1 - 0.06 = 0.94.

The probability that none of the 11 patients will have the side effect can be calculated as:

P(X = 0) = (0.94)^11 ≈ 0.5147

So, the probability that none of the patients will have the mild side effect is approximately 0.5147 or 51.47%.

(ii) The probability that at least one patient will have the mild side effect can be calculated as the complement of the probability that none of the patients will have the side effect.

In other words, it is 1 minus the probability of none of the patients having the side effect.

P(at least one patient has the side effect) = 1 - P(X = 0) = 1 - 0.5147 ≈ 0.4853

So, the probability that at least one patient will have the mild side effect is approximately 0.4853 or 48.53%.

(i) To find the probability that none of the patients will have the mild side effect, we use the binomial distribution formula.

The probability of success (having the side effect) is given as 0.06, and the probability of failure (not having the side effect) is 1 - 0.06 = 0.94.

We raise the probability of not having the side effect to the power of the number of trials (11 patients) to find the probability that none of them will have the side effect.

(ii) To find the probability that at least one patient will have the mild side effect, we use the complement rule.

The complement of none of the patients having the side effect is at least one patient having the side effect.

By subtracting the probability of none of the patients having the side effect from 1, we find the probability of at least one patient having the side effect.

These probabilities are important in assessing the likelihood of experiencing the mild side effect when using the new drug.

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Answer:

y = - 3

Step-by-step explanation:

the midline is a horizontal line positioned midway between the maximum and minimum values of the graph.

maximum = - 1 and minimum = - 5

then

(- 1 + (- 5)) ÷ 2 = (- 1 - 5) ÷ 2 = - 6 ÷ 2 = - 3 so equation of midline is

y = - 3

1) 2a - 100

Substituting the value of a here,

[tex] \rm 2(32) - 100 [/tex]

[tex] \rm 64 - 100 [/tex]

[tex] \rm -36 [/tex]

2) b (-12)

Substituting the value of b here,

[tex] \rm 150 (-12) [/tex]

[tex] \rm -1800 [/tex]

3) 4a + b

Substituting the values of a and b here,

[tex] \rm 4(32) + 150 [/tex]

[tex] \rm 128 + 150 [/tex]

[tex] \rm 278 [/tex]

4) 9b - 2a

Substituting the values of a and b here,

[tex] \rm 9(150) - 2 (32) [/tex]

[tex] \rm 1350 - 64 [/tex]

[tex] \rm 1286 [/tex]

The answers are:

below in [tex]\bold{bold}[/tex]

Work/explanation:

Plug in 32 for a

[tex]\sf{2(32)-100}[/tex]

[tex]\sf{64-100}[/tex]

[tex]\bf{-36}[/tex]

____________

[tex]\sf{b(-12)}[/tex]

[tex]\sf{150\cdot(-12)}[/tex]

[tex]\bf{1,800}[/tex]

____________

[tex]\sf{4a+b}[/tex]

[tex]\sf{4(32)+150}[/tex]

[tex]\sf{128+150}[/tex]

[tex]\bf{278}[/tex]

____________

[tex]\sf{9b-2a}[/tex]

[tex]\sf{9(150)-2(32)}[/tex]

[tex]\sf{1,350-64}[/tex]

[tex]\bf{1,286}[/tex]

____________

The discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.

To determine the net present value (NPV) when the discount rate is increased by 12%, we need to recalculate the NPV using the new discount rate.

Given:

Current NPV = Rs. 6172

Current discount rate = 9%

Increase in discount rate = 12%

To find the new NPV, we can use the formula:

New NPV = Current NPV / (1 + Increase in discount rate)

Calculating the new NPV:

New NPV = 6172 / (1 + 0.12)

New NPV = 6172 / 1.12

New NPV ≈ Rs. 5514.29

Therefore, if the discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.

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Answer:step 4

Step-by-step explanation: I just took the test pookies

The slope-intercept form of the equation of the line that passes through (-2, -1) and is perpendicular to y + 15 = x + 10 is y = -x - 3.

To find the slope-intercept form of the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.

The given line equation is y + 15 = x + 10. To rewrite it in slope-intercept form (y = mx + b), we isolate y:

y = x + 10 - 15

y = x - 5.

From this equation, we can see that the slope of the given line is 1.

To find the slope of the line perpendicular to this, we take the negative reciprocal of 1, which is -1.

Now that we have the slope (-1) and a point (-2, -1) that the line passes through, we can use the point-slope form of a line to find the equation.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Plugging in the values (-2, -1) and -1 for x1, y1, and m respectively, we get:

y - (-1) = -1(x - (-2))

y + 1 = -1(x + 2)

y + 1 = -x - 2.

To rewrite this equation in slope-intercept form (y = mx + b), we isolate y:

y = -x - 2 - 1

y = -x - 3.

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