What is the surface area of this composite solid? show your work

Answer:

[tex]\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}[/tex]

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

[tex]\boxed{f(x) = A \sin (B(x + C)) + D}[/tex]

where:

Given values:

Calculate the value of B:

[tex]\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16[/tex]

Substitute the values of A, B C and D into the standard formula:

[tex]f(x) = 5 \sin (16(x + 0)) + 7[/tex]

[tex]f(x) = 5 \sin (16x) + 7[/tex]

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

[tex]\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}[/tex]

41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

We have,

41.

a.

1/3 x 5/6

= 5/18

This means,

Out of the 18 parts, we shade 5 parts

b.

2/9 x 2/3

= 4/27

This means,

Out of the 27 parts, we shade 4 parts

42.

String = 15 feet

Length of each piece = 1/4 feet

Now,

The number of 1/4 feet pieces.

= 15/(1/4)

= 15 x 4

= 60 pieces

43.

Original pizza = 1

Half pizza = 1/2

Number of people = 3

Now,

The fractional part for each person.

= 1/2 ÷ 3

= 1/6

44.

a.

7/6 x 9

= 7/2 x 3

= 21/2

= 10(1/2)

b.

1/7 ÷ 3

= 1/(7 x 3)

= 1/21

c.

4/5 x 3(2/3)

= 4/5 x 11/3

= 44/15

= 2(14/15)

d.

2 ÷ 1/9

= 2 x 9/1

= 18

Thus,

41.

Out of the 18 parts, we shade 5 parts

Out of the 27 parts, we shade 4 parts

42.

There are 60 pieces.

43.

The fractional part for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

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Answer:

Area = 40

Perimeter = 26

Step-by-step explanation:

length = 8

width = 5

Area = 8 x 5 = 40

Perimeter = 2(8 + 5) = 26

Answer: 1080

Step-by-step explanation:

12x10x9=1080

Hoped this helped?!

In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.

Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.

Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.

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The full question is:

In the year 2000 the world population was

Both the angles are supplementary angles hence the value of x is 8°.

To solve for the value of x in the given scenario, we can use the fact that the interior angles between two parallel lines are supplementary, meaning they add up to 180 degrees.

Given:

Angle 1: (8x + 1)

Angle 2: 115°

Since these two angles are supplementary, we can set up the equation:

(8x + 1) + 115 = 180

Now we can solve for x by simplifying and isolating the variable:

8x + 1 + 115 = 180

8x + 116 = 180

8x = 180 - 116

8x = 64

To isolate x, we divide both sides of the equation by 8:

8x/8 = 64/8

x = 8

Therefore, the value of x is 8.

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The volume of the trapezoidal prism is 420 cm³

Volume is the amount of space that is occupied by a three dimensional shape or object.

The volume of a trapezoidal prism is the product of the base area and its height.

For the trapezoidal prism:

Area of base = (1/2)(15 + 5) * 7 = 70 cm²

Volume of Prism = Area of base * height = 70 cm² * 6 cm = 420 cm³

The volume of the figure is 420 cm³

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Rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.

A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.

Here, rhombus and equilateral triangle are regular, and rectangle and triangle are not regular.

Therefore, rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.

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The quadratic function has the following domain: 0 ≤ t ≤ 8.

Herein we find a quadratic equation that models the height of the rocket in time. The domain is the set of all values of t such that all values of h exist.

Mathematically speaking, the domain of quadratic equations is the set of all real numbers, but physically speaking, this domain is formed by the set of all non-negative numbers such that h ≥ 0. The domain is found by algebra properties:

h = - 16 · t² + 128 · t

h = - 16 · t · (t - 8)

Then, the domain of the quadratic function is: 0 ≤ t ≤ 8.

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Answer:

Not a right triangle

Step-by-step explanation:

[tex]10^2+15^2\stackrel{?}{=}18^2\\100+225\stackrel{?}{=}324\\325\neq324[/tex]

As the sides of the triangle do not follow the Pythagorean Theorem, then the triangle is not a right triangle.

The population reached in the year 2079 is 1,65,400 and the total population in the year 2081 would be 1,80,623.

To find the population reached in the year 2079, we need to consider the initial population and the growth rate, as well as the number of people who migrated.

The initial population in 2078 was 1,20,000. The population growth rate is 4.5%, which means the population will increase by 4.5% each year.

To calculate the population in 2079, we first need to calculate the increase in population due to the growth rate:

Population increase due to growth rate = 1,20,000 * (4.5/100) = 5,400

Then we add the number of people who migrated:

Total population in 2079 = Initial population + Population increase due to growth rate + Number of migrants

= 1,20,000 + 5,400 + 20,000

= 1,45,400 + 20,000

= 1,65,400

To calculate the total population in the year 2081, we need to consider the growth rate and the population in 2080.

The population in 2080 would be the population in 2079 plus the population increase due to the growth rate:

Population increase due to growth rate in 2080 = 1,65,400 * (4.5/100) = 7,444

Total population in 2080 = 1,65,400 + 7,444

= 1,72,844

To calculate the total population in 2081, we need to consider the growth rate and the population in 2080:

Population increase due to growth rate in 2081 = 1,72,844 * (4.5/100) = 7,779

Total population in 2081 = Population in 2080 + Population increase due to growth rate in 2081

= 1,72,844 + 7,779

= 1,80,623

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The values from figure is,

x = 2

NS = 3.5

We have to given that,

In the figure below, S is the center of the circle.

And, Suppose that JK = 16, MP = 8, LP = 2x + 4, and SP = 3.5.

Now, We know that,

By figure,

MP = LP

Substitute the given values,

8 = 2x + 4

8 - 4 = 2x

4 = 2x

x = 4/2

x = 2

Hence, We get;

LM = MP + LP

LM = 8 + (2x + 4)

LM = 8 + 2 x 2 + 4

LM = 8 + 4 + 4

LM = 16

Since, We have JK = 16

Hence, We get;

NS = SP

This gives,

NS = 3.5

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The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45 cm 7 mm when they are born,  137 cm 1 mm is the height of the average fourth grader.

Given information,

Baby height is typically 45 cm. 7 mm 45 cm Since there are 10 millimeters in a centimeter, 7 mm is equal to 45.7 cm.

Assume that a fourth-grader is x inches tall.

The average height of a newborn baby (x) = 3 times the height of a fourth-grader.

A fourth-grader's height (x) is equal to 3 x 45.7.

A fourth-grader's height is equal to (x)=137.

Fourth-grader height (x) = 137 cm 1 millimeter

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Answer: There are 16 fluid ounces in 1 pint. To determine the number of pints in the jug, we need to divide the total number of fluid ounces by 16.

Given that the jug contains 36 fluid ounces of apple juice, we divide 36 by 16:

36 fluid ounces ÷ 16 fluid ounces/pint = 2.25 pints

Therefore, the jug contains 2.25 pints of apple juice.

Answer:

13)  4.9 m

14)  0.9 m

Step-by-step explanation:

The given diagram shows the height of the same cactus plant a year apart:

We are told that the cactus continues to grow at the same percentage rate. To calculate the growth rate per year (percentage increase), use the percentage increase formula:

[tex]\begin{aligned}\sf Percentage \; increase &= \dfrac{\sf Final\; value - Initial \;value}{\sf Initial \;value}\\\\&=\dfrac{ 2-1.6}{1.6}\\\\&=\dfrac{0.4}{1.6}\\\\&=0.25\end{aligned}[/tex]

Therefore, the growth rate of the height of the cactus is 25% per year.

As the cactus grows at a constant rate, we can use the exponential growth formula to calculate its height in Year 6.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Exponential Growth Formula}\\\\$y=a(1+r)^t$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value. \\ \phantom{ww}$\bullet$ $r$ is the growth factor (in decimal form).\\ \phantom{ww}$\bullet$ $t$ is the number of time periods.\\\end{minipage}}[/tex]

The initial value is the height in Year 1, so a = 1.6.

The growth factor is 25%, so r = 0.25.

As we wish to calculate its height in Year 6, the value of t is t = 5 (since there are 5 years between year 1 and year 6).

Substitute these values into the formula and solve for y (the height of the cactus):

[tex]\begin{aligned}y&=a(1+r)^t\\&=1.6(1+0.25)^5\\&=1.6(1.25)^5\\&=1.6(3.0517578125)\\&=4.8828125\\&=4.9\; \sf m\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, if the cactus continues to grow at the same rate, its height in Year 6 will be 4.9 meters (to the nearest tenth).

Check by multiplying the height each year by 1.25:

[tex]\hrulefill[/tex]

The given diagram shows the height of the same snowman an hour apart:

We are told that the snowman continues to melt at the same percentage rate. To calculate the decay rate per hour (percentage decrease), use the percentage decrease formula:

[tex]\begin{aligned}\sf Percentage \; decrease&= \dfrac{\sf Initial\; value - Final\;value}{\sf Initial \;value}\\\\&=\dfrac{1.8-1.53}{1.8}\\\\&=\dfrac{0.27}{1.8}\\\\&=0.15\end{aligned}[/tex]

Therefore, the decay rate of the snowman's height is 15% per hour.

As the snowman melts at a constant rate, we can use the exponential decay formula to calculate its height after another 3 hours.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Exponential Decay Formula}\\\\$y=a(1-r)^t$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value. \\ \phantom{ww}$\bullet$ $r$ is the decay factor (in decimal form).\\ \phantom{ww}$\bullet$ $t$ is the number of time periods.\\\end{minipage}}[/tex]

The initial value is the snowman's initial height, so a = 1.8.

The decay factor is 15%, so r = 0.15.

As we wish to calculate the snowman's height after another 3 hours, the value of t is t = 4 (i.e. the first hour plus a further 3 hours).

Substitute these values into the formula and solve for y (the height of the snowman):

[tex]\begin{aligned}y&=a(1-r)^t\\&=1.8(1-0.15)^4\\&=1.8(0.85)^4\\&=1.8(0.5220065)\\&=0.93961125\\&=0.9\; \sf m\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, if the snowman continues to melt at the same rate, its height after another 3 hours will be 0.9 meters (to the nearest tenth).

Check by multiplying the height each hour by 0.85:

The words for which the probability of selecting the letter A at random is 1/3 are:

a) CAB

b) ANT

c) ABOARD

Given data ,

Let the probability of selecting the letter A at random be P ( A ) = 1/3

Now , the number of letters in the words CAB are = 3

The number of A's in the word CAB = 1

So , the probability is P ( A ) = 1/3

Now , Now , the number of letters in the words ANT are = 3

The number of A's in the word ANT = 1

So , the probability is P ( A ) = 1/3

And , Now , the number of letters in the words ABROAD are = 6

The number of A's in the word ABROAD = 2

So , the probability is P ( A ) = 2/6 = 1/3

Hence , the probability is solved

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Answer: z=3

Step-by-step explanation:

a. The variables are x and y which represents 2 shots and 3 shots respectively.

b. The system of equations are;

x + y = 11

2x + 3y = 29

a. Let's define the variables to write the system of equations:

Let x be the number of two-point shots Noah made.

Let y be the number of three-point shots Noah made.

b. We can write a system of equations that model this problem.

Equation 1: x + y = 11

This equation represents the total number of shots Noah made, which is 11.

Equation 2: 2x + 3y = 29

This equation represents the total number of points Noah scored, which is 29. Since each two-point shot is worth 2 points and each three-point shot is worth 3 points, we can multiply the number of two-point shots (x) by 2 and the number of three-point shots (y) by 3 and sum them up to get the total score of 29.

The system of equations that can be used to determine the number of two-point shots Noah made and the number of three-point shots he made is:

x + y = 11

2x + 3y = 29

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When a student is selected at random, the solution for the various possible outcome would be given below as follows:

p(pass or did not study)=0.409

p(pass or did study)=0.312

p(fail and pass)= 0.201

p(pass or fail)= 1

The formula that is used to calculate probability = possible outcome/sample space.

The total number of scores of the statistics students = 93

For p(pass or did not study):

possible outcome = 38

sample size = 93

probability = 38/93 = 0.409

For p(pass or did study):

possible outcome = 29

sample size = 93

probability = 29/93 = 0.312

For p(fail and pass):

p(fail) = 26/93

p(pass) = 67/93

probability = 26/93× 67/93

= 1742/8649

= 0.201

For p(pass or fail);

P(pass) = 67/93

P(fail) = 26/93

Probability of pass or fail = 67/93+26/93

= 93/93 = 1

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Answer:

150

Step-by-step explanation:

| P | Q | ~Q | ~Q → P | ~P | (~Q → P) ⋀ ~P |

|---|---|----|--------|----|----------------|

| T | T | F  | T      | F  | F              |

| T | F | T  | T      | F  | F              |

| F | T | F  | T      | T  | T              |

| F | F | T  | F      | T  | F              |

To construct a truth table for the logical statement (~Q → P) ⋀ ~P, we need to consider all possible truth values for the variables Q and P. The symbol "~" represents negation or "not" in logic, so ~Q denotes "not Q" and ~P denotes "not P".

In the above table, we first list all possible truth values for P and Q and then determine the truth values for ~Q, ~Q → P, and ~P based on these values. Finally, we evaluate the logical statement (~Q → P) ⋀ ~P based on the truth values for (~Q → P) and ~P to determine the overall truth value of the statement for each combination of P and Q.

The output of the above truth table shows that the statement (~Q → P) ⋀ ~P is true only in one case when P is false and Q is true. In all other cases, the statement is false. Therefore, we can infer that the statement is not always true and hence it is not a tautology. The statement is only true in one specific case where P is false and Q is true.

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Where the above is given, Area of Δ ACB ≈ 282.62

The area of a triangle is given as

Area = 1/2 Base x Height

In this case,

Base = AB

Height = CP

Thus, it is correct to state that Area of Δ ACB = 1/2AB * CP.

First we need to find the height and hypotenuse of the triangle.

that is CP and CB.

CB = a/Cos (63)

CB = 26.43227

CP = √(CB²-PB²)

CP = √(26.4322711750232² - 12²)

CP = 23.55133

Area of ΔPCB = (CP x PB)/2

(12 × 23.551326066062)/ 2

= 141.30796

Since ΔPCB = ΔPCA

and ΔACB = ΔPCB + ΔPCA

Thus,

Area of  ΔACB = 141.30796 + 141.30796 = 282.61592

≈ 282.62

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

Answer:

Volume ≈ 153.93804 cm^3

Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.

Step-by-step explanation:

Answer:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

The perimeter of the dilated rectangle C'D'E'F' is 200 units.

To find the perimeter of the dilated rectangle C'D'E'F', we need to determine the new coordinates of its vertices after the dilation.

Given that the scale factor is 5 and the dilation is centered at (0, 0), each coordinate of the original rectangle CDEF will be multiplied by 5 to obtain the corresponding coordinate of the dilated rectangle C'D'E'F'.

The original coordinates of CDEF are:

C (-10, 10)

D (5, 10)

E (5, 5)

F (-10, 5)

To find the coordinates of the dilated rectangle C'D'E'F', we multiply each coordinate by 5:

C' = (-10 × 5, 10 × 5) = (-50, 50)

D' = (5 × 5, 10 × 5) = (25, 50)

E' = (5 × 5, 5 × 5) = (25, 25)

F' = (-10 × 5, 5 × 5) = (-50, 25)

Now, we can calculate the perimeter of the dilated rectangle C'D'E'F' by summing the lengths of its sides.

Length of side C'D':

√[(-50 - 25)² + (50 - 50)²] = √[(-75)² + 0²] = √[5625] = 75

Length of side D'E':

√[(25 - 25)² + (50 - 25)²] = √[0² + 625] = √[625] = 25

Length of side E'F':

√[(25 - (-50))² + (25 - 25)²] = √[75² + 0²] = √[5625] = 75

Length of side F'C':

√[(-50 - (-50))² + (25 - 50)²] = √[0² + 625] = √[625] = 25

Now, we add up the lengths of all four sides to find the perimeter:

Perimeter = C'D' + D'E' + E'F' + F'C'

= 75 + 25 + 75 + 25

= 200

Therefore, the perimeter of the dilated rectangle C'D'E'F' is 200 units.

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