Right triangles. Find the trig ratio. 29
20
21
sin(0)=
Round to the nearest hundredth

Right Triangles. Find The Trig Ratio. 29 20 21sin(0)= Round To The Nearest Hundredth

Answers

Answer 1

Answer: My guess is 0

Step-by-step explanation:

Checked with my math teacher


Related Questions

Evaluate the following improper integral. If the integral diverges, enter "DIV".
[₁
IH
Te dx=

Answers

The calculated value of the integral [tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex] is 0.7358

How to evaluate the integral

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

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex]

The above expression can be integrated using integration by parts method

When integrated, we have

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(x+1\right)\mathrm{e}^{-x}[/tex]

Recall that the x values are from 1 to ∝

This means that

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(\infty +1\right)\mathrm{e}^{-\infty} + \left(1+1\right)\mathrm{e}^{-1}[/tex]

So, we have

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + \frac{2}{e}[/tex]

Solving further, we get

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + 0.7358[/tex]

Evaluate

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0.7358[/tex]

Hence, the value of the integral is 0.7358

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HELP PLSSS!!!!!!!!!!!!!

Answers

Answer:

84

Step-by-step explanation:

A= [tex]\frac{1}{2}[/tex]b*h

A= [tex]\frac{1}{2}[/tex]14*12

A=84

in your view support the method that you find important to enhance the strong number sense. Provides appropriate examples for chosen method​

Answers

The method that you find important to enhance the strong number sense is  the use of manipulatives and hands-on activities.

Example:

Illustrating numbers and executing mathematical operations through block representations can assist students in visualizing addition, subtraction, and multiplication.

How to determine the method

Using manipulatives and interactive activities, numerical concepts can be grasped more tangibly, as learners physically engage with these objects, thereby developing a concrete understanding of mathematics.

Students can enhance their comprehension of measurement and units by employing measurement instruments such as rulers and measuring tapes.

Through participation in these tasks, students cultivate a profound sense of intuition in regard to numbers, operations, and their interconnections, thereby establishing a firm groundwork.

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Find BE, if DC is equal to 27 and FA is equal to 46.

Answers

Considering the triangles, the value of BE is 27

What are similar triangles?

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

In the figure, BE is solved using the following ratio

FD / FA = DC / AE

1 / 2 = 27 / AE

AE = 27 * 2

AE  = 54

BE = 1/2 AE

BE = 27

hence BE = 27

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Geometry
Solve both and show work

Answers

Answer:

For both problems, the correct equation of the line will be presented in three forms.

14)

y - 4 = -5(x + 1)---point-slope form

y - 4 = -5x - 5

y = -5x + 1---slope-intercept form

5x + y = 1---standard form

15)

y + 3x = 13

y = -3x + 13

y - 10 = (1/3)(x - 6)---point-slope form

y - 10 = (1/3)x - 2

y = (1/3)x + 8---slope-intercept form

3y = x + 24

-x + 3y = 24---standard form

x - 3y = -24

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 120.5° is added to the data, how does the mean change and by how much?

The mean stays at 83.5°.
The mean increases by 3.1°.
The mean increases by 3.5°.
The means stays at 80.4°.

Answers

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

To determine how the mean changes when a value of 120.5° is added to the data, we need to recalculate the mean before and after the addition.

Given the average high temperatures:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

To find the original mean, we sum up all the temperatures and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 904 / 12 = 75.33°

Now, let's add the value of 120.5° to the data:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 120.5

To find the new mean, we sum up all the temperatures (including the added value) and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 120.5) / 13 = 1025.5 / 13 ≈ 78.88°

The mean has increased from 75.33° to 78.88°.

Therefore, the mean increases by approximately 3.55° (rounded to the nearest tenth).

The correct answer is: The mean increases by 3.5°.

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

The graph represents a functional relationship.

Answers

The value that is the input of the function is 4.

How to represent a function?

A function relates input and output. In other words,  a function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The independent variable is the x values or the input value while the dependent variable is the y values of the output values.

Hence, the values of the input(x) of the function are 4, 6, 8, 10. 12 etc.

Therefore, base on the option, the input of the function is 4.

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Which graph represents h(x)?
5
T
3-
2
3-2-1₁
hoo
2.
hou
M
32

Answers

The graph that represents the piecewise function, h(x) is the second option

Please find attached the graph that represents h(x) created with MS Excel

What is a piecewise function?

A piecewise function comprises of two or more functions, which are defined based on specified intervals of the input variable.

The possible piecewise function that is represented by h(x), obtained from a similar question on the site can be presented as follows;

[tex]h(x) \begin{cases} \frac{1}{4}\cdot x-4, & \text{ } x\leq0 \\\frac{1}{3}\cdot x - 3, & \text{ } 0 < x \leq 3 \\\frac{1}{2}\cdot x-2, & \text{ } x\geq4\end{cases}[/tex]

Therefore, at x ≤ 0, the y-intercept is -4, for h(x) = (1/4)·x - 4, which corresponds to the second graph.

The range for h(x) at 0 < x ≤ 3 is; h(0) = (1/3)×0 - 3 < h(x) ≤ (1/3)×3 - 3, which can be expressed as; (-3, -2], also corresponding to the second graph

The value of x-intercept of h(x) in the interval x ≥ 4 can be found from the equation; h(x) = (1/2)·x - 2 = 0

(1/2)·x = 2

x = 2 × 2 = 4

The x-intercept, (4, 0), corresponds to the second graph, therefore, the graph that represents h(x) is the second graph

Please find attached the graph that represents the piecewise function, h(x), created with MS Excel

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Helpppp it’s for my homework

Answers

Answer:

A = -5

B = -2

C = 3

Step-by-step explanation:

[tex](A) = (-3)^{2} +4(-3)-2\\(A) = 9+(-12)-2\\(A) = -5\\\\\\(B) = (0)^{2} +4(0)-2\\(B)=0+0-2\\(B)=-2\\\\\\(C)=(1)^{2} +4(1)-2\\(C)=1+4-2\\(C)=3[/tex]

Solve for the measure of the indicated arc.
O Saved 41°
O
49°
45°
51⁰
131
M
?
K
45°

Answers

The calculated measure of x in the circle is 2

How to calculate the measure of x in the circle

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

The circle

The measure of x in the circle can be calculated using the angle intersected by arc theorem

So, we have

1/2(69x + 2) = 70

Multiply both sides by 2

69x + 2 = 140

So, we have

69x = 138

Divide both sides by 69

x = 2

Hence, the measure of x in the circle is 2

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Solve for the value of c.
(2c-3)°
97°

Answers

Answer:

c = 50

Step-by-step explanation:

2c - 3 = 97

2c = 100

c = 50

Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if
any; d. the y-intercept, if any; and e. the missing function value, indicated by the question mark
below.
f(9) = ?

Answers

a. Domain -   [0, 20]

b. Range -   [8, ∞)

c. X-intercepts -   undefined.

d. Y-intercept -   8

e. Missing function value f(9) = 11

What is   the  explanation for the above ?

a. The function's domain is the range of x-values over which the graph is defined.  In this case, the domain is from 0 to 20, inclusive -   [0, 20].

b. The function's range is the set of all possible y-values that the function takes. Since the graph starts from unit 8 on the y-axis, the range would be from 8 to positive infinity -   [8, ∞).

c. since the   graph does not touch the x- axis at any point, we can state that the there is no x-intercept orthat the x -intercept is undefined.

d. The y-intercept is the point where the   graph intersects the y-axis. In this case, the y-intercept is at unit 8 on the y-axis.

e.  Based on the graph the point (9, 11) corresponds to the value of y when x is 9, then f(9) would be equal to 11.

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help me with math pls

Answers

Answer:

V = 1/3 π r^2 h

Step-by-step explanation:

V = 1/3 area base*height

1. work out the area

2. base*height

3. area*answer

4. you get full answer

in general, the y intercept of the function F(x) = (a) (b^x) is the point _____.

Answers

Answer:

(0,a)

Step-by-step explanation:

The y-intercept of a function is the point where the graph of the function intersects the y-axis.

To find the y-intercept of the function F(x) = (a)(b^x), we can substitute x = 0 into the equation and solve for F(0).

When x = 0, we have:

=> F(0) = (a)(b^0)

=>  F(0) = (a)(1)

=> F(0) = a

Therefore, the y-intercept of the function F(x) = a * b^x is the point (0, a).

The following cost estimates were provided for your project: Cost of soil: $80.00 per cubic yard Cost of sand: $100.00 per cubic yard Cost of Sod: $100.00 per roll that is 3’ by 30’ Tree and shrubbery installation: $2500.00 You are at the final phase of your project and are doing final grading and landscaping. The estimates are 8 cubic yards of soil, 3 cubic yards of sand, 3600 square feet of sod, and tree/shrubbery installation. Including a 3 percent contingency, what is the estimated total cost?

Answers

The estimated total cost of the project is $7,663.20.

What is the estimated total cost?

We need to add up the costs of soil, sand, sod, and tree/shrubbery installation, including the contingency.

Soil: 8 cubic yards x $80/cubic yard = $640

Sand: 3 cubic yards x $100/cubic yard = $300

Sod: 3600 square feet / 30 square feet/roll x $100/roll = $1200

Tree and shrubbery installation: $2500

Contingency: 3% x $4640 = $139.20

Total cost: $640 + $300 + $1200 + $2500 + $139.20 = $7,663.20

Therefore, The estimated total cost of the project is $7,663.20

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Please help with an explanation my brain isn’t working

Answers

Answer:

h=1.8 cm

Step-by-step explanation:

Solution Given:

Volume of triangular prism= Area of base * length

Here

Volume of traingular Prism= 63 cm³

base =7 cm

length =10 cm

Area of base = Area of triangle=½*base*height=½*7*h

Now

substituting value in the formula:

63= ½*7*h*10

63=35*h

h=63/35

h=1.8 cm

Therefore, height of the triangular cross section is 1.8 cm.

Selena and Drake are evaluating the expression (StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1, when r = negative 1 and s = negative 2.


Selena’s Work
Drake’s Work

(StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1 Baseline = (r Superscript negative 1 Baseline s) Superscript negative 1 Baseline = StartFraction r Over s EndFraction = StartFraction negative 1 Over negative 2 EndFraction = one-half

(StartFraction (negative 1) (negative 2) Superscript negative 2 Baseline Over (negative 1) squared (negative 2) Superscript negative 3 EndFraction) Superscript negative 1 = (StartFraction (negative 1) (negative 2) cubed Over (negative 1) squared (negative 2) squared EndFraction) Superscript negative 1 = (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1 Baseline = StartFraction 4 Over negative 8 EndFraction = negative one-half


Who is correct and why?
Selena is incorrect because she should have substituted the values for the variables first, and then simplifed.
Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
Drake is incorrect because he should have simplified first, before substituting the values for the variables.
Drake is correct because he substituted the values for the variables first, and simplified correctly.

Answers

Drake is correct, and Selena is incorrect in this scenario.Option D.

Selena's Work:

Selena substituted the values for the variables r = -1 and s = -2 directly into the expression before simplifying. She then simplified the expression and evaluated it.

However, this approach is incorrect because the order of operations requires simplification before substitution. Selena should have simplified the expression first and then substituted the values of r and s.

Drake's Work:

Drake followed the correct order of operations. He simplified the expression first and then substituted the values of r = -1 and s = -2. By simplifying the expression, Drake obtained (-1/-2), which simplifies to 1/2. After substituting the values, Drake evaluated the expression correctly and arrived at the final result of 1/2.

Since Drake followed the correct order of operations and obtained the correct result, he is the one who is correct. Selena's mistake was in not simplifying the expression before substituting the values for r and s.

In mathematical operations, it is important to follow the order of operations (PEMDAS/BODMAS) to ensure accurate results. The correct order is to simplify the expression first, and then substitute the given values for the variables. So Option D is correct.

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Pls help with my homeworkkkkk

Answers

Answer: A= -1, B= -3,C=-4.D=3 i think

A: (-1,0)
B: (0,-3)
C: (1,-4)
D: (3,0)

explanation:
use the graph given and count each point on the x and y axis :)

k(t)=13t−2k, left parenthesis, t, right parenthesis, equals, 13, t, minus, 2

(
3
)
=
k(3)=k, left parenthesis, 3, right parenthesis, equals

Answers

The value of k(3) in the function given is 37

Given the function :

k(t) = 13t - 2

To find k(3) ; substitute t = 3 into the equation

k(3) = 13(3) - 2

k(3) = 39 - 2

k(3) = 37

Therefore, the value of k(3) would be 37.

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solve it pls fast
.........................

Answers

The solution to this integral [tex]\int\limits^{\infty} _{-\infty} e^{-x^{2} } \, dx =\sqrt{\pi}[/tex] is equal to √π.

How to integrate the given function?

In Mathematics, the Gaussian integral is sometimes referred to as the probability integral, and it highly related to the erf function, which represents the integral of the one-dimensional Gaussian function over the interval [-∞, ∞].

Generally speaking, the given integral can be computed by using the advanced techniques of combining two one-dimensional Gaussians and converting into polar coordinates;

[tex]I^2 =\int\int e^{(-(x^2 +y^2))}dxdy\\\\I^2 =\int\int e^{-r^2}rdr d\theta[/tex]

In this context, we would use these integration limits [0, ∞) with respect to "r" and [0, 2π] with respect to "θ" as follows:

[tex]I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0} e^{-r^2}rdr d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0}\frac{1}{2} e^{-u}du d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} [\frac{1}{2} e^{-u}]\limits^{\infty}_{0}d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} (\frac{1}{2} )d\theta\\\\I^2=\frac{1}{2}[\theta]\limits^{2 \pi}_{0}\\\\I^2=\frac{1}{2}(2 \pi)-\frac{1}{2}(0)\\\\I^2=\frac{2 \pi}{2}[/tex]

I² = π

I = √π

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O
Problem !. Draw the Logic Circuit for:
BD + BE + D'F
Problem 2. What is the boolean Expression of F5?
B
X
Y
Z
F5

Answers

The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

in how many ways can first, second, and third prizes be awarded in a contestant with 375 contestants? assume there are no ties

Answers

There are 52,406,250 ways to award the first, second, and third prizes in a contest with 375 contestants, assuming there are no ties.

To solve this problem, we will use permutations.

A permutation is a way of arranging objects or elements in a specific order.

In this case, we want to find the number of permutations of 375 objects taken 3 at a time, because we are selecting three prize winners.

The formula for permutations is: P(n, r) = n!/(n-r)!where n is the total number of objects and r is the number of objects we are selecting.

So in our case, we want to find the number of ways to select 3 prize winners out of 375 contestants:

P(375, 3) = 375!/(375-3)!P(375, 3) = 375!/372!P(375, 3) = 375*374*373P(375, 3) = 52,406,250

Therefore, there are 52,406,250 ways to award the first, second, and third prizes in a contest with 375 contestants, assuming there are no ties.

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For a certain company, the cost function for producing x items is C(x) = 40 x + 150 and the
revenue function for selling x items is R(x) = -0.5(x - 100)2 +5,000. The maximum capacity
of the company is 160 items.

Answers

The company should produce and sell 60 items to maximize its profit. The profit at this level of production will be $2,350.

For a certain company, the cost function for producing x items is C(x) = 40 x + 150 and the revenue function for selling x items is R(x) = -0.5(x - 100)2 + 5,000. The maximum capacity of the company is 160 items.To find the optimal number of items that the company should produce and sell, we need to maximize the revenue function R(x) while also taking into account the cost function C(x).

The profit function P(x) can be expressed as:P(x) = R(x) - C(x).

Substituting the given equations, we get:P(x) = (-0.5(x - 100)2 + 5,000) - (40x + 150)P(x) = -0.5(x - 100)2 - 40x + 4,850.

To maximize the profit, we need to find the value of x that gives the maximum value for P(x). The maximum capacity of the company is 160 items, so we only need to consider the values of x from 0 to 160.

To find the optimal value of x, we can take the derivative of P(x) and set it equal to zero: d P(x)/dx = -x + 100 - 40 = 0.

Solving for x, we get: x = 60. This means that the optimal number of items that the company should produce and sell is 60. At this level of production, the profit will be:P(60) = -0.5(60 - 100)2 - 40(60) + 4,850 P(60) = $2,350.

Therefore, the company should produce and sell 60 items to maximize its profit. The profit at this level of production will be $2,350.

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Which variation is represented by this situation:

A building that is 6 stories tall has a shadow that is 22 meters long. How many stories tall is a building with a shadow that is 40 meters long?

Answers

Answer:

The answer is approximately 11 stories

Step-by-step explanation:

6 stories------->22 meters

x stories---------->40 meters

[tex]x = \frac{6 \times 40}{22} [/tex]

x≈11 stories

John is a furniture maker. The graph shows the number of chairs John makes and the time it takes to make those chairs. Based on the graph, how many chairs can John make in 5 hours?





A.
55
B.
50
C.
45
D.
40

Answers

The correct answer is Option B. 50 chairs can John make in 5 hours from the graph.

John is a furniture maker and the graph shows the number of chairs John makes and the time it takes to make those chairs.

Based on the graph, the number of chairs John can make in 5 hours can be found by following the given steps:

Step 1: Look for the point on the graph where the line intersects the vertical line marking 5 hours.

Step 2: From the point on the graph found in step 1, read the horizontal line and find the point at which it intersects the y-axis.

This point will give us the number of chairs John can make in 5 hours.

According to the graph, John makes 50 chairs in 5 hours.

Therefore, the correct answer is option (B) 50.

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Leon has two boxes with coloured pencils. Boxed A contained 3/8 of all his coloured pencils. Leon removes 2/5 of the pencils from box B to colour a picture. If 15 pencils are used to colour his picture, how many pencils are there in box A?​

Answers

Answer:

Step-by-step explanation:

Let's assume that Leon has 'x' number of coloured pencils. According to the question, Box A contains 3/8 of all his coloured pencils.So, Box B contains (1-3/8) = 5/8 of all his coloured pencils.  Therefore, number of pencils in Box A = (3/8) * x  Also, number of pencils in Box B = (5/8) * x  According to the question, Leon removes 2/5 of the pencils from Box B to colour a picture. So, pencils used from Box B = (2/5) * (5/8) * x = (1/4) * x  And the total number of pencils used for the picture = 15.  So, pencils used from Box A = 15 - (1/4) * x  Now, the total pencils used in the picture = pencils used from Box A + pencils used from Box B  Therefore, 15 = 15 - (1/4) * x + (1/4) * x  Thus, x = 60  Therefore, number of pencils in Box A = (3/8) * 60 = 22.5.  Hence, there are 22.5 pencils in Box A.

solve the exponential equation for x. 2^9x+2 = 16^5x-2

Answers

The value of is 2/11

How to determine the value

To determine the value, we have;

Index forms are mathematical forms used to represent numbers or values that are too large or too small in more convenient forms.

From the information given, we have the expression written as;

2⁹ˣ+2 = 16⁵ˣ -2

Put all the terms in one base form, we have;

2⁹ˣ + 2¹ = 2²⁰ˣ - 2¹

equate the exponents, we have;

9x + 1 = 20x - 1

collect the like terms, we have;

9x - 20x = -2

-11x = -2

Make 'x' the subject of formula, we have;

x = 2/11

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Miguel deposited a certain amount of money in the bank. The bank paid him interest after one year at which point he had $757.12. After the next year he had $787.40. How much money did Miguel originally put into the bank? (Answer to the nearest dollar.)

Answers

The amount that Miguel originally put into the bank is given as follows:

$728.

How to obtain the balance using simple interest?

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

Then the interest accrued is given as follows:

I(t) = Prt.

In which the parameters of the equation are listed and explained as follows:

A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.

The interest accrued from the first year to the second year is of $30.28, hence the rate is given as follows:

30.28 = 757.12r

r = 30.28/757.12

r = 0.04.

Then the principal is obtained as follows:

1.04P = 757.12

P = 757.12/1.04

P = $728.

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Select the correct answer from each drop-down menu.
The figure shown is made up of a cone and a cylinder. The height of the cone is 5 ft and its diameter is 12 ft. The height of the cylinder is 20 ft.
12 ft.
5 ft
4
20 ft
Find the lateral surface area of the cone and the surface area of the sides and bottom of the cylinder.
The lateral surface area of the cone is about
The total surface area of the figure is about
². The surface area of the sides and the bottom of the cylinder is about
1².
n².

Answers

Answer:

The lateral surface area of the cone is about 147.2 ft².

The surface area of the sides and the bottom of the cylinder is about 867.1 ft².

The total surface area of the figure is about 1014.3 ft².

Step-by-step explanation:

The formula for the lateral surface area of a cone is:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Lateral Surface Area of a Cone}\\\\$L.S.A.=\pi r \sqrt{r^2 + h^2}$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius of the circular base. \\ \phantom{ww}$\bullet$ $h$ is the perpendicular height of the cone.\\\end{minipage}}[/tex]

From inspection of the given diagram (attached), we can see that the diameter of the base of the cone is 12 ft.

As the radius of a circle is half its diameter, the radius of the base of the cone is r = 6.

The height of the cone is 5 ft, so h = 5.

Substitute the values of r and h into the formula to calculate the lateral surface area of the cone:

[tex]\begin{aligned}\textsf{Lateral Surface Area of the Cone}&=\pi (6) \sqrt{6^2 + 5^2}\\&=6\pi \sqrt{36 +25}\\&=6\pi \sqrt{61}\\&=6\sqrt{61}\pi \\&=147.219738...\\&=147.2\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]

The surface area of the cylinder part of the figure is made up of the lateral surface area of the cylinder and the area of one circular base.

Therefore the formula to use to calculate the area of the sides and bottom of the cylinder is:

[tex]\boxed{L.S.A.=2\pi r h+\pi r^2}[/tex]

where r is the radius and h is the height of the cylinder.

From inspection of the given diagram, we can see that the radius of the cylinder is r = 6 and the height is h = 20. Substitute these into the formula to find the area of the sides and bottom of the cylinder:

[tex]\begin{aligned}\textsf{S.A. side and bottom of cylinder}&=2 \pi (6)(20)+\pi (6)^2\\&=2 \pi (120)+\pi (36)\\&=240 \pi +36\pi\\&=276 \pi \\&=867.079572...\\&=867.1\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]

The total surface area of the figure is the sum of the lateral surface area of the cone and the sides and bottom of the cylinder. Therefore:

[tex]\begin{aligned}\textsf{Total Surface Area}&=147.219738...+867.079572...\\&=1014.29931...\\&=1014.3\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]

In conclusion:

The lateral surface area of the cone is about 147.2 ft².The surface area of the sides and the bottom of the cylinder is about 867.1 ft².The total surface area of the figure is about 1014.3 ft².

A driver's distance D in miles from a rest stop after x hours is given by D(x) = 72x.
a) How far is the driver from the rest stop
after 3 hours?
b) Find the slope of the graph of D. Interpret
this slope as a rate of change.

Answers

the driver is 24 hours

the slop is 72 (x is always slope)

Answer & Step By Step Explanation:

a) The function D(x) = 72x represents the distance traveled by the driver after x hours. To find out how far the driver is from the rest stop after 3 hours, we simply substitute x = 3 into the function:

[tex]D(3) = 72 * 3 = 216 miles[/tex]

So, the driver is 216 miles away from the rest stop after 3 hours.

b) The slope of the graph of D(x) = 72x is 72. In the context of this problem, the slope represents the rate of change of the distance with respect to time. This is essentially the speed of the driver. So, the driver is traveling at a constant speed of 72 miles per hour.

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