Find the volume of the solid.

The amplitude and period of each function are calculated and listed below

The amplitude and period of each function can be determined using their standard form:

y = A sin (Bx + C) or y = A cos (Bx + C)

where |A| is the amplitude, B is the frequency (or angular frequency), and 2π/B is the period.

Let's apply this formula to each function:

y = cos(2x)

Amplitude = 1

Period = 2π/2 = π

y = -sin(2x)

Amplitude = 1

Period = 2π/2 = π

y = -3sin(3x)

Amplitude = 3

Period = 2π/3

y = (1/2)cos(4x)

Amplitude = 1/2

Period = 2π/4 = π/2

y = 10sin(1/2x)

Amplitude = 10

Period = 2π/(1/2) = 4π

y = 5cos(1/4x)

Amplitude = 5

Period = 2π/(1/4) = 8π

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

Amplitude = 1/3

Period = 2π/(1/3) = 6π

y = 4sin(-2x)

Amplitude = 4

Period = 2π/(-2) = -π

y = -2sin(2πx)

Amplitude = 2

Period = 2π/(1) = 2π

y = -3sin(πx)

Amplitude = 3

Period = 2π/π = 2

y = 1 + (1/2)cos(πx)

Amplitude = 1/2

Period = 2π/π = 2

y = -2 + cos(4πx)

Amplitude = 1

Period = 2π/(4π) = 1/2

The graphs of the functions are added as attachment

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On solving the provided question we can say that As a result, set D denotes a linear function.

The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).

The set of ordered pairs expressing a linear function must meet the requirement that any two locations in the set have a constant rate of change (slope).

We can determine the rate of change between the two supplied positions using set D:

slope = (y2 - y1) / (x2 - x1)

slope = (1 - 2) / (2 - (-1))

slope = -1/3

We may use the slope-intercept form of a linear equation to see if the remaining points in set D fulfil the same rate of change: y = mx + b, where m is the slope and b is the y-intercept.

We can solve for b using the first point in D, (-1,2):

2 = (-1/3)(-1) + b

b = 7/3

So the linear equation for set D is: y = (-1/3)x + 7/3

Now we can check if the remaining points in set D satisfy this equation:

(2, 1): 1 = (-1/3)(2) + 7/3 (satisfies the equation)

As a result, set D denotes a linear function.

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Answer: To calculate the cost of the triangular lot, we need to first find the area of the triangle using the given dimensions. To do this, we can use Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is given by:

area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a + b + c)/2

In this case, we have a = 188, b = 145, and c = 158. Substituting these values into the formula, we get:

s = (188 + 145 + 158)/2 = 245.5

area = √(245.5(245.5-188)(245.5-145)(245.5-158)) ≈ 12463.15 square feet

Now that we have the area of the lot, we can multiply it by the price per square foot to get the total cost:

cost = 12463.15 × $3 = $37,389.45

Therefore, the lot would cost approximately $37,389.45.

Step-by-step explanation:

Step-by-step explanation:

when we are supposed to find each degrees of a certain angle on an equilateral triangle all we have to know is that a triangle is equal to 180° there for each angle or each line is equal to 180° / 3

Answer: The 22% discount was calculated as R551 (rounded to the nearest rand).

Step-by-step explanation:

To calculate the discount, we need to determine what percentage of the original price R2 499 the discount of R551 represents.

The formula to calculate the percentage discount is:

Discount percentage = (Discount amount ÷ Original price) x 100%

Substituting the values given in the question, we get:

Discount percentage = (551 ÷ 2499) x 100%

Discount percentage = 0.22088 x 100%

Discount percentage = 22.088%

Therefore, the discount given was 22%.

Answer:

x = 4

Step-by-step explanation:

given 2 secants drawn from an external point to the circle, then the product of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is

x(x + 4x) = 8(8 + 2)

x(5x) = 8(10)

5x² = 80 ( divide both sides by 5 )

x² = 16 ( take square root of both sides )

x = [tex]\sqrt{16}[/tex] = 4

Two quadratic functions that contains the points (5, 3) and (8, 0) are

In this problem we must find two possible quadratic functions that contains two points: (x, y) = (5, 3), (x, y) = (8, 0). The factor form of the quadratic function is now introduced:

y = a · (x - r₁) · (x - r₂)

Where:

If we know that (x₁, y₁) = (5, 3) and (x₂, y₂) = (8, 0), then the two possible quadratic functions are:

3 = a · (5 - r₁) · (5 - r₂)

3 = a · [25 - 5 · (r₁ + r₂) + r₁ · r₂]

0 = a · (8 - r₁) · (8 - r₂)

0 = 64 - 8 · (r₁ + r₂) + r₁ · r₂

0 = 64 - 8 · r₁ - 8 · r₂ + r₁ · r₂

0 = 64 - 8 · r₁ + (r₁ - 8) · r₂

Now we clear r₂:

r₂ = (8 · r₁ - 64) / (r₁ - 8)

And we eliminate r₂ in the first equation:

3 = a · [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

And variable a is now cleared:

a = 3 / [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

The function is graphed and two possible solutions are introduced below:

(r₁, a) = (6, 1), (r₁, a) = (10, 0.2)

And the values of r₂ are, respectively:

(r₁, a) = (6, 1):

r₂ = (8 · 6 - 64) / (6 - 8)

r₂ = - 16 / (- 2)

r₂ = 8

(r₁, a) = (10, 0.2):

r₂ = (8 · 10 - 64) / (10 - 8)

r₂ = 16 / 2

r₂ = 8

Finally, we complete and graph the resulting quadratic functions.

Case 1:

y = (x - 6) · (x - 8)

y = x² - 14 · x + 48

Case 2:

y = 0.2 · (x - 10) · (x - 8)

y = 0.2 · (x² - 18 · x + 80)

y = 0.2 · x² - 3.6 · x + 16

The graphs of the two quadratic functions are shown in the second image.

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Answer:

66 because 10 percent of 60 is 6 so add 60 and 6

2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

What is scatterplot?

A scatter plot is a particular type of plot or mathematical diagram by using Cartesian coordinates to display values for typically two variables for a set of values. It represents the correlation between two sets of data which may be linear or non linear sometimes strongly positive linear sometimes it may be curvilinear sometimes it may be null.

In the first plot it visibly showing a graph for straight line that is strong positive linear scatter plot. Same for the last but there is a little difference that it is negative linear scatter plot.

For the second one there is a null scatter plot. So there is no correlation.

For the 3rd graph there is a curvilinear relation in the scatterplot.

Hence, 2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

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Answer:

To solve this problem, we can use the concept of direct variation, which states that two quantities vary directly with each other if they can be expressed as y = kx, where y is the dependent variable, x is the independent variable, and k is a constant of variation.

In this case, the distance traveled is the dependent variable and the speed is the independent variable. We are given that the distance traveled is 17.5 miles when the time (or speed) is 15 minutes.

So, we can set up the proportion:

distance / time = constant

17.5 miles / 15 minutes = k

Solving for k, we get:

k = 17.5 / 15

k = 1.16667 (rounded to 5 decimal places)

Now that we have the constant of variation k, we can use it to find the distance traveled in 2 hours (which is equivalent to 2 hours * 60 minutes/hour = 120 minutes).

distance = k * time

distance = 1.16667 * 120

distance = 139.99964 miles (rounded to 5 decimal places)

So, the correct answer is C) 140 miles, as it is the closest rounded value to the calculated distance of 139.99964 miles.

Answer:

28

Step-by-step explanation:

you first do the 4x4=16 then 4x3=12 then do 16+12=28

Answer:

125

Step-by-step explanation:

60% x X = 75

X              = 75/0.6
X              = 125

Answer:

1 pound of jelly beans cost $1.75 , 1 pound of trail mix cost $3.75

Step-by-step explanation:

let j represent 1 pound of jelly beans and t represent 1 pound of trail mix , then

5j + 3t = 20 → (1)

7j + 9t = 46 → (2)

multiplying (1) by - 3 and adding to (2) will eliminate t

- 15j - 9t = - 60 → (3)

add (2) and (3) term by term to eliminate t

(7j - 15j) + (9t - 9t) = 46 - 60

- 8j + 0 = - 14

- 8j = - 14 ( divide both sides by - 8 )

j = [tex]\frac{-14}{-8}[/tex] = 1.75

substitute j = 1.75 into either of the 2 equations and solve for t

substituting into (1)

5(1.75) + 3t = 20

8.75 + 3t = 20 ( subtract 8.75 from both sides )

3t = 11.25 ( divide both sides by 3 )

t = 3.75

then

cost of 1 pound of jelly beans = $1.75

cost of 1 pound of trail mix = $3.75

Answer:

Cost for each pound of jelly beans:  $1.75

Cost for each pound of trail mix:  $3.75

Step-by-step explanation:

Define the variables:

Using the given information and defined variables, create a system of equations:

[tex]\begin{cases}5J+3T=20\\7J+9T=46\end{cases}[/tex]

To solve the system of equations, multiply the first equation by 3 to create a third equation:

[tex]5J \cdot 3+3T \cdot 3=20\cdot 3[/tex]

[tex]15J+9T=60[/tex]

Subtract the second equation from the third equation to eliminate the term in T:

[tex]\begin{array}{crcrcl}&15J & + & 9T & = & 60\\\vphantom{\dfrac12}- & (7J & + & 9T & = & 46)\\\cline{2-6}\vphantom{\dfrac12} &8J&&&=&14\end{array}[/tex]

Solve the equation for J by dividing both sides by 8:

[tex]\dfrac{8J}{8}=\dfrac{14}{8}[/tex]

[tex]J=1.75[/tex]

Therefore, the cost of each pound of jelly beans is $1.75.

To find the cost of one pound of trail mix, substitute the found value of J into one of the original equations and solve for T.

Using the second equation:

[tex]7(1.75)+9T=46[/tex]

[tex]12.25+9T=46[/tex]

[tex]12.25+9T-12.25=46-12.25[/tex]

[tex]9T=33.75[/tex]

[tex]\dfrac{9T}{9}=\dfrac{33.75}{9}[/tex]

[tex]T=3.75[/tex]

Therefore, the cost of each pound of jelly beans is $3.75.

Answer:

the required answer is √5-√6

The option that interchanges the hypothesis with the conclusion is the Converse.

In logic and mathematics, the Converse of an if-then statement switches the positions of the hypothesis (the "if" part) and the conclusion (the "then" part).

It is formed by flipping the original statement.

For example, let's consider the statement: "If it is raining, then the ground is wet."

The hypothesis is "it is raining," and the conclusion is "the ground is wet."

The Converse of this statement would be: "If the ground is wet, then it is raining."

Here, the positions of the hypothesis and the conclusion are interchanged.

It's important to note that the Converse is not always true.

In some cases, the original statement and its converse may have different truth values.

A statement and its converse can be both true, both false, or one true while the other false.

The Converse is a distinct logical operation from other concepts such as the Biconditional and the Inverse.

The Biconditional establishes a two-way relationship between two statements, while the Inverse negates both the hypothesis and the conclusion of the original statement.

Therefore, the option that interchanges the hypothesis with the conclusion is the Converse.

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Answer: Converse

Step-by-step explanation: Took the exam answer above correct

The value of the line AC is  100. 07 inches

Trigonometric identities are equations that involve trigonometric functions such as sine, cosine, and tangent, which hold true for all values of the variables in the equation.

Note that there are six trigonometric identities. They are;

From the information given, we have;

Using the sine identity, we have;

sin 58 = Line AC/118

cross multiply the values

Line AC = 100. 07 inches

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Answer:

b. parallelogram

Step-by-step explanation:

The figure cannot be square because a square has four congruent sides and four right angles, and this figure does not have either of those properties.

The figure cannot be a triangle because a triangle has only three vertices, and this figure has four vertices.

The figure cannot be a trapezoid because a trapezoid has at least one pair of parallel sides, and it is not clear from the given information whether any of the sides are parallel.

The figure could be a parallelogram, which is a quadrilateral with opposite sides parallel. To determine whether this is the case, we can check whether the slopes of opposite sides are equal. Here are the slopes of the sides:

AB: (4-1)/(1-(-4)) = 3/5

BC: (-1-4)/(6-1) = -5/5 = -1

CD: (-4-(-1))/(1-6) = 3/5

DA: (1-(-4))/(-4-1) = -5/5 = -1

We can see that the slopes of opposite sides AB and CD are equal, and the slopes of opposite sides BC and DA are equal. Therefore, the figure is a parallelogram.

The figure cannot be a kite because a kite is a quadrilateral with two pairs of adjacent congruent sides, and this figure does not have that property.

So the answer is: b. parallelogram.

The slope from the table is greater than the slope from the graph hence the table shows a greater rate.

The slope of a graph is the measure of how steep a line is. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically, slope is represented as:

Slope (m) = (change in y)/(change in x)

The slope from the table is;

y2 - y1/x2 - x1

m = 42 - 30/7 - 5

= 6

The slope from the graph is;

8 - 0/1.5 - 0

m = 5.33

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The 18% he gets over the goods purchased exceeds Rs. 6300.

a decrease from the gross amount or value of something: for example, a(1): a reduction from the usual or list price.

Total Purchase Value = Total discount in rs * % discount

= 1520/16 x 100 = 9500

Discount on upto 3200 = 3200 x 14% = 448

Discount on upto 3201-6300 = (6300-3200) x 14% = 496

Balance discount = 1520 - 448 - 496 = 576

Above 6300 purchase amount = 9500 - 6300 = 3200

Discount % = 576/3200 x 100 = 18%

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Complete question:

A customer gets 14% discount on purchasing goods whose value is up to Rs. 3200 and gets 16% discount whose value is between Rs. 3201- Rs. 6300 and customer gets certain % discount while purchase the goods exceeds Rs. 6300. A customer gets a total discount of Rs. 1520 is 16% of the total purchase value. find the %age he gets over the goods purchased exceeds Rs. 6300 ?

The interval(s) for which the function is decreasing are (3, 1) and (4, ∝)

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

The graph

The interval(s) for which the function is decreasing is when

As x increases, the function values decreases

Using the above as a guide and examining the graph, we have the following:

The function is decreasing at (3, 1) and (4, ∝)

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(10) The value that will make the equation a perfect square is 25.

(11) The value that will make the equation a perfect square is 64.

(12) The value that will make the equation a perfect square is 400.

(13) The value that will make the equation a perfect square is 6.25.

To make a perfect square trinomial of the form x² + bx + c, we need to add (b/2)² to both sides.

the perfect square is calculated as;

x² + 10x + __

b = 10,

(b/2)² = 25

the perfect square is calculated as;

x² - 16x + __

b = -16

(b/2)² = 64

the perfect square is calculated as;

x² + 40x + __

b = 40

(b/2)² = 400

the perfect square is calculated as;

x² + 5x + __

b = 5

(b/2)² = 6.25

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a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = [tex](1-p)^{k-1}[/tex]×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

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Answer:

Your late fee is $13.13 (15% of $87.50).

Your past due balance plus the late fee equals $100.63 ($87.50 + $13.13).

Adding the new charges of $75.00 to $100.63, your new total is $175.63.

Therefore, your new total is $175.63.

Answer:

[tex]sin(theta) = \frac{5}{13} [/tex]

The cube root function represented by the graph is h(x) = ∛(x + 3) - 2.

The parent cube root function is f(x) = ∛x

If we translate the parent cube root function 3 units to the left, this means that we replace x with (x + 3) in the function.

This results in the new function g(x) = ∛(x + 3). So, for any input value of x, the output value of g(x) is the cube root of (x + 3).

Similarly, if we translate the parent cube root function 2 units down, this means that we subtract 2 from the function.

So, the new function h(x) = ∛(x + 3) - 2.

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