Use the volume formula to find the volume of the prism.
TIN
OA. 21 cubic units
OB. 42 cubic units
O C. 84 cubic units
OD. 13 cubic units
NY

The values are; Option C. x = 18; y = 6√10

Using the tangent identity, we have;

tan θ = opposite/adjacent

tan θ = 2/6

θ = 18. 4

Then

Angle CDB = 90 - 18. 4 = 71. 5 degrees

Using tangent identity, we have;

tan 71.5 = x/6

cross multiply the values

x = 18

Then, we have using Pythagorean theorem ;

y²= 18² + 6²

y = 360

y = 6√10

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The value of angle m/EFG is 54°.

We are given that;

Arc GH=96

ARC HE=108

Now,

If a polygon is four sided (a quadrilateral), the sum of its angles is 360°

To find m/EFG, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, we can use the length of EF as the opposite side and the length of FG as the adjacent side.

So, we have:

tan(m/EFG) = EF / FG

We are given that EF = 4.6 and FG = 3.

Substituting these values into the equation above, we get:

tan(m/EFG) = 4.6 / 3

we can find that:

m/EFG = tan^-1(4.6 / 3) ≈ 54°

Therefore, by the given quadrilateral the answer will be 54°.

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1. The Value if x= 41.21 and y= 43.85

2. The value of x is 21.71

1. Using Trigonometry

tan 20 = 15/x

x= 41.2121

and, sin 20 = 15/y

y= 43.857

2. Using Pythagoras theorem

H² = P² + B²

So, 24²= x² + y²

45² = (51-y)² + x²

Solving the above equation we get

576 = x² + y²

2025 = 2601 + y² - 102y + x²

Now, 2025 = 2601 - 102y + 576

-102y = -1152

y= 11.2941

So, x = 21.71

3. The measure of <2 = 180 - 72

= 108

This is because angles on same side if transversal is are supplementary.

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The area of the composite figure = (8π+ 6) in².

We have, Height of triangle = 3 in

Radis of Semicircle = 4 in

Now, area of Semicircle

= πr²/2

= 3.14 x 4²/2

= 25.12 in²

= 8π in²

and, Area of Triangle

= 1/2 x base x height

= 1/2 x 4 x 3

= 6

So, the area of the composite figure

= (8π+ 6) in²

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The area of the composite figure is (8π + 12) in.² So option B is correct.

The given figure consists of 2 triangles and a semicircle.

Given,

The base of the triangle = 4 inches.

The height of the triangle = 3 inches

So the area of the triangle is = 1/2 × base× height

                                                =1/2× 4 × 3

So the area of the triangle is = 6 in².

The radius of the semicircle is= 4 inches,

So,

Area of semicircle= πr²/2

                             = π × 4×4/2

                              =8π in².

So the total area of the composite figure is the area of two triangles + the area of the semicircle which is = 6+6 +8π in²

= 8π +12 in².

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Answer: -1/3

Step-by-step explanation: To solve the equation -18t - 6 = 0, we need to isolate the variable t on one side of the equation.

First, we add 6 to both sides of the equation to get:

-18t = 6

Then, we divide both sides by -18 to get:

t = -6/18

Simplifying -6/18 by dividing both the numerator and denominator by 6, we get:

t = -1/3

Therefore, the solution to the equation -18t - 6 = 0 is t = -1/3.

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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The value of x is 58.51 degree.

We have,

Perpendicular= 8

Base = 4.9

Using trigonometry

tan x = Perpendicular/ Base

tan x = 8/4.9

tan x= 1.63265306122449

x = 58.51253064

Thus, the value of x is 58.51 degree.

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The company can maximize profit by producing 25 units of each good A and good B.

The company can maximize profit by choosing the levels of production x and y that satisfy the following conditions:

Marginal revenue for good A = Marginal cost for good A

Marginal revenue for good B = Marginal cost for good B

To put it differently, the organization must manufacture products A and B until the extra income gained from producing an additional unit of each product is the same as the extra expenses involved in creating that unit.

The marginal revenue for good A is given by p = 100 − x, and the marginal revenue for good B is given by q = 100 − y.

The marginal cost for good A is given by 2x + y, and the marginal cost for good B is given by 2y + x.

Substituting these expressions into the above conditions, we get the following system of equations:

100 − x = 2x + y

100 − y = 2y + x

Solving this system of equations, we get x = 25 and y = 25.

Therefore, the company can maximize profit by producing 25 units of each good A and good B.

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The function that describes the table of values is y = 4x + 7

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

The table of values

From the table, we can see that

As x increases by 1

The y values increase by 4

So, we have

m = Slope = 4/1 = 4

The equation is calculated as

y = mx + c

So, we have

y = 4x + c

Using the other points, we have

c = 7

This gives

y = 4x + 7

Hence, the function that describes the table of values is y = 4x + 7

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if you were traveling at 30 mph and were distracted for just one second, you would travel approximately 44.7 feet blindly.

Here we have to calculate,

How many feet you would travel in one second at 30 mph.

In order to find this

Convert mph (miles per hour) to fps (feet per second)

Since we are looking for the distance in feet.

⇒ 1 mph = 1.47 fps

So,

⇒ 30 mph = 44.7 fps

Now that we know how fast you are traveling in feet per second,

Calculate how far you would travel in one second if you were distracted for just one second.

⇒ 44.7 feet per second x 1 second

⇒ 44.7 feet

Hence,

you would travel approximately 44.7 feet .

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The ordered pair that represents the point plotted and labeled A include the following: (−1, 2).

In Mathematics and Geometry, the translation of a graph to the left simply means a digit would be subtracted from the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph upward means a digit would be added to the numerical value on the y-coordinate (y-axis) of the pre-image.

g(x) = f(x) + N

Note: "Point A is one unit left and two units up from the origin. "

Since point A is one unit left and two units up from the origin (0, 0), we can logically deduce the following:

(x, y)                   →           (x - 1, y + 2)

Origin (0, 0)        →           (0 - 1, 0 + 2) = point A (-1, 2).

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Answer:

A: -2 + 3i

B: -1 + -1i

C: 3 + -4i

D: 4 + 1i

Step-by-step explanation:

These are the answers, Basically just normal graphing. run/rise.

I hope this helps! :)))))

The correct answer is,

⇒ as a trapezoid, a rectangle, and two squares

We have to given that,

The composite figure is shown in image.

Now, By given figure,

The figure is make by,

⇒ a trapezoid,

⇒  a rectangle,

⇒ two squares.

Where, Trapezoid is shown in upper side.

And, Rectangle is shown in middle.

And, Two small Squares are shown below.

Thus, The correct answer is,

⇒ as a trapezoid, a rectangle, and two squares

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Answer:

The answer is 126ft³

Step-by-step explanation:

V=1/3LWH

V=1/3×9×6×7

V=3×6×7

V=126ft³

The difference between the slopes of two function is,

⇒ 2

We have to given that,

Mary compared to slope of the function y = 5x + 6 ​to the slope of the table.

Now, We have;

Function is,

y = 5x + 6

Hence, Slope = 5

And, For equation for table,

Let two points on table are (1, 3) and (2, 6).

Hence, Slope of table is,

m = (6 - 3) / (2 - 1)

m = 3/1

m = 3

Thus, The difference between the slopes of two function is,

⇒ 5 - 3

⇒ 2

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Answer:

967 meters

Step-by-step explanation:

1 kilometer is 1000 meter so 1000-33=967

The true statement is; II. Option D

From the information given, we have that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Note that;

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The pressure exerted is given as 4400Pa

The pressure exerted by the cube is calculated as follows:

Pressure = Force / Area

The force is given as 40 N and the area is the area of the bottom face of the cube, which is 30 cm x 30 cm = 900 cm^2.

Therefore, the pressure is:

Pressure = [tex]40 N / 900 cm^2 = 0.044 N/cm^2[/tex]

In pascals, the pressure is:

Pressure = [tex]0.044 N/cm^2 * 10^6 Pa/N/m^2 = 4400 Pa[/tex]

Therefore, the pressure exerted is given as 4400Pa

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The Question in English

A cube of side 30 cm is resting on the table exerting a table of 40 N what pressure does it exert?

Answer:

2002.7 (1 d.p.).

The value of the exports reached $8.8 billion during the year 2002.

Step-by-step explanation:

The function modelling the approximate value of China's exports of automobiles and parts (in billions of dollars) is:

[tex]f(x)=1.8208e^{0.3387x}[/tex]

where x = 0 corresponds to 1998.

To find the year when the exports reach $8.8 billion, substitute f(x) = 8.8 into the given equation, solve for x, then add this value to 1998.

[tex]\begin{aligned}1.8208e^{0.3387x}&=8.8\\\\e^{0.3387x}&=\dfrac{8.8}{1.8208}\\\\\ln e^{0.3387x}&=\ln \left(\dfrac{8.8}{1.8208}\right)\\\\0.3387x&=\ln \left(\dfrac{8.8}{1.8208}\right)\\\\x&=\dfrac{\ln \left(\dfrac{8.8}{1.8208}\right)}{0.3387}\\\\x&=4.65153751...\end{aligned}[/tex]

Add the found value of x to the year 1998:

[tex]\implies 1998+4.65153751...=2002.65153...[/tex]

Therefore, the the value of the exports reached $8.8 billion during the year 2002.

As the answer requires the year with at least one decimal place, the final answer is 2002.7 (1 d.p.).

The equation of the line of best fit is: y = (-2/3)x + 26/3

To estimate the line of best fit using two points on the line, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given the two points (7, 4) and (10, 2), we can calculate the slope (m) using the formula:

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

Substituting the coordinates of the points:

m = (2 - 4) / (10 - 7)

m = -2 / 3

Now that we have the slope, we can substitute it into the equation and solve for the y-intercept (b). Let's use the coordinates of one of the points, such as (7, 4):

4 = (-2/3)(7) + b

4 = -14/3 + b

To find the value of b, we can rearrange the equation:

b = 4 + 14/3

b = 12/3 + 14/3

b = 26/3

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The percentage of the men  that weighed between 57 kg and 75 kg is 68%.

The percentage of the men  that weighed between 57 kg and 75 kg is calculated by applying normal distribution formula.

In a standard normal distribution curve, we have the following;

One standard deviation below the mean = M - S.D = 34%

One standard deviation above the mean = M + S.D = 34%

The number of men that would weigh 57kg is calculated as;

M - S.D = 66 - 9

M - S.D = 57

The number of men that would weigh 75kg is calculated as;

M + S.D = 66 + 9

M + S.D = 75

So we can see that 57 and 75 lie between one standard deviation below the mean and one standard deviation above the mean.

The total probability = 34% + 34% = 68%

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Answer:

The answer are

B and C

Step-by-step explanation:

r=d/2=12/2=6

r=16/2=8

Circumference=2pir

C=2×6pi

C=12pi

C=2pir

C=2×8pi

C=16pi

Answer:

option A

2/11

Step-by-step explanation:

odds in favor of an event are calculated as,

number of favorable outcomes : number of unfavorable outcomes

here the favorable outcomes is either a jack or a 10

(8 cards from a deck of 52 playing cards)

all the rest of the cards are unfavorable outcomes

(44 remaining cards of the deck)

thus,

odds in favor = 8 : 44

= 2 : 11

If the graph of [tex]f(x) = 4e^{0.1x}[/tex] is blue, then the graph of [tex]f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}[/tex] is: C. red.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

For the rate of change of the blue exponential function [tex]f(x) = 4e^{0.1x}[/tex], we have the following:

b = [tex]e^{0.1}[/tex]

b = 1.11

For the rate of change of this exponential function [tex]f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}[/tex], we have the following:

b = 1 + 0.1/0.5

b = 1.2

Therefore, this exponential function [tex]f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}[/tex] is represented by the red line on the graph.

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The best measure of center for the given data is the median and the median is 17.

We have,

The best measure of center for the given data is the median because it represents the middle value when the data is arranged in ascending order.

In this case, the data is:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

To find the median, we look for the middle value.

Since there are 13 numbers in total, the middle value is the 7th number, which is 17.

Therefore, the median is 17.

The mean, on the other hand, may not be the best measure of center in this case because it can be affected by extreme values.

Since we don't have information about the distribution of the data or the presence of outliers, the median is a more robust measure that gives a better representation of the central tendency of the data.

Thus,

The best measure of center for the given data is the median and the median is 17.

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As per the given details, the starting height of the ball is 5 units from the ground.

Setting h(t) = 0:

-16t² + 112t + 5 = 0

The solutions are t = 0.125 and t = 7.

The vertex of the parabola given by h(t) = -16t² + 112t + 5 can be found using the formula t = -b / (2a).

In this case, a = -16 and b = 112.

t = -112 / (2 * -16)

t = -112 / -32

t = 3.5

h(3.5) = -16(3.5)² + 112(3.5) + 5

h(3.5) = -196 + 392 + 5

h(3.5) = 201

So, the maximum height of the ball is 201 units.

The time when the maximum height occurs is t = 3.5 seconds.

Thus, plotting points using various t values and figuring out the appropriate values of h(t) will allow us to graph the function.

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The volume of the biggest candle given the volume of the smallest candle would be = 90.75cm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder =πr²h

π = 3.14

r = radius

Volume of the smallest candle = 3.14 x 5 x 1.7² = 45.37 cm³

But the scale factor = 2

Volume of the largest candle = 45.37 cm³ x 2 = 90.75cm³

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Complete question:

Mrs. Lopez made decorative candles in different

sizes for sale at her church. All of the candles are in

cylindrical jars. The size of the largest candle was bigger

than the smallest candle by a scale factor of two. If the

height and radius of the smallest candle are 5 cm and

1.7 cm, respectively, calculate the volume of the biggest

candle. Use 3.14 for T. Round to the nearest hundredth.

Based on the formula of Venn Diagram, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram is a pictorial representation of data such that the relationships between two or more data sets are highlighlighted for similarities and differences.

A Venn Diagram may use overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, we can conclude that 26 customers purchased both shirts and pants, using the formula of Venn Diagram.

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The yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

The function f(x) = 1,000 * 1.02^t represents the amount in Karl's savings account over t years. The number 1.02 is the growth factor, which is equal to (1 + r), where r is the yearly interest rate.

To find the yearly interest rate, we need to solve the equation:

1.02 = 1 + r

Subtracting 1 from both sides of the equation:

0.02 = r

Therefore, the yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

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The measurements of the angles are 15 degrees, 45 degrees and 120 degrees.

We are given that;

The statement of triangle

Now,

Let x be the smallest angle, then the largest angle is 8x and the middle angle is 3x. Using the triangle angle sum theorem, we can write an equation:

x + 8x + 3x = 180

Simplifying, we get:

12x = 180

Dividing by 12, we get:

x = 15

This means that the smallest angle is 15 degrees. To find the other angles, we can multiply x by 8 and 3:

8x = 8 * 15 = 120 3x = 3 * 15 = 45

Therefore, by the angle the answer will be 15 degrees, 45 degrees and 120 degrees.

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The complete question is;

A triangle has angle measures that are related as follows: -the largest angle is eight times the smallest angle -the middle angle is triple the smallest angle find the measurements of the angles.