Find the surface area of the triangular prism.

A drawing of a triangular prism. The base is a right triangle with base 9 inches, height 12 inches, and third side 15 inches. The height of the prism is 29 inches.

The surface area is
square inches.

the runner still needs to run a distance of 15 km to finish the marathon.

To find out how much distance remains to be run in the marathon, we can first calculate how far the runner has already run in the last 3 hours. We can use the formula:

distance = speed x time

where speed is in meters per second and time is in hours.

The runner has been running at a constant speed of 5/3 m/s for 3 hours, so the distance covered so far is:

distance = (5/3) m/s x 3 hours x 3600 seconds/hour

distance = 6000 meters or 6 km

Therefore, the runner has already completed 6 km of the marathon, which means that the remaining distance to be run is:

remaining distance = total distance - distance already covered

The total distance of the marathon is 21 km, so the remaining distance is:

remaining distance = 21 km - 6 km

remaining distance = 15 km

Therefore, the runner still needs to run 15 km to finish the marathon.

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value of variable x on the parallel line is 12.

In geometry, a co exterior angle is an angle that is formed outside of a geometric figure by extending one of its sides. More specifically, a co exterior angle is formed when a transversal intersects two parallel lines, and it is an angle that is located outside of the parallel lines and on the same side of the transversal as one of the angles formed by the intersection.

Given

m ║n

8x+6 and 9x-30 are co exterior angle

8x+6+9x-30=180°

17x-24=180°

x=12

hence, value of variable x on the parallel line is 12.

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The area of the circle is 200.96 square kilometers, the area of the polygon is 181.02 square kilometers and the shaded region is 19.94 square kilometers.

The area A of a circle with radius r can be found using the formula:

A = πr^2

Plugging in the given value of radius, we get:

A = π(8 km)^2

Simplifying the expression, we get:

A = 64π km^2

So, we have

A ≈ 64 x 3.14 km^2

A ≈ 200.96 km^2

To find the area of an octagon with a radius of 8 km, we can break it up into eight congruent isosceles triangles.

So, we have

Area = 8 * Area of triangle

This gives

Area = 8 * 1/2 * r² sin(central angle)

So, we have

Area = 8 * 1/2 * 8² sin(45)

Evaluate

Area = 181.02

The shaded area is

Shaded = 200.96 - 181.02

Shaded = 19.94

Hence, the shaded area is 19.94 square kilometers.

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The x- and y-intercepts of the function f(x) = 2x² + x + 5 is A.

we put x as equal to 0 first and we get y = 5 (y=f(x))

once we get y = 5 we can replace it in the equation and we get 2x^2+x=0 solving the quadratic equation, we get x=0, -1/2

The quadratic equation can be solved by taking x common then we are left with (2x+1).

the x we take common is equal to 0

(2x+1) = 0 gives x=-1/2

hence the x intercept = -1/2, 0 and y intercept =5

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Step-By-Step:

The height triangle has a height of 17.3 yards and a width of 12 yards. 3. Finally, connect the two triangles to create the pyramid's surface area. The surface area of the pyramid is 116.7 yards².

Answer:

116.7 yards².

Answer:

The first step is to find the area of the base triangle:

Area = (1/2) x base x height

Area = (1/2) x 20 yards x 17.3 yards

Area = 173 square yards

To find the surface area of the pyramid, we need to find the areas of the four triangular faces and add them to the base area.

Area of a triangular face = (1/2) x base x height

Area of each face = (1/2) x 20 yards x 12 yards

Area of each face = 120 square yards

Now we can add up all the areas:

Surface area = base area + area of four faces

Surface area = 173 square yards + 4 x 120 square yards

Surface area = 653 square yards

Therefore, the surface area of the pyramid is 653 square yards.

let's call our number hmmm Z, now, let's reduce it by 17%, so 100% - 17% = 83%, so the new size for Z is 83% off the original, hmm how much is that?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{83\% of Z}}{\left( \cfrac{83}{100} \right)Z}\implies 0.83Z[/tex]

now, let's increase it by 12%, so the new size will be 100% + 12% = 112%, so 112% of 0.83Z, let's check how much is that

[tex]\stackrel{\textit{112\% of 0.83Z}}{\left( \cfrac{112}{100} \right)0.83Z}\implies 0.9296Z[/tex]

now, let's convert that to a percent format by simply multiplying it by 100, so that'd be 100 * 0.9296Z = 92.96% of Z.  Well, hell 92.96% is less than 100%, so is really 100% - 92.96% = 7.04% less.

So, instead of all that rigamarole, we could have just reduced Z by 7.04% in one fell swoop and obtain the same thing.

We find sets of three positive single digit integers with a mean of 4 and a range of 5 is {1, 5, 6} and another possible set is {2, 4, 6}.

Here mmr is mean, median, and range of a set of numbers. The mean of a set of numbers is the sum of all the numbers divided by the total number of numbers in the set. The median of a set of numbers is the middle number when the numbers are arranged in order.

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

To find two sets of three positive single digit integers with a mean of 4 and a range of 5, we can use the formula:

Mean = (sum of numbers) / (number of numbers)

Since we want the mean to be 4, the sum of the three numbers in each set must be 12. Since we want the range to be 5, the largest number in each set must be 5 more than the smallest number.

One possible set of three numbers that satisfies these conditions is {1, 5, 6}. The mean of this set is (1+5+6)/3 = 4, and the range is 6-1 = 5.

Another possible set of three numbers that satisfies these conditions is {2, 4, 6}. The mean of this set is (2+4+6)/3 = 4, and the range is 6-2 = 4.

Therefore, two sets of three positive single digit integers with a mean of 4 and a range of 5 are {1, 5, 6} and {2, 4, 6}.

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The probability that the reporter gets an assignment in the United States or Asia is 15/37.

To find the probability that the reporter gets an assignment in the United States or Asia, we first need to determine the total number of assignments in the pool.

Total number of assignments = 8 + 29 + 15 + 22 = 74

Next, we need to determine the number of assignments that are in the United States or Asia.

Number of assignments in the United States or Asia = 8 + 22 = 30

Finally, we can calculate the probability of the reporter getting an assignment in the United States or Asia by dividing the number of assignments in the United States or Asia by the total number of assignments:

Probability of getting an assignment in the United States or Asia = (Number of assignments in the United States or Asia) / (Total number of assignments)

Probability of getting an assignment in the United States or Asia = 30/74

Therefore, the probability of the reporter getting an assignment in the United States or Asia is 30/74, which can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 2:

Probability of getting an assignment in the United States or Asia = 15/37

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(1)  The scale factor for this dilation is 1/6.

(2) The scale factor for this dilation is 6.

(3) False. A dilation with a scale factor less than 1 is a reduction, not an enlargement.

1. To find the scale factor for the dilation with center at the origin that maps point M(-12,18) to M(-2,3) we can use the formula:

new coordinate / old coordinate = scale factor

For the x-coordinate:

-2 / -12 = 1/6

For the y-coordinate:

3 / 18 = 1/6

Since both coordinates have the same scale factor, we can conclude that the scale factor for this dilation is 1/6.

2. To find the scale factor for the dilation with center at the origin that maps point M(-2,3) to M'(-12,18) we can again use the formula:

new coordinate / old coordinate = scale factor

For the x-coordinate:

-12 / -2 = 6

For the y-coordinate:

18 / 3 = 6

Since both coordinates have the same scale factor, we can conclude that the scale factor for this dilation is 6.

3. False. A dilation with a scale factor less than 1 is a reduction, not an enlargement. An enlargement is a dilation with a scale factor greater than 1.

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In conclusion the area of the segment is approximately 32.76 square units.

How to find?

To find the area of a segment of a circle, we can use the formula:

Area of segment = (θ/360)πr²2 - (1/2)rsin(θ)

where:

θ is the central angle of the segment in degrees

r is the radius of the circle

π is a constant approximately equal to 3.14

sin is the sine function

In this case, the central angle is 50° and the radius is 15. Substituting these values into the formula, we get:

Area of segment = (50/360)π(15)²2 - (1/2)(15)sin(50)

= (5/36)π(225) - (1/2)(15)(0.766)

= 32.76 square units (rounded to two decimal places)

Therefore, the area of the segment is approximately 32.76 square units.

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The measure of angle 10 is 30 degrees.

What is an angle?

we can see that angle 10 and angle 11 form a straight line, and angle 9 and angle 10 form a triangle with angle 11.

Since angle 11 is a right angle with a measure of 90 degrees, the sum of angles 9 and 10 in the triangle must be 90 degrees.

We know that the measure of angle 9 is 60 degrees, so we can solve for the measure of angle 10 as follows:

angle 9 + angle 10 = 90 degrees

60 degrees + angle 10 = 90 degrees

angle 10 = 90 degrees - 60 degrees

angle 10 = 30 degrees

Therefore, the measure of angle 10 is 30 degrees.

What is triangle ?

A triangle is a closed geometric shape that consists of three line segments that connect three non-collinear points. The points where the line segments intersect are called the vertices of the triangle, and the line segments themselves are the sides of the triangle.

Triangles are two-dimensional objects that lie flat in a plane, and they have a variety of properties and characteristics that make them important in mathematics and other fields. The angles and sides of a triangle can be measured and related to one another through various geometric formulas and theorems, and triangles are used in a wide range of applications, from basic geometry and trigonometry to engineering, physics, and computer graphics.

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Complete question is: If the measure of angle 11 is 90 degrees, and the measure of angle 9 is 60 degrees, the measure of angle 10 is 30 degrees.

Answer:

11? I only think this because it says that EBD are collinear and it equals 99 so for (9x) to equal 99, it would have to be nine times 11.

first part.

The probability that the medicine is effective on each of three patients is 0.512 or 51.2%.

second part.

The probability that the medicine is effective on fewer than two of the next three patients is 0.104 or  10.4%.

Let p be the probability that the medicine is effective for a given patient.  p = 0.8.

6.  calculating the probability that the medicine is effective for all three patients. , we will multiply their individual probabilities of being effectively treated, because  the patients are independent

P(event 6) = p * p * p = 0.8 * 0.8 * 0.8 = 0.512 or 51.2%.

7.

event 7, we will  calculate the probability that the medicine is effective on fewer than two of the next three patients.

We apply the binomial distribution with n = 3 (the number of patients) and p = 0.8 (the probability of success).

The probability mass function for the binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

P(event 7) = P(X=0) + P(X=1)

= (3 choose 0) * 0.8^0 * 0.2^3 + (3 choose 1) * 0.8^1 * 0.2^2

= 0.008 + 0.096

= 0.104 or  10.4%.

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One possible set of points: (-9, 1), (-3, 5), (3, 9) which would have a positive linear association if they were graphed in a scatterplot.

A scatterplot is a graph that displays the relationship between two quantitative variables. It is a useful tool for exploring patterns and relationships in data, and can help identify trends, outliers, and potential correlations.

In the given question,

To create a set of 3 points with a positive linear association, we want to choose three points where the y-coordinate increases as the x-coordinate increases. Here's one possible set of points:

(-9, 1), (-3, 5), (3, 9)

If we graph these points on a scatterplot, we can see that there is a clear positive trend. As x increases, y also increases, suggesting a positive linear association between the two variables.

Note that there are many other sets of points we could choose that would also have a positive linear association. The key is to choose points where the y-coordinate tends to increase as the x-coordinate increases.

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Based on the information provided, the total tax this person will need to pay is $2,622,2.

The amount of money you pay for taxes depends on your income as there are specific percentages to be paid. In the case the income is $25000, this income matches the range $7,825 - $31,850, and therefore you should pay 50 plus 15 percent of the amount over 7,825. Based on this, let's calculate the money to be paid:

$25,000 - $7852 = $17, 148 x 0.15 (15%) = $2,572.2 + $50 = $2622.2

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The value of y is 7.5 for the given similar triangle.

The sides of comparable triangles are relative to one another. For instance, if the proportion of the lengths of two comparing sides of one triangle to another is 2:1, then the other two relating sides will likewise be in the proportion of 2:1.

According to the figure; two triangles are similar because its identities,

So, (2y + 25) = 2 times of (2y + 5)

we can write as,

⇒ (2y + 25) = 2 × (2y + 5)

⇒ 2y + 25 = 4y + 10

⇒ 2y - 4y = 10 - 25

⇒ - 2y = - 15

⇒ y = 15/2 = 7.5

Therefore, the value of y is 7.5 of the given similar triangle.

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Answer:

even

Step-by-step explanation:

It lands on 10, and 8, take that, divide by 2, and mutiply by 8.

Answer: The first graph

Step-by-step explanation: because the vertex is (3,-1)

Then plug in number like is 1 is x solve for y which will be -3

if x is 2, y is -3/2

x is 3, y is -1

x is 4, y is -3/2

x is 5, y is -3

Answer:

Vertex at (3,-1) and flipped upside down (opening downward)

*looks like the first one of the first attachment*

Step-by-step explanation:

The normal untransformed parabola is a U-ish, V-ish curve that has its vertex at (0,0) and it opens upward. There are "nice" points at (1,1) and (2,4) also at (-1,1) and (-2,4) Your parabola has had four changes made to it:

□The negative sign in front on your equation will FLIP the whole thing upside down so it opens downward.

□The 1/2 in front will "smash" the parabola so it is flatter and wider.

□The - 3 that's in close next to the x will shift (slide, translate) the whole thing to the right 3 units **left and right shifts are kind of the opposite of what you might think: - shifts right and + shifts left**

□The -1 tacked on to the end will shift (slide, translate) the whole thing down one unit. **more intuitive, - shifts down and + shifts up**

The acceleration function is a(t) = 6(t - 3).

Acceleration is the rate at which an object changes its velocity. The acceleration function is a mathematical function that gives the acceleration of an object at any given time

To find the acceleration function, we need to take the second derivative of the given velocity function f(t).

f(t) = (t - 3)^3 + t

First, let's find the first derivative of f(t)

f'(t) = 3 × (t - 3)^2 + 1

Now, let's find the second derivative of f(t) ( the acceleration function )

a(t) = f''( t )

= d/dt [3 × (t - 3)^2 + 1]

Do the derivation

= 6(t - 3)

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The given question is incomplete, the complete question is:

The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)^3 + t. find the acceleration function a(t).

Answer:

an = 6 * 2^(n-1)

Step-by-step explanation:

To find the general term of the sequence 6, 12, 24, 48, ... , we need to observe that each term is obtained by multiplying the previous term by 2. Therefore, the sequence is a geometric sequence with first term a = 6 and common ratio r = 2.

The formula for the nth term of a geometric sequence is:

an = a * r^(n-1)

Substituting a = 6 and r = 2, we get:

an = 6 * 2^(n-1)

Therefore, the general term of the sequence 6, 12, 24, 48, ... is given by the formula an = 6 * 2^(n-1).

Answer:

To determine which option is the most cost-effective, you can use some simple math. Let's assume you need to park for 8 hours:

Park and Ride:

Parking cost: 8 hours x £0.40 = £3.20

Bus fare: £0.60 x 2 (round trip) = £1.20

Total cost: £4.40

Free parking at the railway station:

Train fare: £3.50 x 2 (round trip) = £7.00

Total cost: £7.00

Based on the calculations above, the Park and Ride option is cheaper for an 8-hour parking period. However, you should also consider factors such as convenience and travel time when making your decision. If the railway station is closer to your destination or has more frequent train services, it may be the better option despite the higher cost.

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Answer:

∡7 = 70°

Step-by-step explanation:

∡7 and ∡8 are supplementary angles

∡7 + ∡8 = 180°

If:

∡8 = 110°

Then:

∡7 = 180 - 110

∡7 = 70°

The unknown angles on the straight line is as follows:

∠ZOX = 64 degrees

The sum of angles in a line segment is 180 degrees. Therefore, let's find the angle ∠ZOX as follows:

∠YOX = ∠YOZ + ∠ZOX

Therefore,

∠ZOX = ∠YOX -  ∠YOZ

∠YOX = 180°

Therefore,

5x + 6 + 3x - 2 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176 / 8

x = 22

Hence,

∠ZOX = 3x - 2

∠ZOX = 3(22) - 2

∠ZOX = 66 - 2

∠ZOX = 64 degrees

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The equation for a cosecant function with vertical asymptotes found at x = nπ such that n is an integer is `y = csc(x - nπ)`.

The cosecant function is the reciprocal of the sine function. The cosecant of a particular angle in a right triangle is the ratio of the hypotenuse to the side opposite the angle.

The cosecant function is written as follows: `csc(x) = 1/sin(x)`

Asymptotes are straight lines or curves that a graph approaches but never touches.

As a result, the graph of a curve gets closer and closer to the asymptote as it moves further away from the origin, but it never touches it.

For a function to have vertical asymptotes at `x = nπ`, the denominator of the function should equal zero. In the cosecant function, the denominator is equal to `sin(x - nπ)`.

Therefore, the vertical asymptotes are where `sin(x - nπ) = 0`.

The general form of the cosecant function is `y = A csc(B(x - C)) + D`.

The constants A, B, C, and D are used to alter the form of the graph of the cosecant function.

They can be used to alter the amplitude, period, phase shift, and vertical displacement of the graph, respectively.

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Answer:

y^10

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.

Part A: If assuming 0 means the white part, then nο.

Part B: If assuming 0 means the black part, then yes.

The prοbability οf an οccurrence is a figure that represents hοw likely it is that the event will take place. In terms οf percentage nοtatiοn, it is expressed as a number between 0 and 1, οr between 0% and 100%. The higher the likelihοοd, the mοre likely it is that the event will take place.

Part A: If assuming 0 means the white part, then nο, there is a chance tο hit the black circle but the circle is οnly abοut 1/9th, then the whοle target, sο putting it in numbers, it wοuld be abοut 1/9 cοmpared tο 8/9.

8/ 9 has a higher chance.

Part B: If assuming 0 means the black part, then yes, as I said in Part A, it's basically cοmparing 1/9 tο 8/9.

1/9 being the black part and 8/9 being the white [tex]8/9 > 1/9[/tex] which means the white pοrtiοn has a higher prοbability.

Hence, Part A: If assuming 0 means the white part, then nο.

Part B: If assuming 0 means the black part, then yes.

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the number of students who take only Physics is 15.

An equation is a mathematical statement that shows that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.

Let's denote the number of students who take only Physics by x.

We can use these equations to solve for x, the number of students who take only Physics:

Substituting the expression for the number of Physics students in terms of the number who take both, we get:

20 = number who take both + 3(number who take both)

20 = 4(number who take both)

number who take both = 5

this value in the expression for the number of Physics students, we get:

number of Physics students = 3(number who take both) = 15

Finally, we can use the first equation to solve for the number of students who take only Physics:

40 = 15 + 2(number of students who take only Physics) - 5

40 = 10 + 2(number of students who take only Physics)

number of students who take only Physics = 15

Therefore, the number of students who take only Physics is 15.

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Answer:

{f(x) ∈ ℝ | f(x) ≥ –3}

Step-by-step explanation:

f(x)=|x|-3

|x| have range x≥0 .

f(x)≥0-3

f(x)≥-3

First answer {f(x) ∈ ℝ | f(x) ≥ –3}