Find the surface area and volume of the prism.


The surface area of the prism is _________ cm2.
The volume of the prism is __________ cm3.

The function (f - g)(x) is given as follows:

C. (f - g)(x) = |7x + 1| - 6.

The functions for this problem are defined as follows:

To obtain the subtraction of f(x) by g(x), we merely subtract the definitions, as follows:

(f - g)(x) = f(x) - g(x).

Hence:

(f - g)(x) = |7x + 1| - 8 - (-2)

(f - g)(x) = |7x + 1| - 8 + 2.

The like terms in the expression are given as follows:

-8 + 2 = -6.

Hence the subtraction function for this problem is defined as follows:

(f - g)(x) = |7x + 1| - 6.

Meaning that option C is the correct option.

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The difference between the given statements is that opposite sides are congruent means that all four sides of the quadrilateral are equal in length.

While one pair of parallel sides means that two sides of the quadrilateral are parallel and have the same length, the other two sides may or may not have the same length.

These two conditions define different types of quadrilaterals like a rectangle and a parallelogram, respectively.

So the answer is "construct a quadrilateral with one pair of opposite sides congruent and parallel."

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The compound inequality for the graph shown above include the following:

x < -4.

x ≤ 5.

In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.

Since the first point is at -4 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.

Additionally, the second point is located at 5 and the arrow points to the left of the number line with a shaded circle, it represents the greater than (>) inequality symbol and should be written as x ≤ 5.

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A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.

To find out what the simplest form is of the ratio 5: 2[tex]\frac{1}{2}[/tex], we can divide both sides by 2[tex]\frac{1}{2}[/tex].

The ratio simplified is 2: 1.

To determine the simplest form of the ration 5 : [tex]2\frac{1}{2}[/tex] , we can first simplify the mixed fraction [tex]2\frac{1}{2\\}[/tex]

So, [tex]2\frac{1}{2\\}[/tex] = [tex]\frac{5}{2}[/tex]

∴ 5 : [tex]2\frac{1}{2\\}[/tex] = 5 : [tex]\frac{5}{2}[/tex]

            = ( 5 x 2 ) : ( [tex]\frac{5}{2\\}[/tex] x 2 )

            =  10 : 5

            =  [tex]\frac{10}{5}[/tex] x [tex]\frac{5}{5}[/tex]

            =  2 : 1

Hence, the simplest form of the ratio given is 2 : 1

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The value of the expression (x − y)(x+y)(x² + y²) will be 183.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, when x⁴ = 116, x will be 3.5

Also y² = 11, y will be 3.3

The value of (x − y)(x+y)(x² + y²) will be:

= (3.5 - 3.3) (3.5 + 3.3)(3.5² + 3.3²)

= 0.2 × 6.8 × 134.75

= 183

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The Intermediate Value Theorem tell us that there is a c in the interval [0,1] such that f(c) = k is lies between f(0) and f(1).

The Intermediate Value Theorem is a fundamental concept in calculus that states that given a continuous function f and two real numbers a and b, if k is a real number between f(a) and f(b), then there exists a real number c in the interval [a, b] such that f(c) = k.

In the specific case of [0,1], the Intermediate Value Theorem tells us that if k is a real number between f(0) and f(1), then there exists a real number c in the interval [0,1] such that f(c) = k. This means that for any value of k that falls between the values of the function at 0 and 1, there is a point in the interval [0,1] where the function takes on that value.

So, for what values of k does the Intermediate Value Theorem tell us that there is a c in the interval [0,1] such that f(c) = k? The Intermediate Value Theorem tells us that there is a c in the interval [0,1] such that f(c) = k for any real number k that falls between the values of f(0) and f(1).

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The company that has a better value is: company A.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the total fee that is being charged by company A is denoted by C(x) and it charges $14 per delivery fee and $8 per hour, an equation that models this situation is given by;

C(x) = 8x + 14

When hours, x = 8 hours, the total fee is given by:

C(8) = 8(8) + 14

C(8) = $78.

For company B, the total fee is given by:

C(x) = 10x + 10

C(8) = 10(8) + 10

C(8) = $90.

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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The complete question is:

We have 15 voters and four alternatives, and the individual preference lists are as follows:

Voters 1-3: a d b c

Voters 4-5: b d a c

Voters 6-7: c d a b

Voters 8-9: a d c b

Voters 10-11: b d c a

Voters 12-13: c d b a

Voters 14-15: d b a c

1) The plurality voting procedure? - Voters 1-3: a d b c

2) The Condorcet procedure? - Voters 8-9: a d c b

3) The Hare (instant runoff) system? - Voters 4-5: b d a c

4) The Borda count procedure? - Voters 8-9: a d c b

5) Sequential pairwise voting with agenda bdac? - Voters 8-9: a d c b

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(A) The number of doughnuts that were jelly = 6

(B) The number of doughnuts that were glazed = 14

As per the data given in the question,

We have,

Total number of doughnuts sold = 40

Percentage of jelly doughnuts = 15%

Percentage of doughnuts that's were glazed = 35%

A) The number of doughnuts that were jelly can be found by multiplying the total number of doughnuts by the percentage that was jelly:

40 x 15% = 6 donuts

So there were 6 doughnuts that were jelly.

B) The number of doughnuts that were glazed can be found by multiplying the total number of doughnuts by the percentage that was glazed:

40 x 35% = 14 donuts

So there were 14 doughnuts that were glazed.

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The area between the graph of f and the x-axis on the interval [-8, 0] is 4608 square units.

The two-dimensional region enclosed by the function's graph and the x-axis is referred to as the region between the graph and the x-axis. Calculating the definite integral of the function over the specified interval and deducting the area below the x-axis, if any, will yield the area of this region.

There are two sections to the graph of f(x) = |x3 - 64|: a parabolic section and a linear section. The area between the graph of f and the x-axis is just the absolute value of the definite integral of f(x) over [-8, 0] because the graph of f(x) on the interval [-8, 0] is below the x-axis and contains negative values.

We must first get the antiderivative of f(x) before we can determine the definite integral, which may be accomplished by utilising partial fraction decomposition.

The antiderivative of f(x) = x⁴ - 64 is:

F(x) = (x⁴)/4 + 64x

The definite integral of f(x) over [-8, 0] is:

Area = F(0) - F(-8) = (0⁴)/4 + 64(0) - ((-8)⁴)/4 - 64(-8) = (8⁴)/4 + 64(8) = 4096 + 512 = 4608

Hence, the area between the graph of f and the x-axis on the interval [-8, 0] is 4608 square units.

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the answer which equal to the 1 1/4 are 8 3/4 - 7 1/2 and 9 5/12 - 8 1/6.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

a) 5 2/8 - 4 1/4 = 42/8 - 17/4 = 42-34/8 = 8/8 =1

b) 8 3/4 - 7 1/2 = 35/4 - 15/2 = 35-30/4 = 1 1/4

c) 2 1/8 - 1 7/8 = 17/8 - 15/8 = 2/8

d) 9 5/12 - 8 1/6 = 113 - 98/ 12 = 15/12 = 1 3/12 =1 1/4

So the answer which equal the 1 1/4 is 8 3/4 - 7 1/2 and 9 5/12 - 8 1/6.

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50% of the kittens are black in colour.

Total number of kittens = 6

Out of these, 3 are black, 2 are grey, and 1 is white.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Now, percentage of kittens that are black:

(Total number of Black Kittens/Total number of kittens) x 100 %

= 3/6 x 100 % = 50%

Therefore, 50% of the kittens are black in colour.

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Answer:

62.2 m

Step-by-step explanation:

From 148m away at ground level, the angel of elevation to the tower base is 18 degrees. Imagining this as a right angled triangle, if considering the angle of 18 degrees, 148m is the adjacent and the opposite is the height of the hill:

tanA=opposite/adjacent

tan18=opposite/148

opposite = 57.8357059295m

From 148m away at ground level, the angel of elevation to the tower top is 34 degrees. Imagining this as a right angled triangle, if considering the angle of 34 degrees, 148m is the adjacent and the opposite is the height of the hill+the tower:

tanA=opposite/adjacent

tan34=opposite/148

opposite = 120.062515998m

Knowing the height of the hill and tower is 120.062515998m and the height of the hill is 57.8357059295m, we can say the height of the tower is the difference:

120.062515998 - 57.8357059295 = 62.2268100685 m

Answer:

Subtract the amount of £1 coins from 50p coins:

256-172 = 84

84/3 coins = 28 people paid with 3 coins.

172 people paid using £1 coins

172 + 28 = 200 total people

percent who used 3 coins = 28/200 = 0.13 x 100 = 14% so the answer is 14%

Charlotte makes 500 pounds per week

30 % of 500 she has to pay to the commission per week

if she made 1575 one week how much would she get?

1575 divided by 30%=472.5

472.5 rounded = 473

x=473 or 472.5

Charlotte would make $972.50 in a week in which she made $1575 in sales and  if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.

percentage, a relative value indicating hundredth parts of any quantity.

To calculate how much Charlotte would make in a week in which she made $1575 in sales

we first need to calculate her commission:

Commission = 30% × $1575

= $472.50

Total earnings = Guaranteed salary + Commission

= $500 + $472.50

= $972.50

Therefore, Charlotte would make $972.50 in a week in which she made $1575 in sales.

To calculate how much Charlotte would make in a week if she made x dollars in sales, we can use the same method.

Her commission would be:

Commission = 30% ×x

And her total earnings would be:

Total earnings = Guaranteed salary + Commission

= $500 + 0.3x

So, if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.

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Given that the function of ex is ex, the derivative of y with respect to x is -14e-14x.

The rate of a function's change with regard to one of its variables is known as the derivative. The derivative of y with respect to x in the case of y=e-14x is the rate at which y varies as x changes. The derivative is the derivative of ex, which is ex because derivative  the function is e-14x. Simply multiplying ex by the coefficient of x, which is -14, yields the derivative of y with respect to x. Consequently, derivative -14e-14x is the derivative of y with respect to x. Accordingly, y will drop by 14e-14x units for every unit increase in x.

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The value of the variable 'x' will be 40.50. Then the correct option is D.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔPQS is similar to the triangle ΔRQS. Then the equation is given as,

x / 45 = 18 / 20

x / 45 = 0.90

x = 40.5

The value of the variable 'x' will be 40.50. Then the correct option is D.

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Yes it's linear because the rate of change between x and y remain the same. Every increase of 5 in x results in a decrease of 4 in y, as example from x0 to x5, y goes from 18 to 14, from x5 to 10, y goes from 14 to 10. They decide to double the jump and go from x10 to x20, but as proof of it being linear, y also double the amount it decreases going from 4 to 8.

The name of all the chords that are drawn in Circle C are; SU, UV and TW.

The chord of a circle is a term that is defined as the line segment joining any two points on the circumference of the circle.

Looking at the image and comparing with the definition of chords above, we can say that the chords will be SU, UV and TW. This is because they join two points on the circumference of the given circle with center C

We further see that the segment CV is only the radius of the circle.

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Answer:

Reflection across the x-axis.

Step-by-step explanation:

Use squared paper and plot some coordinate points.

For example: (2,3) and (−3,−2) and reflect them in the x-axis. You should obtain the following results.

(2,−3) and (−3,2) respectively.

(Note that the x-coordinate remains unchanged, while the y-coordinate is the negative of the original point.In general this can be expressed as: Under reflection in the x-axis (x,y)→(x,−y))

The flux of F coming out of the circle C is 126π.

The flux of a vector field, F, out of a surface, S, is given by the formula

Flux = ∮F •  n ds,

where n is a unit normal vector to the surface S.

In this case, the surface S is the circle C with radius 6 centered at the origin and the vector field F is given by F(x, y) = (7x, 11). We can use Green's Theorem to find the flux from the circle C. The equation for the circle is x2 + y2 = 36. Differentiating this equation with respect to x and y gives us the unit normal vector, n = (x/6, y/6).

Plugging these values into the flux formula, we get

Flux = ∮F •  n ds = ∮ (7x, 11) •  (x/6, y/6) ds

= ∮ 7x2/6 + 11y/6 ds

= (7/6) ∮ (x2 + y2) ds

= (7/6) * Area of C

= (7/6) * π * 36

= 126π.

Therefore, the flux of F coming out of the circle C is 126π.

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If Sam runs another mile every 10 minutes, From the 1st mile marker, Tyrone runs another mile every 6 minutes.  Sam and Tyrone meets after  45 minutes

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

Given that,

Sam and Tyrone are running on a trail,

Sam reaches the 4th mile marker at the same time that Tyrone reaches the 1st mile marker

From the 4th mile marker,

Sam runs another mile every 10 minutes,

Speed =  distance/time  = 1/10 mile/minute

Tyrone runs another mile every 6 minutes,

Speed =  distance/time  = 1/6 mile/minute

Time when Sam and Tyrone meet = ?

Suppose,

When x distance covered by Sam then they will meet,

So,  That time distance covered by Tyrone will be, (4-1) + x

And time taken for it will be, t

Now it can be written as,

Time for Sam after 4th mile  = Time for Tyrone after 1st mile

x/(1/10)   =  (3 + x)/(1/6)

10x  =   6(3 + x)

10x  =  18 + 6x

4x  = 18

x  = 9/2

Time t =x/(1/10)   =  (3 + x)/(1/6)

 t =  (9/2)/(1/10)

t = 45 minute

Hence, After 45 minutes they will meet

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The learning preference category that best describes a high school fine arts student who prefers a studio lesson that involves modeling with clay over a virtual field trip to the Louvre is a kinesthetic learner.

Kinesthetic learners are individuals who learn best through hands-on, physical experiences and activities. They tend to be active and enjoy engaging their bodies in learning, such as manipulating objects or performing movements. For this student, modeling with clay provides a hands-on, physical experience that allows them to learn through touch and movement. They can feel the texture and weight of the clay, and manipulate it to create their desired form. This type of learning experience is much more engaging and effective for a kinesthetic learner compared to a virtual field trip to the Louvre, which is primarily a visual learning experience.

In conclusion, a kinesthetic learning preference involves hands-on, physical activities and experiences, and this preference is evident in the student's preference for a studio lesson that involves modeling with clay over a virtual field trip to the Louvre.

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The average rate of change is defined as the change in the dependent variable (y) divided by the change in the independent variable (x), or (y2 - y1) / (x2 - x1).

The average rate of change over the interval [π/2, π] cannot be determined without knowing the specific function. The average rate of change is defined as the change in the dependent variable (y) divided by the change in the independent variable (x), or (y2 - y1) / (x2 - x1). To find the average rate of change, you need to know the values of y at the start and end of the interval, as well as the corresponding x values.

Thus, The average rate of change over the interval [π/2, π] cannot be determined.

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Answer: 7/15

Step-by-step explanation:

8p + 7 = -6p

15p = 7

p = 7/15

[tex] \: [/tex]

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[tex] \: [/tex]

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hope it helps! :)

Therefore, the AAA test of congruency demonstrated that ABE is Congruence to CDE.

Something that is "exactly equal" in terms of size and shape is referred to as congruent. No matter which way we spin, flip, or rotate the shapes, they remain accurate. For instance, you may draw two circles with the same radius, cut them out, and stack them.

In this case, we are aware that AB ll DC - GIVEN

In light of the characteristic of parallel lines,

Let's recall the property of parallel lines:-

"When the pair of alternating angles equals one another, two straight lines become parallel."

Alternate angles are angle ABE and angle CDB.

angle BAE ≅ angle DCE -{alternate angles}

E is a midway, given that.

According to the midpoint theorem, opposite angles are congruent when angle AES and angle CED are compared.

Here, we may see the congruency test from AAA.

Hence its proved that ∆ABE ≅ ∆CDE by AAA test of congruency.

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The fare for a 9-mile journey can be calculated using the formula Fare = £2.50 + £0.90 x miles. To find the fare for a 9-mile journey, we just need to substitute 9 for miles in the formula:

Fare = £2.50 + £0.90 x 9

Fare = £2.50 + £8.10

Fare = £10.60

So, the fare for a 9-mile journey would be £10.60.

It's important to understand how the formula works in order to correctly use it. The first part of the formula, £2.50, is a fixed cost that is added to the fare regardless of the distance traveled. This could represent things like the cost of hiring the taxi, the driver's time, and any other fixed expenses that the taxi company incurs.

The second part of the formula, £0.90 x miles, is the variable cost that is added to the fare depending on the distance traveled. This could represent things like the cost of fuel, wear and tear on the vehicle, and any other expenses that the taxi company incurs as a result of traveling a certain distance. By multiplying the distance traveled by the cost per mile, £0.90, the formula calculates the total variable cost for the journey.

When these two costs are added together, the formula gives the total fare for the journey. In this case, for a 9-mile journey, the total fare would be £10.60.

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