Work out the equation of line B shown below.
Give your answer in the form y = mX + C,
where m and c are integers or fractions in their simplest forms.

Answer:

[tex]\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}[/tex]

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

[tex]SA = 2( A_{\text{base}}) + A_\text{side}[/tex]

First, we can calculate the area of the circular base:

[tex]A_{\text{circle}} = \pi r^2[/tex]

[tex]A_{\text{base}} = \pi (0.75 \text{ in})^2[/tex]

[tex]A_{\text{base}} = 0.5625\pi \text{ in}^2[/tex]

Next, we can calculate the area of the rectangular side:

[tex]A_\text{rect} = l \cdot w[/tex]

[tex]A_\text{side} = (4\text{ in}) \cdot C_\text{base}[/tex]

Since the width of the side is the circumference of the base, we need to calculate that first.

[tex]C_\text{circle} = 2 \pi r[/tex]

[tex]C_\text{base} = 2 \pi (0.75 \text{ in})[/tex]

[tex]C_\text{base} = 1.5 \pi \text{ in}[/tex]

Now, we can plug that back into the equation for the area of the side:

[tex]A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})[/tex]

[tex]A_\text{side} = 6\pi \text{ in}^2[/tex]

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

[tex]SA = 2( A_{\text{base}}) + A_\text{side}[/tex]

[tex]SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2[/tex]

[tex]\boxed{SA = 7.125\pi \text{ in}^2}[/tex]

[tex]\boxed{SA \approx 22.4 \text{ in}^2}[/tex]

The Mujib spent 60% of his money, while Prakash spent 20% of his money.The Mujib spent 60% of his money ($24 out of $40), and Prakash spent 20% of his money ($24 out of $120). Understanding percentages is an important skill, as it allows us to analyze and compare data in a meaningful way.

To work out the percentage of money each person has spent, we first need to determine the amount spent by each person. Both Mujib and Prakash spent $24 each. Now, let's calculate the percentage of money spent by each person.

Mujib had $40 initially and spent $24, so his total spending is $24. To find the percentage, we divide his spending by his initial amount and multiply by 100: ($24 / $40) * 100 = 60%. Therefore, Mujib spent 60% of his money.

Prakash had $120 initially and also spent $24, resulting in a total spending of $24. Similarly, we calculate the percentage of Prakash's spending by dividing his spending by his initial amount and multiplying by 100: ($24 / $120) * 100 = 20%. Hence, Prakash spent 20% of his money.

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The Algebraic expression -3 * 15 simplifies to -45.

The product of -3 and 15 can be represented algebraically as (-3) * 15.

To simplify this expression, we can perform the multiplication operation:

(-3) * 15 = -45

Therefore, the product of -3 and 15 simplifies to -45.

In the given expression, we have multiplied -3 by 15, resulting in a negative value since one of the factors is negative. Multiplying a negative number by a positive number yields a negative product.

So, the algebraic expression -3 * 15 simplifies to -45.

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Answer:

28

Step-by-step explanation:

2 30 mg pills for 60 mg

Twice a day is 4 pills and 7 days a week

So 4x7=28

Answer:

To solve this problem, we can use the formula distance = rate x time.

For the first part of the trip on the highway, Jennifer travels at an average rate of 54 1/2 miles per hour for 3 hours, so the distance she covers is:

distance = rate x time

distance = (54 1/2) x 3

distance = (109/2) x 3

distance = 327/2

distance = 163.5 miles

For the second part of the trip on the smaller route, Jennifer travels at an average rate of 34.25 miles per hour for 3 hours, so the distance she covers is:

distance = rate x time

distance = 34.25 x 3

distance = 102.75 miles

The total distance Jennifer has driven after 6 hours is the sum of the distances she covered on both parts of the trip:

total distance = 163.5 + 102.75

total distance = 266.25 miles

Therefore, the answer is (A) 266.25 miles.

Answer:

A C E

Step-by-step explanation:

judging by the fact that every game is $3.25 2 games is $6.50 3 is 9.75 and so on

Answer:

Step-by-step explanation:

To find out how many cuboids of dimension 5 cm x 5 cm x 3 cm are needed to form a cube, we need to calculate the volume of both the cuboid and the cube.

The volume of the cuboid is:

5 cm x 5 cm x 3 cm = 75 cubic cm

To form a perfect cube, the volume of the cube should be a multiple of the volume of the cuboid. The smallest cube that can be formed using a multiple of 75 cubic cm is a cube with a volume of 75 x 8 = 600 cubic cm.

To find the dimensions of this cube, we need to find the cube root of 600 cubic cm:

cube root of 600 = 8.66 cm

So, the dimensions of the cube are 8.66 cm x 8.66 cm x 8.66 cm.

To find how many cuboids are needed to form this cube, we need to divide the volume of the cube by the volume of the cuboid:

Volume of the cube = 8.66 cm x 8.66 cm x 8.66 cm = 658.39 cubic cm

Number of cuboids required = 658.39 cubic cm ÷ 75 cubic cm = 8.78

Since we can't use a fraction of a cuboid, Anuj will need 9 such cuboids to make a perfect cube.

Answer:

Step-by-step explanation:

Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

The instantaneous velocity of the coin, from the first derivative of the height function of the coin, is; v(2) = -20 m/s

The derivative of a function is the rate at which the function is changing with regards to the input variable, at a point within the domain of the function.

The height of the tower = 100 m

The function for the height of the coin is; h(t) = 100 - 5·t²

The instantaneous velocity of the coin is the rate of change of the height with respect to time, which is obtained from the derivative of the height function as follows;

The instantaneous velocity; v(t) = h(t)/dt = d(100 - 5·t²)/dt = -10·t

The instantaneous velocity for the coin at t = 2 seconds is therefore;

v(2) = -10 × 2 = -20

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The volume of the pyramid is 18069333.33 cubic units

The area of the surface is 313280 square units

The volume of the pyramid is solved using the formula

= 1/2 * base area * height

Where

base area = 440 * 440 = 193600

height = 280

volume of the pyramid = 1/3 * 193600 * 280

volume of the pyramid = 18069333.33 cubic units

The surface area

The surface area is calculated using the formula

= 4 *  area of the triangles

= 4 * 1/2 * 440 * 356

= 313280 square units

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The perimeter of the classroom in feet is 90 feet.

We are given that;

The corners of the classroom are (−12, 15), (−12, −9), (9, 15), and (9, −9).

Now,

Using the given coordinates, we can find the length and width of the rectangle. The length of the rectangle is the difference between the y-coordinates of two opposite corners, which is 15 - (-9) = 24 feet. The width of the rectangle is the difference between the x-coordinates of two opposite corners, which is 9 - (-12) = 21 feet.

P = 2(24 + 21) = 90 feet

Therefore, by the perimeter the answer will be 90 feet.

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In the given triangle, we have a right triangle where one angle is 90 degrees (marked as a square symbol). To find the value of x, we can use the trigonometric ratios sine, cosine, or tangent.

Looking at the triangle, we can see that the side adjacent to the angle x is 8 cm, and the hypotenuse of the triangle is 10 cm.

Using the cosine ratio, which is defined as the adjacent side divided by the hypotenuse, we can set up the equation:

cos(x) = adjacent/hypotenuse

cos(x) = 8/10

To find the value of x, we can take the inverse cosine (arccos) of both sides:

x = arccos(8/10)

Using a calculator, we can determine the approximate value of x:

x ≈ 36.87 degrees

Therefore, the value of x in the given triangle is approximately 36.87 degrees.

Answer:

4 cm

Step-by-step explanation:

Step: 1

Consider a circle inscribed in an isosceles triangle with legs of length 13cm and a base length of 10cm.

Step: 2

Draw-in altitude AD will pass through the center  O and bisects the base into two segments each in 5cm length.

So the triangle is isosceles so the segment BD is 6cm.

Draw in radius OB and radius OA  and length of  OD as h.

Refer to the attachment for step 3 and step 4

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Randall's conversion is incorrect because centimetre value cannot be less than the meter value for an equivalent measurement.

Both meters and centimeters are used to measure the length of distances or objects. As distances becomes longer, the use of meters would be more preferable as they can represent this distances with smaller values than centimeters.

100 cm = 1 m

Therefore,

40 cm = (40/100) m

40cm = 0.4 m

This shows that centimeters values cannot be greater than equivalent meter values .

Hence, Randall is incorrect .

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The option that shows the inverse's graph (with the correspondent domain and range) is option a.

Remember that for a function:

f(x) = y

The inverse f⁻¹(x) is defined as:

f⁻¹(y) = x

Here the original function is defined by the relation:

x: -1,  1,  3, 5, 7

y: 4, 2, 1, 0, 1

Then for the inverse function, the domain and range are:

x: 4, 2, 1, 0, 1

y: -1, 1, 3, 5, 7

Then the domain is 0 ≤ x ≤ 4

And the range is -1 ≤ y ≤ 7

the option with these two is a, so that is the correct option.

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To determine the area of the figure accurately, we need more information or a description of the figure. The measurements provided (4 cm, -3 cm, 8 cm, 6 cm) do not provide enough details to calculate the area. Please provide additional information or a description of the figure so that I can assist you in finding the closest measurement to its area.

Answer:

[tex]\huge\boxed{\sf |AB|\approx 13.9 \ units}[/tex]

Step-by-step explanation:

Point 1 = (x₁, y₁) = (7, 12)

Point 2 = (x₂, y₂) = (2, -1)

So,

x₁ = 7

y₁ = 12

x₂ = 2

y₂ = -1

Using distance formula to solve the question.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\D=\sqrt{(2-7)^2+(-1-12)^2} \\\\D=\sqrt{(-5)^2+(-13)^2} \\\\D = \sqrt{23+169} \\\\D=\sqrt{194} \\\\|AB|\approx 13.9 \ units\\\\\rule[225]{225}{2}[/tex]

The marginal revenue when 20 units are sold is approximately $24.877.

To find the marginal revenue when 20 units are sold, we need to calculate the derivative of the revenue function with respect to the number of units (x) and then evaluate it at x = 20.

The revenue function is given by R(x) = 25x - 0.003x^2.

The definition of the derivative of a function f(x) is:

f'(x) = lim(h->0) [f(x+h) - f(x)] / h

Let's apply this definition to find the derivative of the revenue function:

R'(x) = lim(h->0) [R(x+h) - R(x)] / h

Substituting the revenue function R(x) = 25x - 0.003x^2:

R'(x) = lim(h->0) [(25(x+h) - 0.003(x+h)^2) - (25x - 0.003x^2)] / h

Expanding and simplifying the expression inside the limit:

R'(x) = lim(h->0) [25x + 25h - 0.003x^2 - 0.003h^2 - 0.006xh - 0.003h] - 25x + 0.003x^2) / h

Canceling out the common terms:

R'(x) = lim(h->0) (25h - 0.003h^2 - 0.006xh - 0.003h) / h

Factoring out h from the numerator:

R'(x) = lim(h->0) h(25 - 0.003h - 0.006x - 0.003) / h

Canceling out h:

R'(x) = lim(h->0) 25 - 0.003h - 0.006x - 0.003

Taking the limit as h approaches 0:

R'(x) = 25 - 0.006x - 0.003

Simplifying:

R'(x) = -0.006x + 24.997

Now, to find the marginal revenue when 20 units are sold, we substitute x = 20 into the derivative:

R'(20) = -0.006(20) + 24.997

Calculating:

R'(20) = -0.12 + 24.997

R'(20) ≈ 24.877

Therefore, the marginal revenue when 20 units are sold is approximately $24.877.

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Answer:

7

Step-by-step explanation:

Answer: D (√x < 2)

Explanation: In interval notation, it reads:

0 < x < 4

It goes from 0 to 4.

The expression x² + 17 represents the sum of x squared and 17.

The sum of x squared and 17 we have to write in expression

x squared is the term x² represents x squared.

It means that the variable x is being multiplied by itself.

If x = 3, then x² would be 3 squared, which is 9.

Similarly, if x = -2, then x² would be (-2) squared, which is 4.

The term + 17 represents the constant value 17 being added to x squared. Regardless of the value of x, 17 will always be added to the result of x squared.

By combining these two terms using the addition operator (+), we express the sum of x squared and 17 as a single mathematical expression, which is x² + 17

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Step-by-step explanation:

a)   x = riders     y = racers       ( that is just what I picked...YMMV)

b)   x+y = 321        <======given

c)  25 x + 15 y =  6935    <=====given

Now just graph the two equations.....where they cross is the solution.

Graph below:

The relation that represents a function is: ((- 6, 5), (- 3, 2), (1, 2), (6, 5))

A relation represents a function if each input (x-value) is associated with only one output (y-value).

1. {(0, 3), (2, 4), (0, 6)}:

This relation is not a function because the input 0 is associated with two different outputs, 3 and 6.

2. ((- 7, 5), (- 7, 1), (- 10, 3), (- 4, 3)):

This relation is not a function because the input -7 is associated with two different outputs, 5 and 1.

3. ((- 6, 5), (- 3, 2), (1, 2), (6, 5)):

This relation is a function since each input is associated with a unique output.

4. {(2, 0), (6, 2), (6, - 2)}:

This relation is not a function because the input 6 is associated with two different outputs, 2 and -2.

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Predicates are used to express statements, properties, or relationships between entities in a formal and systematic way, allowing for logical reasoning and analysis. They are an essential component of predicate calculus, which is a branch of mathematical logic.

In logic and linguistics, a predicate is a term used to describe or assert something about a subject. It is a fundamental concept in predicate logic, which is a formal system for reasoning about statements and their relationships.

In a logical statement, a predicate is typically a function or a relation that takes one or more arguments and returns a truth value (either true or false) when those arguments are substituted into it. The arguments of a predicate are usually referred to as its subjects.

For example, in the statement "Socrates is mortal," the predicate is "is mortal," which asserts the property of being mortal about the subject "Socrates." In this case, the predicate is a unary relation since it takes only one argument.

Predicates can also take multiple arguments. For instance, in the statement "John loves Mary," the predicate is "loves," which relates the subject "John" to the object "Mary." In this case, the predicate is a binary relation.

In general, predicates are used to express statements, properties, or relationships between entities in a formal and systematic way, allowing for logical reasoning and analysis. They are an essential component of predicate calculus, which is a branch of mathematical logic.

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The value of x that makes the relation a function is 3.

Option A is the correct answer.

We have,

A = (5, 3), (4, 9), (7, 2), (x, 6)

Given the points (5, 3), (4, 9), (7, 2), and (x, 6), we need to ensure that x does not repeat in the relation.

If we substitute the given values of x (3, 4, 5, 7) into the relation, we find:

For x = 3: (3, 6)

For x = 4: (4, 6)

For x = 5: (5, 6)

For x = 7: (7, 6)

Now,

A function can not have the same output for the same input.

So,

(4, 6) and (4, 9) are not possible.

(5, 6) and (5, 3) are not possible.

(7, 6) and (7, 2) are not possible.

And,

(3, 6) is possible

Thus,

The value of x that makes a function is 3.

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The range of the cost of their family grocery bill is $119.91.

The range of the cost of the Michaels family grocery bill can be calculated by finding the difference between the highest and lowest values.

In this case, the highest value is $176.97, and the lowest value is $57.06.

Range = Highest value - Lowest value

Range = $176.97 - $57.06

Range = $119.91

Therefore, the range of the cost of their family grocery bill is $119.91.

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The probabilities for the size of homes that future buyers will desire are as follows:

2BR: 0.10 or 10%

3BR: 0.35 or 35%

4BR: 0.30 or 30%

5BR: 0.15 or 15%

6BR: 0.10 or 10%

We have,

To determine the probabilities for the size of homes that future buyers will desire, we can use the information provided in the table.

Let's calculate the probabilities for each size of home:

Probability of purchasing a 2BR home: 10%

Probability of purchasing a 3BR home: 35%

Probability of purchasing a 4BR home: 30%

Probability of purchasing a 5BR home: 15%

Probability of purchasing a 6BR home: 10%

To find the probabilities, we divide each percentage by 100:

Probability of purchasing a 2BR home: 10% / 100 = 0.10

Probability of purchasing a 3BR home: 35% / 100 = 0.35

Probability of purchasing a 4BR home: 30% / 100 = 0.30

Probability of purchasing a 5BR home: 15% / 100 = 0.15

Probability of purchasing a 6BR home: 10% / 100 = 0.10

Therefore,

The probabilities for the size of homes that future buyers will desire are as follows:

2BR: 0.10 or 10%

3BR: 0.35 or 35%

4BR: 0.30 or 30%

5BR: 0.15 or 15%

6BR: 0.10 or 10%

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To determine the probability of Luke getting all three prizes in three boxes of cereal, we need to find the probability of each individual event happening and then multiply those probabilities together.

The probability of getting a movie ticket coupon is 20% or 0.2.

The probability of getting a drink coupon is 30% or 0.3.

The probability of getting a popcorn coupon is 40% or 0.4.

Since Luke spins the spinner three times, the probability of getting all three prizes is calculated by multiplying the probabilities together:

P(all three prizes) = P(movie ticket) * P(drink) * P(popcorn)

= 0.2 * 0.3 * 0.4

= 0.024 or 2.4%

Therefore, based on the simulation, the probability that Luke gets all three prizes in three boxes of cereal is 2.4%.

Answer:

Step-by-step explanation:

[tex]n^{5}= 1254\\n^{5} = 2.3.11.19[/tex]

Therefore it is not possible that n is a perfect power of 5

           it is approximately 4.16

Answer:

n ≈ 4.165

Step-by-step explanation:

To solve this, you need to take the 5th root of both sides:

[tex]n^5=1,254[/tex]

[tex]\sf{\sqrt[5]{n^5} =\sqrt[5]{1254}}[/tex]

On the lhs we're only left with n as n^5 and the 5th root cancel each other out.

On the right-hand side we need to calculate:

[tex]n\approx4.165[/tex]