what’s the distributive property for 3(2x -1)*

Option C "1/20" and option E "15" are equivalent to 5% of 300.

When finding 5% of 300, we can use the formula (5/100) * 300 = 15. Hence, 15 is one of the expressions equivalent to 5% of 300. Another way to express 5% is as a fraction, which is 1/20. Therefore, 1/20 is also equivalent to 5% of 300. To arrive at this result, we first find that 5% is the same as dividing by 20, which is where the fraction 1/20 comes from.

Thus, options C and E, "1/20" and "15," respectively, are both correct answers.

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Answer:

-15

Step-by-step explanation:

-15

Hope it helps.

Do comment if you have any query.

Answer:

A = 14 mm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

Here b = 14 and h = 2 , then

A = \(\frac{1}{2}\) × 14 × 2 = 7 × 2 = 14 mm²

Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.

To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).

The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:

2x + 3y = 15

3y = -2x + 15

y = (-2/3)x + 5

The slope of the given line is -2/3.

Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.

Now, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:

y - (-5) = (-2/3)(x - (-3))

y + 5 = (-2/3)(x + 3)

To convert this equation into slope-intercept form, we can simplify and rearrange:

y + 5 = (-2/3)x - 2

y = (-2/3)x - 2 - 5

y = (-2/3)x - 7

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The average daily earning for the electrician is $303.10.

To find the average daily earning, we first need to find the total earnings for the week.

The electrician worked a total of 35 hours during the week (8 + 7 + 5.5 + 10 + 4.5 = 35).

Multiplying the total hours worked by the hourly rate gives us the total earnings for the week:

35 hours x $43.30/hour = $1,515.50

To find the average daily earning, we divide the total earnings by the number of days worked.

The electrician worked 5 days during the week, so:

$1,515.50 / 5 days = $303.10

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The maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

The maximum number of people who can stand in each side of a boat can be determined using Archimedes' Principle. This principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water it displaces.

Using this principle, the maximum number of people who can stand in each side of a boat can be calculated using the equation:

F_B = m_p * g

Where F_B is the buoyant force, m_p is the total mass of all the people standing in the boat, and g is the acceleration due to gravity.

To determine the maximum number of people, we must first calculate the mass of the boat, m_b. We can do this by multiplying the volume of the boat (V) by the density of the material the boat is made of (ρ).

m_b = V * ρ

Next, we can calculate the total mass of all the people standing in the boat, m_p. This can be calculated by multiplying the total number of people (n) by the average mass of a person (m).

m_p = n * m

Finally, we can calculate the maximum number of people who can stand in each side of the boat by rearranging the equation for F_B and solving for n.

n = (F_B) / (m * g)

Therefore, the maximum number of people who can stand in each side of the boat is equal to the buoyant force divided by the average mass of a person multiplied by the acceleration due to gravity.

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Answer:

Step-by-step explanation:

Divide height by width for the scale difference 'x'

Divide height 20ft by 'x' for the width.

Based on the given information, Jane should not search for the doll any more. The cost of searching outweighs the potential savings she might gain by finding a lower price.

In this scenario, Jane has already visited one shop and found the doll priced at $100. She knows that the doll is offered at three different prices: $120, $100, and $80, with unknown probabilities (represented as odds). Each additional search incurs a cost of $5.

To determine whether Jane should search for the doll again, we need to compare the expected cost of searching with the potential savings. Given the information provided, we do not have the probabilities associated with each price, so we cannot calculate the exact expected savings. However, we can make an informed decision based on the given information.

Since the current price of the doll is $100 and the potential savings from finding a lower price are uncertain, Jane should consider the cost of searching. With a search cost of $5 per search, it is unlikely that the potential savings from finding a lower price would offset the additional cost incurred by searching. Therefore, it is advisable for Jane not to search for the doll any more, as the cost of searching exceeds the expected savings.

It's important to note that a definitive decision would require more information, such as the probabilities associated with each price. However, based on the given information, the best course of action for Jane is to refrain from further searching.

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The dimension of a vector space is equal to the number of linearly independent vectors in its basis.

In the given basis B = {(0,2,1),(0,2,1),(1,0,0)}, we can see that the first two vectors (0,2,1) and (0,2,1) are identical and therefore not linearly independent. Therefore, the dimension of the vector space is equal to the number of linearly independent vectors in the basis, which is 2.

So, the dimension of the vector space whose basis are B = {(0,2,1),(0,2,1),(1,0,0)} is equal to 2.

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Answer:600

Step-by-step explanation:

300,000/ 500 =600

The height of the building from which the angle of elevation is 32 degrees is 127.87m.

The angle of elevation is found to be 32 degrees and when moving 50 closer to the building, the angle of elevation is 53.

Let us say that the height of the building is X.

Now, let us say the distance between the building and the person is Y.

So, we write,

tan(32°) = X/Y

Also, tan(53°) = X/(Y-50)

0.62 = X/Y and 1.32 = X/(Y-50)

0.62Y = 1.32Y - 66

66 = 0.32Y

Y = 206.25 m

Now, we know, X = 206.25m x 0.62

X = 127.87m

So, the height of the building is 127.87m.

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Julie will have driven a total distance of 289 miles if she travels from York to Corby via Derby.

Starting from York, Julie needs to travel to Derby. The distance between York and Derby is given as 89 miles. So, we know that Julie will have driven 89 miles once she reaches Derby.

Next, Julie needs to travel from Derby to Corby, but the given information is a bit tricky here. The distance from Derby to Corby is not given directly. Instead, we are given two distances - Derby to Dory and Dory to Corby.

To find the distance from Derby to Corby, we need to add the distances between Derby and Dory, and Dory and Corby. From the question, we know that the distance between Derby and Dory is 127 miles and the distance between Dory and Corby is 73 miles. Adding these two distances gives us the total distance from Derby to Corby, which is 200 miles.

Finally, we can add up the distances traveled between each location to find the total distance traveled by Julie. Adding the distances of each leg of the journey, we get:

89 miles (York to Derby) + 200 miles (Derby to Corby via Dory) = 289 miles

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Complete Question:

If Julie drives from York to Corby via Dory how many miles will she have driven?

York 89

Derby 127 73

Corby

The second situation costs less by

The cost of the first situation is

Adult = 8 * 2 = 16

drink = 2 * 2 = 4

popcorn = 2 * 2 = 4

Total = $24

Second situation

rent a video = $3.50

buy a 2 liter of cola = $1.60

a bag of microwave popcorn = $1.98.

Total = $7.03

The second situation costs less by

$24 - $7.03

= $16.92

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Answer:

12x - 18

Step-by-step explanation:

3 x 4x = 12x

3 x -6 = -18 (Negative and positive make a negative.)

12x - 18

The arrival rate is approximately 32.79 customers per hour.

To find the arrival rate in customers per hour, we need to convert the given information to an hourly basis.

Cars arrive at a rate of 6 cars every 11 minutes.

The average service time is 3 minutes per customer.

To calculate the arrival rate in customers per hour, we need to convert the time frame to hours and divide the number of cars by the time:

Arrival rate = (Number of cars) / (Time in hours)

Number of cars = 6 cars

Time = 11 minutes

To convert 11 minutes to hours:

11 minutes * (1 hour / 60 minutes) = 11/60 hours ≈ 0.183 hours

Arrival rate = 6 cars / 0.183 hours

Arrival rate ≈ 32.79 cars per hour

Therefore, the arrival rate is approximately 32.79 customers per hour.

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Answer:Betty earned $8 per hour babysitting

Step-by-step explanation:

Number of hours worked per day =3

Number pf nights worked =12

Number of hours wored for 12 nghts =3x12=36hours

Now if 36 hours  earned her $288

1 hour will earn her=( 288 x 1) / 36 = 8 hours

Answer:

The Rule for Horizontal Translations:

if y = f(x), then y = f(x-h) gives a vertical translation. The translation h moves the graph to the left when h is a postive value and to the right when h is a negative value.

Step-by-step explanation:

First, let us look at the parent function f(x) = |x|. The graph of this function looks like the following.

Notice that it is symmetric about the y-axis and looks like a v. Now, that we have the parent function and its graph. Let's look at thow the four transformations happen.

Part I: Horizontal and Vertical Translations

First, we must have a definition of the two types of translations. A vertical translation moves the graph up or down. An example of that would be:

Here, the red graph has been moved up 10 units and the blue graph has been moved down 10 units. These are the two types of vertical translations.

The other type of translation is a horizontal translation. A horizontal translation moves the graph left or right. An example of this would be:

Here, the red graph has been moved to the left 10 units and the blue graph has been moved to the right 10 units.

Now that we have seen some examples of the these, let's see if we can figure out why these translations happen.

Here is an equation of one of the vertical translations: , which of the graphs do you think it is? If you said the red one, you are correct.

Now, what do you think the equation of the blue graph is? If you said, , then you are correct again.

What does this lead us to any generalizations about how to make vertical translations with regard to our parent function? If you need a little more help, click here to start a movie of the parent function moving through vertical translations.

Now, we have hopefully come up with a generalization for our parent funcion, f(x) = |x|.

The Rule for Vertical Translations:

if y = f(x), then y = f(x) + k gives a vertical translation. The translation k moves the graph upward when k is a postive value and downward when k is negative value.

Here is an equation of one of the horizontal translations: , which of the graphs do you think it is? If you said the red one, you are correct.

Now, what do you think the equation of the blue graph is? If you said, , then you are correct again.

What does this lead us to any generalizations about how to make vertical translations with regard to our parent function? If you need a little more help, click here to start a movie of the parent function moving through horizontal translations.

Now, we have hopefully come up with a generalization for our parent funcion, f(x) = |x|.

The Rule for Horizontal Translations:

if y = f(x), then y = f(x-h) gives a vertical translation. The translation h moves the graph to the left when h is a postive value and to the right when h is a negative value.

Hope this helps, have a nice day/night! :D

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Given polynomial function is f(x) = 9(x-6)(x-5)^2Given polynomial function has three zeros 6, 5, 5For each zero of the given polynomial, we need to give multiplicity and state whether the graph crosses the x-axis or touches the x-axis and turns around, for each zero. Multiplicity of a zero is the number of times the factor (x – c) occurs in the factored form of the given polynomial.

For the zero 6, the multiplicity is 1 and the graph crosses the x-axis. For the zero 5, the multiplicity is 2 and the graph touches the x-axis and turns around. For the zero 5, the multiplicity is 2 and the graph touches the x-axis and turns around. Given polynomial function is f(x) = 5(x+3)(x+4)^3Given polynomial function has two zeros -3, -4For each zero of the given polynomial.

We need to give multiplicity and state whether the graph crosses the x-axis or touches the x-axis and turns around, for each zero. Multiplicity of a zero is the number of times the factor (x – c) occurs in the factored form of the given polynomial. For the zero -3, the multiplicity is 1 and the graph crosses the x-axis. For the zero -4, the multiplicity is 3 and the graph touches the x-axis and turns around.

Given polynomial function is f(x) = x^3 +2x^2 - 9x -18Given polynomial function has three zeros.To find the zeros, let's use the Rational Zero Theorem. Rational Zero Theorem states that if a polynomial has integer coefficients, then every rational zero is of the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.

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The range of the function f(x) = 2x +2 will be all real numbers.

Given that:

Function: f(x) = 2x + 2

The domain means all the possible values of x and the range means all the possible values of y.

The function is a linear function. And the domain and the range of the linear function will be all real numbers.

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Answer:

x=3, and y= 4 is a correct answer

Answer:

x = 2

y = -3

Step-by-step explanation:

y = -x - 1 and 5x - 2y = 16 replace y with -x-1 in the second equation

5x - 2(-x-1) = 16

5x + 2x + 2 = 16 add like terms

7x + 2 = 16 subtract 2 from both sides

7x = 14 divide both sides by 7

x = 2 now we can use this information to find y

y = -x-1 replace x with the value we found

y = -2-1

y = -3

Carina has developed c) explicit knowledge, which refers to knowledge that is codified, easily transferable, and can be communicated through various mediums such as manuals, checklists, and flowcharts.

Her well thought-out process documents and checklists are examples of explicit knowledge.Additionally, Carina possesses tacit knowledge, which is personal knowledge gained through experience and is difficult to codify or communicate. Her experiential knowledge gained through on-the-job learning is an example of tacit knowledge.

However, Carina's informal training tools such as checklists and flowcharts can also be considered as on-the-job learning methods that have helped her acquire both explicit and tacit knowledge over time.

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What is the value of 3⁴

▶️ 3⁴ = 3×3×3×3

▶️ 3⁴ = 81

The value of 3⁴ is 81..

Answer:

false

Step-by-step explanation:

I hope this helps!!

Answer:

3⅓ moves he have to make in garden

Answer:

\(\frac{64.5}{38.7}: \frac{5}{3}\)

Step-by-step explanation:

5 : 3

5 + 3 = 8

103.2 ÷ 8

12.9

12.9 × 3

38.7

12.9 × 5

64.5

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer:

3 hours

Step-by-step explanation:

She has 224-59=165 miles left to drive. Since her speed is 55 mph, time is equal to distance/speed, so 165mi/55mph = 3 hours

Answer:

Option D

Step-by-step explanation:

Convert to slope-intercept form:

\(4x-2y=2\)

\(-2y=2-4x\)

\(y=-1+2x\)

\(y=2x-1\)

Find the x-intercept by plugging in y=0:

\(y=2x-1\)

\(0=2x-1\)

\(1=2x\)

\(\frac{1}{2}=x\)

\(x=\frac{1}{2}\)

Therefore, the x-intercept is \((\frac{1}{2},0)\)

Find the y-intercept by plugging in x=0:

\(y=2x-1\)

\(y=2(0)-1\)

\(y=0-1\)

\(y=-1\)

Therefore, the y-intercept is \((0,-1)\)

So, the correct answer is option D.

Answer:

D

Step-by-step explanation:

1. To find the x intercepts, set y equal to 0 and solve for x

4x - 2y = 2

4x -2(0) = 2

4x - 0 = 2

4x = 2

x = 1/2

2. To find the y intercepts, set x equal to 0 and solve for y

4x - 2y = 2

4(0) - 2y = 2

0 - 2y = 2

-2y = 2

y = -1