dilate triangle LMN by a scale factor of four using the origin as the center of dilation label the image triangle LMN and give the coordinates for each of the vertices

The amount earned as commission in the month of June is $2700

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

Commission percentage = 5%

Total sales in the month of June = $54000

The amount earned as commission in the month of June is then calculated as

Amount = Commission percentage x Total sales in the month of June

Substitute the known values in the above equation

So, we have

Amount = 5% x 54000

Evaluate

Amount = 2700

Hence, the commission amount is $2700

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The Volume of the model sphere is given as

Given that the diameter is 5inches, the radius will be

substituting r in the formula will give

Hence, the volume of the model sphere is approximately 321.39 cubic inches

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

How to find the soccer portion of the pie chart?

In mathematics, the complete pie chart is 360° and to calculate the soccer portion using standard formula which states that the division of the total hours spent on soccer and total sports hours multiply with 360°.

According to the question, the given data states that the pie chart is 360° which represents the total sports hours as 50 hours.

Therefore, the soccer portion is:

= Total hours spent on walking / Total sports hours x 360°

= 10 / 50 x 360°

= 72°

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

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The probability that the entire cargo will be approved is 0.078 = 7.8% using the Binomial probability distribution, while 92.2% will be refused. As a result, many will be rejected.

By Binomial probability distribution,

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] , various combinations of x items from a collection of n elements given by,

[tex]C_{n,x}[/tex] = n! ÷ x! (n - x)!

n=42, as 42 tablets are tested.

p=0.06 as 6% is defective.

If at most there is 1 defective piece then it will be accepted.

Therefore,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

P(X = 0) = [tex]C_{42,0}[/tex] × [tex](0.06)^{0}[/tex] × [tex](0.94)^{42}[/tex] = 0.074

P(X = 1) = [tex]C_{42,1}[/tex] × [tex](0.06)^{1}[/tex] × [tex](0.94)^{41}[/tex] = 0.0047

Thus,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X ≤ 1) = 0.074 + 0.0047

P(X ≤ 1) = 0.0787

The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.

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Answer:

  U'(12, 15)

Step-by-step explanation:

Given point U(4, 5) is part of figure STUVW that is dilated by a factor of 3 about the origin, you want the coordinates of U'.

Dilation about the origin multiplies each coordinate value by the scale factor:

  U' = 3U

  U' = 3(4, 5) = (12, 15)

The coordinates of U' are (12, 15).

Answer:

Part A:

Option 1

3x + 8 = 5x - 20 (vertically opposite angles)

2x = 28

x = 14

3x + 8 + 5x + 4y = 180° (adjacent angles on a straight line)

8x + 4y = 172

Substitute x = 14 into equation to find y.

8(14) + 4y = 172

4y = 60

y = 15

Hence, x = 14 and y = 15.

Part B:

Option 4

Unlabeled angle = 5x + 4y (vertically opposite angles)

Substitute x and y to find angle measure.

5(14) + 4(15) = 130°

Hence, measure of unlabeled angle is 130°.

Considering the definition of an equation, the equation 0.925p= p - 599 models the following situation: the sale prices of the motorcycles in both dealers are equal.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:

Being "p" the motorcycle’s original price, you know that:

If the sale prices are equal, the equation in this case is:

Sale price A= Sale price B

0.925p= p - 599

Finally, the equation 0.925p= p - 599 represent the situation.

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Answer:

this is true

Step-by-step explanation:

Answer: 22

Step-by-step explanation:

Let the sides have lengths [tex]x-4, x-2, x[/tex]. Since the perimeter is 60,

[tex]x-4+x-2+x=60\\\\3x-6=60\\\\3x=66\\\\x=22[/tex]

So, the length of the longest side is 22 units.

Answer:

Yes

Explanation:

A set S is said to be closed under addition if:

For a, b in S, a+b is in S.

If we add two even numbers, the result will always be an even number.

Therefore, the set of even number is closed under the operation of addition

We have a line defined by two points, P(-4,9) and Q(12,1).

Knowing two points of the line, we can calculate the slope with the formula:

In this case, the slope will be:

With the slope and one point we can express the equation in slope-point form:

The x-intercept is the value of x that makes the function f(x) become 0.

In this case, we have to find x so that y = 0.

We can replace y in the equation and calculate x as:

Then, for the x-intercept is x = 14.

Answer:

a) The equation of the line is y = (-1/2)*x+7

b) The x-intercept is x = 14.

Answer:

-5  < x < 17/5

Step-by-step explanation:

add three onto all sides -10 < 5x < 17

then divide all sides by -5  < x < 17/5

The parent function is given as:

f(x) = x²

y = x²

The graph is reflected across the x - axis

The x axis remains the same but the y axis is negated

g(x) = -x²

It is translated 4 units left

The function g(x) becomes

g(x) = -(x - 4)²

It is the translated 2 units down

g(x) = -(x - 4)² - 2

Simplifying the above equation:

g(x) = - (x² - 8x + 16) - 2

g(x) = -x² + 8x - 16 - 2

g(x) = -x² + 8x - 18

The height of cylinder when volume of 480 cubic meters is  480/r^2.

Volume serves as a measure for an object's storage capacity. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water when filled to the brim. The amount of space a three-dimensional object occupies is another way to define volume.

A solid's volume can be calculated by counting how many unit cubes it contains, such as in the case of a cube or cuboid. The best way to understand volume is to think of it as the area surrounded or occupied by any solid object or object with three dimensions. This can be seen by performing the following easy exercise at home:

volume of cylinder V is = πr²h

where, r  = radius of cylinder

h = height of cylinder

V = 480π cubic meters

Now, calculate its height in terms of cylinder radius using the volume of cylinder formula:

V = πr²h

480π =  πr²h

h = 480π/ πr²2

h = 480/r²

Therefore, The height of cylinder when volume of 480π is  480/r².

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Explanation

Part A: The quotient of y and seven is eight.

Answer: y/7 =8

Part B: Thrice a number is eighteen

Answer: 3x = 18

Part C: The sum of twice a number and five is nine

Answer: 2x+5 =9

Part D: A number decreased by seven is twenty- eight

Answer: x-7 =28

Solution

We are given the equation

We want to find y when x = -3. We only need to put x = -3

Therefore, the answer is

Problem

Henry purchased compact disks for $112. The compact discs cost $16 each.

Which of the following equations could you use to find how many compact disks, x, Henry purchased?

Solution

We can set up the following notation:

x= number of disks

total cost = (number of disks)* (unitary price)

Total cost = $112

number of disks =x

unitary price = $16

Replacing we got:

112 = x*16

For this case the correct equation would be given by:

$112 = $16x

The fraction of gasoline used is:

We need to convert this fraction to decimal and to percentage to find the answer.

Converting 7/8 to decimal:

For this we have to do the division between 7 and 8:

Thus, the decimal form of 7/8 is 0.875

Converting 7/8 to percentage:

we use the result that we previously get of 7/8 as a decimal: 0.875, and to convert it to percentage we multiply it by 100:

7/8 to percentage is equal to 87.5%

Answer: 0.875 and 87.5%

Given the following question:

Part A:

75 dollars to spend on gaS

Gas per gallon costs $2.80

With 75 dollars you can buy "26.8 gallons of gas."

Part B:

We know we can travel 230 miles with 26.8 gallons of gas, now we have to find out how many miles can we travel PER gallon of gas.

"10.4 miles" per gallon

1) Picking points G( 14,13) , H (-11, 0) and R(-3,7) , S(-4,-5) let's find their slopes using the slope formula

And R(-3,7) , S(-4,-5)

Since the condition to be parallel is share the same slope, and to be perpendicular one line must have the reciprocal and opposite slope in comparison to the first one. We can state that neither that line is parallel nor perpendicular.

3) So the answer is GH is not parallel nor perpendicular.

Hello! First, let's write some important information contained in the exercise:

committee = 6 students

class: 28 students:

- 10 males

- 18 females

Let's consider the rule: At least three females must be on the committee, so we have some cases, look:

_F_ * _F_ * _F_ * __ * __ * __

3 females and 3 males

_F_ * _F_ * _F_ * _M_ * _M_ * _M_

4 females and 2 males

_F_ * _F_ * _F_ * _F_ * _M_ * _M_

5 females and 1 male

_F_ * _F_ * _F_ * _F_ * _F_ * _M_

6 females and 0 male

_F_ * _F_ * _F_ * _F_ * _F_ * _F_

Now, we have to use the formula below and find the number of possible combinations:

Let's calculate each option below:

3 females:

3 males:

3 females and 3 males: 816 * 120 = 97920

4 females:

2 males:

4 females and 2 males: 3060* 45 = 137700

5 females:

1 male:

5 females and 1 male = 8568 * 10 = 85680

6 females and 0 male:

6 females and 0 male: 18564 * 1 = 18564

To finish the exercise, we have to sum the four options:

97920 + 137700 + 85680 + 18564 = 339864

So, right answer A: 339864.

This can be solved using ratio and proportions.

What is ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive. A ratio in mathematics illustrates how many times one number contains another.

First, we find the ratio of trees planted to trees cut

= 48/8 = 6

So, no. of trees to be planted when 5 trees are cut = 5x6 = 30

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Step 1: State the given in the question

Given that 3 out 20 cars passing through an intersection did not fully stop

Step 2: State what to be determined

We are to determine the probability that a car arriving at this intersection that will not fully stop

Step 3: State the formula for finding probability

The formula for finding the probability of an en event, E, from a sample S, is the ratio of the number of elements of event E to the total number of elements in the sample S.

This can be represented mathematically as

Step 4: Use the formula to solve the probability

If the event E is cars passing through an intersection did not fully stop. Then, the number of elements in the event E is given as 3. That is:

The sample is the total number of cars, which is given as 20. This means that

Therefore, the probability of the event occuring would be P(E). This is as calculated below:

Hence, the probability that a car arriving at this intersection will not fully stop is 3/20 or 0.15

A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?​

Let

A -----> you

B-----> a bird

C-----> top of the tree

see the following image

step 1

In the right triangle ABD

tan(42)=BD/AD

substitute given values

tan(42)=BD/40

BD=40*tan(42)

BD=36 ft

step 2

In the right triangle ACD

tan(32)=CD/AD

CD=AD*tan(32)

CD=40*tan(32)

CD=25 ft

step 3

Find the difference BD-CD

36-25=11 ft

therefore

Take into account that vector v can be written as follow:

where (x,y) and (xo,yo) are two points on the vector.

In this case, we can use (xo,yo) = R(-2,12) and (x,y) = S(-7,6). By replacing these values into the expression for vector v, we obtain:

Now, consider that the magnitude of v is the square root of the sum of the squares of the components. Then, we have for the magnitud of v:

Hence, the magnitude of v is approximately 7.810.

Now, consider that the tangent of the angle of the direction of the vector is equal to the quotient between the y component over the x component of the vector:

Hence, the direction of vector v is approximately 230.194 degrees.

You will need to make b the subject of the formula:

This you do by subtracting 0.25 from both sides of the equation:

b + 0.25 = 1.15 becomes:

For the description "The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations." Graphing method for solving systems is in play. Option A

This is further explained below.

Generally, Construct a graph using the first equation.

Create a graph using the same rectangular coordinate system for the second equation.

Find out whether the lines overlap, if they run parallel to one another, or if they are the same line.

In conclusion, Find a solution to the problem that we are having. In the event that the lines meet, locate the location where they do so.

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CQ.

Identify which method for solving systems is being described by this fact:

The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

answer choices

Graphing

Substitution

Elimination (adding or multiplying)

Answer:

900

Step-by-step explanation:

because I know answer