1. A sum of money is to be shared among three friends Paul, Mark and Anna in the ratio 2: 3: 5 respectively. If Paul received $ 48,000. Determine


a. Anna’s Share
b. Mark’s share.
c. The total sum

The reflection across x-axis has the following rule applied

The rotation of 180° about the origin has the rule

In this case, the new image are not the same, that is to say

Therefore, they are not the same.

flowchart proof

1) Lines m and l are parallel ------> given

2) ∠1 ≅ ∠2 -----> by alternate interior angles

3) ∠3 ≅ ∠2 -----> by vertical angles

4) ∠1 ≅ ∠3 ----> by the transitive property

Mr. Thompson weighs 260 pounds and he loses 4 pounds each month.

The equation will be :

w = 260 - 4m

where w is the weight after m months

when w = 220 pounds, the number of months will be :

220 = 260 - 4m

4m = 260 - 220

4m = 40

m = 40/4

m = 10

The answer is 10 months

The length of the rafter when the architect design a house is 12.778m.

The information illustrates that the architect designs a house that is 10 m wide and that the rafters holding up the roof are equal length and meet at an angle of 65°.

The rafters extend 0.4 m beyond the supporting wall. Then, the length will be:

cos65° = BC / AC

cos 65° = (5 + 0.4)/x

cos 65° = 5.4/x

x = 5.4 / 0.4226

x = 12.778m

The length is 12.778m

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There is the required value would be 6 in the box.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

If you are in the partition XY in the ratio 3 to 4 from point X to point Y

To determine multiply the length of XY.

XY = 14 units then 3/7 of 14

= 3/7 × 14

Apply the multiplication operation,

= 42/7

Apply the division operation,

= 6

Hence, the required value would be 6 in the box.

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The exponential equation which represents the amount of raw sugar t hours after the process begins is; A = 1,000 (0.8)^(t/5).

It follows from the task content that the amount of raw sugar left after the process begins is to be determined according to the information given.

Since, 20% of the available raw sugar is changed to a refined sugar every 5 hrs, it follows that only 80% of the raw sugar is left after each successive time interval period.

Hence, the exponential model of the situation is such that;

A = 1,000(0.8)^(t/5).

Where t = number of hours after the process begins.

Therefore, the required equation is; A = 1,000(0.8)^(t/5).

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Answer:

75?

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

3 divided by 5

0.6x125

Answer:

15

Explanation:

Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.

So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;

The angle that the architect should cut to frame the base is 15 degrees

We have the following equation:

y - 4 = 1/3 (x + 2)

We clear y in order to be more unterstandable:

y - 4 = 1/3 (x + 2)

y = 1/3 (x + 2) + 4

y = 1/3 x + 2/3 + 4

y = 1/3 x + 2/3 + 12/3

y = 1/3 x + 14/3

In order to find the answer we are going to determine x value when y = 4:

y = 1/3 x + 14/3

4 = 1/3 x + 14/3

4 - 14/3 = 1/3 x

12 - 14 = x

-2 = x

Then, it passes through the point (-2 , 4), so we can discard options A and B (because it doesn't pass through (2, 4))

We know a linear equation is given by:

y = mx + b, where m and b are numbers: m is the slope of the line and b the y-intercept.

In this case y = 1/3 x + 14/3, the slope is 1/3. We know m is given by

m = Δy/Δx

Since in this case

m = 1/3 = Δy/Δx

Then

Δx = 3 and Δy = 1

That means that if it changes 3 units on the x-axis, then it changes 1 unit on the y-axis

Answer:

Step-by-step explanation:

the equation is written in slope intercept form

y= mx + b with m= slope and b= y-intercept

so in your equation

y=2/3x + 1,

the slope is 2/3 and the y-intercept is (0,1)

slope is also known as rise/run

so to move from one point to another, starting at (0,1) (since you know that point is on the line) you would move up 2 units and to the left 3 units.

hope this helped!

Part A

If Emily needs 24 feet of wire, then she has to spend $14.4

Part B

If Andy needs 13 yards of wire, then he has to spend $23.4

From the given graph choose one option

The length of the wire = 120 inches

The cost of 120 inches of wire = $6

Cost of 1 inch of wire = 6/120

= $0.05

Part A

The length of the wire = 24 feet

Convert the feet to inches

24 feet = 288  inches

The cost of 288 inches of wire = 0.05×288

= $14.4

Part B

The length of the wire = 13 yards

Convert the yards to inches

13 yards = 468 inches

The cost of 468 inches of wire = 0.05×468

= $23.4

Hence,

Part A

If Emily needs 24 feet of wire, then she has to spend $14.4

Part B

If Andy needs 13 yards of wire, then he has to spend $23.4

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Solution

step 1

Explain similarity

Both triangles are similar therefore the ratio of their corresponding sides must be equal.

Step2

State the corresponding sides

Step 3

Find x

Hence option A

Sebastian buy 134 cookies.  

Given,

He bought 4 boxes of shortbread cookies

and, 3 boxes of peanut butter cookies.

There are 20 shortbread cookies in each box.

but only 18 peanut butter cookies in each box.

To find the how many cookies did Sebastian buy in all?

Now, According to the question:

Formulate the above conditions:

18 x 3 + 20 x 4

Calculate the product or quotient

54 + 20 x 4

54 + 80

= 134

Hence, Sebastian buy 134 cookies.  

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1) Gathering the data

282 miles

2 1/2 hour We can rewrite that as 2.5

2) Let's use a proportion, or rather a formula for that

282 miles ------- 2.5

x -------------------- 1

2.5x = 282

x=282 /2.5

x =112.8 miles per hour

In one 1 hour, this train is able to get 112.8 miles if this train maintains its velocity

Answer:

B

Step-by-step explanation:

None

in this problem we have a vertical line

The equation of a vertical line is equal to the x-coordinate of the point that passes through it

so

in this case

the equation of the line is

x=-1

Given:

To find: The value of x (box)

Explanation:

Multiplying 30 on both sides. We get,

Solving we get,

Thus, the value of x is 24.

Final answer: The missing value is 24.

SOLUTION:

Step 1:

In this question, we are given the following:

The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?

Step 2:

The details of the solution are as follows:

Since side DE = 45, side HI = 36, and side DF = 30.

Then, the length of side HJ =

The value of the missing variable x is; x = 37

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

Now, from the given problem, we see that we have two parallel lines with a transversal crossing them Thus, we can say that the two given angles are corresponding angles and as such they are congruent. Thus;

3x + 4 = 115

3x = 115 - 4

3x = 111

x = 111/3

x = 37

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The given system of equation:

y = 3x - 5 (1)

y = -6x + 4 (2)

We can solve the system of equation by using elimination method :

Elimination Method: In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Subtract the equation (1) & (2)

So, we get x = 1

Substitute the value of x in the equation (1)

y = (-2)

So, the solution of the system of equations are : (x,y) = (1,-2)

Answer: (x,y) = (1,-2)

Answer:

  x = 3

Step-by-step explanation:

Given the sequence x, 7, 11, 15, ... 399, where 399 is the 100th term, you want to know the first term, x.

The differences of the first few terms are ...

  11 -7 = 4

  15 -11 = 4

This suggests an arithmetic sequence with a common difference of 4.

The first term, x, will be 4 less than the second term:

  x +4 = 7

  x = 7 -4 = 3

The value of x is 3.

__

Check

The n-th term of an arithmetic sequence with first term a1 = 3 and common difference d = 4 is ...

  an = a1 +d(n -1)

  an = 3 +4(n -1) = 4n -1

Then the 100th term is ...

  a100 = 4(100) -1 = 399 . . . . consistent with the given information

R90° transformation results in an image point that is (6, -8).

The plane is divided into four infinite areas known as quadrants, each of which is bounded by two half-axes, using two-dimensional Cartesian axes.

These are commonly numbered from 1 to 4, and are denoted by Roman numerals: the coordinates for I are I (+, +), II (-, +), III (-, -), and IV (+, -).

We are aware that there are four quadrants: I (x, y), II (-x, y), III (-x, -y), and IV (-x, -y) (x, -y)

We can infer that the points are in quadrant III from the supplied point, which is (-6, -8). (-x, -y).

Now, if we turn right 90 degrees and enter sector IV (x, -y), the supplied point will change to (6, -8)

hence, following the transformation of R90°, we have the image point is (6, -8).

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Answer:

P = 80 units

Explanation:

Let's label some points in the triangle as:

Since the sides of the triangles are tangent to the circumference, we can write the following relationships:

XC = YC

AZ = AY

BX = ZB

So, the length of the missing side XC is equal to:

XC = YC = 14

On the other hand, the length of AB is the sum of the length of AZ and ZB, so we can calculate ZB as:

AB = AZ + ZB

26 = AY + ZB

26 = 18 + ZB

26 - 18 = ZB

8 = ZB

Because AZ and AY have the same length.

Finally, the measure of BX is equal to:

BX = ZB

BX = 8

Therefore, the perimeter of the triangle is:

Perimeter = AY + YC + AZ + ZB + BX + XC

Perimeter = 18 + 14 + 18 + 8 + 8 + 14

Perimeter = 80

So, the answer is 80 units.

Meal prepared a day = 80 meals

Vegetarian meals will be

Non vegetarian meals = 80 - 30 = 50 meals

Given the data that we have here where the number of people in the survey is 10, s = 2 and mean = 49, the margin of error is given as 0.76

The margin of error can be used to provide the data that has to do with the amount of sampling error that would be in a given data statistic.

We would have to calculate the amount of error using the data that we have below.

We have the following values

number n = 10

mean u = 49

standard deviation sd = 2

The level of confidence c i = 80% = 0.80

we have to find the critical value

degree of freedom = 1 - 0.80

= 0.20

zα/2

= 0.20 / 2 = 0.10

= 1.383

The margin of error

= zα / 2 * s / √n

= 1.383 * 2/√10

= 1.383 x 2 / 3.623

= 1.383 x 0.552028

= 0.7634

The calculated margin of error is given as  0.7634

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Consequently, it costs $62.70 to make cupcakes for two hours.

By making use of functions, We have: n(h) = 3h, The cost in terms of hours h is given by C(3h) = 60+1.35h, and Lisa's cost for making cupcakes for 2 hours is $62.70

According to the question, Lisa makes 3 dozen cupcakes an hour. To calculate how many she makes in h hours, we will apply the equality postulate as stated.

3 dozens = 1 hour

Hour = n(h)

Cross Multiplying,

n(h) × 1 = 3×h

n(h) = 3h

Therefore, n(h) = 3h is the function that predicts the number of cupcakes Lisa produces in h hours.

We shall locate the composite function C(n(h)) to obtain the cost function in hours.

C(n(h)) = C(3h) (3h)

If C(n) = 60 + 0.45n, then

By replacing n with 3h in the function as indicated, C(3h) is obtained;

C(3h) = 60+0.45(3h) (3h)

C(3h) = 60+1.35h

Thus, 60+1.35h is the cost function expressed in hours.

We will change h = 2 into the calculation C(h) = 60+1.35h to obtain the cost of baking cupcakes for 2 hours.

C(2) = 60+1.35(2) (2)

C(2) = 60+2.70

C(2) = 62.70

Consequently, it costs $62.70 to make cupcakes for two hours.

Complete Question:

Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n. The function that models the number of cupcakes Lisa makes in h hours is n(h)=___. The cost in terms of hours h is given by ___. Lisa's cost for making cupcakes for 2 hours is___

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The answer is 75%