Question 4 (10 points)

(02. 07 MC)


The figure shows triangle ABC and line segment PQ, which is parallel to BC:


Triangle ABC has a point P on side AB and point Q on side AC. The line PQ is parallel to the line BC.

Part A: Is triangle ABC similar to triangle APQ? Explain using what you know about triangle similarity. (5 points)


Part B: Which line segment on triangle APQ corresponds to line segment BC? Explain your answer. (3 points)


Part C: Which angle on triangle APQ corresponds to angle B? Explain your answer. (2 points)

The probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.

We have following information,

the demand for the polymer is distributed normally .

Mean (μ) = 250 gallons and Standard deviations (σ) = 125 gallons

Selling price of poymer = $25 per gallons

cost price of raw material for polymer= $ 10 per gallons

Salvage value = $(-5)/ gallon

Now, Using the formula for normally distributed sample,

Z = ( X - μ ) /σ

where , X---> sample mean

μ ----> population mean

σ----> standard deviations

Z -----> Z-value

from question it is clear X = 150

putting all the values of variables in above formula we get, Z = ( 150-250)/125 = -100/125

= - 0.8

(-0.8) value of z = 0.21 = 21% , the value of z is measure from normal distribution table.

They will run out of raw material if demands exceds this quantity or

Probability ( out of stock ) = 1 - 0.21 = 0.79 = 79%

So, the probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.

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#Complete Question :

Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop's purchases raw material for $10 per gallon and Goop mrust spend $5 per gallon to dispose off all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) That is to say, the salvage value is $(-5)/gallon. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost. ?

1. Suppose Good purchases 150 gallons of raw material. What is the probability that they will run out of raw material? ?

The factory produced 1.404 x 10⁶ sweets in a year

Standard form is a way of writing very large numbers or very small numbers in a simpler form. It is also called scientific notation

Given that: The factory produces 270000000 sweets every

week.

To know how many sweets the factory produces in a year, we will multiply the quantity produced in a week by 52 since there are 52 weeks in a year. Thus:

Number of sweet in a year = Weekly production x 52

                                 = 270000000 x 52 = 14040000000 sweets

To express 140400000000 in standard form, we will move the position of the decimal point to the back of the first number(1) and take note of the number of steps we take to get there. The  number of steps will then be  used as the power of 10:

14040000000 = 1.404 x 10⁶

Therefore, the number of sweets produced by the factory in a year in standard form is 1.404 x 10⁶ sweets

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The correct number in the function f (3) will be;

⇒ f (3) = 2

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The graph is shown in figure.

Now,

Clearly, By the image of the graph;

At x = 3,

The function is defined as;

⇒ f (3) = 2

Thus, The correct number in the function f (3) will be;

⇒ f (3) = 2

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There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal ≤

Greater than and equal ≥

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

-2/5 = -0.4

-11/3 = -3.67

-2.5

Now,

We see that,

-0.4 is greater than -2.5 and -2.5 is greater than -3.67.

This can be represented as an inequality:

-3.67 < -2.5 < -0.4

Thus,

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

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Answer:

  A, B, F

Step-by-step explanation:

You want to know the errors made in graphing y = -3x +2 by plotting the y-intercept of 2 and then plotting another point 3 down and 2 left of that.

The appropriate graph would be created by plotting the y-intercept at 2, then moving down 3 units and 1 unit right from there, because the slope is -3.

The y-intercept is correctly plotted at y=2.

The next point is incorrectly plotted down 3 units and 2 units left of the y-intercept. It should be plotted down 3 units and 1 unit right.

The slope is -3, or -3/1. For a negative slope, the rise or run, but not both, will be negative. We don't know the student's rationale for using 2 as the "run" in ...

  slope = rise/run

The best error descriptors seem to be ...

A)  The student used the y-intercept, 2, for the denominator of the slope. The slope should be −3 or −3/1 .

B)  The student said that, because the slope is negative, both rise and run are negative. When the slope is negative, either the numerator is negative or the denominator is negative, not both.

F) After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 1 unit, because the slope is −3/1, not −3/−2.

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Using the angle of elevation, the height of the tower is 9.2 ft.

He is  5 ft tall. The angle of elevation of the tower is 23 degree.

He is standing 10 feet away from the base of the tower.

The height of the tower can be found as follows;

The situation forms a right angle triangle.

The height of the tower can be found using trigonometric ratios.

Hence,

tan ∅ = opposite / adjacent

where

tan 23° = h / 10

cross multiply

h = 10 tan 23°

h = 4.2447481621

h = 4.2 ft

Therefore,

height of the tower = 4.2 + 5 = 9.2 ft

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The fault with Jerome's approach as required in the task content is; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.

Commutative property of addition is a property of addition which posits that Changing the order of addends does not change the sum.

On this note, the use of the commutative property of addition on the given expression; 3 - 6 + 5 would yield the expression; 3 + 5 - 6.

Consequently, the fault with Jerome's approach is that; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.

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Answer:

y = 119

30 =x

Step-by-step explanation:

61 and y are same side interior angles and they add to 180

61+y = 180

y = 180-61

y = 119

y and 6x-61 are vertical angles and they are equal

y = 6x-61

119 = 6x-61

Add 61 to each side

119 + 61 = 6x

180 = 6x

Divide each side by 6

180/6 = x

30 =x

Answer:

y = 119°

x = 30°

Step-by-step explanation:

We know that if two lines are parallel, the co - interior angles are added up to 180°°.

Accordingly,

y + 61 = 180

y = 180 - 61

y = 119°

Also, we know that, vertically opposite angles are equal to each other.

y = 6x - 61

119 = 6x - 61

Now, we have to make x the subject.

For that, first, add 61 for both sides.

119 + 61 = 6x

180 = 6x

Now, divide both sides by 6.

30° = x

This is an example of Cluster random sampling.

Cluster sampling refers to probability sampling when the population is divided into multiple smaller groups, also called clusters, and then further sampling is performed to check the data.

Here we can see that the principal had selected 222 boxes randomly over here. This implies that she had taken a group of boxes randomly. Then she proceeded to check every t-shirt in this box.

Therefore here we see that the population i.e the boxes were divided into smaller groups. The 222 boxes are the clusters here. Therefore we can conclude that the principal uses the cluster random sampling method.

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The value of the 48 cm will be equal to 480 mm.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that the number is 48 cm. Here 48 cm is the length of any object the value of 48 cm in the unit mm will be calculated as below,

1 cm = 10 mn

48 cm = 48 x 10 mm

48 cm = 480 mm

Therefore, the value of the 48 cm will be equal to 480 mm.

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The domain of h(z) would be (-8,3).

The range of h(z) would be (2,9).

Point (4,8) would be moved to (0,8)

What are the domain and range of a function?

The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.

A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)

For the function f(x):

Domain: (-4,7)

Range: (2,9)

The function f(x+4) is equal to 1 (f(x+4)).

This shows, inputs: -4, outputs: 1

Domain of f(x+4):

add -4 to the Domain values of f(x)

Domain:(-4-4,7-4)=(-8,3)

Range of f(x+4):

Multiply the range values of f(x) by 1

Range: (1*2,1*9)= (2,9)

Find, where the point (4,8) would be moved:

add -4 to 4, and multiply 8 by 1

(4-4,8*1)

=(0,8)

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The average skid mark for the car is 98.5 feet.

The average skid mark can be calculated by the formula -

S = ✓30Dfn, where s is speed of car, D is skid distance, f is drag factor and n is braking efficiency. Keep the values in formula to calculate the value of D.

57 = ✓30 × D × 1.1 × 1

Performing multiplication on Right Hand Side of the equation

57 = ✓D × 33

Taking square on both sides of the equation

D = 57² ÷ 33

Taking square on numerator on Right Hand Side of the equation

D = 3249 ÷ 33

Performing division on Right Hand Side of the equation

D = 98.45 feet

Rounding to the nearest tenth of a foot

D = 98.5 feet

Hence, the average skid mark is 98.5 feet.

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The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

The given equation of the line is

5x - 2y = -6

Ax + By = C1

Bx - Ay = C2

are perpendicular.

Then the perpendicular to the line 5x - 2y = -6 is 2x + 5y = C2

We have to find the value of C2

The line is passing through the point (5, -4)

Substitute the values in the equation and find the value of C2

2(5) + 5(-4) = C2

C2 = 10 -20

= -10

The equation will be 2x + 5y = -10

Rearrange the terms and make it slope intercept form

2x + 5y = -10

5y = -10 -2x

5y = -2x - 10

y = (-2/5)x - 2

Hence,  equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

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Step-by-step explanation:

the answer is Y=-1/2×+5

Explanation:

You put the gradient in M for Y=M×+C (substitute) then you substitute the coordinates it has given you into the X and Y part of linear equation. (x,y)

Answer:

10t + 20

Step-by-step explanation:

17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.

A percentage is a number or ratio expressed as a fraction of 100.

Given that, there are 14 litres of a solution which is 90% acidic,

Let water added be x, then according to question,

0.90*14 = 0.40(x+14)

12.6 = 0.40x + 5.6

0.40x = 7

x = 17.5

Hence, 17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.

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The subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18) is given as follows:

1.3t³ - 0.2t² - 32t + 18.

Polynomials are subtracted subtracting the like terms, which are the terms that have the same symbolic variable and the same exponent.

For this problem, the subtraction is given by the expression presented as follows:

(1.3t³ + 0.4t² - 24t) - (0.6t² + 8t - 18).

The like terms of the expression are given as follows:

Hence the result of the subtraction of the polynomials is given as follows:

1.3t³ - 0.2t² - 32t + 18.

The problem asks for the subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18).

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Answer:

2<y<6

Step-by-step explanation:

12 < 8y-y^2

y^2 -8y +12 <0

(y-6)(y-2)<0

y < 6

y < 2

 2.       6

-       -        +

-       +.       +

+.      -         +

2<y<6

Answer:

Step-by-step explanation:

Yes, of course!

A parabola's direction is based on whether its "a" value is positive or negative and whether it is opening vertically or horizontally (y= or x =)!

Answer:

1022

Step-by-step explanation:

360+600+12+45+9=1022

Answer:

18x−33−f(x)=0

Solve for f by simplifying both sides of the equation, then isolating the variable.

The transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

The given functions are f(x)=-1/4 x-2 and r(x)=4f(x).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

r(x)=4f(x)

So, r(x)=4(-1/4 x-2)

⇒ r(x)=-x-2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Vertical: stretch

The graph of the functions is given below.

Therefore, the transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

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Assuming it is a standard deck of 52 cards and a standard dice of 6 faces.

There are 13 heart cards in a standard deck, therefore the odd of getting a heart is 13 : 52 = 1/4.

There is only 1 six in a standard dice, therefore the odd of getting a six is 1/6.

For these events to happen simultaneously, we multiply the chances.

Therefore, the chance of getting a heart in a deck of cards and a six on a dice is 1/4 x 1/6 = 1/24.

Answer:

heart from a deck of cards= 13/52 = 1/4

getting a six on a dice= 1/6 = 1/6

Step-by-step explanation:

heart from a deck of cards :

In the context of ordinary maths questions the answer is so obvious as to almost not be worth mentioning. There are 52 cards in an ordinary deck and 13 of them have heart pips, so 13/52 = 1/4.

six from a dice :

There is a 1/6 chance of rolling a 6. There are only 6 sides on a die, and only 1 of them is 6, so there is a 1/6 chance of rolling a 6.

at the same time is:

13/15 + 1/6 = 31/30 = 1/30

Answer:

11.6666666 (infinitely)

The missing values in the ratio table include the following:

A = 2

B = 6

In Mathematics, a proportional relationship can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order for the ratio of the number of people to liters of ginger ale needed to have a proportional relationship, the variables x and y must have the same constant of proportionality.

Next, we would calculate the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 24/4

Constant of proportionality (k) = 6.

Now, we can determine the value of A and B:

A = x/k

A = 12/6

A = 2

For the value of B, we have:

B = x/k

B = 36/6

B = 6.

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Answer: A=2 and B=6

Step-by-step explanation: I hope this helped you

:D

The amount of tax paid per tonne of sand is $14.835 as the sand costs $98.90 per tonne.

In mathematics, a percentage is a value or ratio expressed as a fraction of 100.

The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.

Given,

The cost of one Tonne of sand=$98.90

The tax on one Tonne=15%

The  amount of tax per Tonne of sand is,

=(15/100)×98.90

=$14.835

Hence, the amount of tax paid per tonne of sand is $14.835.

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Answer:

N=138

Step-by-step explanation:

(4x+6) + N = 180

In order to complete this problem we need to solve for x. 4x+6=7x-21

Subtract on both sides

Subtract again

Divide

x=9

Plug it in now so 4 times 9 plus 6. 36, plus 6 = 42.

plug it in to the equation 42+N=180

                                         -42       -42

                                                    138 = N