Unit 2 lesson 5 practice problem 3 in math workbook

You get 15 points if you answer this.

The correct system of equations that could be used to find x, the cost of a medium drink, and y, the cost of a large popcorn, is:

A) 2x + y = 13.85 3x + 2y = 23.9

To arrive at these equations, you can use the information given in the question to set up a system of linear equations. You know that 2 medium drinks and a large popcorn cost $13.85, so you can write:

2x + y = 13.85

where x is the cost of a medium drink and y is the cost of a large popcorn.

You also know that 3 medium drinks and 2 large popcorns cost $23.90, so you can write:

3x + 2y = 23.9

Then , you can solve the system of equations for x and y using any method you prefer, such as elimination or substitution. For example, one way to solve the system is to multiply the first equation by 3 to eliminate y:

6x + 3y = 41.55

Then you can subtract the second equation from this equation:

6x + 3y - (3x + 2y) = 41.55 - 23.9

Simplifying this equation gives:

3x + y = 17.65

You now have two equations to solve for x and y:

3x + y = 17.65 3x + 2y = 23.9

This system of equations is equivalent to the system shown in answer A.

Answer:

A

Step-by-step explanation:

The answer is (A) because, first off you have 2 medium drinks. So that is 2x. Second you only have 1 large popcorn. So that is just y. Right now the equation is 2x + y =$13.85. The next part of the problem is the same thing. You have only 1 more medium drink this time, so it is 3x. Then you have 1 more large popcorn, so that is 2y. The final part of the equation is 3x + 2y =$23.90. Since 23.90 is just a decimal you can just get rid of the 0. Now the equation should look like this, 2x + y=$13.85

3x + 2y=$23.9

Using the slope concept, it is found that the angle measurement has to be within 1.2º of 30º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, considering the horizontal distance and the actual angle, the following equation is applied to find the actual height:

\(\tan{30^\circ} = \frac{h}{25}\)

\(h = 25\tan{30^\circ}\)

h = 14.43.

For an error of 5%, the bounds of h are as follows:

\(h_{min} = 0.95 \times 14.43 = 13.71\)

\(h_{max} = 1.05 \times 14.43 = 15.15\)

Hence, the angles will be given by:

\(\tan^{\alpha} = \frac{13.71}{25}\)

\(\alpha = \tan^{-1}{\left(\frac{13.71}{25}\right)}\)

\(\alpha = 28.8\)

\(\tan^{\alpha} = \frac{15.15}{25}\)

\(\alpha = \tan^{-1}{\left(\frac{15.15}{25}\right)}\)

\(\alpha = 31.2\)

Hence the angle measurement has to be within 1.2º of 30º.

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Surveying 200 likely voters from each group of libertarians, independents, Democrats, and Republicans is an example of stratified sampling.

The survey conducted, which involves sampling 200 likely voters from each group of libertarians, independents, Democrats, and Republicans, exemplifies stratified sampling. Stratified sampling is a sampling technique where the population is divided into distinct subgroups or strata based on certain characteristics, and then samples are selected from each subgroup in proportion to their representation in the population.

In this case, the four political groups serve as the strata, and by selecting an equal number of likely voters from each group, the survey aims to ensure that each group is adequately represented in the sample. Stratified sampling allows for more accurate analysis and conclusions by considering the characteristics of each subgroup separately, enhancing the overall validity and reliability of the survey results.

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Answer:

x=4

y= 5

Step-by-step explanation:

6x+y=29

3x-y=7

Let's add them together

9x = 36

x= 4

Then put 4 back in the equation for x

6(4) + y =29

24 + y = 29

y= 5

The equation in slope-intercept form of the line that passes through (6, −1) and (3, −7) is:y = 2x − 13.

To write an equation in slope-intercept form of the line that passes through (6, −1) and (3, −7), you will use the point-slope form, as follows:

y − y1 = m(x − x1),

where:

m = slope (or gradient) of the line, and

(x1, y1) = the coordinates of a point on the line.

Let us calculate the slope (gradient) of the line using the given points:

(6, −1) and (3, −7).

m = (y2 − y1)/(x2 − x1)

m = (−7 − (−1))/(3 − 6)

= −6/−3

= 2

Thus, the slope of the line is 2.

Using the coordinates of one of the points, say (6, −1), in the point-slope form, we obtain:

y − y1 = m(x − x1)y − (−1)

= 2(x − 6)y + 1

= 2x − 12

Subtracting 1 from both sides, we get:

y = 2x − 13

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Answer:

 The quotient is x² + 6x +3

       Remainder  = -1      

 Step-by-step explanation:

Explanation:-

Given Polynomial equation

   f(x) = x³+5x²−9x−7

By using synthetic division

  x = 2           1       5       -9      -7

                      0       1       12     6

                  1      6         3     -1          

 The quotient is x² + 6x +3

       Remainder  = -1      

Answer:

Not Proportional

Step-by-step explanation:

Answer:

Proportional

Step-by-step explanation:

I just took the test

Have a nice day!

The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.

The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.

Expected winnings per ticket

= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0

If we condense the equation, we obtain:

Calculating the total wins anticipated per ticket

= $0.50 + $1.00 + $1.88 + $0.75 + $0

Expected winnings per ticket = $3.13

Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.

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Complete question:

For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:

a) $5.36

b) $5.63

c) $5.33

d) $5.66

Answer:

There are many different ways to portray your findings for an individual to view and understand. However, each have their pros and cons. When using a table, all of the specific numbers of your data can clearly be seen and compared with one another without having to analyze a picture. However, since there is no visual correlation that shows the growth and decline of your data, someone who best comprehends visually may not be able to understand your findings. It sis best to vary your sources of displaying information to make sure that it is all able to be understood by any viewer. When using a graph, you have a clear visual representation of the correlation of your variables in your experimentation. This allows the viewer to comprehend your data as a picture and see the change as the picture moves. However, it take further analysis and cross referencing to get specific quantitative data as you are required to read across and down the graph. And finally, when using equations you can show the direct way that the change was caused in your experiment. Each equation has a specific input and output. However, the drawback is the person viewing your data may have to solve the equations themselves to find out your data or simply be confused as equations don’t directly show data, but rather how to find it. It is important to have a varied combination of these things to allow for your data to be throughly understood by anyone viewing it. I hope this helps! :)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

The slope is always the value with the x.

Answer:

Slope = - 1/2x

Step-by-step explanation:

Answer:

320,000

Step-by-step explanation:

Step-by-step explanation:

a, The definite integral that represents the total work done is  ∫∫∫R g(P) * h(P) dV. b, The work done in forming Mount Fuji, assuming a right circular cone shape with given dimensions and a constant density of 200 lb/ft³, is approximately 8.216 × 10¹³ lb·ft.

(a) To find the definite integral that represents the total work done in forming the mountain, we need to integrate the product of the weight density and the height over the volume of the mountain.

Let's denote the weight density as g(P) and the height as h(P), and assume the mountain is formed within a region R. The total work done in forming the mountain can be expressed as

Work = ∫∫∫R g(P) * h(P) dV

Here, dV represents an infinitesimal volume element within the region R.

(b) Let's calculate the work done in forming Mount Fuji using the given information. We have

Radius of the cone, r = 62,000 ft

Height of the cone, h = 12,400 ft

Density of the material, g(P) = 200 lb/ft³

The region R is the volume of the cone formed by Mount Fuji. The volume of a right circular cone is given by

V = (1/3) * π * r² * h

Substituting the values, we get:

V = (1/3) * π * (62,000 ft)² * (12,400 ft)

Now, we can calculate the work done using the definite integral

Work = ∫∫∫R g(P) * h(P) dV

= ∫∫∫R (200 lb/ft³) * h(P) dV

= (200 lb/ft³) * ∫∫∫R h(P) dV

Since the density is constant, we can pull it out of the integral:

Work = (200 lb/ft³) * ∫∫∫R h(P) dV

= (200 lb/ft³) * V

Substituting the value of V, we get:

Work = (200 lb/ft³) * (1/3) * π * (62,000 ft)² * (12,400 ft)

Calculating this expression, we get:

Work = (200 lb/ft³) * (1/3) * π * (62,000 ft)² * (12,400 ft)

≈ 8.216 × 10¹³ lb·ft

Therefore, the work done in forming Mount Fuji, assuming the given values and the land initially at sea level, is approximately 8.216 × 10¹³ pound-feet (lb·ft).

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The required probability of rainfall duration falls for at least 2 hours, at most 3 hours and between 2 and 3 hours is given by  0.5896, 0.6808, and 0.2704 respectively.

Rainfall duration at Toronto Pearson International Airport follows,

An exponential distribution with a mean value of 2.725 hours

Probability that the duration of a particular rainfall event is at least 2 hours is,

Probability that the rainfall duration is greater than or equal to 2 hours.

Let X be the duration of a rainfall event,

P(X ≥ 2) = 1 - P(X < 2)

The cumulative distribution function (CDF) of an exponential distribution with mean value λ is,

F(x) = 1 - e^(-λx)

Substituting λ = 1/2.725 (since the mean value is 2.725 hours) and x = 2,

P(X < 2)

= F(2)

= 1 - e^(-1/2.725 × 2)

≈ 0.4104

Probability that the duration of a particular rainfall event is at least 2 hours is,

P(X ≥ 2)

= 1 - P(X < 2)

≈ 0.5896

Probability that the duration of a particular rainfall event is at most 3 hours,

Probability that the rainfall duration is less than or equal to 3 hours.

Using the CDF of the exponential distribution,

P(X ≤ 3)

= F(3)

= 1 - e^(-1/2.725 × 3)

≈ 0.6808

Probability that the duration of a particular rainfall event is at most 3 hours is approximately 0.6808.

Probability that the duration of a particular rainfall event is between 2 and 3 hours,

Probability that the rainfall duration is greater than or equal to 2 hours and less than or equal to 3 hours.

P(2 ≤ X ≤ 3)

= P(X ≤ 3) - P(X < 2)

= F(3) - F(2)

= e^(-1/2.725 × 2) - e^(-1/2.725 × 3)

≈ 0.2704

Probability that the duration of a particular rainfall event is between 2 and 3 hours is approximately 0.2704.

Therefore , the probability that the duration of rainfall is at least 2 hours, at most 3 hours and between 2 and 3 hours is equals to  0.5896, 0.6808, and 0.2704 respectively.

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Answer:

Step-by-step explanation:

Yes it is correct. :)

Answer:

Yeah, You're correct

Step-by-step explanation:

Have a nice day

Answer:

6:

x=  6(y−2)/5

8:a=−(b+c+4)

b=−(a+c+4)

Step-by-step explanation:

Answer: y=4/3x -3

Therefore the slope is 4/3

Step-by-step explanation:

distribute your x to the other side and divide

Answer:

4/3

Step-by-step explanation:

8x-6y=18

-6y=18-8x

divide all terms by -6

y=-3+4x/3

y=4x/3 -3

y=4/3x -3

slope 4/3

Answer:

The river is 3.15 feet deep.

Step-by-step explanation:

First let's recognize what we need to find: the depth of the river

We know last year the river was 4.2 feet deep, but it dropped 25%. This means we also need to find how much it dropped. To find this, we need to know what 25% of 4.2 is. Write an equation for this.

y = 25% of 4.2

y = 0.25 • 4.2

y = 1.05

This means that the river dropped 1.05 feet. To know its depth now, we need to subtract 1.05 from 4.2. Write an equation for this.

d = 4.2 - 1.05

d = 3.15

The river is 3.15 feet deep.

Hope this helps!

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π               → A = π - (B + C)

                                               → B = π - (A + C)

                                               → C = π - (A + B)

Use Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Use the following Cofunction Identity: cos (π/2 - A) = sin A

Proof LHS → RHS:

LHS:                        sin A - sin B + sin C

                             = (sin A - sin B) + sin C

\(\text{Sum to Product:}\quad 2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Given:}\qquad 2\cos \bigg(\dfrac{\pi -(B+C)}{2}+\dfrac{B}{2}}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi -C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(.\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2} -\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Cofunction:} \qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Factor:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\bigg]\)

\(\text{Given:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad =2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi}{2} -\dfrac{(A+B)}{2}\bigg)\bigg]\)

\(\text{Cofunction:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)\bigg]\)

\(\text{Sum to Product:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ 2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{LHS = RHS:}\quad 4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)=4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\quad \checkmark\)

In this scenario, we have two parallelograms, ghlj and gstu. The given information states that gstu is inside of ghlj. We are then asked to determine why angle ∠l is congruent to angle ∠t.

To understand why ∠l is congruent to ∠t, we need to look at the properties of parallelograms. In a parallelogram, opposite angles are congruent. In other words, if two sides of a parallelogram are parallel, then the opposite angles formed by these sides will be equal.

Looking at parallelogram ghlj, we see that side gh is parallel to side sj (given information). This means that angle ∠l and angle ∠t are opposite angles and therefore congruent.

In conclusion, the reason why ∠l is congruent to ∠t is due to the property of parallelograms. Since gstu is inside ghlj, side gh is parallel to side sj. This parallelism leads to the congruence of the opposite angles ∠l and ∠t.

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Answer:

(x,y) —> (–1 ,1)

I hope I helped you ^_^

Answer:

x=4

Step-by-step explanation:

4(3+2x)+2=46

12+8x+2=46

12+8x=44

8x=32

x=4

Answer:

4

Step-by-step explanation:

You need to start with the 2x inside the parenthesis

If you put 4 in place of x you get 8

8+3=11

then because there isnt any sign between 4 and the parenthesis you multiply

4x11=44

then its easy

44+2=46

Answer:

13.16 inches

Step-by-step explanation:

56.43 - 43.27 = 13.16

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

Answer:

C is correct I think.

Step-by-step explanation:

Tell me if I am right.

Have a nice day!

Answer:

25/2 or 12 1/2 or 12.5

Step-by-step explanation:

Hi! The answer is going for be D (400)

Step-by-step explanation:

Out of 100 women, 8 were married 2 or more times which is 8% or 0.08

So out of 5000 women, the number of women married 2 or more times is: 0.08*5000 = 400

x/5000 = 8/100

x/50=8/1

x=400

Hope this helps! Have a good day!

Answer: x=-29

Step-by-step explanation:

0.35(x+4)=0.25(x-6)

0.35x+1.4=0.25x-1.5

0.35x+2.9=0.25x

-0.1x=2.9

x=-29

From the given table, let's complete the stem and leaf plot.

Part (a):

From the given table, we have 27 data.

It consists of just the data for the round-trip commute time for the employees.

Therefore, data were collected for 1 quantitative variable.

Part (b):

The data constitute a sample

Part (c):

To compute the stem and leaf plot, we have:

Stems------------->Leaves

5--------------------> 0, 0, 3, 3, 3, 4, 7, 7, 9

6----------------------> 0, 1, 3, 4, 5, 7, 8, 8

7------------------------> 0, 3, 4, 4, 5

8------------------------>0, 1, 9

9-------------------------> 0, 4

Part d:

The shape of the data can be said to be right skewed .