How to find the probability? Please show your work. Thanks!

Answer:

Step-by-step explanation:

First you would multiply 12 by four since each person has to have a ticket ($48) next you would multiply 4.50 by two since they bought two buckets of popcorn ($9) then you would multiply 4.75 by four since they each bought their own drink ($15) then you would all three of those totals together to get the final cost of everything ($72)

Hoped that answered your question!

Answer:

$92.75

Step-by-step explanation:

Krystal and 4 friends were going to the movies.

Total person = 5

The cost of each ticket = $12.00

They bought 2 buckets of popcorn at $4.50 each

They all bought soda at $4.75 each.

Total money they spent = (12 × 5) + (4.50 × 2) + (4.75 × 5)

                                        = 60 + 9.00 + 23.75

                                        = $92.75

They spent $92.75 in total.

Answer:

y = b + kn

Step-by-step explanation:

In any given year, the salary of each will be given by the equation

y = b + kn where

y = Salary

b= Initial salary before increment

k= Increment

n= is the year in question

Thus, this can be proven by equating the salaries of both workers.

Jose's salary will be $48,000 + $2800n

Victor's salary will be $59000 + $1700n

Thus, to get the particular year, we equate both as

$48,000 + $2800n = $59000 + $1700n

$2800n -$1700n =$59,000 - $48,000

       $1100n =$11000

Canceling the dollar signs throughout, we get

n = 11000/1100 = 10 years.

If you worked his out, you will get that in the 10th year, both salaries will be $76,000.

Thus, the equation is

y = b + kn

with the variables as explained above.

Answer: 48,000 + 2,800x = 59,000 + 1,700x

Step-by-step explanation:

Answer:

[tex]2^{12}=4,096[/tex]

Step-by-step explanation:

You know that [tex]3x-y=12[/tex] and have to find

[tex]\dfrac{8^x}{2^y}[/tex]

Use the main properties of exponents:

1. [tex](a^m)^n=a^{m\cdot n}[/tex]

2. [tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]

Note that

[tex]8=2^3,[/tex]

then

[tex]7^x=(2^3)^x=2^{3\cdot x}=2^{3x}[/tex]

Now

[tex]\dfrac{8^x}{2^y}=\dfrac{2^{3x}}{2^y}=2^{3x-y}[/tex]

Since [tex]3x-y=12,[/tex] then [tex]2^{3x-y}=2^{12}=4,096[/tex]

Final answer:

The value of the expression [tex]\(\frac{8^x}{2^y}\)[/tex] given the equation 3x - y = 12 is 4096, since 8 can be expressed as 2^3 and the properties of exponents allow us to simplify the expression to 2^12.

Explanation:

The question involves determining the value of a mathematical expression given a specific equation.

Given the equation 3x - y = 12, we want to find the value of [tex]\(\frac{8^x}{2^y}\)[/tex].

This can be done by recognizing that 8 is a power of 2, specifically 8 = 2^3.

Thus, [tex]\(8^x = (2^3)^x = 2^{3x}\)[/tex]. Substituting back into the original expression, we get [tex]\(\frac{2^{3x}}{2^y}\)[/tex].

Using the properties of exponents, when dividing terms with the same base, we subtract the exponents: [tex]\(2^{3x - y}\)[/tex].

Since we know 3x - y = 12, we substitute 12 in place of 3x - y, giving us 2^12.

Therefore, the answer is 2^{12}, or 4096.

Answer:

1) x = 6, y = -2 + 1/3x

2)

Step-by-step explanation:

1) x-3y=6

-3y=6-x, 6-x/-3y

y = -2 + 1/3x

x - 3(-2+1/3x) = 6

x - 6 + x = 6

2x =12

x = 6

2) x=3y+4

-3y = -x+4

y = -x/-3 +4/-3

y = 1/3x + -4/3

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

I am unsure about x on number two...

Did you ever get the answer for this?

Answer:

The order is Congruent, not congruent, not congruent, not congruent,congruent, not congruent

Step-by-step explanation:

-

Answer: A. 0.20

Step-by-step explanation:

Let A be the event of employees needed corrective shoes and B be the event that they needed major dental work .

We are given that : [tex]P(A)=0.08\ ;\ P(B)=0.15\ ;\ P(A\cap B)=0.03[/tex]

We know that [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Then,   [tex]P(A\cup B)=0.08+0.15-0.03= 0.20[/tex]

Hence, the probability that an employee selected at random will need either corrective shoes or major dental work : [tex]P(A\cup B)= 0.20[/tex]

hence, the correct option is (A).

The probability that an employee selected at random will need either corrective shoes or major dental work is 0.20.

The subject of this problem is probability. To find the probability that an employee selected at random will need either corrective shoes or major dental work, you need to add the probabilities of each individual event and then subtract the probability of both events occurring, as this is counted twice.

So, the probability is calculated as:

P(Corrective Shoes or Major Dental Work) = P(Corrective Shoes) + P(Major Dental Work) - P(Both)

Substituting the values from the problem, we have:

P(Corrective Shoes or Major Dental Work) = [tex]0.08 + 0.15 - 0.03 = 0.20[/tex]

So, the probability that an employee selected at random will need either corrective shoes or major dental work is 0.20, matching answer choice A.

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Answer:

when x= -7

h(-7) = (-7)^2 -5

= (-1)^2*(7)^2-5

= 1*49-5

= 49-5

=44

Therefore , h(-7)=5

Answer:

h(- 7) = 44

Step-by-step explanation:

To evaluate h(- 7) substitute x = - 7 into h(x), that is

h(- 7) = (- 7)² - 5 = 49 - 5 = 44

Answers and explanations:

87. The domain of added functions includes the restrictions of both. So the range of the added function in this question is [-4, 3]

88. When finding the domain of a divided function we do the same as adding, but with an extra rule: g can't equal zero. So for this question the domain is (-4, 3)

89. To graph f + g you add the y-values for each x-value. I added a picture to help explain this one!

Answer:

87. [-4, 3]

88. (-4, 3)

89. See Attachment

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

*Notes:

Step 1: Define

Identify the domains of each function.

Domain of f(x): [-4, 3]

Domain of g(x): [-5, 5]

Step 2: Find 87.

Determine the x-values for each function that overlap/intersect.

f(x) and g(x) have intersect from -4 to 3.

Domain f + g: [-4, 3]

Step 3: Find 88.

Determine the x-values for which g(x) = 0.

The function g(x) equals 0 at x = -4 and x = 3. Therefore, these x-values are excluded in the domain.

Domain of f/g: (-4, 3)

Step 4: Find 89.

To draw a graph of the f + g, we must combine the y-values for each x-value domain in a t-chart and plot by hand.

x   |   f(x)          x   |  g(x)          x   |  f + g

-4     5             -4     0             -4      5

-3     4             -3      1             -3      5

-2     3             -2     2             -2      5

-1      3             -1      2             -1       5

0      2             0       1             0       3

1        1              1       1              1       2

2      -1             2       1              2      0

3      -3             3      0             3      -3

The correct option is (c) $1,354,500 The total sale price of Farmer Donald's property is calculated by converting square miles to acres (1 square mile = 640 acres), adding the additional 5 acres, and then multiplying by the sale price per acre to get the total of $1,354,500.

To calculate the total sale price of the property Farmer Donald is selling, we need to find the total number of acres for both parcels of land and then multiply that by the price per acre.

First, we convert the one square mile to acres, knowing that one square mile equals 640 acres:

Parcel 1: 1 square mile = 640 acres

Parcel 2: 5 acres

Adding the two parcels together gives us:

Total acres = 640 acres + 5 acres = 645 acres

Next, we multiply the total acres by the price per acre:

Total sale price = 645 acres \\u00D7 $2,100 per acre

Total sale price = $1,354,500

Therefore, the total sale price of the property is $1,354,500.

Answer:

  1152 in²

Step-by-step explanation:

Barack can change the units using a suitable multiplier. It will have a numerator equal to its denominator, and will have units that cancel the square feet and give square inches:

  8 ft² × ((12 in)/(1 ft))² = 8×12×12 in² = 1192 in²

_____

12 in = 1 ft . . . so numerator is equal to denominator

Answer:

She needs 300 mililiters of Solution B so that the resulting mixture is a 12% alcohol

Step-by-step explanation:

In this problem you have to take into account that when you are talking about solutions you can't just add the porcentaje because each percentaje represent how many mililiters of the total of the solution are, in this case of alcohol.

So for solving this problem we are first going to establish the variables, because it si solved using a system of equations. In that way we are going to say that:

VT: represents the total volume of the resulting mixture of solution A and solution B at 12% of alcohol

VA: represent the mililiters of solution A, in the problem they say that this value it equals to 400 ml

VB: Represent the mililiters of solution B, that is what we need to find.

From now on, we are just going to use this variables but always keep in mind what does they represent.

VaT: Represent the total volume of alcohol in the resulting mixture solution at 12%

VaA: Represent the volume of alcohol in solution A

VaB: Represent the volume of alcohol in solution B

What comes next? we need to describe the equations from the information we have so that we create a system that can be solve after.

What can we first say about the total volume (VT)? That it is the result of the adition of solution A and B so we can state the following equation:

VT = VA + VB

As we know that VA equals to 400ml we can replace to get:

1) VT = 400ml + VB

But what happens with the other information we have? We now need to take into account the concentration of each solution, so as we can´t add the percentages of alcohol but we can add the volumes of alcohol in each solution we can say that:

2) VaT = VaA + VaB

Now we are going to start to reduce the number of variables changing does that we don't know for those that we do to solve the problem, starting first with the volumes of alcohol.

A porcentaje represents a part of the total volume so to know how much alcohol does each of the solutions has we must do rules of three so that we can leave all the variables in terms of VT, VA and VB:

- VT  → 100%

VaT → 12%

VaT = [tex]\frac{12.VT}{100}[/tex] = 0,12.VT

- VA  → 100% In this case we know that VA = 400

VaA → 6%

VaA = [tex]\frac{6x400}{100}[/tex]

VaA = [tex]\frac{6x4}{1}[/tex]

VaA=24ml

VaB  → 100%

VaB → 20%

VaB = [tex]\frac{20.VB}{100}[/tex] = 0,20.VB

Now we are going to replace this information in the equation number two to get the following expresion:

3) 0,12.VT = 24ml + 0.20VB

At this point we have a system of two equations (remember equation 1) with two variables VT and VB so we are going to do some algebra to clear the variables.

- Replace VT of equation 1 in equation 3

Remeber that VT = 400ml + VB so now we are going to put this information in equation 3) 0,12.VT = 24ml + 0.20VB to get:

4) 0,12 (400ml + VB) = 24ml + 0.20VB

- Use the distributive operation to solve the parentesis

0,12x400ml + 0.12.VB = 24ml + 0.20VB

5) 48ml + 0.12VB = 24ml + 0.20VB

- Organize the information in one side the ones with variables and in the other side just numbers:

0.12VB - 0.20VB = 24ml - 48ml

-0.08 VB = -24ml (do the operations)

As it is a minus in both sides we can divide it and cancel the sign to have:

0,08VB = 24 ml (to clear VB, we must divide in both sides by 0,08)

[tex]\frac{0,08.VB}{0,08} = \frac{24ml}{0.08}[/tex] after doing the division we get:

with this you already get the answer of how many mililiters of solution B does she use to get a resulting mixture of 12%.

To verficate we must do the following process:

VT = 300ml + 400ml = 700ml

The total volume of the solution is 700 ml of which 12% equals to:

VaT = 0,12. VT = 0,12(700ml) = 84 ml

VaA = 24ml (Volume of alcohol in solution A, we already calculated)

VaB = 0,20 VB = 0,20(300ml) = 60ml (Volume of alcohol in solution B)

VaT = VaA + VaB  (Prove the equation with the values we obtain)

84ml = 24ml + 60ml

84 ml = 84ml

As the equation is the same we have verificated our result.

Robyn needs to use 300 mL of Solution B to achieve a 12% alcohol solution when mixed with 400 mL of Solution A. This was calculated by setting up an equation based on the concentrations and solving for the quantity of Solution B.

To solve this problem, we need to find out how much Solution B (20% alcohol) Robyn needs to add to 400 mL of Solution A (6% alcohol) to get a 12% alcohol solution.

Step-by-Step Solution

First, let's set up the equation assuming she uses x milliliters of Solution B:

Since Solution A is 6% alcohol, in 400 mL of Solution A, there is:

Next, for Solution B, which is 20% alcohol, the amount of alcohol in x mL of Solution B is:

We need the resulting mixture to have a 12% concentration. The total volume of the mixture will be:

The total amount of alcohol in this mixture will be 12% of the total volume:

Simplify and solve for x:

So, Robyn needs to use 300 mL of Solution B.

Answer:

The required probability is : [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Three married couples have purchased theater tickets and are seated in a row consisting of just six seats.

First we will check the total arrangements that is 6! ways.

6! = [tex]6\times5\times4\times3\times2\times1=720[/tex]

Jim and Paula can sit at far left in 2 ways and the remaining 4 in 4! ways,.

So, probability will be = [tex]2\times\frac{4!}{6!}[/tex]

= [tex]2\times\frac{24}{720}[/tex]

= [tex]\frac{48}{720}[/tex]

= [tex]\frac{1}{15}[/tex]

Answer:

  3/4 bag

Step-by-step explanation:

4.5 divided 6 ways makes each part ...

  4.5/6 = 0.75 = 3/4

Each person gets 3/4 bag.

Answer:  The correct option is

(A) Both the statement and its contrapositive are true.

Step-by-step explanation:  We are given to check whether the following conditional statement and its contrapositive is true or false :

"If an angle is a right angle, then the angle measures 90°".

Let us consider that

p : an angle is a right angle

and

q : the angle measures 90°.

So, the conditional statement is p ⇒ q. This is true, because the measure of a right angle is 90°.

The contrapositive of "p ⇒ q" is "not q ⇒ not p".

That is, if the measure of an angle is not 90°, then the angle is not right angle.

This is also true, because only angles with measure 90° are right angles.

Thus, the given statement and its contrapositive are TRUE.

Option (A) is correct.

Answer:

The answer to your question is: cost = $4000

Step-by-step explanation:

Data

Volume = 8000 ft³

cost = $10 / square foot

Process

It's a  cube then we find the length of one side

Volume = l³ = 8000

                l = ∛8000

                I = 20 ft

Now, calculate the area of the floor,

Area = l x l

        = 20 x 20

        = 400

Finally, find the cost of the floor

cost = area x price

cost = 400 x 10

       = $4000

Final answer:

To calculate the cost of the hardwood floor for a cubic room with a volume of 8,000ft³, we first find the length of one side of the cube (20ft), then calculate the floor area by squaring that length (400ft²), and multiply it by the contractor's charge ($10/ft²) to get the total cost ($4000).

Explanation:

The question involves calculating the cost of adding hardwood floors to a cubic room, with knowledge of its volume. First, we need to find the length of one side of the cube to determine the floor area. Since the volume of a cube is found by cubing the length of one side, we find the cube root of the room's volume:

∛(8,000ft³) = 20ft (this is the length of one side of the cube).

Then the area of the floor, which is a square, is calculated by squaring the length of the side:

Area = side² = (20ft)² = 400ft².

Finally, to find the cost, we multiply the area by the contractor's charge per square foot:

Cost = area × charge per square foot = 400ft² × $10/ft² = $4000.

Therefore, the hardwood floor will cost $4000.

Answer:

a. The dependent variable for this study is the "number of colds each individual experiences during the 3-month winter season" because it depends on the doses of vitamins and placebo.

b. The dependent variable is discrete because the number of colds is like 1,2,3,... so on.

c. The scale of measurement of the dependent variable is Ratio because the number of cold experiences can be 0.

Answer:

B.No. It describes the​ midrange, not the median.

Step-by-step explanation:

Further,

The range is the difference between the least and largest value of data. It measures skewness using all data points.

Mean is calculated as the ratio of the sum of all the observations to the total number of observations.

Median is the middle value of the data after arranging them in ascending order.

Answer:

  -11a +5

Step-by-step explanation:

(5a-6a-4) -(7a+3a-9) = a(5-6-7-3) -4+9 = -11a +5

Answer:

  r = 29

Step-by-step explanation:

We assume your diagram is showing ...

To find r, use the relationship between the side lengths of the triangle.

__

In a 30°-60°-90° triangle, the ratio of shortest to longest sides is 1 : 2. Therefore, we have ...

 CD/CA = r/(r+29) = 1/2

  2r = r +29 . . . . . . multiply by 2(r+29)

  r = 29 . . . . . . . . . .subtract r

_____

The knowledge of 30°-60°-90° triangle relationships can come from any of several sources. One such source is consideration of what happens when you cut an equilateral triangle along its altitude. (The short side is half the long side of the resulting 30-60-90 triangle.)

Another source is the sine ratio of the 30° angle (trigonometry). Sin(30°) = CD/CA = 1/2.

Answer: Infinite solutions. It is the same line

Step-by-step explanation:

The survey design described is a statistical study on college student eating habits, specifically focusing on sweet potato consumption, to obtain quantitative data about behaviour patterns.

The student in question is surveying to gather data on a particular behavioural pattern, in this case, the frequency of sweet potato consumption among college students. To achieve results that reflect the larger student body of the college, a random sample of 200 students is selected to answer the survey question. Completing the survey comprises the collection of quantitative data, which can later be analyzed statistically. Surveys are a common method in statistics to investigate various questions and hypotheses. For example, a survey similar to this might be performed to evaluate the number of movies students watch in a week or determine the daily average study time for freshmen students. The effectiveness of the survey method relies on a representative sample accurately reflecting the population of interest.

Answer:

Step-by-step explanation:

2 if you mean 1 of each so it would be 50 cards

The cards left are in the deck now is  38.

A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.

According to the question

Total number of cards in deck = 52

Total number of spades of card in deck = 13

Bill removed the spades from deck of card = 10

Bill removed the king of hearts from a deck of cards = 4

Total cards removed from deck and thrown in trash  = 10 + 4

                                                                                        = 14

Cards left in the deck of card = 52 - 14

                                                 = 38

Hence, the cards left are in the deck now is  38.

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Answer:

The answer to your question is:

Step-by-step explanation:

1.-  1.09                                              In the table the order will be

2.- 0.99                                            1.- 6

3.- 0.919                                           2.- 10

4.- 0.66                                            3.- 7

5.- 0.647                                          4.- 11

6.- 0.394                                          5.- 5

7.-  0.298                                         6.- 4

8.- 0.256                                         7.- 9

9.- 0.23                                           8.- 8

10.- 0.136                                        9.- 1

11.- 0.112                                          10.- 2          11.- 3

Answer:

d. $119,743.59

Step-by-step explanation:

actual value (AV)=$180,000

purchase price (PP) =$142,000

intial value (IV) =$18,000

useful live (UL)= 39 years

First, we subtract the value of the property from the purchase value or IV to know the value to be depreciated:

PP-IV= $142,000-$18,000 = $124,000

Then we find out the yearly depreciation by dividing $124,000 into useful live (UL) years:

$124,000/39 = $3,179.49 This is the amount that the property depreciates every year.

But after 7 years the depreciation is: $3,179.49*7= $22,256.41  

We subtract the depreciation in the 7 years from the purchase price (PP) and that's the present book value of the property:  

$142,000-$22,256.41=$119,743.6

To find the present book value of the property, subtract the land value from the purchase price to get the initial building value. Then, calculate the total depreciation over the seven years and subtract this from the initial building value. Finally, add back the land value.

To find the present book value of the property, we need to first determine the value of the structure. We can do this by subtracting the value of the land ($18,000) from the purchase price of the property ($142,000), according to the details given. So, the initial value of the building is $124,000.

Since we use the straight-line method of depreciation, the structure depreciates at a constant amount each year over its useful life. So, the yearly depreciation expense is 124,000 / 39 = $3,179.49.

Then, we'll calculate the total depreciation over the seven years, which is 3,179.49 * 7 = $22,256.43.

Lastly, we'll subtract this total depreciation from the original building value ($124,000 - $22,256.43). This yields a present book value of $101,743.59 for the structure. When we add back the value of the land ($18,000) which does not depreciate, we obtain a total present book value of $119,743.59 for the property.

Therefore, the current book value of the property is d. $119,743.59.

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Answer:

(2,3)

Step-by-step explanation:

We are given that triangle PQR lies in the xy-plane, and coordinates of Q are (2,-3).

Triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R',

We have to find the coordinates of Q'.

The coordinates of Q(2,-3).

180 degree clockwise  rotation about the origin  then transformation rule

[tex](x,y)\rightarrow (-x,-y)[/tex]

The coordinates (2,-3) change into (-2,3) after 180 degree clockwise rotation about origin.

Reflect across y- axis the transformation rule

[tex](x,y)\rightarrow (-x,y)[/tex]

Therefore, when reflect across y- axis then the coordinates (-2,3) change into (2,3).

Hence, the coordinates of Q(2,3).

After applying the sequence of transformations, the coordinates of Q′ are Q' (2, 3).

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Additionally, the mapping rule for the rotation of any geometric figure 180° clockwise or counterclockwise about the origin is represented by the following mathematical expression:

(x, y)             →            (-x, -y)

Q (2, -3)       →    Q" (-2, 3)

By applying a reflection over the y-axis to the coordinates of the point (4, -9), we have the following new coordinates for the image;

(x, y)                →      (-x, y)

Q" (-2, 3)         →      Q' (2, 3).

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Answer:

  35 years

Step-by-step explanation:

The proportion p that remains after y years is ...

  p = (1/2)^(y/5.27)

In order for 1/100 to remain (the level decays from 100 times to 1 times), we have ...

  .01 = .5^(y/5.27)

  log(0.01) = y/5.27·log(0.5) . . . take logs

  y = 5.27·log(0.01)/log(0.5) ≈ 35.01 ≈ 35 . . . . years

Given that the radioactive isotope cobalt-60 has a half-life of 5.27 years, it will take around 36.89 years for it to decay to a level that is safe for human habitation, assuming the initial level is 100 times the safe limit.

The subject of this question is the half-life of radioactive substances, specifically cobalt-60. The half-life is the time it takes for half of the radioactive atoms to decay. Cobalt-60 has a half-life of 5.27 years. This implies that 50% of the cobalt-60 will remain after 5.27 years, 25% will remain after 10.54 years (two half-lives), 12.5% will remain after 15.81 years (three half-lives), and so forth.

Understanding this concept, we can calculate when the region will be habitable. Currently, the radiation level is 100 times the acceptable limit. We need to determine how many half-lives it will take for the radiation level to reduce to 1% i.e., 1/100 of its original level. Since each half-life reduces the radiation by half, this is equivalent to finding when the cobalt-60 will be reduced to a fraction of 1/(2^n), where 'n' is the number of half-lives. Using n = 7 gives us 1/128, which is less than 1/100 (it will need to be less to be within safe levels).

So, it will take approximately 7 half-lives for the area to become safe for human habitation again. Since the half-life of cobalt-60 is 5.27 years, it will therefore take about 7 * 5.27 = 36.89 years for the region to become habitable once more.

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Answer:

$10.00

Step-by-step explanation:

Let Stephanie's weekly allowance = x

She spent half of her weekly allowance playing arcade games = [tex]\frac{x}{2}[/tex]

Her parents let her clean the oven for = [tex]\frac{x}{2}+7[/tex].

She ended with $12

So the equation will be  [tex]\frac{x}{2}+7=12[/tex]

[tex]\frac{x}{2}[/tex] = 12 - 7

[tex]\frac{x}{2}[/tex] = 5

x = 5 × 2

x = 10 dollars

Her weekly allowance would be $10.00

Final answer:

To find Stephanie's weekly allowance, we set up an equation where half of her allowance plus $7 equals $12, which results in a calculation showing that her weekly allowance is $10.

Explanation:

Stephanie spent half of her weekly allowance on arcade games and earned an additional $7 by cleaning the oven. We're told that after this, she ends up with $12. To find Stephanie's weekly allowance, let's denote her allowance as A. Since she spent half of it on games, she was left with A/2. By cleaning the oven, she received $7, so her total money became A/2 + $7 = $12. To find the allowance, we solve the equation:

Therefore, Stephanie's weekly allowance is $10.

Answer:

  67 points

Step-by-step explanation:

To find the difference between the winning and losing scores, subtract the losing score from the winning score:

  50 -(-17) = 50 +17 = 67

The difference is 67 points.