Mrs.Thomas sells online math and reading games. His revenue for each game (in dollars) is modeled by the given equations, where x is the number of days since the games went on sale.
Math Game: M(d)=2x^2+8x+2
Reading Game: R(d)=3x+5
Solve the system algebraically. After how many days is the revenue for each game the same? Show your work and explain your answer.
Graph this system to show the solutions. Label each axis appropriately.
Mr. Thomas would take 0.5 (half) day for the revenue for each game to be the same.
Revenue is the total amount of money made from selling a particular number of items.
The revenue for math game is:
M(d)=2x² + 8x + 2
While the revenue for Reading Game is:
R(d)=3x+5
For the revenue of each game to be the same, hence:
M(d) = R(d)
2x² + 8x + 2 = 3x + 5
2x² + 5x - 3 = 0
x = -3 or x = 0.5
Since the number of days cannot be negative, hence it would take 0.5 (half) day for the revenue for each game to be the same.
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A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inches in the drawing to inches in the actual room?
Enter the correct answer in the box.
Answer:
The scale is 1:18 for the entire room, 1 inch in the diagram for 18 inches IRL
Step-by-step explanation:
12 inches = 1 foot
Convert the feet to inches, then divide both sides of the ratio by the # of inches in the diagram
So for length:
10:(15*12)
10:180
1:18
And for width:
8:12(12)
8:144
1:18
Answer:
18 inches
Step-by-step explanation:
The question asks for scale of inches in the drawing and the actual room, so first convert 15 ft and 12 ft into inches.
1 foot= 12in x 1ft= 12 inches
15 feet= 12in x 15ft = 180 inches
12 feet= 12in x 12ft = 144 inches
The room is 180 inches long and 144 inches wide.
To find the scale, set up a proportion to the drawing to the room.
[tex]\frac{10}{8} =\frac{180}{144}[/tex]
You can see that the scale is 18 inches because to get from 180 to 10, you multiply by 18, and the same thing as 8, you would multiply 8 by 18 to get to 144.
What is -105/-77 simplified?
Answer:
[tex]\frac{-15}{-11}[/tex]
Step-by-step explanation:
To simplify more known as reduced we have to find the fraction as and equivalent fraction
DefinitionEquivalent Fraction - are the fractions that have different numerators and denominators but are equal to the same value.
Look for the GCFTo find the we must list out the of and
[tex]77:1, 7, 11 ,77\\\\1, 3, 5, 7, 15, 21, 35 , 105[/tex]
Our [tex]GCF[/tex] is [tex]7[/tex]
Our fraction[tex]\frac{-105}{-77}[/tex]ReduceDefinition of reduce - reduction refers to the rewriting of an expression into a simpler form
Divide the numerator and denominator by [tex]7[/tex]
Our fraction is [tex]\frac{-15}{-11}[/tex]help plsssssssssssss
Answer:
with what
Step-by-step explanation:
Answer:
help with? there's nothing there
Help help help math help please
Answer:
x + 15
Step-by-step explanation:
9x + 25 + x + 5 = 180
9x + x + 25 + 5 = 180
10x + 30 = 180
10x = 180 - 30
10x = 150
x = 150÷10
x = 15.
In a game, you toss a fair coin and a fair six-sided die. If you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. Otherwise, you lose $6. What is the expected profit of one round of this game?
Using probabilities, it is found that the expected profit of one round of this game is of $0.
A probability is the number of desired outcomes divided by the number of total outcomes.
One of the two sides of the coin are heads.2 of the 6 sides of the dice are 3 or 6.Hence, since the coin and the dice are independent, the probability of winning is:
[tex]p = \frac{1}{2} \times \frac{2}{6} = \frac{1}{6}[/tex]
The expected value is the sum of each outcome multiplied by its respective probability.
In this problem:
[tex]\frac{1}{6}[/tex] probability of earning $30.[tex]\frac{5}{6}[/tex] probability of losing $6.Then:
[tex]E(X) = 30\frac{1}{6} - 6\frac{5}{6} = 5 - 5 = 0[/tex]
The expected profit of one round of this game is of $0.
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The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.07 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answer:
93.684
Step-by-step explanation:
They just give a 5% bonus to the price of the lunch
1.8.3 practice - functions
3. Water freezes at 0 Celsius and 32 Fahrenheit. Water boils at 100 Celsius and 212 Fahrenheit.
Answer:
A. C(F) = 5/9F -(17 7/9)
B. slope: 5/9
C. y-intercept: -17 7/9
Step-by-step explanation:
A.The question tells us that the independent variable is the temperature in degrees Fahrenheit. Then the given ordered pairs are ...
(F, C) = (32, 0) and (212, 100)
The slope can be found from the slope formula:
m = (y2 -y1) / (x2 -x1)
m = (100 -0)/(212 -32) = 100/180 = 5/9
The y-intercept can be found from the slope-intercept equation for a line:
y = mx +b
b = y -mx
Using the first point, we have ...
b = 0 -(5/9)(32) = -160/9 = -17 7/9
Using the found values for m and b, the slope-intercept equation can be written ...
C(F) = 5/9F -(17 7/9)
__
B.The slope was found in part A to be 5/9. This means each degree Fahrenheit corresponds to 5/9 of a degree Celsius.
__
C.The y-intercept was found in part A to be -17 7/9. This means 0 °F corresponds to -17 7/9 °C.
Ivy bought a bike for $67.82. The sales tax was $4.79. How much money did Ivy spend on the bike before taxes?
Answer:
Step-by-step explanation:
$63.03 money
Which linear equation would produce a y-intercept of (0,-7) and a slope of 5?
I need it no link no bot right, please
Answer: fifths
Step-by-step explanation:
fifths because you would divide the 3 loves with the amount of people there is.
42 out of 56 students have cell phone. What percent of students said they owned a cell phone
Answer:
75%
Step-by-step explanation:
now we can see that our fraction is 75/100 which means that 42/56 as a percentage is 75%
thanks i'll mark brainliest
Answer:
m <5=91 is the correct response to this question
Find the volume of a coffee can with r=7.5 cm, h= 16.8 cm, to the nearest cubic centimeter.
Answer:
V = 2968.8 cm³ or 2969 cm³
Step-by-step explanation:
Given the radius, r = 7.5 cm, of a cylindrical coffee can whose height, h = 16.8 cm:
We can find the volume of a cylinder by using the following formula:
V = πr²h
Substitute the given values into the formula:
r = 7.5 cm
h = 16.8 cm
V = πr²h
V = π(7.5)²(16.8)
V = π × 56.25 × 16.8
V = 2968.8 cm³ or 2969 cm³
Therefore, the volume of a coffee can is 2969 cm³.
If g(x)=x^2-5x+8, find g(8)
Answer:
Option A) 32
Step-by-step explanation:
Given the quadratic function, g(x) = x²- 5x + 8:
In order to evaluate and determine the output value given g(8), substitute the input value into the function:
g(x) = x²- 5x + 8
g(8) = (8)²- 5(8) + 8
g(8) = 64 - 40 + 8
g(8) = 32
Therefore, the correct answer is Option A) 32.
A bicycle has a listed price of $660.95 before tax. If the sales tax rate is 7.25%, find the total cost of the bicycle with sales tax included.
Round your answer to the nearest cent, as necessary
9514 1404 393
Answer:
$708.87
Step-by-step explanation:
The price with tax included is ...
660.95 + 0.0725×660.95 = 660.95(1 +0.0725) = 708.87
The total cost of the bicycle with tax is $708.87.
Answer:
$ 708.87
Step-by-step explanation:
Think that, a bicycle has listed price of $ 100,
Listed price Tax rate Total cost of the bicycle with sales tax
$ 100 7.25 107.25
$ 660.95 x
Let the Total price of the bicycle be x
Now you can create a equation like this,
[tex]\frac{100}{660.95}=\frac{107.25}{x}[/tex]
Use cross multiplication, and find out the total cost of the bicycle with sales tax.
[tex]100x=660.95*107.25[/tex]
[tex]100x=70886.8875[/tex]
[tex]\frac{100x}{100} =\frac{70886.8875}{100} \\[/tex]
[tex]x=708.8688[/tex]
Therefore, the total cost of the bicycle with sales tax is,
≈ $ 708.87
Hope this helps you.
Let me know if you have any other questions :-)
please need help on this question thanks. see the screenshot
Check the picture below.
F = sales for Friday
we know that the total of weekend sales for Germany was F + 317 + 405.
we also know that 405 is really 37.19% of that amount, say "x", which is the 100%, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 405&37.19\\ x&100 \end{array}\implies \cfrac{405}{x}=\cfrac{37.19}{100}\implies 40500=37.19x \\\\\\ \cfrac{40500}{37.19}=x\implies 1089~\approx ~ x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{friday}{F} + \stackrel{sat/sun}{317} + \stackrel{monday}{405} \approx 1089\implies F +722 \approx 1089\implies \boxed{F\approx 367}[/tex]
What is x
5x + 5 = 40
100 POINTS ANSWER PLZ
On saturday endsay walked 3 1/2 miles in 1 2/5 hours what was her walking pace in miles per hour? write in somplest form
Answer:
2 1/2 mph
Step-by-step explanation:
Answer:
4 9/10
Step-by-step explanation:
trust me i tried posting a pic of my work but it wont load but it is 4 9/10
what is the slope intercept form of 12x+4y=-12
Answer:
y=-3-3x
Step-by-step explanation:
Transpose the equation for y
y=-12/4-12x/4
y=-3-3x
geomtry plzzzzz help. me
Answer:
N=3.5
Step-by-step explanation:
it is 3.5 because it said line p is the perendicular bisector so the triangle has to be equal. so the line ZY=XY
14/4=3.5
What is the common difference in the arithmetic sequence 13, 26, 39, 52, 65?
They all have a difference of 13.
So each time 13 is added to get the next number.
Can someone please help me with #14 and #15?
14.Given y=2(x - 10)+3, write an equation in point slope and slope intercept form that is:
a) Parallel and goes through (-4,1).
b) Perpendicular and goes through (-4,1).
15.Given 5x+2y=7
a.Find an equation parallel to the equation and through (0,10).
b.Find an equation perpendicular to the equation and through (0,10).
This picture is an example of what the answers should look like.
Problem 14, Part (a)
The given equation y = 2(x-10)+3 has a slope of m = 2. Anything parallel to this will also have the same slope, but a different y intercept.
Let's find the point slope form of the parallel line through (-4,1)
[tex]y-y_1 = m(x - x_1)\\\\y-1 = 2(x - (-4))\\\\y-1 = 2(x + 4)\\\\[/tex]
The point slope form is: y-1 = 2(x+4)Now solve for y to get the slope intercept form.
[tex]y-1 = 2(x + 4)\\\\y = 2(x + 4)+1\\\\y = 2x + 8+1\\\\y = 2x + 9\\\\[/tex]
The slope intercept form is: y = 2x+9============================================================
Problem 14, Part (b)
The original slope is m = 2. Apply the negative reciprocal to go from 2/1 to -1/2. The perpendicular slope is -1/2.
Using the same point (-4,1), we find that the point slope form is...
[tex]y-y_1 = m(x - x_1)\\\\y-1 = -\frac{1}{2}(x - (-4))\\\\y-1 = -\frac{1}{2}(x+4)\\\\[/tex]
The point slope form is: y-1 = (-1/2)*(x+4)Now solve for y
[tex]y-1 = -\frac{1}{2}(x+4)\\\\y = -\frac{1}{2}(x+4)+1\\\\y = -\frac{1}{2}x-2+1\\\\y = -\frac{1}{2}x-1\\\\[/tex]
The slope intercept form is: y = (-1/2)x - 1============================================================
Problem 15, Part (a)
Anything parallel to Ax+By = C will be in the form Ax+By = D. The only thing changes is the C becomes D, where [tex]C \ne D[/tex]. If C = D, then we'd be talking about the exact same line rather than two parallel lines.
We're given 5x+2y = 7. The answer is in the form 5x+2y = D. Plug in (x,y) = (0,10) to find the value of D
5x+2y = D
D = 5x+2y
D = 5(0)+2(10)
D = 20
The equation 5x+2y = D updates to 5x+2y = 20
Answer: 5x+2y = 20============================================================
Problem 15, Part (b)
If you are given Ax+By = C, then anything perpendicular to this is Bx-Ay = D. Here it's possible that C = D; however, it's likely that they'll be different.
The given equation 5x+2y = 7 is perpendicular to anything of the form 2x-5y = D. We'll plug in the given point to find D.
2x-5y = D
D = 2x-5y
D = 2(0)-5(10)
D = -50
Answer: 2x-5y = -50Multiply 3 by 25% of 40.
[tex]3 \times 25\% \times 40 = 3 \times \dfrac{25}{100} \times 40 = 3 \times 10 =30[/tex]
The value of the numerical expression 3 × 25% × 40 will be 30.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 3 × 25% × 40
Simplify the expression, then the value of the expression will be given as,
⇒ 3 × 25% × 40
⇒ 3 × 0.25 × 40
⇒ 30
The value of the numerical expression 3 × 25% × 40 will be 30.
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Theresa ran 7.56 miles this week. Write her distance as a mixed number and as an improper fraction.
Answer:
Mixed=7 14/25 improper=189/25
Step-by-step explanation:
can someone help me ?
Which of the following are true?
3^6 x 3^-3 = 27
3^3 x 3^-6 = 1/27
3^2 x 3^1 = 27
3^4 x 3^-1 = 1/27
Answer:
i think that all of them EXCEPT the last one are correct. Explained below
Need this ASAP please
a) x²+6x
b)5x²-x
c)12x²+15x
d)8x²-12xy
A Gardner has 1 1/4 cubic feet of soil available for filling pots. Each pot will need 2/5 cubic foot to be filled. What is the greatest number of pots that the gardener fill
The greatest number of pots that can be filled is 3.
In order to determine the greatest number of pots that can be filled, the quantity of soil available would be divided by the capacity of each pot.
Number of pots that can be filled = 1 1/4 ÷ 2/5
= 5/4 ÷ 2/5
= 5/4 x 5/2 = 25/8 = 3 1/8
Thus, the greatest number of pots that can be filled is 3.
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this cubiod is made from 6 small cubes write how many small cubes there are in this cubiod
Pleas help
Answer:
16 I guess.
Step-by-step explanation:
lolololololol?
La probabilidad de que julio salga con carla es 0.75 , y la probabilidad de que salga con marisol es de 0.50. Si la probabilidad de que salga con carla o marisol es 0.85; calcular la probabilidad de que salga con ambas a la vez
La probabilidad de que Julio salga con Marisol y Carla al mismo tiempo es 0.40
What is the addition rule of probability for two events?For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Given that;
The probability that Julio goes out with Carla is 0.75, and
the probability that he goes out with Marisol is 0.50.
The probability that he goes out with Carla or Marisol is 0.85
To find:
The probability that he will date both at the same time.
Let we take:
A = event that Julio goes with Carla
B = event that Julio goes with Marisol, then, the given expression is symbolically represented as:
[tex]P(A) = 0.75\\[/tex][tex]P(B) = 0.50[/tex][tex]P(A \cup B) = 0.85[/tex]To find: [tex]P(A \cap B)\\[/tex]
Using the addition rule, we get:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)\\0.85 = 0.75 + 0.50 - P(A \cap B)\\P(A \cap B) = 1.25 - 0.85 = 0.40[/tex]
Thus, the probability that Julio will date Marisol and Carla at the same time is 0.40
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The probability that Julio will date Marisol and Carla at the same time is 0.40.
Here, we have, For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given that;
The probability that Julio goes out with Carla is 0.75, and
the probability that he goes out with Marisol is 0.50.
The probability that he goes out with Carla or Marisol is 0.85
To find:
The probability that he will date both at the same time.
Let we take:
A = event that Julio goes with Carla
B = event that Julio goes with Marisol, then, the given expression is symbolically represented as:
P(A) = 0.75
P(B) = 0.50
P(A∪B)= 0.85
To find: P(A ∩ B)
Using the addition rule, we get:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.85 = 0.75 + 0.50 - P(A ∩ B)
P(A ∩ B) = 0.40
Thus, the probability that Julio will date Marisol and Carla at the same time is 0.40.
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complete question:
The probability that Julio dates Carla is 0.75, and the probability that he dates Marisol is 0.50. If the probability that he goes out with carla or marisol is 0.85; Calculate the probability that he will date both at the same time.