write the quadratic equation y=x2-6x+7 in vertex form. y=
Which equation, when solved, results in a different value of x than the other three?
Equation of option (d) is having different value of x than other 3 equations.
So, option (d) is correct option.
How to solve equation?Write down the problem.Remember the order of operations: DMAS, which stands for Multiplication/Division, and Addition/SubtractionDo the multiplication.Do the addition and subtraction.Keep the variable at L.H.S and alone.To do this, just divide both sides of the equation by coefficient of x to find x.Solving equations
(a) (-7/8)x-(3/4)=20
adding 3/4 on both sides, we get
(-7/8)x = 20+(3/4)
multiplying (-8/7) on both sides, we get
x = -23.71
(b) (7/8)x+(3/4)=-20
subtracting 3/4 on both sides, we get
(7/8)x = -20-(3/4)
multiplying (8/7) on both sides, we get
x = -23.71
(c) 7(-1/8)x-(3/4)=20
adding 3/4 on both sides, we get
(-7/8)x = +20+(3/4)
multiplying (-8/7) on both sides, we get
x = -23.71
(d) (-7/8)×(-8/7)x-(3/4)=20×(-8/7)
⇒ x-(3/4) = -22.85
adding 3/4 on both sides, we get
x = -22.85+(3/4)
x = -22.10
So equation in option (d) has different value of x than all other equation.
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Sunil drove 63.9823 km to visit his grandmother. When he reached his grandmother's house he noticed that the car had used up 3.31 litre of petrol. How many km can the car go in 1 litre?
The km per liter based on the information that Sunil can drive is 19.33 km.
How to illustrate the expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Sunil drove 63.9823 km to visit his grandmother. When he reached his grandmother's house he noticed that the car had used up 3.31 litre of petrol.
Therefore, the km per liter will be:
= 63.9823 / 3.31
= 19.33 km per liters
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May someone help me with this.
Step-by-step explanation:
since I don't see the options, I can only tell you what it is supposed to be and you need to pick the best fitting option :
the score of the test is simply
the number of correctly answered questions times 3 (as every correctly answered question is with 3 points).
the equation is therefore
y = R(x) = 3x
the independent variable x represents the number of correctly answered questions,
and the dependent variable is y, the test score, because the test score depends on the number of correctly answered questions.
so,
R(25) = 3×25 = 75, meaning 25 correctly answered questions × 3 results in the score of 75.
NO LINKS!!
Let Q represent a mass (in grams) of carbon (^14C), whose half-life is 5,715 years. The quantity of carbon-14 present after t years is given by the following
Q = 11(1/2)^(t/5715)
a. Determine the initial quantity (when t=0) g
b. Determine the quantity present after 2000 years. (Round your answer to 2 decimal places).
c. What is the graph of the function over the interval t = 0 to t = 10,000
Answer:
(a) 11 g
(b) 8.63 g
(c) Attached
Step-by-step explanation:
Given function:
[tex]Q = 11 \left(\dfrac{1}{2}\right)^{\dfrac{t}{5715}}[/tex]
where:
Q = quantity of carbon-14 presentt = time (in years)Part (a)Substitute t = 0 into the given function to determine the initial quantity:
[tex]\begin{aligned} t=0 \implies Q &= 11 \left(\dfrac{1}{2}\right)^{\dfrac{0}{5715}}\\\\&=11\left(\dfrac{1}{2}\right)^0\\\\&=11\left(1\right)\\\\&=11\; \rm g\end{aligned}[/tex]
Part (b)Substitute t = 2000 into the given function to determine the quantity present after 2000 years:
[tex]\begin{aligned} t=2000 \implies Q &= 11 \left(\dfrac{1}{2}\right)^{\dfrac{2000}{5715}}\\\\&=11\left(0.784697887...\right)\\\\&=8.63\; \rm g\;\; \sf (2 \; d.p.)\end{aligned}[/tex]
Part (c)[tex]\begin{aligned} t=10000 \implies Q &= 11 \left(\dfrac{1}{2}\right)^{\dfrac{10000}{5715}}\\\\&=11\left(0.297346855...\right)\\\\&=3.27\; \rm g\;\; \sf (2 \; d.p.)\end{aligned}[/tex]
The graph of the function over the interval t = 0 to t = 10000 is attached.
A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75. If the manager spent a total of $38.50, how many pens did the store manager purchase?
The store manager purchases 7 pens which can be determined by the concept of equations.
What are equations?According to question store manager purchased a total of 15 pens and markers. So, let us assume the total number of pens =x and the total number of markers = y
The above statement gives us the equation as follows:
x + y=15
The statement each pen cost $3.50, and each marker cost $1.75 and the manager spent a total of $38.50 gives us the equation as follows:
3.50x +1.75 y=38.50
By solving both the equation on multiplying first eq by 3.50 gives
3.50x+3.50y=52.5
Subtracting the above two equations gives
1.75y=14
y=8
Putting value of y in first equation gives x=7
As we had assumed that the total number of pens = x
Hence, the total number of pens =7
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Find the unit rate.
1. A sloth moves 10 feet in 2 hours. It moves
2. The car travels 165 miles in 3 hours. It travels
feet per hour.
3. There are 48 bottles of water in 4 cases. There are
4. Juice cost $3.60 for 12 ounces. It costs
miles per hour.
per ounce.
bottles per case.
Step-by-step explanation:
1.
10 ft in 2 hours = 10/2 / 1 hour = 5 ft/h
2.
165 miles in 3 hours = 165/3 / 1 hour = 55 m/h or mph
3.
48 bottles in 4 cases = 48/4 / 1 case = 12 bottles per case
4.
$3.60 for 12 oz = 3.6/12 / 1 oz = $0.30 per ounce
A. (f•g)(x)
B. (f•g)(-3)
f(x) = x^2+3x-2
g(x)= x-2
Answer: A. x^3 +x^2-8x+4 B. 10
Step-by-step explanation: (f•g)(x) is the same as f(x) • g(x)
A. (x^2+3x-2) • (x-2) = (x^3+3x^2-2x) -(2x^2+6x-4) -> x^3 +x^2-8x+4
B. plug in -3 for x -> (-3)^3 + (-3)^2 -8(-3) + 4 -> 10
Keyshawn is asked to compare and contrast the domain and range of two functions F(x)=5x g(x)=5^x which statements could he include in his explanation
Domain is the input and range is the output of a function. By considering the options The domain of both function is all real number and The range of g(x) >0 are the correct answers.
What is Domain?Domain is the input of a function.
What is range?Range is the output of a function.
The domain of both functions is the set of all real numbers, since both functions are defined for all values of x.
The range of the function g(x)=5^x is the set of all positive real numbers, since any positive real number can be obtained by raising 5 to the power of a real number
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A service club agrees to donate at least 500 hours of community service. A full member is to give 4 hours, and a pledge gives 6 hours.
(a) Write the inequality that expresses this information.
(b) Graph the inequality.
(a) 4x + 6y ≥ 500 , (b) The graph of this inequality is a line with a slope of 4/6 and a y-intercept of 500/6.
(a) The inequality expresses the total hours of community service that must be given, which is at least 500 hours. The 4x term represents the hours given by the full members, and the 6y term represents the hours given by the pledges. The ≥ symbol means that the sum of these two terms must be greater than or equal to 500.
(b) To graph the inequality, you first need to find the y-intercept, which is 500/6. Then you need to find the slope, which is 4/6. This means that the line has a positive slope and passes through the point (0, 500/6). The graph of the inequality is a line that passes through this point and has a positive slope of 4/6.
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My question is what is the answer to this question when
7p+5 when p=12
Answer:89
Step-by-step explanation:math
Answer:89
Step-by-step explanation:7p+5
This means 7 *p+5
Where we see the p we put in 12
We get 7*12+5=89
The profit, p(x), that Rivka’s Delivery Service makes from delivering packages between local businesses is P(x), where x is the number of $0.10 price increases for each delivery. Use the graph below to answer the question.
2.5 price hikes are often required to optimize profit.
How do you calculate the cost per unit?
To get the unit price of an item, we divide the price of a specific number of units by the number of units. If 12 ounces of soup cost $2.40, for instance, divide $2.40 by 12 ounces to get the unit price of soup, which is $0.20 per ounce.
x = the number of price hikes
y = Earnings
Additionally from the query, we have
starts at (0, 50)
expands to (2.5, 81.25)
Reduce through (6.531, 0)
It follows that
the most is (2.5, 81.25)
Remember that
x = the number of price hikes
Thus, we have
x = 2.5
Hence, the number of price increases is 2.5
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The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the ____ state. primary steady start-up transientintroductory
The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the primary state.
In the queue system, what are the three states?1) Orderly queue, also known as FIFO (First In, First Out) or FCFS (First Come, First Serve).
2) Stack, also known as LCFS (Last Come First Serve), or LIFO (Last In First Out).
3) SIRO (Serve in Irregular Request).
What is the queuing system's steady state?Let P n(t) represent the probability of having n customers in the system at time t. This is the steady state of a queueing system, where the probability of the number of customers in the system is independent of t.
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Harry and Tim both made New Year’s Resolution. Harry made 5 more resolutions than Tim. Together they made 13 resolutions. How many resolutions did Harry make?
Answer:
Harry made 9 resolutions.
Step-by-step explanation:
Tim made x resolutions.
Harry made five more, x + 5.
Harry and Tim's together was 13.
x + x + 5 = 13
combine like terms.
2x + 5 = 13
subtract 5
2x = 8
divide by 2
x = 4
Tim made 4 resolutions.
Harry made 4 + 5, that is, 9 resolutions.
Check:
Harry and Tim together is 13.
4 + 9 = 13
Harry made 9 resolutions.
you have 84 feet of fencing to enclose a rectangular plot that borders on a river. if you do not fence the side along the river, fidn the length and width of the plot that will maximise the area
Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .
What is area?A region's size on a planar or curved surface can be expressed mathematically as its area. The term "surface area" refers to the area of a surface or the border of a three-dimensional object, whereas the term "plane area" refers to the area of a shape or planar lamina.
Here,
Here, take note that the shape is still a rectangle and the fencing is still 84 feet long.
As a result, the area is equal to xy and the sum of the sides NOT along the river is 84.
Thus, 2x + y = 84 and A = xy are the two equations.
We must find A as a function of x or y to determine the area with the largest value. My recommendation is to solve the first equation for y and substitute that value into the second equation.
A(x) = x and y = 84 - 2x (84-2x)
Currently, we must maximize A(x) = 84x - 2.
Recall that if we determine the vertex's x value by substituting, x = -b/(2a), we may find the vertex's y value.
Therefore, x = -84/(-4) = 21 ft because a = -2 and b = 84. If x = 21, y = 84 - 2(21) = 42
Thus, the dimensions are 21 by 42, and the maximum size is 21 by 42, or 882 square feet.
Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .
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Enola wants to invest $8,600.00 in a savings account that pays 5.1% simple interest.
How many years will it take for this investment to triple in value?
Round your answer to the nearest tenth of a year.
years for this investment to triple in value.
It will take _____ years for this investment to triple in value.
Step-by-step explanation:
To find the number of years it will take for Enola's investment to triple in value, we can use the formula for simple interest:
I = P * r * t
where I is the total interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the number of years.
Since the investment will triple in value, the total interest earned will be equal to two times the initial investment, or 2 * $8,600.00 = $17,200.00. Substituting these values into the formula and solving for t, we get:
$17,200.00 = $8,600.00 * 5.1% * t
t = $17,200.00 / ($8,600.00 * 5.1%) = 3.28 years
Rounding this value to the nearest tenth of a year, we get t = 3.3 years. Therefore, it will take approximately 3.3 years for Enola's investment to triple in value.
Q30: Work out the surface of the following prism
Surface area of the given prism is 6 square cm .
How to Calculate the Surface Area of Prism?
The steps to determine the surface area of the prism are:
Step 1: Note down the given dimensions of the prism.
Step 2: Substitute the dimensions in the surface area of prism formula (2 × Base Area) + (Base perimeter × height).
Step 3: The value of the surface area of the prism is obtained and the unit of the surface area of the prism is placed in the end (in terms of square units).
The lateral area is the area of the vertical faces, in case a prism has its bases facing up and down. Thus, the lateral surface area of prism = base perimeter × height
The total surface area of a Prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height).
Area of triangular cross-section:
Area = 1/2 . b . h
Area = 1/2 . 4. 3
Area = 6 square cm
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At Jalisco Electronics, assemblers are paid according to the following differential piece 4. rate scale: 1–20 units in a day, $4.50 each; 21–30 units, $5.50 each; and $7 each for every
unit over 30. Adrian Ortega assembled 70 units in one week. Find his gross pay.
The gross pay of Adrian Ortega for assembling 70 units of electronics in a week is $425
What is his gross pay?Gross pay refers to the total payment earned over a period of time.
1–20 units in a day = $4.50 each21–30 units = $5.50 eachOver 30 units = $7 eachAdrian Ortega assembled 70 units in one week
Pay for 1–20 units = $4.50 × 20
= $90
Pay for 21 - 30 units = $5.50 × 10
= $55
Pay for 30 - 70 = $7 × 40
= $280
Gross pay = $90 + $55+ $280
= $425
Therefore, Adrian Ortega is paid $425 in a week for assembling 70 electronics.
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given the function that indicates the time it takes to double an investment compounded continiuosly at 6.35% then solve for t
10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.
Given that,
We have to find how long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.
We know that,
P = $1000
r = 6.35% = 0.635
n=12
A = $2000
A = P(1+r/n[tex])^{nt}[/tex]
2000 = 1000(1+0.635/12[tex])^{12t}[/tex]
2= (1+0.635/12[tex])^{12t}[/tex]
log2= log(1+0.635/12[tex])^{12t}[/tex]
log2= 12t×log(1+0.635/12)
t=log2/12×log(1+0.635/12)
t≈10.9 years.
Therefore, 10.9 years long will it take for $1000 to double at a 6.35% annual interest rate that is compounded every month.
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A newsletter publisher believes that 43% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.02 level of significance, the testing firm fails to reject the null hypothesis.
The conclusion regarding the test of the hypothesis is given as follows:
There is not sufficient evidence at the 0.02 level of significance that the percentage is not of 43%.What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the percentage is not of 43% = proportion of 0.43, hence:
[tex]H_0: p = 0.43[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the percentage is not of 43%, hence:
[tex]H_1: p \neq 0.43[/tex]
The decision was to not reject the null hypothesis, meaning that there is not sufficient evidence at the 0.02 level of significance that the percentage is not of 43%.
Missing InformationThe problem asks to identify the correct conclusion from these two options:
There is not sufficient evidence at the 0.02 level of significance that the percentage is not of 43%.There is sufficient evidence at the 0.02 level of significance that the percentage is not of 43%.More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
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The table shows the colour of the bicycles in
a bike shed.
Bookwork code: S79 EX
<
< Back
Colour Frequency
Silver
3
Green
1
a) What fraction of the bicycles are silver?
Give your answer in its simplest form.
b) How many sections on this pie chart
would you shade to show the bicycles that
are silver?
✓ Scroll down
Watch video
Answer >
A fraction of the bicycles which are silver is 3/4.
You should shade three (3) sections on the pie chart to show the number of bicycles that are silver.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.
Based on the information provided, we can logically deduce the following parameters;
Number of silver bicycles = 3 silver bicycles.
Number of green bicycles = 1 green bicycles.
Therefore, the total number of bicycles is equal to 4 bicycles.
For the fraction of silver bicycles, we have;
Fraction = 3/4 bicycles.
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Use algebraic rules of equations to predict the solution type to the system of equations
The solution type to the system is one solution or consistent system
How to predict the solution type to the system?From the question, we have the following parameters that can be used in our computation:
f(x) = [x + y = 4
[y = 2x - 1
Substitute y = 2x - 1 in the equation x + y= 4
So, we have the following representation
x + 2x - 1 = 4
Evaluate the like terms
3x = 5
So, we have
x = 5/3
Substitute x = 5/3 in y = 2x - 1
So, we have the following representation
y = 2 * 5/3 - 1
Evaluate
y = 2.33
Because x and y have real values
Then, the solution type is a consistent system
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Of the 24 fast-food businesses on Valley Mills Drive, the number that have a drive-up window, outside seating, or a pay telephone is summarized as follows:
18 have a drive-up window.
17 have outside seating.
8 have pay telephones.
12 have a drive-up window and outside seating.
6 have outside seating and a pay telephone.
5 have a drive-up window and a pay telephone.
4 have all three.
Find the number of businesses that have the following.
(a) a drive-up window and no outside seating
(b) a drive-up window and outside seating, but no pay telephone
(c) no pay telephone
(d) only a drive-up window
(e) outside seating or a pay telephone
By using a Venn diagram, we can conclude that:
a. 10 businesses have a drive-up window and no outside seating
b. 4 Businesses have a drive-up window and outside seating, but no pay telephone
c. 20 businesses have no pay telephone
d. 9 businesses have only a drive-up window
e. 8 businesses have outside seating or a pay telephone
A Venn diagram is a diagram consisting of overlapping circles to illustrate the logical relationship between two or more sets of items.
In the question, there are 3 sets of criteria that describe the condition of the fast-food businesses in Valley Mills Drive: whether or not there is a drive-up window, outside seating, or a pay telephone.
Let d denotes the number of businesses that have the three criteria.
If a denotes the number of businesses that have drive-up window and outside seating only, then:
drive-up window and outside seating = a + d
12 = a + 4
a = 8
If b denotes the number of businesses that have outside seating and a pay telephone only, then:
outside seating and a pay telephone = b + d
6 = b + 4
b = 2
If c denotes the number of businesses that have drive-up window and a pay telephone only, then:
drive-up window and a pay telephone = c + d
5 = c + 4
c = 1
If x denotes the number of businesses that have drive-up window only, then:
have a drive-up window = a + c + d + x
18 = 4 + 1 + 4 + x
18 = 9 + x
x = 9
If y denotes the number of businesses that have outside seating only, then:
have outside seating = a + b + d + y
17 = 4 + 2 + 4 + y
17 = 10 + y
y = 7
If z denotes the number of businesses that have pay telephone only, then:
Have pay telephone = b + c + d + z
8 = 2 + 1 + 4 + z
8 = 7 + z
z = 1
Then we can draw a Venn diagram to illustrate those numbers to get a better illustration in answering the questions.
a. a drive-up window and no outside seating = c + x = 1 + 9 = 10
b. a drive-up window and outside seating, but no pay telephone = a = 4
c. no pay telephone = x + y + a = 9 + 7 + 4 = 20
d. only a drive-up window = x = 9
e. outside seating or a pay telephone = y + z = 7 + 1 = 8
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A line passes through the point (4, -8) and has a slope of 5/2
Write an equation in slope-intercept form for this line.
help me pls this is due in 30 minutes
y=5/2x+24
Step-by-step explanation:
use the formula y-y1=m(x-x1)
5/2 symbolizes m
put in 4 for y1 and put in -8 for x1
y-(4)=(5/2)(x-(-8)
y-4=5/2(x+8)
y-4=5/2x+20
y=5/2x+24
Answer:
y = 5/2x -18
Step-by-step explanation:
You want the slope-intercept equation for the line with slope 5/2 through point (4, -8).
Point-slope formIt can work well to start with the point-slope equation and rearrange it to the desired form.
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y -(-8) = 5/2(x -4) . . . . . line with slope 5/2 through point (4, -8)
Slope-intercept formAdd -8 and eliminate parentheses
y = 5/2x -10 -8
y = 5/2x -18 . . . . . . . . simplify
The desired equation is y = 5/2x -18.
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What is the value of the missing exponent in the equation 7.4 ÷ 10□ = 0.074?
either 1
or 2
or 3
or 0
Answer:
The result is 0.074 ÷ 1000 = 0.00074, which means that 10□ = 1000, so the value of the missing exponent is 3.
Step-by-step explanation:
Which expression is equivalent to 8(6s+6)?
Answer:
48s + 48
Step-by-step explanation:
Create a multiplication equation with a solution of 2/7
Answer:
1 / 7 · 2 = 2 / 7
Find the point of intersection between a line that is tangent to the function
() = x^2 + 4 at = −1 ,
and the function
() = x^2 − 4
There is no point of intersection between a line that is tangent to the function () = x² + 4 at = −1 , and the function () = x² − 4
What is the point of intersection about?To find the point of intersection between the line that is tangent to the function y = x² + 4 at x = −1 and the function y = x² − 4 , we can set the two equations equal to each other and solve for x. This will give us the x-coordinate of the point of intersection.
Setting the two equations equal to each other, we have:
x^2 + 4 = x² - 4
This simplifies to:
2 = -8
This equation has no solutions, so the two functions do not intersect. This means that the point of intersection does not exist.
Alternatively, we could see that the two functions have different slopes at the point x = −1 .
The function y = x² + 4 has a slope of 2x at this point, which is equal to -2 . The function y = x² − 4 has a slope of 2x , which is equal to -2 at this point as well.However, since the two functions have different y-intercepts, they cannot be tangent to each other at this point. Therefore, the point of intersection does not exist.
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Miguel earns extra money working two weekends with his dad. He is saving to buy a new bike that costs $140. Heather says that Miguel needs to earn more than $6 for each hour that he works to have enough money to buy the bike. Her work is shown below. Write an inequality to explain why she is incorrect
An inequality to explain the reason Heather is incorrect is t > $8.75.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).From the histogram, we can logically deduce the following information;
Miguel’s work record during Weekend 1 = 9 hours.
Miguel’s work record during Weekend 2 = 7 hours.
Therefore, the total number of hours which Miguel worked in two Weekends is given by;
Total hours = 9 hours + 7 hours
Total hours = 16 hours.
Next, we would calculate the amount of money that Miguel would earn per hour;
Amount = $140/16
Amount = $8.75 per hour.
Note: Let the variable t represent the total earnings.
In conclusion, the correct inequality is t > $8.75.
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There were 616 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $6543.50. How many of each kind of ticket were purchased?
The number of the tickets purchased for upper reserve is 146 and lower is 470.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that there were 616 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $6543.50.
The equations will be formed as,
L + U = 616
12.5L + 8U = 6543.5
Solve the above equations,
12.50L + 8 (616-L) = 6543.5
12.5L + 4928 - 8L = 6543.5
12.50L - 8L = 6543.5 - 4428
4.50L = 2118.5
L = 470
U = 616 - 470
U = 146
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