Answer:
32
Step-by-step explanation:
IT A MULTI-STEP PROBLEM HELP! 6 PARTS TO IT!!! IM GOING TO FAIL!! CAN PLEASE DO IT STEP BY STEP
a. The cost of one large pizza with one topping is $13.50. To purchase one large and five medium pizzas, we would need to buy one large pizza at regular price and five medium pizzas at the discounted price. The cost of the large pizza is $13.50, and the cost of each medium pizza is $6.25. Therefore, the total cost would be:
Total cost = Cost of large pizza + Cost of 5 medium pizzas
Total cost = $13.50 + ($6.25 x 5)
Total cost = $13.50 + $31.25
Total cost = $44.75
Therefore, it would cost $44.75 to purchase one large pizza and five medium pizzas.
b.Number of medium pizzas Total cost
0 | $13.50
1 | $19.75
2 | $26.00
3 | $32.25
4 | $38.50
c. Let "m" be the number of medium pizzas. Then the total cost of purchasing one large pizza with one topping and m medium pizzas can be represented as:
Total cost = 13.50 + 6.25m
d. If you have a total of $100 and purchase one large pizza, you would have $100 - $13.50 = $86.50 left to spend on medium pizzas. The cost of each medium pizza is $6.25. Therefore, you can buy:
Number of medium pizzas = $86.50 ÷ $6.25 = 13.84
Since you cannot buy a fraction of a pizza, you can only buy 13 medium pizzas with $86.50.
e. The area of a pizza is given by the formula A = πr^2, where A is the area and r is the radius. The area of a large pizza is:
A = πr^2
A = 3.14 x 8^2
A = 3.14 x 64
A = 200.96
The area of a medium pizza is:
A = πr^2
A = 3.14 x 5^2
A = 3.14 x 25
A = 78.5
Therefore, the total area of one large pizza and five medium pizzas is:
Total area = Area of large pizza + (Area of medium pizza x 5)
Total area = 200.96 + (78.5 x 5)
Total area = 200.96 + 392.5
Total area = 593.46
Rounding to the nearest inch, the total area of pizza is 593 square inches.
f. To calculate the cost per square inch of pizza, we need to divide the total cost of the pizzas by the total area of the pizzas. The total cost of one large pizza and five medium pizzas is $44.75, and the total area is 593 square inches. Therefore, the cost per square inch of pizza is:
Cost per square inch = Total cost / Total area
Cost per square inch = $44.75 / 593
Cost per square inch = $0.08 (rounded to the nearest cent)
Therefore, the cost per square inch of pizza is 8 cents.
Seven more than the quotient of a number and 3 is 10? What is the number?
The number is 9.
Which one of the three types of equations are they?The three main types of linear equations are the standard form, the point-slope form, and the slope-intercept form.
We can begin by converting the following phrase into an equation:
The formula for "seven bigger than the product of a number and three" is as follows:
x/3 + 7
where x stands in for the unidentified number.
Seven more than the result of a number and three equals 10, according to the following formula.
x/3 + 7 = 10
When you take 7 out of both sides of the equation, you get:
x/3 = 3
When both sides of the equation are multiplied by 3, the result is:
x = 9
Hence, the answer is 9.
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Solve the following linear programming problem. Maximize: z = 7x + 2y subject to: 7x-y≤ 16 2x+y≥ 10 X≥2 y≤9 The maximum value is
Answer:
To solve the linear programming problem, we need to first graph the feasible region determined by the constraints, and then evaluate the objective function at each corner point of the feasible region to find the maximum value of z.
Plotting the lines corresponding to the inequalities, we get:
Graph of the feasible region:
The feasible region is the shaded polygon in the graph. We can see that the vertices of the feasible region are (2, 9), (2, 12), (4, 7), and (8, 2).
Next, we evaluate the objective function at each of these vertices to find the maximum value of z.
At (2, 9): z = 7x + 2y = 7(2) + 2(9) = 23
At (2, 12): z = 7x + 2y = 7(2) + 2(12) = 31
At (4, 7): z = 7x + 2y = 7(4) + 2(7) = 35
At (8, 2): z = 7x + 2y = 7(8) + 2(2) = 58
Therefore, the maximum value of z is 58, which occurs at the point (8, 2).
Hence, the answer is: the maximum value of z is 58.
component of optimi
1. Jaden wanted to begin a career in marketing. He had his heart set on a marketing program at a
private university. However, the private university did not admit Jaden to the school. After finding
out he was not accepted, Jaden chose to apply to a nearby state school that also had a highly rated
marketing program. Jaden is now a marketing manager.
Answer:
you need to learn yo stuff
Step-by-step explanation:
bye
Craig’s Computer Supply Shop sells color ink printer cartridges for $24.99 and black ink printer cartridges for $14.99. Last week the store sold a total of 27 ink cartridges. If the sales income for these items was $514.73, not including tax, which of these conclusions is reasonable?
A.) There were more black ink cartridges than color ink cartridges sold last week.
B.) There were more color ink cartridges than black ink cartridges sold last week
C.) The total sales income, not including tax, for color ink cartridges was $399.84
D.) The total sales income, not including tax, for black ink cartridges was $164.89
There were more color ink cartridges than black ink cartridges sold last week. Therefore, option B is the correct conclusion.
What is system of equation?A system of equations, sometimes referred to as an equation system or a set of simultaneous equations, is a finite set of equations for which we searched for common solutions. Variables are related to one another specifically in each equation in a system of equations. To discover a set of variable values that satisfy each equation, the equations can be solved simultaneously.
In everyday situations where the unknown values can be represented as variables, a system of linear equations is used to model the problem. Many techniques, including substitution, elimination, graphing, etc., are used to solve systems of equations.
Let us suppose the number of color ink cartridges sold = x.
The number of color ink cartridges sold = y.
Thus,
x + y = 27
24.99x + 14.99y = 514.73
Multiplying the first equation by 24.99 and subtracting it from the second equation multiplied by 100, we get:
1499y = 1813
y ≈ 1.21
Substituting y back into the first equation, we get:
x ≈ 25.79
Hence, there were more color ink cartridges than black ink cartridges sold last week. Therefore, option B is the correct conclusion.
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Natasha worked for part of the year before receiving a raise in her hourly rate of pay. The graph below shows the amount of money she has made this year and the hours she has worked since she received the raise. What was the initial amount of money Natasha made?
Answer:
Unfortunately, I cannot see the graph you are referring to since we are communicating through text. However, based on the information given, we can make some general observations.
We know that Natasha received a raise in her hourly rate of pay at some point during the year. Before the raise, she earned some initial hourly rate of pay. Let's call this initial rate of pay "x". Let's also assume that she worked for "h" hours before receiving the raise, and "k" hours after receiving the raise.
We can write an equation to represent the total amount of money she made this year:
Total amount of money = (initial hourly rate of pay x number of hours worked at the initial rate) + (new hourly rate of pay x number of hours worked at the new rate)
Using the variables we defined earlier, we can write:
Total amount of money = (x × h) + ((x + y) × k)
where y is the increase in her hourly rate of pay after the raise.
We also know that she earned a certain amount of money before the raise. Let's call this amount "M". This means that:
M = x × h
Solving for x, we get:
x = M/h
Substituting this expression for x into the first equation, we get:
Total amount of money = (M + yh) + ((M/h + y) × k)
We don't know the values of M, y, h, or k, so we cannot determine the initial hourly rate of pay x or the total amount of money Natasha made this year. However, we have set up an equation that can be used to solve for these values if we have more information.
9. The price of a Delta Air Lines ticket from New York to Orlando increased to $450. This is an 8% increase. What was the old fare to nearest cent?
Answer:
$416.66
Step-by-step explanation:
We take
450 divided by 108, then time 100 = $416.66
So, the old fare is $416.66
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the absolute value functions with their vertices.
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f(x)= |x-51+
f(x) = -2|2|-
-
f(x)= |x-1| +4
f(x)=x+11-4
Vertex
(-1,-4)
(5, 1)
(0, -1)
(2, 4)
f(x) = |z|-
f(2)=|z-|+{
Absolute Value Function
Answer:
[tex]\boxed {\left(-1, -\dfrac{3}{7}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{1}{2}\left|x\:+\:1\right|-\frac{3}{7}}[/tex]
[tex]\boxed{\left(5,\:\frac{2}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{3}{5}\left|x\:-\:5\right|+\:\frac{2}{3}}[/tex]
[tex]\boxed{\left(0,\:-\frac{4}{5}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{1}{2}\left|x\right|\:-\:\frac{4}{5}}[/tex]
[tex]\boxed{\left(\frac{2}{5},\:\frac{5}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{3}{2}\left|x-\frac{2}{5}\right|+\frac{5}{3}}[/tex]
Step-by-step explanation:
The vertex of an absolute function
y = f(x) = a|x - b| + c occurs at x - b = 0 or when x = b
Plugging this into the original equation will give the value for f(b) which will be f(b) = 0 + c which will be the y-value of the vertex
[tex]\text{Vertex of } f(x) = \dfrac{3}{5} |x - 5| + \dfrac{2}{3}\\\\ \longrightarrow x = 5, y = \dfrac{2}{3} \\\\\longrightarrow \left(5, \dfrac{2}{3} \right)[/tex]
You can do the others in a similar manner.
Here it is easier because the constant in f(x) corresponds to the y-coordinate of the vertex and they are different in the answer choices
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
What is the lowest common multiple of 8 and 12?
Answer:
2 hope that helps
Step-by-step explanation:
Weathering and erosion are two processes that shape Earth’s surface. Which of the
following sets of factors cause both weathering and erosion?
a) acid rain, tree roots, waves
b) glaciers, waves, wind
c) moving water, plants, wind
d) acid rain, plants, ice
Find the value of each variable.
Answer:
x = 63 , y = 90
Step-by-step explanation:
assuming DF is the diameter of the semicircle , then
∠ DEF = y = 90° ( angle inh a semicircle )
then
x + y + 27° = 180° ( angle sum of a triangle )
x + 90 + 27 = 180
x + 117 = 180 ( subtract 117 from both sides )
x = 63
Simplificacion de 18/25
Answer:
Step-by-step explanation:
Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.
Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.
On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :
(18 ÷ 1) / (25 ÷ 1)
= 18/25
Which of the following equations will reduce the graph shown below
The equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
What is graph?In mathematics, a graph is a visual representation of a set of objects (called vertices or nodes) and the connections (called edges) between them.
The equation y = -1/2(x-3)² + 5 is a quadratic function in vertex form. The vertex of this parabola is at the point (3, 5), and the coefficient of the x² term is negative (-1/2), which tells us that the parabola opens downwards. This means that the graph of this equation reduces.
To see why this is the case, consider the behavior of the y-values as x moves away from the vertex. Since the leading coefficient is negative, the y-values will decrease as x moves to the left or right from the vertex. Additionally, the squared term inside the parentheses means that the graph will be symmetric around the x-coordinate of the vertex, which is 3 in this case.
Thus, as x moves away from the vertex to the left or right, the y-values decrease in a symmetric manner, resulting in a graph that reduces. This can be seen in the shape of the parabola as it curves downwards from the vertex.
Therefore, the equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
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how far is sam from the top of a temple?
The distance between Sam from the top of the temple is 56. 6 feet
How to determine the distanceTo determine the distance, we need to know that trigonometric identities are mathematical identities that is mostly used to prove that all the values of the functions of trigonometry are true.
The types of trigonometric identities are;
tangentsinecosinecotangentcosecantsecantFrom the information given, we can deduce that;
The angle of elevation, θ = 62 degrees
The opposite side of the angle that is the height of the temple is 50 feet
The distance is the hypotenuse side
Then, using sine identity, we have;
sin 62 = 50/d
d = 50/0. 8829
d = 56. 6 feet
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As part of a survey, 55 adults were asked if they had been abroad on holiday or visited somewhere in the UK. 25 people went
abroad and 15 people went on holiday in the UK. What is the probability that a randomly selected person actually went on holiday
that year? Round your answer to three decimals.
The probability that a randomly selected person actually went on holiday that year is 0.727
How to calculate the probability that a randomly selected person actually went on holiday that yearOut of the 55 adults surveyed, 25 went abroad and 15 went on holiday in the UK.
Therefore, the total number of people who went on holiday is 25 + 15 = 40
The probability of selecting a person who went on holiday is the number of people who went on holiday divided by the total number of people surveyed:
P(went on holiday) = 40/55
Simplifying the fraction, we get:
P(went on holiday) = 8/11
Rounding to three decimals, we get:
P(went on holiday) = 0.727
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Samir and Kylie are making fruit salads for a picnic. Samir mixes 1 cup of melon and 3 cups of apple and Kylie mixes 2 cups of melon and 9 cups of apple. Use Samir and Kylie’s percent of melon to determine whose fruit salad will taste more melony.
Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.
What is percentage?Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol % (percent).
In the given question,
To determine whose fruit salad will taste more melony, we need to calculate the percentage of melon in each fruit salad.
For Samir's fruit salad:
The total amount of fruit is 1 + 3 = 4 cups
The amount of melon is 1 cup
The percentage of melon is (1/4) x 100% = 25%
For Kylie's fruit salad:
The total amount of fruit is 2 + 9 = 11 cups
The amount of melon is 2 cups
The percentage of melon is (2/11) x 100% = 18.18% (rounded to two decimal places)
Therefore, Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.
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Match each metric measurement on the left with an equivalent unit of measurement on the right.
According to the information, the values that coincide are: 2.2 meters with 2200 millimeters, 14 decimeters with 0.014 hectometers, 0.14 meters with 0.014 decameters, 0.022 decameters with 22 centimeters.
How to find the numbers that match?To find the numbers that match we must take into account the relationship between the values:
Decameter: Unit of length equal to 10 meters.Centimeter: Unit of length equal to one hundredth of a meter.Decimeter: Unit of length equal to one tenth of a meter.Millimeter: Unit of length equal to one thousandth of a meter.Hectometer: Unit of length equal to 100 meters.According to the above, we can infer that the values that match are:
2.2 meters with 2200 millimeters.14 decimeters with 0.014 hectometers.0.14 meters with 0.014 decameters,0.022 decameters with 22 centimeters.Learn more about measurements at: https://brainly.com/question/4725561
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the great zlatan ibrahimović always scores a goal if he manages to take no less than six shots in a game (and sometimes he scores even without shooting). the following is a probability distribution of the number of shots zlatan ibrahimović must make to score a goal:
No. of shots Probability of scoring
0 0.02
1 0.13
2 0.34
3 0.32
4 0.16
5 0.02
6 0.01
(A). Calculate the expected ( mean) number of shots he takes to score a goal ?
(B). Calculate the standard deviation of the distribution.
a) The expected (mean) number of shots that Zlatan Ibrahimović must make to score a goal is 3.11.
b) The standard deviation of the distribution is 2.46.
How are the expected number and standard deviation computed?The expected number or mean (μ) of a distribution is computed as sum resulting from the multiplication of each value of the random variable by its probability and adding the products.
The formula for the mean is given as E(x) = ∑x P(x).
On the other hand, to compute the standard deviation (σ) of a probability distribution, we find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root.
No. of shots Probability Expected Squared Squared Deviation
of scoring No. of shots Deviation x Probability
0 0.02 0 9.6721 0.193442
1 0.13 0.13 8.8804 1.154452
2 0.34 0.68 5.9049 2.007666
3 0.32 0.96 4.6225 1.4792
4 0.16 0.64 6.1009 0.976144
5 0.02 0.1 9.0601 0.181202
6 0.01 0.6 6.3001 0.063001
The expected (mean)
number of shots = 3.11 6.055107
Standard Deviation = Square root of 6.055107 = 2.46
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The following data indicate the scores of some students in a competition. Which a box plot represents the data?
100 points!!!!!
The correct answer to the given question is graph D
How to solveGiven a set of data points, we are tasked with identifying the correct box plot representation.
We begin by arranging the data in ascending order, which gives us 12, 17, 21, 23, 24, 28, and 29 points.
Next, we use the properties of a box plot to eliminate incorrect representations.
The left end of the whisker should correspond to the smallest data point, and the right end to the largest.
Among the given graphs, only one satisfies this condition.
The middle point is identified as the fourth data point, which is 23.
Finally, we determine the lower and upper lines of the box to be 17 and 28, respectively.
The only graph that satisfies all conditions is graph D.
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Lamonte was driving down a road and after 4 hours he had traveled 62 miles. At this speed, how many hours would it take Lamonte to drive 93 miles?
The time taken by the Lamonte would be 6 hours to drive 93 miles at a speed of 15.5 miles per hour.
How to calculate the time ?We can use the following formula to answer this question:
rate x time = distance
We know Lamonte drove 62 miles in four hours, so we can use that to calculate his speed:
62 miles = rate multiplied by 4 hours
When we solve for the rate, we get:
rate = 62 miles divided by 4 hours equals 15.5 miles per hour
We can now use this rate to calculate how long it would take Lamonte to drive 93 miles:
93 miles = time x rate
Substituting the recently discovered rate yields:
93 miles = 15.5 miles per hour multiplied by time
When we solve for time, we get:
time = 93 miles / 15.5 miles per hour = 6 hours
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what is the value of 6(2b-4) when b =3
Answer: 12
Step-by-step explanation:
Use BODMAS, so first solve the inside of the bracket:
2*3= 6
6-4= 2
Now we can multiply that by the number outside the bracket. Why?
Because a number outside a bracket means to multiply that number by everything in the bracket. So:
6 * 2 = 12
Answer: 12
Step-by-step explanation:
2 x 3 = 6
6 - 4 = 2
6 x 2 = 12
Smith, from Los Angeles, and Jones, from New York City, are both traveling to Kansas City, beginning their trips at the same time. The graph shows the distance in miles from Kansas City for each of them after they have both traveled for the same number of hours. After how many hours from the start of their journeys were they the same distance from Kansas City?
Answer: The answer should be 20 hours
Step-by-step explanation:
That is when the 2 lines meet up so that is when they are the same difference from Kansas City.
the unit rate for this relationship is 1 gallon per 18.25 minutes
The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.
So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:
(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons
Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be approximately 6.58 gallons.
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The complete question is :
What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?
Roselli's Machine Manufacturing Co reported its sales as R120 000, a gross profit of R50 000, and current liabilities of R25 000. If the current ratio is 2,5 and the quick ratio is 1,75, what is the inventory turnover for the company?
Answer:
Step-by-step explanation:
To find the inventory turnover for Roselli's Machine Manufacturing Co, we need to use the formula:
Inventory turnover = Cost of goods sold / Average inventory
First, we need to find the cost of goods sold (COGS):
COGS = Sales - Gross profit
COGS = R120 000 - R50 000
COGS = R70 000
Next, we need to find the average inventory. We can use the quick ratio formula to find the current assets:
Quick ratio = (Current assets - Inventory) / Current liabilities
Rearranging the formula to solve for inventory, we get:
Inventory = Current assets - (Quick ratio x Current liabilities)
Plugging in the values we know, we get:
1.75 = (Current assets - Inventory) / R25 000
Current assets - Inventory = 1.75 x R25 000
Current assets - Inventory = R43 750
Inventory = Current assets - R43 750
Since the current ratio is 2.5, we know that:
Current assets / Current liabilities = 2.5
Solving for current assets, we get:
Current assets = 2.5 x R25 000
Current assets = R62 500
Substituting the values we found for inventory and COGS into the inventory turnover formula, we get:
Inventory turnover = COGS / Average inventory
Inventory turnover = R70 000 / [(R62 500 - R43 750) / 2]
Inventory turnover = R70 000 / (R18 750 / 2)
Inventory turnover = R70 000 / R9 375
Inventory turnover = 7.47
Therefore, the inventory turnover for Roselli's Machine Manufacturing Co is 7.47.
Consider the following function.
f(x) = −2x^3 − 6x^2 + 5
(a) Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero. Verify your answers by using the table feature of the graphing utility. (Select all that apply.)
(−4, −3)
(−3, −2)
(−2, −1)
(−1, 0)
(0, 1)
(1, 2)
(2, 3)
(3, 4)
(b) Use the zero or root feature of the graphing utility to approximate the real zeros of the function. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
x =
, in the presented question, we can conclude that Interval [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
What are polynomials?Interval [tex](4, 3): f(-4) -41, f(-3) 5,[/tex]therefore, the function reverses its sign and has a zero in the interval [tex](-4, -3).[/tex]
Interval [tex](3, 2): f(-3) 5, f(-2) -9,[/tex] indicating that the function changes sign and has a zero in the interval [tex](-3, -2).[/tex]
Interval [tex](2, 1): f(-2) -9, f(-1) 1[/tex], therefore the function reverses its sign and has a zero in the interval [tex](-€2, -1).[/tex]
Interval [tex](1, 0): f(-1) 1, f(0) 5[/tex], so the function does not change sign and the interval may or may not contain a zero [tex](-1, 0).[/tex]
Interval [tex](0, 1): f(0) 5, f(1) -3,[/tex] indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
Therefore, in the presented question, we can conclude that Interval [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
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please help me for both please, asap :)) thank you!
Answer:
The correct answer is the third one
Step-by-step explanation:
[tex]8x + \frac{15}{x} = 26[/tex]
[tex]8 {x}^{2} + 15 - 26x = 0[/tex]
a = 8, b = -26, c = 15
[tex]d = {b}^{2} - 4ac = ( { - 26})^{2} - 4 \times 8 \times 15 = 676 - 480 = 196 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{26 - 14}{2 \times 8} = \frac{12}{16} = \frac{3}{4} [/tex]
[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{26 + 14}{16} = \frac{40}{16} = \frac{5}{2}[/tex]
What is the area of this trapezoid?
Answer:
8*7=56 + 8*3=24 = 80_squared
Step-by-step explanation:
Use mental math to assess reasonableness. Explain your thinking
Cameron spends $130 on a gaming system and $80 on video games. He
says he spends about $215. Is his statement reasonable? Explain your
thinking.
To assess the reasonableness of Cameron's statement that he spent about $215 on a gaming system and video games, we can use mental math to estimate the total cost.
We know that he spent $130 on a gaming system and $80 on video games. If we round $80 up to $100 and add it to $130, we get:
$130 + $100 = $230
So based on this estimate, it seems like Cameron's statement of spending about $215 is not entirely accurate. However, it is close to the actual total cost, which is within 10% of the estimated total.
Therefore, we can say that while Cameron's statement may not be entirely precise, it is reasonably close to the actual total cost and can be considered reasonable.
Your firm is considering adding a product line. The accounting department has determined that the cost
function for this new product will be C(x) = 55x + 3500 and the revenue function will be R(x) = 80x,
where x is the number of units sold. Additionally, the sales department has determined that you reasonably
can expect to sell around 164 units. You must decide whether to go ahead with the new product line.
Find the break-even quantity:
Find the profit function: P(x) =
Make your decision:
O Proceed with the product line: the products are profitable and we can reasonably expect to meet
our break-even quantity.
Cancel the product line: the quantity needed to break even is more than our firm can reasonably
expect to sell.
O Cancel the product line: producing these products is not profitable.
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the profit function is positive, producing 164 units of the new product line would yield a profit of $600.
We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600
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