The number of times more high school football players were there is 500.
Given that, in 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States.
Here, the number of times more high school football players were there
= 1×10⁶/2×10³
= 1×10³/2
= 1000/2
= 500
Therefore, the number of times more high school football players were there is 500.
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"Your question is incomplete, probably the complete question/missing part is:"
In 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States. About how many times more high school football players were there?
if there are 15 people from the bronx, brooklyn, manhattan queens and staten island and each borough has 3 people, if the people from each borough insist on standing together, how many possible ways are there to stand
There are 10,080 possible ways for the 15 people to stand if the people from each borough insist on standing together.
If there are 15 people from the Bronx, Brooklyn, Manhattan, Queens, and Staten Island, and each borough has 3 people, then there are 5 groups of 3 people. If the people from each borough insist on standing together, we can treat each group of 3 people as a single entity. So, we have 5 entities that need to be arranged.
The number of ways to arrange these 5 entities is 5!, which is equal to 120. However, within each group of 3 people, there are 3! ways to arrange the people. So, we need to multiply the number of ways to arrange the groups by the number of ways to arrange the people within each group. We will get the answer
5! × (3!)⁵ = 120 × 3⁵ = 10,080
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Ashley made 4 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 4 necklaces was $29.20 . If the beads cost a total of $13.60 , how much did each pendant cost?
$3.90
29.20-13.60=15.6
15.6/4= 3.90
Help please!!!!
Whoever answers right gets brainliest!
The simplified form of given expression a³/a⁶b⁻¹ is b/a³.
Hence, the correct option is C.
Exponents are a shorthand notation used in mathematics to represent repeated multiplication of a number by itself. The exponent is a small number written to the right and above a base number, and indicates how many times the base should be multiplied by itself.
In the given expression, a³/a⁶b⁻¹
We can apply the rules of exponents, and we get
= a³⁻⁶/b⁻¹
= a⁻³/b⁻¹
= b/a³
Hence, the correct option is C.
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[tex]-2-\frac{5}{4} x=13\\[/tex]
Therefore, the solution to the equation -2 - 5/4x = 13 is x = -12.
What is equation?A mathematical statement proving the equality of two expressions is known as an equation. Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. In addition to representing a connection between variables, an equation may also be used to find an unknown number. As they enable us to define and evaluate connections between things and make predictions about how they will behave under various circumstances, equations are a crucial tool in many domains, including mathematics, physics, engineering, and many more.
To solve for x in the equation -2 - 5/4x = 13, you can follow these steps:
Add 2 to both sides of the equation to isolate the fraction on the left side:
-2 - 5/4x + 2 = 13 + 2
-5/4x = 15
Multiply both sides of the equation by -4/5 to get x by itself:
(-4/5) * (-5/4x) = (-4/5) * 15
x = -12
Therefore, the solution to the equation -2 - 5/4x = 13 is x = -12.
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I complete lost on this problem can you help me solve it
The line described by y = 3/4x+5 is tangent to a circle at the point (0, 5). The line described by 3x + 4y = 38 is tangent to the same circle at the point (6, 5). Find the equation of the circle.
Answer:
(x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25
Step-by-step explanation:
The equation of a circle can be written in the form (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Since the lines are tangent to the circle at points (0,5) and (6,5), we can use these points to find the center and radius of the circle.
First, let’s find the slope of each line. The slope of the line y = 3/4x+5 is 3/4. The slope of the line 3x + 4y = 38 can be found by rearranging it into slope-intercept form: y = (-3/4)x + 19/2. So the slope of this line is -3/4.
Since the lines are tangent to the circle, they are perpendicular to the radius at their point of tangency. This means that the center of the circle lies on the line that passes through (0,5) and has a slope of -4/3, and also on the line that passes through (6,5) and has a slope of 4/3.
Let’s find the equation of these two lines. The line passing through (0,5) with a slope of -4/3 has an equation y - 5 = (-4/3)(x - 0), or y = (-4/3)x + 5. The line passing through (6,5) with a slope of 4/3 has an equation y - 5 = (4/3)(x - 6), or y = (4/3)x - 3.
The center of the circle is at the intersection of these two lines. To find it, we can set their right-hand sides equal to each other and solve for x: (-4/3)x + 5 = (4/3)x - 3. Solving this equation gives us x = 24/5. Substituting this value into either equation for y gives us y = (4/3)(24/5) - 3 = 21/5.
So the center of the circle is at (24/5, 21/5). To find its radius, we can use either point of tangency. Let’s use (0,5). The distance between this point and the center is given by sqrt((0-24/5)^2 + (5-21/5)^2), which simplifies to sqrt(481)/5.
Therefore, the equation of the circle is (x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25.
Cheryl and her sister Diane walk to school along the same route. Cheryl walks at an average of
80 steps per min while Diane walks at an average of 90 steps per min. Cheryl takes steps
of 81 cm each. She takes 12 min to walk to school.
A) If each of Diane's steps in 72 cm, how long does Diane take to walk to school?
Answer: Let's first convert Cheryl's walking speed to meters per minute. Since she takes 80 steps per minute and each step is 81 cm, her walking speed is:
80 steps/min x 81 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
Now, let's find out the distance Cheryl walks to school. Since she walks for 12 minutes at a speed of 64.8 m/min, the distance she covers is:
distance = speed x time = 64.8 m/min x 12 min = 777.6 m
Next, let's find out how many steps Diane takes per minute on average:
90 steps/min
Since each of Diane's steps is 72 cm long, her walking speed is:
90 steps/min x 72 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
So Diane's walking speed is the same as Cheryl's. To find out how long it takes Diane to walk to school, we can use the formula:
distance = speed x time
Since Diane and Cheryl walked the same distance, we can use the distance we found for Cheryl:
777.6 m = 64.8 m/min x time
Simplifying this equation, we get:
time = 12 minutes
Therefore, Diane takes 12 minutes to walk to school.
Answer:
12 min
Step-by-step explanation:
You want to know how long it takes Diane to walk to school if she takes 90 steps of 72 cm per minute, while Cherly takes 80 steps of 81 cm per minute and traverses the distance in 12 minutes.
SpeedThe speed of each girl is the product of the number of steps per minute and the length of the step:
Cheryl: (80 step/min)(81 cm) = 6480 cm/min
Diane: (90 step/min)(72 cm) = 6480 cm/min
Both girls travel at the same speed, so will take the same amount of time to get to school. It takes Diane 12 minutes to walk to school.
Need the slope(m) of the function.
the y intercept of the function.
and the slope intercept form f(x)=mx+b of the function.
Answer:
We can calculate the slope by taking 2 points on the line. I took A(4,4) and B(-4,0), so we get m=1/2.
2. y-intercept is the point where a line crosses the y-axis which is (0,2)
3. We have f(x)=1/2x +b
By taking a particular point on the line,we get :
2=1/2(0)+b
==》 b=2
So the slope intercept form is
y=1/2x+2
Confusing
Kerrin is making an input-output table for the rule "add 5." What is the output value for an input value of 5?
Options:
A: 0
B :5
C: 10
D: 25
The calculated output value for an input value of 5 is (c) 10
What is the output value for an input value of 5?From the question, we have the following parameters that can be used in our computation:
Kerrin is making an input-output table for the rule "add 5."
This means that
Output = input + 5
In this case, we have
input = 5
substitute the known values in the above equation, so, we have the following representation
Output = 5 + 5
Evaluate
Output =10
Hence, the output is 10
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A sixth-grade class collected data on the number of letters in the first names (name lengths) of all the students in class. Here is the dot plot of the data they collected:
How many students are in the class?
Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.
How to know the number of students based on the dot plot?Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.
Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.
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Help me please I got an exam tomorrow
Answer:
Domain(-infinity,infinity) Range(-infinity,infinity) Zeros(0,0), (-4,0), (8,0) and (4,0) y-intercept at 0, even, y-axis, 2, -4
Step-by-step explanation:
qwtq4rg
Find the value of linear correlation coefficient r (statistics)
Answer:
r=1
Step-by-step explanation:
The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and weight are correlated (they will be - the taller people are, the heavier they're likely to be).
If g(q) = 2q-4 / q-A
and g(-3) = 2, what is the value of A?
Answer:
To find the value of A, we can substitute g(-3) = 2 into the given equation and solve for A.
g(q) = (2q-4) / (q-A)
2 = (2(-3)-4) / (-3-A)
Multiplying both sides by (-3-A), we get:
2(-3-A) = -10 - 2A
Expanding the left side, we get:
-6 - 2A = -10 - 2A
Adding 2A to both sides, we get:
-6 = -10
This is a contradiction, which means that there is no value of A that satisfies the given conditions. Therefore, the answer to the question is:
There is no value of A that satisfies the given conditions.
Triangle ABC is dilated to create triangle A'B'C'. If AB=12 and A'B'=9, what is the scale factor of the dilation?
If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.
The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.
In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:
So, scale factor = A'B'/AB,
Substituting the values,
We get,
Scale factor = 9/12,
Scale Factor = 3/4,
Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.
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Seven undergraduate students tagged A, B, C, D, E, F & G are to be allocated seven bed spaces in a hall in the University’s hostel. Student A doesnot want a bed next to student B because he is aware that student B snores. In how many ways can the bed spaces be allocated to them if the concern of student A is to be honoured?
By permutation and combination we can say there are 25200 ways to allocate the bed
What exactly are permanence and combination?Mathematical concepts like permutation and combination count the number of possible arrangements or choices for an object.
The quantity of possible arrangements of objects in a given order is referred to as a permutation.
Combination refers to the variety of possible selections of objects that are made without respect to their sequence.
The number of ways to distribute the seven students' beds in a way that ensures student A doesn't share a bed with student B is equal to the number of ways to distribute the six students' beds in a way that ensures student A doesn't share a bed with student B multiplied by two. (since there are two possible positions for student B).
The following formula can be used to determine how many options there are to distribute the six available beds among the students so that Student A does not have a bed next to Student B:
In this instance, seven students with the identifiers A, B, C, D, E, F, and G will each receive seven bed places in a dormitory at the university. Because he is aware that student B snores, student A does not want to share a bed with him. As a result, we can group students A and B together and arrange them in six different ways.
Then we can arrange the remaining students C, D, E, F and G in 5! ways. Therefore, the total number of ways to allocate bed spaces to them if the concern of student A is to be honored is 6! * 5! = 17,280 .
the bed spaces to seven students such that student A does not get a bed next to student B
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On their farm, Adam’s family maintains a storage that can hold 14.3 cubic yards (yd3) of grain. Use the fact that 1 yard is approximately equal to 0.9144 m to convert this volume to m3. Round your answer to the nearest hundredth. Do not type the units in the space below.
The storage can hold approximately 10.94 cubic meters of grain.
Unit conversion:
Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.
To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.
Here we have
Adam’s family maintains storage that can hold 14.3 yd³ of grain.
Given that 1 yard is approximately equal to 0.9144 meters
To convert cubic yards (yd³) to cubic meters (m³),
Use the conversion factor:
1 yd³ = (0.9144 m)³
So, we can convert 14.3 cubic yards of grain to cubic meters as follows:
14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³
Rounding this answer to the nearest hundredth gives us:
10.94 m³ rounded to the nearest hundredth = 10.94 m³
Therefore,
The storage can hold approximately 10.94 cubic meters of grain.
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Alan and his mom are planting vegetables in their garden. Alan has finished planting 4 rows of carrots so far and is planting new rows at a rate of 2 rows per hour. His mom has finished 7 rows of tomatoes and will continue planting at 1 row per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed? Write a system of equations, graph them, and type the solution.
Alan and his mom will each have completed 10 rows after 3 hours.
What do you mean by term Expressions ?An expression is a combination of numbers, variables, and/or operations (such as addition, subtraction, multiplication, division, exponents, and roots) that are grouped together to represent a value.
Let x be the number of hours it takes for Alan and his mom to have planted the same number of rows.
Alan will have planted 4 + 2x rows of carrots, and his mom will have planted 7 + x rows of tomatoes.
Setting these two expressions equal to each other gives:
4 + 2x = 7 + x
Solving for x, we get:
x = 3
Thus, after 3 hours, Alan will have planted:
4 + 2(3) = 10 rows of carrots
And his mom will have planted:
7 + (3) = 10 rows of tomatoes
Therefore, they will each have completed 10 rows of vegetables after 3 hours.
To graph these equations, we can plot them on a coordinate plane, where the x-axis represents the number of hours and the y-axis represents the number of rows planted.
Alan's equation is y = 2x + 4, and his mom's equation is y = x + 7.
The graph of these two equations intersect at the point (3, 10), which represents the moment when they have each planted 10 rows.
Therefore, Alan and his mom will each have completed 10 rows after 3 hours
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find the least common multiple of x^2-25 and x-5
Answer: The least common multiple is (x−5) (x−5)
Step-by-step explanation:
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
Use the following formula to find the correct answers: FV = PV. (1+i)"
You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years. How much money will you have by then?
O$677.23
O $746.93
$467.39
O $725.30
The savings amount balance in the account is $ 467.39
Given data ,
You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years.
Using the formula FV = PV * (1 + i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of periods, we can calculate the future value of the savings account after 15 years.
PV = $300 (the initial deposit)
i = 0.03 (the interest rate per period)
n = 15 years (the number of periods)
FV = $300 (1 + 0.03)^15
FV = $300 ( 1.5579 )
FV = $467.39
Hence , after 15 years, the savings account will have a balance of $ 467.39
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Which transformation would move Point A(-5, -2) to Quadrant IV? Mark all that apply.
To move Point A(-5, -2) to Quadrant IV, we need to apply one or more transformations that result in a reflection about the x-axis and/or a rotation of 180 degrees. The following transformations would move Point A to Quadrant IV:
Reflection about the x-axis: This transformation would change the sign of the y-coordinate, making it positive. So, the image of A after this transformation would be (−5, 2).
Rotation of 180 degrees about the origin: This transformation would change the sign of both the x and y-coordinates, making them positive. So, the image of A after this transformation would be (5, 2).
Therefore, either a reflection about the x-axis or a rotation of 180 degrees would move Point A to Quadrant IV.
Find the length of the third side. If necessary, round to the nearest tenth.
6 and 10
The length of the third side is 8units
What is Pythagoras theorem?Pythagoras theorem states that : the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
If a and b are the legs of the triangle and c is the hypotenuse,then
c² = a²+b²
For example , if a = 3 and b = 4 , then
c = √3²+4²
c = √ 9+16
c = √25
c = 5units.
Similarly, c = 10, a= 6, and b is unknown
therefore
10²= 6²+b²
b² = 10²-6²
b² = 100-36
b² = 64
b = √64
b = 8units
therefore the length of the third leg is 8units.
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Pleasee help me I donk know what is the answer for the white space
The row operation performed to obtain [0 0 -3 9] is R₃ - R₂.
What is row operation in matrix?A row operation in a matrix involves making a change to one or more rows of the matrix. The three elementary row operations are, interchanging rows, rows addition, and rows multiplication.
The given matrix;
[9 -2 -9 9] [9 -2 -9 9]
[1 2 -6 -1] into [1 2 -6 -1]
[1 2 -9 8] [0 0 -3 9]
If we perform R₃ - R₂, that is row 3 minus row 2, we will have the following;
[1 2 -9 8] - [1 2 -6 -1]
= [(1-1) (2-2) (-9 + 6) (8 + 1)]
= [0 0 -3 9]
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7: An entrance examination for a job consists of 25% English, 30% Mathematics, 25% computer and 20% accounting, and the passing mark is 45. If an applicant sat for the examination and scored 60% in English, 35% in Mathematics, 80% in computer and 50% in Accounting, do you think she will be accepted?
Answer: The overall score obtained is 55.5, which is higher than the passing mark of 45. Therefore, the applicant will be accepted.
Step-by-step explanation:To determine if the applicant will be accepted, we need to calculate their overall score based on the percentage weights and passing mark given for each subject.
The overall score can be calculated as follows:
Overall score = (0.25 x English score) + (0.3 x Math score) + (0.25 x Computer score) + (0.2 x Accounting score)
Substituting the given scores, we get:
Overall score = (0.25 x 60) + (0.3 x 35) + (0.25 x 80) + (0.2 x 50)
= 15 + 10.5 + 20 + 10
= 55.5
It’s similar figure with proportions
Answer:
x = 72 cm
Step-by-step explanation:
Because the two figures are similar, we can create a proportion between one set of similar sides (i.e., the side measuring 48 cm and the side measuring 6 cm) and another set (the side measuring x cm and the side measuring 9 cm. This, will allow us to solve for x:
[tex]\frac{6}{48}=\frac{9}{x}\\ 432=6x\\ 72=x[/tex]
Another way to solve would have been to notice that the scale factor used to create the bigger puzzle piece is 8 since 6 * 48. In order for the smaller figure to be considered similar to the larger, every side had to be multiplied by the same scale factor. Since the scale factor is 6, x must be 72 cm as 9 * 8 = 72
9. Which of the following functions represents a vertical shift of the function f(x) = x? a. f(x) = 2x b. f(x) = x + 5
c. f(x) = x2 d. none of the above 9.____________________
10. Which of the following functions represents a horizontal shift of the function f(x) = x2?
a. f(x) = (x+2)2 b.f(x) = 3x2
c. f(x) = x2 + 2 d. none of the above
b. f(x) = x + 5, which represents a vertical shift of 5 units upwards. f(x-a) = (x-a)^2, where a is a constant.
How to find the functions that represents a vertical shift9) The function f(x) = x represents a linear function with a slope of 1 and y-intercept of 0. To shift the graph vertically, we need to add or subtract a constant from the function. Thus, the function that represents a vertical shift of f(x) = x would be of the form f(x) = x + b, where b is a constant.
Out of the given options, the correct answer is b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.
10) To shift the graph of f(x) = x^2 horizontally, we need to add or subtract a constant inside the function, affecting the position of the vertex of the parabola. Thus, the function that represents a horizontal shift of f(x) = x^2 would be of the form f(x-a) = (x-a)^2, where a is a constant.
Out of the given options, the correct answer is a. f(x) = (x+2)^2, which represents a horizontal shift of 2 units to the left.
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9. Economists in the country of Flatland, a closed economy, have collected the following information about their economy for a particular year: Y=15,000; C=9,000; T=3,000; G=3,600. The economists also estimate that the investment function is I=3,900-100r, where r is the country’s real interest rate, expressed as a percentage.
Calculate private saving, public saving, national saving, investment, and the equilibrium real interest rate. Does the government of Flatland have a budget surplus or budget deficit?
Answer:
Private saving (Sprivate) is equal to disposable income minus consumption:
Sprivate = Y - T - C = 15,000 - 3,000 - 9,000 = 3,000
Public saving (Spublic) is equal to government revenue minus government spending:
Spublic = T - G = 3,000 - 3,600 = -600
National saving (S) is equal to the sum of private and public saving:
S = Sprivate + Spublic = 3,000 - 600 = 2,400
Investment (I) is given by the investment function:
I = 3,900 - 100r
Equating investment to national saving gives:
I = S
3,900 - 100r = 2,400
Solving for r:
r = 15%
Therefore, the equilibrium real interest rate is 15%.
Substituting r = 15% into the investment function gives:
I = 2,400
Therefore, investment is 2,400.
Finally, to determine if the government has a budget surplus or deficit, we need to calculate the government's budget balance, which is equal to government revenue minus government spending:
Budget balance = T - G = 3,000 - 3,600 = -600
Since the budget balance is negative, the government of Flatland has a budget deficit.
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
23098376=890754730.0%
Suppose that the production of plastic creates a social cost which is depicted in the graph above. Without any government regulation, how much plastic will be produced?
Suppose that the production of plastic creates a social cost which is depicted in the graph above. Without any government regulation, about 650 units of plastic will be produced. (Option C)
Why is this so?This is because, when the market forces are left to play out, competition drives efficiency upwards, which enable suppliers to produce at lower price thus offering consumers more quantity demanded for lower prices.
Hence, without government intervention, the unit produced will be 650 at the price of 7.
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Solve the equation for x -4X+3=11
Answer:
x = -2
Step-by-step explanation:
-4x + 3 = 11
Subtract 3 from both sides:
-4x = 8
Divide both sides by -4:
x = -2
HELPPPP !!
Mr. Olaffsen opened a sandwich shop and a smoothie stand in his neighborhood.
The following table and equation show function f, representing Mr. Olaffsen's profit, in dollars, x months since opening the sandwich shop.
__________________________________________________________________
x 1 2 3 4 5 6 7
f(x) 12,000 15,500 18,000 19,500 20,000 19,500 18,000
__________________________________________________________________
The following table and equation show function g, representing Mr. Olaffsen's profit, in dollars, x months since opening the smoothie stand.
__________________________________________________________________
x 1 2 3 4 5 6 7
g(x) 9,300 12,000 14,100 15,600 16,500 16,800 16,500
__________________________________________________________________
Select the true statement.
A.) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,000.
B.) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,500.
C. ) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,200.
D. ) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700.
The true statement is that the difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700. (option d).
To determine the maximum profit earned by each business, we need to find the vertex of each quadratic function. The vertex of a quadratic function of the form ax² + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the maximum value of the function.
The equations for the two functions are:
f(x) = -500x² + 9000x + 7500 g(x) = -500x² + 7500x + 4200
To find the vertex of f(x), we need to first rewrite the function in standard form:
f(x) = -500(x² - 18x - 15)
Completing the square, we get:
f(x) = -500(x - 9)² + 12000
So the vertex of f(x) is (9, 12000), which represents the maximum profit earned by the sandwich shop.
Similarly, to find the vertex of g(x), we rewrite the function in standard form:
g(x) = -500(x² - 15x - 8.4)
Completing the square, we get:
g(x) = -500(x - 7.5)² + 14100
So the vertex of g(x) is (7.5, 14100), which represents the maximum profit earned by the smoothie stand.
Finally, we can calculate the difference between the maximum profits earned by both businesses as:
12000 - 14100 = -2700
Therefore, the correct answer is option (d).
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Solve for x. Round to the nearest tenth, if necessary.
Using the sine ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Sine Ratio?The sine ratio is part of the trigonometry ratios that can be applied to solve a right triangle, and it is written as:
sin ∅ = length of the opposite side / length of the hypotenuse of the right triangle
We are given the following information from the image above:
Reference angle (∅) = 75 degrees
length of the opposite side = x
length of the hypotenuse = 9
Plug in the values:
sin 75 = x/9
9 * sin 75 = x
x = 8.7 [to the nearest tenth]
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