Scott starts with 25 plus the 100 from his grandfather making 125 then subtract 50 that he traded so you get 75
The table shows the profits (y) in millions of dollars for Buffalo Wild Wings for each year (x) from 2007 through 2013, where x=7 represents 2007.
Year x | Profits y
7 | 19.7
8 | 24.4
9 | 30.7
10 | 38.4
11 | 50.4
12 | 57.3
13 | 71.6
a.) sketch a graph
b.) use the slopes to determine the years in which the profits showed the greatest or least increases.
c.) find the equation of a line between 2007 and 2013
d.) interpret meaning of the slope and line from part (c) in the context of the problem
e) use the equation from part (c) to estimate the profit for Buffalo wild wings in 2017. Do you think that it is an accurate estimate. Explain.
a) See attached diagram.
b) The slope can be obtained by the formula:
[tex]m_i=\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i}.[/tex]
Now
[tex]m_1=\dfrac{24.4-19.7}{8-7}=4.7;[/tex][tex]m_2=\dfrac{30.7-24.4}{9-8}=6.3;[/tex][tex]m_3=\dfrac{38.4-30.7}{10-9}=7.7;[/tex][tex]m_4=\dfrac{50.4-38.4}{11-10}=12;[/tex][tex]m_5=\dfrac{57.3-50.4}{12-11}=6.9;[/tex][tex]m_6=\dfrac{71.6-57.3}{13-12}=14.3;[/tex]The greatest increases were from 2012 till 2013 years and the least increases were from 2007 till 2008 years.
c) Using graphing calculator, the equation of the line (black line in the diagram) is
[tex]y\approx 0.71x^2-5.58x+23.76.[/tex]
d) Since the slopes are different, this line is not straight. From the given data you can predict that the "best fit" is quadratic function.
e) In 2017, find
[tex]y(17)\approx 0.71\cdot 17^2-5.58\cdot 17+23.76\approx 134.09[/tex]
Answer:
Step-by-step explanation:
Perform the indicated operation.
1/3÷3/8
A) 1/8
B)8/9
C)1 1/8
1/3÷3/8
Multiply by reciprocal
1/ 3÷ 8/3
Now multiply across
1×8/3×3
Solve
8/9
Your answer is b .
REVIEW:
Numerator is the number on the top in a fraction. Denominator is the number at the bottom of a fraction.
[tex]\frac{1}{2} \rightarrow \frac{numerator}{denominator}[/tex]
Here is your equation:
[tex]\frac{1}{3} \div \frac{3}{8}[/tex]
When dividing fractions, you have to Keep, Change, then Flip.
[tex]Keep\ \frac{1}{3} \\ Change\ \div\ to\ \times \\ Flip\ \frac{3}{8} \rightarrow \frac{8}{3}[/tex]
Here is your new equation:
[tex]\frac{1}{3} \times \frac{8}{3}[/tex]
Multiply the numerators and denominators together:
[tex]\frac{1}{3} \times \frac{8}{3} = \frac{8}{9}[/tex]
Your answer is A. [tex]\frac{8}{9}[/tex]
If you have any questions, feel free to ask! :)
Mandana is ordering new tile for her kitchen floor. The area of the floor is 119.9 square feet, and she wants to order between 15% and 20% extra of the materials. Which of the following is a reasonable amount of tile for Mandana to order?
A.
134 square feet
B.
140 square feet
C.
137 square feet
D.
145 square feet
To find a reasonable amount of tile for Mandana to order, we need to calculate 15% and 20% of the area of her kitchen floor and add that to the original area. Therefore, options B and D can be considered as reasonable amounts of tile for Mandana to order.
Explanation:To find a reasonable amount of tile for Mandana to order, we need to calculate 15% and 20% of the area of her kitchen floor and add that to the original area.
15% of 119.9 square feet is 0.15 * 119.9 = 17.985 (approximately 18 square feet).
20% of 119.9 square feet is 0.20 * 119.9 = 23.98 (approximately 24 square feet).
Adding the additional tile to the original area, the reasonable amounts of tile for Mandana to order would be:
A. 119.9 + 18 = 137.9 square feet (approximately 138 square feet)B. 119.9 + 24 = 143.9 square feet (approximately 144 square feet)C. 119.9 + 18 = 137.9 square feet (approximately 138 square feet)D. 119.9 + 24 = 143.9 square feet (approximately 144 square feet)Therefore, both options B and D, which are 140 and 145 square feet respectively, can be considered as reasonable amounts of tile for Mandana to order.
Final answer:
To find a reasonable amount of tile for Mandana to order, calculate the range of 15% to 20% extra of the materials by multiplying the area of the floor by each percentage. Add the extra amount to the area of the floor to get the reasonable amount of tile to order.
Explanation:
To find a reasonable amount of tile for Mandana to order, we need to calculate the range of 15% to 20% extra of the materials she needs. First, we find the extra amount by multiplying the area of the floor by each percentage. The extra amount ranges from 17.985 to 23.98 square feet. Finally, we add the extra amount to the area of the floor to get the reasonable amount of tile to order, which ranges from 137.985 to 143.98 square feet. Therefore, option C (137 square feet) is a reasonable amount of tile for Mandana to order.
The table shows the side lengths and perimeters of four squares. Side Length (x) Perimeter (y) 4.5 18 8.5 34 10.25 41 13.75 55 Which equation represents the relationship between the side length, x, and the perimeter, y?
Answer:
The equation will be: [tex]y=4x[/tex]
Step-by-step explanation:
Side lengths[tex](x)[/tex] ⇒ 4.5 8.5 10.25 13.75
Perimeter [tex](y)[/tex] ⇒ 18 34 41 55
First we will pick any two ordered pairs in form of point like [tex](x,y)[/tex]. So, here [tex](x_{1}, y_{1})= (4.5, 18)[/tex] and [tex](x_{2}, y_{2})= (8.5, 34)[/tex]
Now, the slope will be: [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{34-18}{8.5-4.5}=\frac{16}{4}=4[/tex]
So, the equation using the point-slope form will be..............
[tex]y-y_{1}=m(x-x_{1})\\ \\ y-18=4(x-4.5)\\ \\ y-18=4x-18\\ \\ y=4x[/tex]
Thus, the equation that represents the relationship between the side length[tex](x)[/tex] and the perimeter[tex](y)[/tex] will be: [tex]y=4x[/tex]
Answer:
y=4x
Step-by-step explanation:
if <a and <b are vertical and <a =115°,detemine <b what is it??!
The vertical angles have equal measures.
Therefore, if ∠ a and ∠b are vertical angles, then m∠a = m∠b.
Answer: m∠b = 115°
Need help to Solve A=TX, for X
A=TX
Rewrite it
Tx=a
Divide t both sides to get x alone
Tx/t=a/t
Solve
X= a/t
2 1/2, 2.4,2.35,2 1/8 greatest to least
2 1/2
2.4
2.35
2 1/8
Exactly how you had it
The first term of an arithmetic sequence is -3 and the fifteenth term is 53 what is the common difference of the sequence
Solution
The 1st term = -3
15th term = 53
15th term = a + d(n-1)
53 = -3 + d(15- 1) [Here n = 15)
53 + 3 = d(14)
14d = 56
d = 4
The common difference is 4.
**PLEASE NEED HELP BADLY ASAP**
Minimum value is when x = 6 and y = -7
Answer
C) (6 , -7)
The minimum would be the lowest point of the line.
The lowest point in the picture is in the lower right hand corner which is located at (6,-7)
What is the value of the expression “eight more than three time the difference of four and a number” when n=3?
Hey there!!
Let's take the number as ' n '
Three times the difference of a four and number.
... 3 ( 4 - n )
Eight more than the expression.
... 8 + 3 ( 4 - n )
' n ' is given as ' 3 '.
Plugging in :
... 8 + 3 ( 4 - 3 )
... 8 + 3 ( 1 )
... 8 + 3
... 11
The required answer is 11.
Hope my answer helps!!
On Wednesday the high temperature was 7°C in the low temperature was -2°C. what is the temperature difference that day?
The difference is 9 degrees
whats the estimate of 1.537 times 242 and answer
Note that you are estimating.
Estimate each to the nearest whole number
Note that when rounding, look at the digit to the right of the one you want to round to. If the digit is 5 or greater round up, if 4 and lower, round down.
1.537 rounded to the nearest whole number is 2
2 x 242 = 484
484 is your answer
hope this helps
round 9 991 to the nearest thousands
9,990 first digit is like 1, then 10, then 100, then 1000 so the fourth digit being 1 goes to 0 when rounding
When rounding to the nearest thousand, you look at the following number to know if you go up or stay. In the case of 9,991:
9,991 If the 2nd largest digit is ≥ 5, then round up.
10,000
Therefore, you would round 9.991 to 10,000.
Hope this helps! :)
Edit: I literally solved for the wrong thing earlier lol; fixed it.
You and your mom enter a drawing with 3 different prizes. A total of 8 people entered the drawing, and prizes are awarded randomly.There are 336 ways to award the prizes.What is the probability that you win first prize and your mom wins second prize?
A. 8/336
B. 1/8
C. 6/336
D. 1/336
Answer: [tex]\frac{6}{336}[/tex]
Step-by-step explanation:
Given: The Number of different prizes = 3
The number of people entered the drawing room = 8
The number of ways to select for 3 prizes, such that you win first prize and your mom wins second prize = You × Mom × Rest of people
[tex]1\times1\times(8-2)=1\times6=6[/tex]
The total number of ways to award the prizes = 336
Therefore, the probability that you win first prize and your mom wins second prize=[tex]\frac{6}{336}[/tex]
a construction crew built 4 1/2 miles of Road and 3 3/8 days. What is the unit rate in miles per day? Write your answer as a fraction or mixed number in simplest form.
The construction crew took [tex]3\frac{3}{8}[/tex] days to build [tex]4\frac{1}{2}[/tex] miles of road.
Therefore, in 1 day, the crew built [tex]\frac{4\frac{1}{2} }{3\frac{3}{8} }[/tex] miles of road
= [tex]\frac{\frac{9}{2} }{\frac{27}{8} } =\frac{9}{2}times\frac{8}{27}=\frac{4}{3}[/tex] miles of road
Thus, the required rate is [tex]\frac{4}{3}[/tex] miles or [tex]1\frac{1}{3}[/tex] miles per day.
In a recent year 22% of email users said they spend less time using email because of spam what fraction of email users is this
Answer:
22/100 divided by 2 equals 11/50
Step-by-step explanation:
22/100=11/50
22/100=22%
22/100=0.22
George claims that he is 3 years less than 3 times as old as his niece Pam will be one year from now. Let p= Pam’s age now. Write an expression to represent George’s age. Then simplify the expression.
G = George's age
G = 3(P+1) - 3
G = 3P + 3 - 3
G = 3P
The ratio of chocolate cookies to sugar cookies in a bakery box is 2:1. What is the ratio of sugar cookies to total cookies?
What is the pattern rule for this pattern 5-8-14-23-55?
Final answer:
The sequence 5-8-14-23-55 does not follow a clear linear or geometric pattern rule based on the differences between its terms. A simple pattern is not evident, and more context is required to determine if there's a complex rule or an error with the given numbers.
Explanation:
The sequence provided, 5-8-14-23-55, does not have a clear linear or geometric progression that is immediately evident. To determine the pattern rule, we need to look at the differences between successive terms:
8 - 5 = 3
14 - 8 = 6
23 - 14 = 9
55 - 23 = 32
The differences between the first few terms are incremental by 3, but the last increment does not follow this progression. Therefore, there is no single common pattern rule applicable to the entire sequence given. If more context or additional numbers in the sequence are provided, it may be possible to discern a more complex rule or recognize if the last term is an error.
How many 3/4 cup servings of trail mix are in a 8 cup bag?
Diana sold 336 muffins at the bake sale bob sold 287 muffins. Bob estimates that he sold 50 fewer muffins than Diana. How did he estimate? Explain
he subtracted both numbers and got 49
The sum of two numbers is 125. Five times one number minus three times the other is 41. Determine the numbers using one single variable
To find the two numbers, we can assign a variable and set up an equation based on the given information. By solving the equation algebraically, we can determine that the two numbers are 52 and 73.
Explanation:To solve this problem, we can assign a variable to one of the numbers.
Let's say the first number is x.
Then, the second number would be 125 - x, since the sum of two numbers is 125.
Next, we can set up an equation with the given information: 5x - 3(125-x) = 41.
Simplifying this equation, we get 5x - 375 + 3x = 41.
Combining like terms, we have 8x - 375 = 41.
Adding 375 to both sides, we get 8x = 416. Finally, dividing both sides by 8, we find that x = 52. Therefore, the two numbers are 52 and 73 (125-52).
Learn more about Algebra here:https://brainly.com/question/24875240
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What is the value of f(-3)
F(x)={ -2 if x<-3
4x if -3 _^< x _^<-1
X^2 if x >-1
[tex]f(x)=\left\{\begin{array}{ccc}-2&if&x < -3\\4x&if&-3\leq x\leq-1\\x^2&if&x > -1\end{array}\right\\\\-3\leq-3\leq-1\to f(x)=4x\\\\f(-3)=4(-3)=-12[/tex]
I know the answer to the problem 94x27=2538 but can't figure out how to show my work in core math.
94*27=2538
90*20+4*7+20*4+90*7=2538
1800+28+80+630=2538
2538=2538
which equations are equal to x+x+x+2
x times 3 plus 2: answer
Which expression is equal to f(x) + g(x)
Answer.
The Answer is C.
Which product is negative?
−2⋅(−4)⋅8⋅(−1)
−7⋅(−3)⋅(−5)⋅(−8)
−3⋅(−4)⋅(−9)⋅0
6⋅(−2)⋅(−3)⋅1
When I had these kinds of problems, I'd count how many negatives there were. If there more or less negatives to positives, then it is negative. If there's the same amount of positives and negatives, then it's positive since they cancel out! The answer to this is A. (-2)(-4)(8)(-1)=-64.
In mathematics, the product −2⋅(−4)⋅8⋅(−1) is negative. This occurs because it has an odd number (three) of negative numbers being multiplied, leading to a negative product. The other options will give either a positive product or zero.
Explanation:In the realm of mathematics, when we multiply equal numbers of positive and negative values, we arrive at positive products. However, when we multiply an unequal number of positive and negative values, the product is negative. Let's apply this rule to the given products:
−2⋅(−4)⋅8⋅(−1): It contains three negative numbers, hence product will be negative.−7⋅(−3)⋅(−5)⋅(−8): It contains four negative numbers, hence product will be positive.−3⋅(−4)⋅(−9)⋅0: As one of the numbers is zero, the product will be zero.6⋅(−2)⋅(−3)⋅1: It has two negative numbers, so the product will be positive.
Among the provided choices, only the first product, −2⋅(−4)⋅8⋅(−1), will yield a negative product.
Learn more about the Multiplication of Positive and Negative Numbershttps://brainly.com/question/32838038
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Gavin is thinking of a number.8 more than the product of 7 and the number is 120. find the number.
7x + 8 = 120
Subtract 8 from both sides.
7x = 112
Divide both sides by 7.
x = 16
an employee is marking up new merchandise by 35%. the price they paid for an item is $120. what price will the employee place on the item?
A:$150
B:$155
C:$165
D:$162
please show work thank you!
What is the perimeter of a triangle with sides 14 in 8 in and 16 in in length
Answer: The answer to this question is 38 in.
Step-by-step explanation: All we have to do here is to add all the sides and here's the formula P=s+s+s where s stands for side. We substitute in the values P= 14+8=16 and the result is P= 38 in. Hope this helps!