Answer:
After 10 months, both salespersons will sell 160 cars.
Step-by-step explanation:
We are given two different salesperson's statistics of sales. We can use this information to set up a system of equations and solve for our variable.
Let us name the first salesperson Person 1 and the other salesperson Person 2.
Person 1 sells 30 cars this year and sells an average of 13 cars a month.We can represent this with a linear equation (form of y = mx + b) to see the linear relationship at which they sell cars.Because they sell an average of 13 cars each month, this is a recurring amount. Therefore, this is m, or our slope.Because they've already sold 30 cars this year, this is our y-intercept, or b, a.k.a. our starting point of sales.Therefore, we are able to set up the equation for Person 1. This equation is [tex]\text{y = 13x + 30}[/tex].Now, for Person 2:
Person 2 sells an average of 11 cars per month and has sold 50 cars already this year.Their sales can be represented the same way - with a linear equation. Therefore, their sales are modeled with the slope-intercept form of an equation of a line (y = mx + b).Considering they have already sold 50 cars, this is where their average sales would start. Therefore, 50 is the y-intercept, or b, of our equation.Since they sell an average of 11 cars per month, they increase their sales by 11 each month. This means that because their sales rise, this is our slope, or m, of our equation.With this information, our equation becomes [tex]\text{y = 11x + 50}[/tex].Now, because we have these equations, we can set up a table that will determine the number of months that will elapse before the salespersons will sell the same amount of cars.
For Person 1, the equation will be the increase of the y-value by 13 cars after an initial sale of 30 vehicles. Therefore, we can create a table of values.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 30 \\ \cline{1-2} 1 & 43 \\ \cline{1-2} 2 & 56 \\ \cline{1-2} 3 & 69 \\ \cline{1-2} 4 & 82 \\ \cline{1-2} 5 & 95 \\ \cline{1-2} 6 & 108 \\ \cline{1-2} 7 & 121 \\ \cline{1-2} 8 & 134 \\ \cline{1-2} 9 & 147 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]
For Person 2, we can use the same formatting to create a table. However, the rule changes - we must start at 50 cars being sold and increase it by only 11 cars a month.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 50 \\ \cline{1-2} 1 & 61 \\ \cline{1-2} 2 & 72 \\ \cline{1-2} 3 & 83 \\ \cline{1-2} 4 & 94 \\ \cline{1-2} 5 & 105 \\ \cline{1-2} 6 & 116 \\ \cline{1-2} 7 & 127 \\ \cline{1-2} 8 & 138 \\ \cline{1-2} 9 & 149 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}[/tex]
Now, we need to see where the y-values are the same in both tables. We can see that we have a value of (10, 160) in both tables, so after 10 months, the salespersons will sell the same amount of cars.
There is an alternative method of solving the problem that is much quicker and will require much less work.
We are given two equations that are both equal to y. Therefore, we can set them equal to each other (dropping the y) and solving for x.
Our value of x will be the amount of months in which the sales are equal.
[tex]\displaystyle{13x+30=11x+50}\\\\2x + 30 = 50\\\\2x = 20\\\\\boxed{x = 10}[/tex]
Therefore, after 10 months of sales, the salespersons will have sold the same amount of cars. We can plug this information into one of the equations to see how many cars will be sold at that point.
[tex]y = 13(10) + 30\\\\y = 130 + 30 \\\\y = 160[/tex]
In 10 months, 160 cars will be sold. If we set the equations equal to each other and substitute x, we should get a true statement.
[tex]13(10)+30=11(10)+50\\\\130 + 30 = 110 + 50\\\\160 = 160[/tex]
Because we get a true statement, each salesperson will sell 160 cars after 10 months of initial sales.
URGENT URGENT helppps plz
Answer:
1) Bigger sector = 168.8pi
1) Smaller sector = 56.3pi
2) Bigger sector = 529.9
3) Smaller sector = 176.6
Step-by-step explanation:
1) Bigger sector = [tex]\frac{270}{360}[/tex]×pi×15×15
= 168.75pi
1) Smaller sector = [tex]\frac{360-270}{360}[/tex]×pi×15×15
= [tex]\frac{90}{360}[/tex]×pi×15×15
= 56.25pi
2) Bigger sector = [tex]\frac{270}{360}[/tex]×3.14×15×15
= 529.875
2) Smaller sector = [tex]\frac{360-270}{360}[/tex]×3.14×15×15
= [tex]\frac{90}{360}[/tex]×3.14×15×15
= 176.625
130 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The
(incomplete) results are shown below:
Cumulative Frequency
# of times floss per week
0
1
12
Frequency
12
21
13
Relative Frequency
0.0923
0.1615
0.1
0.1385
33
2
46
64
20
0.1538
100
0.1308
117
0.1
130
Answer:
a. The answers obtained are as follows:
Frequency for flossing 7 times per week = 24
Relative frequency for flossing 4 times per week = 0.1231
Cumulative Frequency at flossing 1 time per week = 22
b. The Cumulative Relative Frequency at flossing 7 time per week is 100%.
Step-by-step explanation:
Note: This question is not complete and the data in it are merged together. The complete question is therefore provided with the sorted data before answering the question. See the attached pdf file for the complete question.
The explanation to the answers is now provided as follows:
a. Complete the table (Use 4 decimal places when applicable)
Note: See part a of the attached excel for the complete table (answers are in bold red color)
Frequency is the rate at which something or an event occurs in a particular sample.
Since we already have frequency for others flossing times per week and we have 130 adults as the sample, the frequency for flossing 7 times per week is calculated by deducting the frequencies of others from 130 as follows:
Frequency for flossing 7 times per week = 130 – 10 – 12 – 14 – 18 – 16 – 21 – 15 = 24
Relative Frequency refers to the fraction of times an event occurs. The relative frequencies in this question are calculated by dividing each frequency by the total number of adults in the sample, i.e. 130. The relative frequency for flossing 4 times per week is therefore calculated as follows:
Relative frequency for flossing 4 times per week = Frequency for flossing 4 times per week / Total number of adults in the sample = 16 / 130 = 0.1231
Cumulative Frequency is calculated by adding the current frequency to the previous Cumulative Frequency. The Cumulative Frequency at flossing 1 time per week is therefore calculated as follows:
Cumulative Frequency at flossing 1 time per week = Cumulative Frequency at flossing 0 time per week + Frequency at flossing 1 time per week = 10 + 12 = 22
b. What is the cumulative relative frequency for flossing 7 times per week? %
Note: See part b of the attached excel for the complete table (answer is in bold red color)
The cumulative relative frequency refers to the accumulation of the previous relative frequencies.
Cumulative Relative Frequency is calculated by adding the current relative frequency to the previous Cumulative Relative Frequency. It should be noted that the first cumulative relative frequency equal to the first relative frequency.
The Cumulative Relative Frequency at flossing 7 time per week is therefore calculated in the attached excel file as follows:
Cumulative Relative Frequency at flossing 1 time per week = Cumulative Relative Frequency at flossing 6 times per week + Relative Frequency at flossing 7 times per week = 0.8154 + 0.1846 = 1.0000
Since the question indicates that the Cumulative Relative Frequency at flossing 7 time per week should be stated in percentage term, we therrefore have:
Cumulative Relative Frequency at flossing 7 time per week = 1.0000 * 100 = 100%.
What are the x-intercept and y-intercept of the graph of y=−12x+4? please answer asap will give brainliest
Answer:
x= 1.16 y=14 ...........
Answer:
x intercept= -1/2
y intercept= 4
Step-by-step explanation:
its easy, the answers are in the equation- y=−1/2x+4
Use A Diagram To Show That (3x+1)(x+2) Is Equivalent To 3x2+7x+2. Show Your Work.
Is (x+4) Equivalent To 2x2+8x+8? Explain Or Show Your Reasoning.
Answer:
1) Please find attached the diagram showing the answer to the question
The area of the diagram is (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
2) When x = 1, (1 + 4)² = 25 ≠ 2 × 1² + 8 × 1 + 8 = 18
Therefore, (x + 4)² is not equivalent to 2·x² + 8·x + 8
Step-by-step explanation:
1) In the attached diagram, we have;
For x = 1
(3x + 1)(x + 2) = (3 + 1)(1 + 2)
Therefore, the length of the sides of the rectangle are;
Height = 4, and Width = 3
For x = 1, x² = 1² = 1
∴ 3·x² = 3, 7·x = 7 × 1 = 7, and 2 = 2
Therefore, from the diagram, we have;
The area = (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
The diagram for when x = 3 is also included
2) For (x + 4)², we have;
When x = 1, (x + 4)² = (1 + 4)² = 25
However;
When x = 1, 2·x² + 8·x + 8 = 2 × 1² + 8 × 1 + 8 = 18
Therefore;
(x + 4)² is not equivalent to 2·x² + 8·x + 8
1) Please find attached the diagram showing the answer to the question
The area of the diagram is (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
2) When x = 1, (1 + 4)² = 25 ≠ 2 × 1² + 8 × 1 + 8 = 18
Therefore, (x + 4)² is not equivalent to 2·x² + 8·x + 8
Step-by-step explanation:
1) In the attached diagram, we have;
For x = 1
(3x + 1)(x + 2) = (3 + 1)(1 + 2)
Therefore, the length of the sides of the rectangle are;
Height = 4, and Width = 3
For x = 1, x² = 1² = 1
∴ 3·x² = 3, 7·x = 7 × 1 = 7, and 2 = 2
Therefore, from the diagram, we have;
The area = (3x + 1)(x + 2) = 3 dark green squares + 7 light green squares + 2 Plain squares
∴ (3x + 1)(x + 2) = 3·x² + 7·x + 2
The diagram for when x = 3 is also included
2) For (x + 4)², we have;
When x = 1, (x + 4)² = (1 + 4)² = 25
However;
When x = 1, 2·x² + 8·x + 8 = 2 × 1² + 8 × 1 + 8 = 18
Therefore;
(x + 4)² is not equivalent to 2·x² + 8·x + 8
Answer: 1) Please find attached the diagram showing the answer - 1
Answer: 1) Please find attached the diagram showing the answer - 1
Answer: 1) Please find attached the diagram showing the answer - 2
Explore all similar answers
Your Local grocery store is having a special on soda. They're selling a 12-pack of 12-oz cans for $4.75. The 20-oz bottles are also on sale for $0.90. Should "you" buy one 12-pack of 12-oz cans or seven 20-oz bottles?
Answer:
12 pack
Step-by-step explanation:
Buying 12-pack of 12-oz cans will be the better choice.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given here , pack of 12 oz cans at $4.75 and hence volume of such 12 packs = 12 × 12 = 144 oz
and seven 20 oz bottles at $ 6.3 the volume is = 20 × 7 = 140 0z
Hence clearly 12-pack of 12-oz is the better choice
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
Explain what is happening at this step in the solving equation process.
1. 10 − 6 x = 4 + 5 x
2. 7-6x=1+5x
Answer:
1. After solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]
2. After solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]
Step-by-step explanation:
We need to Solve the equations.
1. [tex]10 - 6 x = 4 + 5 x[/tex]
Step 1: Subtract 5x on both sides
[tex]10 - 6 x-5x = 4 + 5 x-5x\\10-11x=4[/tex]
Step 2: Subtract 10 on both sides
[tex]10-11x-10=4-10\\-11x=-6[/tex]
Step 3: Divide both sides by -11
[tex]\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}[/tex]
So, after solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]
2. [tex]7-6x=1+5x[/tex]
Step 1: Subtract 5x on both sides
[tex]7 - 6 x-5x = 1 + 5 x-5x\\7-11x=1[/tex]
Step 2: Subtract 7 on both sides
[tex]7-11x-7=1-7\\-11x=-6[/tex]
Step 3: Divide both sides by -11
[tex]\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}[/tex]
So, after solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]
Terry says, “I have 8 cousins."
Rita
says, “Then
you have one less than three times as many as I do." How
many cousins does Rita have?
Answer:
Rita has three cousins.Step-by-step explanation:
We must reverse this operation in order to solve it.
First, add one cousin to 8.
8 + 1 = 9.
Then, divide 9 by 3.
9 / 3 = 3.
Rita has three cousins.m = ab + 3c Solve for a
Answer:
[tex]\frac{M-3c}{b}=a[/tex]
Step-by-step explanation:
[tex]M=ab+3c\\M-3c=ab\\\frac{M-3c}{b}=a[/tex]
Answer:
[tex]\frac{m - 3c}{b} = a[/tex]
Step-by-step explanation:
m = ab + 3c
-3c - 3c
m - 3c = ab
[tex]\frac{m - 3c}{b} = \frac{ab}{b}[/tex]
[tex]\frac{m - 3c}{b} = a[/tex]
Helps me solve this problem please
Answer:
0,2
Step-by-step explanation:
Anyone know if so help please
|\SERIOUS/|
ive been feeling down for multiple days now and i just feel like giving up like i try and people say i can do more so i try harder and they keep saying i can do more and i feel like so much would be better in life if i wasnt on this planet (mars sounds good(: ) and there would be so much less stress and less anxiety in my house without me and everything i touch i either mess up or break and i cant do anything right ever and i try and try and try and try but nothing ever goes right and so im just giving up im not going to be posting for a while so this is the last post for the year maybe
Answer:
Do not post random subjects in mathematics.
Also, pain is temporary.
If you end your life you just pass it onto someone else.
Try to find people online that understand you. The reason why you can't do anything is because you keep telling yourself that. This sounds cringe but try new things and venture. Try meditation or yoga. If you aren't an open person then you can do breathing exercises in private. While you take in your breath think positively. I hope this advice can help you! Never give up!
Answer:
no
Step-by-step explanation:
PLEASE PLEASE HELP.
Answer:
120 square feet
Step-by-step explanation:
they are similar so they are in a ratio 20/10=2 so smaller triangle is twice the larger one 6×2=12ft
area of triangle =1/2×base×height
=1/2×20×12
=120 square feet
a corner self is 1/4 of a circle and has the radius of 10.5 inches. enter the area of the self in square inches. can you round it to nearest hundredth?
Answer:
The area of the shelf is 86.59 square inches
Step-by-step explanation:
The formula of the area of the circle is A = π r², where
r is the radius of the circle∵ The corner shelf is [tex]\frac{1}{4}[/tex] of a circle
→ That means its area is [tex]\frac{1}{4}[/tex] the area of the circle
∴ The area of the corner shelf = [tex]\frac{1}{4}[/tex] × area of the circle
∵ Area of the circle = π r²
∴ The area of the corner shelf = [tex]\frac{1}{4}[/tex] × π r²
∵ The radius of the shelf is 10.5 inches
∴ r = 10.5 inches
→ Substitute the values of r in the formula of the area
∴ The area of the corner shelf = [tex]\frac{1}{4}[/tex] × π × (10.5)²
∴ The area of the corner shelf = 86.59014751
→ Round it to the nearest hundredth
∴ The area of the corner shelf = 86.59 square inches
∴ The area of the shelf is 86.59 square inches
What is a question that could be used to collect categorical data??
Dale will run at most 29 miles this week. So far, he has run 17 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.
Answer:
17+t=19
Step-by-step explanation:
there u go buddy :(
A ring was thrown 12 feet up in the air. After falling back down to the pool level it went 5 feet under that water. How far did the ring travel
Answer: 17 feet
Step-by-step explanation:
y-2 = -3(x + 6), write the equation of the line in slope intercept form.
Answer: y=-3x-16
Step-by-step explanation:
Slope-intercept form is y=mx+b, where m is slope and b is y-intercept.
y-2=-3(x+6) [distribute]
y-2=-3x-18 [add both sides by 2]
y=-3x-16
Now, we see that the equation above matches the slope-intercept form equation. You can see that m=-3 and b=-16.
Bonus (3 points)
Graph the parabola using the indicated information (you may NOT use decimals) You must show all work to
receive credit.
y = 2^2 + 17x +30
a. equation of the axis of symmetry
b. coordinates of the vertex
c. calculate the coordinates of the x-intercepts
Answer:
c
Step-by-step explanation:
Which of the following shows a translation of f(x) two units to the right?
f(x + 2)
f(x - 2)
f(x) - 2
f(x) + 2
Answer:
f(x-2)
Step-by-step explanation:
This is because f(x)-2 or f(x)+2 is moving it up or down and f(x+2) seems like it would be the right answer but it is reversed when it's in parenthesis so it would actually be moving 2 to the left.
Answer:
its f (x-2)
Step-by-step explanation:
i got this on my quiz and i got it right! i hoped this helped!!!
For exercises 4-6, use the imaginary unit to write an equivalent expression for
the radicals.
Just number 4 and 6
32x+8+5=113 2x+8 +5=11 simplify in radical form
Answer:
The answer is in the picture below
Step-by-step explanation:
5. A girl is told to buy some melons and oranges. Melons are 50c each and oranges 25c each, and she has $2 to spend. She must not buy more than 2 melons and she must buy at least 4 oranges. She is also told to buy at least 6 fruits all together.
Let x be the number of melons
Let y be the number of oranges.
a) Write down four inequalities which must be satisfied.
b) Draw a graph and use it to list the combinations of fruit that are open to her.
Answer:
a) The four inequalities are;
1) x ≤ 2
2) y ≥ 4
3) x + y ≥ 6
4) 0.5 × x + 0.25 × y ≤ 2
b) The limits of the combinations of fruits that are opened to her, derived using the Chart function on Microsoft Excel are;
1) (0, 8) which is 0 melons and 8 oranges
2) (0, 6) which is 0 melons and 6 oranges
3) (2, 4) which is 2 melons and 4 oranges
Step-by-step explanation:
The price per Melon = 50c = $0.5
The price per orange = 25c = $0.25
The amount she has to spend = $2
The number of melons she must buy ≤ 2
The number of oranges she must buy ≥ 4
The total number of fruits she should ≥ 6
Let x be the number of melons
Let y be the number of oranges
a) The four inequalities are;
1) x ≤ 2
2) y ≥ 4
3) x + y ≥ 6
4) 0.5 × x + 0.25 × y ≤ 2
b) Please find attached the required graph of the combination of fruits the girl buys created with Microsoft Excel
The combinations of the vertices of the feasible combinations that are opened to her, obtained from the creation of the combined graph, using Microsoft Excel are;
1) (0, 8) which is 0 melons and 8 oranges
2) (0, 6) which is 0 melons and 6 oranges
3) (2, 4) which is 2 melons and 4 oranges
the average American uses 83 gallons of water every day. of you lived in Africa you lived in Africa you would have to walk to collect this water and carry it home. It takes 3 hrs to collect 5 gallons of water.how many hrs to collect 83 gallons of water? round answer to 1 place decimal.
Answer:
50g
Step-by-step explanation:
83g
3hrs=5g
83/5=16.6
16.6x3=49.8=50g
CAUSE EFFECT Desire to turn U.S. citizens against Germany Which of the following government agencies would complete the chart? War Industries Board Selective Service Act The National War Labor Board Committee of Public Information
Answer:
Committee of Public Information
Step-by-step explanation:
The correct answer in the cause to turn US citizens against Germany should be the Committee of Public Information which was created in World War I.What is the bottom one? One in blue? Please help worth a lot of points.
Step-by-step explanation:
it's blurry i can't clearly see
Answer:
-7/8
Step-by-step explanation:
change the denominator and numerator of -1/2 by multiplying both by 4.
Then you get -4/8 instead of -1/2. This allows you to then subtract the -3/8 with -4/8 which equals -7/8.
Divide. Express your answer in simplest form.
8 divided by 2 4/9
Answer:
Step-by-step explanation:
8 ÷ 2 4/9
36/11 or 3 3/11 or 3.27
Answer:
In exact form it is 36/11. In decimal form it is 3.277777 going on forever. And last is mixed number form 3 3 11.
Step-by-step explanation:
Please help me
Excellent help needed
Answer:
All of the following have the same solution except b + 2 = 8
Answer:
the answer is D.
Step-by-step explanation:
A. [tex]50 = 5 m = 10=m[/tex]
B. [tex]x-6=4 = x=10[/tex]
C. [tex]w/5=2 = w=15[/tex]
D. [tex]b+2=8 = b=6[/tex]
hope this helps and feel free to give brainiest
which equation is a point slope form equation for line AB? y+1=−32(x−4) y+1=32(x−4) y+1=−23(x−4) y+1=23(x−4) A graph with a line running through point A, with coordinates (4, -1), and point B, with coordinates (-2, 3)\]
Answer:
3
Step-by-step explanation:
Dan earns £8.80
per hour. How much will he earn for 7 hours work
Answer:£61.6 in 7 hours
Step-by-step explanation:
£8.80*7=£61.6
Answer the following parts asked.
Answer:
[tex]f(n) = 15 + (n + 1)[/tex]
Step-by-step explanation:
Tina earns $15 every week when she mows the lawn.
We would put $15 because she earns $15 every week.
She earns 15 every week, so we would put (n + 1).
Our final answer would be [tex]f(n) = 15 + (n + 1)[/tex]
Answer:
The explicit rule is:
[tex]f(n)=60+15(n-1)[/tex]
After 15 week, Tina will have $270 in her savings account.
Step-by-step explanation:
Let’s write down our sequence so we can see it better.
For the first week (i.e. the first term), Tina has $60.
For the second week (i.e. the second term), Tina has $75.
And for the 3rd, 4th, 5th, and 6th week, Tina has $90, $105, $120, and $135, respectively.
Therefore, we can write the following sequence:
60, 75, 90, 105, 120, 135...
Note that our initial term a is 60.
And our common diffference will be 15.
Let’s find the explicit rule. The standard format for an explicit rule is:
[tex]f(n)=a+d(n-1)[/tex]
Where a is the initial term and d is the common difference.
Let’s substitute 60 for a and 15 for d. Hence, our explicit formula is:
[tex]f(n)=60+15(n-1)[/tex]
So, to find the amount Tina will have in her savings account in 15 weeks, we will substitute 15 for n and evaluate. So:
[tex]f(15)=60+15(15-1)[/tex]
Evaluate:
[tex]\begin{aligned} f(15)&=60+15(14) \\ f(15)&=60+210 \\ f(15)&=270 \end{aligned}[/tex]
Hence, after 15 weeks, Tina would have $270 in her savings account.