Answer:
312
Step-by-step explanation:
A car salesperson has already sold 30 cars this year. He sells an average of 13 cars per month. Another salesperson has already sold 50 cars this year. She sells an average of 11 cars per month. After how many months will the salespeople have sold the same number of cars?
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.
Choose the slope and y-intercept that
correspond with the graph.
GUYS HELP! IS THIS CORRECT???
ILL MARK YOU BRAINIEST!
Answer:12
Step-by-step explanation:
it’s 12 because 4 x 3 = 12
Answer:
48π units³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius of the base and h the height )
Here r = 4 and h = 3 , thus
V = π × 4² × 3
= π × 16 × 3
= 48π units³ ← exact answer
By 10 a.m., Andrew has read 85% of his emails he received on Tuesday. If Andrew received 40 emails, how many emails has he read so far?
Answer: 35
Step-by-step explanation: 85% of 40 basically you multiply 0.85 by 40 :)
If k(x) = x^2 and p(x) = k(x) + n, what is the value of n?
Pleaseee help ASAP!
I will give brainliest :)
Answer:
The value of n is -6
Step-by-step explanation:
If the function f(x) is translated k units up, then its image is g(x) = f(x) + kIf the function f(x) is translated k units down, then its image is g(x) = f(x) - kThe vertex form of the quadratic function is f(x) = a(x - h)² + k, where a is the coefficient of x² and (h, k) is the vertex∵ k(x) = x²
→ Its graph is a parabola with vertex (0, 0)
∴ The vertex of the prabola which represents it is (0, 0)
∵ The given graph is the graph of p(x)
∵ Its vertex is (0, -6)
∴ h = 0 and k = -6
∵ a = 1
→ Substitute them in the form above
∴ p(x) = 1(x - 0)² + -6
∴ p(x) = x² - 6
→ Substitute x² by k(x)
∴ p(x) = k(x) - 6
∵ p(x) = k(x) + n
→ By comparing the two right sides
∴ n = -6
∴ The value of n is -6
Look at the attached figure for more understanding
The red parabola represents k(x)
The blue parabola represents p(x)
The value of the n is -6.
Equation of a parabolay = a(x-h)2 + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to usk(x) = x^2
p(x) = k(x) + n
Substitutionsubstituting the value of k(x) in p(x).p(x) = k(x)+n
p(x) = x² + n
ComparingComparing with the Equation of a parabola,
y = a(x-h)2 + k
p(x) = x² + n
Therefore, the value of n is k which is the y coordinate of the vertex of the parabola.
Coordinates of the vertex of the parabolaLooking at the coordinates of the vertex of the parabola,
(h, n) = (0, -6)
Hence, the value of the n is -6.
Learn more about Parabola:
https://brainly.com/question/4443998
1 + b/2 = 19, b = ____?
Answer:
b = 8.5
Step-by-step explanation:
hope this halps ya!
For #11, make sure you answer all parts of the question.
11) The converse of an “if-then” statement reverses the “if” and “then” parts. The converse of a true “if-then” statement may or may not be true.
Write the converse of each true statement below and tell whether it is true or false. If it is false, give a counterexample.
If a polygon is a parallelogram, then it has four sides.
If Gil lives in France, then he lives in Europe.
If a parallelogram has four congruent angles, then it is a rectangle.
If two circles have the same diameter, then they are congruent.
If Daphne has the flu, then she is ill.
Write a true “if-then” geometry statement for which the converse is true. Give the converse.
Write a true “if-then” geometry statement for which the converse is false. Give the converse. Prove the converse is false by giving a counterexample.
1. When one-half of a number is subtracted
from its thrice, it gives 2500. Find the
number.
Answer:
let the number be x
thrice of the number=3x
one-half of the number=(1/2)x
so from the expression we:
3x-x/2=2500
(6x-x)/2=2500
6x-x=2*2500
5x=5000
x=5000/5
x=1000
Pleaseee someone resolve this quick!!!!!!
please help me........please:)
Step-by-step explanation:
2/3 x 2/2 = 4/6
2/3 x 3/3 = 6/9
2/3 x 4/4 = 8/12
At the beach, you would like to fill 5 buckets with seashells. You have
8 minutes to do so. If you set a steady pace, how much of a bucket
should you fill in each minute?
A. bucket
2nter your text here
B. bucket
c. bucket
The CD Warehouse is having a clearance sale. A CD player that originally sells for $60 is now priced at $36. What is the percent decrease in the price?
Answer: 24
Step-by-step explanation:
i did the problem and got it right
ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (2, 2), B = (4, 3), and C = (6, 3), what is the length of ?
Answer:
Fourth option is correct. The length of B'C' is 1 unit.
Step-by-step explanation:
The vertices of triangle ABC are A = (2, 2), B = (4, 3), and C = (6, 3).
Distance formula:
The length of BC is 2 units.
It is given that ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′.
It means the ΔABC and ΔA′B′C′ are similar and corresponding sides of ΔA′B′C′ and ΔABC are proportional.
The scale factor is 0.5.
Therefore the length of B'C' is 1 unit and fourth option is correct
Answer:
D= 1 unit
Step-by-step explanation:
If 18 meters of high-resistance wire with a diameter of 1.2 mm has a resistance of 10 ohms, what is the resistance of 27 m of the same type of wire with a diameter of 1.5 mm?
Please help me! Im making the first correct answer brainliest!
Answer:
The answer is most likely c.)
Step-by-step explanation:
It says that they sold 40 scarves and hats at the Winter Festival, but it never told us exactly how many hats total and how many scarves total that they sold. So we leave it as "s+h=40" Next we have the price of the scarves and hats, not the numbers sold. Since the scarves cost $18 and the hats cost $14, we know that a certain amount of each equals $700. Since we don't know the exact number of each that were sold, we leave it at "18s+14h=700." Sorry if you got a bit lost.
what is2/3 divided by 4/5
Step-by-step explanation:
2 /4
3. 5
doing reciprocal
2× 5
3. 4
= 8×15
12
= 120
12
=10 ans
hope it help u..
The ratio of goldfish to gallons of water is 7 to 2. how many goldfish can you get if you have 16 gallons of water?
Answer:
56
Step-by-step explanation:
Need answers for parallelogram LMNO
Answer:
what does lmno means
Step-by-step explanation:
please walk me through how to do this so I can di the other questions
Answer:
Axis is a vertical line at x = 2
Vertex is (2, -1)
y-intercept is (0, 3)
Solutions are x = 1 and x = 3
Step-by-step explanation:
To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y
Let us do that
Use x = -1, 0, 1, 2, 3, 4, 5
∵ y = x² - 4x + 3
∵ x = -1
∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8
→ Plot point (-1, 8)
∵ x = 0
∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3
→ Plot point (0, 3)
∵ x = 1
∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0
→ Plot point (1, 0)
∵ x = 2
∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1
→ Plot point (2, -1)
∵ x = 3
∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0
→ Plot point (3, 0)
∵ x = 4
∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3
→ Plot point (4, 3)
∵ x = 5
∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8
→ Plot point (5, 8)
→ Join all the points to form the parabola
From the graph
∵ The axis of symmetry is the vertical line passes through the vertex point
∵ x-coordinate of the vertex point is 2
∴ Axis is a vertical line at x = 2
∵ The coordinates of the vertex point of the parabola are (2, -1)
∴ Vertex is (2, -1)
∵ The parabola intersects the y-axis at point (0, 3)
∴ y-intercept is (0, 3)
∵ x² - 4x + 3 = 0
∵ The solutions of the equation are the values of x at y = 0
→ That means the intersection points of the parabola and the x-axis
∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)
∴ Solutions are x = 1 and x = 3
This month. Quincy buys honey at a price of $8.80 per pound. He sells the honey at a 25% markup. What is the selling price for a pound of honey?
THIS IS 7TH GRADE MATH, PLEASE HELP!!
Answer:
Company B is offering the lowest price/lb at $12.72/lb.
Step-by-step explanation:
If you know trig please help! Will give brainliest!
Answer:
sin^2α
Step-by-step explanation:
I will just pose x instead of alpha here to make things simpler
[tex]\tan ^2\left(x\right)\left(2\cos ^2\left(x\right)+\sin ^2\left(x\right)-1\right)\\\\[/tex]
we know that sin^2x = 1 - cos^2x so...
[tex]=\left(-1+1-\cos ^2\left(x\right)+2\cos ^2\left(x\right)\right)\tan ^2\left(x\right)[/tex]
[tex]=\cos ^2\left(x\right)\tan ^2\left(x\right)[/tex]
we can rewrite using trigonometric identities (tan = sin/cos)...
[tex]=\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2\cos ^2\left(x\right)\\= \sin ^2\left(x\right)[/tex]
Is 9 a possible solution for -2x + 4 ≥ -14?
Answer:
Yes
Step-by-step explanation:
-2(9)+4= -14 and -14 is equal to -14.
What is the absolute value of 8.7
Answer:
absolute value of 8.7 is 8.7
The weight of a suitcase checked onto a plane by a male, is a random variable with mean 42 pounds and standard deviation 16 pounds. The mean and standard deviation of the weight of a suitcase checked on to a plane by a female, is a random variable with mean 40 pounds and a standard deviation of 10 pounds. (For the purposes of this problem, a married couple consists of one male and one female. All suitcases are considered independent of each other even if from the same person.) What is the mean and standard deviation for the weight of the suitcases for a married couple, with one suitcase per person? What is the mean and standard deviation for the 6 suitcases checked onto the plan by 2 married couples, if each couple checked on 2 female suitcases and 1 male suitcase? In a cost cutting move the airlines is now charging $1.50 per pound for checked luggage. What is the mean and standard deviation for the cost of: A suitcase checked by a female 2 suitcases checked by a male. In an unexplained move, a worker at the airport adds a 5 pound graphing calculator to each male’s suitcase. What is the new mean and standard deviation for the weight of a male’s suitcase? What are the mean and standard deviation for the weight of the suitcases of a married couple, if the man’s suitcase is given the 5 pound calculator added to it?
Answer:
1) The mean = 41
The standard deviation = 13.379
2) The mean = 40.67
The standard deviation = 12.365
3) The mean and standard deviation will remain the same
4) The new mean = 44.5
The new standard deviation = 13.58
5) The mean = 42.25
The standard deviation = 13.83
Step-by-step explanation:
The combines mean is given by the formula;
[tex]\overline {x_{12}} = \dfrac{n_1 \bar x + n_2 \bar x}{n_1 + n_2}[/tex]
The combined standard deviation is given as follows;
[tex]\sigma_{12} = \sqrt{\dfrac{n_1 \times \left (\sigma^2_{1} + d^2_1 \right) + n_2 \times \left (\sigma^2_{2} + d^2_2 \right)}{n_1 + n_2} }[/tex]
d₁ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_1}[/tex]
d₂ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_2}[/tex]
Substituting the known values, we have;
[tex]\overline {x_{12}} = \dfrac{ 42 + 40}{2}=41[/tex]
d₁ = 41 - 42 = -1
d₂ = 41 - 40 = 1
[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 1 \right) + \left (10^2 +1 \right)}{2} } = 13.379[/tex]
2) When n₁ = 1, n₂ = 2, we have;
[tex]\overline {x_{12}} = \dfrac{ 2 \times 42 + 4 \times 40}{6} \approx 40.67[/tex]
d₁ = 40.67 - 42 = -1.33
d₂ = 40.67 - 40 = 0.67
[tex]\sigma_{12} = \sqrt{\dfrac{ 2 \times \left (16^2 + 1.33^2 \right) + 4 \times \left (10^2 +0.67^2 \right)}{6} } \approx 12.365[/tex]
3) The mean and standard deviation will remain the same
4) The new mean = (42 + 47)/2 = 44.5
The new standard deviation [tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +2.5^2\right)}{2} } \approx 13.58[/tex]
5) [tex]\overline {x_{12}} = \dfrac{ 44.5 + 40}{2}=42.25[/tex]
[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +4.5^2\right)}{2} } \approx 13.83[/tex]
HELLLLLLLLLLLLLPPPPPPPPPPPPP please
Can someone please help me in this.
20% of what number is 47?
Answer:
235
Step-by-step explanation:
Answer:
235
20 percent (calculated percentage %) of what number equals 47? Answer: 235.
Step-by-step explanation:
I hope this Helps c:
PLEASE THIS IS URGENT
Answer:
B
Step-by-step explanation:
I am sorry if this is wrong
hello everyone.
please answer……
The first water pipe fills the tank in 8 minutes and the second in 16 minutes. If both pipes are open in one minute, what part of the tank will not be filled with water?
have a nice day.good bye
Answer:
13/16 is the answer. Bad handwriting but try to understand .