Final answer:
Using the two given points $(82, 4)$ and $(42, 9)$, the slope is calculated to be $-1/8$. Subsequently, by using the point-slope form of the line equation and simplifying, we find that the linear relationship between price and demand is described by $y = -1/8x + 57/4$, which corresponds to choice A.
Explanation:
To determine the linear equation that best models the price-demand relationship for the mini-recorders, we are given two points. At a price of $82, the demand is 400 recorders (4 hundred), and at a price of $42, the demand is 900 recorders (9 hundred). In the mathematical representation, these points are (82, 4) and (42, 9), where x is the price and y is the demand in hundreds.
To find the slope (m) of the line, we use the slope formula:
m = (y2 - y1) / (x2 - x1), which gives us m = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8.
Now, we can use the point-slope form to find the equation of the line. Let's use the point (82, 4):
y - y1 = m(x - x1)
y - 4 = (-1/8)(x - 82)
Multiplying out the right-hand side of the equation, we have:
y - 4 = (-1/8)x + (82/8)
y - 4 = (-1/8)x + 10.25
Moving 4 to the other side to get 'y' by itself, the equation becomes: y = (-1/8)x + 10.25 + 4
This simplifies to:
y = (-1/8)x + 14.25
Converting 14.25 into quarters gives us 14.25 = 57/4. Hence the equation becomes:
y = (-1/8)x + 57/4 which matches choice A.
Final answer:
The correct equation that models the price-demand relationship is y = -1/8x + 57/4, where y is the demand in hundreds and x is the price per mini-recorder.
Explanation:
To find the equation that models the price-demand relationship, we need two points to determine the line: (x1, y1) = (82, 4) and (x2, y2) = (42, 9). The demand, y, is in hundreds of recorders and x represents the price per mini-recorder. The slope (m) of the line is given by the change in demand over the change in price: m = (y2 - y1) / (x2 - x1) = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8. To find the y-intercept (b), we use one of the points and the slope in the linear equation formula y = mx + b. Using the point (82, 4), we have 4 = (-1/8)(82) + b. Solving this equation gives us b = 4 + (1/8)(82) = 4 + 10.25 = 14.25. Now the linear equation is y = -1/8x + 14.25. Since y needs to be in hundreds for the units to match the point given (400, 900), we must divide b by 100, resulting in b = 14.25 / 100 = 57/4. The final price-demand relationship is y = -1/8x + 57/4.
Which expression is equivalent to 2(9 + 7)?
Leon lives in North Dakota, which has a sales tax of 5%. He just bought a home theater system whose full price was $450, but after sending in a rebate form, he later received a check in the mail for $75. What was the total amount that Leon ended up paying after receiving the rebate? A. $397.50 B. $472.50 C. $393.75 D. $375.00
Answer:
$397.50
Step-by-step explanation:
$450×5%=22.5 (Tax)
$450+22.5=$472 (Full Price of Item)
$472-$75=$397.5 (With Rebate)
final answer=$397.5
The maximum height of a vehicle that can safely pass under a bridge is 12 feet 5 inches. A truck measures 162 inches in height. Which best explaims whether or not the truck can pass safely under the bridge?
how do you solve the function 5x-4=-2(3x+2)
What is the center of a circle given by the equation (x-3)2+(y-9)2=16
What are the like terms of 8c - 12 - 5c +4
Matteo is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by y^2=6x where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite? (–1.5, 0) (0, –1.5) (0, 1.5) (1.5, 0)
Answer: (1.5, 0)
Step-by-step explanation:
Given : The shape of his satellite can be modeled by [tex]y^2=6x[/tex] where x and y are modeled in inches.
Now,the given equation [tex]y^2=6x[/tex] is a equation of parabola.
Here, coefficient of x is positive, hence the parabola opens rightwards.
On comparing this equation with standard equation [tex]x^2=4mx[/tex], we get
[tex]4m=6\\\Rightarrow\ m=\frac{6}{4}=1.5[/tex]
In standard equation, coordinates of focus=(m,0)
Thus for given equation coordinates of focus=(1.5,0)
Answer:
Answer: (1.5, 0)
Step-by-step explanation:
A substance with a density of 1.0 gram per cubic centimeter has a mass of 1.0 kilogram if its volume is 100 cubic centimeters. True or false ? Please answer with explanation
There are 150 marigold plants in a back yard. Each month, the number of marigold plants decreases by 15%. There are 125 sunflower plants in the back yard. Each month, 8 sunflower plants are removed. Part A: Write functions to represent the number of marigold plants and the number of sunflower plants in the back yard throughout the months. (4 points) Part B: How many marigold plants are in the back yard after 3 months? How many sunflower plants are in the back yard after the same number of months? (2 points) Part C: After approximately how many months is the number of marigold plants and the number of sunflower plants the same? Justify your answer mathematically. (4 points)
Let us first assign variables. We say that:
X = number of marigold plants
Y = number of sunflower plants
n = number of months
We can see that in the given problem, X is decreasing by a percentage, this means that we have to set-up a geometric equation while for Y the decrease is linear so we set-up an arithmetic equation.
Part A.
For marigold plants X, a geometric sequence has a general form of:
X = Xo * (1 + r)^n
where r = -15% = -0.15 (negative since it is decreasing)
Xo = the initial amount of marigold plants = 150
X = 150 * (1 – 0.15)^n
X = 150 (0.85)^n
For the sunflower plants Y, an arithmetic sequence has a general form of:
Y = Yo + d * n
where d = -8 and Yo = 125
Y = 125 – 8 n
Part B. For n = 3
X = 150 (0.85)^3 = 92.12 = 92
Y = 125 – 8 (3) = 101
Part C. From Part B we see that the two values are very far from each other when n = 3, therefore they must be similar when n < 3. So we try n = 2
X = 150 (0.85)^2 = 108.38 = 108
Y = 125 – 8 (2) = 109
Therefore the two plants have approximately similar amount after 2 months.
If x = -6 and y = -9, find xy - 3x + 2y
PLEASE HELP!!! 40 points!!! 1) A school puts on a play. The play costs $1,200.00 in expenses. The students charge $4.00 for tickets. There will be 1 performance of the play in an audiotorium that seats 500 people. What is the domain of the function that shows the profit as a function of the number of tickets sold? A)The domain is all real numbers from negative 1,200 to positive 2,000. B) The domain is all integers from negative 1,200 to positive 2,00. C) The domain is all integers from 0 to 500. D) The domain is all real numbers from 0 to 500.
A parachutist descends 64 feet in 4 seconds. Express the rate of the parachutist's change in height as a unit rate.
The unit rate of the parachutist's change in height is __ feet per second.
To find the unit rate of the parachutist's change in height, we divide the total distance descended (64 feet) by the total time (4 seconds). This yields a unit rate of 16 feet per second.
Explanation:In order to calculate the unit rate of this parachutist's descent, we need to set up a fraction with the total distance descended over the overall time. In this case, the parachutist descends 64 feet in 4 seconds.
We then solve for the unit rate by dividing the distance descended (64 feet) by the time it took to descend (4 seconds). So, the calculation would be 64 ÷ 4 = 16.
So, the unit rate of the parachutist's change in height is 16 feet per second.
Learn more about Unit Rate here:https://brainly.com/question/22607023
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What is the domain of the function f (x)=x^2+1
A student attempted to generate an equivalent expression using the distributive property, as shown below: 4(x + 2) = x + 8 What was the mistake made?
What is the length of leg y of the right triangle? A right triangle with hypotenuse 85 and legs 84 and y 1 9 13 26 Question 11(Multiple Choice Worth 1 points)
a^2 +b^2 = c^2
a^2 +84^2 = 85^2
a^2 + 7056 =7225
a^2 = 169
a= sqrt(169)
a=13
length of leg y = 13
Which situation will have the greatest number of possible outcomes? A. The number of 5-digit zip codes, where the digits cannot be repeated. B. The number of 5-digit zip codes, where the digits increase. C. The number of 5-digit zip codes, where the digits can be repeated. D. The number of 5-digit zip codes, where the digits are the same.
find the quotient -7 divided by 14/3
Help me please!! Thanks you
height = sqrt (26^2 - 10^)
10^2 = 100
26^2 = 676
sqrt ( 676-100)=
sqrt(576) = 24
height is 24 ft
what is sine times secant
What is the equation of this line of best fit in slope-intercept form?
y = −6x + 3/4
y = 6x + 3/4
y =-3/4 x + 6
y =3/4 x + 6
PLEASE HELP!!! Get brainliest answer if right @peredhel
Use a special right triangle to write cos 30
Solve 8x 2 - 2x - 1 = 0
{-1/4, 1/2}
{-1/2, 1/4}
{1/2}
What is the LCD of 1/6 and 5/12 and 11/18
What is 0.77 estimated
.736 rounded to the nearest hundredth
A standard showerhead in Nathan's house dispenses 11 gallons of water per minute. Nathan changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x How much water does Nathan save each day with the change in showerheads if he uses the shower for 8 minutes each day? 8 gallons 24 gallons 33 gallons 64 gallons
Answer: 64 gallons
hope it helps XD :))
What is the smallest value in the stem and leaf plot below?
STEM | LEAVES
0 | 2 3 3 7
1 | 0 0 7
3 | 4 4 5 5
Key: 3 | 5 means 35
A:2
B: 20
C: 35
D: 2337
Final answer:
The smallest value in the provided stem-and-leaf plot is 2, corresponding to the lowest stem of 0 with the lowest leaf of 2.
Explanation:
The student's question is asking for the smallest value displayed in a provided stem-and-leaf plot. The stem-and-leaf plot shows numbers divided into stems (tens place) and leaves (ones place), which tells us unique values in the dataset. In this case,
STEM | LEAVES
0 | 2 3 3 7
1 | 0 0 7
3 | 4 4 5 5
According to the provided key, which states that '3 | 5' means '35', we can see that the smallest stem is '0' and the smallest leaf in the '0' stem row is '2', combining these gives us the smallest value in the plot. Therefore, the smallest value in the stem and leaf plot is 2, which corresponds to option A: 2.
What is 5xy cubed? To better rephrase it, what is 5xy to the power of 3?
I know the answer but my meme dealer needs points
Answer: 12 (C)
Step-by-step explanation: Im a "Meme Dealer" but not yours.
Order least to greatest
0, -14,13,-12,-16,17
-16,-14,13,-12,0,17
-12,0,13,-14,-16,17
-12,-14,-16,-,13,17
0,12,13,-14,-16,17
Which is the farthest to the right on a number line
-15
-1
0
1
Find -5
-5
5
1/5
-1/5
The correct order from least to greatest is -16, -14, -12, 0, 13, 17. The number farthest to the right on the number line is 1, and 'finding -5' means locating the number -5 on a number line.
The question involves ordering numbers from least to greatest and finding the position of a number on a number line. To order numbers from least to greatest, you look for the smallest or most negative number and move towards the largest or most positive number. When placed on a number line, negative numbers are to the left of zero, and positive numbers are to the right of zero. Therefore, the correct order from least to greatest is -16, -14, -12, 0, 13, 17.
Moreover, the number farthest to the right on a number line from the options given is 1 because it is the greatest number listed and is positioned to the right of all the other numbers.
Finally, to 'find -5', it simply means to locate the number -5 on the number line. It is negative, so it will be to the left of zero.