Jack plotted the graph below to show the relationship between the temperature of his city and the number of ice cream cones he sold daily: Main title on graph is Ice Cream Cone Sale. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 60 on y axis at increments of 10. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of Ice Cream Cones Sold. Dots are made at the ordered pairs 0, 5 and 5, 15 and 7.5, 15 and 10, 24 and 10, 28 and 12, 32 and 12.5, 25 and 12.5, 30 and 15, 35 and 15, 40 and 17.5, 35 and 20, 45 and 22.5, 36 and 23, 46 and 25, 55 and 27.5, 60. Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold. (5 points) Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Answers
Answer:
(a) The amount of ice cream increase as temperature increases
(b)
[tex]y = 2x + 5[/tex] --- equation
[tex]y = 5[/tex] --- y intercept
[tex]m = 2[/tex] --- slope
Step-by-step explanation:
Given
See attachment for graph
Solving (a): The relationship between the variables
From the attached graph, the dots on the graph increases towards up-right direction. This implies that there is a positive correlation between the variables.
In other words;
The amount of ice cream increase as temperature increases
Solving (b): The line of best fit
First, we draw a line through the points (the line should have almost equal points on both sides; see attachment 2).
From (2), we select any 2 points on the line:
[tex](x_1,y_1) = (15,35)[/tex]
[tex](x_2,y_2) = (0,5)[/tex]
The slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{5-35}{0-15}[/tex]
[tex]m = \frac{-30}{-15}[/tex]
[tex]m = 2[/tex]
So, the line of best fit is:
[tex]y = m(x - x_1) + y_1[/tex]
Substitute known values:
[tex]y = 2(x - 0) + 5[/tex]
[tex]y = 2(x) + 5[/tex]
[tex]y = 2x + 5[/tex]
The y-intercept is when [tex]x=0[/tex]
So, we have:
[tex]y = 2*0 + 5[/tex]
[tex]y = 0 + 5[/tex]
[tex]y = 5[/tex]
Related Questions
Question 7 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 5 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 13 feet. What is the length of the other
diagonal?
O A. 12 feet
B. 13 feet
O C. 5 feet
O D. 17 feet
Answers
Answer:
13
Step-by-step explanation:
The diagonals of rectangle are equal in length.
Find the length of UC? Please help
Answers
Answer:
The choose C. 18
Step-by-step explanation:
UC —> 105+82=187 —> 96+22+51=169 —> 187–169=18
I hope I helped you^_^
What is the domain of g(x)
X is a real number
Answers
Answer:
The doing would be x
Step-by-step explanation:
since you are calculating domain for a specific value it would be the corresponding g(x) value which is the domain
Find the 5th term of each geometric sequence. 32,80, 200
Answers
Answer:
12.8
Step-by-step explanation:
Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.
Given all of this information, answer the following questions:
1. What is the original loan amount, i.e. how much were the total costs for tuition plus room & board for the four years that Penny attended the college?
2. What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)
3. Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)
Answers
Answer:
27,880 for tutitions + 45,280 for room and board= 73,160 total
HELP PLEASE 100 POINTS
Answers
Answer:
Step-by-step explanation:
That's an awful lot of points. You don't have to give that many. 10 or 15 points would be more than enough.
The graph touches the x axis at 1 point. That means its basic formula is y = (x - a)^2
Since it upside down, the formula is y = -(x - a)^2. A couple of other things are true.
a = 1 because that's where the graph touches the x axis. y = - x^2 has shifted 1 unit to the right.
Finally the y intercept is -4 which means that the final equation is y = -4(x-1)^2
That's all preliminary. The actual question is, what does the discriminate look like?
y = -4(x^2 - 2x + 1)
y = -4x^2 + 8x - 4
a = - 4
b = 8
c = - 4
sqrt(b^2 - 4ac)
sqrt(8^2 - 4(-4)(-4) )
sqrt(64 - 64) = 0
The answer is the third one. The answer will always be 0 when the graph touches the x axis and does not go through it.
Yesenia drove 45.3 miles on Monday and 3.8
miles more on Tuesday. How many miles did she
drive in all?
Answers
Answer:
49.1 milez
Step-by-step explanation:
Total miles driven=45.3+3.8=49.1 miles
Select the correct answer from each drop-down menu.
The table shows certain values of a cubic function.
Answers
Answer:
7 and - infinity
Step-by-step explanation:
The function is decreasing in nature. The function has a maxima when x is near 7 and as the function is decreasing, the function will approach -infinity as x approaches positive infinity.
The entrance ticket for a carnival costs $89.97, which includes a royal meal
that costs $10.85, 1 play station game, and 3 water rides (Each water ride
costs the same price). The cost of a water ride is twice as that of a play
station game. Find the cost of a water ride. Estimate to the nearest tenths.
Answers
Answer:
Cost of a play station game = $11.3
Cost of each water ride = $22.6
Step-by-step explanation:
Entrance tickets = $89.97
Royal meal = $10.85
Cost of a play station game = x
Cost of each water ride = 2x
Find the cost of a water ride
Entrance tickets = Royal meal + 1 play station game + 3 water rides
89.97 = 10.85 + 1(x) + 3(2x)
89.97 = 10.85 + x + 6x
89.97 = 10.85 + 7x
89.97 - 10.85 = 7x
79.12 = 7x
x = 79.12/7
x = 11.302857142857
Approximately to the nearest tenth
x = $11.3
Cost of a play station game = x = $11.3
Cost of each water ride = 2x
= 2(11.3)
= $22.6
Which graph represents the step function f(x)=⌊x+2⌋?
Answers
Answer:
biyotiptol graph by using pen
If sec^2 teta (1+sin teta) (1-sin teta) = k, find k
Pls help no spamming
Answers
[tex]\boxed{\sf 1-sin^2\theta=cos^2theta}[/tex]
[tex]\boxed{\sf cos^2\theta=\dfrac{1}{sec^2\theta}}[/tex]
Solution:-
Let's do
[tex]\\ \sf\longmapsto k=sec^2\theta(1+sin\theta)(1-sin\theta)[/tex]
[tex]\\ \sf\longmapsto k=sec^2\theta(1-sin^2\theta)[/tex]
[tex]\\ \sf\longmapsto k= sec^2\theta(cos^2\theta)[/tex]
[tex]\\ \sf\longmapsto k=sec^2\theta\times \dfrac{1}{sec^2\theta}[/tex]
[tex]\\ \sf\longmapsto k=1[/tex]
[tex]\color{lime}\boxed{\colorbox{black}{Answer : - }}[/tex]
[tex] \sec^{2} θ(1 + \sinθ)(1 - \sinθ) = k[/tex]
[tex] \sec^{2} θ \: (1 - { \sin}^{2} θ) = k[/tex]
[tex] { \sec }^{2} θ \cos^{2} θ = k[/tex]
[tex] \sec ^{2} θ. \frac{1}{ {sec}^{2}θ } = k[/tex]
[tex]1 = k[/tex]
Therefore:
[tex] \color{red}k = 1[/tex]
What is the estimate for 312+138+207
Answers
Answer:
657
Step-by-step explanation:
312 + 138 + 207
= 450 + 207
= 657
Answer:
600
Step-by-step explanation:
To round your answer, you check the tenths place to see if it is under 5 or above 5. If it is under 5, your answer will stay in the number the hundreds place is in currently. If it is above 5, you will add one to the hundreds place.
312: there is one in the tenths place, so it will stay as 300.
138: there is three in the tenths place, so it will stay as 100.
207: there is a zero in the tenths place, so it will stay as 200.
If you are doing it with the one's place, it is the same method. Either round up or down.
300 + 100 + 200 = 600
The answer is 600.
Find the measure of the missing angle.
156°
a =
Answers
Answer:
Below!
Step-by-step explanation:
A straight line = 180 degrees, so all you need to do to find angle a is to subtract 156 from 180!
180 - 156 = 24 degrees
Hope this helped!
which has a steeper slope y-1/2x or y=2/3x?
Answers
Answer:
y=2/3x
Step-by-step explanation:
2/3 is greater than 1/2. It doesn't matter if one of the slopes are negative.
A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?
(–1, 2)
(1, 3)
(8, 11)
(9, 12)
i really dont get this at all can someone help me and explain
Answers
Answer:
(8,11)
Step-by-step explanation:
1st line
y = x+ 3
We need to find the equation of the other line
We have two points (3, 1) and (4, 3)
Slope
m = (y2-y1)/(x2-x1)
= ( 3-1)/(4-3)
= 2/1 = 2
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y =2x+b
Using the point (4,3)
3 = 2(4)+b
3 = 8+b
3-8=b
-5 =b
y = 2x-5
We have 2 lines
y =x+3 and y = 2x-5
Setting them equal to each other
x+3 = 2x-5
Subtract x from each side
x+3-x = 2x-5-x
3 = x-5
Add 5 to each side
3+5 =x-5+5
8=x
Now we can find y
y =x+3
y = 8+3
y=11
Answer:
c (8,11)
Step-by-step explanation:
the ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1, 60), (2, 240), (3, 960), (4, 3840)}
what is the function equation in sequence notation?
wt = ____
Answers
Answer:
w = 15 (4^t)
Step-by-step explanation:
Let w be what the function is equal to
Let t be the input variable
equation :
w = k a^t
Plug in any two of the points to solve for k and a
for example, let's take (1, 60) and (2, 240):
60 = k * a^1
k = 60 / a
240 = k a^2
Substituting:
240 = 60/a (a^2)
a = 4
k = 15
The function is
w = 15 (4^t)
Which equation can be solved using the one-to-one property?
3X = 10
4In x = 2
log x = 5
4* = 47x+2
Answers
Answer:
3x=10
Step-by-step explanation:
x=10-3
x=7
i hope this answer will help u
Answer:
4x = 47x+2
Step-by-step explanation:
Using the one–to–one property, you can set x = 7x + 2.
Help help help help help help help help help help help help
Answers
Answer:
$32.07
Step-by-step explanation:
I am not sure - are we seeing the full information about this problem ?
because the problem description is strangely vague and confusing, as it uses "total cost" two times for not the same thing ...
either total cost means including tax or not including tax. but it cannot mean both ...
I think the most likely understanding of this problem is that the first price is without tax, and now we need to calculate and add the extra 6% tax to get the really total price to be paid.
I will solve this now based on this assumption.
100% = $30.25
1% = 100%/100 = 30.25/100 = $0.3025
6% = 6×1% = 6×0.3025 = $1.815 ≈ $1.82
the total price is then calculated either by
100% + 6%
or by
106% = 100%×1.06 = 30.25×1.06 = $32.065 ≈ $32.07
in both cases we get the same result, of course.
Answer:
32.171
Step-by-step explanation:
factorise [tex]x^{2} - 121[/tex]
Answers
Answer:
(x+11)(x-11)
Step-by-step explanation:
Hello!
We are given the expression x²-121, and we want to factor it
The expression is a difference of squares expression.
The formula for the difference of squares is written as a²-b² can be factored as (a-b)(a+b)
121 is 11 squared, and x² is x squared
So that means that a=x, and b=11 in this case
Now substitute those values into the formula
a²-b²=x²-121=(x+11)(x-11)
Hope this helps!
Answer:
(x-11)(x+11)
Step-by-step explanation:
x^2 -121
x^2 -11^2
This is the difference of squares a^2 - b^2 = (a-b)(a+b)
(x-11)(x+11)
SEE QUESTION IN IMAGE
Answers
Answer:
(b)
Total frequencies:
25 - 4 = 21Multiples of 3 or 5:
6, 9, 10, 12, 15, 18, 20, 21, 24, 25 - total of 10Required probability:
P(3x or 5x) = 10/21(c)
Limes = 10 + 6 = 16Apples = 8 + 6 = 14Total = 16 + 14 = 30(i) Good limes = GL = 10
P(GL, GL) = 10/30*9/29 = 3/29(ii) Good fruits = GF = 10 + 8 = 18
P(GF, GF) = 18/30*17/29 = 51/145(iii) Good apple = GA = 8, Bad lime = BL = 6
P(GA&BL or BL&GA)) = 8/30*6/29 + 6/30*8/29 = 16/145resolve (5x+4) /( (x-4)( x+2))
Answers
Answer:
Step-by-step explanation:
Hello!
(5x+4) /( (x-4)( x+2))
(5x+4)/ (x² +2x -4x -8)=
(5x+4) /( x²-2x -8)
use the prime factors of 3136 and 2744 to evaluate:✓3136/3✓2744
Answers
Answer:
3136 = 2^6 × 7^2
2744 = 2^3 x 7^3
✓3136/3✓2744 = ✓(2^6 × 7^2)/3✓(2^3 x 7^3) = (2^3 x 7)/3 x 14(✓14) = 56/42✓14 =4/3✓14
assume abc=def. if ab=5, ac=9 and ef=7, what is the length of bc?
Answers
Answer:
bc= 7
Step-by-step explanation:
Help me solve for t please
Answers
Answer:
[tex]t = \frac{ v_{1} - v_{0}}{a} \\[/tex]
Step-by-step explanation:
[tex]a = \frac{v_{1} - v_{0}}{t} \\ a \times t = v_{1} - v_{0} \\ \frac{at}{a} = \frac{ v_{1} - v_{0} }{a} \\ t = \frac{ v_{1} - v_{0}}{a} \\ [/tex]
what is the area of the figure below?
Answers
Answer:
15x^9
Step-by-step explanation:
A=l x w
5x^4 times 3x^5 is basically 3*5*x^4*x^5
when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9
explanation would be appreciated. i don’t understand
Answers
Answer:
[tex]28\sqrt{3}[/tex]
Step-by-step explanation:
The area of the big triangle is 1/2 b h = 1/2*6*(12^2 = 6^2 + x^2)
that ends up being [tex]\sqrt{108} = 36\sqrt{3}[/tex]
the small triangle are needs to be subtracted....
[tex]\frac{\left(4\cdot \:sin\left(90\right)\right)}{sin\left(30\right)}[/tex] that is the length of the unknown side...
1/2 B * h of that triangle get you to [tex]8\sqrt{3}[/tex]
just subtract the two areas
Answer:
(B) 28√3
Step-by-step explanation:
The area of quadrilateral ABED is equal to the area of triangle CDE subtracted from the area of triangle ABC.
Area of triangle CDE:
Triangle ABC is equilateral. All sides have length 12.
AB = BC = AC = 12
BE = 8
BE + EC = BC
8 + EC = 12
EC = 4
In an equilateral triangle, all angles measure 60°.
m<C = 60°
m<CDE = 30°
Triangle CDE is a 30-60-90 triangle.
DE = EC√3
DE = 4√3
area of triangle CDE = bh/2
area of triangle CDE = (EC)(DE)/2
area of triangle CDE = (4)(4√3)/2
area of triangle CDE = 8√3
Area of triangle ABC:
Side AC is a base of triangle ABC.
AC = 12
(1/2)AC = 6
The altitude of triangle ABC from side AC to vertex B measures
h = 6√3
area of triangle ABC = bh/2
area of triangle ABC = (AC)(h)/2
area of triangle ABC = (12)(6√3)/2
area of triangle ABC = 36√3
area of quadrilateral ABED = area of triangle ABC - area of triangle CDE
area of quadrilateral ABED = 36√3 - 8√3
area of quadrilateral ABED = 28√3
how many subsets can be formed of a set A={a,b}
Answers
Answer:
4
Step-by-step explanation:
(a,a),(a,b),(b,a),(b,b)
5.
Krishna got on an elevator on the 12" floor and went up 3 floors. If he then went down 8 floors,
what floor is krishna now on?
Answers
Answer:
Krishna is at the 7th floor
Step-by-step explanation:
Given
[tex]Start = 12[/tex]
[tex]Up = 3[/tex]
[tex]Down = 8[/tex]
Required
The current floor
This is calculated as:
[tex]Floor = Start + Up - Down[/tex]
[tex]Floor = 12 + 3 - 8[/tex]
[tex]Floor = 7[/tex]
equation of the line which passes through point (0,5) at gradient of - 1
Answers
Answer:
y = - x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here gradient (slope) = - 1 and (0, 5) ⇒ c = 5
y = - x + 5 ← equation of line
PLS TELL ME HOW TO FIND THIS ANGLE
Answers
Answer:
it is 80⁰
Step-by-step explanation:
cuz the it vertical angle
and to find a just get
180-80-70
