Answer:
First Part;
As the temperature in the city increases, the number of cups of hot chocolate sold decreases
Second Part;
The approximate value of the slope in number of cups sold per change in temperature is -0.12222
The approximate value of the y-intercept is 20.944 degrees temperature
Step-by-step explanation:
Question;
First Part
What is the relationship between temperature in the city and the number of cups of hot chocolate sold, using your own words
Second Part
How can the line of best fit be made. Give the approximate values of the slope and the y-intercept of the line of best fit
Explanation
The data points are presented in the following table;
[tex]\begin{array}{lcl}x&&y\\20&&20\\30&&18\\40&&20\\35&&15\\50&&20\\45&&20\\60&&14\\65&&18\\80&&10\\70&&8\\40&&2\end{array}[/tex]
A scatter plot is formed from the given data using MS Excel
First part;
From the values of the number of cups sold, y, and the temperature at which they are sold, x, there is correlation between the x and y values, such that as the temperature increases, the number of cups sold decreases, the becomes more rapid as the temperature increases past 50, such that the reason for taking the hot chocolate decreases with increasing temperature
Second Part;
The line of best fit can be found using the least squares regression formula to draw a straight line from the regression equation as follows;
y = a + b·x
[tex]b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }[/tex]
a = [tex]\bar y[/tex] - b·[tex]\bar x[/tex]
Where;
b = The slope
a = The y-intercept
From MS Excel, we have;
[tex]\bar y[/tex] = 15, [tex]\bar x[/tex] = 48.63636
[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) = -410[/tex]
[tex]\sum \left(x_i - \bar x\right )^2 = 3354.545[/tex]
Therefore;
[tex]b = \dfrac{-410}{3354.545} = -0.12222[/tex]
The approximate value of the slope, b = -0.12222 (number of cups sold per unit change in temperature)
a = 15 - (-0.12222)×48.63636 ≈ 20.944
The approximate value of the y-intercept, a = 20.944 (in degrees of temperature).
Write an equation that PASSES THROUGH (3, -1) and is PARALELL to y = 6x - 4
show work
Answer:
y = 6x - 19
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 )
y = 6x - 4 ← is in slope- intercept form
with slope m = 6
Parallel lines have equal slopes , then
y = 6x + c ← is the partial equation
To find c substitute (3, - 1) into the partial equation
- 1 = 18 + c ⇒ c = - 1 - 18 = - 19
y = 6x - 19 ← equation of parallel line
A rectangle has an area of 161.2m2.
One of the sides is 5.2m in length.
Work out the perimeter of the rectangle
Answer:
72.4 m
Step-by-step explanation:
The area of a triangle is
A = l*w
161.2 = 5.2 *w
Divide each side by 5.2
161.2/5.2 = w
31 =w
Now find the perimeter
P =2 (l+w)
P =2 ( 5.2+31)
P =2( 36.2)
P =72.4
At the grocery store last week, small boxes of facial tissue were on sale at 4 boxes for $5. This week they mark a new price at 5 boxes for $4. What is the percent decrease in the price per box this week?
Answer: 36%
Step-by-step explanation:
Since the price last week, was 4 boxes for $5. Therefore, the price per box will be:
= $5/4
= $1.25 per box
This week they mark a new price at 5 boxes for $4. The price per box will be:
= $4/5
= $0.8 per box
The percent decrease in the price per box this week will be:
= (1.25 - 0.80)/1.25 × 100
= 0.45/1.25 × 100
= 36%
The Percentage decrease is 36%
Worth 10 points please help me
Answer:
(2,1)
Step-by-step explanation:
one half of (4,2) would be (2,1)
easy math, just a little tricky logic
can someone pls pls help me?
Answer:
its 30 or 24
Step-by-step explanation:
but its most likely 30
Which system of equations has infinitely many solutions?
to multiply two fractions multiply the numerator by the and the denominator by the
Answer:
Multiply the numerator by the numerator and the denominator by the demoninator.
Step-by-step explanation:
Answer:
Nope, to multiply two fractions = numerator × numerator / denominator × denominator
Step-by-step explanation:
For Example:
[tex]\frac{5}{3}[/tex] × [tex]\frac{8}{2}[/tex]
Multiply 5 by 8
40
Multiply 3 by 2
6
Result: [tex]\frac{40}{6}[/tex]
Finally Simplify
[tex]\frac{40}{6} =[/tex] [tex]40[/tex] ÷ 6 = [tex]6\frac{4}{6}[/tex] or 6.6 as a decimal
What is the value for x?
69
(5x + 2)
Enter your answer in the box
(9y-3)
Answer:
[tex]5x + 2 \\ x = 5 - 2 \\ x = 3 \\ \\ 9y - 3 \\ y = 9 + 3 \\ y = 12[/tex]
Simplify by factorising first
Answer:
x+8
Step-by-step explanation:
Simplify the numerator
list the factors of 16
16: 1, 2, 4, 8, 16
look for two factors that add up to the b value
in this case it is 18
by looking at the factors 2 and 8 add up 10
so you can rewrite the numerator as [tex]x^{2}+2x+8x+16[/tex]
Split the trinomial into two separate binomials each having one of the factors that add up to 10
So it should be [tex]x^{2} +2x and 8x+16[/tex]
Factor both binomials
you can factor an x from the first one
Then it is x(x+2)
Factor an 8 from the second one
8(x+2)
So it should be [tex]x(x+2) 8(x+2)[/tex]
This can rewritten as (x+8)(x+2)
So now you have [tex]\frac{(x+2)(x+8)}{x+2)}[/tex]
simplify it by canceling out the two (x+2)'s
this is because (x+2)/(x+2) is 1
Finally you get x+8
i need help with this problem
Answer:
Step-by-step explanation:
Her angle of depression is the same measure as the angle of inclination inside the triangle. That's the base angle that is not the right angle. The height of the triangle is the 10,000 feet she is up in the air, and the reference angle is 20, and we are looking for the measure of the base of this right triangle. The trig ratio that uses the side opposite over the side adjacent is the tangent ratio:
[tex]tan(20)=\frac{10000}{x}[/tex] and
[tex]x=\frac{10000}{tan20}[/tex] so
x = 27474.77 feet
-7 2/3 + (-5 1/2) + 8 3/4
Answer:
the answer would be -1339/24
Apply the distributive property to create an equivalent expression.
\dfrac12(2a - 6b+ 8) =
2
1
(2a−6b+8)=start fraction, 1, divided by, 2, end fraction, left parenthesis, 2, a, minus, 6, b, plus, 8, right parenthesis, equals
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]a-3b+4[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying the Equation...}}\\\\\frac{1}{2}(2a-6b+8)\\----------------\\\rightarrow\frac{1}{2}* 2a = a\\\\ \rightarrow\frac{1}{2}*-6b = -3b\\\\\rightarrow\frac{1}{2}*8 = 4\\\\\text{\underline{Therefore:}}\\\\\frac{1}{2}(2a-6b+8)\rightarrow \boxed{a-3b+4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer: a-3b+4
Step-by-step explanation:
Credits to guy up there
I NEED THIS NOW NO LINKS OR ILL REPORT PLZZZ
Answer:
2x + 4
Step-by-step explanation
Answer:
it's B, because 2*x and 2*-6 give 2x-12+16 which is 2x+4
using appropriate properties find the value of 3/5×(-3)/10+1/15-3/5×1/5 please help me out
3/5×(-3)/10 + 1/15 - 3/5×1/5 = -7/30 ≅ -0.2333333
I hope this helps!
PLEASE HELP!! Which variable is most important to the following problem?
Jackie played the first 8 minutes of a basketball game. Layla then replaced
her for the rest of the half. Layla started the second half and was replaced by
Jackie with 9 minutes left in the game. If each half is 16 minutes long, how
long did Jackie play?
A. The number of players who played during the game
B. The number of minutes Layla played in the second half
C. The total number of minutes Jackie played
D. The length of the half
Answer:
Step-by-step explanation:
d
How long would the processing take to develop 1000 negatives if it takes 5 minutes to develop 100 negatives? minutes Type the correct answer, then press Enter.
Answer:
50 minutes
Step-by-step explanation:
First you need to find out how many times 100 will fit into 10
1000/100 = 10
then you need to multiply it by 5, because each 100 negatives takes 5 minutes.
10 * 5 = 50
your answer is 50.
3. Apply what you have learned to answer the following question. Select the correct choice
and explain your reasoning
Which equation has the same number of solutions as 914x + 2) 71588) -
А
C
3(8x 12) 5(
39)
B flor + 9) - / 12x + 8
D
3(180 + 10) = 313x + 2) -
A
О ООО
Answer:
shshghhhsjsjjsjsjs
Step-by-step explanation:
snnsbzhhhshs
In each part, a and b represent the length of a leg of a right triangle, and c represents the length of its hypotenuse. Find the missing length, given the other two lengths.
Answer:
c=13 and a=20
Step-by-step explanation:
Here you need to use the Pythagoras theorem :
c²=a² + b²
c = √a² + b²
c = √(12)²+(5)²
c= √144+25
c = √169
c = 13
2) c²=a²+b²
b= √c²-b²
b= √(29)²-(21)²
b = √400
b = 20
In 2 you change your formula just so that it can be easier and just calculate your length straight forward but you can also just do it in the original equation
how many eggs are 5 dozen
Answer:
A dozen is 12.
12*5 = 60 eggs
5 dozen eggs are equal to 60 eggs.
A dozen is a unit of measurement equal to 12 items. So, 5 dozen is equivalent to 5 times 12, which gives us a total of 60 items.
When referring to eggs, the term "dozen" is commonly used to represent a quantity of eggs. In this case, if we have 5 dozen eggs, it means we have 5 sets of 12 eggs each.
To calculate the total number of eggs, we multiply the number of dozens (5) by the number of eggs in a dozen (12):
5 dozen x 12 eggs/dozen = 60 eggs
Therefore, 5 dozen eggs are equal to 60 eggs. This means that if you have 5 sets of 12 eggs, you would have a total of 60 eggs.
To learn more about multiplication;
https://brainly.com/question/19634536
#SPJ6
- If 4x = 4, what is the value of 3y ?
2y
X
A)
3
4
B)
ما در
C)
2
D) 2
Answer:
C
Step-by-step explanation:
[tex] \frac{4x}{2y} = 4[/tex]
Simplify fraction:
[tex] \frac{2x}{y} = 4[/tex]
Divide both sides by 2:
[tex] \frac{x}{y} = 2[/tex]
[tex] \frac{x}{y} = \frac{2}{1} [/tex]
[tex] \frac{y}{x} = \frac{1}{2} [/tex]
[tex] \frac{3y}{x} [/tex]
[tex] = 3( \frac{y}{x} )[/tex]
[tex] = 3( \frac{1}{2} )[/tex]
[tex] = \frac{3}{2} [/tex]
Step-by-step explanation:
everything can be found in the picture
Which of the following must be true to prove triangle ABC = ~ triangle DEF by the AAS theorem? I need help to understand this, can someone show me step by step on how to do this?
June 14th Jim Thompson Homework
Answers:
8) Choices E, F and G9) r = -0.9510) 0.9 (choice C)11) Choice C. y1 = mx1+b12) Choice B. Slope13) Choice C. y intercept========================================================
Explanations:
8) Positive r values always go with positive regression slopes. The r value will likely not equal the slope, but they share the same sign.
------------------------------
9) The data set isn't given so I'm not sure. But it seems like your teacher just wants to know a hypothetical situation in which r value will produce the best fit. That would be r = -0.95 since we're the furthest from zero. The closer you are to r = 1 or r = -1, the better the fit.
------------------------------
10) The blue regression line, aka line of best fit, is fairly close to all of the data points. Also, the blue line has a positive slope. This means r is fairly close to 1. So that's why we go with r = 0.9
------------------------------
11) The general equation is y = mx+b. We simply replace x,y with x1,y1.
------------------------------
12) When considering y = mx+b, the m is the slope. I'm not entirely sure where the m comes from, but I've read some sources that say 'm' somehow represents 'mountain' which involves slopes. This could have simply been a memorization tool and not the actual reason why m was chosen to be the slope.
As an example, y = 2x+5 has slope 2.
------------------------------
13) The b in y = mx+b is the y intercept. It's the initial value.
It always occurs when x = 0 since
y = mx+b
y = m*0+b
y = b
Meaning the point (0,b) is the location of the y intercept.
For example, y = 2x+5 has y intercept 5 located at the point (0,5).
Based on the picture below (note that it is not drawn to scale), Maggie says that . Is she correct? Explain why or why not.
Answer:
Step-by-step explanation:
By using the property of similar triangles,
"Corresponding sides of two similar triangles are proportional"
If ΔSMA ~ ΔPOD
[tex]\frac{SM}{PO}=\frac{MA}{OD}=\frac{SA}{PD}[/tex]
[tex]\frac{6}{10}=\frac{5}{10}=\frac{5}{12}[/tex]
[tex]\frac{3}{5}=\frac{1}{2}=\frac{5}{12}[/tex]
Since, ratios of corresponding sides are not equal,
Therefore, the given triangles are not similar.
Every Friday the boss buys pizza for his workers. Last week the workers finished 5 pizzas. This week
they finished 5 pizzas. Write the ratio of pizzas eaten last week to pizzas eaten this week.
Remember ratios must have two whole numbers.
Answer:
1:1 because they ate the same amount both weeks
The formula to convert °F to °C is C = C equals StartFraction 5 Over 9 EndFraction left-parenthesis F minus 32 right-parenthesis.(F – 32).
Answer:
True
Step-by-step explanation:
The formula to convert Fahrenheit degrees to Celcius degrees is [tex]C=5/9*(F-32)[/tex]
16. Solve y2 - 17x + 30 = 0 by factoring.
Answer:
x = 15 , x = 2
Step-by-step explanation:
[tex]x^2 -17x + 30 =0\\\\x^2 -2x-15x +30=0\\\\x(x-2)-15x(x-2) =0\\\\(x-15)(x-2)=0\\\\[/tex]
x = 15 , x = 2
Share $600 between Anna and Raman in the ratio 3:7 and 1:4
Answer:
3 : 7 =>
Anna = $180
Raman = $420
1 : 4 =>
Anna = $120
Raman = $480
Step-by-step explanation:
Shares when ratio is 3 : 7
Anna : Raman = 3 : 7
Sum of ratio 10
Anna's share=
[tex]\frac{3}{10} \times 600 = \$ 180[/tex]
Raman 's share=
[tex]\frac{7}{10} \times 600 = \$ 420[/tex]
Shares when ratio is 1 : 4
Anna : Raman = 1 : 4
Sum of ratio = 5
Anna 's share =
[tex]\frac{1}{5} \times 600 = \$ 120[/tex]
Raman's share =
[tex]\frac{4}{5} \times 600 = \$ 480[/tex]
Joseph has 16 metres of rope. He wants to cut pieces of rope that are 0.2 metres long.
How many pieces can he cut?
Ignore the answer I put
Answer:
80
Step-by-step explanation:
Given that :
Length of rope = 16 m
Length per Piece of rope to cut = 0.2 m
The number of pieces of rope that can be cut :
Length of rope / length per piece of rope
16 / 0.2
= 80
Hence, 80 pieces of 0.2 m rope will be cut
These prisms are similar. Find the volume
of the larger prism in decimal form.
5 m
7 m
Volume = 50 m3
Volume = [ ? ] m3
PLEASE HELP IM OVERDUE
Answer:
98 m³
Step-by-step explanation:
For similar shapes
The ratio of the cube of the corresponding length of similar shapes is equal to the ratio of their volume.
Applying,
L³/L'³ = V/V'............... Equation 1
Where, L = Length of the smaller prism, L' = Length of the larger prism, V = Volume of the smaller prism, V' = Volume of the larger prism
From the question,
Given: L = 5 m, L' = 7 m, V = 50 m³
Substitute these values into equation 1
5²/7² = 50/V'
25/49 = 50/V'
V' = (50×49)/25
V' = 98 m³
Answer: 137.2
Step-by-step explanation:
I'm just making the correct answer an actual answer instead of a comment so it's easier to see
can someone pls pls help me?
Answer:
i think 88
Step-by-step explanation:
(it's been a while since I've done this so I'm not too sure it's correct)
The formula we need to use is
2πr(angle/360)
we need the radius (r)
To get r we need angle AES
180-80= 100
using the equation from before
88=2πr*(100/360)
raidus: 50.42
Then to get the length CD we need angle DEC
180-80=100
2π*50.42*(100/360)=88
there probably was some kind of shortcut we could've used to figure this out faster but whatever