Answer:
a. $18.36 for 3 pizzas : k = 6.12
b. $4.17 for 3 pounds of bananas . k = 1.39
c. $16.48 for 4 pounds of potatoes . k = 4.12
d. 2 cups of flour to make 24 cookie . k = 12
Step-by-step explanation:
PROPORTIONALITY:
Two quantities x and y are said to proportional to each other
if for x ∝ y , x = y k.
Here, k is called the PROPORTIONALITY CONSTANT.
⇒ [tex]x\propto y \implies k = \frac{x}{y}[/tex]
Now, for the given quantities:
a. $18.36 for 3 pizzas [box]
Here, [tex]k = \frac{18.36}{3} = 6.12[/tex]
So, the proportionality constant is 6.12.
b. $4.17 for 3 pounds of bananas [box]
Here, [tex]k = \frac{4.17}{3} = 1.39[/tex]
So, the proportionality constant is 1.39.
c. $16.48 for 4 pounds of potatoes [box]
Here, [tex]k = \frac{16.48}{4} = 4.12[/tex]
So, the proportionality constant is 4.12.
d. 2 cups of flour to make 24 cookies
Here, [tex]k = \frac{24}{2} = 12[/tex]
So, the proportionality constant is 12
Which of the following correlation coefficients would correspond to a strong linear relationship in a data set?
A. 0
B. 0.5
C. 0.9
D. 100
Answer:
The correct answer is C.
Final answer:
The correlation coefficient of 0.9 indicates the strongest linear relationship among the provided options, and the weakest relationship is indicated when the coefficient is closest to 0.
Explanation:
The correlation coefficient that corresponds to a strong linear relationship in a data set is typically close to either -1 or +1. Based on the given options, the correlation coefficient of 0.9 (Option C) would indicate the strongest linear relationship, suggesting a very strong positive linear relationship between the two variables. Correlation coefficients close to 0 indicate weak relationships, and a value of exactly 0 implies no linear relationship at all. A perfect positive linear relationship has a correlation coefficient of +1, whereas a perfect negative linear relationship has a correlation coefficient of -1. Therefore, even negative coefficients such as -0.90 can also indicate a strong, but negative, linear relationship.
Hence, for the second part (Q4), the weakest relationship would be when the correlation coefficient is closest to 0 (Option A).
Evaluate the expression. 8 x 7 - 12 ÷ 6 please anwser fast
Answer:
54
Step-by-step explanation:
8*7-12/6=56-2=54
Answer:
56-2=54
Step-by-step explanation:
8×7 - 12÷6 =56 - 2= 54
What is the minimum cuts
needed to cut a circle into 8
equal parts?
What is the minimum cuts needed to cut a circle into 8 equal parts ?
A : 4 cuts
Answer:
4 cuts.Step-by-step explanation:
When we have a circle, each cut (supposing the curst are in the exact middle) which give use two haves. So, if we cut one time, we'll have two equal parts, if we cut a second time, we'll have 4 equal parts, a third time, we'll get us 6 equal parts, and if we cut a fourth time, we'll have 8 equal parts.
So, whenever we have this kind of problem dividing circles, we just say that each cut in the exact middle equals two equal haves, so if we have 4 cuts, we just multiply them by 2, 4(2)=8. Therefore, we have 8 equal parts.
Sandria earned $24 babysitting. She owes her friend $7 for dinner, and she owes her mom $4. She will make $15 later this week for mowing the yard.
How much money will she have at the end of the week?
Answer:
28
Step-by-step explanation:
24-7-4=13
13+15=28
Solve 3x - 5 = 16.
9
8
6
7
Answer:
7
Step-by-step explanation:
3(7)=21-5=16
Mr. lee drive 8 miles from his house to Parkside Parkside is 4 miles south of Springfield from Parkside he drove 3 miles to Springdale then he drove 20 miles from Springdale to Brookville how far did Mr. Lee Drive in all
Mr Lee drive 31 miles from his house to Brookville
Solution:Given that
Mr. Lee drove 8 miles from his house to park side .
Parkside is 4 miles south of springfield.
From Parkside he drove 3 miles to springdale
Then he drove 20 miles from springdale to brookville.
Need to determine how far Mr Lee drive in all, from his house to Brookville.
Complete drive of Mr Lee from his house to Brookville is equal to 8 miles from his house to park side then 3 miles from Parkside to springdale , then 20 miles from springdale to brookville.
=> Complete drive of Mr Lee from his house to Brookville in miles = 8 + 3 + 20 = 31 miles
Thomas rents a car for his vacation. the mileage included with the rental is 54 miles. For every mile he drives over 54 miles, he needs to pay $1 4/5. If he drives 69 miles, how much extra does he need to pay?
Answer:
Thomas needs to pay additional US$ 27 for the 15 extra miles not included in the mileage.
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Mileage included with the rental = 54 miles
Additional mile over 54 miles = US$ 1 4/5
Distance finally driven by Thomas = 69 miles
2. Let's calculate how much additional money Thomas needs to pay.
Extra miles driven by Thomas = Distance finally driven - Mileage included
Extra miles driven by Thomas = 69 - 54
Extra miles driven by Thomas = 15
Cost of the additional miles = 15 * 1 4/5
Cost of the additional miles = 15 * 1.80 ⇒ 4/5 = 0.80
Cost of the additional miles = 27
Thomas needs to pay additional US$ 27 for the 15 extra miles not included in the mileage.
62 is 50% of what number?
Answer:
62 is 50% of 31
Step-by-step explanation:
For example: 50% of 62 = 31; Example 2: Calculate a percentage based on 2 numbers. For example: 31/62 = 50%
Answer:
31
To calculate a percentage of some number, change the percentage into a decimal, and the word "of" into multiplication
A long-distance telephone company charges a rate of 8 cents per minute or a 50-cent minimum charge per completed call, whichever is greater. Find the cost, in cents per minute, for a 3-minute call.
Answer:
Cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.
Step-by-step explanation:
We are given the following in the question:
Plan A
A rate of 8 cents per minute.
Plan B
A 50-cent minimum charge per completed call.
We have to find the cost, in cents per minute, for a 3-minute call.
Cost according to plan A:
[tex]\text{Cost per minute}\times \text{Call length in minutes}\\= 8 \times 3\\=24 \text{cents}[/tex]
Cost according to plan B:
50 cents for a 3 minute call
Rate =
[tex]\displaystyle\frac{\text{Total cost}}{\text{Duration of call}} = \frac{50}{3} = 16.67 \text{ cents per minute}[/tex]
The company chooses the plan with greater cost, thus, it chooses plan B.
Thus, cost of a 3 minute call is 50 cents at a rate of 16.67 cents per minute.
One number is four times another number. The sum of their reciprocals is 1/4 . What are the numbers?
No, the numbers are not 4/5 and 16/5
Answer:
x=2, y=8
Step-by-step explanation:
Set up the equations:
4x=y
1/4x+1/y=1/4
---------------------
1/y+1/y=1/4
2/y=1/4
cross product
y*1=2*4
y=8
4x=8
x=8/4=2
The required numbers are given as 5 and 20, as of the given conditions.
Given that,
One number is four times another number. The sum of their reciprocals is 1/4.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Let the number be x,
According to the question,
y = 4x - - - - -{1}
and
1 / y + 1/ x = 1/4
1 / 4x + 1/x = 1/4
x = 5
Now,
y = 4 [5] = 20
Thus, the required numbers are given as 5 and 20, as of the given conditions.
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What is the answer:
19 7/5-6 1/3- 5 5/6
Answer:
247/30
Step-by-step explanation:
19 7/5-6 1/3-5 5/6
19 7/5=102/5
6 1/3=19/3
5 5/6=35/6
----------------------
102/5-19/3-35/6
612/30-190/30-175/30=247/30
Answer:
8 7/30
Step-by-step explanation:
need help solving with working much appreciated
Answer:
i. g = 70°
ii. x = 85°
Step-by-step explanation:
Given:
Let first we name the triangle
i. ) Δ PQR , m∠ PRQ = 40°
ii. ) Δ ABC is a right angle at B and a line B- D-C
m∠ DAC = 25°
m∠ ACD = 60°
m∠ BDA = x°
To Find:
i. g = ?
ii. x = ?
Solution:
i.
In Δ PQR , PR ≅ QR ...........{Given]
∴ Δ PQR is an Isosceles Triangle.
c.........{ Base angles of Isosceles triangle are equal }
∴ m∠ PQR = m∠ RPQ = g
Now sum of all the angles in a triangle is 180°
∴ m∠ PQR + m∠ RPQ + m∠ PRQ = 180°....{Angle sum property of Triangle}
[tex]g + g + 40 = 180\\2g=180-40\\2g=140\\g=\frac{140}{2} \\g=70\°[/tex]
∴ g = 70°
ii.
We know sum of all the angles in a triangle is 180°
In Δ DAC
m∠ DAC + m∠ ACD + m∠ ADC = 180°.....{Angle sum property of Triangle}
[tex]25+60+ \angle ADC = 180\\[/tex]
[tex]\angle ADC = 180-85\\\angle ADC =95\\[/tex]
Now By Linear Pair Angle Property
m∠ ADB + m∠ ADC = 180° ........{Linear Pair Angle Property}
[tex]x+95=180\\x=180-95\\x=85[/tex]
∴ x = 85°
Suppose the x-axis of a density graph represents someone's height in inches.
If the area under the density curve from 60 inches to 70 inches is 0.55, what
is the probability of someone's height being anywhere from 60 inches to 70
inches?
A.70%
B.55%
C.65%
D.60%
Simplify (-8)(-2) + 11
Answer:
27
Step-by-step explanation:
-8 * -2 = 16
16 + 11 = 27
Last Monday, two law students met up at café Literatura after school to read the pages they were assigned in the legal methods class. Alejandro can read 1 page per minute, and he has read 28 pages so far. Carly, who has a reading speed of 2 pages per minute has read 12 pages so far.
Part A: Define the variables and write two equations to represent the number of pages that each student read.
Variables:
Alejandro:
Carly:
Answer:
Step-by-step explanation:
Variables:
let x be the number of minutes
let y be the total number of pages read
Use the form y = mx + b
"b" is irrelevant in this context because the initial value is 0 (they have not read it before or it is not given)
m is the rate, how fast they can read, how many pages each minute
Alejandro:
28 = 1x <=Simplify because any number multiplied by 1 is itself.
28 = x
Carly:
12 = 2x
0.03542 as a percent
Answer:
3.542 or 3/271/500
Step-by-step explanation:
0.03542×100
= 1771/50000 ×100
=1771/500
=3.542 or 3/271/500
Simplify the expressions:
2(3a+1)-5a
Answer:
6a+2-5a
ascending
2+a
descending
a+2
6[4x(72-36) divided by 3
Three consecutive integers have a sum of 132
Answer:
43+44+45
Step-by-step explanation:
X + X + 1 + X + 2 = 132
3X + 3 = 132
3X + 3 - 3 = 132 - 3
3X = 129
3X/3 = 129/3
X = 43
consecutive means numbers after
5 divide 3/4 in simplest
Answer:
20/3
Step-by-step explanation:
5/(3/4)=(5/1)(4/3)=20/3
Solve the inequality. Graph the solution.
6n < 90
Answer:
[tex]\displaystyle 15 > n[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6n}{6} < \frac{90}{6} → n < 15[/tex]
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
** The above answer is written in reverse, which is the exact same result.
≥, ≤ → Solid Circle [●]
>, < → Blank Circle [○]
I am joyous to assist you anytime.
slope intercept form slope:⅖ y-intercept:-2
Answer:
y= ⅖x - 2
Step-by-step explanation:
Formula: y = mx + b (m is the slope and b is the y intercept)
Info given:
m= 2/5
b= -2
Plug the info given into the formula, you get (2/5)x -2
How is the number 6.24 x 10^-4 expressed in regular numbers?
Answer:
The scientific notation, 6.24 x 10^-4, means that the 6.24 is multiplied to 10 which is raised to exponent -4. 10^-4 has a regular number value of 0.0001. So, to find the answer you should multiply 6.24 by 0.0001 which gives an answer of 0.000624.20
Step-by-step explanation:
What is the factored form of 8x^2+ 12x? 4(4x^2+8x) 4x(2x+3) 8x(x+4) 8x(x^2+4)
Answer:
4x(2x+3)
Step-by-step explanation:
The answer is 4x(2x+3)
「14+ (-4) +6+(-16) = _
Answer:
0
Step-by-step explanation:
14+ (-4) +6+(-16) = _
10+6+(-16) =
16+(-16) = 0
Answer:
0
Step-by-step explanation:
14 + (-4) + 6 + (-16) =
10 + 6 + (-16) =
16 + (-16) =
0
Name the only type of polygon that must be regular if it is equiangular?
an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon
The only type of polygon that must be regular if it is equiangular is a regular polygon.
Here, we have,
we know that,
A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
an equiangular polygon is a polygon whose vertex angles are equal.
If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon.
Hence, The only type of polygon that must be regular if it is equiangular is a regular polygon.
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When a window is open, the temperature in a room falls 5°F every 15 minutes. Before the window is opened, the temperature was 70°F . Pls Help Me! Will mark Brainliest
Use the Ray tool to make a graph that shows the temperature of the room, T, after the window has been open for m minutes.
Answer:
See attached graph
Step-by-step explanation:
Let m be the number of minutes passed and T be the temperature (in F°)
Before the window is opened, the temperature was 70°F, then at m = 0 minutes, T = 70°F
When a window is open, the temperature in a room falls 5°F every 15 minutes. This means
at m = 15, T = 70°F - 5°F = 65°F
at m = 30, T = 70°F - 10°F = 60°F
at m = 45, T = 70°F - 15°F = 55°F
and so on.
Plot points (0,70), (15,65), (30, 60), (45, 55) and connect them with a straight line. This is the graph that shows the temperature of the room, T, after the window has been open for m minutes.
The circumference of a circle is 113 pi. What is the radius?
Answer:
R=18 (17.98)
Step-by-step explanation:
Since c=dπ
113=dπ
SOlve for d
113=dπ
/π /π
36=d (35.96)
Divide by 2, since the radius is the half of diameter
r=18 (17.98)
Solve for x in the following situation. Show your work.
11x-4/50=70/60
Answer:
x=17/150
Step-by-step explanation:
11x-4/50=70/60
11x-2/25=7/6
11x=7/6+2/25
11x=187/150
x=(187/150)/11
x=(187/150)(1/11)
x=187/1650
simplify,
x=17/150
Answer:
x=17/150
Step-by-step explanation:
Is 312 evenly divisible by 3?
Answer:
Yes
Step-by-step explanation:
312/3=104