Baruti, a ranger in Kruger National Park in South Africa, collected data about the elephant population in the park. She compared the foot lengths of the elephants and their shoulder height (both in centimeters) and created the following scatter plot. A line was fit to the data to model the relationship.
10
10
20
20
30
30
40
40
50
50
40
40
80
80
120
120
160
160
200
200
240
240
280
280
320
320Shoulder height (cm)Foot length (cm)
Which of these linear equations best describes the given model?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
y
^
=
6
x
−
20
y
^
=6x−20y, with, hat, on top, equals, 6, x, minus, 20
(Choice B)
B
y
^
=
6
x
+
20
y
^
=6x+20y, with, hat, on top, equals, 6, x, plus, 20
(Choice C)
C
y
^
=
3
2
x
−
20
y
^
=
2
3
x−
Answers
The linear function that best represents the relationship between the foot lengths of the elephants and their shoulder height is given as follows:
y = 5.71x - 5.65.
How to obtain the linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients of the function are defined as follows:
m is the slope, representing the rate of change of the output y relative to the input x.b is the y-intercept, representing the numeric value of y when x = 0.From the image given at the end of the answer, two points of the line are given as follows:
(15, 80) and (50, 280).
Given two points, the slope is obtained as the change in y divided by the change in x, hence:
m = (280 - 80)/(50 - 15) = 5.71.
Hence:
y = 5.71x + b.
When x = 15, y = 80, hence the intercept b is obtained as follows:
80 = 5.71(15) + b
b = 80 - 5.71(15)
b = -5.65.
Hence the equation is given as follows:
y = 5.71x - 5.65.
Missing InformationThe graph is given by the image shown at the end of the answer.
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Related Questions
How can the area of this triangle be determined by forming a rectangle? Select from the drop-down menus to correctly complete the statements. Copy and rotate the triangle and place it next to the existing triangle to form a rectangle. The length of the rectangle is Choose. Units. The width of the rectangle is Choose. Units. The area of the rectangle is Choose. Square units. The area of the triangle is half the area of the rectangle, so the area of the triangle is Choose. Square units.
Answers
The area of the triangle can be found by copying the triangle and putting the bases together such that it forms the diagonals of the triangle.
What is the area of the triangle?The area of the triangle is half the product of the height of the triangle and the base of the triangle.
As we know that the area of a rectangle is double the area of a triangle,
therefore, in order to calculate the area of a triangle we need to convert it to a rectangle and then divide the area of the rectangle by 2.
Also, we know that the diagonal of a rectangle divides it into two equal triangles, therefore, we will put the triangle along the diagonal of the base.
Thus, to find the area of the triangle we will copy the triangle and put the base of the together such that it forms the diagonals of the triangle.
Since the triangles are put on each other along the base, therefore, the height(h) of the triangle will be the length of the rectangle, and the breadth of the triangle will be equal to the base of the triangle(b).
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Ai need help please 43
Step-by-step explanation:
please just need help
please help I realy need help HHHHEEELLLPPPP
Answers
Answer: 63/100
Step-by-step explanation: it is in its most simplified form
5x+15+10x+7
5(x+3)+2x+7
Answers
Step-by-step explanation:
1. Combine Like Terms (Add):
[tex]5x+15+10x+7[/tex]
[tex]15x+22[/tex]
2. Use Distributive Property:
[tex]5(x+3)+2x+7[/tex]
[tex]5x+15+2x+7[/tex]
Combine Like Terms:
[tex]7x+22[/tex]
What is the percent of change from 55 to 22?
Answers
Answer:
40 percent
Step-by-step explanation:
22/55 = 0.4
0.4 = 40%
check answer: 55 x 0.4 = 22
PLEASE HELP ITS DUE TODAY PLEASE HELP ASAP 15 POINTS PLEASE HELP
Answers
Answer:
210 cm³
Step-by-step explanation:
volume = W x L x H
(where W = width, L = length and H = height)
By inspection of the diagram,
W = 6 cm
L = 7 cm
H = 5 cm
Therefore, volume = 6 x 7 x 5 = 210 cm³
Answer:
210 cm³
Work:
6×7=42
42×5=210
Step-by-step explanation:
When finding volume of a cube or rectangular prism you do the same thing as when you find the area of a square or rectangle, which is multiply the dimensions.
We see it is 7 cubes long, 6 cubes wide, and 5 cubes tall. To find the volume multiply all of these values together.
7×6×5=210
So, the volume of the prism is 210 cubes. Sense each cube is 1 cm³ the answer to the problem is 210 cm³
Two positive integers differ by 9. If the squares of the integers are added, the result is 125. Find
the two integers.
Answers
Answer:
x - y =9
x^2 + y^2 = 125
2^2 + 11^2 = 125
11-2 = 9
Thus, the two numbers are 2 & 11.
Hope this helps!
The equation for the area of a circle is given.
A=πr2
If the radius (r) of the circle is 3, what is the area in terms of π?
3π
3π2
9π
9π2
Answers
[tex]A=\pi r^2; r=3 =>\\\\A=\pi \times3^2\\A=9\pi[/tex]
Answer: [tex]9\pi[/tex]
find the mean of 12 ,10,12,14,8,15,8,9,6,5
Answers
Answer:9.9
Step-by-step explanation:
Add up the scores and dividing the total by the number of scores.
Answer:
9.9
Step-by-step explanation:
12+10+12+14+8+15+8+9+6+5 =99
99÷10=9.9
Find the equation (in terms of x ) of the line through the points (-4,-4) and (2,4)
Answers
Answer:
[tex]y=\frac{4}{3}x+\frac{4}{3}[/tex]
Step-by-step explanation:
Let [tex](x_1,y_1)\rightarrow(-4,-4)[/tex] and [tex](x_2,y_2)\rightarow(2,4)[/tex]:
Determine slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{4-(-4)}{2-(-4)}\\ \\m=\frac{4+4}{2+4}\\ \\m=\frac{8}{6}\\ \\m=\frac{4}{3}[/tex]
Use either coordinate point to find "b", the y-intercept
[tex]y=mx+b\\\\4=\frac{4}{3}(2)+b\\ \\4=\frac{8}{3}+b\\ \\\frac{4}{3}=b[/tex]
Final Equation
[tex]y=\frac{4}{3}x+\frac{4}{3}[/tex]
The heart rate of 10 football players is sampled. The rates, measured in beats per minute, are
62, 74, 74, 64, 76, 64, 80, 76, 68, 76
What is the best estimate of the population mean for heart rate among football players?
Enter your answer in the box.
beats/min
PLEASE ANSWER ASAP
Answers
Answer:
I know that I saw that on social
Answer:
71.4
Step-by-step explanation:
add all together and divide by the number of players.
At a grocery store, tasting cups are used to let customers try a
new brand of chicken stock. An ounce of chicken stock can be filled up by 5 tasting
cups. Each carton of chicken stock is 16 oz. if 5,630 customers tried the chicken stocks in
one day, they drank about ____ cartons of chicken stock.
A. 70
B. 110
C. 350
Answers
Madaly was extremely excited to go on vacation. HELP!!!!
The underlined part of the sentence can best be described as a/an...
adjective phrase.
prepositional phrase.
adverbial phrase.
noun phrase.
Answers
The underlined part of the sentence can best be described as an adjective phrase.
Parts of speechIn formation of sentences in English language, the words that are used usually include the following parts of speech:
nounspronounsverbsadjectivesadverbsprepositionsconjunctionsinterjectionsAn Adjective is a word that describes or modifies a noun or a pronoun. While adjective phrase is the phrase that can be used to modify or describe a noun in a sentence.
From the sentence given, extremely excited is adverbial phrase used to modify the noun vacation.
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An executive for the movie production company wants to create a function that models this data. . Create a function that can be used to model the data shown in the table . Be sure to define the variables and provide justification for your choice of function . Discuss any possible domain restrictions which should be placed on your model . Use your model to estimate the box office gross the company should expect in week 10 .
Answers
Functions can be modeled by equations, tables and graphs
The equation that models the function is [tex]y = \frac 14x +1[/tex]The domain of the function is the set of whole numbersThe company should expect 4 box office gross in week 10 How to determine the functionFrom the question, we have the following ordered pairs
(x,y) = (0,1) and (4,2)
The function is a linear function.
So, we start by calculating the slope (m) using:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
Substitute known values
[tex]m = \frac{2 - 1}{4 - 0}[/tex]
[tex]m = \frac{1}{4}[/tex]
The equation is then calculated as:
[tex]y = m(x -x_1) +y_1[/tex]
This gives
[tex]y = \frac 14(x -0) +1[/tex]
[tex]y = \frac 14x +1[/tex]
The domain of the above function is the set of whole numbers
Substitute 10 for x, to calculate the number of box office gross for week 10
[tex]y = \frac 14 * 10 +1[/tex]
[tex]y = 3.5[/tex]
Approximate
[tex]y = 4[/tex]
Hence, the company should expect 4 box office gross in week 10
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Round your answer to the nearest hundredth.
Answers
Given b=4 and ∠β=20°,
a = 10.98991
c = 11.69522
∠α = 70° = 1.22173 rad = 7/18π
h = 3.75877
area = 21.97982
perimeter = 26.68513
inradius = 1.64735
circumradius = 5.84761
a
b
c
Calculation Steps
The following is one way to perform the calculation. It may not be the best way.
c =
b
sin(β)
= 11.69522
a = √c2 - b2
= √11.6952176006522 - 42
= √120.77811472661
= 10.98991
∠α = 90° - ∠β
= 70° = 1.22173 rad = 7/18π
area =
a × b
2
=
10.989909677818 × 4
2
= 21.97982
perimeter = a + b + c
= 10.989909677818 + 4 + 11.695217600652
= 26.68513
inradius =
a × b
a + b + c
=
43.959638711274
26.685127278471
= 1.64735
circumradius =
c
2
=
11.695217600652
2
= 5.84761
- ror
Write and equation in slope intercept form of the line that has a slope of -6 and passes through the point (3,-4).
Answers
Hi! I will help you with a smile!
First of all, we have the slope of the line and a point that it passes through.
Let’s write the line’s equation in Point-Slope Form:
y-y1=m(x-x1)
Where
y1 is the y-coordinate of the point, m is the slope of the line, and x1 is the x-coordinate.
In this case, y1=-4, m=-6, and x1=3
Solve:
y-(-4)=-6(x-3)
y+4=-6x+18
y=-6x+18-4
y=-6x+14 (Answer)
Hope it helps.
Do comment if you have any query regarding my answer.
Answered by
PeacefulNature :-)
Answer:
y = -6x+14
Step-by-step explanation:
m = -6 ,given as x an y (3,-4)
solution y-y1 = m(x-x1)
y-(-4) = -6(x-3)
y+4 = -6x+18
then y = -6x+18-4
y = -6x+14
The admission fee at a water park is $9 for children and $15 for adults. On a certain day, 220
people entered the park, and the admission fees collected totaled $2640. How many children and
how many adults were admitted? Let x represent the number of children and y represent the
number of adults.
Total Equation:
Cost Equation:
The number of children admitted was
The number of adults admitted was
Answers
hope this helps :)
help asap! brainlist will be given!
Answers
for b, the answer would be 15 because as i explained before, the bigger segment is double the size of the smaller segment inside the figure
for c and d, i’m not so sure on the results
I add 12 to a certain number and then double the result. The answer is 42. Find the original number
Answers
2x+24=42
2x=42-24
2x=19 divided by two
X=9.5
A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 13°
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22°
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.
Answers
Answer:
198.6
Step-by-step explanation:
see pic
The bottom of ladder must be placed 3 feet from wall.The ladder is 10 feet long. How far above the ground does the ladder touch the wall?
Answers
Answer:
9.54ft
Step-by-step explanation:
This problem uses pythagoras theorem as the ladder and the wall make a triangle.
A
B C
Points A, B and C represent this problem. BC is 3ft, AC is 10ft and AB is x, now we sub this information into pythagoras theorem formula
3^2+b^2=10^2
Rearranged this is,
b^2=10^2-3^2
b^2=91
b=[tex]\sqrt{91}[/tex]
b=9.54
The above is rounded to two decimal places
width is 4 cm hight 8 cm how much square
Answers
Answer: The square is 32
Step-by-step explanation:
In - order to find the size of the square you must do width times height . . .
What is 4 x 8 ? 32
Please help!!! What is the equation of the function given the following table of values?
Answers
Answer:
C
Step-by-step explanation:
if you plug in the X values, you get the corresponding Y values.
There are 11 rainbows that total 1,011 miles in total. What is the mean length of the rainbows?
Answers
It can be seen that the value of the mean computed will be 91.9 miles.
How to calculate the meanA mean simply means the average of a set of numbers. In this case, there are 11 rainbows and thete are total of 1,011 miles.
Therefore, the mean of the numbers will be:
= 1011/11
= 91.9 miles.
In conclusion, the correct option is 91.9 miles.
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If im going 30 km per hour and i need to go 500 metres how long would it take
Answers
Answer:
1 minute
Step-by-step explanation:
1km = 1000m
30km = 30000m
30km ÷ 60 = 500m
it takes one hour to go 30km or a ratio of 30km to 1hour. 1hour is also 60minutes. 30:60
divide both sides by 60 gets 500m and the amount of time to go that distance 1 minute
Answer:
1/60 hr or 1 minute
Step-by-step explanation:
30 km per hour
30 km : 1 hr
convert 500 metres to km
1 km = 1000 metres
500 ÷ 1000 = 0.5 km
using ratios
30 km : 1 hr
0.5 km : x hr
to get from 30 to 0.5 multiply by 1/60 ( we got this from doing 0.5 ÷ 30) , so do the same to the other side
1 hr × 1/60 = 1/60 hr
you can convert to minutes = 1/60 × 60 = 1 minute
Use the bar diagram to write an equation. Then solve for x.
Answers
Answer:
we need to know the question
Step-by-step explanation:
What is the ratio for 128 eggs per 72 strips of bacon
Answers
Answer:
128:72
Or
16:9 (simplified)
Hope this helps!
The magic number is -15. Combine each statement with the magic number and determine if it will result in zero. _______ a. An elevator rises 15 floors. _______ b. $15 is withdrawn out of your account. _______ c. The temperature rises 15 degrees.
Answers
Answer:
A. is 0
B. is -30
C. is 0
Step-by-step explanation:
Hope this helps!
The correct answers are:
0-300CalculationsWe are asked to combine the magic number -15 with the given statements.
Hence, if we combine the magic number with the given statements, we would have:
a. -15 + 15 = 0
b. -15 + (-15)= -30.
c. -15 + 15 = 0.
Hence, the answers are 0, -30 and 0 respectively.
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Please help me figure these out!
Answers
Step-by-step explanation:
just u have to put the values of sin and cos and you will get the answer
hope u get help
Use IF functions to calculate the regular pay and overtime pay based on a regular 40-hour workweek in cells E5 and F5. Pay overtime only for overtime hours. In cell G5, calculate the gross pay based on the regular and overtime pay. Abram’s regular pay is $398. With 8 overtime hours, Abram’s overtime pay is $119.40.
Answers
Excel formulas are expressions used to perform computation.
The Excel formula to enter in cell E5 is =IF(D5<$B$21,D5,$B$21) * C5The Excel formula to enter in cell E5 is =IF(D5>$B$21,(D5-$B$21) * C5 * $B$22, 0)The regular payFrom the complete question, cell B21 represents base work hour
So, we start by checking if the work hour in cell D5 is less than the base work hour in cell B21
If yes, the work hour remains D5; otherwise the work hour is cell B21
The work hour is then multiplied by the rate in cell C5
Hence, the Excel formula to enter in cell E5 is =IF(D5<$B$21,D5,$B$21) *
The overtime payHere, we start by checking if the work hour in cell D5 is greater than the base work hour in cell B21
If yes, the overtime hour the difference between D5 and B21; otherwise the overtime hour and pay is 0
The over time hour if there is, is then multiplied by the rates in cells C5 and B22
Hence, the Excel formula to enter in cell E5 is =IF(D5>$B$21,(D5-$B$21) * C5 * $B$22, 0)
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Write the slope-intercept form of
the equation of the line described
through: (2.0), perp. to y=-2x+2
Answers
Answer: Y= 1/2X+5
Step-by-step explanation: Equation of the line
The slope-intercept form of a line is given by:
Being:
m = the slope of the line
b = the y-intercept
We can also use the point-slope form of the line:
Being:
(h,k) = A point that belongs to the line
Two lines of slopes m1 and m2 are perpendicular if:
We are given the line:
Whose slope is m1=-2
Thus, the perpendicular line has a slope of:
The required line contains the point (-8,1), thus the equation is:
Removing the parentheses:
Adding 1:
Operating: