Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and
16 minutes to lay down 44 cubic yards of mulch.
Plot five data points and the line that represent this direct variation relationship.
Answers
Answer with explanation:
Given: Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and 16 minutes to lay down 44 cubic yards of mulch.
Here, Time(Independent variable (x)) is directly proportion to the Volume of mulch(dependent variable (y)) lied by Charlie.
Let k be the constant of proportionality, such that
[tex]k=\dfrac{y}{x}[/tex]
For x= 4 and k= 11, [tex]k=\dfrac{11}{4}[/tex]
Required equation: [tex]y=\dfrac{11}{4}x[/tex]
Two points are given in question: (4,11) , (16,44).
Take x= 8 , [tex]y=\dfrac{11}{4}(8)=22[/tex]i.e. point (8,22)
Similarly, for x= 12, y=33 i.e. point (12, 33)
For x= 20 , y= 55 i.e. point (20,55)
Five data points: (4,11) , (16,44), (8,22), (12, 33), (20,55).
Now, we plot these points on graph and join them
Answer:
Here
Step-by-step explanation:
Related Questions
If a polynomial function f(x) has roots -9 and 7 -i, which must be a factor of f(x)
Answers
Answer:
(x + 9) (x - 7)
Step-by-step explanation:
when we put x + 9 = 0 then x = -9 as it's the root of the fuction.
same thing here: x - 7 = 0 then x = 7
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were in either college or high school:
High Low Q1 Q3 IQR Median Mean σ
College 20 6 8 18 10 14 13.3 5.2
High School 20 3 5.5 16 10.5 11 11 5.4
Which of the choices below best describes how to measure the spread of these data?
(Hint: Use the minimum and maximum values to check for outliers.)
Both spreads are best described by the IQR.
Both spreads are best described by the standard deviation.
The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answers
Answer:
The correct option is;
Both spreads are best described by the standard deviation
Step-by-step explanation:
The given information are;
, College High School
High, 20 20
Low, 6 3
Q₁, 8 5.5
Q₃, 18 16
IQR, 10 10.5
Median, 14 11
Mean, 13.3 11
σ, 5.2 5.4
Checking for outliers, we have
College
Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7
Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33
For high school
Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25
Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75
Therefore, there are no outliers and the data is representative of the population
From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2
The difference between the low and the high is also approximately 3 standard deviations
Therefore the college spread is best described by the standard deviation
Similarly for the high school students, the IQR is approximately two standard deviations, the difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4
Therefore the high school spread is also best described by the standard deviation.
Answer:
Both spreads are best described by the standard deviation
Step-by-step explanation:
In the table, describe the shape of the cross section formed when a particular plane passes through the cylinder.
Answers
triangle is the best answer
Answer:
Step-by-step explanation:
Please help out show work ty!
Answers
Answer:
C
Step-by-step explanation:
This is because it has a constant rate of change.
5 x 1.5 = 7.5
6 x 1.5 = 9
7 x 1.5 = 10.5
You can find this image by dividing y by x and testing this rate of change on the other y values. Thus C is correct.
Please Help! Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point
Answers
Answer:
The last choice (3,2), because both lines pass through this point.
Step-by-step explanation:
For a point to be a solution to a system of linear equations, both equation's lines have to pass through that same point.
Answer: (3, 2), because both lines pass through this point
Step-by-stepexplanation:
This can be solved by substitution. The graph will show the same result.
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n)=-6+(n-1)(1/5) A)-6,-5 1/5, -4 B)5, -5 1/5,1 4/5 C)-6, -5 2/5, -4 1/5 D) 0, 3/5, 1 4/5
Answers
Step-by-step explanation:
An arithmetic sequence is given by relation as follows :
[tex]A(n)=-6+(n-1)\dfrac{1}{5}[/tex]
For the first term, put n = 1. So,
[tex]A(1)=-6+(1-1)\dfrac{1}{5}\\\\A(1)=-6[/tex]
For fourth term, put n = 4. So,
[tex]A(4)=-6+(4-1)\dfrac{1}{5}\\\\A(4)=\dfrac{-27}{5}\\\\A(4)=-5\dfrac{2}{5}[/tex]
For tenth term, put n = 10. So,
[tex]A(10)=-6+(10-1)\dfrac{1}{5}\\\\A(10)=-6+\dfrac{9}{5}\\\\A(10)=\dfrac{-21}{5}\\\\A(10)=-4\dfrac{1}{5}[/tex]
Hence, the correct option is (C).
Answer:
the answer in C)-6, -5 2/5, -4 1/5
Kate opens a savings account with a deposit of $1250. After 2 years, she has
receives $112.50 in interest. What is the annual interest rate?
Answers
Answer:
4.5%
Step-by-step explanation:
Simple interest:
I = Prt
112.5 = 1250(r)(2)
1250r = 56.25
r = 0.045 = 4.5%
Answer: 4.5%
The hardcover version of a book sells for 15 dollars and the paperback sells for 11.50. If a store sells 70 copies of the book in one month and charges 917 dollars how many hardcover versions were sold
Answers
Answer: 32 copies of hardcover version.
Step-by-step explanation: Suppose the quantity of hardcover version copies sold is H and the paperback copies is P.
1) A store sells a total of 70 copies:
H + P = 70
2) One hardcover is sold for $15 and one paperback for $11.50. In one month was charged $917:
15H + 11.5P = 917
Solving the system of equations:
H + P = 70 (I)
15H + 11.5P = 917 (II)
Since it is asked for the hardcover version, find H.
Multiply equation (I) by -11.5:
-11.5H - 11.5P = - 805 (III)
Add (II) and (III):
-11.5H - 11.5P = - 805
15H + 11.5P = 917
3.5H = 112
H = 32
In one month, it was sold 32 hardcover version of a book.
The direct distance from a starting point to a finish line is 20 miles. Unfortunately, you can't take the direct route. If you travel 16 miles west, how many miles south must you travel to reach the finish line? A. 12 B. 16 C. 4
Answers
Answer:
12
Step-by-step explanation:
Use the explicit formula 8. = a + (n-1). d to find the 500th term of the
sequence below.
24, 31, 38, 45, 52, ...
A 3545
B. 3517
C. 3524
D. 3493
Answers
Answer:
The 500th term is 3,517
Step-by-step explanation:
Here in this question, we are given an explicit formula to calculate the 500th term of the sequence
The formula to use is ;
a + (n-1)d
where a refers to the first term which is 24 in this case, while d is the common difference which is the difference between success terms and that is 52-45 = 45-38 = 7 and finally n is 500
Now we make a substitution into the formula and we have
24 + (500-1)7
= 24 + (499)7
= 24 + 3493 = 3,517
Solve by the quadratic formula: x^2= 6x-4
Answers
Answer:
3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].
Step-by-step explanation:
x^2 = 6x - 4
x^2 - 6x + 4 = 0
Now, we can use the quadratic formula to solve.
[tex]\frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex], where a = 1, b = -6, and c = 4.
[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4 * 1 * 4} }{2 * 1}[/tex]
= [tex]\frac{6\pm\sqrt{36 - 4 * 4} }{2}[/tex]
= [tex]\frac{6\pm\sqrt{36 - 16} }{2}[/tex]
= [tex]\frac{6\pm\sqrt{20} }{2}[/tex]
= [tex]\frac{6\pm2\sqrt{5} }{2}[/tex]
= 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex]
x = 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].
Hope this helps!
Please explain: Find the measure of angle A. a. 32 b. 57 c. 59 d. No angle exists.
Answers
Answer:
The answer is option B.
57°Step-by-step explanation:
To find Angle A we use cosine
cos ∅ = adjacent / hypotenuse
From the question
The adjacent is 14
The hypotenuse is 26
So we have
cos A = 14/26
cos A = 7/13
A = cos-¹ 7/13
A = 57.42
A = 57° to the nearest degreeHope this helps you
Answer:
57 deg
Step-by-step explanation:
(see attached for reference)
we are given a right triangle together with the lengths of one side (= 14 units) and the hypotenuse (= 26 units)
Using the trigonometry formulas, we can find angle A
cos A = adjacent length / hypotenuse
cos A = 14 / 26
A = cos⁻¹ (14/26) (use calculator)
A = 57.42 deg
A = 57 deg (rounded to nearest whole degree)
11 POINTS! GEOMETRY!! Find the area of the composite function and explain how you broke the shape into pieces to find the area.
Answers
Answer:
370 mm²
Step-by-step explanation:
The area of this figure can be calculated by taking the whole figure as a full rectangle, and consider the part that is cut out from the middle of the shape as another rectangle.
Find the area of the cut-out part and subtract from the area of the full rectangular shape to get the area of the composite figure.
=>Area of full rectangular shape:
Length = 30 mm
Width = 15 mm
Area = L * B = 30*15 = 450 mm²
=>Area of the cut-out Rectangle part:
Length = 10 mm
Width = 8 mm
Area = 10*8 = 80 mm²
=>Area of composite figure = 450 mm² - 80 mm² = 370 mm²
Factorize: 14x^6-45x^3y^3-14y^6
Answers
Answer:
(7x^3+2y^3)(2x^3−7y^3)
pls help me for question no.4
Answers
Answer:
Area of the composite figure = 75.25 cm²
Step-by-step explanation:
Question (4). Given figure is a composite figure having,
(1). Right triangle STU
(2). A kite PSUV
(3). A trapezoid PQRS
Now we will calculate the area of each figure.
(1). Area of the right triangle = [tex]\frac{1}{2}(\text{ST})(\text{TU})[/tex]
= [tex]\frac{1}{2}(3.5)(3)[/tex]
= 5.25 cm²
(2). Area of the kite PSUV = [tex]\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})[/tex]
= [tex]\frac{1}{2}(\text{PU})(\text{SV})[/tex]
= [tex]\frac{1}{2}(\text{TS+RQ})(\text{SV})[/tex]
= [tex]\frac{1}{2}(3.5+7)(6)[/tex] [Since SV = 2 × 3 = 6 cm]
= [tex]3\times 10.5[/tex]
= 31.5 cm²
(3). Area of the trapezium = [tex]\frac{1}{2}(b_1+b_2)(h)[/tex] [Where [tex]b_1[/tex] and [tex]b_2[/tex] are the bases and h is the distance between the bases]
= [tex]\frac{1}{2}[(7-3)+7](7)[/tex]
= [tex]\frac{77}{2}[/tex]
= 38.5 cm²
Total area of the given figure = 5.25 + 31.5 + 38.5
= 75.25 cm²
One equation 0f a pair of dependent linear equations is -5x+7y=2.The second equation can be a)10x-14y=-4 b)-10x-14y+4=0 c)-10x+14y+4=0 d)10x+14y=-4
Answers
Answer:
a) 10x - 14y = -4
Step-by-step explanation:
Two equations linear dependent if you can write one as a multiple of the other. It means that the equation that is a linear dependent with -5x+7y=2 is:
10x - 14y = -4
Because it can be written as:
-2(-5x+7y) = -2(2)
So, this equation is equivalent to -5x + 7y = 2
PLS HELP THE 1ST PERSON TO ANSWER THIS CORRECTLY AND EXPLAINS IT ILL MARK BRAILIEST. What is the solution to the equation 3.6m − 2.7 = −1.8m? m = 0.25 m = 0.5 m = 1.25 m = 1.5
Answers
Answer:
m=0.5
Step-by-step explanation:
Copy the equation.
3.6m-2.7=-1.8m
Subtract 3.6m from both sides.
-2.7=-5.4m
Divide by -5.4 on both sides.
0.5
Which of the following correlation coefficients would correspond to a strong linear relationship in a data set? a. 0 b. 7 c. 0.9 d. 0.4
Answers
The correlation coefficient r is always between -1 and 1, inclusive of both endpoints. We can write [tex]-1 \le r \le 1[/tex]
If r = 0, then we have no linear correlation at all. If r = 1, then we have perfect positive correlation. If r = -1, then we have perfect negative correlation.
We see that r = 0.9 is close to r = 1, so we have strong positive linear correlation going on here.
plz answer this question
Answers
Answer:
D is correct one
Step-by-step explanation:
The pattern consists of repeating 4 faces
1000 is fully divisible by 4
1000/4= 250The 1000th face ends the pattern of 4
The next, 1001th one is the very first face
Correct choice is D
PLEASE HELP Question 1(Multiple Choice Worth 4 points) (08.03)A system of equations is given below: y = –2x + 1 6x + 2y = 22 Which of the following steps could be used to solve by substitution? 6x + 2(−2x + 1) = 22 −2x + 1 = 6x + 2y 6(−2x + 1) + 2y = 22 6(y = −2x + 1) Question 2(Multiple Choice Worth 4 points) (08.03)Solve the system of equations and choose the correct answer from the list of options. d + e = 15 −d + e = −5 Label the ordered pair as (d, e). (0, 0) (10, −5) (5, 10) (10, 5) Question 3(Multiple Choice Worth 4 points) (08.03)A set of equations is given below: Equation H: y = −x + 2 Equation J: y = 3x − 4 Which of the following steps can be used to find the solution to the set of equations? −x = 3x − 4 −x +2 = 3x −x + 2 = 3x − 4 −x + 1 = 3x + 2 Question 4(Multiple Choice Worth 4 points) (08.03)A set of equations is given below: Equation M: y = 3x + 4 Equation P: y = 3x + 7 Which of the following options is true about the solution to the given set of equations? No solution One solution Two solutions Infinite solutions Question 5(Multiple Choice Worth 4 points) (08.03)Solve the system of equations and choose the correct answer from the list of options. x + y = −3 y = 2x + 2 five over 3 comma 4 over 3 negative 5 over 3 comma negative 4 over 3 negative 3 over 5 comma negative 3 over 4 3 over 4 comma 3 over 5
Answers
Answer:
6x + 2(−2x + 1) = 22
Step-by-step explanation:
Answer: The answer is 6x + 2(−2x + 1) = 22
x-15 = 8
A. x= 23
B. x = 7
C. x=-23
D. x=-7
Answers
Answer:
[tex]\boxed{ x = 23}[/tex]
Step-by-step explanation:
=> x - 15 = 8
Adding 15 to both sides
=> x - 15 + 15 = 8 + 15
=> x = 23
Answer:
A. x = 23
Step-by-step explanation:
Step 1: Write out equation
x - 15 = 8
Step 2: Add 15 to both sides (Addition Equality)
x - 15 + 15 = 8 + 15
x = 23
Instructions: Find the measure of the indicated angle to the
nearest degree
Answers
Answer:
? = 33
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp / adj
tan ? = 13/20
Take the inverse tan of each side
tan ^-1 tan ? = tan ^-1 ( 13/20)
? = 33.02386756
To the nearest degree
? = 33
Answer:
33.
Step-by-step explanation:
inverse tan (13/20) = 33.023867579302
9 is subtracted from 3 times the sum of 4 and 2
Answers
Answer:
9
Step-by-step explanation:
3 times the sum of 4 and 2 = 3*(4+2)
= 3 * 6
= 18
18 - 9 = 9
John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for pi , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%
Answers
Answer: A. 51%
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex] , where r = radius of the circle.
In the figure below, we have the complete question.
According to that,
Radius of outer circle = 7ft
Radius of inner circle = 5ft
The probability that the thumbtack will be placed on the inner circle
[tex]=\dfrac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=\dfrac{\pi (5)^2}{\pi (7)^2}\\\\=\dfrac{25}{49}[/tex][π is canceled from numerator and denominator
in percent, [tex]\dfrac{25}{49}\times100=51.0204081633\%\approx51\%[/tex]
So, the probability that the thumbtack will be placed on the inner circle = 51%
Hence, the correct option is A. 51%.
Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x??
These are the options
O 12/21
O 1 2 191
O 1+2,1191
O 12.191
Answers
[tex]x^2-2x+20=0\implies D=b^2-4ac<0\implies x_1,x_2\notin\mathbb{R}[/tex].
There are no real solutions to the quadratic equation.
Hope this helps.
The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard
deviation 7.1%. What is the standardized score for a student who scores 60% on this test?
on 70
Answers
Answer:
-0.704 (corrected to 3 significant figures).
Step-by-step explanation:
Standardized score = (actual score - mean) / standard deviation
Standardized score = (60% - 65%) / 7.1%
= -0.704 (corrected to 3 significant figures).
Standardized score = (actual score - mean) / standard deviation
= (60% - 65%) / 7.1%
= -0.704 (corrected to 3 significant figures).
What is supposed by way of ordinary distribution?A regular distribution is an association of facts set in which maximum values cluster in the center of the range and the relaxation taper off symmetrically in the direction of either intense.
What are everyday distributions with examples?Peak, beginning weight, studying potential, activity satisfaction, or SAT scores are only some examples of such variables. due to the fact that commonly distributed variables are so not unusual, many statistical checks are designed for commonly disbursed populations.
Learn more about the normal distribution here: https://brainly.com/question/4079902
#SPJ2
Please find out the answer and I will mark your answer as the brain test with a five-star rating and a thank you. But only if the answer will be proper and neat...
Answers
Answer:
Below
Step-by-step explanation:
Let x be that missing number
One third of it is x/3
One-ninth of it is x/9
Multiply x/3 and x/9
● (x/3)*(x/9) = (x^2/27)
● (x^2/27) = 108
Multiply both sides by 27
● (x^2/27)*27 = 108*27
● x^2 = 2916
● x = √(2,916) or x = -√(2,916)
● x = 54 or x = -54
So there are two possibilities 54 and -54.
a1/3×1/9=!08
if you multiply you should get 1/27a=108
in order to let a alone multiply both sides by 27
and now your a which is unknown will equal 2916.
What is the length of AC?
Please help me ASAP!!!
Answers
Answer:
a
Step-by-step explanation:
A track coach is trying to improve the 50 -meter-dash times of the track team. He times each student and then implements a month-long training program. At the end of the program, he timed each of the students again. The box plots show the number of seconds it took the students to run the 50 -meter-dash before and after the program. Using the plots, how much did the median change?
Answers
Answer:
-5
Step-by-step explanation:
Given the two box plots showing the number of seconds the students completes the 50-meter-dash race before and after the program, we are to determine the difference between the median value of seconds before and after the program.
Median in a box plot is represented by the vertical line that divides the rectangular box in a box plot.
Thus, the median before the program = 15 seconds
The Median after the program = 10 seconds
The median change = 10 - 15 = -5 seconds.
This means, after the program, most of the students now finish the 50-meter-dash faster, about 5 seconds less the former seconds used before the program.
Answer:
-5
Step-by-step explanation:
i did it on Imagine Math and i got it correct!
Use multiplication to solve the proportion.
9/5 = z/20
Answers
Answer:
36
Step-by-step explanation:
9/5 = z/20
First, we have to divide what we know
9/5 = 1.8
1.8 = z/20
Next, we have to multiply both sides of the equation by 20 to cancel out the division sign
1.8•20 = z/20•20
36 = z