Answer:
the first option (1,3) and (1,-2)
Step-by-step explanation:
it is unusual to have neighboring corners of a rectangle called A and C. normally the neighbors of A are B and D. but ok.
A and C have the same x coordinate (-3). so, A is directly above C. the distance between them is therefore only the difference between their y coordinates.
AC = 3 - -2 = 3 + 2 = 5
the area of the rectangle is length × width, so
20 = AC × AB = 5 × AB
AB = 20/5 = 4
in a rectangle all angles are 90 degrees.
so, to find B we need to draw a line of 4 units from A to the right, perpendicular to AC. that means that now the y coordinate is the same as for A (3), and the distance to A is just the difference in the x coordinate :
4 = Bx - -3 = Bx + 3
Bx = 1
=> B = (1, 3)
to maintain the rectangle shape now D has to be right under B and to the right of C with the same distances
DB = AC = 5
DC = AB = 4
due to the special orientation of the rectangle (the sides are all parallel to the x- and y-axis) we can simply add the distances to the corresponding coordinates, or just deduct from the other points :
D has to have the same x coordinate as B (1).
D has to have the same y coordinate as C (-2).
so, D = (1, -2)
After the first exam in a statistics course, the professor surveyed 14 randomly-selected students to determine the relation between the amount of time they spent studying for the exam and exam score. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is: y=6.3333x+53.0298.
Required:
a. Predict the exam score of a student who studies 2 hours.
b. Interpret the slope.
c. What is the mean score of students who did not study?
d. A student who studies 5 hours for the exam scored 81 on the exam. Is this student's exam score above or below average among all students who studies 5 hours?
Solution :
Given :
Equation :
y = 6.3333 x + 53.0298
Here, x = number of hours studied
y = the exam score
a). To predict the exam score, we have to replace x in the least square regression line by 2 :
y = 6.3333 x + 53.0298
y = 6.3333 (2) + 53.0298
= 65.6964
Thus he predicted exam score is 65.6964
b). The slope is the co-efficient of x in the least squares regression line :
Slope = 6.3333
The slope represents the average increase in y as x increases by 1.
The exam score increases on average by 6.3333 points per hour studied.
c). The mean score of the [tex]\text{ students who did not study}[/tex] (studied 0 hours) is obtained by replacing x in the least squares regression line by 0 :
y = 6.3333 x + 53.0298
y = 6.3333 (0) + 53.0298
= 53.0298
d). To predict the exam score of a student who studied 5 hours, we replace x in the least squares regression line by 2 :
y = 6.3333 x + 53.0298
y = 6.3333 (5) + 53.0298
y = 84.6963
Thus the average exam score of a student who studied 5 hours is 84.6963
Since the actual exam score 81 is less than the average exam score of 84.6963 the student's exam score is below the average.
A health care organization, StarCare, wants to implement a program to increase use of diabetes care services. In the past StarCare has billed insurance companies $350 per group session on cardiac care, a similar service, and thus plans to bill $350 for the diabetes group sessions. Operational expenses for the diabetes care services will be $1,000. Because StarCare is concerned with quality of services, it plans to have a consistent group size of 20 participants. However, the number of group facilitators will vary based on the number of diabetes care group participants. For every participant, it costs StarCare $300 in facilitator salary and other expenses. StarCare will only do one session if it is profitable. Based on this information, what are the (a) fixed costs for the proposed diabetes care program and the (b) the total variable costs for 20 participants?
Answer:
a) The fixed cost is $1350.
b) Total variable cost is $6000.
Step-by-step explanation:
a) The fixed cost = Operational cost + Insurance company bill.
= $ 1000 + 350 = $1350.
b) Variable cost:-
The number of facilitators = 20.
The salary for each facilitator = $300.
Total variable cost = $300 x 20 = $6000.
You and a friend are driving go-karts on two different tracks. As you drive on a straight section heading east, your friend passes above you on a straight section heading south. Are these sections of the two tracks???
Yes, these sections of the two tracks, because cross each other while moving in perpendicular directions.
Given that,
You and a friend are driving go-karts on two different tracks. As you drive on a straight section heading east, your friend passes above you on a straight section heading south.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
As given in the question they both move in a different direction that is perpendicular to each other which implies one of them pass over the other by any means such as a subway or bridge.
Thus, Yes, these sections of the two tracks, because cross each other while moving in perpendicular directions.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Over a season in a women's basketball league Jackson scored 40 more points than the second-highest scorer, Leslie. Together, Jackson and Leslie scored 1202 points during the season. How many points did each player score over the course of the season?
Answer:
Step-by-step explanation:
x+x+40=2
+ 4 0
2x+31=1205
2x=1205-31
2x=1174
x=1174/2
x=587
leslie will hace 587 score and
jackson =587+31= 618
On a piece of paper graph y ≥2x
Answer:
Step-by-step explanation:
need answer please !!!!!
Answer: -9
Step-by-step explanation:
f(x)=-5x-4
f(1)=-5(1)-4
=-5-4
f(1) =-9
can someone help me thanks
Let x be the length of the third side.
Thus:
[tex]\mathsf{25^2=17^2+x^2}\\\\\mathsf{625=289+x^2}\\\\\mathsf{x^2=625-289}\\\\\mathsf{x^2=336}\\\\\mathsf{x=\sqrt{336}}\\\\\boxed{\mathsf{x=4\sqrt{21}}}[/tex]
a salesperson earns 5.5% commission on $21000 with a retainer of $23. what is the total earned?
Answer: 1178
Step-by-step explanation:
You can make 5.5% 0.055
Multiply 0.055 by $21000
0.055 x $21000 = 1155
Then you have to add 23
1155+23=1178
Which of the following are true of linear functions? Select all that apply.
There is exactly one output for each input.
The graph of a linear function is a straight line.
A linear function can cross the y-axis in two places.
A linear function has a constant rate of change.
A linear function must cross the x-axis.
Answer:
"there is exactly one output for each input" is cotrrect
"the graph of a linear function" is correct
Step-by-step explanation:
Jackson is making brownies. He uses the following ingredients.
Ingredients Amount for 1
Batch of Brownies
Flour 3 cups
Sugar 2 cups
Butter 1/3 cup
Cocoa Powder 1/4 cup
Jackson has 1 cup of butter. If he wants to use all the butter, how many batches of brownies can he make?
Part A
Which equation can you use to solve the problem?
A. 1 ÷ 3 = 3
B. 1 ÷ 1/3 = 3
C. 1 × 1/3 = 1/3
D. 1 + 1/3 = 1/3
Part B
Jackson used all the butter to make the brownies.
If each brownie is 1/9 of a batch, how many brownies did he make?
Enter your answer in the box.
brownies
Answer:
Part A = B. 1 ÷ 1/3 = 3
Part B = 27 brownies
Step-by-step explanation:
Part A
From the ingredients given in above question:
1/3 cup of butter = 1 batch of brownies
Hence: 1 cup of butter = x
Cross Multiply
1/3 cup of butter × x = 1 cup of butter × 1 batch of brownies
x = 1 cup of butter × 1 batch of brownies/1/3 cup of butter
x = 1 batch of brownies ÷ 1/3
x = 1 batch of brownies × 3/1
x = 3 batches of brownies
Hence, the number brownies Jackson can make with 1 cup of butter Is 3 batches of brownies
Therefore, the equation you can use to solve the problem is Option B. 1 ÷ 1/3 = 3
Part B
If each brownie is 1/9 of a batch, how many brownies did he make?
We know from Part A that Jackson made 3 batches of brownies hence:
1/9 of a batch of brownies = 1 brownie
3 batches of brownies = x
Cross Multiply
1/9 of a batch of brownies × x = 1 brownie × 3 batches of brownies
x = 1 brownie × 3 batches of brownies/ 1/9 of a batch of brownies
x =( 3 ÷ 1/9) brownies
x = ( 3 × 9/1) brownies
x = 27 brownies
Therefore, the number of brownies he made was 27 brownies.
SOMEONE HELP ME PLEASE
Answer:
.12
Step-by-step explanation:
set up two ratios the same way [tex]\frac{x}{y}[/tex]
[tex]\frac{4.8}{.09}[/tex] = [tex]\frac{6.4}{y}[/tex]
cross multiply and solve for y
4.8(y) = .09(6.4)
4.8y = .576
y = .12
What is the area of the parallelogram shown? 8 and 12
Answer:
96
Step-by-step explanation:
A=bh=8·12=
NEXT TIME SHOW THE PICTURE BUT YOU GOOD FOR RN.
During which period did humans first appear on Earth?
Quaternary
Neogene
Paleogene
Cenozoic
Answer:
According to Science, Quaternary.Step-by-step explanation:
I took the quiz.
But really, the Earth is not that old. just a couple thousand years old.
There is no such thing as 2.3 million billion years ago. There is someone with a greater power above who created everything.
Hope this helps and have a great day!
:)
Answer:
A. Quaternary
Step-by-step explanation:
What is 1/5 + 7/8 PLS HELP ME if you help me I’ll give you 20 points!
Answer:
1.075 or 43/40
Step-by-step explanation:
Answer:
1 3/40
Step-by-step explanation:
Write the equation and show work please
Answer:
y=-3x-5
Step-by-step explanation:
(-1, -2) (0, -5)
use slope formula
ΔY = (-5 – -2) = -3
ΔX = (0 – -1) = 1
m = -3
y=mx+b
-5 = -3(0)+b
b = -5
y=-3x-5
Assessment started: undefined.
Item 1
Stan scored 548,751 points on a computer game.
What was his score rounded to the nearest thousand?
Answer:
549,000
Step-by-step explanation:
A credit card company advertises an APR of 14.7 compounded daily. What is the effective interest rate.Round your answer to two decimal places
Answer:15.83
Step-by-step explanation:
15.83 cuz I did it
The following table shows the number of classes that each teacher in the math department at Wilburton High School teaches. Find the median number of classes.
Answer:
4 classes
Step-by-step explanation:
4+3+5+9+3+4=28
28/6=4.6
What is the improper fraction of 20-7
Answer:
20/7 or 13
Step-by-step explanation:
Answer:
20/7 doesn't reduce, so it's 20/7
if you mean 20- 7 it's 13
the proper fraction would be 2 remainder 6, 2.6, 2 and 6/10, or 2 and 3/5 simplified.
What is the equation of the circle?
help!!! Choose the product . - 6p ^ 3 * (3p ^ 2 + 5p - 1)
Answer:
[tex]-18p^{5} -30p^{4} +6p^{3}[/tex]
Step-by-step explanation:
[tex](-6p^{3} )(3p^2+5p-1)[/tex]
[tex](-6p^3)(3p^2)+(-6p^3)(5p)+(-6p^3)(-1)[/tex]
[tex]-18p^{5} -30p^{4} +6p^{3}[/tex]
hope this helps.....
Write each as an algebraic expression
1) the difference of 10 and 5
3) u decreased by 17
5) x increased by 6
7) the sum of q and 8
9) twice q
11) the quotient of 18 and n
Help me if you don't know, don't touch it
9514 1404 393
Answer:
(a) 628 cm³
Step-by-step explanation:
Put the given numbers into the formula and do the arithmetic.
V = πr²h
V = (3.14)(5 cm)²(8 cm) = 628 cm³
Suppose that the lifetimes of TV tubes are normally distributed with a standard deviation of 1.1 years. Suppose also that exactly 20% of the tubes die before 4 years. Find the mean lifetime of TV tubes. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
0
The circumference of a circle is 9.22cm
Find the length of the diameter.
Give your answer rounded to 2 DP.
de
cm
Answer:
Step-by-step explanation:
circumference of a circle = 2πr
9.22 cm = 2*3.14*r
9.22 cm = 6.28*r
9.22 cm /6.28 = r
1.4681 = r
diameter of a circle = 2*r
=2*1.4681
=2.9362
=2.9 cm
Answer:
The Length of diameter of circle is 2.93cm.
Step-by-step explanation:
Given :-Circumference of circle = 9.22 cmTo Find : -Length of diameter, dFormula Used :-Circumference of circle = π × dwhere , d is the length of diameterSolution:-Using formula
Circumference of circle = π × d
substitute the values
9.22 cm = π × d
Using value of π = 3.14
9.22 cm = 3.14 × d
divide each side by 3.14
9.22 cm / 3.14 = 3.14 × d /3.14
2.93 cm = d
Hence, The Length of diameter of circle is 2.93cm.
What value of x is in the solution set of 2(3x - 1) > 4x - 6?
Answer:
-1
Step-by-step explanation:
Distribute
6x - 2 >= 4x - 6
2x >= -4
x >= -2
The measure of an angle ABC is 50°,AD bisects angle BAC, and DC bisects angle BCA. The measure of angle ADC is what?
9514 1404 393
Answer:
115°
Step-by-step explanation:
Let A, B, C represent the vertex angle measures of ΔABC. Then the sum of angles in ΔADC is ...
A/2 +∠ADC + C/2 = 180°
Multiplying by 2 gives ...
A + C + 2×∠ADC = 360°
From the given information, we know ...
A + C + 50° = 180° . . . . . sum of angles in ΔABC
This lets us write an expression for (A +C):
A + C = 130° . . . . . . . . subtract 50° from the previous equation
Substituting for A+C, we get ...
130° + 2×∠ADC = 360°
2×∠ADC = 230° . . . . . . . . . subtract 130°
∠ADC = 115° . . . . . . . . . . . divide by 2
A. -2/9
B. -1/3
C. 1/3
D. 2/9
Answer:
C. 1/3
Hope this helps!:)
Answer:
1/3
Step-by-step explanation:
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
f(x) = -2/9x + 1/3
The slope is -2/9 and the y intercept is 1/3
Factor 24m - 12p + 72 to identify the equivalent expressions.
CHOOSE TWO ANSWERS!!!
A.6(4m+2p+12)
B.2(12m-6p+36)
C.12(2m-p+6)
D.24(m-12p+3)
Answer:
B and C
Step-by-step explanation:
If you take the least common factor you'd see that it could be factored to 2(12m-6p+36)
If you take the greatest common factor then it could be factored to 12(2m-p+6)
Maria has a job selling shoes, and earns a
6% commission on all sales made. How much in
commissions should Maria earn if $778.00 of
shoes are sold?
Answer:
Commission: $46.68
Step-by-step explanation:
https://www.commission-calculator.com/
By using this calculator, it shows you exactly the commission rate.
