Answers
It is observed that the mean line of the data should pass through the points (3,3), (2,4), (1,5), (0,6), (-1,7).
Consider that the equation of a line passing through two given points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]So the equation of the best fit line passing through (3,3) and (0,6) will be,
[tex]\begin{gathered} y-3=\frac{6-3}{0-3}(x-3) \\ y-3=\frac{3}{-3}(x-3) \\ y-3=-(x-3) \\ y-3=-x+3 \\ y=-x+6 \end{gathered}[/tex]Thus, option C is the correct choice.
Related Questions
In a circle, diameter AB is perpendicular to chord CD at point L. Which statement will always be true about this circle?A. CL=LDB. AL>LBC. CL⋅LD=ABD. BL>LA
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The chord is CD and the diameter AD of the circle are perpendicular to each other at point L. According to the perpendicular bisector theorem, if the diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc. This means that chord CD is bisected by the diameter of the circle at point L. In this case this means CL = LD
A quilt maker sews both large and small quilts. A large quilt requires 8 yards of fabric while the small quilt requires 3 yards of fabric. How many of each size quilt did she make if she used a total of 90 yards of fabric to make 15 quilts?
Answers
Answer:
The number of each size quilt is;
[tex]\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}[/tex]Explanation:
Given that a large quilt requires 8 yards of fabric while the small quilt requires 3 yards of fabric.
Let x represent the number large quilt and y the number of small quilt.
If she used a total of 90 yards of fabric to make 15 quilts then we have;
[tex]\begin{gathered} 8x+3y=90\text{ ---------1} \\ x+y=15\text{ ----------2} \end{gathered}[/tex]let us solve the system of equations by substitution. From equation 2;
[tex]x=15-y[/tex]substituting into equation 1;
[tex]\begin{gathered} 8x+3y=90 \\ 8(15-y)+3y=90 \\ 120-8y+3y=90 \\ 120-5y=90 \\ 5y=120-90 \\ 5y=30 \\ y=\frac{30}{5} \\ y=6 \end{gathered}[/tex]substituting the value of y;
[tex]\begin{gathered} x=15-y \\ x=15-6 \\ x=9 \end{gathered}[/tex]Therefore; the number of each size quilt is;
[tex]\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}[/tex]Find the x- and y-intercepts of the graph of the function f (x) = -2|x – 1| +6.Enter your answers as points, (a,b).Enter the x-intercepts in order of increasing x-value.
Answers
Given the function:
[tex]fx=-2|x-1|+6[/tex]Let's find the x-intercepts and the y-intercepts of the graph.
• x-intercepts:
To find the x-intercept, substitute 0 for f(x) and solve for x:
[tex]\begin{gathered} 0=-2|x-1|+6 \\ \end{gathered}[/tex]Subtract 6 from both sides:
[tex]\begin{gathered} 0-6=-2|x-1| \\ \\ -6=-2|x-1| \end{gathered}[/tex]Divide both sides by -2:
[tex]\begin{gathered} \frac{-6}{-2}=\frac{-2|x-1|}{-1} \\ \\ 3=|x-1| \\ \\ x=\pm3+1 \\ \\ x=3+1,-3+1 \\ \\ x=-2,\text{ 4} \end{gathered}[/tex]Therefore, the x-intercepts are:
x = -2, 4
• y-intercept:
To find the y-intercept, set the value of x to zero and solve for f(x).
[tex]\begin{gathered} f(x)=-2|x-1|+6 \\ \\ f(0)=-2|0-1|+6 \\ \\ f(0)-2|-1|+6 \\ \\ f(0)=-2(1)+6 \\ \\ f(0)\text{ =}-2+6 \\ \\ f(0)=4 \end{gathered}[/tex]Yes, therefore, the y-intercept is:
y = 4
ANSWER:
• x-intercepts: x = -2, 4
,• y-intercept: y = 4
Geometry MAFS.912.G-C0.3.9 11. Peach Street and Cherry Street are parallel. Apple Street intersects them as shown in the diagram below. Apple Street 12 RS Peach Street Cherry Street If mZ1 = 2x +36 and m22 = 7x-9, what is m 1? A 9 B. 17 C. 54 D. 70
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therefore,
[tex]m\angle1=2(17)+36=34+36=70[/tex]Can you pls help me with this question thank you
Answers
First, identify an expression for the phrase "twice a number v".
The word "twice" means "two times" or "double", and refers to a multiplication by the number 2.
Then, "twice a number v" can be written using algebraic language as 2v.
So, the phrase "twice a number v plus 52" is equivalent to "2v plus 52", which can be expressed in algebraic languaje as 2v+52.
Therefore, the correct choice is option A) 2v+52
A frequency table of gradəs has five classes (A, B, C, D, F) with frequencies of 4, 10, 17,6, and 2 respectively. Using percentages, what are the relativefrequencies of the five classes?Complete the table.Grade Frequency Relative frequencyА4%B10%с176F2%(Round to two decimal places as needed.)%62
Answers
GRADE FREQUENCY RELATIVE FREQUENCY % RELATIVE FREQUENCY
A 4 4/39 4/39 x 100 = 10.26
B 10 10/39 10/39 x 100 = 25.64
C 17 17/39 17/39 x 100 = 45.59
D 6 6/39 6/39 x 100 = 15.38
F 2 2/39 2/39 x 100 = 51.28
∑F = 39
Mike rolls a die 30 times and gets the frequency shown in the table below. What is the relative frequency (experimental probability of rolling a 3 or a 4?
Answers
Given:
Number of times the die rolled = 30
Number of times got 3 = 7
Number of times got 4 = 6
Required: Experimental probability of rolling a 3 or a 4.
Explanation:
Experimental probability is defined as
[tex]P(\text{event\rparen=}\frac{\text{ Number of times event occur}}{\text{ Total number of events}}[/tex]Number of times got a 3 or a 4 = 7+6 = 13
So,
[tex]\begin{gathered} P(\text{rolling a 3 or a 4\rparen=}\frac{\text{ Number of times got a 3 or a 4}}{\text{ Total number of trials}} \\ =\frac{13}{30} \end{gathered}[/tex]Option C is correct.
Final Answer: Experimental probability of rolling a 3 or a 4 is 13/30.
f(x)=(−x+3)(x+5)Use the Parabola tool by plotting the vertex first and then another point on the parabola.
Answers
Answer:
Explanation:
Here, we want to get the plot of the parabola
We start by getting its vertex
We have that as follows:
[tex]\begin{gathered} f(x)\text{ = (-x+3)(x+5)} \\ f(x)=-x^2-2x+15 \end{gathered}[/tex]We have the vertex form as follows:
[tex]\begin{gathered} f(x)\text{ = }-1(x+1)^2+16 \\ \text{compared with the general vertex form:} \\ f(x)=a(x-h)^2+k \\ \text{vertex is (h,k)} \end{gathered}[/tex]The vertex here is thus (-1,16)
To get the other point, we can equate the values in the brackets to zero and solve for x
We have that as:
[tex]\begin{gathered} -x+3\text{ = 0} \\ x\text{ = 3} \\ x+5\text{ = 0} \\ x=\text{ -5} \end{gathered}[/tex]The other points are thus (3,0) and (-5,0)
Thus, we can join (-1,16) with either (3,0) and (5,0) as shown below:
As a Nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patients doctor indicated that you should mix 150 milligrams of Medication A with 225 milligrams of Medication B. However this week, the doctor said to only use 165 milligrams of Medication B. How many milligrams of Medication A should be mixed this week? Answer_____milligrams
Answers
Answer: This problem can be solved using the concept of mathematical proportions, the equation that can be constructed for the problem is as follows:
[tex]\begin{gathered} \frac{A_1}{B_1}=\frac{A_2}{B_2} \\ \\ \\ \frac{A_{1}}{B_{1}}=\frac{150mg}{225mg} \\ \\ \\ \frac{A_{2}}{B_{2}}=\frac{A_2}{165mg} \\ \\ \therefore\Rightarrow \\ \\ \\ \frac{150mg}{225mg}=\frac{A_{2}}{165mg}\Rightarrow(1) \end{gathered}[/tex]Solving equation (1) gives the answer, the solution to the equation (1) is as follows:
[tex]\begin{gathered} \begin{equation*} \frac{150mg}{225mg}=\frac{A_2}{165mg} \end{equation*} \\ \\ \\ A_2=(\frac{150}{225}\times165)mg=110mg \\ \\ A_2=110mg \end{gathered}[/tex]Therefore the answer is 110mg.
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function. v(t)=25,900(0.86)^t Find the intial value of the car and the value after 13 years. Round your answers to the nearest dollor as necessary.
Answers
To find the initial value of the car replace when t=0
[tex]\begin{gathered} V(0)=25,900(0.86)^0 \\ V(0)=25,900 \end{gathered}[/tex]To find the value after 13 years use t=13
[tex]\begin{gathered} V(13)=25,900(0.86)^{13} \\ V(13)=3645.69\approx3646 \end{gathered}[/tex]Ping says that subtracting 2- 1 1/3 yields the same result as computing 2-1+ 1/3. Quon disagrees. He thinks its the same result as computing 2-1- 1/3. Is either correct? Explain.
Answers
2 - 1 1/3 is
2 - 4/3 = (6-4)/3 = 2/3
2 - 1 + 1/3 is
1 + 1/3 = 4/3
According to Q
A triangle has 2 sides of length 15 and 19 what is the smallest possible whole number length for the 3rd side
Answers
We have a triangle with 2 sides of length 15 and 19.
We have to find the smallest possible whole number length for the 3rd side.
We can draw this as:
The third size is x.
If we reduce h, approaching to 0, x is minimized.
When h is very close to 0 (if h=0, the triangle cease to exist), the value of x can be written as a little bigger than the difference between the largest side (19) and the other side (15).
Then, x is, in the limit h-->0:
[tex]x+15>19\Rightarrow x>19-15=4\Rightarrow x>4[/tex]As x>4, the next whole number is 5.
NOTE: if x=4, the triangle does not exist, as there is no height or 3 angles.
Answer: The smallest whole number length for the 3rd side is 5.
Use order of operations and the mathematical properties of numbers to simplify
these numbers.
6x7-7x3 =
Answers
Answer:
21
Step-by-step explanation:
[tex]6*7-7*3[/tex]
Utilizing PEMDAS, we know that all multiplication comes before subtraction.
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Knowing this, multiply the four terms:
[tex]42-21[/tex]
Now subtract:
[tex]21[/tex]
Solve the following trigonometric equation on the interval [0, 2π]12sin2x−3=0
Answers
Given the expression:
[tex]12sin^2(x)-3=0[/tex]To solve the expression, follow the steps below:
Step 01: Add 3 to both sides.
[tex]\begin{gathered} 12sin^2(x)-3+3=0+3 \\ 12sin^2(x)=3 \end{gathered}[/tex]Step 02: Divide both sides by 12.
[tex]\begin{gathered} \frac{12sin^2(x)}{12}=\frac{3}{12} \\ sin^2(x)=\frac{1}{4} \end{gathered}[/tex]Step 03: Take the square root of both sides.
[tex]\begin{gathered} \sqrt{sin^2(x)}=\pm\sqrt{\frac{1}{4}} \\ sin(x)=\pm\frac{1}{2} \end{gathered}[/tex]Step 04: Evaluate the results.
First, let's evaluate sin(x) = 1/2.
Sin(x) is positive in the first and in the second quadrant. Then,
[tex]\begin{gathered} sin^{-1}(\frac{1}{2})=x \\ x=\frac{\pi}{6},x=\frac{5}{6}\pi \end{gathered}[/tex]Second, let's evaluate sin(x) = -1/2.
Sin(x) is negative in the third and in fourth quadrant. Then,
[tex]\begin{gathered} sin^{-1}(-\frac{1}{2})=x \\ x=\frac{7}{6}\pi,x=\frac{11}{6}\pi \end{gathered}[/tex]Answer:
[tex]x=\frac{\pi}{6},x=\frac{5}{6}\pi,x=\frac{7}{6}\pi,x=\frac{11}{6}\pi[/tex]In the diagram, m of angle Q= 75º and Measure of arc QS = 133 degrees. Find Measure of QR. PLEASE HELP!
Answers
It is given that angle Q is 75 degrees and arc QS is 133 degrees.
Use inscribed angle theorem on angle RQS to get:
[tex]\begin{gathered} \angle RQS=\frac{1}{2}mRS \\ m(RS)=2\angle RQS \\ m(RS)=2\times75=150^{\circ} \end{gathered}[/tex]It is known that the sum of all arcs of circle is 360 degrees so it follows:
[tex]\begin{gathered} m(QS)+m(RS)+m(RQ)=360 \\ 133+150+m(RQ)=360 \\ m(RQ)=360-150-133=77^{\circ} \end{gathered}[/tex]Hence the measure of arc QR is 77 degrees.
O
1) if b is a root of a polynomial equation then (x-b) is a ______of the polynomial2). polynomial equation y=x^2+x-6 root=2 ,factor=__
Answers
If b is a root of a polynomial equation then (x - b) is a FACTOR of the Polynomial
Question 2
polynomial y = x^2 + x + 6
If root = 2
Then the factor is iven by
(x - 2)
find f(-3) for the equation below f(x)=-2x+3
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In this problem, we are applying function notation. When we see a function written as
[tex]f(x),[/tex]we read it as "f of x" or "f as a function of x."
We will take the value of x and substitute it into the quation.
The function rule states
[tex]f(x)=-2x+3[/tex]Since we are given f(-3), we will substitute each x-value (inside parentheses), and simplify:
[tex]f(-3)=-2(-3)+3=6+3=9[/tex]Therefore, f(-3) = 9.
find the values of x and y if l || m.
Answers
Explanation
Step 1
when a lines intersects a pair of parallel lines , diverse angles are created
All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent,so ( in the image yellow angles are corresponding, so)
[tex]\begin{gathered} (5x+14)=(7x-30) \\ \end{gathered}[/tex]solve for x
[tex]\begin{gathered} (5x+14)=(7x-30) \\ \text{subtrac 5x in both sides} \\ (5x+14)-5x=(7x-30)-5x \\ 14=2x-30 \\ \text{add 30 in both sides} \\ 14+30=2x-30+30 \\ 44=2x \\ \text{divide both sides by 2} \\ \frac{44}{2}=\frac{2x}{2} \\ 22=x \end{gathered}[/tex]Step 2
now, yellow angle and ble angles are supplementary( Two Angles are Supplementary when they add up to 180 degrees),so
[tex]\begin{gathered} (3y+11)+(7x-30)=180 \\ \end{gathered}[/tex]let
x=22
and solve for y
[tex]\begin{gathered} (3y+11)+(7x-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ (3y+11)+(7\cdot22-30)=180 \\ 3y+11+124=180 \\ 3y+135=180 \\ \text{subtract 135 in both sides} \\ 3y+135-135=180-135 \\ 3y=45 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{45}{3} \\ y=15 \end{gathered}[/tex]I hope this helps you
I need help with this please, thank you very much
Answers
1. translation 1 unit left and 6 units down
[tex]h(x)=6(2^x)-1[/tex]2. Stretch vertically by a factor of 6 and translate 1 unit down
[tex]j(x)=2^{6x}-1[/tex]3. Compress horizontally by a factor of 6 and translate 1 unit down
[tex]k(x)=2^{x+6}+1[/tex]4. Translation 6 units left and 1 unit up
i need help finding the bottom layer of the cake
Answers
In a trpezium, the median line is always parallel to the bases. The expression for the length of the median of trapezium is :
[tex]\text{length of mediam=}\frac{Sum\text{ of parallel sides}}{2}[/tex]In the trapezium: NM = ML=LK=PQ=QR=RS
we have : NP = 8, LR =20
Conisder the case of trapezium NPLR, where MQ is the median
From the expression of the length of median:
[tex]\begin{gathered} MQ=\frac{NP+LR}{2} \\ MQ=\frac{8+20}{2} \\ MQ=\frac{28}{2} \\ MQ=14 \end{gathered}[/tex]Now, consider the case of trapezium MQSK, where LR is act as median, MQ= 14, LR =20
From the expression of the length of median
[tex]\begin{gathered} \text{length of median=}\frac{Sum\text{ of parallel sides}}{2} \\ LR=\frac{MQ+KS}{2} \\ 20=\frac{14+KS}{2} \\ 14+KS=40 \\ KS=40-14 \\ KS=26\text{ inches} \end{gathered}[/tex]So, the diameter of the bottom KS is 26 inches
Answer : the diameter of the bottom KS is 26 inches
rotate the following ploygon 90 degrees ccw. List the new image coordinates. write the general rule.
Answers
The general rule for a 90° counterclockwise rotation is
[tex](x,y)\rightarrow(-y,x)[/tex]We have to apply this rule to each point on the given table.
[tex]\begin{gathered} A(2,3)\rightarrow A^{\prime}(-3,2) \\ B(5,3)\rightarrow B^{\prime}(-3,5) \\ C(1,5)\rightarrow C^{\prime}(-5,1) \\ D(6,5)\rightarrow D^{\prime}(-5,6) \end{gathered}[/tex]Therefore, the new image coordinates areA'(-3,2)
B'(-3,5)
C'(-5,1)
D'(-5,6)
Asuka is planting grass seeds on her new lawn. The dimensions of her lawn are 4 ft by 3 ft. The instructions to plant the grass seeds suggest planting 16 seeds for every squarefoot How many seeds should Asuka use to plant her entire lawn? foot
Answers
Since she can plant 16 seeds per square foot, then
We must find the area of the lawn
Since the lawn is shaped a rectangle of dimensions 4 ft and 3 ft, then
[tex]\begin{gathered} A=L\times W \\ A=4\times3 \\ A=12ft^2 \end{gathered}[/tex]Since 1 square foot = 16 seed, then
12 square feet = 12 x 16 = 192 seeds
She will need 192 seeds to plant the entire lawn
What answer was rounded to the tenths place 4.1,4.100,or 4
Answers
Answer:
4.1
Explanation:
In the number:
[tex]1.234[/tex]• The place value of 2= 2 tenths
,• The place value of 3= 3 hundredths
,• The place value of 4= 4 thousandths
The digit rounded to the tenths place is that which have just a digit after the decimal sign.
The correct choice is 4.1
ADBA. 9°B. 10°C. 81°D. 91°99⁰CABCD is a quadrilateral. If mZC = (x²)°, find mZC..
Answers
Since ABCD is a quadrilateral, the sum of internal angles is equal to 360°.
Using this property, let's find the measure of angle C:
[tex]\begin{gathered} A+B+C+D=360°\\ \\ 90+99+C+90=360\\ \\ C+279=360\\ \\ C=360-279\\ \\ C=81° \end{gathered}[/tex]The measure of angle C is 81°, therefore the correct option is C.
81/50 as a percentage
Answers
Given:
[tex]\frac{81}{50}[/tex][tex]\begin{gathered} \frac{81}{50}=\frac{81}{50}\times100\text{ \%} \\ =162\text{ \%} \end{gathered}[/tex]Answer:
162%
Step-by-step explanation:
[tex]\frac{81}{50} (100)=1.62(100)=162[/tex]
Hope this helps
a panel containing three on off switches in a row is to be set. assuming no restrictions on individual switches.use the fundamental counting principle to find the total number of possible panel settings.
Answers
Using the fundamental counting principal, we get that every switch has 2 options, on or off. So the total possible outcomes are:
[tex]2\times2\times2=2^3=8[/tex]Find the number of ways of arranging N people in a straight line, if two particular people must always be separate
Answers
Answer:
N! - 2(N - 1)!
Step-by-step explanation:
It’s the number of ways N people can be arranged in a straight line without restriction minus the number of arrangements in which the 2 people are together.
The number of ways N people can be arranged in a straight line without restriction = N!
The number of arrangements in which the 2 people are together = the number of possible positions for the left-hand person multiplied by the number of people who can be that person, multiplied by the number of possible arrangements for the other N - 2 people
= (N - 1) * 2 * (N - 2)!
= 2 (N - 1)!
So the number of ways N people can be arranged in a straight line if 2 particular people must be separated = N! - 2(N - 1)!
#SPJ1
Lucas read 30% of his book containing 480 pages. What page is he going to read next? How many pages has he read so far?
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First, calculate the number of page read by Lucas. Calculate the 30% of 480, as follow:
(30/100)(480) = 144
Next, subtract the previous result to 480:
480 - 144 = 336
Hence, Lucas is going to read 336 pages
You roll a 6-sided die two times.What is the probability of rolling an odd number and then rolling a 1?Simplify your answer and write it as a fraction or whole number.
Answers
The sample space for rolling a die twice is shown below
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
Total number of outcomes = 36
Outcomes involving an odd number followed by 1 = 1,1 3,1 5,1
Thus, number of favorable outcomes = 3
Probability = number of favorable outcomes/total number of outcomes
the probability of rolling an odd number and then rolling a 1 = 3/36
the probability of rolling an odd number and then rolling a 1 = 1/12
find the average rate of change in the simplest form of the function over the interval 4
Answers
Suppose the function is f.
Then the average rate
f(4) = 5
and f(5) = 10
Hence,
[tex]\text{average rate of change =}\frac{f(5)-f(4)}{5-4}=\frac{10-5}{5-4}=\frac{5}{1}[/tex]Hence the average rate of change over the interval 4