Answer:
(382/(292-101))+8=10
(382/191)+8=10
(2)+8=10
10=10
Estimate the square root to the nearest whole numberV450question 1
We need to solve the next square root
[tex]\sqrt[]{450}=21.21[/tex]The nearest whole number is 21
If a golden rectangle has a length of 1 cm, what is its width (shorter side) rounded to the NEAREST TENTH?
In any golden rectangle the following poreperty should hold:
[tex]\frac{a+b}{a}=\frac{a}{b}[/tex]where a+b is the length and a is the width. We know that the length of the rectangle is 1, then:
[tex]\begin{gathered} a+b=1 \\ b=1-a \end{gathered}[/tex]Plugging this values in the first equation we have:
[tex]\frac{1}{a}=\frac{a}{1-a}[/tex]Solving this equation for a:
[tex]undefined[/tex]write an equation to represent"three consecutive integers is 12 less than 4 times the middle integer'
Consider that the three consecutive integers are:
least integer = n
middle integer = n + 1
greatest integer = n + 2
THe expression "three consecutive integers is 12 less than 4 times the middle integer" can be written as follow:
n + (n + 1) + (n + 2) = 4(n +1) - 12
In order to find the numbers, proceed as follow:
n + (n + 1) + (n + 2) = 4(n +1) - 12 cancel parenthesis
n + n + 1 + n + 2 = 4n + 4 - 12 simplify like terms
3n + 3 = 4n - 8 subtract 4n and 3 both sides
3n - 4n = - 8 - 3
-n = -11
n = 11
Hence, the three consecutive integers are:
n = 11
n + 1 = 12
n + 2 = 13
A student in MAT110 this semester has the following grades at the end of the semester, after two quizzes and one lab grade are dropped: Quiz average: 95 Lab average: 89 Tests: 52, 82, 88 Final Exam: 73 Question 1 of 5 20 Points Find the student's course average rounded to the nearest whole number. You'll need to consult your syllabus (and/or the feedback given) for weighting percentages and other grading information.Weights:Quiz = 25%Lab = 25%Test = 35%Final = 15%
The overall course average is the average weight of all the quizzes, tests, finals, labs.
First we need the average for all the information:
Quiz Average: 95 (given)
Lab Average: 89 (given)
Test Average >> we have to find by summing and dividing by number of tests
[tex]\text{average}=\frac{52+82+88}{3}=74[/tex]Final Exam: 73 (1 exam, so this is the average).
Thus, the information we have:
Quiz Avg = 95
Lab Avg = 89
Test Avg = 74
Final Avg = 73
Now, we multiply the scores with the respective weightage(in decimal) and sum it. We get:
[tex]95\mleft(0.25\mright)+89\mleft(0.25\mright)+74\mleft(0.35\mright)+73\mleft(0.15\mright)=82.85[/tex]Rounded to nearest whole number: 83
Answer:Course Average = 83 (rounded to nearest whole number)
Which set of parametric equations represents the function y=x^2+4x-5? Select all that apply.
Solution
- The way to solve the equation is to take the expression for x i.e. x = 2t, and substitute into the expression for y(x).
- The result must be the corresponding y-value in terms of t.
- This is done below:
Option A:
[tex]\begin{gathered} x=2t \\ y(x)=x^2+4x-5 \\ \\ \text{ put }x(t)=2t \\ \\ y(x(t))=(2t)^2+4(2t)-5 \\ y(x(t))=y(t)=4t^2+8t-5 \\ \\ \therefore y(t)=4t^2+8t-5\text{ \lparen OPTION A\rparen} \end{gathered}[/tex]Option B:
[tex]\begin{gathered} x=t+1 \\ y=x^2+4x-5 \\ \\ y(x(t))=y(t)=(t+1)^2+4(t+1)-5 \\ t^2+2t+1+4t+4-5 \\ y(t)=t^2+6t\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]Option C:
[tex]\begin{gathered} x=t-3 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t-3)^2+4(t-3)-5 \\ =t^2-6t+9+4t-12-5 \\ =t^2-2t-8\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]Option D:
[tex]\begin{gathered} x=t^2 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t^2)^2+4(t^2)-5 \\ =t^4+4t^2-5\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]Option E:
[tex]\begin{gathered} x=t+1 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t+1)^2+4(t+1)-5 \\ =t^2+2t+1+4t+4-5 \\ =t^2+6t\text{ \lparen OPTION E IS CORRECT\rparen} \end{gathered}[/tex]Final Answer
The answers are OPTIONS A AND E
hi, need help how the graph looks like for this [tex]y \ \textless \ \frac{1}{2} x - 2[/tex][tex]y \leqslant - 2x + 4[/tex]
Solution:
Given:
[tex]\begin{gathered} y<\frac{1}{2}x-2 \\ y\leq-2x+4 \end{gathered}[/tex]Using a graph plotter, the graph of the two inequalities is shown;
In one month, Jason eams $32.50 less than twice the amount Keyin earns, Jason earns $212.50write and solve an equation to solve for the amount of money that kevin earns
Let the amount Kevin earns be represented with K
Let the amount Jason earns be represented with J
Jason earns $32.50 less than twice Keyin earns can be represented by
J = K - 32.5 ----- equation 1
Jason earns $ 212.5
J = 212.5 ----- equation 2
From equation 1, we can write the equation to solve for what Kevin earns
J = K - 32.5
Making K the subject of the formula
K = J + 32.5
Putting J = 212.5 into the equation above
K= $ 212.5 + $ 32.5
K = $ 245
Kevin earns $245
I would like to know if I answered the question correctly
INFORMATION:
We have the next system of equations:
[tex]\begin{cases}{x-5y=-16} \\ {9x+9y=72} \\ {4x-6z=-8}\end{cases}[/tex]And we need to determine if (4, 4, 4) is a solution of the system.
STEP BY STEP EXPLANATION:
To know if the ordered triple is a solution of the system, we need to that (4, 4, 4) means x = 4, y = 4 and z = 4.
Then, to know if it is a solution we must replace the values on each equation to verify if the values are solutions
We have three equations:
1. x - 5y = -16
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 4-5\cdot4=-16 \\ 4-20=-16 \\ -16=-16 \\ \text{ TRUE} \end{gathered}[/tex]2. 9x + 9y = 72
Replacing x = 4 and y = 4, we obtain
[tex]\begin{gathered} 9\cdot4+9\cdot4=72 \\ 36+36=72 \\ 72=72 \\ \text{ TRUE} \end{gathered}[/tex]3. 4x - 6z = -8
Replacing x = 4 and z = 4, we obtain
[tex]\begin{gathered} 4\cdot4-6\cdot4=-8 \\ 16-24=-8 \\ -8=-8 \\ \text{ TRUE} \end{gathered}[/tex]Finally, since the three equations are true when x = 4, y = 4 and z = 4, the ordered triple is a solution
ANSWER:
Yes
The hypotenuse of a right triangle is 1 centimeter longer than the longer leg. The shorter leg is 7 centimeters shorter than the longer leg. Find the length of the shorter leg of the triangle.
Answer:
[tex]\text{Shorter leg= 5cm}[/tex]Step-by-step explanation:
As a first step to go into this problem, we need to make a diagram:
Let x be the measure of the longer leg.
Now, understanding this we can apply the Pythagorean theorem to find x, it is represented by the following equation:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where,} \\ a=\text{longer leg} \\ b=\text{shorter leg} \\ c=\text{hypotenuse } \end{gathered}[/tex]Substituting a,b, and c by the expressions corresponding to its sides:
[tex]\begin{gathered} x^2+(x-7)^2=(x-1)^2 \\ \end{gathered}[/tex]apply square binomials to expand and gather like terms, we get:
[tex]\begin{gathered} x^2+x^2-14x+49=x^2-2x+1 \\ 2x^2-x^2-14x+2x+49-1=0 \\ x^2-12x+48=0 \end{gathered}[/tex]Now, factor the quadratic equation into the form (x+?)(x+?):
[tex]\begin{gathered} (x-4)(x-12)=0 \\ x_1=4 \\ x_2=12 \end{gathered}[/tex]This means, the longer leg could be 4 or 12, but if we subtract 7 to 4, we get a negative measure for the shorter leg, that makes no sense.
Therefore, the long leg is 12 cm.
Hence, if the shorter leg is 7 centimeters shorter than the longer leg:
[tex]\begin{gathered} \text{Shorter leg=12-7} \\ \text{Shorter leg=}5\text{ cm} \end{gathered}[/tex]Tell whether x and y show direct variation, inversevariation, or neither. Explain your reasoning.X 24.68y -5 -11 -17 -23The products xy areThe ratios Y areХSo, X and y show
Neither
1) Firstly, we can start filling in the blanks.
2) The products xy are:
[tex]xy=-10,-44,-102,-184[/tex]We're simply multiplying each x-entry by its output y.
The ratios y/x are:
[tex]\frac{y}{x}=-\frac{5}{2},-\frac{11}{4},-\frac{17}{6},-\frac{23}{8}[/tex]So, x and y show:
Note that xy is not constant, for their product differs. So it is not an
inverse variation.
On the other hand, y/x is not constant as well. So it is not a direct variation.
3) Hence, it's neither direct nor inverse.
x-(7.65 + 3.18)=4 solve for x
Answer:
The value of x is;
[tex]x=14.83[/tex]Explanation:
Given the equation;
[tex]x-(7.65+3.18)=4[/tex]Solving for x;
[tex]\begin{gathered} x-(10.83)=4 \\ x=4+10.83 \\ x=14.83 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=14.83[/tex]which statement is the contrapositive of the given statement statement if you play a sport then you wear a helmet
We will have that the contrapositive statement is:
*If you do not wear a helmet, then you do not play a sport.
what are the unit prices for 100 sheets for $.99 and 500 sheets for $4.29
Answer:$.0099/sheet; $.00858/sheet;500 sheets
Step-by-step explanation:
Solve the system by the addition method x + 2y = - 26x + 3y = - 30
We are asked to solve the following system of equations via the addition method:
x + 2 y = - 2
6 x + 3 y = - 30
so via the addition method we will try to eliminate one of the variables by multiplying for the appropriate factor that would ease tha process. We notice that if wemultiply the whole first eqaution by the factor (-6), we will be able to in the second step eliminate the term in "x" by combining both equations term by term.
So we do that: Multiply the whole first equation by "-6":
(-6) (x + 2 y ) = (-6) (-2)
- 6 x - 12 y = 12
now we combine this with the second equation term by term to eliminate the term in x:
- 6 x - 12 y = 12
+
6 x + 3 y = - 30
_______________
0 - 9 y = - 18
Now divide both sides by "-9" to isolate y:
y = - 18 / (-9)
y = 2
Now we use y = 2 in the very first equation to solve for the variable x:
x + 2 y = - 2
x + 2 (2) = -2
x + 4 = - 2
subtract 4 from both sides:
x = - 2 - 4
x = - 6
A parabola can be drawn given a focus of (-7,3) and a directrix of x = 9. What canbe said about the parabola?
The focus of a parabola is given by:
[tex]F(h,k+p)[/tex]and the directrix is given by:
[tex]y=k-p[/tex]since the directrix is x = 9, we can conclude it is a horizontal parabola, so:
[tex]\begin{gathered} x=9=k-p \\ so\colon \\ k=9+p \end{gathered}[/tex][tex]\begin{gathered} F(-7,3)=(h,k+p) \\ h=-7 \\ k+p=3 \\ 9+p+p=3 \\ 9+2p=3 \end{gathered}[/tex]solve for p:
[tex]\begin{gathered} 2p=3-9 \\ 2p=-6 \\ p=-\frac{6}{2} \\ p=-3 \end{gathered}[/tex][tex]\begin{gathered} k=3-p \\ k=3-(-3) \\ k=6 \end{gathered}[/tex]We can write the parabola in its vertex form:
[tex]\begin{gathered} x=\frac{1}{4p}(y-k)^2+h \\ so\colon \\ x=-\frac{1}{12}(y-6)^2-7 \end{gathered}[/tex]It is a horizontal parabola that opens to the left, and has vertex located at (-7,6)
How many kilometers could the red car travel in 12 hours? Write an equation to show your work.
The kilometers that the red car travel in 12 hours is 2604 kilometers.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
From the diagram, it should be noted that the red car has a speed of 217 km per hours.
Therefore, the distance traveled in 12 hours will be:
Distance = Speed × Time
= 217 × 12
= 2604 km
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Write a word problem that involves a proportional relationship and needs more than one step to solve.Show how to solve the problem
To write a word problem that involves a proportional relationship:
Sam bought 4kg of apples for $12. How many kilograms of apples, he can buy for $30?
Sam bought 4kg of apples for $12.
So, cost of 1 kg of apples is,
[tex]\frac{12}{4}=3[/tex]Let x be the number of kg apples.
Therefore, He can buy 3x kg apples for $30.
So,
[tex]\begin{gathered} 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]Therefore, He can buy 10 kg apples for $30.
Lincoln Middle School plans to collect more than 2,000 cans of food in a food drive. So far, 668 cans have been collected. Write and solve an inequality to find numbers of cans the school can collect on each of the final 7 days of the drive to meet this goal.Which inequality represents the solution to this situation?
Inequalities
Let's call c the number of cans of food.
The school wants to collect more than 2,000 cans in a food drive.
668 cans have been collected so far.
The number of cans needed to reach the goal is 2,000 - 668.
These cans will be collected in 7 days, thus:
7c > 2,000 - 668
Operating
7c > 1,332
Dividing by 7:
c > 1,332 / 7
c > 190.29
This is the average number of cans needed to collect each day.
The first choice is correct
Elena is organizing her craft supplies. She estimatesthat her jars will fit 1,000 buttons or 50 large beads.They actually fit 677 buttons or 22 large beads. DoesElena's estimate about the buttons or her estimateabout the large beads have less percent error? To thenearest percent, how much less?
Step 1
Given;
[tex]\begin{gathered} Elena-\text{ estimates her jar will take 1000 buttons or 50 large beads} \\ Her\text{ Jar actually takes 677 buttons or 22 large beads} \end{gathered}[/tex]Required; To find if Elena's estimates have percentage error, to which percent, and how much less
Step 2
State the formula for percentage error
[tex]\text{ \% error=}\frac{|Approximate-exact|}{exact}\times100[/tex][tex]Elena^{\prime}s\text{ estimate about the button has a percentage error }[/tex][tex]\begin{gathered} For\text{ buttons} \\ Approximate=1000 \\ Exact=677 \end{gathered}[/tex][tex]\text{ \%error=}\frac{|1000-677|}{677}\times100=47.71048744\text{\%}[/tex][tex]\begin{gathered} For\text{ large beads} \\ \operatorname{\%}\text{error=}\frac{\text{\lvert50-22\rvert}}{22}\times100 \end{gathered}[/tex][tex]\text{ \% error=}\frac{28}{22}\times100=127.272727...\text{\%}[/tex]Percent errors tells you how big your errors are when you measure something in an experiment. Smaller values mean that you are close to the accepted or real value. For example, a 1% error means that you got very close to the accepted value, while 45% means that you were quite a long way off from the true value.
The percentage error for buttons with about 47.71% is less than that of the large beads which is about 127.273%.
How much less of the percentage error to the nearest percent will be;
[tex]\begin{gathered} =79.56223986 \\ \approx80\text{\%} \end{gathered}[/tex]Find y if the point (5,y) is on the terminal side of theta and cos theta = 5/13
For this problem we have a point given (5,y) and we know that this point is on a terminal side of an angle, we also know that:
[tex]\cos \theta=\frac{5}{13}[/tex]If we know the cos then we can find the sin on this way:
[tex]\sin \theta=\frac{y}{13}[/tex]Then we can apply the following identity from trigonometry:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]Using this formula we got:
[tex](\frac{5}{13})^2+(\frac{y}{13})^2=1[/tex]And we can solve for y:
[tex]\frac{y^2}{169}=1-\frac{25}{169}=\frac{144}{169}[/tex]And solving for y we got:
[tex]y=\sqrt{169\cdot\frac{144}{169}}=\sqrt{144}=\pm12[/tex]And the two possible solutions for this case are y=12 and y=-12
Tim is building a model of a castle with small wooden cubes. So far Tim has constructed part of a security world castle,as shown below. Each wooden cube has a side length of 1/8ft
From the given model, the length of the wall is 9/8 ft, the width of the walk is 1/2 ft, and the height of the wall is 11/8. The volume of the portion of security wall that Tim has constructed so far is 99/128 cu ft.
What is the Volume of the Block?From the given image of the building model we see that part of a security world castle is shown.
We see that the length has 9 blocks.
Since the length has a total of 9 blocks and each side length is 1/8 ft, then we say that;
Length = 9*(1/8) = 9/8 ft
We also observe that the height has 11 blocks and as such;
height = 11*(1/8) = 11/8 ft
Meanwhile the width will have a length of: 1/2 ft
Formula for volume is;
Volume = length * height * width
Thus;
Volume = (9/8) * (11/8) * (1/2)
Volume = (9 * 11 * 1)/(8 * 8 * 2)
Volume = 99/128 cu ft
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Complete question is;
Tim is building a model of a castle with small wooden cubes. So far Tim has constructed part of a security world castle,as shown below. Each wooden cube has a side length of 1/8ft
Based on the model,the length of the wall is ___ft, the width of the walk is 1/2 ft, and the height of the wall is ___. The volume of the portion of security wall that Tum has constructed so far is ___ cu ft.
Lesson 6.02: Finn's fish store has 5 tanks of goldfish; each tank holds 40 fish. He collects andinspects 5 fish from each tank and finds that 4 fish have fin rot. Find the estimated numbergoldfish in the store that have fin rot. SHOW ALL WORK!
Answer:
Explanation:
We are told that of each 5 fish inspected in the tank, 4 have fin rot, therefore, the probability o getting a fin rot is
[tex]\frac{4}{5}\times100\%=80\%[/tex]This means 80% of the fish in a tank have fin rot.
Now, for one tank 80% of 40 fish is
[tex]\frac{80\%}{100\%}\times40=32[/tex]Now, since there are 5 fish tanks in the store and 32 fish in each have fin rot; therefore, the total number of fish that have fin rot will be
[tex]32fish\times5=160\text{fish}[/tex]Hence, the estimated number of fish with fish rot in the store is 160.
Find the area of the parallelogram. 6.5 cm 3.1 cm 3 cm O 9.3 cm^2 O 19.5 cm^2 O 20.15 cm^2 O 60.45 cm^2
Data
length = 6.5 cm
height = 3 cm
side = 3.1 cm
Formula
Area = base x height
Substitution
Area = (6.5 x 3)
Result
Area = 19.5 cm^2
Next
The right answer is the second choice
12 + 1.5x >= 20
convert r= 5/ 1+3sinθ to a rectangular equation
Given:
[tex]r=\frac{5}{1+3\sin \theta}[/tex]Find: Rectangular equation.
Sol:
[tex]r^2=x^2+y^2[/tex][tex]\begin{gathered} y=r\sin \theta \\ \sin \theta=\frac{y}{r} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{5}{1+3\sin \theta} \\ r=\frac{5}{1+\frac{3y}{r}} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{5r}{r+3y} \\ r+3y=5 \\ r=5-3y \\ r^2=(5-3y)^2 \end{gathered}[/tex]Put the value in rectangular equation:
[tex]\begin{gathered} x^2+y^2=r^2 \\ x^2+y^2=(5-3y)^2 \end{gathered}[/tex]Answer please the picture scanner deal won’t scan over this and i don’t know how to type it out
Solution
We are given the arithmetic sequence
[tex]\begin{gathered} a_1=5 \\ a_n=a_{n-1}-4 \end{gathered}[/tex]To find an explicit formula
[tex]\begin{gathered} First\text{ }Term=5 \\ a=5 \end{gathered}[/tex]From the second recursive formula
[tex]\begin{gathered} a_n-a_{n-1}=-4 \\ Common\text{ }Difference=-4 \\ d=-4 \end{gathered}[/tex]The nth term of an Arithmetic sequence is given by
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=5+(n-1)(-4) \end{gathered}[/tex]Therefore, the answer is
[tex]a_{n}=5+(n-1)(-4)[/tex]Team Arrow shoots an arrow from the top of a 1600-foot building on Earth-51. The arrow reaches a maximum height of 1840 feet after 4 seconds.Write an equation for the height of the arrow, h, in feet as a function of the number of seconds, t, since the arrow was shot.Round to 3 decimal places as needed. After how many seconds will the arrow reach the ground?Round to 3 decimal places as needed.
We will have the following:
***First:
[tex]h=h_0+v_0\cdot t+\frac{1}{2}g\cdot t^2[/tex]Now, we will determine the value for the speed:
[tex]1840=1600+v_0\cdot(4)+\frac{1}{2}(-32.17)\cdot(4)^2\Rightarrow240=4v_0-\frac{25736}{25}[/tex][tex]\Rightarrow\frac{31736}{25}=4v_0\Rightarrow v_0=\frac{7934}{25}\Rightarrow v_0=137.36[/tex]So, the equation for the height of the arrow (h) in feet as a function of the number of seconds t is:
[tex]h=1600+317.36t+\frac{1}{2}gt^2[/tex]Here "g" is the gravitational pull of earth.
***Second:
We will determine how much time it would take for the arrow to hit the ground as follows:
[tex]0=1600+317.36t+\frac{1}{2}(-32.17)t^2\Rightarrow-\frac{3217}{200}t^2+317.36t+1600=0[/tex][tex]\Rightarrow t=\frac{-(317.36)\pm\sqrt[]{(317.36)^2-4(-\frac{3217}{200})(1600)}}{2(-\frac{3217}{200})}\Rightarrow\begin{cases}t\approx-4.163 \\ t\approx23.893\end{cases}[/tex]So, afeter 23.893 seconds the arrow would hit the ground.
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.six subtracted from a number
Find d and then find the 20th term the sequence. Type the value of d (just the number) in the first blank and then type the 20th term(just the number) in the second blank.a1=6 and a3=14
We have that an arithmetic sequence can be defined by the following explicit formula:
[tex]a_n=a_1+(n-1)\cdot d[/tex]where n represents the index of each term in the sequence and d represents the common difference beteen each term. a1 is the first term of the sequence.
In this case we have that the first term is a1 = 6, and also we have that a3=14. We can use the formula to find the common difference:
[tex]\begin{gathered} a_3=a_1+(3-1)d \\ \Rightarrow a_3=a_1+2d \\ \Rightarrow14=6+2d \end{gathered}[/tex]solving for d, we get:
[tex]\begin{gathered} 2d+6=14 \\ \Rightarrow2d=14-6=8 \\ \Rightarrow d=\frac{8}{2}=4 \\ d=4 \end{gathered}[/tex]therefore, the value of d is d = 4.
We have now the explicit formula for the sequence:
[tex]\begin{gathered} a_n=6_{}+4(n-1) \\ \end{gathered}[/tex]then, for the 20th term, we have to make n = 20 on the formula, and we get the following:/
[tex]\begin{gathered} a_{20}=6+4(20-1)=6+4(19)=6+76=82 \\ \Rightarrow a_{20}=82 \end{gathered}[/tex]therefore, the 20th term is 82
The number of newly reported crime cases in a county in New York State is shown inthe accompanying table, where x represents the number of years since 2006, and yrepresents number of new cases. Write the linear regression equation that representsthis set of data, rounding all coefficients to the nearest tenth. Using this equation,estimate the calendar year in which the number of new cases would reach 767.Years since 2006 (x) New Cases (y)099619232882389248405813
Solution
For this case we have the following data:
x y
0 996
1 923
2 882
3 892
4 840
5 813
sum xi = 15
sum yi = 5346
sum xi yi = 12788
sum xi^2 = 55
And we want to find and equation like this one:
y= mx+ b
So then we can estimate the slope using least squares and we have:
[tex]m=\frac{n\sum ^n_{i=1}x_iy_i-\sum ^n_{i=1}x_i\sum ^n_{i=1}y_i}{n(\sum ^n_{i=1}x^2_i)-(\sum ^n_{i=1}x_i)^2}[/tex]Replacing we have:
[tex]m=\frac{6\cdot12788-(15\cdot5346)}{6(55)-(15)^2}=\frac{-3462}{105}=-32.971[/tex]m= -32.971
And the intercept would be:
[tex]b=\frac{\sum^n_{i=1}y_i}{n}-m\cdot\frac{\sum^n_{i=1}x_i}{n}=\frac{5346}{6}-(-32.971)\cdot\frac{15}{6}=973.429[/tex]b= 973.428
Then the equation would be:
y= -32.971x+ 973.428
And we can find the value of x for y = 767 and we got::
767 = -32.971x+ 973.428
Solcing for x we have:
767- 973.428 = -32.971 x
x= 6.26
Regression Equation: y= -32.9x + 973.4
Final Answer: 2012
What is the slope of the line containing (-2,5) and (4,-4)?A.3/2B.-3/2C. -2D. 2
Answer:
B.-3/2
Step-by-step explanation:
To find the slope, we need to take two points from a line. I am going to call them:
(x1,y1) and (x2,y2).
The slope is:
[tex]a=\frac{y2-y1}{x2-x1}[/tex]In this question:
(x1,y1) = (-2,5)
(x2,y2) = (4, -4)
So
[tex]a=\frac{y2-y1}{x2-x1}=\frac{-4-5}{4-(-2)}=\frac{-9}{4+2}=-\frac{9}{6}=-\frac{3}{2}[/tex]So the correct answer is:
B.-3/2