Using the data in this table, what would be the line ofbest fit ( rounded to the nearest tenth)?
Solution
Note: The formula to use is
[tex]y=mx+b[/tex]Where m and b are given by
the b can also be given as
[tex]b=\bar{y}-m\bar{x}[/tex]The table below will be of help
We have the following from the table
[tex]\begin{gathered} \sum_^x=666 \\ \sum_^y=106.5 \\ \operatorname{\sum}_^x^2=39078 \\ \operatorname{\sum}_^xy=6592.5 \\ n=10 \end{gathered}[/tex]Substituting directing into the formula for m to obtain m
[tex]\begin{gathered} m=\frac{10(6592.5)-(666)(106.5)}{10(39078)-(666)^2} \\ m=\frac{-5004}{-52776} \\ m=0.09481582538 \\ m=0.095 \end{gathered}[/tex]to obtain b
[tex]\begin{gathered} \bar{y}=\frac{\operatorname{\sum}_^y}{n} \\ \bar{y}=\frac{106.5}{10} \\ \bar{y}=10.65 \\ and \\ \bar{x}=\frac{\operatorname{\sum}_^x}{n} \\ \bar{x}=\frac{666}{10} \\ \bar{x}=66.6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} b=\bar{y}- m\bar{x} \\ b=10.65-(0.095)(66.6) \\ b=4.323 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=mx+b \\ y=0.095x+4.323 \end{gathered}[/tex]To the nearest tenth
[tex]y=0.1x+4.3[/tex]The least square method didn't give an accurate answer, so we use a graphing tool to estimate instead
Here
m = 0.5 (to the nearest tenth)
b = -23.5 (to the nearest tenth)
The answer is
[tex]\begin{gathered} y=mx+b \\ y=0.5x-23.5 \end{gathered}[/tex]A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds. How thick will the paper be if you could fold it 10 times?About an inchAbout 2 inchesAbout 3 inchesAbout 4 inches
Given: A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds.
Required: To determine the thickness of the paper if the paper is folded 10 times.
Explanation: The thickness of the paper is given by the function
[tex]y=\frac{2x}{1000}[/tex]Here, x is the number of folds=10
Hence,
[tex]\begin{gathered} y=\frac{2\times10}{1000} \\ =0.02\text{ inches} \end{gathered}[/tex]Final Answer: After 10 folds, the thickness of the paper is 0.02 inches.
A bag contains 8 red marbles, 2 blue marbles, 5 white marbles, and 7 black marbles. What is the probability of randomly selecting:A white marble:A red marble:A red marble, white or blue marble: A black marble: A green marble:
A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 500 contains 100 green, one-headed Jolos; 125 purple, two-headed Jolos; and 270 one headed-jolos.How many green Jolos are there in Balan's colony?A. 105B. 170C. 205D. 230
According to the table, there are 270 one-headed in total, and there are 500 Jolos, we just have to subtract to find the total of two-headed Jolos
[tex]500-270=230[/tex]There are 230 two-headed Jolos.
Now, we subtract the total of two-headed Jolos and the two-headed purple Jolos to find the total green.
[tex]230-125=105[/tex]There are 105 two-headed green Jolos.
At last, we have to sum the number of one-headed green Jolos and the two-headed green Jolos,
[tex]100+105=205[/tex]Hence, there are 205 green Jolos in total.Here is a system of equations.y=-3x+3y=-x-1Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many solutions.-6
From the given system, we can observe that the y intercepts of the equations are 3 and -1 respectively.
Also we can find the x intercepts by replacing y for 0 and solving for x:
[tex]\begin{gathered} 0=-3x+3 \\ -3=-3x \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} 0=-x-1 \\ 1=-x \\ x=-1 \end{gathered}[/tex]It means that the x intercepts of the lines are 1 and -1 respectively.
Using these points we can graph both lines, this way:
According to this graph, the intersection of these lines is at (2, -3). This represent the solution of the system, therefore, the solution of the system is x=2 and y=-3.
gB - N³B = d what does B equal?
Answer:
[tex]b \: = \frac{d}{(g - {n}^{3} )} [/tex]
Help on math question precalculus ChoicesVertical shift Period DomainRange Phase shift Amplitude
All the x-values that satisfy the function - Domain
Translating the sine or cosine curve up or down - Vertical shift
How long a given function takes to repeat itself - Period.
A horizontal shift of a sine or cosine function- Phase shift
All the y-values that satisfy the function- Range
Distance from the horizontal axis or midline to the maximum and minimum points - Amplitude
Simplify (sqrt)98m^12Using factor tree. Please draw. Quick answer = amazing review. Not a graded or timed assessment. Please use factor tree or split up using perfect squares
The simplified expression is 7m⁶ √2
STEP - BY - STEP EXPLANATION
What to find?
Simplify the given expression.
Given:
[tex]\sqrt[]{98m^{12}}[/tex]To simplify the above, we will follow the steps below:
Step 1
Apply radical rule:
[tex]\sqrt[]{ab}=\sqrt[]{a}\text{ . }\sqrt[]{b}[/tex]That is;
[tex]\sqrt[]{98m^{12}}=\sqrt[]{98}\times\sqrt[]{m^{12}}[/tex]Step 2
Simplify each value under the square root.
[tex]\sqrt[]{98}=\sqrt[]{49\times2}=\sqrt[]{49}\times\sqrt[]{2}=7\sqrt[]{2}[/tex][tex]\sqrt[]{m^{12}}=(m^{12})^{\frac{1}{2}}=m^{\frac{12}{2}}=m^6[/tex]Therefore, the simplified expression is:
[tex]\sqrt[]{98m^{12}}=7m^6\text{ }\sqrt[]{2}[/tex]Write a explicit formula for the given recursive formulas for each arithmetic sequence
9,15,21,27 and 7,0,-7,-14
In arithmetic progression, 9,15,21,27,33,39 is a₅ and a₆ .
What is arithmetic progression?
A series of numbers is called a "arithmetic progression" (AP) when any two subsequent numbers have a constant difference. It also goes by the name Arithmetic Sequence.a₁ = 9
a₂ = 15
a₃ = 21
Notice that a₂ - a₁ = 6 and a₃ - a₂ = 6
We can deduce that aₙ₊₁ = aₙ + 6
We can test this on the 4th term : a₄ should equal 21 + 6 = 27
Since this checks out we can say that the sequence is an arithmetic progression with a common difference of 6.
a₅ = 27 + 5 = 33
and
a₆ = 33 + 6 = 39
7,0,-7,-14
find the common difference by substracting any term in the sequence from the term that comes after it.
a₂ - a₁ = 0 - 7 = -7
a₃ - a₂ = -7 - 0 = -7
a₄ - a₃ = -14 - -7 = -7
the difference of the sequence is constant and equals the difference between two consecutive terms.
d = -7
Learn more about arithmetic progression
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Find the negative member of the solution set for |2x -4| =6
The negative solution of the absolute value function is x = - 1.
What is the negative solution of an absolute value set?In this problem we need to solve for x in an absolute value function, whose procedure is done by the use of algebra properties:
Step 1 - Initial condition:
|2 · x - 4| = 6
Step 2 - By definition of absolute value:
2 · x - 4 = 6 or - 2 · x + 4 = 6
Step 3 - By compatibility with addition, existence of additive inverse, associative, commutative and modulative properties:
2 · x = 10 or - 2 · x = 2
Step 4 - By compatibility with multiplication, existence of multiplicative inverse, associative, commutative and modulative properties we get this result:
x = 5 or x = - 1
The negative solution of the function is x = - 1.
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Consider similar figure QRS and TUV below Where QRS is the pre image of TUV.Part A: What is the scale factor ? Part B:Find the the length of RS.
Consider similar figure QRS and TUV below Where QRS is the pre image of TUV.Part A: What is the scale factor ? Part B:Find the the length of RS.
Part A
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
so
In this problem
we have that
QS/TV=QR/TU=RS/UV
that means, that the scale factor is
scale factor=TV/QS
substitute the given values
scale factor=2.8/7=0.4
scale factor=0.4Part B
Find the the length of RS
we have that
The length of RS is equal to the length of UV divided by the scale factor
so
RS=5.7/0.4
RS=14.25Part 2
How many terms are existed in between 10 to 1000 which are divisible by 6?
Answer:166
Step-by-step explanation: There are 166 integers between 1 and 1,000 which are divisible by 6
48. In the parabola, y = 3x ^ 2 + 12x + 11 focus is located at a distance p > 0 from the vertex. Then p=a. 3b. 1/3c. 12d. 1/12e. None of the above
Given the equation,
[tex]y=3x^2+12x_{}+11[/tex]We are to solve for the vertex first, in order to solve for the vertex.
[tex]3x^2+12x+11=y[/tex]factor all through by 3
[tex]\begin{gathered} \frac{3x^2}{3}+\frac{12x}{3}+\frac{11}{3}=y \\ 3(x^2+4x+\frac{11}{3})=y\ldots\ldots.1 \end{gathered}[/tex][tex]x^2+4x=-\frac{11}{3}\text{ complete the square for the inner expression}[/tex][tex]\begin{gathered} x^2+4x+(\frac{4}{2})^2=-\frac{11}{3}+(\frac{4}{2})^2 \\ (x+2)^2=-\frac{11}{3}+4=\frac{1}{3} \\ =(x+2)^2-\frac{1}{3} \end{gathered}[/tex]Put (x+2)²-1/3 into equation 1
[tex]3((x+2)^2-\frac{1}{3})=y\ldots\ldots2[/tex]The vertex is at (-2,-1)
Note:
[tex]\begin{gathered} \text{vertex}=(h,k) \\ \text{focus}=(h,k+\frac{1}{4a}) \end{gathered}[/tex]P is the distance between the focus and the vertex.
[tex]\begin{gathered} (h-h,k+\frac{1}{4a}-k)=(0,\frac{1}{4a}) \\ \end{gathered}[/tex]where,
[tex]a=3\text{ from equation 2}[/tex]Therefore,
[tex]\begin{gathered} p=(0,\frac{1}{4\times3})=(0,\frac{1}{12}) \\ p=(0,\frac{1}{12}) \end{gathered}[/tex]Hence,
[tex]p=\frac{1}{12}[/tex]The correct answer is 1/12 [option D].
5 cm3 cm3 cm5 cm3 cmPrisma5 cmPrism BWhich of the following statements are true about the solids shown above?Check all that apply.A. Prisms A and B have different values for lateral surface area.O B. Prism B has a total surface area of 110 cm?O C. Prism A has a lateral surface area of 60 cm?D D. Prism B has a larger surface area.
Note that the lateral surface area is the area of the faces of the solid, excluding the cross-sectional faces i.e. faces which are perpendicular to the longitudinal axis.
The lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_A=2(5\times3)+2(5\times3)_{} \\ LSA_A=30+30 \\ LSA_A=60 \end{gathered}[/tex]Similarly, the lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_B=2(3\times5)+2(5\times5)_{} \\ LSA_B=30+50 \\ LSA_B=80 \end{gathered}[/tex]Clearly, prisms A and B have different values of lateral surface area.
So option A is the correct statement.
The total surface area is the sum of all the faces of the solid.
Since we have already calculated the LSA i.e. sum of area of 4 faces of the prism, we can add the area of the two remaining cross sectional faces to get the total area.
The total cross section area of prism B is calculated as,
[tex]\begin{gathered} A_B=2(5\times3) \\ A_B=30 \end{gathered}[/tex]So the total surface area of prism B becomes,
[tex]\begin{gathered} TSA_B=LSA_B+A_B_{} \\ TSA_B=80+30 \\ TSA_B=110 \end{gathered}[/tex]The total surface area of prism B is 110 sq. cm.
So option B is also correct.
Note that we have already found that the lateral surface area of prism A is 60 sq. cm.
Therefore, option C is also correct.
The total cross section area of prism A is calculated as,
[tex]\begin{gathered} A_A=2(3\times5) \\ A_A=30 \end{gathered}[/tex]So the total surface area of prism A becomes,
[tex]\begin{gathered} TSA_A=LSA_A+A_A \\ TSA_A=60+30 \\ TSA_A=90 \end{gathered}[/tex]The total surface area of prism A is 90 sq. cm.
It is oberved that prism B has a larger surface area.
So, option D is also correct.
Hence, we can conclude that all the given statements are correct.
NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17. 8(x + 1) = 24. 5(x - 2) = 20. 34 - 7x = 20. 31 - x = 29. 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
We are to solve for x in all the equations and select the ones that occur more than one solution.
Hence,
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4}=5 \\ \therefore x=5 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2=6 \\ \therefore x=6 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ 2=x \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1=2 \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 14=7x \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \\ \Rightarrow x=2 \end{gathered}[/tex]Lastly,
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3}=5 \\ \therefore x=5 \end{gathered}[/tex]Hence, the numbers that represent solutions to more than one of the six equations are
[tex]\begin{gathered} x=2\text{ \lparen Option 2\rparen} \\ x=5\text{ \lparen Option 5\rparen} \end{gathered}[/tex]Julie wants to purchase a jacket that costs $125. So far she has saved $42 and plans tosave an additional $25 per week. She gets paid every Friday, so she only gets money toput aside once a week. How many weeks, x, will it take for her to save at least $125?
cost of the jacket = $125
money saved = $42
extra savings = $25/week
Ok
125 = 42 + 25w
w = number of weeks
Solve for w
125 - 42 = 25w
83 = 25w
w = 83/25
w = 3.3
She needs to save at least 3.3 weeks
Consider the function f (x) = x2 – 3x + 10. Find f (6).
The given function is f(x) = x^2 - 3x + 10
this means that the expression is a function of x
f(6) means replace x with 6
f(6) = (6)^2 - 3(6) + 10
f(6) = 36 - 18 + 10
f(6) = 18 + 10
f(6) = 28
The answer is 28
Finding the time given an exponential function with base e that models a real-world situation
We are solving for the value of t if C(t) = 19. We can rewrite the equation into
[tex]19=5+17e^{-0.038t}[/tex]Solving for t, we have
[tex]\begin{gathered} 17e^{-0.038t}=19-5 \\ 17e^{-0.038t}=14 \\ e^{-0.038t}=\frac{14}{17} \\ -0.038t=\ln \frac{14}{17} \\ -0.038t=-0.1941 \\ t=\frac{-0.1941}{-0.038} \\ t\approx5.1 \end{gathered}[/tex]The bottled water will achieve a temperature of 19 degrees C after 5.1 minutes.
Answer: 5.1 min
The midpoint of AB is M(4,1). If the coordinates of A are (2,8), what are thecoordinates of B?
Which graphed matches the equation y+6= 3/4 (x+4)?
To start, it is important to find the slope intercept form of the equation
[tex]\begin{gathered} y+6=\frac{3}{4}(x+4) \\ y+6=\frac{3}{4}x+3 \\ y=\frac{3}{4}x+3-6 \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]Once we have the slope intercept form we know that the y intercept is -3 and the slope is positive, it means the line is increasing
The graph will look like this
Can someone give me the answer for my last blank
Answer:
[tex]-\frac{1}{2}[/tex]Step-by-step explanation:
Since we have that:
[tex]p=-0.5[/tex]We'll have that:
[tex]\frac{1}{4p}\rightarrow\frac{1}{4(-0.5)}\rightarrow-\frac{1}{2}[/tex]Therefore, we can conclude that the answer is:
[tex]-\frac{1}{2}[/tex]hello can you help me with this trigonometry question and in the question I have to answer it in radians hopefully you can help me please
Answer
(34π/7) = (6π/7) in the range of 0 and 2π.
Explanation
We are asked to find an angle between 0 and 2π that are coterminal with (that is, equal to) (34π/7).
34π/7 is 4.857π in decimal form, indicating that it is outside the required range. To find its equivalent in the required range, we keep going a full revolution (2π) till we get there.
(34π/7) - 2π = (20π/7)
This is 2.857π, which is still outside the required range, so, we subtract another revolution from this
(20π/7) - 2π = (6π/7)
This is 0.857π and it is solidly in the required region.
Hope this Helps!!!
9 to the power of -3 as a fraction or number without exponents (simplified fractions).
Answer:
1/729
Step-by-step explanation:
A number raised to a negative exponent is the same as 1 divided by the number raised the the exponent
9⁻³
1/9³
1/729
which of the following is the equation that represents the function given in the table
To determine which of the given equations represents the function given in the table, let us analyze each of them.
The first two equations do bring not integer numbers in such a way that, if we substitute any of the x values given, we will find a y value which is not an integer. This means that both are not the ones we are looking for.
Now, to determine if the third or the fourth is the one, let us substitute one of the x values on it, and if the y value matches, it means that it might be correct.
Checking the fourth, let's use the values:
[tex]\begin{gathered} x=-2 \\ y=16 \end{gathered}[/tex]Substituting the value of x in the equation of the fourth option, we have:
[tex]\begin{gathered} y=6\times(-2)-5 \\ y=-12-5 \\ y=-17 \end{gathered}[/tex]Because the y value found was not the one given, the option is wrong!
Let's check the third option with the same values of x and y:
[tex]\begin{gathered} y=-5\times(-2)+6 \\ y=10+6 \\ y=16 \end{gathered}[/tex]It matches. This substitution alone does not assure this is the right answer, but once it can not be anyone of the other three, and once we expect that one of the four is the function, this match becomes enough for our final answer:
C) y = -5x + 6
I just need to answer the question number one NOT two .I just need a brief explanation with the answer
The bedroom of the apartment has 4 walls.
2 of them have the following dimensions: 16ft x 8ft.
2 of them have the following dimensions: 10ft x 8ft.
Find the area of each wall and then add them to find the total area:
[tex]\begin{gathered} Aw1=16ft\cdot8ft=128ft^2 \\ Aw2=10ft\cdot8ft=80ft^2 \end{gathered}[/tex][tex]\begin{gathered} TA=2\cdot Aw1+2\cdot Aw2 \\ TA=2\cdot128ft^2+2\cdot80ft^2 \\ TA=256ft^2+160ft^2 \\ TA=416ft^2 \end{gathered}[/tex]It means that the total area to be covered is 416ft^2.
Now, divide this area by the area that can be covered by one roll of wallpaper to find the number of rolls needed:
[tex]n=\frac{416ft^2}{50ft^2}=8.32[/tex]It means that 8.32 rolls are needed to cover the bedroom. You will have to buy 9 rolls.
Find the volume of the pyramid. Round your answer to the nearest tenth.16 in.5 in.3 in.The volume of the pyramid isin?
Recalls that the formula for the volume of a pyramid is given by the product of the area of its base times the height, and all of that divided by 3
Then we start by calculating the area of the base:
Since the base is a rectangle of 3in by 5in, then its area is 15 square inches.
Now this area times the pyramid's height and divided by 3 gives:
Volume = AreaBase x Height / 3
Volume = 15 x 16 / 3 = 80 in^3 (eighty cubic inches)
Then, please just type the number 80 in the provided box (notice that the cubic inches unit is already written on the right of it.
Sarina throws a ball up into the air, and it falls on the ground nearby. The ball's height, in feet, is modeled by the function ƒ(x) = –x2 – x + 3, where x represents time in seconds. What's the height of the ball when Sarina throws it?Question 12 options:A) 1 footB) 3 feetC) 4 feetD) 2 feet
Answer:
3 feet
Explanation:
We are told from the question that the ball's height, in feet, is modeled by the below function;
[tex]f(x)=-x^2-x+3[/tex]where x = time in seconds
To determine the height of the ball when Sarina throws the ball, all we need to do is solve for the initial height of the ball, i.e, the height when x = 0. So we'll have;
[tex]\begin{gathered} f(0)=-(0)^2-(0)+3 \\ f(0)=3\text{ f}eet \end{gathered}[/tex]How do you solve the y-intercept of y = 9x + 9 and what is it simplified?
to know y -intercept we only need to replace x by 0. And we get
[tex]y=9\cdot0+9=9[/tex]so the y-intercept is 9
Your friend Pat bought a fish tank that has a volume of 175 liters. The brochure for Pat's tank lists a "fun fact that it would take 7.43 x 1018 tanks of that sizeto fill all the oceans in the world. Pat thinks the both of you can quickly calculate the volume of all the oceans in the world using the fun fact and the size ofher tankPart a.) Given that 1 liter = 1.0 x 10-12 cubic kilometers, rewrite the size of the tank in cubic kilometers using scientific notation.b) Determine the volume of all the oceans in the world in cubic kilometers using the "fun fact"
The tank has a volume of 175 liters
Fun fact: it would take 7.43*10¹⁸ tanks that size to fill all the oceans in the world.
a) Using the convertion 1 liter = 1.0*10⁻¹²km³ you have to rewrite the size of the tank.
For this you have to use cross multiplication:
1 Lts = 1.0*10⁻¹²
175Lts=x
[tex]x=175\cdot1.0\cdot10^{-12}=1.75\cdot10^{-10}[/tex]The volume of the tank is equal to 1.75*10⁻¹⁰ km³
b)
You know that one tank has a volume of 1.75*10⁻¹⁰ km³
To know what volume would 7.43*10¹⁸ tanks of the same size have, multiply the volume of one tank by the number of tanks.
[tex]1.75\cdot10^{-10}\cdot7.43\cdot10^{18}=1300250000\operatorname{km}^3[/tex]Using the fun fact, the determined volume of all oceans in the world is 1300250000km³
Determine whether the statement is true or false, and explain why.
If a function is positive at x = a, then its derivative is also positive at x = a.
Choose the correct answer below.
OA. The statement is true because the sign of the rate of change of a function is the same as the sign of its value.
OB. The statement is false because the derivative gives the rate of change of a function. It expresses slope, not
value.
OC. The statement is false because the sign of the rate of change of a function is opposite the sign of its value.
OD. The statement is true because the derivatives of increasing functions are always positive.
Answer: B. The statement is false because the derivative gives the rate of change of a function. It expresses slope, not value.