Answers
We will have to find the equation that follows the form:
[tex]a+bx=y[/tex]That is:
*The value of a is:
[tex]a=547.4666667[/tex]*The value of b is:
[tex]b=29.91428571[/tex]So, the linear regression is:
[tex]y=29.91428571x+547.4666667[/tex]We can see it graphically as follows:
Here we can see the linear regression line and the points used.
***How to manually determine linear regressions***
We will start as follows:
We will have to use the following expressions in order to manually find the linear regression:
[tex]b=\frac{n(\sum^{}_{}xy)-(\sum^{}_{}x)(\sum^{}_{}y)}{n(\sum^{}_{}x^2)-(\sum^{}_{}x)^2}[/tex]And:
[tex]a=\frac{\sum ^{}_{}y-b(\sum ^{}_{}x)}{n}[/tex]Here we have that n is the number of values on the dataset. So, we solve for b as follows [Based on the problem given]:
*We will determine the values of n, the sum of x, the sum of y, xy, x^2 & y^2 as follows:
Sum of x:
[tex]\sum ^{}_{}x=1+2+3+4+5+6\Rightarrow\sum ^{}_{}x=21[/tex]Sum of y:
[tex]\sum ^{}_{}y=588+298+640+650+707+730\Rightarrow\sum ^{}_{}y=3913[/tex]Value of n: We have that the number of datasets given is 6 [6 pairs of values on the table].
[tex]n=6[/tex]*The sum of xy:
[tex]\sum ^{}_{}xy=(1)(588)+(2)(598)+(3)(640)+(4)(650)+(5)(707)+(6)(730)\Rightarrow\sum ^{}_{}xy=14219[/tex]*The sum of X^2:
[tex]\sum ^{}_{}x^2=1^2+2^2+3^2+4^2+5^2+6^2\Rightarrow\sum ^{}_{}x^2=91[/tex]*The square of the sum of x:
[tex](\sum ^{}_{}x)^2=21^2\Rightarrow(\sum ^{}_{}x)^2=441[/tex]Now that we have all the values, we replace in the first equation and solve for b:
[tex]b=\frac{(6)(14219)-(21)(3913)}{(6)(91)-(441)}\Rightarrow b=29.91428571[/tex]And we solve now for a:
[tex]a=\frac{(3913)-(29.91428571)(21)}{(6)}\Rightarrow a=548.4666667[/tex]And then we simply replace on the expression:
[tex]y=bx+a[/tex]And the expression after the replacement of a & b is the linear regression.
Related Questions
Blake buys a one-quart bottle of juice for $6.40. What is the unit rate of the cost ofthe juice per fluid ounce?1 gallon 4 quarts1 quart 2 pints1 pint cups1 cup= 8 fluid ounces2Before you try that problem, answer the question below.How many fluid ounces of juice did Blake buy?
Answers
So the information we have is Blake buys a one-quart bottle of juice for $6.40
So we can say the juice cost 6.40 $/quart
so now, let's find the relationship between quart and ounces
1 quart =2 pints
1 pint =2 cups
1 cup = 8 fluid ounces
So
[tex]\begin{gathered} 1\text{quart}=2\text{ pints=2}\cdot(2\text{ cups)} \\ 1\text{ quart= 4 cups} \\ 1\text{ quart=4}\cdot(8\text{ ounces)} \\ 1\text{ quart=32 ounces} \end{gathered}[/tex]so for the question:
How many fluid ounces of juice did Blake buy?
she bought 1 quart of juice and we said 1 quart=32 ounce, so the answer is: She bought 32 ounces of juice.
And for the first question: What is the unit rate of the cost of
the juice per fluid ounce? we can do:
[tex]6.40\frac{Dollars}{quart}\cdot\frac{1\text{ quart}}{32\text{ ounces}}=\frac{6.40}{32}\frac{dollars}{ounces}[/tex]So the answer is:
0.2 $/ounces ($ per ounce)
An equation of the parabola shown in the xy-plane is y = ax² - c, where a is a constant and c is an integer. What is the value of c ?
Answers
To find c we notice that this value happens when x=0, then we have the equation:
[tex]y=-c[/tex]Now, from the graph we notice that when x=0 the value of y=-10, then we have:
[tex]\begin{gathered} -10=-c \\ c=10 \end{gathered}[/tex]Therefore the value of c is 10.
The Epson Stylus 850 can print Helen's class project in 12 minutes. The Epson Stylus 500 can print the project in 42 minutes. If the two printers work together, how long would they take to print out the project?A) 9 minB) 9 1/3 minC) 84 minD) 3/28 min
Answers
The epson stylus 850 can print Helen's project in 12 mins
TThe epson stylus 500 can print that same project in 42 minutes
Work = rate x time
the two printers are working on the same assignment
therefore, we will be adding their rate
for epson 850
work = rate x time
work= 1
time = 12mins
1 = rate x 12
make rate the subject of the formula by dividing bott sides by 12
1 / 12 = rate x 12 / 12
rate = 1/ 12
for epson 500
work = rate x time
time = 42 mins
work = 1
applying the same process
1 = rate x 42
rate = 1/42
since they are both working together
Total rate = 1 /12 + 1/42
lcm is 84
since 12 and 42 are factors of 84
Total rate = 1/12 + 1/42
total rate = 84 * 1 /12 + 84*1 / 42 /84
total rate = 7 + 2 / 84
total rate = 9/84
to calculate the time they worked together
work = rate x time
1 = 9/84 x time
make time the subject of the formula
1 / 9/84 = time
time = 84/9
time = 28 / 3
Time = 9 1/3 min
Option B
i need help asap please help worth alot points
Answers
There are 24 question in the picture. We have to solve the problem by multiplication and division.
Given that,
There are 24 question in the picture.
We have to find the multiplication and division for the given question.
Multiplication condition:
Plus multiply minus is equal to minus
Plus multiply plus is equal to plus
Minus multiply minus is equal to plus
Minus multiply plus is equal to minus
Division condition:
Plus divided by minus is minus
Plus divided by plus is plus
Minus divided by minus is plus
Minus divided by plus is minus
1. -2×5= -10
2. -16÷-8= 2
3. 60÷-5= -12
4. 11×-1= -11
5. 18÷-2= -9
6. 28÷-4= -7
7. 7×-8= -56
8. -8×11= -88
9. -70×-3= 210
10. -60÷-2= 30
11. 8×-90= -720
12. -80÷40= -2
13. 300÷-6= -50
14. -80×50= -4000
15. -200÷40= -5
16. -70×-60= 4200
17. -3×2= -6
18. -16÷-4= 4
19. 5×-6= -30
20. 12÷-3= -4
21. -18÷6= -3
22. 7×9= 63
23. -60÷-6= 10
24. -8×-5= 40
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pls help: find the probability of rolling a die five times and getting at least one three
Answers
The probability of getting at least one 3 when a die is rolled 5 times is 0.59 .
What is probability?
The area of mathematics known as probability deals with numerical estimates of how likely an event is to occur.
A die is rolled 5 times.
The sample space is [tex]6^{5}=7776[/tex].
Probability of getting no 5 is [tex]\frac{5}{6}[/tex].
Probability of getting at least one 5 = 1- probability of getting no 5
[tex]1-(\frac{5}{6}) ^{5} \\\\\frac{7776-3125}{7776}\\ \\\frac{4651}{7776}\\ \\0.59[/tex]
Hence Probability of getting at least one 5 is 0.59.
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there are 4 swimmers in a race. there will be 1st, 2nd and 3rd place prize awarded. In how many different ways can the prizes be awarded?
Answers
From the problem we will have that:
[tex]\begin{gathered} _4P_3=\frac{4!}{(4-3)!}\Rightarrow_4P_3=\frac{24}{(1)} \\ \\ \Rightarrow_4P_3=24 \end{gathered}[/tex]There will be 24 possible ways to award the 3 prizes between 4 people.
what is a reasonable minimum value for the dependent variable? explain how you arrived at your answer
Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} f(x)=-16x^2+64 \\ x\text{ is the time in seconds} \\ f(x)\text{ is the distance of the pumpkin from the ground} \\ \\ \text{ When the pumpkin is on the ground, its distance from the ground is zero. Thus,} \\ f(x)=0,\text{ when the pumpking is on the ground.} \\ \\ -16x^2+64=0 \\ \text{ Subtract 64 from both sides} \\ -16x^2=-64 \\ \text{ Divide both sides by -16} \\ x^2=-\frac{64}{-16} \\ \\ x^2=4 \\ \text{ Take the square root of both sides} \\ \\ x=\pm\sqrt{4} \\ x=+2\text{ or }-2 \\ \\ \text{ Since we cannot have negative time, } \\ x=2\text{ seconds} \end{gathered}[/tex]Final Answer
It takes 2 seconds for the pumpkin to hit the ground
WXYZ is a quadrilateral graphed in the coordinate plane with vertices W(0,5),X(-3,2), Y(0,-4), and Z(3,2). What are the lengths of the sides of the quadrilateral, and what is the correct name for the figure?
Answers
Given: WXYZ is a quadrilateral graphed in the coordinate plane with vertices W(0,5), X(-3,2), Y(0,-4), and Z(3,2).
Required: To determine the side length and type of quadrilateral.
Explanation: The distance between two points is given by the formula-
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The length of side WX is-
[tex]D=\sqrt{(-3-0)^2+(2-5)^2}[/tex]Further solving as-
[tex]\begin{gathered} D=\sqrt{9+9} \\ D=3\sqrt{2}\text{ units} \\ D=4.24\text{ units} \end{gathered}[/tex]Similarly, the side length XY is-
[tex]\begin{gathered} D=\sqrt{(0+3)^2+(-4-2)^2} \\ D=\sqrt{45} \\ D=6.71\text{ units} \end{gathered}[/tex]And, the side length YZ is-
[tex]\begin{gathered} D=\sqrt{(3-0)^2+(2+4)^2} \\ D=\sqrt{45} \\ D=6.71\text{ units} \end{gathered}[/tex]Finally, the side length WZ is-
[tex]\begin{gathered} D=\sqrt{(3-0)^2+(2-5)^2} \\ D=3\sqrt{2} \\ D=4.24\text{ units} \end{gathered}[/tex]Now, since the adjacent sides of the quadrilateral WXYZ are equal, the quadrilateral is a Kite.
Final Answer:
The length of side WX=4.24 units.
The length of side XY=6.71 units.
The length of side YZ=6.71 units.
The length of side ZW=4.24 units.
The best name for this quadrilateral is Kite.
A particular fruit's weights are normally distributed, with a mean of 406 grams and a standard deviation of 27 grams.The heaviest 14% of fruits weigh more than how many grams?Give your answer to the nearest gram.
Answers
Given
mean of 406 grams and a standard deviation of 27 grams.
Find
The heaviest 14% of fruits weigh more than how many grams?
Explanation
given
mean = 406 gms
standard deviation = 27 gms
using standard normal table ,
[tex]\begin{gathered} P(Z>z)=14\% \\ 1-P(Zso , [tex]\begin{gathered} x=z\times\sigma+\mu \\ x=1.08\times27+406 \\ x=435.16 \end{gathered}[/tex]Final Answer
Therefore , The heaviest 14% of fruits weigh more than 435.16 gms
Describe the set of values that is greater than the quadratic function with zeros –5 and –13 and includes the
point (–9, –32).
Answers
Answer: y>2(x+5)(x+13)
Step-by-step explanation:
edg
Answer:
Answer: y>2(x+5)(x+13)
Step-by-step explanation:
A.) If angle 3 = 5x-1 and angle 5-3x+11, then x= B.) If angle 3 = 5x-1, and angle 5 = 3x + 11, then the measure of angle 3= C.) If 23 = 5x-1, and 25 = 3x+ 11, then the measure of angle 1= D.) If angle 3 = 5x-1, and angle 5 = 3x + 11, then the measure of angle 2 =
Answers
1) Gathering the data
∠3 = 5x -1
∠5=3x +11
∠3=?
2) The angles ∠3 and ∠5 are alternate interior angles, therefore they are congruent ones. So we can write:
5x -1 = 3x +11
5x -3x = 11 +1
2x = 12
x = 6
The measure of angle m∠3 =
5(6) -1
30-1
29º As ∠5 is also congruent then m∠5= 29º
3) ∠1 According to the Vertical Angle Theorem has the same measure as the ∠3, So we can say that ∠1 = 29º
∠2 is supplementary to ∠1
m∠2=180 -29
m∠2=151º
how do you rewrite an expression with parenthesisthe question is 5(x+2)
Answers
We have the following:
[tex]5(x+2)=5x+10[/tex]the answer is 5x + 10
The given table of values represents a linear equation. What is the slope?
X 1 2 3 4 y 5 8 11 14
Answers
The slope of the straight line is 3.
What is slope of a line?
Slope is the measure of steepness. Slope is determined by the tangent of angle a line makes with the x-axis. It is calculated as rise over run. Mathematically for the coordinates (a, b) (c, d) it can be given as [tex]\frac{d-b}{c-a}[/tex].
We are given a table which contains some coordinates of a straight line
We have to find the slope of the line
This can be done as
Slope[tex]=\frac{8-5}{2-1}[/tex]
Slope[tex]=3[/tex]
Hence the slope of the line is 3.
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Assume that there is a 10% rate of disk drive failure in a year.
a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
b. If copies of all your computer data are stored on independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answers
The probability that at least one drive is working is 0.99 and the probability that at least one drive is working out of 3 drives is 0.999 .
Probability is the branch of mathematics which deals with the likelihood of an occurrence of an event.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's true probability is a single decimal number between 0 and 1, where, mathematically speaking, 0 denotes the event is impossible and 1 denotes certainty.
Given the probability on one disk failing is 0.1
Probability that both disk fails = 0.1 × 0.1 = 0.01
Now let us calculate the probability that at least one disk does not fail.
We have to find the complement of the above.
Required probability = 1 -0.01 = 0.99
Similarly when 3 independent disc are involved.
Probability that all the disc fails = 0.1 × 0.1 × 0.1 = 0.001
At least one survives = 1 - 0.001 = 0.999
Therefore the probability that at least one drive is working is 0.99 and the probability that at least one drive is working out of 3 drives is 0.999 .
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Check each answer to see whether the student evaluated the expression correctly. If the answer is incorrect cross out the answer and write the correct answer. 6w-19+k when w-8 and k =26(2)-19+8=12-19+8=1
Answers
we have the expression
6w-19+k
Evaluate the given expression for
w=8 and k=2
so
substitute
6(8)-19+2=31
therefore
The answer is incorrect
the correct answer is 31
Which of the graphs on the right is the graph of C?
Answers
Answer: D
Step-by-step explanation:
The cost function gives that 75 is the initial cost and adds 0.25 per copy. the only graph that has a positive slope and has a y-intercept of 75 is D.
The dial on a combination lock contains markings which represent the numbers from 0 to 39. How many 3-
number combinations are possible if the first and the second must be different odd numbers, while the third
number must not be an odd number?
a. 7600
b. 8000
c. 59280
d. 57720
e. 43520
Answers
Answer:
C
Step-by-step
c
Help me out with this pls
Answers
Answer:
7.5
0
5
1
3.67
Step-by-step explanation:
absolute value (the ||) means negative numbers become positive
it does not change values that are already positive
abs of 7.5 is 7.5
abs of 0 is 0
abs of -5 is 5
abs of -1 is 1
abs of -3.67 is 3.67
McMichael Inc. collects 25% of its sales on account in the month of the sale and 75% in the month following the sale. If sales on account are budgeted to be $523,000 fo September and $465,000 for October, what are the budgeted cash receipts from sales on account for October?
Answers
The budgeted cash receipts from sales on account for October is $479500.
Define sale.A sale is a deal in which two or more parties exchange goods or services for cash or other assets. A sale in the financial markets is an arrangement involving the cost of a security and its delivery for agreed-upon payment between a buyer and a seller. Sales in general business operations refer to any exchanges of money or value for the right to possess a good or get a service. Sales, in the context of accounting, refers to the income generated by a corporation via the selling of goods or services (net sales).
Given Data
McMichael Inc. collects 25% of its sales on account in the month of the sale and 75% in the month.
If sales on account are budgeted to be $523,000 to September and $465,000 for October.
We can respond as follows based on the data provided in the question:-
25% of sales from October plus 75% of sales from September equal the budgeted cash receipts from sales.
Sales revenue budgeted for in cash is
($523,000 (25%)) + ($465,000 (75%))
130750 + 348750
479500
The budgeted cash receipts from sales on account for October is $479500.
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Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y+1=-3(x-4)
Answers
The given equation is expressed as
y + 1 = - 3(x - 4)
The first step is to expand the bracket by multiplying each term inside the bracket by the term outside. It becomes
y + 1 = - 3x + 12
3x + y = 12 - 1
3x + y = 11
A = 3
B = 1
C = 11
May I please get help with this problem? For I have Ed tried many times but still could not get the right answer
Answers
Given the square root of 64
[tex]\sqrt[]{64}[/tex]As we know 64 = 8 x 8
So, the square root of 64 = 8
[tex]\sqrt[]{64}=\sqrt[=]{8\times8}=8[/tex]So, the answer will be 8
A 6 3/4-inch candle burns down in 9 hours. How far has it burned after 6 hours? Use the dropdown menu to state your answer as a decimal, mixed number, or improper fraction.
Answers
The question can be solved using fractions, 4 and 1/2 inches of the candle will burn in 6 hours.
What is fractions?
The components of an entity or group of entities are represented as fractions. A fraction consists of two components. The numerator is the number at the top of the line (slash). It tells us how many equal portions of the whole or collection were taken. The denominator is the figure that appears below the line (slash). It displays the total number of identical objects in a collection or the total number of equal portions.
As given in the question, 6 3/4-inch (27/4) inch candle burns down in 9 hours.
We have to find the candle burnt in 6 hours.
Fraction for 9 hours = Fraction for 6 hours
So,
27/4:9 = x:6
We can also write it as,
(27/4)9 = x/6
x = 4.5 inch
It could also be written as 4 1/2 inches.
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Write an equation that models the linear situation:
A fitness club charges $5 for each class in addition to $150 for the year’s membership.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
n = number of fitness classes attended
C(n) = total cost of fitness club, including classes, for the year (dollars)
Question 2
Write an equation that models the linear situation:
A car rental company charges 5 cents per mile in addition to the base fee of $20.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
m = distance the rental car has been driven (miles)
C(m) = total cost of renting a car (dollars)
Question 3
Write an equation that models the linear situation:
A train starts a trip and it travels at a steady (average) speed of 70 miles per hour.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
t = time traveled (hours)
d(t) = distance traveled (miles)
Write an equation that models the linear situation:
A diver that was 300 feet below the surface of the ocean rises towards the surface 30 feet every minute.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
t = amount of time the diver rises towards the surface (minutes)
L(t) = sea-level position of the diver (feet)
Answers
The linear functions for each case are given as follows:
1. C(n) = 5n + 150.
2. C(m) = 0.05m + 20.
3. L(t) = 30t - 300.
What is a linear function?A linear function, in slope-intercept format, is given by:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For each item in this problem, we have that the meaning of the coefficients is explained as follows:
The rate per class/mile/rise represents the slope.The initial fees or the initial position represents the intercept.Hence the functions are given as follows, considering the stated variables:
1. C(n) = 5n + 150.
2. C(m) = 0.05m + 20. (5 cents = $0.05).
3. L(t) = 30t - 300. (300 feet below the surface is represented by a negative value, while a rise is represented by a positive value).
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Solve P=3(l+w) for l
Answers
Answer:
l=p/3-w
Step-by-step explanation:
To solve this problem, first distribute.
P=3l+3w
Now, subtract 2w on both sides
p-3w=3l
finally, divide both sides by 3.
3l/3=l
p/3=p/3
-3w/3=-w
The answer would be l=p/3-w
Kai took five tests this semester. His scores are listed below. 92, 88, 90, 96, 84What is the mean absolute deviation of Kai's test scores?4.03.22.01.6
Answers
the mean can be calculate with this equation:
[tex]m=\frac{x_1+x_2+\cdots}{n}[/tex]So in our problem will be:
[tex]\begin{gathered} m=\frac{92+88+90+96+84}{5} \\ m=90 \end{gathered}[/tex]Divide. Round your answer to the
nearest whole number.
3.37 54.308
Answers
Answer:
16
Step-by-step explanation:
please help this is for my study guide thanks! (at the end it says round to the nearest hundredth)
Answers
Given the figure of a cylinder:
As shown the radius of the cylinder = r = 11 ft
The height of the cylinder = h = 18 ft
the volume of the cylinder is given by the formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]where: π = 3.14
Substitute with the given values:
[tex]V=3.14\cdot11^2\cdot18=6838.92[/tex]so, the answer will be:
The volume = 6,838.92 ft³
What are the solutions to the equation 6x2 - x - 40 = 0? A. x = -8/3, x = -5/2B. x = -8/3, x = 5/2 С. x = -2, x = 3 D. x = -6, x = 2
Answers
what is the correct algebraic reprentation for a translation 5 units right and 4 units down?
Answers
We want to write the correct algebraic representation for a translation 5 units right and 4 units down.
Which means 5 units along the positive x axis and 4 units along the negative y axis.
So, we have;
[tex](x,y)\rightarrow(x+5,y-4)[/tex]Therefore, the correct algebraic
Solve the following equation for all values of x:2 +3−28=9+27
