Consider the following data for a dependent variable y and two independent variables, ₁ and 2. x1 22 30 12 45 11 25 18 50 17 41 6 50 19 75 36 12 59 13 76 17 The estimated regression equation for thi
Answers
69.56 + 0.32x₁ - 0.18x₂ is the equation that fits the given data for the dependent variable y and the two independent variables x₁ and x₂.
The given data for a dependent variable y and two independent variables, x₁ and x₂, are as follows:
x₁: 22, 30, 12, 45, 11, 25, 18, 50, 17, 41, 6, 50, 19, 75, 36, 12, 59, 13, 76, 17
y: 50, 90, 50, 80, 60, 80, 50, 70, 60, 70, 50, 70, 90, 80, 70, 60, 80, 50, 70, 60
The estimated regression equation for the given data is given by:
y = 69.56 + 0.32x₁ - 0.18x₂
Here:
y represents the dependent variable.
x₁ and x₂ are the two independent variables.
Therefore, the equation that fits the given data for the dependent variable y and the two independent variables x₁ and x₂ is y = 69.56 + 0.32x₁ - 0.18x₂.
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Related Questions
Let R be the region bounded by the following curves. Find the volume of the solid generated by revolving the shaded region shown to the right about the x-axis. y=6 -3x, y = 0, and x = 0 AY Y6-3x The volume of the solid is cubic units. (Type an exact answer.)
Answers
Therefore, the volume of the solid generated by revolving the shaded region about the x-axis is (20π/3) cubic units.
To find the volume of the solid generated by revolving the shaded region about the x-axis, we can use the method of cylindrical shells.
The region bounded by the curves y = 6 - 3x, y = 0, and x = 0 forms a triangular region in the first quadrant. Let's find the limits of integration for x.
The line y = 0 intersects with the curve y = 6 - 3x at x = 2. Therefore, the limits of integration for x will be from x = 0 to x = 2.
Now, let's consider a vertical strip at a specific x-value within this region. The height of this strip is given by the difference between the curves y = 6 - 3x and y = 0, which is (6 - 3x) - 0 = 6 - 3x.
The width of the strip is dx.
The circumference of the shell is the distance traveled by revolving the strip around the x-axis, which is given by 2πx.
The volume of the shell is then given by the product of the circumference and the height, which is (2πx) * (6 - 3x) * dx.
Integrating this expression from x = 0 to x = 2 will give us the total volume of the solid:
V = ∫[0 to 2] (2πx) * (6 - 3x) dx.
Simplifying and evaluating the integral, we get:
V = 2π ∫[0 to 2] \((6x - 3x^2) dx.\)
V = 2π \([3x^2/2 - x^3/3]\) evaluated from 0 to 2.
V = 2π \([(3(2)^2/2 - (2)^3/3) - (3(0)^2/2 - (0)^3/3)]\)
V = 2π [(3(4)/2 - (8)/3) - 0].
V = 2π [(6 - 8/3)].
V = 2π [(18/3 - 8/3)].
V = 2π (10/3).
V = (20π/3) cubic units
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two point charges are placed on the x-axis as follows: charge q1 = 3.99 nc is located at x= 0.205 m , and charge q2 = 5.01 nc is at x= -0.302 m .
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Two point charges, q1 = 3.99 nC located at x = 0.205 m and q2 = 5.01 nC at x = -0.302 m, are placed on the x-axis. The electric field and direction at a given point can be calculated using the principle of superposition.
The electric field at a point due to a point charge is given by Coulomb's law, E = kq/r^2, where E is the electric field, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the point where the electric field is being measured. To calculate the net electric field at a point due to multiple charges, we use the principle of superposition, which states that the total electric field at a point is the vector sum of the electric fields due to each individual charge.
In this case, we have two charges, q1 = 3.99 nC and q2 = 5.01 nC. The electric field at a point P on the x-axis, due to q1, can be calculated as E1 = kq1/r1^2, where r1 is the distance between q1 and point P. Similarly, the electric field at point P due to q2 can be calculated as E2 = kq2/r2^2, where r2 is the distance between q2 and point P. To find the net electric field at point P, we add the electric fields vectorially, E_net = E1 + E2.
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Choose all of the numbers below that are perfect squares. You must select all that apply.
200
361
121
50
225
4
please help meh
Answers
Answer:
361 121 225 4
Step-by-step explanation:
you can square root these numbers to get a whole number
1/3h=6 I don’t know how to solve it
Answers
Solution
H=18
1. Rey Mercado has a house valued at $250,000. His mortgage is
for $180,000. How much money can he borrow if the bank will
lend 80 percent of the equity in the home?
2. Your credit card was stolen. You reported the theft within
24 hours. Before the theft was reported, the thief charged
$2,450 at a jewelry store and $1,245 at an electronics store.
How much of the fraudulent charges will you have to pay?
3. Jacki Marshall owes a balance of $5,000 on one credit card that charges 19 percent interest. She can pay off the balance in two years with monthly payments of $252.04. She has another credit card with a balance of $7,500 that charges 20 percent interest.
She can pay off the balance in two years with monthly payments of $381.72. Jacki owns a home valued at $150,000. She can get a home equity loan for $12,500 at 8 percent interest. Jacki can repay the loan in two years with monthly payments of $565.34. How much money will Jacki save if she takes out a home equityloan to pay off the credit card balances?
Answers
Answer:
1. $56,000
2. $3,695
3. $1,644.48
Step-by-step explanation:
1. Equity = valuation - mortgage
= $250,000 - $180,000
= $70,000
80% = 80/100 = 0.8
Therefore, 80% of the equity = 0.8 × $70,000
= $56,000
2. Total charges = jewelry charge + electronics charge
= $2,450 + $1,245
= $3,695
3.
First credit card:
Total payment = two years × monthly payments
= 2 × 12 × $252.04
= $6,048.96
Interest = total payment - balance
= $6,048.96 - $5,000
= $1,048.96
Second credit card:
Total payment = two years × monthly payments
= 2 × 12 × $381.72
= $9,161.28
Interest = total payment - balance
= $9,161.28 - $7,500
= $1,661.28
Home equity loan:
Total payment = two years × monthly payments
= 2 × 12 × $565.24
= $13,565.76
Interest = total payment - balance
= $13,565.76 - $12,500
= $1,065.76
Money saved = (total of interest from credit cards) - home equity loan interest
= ($1,048.96 + $1,661.28) - $1,065.76
= $1,644.48
Explain why for any value of the answer to y² +3pis always positive when p is positive.
Answers
If y is any real number, then y² is always nonnegative (i.e. not negative).
Examples:
y = -10 leads to y² = (-10)² = 100y = 0 leads to y² = (0)² = 0y = 7 leads to y² = (7)² = 49There's no way to have y² be a negative value.
So everything relies on the 3p
If p > 0, then 3p > 0 after multiplying both sides by 3.
Therefore, p being positive means 3p is also positive.
Adding a positive number onto y² is some other positive number (either that value itself or larger).
Overall, y²+3p > 0 if p > 0
The sampling distribution of the sample mean _____.a. shows the distribution of all possible values of μb. is an unbiased estimatorc. is the probability distribution showing all possible values of the sample meand. is used as a point estimator of the population mean μ.The standard error of the proportion will become larger as _____.a. p approaches 1b. n increasesc. p approaches 0d. p approaches .5
Answers
C- is the probability distribution showing all possible values of the sample mean. D- p approaches 0.5
The sampling distribution mean is the physical to the population mean. A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
Thus, the correct answer is C
The term "standard error" refers to the sampling standard deviation of the sample statistic or sample proportion. The population percentage can be accurately estimated using the sample proportion.
Thus, the correct answer is D
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The sampling distribution mean is the physical to the population mean. A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
PLEASE HELP!!
Water is dripping into an enclosed classroom at the rate of 78,000 drops per second. Unfortunately, the door is locked and the teacher does not have a key.
A professional lock smith has been called to come over and
unlock the door, but he is stuck in heavy traffic and will
not be able to arrive for 24 hours. Will the lock smith arrive in time to save the class gerbil?
Volume= 37,956,672cm^3
Length=416cm
Width=333cm
Height=274cm
Answers
Answer:
No.
Explanation:
Let's assume that the average drop is 0.05cm³.
0.05cm³ * 78000drops/sec * 60secs * 60mins * 24hrs = 336,960,000cm³ which is more than the volume of the room.
In order for the locksmith to arrive in time the average drop would have to be less than 0.00056cm³ which probably isn't happening here. And even then the gerbil has probably already drowned unless its cage is at the very top of the room and the locksmith is a wizard.
$800 is deposited in an account with a 9% interest rate, compounded continuously. what is the balance after 12 years?
Answers
Answer:
The formula for calculating the compound amount is:
A = P( 1 + R ) ^ T
Put in the numbers and calculate:
A = 800( 1.09 ) ^ 2
A = 800 x 1.1881
A = 950.48
I = A - P
I = 950.48 - 800
I = 150.48
on this necklace the ratio of black beads to white beads is 1:4 How many more black beads do you need to add to make the ratio of black to white 4:1 ?
WILL GIVE BRAINLIEST!!!
Answers
1:4 = 1 black bead and 4 white beads
4:1 = 16:4
16 - 1 = 15 black beads
Write 24 as a product of prime factors.
Answers
Answer:
2 x 2 x 3 x 2
Step-by-step explanation:
Let's slowly break down 24 into shorter pieces.
24 = 4 x 6
=> 2 x 2 x 3 x 2
Since all of the numbers are prime numbers, the following product is the product of prime factors.
Hoped this helped.
Solve for n: 3 x n = 2 x 9
I need help
Answers
Answer:
18
Step-by-step explanation:
CALCULATER
joe needs to transfer 28 quarts of oil into containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error
Answers
This question is incomplete
Complete Question
Joe needs to transfer 28 quarts of oil into gallons containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error
Joe's error:
28 quarts × 4 quarts/ 1 gallon
= 28 quarts/1 × 4 quarts/ 1 gallon
= (28 × 4)/ ( 1 × 1) = 112 gallons
Answer:
7 gallons is the correct answer
Joe needs to transfer 28 quarts of oil into 7 gallons
Step-by-step explanation:
Joe's error:
28 quarts × 4 quarts/ 1 gallon
= 28 quarts/1 × 4 quarts/ 1 gallon
= (28 × 4)/ ( 1 × 1) = 112 gallons
Correcting Joe's error, we have:
4 quarts = 1 gallon
28 quarts = x
Cross Multiply
4 quarts × x = 28 quarts × 1 gallon
x = 28 quarts × 1 gallon/ 4 quarts
x = 7 gallons
= 28 quarts/x gallons × 1 gallon/4 quarts
= (28 × x)/ ( 1 /4) = 7 gallons
Therefore, Joe needs to transfer 28 quarts of oil into 7 gallons
En un comedor llenan termos con mate cocido con leche para servir la merienda. Juana, la cocinera, llena los termos de manera que 1/3 sea leche caliente y el resto, mate cocido. Perla, su ayudante, prepara los termos de otra manera: sabe que en cada uno entran 5 jarras de liquido, así que los completa con 3 jarras de mate cocido y 2 de leche. c) La semana que viene cambiarán los termos por otros más grandes , de 4,5 litros de capacidad. ¿Qué cantidad de mate cocido y de leche pondrá Juana en cada termo nuevo? ¿Y Perla?
Answers
Answer:
Juana pondrá 1.5 litros de leche caliente y 3 litros de mate cocido en cada termo de 4.5 litros de capacidad.
Perla pondrá 1.8 litros de leche caliente y 2.7 litros de mate cocido en cada termo de 4.5 litros de capacidad.
Step-by-step explanation:
Aquí podemos constatar dos formas distintas de preparar mate cocido con leche. Juana llena los termos con un tercio de la capacidad de los termos con leche caliente y dos tercios de la capacidad de los termos con mate cocido.
En cambio, Perla llena los termos con dos quintos de la capacidad de los termos con leche caliente y tres quintos de la capacidad de los termos con mate cocido.
Entonces, las capacidades correspondientes de cada ingrediente se obtiene al multiplicar la capacidad total por la razón correspondiente. A continuación, presentamos los resultados según la receta de cada persona:
Juana - Leche Caliente
\(x = \frac{1}{3}\times 4.5\,L\)
\(x = 1.5\,L\)
Juana - Mate Cocido
\(x = \frac{2}{3}\times 4.5\,L\)
\(x = 3\,L\)
Juana pondrá 1.5 litros de leche caliente y 3 litros de mate cocido en cada termo de 4.5 litros de capacidad.
Perla - Leche Caliente
\(x = \frac{2}{5}\times 4.5\,L\)
\(x = 1.8\,L\)
Perla - Mate Cocido
\(x = \frac{3}{5}\times 4.5\,L\)
\(x = 2.7\,L\)
Perla pondrá 1.8 litros de leche caliente y 2.7 litros de mate cocido en cada termo de 4.5 litros de capacidad.
Cayden has several screws on a scale, and the scale reads 80.955 cayden add 1 more screw and the scale reads 84.81
Answers
Answer:
-3.855
Step-by-step explanation:
Not sure if you need the weight of each screw! but you just subtract 80.955-84.81
Answer:
1
Step-by-step explanation:
itnisbbsndnfnfnfnnfnfnfncjcjccjcj
Choose all of the vectors shown below that (1²2) are parallel to (7²) (12²) (-22) (3) 12/ (ő) 4 24 3 13/
Answers
There are no vectors among the options provided that are parallel to (1²2).
To determine if two vectors are parallel, we can compare their direction ratios.
Two vectors are parallel if their direction ratios are proportional.
Let's compare the given vector (1²2) with each of the options provided:
Vector (7²) (12²) (-22) (3) 12/ (ő) 4 24 3 13/:
Comparing the direction ratios, we have:
1/7 = 2/12 = 2/-22 = 3/4 = 24/3 = 12/13.
Since the direction ratios of the given vector (1²2) are not proportional to the direction ratios of any of the options, none of the options are parallel to (1²2).
summary, none of the vectors (7²) (12²) (-22) (3) 12/ (ő) 4 24 3 13/ are parallel to the given vector (1²2).
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Maria calls her mother 5 times every week. Let w represent the number of weeks and c represent the total number of times Maria calls her mother. DO NOT use spaces in your equation.
Answers
Answer:
Equation: 5w = c
Step-by-step explanation:
\({ \tt{w \: \alpha \: c}} \\ { \tt{w = kc}}\)
k is a constant of proprtionality
\({ \tt{1 = (k \times 5)}} \\ { \tt{k = \frac{1}{5} }}\)
» Therefore, equation becomes:
\({ \tt{w = \frac{1}{5}c }} \\ \\ { \boxed{ \tt{5w = c}}}\)
Please someone help me
Answers
Paul surveyed students in a high school about their favorite sport of the 1, 200 students in the school, 67 tenth-grade students were surveyed. More than half of the 67 students said their favorite sport is basketball. Based on the survey, Paul concluded that the favorite sport of most high school students is basketball.
Why is Paul's conclusion incorrect?
1 Paul surveyed too many students.
2 Paul's survey sample only included tenth graders.
3 Paul did not survey any middle school students.
4 Paul did not include enough sports in the survey.
Answers
Answer:
2 Paul's Survey sample only included tenth graders
Step-by-step explanation:
The reson why this is your answer is simple
Because this is true, he ONLY surveyed tenth-graders. He should have found for all of the students, including the other 1,100 students that didn't get surveyed.
Thanks!
square root of 50 multiplied by square root of 7d squared
Answers
A triangular pyramid with an equilateral base has a side length of 10 centimeters and a surface area of 214.5 square centimeters. Find its slant height. No photo given.
Answers
the The Solution:
Step 1:
We shall split the triangular pyramid into its component surfaces.
3 triangles + 1 triangle.
Step 2:
We shall find the area of the triangle in fig 1., by using Heron's formula.
\(\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{Where A= area} \\ a=10\text{ ; b= 10 ; c=10} \\ s=\frac{a+b+c}{2}=\frac{10+10+10}{2}=\frac{30}{2}=15 \\ So, \\ A=\sqrt[]{15(15-10)(15-10)(15-10)} \\ A=\sqrt[]{15\times5\times5\times5} \\ A=25\sqrt[]{3}cm^2 \end{gathered}\)Step 3:
We shall state the formula for calculating the total surface area of the triangular pyramid.
\(\begin{gathered} \text{SA = Area of fig1 triangle + 3(}\frac{1}{2}bh) \\ \text{Where SA =surface area =214.5 cm}^2 \\ \text{Area of fig 1 triangle = 25}\sqrt[]{3}cm^2 \\ b\text{ =base =10 cm} \\ h=\text{slant height =?} \end{gathered}\)Step 4:
We shall substitute the above values into the formula.
\(\begin{gathered} 214.5=25\text{ }\sqrt[]{3}\text{ + 3(}\frac{1}{2}\times10\times h) \\ 214.5=25\text{ }\sqrt[]{3}+3(5h) \\ 214.5=43.3+15h \\ \text{Collecting the like terms, we get} \end{gathered}\)\(\begin{gathered} 214.5-43.3=15h \\ \text{Dividing both sides by 15, we get} \\ 171.2=15h \\ h=\frac{171.2}{15} \\ h=11.413\approx11.4\text{ cm} \end{gathered}\)Step 4:
The presentation of the Answer.
The slant height is 11.4 centimeters.
Thus, the correct answer is 11.4 centimeters.
24 pencils cost $1.20 how much will 6 pencils cost?
Answers
Answer:
30 cents
Step-by-step explanation:
Answer:
30 cents
Step-by-step explanation:
1.2 divided by 24=.05= 5 cents
.05 times 6= .3=30 cents
Hope this helped!! :)
Brainliest!?!?!
Stay safe and have a wonderful day/afternoon/night!!!
Can someone help me answer 4-13
Need done tonight!!
Answers
3(x+2)=4(x+1)
3x+6=4x+1
so that means x=2
Please help!!! Find the equation of the line, use exact numbers:
y=__x+__
(__ means to fill in)
Answers
how many teaspoons are f vanilla will i use?
Answers
Answer:
9 teaspoons of vanilla
Step-by-step explanation:
12/4=3
3*3=9
Answer:
teaspoons of vanilla =9
Step-by-step explanation:
we can make it as a ratio
So we have (3 for teaspoons and 4 tablespoons)
3:4
Then x : 12
x=(12/4)*3=9
hope this helps
juan rolls a fair regular octahedral die marked with the numbers $1$ through $8$. then amal rolls a fair six-sided die. what is the probability that the product of the two rolls is a multiple of $3$?
Answers
The probability that the product of the two rolls is a multiple of 3 is 1/2.
Probability:
Probability mean the fraction of the possibility of the required event.
The formula for the probability is
P(E) = n(E)/n(S)
Where
P(E) = Probability of the event
n(E) = number of required event
n(S) = Total number of event
Given,
Juan rolls a fair regular octahedral die marked with the numbers 1 through 8.
Then Amal rolls a fair six-sided die.
Here we need to find the probability that the product of the two rolls is a multiple of 3.
We know that,
On both dice, only the faces with the numbers 3,6 are divisible by 3.
Let
P(a) = 2/8
P(a) = 1/4
it is the probability that Juan rolls a 3 or a 6,
and Similarly,
P(b) = 2/6
P(b) = 1/3
Is the probability of Amal does.
By the Principle of Inclusion-Exclusion,
\(\[P(a \cup b) = P(a) + P(b) - P(a \cap b) = \frac{1}{4} + \frac{1}{3} - \frac{1}{4} \cdot \frac{1}{3} = \frac{1}{2} \Rightarrow \mathrm{(C)}\]\)
Thus the total probability is 1/2.
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What is the yield to maturity (YTM) on a simple loan for $1,500 that requires a repayment of $7,500 in five years' time? The yield to maturity is ?
Answers
The yield to maturity on a simple loan for $1,500 that requires a repayment of $7,500 in five years' time is 37.14%.
Yield to maturity (YTM) is the total return anticipated on a bond or other fixed-interest security if the security is held until it matures. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. In this problem, the present value (PV) of the simple loan is $1,500, the future value (FV) is $7,500, the time to maturity is five years, and the interest rate is the yield to maturity (YTM).
Now we will calculate the yield to maturity (YTM) using the formula for the future value of a lump sum:
FV = PV(1 + YTM)n,
where,
FV is the future value,
PV is the present value,
YTM is the yield to maturity, and
n is the number of periods.
Plugging in the given values, we get:
$7,500 = $1,500(1 + YTM)5
Simplifying this equation, we get:
5 = (1 + YTM)5/1,500
Multiplying both sides by 1,500 and taking the fifth root, we get:
1 + YTM = (5/1,500)1/5
Adding -1 to both sides, we get:
YTM = (5/1,500)1/5 - 1
Calculating this value, we get:
YTM = 0.3714 or 37.14%
Therefore, the yield to maturity on a simple loan for $1,500 that requires a repayment of $7,500 in five years' time is 37.14%.
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What is the scale factor from ABC to DEF?
Answers
Answer:
0 so D
Step-by-step explanation:
The shape didnt change at all. All the sides are 5 for both triangles.
Explanation: any side you have is multiplied by some sort of scale factor. In this instance, if you multiply the sides of ABC by a scale factor of 1, you will get the similar side lengths of DEF (the same as ABC)
Answer D may be tempting but multiplying your sides by 0 would make the triangle…well disappear :D
Write the verbal sentence as a equation. 3 times the sum of a number and 2 is 12.
Answers
Answer:
3(x+2)=12
Step-by-step explanation:
let the number be x
the sum=x+2
the answer
3(x+2)=12
Instructions: Find the measure of the indicated angle to the nearest
degree.
?
35
19
?
Answers
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the opposite side and the adjacent side. Therefore, we should use the tangent function.
tan(x) = 19 / 35
x = tan^-1(19/35)
x = 28 degrees
Hope this helps!