A simple linear regression model is appropriate when the response variable is influenced by only one explanatory variable.
A simple linear regression model assumes a linear relationship between the response variable (y) and a single explanatory variable (x).
It is suitable when we want to understand how changes in the explanatory variable affect the response variable.
In the given options, the situation where the response variable y is influenced by one explanatory variable aligns with the requirements of a simple linear regression model.
This means that the relationship between y and x can be adequately described by a straight line.
The model aims to estimate the slope and intercept of this line, allowing us to make predictions and draw conclusions about the impact of the explanatory variable on the response variable.
If the response variable y is influenced by two or more explanatory variables, a multiple linear regression model would be more appropriate.
Multiple linear regression allows for the analysis of the combined effects of multiple predictors on the response variable, accounting for their individual contributions.
Similarly, if the explanatory variable x is influenced by two or more response variables, a different modeling technique, such as multivariate regression, would be more suitable.
Therefore, the situation where the response variable y is influenced by one explanatory variable is the scenario where a simple linear regression model is appropriate.
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If sinx + sin^2x = 1 then, show that cos^12x + 3cos^10x + 3cos^8x + cos^6x = 1
This can be proved by using identities of trigonometry.
Prove that cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1:Given that,
sin x + sin²x = 1 ⇒ sin x = 1 - sin²x
⇒ sin x = cos²x (∵sin²x + cos²x = 1)
We have to prove that,
cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1
LHS = cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x
= sin⁶x + 3sin⁵x + 3sin⁴ + sin³x
= (sin²x)³ + 3(sin²x)²sin x + 3(sin²x) (sin x)² + (sin x)³
= (sin²x + sin x)³ (∵(a+b)³ = a³ + 3a²b + 3 ab² + b³)
= 1³ = 1 = RHS
LHS = RHS
Hence the equation is proved since both sides of the equation are equal.
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A sequence of transformations maps Triangle ABC onto triangle ABC prime prime. The type of transformations that maps triangle ABC onto Triangle prime ABC is a _____. When Triangle prime ABC is reflected across the line x=2 to form triangle triangle prime prime ABC vertex _____ of triangle ABC will have the same coordinates as B prime.
The type of transformations that maps triangle ABC onto Triangle prime ABC is a Reflection across the line y=x ; translation 10 units to the right and 4 units up.
What is the reflection about?Note that: Triangle ABC has vertices at points which are:
A(-6,2), B(-2,6) and C(-4,2).
Therefore, the reflection across the line y=x has the rule of"
(x, y) ---(y, x).
Hence:
A(-6,2) -- A''(2,-6);
B(-2,6)--- B''(6,-2);
C(-4,2)----C''(2,-4).
2. The translation 10 units to the right and 4 units up is:
(x, y)----(x+10,y+4).
Hence
A''(2,-6)----A'(12,-2);
B''(6,-2)----B'(16,2);
C''(2,-4)----C'(12,0).
Therefore, Points A'B'C' are said to be exactly of the vertices of that of triangle A'B'C'.
Hence, The type of transformations that maps triangle ABC onto Triangle prime ABC is a Reflection across the line y=x ; translation 10 units to the right and 4 units up.
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PLEASE ANSWER ASAP
What is the solution to the following system of equations?
Answer:
(-3, 1)
Step-by-step explanation:
the easiest thing to do is look at the graph and find the point where the two lines intersect
5
Sample Space and Venn Diagrams: Mastery Test
Type the correct answer in each box. If necessary, use / for the fraction bar.
A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag.
The probability of not drawing a black marble is
. The probability of drawing a red marble is
m. All rights reserved.
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The probability of not drawing a black marble is 4/5
The probability of drawing a red marble is 3/10
What are the probabilities?Probability determines the odds of the occurrence of a random event. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of not drawing a black marble = total marbles that are not black / total number of marbles
(5 + 3) / (5 + 3 + 2) = 8/10 = 4/5
The probability of drawing a red marble = total number of red marbles / total number of marbles
= 3/10
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Answer:
See image
Step-by-step explanation:
Plato
Which expression is equivalent to the following complex fraction?
1 + StartFraction 1 Over y EndFraction divided by 1 minus StartFraction 1 Over y EndFraction
StartFraction (y + 1) (y minus 1) Over y squared EndFraction
StartFraction y + 1 Over y minus 1 EndFraction
StartFraction y minus 1 Over y + 1 EndFraction
StartFraction y squared Over (y + 1) (y minus 1) EndFraction
The equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]
How to determine the equivalent fraction?The fraction is given as:
[tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex]
Take the LCM
[tex]\frac{y + 1}{y} \div \frac{y-1}y[/tex]
Express as products
[tex]\frac{y + 1}{y} \times \frac{y}{y-1}[/tex]
Evaluate the product
[tex]\frac{y + 1}{y-1}[/tex]
Hence, the equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]
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To calculate accurate ____________________ (vital/hospital) statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
To calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
What are vital statistics?The term "vital statistics" refers to the collection of data on live births, deaths, migration, fetal deaths, marriages, and divorces. Civil registration, an administrative system used by governments to record vital events that occur in their populations, is the most prevalent method of gathering information on these events. Efforts to increase the quality of vital statistics will thus be inextricably linked to the growth of countries' civil registration systems. Since the nineteenth century, civil registration has followed the practice of churches keeping such records. To compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.As it is given in the description itself, to compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.
Therefore, to calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
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sin (x+y)/sin (x-y) =
No directions given here. What exactly do you need to be done with this trigonometric function?
Select the correct answer from each drop-down menu.
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is. The center of the circle is at the point, and its radius is units
Step-by-step explanation:
the equation in the standard form is :
( x - 2 ) 2+ ( Y + 3 ) 2 = 18
the center is at the point ( 2, - 3 ).
its radious is : /18 = 3/ 2 units
Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury? 0.05 – 0.1y = 0.12 – 0.06y 0.05y 0.1 = 0.12y 0.06 0.05 0.1y = 0.12 0.06y 0.05y – 0.1 = 0.12y – 0.06
The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.
In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.
First, we will find the equations showing the level of mercury in each body of water.
For the first water body:
Initial measure of mercury = 0.05 ppb.
Rate of rising = 0.1 ppb each year.
Number of years = y.
Thus, the equation showing level of mercury = 0.05 + 0.1y.
For the second water body:
Initial measure of mercury = 0.12 ppb.
Rate of rising = 0.06 ppb each year.
Number of years = y.
Thus, the equation showing level of mercury = 0.12 + 0.06y.
We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.
As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:
0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.
Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.
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For the complete question, refer to the attachment.
Use the following function rule to find h(w–5). Simplify your answer.
h(y)=y²–y–5
h(w–5)=
The value of the function is h(w - 5) = w^2 - 11w +25
How to determine the function?The function is given as:
h(y) = y^2 - y - 5
Substitute w - 5 for y
h(w - 5) = (w - 5)^2 - (w - 5) - 5
Expand the equation
h(w - 5) = w^2 - 10w + 25 - w + 5 - 5
Evaluate the like terms
h(w - 5) = w^2 - 11w +25
Hence, the value of the function is h(w - 5) = w^2 - 11w +25
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May someone please explain to me how exponents can be used to represent fractions between 0 and 1???
The fraction m/n that lies between 0 and 1 is equivalent to the real number m · n⁻¹, where m, n > 0 and m < n.
How can rational numbers between 0 and 1 be represented in terms of exponents?
By algebra, we know that fractions, a kind of rational numbers, are real numbers of the form m/n, where m and n are integers and n ≠ 0.
In addition, the operator "/" means division, an operator derived from the existence of multiplicative inverse and fundamental operation of multiplication in the real field.
Thus, the rational number m/n is equivalent to the number m · n⁻¹. If the rational number is between 0 and 1, then m, n > 0 and m < n.
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If the class sizes in a school from 18 to 24 what is the range?
Answer:
18 students
Step-by-step explanation:
Answer:
the range between 18 and 24 is 6
Step-by-step explanation:
24-18=6
Terrence’s car contains 8 gallons of fuel. He plans to drive the car m miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of m?
The correct option is A. m ≤ (8)(20)
The inequality which gives the possible values of 'm' is m ≤ (8)(20).
What is inequality?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
According to the question;
Terrence's car contains 8 gallons of fuel.
Terrence can drive the car 'm' miles using the fuel currently in the car.
The car can drive 20 miles per gallon of fuel,(which is maximum fuel capacity of the car to drive).
Then,
The total miles 'm' covered by the car is 8×20 which is maximum capacity of the car to travel.
Thus, total miles covered by the car are less than the maximum value which is given by the inequality-
m ≤ (8)(20)
Therefore, the inequality which gives the possible values of 'm' is m ≤ (8)(20).
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The complete question is-
Terrence's car contains 8 gallons of fuel. He plans to drive the car 'm' miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of 'm'?
answer choices
A. m ≤ (8)(20)
B. m ≥ (8)(20)
C. 8 ≤ 20m
D. 8 ≥ 20 m
What can you say about the continuous function that generated the following table of values?
table
x y
0.125 -3
0.5 -1
2 1
8 3
64 6
A.not enough information to answer the question
B. the function has more than one x-intercept
C.the function has exactly one x-intercept
D.the function has no x-intercept
Option C. The function that has the table here has exactly one x-intercept.
How to find the interceptAs the signs of the functions are changing, we can see that there is a crossing to the x axis.
This tells us that the zero value that we see is the x intercept and there is no other x intercept in the question.
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Can somebody please help me I have exam tomorrowwww
Answer:
3x²y (2x²-3y²+ 4y)
Step-by-step explanation:
Factor the expression 6x^4y-9x²y³+12x²y².
First, check if there is a GCF. The GCF is 3x²y.
3x²y (2x²-3y²+ 4y).
This equation cannot be factored further. Therefore, the answer is
3x²y (2x²-3y²+ 4y).
Hope this helps!
Answer:
3x²y(-3y²+4y+2)
Step-by-step explanation:
6x⁴y-9x²y³+12x²y²
solution:
first common
3x²y(2x²-3y²+4y)
3x²y(-3y²+4y+2)
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
By definition of surface area, the composite figure reports an area of 233.6 square centimeters.
How to calculate the surface area of a composite figure
In this question we need to determine the surface area of a composite figure, which is the sum of all the areas of the faces, which are combinations of triangles and quadrilaterals. Now we proceed to calculate the surface area:
A = 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (3.6 cm) + 2 · (8 cm) · (2 cm) + 4 · (1/2) · (3 cm) · (2 cm)
A = 233.6 cm²
By definition of surface area, the composite figure reports an area of 233.6 square centimeters.
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Compare the theoretical probability to the experimental probability of landing on H.
The correct statement comparing the theoretical and experimental probabilities is given as follows:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:
T(H) = 1/4.
The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:
E(H) = 28/100 = 7/25.
Hence the correct statement is:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
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Explain all of the steps needed to simplify the equation 8(x+2) = 4(2x+9) using the order of operations.
Answer:
First, use the distributive property and distribute 8 to the [tex](x,2)[/tex] in the first part of the equation to get [tex]8x + 16[/tex].
Next, also use the distributive property to distribute the 4 to the [tex](2x+9)[/tex] in the second part of the equation to get [tex]8x+36[/tex].
The simplified equation looks like this: [tex]8x+16=8x+36[/tex].
PLEASE ANYONE: The tennis club has 5 new members each member buys a racet and a tube of balls. If 6 racket cost $186.00 and 6 tubes of balls cost $27.00 how much do the 5 people pay for rackets and balls?
Answer:
Total cost is $177.50.
Step-by-step explanation:
Rackets:
Divide the cost for racket by 6 to find the cost per racket.
186÷6=31
Multiply 31 by 5 to find the cost for 5 rackets.
31×5=155
$155
Tubes of balls:
Divide 27 by 6 to find the cost per a tube of balls.
27÷6=4.50
Multiply 4.50 by 5 to find the cost for 5 tubes of balls.
4.50×5=22.50
$22.50
Add the amounts for rackets and tubes of balls to find the total cost.
155+22.50=177.50
The total cost is $177.50.
Hope this helps!
Solve for x.
A. 5
B.7
OC. 6
OD. 8
3
X
5
4
Answer:
6
Step-by-step explanation:
[tex]5(5+3)=4(x+4) \\ \\ 40=4(x+4) \\ \\ 10=x+4 \\ \\ x=6[/tex]
The number of goldfish in a tank is 22, and the volume of the tank is 56 cubic feet. what is the density of the tank? 0.34 goldfish per cubic foot 0.39 goldfish per cubic foot 1.41 goldfish per cubic foot 2.55 goldfish per cubic foot
Option B is correct. 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet. This can be obtained by using the formula of density.
Calculate the density of tank:Given that there are 22 goldfishes,
mass of tank = 22 goldfishes
volume of tank = 56 cubic feet
Density = mass/volume= 22/56
= 0.39 goldfish per cubic feet
Hence 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet.
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Answer: 0.39 goldfish
Step-by-step explanation:
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
Inequality expressionInequality are expressions not separated by an equal sign. Given the inequality expression:
3(8 – 4x) < 6(x – 5)
Expand
24 - 12x < 6x - 30
Collect the like terms
-12x-6x < -30 - 24
-18x <-54
x > 3
Hence the number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
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helppppppp please help help
The y-value of the terminal point of the vector is 3.
How to determine the resulting vector by applying rotation about the origin
In this question we must apply a matricial form of rotation, which is a kind of rigid transformation. This transformation is defined by the following formula:
[tex]\vec A' = \vec T\cdot \vec A[/tex], where [tex]\vec A' , \vec A \in \mathbb{R}_{1 \times 2}[/tex], [tex]\vec T \in \mathbb{R}_{2 \times 2}[/tex]
If we knw that [tex]\vec A = \left[\begin{array}{c}- 4\\3\end{array}\right][/tex] and [tex]\vec T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], then the transformed vector column is:
[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}-4\\3\end{array}\right][/tex]
[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}4\\3\end{array}\right][/tex]
The y-value of the terminal point of the vector is 3.
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Select the correct answer.
Choose the system of inequalities that best matches the graph below.
Considering the linear functions on the graph, the inequality that matches the situation is:
B.
[tex]y \geq \frac{1}{2}x + 2[/tex][tex]y \leq 2x + 1[/tex]What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The lower bound of the interval is a linear function with y-intercept of b = 2, that also passes through (2,3), hence the slope is:
m = (3 - 2)/(2 - 0) = 1/2.
Hence the inequality is:
[tex]y \geq \frac{1}{2}x + 2[/tex]
The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:
m = (5 - 1)/(2 - 0) = 2.
Hence the inequality is:
[tex]y \leq 2x + 1[/tex]
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You draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
The events are not independent
How to determine the type of events?Say that there are n marbles in the bag
When the first red marble is drawn, the number of marbles in the bags becomes n - 1
This means that the first red marble has changed the probability of drawing the second red marble
This represents a dependent event
Hence, the events are not independent
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A group of birds are flying, they meet another group of birds. They ask 'hello hundred.' They replied we are not 100. we need half of us plus you to be hundred. How many birds are needed?
Answer:
Step-by-step explanation:
You answer
Y is inversely proportional to the square of x. If Y = 2 when x = 8, then Y = , when x is_______.
The value of x when y =2 is 8
How to solve for x?The inverse proportion to the square of x represented as:
k = yx^2
Where
k represents the constant of proportion
When y = 2, x = 8.
So, we have:
k =2 * 8^2
k =128
Substitute k = 128 in k = yx^2
So, we have:
yx^2 = 128
When y = 2, we have:
2x^2 = 128
Divide by 2
x^2 = 64
Take the square roots
x = 8
Hence, the value of x when y =2 is 8
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Im the diagram shown JKL~ MNP. Find MP and PN.
Answer: [tex]MP=10, PN=6[/tex]
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so:
[tex]\\\\frac{MP}{5}=\frac{8}{4}\\\\MP=10\\\\\frac{PN}{3}=\frac{8}{4}\\\\PN=6[/tex]
solve for r as a percentage f(7000)=20000(1-r)^10
The value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%
How to solve for r as a percentage?The equation is given as:
7000 = 20000(1-r)^10
The above equation is an exponential decay function.
So, we have:
7000 = 20000(1-r)^10
Divide both sides of the equation by 20000
0.35 = (1-r)^10
Take the 10th root of both sides
0.35^(1/10) = 1 - r
Evaluate the exponent
0.9 = 1 - r
Add r to both sides
0.9 + r = 1
Subtract 0.9 from both sides
r = 1 - 0.9
Evaluate
r = 0.1
Express as percentage
r = 10%
Hence, the value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%
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find the sum of the average monthly rainfall. this is on i ready okay so please help.
Based on the average monthly rainfall amounts as shown in the graph, the sum of the average monthly rainfall 11/12 inches.
What is the sum of the average monthly rainfall?The average can be found by adding up the monthly rainfall and dividing by 12 months.
Solving gives:
= (1/8 + 1/8 + 1/8 + 2/8+ 2/8 + 5/8 + 7/8 + 9/8 + 13/8 + 15/8 + 16/8 + 16/8) / 12
= (88/8) / 12
= 11/12 inches
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