So, for f(x)=xa(9-x)b on the interval 0≤x≤9, the maximum value of f(x) is 0, and a and b are positive numbers.
What is function?A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences. Functions are broadly classified into four categories. Element-based: one-to-one function, many-to-one function, onto function, one-to-one and onto function, into function
Here,
f(x)=xa(9-x)b
If we put x=0,
f(x)=0
If we put x=9,
f(x)=0
So, the maximum value of f(x) is 0 for f(x)=xa(9-x)b on the interval 0 ≤ x ≤ 9 and a and b are positive numbers.
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the question is in the screen shot need this answered by 11:59 pm
Based on the line of best fit that models the data points, the y-value when x = 24 is equal to 20.
How to determine a line of best fit for the data set?In order to determine a linear equation for the line of best fit that models the data points described above, we would have to calculate the slope of the trend line.
Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided, we have the following points:
Points on x-axis = (4, 8).
Points on y-axis = (5, 8).
Substituting the given points into the formula, we have;
Slope, m = (8 - 5)/(8 - 4)
Slope, m = 3/4
Slope, m = 0.75
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the y-intercept.Note: The y-intercept is equal to 2 based on the ordered pair (0, 2).
A linear equation for the line of best fit in slope-intercept form is given by:
y = 0.75x + 2
When x = 24, the value of y is;
y = 0.75(24) + 2
y = 18 + 2
y = 20.
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there are 8 students in the class. two of them should be selected as the best students in the class. how many different ways can this be done?
Since, there are 08 students in the class, among 02 of them should be selected as the best students in the class. In 28 different ways this can be done.
Use the formula of combinations given as ⁿ[tex]C_{r}[/tex] to find the numbers of possible ways to select r things out of a total of n things. Let n be the total number of students in the class and r as the number of students required to be selected as best students in the class. Now, use the formula
ⁿ[tex]C_{r}[/tex] = [tex]\frac{r!}{(n- r)!}[/tex] to simplify the expression .
Given that a class has 8 students in which 2 students will be selected for a best students in the class. .
Therefore, n = 08 and r = 02, substituting these values in the formula we get,
Number of possible ways of selection = ⁿ [tex]C_{r}[/tex] = ⁸C₂
Now,
Number of possible ways of selection = [tex]\frac{8!}{2! ( 8 - 2)!}[/tex]
Or, Number of possible ways of selection = [tex]\frac{8!}{2! 6!}[/tex]
Solving further,
Number of possible ways of selection = 8 × 7× 6!/ 2× 1 ×6!
Number of possible ways of selection = 4 × 7 = 28
Hence, the total number of ways to select the required number of students is 28.
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How do you use the distributive property to rewrite and evaluate 15(2 1/3)?
The value of the equation after the evaluation is 35
The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.
The distributive property is straightforward to recall. Numerous mathematical features allow us to make algebraic expressions as well as arithmetic calculations simpler.
Using the distributive property we can rewrite this expression as:
[tex]15(2\frac{1}{3} )= (15*2)+(15*\frac{1}{3} )[/tex]→[tex]30[/tex]→[tex]\frac{15}{3}[/tex]→[tex]30+5[/tex]→[tex]35[/tex]
Evaluating the equation:
[tex]15(2\frac{1}{3} )=15*(\frac{7}{3} )=35[/tex]
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which expressions are equivalent to 7^-2 times 7^6?
The expressions presented in options A and D are equivalent to the given expression.
Power Rules
Knowing some of the main power rules.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive.Zero Exponent. When you have an exponent equal to zero, the result must be 1.An algebraic expression is considered equivalent when they are equal.
Thus, for solving this question, you should:
identify which power rules you will applysolve each expression of the questioncheck with the results is equal to the given expression: [tex]7^{-2}*7^6=7^4[/tex]Let's solve each option.
Option A[tex]\frac{7^2}{7^{-2}}[/tex]= 7² *7²= [tex]7^4[/tex] - this equation is equivalent to the given algebraic expression.
Option B[tex]\frac{7^6}{7^{-2}}=7^6*7^2=7^8[/tex] - this equation is not equivalent to the given algebraic expression.
Option C[tex]7^{-12}=\frac{1}{7^{12}}[/tex] - this equation is not equivalent to the given algebraic expression.
Option D(7²)2= [tex]7^4[/tex] - this equation is equivalent to the given algebraic expression.
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In the given figure, write the relation between AB and CD as well as AB and AE.
Answer:
see explanation
Step-by-step explanation:
since both AB and CD are at right angles to AE then
AB and CD are parallel lines.
since AB and AE are at right angles to each other then
AB and AE are perpendicular lines
no LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
Trigonometric Substitution Suppose √x=siny. (a) Use the substitution x=sin2 y,dx=2 sin y cos ydy to show ∫1/2 0 √xdx/√1−x = ∫π/4 0 2 sin2 ydy (b) Use the identity given in Exercise 49 to evaluate the definite integral without a calculator.
The value of the definite integral is [tex]\frac{\pi }{4} - \frac{1}{2}[/tex]
Using microscopic slivers or stripes of the region, a definite integral is a formal estimate of the area beneath a function. Integrals can reflect a region's (signed) area, the total value of a function that changes over time, or the amount of a given thing given its density.
Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.
Given,
[tex]\int\limits^\frac{1}{2} _0 {\frac{\sqrt{x} }{\sqrt{1-x} } } \, dx = \int\limits^\frac{\pi }{4} _0 {2sin^{2}y } \, dy[/tex]
[tex]\int\limits^\frac{1}{2} _0 {\frac{\sqrt{x} }{\sqrt{1-x} } } \, dx = \frac{\pi }{4} - \frac{1}{2}[/tex]
[tex]\int\limits^\frac{\pi }{4} _0 {2sin^{2}y } \, dy = \frac{\pi }{4} -\frac{1}{2}[/tex]
∴[tex]\frac{\pi }{4} - \frac{1}{2}[/tex] = [tex](\frac{\pi }{4} - \frac{1}{2})[/tex]
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what is the initial value and rate of change in y=3x-5
PLESE HELP
Answer:
the rate of change is 3x(slope)
jim is considering pursuing an ms in information systems degree. he has applied to two different universities. the acceptance rate for applicants with similar qualifications is 30% for university x and 40% for university y. what is the probability that jim will not be accepted at either university?
Probability that jim will not be accepted at either university is 0.42
He has applied to two different universities.
the acceptance rate for applicants with similar qualifications is 30% for university x
the acceptance rate for applicants with similar qualifications is 40% for university Y
Here, getting accepted into the two different universities are two independent events.
P(A or B) = P(A) x P(B)
Probability of not getting accepted in university X is 1 - 0.30
Probability of not getting accepted in university Y is 1 - 0.40
Probability that jim will not be accepted at either university
P'(X or Y) = P'(X) x P'(Y)
=(1 - 0.30) x(1 - 0.40) = 0.70 x 0.60 = 0.42
Therefore, Jim will not be accepted at either university has a probaility of 0.42 or 42%
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Which numbers below are even? Check all that apply.
A. 5464
B. 1126
C. 9092
D. 6669
E. 4950
F. 6921
Answer: A, B, C, E
Step-by-step explanation:
how many revolutions will the circular helix make in a distance of 10 units measured along the z axis
At a = √25/π^2 - 0.04 revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.
In the given question, we have to find how many revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.
r = acosti + asintj + 0.2tk, length = 10 unit
So |r| = [tex]\int^{2\pi}_{0}\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt[/tex]
From the given equation,
x = acost, y = asint, z = 0.2t
dx/dt = -asint, dy/dt = acost, dz/dt = 0.2
10 = [tex]\int^{2\pi}_{0}\sqrt{(-a\sin t)^2+(a\cos t)^2+(0.2)^2}dt[/tex]
10 = [tex]\int^{2\pi}_{0}\sqrt{a^2\sin^2 t+a^2\cos^2t+0.04}dt[/tex]
As we know that sin^2x+cos^2x = 1. So
10 = [tex]\int^{2\pi}_{0}\sqrt{a^2+0.04}dt[/tex]
10 = [tex]\sqrt{a^2+0.04}\int^{2\pi}_{0}dt[/tex]
10 = [tex]\sqrt{a^2+0.04}\cdot[t]^{2\pi}_{0}[/tex]
10 = √(a^2+0.04)∙[2π-0]
2π√(a^2+0.04) = 10
Divide by 2π on both side, we get
√(a^2+0.04) = 5/π
Taking square on both side, we get
a^2+0.04 = 25/π^2
Subtract 0.04 on both side, we get
a^2 = 25/π^2 - 0.04
taking square root on both side, we get
a = √25/π^2 - 0.04
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The right question is:
How many revolutions will the circular helix
r = acosti + asintj + 0.2tk
make in a distance of 10 units measured along the z-axis?
If Monica has 60 arces of land and each goat required 1/3 of an acre, how many goats can her land support?
A. 100
B. 180
C. 300
D. 120
Answer: B.180
Step-by-step explanation:
number of acres = 60
area required for one goat = 1/3 of an acre
number of goats one acre can hold = 3
number of goats her land can support = 60*3 = 180
Which of these expressions is equivalent to log (20 35)
Answer:
log_20(35)= 1.5372435736805
Step-by-step explanation:
what percentage of observed variation in hardness can be explained by the linear relationship between hardness and elapsed time? (round your answer to one decimal place.)
95.1% of the proportion of observed variation in hardness can be explained by the simple linear regression model relationship between hardness and elapsed time.
Linear regression model:
In statistics, linear regression model defined the relationship between a dependent variable, y, and one or more independent variables, X.
Given,
Here we need to find the percentage of observed variation in hardness can be explained by the linear relationship between hardness and elapsed time.
In order to find the percentage we must know the definition of observed variation which means the combined variation that is derived from all sources.
In order to solve this let us consider that the linear regression model is used by statisticians to predict the value of the response variable for given values of the predictor variables.
So, if there are two variables involved in the regression analysis, then the model is called a bivariate one.
Where as If there are more than two independent variables, then the regression model is known as the multiple regression model.
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Calculator
What is the measure of angle A in this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the hundredths place (2 decimal places).
Answer: 73.74
Step-by-step explanation: I just used a calculator. I hope it's right. Check me if I'm wrong.
HELP ASAP WITH SLOPE PLEASE
the options are:
1
undefined
0
-1
Answer: 0
Step-by-step explanation:
Answer: 0
Step-by-step explanation:
Slope is a value that describes the steepness and direction of a line.
A line with a negative slope, said to be decreasing, runs downwards from left to right.
A line with a positive slops, said to be increasing, runs upwards from left to right.
A horizontal line has a slope of zero because y does not change. A vertical line has an undefined slope because you cannot divide by zero (x does not change).
I hope this helps to understand :)
The quotient of y and 3 added to 9 equals 10
Answer:
Step-by-step explanation:
Are you after a solution for y?
quotient of y and 3 is a fancy word for division
y/3+9=10
To solve for y subtract 9 from both sides
y/3+9-9=10-9
y/3=1
To solve for y
multiply both sides by 3
3(y/3)=1*3
y=3
What is the actual distance between Toledo and Colubus?
The equation is y = 2.5. And the actual distance in the third case and the distance on the map in the fourth case will be 120 miles and 90 mm, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the distance on the map and 'y' be the actual distance. Then the equation of the line is given as,
(y - 25) = [(50 - 25) / (20 - 10)](x - 10)
y - 25 = 2.5x - 25
y = 2.5x
If x = 48 mm, then the actual distance is given as,
y = 2.5(48)
y = 120 miles
If y = 225 miles, then the distance on the map is given as,
225 = 2.5x
x = 90 mm
The graph is given below.
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the latest rare disease, expy, has entered your math classroom of 30. the students affected by the disease is modeled by the logistic function , where p(t) represents the number of students that understand exponential functions and t is time in days. clearly label each answer part. a) how many students understand exponential functions initially? (3 points) show your initial set-up and give your final answer. each step does not need to be shown. b) how many students will understand exponential functions after 3 days? (3 points) show your initial set-up and give your final answer. each step does not need to be shown. c) how many days will it take for 24 students to understand exponential functions? (4 points, multiple-choice) f) t
Therefore the answer to when math classroom of 30. the students affected by the disease is modeled by the logistic function is first case : 6 , second case : 15.68 and third case : 5.18
What is function ?A function is a particular relation that transfers every element in set A to exactly one element in set B. There cannot be an empty set in either A or B. For a specific input, a function defines a specific output.
Here ,
Given:
P(t) = [tex]\frac{180}{5 + 25e^{-0.45t} }[/tex]
First case :how many students understand exponential functions initially is
Where t is number of days
t=0
P(0)= [tex]\frac{180}{5 + 25e^{-0.45(0)} }[/tex]
P(0)=180/(25+5)
P(0)=6
Second case: how many students will understand exponential functions after 3 days
t=3
P(3)=[tex]\frac{180}{5 + 25e^{-0.45(3)} }[/tex]
P(3) ≈ 15.68
Third case: how many days will it take for 24 students to understand exponential functions
t=24
P(24)=[tex]\frac{180}{5 + 25e^{-0.45(24)} }[/tex]
P(24) ≈ 5.18
Therefore the answer to when math classroom of 30. the students affected by the disease is modeled by the logistic function is first case : 6 , second case : 15.68 and third case : 5.18
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solve for x please help asap! will give brainlest
Answer:
80+60+3x+4=180
140+3x+4=180
144+3x=180
3x=180-144
3x=36
x=12
Answer:
x = 12
Step-by-step explanation:
All triangles equal to 180 degrees so, we can set up this expression:
180 = (3x + 4) + 80 + 60
All we have to do is solve:
180 = (3x + 4) + 80 + 60
180 = 3x + 4 + 140
180 = 3x + 144
-144 -144
36 = 3x
/3 /3
12 = x
p and q are two numbers such that p > q
When you subtract 5 from p and subtract 5 from q the answers
are in the ratio 9 : 1
When you add 20 to p and add 20 to q the answers
are in the ratio 7 : 3
Find the ratio p: q
Give your answer in its simplest form.
The ratio of p : q in its simplest form is 5 : 1
How to write ratio in its simplest formThe unknown numbers are p and q
(p - 5) / (q - 5) = 9/1
(p + 20) / (q + 20) = 7/3
From equation (1)
cross product
1(p - 5) = 9(q - 5)
p - 5 = 9q - 45
p = 9q - 45 + 5
p = 9q - 40
From equation (2)
3(p + 20) = 7(q + 20)
3p + 60 = 7q + 140
Substitute p = 9q - 40 into 3p + 60 = 7q + 140
3p + 60 = 7q + 140
3(9q - 40) + 60 = 7q + 140
27q - 120 + 60 = 7q + 140
27q - 60 = 7q + 140
27q - 7q = 140 + 60
20q = 200
divide both sides by 20
q = 200/20
q = 10
Substitute q = 10 into p = 9q - 40
p = 9q - 40
p = 9(10) - 40
p = 90 - 40
p = 50
In conclusion, the ratio of p to q = 50 : 10
= 50/10
= 5/1
= 5:1
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A line passes through the points (20, 2) and (10, 1). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
[tex]y = \frac{1}{10}x[/tex]
Step-by-step explanation:
⭐ What is slope-intercept form?
[tex]y = mx + b[/tex]"m" is the slope"b" is the y-intercept (the y-value for when x = 0)First, we need to find the value of "m" using the slope formula.
⭐ What is the slope formula?
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex][tex](x_1,y_1)[/tex] is a coordinate that you are given[tex](x_2,y_2)[/tex] is another coordinate that you are givenSubstitute the two coordinates you are given into the slope formula.
[tex]m = \frac{1-2}{10-20}[/tex]
[tex]m = \frac{-1}{-10}[/tex]
[tex]m = \frac{1}{10}[/tex]
Substitute the value of "m" into the slope-intercept form equation.
[tex]y = \frac{1}{10}x + b[/tex]
Next, we need to find the value of "b". To do so, substitute a coordinate that you are given into the equation and solve for "b".
I am going to use (10,1), but you can also use (20,2).
[tex]1 = \frac{1}{10} (10) + b[/tex]
[tex]1 = 1 + b[/tex]
[tex]0 = b[/tex]
Substitute the value of "b" into the slope-intercept form equation.
[tex]y = \frac{1}{10}x[/tex]
Consider the line y = 2x - 3. Write the equation of the line that is perpendicular to this line and that contains the point (-5, 3) Please help!!!
Considering the definition of perpendicular line, the equation of the perpendicular line is y= -1/2x + 1/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 2x -3
where:
The slope m is 2.The ordinate to the origin b is -3.If you multiply the slopes of two perpendicular lines, you get –1, you get:
2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 2
slope perpendicular line= -1/2
The line passes through the point (-5, 3). Replacing the point and the slope in the expression for a line:
3= (-1/2)× (-5) + b
3= 5/2 + b
3 -5/2 = b
1/2= b
Finally, the perpendicular line is y= -1/2x + 1/2.
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The sum of two numbers is 20. What is the least possible sum of their squares and what are the numbers?
The numbers are 10 and 10. And the sum of their squares will be 200.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
The sum of the two numbers is 20.
Let the first number be 'x'. Then the other number is (20 - x). Then the equation is given as,
y = x² + (20 - x)²
Differentiate the function, then we have
y' = 0
2x + 2(20 - x)(-1) = 0
x - 20 + x = 0
2x = 20
x = 10
Then the other number is given as,
⇒ 20 - 10
⇒ 10
The sum of their squares is given as,
⇒ 10² + 10²
⇒ 100 + 100
⇒ 200
The numbers are 10 and 10. And the sum of their squares will be 200.
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Label the illustrations based on the Gestalt principles of grouping:
a. closure
b. proximity
c. continuity
d. illusory contours
e. similarity
The illustration based on the Gestalt principles of grouping are:
(A) Closure principle.
(B) Proximity principle.
(C) Continuity principle.
(E) Similarity principle.
What are Gestalt principles of grouping?The principles of grouping, also known as the Gestalt rules of grouping, are a collection of psychological concepts first put out by Gestalt psychologists to explain why people naturally perceive items as structured patterns and objects, or Prägnanz.
Gestalt psychologists asserted that these principles hold true because the mind is predisposed to recognize patterns in the stimulus based on predetermined rules.
Gestalt grouping guidelines include:
Continuity principle.
Similarity principle.
Proximity principle.
Closure principle.
Common region principle.
Figure-ground principle.
Focal point principle.
Therefore, the illustration based on the Gestalt principles of grouping are:
(A) Closure principle.
(B) Proximity principle.
(C) Continuity principle.
(E) Similarity principle.
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Yuri and Trina sold boxes of cookies. Yuri sold 14 boxes, while Trina sold n boxes. Together, they sold a total of 37 boxes. Which equation represents the number of boxes Trina sold? How many boxes did she sell?(1 point)
n + 37 = 14; Trina sold 23 boxes.
n + 14 = 37; Trina sold 23 boxes.
.
n − 37 = 14; Trina sold 51 boxes.
n − 14 = 37; Trina sold 51 boxes.
Answer: n + 14 = 37; Trina sold 23 boxes
Step-by-step explanation:
Answer:
The equation that represents the number of boxes Trina sold is: n + 14 = 37.
To solve for n, we can subtract 14 from both sides of the equation:
n + 14 - 14 = 37 - 14
n = 23
Therefore, Trina sold 23 boxes.
Step-by-step explanation:
Please help soon on functions problem, thanks!
Answer:
g(0) = 3
Step-by-step explanation:
x=0 fits perfectly in the range -1<x<2: -1<0<2 √
Hence:
g(x)=3 when x=0
Since x=0:
g(x) = g(0) = 3
To test if x is a good predictor of y in Simple Linear Regression we need to determine whether:
A. the slope is significantly different from zero.
B. the intercept is significantly different from zero.
C. the response variable is significantly different from zero.
D. the predictor variable is significantly different from zero.
E. the error term is significantly different from zero.
F. the F test statistic is significantly different from zero
Option A is correct.
For testing, if x is a significant predictor of y in simple linear regression, we need to determine if the slope is significantly different from zero.
What is linear regression?
A statistical technique known as linear regression is used to represent the connection between a scalar answer and one or more explanatory factors. When there is just one explanatory variable, simple linear regression is employed; when there are numerous explanatory variables, multiple linear regression is utilized.
Based on the value of another variable, linear regression analysis makes predictions about the value of the first variable. The dependent variable is the one you're trying to forecast. The independent variable is the one you are utilizing to make a prediction about the value of the other variable.
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1. Find the equation of the straight line that passes through the points (0, -1) and (-1,0).
2. For this problem, please use the point-gradient form of the equation that passes through
the points (2, -4) and has gradient/slope 3.
3. Find the equation of the straight line that is parallel to the line y = x-2 and goes through
the point (0,1). Use Desmos Graphing Calculator to check your answer.
1. The equation of the straight line is y = -x -1.
2. The equation of the point-gradient form is 3x -y - 10.
3. The equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.
What is a straight line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things. In daily language, a line segment with two points designating its endpoints is also referred to as a "line."
Here, we have
1. The slope-intercept form of the equation of a line is:
y = mx + b
We are fortunate to be given the y-intercept, the point(0,-1) therefore, the value, b, in the slope-intercept form is -1:
y = mx - 1
Substitute the other point(-1,0) into the equation and then solve for the value of m:
0 = -m - 1
m = -1
y = -x -1
Hence, the equation of the straight line is y = -x -1.
2. We know that the equation of a line passing through the point (x₀, y₀ ) whose slope is m is (y - y₀) = m(x -x₀)
The equation of a line passing through the point(2,-4) and the slope is 3.
(y+4) = 3(x-2)
y + 4 = 3x - 6
3x -y - 10
Hence, the equation of the point-gradient form is 3x -y - 10.
3. Consider the given equation: y = x-2
Since, the line is parallel to given line. so slope will be same.
slope = 1
We know that the second line will also have a slope of 1, and we are given the point (0,1). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.
y = mx + b
1 = b
Now, we put the value of b in the equation and we get
y = x + 1
Hence, the equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.
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Use the table below to answer question 1-4 related to the Miller’s monthly expenses.
1. What do the millers pay each month to repay their mortgage loan?
2. What is Miller’s average monthly expenditure for the telephone?
3. Transportation costs include car payments and costs for gasoline,repairs and so on. What is their average monthly expenditure for transportation costs?
4. Can you determine how much they save each month? Why or why not?
1. The Millers pay $675 monthly to repay their mortgage loan.
2. The average monthly expenditure for the telephone for Millers is $41.00.
3. The Millers' average monthly expenditure for transportation costs is $592.46.
4. The information is not available for determining the amount the Millers' monthly savings.
What is the average cost?The average cost is the mean, which represents the quotient of the total costs and the number of months.
We compute the average cost using the division operation.
Average telephone expenses:July $37.85
August $47.29
September $37.85
Total costs = $122.99
Average cost = $41.00 ($122.99 ÷ 3)
Average Transportation Costs:July August September
Gasoline $118.60 $123.36 $96.74 $338.70
Car loan 278.50 278.50 278.50 835.50
Car repair 126.36 278.50 198.31 603.17
Total costs $523.46 $680.36 $573.55 $1,777.37
Average monthly transportation cost = $592.46 ($1,777.37 ÷ 3)
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Determine which of the following are examples of independent events.
Rolling a 5 on one die and rolling a 5 on a second die.
Choosing a cookie from the cookie jar and choosing a jack from a deck of cards.
Winning a hockey game and scoring a goal.
Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.
What is independent events?
Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances involve independent occurrences of the two events.In probability, two events are deemed independent if the knowledge that one occurred has no impact on the likelihood of the other event.Winning a hockey game and scoring a goal is dependent because if we score a goal then only we can win the game.
Hence, Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.
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