The answer choice which correctly represents a scenario modelled by the given equation as required is; A pair of boots is on sale for 65 percent of the original cost. The original price of the boots is x, $56.12.
Which scenario is best modelled by the given equation?As evident in the task content; the given equation is; (x) (0.65) = 36 dollars and 48 cents which can be written algebraically as;
0.65x = 36.48
x = 36.48 / 0.65
x = $56.12.
On this note, by observation; it follows that 0.65 is equivalent to 65% and hence, it can be inferred that;
The original price of the boots is; x which is equal to $56.12 and whose 65% equivalent is; $36.48.
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Answer:
c on edge
Step-by-step explanation:
i hate edge
Help asap :)
Are the following functions inverses of one another ?
Use function composition to explain your answer :)
It is proved that f(g(x)) = g(f(x)) = x , So f(x) and g(x) are inverses of one other
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
We are given the function as;
f(x) = 5x + 2
g(x) = (x -2)/ 5
If two functions f(x) and g(x) are inverses of each other, their compositions will equal
f(g(x)) = 5[ (x -2)/ 5] + 2
f(g(x)) = x - 2 + 2
f(g(x)) = x
Now,
g(f(x)) = ((5x + 2) -2)/ 5
g(f(x)) = (5x + 2 -2)/ 5
g(f(x)) = x
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Can u pls help me out with my math
The evaluation of the equations in the questions are as follows;
10. The equation 18·y - 10 = 2 + 18·y has no solutions
11. x = 0
12. x = 20
13. The consecutive integers are -46 and -45
What is an equation?An equation is a statement which indicates the equivalence between two expressions.
10. 18·y - 10 = 2 + 18·y
18·y - 18·y - 10 + 10 = 2 + 18·y - 18·y + 10
0 = 12
The equation 18·y - 10 = 2 + 18·y is a contradiction with no solution.
11. 2·(6·x - 4) - 16x = 4·(3·x - 2)
2·(6·x - 4) - 16x = 12·x - 8 - 16·x = -8 - 4·x
4·(3·x - 2) = 12·x - 8
2·(6·x - 4) - 16x = -8 - 4·x = 4·(3·x - 2) = 12·x - 8 therefore
-8 - 4·x = 12·x - 8
16·x = 0
x = 0 ÷ 16 = 0
x = 0
12. (3/4)·x + 2 = (3/5)·x + 5
(3/4)·x + 2 - (3/5)·x - 2 = (3/5)·x + 5 - (3/5)·x - 2
(3/4)·x - (3/5)·x = 5 - 2 = 3
(3/20)·x = 3
x = 3 × 20 ÷ 3 = 20
x = 20
13. The sum of the two integers = -91
Let a represent one of the integers, therefore, based on the details;
The other integer = a + 1
a + a + 1 = -91
2·a = -91 - 1 = -92
a = -92 ÷ 2 = -46
One of the integers, a = -46
The other integer, a + 1 = -46 + 1 = -45
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Write as a mathematical expression. The product of 5 and x.
O 5/x
O 5+x
O 5-x
O 5x
Answer:
5x
Step-by-step explanation:
The word "product" is used for multiplication.
What is the measure of each base angle of an isosceles triangle if its vertex?
The measure of each base angle of an isosceles triangle is is 65 degree.
In an isosceles triangle, the two base angles are congruent, or equal in measure. To find the measure of one of the base angles, we can use the fact that the measures of the angles in a triangle always add up to 180 degrees. This means that if we know the measure of the vertex angle, we can use this information to find the measures of the base angles.
we have an isosceles triangle with a vertex angle that measures 50 degrees. To find the measure of a base angle, we can use the following formula:
(180 - measure of vertex angle)/2 = measure of base angle
Plugging in the given value of 50 degrees for the measure of the vertex angle, we get:
(180 - 50)/2 = measure of base angle
Solving this equation, we find that the measure of a base angle is 65 degrees. Therefore, if the vertex angle of an isosceles triangle measures 50 degrees, the measure of a base angle is 65 degrees.
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Complete question:
What is the measure of one of the base angles in an isosceles triangle if the measure of the vertex angle is 50 degrees?
The base angle of an isosceles triangle measures 54°. 72 is the measure of its vertex angle
We know that the sum of all the angles of any triangle is 180
We have to use the above property in order to find the measurement of the vertex angle.
Now our triangle is isosceles , that is the two equal sides will be containing equal angle. One of them is given as 54
And hence the other will also be 54.
Let the vertex angle be x
180=54+54+×
180=108+×
x=180-108
x=72
Hence the vertex angle is 72
complete question is
The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?
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Which of these expressions will give the unpaid balance after 7 years on a $60,000 loan with an apr of 8. 4%, compounded monthly, if the monthly payment is $516. 90?.
The option c will give the unpaid balance after 7 years on a $60,000 loan with an apr of 8. 4%, compounded monthly, if the monthly payment is $516. 90.
The profit you receive on money is known as compound interest. The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.
For the given situation,
Principal value, p = $60000
Rate of interest, r = 8.4% = 0.084
Monthly payment, pm = $516.90
Number of years, T = 7 years
Compounded monthly, n= 12
The formula of unpaid balance on loan is
[tex]B = p\left(1+\frac{r}{n}\right)^{nT}+pm\left(\frac{1-\left(1+(r/n)^{nT}\right)}{r/n}\right)[/tex]
Now putting the values
[tex]B = 60,000\left(1+\frac{0.084}{12}\right)^{12\cdot 7}+516.90\left(\frac{1-\left(1+(0.084/12)^{12\cdot7}\right)}{0.084/12}\right)[/tex]
Simplifying
[tex]B = 60,000\left(1+0.007\right)^{84}+516.90\left(\frac{1-\left(1+0.007^{84}\right)}{0.007}\right)[/tex]
Hence, the option c is correct.
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The complete question is:
Which of these expressions will give the unpaid balance after 7 years on a $60,000 loan with an apr of 8. 4%, compounded monthly, if the monthly payment is $516. 90?
(1) [tex]B = 60,000\left(1+0.0084\right)^{7}+516.90\left(\frac{1-\left(1+0.0084^{7}\right)}{0.0084}\right)[/tex]
(2) [tex]B = 60,000\left(1+0.007\right)^{7}+516.90\left(\frac{1-\left(1+0.007^{7}\right)}{0.007}\right)[/tex]
(3) [tex]B = 60,000\left(1+0.007\right)^{84}+516.90\left(\frac{1-\left(1+0.007^{84}\right)}{0.007}\right)[/tex]
(4) [tex]B = 60,000\left(1+0.0084\right)^{84}+516.90\left(\frac{1-\left(1+0.0084^{84}\right)}{0.0084}\right)[/tex]
The unpaid balance after 7 years on a $60,000 loan with an APR of 8.4% compounded monthly, if the monthly payment is $516.90, is $1,163.53.
This can be calculated using the formula for future value of an annuity. The formula is FV = PMT(1 + i)^n - 1/i where FV is the future value, PMT is the periodic payment, i is the interest rate per period and n is the total number of payments.
Calculate the interest rate per period:
i = 0.084/12 = 0.0070
Calculate the total number of payments:
n = 7 * 12 = 84
Calculate the future value of the annuity:
FV = $516.90 (1 + 0.0070)^84 - 1/0.0070
FV = $516.90 (1.0070)^84 - 1/0.0070
FV = $516.90 (2.5408) - 1/0.0070
FV = $1,306.39 - 142.86
FV = $1,163.53
Therefore, the unpaid balance after 7 years on a $60,000 loan with an APR of 8.4% compounded monthly, if the monthly payment is $516.90, is $1,163.53.
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A sawoman cams 8% commission on at the merchandise that the sets Last month she sold $7000 worth of merchandise. How much commission (in dollars) did she warm last month?
He made $480 in commission last month
What is a Commission?This refers to the fee paid to an agent or employee for transacting a piece of business or performing a service
First, convert 8% into a decimal
8%/100
= 0.08
Multiply the decimal by his sales
0.08 * 6000
480
Therefore, he made $480 in commission last month
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a line with a slope of 4 and passes through (2,4). what is the equation of the line in point slope form
Answer: In point slope form It would be y = 4x - 4
Step-by-step explanation: The point-slope form of a line is given by the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
In your case, the slope of the line is 4, and the point that the line passes through is (2,4). Plugging these values into the point-slope formula, we get:
y - 4 = 4(x - 2)
Simplifying, we get:
y - 4 = 4x - 8
Adding 4 to both sides, we get:
y = 4x - 4
27. The equation shown models the average depth
y, in feet, of a lake, x years after 2016, where
0
In what year does this model predict a relative
minimum value for the depth? SEE EXAMPLE 5
2016, x=0
depth: y=x4-9x³ + 24x²-31x + 66
Lake Bottom
The given model predicts a relative minimum value for the depth in 2021 year.
What are the Maxima and Minima of a Function?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
The given equation is shown models the average depth y, in feet, of a lake, x years after 2016, where 0 < x < 6
y = x⁴- 9x³ + 24x²-31x + 66
From the attached graph it is noticed that the lowest point of the function is (4.441, 2.357), therefore the local minima is (4.441, 2.357).
So, x is years after 2016 is 4.441 which means this model predicts a relative minimum value for the depth in the 2021 year.
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Seen previously.Four standard six-sided dice are to be rolled. What is the probability that the product of the numbers on the top faces will be prime
The probability that the product of the numbers on the top faces of four standard six-sided dice will be prime is approximately 0.09%.
To calculate this probability, a table can be created that outlines the 36 possible combinations of numbers on the top faces of four dice. From this table, the number of prime products can be determined. As there are only three primes (2, 3, and 5) in the 36 possible products, the probability of rolling a prime product is 3/36, which is approximately 0.09%. This means that the probability of rolling a prime product on four standard six-sided dice is very low, approximately 0.09%.
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What are the 5 examples of quadratic function?
Five examples of quadratic functions are: f(x) = -2x² + 2x - 5, f(x) = x² - 7x - 4, f(x) = x² - 4x + 4, f(x) = 2x² - 3x - 2, f(x) = x² + 2x + 4
A quadratic function is polynomial of degree 2. The standard form of a quadratic function is:
f(x) = ax² + bx + c, with a ≠ 0
5 examples of quadratic function:
1. Quadratic function with negative leading coefficient, or a is negative,
f(x) = -2x² + 2x - 5
The graph of this function opens downward
2. Quadratic function with positive leading coefficient, or a is positive,
f(x) = x² - 7x - 4
The graph of this function opens upward
3. Quadratic functions that have only 1 root
f(x) = (x - 2)²
f(x) = x² - 4x + 4
4. Quadratic functions that have 2 different real roots
f(x) = 2x² - 3x - 2
5. Quadratic functions that have complex conjugate roots
f(x) = x² + 2x + 4
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If the measure of interior angle of a regular polygon is 108°,then find the number of sides.
Answer: If the measure of interior angle of a regular polygon is 108°,then the number of sides are 5.
Step-by-step explanation:
Given:
108° equals one internal angle of a regular polygon.
The sum of an regular polygon's internal angles = (n - 2) 180°.
The interior angle of a regular polygon equals [(n - 2) 180°] divided by n.
By equating them, we obtain
108 = [(n - 2) × 180°]/n
By additional simplification
108n = 180n - 360
180n - 108n = 360
So we get
72n = 360
n = 5
Therefore, it is a pentagon, a polygon with five sides.
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You roll a number cube and flip a coin. What is the probability of rolling a number less than 2 and flipping tails? Write your answer as a mixed number.
The probability of rolling a number less than 2 and flipping tails as required is; 1/12.
Which fraction represents the probability of rolling a number less than 2 and flipping a tail?It follows from the task content that one rolls a die and flips a coin.
It is noteworthy to know that the probability of rolling a number less than 2 from a six-sided die is; 1 / 6. since, only 1 is less than 2 on the face of the die.
Also, the probability of flipping a tail is; 1/2.
On this note, the combined probability of rolling a number less than 2 and a flipping tail is; 1/6 × 1/2 = 1 / 12.
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What is improper fraction Class 6?
Answer: A fraction where the denominator (bottom number) is smaller than the numerator (top number). Examples: [tex]\frac{14}{9}[/tex], [tex]\frac{95}{40}[/tex], [tex]\frac{78}{13}[/tex]
Step-by-step explanation:
The equation of line l is y = 3x + 2. What is the slope of a line perpendicular to l
A. 1/3
B. 0
C. 3
D. none of the answers
E. -3
Are there 4 types of task analysis?
In general, there are five kinds of task analyses:
job or performance analysis learning analysis cognitive task analysis content or subject matter analysis activity analysisWhat is Task AnalysisTask analysis is the process of learning about ordinary users by observing them in action to understand in detail how they perform their tasks and achieve their intended goals. Tasks analysis helps identify the tasks that your website and applications must support and can also help you refine or re-define your site’s navigation or search by determining the appropriate content scope.
Purpose of Task AnalysisIn their book User and Task Analysis for Interface Design, JoAnn Hackos and Janice Redish note that performing a task analysis helps you understand:
What your users’ goals are; what they are trying to achieveWhat users actually do to achieve those goalsWhat experiences (personal, social, and cultural) users bring to the tasksHow users are influenced by their physical environmentHow users’ previous knowledge and experience influence:How they think about their workThe workflow they follow to perform their tasksLearn more about task analysis at https://brainly.com/question/22720305.
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Use synthetic division to find the result when 3x^4+8x^3+14x^2+25x+10 is divided by x+2
Answer: -2 | 3 8 5 8 12 __-6 -4 -2 -12 3 2 1 6 | 0 Therefore, Advertisement New questions in Mathematics
Step-by-step explanation: e
April wants to multiply 6 and 42 using the distributive property. Which of the following number sentences shows how she could do it?
The number sentence that shows that April can use the distributive property is; Option D: 6 × (40 + 2) = (6 × 40) + (6 × 2)
How to use the distributive property?The distributive property of algebra states that you can "distribute" the contents of one parentheses into the other to find an answer.
For example, we have the equation; a(b + c)
Using distributive property, we now have;
ab + ac
No, we are told that April wants to multiply 6 and 42 using the distributive property. Looking at the options, we can tell that the number sentence that shows she can do it is option D. This can be shown as;
6 × (40 + 2) = (6 × 40) + (6 × 2)
This is because 42 can also be expressed as 40 + 2 and multiplying both by 6 shows distributive property in use.
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The missing options are;
6 × 42 = 42 × 6
6 × (40 + 2) = (6 × 40) + 2
(6 × 42) × 1 = 6 × (42 × 1)
6 × (40 + 2) = (6 × 40) + (6 × 2)
The slope of the line that passes through the points \left( 0 , 3 \right) \ \mathrm{and} \ \left( 5 , 13 \right)(0,3) and (5,13) is
The slope of the line that passes through the points (0, 3) and (5, 13) as required is; 2.
What is the slope of the line through the points; (0, 3) and (5, 13)?As evident in the task content, it follows that the slope of the line which passes through the points (0, 3) and (5, 13) is to be determined.
Since the slope of a line is given by the formula;
Slope, m = ( y₂ - y₁ ) / ( x₂ - x₁ ).
The slope of the line in discuss is therefore;
Slope, m = ( 13 - 3 ) / ( 5 - 0 )
m = 10 / 5
m = 2.
Ultimately, the slope of the line in discuss is; 2.
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Fair tickets for 2 adults and 3 children cost $34. An adult ticket costs $2 more than a child ticket. What is the price of an adult ticket
The price of an adult ticket is $8.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.
Let x = price of an adult ticket
If an adult ticket costs $2 more than a child ticket, then
price of a child ticket = x - 2
If fair tickets for 2 adults and 3 children cost $34, then
2x + 3(x - 2) = 34
Simplify the equation and solve for the value of x.
2x + 3(x - 2) = 34
2x + 3x - 6 = 34
5x = 40
x = 8
price of an adult ticket = $8
price of a child ticket = x - 2 = $6
Hence, the price of each ticket is $8 and $6 for adult and child, respectively.
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Find the HCF and LCM of: -
y²-11y + 10, y² +9y-10, y ²-1
Answer:
(y-1)
Step-by-step explanation:
lets take the expression
1st expression: y²-11y+10
y²-10y-y+10
y(y-10)-1(y-10)
(y-10)(y-1)
2nd expression:y²+9y-10
y²+10y-y-10
y(y+10)-1(y+10)
(y+10)(y-1)
3rd expression:y²-1
(y-1)(y+1)
*HCF=(y-1)
*LCM=(y-1)(y+1)(y-10)(y+10)
(y²-1)(y²-10²)
Imagine that the stone is part of an arch, and that there is an isosceles triangle JEF formed by extending sides GE and HF downward.
Use the measure of the angles of the trapezoid to find to measure of the base angles JEF and JFE. Add these measurements to your drawing
(USE PICTURED TO HELP ANSWER THE PROBLEM)
The measure of the base angles of the isosceles triangle ∠JEF and ∠JFE are;
m∠JEF = m∠JFE = 80°
What is an isosceles triangle?An isosceles triangle is a triangle that has a pair of congruent sides and a pair of congruent angles.
The trapezoid in the question, based on the drawing in a similar online question, is formed by dividing the semicircular arc into 9 smaller (congruent) arcs.
The number of arcs the semi circular arc is divided by the dimensions and radial location of the stone = 9
The vertex angle of each isosceles triangle = 180° ÷ 9 = 20°
The measure of the base angles of the triangle ΔJEF = (180° - 20°) ÷ 2 = 80°
The base angles of the isosceles triangle ΔJEF = ∠JEF and ∠JFE
The measure of the base angles of the isosceles triangle are;
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Answer:
If you're talking about the 5.6.4 Journal: The Stone Arch assignment, then the actual answer is
JEF = 84
JFE = 84
Step-by-step explanation:
Bonus* for number 12 the answer will be 12 degrees.
I did the assignment and got an A+
Hope I was able to help
What is the sum? startfraction 3 over x squared minus 9 endfraction + startfraction 5 over x + 3 endfraction startfraction 8 over x squared + x minus 6 endfraction startfraction 5 x minus 12 over x minus 3 endfraction startfraction negative 5 x over (x + 3) (x minus 3) endfraction startfraction 5 x minus 12 over (x + 3) (x minus 3).
The sum of the given expression is [tex]\dfrac{(-7x - 45)}{(x - 3)(x + 3)(x - 2)}[/tex].
To find the sum of the given expression, we can simplify and combine the fractions with the same denominator. Let's break it down step by step:
When used to indicate a mathematical computation or connection, numbers, variables, operators, and mathematical symbols are called expressions. It might include variables, constants, addition, subtraction, multiplication, division, exponentiation, and other mathematical operations.
The expression is:
[tex]\dfrac{3}{(x^2 - 9)} + \dfrac{5}{(x + 3)} - \dfrac{8}{(x^2 + x - 6)} - \dfrac{(5x - 12)}{(x - 3)} - \dfrac{5x}{(x + 3)(x - 3)}[/tex]
First, let's simplify the denominators:
[tex]x^2 - 9 = (x - 3)(x + 3)\\x^2 + x - 6 = (x - 2)(x + 3)[/tex]
Rewrite the expression with the simplified denominators:
[tex]\dfrac{3}{(x - 3)(x + 3)} + \dfrac{5}{(x + 3)} - \dfrac{8}{(x - 2)(x + 3)} - \dfrac{(5x - 12)}{(x - 3)} - \dfrac{5x}{(x + 3)(x - 3)}[/tex]
Combine the fractions with the same denominator:
[tex]\dfrac{((3x - 6) + (5x - 15) - (8x - 24) - (5x^2 - 12x + 15x - 36) - (5x^2 - 10x))}{((x - 3)(x + 3)(x - 2))}[/tex]
Simplifying further,
[tex]\dfrac{(-7x - 45)}{(x - 3)(x + 3)(x - 2)}[/tex]
Therefore, the sum of the given expression is [tex]\dfrac{(-7x - 45)}{(x - 3)(x + 3)(x - 2)}[/tex].
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in one particular suburb there are 24 families that own a boxer. If these owners make up 16% of all dog owners in he suburb, then how many dog owners are there in this neighborhood
Answer:
150
Step-by-step explanation:
x = number of dog owners
x(0.16) = 24
x = 24/0.16 = 150
HELP ME ASAP, NEED TO DO MY WORK INSTANTLY
THIS IS THE QUESTION; Roberto has 4 times as many toy cars as John. Roberto has 20 toy cars. Which equation can you use to find the amount of cars that John has?
ANSWERS: 4 x 20 = a, 20 - 4 = a, a x 4 = 20, a x 20 = 4
WHICH ONE DO I PICK?!
Answer:
4x = 20
Divide.
x = 20 / 4
x = 5
John has 5 cars
Answer: A.
Step-by-step explanation: Roberto has 4 times as many toy cars as John and Roberto has 20 toy cars so it is 4 x 20 = a
A 6 ft tree casts a 21 ft shadow. How
tall is a tree which casts a 49 ft shadow?
Answer:
14 ft
GivensWe are given that a 6 ft tall tree casts a 21 ft shadow. We can assume this relationship is proportional, and as such, we can relate this to another tree of an unknown height that is casting a 49 ft shadow. To do this, we need to create a proportion that helps us solve for the unknown tree's height.
SolveTo begin, create a proportional relationship between the two trees, where x is the height of the tree with a 49 ft shadow:
[tex]\displaystyle \frac{6}{21}=\frac{x}{49}[/tex]
Then, cross-multiply the two proportions to create an equation that can be solved for the variable x:
[tex]\displaystyle 6\times49=294\\\\21\times x=21x\\\\294=21x[/tex]
Then, divide both sides of the equation by 21 to isolate the variable:
[tex]\displaystyle \frac{294}{21}=\frac{21x}{21}\\\\x=14[/tex]
Therefore, the tree that casts a 49 ft shadow is 14 ft tall.
A line has a slope of 6 and includes the points (-7, v) and (-4, 9). What is the value of v?
Please help me!
I really want to have time to study for my unit test tomorrow.
Answer:
To solve this problem, we can use the formula for the slope of a line: slope = (y2 - y1)/(x2 - x1).
Plugging in the given values, we get: slope = (9 - v)/(-4 - (-7)).
We can simplify this to: slope = (9 - v)/3.
Since the slope is given as 6, we can set this expression equal to 6 and solve for v:
6 = (9 - v)/3
Multiplying both sides by 3 gives us: 18 = 9 - v
Adding v to both sides gives us: 18 + v = 9
Subtracting 9 from both sides gives us: v = 9 - 18
Finally, we can simplify this to: v = -9
So the value of v is -9.
Answer:
-9
Step-by-step explanation:
(9 - v)/(-4+7)= 6
9 - v = 18
-v = 9
v = -9
in a certain alegabra 2 class of 26 students 16 of them play basketball and 9 of them play baseball there are 5 students who play both sorts what is the probability that a student chosen randomly from the class basketball or baseball
The probability that a student is chosen randomly from the class plays basketball or baseball
10/13= 0.769.
What is probability?Generally, The probability that a student chosen randomly from the class plays basketball is 16/26.
The probability that a student is chosen randomly from the class plays baseball is 9/26.
There are 5 students who play both basketball and baseball, so we need to subtract the probability that a student chosen randomly from the class plays both sports.
The probability that a student plays both sports is 5/26. The total probability that a student chosen randomly from the class plays either basketball or baseball is
16/26 + 9/26 - 5/26
= 20/26
= 10/13.
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Create an equivalent expression for 1.5 cubed over 1.6 raised to the fourth power all raised to the power of negative seven. 1.5 raised to the fourth power over 1.6 cubed 1.6 cubed over 1.5 raised to the fourth power 1.5 to the twenty first power over 1.6 to the twenty eighth power 1.6 to the twenty-eighth power over 1.5 to the twenty first power
(1.53/1.34) is the equivalent expression for 1.5 cubed over 1.6 raised to the fourth power plus all increased to the power of -7. (-6).
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.
given
All numbers raised to the power of negative six are 1.5 cubed over 1.3 raised to the fourth power.
1.53 is equal to 1.5 cubed over 1.3.
1.53 1.3 raised to the fourth power is equal to 1.5 cubed over 1.3.
(1.53/1.34) is the product of 1.5 cubed over 1.3 raised to the fourth power and all increased to the power of negative six (-6)
The expression is therefore (1.53/1.34). (-6).
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In a game involving a standard deck of 525252 playing cards, an individual randomly draws 777 cards without replacement. Let y=y=y, equals the number of kings drawn. Is yyy a binomial variable? why or why not?.
For y = the number of kings drawn, y a binomial variable
In this question we have been given that in a game involving a standard deck of 52 playing cards, an individual randomly draws 7 cards without replacement.
Also, y represents the number of kings drawn
We need to determine whether y a binomial variable or not.
y = "number of kings drawn"
We know that in the standard deck of 52 playing cards there are 4 King cards(each from the 4 suits:; Diamonds, Clubs, Hearts, Spades)
If we draw 7 cards from a standard deck of 52 playing cards, there would be 5 possible values of y.
y = 0 (there would be no king card)
y = 1 (there would be 1 king card)
y = 2 (there would be 2 king cards)
y = 3 (there would be 3 king cards)
y = 4 (there would be 4 king cards)
We know that a binomial variable is a variable that represents two outcomes.
Assume that x = "drawing a king" 7 times, then x is a binomial variable, because it has two outcomes, or you draw a king, or you don't.
Also, as we know a binomial variable can also represent the number of outcomes of each type for several events.
Hence, y is a binomial variable.
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No, yyy is not a binomial variable. A binomial variable is a discrete random variable that follows a binomial distribution and has two possible outcomes - success and failure.
In this case, yyy is not a binary outcome, since it can take on any number from 0 to 777.
To calculate the probability of yyy, we can use the formula P(y) = (n! / ((n-y)!*y!)) * (p^y * (1-p)^(n-y)), where n is the total number of trials (in this case, 777), y is the number of successes (in this case, number of kings), and p is the probability of success (in this case, 4/52). Therefore, the probability of drawing yyy kings from 777 cards is:
P(y) = (777! / ((777-y)!*y!)) * ((4/52)^y * ((48/52)^(777-y))
For example, if y=3, then the probability of yyy is:
P(3) = (777! / (774!*3!)) * ((4/52)^3 * ((48/52)^(774))
= 0.00307%
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For #16-18: A city department of transportation studied traffic congestion on a certain highway. To encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2. The probability distribution of the number of people in passenger cars on the highway is shown in the table.
Number of people
1
2
3
4
5
Probability
0.56
0.28
0.08
0.06
0.02
16. Is the given probability distribution a valid probability distribution? Explain why or why not.
(A) yes because each probability is between 0 and 1, and the sum of all probabilities equals 1.
(B) yes because the number of people are consecutive integers from 1 to 5.
(C) yes because the probabilities are rounded to the same decimal place.
(D) no because the probabilities add to less than 1.
(E) no because the probabilities add to greater than 1.
17. Randomly select a passenger car on the highway. According to the distribution that is the probability it contains 2 or more people?
(A)0.28
(B) 0.36
(C) 0.42
(D) 0.44
(E) 0.56
18. Based on the probability distribution, what is the mean number (expected value) of people in passenger cars on the highway?
(A)0.28
(B) 0.56
(C) 1.7
(D) 2
(E) 3
16) Yes because each probability is between 0 and 1 and sum of all probability equals 1 so option A . 17) (D)= 0.44 18)(C)=1.7
A) yes because each probability is between 0 and 1 and sum of all probability equals 1.
: ( σ <p(x)<1 and Σ p(x)=1)
17) probability that random selected passenger car an highway contain 2 or more people is 0.44
(P(x≥ 2)=p(x=2)+p(x=3)+p(x=4)+p(x=5)
P(x≥ 2=0.44
OR P(x≥ 2)=1-p(x≥ 2)=1-p(x=1)=1-0.56
p(x≥ 2)=0.44
18) Mean number of people in passenger cars are
E(X)=Σxp(x)=(1*0.56)+(2*0.28)+(3*0.08)+(4*0.06)+(5*0.02)
E(X)=1.7
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