The probability that George will win is 1/10 and the probability that Julia will win is 1/20.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.The probability is calculated by dividing the total number of outcomes by the total number of potential events.So, calculate the probability as follows:
Probability formula: P(E) = Favourable events/Total eventsWe know,
The total number of tickets sold is 100.George has 10 tickets and Julia has 5.(A) George's probability of winning:
P(E) = Favourable events/Total eventsP(E) = 10/100P(E) = 1/10(B) Julia's probability of winning:
P(E) = Favourable events/Total eventsP(E) = 5/100P(E) = 1/20Therefore, the probability that George will win is 1/10 and the probability that Julia will win is 1/20.
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The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Find
(a) the co-ordinates of the mid-point of the line PQ,.
The co-ordinates of the mid-point of the line PQ are (6,4).
From the question, we have
The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Mid-point of the line PQ =(10+2)/2 , (12-4)/2
= (6,4).
Midpoint:
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.
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1: A middle School had a school spirit day
In one class the ratio of students who wore
School colors to the number of students who
Didnt was 8 to 5 Ten students didn't wear school
Colors, Determine the number of students who wore School
Colors.
Answer:
The number of students who wore School colors are 8/13. If, Ratio of students who wore School colors to the number of students who didn't are given.
Define ratio.A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division. A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given,
Ratio of students who wore School colors to the number of students who didn't
8:5
Total number of student = 13
Number of students who wore school colors = 8/13
The number of students who wore School colors are 8/13. If, Ratio of students who wore School colors to the number of students who didn't are given.
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Determine if the expression r - 5√r+r² is a polynomial or not. If it is a
polynomial, state the type and degree of the polynomial.
The expression r - 5√r+r² is a polynomial.
What is a polynomial?
Mathematical expressions called polynomials have one variable and many exponents.
The algebraic expression must have all of its exponents be non-negative integers in order for it to be a polynomial. As a general rule, an algebraic expression isn't a polynomial if it contains a radical.
No part of an algebraic expression should be - Variables' square roots. variable powers that are fractional. variable powers that are negative. variables in any fraction's denominator.
Exponents, variables, and constants make up a polynomial. The amount of terms a polynomial has determines its name.
Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.
The idea of the graph of a polynomial equation was first introduced by René Descartes in La géometrie, published in 1637.
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The expression r-5√r+r² is a polynomial. A polynomial is made up of variables, constants, and exponents.
Explain about the polynomial?Polynomials are mathematical expressions with one variable and several exponents.
The algebraic expression is a polynomial if and only if all of its exponents are non-negative integers. In general, if an algebraic expression contains a radical, it isn't a polynomial.
An algebraic expression should not contain any square roots of variables. fractional powers that are changeable. variable powers with negative powers. variables in the denominator of any fraction.
A polynomial is made up of variables, constants, and exponents. A polynomial's name is determined by the number of terms it contains.
There are numerous types of polynomials. respectively a monomial, a binomial, and a trinomial.
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Load the GSS14SSDS-B data set in SPSS and use the frequency procedure to investigate the variability of the respondent's current age (AGE). Click on Analyze, Descriptive Statistics, Frequencies, and then Statistics. Select the appropriate measures of variability.
The level of measurement for the variable AGE is ---
The variance is ---
The standard deviation is ---
The mean is ---
The number of valid responses (n) is ---
Choices:
55.11
48.18,
50.12
1500
Ordinal
18.058
17.073
1490
Nominal
276.584
Interval
291.495
16.054
301.498
Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.
Step-by-step explanation:
the list of your answer options has a different sequence than the picture.
I assume the picture shows us the correct sequence.
the correct answer is
D : the y-values are all greater than our equal to 2
why ?
because the term in absolute value can only go down to 0 but not below. it is an absolute value after all : it is always positive (minimum 0), no matter what.
so, the minimum value of the function is 0 + 2 = 2. it cannot get lower than this.
The face value of a simple discount note is $17,000. The discount is 4% for 160 days. Calculate the following. a. Amount of interest charged for each note. (Round your answer to the nearest cent.) b. Amount borrower would receive. (Round your answer to the nearest cent.)
The amount of interest to be charged on the note, based on the face value of the note, is $302. 22.
The amount the borrower would receive is $16, 697. 78.
How to find the interest charged?The interest charged on the simple discount note can be found by the formula:
= Face value of note x discount rate x number of days / total days in a year
= 17, 000 x 4% x 160 / 360
= $302. 22
The amount that the borrower would receive is then:
= Face value of note - Interest charged on note
= 17, 000 - 302.22
= $ 16, 697. 78
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A 2\frac{1}{2}2 2 1 -inch candle burns down in 10 hours. If b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.
The equation that represents the length of the candle over time will be b = -0.25t.
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.
A 2 ¹/₂ inches candle torches in 10 hours.
Let 'b' be the length of the candle and 't' be the number of hours. Then the equation is given as,
b = -[(2 ¹/₂) / (10)]t
b = -0.25t
The equation that represents the length of the candle over time will be b = -0.25t.
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Which of the following is a Rational Number? √11 √14 √77 15
Answer:
1/2
Step-by-step explanation:
Question content area top
Part 1
A new bank customer with $ wants to open a money market account. The bank is offering a simple interest rate of %.
a. How much interest will the customer earn in years?
Write one quadratic equation that forms a graph through the points (−4,2) and (2,2) and has a
maximum value at the vertex.
Explain please
Quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
Given,
Quadratic equation passes through the points (-4,2) and (2,2)
(x₁, y₁) =(-4,2)
(x₂ ,y₂) = (2,2)
Here,
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
⇒(y - 2) / (x + 4) = (2 - 2) / (2 + 4)
⇒ (y-2) / (x+4) =0
⇒y -2 =0
⇒y = 2
Quadratic equation formed from the given points (-4,2) and (2,2) is y =2.
Which represents the horizontal line and does not have any vertex.
Therefore, quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
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A drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green. What is the probability of picking a shirt that is red or striped?
The probability of picking a shirt that is red or striped is 2/3.
Given, that a drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green.
We have to find the probability of picking a shirt that is red or striped,
P(R ∪ S) = P(R) + P(S) - P(R∩S)
where, R be the event that the shirt is red.
and S be the even that the shirt is striped.
P(R) = 5/12 (as, there are 5 red shirts)
P(S) = 5/12 (as, there are 5 striped shirts)
P(R∩S) = 2/12 (as, there are 5 striped red shirts)
P(R ∪ S) = 5/12 + 5/12 - 2/12
P(R ∪ S) = 8/12
P(R ∪ S) = 2/3
The probability of picking a shirt that is red or striped is 2/3.
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Use the pie chart to answer the following questions:
STEP
1. How many studer ts would you expect to like Comedy in a class of 300
2. How many students would you expect to like Action in a class of 400?
3.How maby studeptstwould you expect to like Romance in a class of 350?
4. How many students would you expect to like Foreign in a class of 225?
5. How many students would you expect to like Horror in a class of 200?
6. How many students would you expect to like Science Fiction in a class of 175?
Comedy 27%
Action 18%
Romance 14%
Drama 14%
Horror 11%
Foreign 8%
Science 8%
fiction
1. The number of students like Comedy in a class of 300 are 81.
2. The number of students like Action in a class of 400 are 72.
3. The number of students like Romance in a class of 350 are 49.
4. The number of students like Foreign in a class of 225 are 18.
5. The number of students like Horror in a class of 200 are 22.
6. The number of students like Science friction in a class of 175 are 14.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The pie chart is,
Comedy 27%
Action 18%
Romance 14%
Drama 14%
Horror 11%
Foreign 8%
Science 8%
Now,
1. The number of students like Comedy in a class of 300 are;
= 27% of 300
= 27/100 x 300
= 81
Thus, The number of students like Comedy in a class of 300 are 81.
2. The number of students like Action in a class of 400 are;
= 18% of 400
= 18/100 x 400
= 72
Thus, The number of students like Action in a class of 400 are 72.
3. The number of students like Romance in a class of 350 are;
= 14% of 350
= 14/100 x 350
= 49
4. The number of students like Foreign in a class of 225 are;
= 8% of 225
= 8/100 x 225
= 18
5. The number of students like Horror in a class of 200 are;
= 11% of 200
= 11/100 x 200
= 22
6. The number of students like Science friction in a class of 175 are;
= 8% of 175
= 8/100 x 175
= 14
Thus, 1. The number of students like Comedy in a class of 300 are 81.
2. The number of students like Action in a class of 400 are 72.
3. The number of students like Romance in a class of 350 are 49.
4. The number of students like Foreign in a class of 225 are 18.
5. The number of students like Horror in a class of 200 are 22.
6. The number of students like Science friction in a class of 175 are 14.
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33 is 15 less than k
What expression is equivalent to -6(t+9)
-6t -54 is the expression equivalent to-6(t+9)
How determine equivalent expressions?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)
Given: -6(t+9)
First, clear the parenthesis by using -6 to multiply t and 9:
-6(t+9) = (-6 x t) + (-6 x 9)
= -6t + (-54)
= -6t -54
Therefore, the -6t -54 is equivalent to -6(t+9)
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Two year ago ernest dorsey purchased a used sports coupe for 8000.00 that is now worth 6000.00 last year he drove it 13569 miles and kept a record od all expenses. His variable costs were gasoline $1589.56 oil changes $245.98 and repairs $548.11 his fix costs were insurance $1105.32 and license $85 find de cost per mile
The cost per mile incurred by Ernest Dorsey for driving the sports coupe for last year was $0.41.
How is the cost per mile derived?The cost per mile is the quotient of the division operation involving the total cost incurred and the driving mileage for the year.
To derive the total cost, add up the value of the car consumed (cost - current value), the annual variable, and fixed costs.
Cost of a used sports coupe last year = $8,000
The current value of the car = $6,000
Used value for the year = $2,000.00 ($8,000 - $2,000)
Yearly variable costs:Gasoline $1,589.56
Oil changes $245.98
Repairs $548.11 $2,383.65
Annual fixed Costs:Insurance $1,105.32
License $85.00 $1,190.32
Total cost for the year = $5,573.97
Driven mileage for the year = 13,569 miles
Cost per mile = $0.41 ($5,573.97/13,569)
Thus, the cost per mile is $0.41.
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Hunter bought 3 chicken wings for $6.60. How much does each wing cost?
Answer:
$2.20
Step-by-step explanation:
6.6/3=2.2
A hexagon has exterior angle measures of (7n + 3), (10n-17)°,
(8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
Find the value of n.
Using the sum of exterior angle, the value of n is 11.
In the given question,
A hexagon has exterior angle measures of (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
We have to find the value of n.
As we know that the sum of exterior angle of any polygon is equal to 360°.
As the given measures are (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
So we can find the value of n by adding the all measures.
So the expression should be
(7n + 3) + (10n-17) + (8n - 16) + (4n+17) + (-n + 16) + (5n - 6)° = 360°
Simplifying the bracket.
7n + 3 + 10n-17 + 8n - 16 + 4n+17 - n + 16 + 5n - 6 = 360°
Solving the expression by solving the same term
(7n+10n+8n+4n-n+5n)+(3-17-16+17+16-6)= 360°
33n-3 = 360°
Add 3 on both side
33n-3+3 = 360°+3
33n = 357°
Divide by 33 on both side
33/33 n= 363°/33
n = 11
Hence, the value of n is 11.
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Find the rectangular coordinates of the point with the polar coordinates (-7,5 π/3)
Rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2 by using the relation between rectangular and polar coordinates
What do you mean by rectangular coordinates?
Rectangular coordinates, commonly known as cartesian coordinates, are a way to represent graphs and show where points are located on a two-dimensional surface or in three-dimensional space.
The origin is the intersection of the two perpendicular axes that make up the Cartesian plane.
The xy plane is another name for the Cartesian plane.
Given polar coordinates are (-7,5π/3)
To change polar coordinates to recatngular coordinate use
x = rcosθ , y = rsinθ
here r = -7 and θ = 5π/3
x = -7cos5π/3 = -7 × 1/2 = -7/2 = -3.5
y = -7sin5π/3 = -7 × -[tex]\sqrt{3}[/tex]/2 = 7[tex]\sqrt{3}[/tex]/2
Therefore, rectangular coordinates are x = -3.5 , y = 7[tex]\sqrt{3}[/tex]/2
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From ratio proportion for the following using
2 different way
45 members of Glee Club to 30 members of Dance
Club
Answer:
see explanation
Step-by-step explanation:
this can be expressed in ratio form and fractional form , that is
45 : 30 ( divide each part by 15 )
= 3 : 2 ← in simplest form
= [tex]\frac{3}{2}[/tex]
Kevin bought a desk on sale for $280.80. This price was 36% of the original price.
What was the original price?
The original price of desk bought by kevin is $780.
What is original price?
To calculate the initial worth of a reduced or sale item, you wish to grasp the sale worth and also the discount proportion. The calculations embody an easy formula that divides the sale worth by the results of one minus the discount in proportion form.
Main body:
Let the original price of desk be x.
After sale price of desk - $280.80
According to question, 36% of original price is what kevin bought it for.
So the equation formed is,
⇒36% of x = 280.80
⇒0.36*x = 280.80
⇒x = 280.80/ 0.36
⇒x = $780
Hence the original price of desk is $780.
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The Gourmand Cooking School runs short cooking courses at its small campus. Management has identified two cost drivers it uses in its budgeting and performance reports—the number of courses and the total number of students. For example, the school might run two courses in a month and have a total of 62 students enrolled in those two courses. Data concerning the company’s cost formulas appear below:
Fixed Cost per Month Cost per Course Cost perStudent
Instructor wages $ 2,970
Classroom supplies $ 310
Utilities $ 1,230 $ 65
Campus rent $ 4,900
Insurance $ 2,400
Administrative expenses $ 4,000 $ 46 $ 4
For example, administrative expenses should be $4,000 per month plus $46 per course plus $4 per student. The company’s sales should average $890 per student.
The company planned to run four courses with a total of 62 students; however, it actually ran four courses with a total of only 52 students. The actual operating results for September were as follows:
Actual
Revenue $ 52,280
Instructor wages $ 11,160
Classroom supplies $ 19,070
Utilities $ 1,900
Campus rent $ 4,900
Insurance $ 2,540
Administrative
expenses $ 3,858
Answer:
whats the question
Step-by-step explanation:
The operating profit for September was $168,418.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Using the given information, we can calculate the following:
Total fixed cost per month.
= Instructor wages + Classroom supplies + Utilities + Campus rent + Insurance + Administrative expenses
= $2,970 + $310 + $1,230 + $4,900 + $2,400 + $4,000
= $15,810
Variable cost per course.
= Cost per course for utilities + Cost per student for administrative expenses
= $65 + $4 = $69
Variable cost per student
= Sales revenue per student - Total variable cost per student
= $890 - $69
= $821
Using the planned number of courses and students, we can calculate the expected revenue:
Expected revenue.
= Planned number of courses x Planned number of students x Sales revenue per student
= 4 x 62 x $890 = $221,120
Using the actual number of courses and students, we can calculate the actual revenue and costs:
Actual revenue
= Actual number of courses x Actual number of students x Sales revenue per student
= 4 x 52 x $890
= $184,640
Total variable cost
= (Variable cost per course x Actual number of courses) + (Variable cost per student x Actual number of students)
= ($69 x 4) + ($4 x 52)
= $412
Total cost
= Total fixed cost + Total variable cost
= $15,810 + $412
= $16,222
Operating profit
= Actual revenue - Total cost
= $184,640 - $16,222
= $168,418
Therefore,
The operating profit for September was $168,418.
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Which equation represents a line which is parallel to the line y = -2x - 7?
y = -2x is line parallel to given line.
What is line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that are endlessly stretched in the opposing directions.
Main body:
The slope-intercept form is
y=mx+b, where
m is the slope and b is the y-intercept.
y=mx+b
Using the slope-intercept form, the slope is −2.
m=−2
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope −2 and a given point (0,0) to substitute for
x₁ and y₁ in the point-slope form
y−y₁=m(x−x₁)
, which is derived from the slope equation
m=(y₂−y₁)/(x₂−x₁).
y−(0)=−2*(x−(0))
Simplify the equation and keep it in point-slope form.
y+0=−2⋅(x+0)
Solve for y.
y=−2x
Hence y = -2x is line parallel to given line.
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Aisha runs a tutoring business. With Plan 1, students may choose to pay $15 per hour. With Plan 2, they may follow the plan shown on the graph.
The student pay initial fess of $20 and addition $10 per hour.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Plan 1:
students pay = $15 per hour.
Plan 2:
From the graph we can see that
slope= Rise/ Run = 10/ 1= 10
and, the graph line starts from 20.
Hence, the student pay initial fess of $20 and addition $10 per hour.
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(3^3*6^6)^-3
what is a simplified version of this
The simplified value of the above expression is 5.00248967e-19
we know,'^' this symbol means by times
[tex]3^{3}[/tex] =27
[tex]6^{6}[/tex] =46,656
27 multiplied by 46,656
[tex]27 \times 46,656 = 1,259,712[/tex]
[tex]1,259,712 ^{-3} = 5.00248967e-19[/tex]
if you want you can apply the BODMAS system here.
it is just a fraction try to simplify it.
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Solve the following simultaneous equations using substitution
Answer:
the answer is 18 lol....
Can you help me with this problems, thank you.
The probability that student will pass the test is 2/7.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.So, the probability that the student will pass the test:
The total number of questions are 50 and 25 questions need to be correct to pass the test.Out of 25, 15 are correct.Out of the remaining 35 questions, 10 questions need to be right to pass the best.Probability Formula: P(E) = Favourable events/Total events
Now, calculate as follows:
P(E) = Favourable events/Total eventsP(E) =10/35P(E) = 2/7Therefore, the probability that student will pass the test is 2/7.
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If q is 2.00 what is the distance from C to A?
Answer: 4.00
Step-by-step explanation:
If the q is 2.00 A to C is double the q. So, 2.00x2= 4.00.
Answer:
AC = 4.00Step-by-step explanation:
Given is a parallelogram.
One of the properties of a parallelogram is its diagonals bisect each other.
It gives us:
AC = 2qAC = 2*2.00 = 4.00HELP!! which expression is equivalent to the given expression 2X^2 -11 X -6
Answer: C.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Jacob held different part-time jobs during his summer holiday. The table below shows the total money he earned for different amounts of time, in hours.
What type of association will the scatter plot for this data represent between the number of hours worked and the total money earned?
1. A positive nonlinear association
2. A positive linear association
3. A negative nonlinear association
4. A negative linear association
Given the table on the total money earned, the type of association the scatter plot would represent is 2. A positive linear association
What is a positive linear association?When two variables are said to have a positive linear association, it means that they move in the same direction together. When one of them increases, the other increases as well. It also means that they are increasing by a uniform amount. For instance, when one variable increases by 3, the other increases by 6, always.
The hours worked here are increasing as well as the money earned by Jacob. The hours worked is increasing by 1, and the money earned is increasing by 4. This is therefore a positive linear association.
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HOW DO YOU SEE IT?. You and your friend go running. The graph shows the distances you and your friend run.
From the graph,
a. Friend runs at constant rate because of the straight line graph
b. the domain of the function representing your run 0 ≤ x ≤ 60
the domain of the function representing your friend's run 0 ≤ x ≤ 60
How to determine who runs at a constant rateThe graph of a straight line shows that the variables are constantly varying hence the graph that has a straight line which is your friend's graph is the graph at constant rate.
The domain of the functionThe domain is controlled by the x direction, it consist of all the values that the s coordinate ca get to
The graph shows that both you and your friend has similar x coordinate and will have same domain
The x coordinate from the beginning of the graph is at 0. At the end it is at at point 60
point 60 is not marked but reading the graph it can be deduced that the last line is point 60. hence the domain is 0 ≤ x ≤ 60
Learn more about linear graph interpretation:
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