if the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces, No , it does not change the value of p(odd number) .
a) The sample space is the set of all possible outcomes. By definition, the elements of a set should not be repeated. Hence, the sample space S = {1, 2, 3}
However, the sample is not equiprobable because each element has different probabilities.
b) P(odd number) = number of odd digits / number of faces = 4/6=2/3
Note that the odd numbers are 1 (on three faces) and 3 (on one face).
c) The fact the die has been biased does not change the possible outcomes. It only changes the probability of getting any given number.
d) Because the 3-face has been loaded, this probability changes. In fact, it is calculated thus:
Let's assume the probability for 1 or 2 is . Then that of 3 is (because it is twice the others). The sum of probabilities must be 1.
x+x+x+x+x+2x=1
7x=1
x=1/7
P(odd number) = 3 * Prob(1) + Prob(3)
=3*1/7 +2/7 = 5/7
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The first and the last terms of two Arithme- tic progressions are the same. The first A.P. has 51 terms with a common difference of 6. Find the number of terms of the 2nd A.P if its common difference is given as 4.
The number of terms of the 2nd A.P if its common difference is given as 4 is 76.
What is common difference?
The difference between consecutive integers in an arithematic sequence is a frequent distinction. Simply subtract the first word from the second term, or the second from the third, or anything similar, to find it. See how we have to add 8 each time to reach the following term? Thus, our common difference is eight.
1st A.P
Let 1st term be a d = 6
Therefore T51 = a + ( 51 - 1 )6
= a + 300
Now 2nd A.P
let the 1st term be a
Therefore for n no. of terms,
lats term, a + ( n - 1 )4
But according to the question:
a + ( n - 1 )4 = a + 300
n - 1 = 300/4
n = 75 + 1
n = 76
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Convert 0.17 to a fraction in simplest form and a percent.
Answer: 17/100, which would be 17%
Step-by-step explanation:
Help I will. Give brainly
Help me please I am in need
At 1 hour, 3 hours and 6.5 hours she travels 36 miles, 108 miles and 234 miles respectively using the concept of average speed of an object.
As per the question statement, Clare covers a distance of 0 miles, 72 miles, 144 miles and 216 miles in 0 hours, 2 hours, 4 hours and 6 hours respectively.
We are supposed to find out the distance travelled by her in 1 hour, 3 hours and 6.5 hours.
We will use the concept of average speed of an object which is as follows
average speed = total distance divided by the total time taken
average speed = 216/6 = 36 miles per hour
Hence at 1 hour, distance = 1 * 36 = 36 miles
at 3 hours, distance = 3 * 36 =108 miles
at 6.5 hours, distance = 6.5 * 36 = 234 miles
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Your friend has $80 when he goes to the fair. He spends $4 to enter the fair and $12 on food. Rides at the fair cost $1.25 per ride.
The function f(x) = -1.25x + 64 can be used to determine how much money he has left over after x rides? What does f(17) represent?
Group of answer choices
Your friend paid for 17 rides and spent $42.75.
Your friend paid for 17 rides and had $37.25 left over.
Your friend paid for 17 rides and had $42.75 left over.
Your friend paid for 17 rides and spent $37.25.
The function f(17) represent your friend paid for 17 rides and had $42.75 left over.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let f(x) represent the amount that the rider has left over after x rides.
f(x) = -1.25x + 64
f(17) = -1.25(17) + 64 = 42.75
f(17) = $42.75
f(17) represent the money left
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Number 21… please explain I don’t know how to do this
Answer:
The lengths of the sides are 18 ft, 18 ft, and 24 ft.
two gears, A and B. are arranged so that the teeth of one gear is mesh with the teeth of another. Gear A turns clockwise and has 54 teeth. Gear B turns counterclockwise and has 36 teeth. If gear A makes 5.5 rotations, how many turns will gear B make?
The number of turns gear B will make is 8.25 turns
How to find the number of turns gear B will makeGiven data
Gear A turns clockwise and has 54 teeth
Gear B turns counterclockwise and has 36 teeth
gear A makes 5.5 rotations
One of the gears is driving the other hence the distance covered by each of the gears is constant.
The distance is the product of the number of rotations and the number of teeth and this should be a constant
Therefore, let the number of rotations of gear B be x
54 teeth * 5.5 rotations = 36 teeth * x rotations
x rotations = ( 54 teeth * 5.5 rotations ) / 36 teeth
x rotations = 54/36 * 5.5
x rotations = 1.5 * 5.5
x rotations = 8.25
We can therefore say that gear B will make 8.25 rotations
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After a 65% reduction, you purchase a new washing machine on sale for $224. What was the original price of the washing machine?
The original price was ___$
Answer:
$369.60
Step-by-step explanation:
65% = 0.65
1.00 + 0.65 = 1.65
$224 * 1.65 = $369.60
the original price was $369.60
Answer:
The original price was 640
Step-by-step explanation:
Let the price be x
100%-65%=35%
35%/100%*x=224
35x=22400
x=640
A rental company charges $85 a day and 30 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill comes to $290. How many miles did he drive?
Answer:
400 miles
Step-by-step explanation:
Let m be the number of miles.
[tex]85(2) + .30m = 290[/tex]
[tex]170 + .30m = 290[/tex]
[tex].30m = 120[/tex]
[tex] m = 400[/tex]
I need help pls its really hard for me rn and teach me how to do it
The sequence that contains all the given terms is:
aₙ = -18 + 6*n
Then the correct option is C.
Which sequence can be used to find the n-th term?
Here we have the elements:
a₃ = 0
a₄ = 6
a₅ = 12
a₆ = 18
a₇ = 24
So each term adds 6 to the previous one, so trivially the relation is of the form:
aₙ = aₙ₋₁ + 6
Now we need to find the first term.
We can rewrite the above equation as:
aₙ₋₁ = aₙ - 6
Then we willget:
a₂ = a₃ - 6 = 0 - 6 = -6
a₁ = a₂ - 6 = -6 - 6 = -12
a₀ = a₁ - 6 = -18
Then the sequence is:
aₙ = -18 + 6*n
Then the correct option is C.
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What number makes the fractions equivalent?
different numerators and denominators but are equal to the same value.
-
if you need a specific number answer from a problem, you'd need to attach a picture
4p−5(p+6) Help plssss
Answer: -p - 30
Step-by-step explanation:
We will simplify the expression.
Given:
4p - 5(p + 6)
Distirubte the negative 5:
4p - 5p - 30
Combine like terms:
-p - 30
3) Mr. G. was once offered a job as a car salesperson. Below is a partial compensation table they used to calculate monthly pay. (10 points)
Number cars sold 5 6 7 8 9 10
Salary 2750 3200 3650 4100 4550 5000
a. Is this linear? How do you know?
b. Suppose Mr. G thought he could sell 23 cars during one month. What would his total monthly pay be? Show your work!
c. If the gross pay is $6,800, how many cars were sold? Show your work!
The relation on the table of values is a linear model,
The total monthly pay is $10850 when he sells 23 cars in one monthThe number of cars is 14 if the gross pay is $6,800How to determine if the relation is linear?The table of values is given as
Number cars sold 5 6 7 8 9 10
Salary 2750 3200 3650 4100 4550 5000
On the table of values, we can see that:
As the number of cars increase by 1, the salary increases by 450
This means that the table has a constant rate of 450
Relations that have a constant rate are linear relations
Hence, the table of values is a linear relation
The total monthly payIn (a), we have
Slope, m = 450
A linear equation is represented as
y = m(x - x1) + y1
So, we have
y = 450(x - 5) + 2750
Evaluate
y = 450x + 500
When the number of cars is 23, we have
y = 450 x 23 + 500
Evaluate
y = 10850
Hence, the total monthly pay is $10850
The number of carsHere, we have
y = 6800
This gives
450x + 500 = 6800
This gives
450x = 6300
Evaluate
x = 14
Hence, the number of cars is 14
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Two fish tanks have measurements as shown.
Which tank has a greater volume? How much greater is its volume?
Use the drop-down menus to explain and show your answer.
8 ft
Choose.
Fish Tank A
The volume of fish tank A is Choose...
volume is greater by ose
Fish Tank B
Area of base: 25 ft²
Area of base: 40 ft²
4 ft
cubic feet, and the volume of fish tank B is
has a greater volume. Its
cubic feet. So fish tank Choose....
cubic feet
Step-by-step explanation:
sgshshsbhehdbdbdbsbehebebdbebd
A scale drawing of a car is presented in the following three scales. Order the scale drawings from smallest to largest. Explain your reasoning. (There are about 1.11.1 yards in a meter and 2.542.54 cm in an inch)
help me please ;-;
The order of the scales from smallest to largest would be,
inch, centimeter, yard, meter
In this question, we have been given a scale drawing of a car is presented in the following three scales.
We need to order the scale drawings from smallest to largest.
We know that,
1 cm = 2.54 inch
and 1 meter = 1.1 yards
We know that the metric conversion,
1 meter = 100 centimeters
And 1 cm = 2.54 inch
So, 1 meter = 254 inches
This means, meter is the largest scale and inch is the smallest scale.
1 yd = 91.44 cm
This means, yard is greater than centimeter.
Therefore, the order of the scales from smallest to largest would be,
inch, centimeter, yard, meter
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Plot the following ordered pairs on the same Cartesian plane for each one.
1.(2,3)
2.(0,-7)
3.(-5,9)
A graph of the given ordered pairs has been plotted as shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.
In conclusion, a graph which represents the given ordered pairs shows a discrete function.
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a library subscribes to two different weekly news magazines, each of which is supposed to arrive in wednesday's mail. in actuality, each one may arrive on wednesday, thursday, friday, or saturday. suppose the two arrive independently of one another, and for each one p(wed.)
The two come separately, and the p(wed.) value for each one is 0.0841. It is founded on likelihood on probability.
What does probability mean in math?Probability is a way to gauge how likely something is to happen. Many things are hard to predict with complete certainty. We can only forecast how likely an event is to occur using it, or how likely it is to occur.
The probability is typically defined as the proportion of positive outcomes to all outcomes in the sample space. Probability of an event P(E) = (Number of favourable outcomes) is how it is stated (Sample space).
based on the facts provided;
p(0) = p(w,w)
= 0.29² = 0.0841
p(1) = p(t, w+t) + p(w, t)
= 2p(w,t) +p(t,t) = 2·.29·.37 + .37² = 0.3515
p(2) = p(f, w+t+f) +p(w+t, f)
= 0.16(2(.29+.37)+.16) = 0.2368
p(3) = p(s, w+t+f+s) +p(w+t+f, s)
= 0.18(2(.29+.37+.16) +.18) = 0.3276
In summary, your pmf is ...
y : p(y)
0 : 0.0841
1 : 0.3515
2 : 0.2368
3 : 0.3276
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What is the total surface area??
Check the picture below.
[tex]\stackrel{\textit{\LARGE Areas}}{ \stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(\underset{b}{8})(\underset{h}{6}) \right]}~~ + ~~\stackrel{\textit{three rectangles}}{(14)(6)~~ + ~~(14)(8)~~ + ~~(14)(10)}} \\\\\\ 48~~ + ~~84~~ + ~~112~~ + ~~140\implies \text{\LARGE 384}~cm^2[/tex]
Probability of an event
A class is made up of 10 boys and 10 girls. Half of the boys wear glasses. A student is selected at random from the class. What is the probability that the
student is a boy with glasses?
Write your answer as a fraction in simplest form.
Answer: ¼ or 25% or 0.25
Step-by-step explanation:
5 boys = 25% of the class
5/20
¼ or 25% or 0.25
is y-4x=9 a linear equation
Answer:
it is a linear equation
Step-by-step explanation:
please help, question is on the image.
The number of gigabytes Salma can use while staying in her budget is less than 4.
What is meant by the term inequality?In mathematics, an inequality is a connection between two expressions and values that aren't equal to each other.
Rule 1: Once inequalities are linked, they can be crossed. As a result, if an is greater than b and b is higher than c, a will be greater than c as well.Rule 2: When you swap the values, this same sign also flips.Rule 3: An inequality could be either > or, but not both at the same time.As per the given question;
The total budget of Salma is $75.
The flat cost is $55.
The cost per gigabytes is $5.
Let the number of gigabytes used be 'x'.
Then, the inequality becomes.
55 + 5x < 75
Subtracting 55 from both sides.
55 + 5x - 55 < 75 - 55
5x < 20
Divide both sides by the 5
x < 4
Thus, the number of gigabytes Salma can use while staying in her budget is less than 4.
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What are the y-intercept and the slope of the graph of the following equation? 3x+4y=12
[tex]3x+4y=12\implies 4y=-3x+12\implies y=\cfrac{-3x+12}{4} \\\\\\ y = \cfrac{-3x}{4}+\cfrac{12}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{4}}x+\stackrel{\stackrel{b}{\downarrow }}{3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Grace has a coupon for $2 off the regular price of each pair of jeans she buys. She buys 4 pairs of jeans with a regular price of $23 each. What is the total cost for her jeans?
The total cost for her jeans will be $84.
How to calculate the cost?From the information, Grace has a coupon for $2 off the regular price of each pair of jeans she buys and she buys 4 pairs of jeans with a regular price of $23 each.
The total cost for her jeans will be:
= (4 × $23) - (4 × $2)
= $92 - $8
= $84
Therefore, it should be noted that the total cost is $84.
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help i’m haveing a hard time
The result of the function f(x)=x+6 when x= -2,0 and 5 is
f(-2)= 4
f(0)= 6
f(5) = 11
The function is f(x) = x+6
The function is an expression that shows the relationship between one variable and another variable. One variable will be independent variable and another variable will be dependent variable.
The given function f(x) = x+6 when x =-2, 0 and 5. Here we have to substitute the values of x in the given function
f(x) = x+6
f(-2) = -2+6
= 4
f(0) = 0+6
= 6
f(5) = 5+6
= 11
Hence, the result of the function f(x)=x+6 when x= -2,0 and 5 is
f(-2)= 4
f(0)= 6
f(5) = 11
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Mark wanted to know the area of his backyard. his parents told him that the yard was 4/5 of a mile wide and 1/2 of a mile long. what is the area of his yard ?
Answer:
A = 0.041138659 Sq. Mi.
Step-by-step explanation:
now I'm guessing that mark's backyard is GIGANTIC
and according to the info the question gave I know his back yard is also a Rectangle, knowing this we can safely say the formula to find the Area of a rectangle: A = LW to break this down it's like saying:
Area = length × width
the question already states that the width was 4/5 of a mile and the length was 1/2 of a mile we would convert the miles to feet
1 mile = 5,280 ft
4/5 × 5,280 = 4,224 ft
so, 4/5 of a mile would be 4,224 ft
similarly, 1/2 of a mile would be 2,640
1/2 × 5,280 = 2,640
GREAT we found our new length and width
length= 2,640 ft
width=4,224 ft
plug it in the formula
A= L×W
A= 2,640 ft · 4,224 ft
A= 1,146,880 sq. ft.
change that into square miles by dividing by 27878000
0.041138659 Square Miles
Simplify.
3/2(x+3/4)−(x+1)
Answer:
x/2 + 1/8
Step-by-step explanation:
3/2(x+3/4) - (x+1)
3/2x + 9/8 - x -1
x/2 + 1/8
The diference between two numbers is 3 their sum is 27. What is the smaller number?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
x - y = 3
x + y = 27
add them:
2x = 30
x = 15
from x+y=27, we can see that y = 12
Construct RS so that RS is bisector to PQ
Draw the image of \triangle ABC△ABCtriangle, A, B, C under a dilation whose center is CCC and scale factor is 222.
The image of triangle ABC△ABC triangle, A, B, C under a dilation whose center is CCC and scale factor is 222. The dimensions of the new triangle are 8.2, 12.8, and 10.2 units. The graph of the Δ is given below.
What is a transformation of a point?A spatial transformation is each mapping of the feature space to itself and it maintains some spatial correlation between figures.
The △ABC is given below.
The dimensions of triangle are approximately 4.1, 6.4, and 5.1.
And scale factor of the dilation is 2.
If △ABC is dilated by the scale factor of 2 as a center of C.
Then dimensions of the new △A'B'C will be
A'C = AC × 2
A'C = 4.1× 2
A'C = 8.2 units
B'C = BC × 2
B'C = 6.4 × 2
B'C = 12.8 units
B'A' = BA × 2
B'A' = 5.1 × 2
B'A' = 10.2 units
Then the dimensions of new triangle are 8.2, 12.8, and 10.2 units.
The graph of triangle is given below:
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What is 3.68086257145 divided by 6.533 * 4,085,0811
When 3.68086257145 divided by 6.533 * 4,085,0811 we get 1.379228624370833401829E-8
The methods of division are of three types according to the difficulty level. These are the chunking method or division by repeated subtraction, short division method or bus stop method and long division method.
The division of two numbers can be calculated using the following formula:
Dividend / Divisor = Quotient + Remainder.
The number that is being divided in this case is known as the dividend. The number that divides the number (dividend) into equal parts is known as the divisor.
The quotient is the result of the division operation.
The remainder is the leftover number in the division operation.
We have been given that
3.68086257145 divided by 6.533× 4,085,0811
First we simplify multiplication part
6.533× 4,085,0811 = 266878348.263
Now
3.68086257145 divided by 266878348.263
3.68086257145 ÷ 266878348.263
= 1.379228624370833401829E-8
Hence , 1.379228624370833401829E-8 is the result of the 3.68086257145 divided by 6.533× 4,085,0811 .
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