The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
Permutation:
Permutations are different ways of arranging objects in a particular order. This can also be expressed as rearranging the elements in linear order of an already ordered set. The symbol are used to denote the number of permutations of n distinct objects obtained for each r. Block bus, train and plane timetables, postcode and phone number assignments. These are some situations where permutations are used.
Example: There are 5 chairs and 3 people need to sit on them. There are 5 ways to place the first person. 2nd person 4 seats, 3rd person 3 seats. So to find the number of ways to place her 3 on 5 chairs, multiply these ways. Make 5×4×3 streets. So we can do it 60 ways. 5 × 4 × 3 is written as (5!) / (2!) (or) (5!) / (5 - 3).
Combination:A combination is a selection of elements from a set with different members, so the order of selection does not matter (unlike a permutation). For example, if he is given three fruits, such as apples, oranges, and pears, he has three binary combinations that he can draw from this set. An apple and a pear. apples and oranges. Or pear and orange. More formally, a k-combination of a set S is a subset of the k distinct elements of S. Two combinations are identical only if each combination has the same members.
According to the Question:
The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
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A copy machine can print 480 copies every 4 minutes. How many copies can it print in 1 minute
Answer: 120 copies
Step-by-step explanation:
Takes 480 divided by 4 = 120 copies per minute
Use the quadratic formula to solve the quadratic equation 2x² - 2x - 5 = 0.
Separate multiple solutions with commas if necessary.
Answer: 1-squareroot of 11 (Nominator) over 2 (dominator), 1+ of 11 (Nominator) over 2 (dominator
Step-by-step explanation:
thirty percent of one hundred
Answer:30
Step-by-step explanation:
30%x100
the comparison distribution for an independent-samples t test is a distribution of; which of the following is the correct formula for computing the one-sample t-test; one important difference between variance terms for between-groups and within-groups is that; the formula for the total degrees of freedom for the independent-samples t test is; for the following original data, calculate the mean of the difference scores.; which report of statistical results is in appropriate apa format?; for the following data, what is the standard error of the difference scores; the fifth step in conducting the single-sample t test is
A distribution of the means of two independent groups serves as the comparison distribution for an independent-samples t-test.
By using the one-sample t-test formula
If s is the sample standard deviation, n is the sample size, and x is the sample mean, is the population mean.
The between-groups variance measures the variability of the group means, whereas the within-groups variance measures the variability of the individual scores within the groups. This is a key distinction between variance terms for between-groups and within-groups.
By using the formula,
df = (n1 - 1) + (n2 - 1) (n2 - 1)
where the sample sizes for the two groups are n1 and n2.
The mean of the differences between the scores in the two groups can be used to compute the mean of the difference scores for the original data. The mean of the difference scores would be determined as follows, for instance, if the first group has scores of 3, 5, and 7, while the second group has scores of 4, 6, and 8.
[tex]\frac{(3 - 4) + (5 - 6) + (7 - 8)}{3}[/tex]
= [tex]\frac{(-1 + -1 + -1)}{3}[/tex]
= [tex]\frac{- 3}{3}[/tex]
= -1
The name of the statistical test, the sample sizes, the averages and standard deviations of the groups, the estimated t-value and degrees of freedom, and the p-value would all be included in a report of statistical results that follows proper APA format. The research question and hypothesis being examined should be stated clearly in the report, together with a discussion of the findings and their implications.
The standard error of the difference scores for the provided data can be calculated as
SE = [tex]((\frac{s12}{n1}) + (\frac{s22}{n2}))[/tex]
where n1 and n2 are the sample sizes, s1 and s2 are the standard deviations of the two groups, and
Calculating the t-value and comparing it to the critical value of t from the appropriate degrees of freedom in the t-distribution is the fifth step in performing a single-sample t-test. The null hypothesis can be rejected if the estimated t-value is greater than the critical value since it shows that the observed differences between the sample and the population are statistically significant.
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What is the 3rd term when 5 3x2 − 5x4 2x3 is arranged in descending order?
-5x^4 is the 3rd term when 5 3x2 − 5x4 2x3 is arranged in descending order.
Given ,
the 3rd term when 5 3x2 − 5x4 2x3 is arranged in descending order.
It is said to be in descending order if the information is arranged from highest to lowest. Examples of numbers that are organized in descending order include 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1. In other words, the order is said to be declining if the numbers are listed from largest to smallest.
5 3x^2 - 5x^4 2x^3
=> 5x^4 - 5 3x^2 2x^3
=> 5x^4 - 10x^5
=> -5x^4
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Work out the value of x . The diagram is not drawn to scale.
After calculating the angles, we know that the value of x is (C) 99°.
What are angles?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex.
The name "angel" comes from the Latin word "angulus," which means "corner."
Angles are also produced when two planes intersect.
These are what are known as dihedral angles.
So, according to the given figure of the diagram:
We can say that:
y + 116 = 180
y = 180 - 116
y = 64°
Now, calculate for x inside the given figure:
125 + 72 + 64 + x = 360
261 + x = 360
x = 360 - 261
x = 99°
Therefore, after calculating the angles, we know that the value of x is (C) 99°.
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pls help what is 5x=20 shown work
Answer: x = 4
Step-by-step explanation:
Divide each term in 5x = 20 by 5 and simplify
[tex]\frac{5}{5} x[/tex] = [tex]\frac{20}{5}[/tex]
[tex]x=4[/tex]
Answer:
x=4
Step-by-step explanation:
5x4=20
In which part of the map will the scale factor be less than 1?
When the scale factor of the map is less than 1, then the location will be above the map projection plane
The scale factor is used in the UTM mapping systems.
UTM stands for Universal Transverse Mercator, it is the coordinate grid used for the map projection.
The scale factor is an important part in the UTM mapping. Because it is used to show the distortion from the mapping system. Distortion is because of the Earth is mapped into flat surface.
So we can divide the surface into two, the surface above the mapping projection and the surface below the mapping projection
If the scale factor is less than 1 the location will be above the map projection plane and if the scale factor is greater than 1 the location will be below the map projection plane
Therefore, the scale factor less than 1 shows the location above the projection
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Multiplying improper fractions 5/4 x 16/3
Answer: 20/3
Step-by-step explanation:
When we multiply improper fractions, we multiply the numerator by numerator and denominator by denominator. So we do:
5/4 * 16/3
= 80/12
= 20/3
So the answer is 20/3.
worth 100 pts
find the value of x in the parallelogram below.
Answer: 103
Step-by-step explanation:i think
Answer: 140 I think actually
Step-by-step explanation: Because if you use the well comonlmonly used method you would see that MAYBE the equivilancalence is 140, not 130.
Cora went to the candy store and bought 1/2 of a pound of candy. If 1/2 of Cora's candy was chocolate, how many pounds of chocolate candy did Cora buy?
Answer:
1/4
Step-by-step explanation:
[tex]\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{2 \cdot 2}=\frac{1}{4}[/tex]
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Question 4 of 5 ✓
Yellow Taxi service charges a $15 flat fee plus $2.50 per mile traveled. The charges for
miles
Black and White Taxi service are shown in the graph, where x is the numb
and y is the total cost.
2
AA
Part B
cdn.assess.prod.mheducation.com
*HW 12/7/22* Module 4- Put It All Together 2
y
C
(202) 1%
Save and Exit
O 1 2 3 4 5 6 7 8 9 x
Johnny needs, to travel 5 miles. How much will it cost Johnny if he pays the least
amount possible?
miles
0
00
How far does Johnny need to travel so that the cost is the same for both taxi services?
Johnny will pay a least possible amount of $25 and for 10 miles, the cost for both services will be same.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given are two taxi service companies.
For Yellow Taxi service, John will pay -
C(x) = 15 + 2.5x = 15 + 2.5 x 5 = 15 + 12.5 = 27.5
C(x) = $27.5
For white taxi service, we can write -
C(x) = 10 + {(16 - 10)/(2 - 0)}x
C(x) = 10 + 3x = 10 + 3 x 5 = $25
C(x) = $25
Johnny will pay $25 as the least possible amount.
For equal amount, we can write -
10 + 3x = 15 + 2.5x
3x - 2.5x = 15 - 10
0.5x = 5
x/2 = 5
x = 10
Therefore, we can write -
Johnny will pay $25 as the least possible amount.For 10 miles, the cost will be same.To solve more questions on equations, expressions and polynomials, visit the link below -
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m = P- 26
2
p = 68.3
b = 8.7
correct to 1 decimal place. correct to 1 decimal place.
Work out the lower bound for m.
The lower bound for given equation of M is 25.45.
What is lower bound?
An element of K that is greater than or equal to each element of S is referred to as an upper bound or majorant in mathematics, particularly in order theory.
An element of K that is less than or equal to each element of S is referred to as a lower bound or minorant of S.
Let,
[tex]M = \frac{p-2b}{2} \\p = 68.3\\b = 8.7[/tex]
We have to find the lower bound for M.
Plug the values of p and b in the given equation.
[tex]M = \frac{68.3 - 2(8.7)}{2}\\ M = \frac{68.3 - 17.4}{2} \\M = \frac{50.9}{2}\\ M = 25.45[/tex]
Hence, the lower bound for M is 25.45.
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WILL GIVE 50 POINTS PLEASE HELP
Which gives the correct values for points A, B, C, and D?
A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. Point A is at negative 2. Point B is 1 mark to the right of negative 2. Point C is 1 mark to the left negative 1. Point D is 1 mark to the left of 0.
A = negative 2, B = negative 1 and three-fourths, C = negative 1 and one-fourth, D = negative one-fourth
A = negative one-fourth, B = negative 1 and three-fourths, C = negative 1 and one-fourth, D = negative 2
A = negative 2, B = negative three-fourths, C = negative one-fourth, D = one-fourth
A = negative one-fourth, B = negative 1 and one-fourth, C = negative 1 and three-fourths, D = negative 2
Answer:
The correct values for points A, B, C, and D on a number line going from negative 2 to positive 2 in increments of 1 are:
A = negative 2
B = negative 3/4
C = negative 1/4
D = 1/4
This can be determined by noting that each mark on the number line represents a distance of 1/4, and by counting the number of marks to the right or left of the given points. For example, point B is 1 mark to the right of negative 2, which means it is located at negative 2 + 1/4 = negative 3/4. Similarly, point C is 1 mark to the left of negative 1, which means it is located at negative 1 - 1/4 = negative 1/4. The other points can be determined in the same way.
Step-by-step explanation:
Answer:
It is A the 1st one
Step-by-step explanation:
A = negative 2, B = negative 1 and three-fourths, C = negative 1 and one-fourth, D = negative one-fourth
Are the following two functions inverses of one another ? Use function composition to determine your answer
Answer:
Step-by-step explanation: No f(x) is not an inverse of g(x)
1 pts the number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day. a random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. describe the sampling distribution of the sample mean
The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day centered around population mean.
This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.
1. The number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day.
2. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated.
3. The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day.
4. This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.
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can somebody please help me this is the last question to pass this class and i need it by 11:59 pls i’ll give brainiest
Answer:
Step-by-step explanation:
To solve use tangent(63) to solve for x
tan(63)=x/90
Multiple by sides by 90
90tan(63)=x
x=176.6
Answer:
176.6
Step-by-step explanation:
tan(63°) = x/90
1.962 • 90 = 176.58
When I round to the nearest tenth I get 176.6
I hope this helps:)
the number of cells of a certain type of bacteria increase continuously at a rate equal to two more than three times the number of bacteria present. if there are 10 present at the start and 42 present t hours later, what is the value of t?
The time take would be 1 hour and 18 minutes
What is Linear Equation in One Variable?
Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable).
Solution:
Given: Growth rate of bacteria = (3*I + 2)*t
I is the Initial Number of Bacteria
t is the time in hours
So,
42 = (3*10 + 2)t
42 = 32*t
t = 1.3 hours
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a total of shows when we roll two fair dice. a. find the probability of the given event. b. find the odds against the given event.
The probability of the given event is 1/9.
The odds against the event are 8 to 1.
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 proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
When we roll 2 dice, then
Sample space i. e possible outcomes are
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(S) = 36
Let A be the event of getting a total of 5.
Therefore,
A = {(1, 4), (2, 3), (3, 2), (4, 1)}
⇒ n(A) = 4
⇒ P(A) = Probability of A = n(A) / n(S) = 1 / 36 = 1/9
(a) Probability of given event = 1/9
(b) Odds against the event = 1- P(A) / P(A)
= (1 - 1/9) / (1/9)
= (8/9) / (1/9)
= 8/9 x 9/1
Odds against the event = 8/1
The reduced odds against the event are 8 to 1.
Hence, the probability of the given event is 1/9.
The odds against the event are 8 to 1.
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it takes exactly 26 paper clips laid end to end to make a length of 17 7/8 inches estimate the length of each paper clip
The estimated length of each paper clip is 0.6785 inches.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, it takes exactly 26 paper clips laid end to end to make a length of [tex]17\frac{7}{8}[/tex] or (17×8 + 7)/8 = 143/8 inches.
∴ The length of each clip is (143/8)/26 inches.
= 0.6785 inches.
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Select the correct choices to complete the sentence.
Reggie bought 40 tokens to use at a family fun center. He used some of the tokens to ride go-carts and use the batting cages. He now has 28 tokens left. What is the percent of decrease in the number of tokens? Round to the nearest tenth percent if necessary.
The percent of decrease in the number of tokens is 30%.
What is the percent of decrease in the number of tokens?From the information illustrated, Reggie bought 40 tokens to use at a family fun center. He used some of the tokens to ride go-carts and use the batting cages. He now has 28 tokens left.
The number used will be:
= 40 - 28
= 12
Therefore, the percentage decrease will be:
= Number used / Total tokens × 100
= 12 / 40 × 100
= 30%
The percentage is 30%.
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Which is NOT an ordered pair??
The ordered pair which does not satisfy the equation f ( x ) = ( 1/2 ) x - 7 is
A ( 2 , 8 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = ( 1/2 ) x - 7
The value of f ( x ) = y
So , the ordered pair will be of the point A ( x , y )
a)
( 1 , -6 1/2 )
The value of the point A ( x , y ) = A ( 1 , -6 1/2 )
So , the equation is f ( x ) = ( 1/2 ) x - 7
Substitute the value of x and y in the equation , we get
y = ( 1/2 ) x - 7
-6 1/2 = ( 1/2 ) 1 - 7
-6 1/2 = 1/2 - 7
-6 1/2 = -6 1/2
Therefore , the ordered pair A ( 1 , -6 1/2 ) satisfies the equation
b)
( 2 , 8 )
The value of the point A ( x , y ) = A ( 2 , 8 )
So , the equation is f ( x ) = ( 1/2 ) x - 7
Substitute the value of x and y in the equation , we get
y = ( 1/2 ) x - 7
8 = ( 1/2 ) 2 - 7
8 = 1 - 7
8 ≠ -6
Therefore , the ordered pair A ( 2 , 8 ) does not satisfy the equation
c)
( -2 , -8 )
The value of the point A ( x , y ) = A ( -2 , -8 )
So , the equation is f ( x ) = ( 1/2 ) x - 7
Substitute the value of x and y in the equation , we get
y = ( 1/2 ) x - 7
-8 = ( 1/2 ) ( -2 ) - 7
-8 = -1 - 7
-8 = -8
Therefore , the ordered pair A ( -2 , -8 ) satisfies the equation
d)
( 0 , -7 )
The value of the point A ( x , y ) = A ( 0 , -7 )
So , the equation is f ( x ) = ( 1/2 ) x - 7
Substitute the value of x and y in the equation , we get
y = ( 1/2 ) x - 7
-7 = ( 1/2 ) ( 0 ) - 7
-7 = 0- 7
-7 = -7
Therefore , the ordered pair A ( 0 , -7 ) satisfies the given equation
Hence , the ordered pair A ( 2 , 8 ) does not satisfy the equation
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What integer describes 50 feet below the sea level?
Answer:
Step-by-step explanation:
-50 since an integer is the opposite of a whole number positive or negative.
Answer: -50
Step-by-step explanation:
Use substitution to determine whether the given ordered pairs are solutions of the given equation.
Is the ordered pair
Part 1 of 2
:7a+8b=3
O Points: 0 of 1
a solution of the equation 7a+8b=3? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
For the given pair of equations, the given ordered pair does not represent the solution.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is the equation -
7a + 8b = 3
For [a] = 0 and [b] = 1, we can write -
7 x 0 + 8 x 1 = 3
8 ≠ 3
Therefore, the points does not represent the solution to the equation given.
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How do you enlarge by a scale factor of 1?
To enlarge a figure by scale factor of 1 , multiple the coordinates of pre-image by 1 though scale factor 1 won't affect anything .
Scale factor is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It is the ratio of the sizes of the original figure with the dilated figure.
The scale factor can either increase the size of an object or decrease the size of an object.
The basic formula:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
Enlarging a shape means to change its size. To enlarge a shape, multiply all lengths of the shape by the scale factor. The scale factor tells us how many times larger the shape will be.
When the scale factor is 1 , a copy of a pre-image form . No, change in the image will happen . You will produce you an original image.
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A health club charges a one-time sign-up fee and a monthly membership fee. The equation y=57x+30y=57x+30 represents what the health club charges. Find the rate of change.
The required rate of change for the given equation is 57.
What is the rate of change?
A measure of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.
For the given equation,
Health club charges a one-time sign-up fee and a monthly membership fee
y = 57x +30
So, the rate of change, [tex]\frac{dy}{dx}[/tex] = 57
hence, the required rate of change for the given equation is 57.
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You make a rectangular quilt that is 5 feet by 4 feet. You use the remaining 10 square feet of fabric to add a border of uniform width to the quilt. What is the width of the border?.
Answer:
0.5ft
Step-by-step explanation:
price of two games in ratio a:b. If both prices decreased by £10, ratio = 3:5. If both prices increase by £5, ratio = 3:4. Work out ratio a:b.
The ratio of a: b is = 5:7
The price of the two games are in the ratio a:bWhen the prices are both decreased by £10, the ratio becomes 3:5When the prices are both increased by £5, the ratio becomes 3:4
Here the ratio is a:b
When the prices are both decreased by £10, the new ratio
= a-10 : b-10
When the prices are both increased by £5, the new ratio
= a+5 : b+5
By the given conditions,
a-10 : b-10 = 3:5
or, [tex]\frac{a-10}{b-10\\}[/tex] =[tex]\frac{3}{5}[/tex]
or, 5(a-10) = 3(b-10)
or, 5a -50 = 3b-30
or, 5a -3b = 20 .... ...(1)
and a+5 : b+5 =3 : 4
or,[tex]\frac{a+5}{b+5}[/tex] = [tex]\frac{3}{4}[/tex]
or, 4(a+5) = 3(b+5)
or, 4a +20 = 3b+15
or, 4a-3b= -5 .... ...(2)
subtract the equation(2) from equation(1)
5a -3b - (4a -3b) =20 - (-5)
or, 5a-3b-4a+3b = 20+5
or, 5a-4a = 25
Therefore, a =25
Putting a=25 in equation (1), we get
125-3b=20
or, 3b= 105
therefore, b=35
a :b =25:35
= 5:7
Hence, the ratio of a: b = 5:7
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rom a club of 12 people, in how many ways can a group of two members be selected to attend a conference?
Answer:
66
Step-by-step explanation:
[tex]\binom{12}{2}=\frac{12!}{10!21}=\frac{12 \cdot 11}{2}=66[/tex]
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In a game, the probability of winning is 20%. If i play 48 times, how many times should I expect to win?
Answer: 20/48=0.416 repeat
Step-by-step explanation: All I know for probability is you divide the chances of winning by total number of chances winning. Example if you by one panthers hockey ticket with 100 of other panthers hockey tickets being sold the probability is 1/100. I hope this helps