The probability that:
a dictionary is selected = [tex]\frac{1}{9}[/tex]two novels and a book of novels is selected = [tex]\frac{5}{14}[/tex]What is probability?Probability refers to the possibility of the occurrence of an event.
P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]
Now,
(a) Total number of books = 5 + 3 + 1 = 9
Probability of getting a dictionary = [tex]\frac{1}{9}[/tex]
(b) Number of ways to select 3 books out of 9 books = [tex]\binom{9}{3}[/tex] = [tex]\frac{9!}{3!(6!)} = \frac{9\times\ 8 \times 7}{6}[/tex] = 84
Number of ways to select 1 out of 3 books of poems = [tex]\binom{3}{1} = \frac{3!}{2!}[/tex] = 3
Number of ways to select 2 out of 5 novels = [tex]\binom{5}{2} = \frac{5!}{2! 3!} = \frac{5\times 4}{2} = 10[/tex]
Thus, the probability of getting 2 novels and 1 book of poem = [tex]\frac{3\times10}{84} = \frac{10}{28} = \frac{5}{14}[/tex]
To learn more about probability, refer to the link: https://brainly.com/question/25870256
#SPJ4
(COMPLETE QUESTION:
If three books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) a dictionary is selected? (b) 2 novels and 1 book of poems are selected?)
12 1/2 divided by 5 1/2
Answer:
25/11
Step-by-step explanation:
Convert to improper fractions
25/2 ÷ 11/2
take reciprocal of divisor and multiply
25/2 x 2/11
50/22
25/11
jamie and imani each play softball. imani has won 5 fewer games than jamie. is it possible for jamie to have won 11 games if the sum of the games imani and jamie have won together is 30? yes; jamie could have won 11 games because 2x − 5
The total number of games won by Jamie is not 11 according to the conditions given in the question.
What is an equation?
The equation is illustrated as a mathematical statement having an equal symbol in between two expressions, '='. It depicts that both sides of the equal sign are equal to each other.
Calculation of the number of games played by Jamie
Let us assume that x and y be the number of games that Jamie and Imani have won
According to the question, Imani has won 5 fewer games than Jamie i.e.
y = x - 5 —-- 1
The total number of games won by Jamie and Imani together is 30
x + y = 30
Using equation 1, put the value of y,
x + x - 5 = 30
2x - 5= 30
Now, substitute x by 11, and we get that the equality does not net
Thus, we can conclude that 11 is not the number of games won by Jamie
Hence, the total number of games won by Jamie is not 11 using the given equations.
To learn more about the equations, visit here:
https://brainly.com/question/13763238
#SPJ4
Directions Round each amount to the nearest cent, dime and dollar
1. $32.518
Answer:
$32.52
Step-by-step explanation:
Hope it helps! =D
i need help with thisxx
Using translation concepts, we have that:
The x-coordinates in the image are the opposite of the y-coordinates in the pre-image.The y-coordinates in the image are the same as the x-coordinates of the pre-image.Therefore, the triangle was rotated clockwise 270º about the origin.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the vertices of the pre-image are given as follows:
D(-5,2), E(1,5), F(0,-1).
The vertices of the transformed image are given by:
D'(-2, -5), E'(-5,1), F(1,0).
From this, we the rule is given by:
(x,y) -> (-y,x).
Which is equivalent to the rotation rule of a rotation of 270º clockwise.
Hence:
The x-coordinates in the image are the opposite of the y-coordinates in the pre-image.The y-coordinates in the image are the same as the x-coordinates of the pre-image.Therefore, the triangle was rotated clockwise 270º about the origin.More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
A small airplane flew 104 miles in 50 minutes.at this rate,how many miles can it fly in one hour? (50 minutes = 5/6 hour)
Answer:
124.8 miles
Step-by-step explanation:
We know that if the rate of change of distance with respect to time remains constant, then the distance and time are proportional .Given : A small airplane flew 104 miles in 50 minutes. Let x be the distance traveled in 1 hour. Also, it is given that Then we have the following proportional equation:-
Hence, it can fly 124.8 miles in an hour.
Under her cell phone plan, Violet pays a flat cost of $38 per month and $3 per gigabyte. She wants to keep her bill under $80 per month. Which inequality can be used to determine xx, the maximum number of gigabytes Violet can use while staying within her budget? A) 80>3x+38 B) 80>3(38+x) C) 80<3x+38 D) 80<3(38+x)
the inequality is:
$38 + $3*x < $80
And the solution is:
x < 14.
How to find the inequality?We know that Violet's plan has a flat cost of $38 plus $3 per gigabyte.
So, if we define x as the number of gigabytes that Violet uses, then the monthly cost is given by:
C(x)= $38 + x*$3
And she wants to spend less than $80 per month, so we can write the inequality:
$38 + $3*x < $80
Solving that for x we get:
$3*x < $80 - $38 = $42
x < $42/$3
x < 14
We conclude that she needs to use less than 14 gigabytes per month.
If you want to learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
Pls pls help whoever gets it right gets a crown
Answer:
[tex]\frac{15}{56} a^2[/tex]
Step-by-step explanation:
Harry tosses a nickel 4 times. The probability that he gets at least as many heads as tails is.
The answer is 4/8 or 1/2 or 0.5 or 50%
Step-by-step explanation:
A nickel has two faces, heads and tails
Equation of probability = Number of chances/Total Numbers of chances
So, 4 chances of heads / 8 chances of heads or tails, thus, there is a chance of 50% if Harry tosses the coin 4 times to get a head
In the following diagram MATH is a rectangle with an inscribed circle. The circle has a diameter of 8 centimeters and the rectangle has a height of 12 centimeters
What is the most specific name for the figure? I NEED THE ANSWER
Answer:
D. Rhombus
Step-by-step explanation:
The most specific name for this figure is a rhombus.
Hope this helps!
Please mark as brainliest if correct!
MatemáticasJavier pagó $92 por 5 libretas y 3 lápices. Laura compró 2 libretas y 6 lápices, y pagó $56, ¿cuál es el
precio de cada libreta y de cada lápiz?
A) $11 por una libreta y $5 por un lápiz.
B)
$13 por una libreta y $9 por un lápiz.
C)
$16 por una libreta y $4 por un lápiz.
D) $10 por una libreta y $6 por un lápiz.
If Javier paid $92 for 5 notebooks and 3 pencils and Laura paid $56 for 2 notebooks and 6 pencils, then the price of each notebook is $16 and that of each pencil is $4, calculated using linear equations.
As per question statement, Javier paid $92 for 5 notebooks and 3 pencils while Laura paid $56 for 2 notebooks and 6 pencils.
We are required to calculate the price of each notebook and each pencil.
To solve this question, let us assume that the price of each notebook is "x" and that of each pencil is "y". Now, we will form two linear equations, each with the two assumed variables, based on the conditions mentioned in the question statement, and solving the equations, we will obtain our desired answer.
Since Javier bought 5 notebooks and 3 pencils for $92 and the price of each notebook is assumed to be "x" and that of each pencil is assumed to be "y", we can write that
[tex][(5x+3y)=92]...(1)\\or,5x = 92-3y\\or,x=\frac{(92-3y)}{5}...(2)[/tex]
And in Laura's case, she bought 2 notebooks and 6 pencils for $56, i.e.,
[tex][(2x+6y)=56]...(3)\\or, 2(x+3y)=56\\or, (x+3y)=\frac{56}{2}\\ or,(x+3y)=28\\or,x=(28-3y)...(4)[/tex]
Now, equating (2) and (4), we get,
[tex]x=\frac{(92-3y)}{5}=(28-3y)\\ or, \frac{(92-3y)}{5}=(28-3y)\\ or, (92-3y)=5(28-3y)\\or, 92-3y=140-15y\\or,(15y-3y)=140-92\\or,12y=48\\or,y=\frac{48}{12}=4[/tex]i.e., Price of each pencil is $4.
Now, using (y = 4) in the equation (4), we get,
[tex]x=[28-(3*4)]\\or,x=(28-12)\\or,x=16[/tex]i.e., Price of each notebook is $16.
Hence, the correct answer is
option(C) $16 for a notebook and $4 for a pencil.
linear equations: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and hence comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.Variable: n Mathematics, a variable is a symbol or a representative of a value, which is unknown.To learn more about Linear Equations, click on the link below.
brainly.com/question/27664510
#SPJ9
What power of 7 is 40 353 607?
Answer:
[tex] {} {7}^{x} = 40353607[/tex]
[tex]x = log_{7}(40353607) [/tex]
[tex]x = 9[/tex]
The diagram shows a rectangle.
The area of the rectangle is 12b²-30b
Write an expression for
a
b
the length of the rectangle
the perimeter of the rectangle.
6b
A
length
N
Answer: The diagram shows a rectangle.
The area of the rectangle is 12b²-30b long a+b+a your answer is aStep-by-step explanation:
A rectangle Expression for "a": a = 12b - 30,Expression for "b": b = (12b² - 30b) / (12b - 30),Length of the rectangle: Length = a = 12b - 30,Perimeter of the rectangle: Perimeter = 2 × (13b - 30)
Let's break down the given information step by step:
The area of the rectangle is given as 12b² - 30b.
The expression for "a":
The area of a rectangle is equal to its length (a) multiplied by its width (b). So, set up the following equation:
Area = Length ×Width
12b² - 30b = a × b
To find the expression for "a," divide both sides of the equation by "b":
a = (12b² - 30b) / b
Simplify the expression for "a":
a = 12b - 30
The expression for "b":
From the same equation as above, that:
Area = Length × Width
12b² - 30b = a × b
To find the expression for "b," divide both sides of the equation by "a":
b = (12b² - 30b) / a
Substitute the value of "a" from the previous expression:
b = (12b² - 30b) / (12b - 30)
The length of the rectangle:
The length of the rectangle is represented by "a," so the expression for the length is: a = 12b - 30
The perimeter of the rectangle:
The perimeter of a rectangle is given by the formula: Perimeter = 2 ×(Length + Width)
Since the rectangle has two pairs of equal sides (opposite sides are equal in a rectangle), the expression for the perimeter will be:
Perimeter = 2 × (a + b)
Substitute the value of "a" from the expression we found earlier:
Perimeter = 2 × ((12b - 30) + b)
Simplify the expression for the perimeter:
Perimeter = 2 ×(13b - 30)
To know more about rectangle here
https://brainly.com/question/15019502
#SPJ2
Which of the following is equivalent to the expression 6z - 9?
A. The quotient of 6 times a number z and 9
B. 6 times the difference of a number z and 9
C. 6 less than the product of 9 and a number z
D. 9 less than 6 times a number z
Answer:
c is the correct answer!
A collector has a box of 32 figurines. The value of each figurine increased by $2.32 over the past year. The box of figurines is now worth $114.24. What was the original cost, x, of one figurine? The original cost of one figurine was . Convince Me! Can the equation 32x + 2.32 = 114.24 be used to find the original cost of each figurine in the problem above? Explain.
Answer:
Step-by-step explanation:
$1.94.Step-by-step explanation:Initial box of figurine = 32Price increase = 2.32Current worth = $144.24Let x be the initial cost of boxes of figurine. (32 * x) * 2.32 = $144.24.74.24x = $144.24.x = $144.24/74.24= $1.94.Therefore the original cost of the box of figurine is $1.94.
When 18 is subtracted from six times a certain number, the result is − 42. What is the number?
Answer: the unknown number is -4.
Step-by-step explanation:
Hope this helps!
Answer:
-4
Step-by-step explanation:
6x-18=-42
6x=-42+18
6x=-24
x=-24/6
x=-4
Elementary and middle school groups typically run for __________, depending on administrator and teacher support for allowing students to miss class for the group sessions.
Elementary and middle school groups typically run for 6 to 8 weeks, depending on administrator and teacher support for allowing students to miss class for the group sessions.
What is elementary education?
Elementary education, can as well be described as the primary education, which is the first stage of education that is followed in the traditional formal education, children at about age 5 to 7 are those that are usually found in the elementary seetings of school.
Its should be noted that Elementary and middle school groups typically run for 6 to 8 weeks, depending on administrator .
Learn more about Elementary School on:
https://brainly.com/question/25887038
#SPJ4
What is −10 + |−4| − |−12|?
−6
−12
−18
−22
Answer:
24
Step-by-step explanation:
3/8 × 11=
3/4 × 2 =
.
[tex]{ \bold{(i)}} \: { \blue{ \tt{4.125}}}[/tex]
[tex]{ \bold{(ii)}} \: { \blue{ \tt{1.50}}}[/tex]
Step-by-step explanation:
[tex]{ \bold{(i)}} \: { \green{ \bold{ \frac{3}{8}}}} \times { \green{ \bold{11}}}[/tex]
[tex] = { \green{ \bold{0.375}}} \: \times \: { \green{ \bold{11}}}[/tex]
[tex] = { \red{ \tt{4.125}}}[/tex]
[tex]{ \bold{(ii)}} \: { \green{ \bold{ \frac{3}{4}}}} \: \times \: { \green{ \bold{2}}}[/tex]
[tex] = { \green{ \bold{0.75}}} \: \times \: { \green{ \bold{2}}}[/tex]
[tex] = { \red{ \tt{1.50}}}[/tex]
which expressions can we use to describe how many more seconds tatenda spends than ciara spends mowing lawns during 4 weeks?
The expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks is 4(700t- 750c) .
What is an expression in math example?
2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient, or a value multiplied by the variable. The number 2 is the coefficient of x in the formula 2x + 3, which indicates 2 times x plus 3.time taken by tatenda to mow a square meter of lawn = t seconds
time taken by Ciara to mow a square meter of lawn = c seconds
area mowed by tatenda in a week = 700 square meters
area mowed by Ciara in a week = 750 square meters
the expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks
time taken by tatenda for mowing in 4 weeks = 4 * 700 * t seconds
time taken by Ciara for mowing in 4 weeks = 4 * 750 * c seconds
more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks = [4 * 700 * t ] - [4 * 750 * c]
= 4(700t- 750c)
Therefore, the expression used to calculate how many more seconds Tatenda spends than Ciara spends mowing lawns during 4 weeks is 4(700t- 750c).
Learn more about mathematical expression
brainly.com/question/14462529
#SPJ4
Previous 40 Question 1 Find and interpret the mean absolute deviation of the data. 24, 26, 28, 28, 30, 30, 32, 32, 34,36
The mean absolute deviation of the data is 0
The mean absolute deviation of given data is 0.Given that
The data from question:24, 26, 28, 28, 30, 30, 32, 32, 34,36
To find
the mean absolute deviation of the data.So, according to the question
We have,
The data from question:24, 26, 28, 28, 30, 30, 32, 32, 34,36
The mean of that data[tex]mean = \frac{sum\;of\;data}{number\;of\;data}[/tex]
= [tex]\frac{24+26+ 28+ 28+ 30+30+ 32+ 32+ 34+36}{10}[/tex]
= [tex]\frac{300}{10}[/tex]
mean of data = 30
For mean absolute deviation of the data, first we have to find the difference of each data value from mean of data.
So,
24 - 30 = -6
26 - 30 = -4
28 - 30 = -2
28 - 30 = -2
30 - 30 = 0
30 - 30 = 0
32 - 30 = 2
32 - 30 = 2
34 - 30 = 4
36 - 30 = 6
The sum of data after subtracting it's mean∑D = | (-6-4-2-2+0+0+2+2+4+6) |
∑D = 0
The mean absolute deviation of the data,MAD = [tex]\frac{The \;sum \; of \; data \;after \; subtracting \;it's \;mean }{number \;of \;data}[/tex]
MAD = [tex]\frac{\sum D}{10}[/tex]
MAD = [tex]\frac{0}{10}[/tex] = 0
the mean absolute deviation of the data = 0.
To learn more about mean please click on the link:
https://brainly.com/question/10528201
#SPJ9
a basketball player recorded the number of baskets he could make depending on how far away he stood from the basketball net. the distance from the net (in feet) is plotted against the number of baskets made as shown below.
If a player is standing 10 feet from the net, he could make approximately option (b) 5 baskets.
What is Distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.A basketball player recorded the number of baskets he could make depending on how far away he was standing from the net.
The distance from the net in feet is plotted against the number of baskets made.
Now, we see from the graph that when the distance from the net in feet is 10, the ordinate of the point is 5.
So, he could make approximately 5 baskets.
So, the answer is
Using the best fit line, if a player is standing 10 feet from the net, he could make approximately option (b) 5 baskets.
Learn more about distance
brainly.com/question/18246609
#SPJ4
The complete question is -
A basketball player recorded the number of baskets he could make depending on how far away he stood from the basketball net. The distance from the net (in feet) is plotted against the number of baskets made as shown below. Distance from Net vs. Number of Baskets 25 20 15 . Number of Baskets 10 5 0 0 2 10 12 4 6 8 Distance from Net (feet) Using the best-fit line, approximately how many baskets can the player make if he is standing ten feet from the net?
Plsssss helppp 20 points HELPP
a 5-letter password is to be constructed from the following letters: {a, b, c, d, e}. the password must contain exactly 3 of the letters. (obviously at least one of them will need to be used more than once to create a 5-letter password.)
If A,B, and C are the letters selected and we use A twice, B twice, and C once. The number of ways different passwords exist in this scenario are 30.
What is a password?
A password, sometimes known as a passcode (in devices made by Apple, for instance), is a hidden piece of information that is typically a long string of characters and is used to verify a user's identity. Passwords were always thought to be memorized, but today's average person has access to a huge number of password-protected services, making it difficult to remember a different password for each one. The secret is kept by a party known as the claimant, and the person confirming the claimant's identity is known as the verifier, according to the nomenclature of the NIST Digital Identity Guidelines. The verifier can determine the identity of the claimant when the claimant successfully uses a recognized authentication technique to show the verifier that they know the password.
A, B and C are selected
A is used twice B is used twice and C is once
Total ways = 5!/2!.2! = 30
To learn more about password ,visit:
https://brainly.com/question/14580131
#SPJ4
write the equation of each line in slope-intercept form. then graph the line described by the equation
passes through (5,-4) and (-6,5)
(the question is number 6)
Proof diagram (50 points)!
Use the proof diagram to complete the question. State the missing reason in this proof for the letter given
The converse of corresponding angles theorem that proves that p║r is stated in the proof explained below (see proof below).
What is the Converse of Corresponding Angles Theorem?If two corresponding angles are congruent to each other, the converse of the corresponding angles theorem states that the lines on which both corresponding angles lie are parallel to each other.
What is the Vertical Angles Theorem?The vertical angles theorem is the theorem that justifies that when two angles are vertically opposite to each other, then they are congruent angles.
Given that, angle 1 is congruent to angle 5, to prove that lines p and r are parallel to each other, the statements and reasons stated below explains why they are parallel lines:
Statement Reason
1. <1 ≅ <5 Given
2. <4 ≅ <1 a. vertical angles theorem
3. <4 ≅ <5 b. transitive property
4. p║r c. converse of corresponding angles
theorem
Therefore, the converse of corresponding angles theorem that proves that p║r is stated in the proof explained above.
Learn more about the converse of corresponding angles theorem on:
https://brainly.com/question/7066290
#SPJ1
What is the slope of the line shown in the graph?
Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]
for the data in the excel file grade point averages, find 90%, 95%, and 99% confidence intervals for the mean gpa. compute the confidence intervals using the appropriate formulas and verify your results using the excel confidence intervals template.
The labels in the spreadsheet are in column B, while the score values are in column A. Column C's cells are where the command operations take place. The test results are distributed between 82.516 and 87.85 by adding and subtracting the test score confidence value of 2.667 from the mean of 85.183. Excel instantly translates the formula to the result when you enter the command functions and press "Enter," giving the confidence level of 97% given the alpha value of 0.03, or 3%.
What is excel confidence interval function ?The Excel Statistical Functions section contains the CONFIDENCE Function. The confidence interval for a population mean will be calculated using the normal distribution, and it will then be returned. For financial analysis, Excel's confidence interval tool is quite helpful. That enhances financial decision-making by enabling financial analysts to anticipate and adjust for a variety of financial goals. To do this, financial data is graphically represented together with a set of distribution parameters. Based on the statistical data offered by the normal distribution, analysts can make better financial decisions. For example, they can determine the relationship between revenue made and income spent on luxuries.
To know more about excel confidence interval function, visit:
https://brainly.com/question/14601622
#SPJ4
Determine if the lines are parallel, perpendicular or neither.
y= -4x - 2 and 12x + 3y = 27
Predict whether atoms of chlorine or atoms of sulfur would be more likely to attract electrons and, therefore, be more reactive. Explain your reasoning.
Chlorine will be more reactive.
Reactivity of elementsFrom the question, we are to predict whether the atoms of chlorine or atoms of sulfur would be more likely to attract electrons
The electronic configuration of chlorine (Cl) is
2,8,7
This means Cl needs only one electron to complete its octet configuration
and
The electronic configuration of sulfur (S) is
2,8,6
This means sulfur needs two more electrons to complete its octet configuration
Since chlorine needs fewer electrons to complete its octet configuration, then it will be more likely to attract electrons.
Thus, chlorine will be more reactive.
Learn more on Reactivity of elements here: https://brainly.com/question/23767405
#SPJ1