The number of books each boy had based on the 3:1 ratio of the books remaining is 34 books
What is a ratio?A ratio is a quantitative expression of the relationship between two values that indicates the relative proportion of each amount.
The initial number of books Ben had = The initial number of books Charlie has
The number of books Ben gave away = 16 books
The number of books Charlie gave away = 28 books
The ratio of the number of books Ben and Charlie had left is 3:1
Let x represent the number of books each of them initially have. Representing the numbers as a ratio gives;
The number of books Ben had left = x - 16
The number of books Charlie had left = x - 28
[tex]\dfrac{x - 16}{(x - 16) + (x - 28)} = \dfrac{3}{3+1}[/tex]
Which gives; [tex]\dfrac{x - 16}{(2\cdot x - 44) } = \dfrac{3}{4}[/tex]
4 × (x - 16) = 3 × (2·x - 44)
6·x - 4·x = 3×44 - 4×16 = 68
2·x = 68
x = 68 ÷ 2 = 34
The number of books each boy had at first = 34 booksLearn more about ratios here:
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(x+2)(x+3)(x+4) can be written in the form [tex]x^{3}[/tex] + a[tex]x^{2}[/tex] + bx c where a, b and c are positive integers.
Work out the values of a, b and c.
a = (Answer here) (1)
b = (Answer here) (1)
c = (Answer here) (1)
Answer:
a = 9 ; b = 26 ; c = 24
Step-by-step explanation:
(x^2+3x+2x+6)(x+4)
(x^2+5x+6)(x+4)
x^3+5x^2+6x+4x^2+20x+24
x^3+9x^2+26x+24
Solve the equation 750 +0.05x = 1,100+ 0.025x for x.
O x = 140
O x = 350
O x = 1,850
O x = 14,000
Answer:
a
Step-by-step explanation:
The value of x will be; x = 14,000
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that the equation 750 +0.05x = 1,100+ 0.025x
Here, we need to solve for x;
750 +0.05x = 1,100+ 0.025x
combine the like terms;
750 - 1,100= -0.05x + 0.025x
-350 = - 0.025x
x = 14,000
Therefore, the solution will be as;
x = 14,000
The value of x will be; x = 14,000
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Factorise
(a) 4ab + 6abc + 8ac
(b) 9x2y + 6xy - 15xy²
(c) 10ab²-8ab + 2a²b
(d) 6xy - 7x²y + 3xy²
a study by tourism ontario revealed that 50% of the vacationers going to toronto visit the cn tower, 40% visit skydome and 35% visit both. what is the probability that a vacationer will visit at least one of these magnificent attractions?
0.55 is the probability that a vacationer will visit at least one of these magnificent attractions.
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
Calculation50% of the vacationers going to toronto visit the CN tower= 0.5
40% visit skydome= 0.4
35% visit both=0.35
P( At lease one) = P(Toronto) + P(Skydome) - P(Both)
P( At lease one) = 0.4 + 0.5 - 0.35
P( At lease one) = 0.55
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What is an equation of the line that passes through the points (-7, 3) and (5, 3)?
the equation of the line passing through the given points is y = 3
What is an equation of the line?
An expression which is satisfied by every point on the line is known as equation of the line. generally it is given in y = mx + c form where m is the slope and c is the y-intercept
We are given two point (-7,3) and (5,3)
We first find the slope of the lines passing through the given points
Slope = [tex]\frac{3-3}{5+7}[/tex]
Slope = 0
Substituting the value in the equation we get
y = c
Now the value of y in both the cases is 3
Substituting that we get c = 3
Hence y = 3 is the required equation of the line
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Line K is represented by the equation y = -3/2x + 1. Line L is perpendicular to line K and passes through the point (6,2). Determine the equation is line L.
Answer:
y = (2/3)y - 2
Step-by-step explanation:
Linear equations of the form y=mx+b, describe the slope, m, and the y-intercept, b (the value of y when x=0).
Line K
y = -(3/2)x + 1 tells us that it has a slope of -(3/2) and crosses the y axis (x=0) at y = 1.
Perpendicular Lines
Perpendicular lines have a useful property in that they have a slope that is the "negative inverse" of the line they are perpendicular to. If, for example, we were ever asked what is the slope of a line perpendicular to Line L (yes, it happens), we could, with minimal effort, respond "It is the negative inverse of -(3/2)," which is a slope of (2/3).
Line L
We just accidently answered a key question when we found the negative inverse of the slope for Line K, (2/3). That will be the slope of Line L that will make it perpendicular to Line K.
Line L will have the form y = (2/3)x + b
This line will be perpendicular to Line K, no matter the value of b. But we want a perpendicular line that goes through point (6,2), so we need to find a value of b that will force it to go through that point.
The role b has in our equation is simply moving it up or down. If b were 0, the line will go through the origin (0,0). If b were 5, it would interect the y axis at 5 (0,5). We could draw a graph and get a pretty good idea what b would have to be for the line to go throgh (6,2), but most prefer the easier route: Use the (x,y) value in the above equation and solve for b. Its easy, and works great:
y = (2/3)x + b for (6,2)
2 = (2/3)(6) + b
b = 2 - (2/3)*(6)
b = 2 - 4
b = -2
The equation for Line L is thus: y = (2/3)y - 2
See the attached graph. Included are equations [marked Demo Line 1 and 2] with 2 random values of b (1 and 0), in order to:
demonstrate how b impacts the line, andsuggest try using DESMOS as a free online graphing tool.
A coin is weighted so that the probability of Heads is five times the probability of Tails. This coin is flipped
twice. What is the probability that both Heads and Tails are flipped?
A.5/36
B.8/25
C.5/24
D.None of the above
If a coin is weighted so that the probability of heads is five times the probabily of tails, that means :
+) P(head) + P(tail) = 1
+) P(head) = 5P(tail)
Therefore, P(head) = 5/6 ; P(tail) = 1/6
For both head and tail to be flipped, the events must happen together.
Therefore, we have the probabilty that both head and tail is flipped = 5/6 x 1/6 = 5/36.
Please help me (check the file attached)
According to the model, the value of -6(10b + 0.8) will be -60b - 4.8.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, this is illustrated as:.
= -6(10b + 0.8)
Open the parentheses
= -60b - 4.8
Therefore, the value is -60b - 4.8.
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Given in a plane the points A(-1,4),B(2,3),C(4,5),D(m,7)
Calculate m knowing that AB // CD
helppppp step by step
Answer:
m = -2
Step-by-step explanation:
slope of AB
(4-3)/(-1-2)= 1/-3 = -1/3
parallel lines have the same slope
slope of CD = -1/3
we can now find the line that passes through the point C
y-5= -1/3(x-4)
y = -1/3 x +4/3 +5
y = -1/3 x + (4+15)/3
y = -1/3 x + 19/3
this line must passes also through the point D
we know its y, so:
7 = -1/3 x + 19/3
(7 * 3) = (-1/3 x + 19/3) * 3
21 = - x + 19
x = 19 - 21
x = -2
3X + 4X - 2 = 12
Please help again I’m not very smart lol
[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]
Step-by-step explanation:
[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]
[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]
[tex]{ \red{ \sf{7x = 14}}}[/tex]
[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]
[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]
what is the probability that a couple will have at least four sons if they plan to have 5 children and if the probability of having a son equals the probability of having a daughter? (enter your probability as a fraction.)
0.1875 is the probability of having a daughter .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.Let X = No. of sons
n = 5 and p = 0.5, because probability of having son and daughter is same.
X follows Binomial distribution with parameter n and p. Then its pmf is,
P(X= x) = \binom{n}{x}p^xq^{(n-x)} \ \ \ \ \ x = 0,1,----5
Now,
P(X= 5) = \binom{5}{5}(0.5)^5 (0.5)^{(5-5)} \\ \\ \\ P(X= 5) = 0.03125
Probability of haveing at least four sons
P(X\ge4) = P(X=4) +P(X=5) \\\\ P(X\ge4) = 0.15625 + 0.03125 \\\\ P(X\ge4) = 0.1875
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Please help thank you
By comparing the fractions of rocks that skip over the poind for Jessica and Henry, we will see that Jessica gets more rocks to skip over the pond.
Who gets more rocks to skip over the pond?We know that for every 9 rocks that Herny throws, 5 skip over the pond. Then the fraction for Henry is:
H = 5/9
While for Jessica we know that for every 12 that she throws, 7 skip over the pond, so her fraction is:
J = 7/12
Now we only need to see which one of the fractions is larger.
If we simplify both we will get:
H = 5/9 = 0.556
J = 7/12 = 0.583
So we can see that Jessica's fraction is larger, which means that she will get more rocks.
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Drag the tiles to the correct boxes. Not all tiles will be used.
Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.
Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.
See photo below. Comment for more clarification.
The sequence below shows a certain company's expected net worth in millions of dollars after 1, 2, 3, 4 years, etc....
8.3, 10.4, 12.5, 14.6,...
Which function models the nth term of this sequence?
Responses
f(n) = 8.3 + 2.1nf(n) = 8.3 + 2.1n
f(n) = 8.3 − 2.1nf(n) = 8.3 − 2.1n
f(n) = 8.3 + 2.1(n+1)f(n) = 8.3 + 2.1(n+1)
f(n) = 8.3 + 2.1(n−1)
f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given,
The sequence below shows a certain company's expected net worth in millions of dollars after 1, 2, 3, 4 years, etc....
8.3, 10.4, 12.5, 14.6,...
The given sequence is a arithmetic sequence.
The first term is 8.3
The common difference is 2.1
The nth term of arithmetic sequence aₙ=a+(n-1)d
the nth term of this sequence=8.3+(n-1)2.1
f(n)=8.3+(n-1)2.1
Hence, f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.
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Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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how many 4-letter passwords can be formed using the letters a, b, c, d, e, f, g if repetition of letters is not allowed and the first letter can only be a, b or c?
840 are 4-letter passwords can be formed using the letters by permutation .
What are some examples of permutation?
A permutation is a set up of things in a specific order. In this arrangement, the components or components of sets are organized in a linear or sequential order. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. The components of set A cannot be arranged in any other way, as you can see.We are to count all possible 4-letter passwords that can be generated from the letters a, b, c, d, e, f, g .
There are 7 letters in total.
n = 7 r = 4
P(n , r ) = 7!/( n - r )!
P( 7 ,4 ) = 7!/( 7 - 4)!
= 7!/3!
= 7 * 6 * 5 * 4 * 3 * 2 * 1/3!
= 7 * 6 * 5 * 4
= 840
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what is 1/1/2 x 2/23
Answer:
1/23
Step-by-step explanation:
PLSSSS HELPPPPP MEEE !!!!!
All the angles in a triangle add up to 180 degrees.
40 + x + (5x + 14) = 180
54 + 6x = 180
6x = 126
x = 21 degrees
Answer:
x=21
Step-by-step explanation:
a triangle adds up to 180 degree so to find x we will use the formula
(5x+14)+x+40=180
subtract 40 from each side so we have
(5x+14)+x=140
we have 2 terms with the same factor (x) so combine like terms
6x+14=140
subtract 14 from both sides
6x=126
divide both sides by 6
x=21
check your answer
5(21)+14
105+14=119
119+ 21+40=180
so x is equal to 21
Linda had 45 fliers to post around town. Last week, she posted 1/3 of them. This week, she posted 3/5 of the remaining fliers. How many fliers has she still not posted?
Answer:
Step-by-step explanation:
The number of fliers that he has not posted is 9
What is proportion?
Proportion can be defined as the mathematical comparison of two elements or numbers.
From the information given, we have that;
• Total number of fliers is 45
• First week, 1/3 of the floors were posted
• This week, 3/5 of the remaining were posted.
To determine the number of fliers remaining, we have that;
Remaining fliers for the First week
= 45 × 1/3
Multiply and find the quotient
= 15 fliers
Fliers remaining after the last week
= 15 × 3/5
Multiply and find the quotient
= 45/5
= 9 fliers
Thus, the number of fliers the he has not posted is 9
Lin rode a bike 20 miles in 150 minutes. She rode at a constant speed. How long did it take her to ride 6 miles
Answer: 45 minutes
Step-by-step explanation:
She rides 150/20 minutes per mile which is 7.5 minutes per mile. So it would take her 45 minutes to ride 6 miles because 6 × 7.5 = 45.
3) an applicant for a job has to take an aptitude test. suppose that the time it takes to finish the test is normally distributed with mean time 69 minutes and standard deviation 8 minutes. determine how much time an applicant should be given so that 97 percent of them will be able to complete the test.
An applicant needs 84.04 minutes to finish the test in order for 97 percent of them to pass.
An aptitude test is required of job candidates. Let's assume that the test's completion time has a mean of 69 minutes and a standard deviation of 8 minutes.
To get how much time an applicant should be given so that 97 percent of them will be able to complete the test.
Mean (μ) = 69
standard deviation (σ) =8
Hence, due to population standard deviation (σ) is known to use the normal distribution.
x_ Norm (μ,σ)
x_ Norm (69,8)
Therefore, x_ random variable that represents the time of applicant;
P(X<x) = 0.97
Corresponding to the left tail area of 0.97 lies in the z-table of z row of 1.8 and column 0.08.
P(z < 1.88) = 0.97
z < 1.88
(X - μ)/σ < 1.88
X < 1.88 (8) + 69
X < 84.04
The time taken by an applicant so that 97 percent of them will be able to complete the test is 84.04 minutes.
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Does the relation shown in the diagram below represent a function? Explain why or why not
The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.
Given that,
In the picture we can see the domain and range.
We have to find if the domain and range is function or not.
Each of the sets of domain values has precisely one range value, according to the mapping.
Every domain value in a relation must have precisely one range value in order for it to be referred to as a function. It is not recommended to assign or map a domain value to more than one range value.
Therefore, The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.
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Which angles are congruent to <5
Answer:
1, 3, 7 (<5 is also congruent to <5, but this is not a choice.)
Step-by-step explanation:
The angles congruent to <5 are:
<1 by corresponding angles.
<3 by alternate interior angles.
<7 by vertical angles.
<5 by the theorem: congruence of angles is reflexive.
a catering company needs 8.75 lb of shrimp for a small party. they buy lb of jumbo shrimp,3 2 3 lb of medium-sized shrimp, and some mini-shrimp. how many pounds of mini-shrimp do they2 5 8 buy?
Finally, we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.
Given that;
A catering company needs 8.75 lbs of shrimp for a small party. they buy [tex]3\frac{2}{3}[/tex] lbs of jumbo shrimps, [tex]2\frac{5}{8}[/tex] lbs of medium-sized shrimps, and some mini-shrimps.
The total of 8.75th is changed as [tex]8\frac{3}{4}th\\[/tex]
Sum of [tex]3\frac{2}{3}[/tex] + [tex]2\frac{5}{8}[/tex] this is bought by the company.
So, to purchase the remaining [tex]8\frac{3}{4}th\\[/tex] - [tex]3\frac{2}{3}[/tex] - [tex]2\frac{5}{8}[/tex]
We use a common denominator of 24 for the fraction parts.
Change [tex]8\frac{3}{4}[/tex] as [tex]8\frac{18}{24}[/tex]
Similarly, convert;
[tex]3\frac{2}{3}[/tex] as [tex]3\frac{16}{24}[/tex]
[tex]2\frac{5}{8}[/tex] as [tex]2\frac{15}{24}[/tex]
By solving all the above conversions, we get;
[tex]\frac{42-16-15}{24}[/tex] = 11/24
Considering all the factors together we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.
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Sohan rolled a number cube 90 times. The outcome of ""6"" occurred 18 times. What is the experimental probability of rolling a 6?
The value of the experimental probability of rolling a 6 is found as 1/5.
Define the term experimental probability?A probability that has been established by a series of tests is called an experimental probability. To ascertain their possibility, a random experiment is conducted and iterated over a number of times; each iteration is referred to as a trial. The purpose of the experiment is to determine the likelihood that a particular occurrence will occur or not.For the given question-
Sohan made 90 turns of the number cube. There were 18 occurrences of the result of "6."Thus, by the definition of the probability-
Probability (getting 6) = number of occurred outcomes/ Total outcomes
Probability (getting 6) = 18/90
Probability (getting 6) = 1/5
Thus, the value of the experimental probability of rolling a 6 is found as 1/5.
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Which expression is equal to 6(r2 – 3) + 2(r2 + 1)?
8r squared - 20
6r squared -2
8r squared -16
6r squared +2r-16
pls, help 20 points!
Answer:8r squared -16
Step-by-step explanation:
what is the probability that you will receive at most 30 winning tickets? (round to four decimal places.) 0.5484 what is the probability that you will receive more than 30 winning tickets? (round to four decimal places.) 1 what is the probability that you will receive fewer than 10 winning tickets? (round to four decimal places.) 0.2206 what is the probability that you will receive at least 10 winning tickets? (round to four decimal places.
Normal distributions are frequently employed in the natural and social sciences to describe real-valued regressors with uncertain distributions, normal distributions are essential to statistics.
The central limit theorem is one reason they are significant.
This claim argues that, in some circumstances, the average of many samples (observations) of a random variable with finite variance and mean is itself a random variable, whose distribution tends to become normal with an increase in sample size.
Because of this, distributions of physical quantities that are meant to be the culmination of multiple separate processes, such as error margins, frequently resemble normal distributions.
Only the normal distribution has additional cumulants after the first two that are zero. It is also the continuous distribution with the highest level of entropy for a given mean and variance.
Assuming that the mean and variance are finite, Geary has shown that the normal distribution is the only distribution in which the mean and variance calculated from a collection of independent drawings are independent of one another.
The normal distribution is a form of elliptical distribution. The normal distribution is symmetric about its mean and non-zero over the whole real line.
Consequently, it could not be an appropriate model for variables that are inherently positive or highly skewed, such as a person's weight or the value of a share.
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Complete the tasks to subtract the polynomials vertically. (1.3t3 0.4t2 â€"" 24t) â€"" (0.6t2 8 â€"" 18t) what is the additive inverse of the polynomial being subtracted? â€""0.6t2 (â€""8) (â€""18t) â€""0.6t2 (â€""8) 18t â€""0.6t2 8 â€"" 18t 0.6t2 (â€""8) 18t
The subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18) is given as follows:
1.3t³ - 0.2t² - 32t + 18.
How to subtract polynomials?Polynomials are subtracted subtracting the like terms, which are the terms that have the same symbolic variable and the same exponent.
For this problem, the subtraction is given by the expression presented as follows:
(1.3t³ + 0.4t² - 24t) - (0.6t² + 8t - 18).
The like terms of the expression are given as follows:
1.3t³ and 0t³ = 1.3t³.0.4t² - 0.6t² = (0.4 - 0.6)t² = -0.2t².-24t - 8t = (-24 - 8)t = -32t.0 - (-18) = 0 + 18 = 18.Hence the result of the subtraction of the polynomials is given as follows:
1.3t³ - 0.2t² - 32t + 18.
Missing InformationThe problem asks for the subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18).
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Monica is 33 years old. Amanda is 18 years older than Brittany and 16 years older than Rita. Brittany is 23 years younger than Monica. How old is Rita?
please help
Isabel got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 7
cents per yard. If after that purchase there was $17.13 left on the card, how many yards of ribbon did Isabel buy?
The number of yards of ribbon Isabel bought is 41 yards.
It is given in the question that:-
Money in prepaid debit card = $ 20
Price of ribbon = 7 cents per yard
Money left on the card after buying the ribbon = $ 17.13
We have to find the number of cards of ribbon Isabel bought.
Money used in buying the ribbon = 20 - 17.13 = $ 2.87
We know that,
$ 1 = 100 cents
Hence, according to the data given in the question, we can write,
$ 2.87 = 287 cents
Yards of ribbon bought = 287/7 = 41 yards.
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