Answer:
(i) Find the smallest number which, on being added 23 to it, is exactly divisible by 32, 36, 48 and 96.
(ii) Find the least length of a rope which can be cut into whole number of pieces of lengths 45 cm, 75 cm and 81 cm.
(iii) Find the greatest number of 4-digits which is exactly divisible by 40, 48 and 60.
(iv) What is the least number of saplings that can be arranged in rows of 12, 15 or 40 in each row?
(v) 210 oranges, 252 apples and 294 pears are equally packed in cartons so that no fruit is left. What is the biggest possible number of cartons needed?
(vi) A certain number of students can be arranged in groups of 3, 4, 6 or 8 with no student left behind. Find the number of students.
(vii) The local bus service has 2 lines of buses that start together at 8 a.m. Buses on line A leave after every 15 minutes while Buses on line B leave after every 20 minutes. In a day, how many times do buses on both line A and B leave together between 8 a.m. and 11 a.m.
(vii) Three painters Ron, Victor and Shelly are painting the rooms of a hotel which are numbered from 15 – 200. Ron has to work in all the rooms. Victor has to work in rooms where the room number is a multiple of 3. Shelly has to work in rooms where the room number is a multiple of 5. In which rooms will they all work together?
(ix) Sara goes to the shopping mall every 6th day. Andy goes to the same shopping mall every 7th day. How many times will they meet in the mall in the month of December and January if we start counting from 1st December?
x) The HCF of two numbers is 6, if one of the numbers is 42, find the other number?
(xi) Find the greatest number of 5-digits which on being divided by 9, 12, 24 and 45 leaves 3, 6, 18 and 39 as remainders respectively
Sam can jump 4 steps at a time and Nina can jump 5 steps at a time. On which of the steps will both meet if both start jumping together?
(xii) Mary has a dance class every 2nd day and painting class every 3rd day. On which of the day will she have both the classes?
(xiii) Find a multiple of 70 which is between 200 and 600 which has odd digits at tens and hundreds place.
(xiv) Find a multiple of 120 which lies between 400 and 500 where the digit at tens place is double the digit at hundreds place.
Given the following data, find the weight that represents the 42nd percentile.
Weights of Newborn Babies
8.3 6.5 6.0 5.4 6.7
6.5 8.1 9.2 6.4 8.0
6.8 9.0 8.7 9.3 8.0
The weight represents the 42nd percentile.
=6.712
This is further explained below.
Find the weight that represents the 42nd percentile.?Generally, the given data is
8.3,6.5,6,6,5,4,6.7,6.5,8: 1,9.2,6.4,8 0,6.8,9.0,8.7,9.3,8.0
The ascending order of the data is
5.4,6.0,6.4,6.5,6.5,6.7,6.8,8.0,8.0,8.1,8.3,8.7,9.0
n=15.
42ndPercentile
=P_{42}
[tex]=42\left(\frac{n+1}{100}\right)^{\text {th }} \text { term } \\[/tex]
[tex]&=42\left(\frac{16}{100}\right) \text { th term } \\[/tex]
=6.72th term
=6th+0.72(72nd -6th) term
=6.7+0.72(6.8-6.7)
=6.712
In conclusion, the weight represents the 42nd percentile.
=6.712
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H E L P :(
What is the ratio of fiction novels to all novels? 11 to 5 2:5 5/11 5 to 2
Answer:
5/11
Step-by-step explanation:
make sure next time to say how much books do you have I have answered a similar question with this wording so I hope this helps :))
Lydia is buying some jewelry for her fried Michelle for her birthday. Each set is $5 and shipping is $4 flat. If Lydia buys 4 jewelry sets, how much will she spend?
When Lydia buys 4 jewelry sets, the amount spent is $24.
How to calculate the value?From the information given, we are told that Michelle is preparing for her birthday and that each set is $5 and shipping is $4 flat. If Lydia buys 4 jewelry sets.
Therefore, the equation will be:
4 + (5 × x)
where x = number of set
4 + 5x
4 + (5 × 4)
= 4 + 20
= $24
The amount is $24.
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When converted to millimeters, the distance 360,000,000 meters is expressed as millimeters in scientific notation.
Answer:
360 million written in scientific notation is 3.6 × 108.
Step-by-step explanation:
According to data from the CDC, about 37.1% of adults (individuals 18 years of age or older) in the United States and 57.9% of children (individuals between 6 months and 17 years of age) in the United States received a flu vaccine during the 2017-2018 flu season.
a) Consider a random sample of 50 adults.
i. Calculate the probability that exactly 20 adults received a flu vaccine.
Using the binomial distribution, there is a 0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.
For each adult, there are only two possible outcomes, either they received the vaccine or they did not. The probability of an adult receiving the vaccine is independent of any other adult, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, we have that:
There is a random sample of 50 adults, hence n = 50.37.1% of adults received the flu vaccine, hence p = 0.371.The probability that exactly 20 adults received a flu vaccine is P(X = 20), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 20) = C_{50,20}.(0.371)^{20}.(0.629)^{30} = 0.1094[/tex]
0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.
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Given the following composite figure, d = 7.5 cm and w = 15.1 cm.
What is the area of the figure?
Answer:
157.41
Step-by-step explanation:
It can be identified that, given the figure, there is a rectangle and 2 semicircles.
Let's find the area of the rectangle first: A=L*w
Plugging in the given values => A=7.5*15.1 which equals 113.25.
Now the area for the semicircles: 1/2(3.14*r^2)
First, we need to find the radius. To find the radius, you just have to divide the diameter by 2. So, 7.5/2=3.75.
We can plug square the radius which is 3.75 and plug it into the formula: 1/2(3.14*3.75^2)=>22.078125.
22.078125 is the area of only one semicircle so we need to multiply it by 2 because we have two semicircles. So, we get 44.15625.
Finally, we can add them all up to find the total area of the figure: 113.25+44.15625=157.40625.
Rounding to the nearest hundredth=>157.41
If a linear function has the points (−5,4) and (−2,−2) on its graph, what is the rate of change of the function?
The rate of change of the linear equation that has the given points on its graph is; -2.
How to Find the Rate of Change of a Linear Function?The rate of change of a linear function can be determined by using the following formula:
Rate of change = change in y / change in x = y2 - y1 / x2 - x1.
Given the following points on a graph of a linear function:
(−5,4) = (x1, y1)
(−2,−2) = (x2, y2)
Plug in the values
Rate of change = change in y / change in x = (-2 - 4) / (-2 -(-5))
Rate of change = -6 / 3
Rate of change = -2 / 1
Rate of change = -2
Thus, the rate of change of the linear equation that has the given points on its graph is; -2.
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When a vehicle is in motion, it has _____.
Answer:
Kinetic energy
Step-by-step explanation:
because when something is in motion it gains kinetic energy
Use the slope formula to find the slope
The slope of line: 1. m= 6 , 2. m= -6 , 3. m= 2.5, 4. m= .5
The slope of the line :
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Tan θ = Δy/Δx can also represent the slope of the line
So, tan θ to be the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The letter ‘ m’ usually represents the slope.
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope,
m = Change in y-coordinates/Change in x-coordinates
m = (y2 – y1)/(x2 – x1)
Therefore, based on the above formula, we can easily calculate the slope of a line between two points.
In other terms, the slope of a line between two points is also said to be the rise of the line from one point to another (along the y-axis) over the run (along the x-axis). Therefore,
Slope, m = Rise/Run
1.
(-1,-1) & (0,5)
m = (y2 – y1)/(x2 – x1)
m = (5 – (-1)) /(0– (-1))
m = (5 +1)/(0 +1)
m = (6)/(1)
m = 6
2.
(3,5) & (4,-1)
m = (-1 – 5)/(4 – 3)
m = (-6)/(1)
m = -6
3.
(2,1) & (4,6)
m = (6 – 1)/(4 – 2)
m = (5)/(2)
m = 2.5
4.
(-5,-2) & (3,2)
m = (2 – (-2))/(3 – (-5))
m = (2 +2/(3 +5)
m = (4)/(8)
m = (2/(4)
m = (1)/(2)
m = 0.5
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Which lines are parallel if the m<2 = m<6? Lines r & s or lines l & m
(Click document to see image)
In the given picture with 4 lines l, m and r, s. The l and m, r and s line are parallel lines.
Given that,
There is a picture with 4 lines l, m and r, s.
We have to check that those lines are parallel or not
To check that the line are parallel we have a condition.
If two lines are cut by the transversal and corresponding angles are congruent then we can say that those 2 lines are parallel.
In the figure we can see that ∠2 and∠6 are congruent.
So, we can say that lines r and s are parallel lines.
Similarly,
In the figure we can see that ∠1 and∠7 are congruent.
So, we can say that lines l and m are parallel lines.
Therefore, the l and m, r and s line are parallel lines.
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A project manager is calculating work forecasts. The manager's team completed of a job in 16 days. At this rate, the
manager says that the team completed of the project each day.
What was the manager's error?
O The manager is correct. There was no error.
O The manager divided by 16 instead of dividing
by 16.
O The manager divided 16 by
instead of dividing
by 16.
O The manager divided 16 by
instead of multiplying 16 by
O The manager divided by 16 instead of multiplying 16 by
The error that the manager made was that B. The manager divided 5/4 by 16 instead of dividing 4/5 by 16.
How to calculate the value?The information illustrates that the project manager is calculating work forecasts and he manager's team completed 4/5 of a job in 16 days.
Therefore, the amount that was done each day will be:
= 4/5 ÷ 16
= 4/5 × 1/16
= 4/80
= 1/20
Therefore, the error that the manager made was that the manager divided 5/4 by 16 instead of dividing 4/5 by 16. This was the reason that he got 5/64.
Therefore, the correct option is B.
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What is the solution to the equation below? Round your answer to two
decimal places.
log₂ x = 2.5
The solution of the logarithmic equation is approximately 5.66 .
The logarithm is a simpler way to write a exponential equation.
The exponential equation nˣ = b is written as logₙ b = x ( read as logarithm of b to the base of n is equal to x).
The various properties of logarithm are:
log x+ log y= log x ylog x - log y= log(x/y)log xⁿ=n log xThe given equation is :
log₂ x = 2.5
This equation is of the form logₐ b=n
We know that from the properties of logarithm logₐ b=n is equivalent to aⁿ=b.
So the given equation can be written as
[tex]x=2^{2.5}[/tex]
Solving we get
x=5.6568....
or, x≈5.66
Therefore the logarithm equation has a solution for x where the value of x is approximately 5.66.
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x to the power of 2 - x + 6
X²-X+6
X²-X¹:there's a invisible ¹ on the variable/XX+6
6XWhat is the solution to
this equation?
5x + 3 = 2x - 6
The solution to this equation is x = -3
How to determine the solution to this equation?
The equation is given as
5x + 3 = 2x - 6
Collect the like terms
5x - 2x = -3 - 6
Evaluate the like terms
3x = -9
Divide both sides by 3
x = -3
Hence, the solution to this equation is x = -3
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Four times the lesser of two consecutive even integers is less than twice the greater number. Find the integers.
There exists no even integer with the given parameters
How to determine the two consecutive even integers?Consecutive even integers are integers that have a difference of 2
i.e x and x + 2
Where x is the lesser number
Using the given mathematical statement, we have
4x < 2(x + 2)
Divide by 2
2x < x + 2
Subtract x from both sides
x < 2
There is no even number less than 2
Hence, there exists no even integer with the given parameters
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I was
following a recipe to make punch for a party. The rect cakks for 2 cups of juice for every 3 cups o
f seltzer. If I have 12 cups of seltzer, how many cups of juice do I need?
You need 8 cups of juice for 12 cups of seltzer.
Representing the first statement in ratio form. So, number of cups of juice: number of cups of seltzer = 2:3. Similarly, for second statement, let the number of cups of juice be x.
Forming the equation with ratio on both sides -
2:3 = x:12
Writing the mentioned equation as fraction to solve for the value of x
x = (2 × 12)/3
Performing multiplication in numerator to find the value of x
x = 24/3
Dividing the numerator and denominator by 3 to find the value of x
x = 8
Therefore, 8 cups of juice is needed for 12 cups of seltzer.
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x+y-z= 6
3x - 2y + z = -5
x + 3y - 2z = 14
Answer:
( x , y , z) = ( 1 , 3 , - 2)
the solution
Find the midpoint of the line segment with the endpoints A and B.
A(10,4); B(8,2)
The midpoint of the line segment is
(Type an ordered pair.)
graph the following. x= -1. y= 5
Answer:
NOT possible to draw
Step-by-step explanation:
Answer:
graph the following
x=-1 y =5
it look like a two line
Step-by-step explanation:
Your weight on the Moon is about 1/6 of your weight on Earth. Write and solve an equation to show how much a person weighs on Earth if he weighs 16 pounds on the moon. How could you check that your answer is reasonable??
Answer:
1/6(x) = 16
Step-by-step explanation:
You can just solve for x which goes as follows:
6 * 1/6 = 6 * 16 - Multiply both sides by 6.
x = 96
Answer:
x=96
Step-by-step explanation:
To figure out the weight of the person on the moon we would need to take their weight and divide by 6. we don't know the weight so it's x. We know the final weight so the x divided by 6 should be 16.
this translates to:
x/6=16
x=16*6
x=96
Is this a function ?
Answer:
no
Step-by-step explanation:
Functions are wavy lines
Answer:
yes
Step-by-step explanation:
what is the answer to this equation 21 x ___=7
Answer:
the answer is 3
Step-by-step explanation:
21 x 3 =7
hope it helps
Answer:
21/7
Step-by-step explanation:
Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3
Please help I will give brainliest
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
You can use the Pythagorean Theorem, which is [tex]a^{2}+ b^{2}= c^{2}[/tex]. So the the distance from -9 to -5 is 4 and the distance from 8 to 6 is 2.
So [tex]4^{2} +2^{2} =c^{2}[/tex]. Which equals [tex]20=c^{2}[/tex].
Then you square root [tex]c^{2}[/tex] to make it c, then you do that to the other side. So you have [tex]\sqrt{20}=c[/tex].
Which equals [tex]2\sqrt{5}[/tex].
Or you can use the Distance Formula, which is [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex].
The [tex]x_{1}[/tex] is -5 and the [tex]x_{2}[/tex] is -9. The [tex]y_{1}[/tex] is 6 and the [tex]y_{2}[/tex] is 8. When you plug that in you get [tex]\sqrt{(-9--5)^{2} +(8-6))^{2} }[/tex]. When you simplify that you get [tex]\sqrt{20}[/tex].
Which equals [tex]2\sqrt{5}[/tex].
Jon placed a ladder 24 feet long against the side of his house. The base of the ladder was 10 feet from the house. What angle did the ladder make with the ground, to the nearest degree.
Answer: 120 degrees (originally said 150 degrees, but thats a weird ladder)
Step-by-step explanation: 6 x 4 = 24, 6 x 60 = 360, 4 = 60, 10 x 2 = 20, 4 x 5 = 20, 60 x 5 = 300. 20 / 2 = 10, 300 / 2 = 150, 150 / 1.17 = 120 most likely
NO LINKS! Please help me
Answer:
hope this explanation helps you
Answer:
[tex]\textsf{b)} \quad -\dfrac{3\sqrt{13}}{13}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.H is the hypotenuse (the side opposite the right angle).[tex]\textsf{If}\; \tan(\theta)=-\dfrac{2}{3} \implies \sf O=2 \; \textsf{and} \; A=3.[/tex]
Use Pythagoras Theorem to calculate the length of the hypotenuse:
[tex]\sf \implies O^2+A^2=H^2[/tex]
[tex]\implies \sf H=\sqrt{O^2+A^2}[/tex]
[tex]\implies \textsf{H}=\sqrt{2^2+3^2}[/tex]
[tex]\implies \textsf{H}=\sqrt{13}[/tex]
Therefore, substituting the values of A and H into the cosine ratio:
[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}[/tex]
[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}\cdot \dfrac{\sqrt{13}}{\sqrt{13}}[/tex]
[tex]\implies \cos \theta=\dfrac{3\sqrt{13}}{13}[/tex]
As the terminal side of the angle is in Quadrant II, and cosine is negative in Quadrants II and III, the exact value of cos(θ) is:
[tex]\implies \cos \theta=-\dfrac{3\sqrt{13}}{13}[/tex]
Find the domain y=1-7x/8-|3x-15|
Using set builder notation, the domain of the given function is;
{x | x ≠ 5}
How to find the Domain of a Function?
The domain is all values of x that makes the given expression undefined.
The given expression is;
y = (1 - 7x)/8 - 1/|3x - 15|
To find the value of x that will make the expression undefined, it means that we will equate the denominator to zero to get;
|3x - 15| = 0
Thus;
3x = 15
x = 15/3
x = 5
Thus, using set builder notation, the domain of the given function is;
{x | x ≠ 5}
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What is the BEST first step for calculating the LCM of 15 and 20
Step-by-step explanation:
The commonly used methods to find the LCM of 15 and 20 are:
1) Division Method
2) Prime Factorization Method
3)Listing Multiples
What is 6 over 9 times 6 over 8 equal
Answer:
0.5
Step-by-step explanation:
Answer: the answer is 0.5 or 1/2
Step-by-step explanation:
(FIRST ANSWER WITH EXPLANATION GETS BRAINLIEST)
Daisy is studying an ant population. On the first day, there are 10 ants. A week later, there are 100 ants. After the third week, there are 1,000 ants. Assuming the ant growth continues at this rate, how many ants would there be after 5 weeks?
Answer:
100,000
Step-by-step explanation
week 1: 10
week 2: 10x10= 100
week 3: 100x10=1,000
week 4: 1,000x10=10,000
week 5: 10,000x10= 100,000
Have an amazing day/night!!
How much money (in dollars) should be invested in an account that earns 5% interest, compounded quarterly, to yield $10,000 in 4 years? Round your answer to the nearest cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$10000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]10000=P\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies 10000=P(1.0125)^{16} \\\\\\ \cfrac{10000}{(1.0125)^{16}}=P\implies 8197.46\approx P[/tex]