Two numbers are 30 and 60 that have 2,3 and 5 as factors.
What is LCM ?LCM is the least common multiple of two or more that two given numbers which is exactly divisible by these given numbers.
According to the given question we have to find two numbers that have 2, 3 and 5 as common factors.
To find least such number which have common factor of 2, 3 and 5 we have to take LCM of 2, 3 and 5.
The LCM of 2, 3 and 5 is 30.
The next such possible higher numbers will be of the form 30k, where k is an integer.
At k = 2,
The number 30k will be 30(2) which is
= 60.
We can find any such form of numbers by putting different integer value of k.
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If there are 11 apples and I eat one and split half of the rest with my friend. How many do i have?
Answer ALL if u cant see all the answers it don't matter all u need is the question
What are the factors of 60a
Answer:
Factors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
Polygon ABCD has the following vertices:
A(−4, 2), B(3, 2), C(3, −5), and D(−4, −2)
Calculate the area of the polygon.
To be able to solve clearly this problem, the best thing to do is to plot the graph (see attached pic). From the graph we can see that the points form a trapezoid.
The base is formed by the segment connecting point A and point B.
While the two heights: shorter one by the segment connecting points A and D, and the longer one by the segment connecting points B and C.
The formula for area of trapezoid is given as:
A = b (h1 + h2) / 2
Where,
b = base of the trapezoid = 3 – (-4) = 7
h1 = shorter height = 2 – (-2) = 4
h2 = longer height = 2 – (-5) = 7
Therefore the area is:
A = 7 (4 + 7) / 2
A = 77 / 2
A = 38.5
The answer is 38.5. I took this exam and I chose 38.5 and got it right, I hope this helps!
If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
The probability helps us to know the chances of an event occurring. The theoretical probability that they have three dogs or three cats is 0.25.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the pet can either be a dog or a cat, therefore,
The probability that all the three pets are dogs is:
[tex]\rm P(X= 3\ dogs) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
The probability that all the three pets are cats is:
[tex]\rm P(X= 3\ Cats) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
Now, we need to calculate the probability that all three pets are either dogs or cats, therefore, the probability can be written as,
[tex]\rm P(3\ Dogs\ or\ 3\ Cats) = P(X = 3\ dogs) + P(X = 3\ cats)[/tex]
[tex]= \dfrac{1}{8}+\dfrac{1}{8}\\\\=\dfrac{2}{8}\\\\ = \dfrac{1}{4} = 0.25[/tex]
Hence, the theoretical probability that they have three dogs or three cats is 0.25.
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the table represents a function. what is the value of f(-1)?
f (-1) = - 3
f (-1) = - 1
f (-1) = 0
f (-1) = 6
The value of f(-1) from the table given is 0
Table of functionsTable of functions are used to find the relationship between variables. The variables x and y can be written as coordinate (x, y)
In order to determine f(-1), we need the value of f(x) at the point where x is 1. From the table, the value of f(-1) is 0
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What is 3^ 2/3 equal to?
3^2/3 means squaring the number 3 to get 9, and then taking the cube root of 9, which is approximately 2.08008.
Explanation:To calculate 3^2/3, we are dealing with an exponential expression where 3 is the base and 2/3 is the exponent. The exponent 2/3 means we must first square the base, which is 3, giving us 3 squared: 32 = 9. Next, we take the cube root (denominator of the fraction exponent) of this result since the exponent is 2/3, meaning the cube root of 9.
To find the cube root of 9, we look for a number which, when multiplied by itself three times, equals 9. Unfortunately, 9 is not a perfect cube, but using estimation or a calculator, we can find that the cube root of 9 is approximately 2.08008. Therefore, the exact expression for 32/3 remains (9)1/3 and the approximate decimal value is 2.08008.
on every 3rd day Ivan goes to the gym. On every fifth day Gavin goes to the gym. What day will Ivan and Gavin will see each other.
The cost of producing key chains with the company logo printed on them consists of a onetime setup fee of $205.00 plus $0.70 for each key chain produced. This cost can be calculated using the formula C=205.00+0.70p, where p represents the number of key chains produced and C is the cost. Use the formula to calculate the cost of producing 1700 key chains
steps in how to solve
Which of these expressions is equal to 6 + (2 + 3) × 5
ini earned $160 during the summer doing chores. She bought 3 dresses worth $12 each using her chore money. How much money was left after she bought the dresses?
What is the average speed (miles/hour) for an object going 1500 feet in 1 minute. Round answer to two decimal places.
there are 3600 seconds per hour
5280 feet per mile
1 foot per second = 3600/5280 = 0.681818 Miles per Hour
60 seconds per minute
so 1500/60 = 25 feet per second
25 x 0.681818 = 17.05 miles per hour
two triangles.are.similar, solve for x if au=20x +108, ub=273, bc= 703, uv=444, AV = 372 and AC=589
If two triangles are similar then the corresponding sides are in proportion. Thus,
AB / AU = BC / UV = AC / AV
AB / (20x+108) = 703 / 444
Where AB is equivalent to:
AB = AU + UB
AB = 20x + 108 + 273
AB = 20x + 381
Therefore going back to the first equation:
(20x + 381) / (20x + 108) = 703/444
444 (20x + 381) = 703 (20x + 108)
8880x + 169164 = 14060x + 75924
14060x - 8880x = 169164 – 75924
5180 x = 93240
x = 93240 / 5180
x = 18 (ANSWER)
The correct value of x is [tex]\(\frac{1}{20}\)[/tex].
To solve for x, we need to use the properties of similar triangles. The sides of similar triangles are proportional. Given that triangles AU V and ABC are similar, we can set up the following proportion:
[tex]\[\frac{AU}{AB} = \frac{UV}{BC} = \frac{AV}{AC}\][/tex]
We are given the lengths of the sides as follows:
- (AU = 20x + 108)
- (UB = 273) (which is part of AB, since (AB = AU + UB)
- (BC = 703)
- (UV = 444)
- (AV = 372)
- (AC = 589)
Using the proportion involving the sides AU, UB, UV, and BC, we have:
[tex]\[\frac{AU}{UB} = \frac{UV}{BC}\][/tex]
Substituting the given values, we get:
[tex]\[\frac{20x + 108}{273} = \frac{444}{703}\][/tex]
Cross-multiplying to solve for x, we have:
[tex]\[(20x + 108) \cdot 703 = 444 \cdot 273\][/tex]
Expanding both sides gives us:
[tex]\[14060x + 76184 = 121172\][/tex]
Subtract (76184) from both sides to isolate the term with x:
[tex]\[14060x = 121172 - 76184\] \[14060x = 49888\][/tex]
[tex]\[x = \frac{49888}{14060}\][/tex]
Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20, we get:
[tex]\[x = \frac{2494.4}{703}\][/tex]
Since (2494.4) is very close to (2496), and \(2496\) divided by (703) is (3.55), which is (20) times (0.1775), we can see that:
[tex]\[x = \frac{1}{20}\][/tex]
Therefore, the value of x is [tex]\(\frac{1}{20}\)[/tex].
What is the value of x in the equation 8 + x = 3? −5 5 11 24
o graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
a.-5/2
b.-2/5
c.2/5
d.5/2
we have
[tex] 2x + 5y = 10 [/tex]
we know that
the formula to calculate the slope is equal to
[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]
Let
[tex] A( 5,0)\\B( 0,2) [/tex]
Step [tex] 1 [/tex]
Find the slope AB
[tex] mAB=\frac{(2-0)}{(0-5)} \\ \\ mAB=-\frac{2}{5} [/tex]
therefore
the answer is the option B
[tex] -\frac{2}{5} [/tex]
the graph in the attached figure
The value of 7 in ___ is 10 times
The value of 7 in ____
how to write place value 35 thousand,26hundredand 16 tens and 12 ones
Which of the following points is a solution to the system of linear inequalities
Which of the following points is a solution to the system of linear inequalities?
{2x+y<-5
{-x+y>0
A.
(4, 1)
B.
(–4, –1)
C.
(–8, –21)
D.
(8, 11)
Answer:
(-4,-1) satisfies the given system of inequalities
Step-by-step explanation:
[tex]2x+y<-5[/tex]
[tex]-x+y>0[/tex]
To find out the solution we check with each option
(4,1) , x=4 and y=1 (Plug in x and y values in the given inequalities)
[tex]2(4)+1<-5[/tex]
[tex]9<-5[/tex] False
(-4,-1) , x=-4 and y=-1 (Plug in x and y values in the given inequalities)
[tex]2(-4)-1<-5[/tex]
[tex]-9<-5[/tex] True
Now plug it in second inequality
[tex]-(-4)-1>0[/tex]
[tex]3>0[/tex] True
(-8,-21) , x=-8 and y=-21 (Plug in x and y values in the given inequalities)
[tex]2(-8)-21<-5[/tex]
[tex]-37<-5[/tex] True
Now plug it in second inequality
[tex]-(-8)-21>0[/tex]
[tex]-13>0[/tex] False
(8,11) , x=8 and y=-11(Plug in x and y values in the given inequalities)
[tex]2(8)+11<-5[/tex]
[tex]-9<-5[/tex] false
a triangle brace has an angle measure of 92 degrees, with a side opposite this angle measuring 10 inches. the base of the triangular brace, which is adjacent to the given angle measure, is 12 inches in length. Which of the following statements is correct
To determine the length of the hypotenuse in a triangle with an angle measure of 92 degrees and a side length of 10 inches, we can use the sine ratio. Calculating the value of Sin(92 degrees) and dividing 10 by that value, we find that the hypotenuse is approximately 10.001525 inches.
Explanation:A triangle brace with an angle measure of 92 degrees and a side length of 10 inches opposite this angle, and a base length of 12 inches adjacent to the given angle. To determine which of the given statements is correct, we need to use trigonometric ratios. We can use the sine ratio in this case.
The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the angle measure is 92 degrees and the side opposite is 10 inches. Let's calculate:
Sin(92 degrees) = Opposite/Hypotenuse
Sin(92 degrees) = 10/Hypotenuse
To solve for the hypotenuse, we can rearrange the equation:
Hypotenuse = 10/Sin(92 degrees)
Using a calculator, we can evaluate Sin(92 degrees) and then divide 10 by that value to find the hypotenuse:
Hypotenuse = 10/0.9998477 = 10.001525 inches (approximately)
Based on this calculation, the correct statement would be that the hypotenuse is approximately 10.001525 inches.
Write 2.95 as the quotient of two integers
For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.
During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.
If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .
When the factors of a trinomial are (x - p) and (x - q) then the constant term of the trinomial is:
A. The quotient of -p and -q
B. The product of -p and -q
C. The difference of -p and -q
D. The sum of -p and -q
The constant term will be the product of -p and -q.
What is a trinomial?A trinomial is an algebraic expression that has three non-zero terms and has more than one variable in the expression.
Given that the factors of a trinomial are (x - p) and (x - q) we need to determine the constant term of the trinomial:
We know that a trinomial in its factors form can be written as,
x² + (α+β)x + αβ, where α and β are factors.
So, here the constant term of the trinomial will be (-p) × (-q) = pq.
Hence the constant term will be the product of -p and -q.
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WALK Heather was out for a leisurely walk at a rate of 3 miles per hour. What was her speed in yards per minute?
Diana is going camping with her family. Their campsite is 5/8 mile away. They walk at a steady speed of 2 1/2 miles per hr. How many minutes will It take them to get to the campsite
The sum of 74 and four times a number is 258. Find the number
The unknown number is 46.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Let the number be x.
The sum of 74 and four times a number is 258,
⇒ [tex]74+4x=258[/tex]
⇒ [tex]4x=258-74[/tex]
⇒ [tex]x=\frac{184}{4}[/tex]
⇒ [tex]x=46[/tex]
Hence we can conclude that the unknown number is 46.
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3 times what gives me a sum of 24? im trying to finish my homework so please help.
Look at the cups shown below (please note that images are not drawn to scale): A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tent
Amount of juice that cup B will hold than cup A when both are completely full is A: 18.8 cubic inches. therefore, Option A: 18.8 cubic inches.
Amount of juice hold by Cup B which is in the shape of a cylinder having width 2 inches that is radius 1 inches and height 7 inches
πr^2h = π × 1^2 ×7 = 7π cubic inches
Amount of juice hold by cup A which is in the shape of a cone having width 2 inches that is radius 1 inches and height 3 inches
1/3 × π × r^2 h
1/3 × π × 1^2 × 3 = πcubic inches
Amount of juice that cup B will hold than cup A when both are completely full = 7π - π = 6π cubic inches
= 6 × 3.14
= 18.84 cubic inches
Option A: 18.8 cubic inches
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Question
Look at the cups shown below (please note that images are not drawn to scale):
A cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches.
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
18.8 cubic inches
21.9 cubic inches
25.1 cubic inches
32.6 cubic inches
Your class is holding elections to choose a leadership committee of 4 students. If there are 30 students in the class, how many different leadership committees would it be possible to elect?
810,000
27,405
120
657,720
Using the combination formula, it is found that it would be possible to elect 27,405 different leadership committees.
The order in which the students are selected to the committee is not important, which means that the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 students are chosen from a set of 30, thus:
[tex]C_{30,4} = \frac{30!}{4!26!} = 27405[/tex]
It would be possible to elect 27,405 different leadership committees.
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Lucia wants to buy some posters over the Internet. Each poster costs $6.67 and has a shipping cost of $9.99 per order. If Lucia wants to spend no more than $30 for her posters, which inequality shows the maximum number of posters, p, that she can buy?