Answer:
The greatest number of kits he can make is 12 kits
Step-by-step explanation:
The greatest common divisor or GCD is called the greatest number that divides exactly two or more numbers at the same time.
The greatest common divisor is usually expressed as GCD(a,b), where a and b are numbers.
Being the divisor of a number is the value that divides the number into exact parts, that is, that the remainder is zero, one way to calculate the GCD is to determine all the divisors of each number, and from these point out the common divisors, of which the major divisor will be the GCD of those numbers. In this case:
Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Divisors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
The common divisors of 36 and 60 are 1, 2, 3, 4, 6 and 12, of which the greatest is 12. So GCD(36,60)=12
Another way to calculate the GCD is through prime factorization, which always starts with the smallest divisible number of the number being analyzed. In this case:
The decomposition of 36 is: 2*2*3*3 = 2²*3²
The decomposition of 60 is: 2*2*3*5= 2²*3*5
Now the common factors with the lowest exponent are chosen and multiplied. The result obtained is the GCD. In this case, the common factors of 36 and 60 are: 2² and 3 and their multiplication gives: 2²*3= 12. So GCD(36,60)=12
The greatest number of kits he can make is 12 kits
Write the following number in standard form.
one hundred four billion, twenty-seven thousand, five hundred seventy-one
140,027,000,571
140,270,571,000
104,000,027,571
104,000,270,571
Answer:
The third one, 104,000,027,571
Step-by-step explanation:
The first and second ones are not the answers because the problem does not say one hundred forty billion.
The last one is not the answer because the problem doesn't say two hundred seventy thousand.
Thus leaving the third one, which fits the description of the number.
What is the surface area of a cube with side length 3/2 units?
Answer:
Surface area = 13.5 unit square.
Step-by-step explanation:
We have given the side length of cube = 3/2 units
Now we have to find the surface area of the cube by using the given information. Therefore we must use the below formula to find the surface area. the formula is as follows:
Surface area = 6 (side)^2
Now plug the given information in the formula.
Surface area = 6 (3/2)^2
Surface area = 13.5 unit square.
Solve: x/3+1/4 =1/3 . Explain your work.
Steps to solve:
x/3 + 1/4 = 1/3
~Subtract 1/4 to both sides
x/3 = 1/12
~Multiply 3 to both sides
x = 1/4
Best of Luck!
Need help ASAP!!!!!!!!!!!!
Answer:
[tex]-\frac{7}{2} x+12[/tex]
Step-by-step explanation:
if you need step by step explanation i will upload.
25 tens=
______hundreds 5 tens
Answer:
2 hundreds.
Step-by-step explanation:
25 tens is equal to 250.
25 x 10 = 250
5 tens = 50, 5 x 10
250 - 50 = 200
200 = 2, hundreds.
Answer:
2 hundreds
Step-by-step explanation:
If you earned 892.50 after depositing 1400 at 4.25% simple interest, how long was it invested ? Using the simple interest formula, solve for t. Formula I=Prt
Answer:
Time t = 15 years
Step-by-step explanation:
Interest = 892.50
Principal = 1400
Rate = 4.25%
Time = unknown
But
interest I = Principal p * rate r * time t
Time t = interest I/(principal P * rate r)
Time t=( 892.50*100)/(1400*4.25)
Time t=89250/5950
Time t = 15 years
What is the polynomial function of least degree whose only zeros are -4,2, and 3?
Answer:
never heard about it
Step-by-step explanation:
The table shown classifies the 35 students in a
college statistics course by year (1st, 2nd, 3rd, 4th)
and type of major (Humanities, Sciences, Other). A
student from this course will be selected at random.
What is the probability that the student's major is
Humanities?
The correct answer is 0.45 or 45%
Explanation:
In this case, the probability of selecting a student whose major is Humanities can be calculated by finding the number of Humanities students, which is considered as the desired outcome, and dividing this by the total of outcomes or students. The process to find the probability is shown below:
[tex]P = \frac{Desired outcomes}{Total outcomes}[/tex]
[tex]P= \frac{Students from Humanities}{Total students}[/tex]
[tex]Students of Humanities = 5 + 5 + 3 + 3 = 16 students[/tex] (Add the students of each year that are part of Humanities)
[tex]Total of students = 35[/tex] (This number is provided in the question but can also be found by adding all numbers in the table)
[tex]P = \frac{16}{35}[/tex]
[tex]P = 0.45[/tex]
Multiply the probability by 100 to know its equivalent in percentages 0.45 x 100 = 45. This means the probability that a student of humanities is selected is 0.45 or 45%.
Two companies report a 15% gain in online sales over the last year. Suppose company Q had 25 online sales and company Z had 150 online sales last year. Do you believe their growth was the same? Justify your answer.
Answer:
Yes, it is possible.
Step-by-step explanation:
It is possible to have same profit rate.
The number of sales may demonstrate that the company Q with 25 online sales is smaller than the company Z with 150 online sales.
Or the company Q may have higher profit rate on individual sales than company Z.
Fill in the next number in the list.
5. 6. 11. 17. 28. 45
5. 6. 11. 17. 28. 45 . 73
Here,5 &6 are given,
Then,
5+6=11
6+11=17
11+17=28
17+28=45
So,
28+45=73
Answer:
73
Step-by-step explanation:
We are adding the two numbers before
5+6 = 11
6+11 = 17
11+17 = 28
17+28 = 45
28+45 =73
In parallelogram RELA you are given that the measure of angle R = 110 degrees. Find the measure of angle E?
Help me solve thiss
Answer:
Angle E = 70°
Step-by-step explanation:
Given parallelogram RELA, where m<R = 110°, to find m<E, recall the properties of a parallelogram.
Angle R and angle E are consecutive angles in parallelogram RELA.
One of the properties of a parallelogram states that any 2 consecutive angles in a parallelogram are supplementary. That is, they add up to 180°.
Therefore:
m<R + m<E = 180°
110° + m<E = 180°
Subtract 110° from both sides
m<E = 180° - 110° = 70°
Find the common ratio of each geometric sequence.
a) 2, 4, 8, ... r = 2
b) -2, 6, -18, L =
c) -3, -12, -48, ... r =
1 1 1
d)
3 927
9
..
e) 0.3, 0.6, 1.2, ... r =
f)
1.
re
.
42
Answer:
d
Step-by-step explanation:
What is 2 cents as a fraction
Which theorem can be used to show that △JKL ~ △MNP?
In this case the answer would be the last option
because it is shrunk by 2/3 on just the x side
D is the only one who has that first transformation
By a theorem of similarity, it can be shown that △JKL ~ △MNP.
What is the similarity?Similar figures are those figures which are identical in shape, but not necessarily in size.
Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.
Another example is all circles are similar circles.
The ratio of corresponding sides of similar objects is always the same.
Any two triangles will be similar if the ratio of their corresponding side is same.
If △JKL ~ △MNP then their corresponding side ratio will definitely same.
If corresponding side is same order in JKL and MNP then,
JK/KL = MN/NP
Hence "By a theorem of similarity, it can be shown that △JKL ~ △MNP".
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I've been stuck on this for about 2 hours but it still doesn't make any sense to me, please helpppppppppp
A piece of carpet is 360 cm long. Mr. Smith cuts it into three pieces in the ratio 2:3:4. Workout the length of the longest piece of carpet.
Answer:
The longest length of carpet is 160 cm.
Step-by-step explanation:
Given that the total ratio(units) of the carpet is 9(2+3+4). So first, you have to find the length of carpet in 1 unit :
[tex]9 \: units = 360 \: cm[/tex]
[tex]1 \: unit = 360cm \div 9[/tex]
[tex]1 \: unit = 40 \: cm[/tex]
Next, you have to find the length of carpet in 4 ratio as the question wants the longest length :
[tex]4 \: units = 40 \: cm \times 4[/tex]
[tex]4 \: units = 160 \: cm[/tex]
Answer:
160cm
Step-by-step explanation:
2+3+4= 9
4/9 x 360= 160cm
I don't have time to calculate I have to go somewhere. HELP ASAP! What is x+300=500
Answer:
x=200
Step-by-step explanation:
x+300=500move the constant to the rightx=500-300x=200Answer:
[tex]x=200[/tex]
Step-by-step explanation:
[tex]x+300=500[/tex]
There is an easy way to solve this.
Let's do
[tex]500-300[/tex]
Since [tex]500-300[/tex] is equal to 200, then x would be 200.
[tex]x=200[/tex]
Hope this helps!
The sum of a number and six is eleven. Find the number.
Answer:
17
Step-by-step explanation:
6 + 11 = 17
Sum (addition of 2 numbers)
Since the sum of a number and six is eleven, the number is equal to 5.
Let the unknown number be n.To find the unknown number:
In this exercise, you're required to determine an unknown number by translating the word sentence into an algebraic equation.
Translating the word sentence into an algebraic expression, we have;
The sum of a number and six is eleven:
[tex]n + 6 =11[/tex]
Next, we would rearrange the equation by collecting like terms:
[tex]n = 11-6[/tex]
n = 5
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please answer thank you!
Answer:
X= -2
Step-by-step explanation:
Given: 16 = -4(x - 1) + 4
Solution:
Subtract 4 from both sides
12 = -4(x -1)
Divide -4 on both sides
-3 = x - 1
Add -1 on both sides
x = -2
A blue scarf is 7/8 of a yard in a race car is 5/8 of a yard find the difference in length of the two scars write your answer as a simplified fraction
Answer:
Difference in length = 1/4 yards
Step-by-step explanation:
Given:
Blue scarf in yard = 7/8 yard
Another car in yard = 5/8 yard
Find:
Difference in length
Computation:
Difference in length = Blue scarf in yard - Another car in yard
Difference in length = 7/8 - 5/8
Difference in length = 2/8
Difference in length = 1/4 yards
16.9 is what percent of 22.9? Round to the nearest percent.
Answer:
74%
Step-by-step explanation:
16.9/22.9。。。。。。。
Answer:
74%
Step-by-step explanation:
22.9=100%
16.9= ?
16.9×100÷22.9=73.8
Round to the nearest % =73.8=74
Answer =74%
The line plot shows the part of an hour that Tamika practiced the piano each day last week. How many hours did Tamika practice the piano last week?
A.4 1/2 B.1 1/2 C. 4 D. 3 3/4
Answer:
it is c
Step-by-step explanation:
got it correct on the quiz
Maya has 120 cupcakes to sell. Each cupcake is covered with one topping. 1/5 of the cupcakes are covered with peanuts. 40 are covered with chocolate chips and the rest are covered with sprinkles. How many cupcakes are covered with sprinkles?
Answer:
24 covered with peanuts
40 covered with choc chips
56 covered with sprinkles
NEED HELP ASAP!!! Please explain your answer. Solve 0 = (3x - 4) / 5
Answer:
x= 1.333333333333 or 1 1/3
Step-by-step explanation:
solve for x, 0 times 5= 0 plus 4 is 4 div by 3 is 1 and 1/3
Check each equation whose graph is the line that
contains the points (4, -7) and (1,5).
y=-4x + 9
y=-4x – 23
y-1 =-4(X-5)
y + 7 = -4(x – 4)
4x + y = 9
DONE
Answer:
Points P ( 4 , - 7 ) and Q ( 1 , 5 ) belong to the equations:
1 ; 4 ; and 5
Step-by-step explanation:
Equations 1 ; 4 and 5 are the same equation
Equation 1 y = - 4*x + 9
Equation 4
y + 7 = - 4 * ( x - 4 ) ⇒ y + 7 = - 4*x + 16 ⇒ y = - 4*x - 7 + 16
y = -4*x + 9
Equation 5
4*x + y = 9 ⇒ y = - 4*x + 9
Now for the equation y = - 4*x + 9
P ( 4 , -7)
For x = 4 y = - 4*(4) + 9 ⇒ y = - 16 + 9 ⇒ y = - 7
Then point P is in the line y = - 4*x + 9
Point Q (1 , 5 )
For x = 1 y = - 4 * ( 1) + 9 ⇒ y = - 4 + 9 ⇒ y = 5
Point Q is in the line y = - 4*x + 9
Equation 2
y = - 4*x - 23
Point P ( 4 , - 7 )
For x = 4 y = 16 - 23 y = - 7
Point P is in the line
Point Q
For x = 1 y = - 4 *(1) - 23 ⇒ y = - 27
Then poin Q is not in the line
Equation 3
y - 1 = - 4 * ( x - 4 )
y - 1 = -4*x + 16 ⇒ y = - 4*x + 17
Point P ( 4 , - 7 )
For x = 4
y = - 16 + 17 ⇒ y = 1
Point P is not in the line
And Point Q ( 1 , 5 )
For x = 1
y = - 4* ( 1 ) + 17 ⇒ y = 13 Q is not in the line
Answer:
1 4 5
Step-by-step explanation:
jus took the test
NEED HELP ASAP (30Points!!) Which answers are examples of the Law of Syllogism? Select each correct answer. A) If there is a children’s movie playing at the cinema, Maria’s mother will take her to see it. When Maria’s mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria. B) If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram. C) If a quadrilateral is a rectangle with 4 equal sides, then it is a square. Quadrilateral ABCD is a rectangle with 4 equal sides. Therefore, quadriateral ABCD is a square. D) Sally goes to the mall every Saturday. Today is Saturday. Therefore, Sally will go to the mall today.
Answer:
The correct answer is: (just took the test)
if a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram
if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria
Step-by-step explanation:
For the given answers the answers that follow the law of syllogism is options A and B.
Given that,
4 statement is given, and we have to pick the statement that follows the low of syllogism.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here
There are only two statements that are following the law of syllogism. ie.
A. If there is a children's movie playing at the cinema, Maria's mother will take her to see it. When Maria's mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children's movie playing at the cinema, Maria's mother will buy popcorn for Maria.
B. If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram.
C. and D. are invalid statement because it does not follow the Law of Syllogism.
Thus, for the given answers the answers that follow the law of syllogism is options A and B.
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7 out of 10 doctors If there are 4200 doctors that prefer Cough-Up brand syrup, how many total doctors are there? * A)6000 B)2940 C)14000 D)1260
Give an expression that generates all angles coterminal with each angle. Let n represent any interger?
1. 60°
2. 120°
Answer:
The expression to this question can be defined as follows:
Step-by-step explanation:
Given angle:
1. 60°
2. 120°
Formula:
[tex]\to \bold{\ angle + 360 \ n}[/tex]
The Expression for point 1:
[tex]\to 60^{\circ} + 360 \ n\\[/tex]
The Expression for point 2:
[tex]\to 120^{\circ} + 360 \ n\\[/tex]
The distance between the point (2,1,1) and the plane x-2y=5 is
The given plane has normal vector
[tex]x-2y=5\implies\mathbf n=\langle1,-2,0\rangle[/tex]
Scaling n by a real number t gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation
[tex]\mathbf r(t)=\langle1,-2,0\rangle t+\langle2,1,1\rangle=\langle 2+t, 1-2t, 1\rangle[/tex]
This line passes through (2, 1, 1) when t = 0, and the line intersects with the plane when
[tex]x-2y=5\implies(2+t)-2(1-2t)=5\implies5t=5\implies t=1[/tex]
which corresponds the point (3, -1, 1) (simply plug t = 1 into the coordinates of [tex]\mathbf r(t)[/tex]).
So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):
[tex]\sqrt{(2-3)^2+(1-(-1))^2+(1-1)^2}=\boxed{\sqrt5}[/tex]
Find the midpoint (1,2)(8,-9)
Answer:
(4,5)
Step-by-step explanation: