Answer:
The gcf of 42 and 84 is 42. The lcm of 4 and 10 is 20.
Step-by-step explanation:
We will now calculate the prime factors of 42 and 84, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42 and 84.We found the factors and prime factorization of 42 and 84. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 84 is 42.
The Least Common Multiple (LCM) of the numbers
4, 10
is
20
because 20 is the smallest number that all of the numbers divide into evenly.
The greatest common factor of 42 and 84 is 42
The least common multiple of 4 and 10 is 20
What is the greatest common factor of 42 and 84?A factor refers to a number or an algebraic expression that divides another number or expression evenly, that is, with no remainder.
42 = 1, 2, 3, 6, 7, 14, 21 and 42.
84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
The greatest common factor of 42 and 84 is 42
least common multiple of 4 and 10
Find the multiples of 4 and 10
4 = 4, 8, 12, 16, 20, 24
10 = 10, 20, 30
The least common multiple of 4 and 10 is 20
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In a symphony orchestra, there are 2 vacancies for cellists only, 4 vacancies for violinists only and 4 vacancies for any of these musicians. In how many ways can these vacancies be filled from 15 applicants, of whom 7 are violinists and 8 are cellists?
Answer:
123480
Step-by-step explanation:
We have to choose:
2 cellists from 8 cellists;4 violonists from 7 violonists;4 cellists or violonists from 9 remaining musicians (8-2=6 - cellists left, 7-4=3 - violonists left, 6+3=9 - left musicians in total)1. 2 cellists from 8 can be chosen in
[tex]C_8^2=\dfrac{8!}{2!(8-2)!}=\dfrac{8!}{2!6!}=\dfrac{6!\cdot 7\cdot 8}{2\cdot 6!}=28[/tex]
different ways.
2. 4 violonists from 7 can be chosen in
[tex]C_7^4=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!3!}=\dfrac{4!\cdot 5\cdot 6\cdot 7}{4!\cdot 2\cdot 3}=35[/tex]
different ways.
3. 4 musicians from 9 can be chosen in
[tex]C_9^4=\dfrac{9!}{4!(9-4)!}=\dfrac{9!}{4!5!}=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9}{5!\cdot 2\cdot 3\cdot 4}=126[/tex]
different ways.
In total, there are [tex]28\cdot 35\cdot 126=123480[/tex] differnt ways to fill all vacancies.
David bought a bag of caramel chocolates and chocolate truffles in the ratio of 4 : 6. If the bag holds 24 caramel chocolates, how many chocolates in all did the bag contain?
Answer:
the number of chocolates in the bag is 60 in total
Step-by-step explanation:
Answer:
60 chocolates in total
Explanation:
If the ratio of caramel chocolates to chocolate truffles is 4:6 and we know there are 24 caramel chocolates, we can create a proportion.(X is the amount of chocolate truffles)
4/24=6/x
Solve for x.
144=4x
X=36
Now that we know how many of each chocolate there is, we can calculate the total by adding them together.
36+24=60 chocolates in total
Find the perimeter of each figure in questions. use 3.14 pi
Answer: 10.5
Step-by-step explanation:Find the perimeter of the figure. Use 3.14 for the pie and round your answer to one decimal.
This looks like a square with a line going from the right corner slanted down to the bottom left, but there is a half circle there so it doesnt actually touch the bottom left. on the right half of the line is 13 in.
A car travels in the direction of 135°. What is its compass heading?
SE ( South East) is the answer I believe
A car travels in the direction of 135° its compass heading is South and East.
We have given the direction of 135°.
North 315 West East ASE South Car travels in a direction of 315.
315 = 270'+ 45".
What is the measure of angle?
The degree measure of an angle is determined by the amount of rotation in degrees from the initial side to the terminal side.
The angle 315" lies between south and east. Making an angle of 45 towards south and east.
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given that (6,-3) is on the graph of f(x), find the corresponding point for the function f(1/3x)
Answer:
The corresponding point for the function [tex]f(\frac{1}{3}x)[/tex] is
(18, -3)
Step-by-step explanation:
By definition if we have a function f(x) and we apply the transformation:
[tex]y = f (hx)[/tex]
Then:
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this case [tex]h=\frac{1}{3}[/tex] this is [tex]0 <h <1[/tex] then the graph is stretched horizontally by a factor [tex]\frac{1}{\frac{1}{3}}=3[/tex]
Therefore the point (6, -3) that belongs to f(x), in the transformed function will be (3*6, -3) This is (18, -3)
Observe the example shown in the attached image
what is the value of the expression below 3 1/4 - 1 78
Answer:1 3/8
Step-by-step explanation:
3 1/4 = 3 2/8
1 7/8 =1 7/8
3 2/8 = 2 10/8
1 7/8 = 1 7/8
2 10/8-1 7/8 =1 3/8
Answer: =1 [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
First, Rewriting our equation with parts separated:
=3 + 1/4 − 1 − 7/8
Then, Solving the whole number parts:
3 − 1= 2
After, Solving the fraction parts
1/4−7/8=?
Find the LCD of 1/4 and 7/8 and rewrite to solve with the equivalent fractions.
LCD = 8
2/8−7/8=−5/8
Then, Combining the whole and fraction parts
2 − 5/8=1 3/8
Next, converting mixed numbers to fractions, our initial equation becomes,
134−158
Finally, doing all the work you answer is going to be :
=1/38* Hopefully this helps:)Mark me the brainliest:)!!
∞ 234483279c20∞
Part A
Which of the following is an expression for a in terms of x?
Part B
What is the maximum area, in square feet, for the garden if 44 feet of fencing are used?
I really need help with this question. I am doing Algebra NJSLAM practice and I’m not sure how to do this problem.
the first choice is correct
The maximum area of the rectangle will be 242 square ft. The expression for a in terms of x will be 44 - 2x. Then the correct option is C.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
If the a, b, and x are 44 ft. Then the expression for a in terms of x will be
We know that b = x
Then we have
a + b + x = 44
a + 2x = 44
a = 44 - 2x
Then the area opf the rectangle will be
Area = (44 - 2x)x
Area = 44x - 2x²
For maximum area the value of x will be 11. Then we have
Area = 44 × 11 - 2 × 11²
Area = 242 square ft
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Marissa Palmer’s charge account statement showed a previous balance of $142.55, a finance charge of $2.82, new purchases of $86.50, and a payment of $80.00. What is her new balance?
Answer:
$151.87
Step-by-step explanation:
The new balance includes the previous balance, plus finance/interests charges, plus the new purchases, minus the payment(s).
So,
Previous balance: $142.55
+ Finance charge: $2.82
+ New purchases: $86.50
= Sub-total: $231.87
- Payment: $80.00
= New Balance: $151.87
Marissa Palmer's new balance after considering her previous balance, finance charge, new purchases, and payment is $151.87.
Explanation:To calculate Marissa Palmer's new balance on her charge account statement, we need to consider several components: the previous balance, finance charge, new purchases, and the payment she made. We start with her previous balance, add any finance charges, add the cost of new purchases, and then subtract any payments. Here's the step-by-step calculation:
Start with the previous balance of $142.55.Add the finance charge of $2.82 to the previous balance, yielding $145.37.Add new purchases of $86.50 to the total, resulting in $231.87.Subtract the payment of $80.00 to find the new balance.When we do the subtraction ($231.87 - $80.00), we find that her new balance is $151.87.
Help please help ,,,,,
Answer:
18 cm²
Step-by-step explanation:
The area labelled A is a triangle.
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 9 and h = 4 ( the same height as the rectangle ), thus
A = [tex]\frac{1}{2}[/tex] × 9 × 4 = [tex]\frac{1}{2}[/tex] × 36 = 18 cm²
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Answer:
15. Radius
16. CF is parallel to AH , Option C
17. Option A , AB congruent to ST
Step-by-step explanation:
15. The line joining the center and any point on the circumference of a circle is the radius if the circle. Here Center is O and is being joined by B which lies on circumference hence OB makes a radius.
16. In a cuboid , all the heights are parallel to each other. Hence CF ║AH ║ BE ║ DG
Hence the right answer is option C
17. If we observe the two quadrilaterals we see that
A overlaps to S , B to T , C to U and D to V
Hence
AB is congruent to ST
i neyd hlpe
4.8 ÷ 0.6
Answer:
8
Step-by-step explanation:
4.8/0.6
4.8/(3/5)
4.8 * 5/3 = 8
Answer:
8
Step-by-step explanation:
The answer is 8 because you just divide the two numbers..
the owner of a video arcade center asked his weekend customers to record their age on a piece of paper and put it in a fishbowl near the cash register. after each day, the owner prepared a box plot to represent the data he collected. what was the the median age of his customers on each day
The median is the number in the middle of a list of numbers
So the middle number on Saturday is 18, and the middle number on Sunday is 22. Your answer is D
Answer:
The Medians on this set of data are 18 on Saturday and 22 on Sunday
Step-by-step explanation:
The median on a set of data is the middle number that separates the lower half from the top half in a set. For us to be able to find the median in a set of numbers, the numbers must first always be arranged from least to greatest. Since the set in the picture is already sorted, we can easily see that the medians are the following,
Saturday: 18
Sunday: 22
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Please help me asap!! Will mark as brainliest!!!200 points !!!!!!!! Find the area of the trapezoid given the coordinates: -3,3 -1,-3 1,-2 3,-3
what are we using ? feet, inches, etc.
Answer:
The answer is 4
Hope this helped
x^2+y^2-16x-161=0 factor it
(x-8)^2+y^2=225 I'm not able to factor it
Please I need help and no dumb answers please and explain please
a= 3
b=4
c=5
The Pythagorean Theorem.
a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9+16=25
25=25
✔
Step-by-step explanation:
I need to master all skills 8 left a lot of questions coming for math lovers
2 hours and 33 minutes have passes
Need help:(.... Simplify (b^5)^2
b^10 would be the correct answer :)
For this case we must indicate an expression equivalent to:
[tex](b ^ 5) ^ 2[/tex]
We have that by definition of properties of powers that is fulfilled:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Now, we can rewrite the given expression as:
[tex](b ^ 5) ^ 2 = b ^ {5 * 2} = b ^ {10}[/tex]
ANswer:
[tex]b^{10}[/tex]
Option A
(30 points of my grade) Emil would like to estimate the probability of 2 or more heads coming up in 3 coin flips.
To do this, he has a computer randomly select 0 or 1 three times, with 0 representing heads and 1 representing tails. The results of 12 trials are shown in the table.
111 011 000 010 100 111
010 111 111 101 000 111
What is Emil's estimated probability, based on this simulation?
Enter your answer as a fraction, in simplified form, in the box.
Answer:
Answer is 5/12 :)
About 14 out of 36 or 7 out of 18 because it’s selecting three numbers 12 times and 14 of them are 0s. And 14 out of 36 simplified is 7 out of 18.
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In 15 minutes Frankita created 15 drawings. In 30 minutes she created 17 drawings. In 45 minutes she created 20 drawings. In 60 minutes she created 24 drawings. If Frankita continues making drawings in the same pattern, how many total drawings will Frankita have created at the end of 90 minutes?
A. 19
B. 28
C. 33
D. 35
Answer:
D. 35
Step-by-step explanation:
the pattern followed by Frankita is:
15 min = 15 drawing
30 min = 17 drawing : increase by 2 (15+2 = 17)
45 min = 20 drawing : increase by 3 (17+3 = 20)
60 min = 24 drawing : increase by 4 (20+4 = 24)
75 min = 29 drawing : increase by 5 (24+5 = 29)
90 min = 35 drawing : increase by 6 (29+6 = 35)
What is 4n squared plus n squared?
Answer:
Step-by-step explanation:
Itś 5n²
I NEED HELP ASAP PLZZZZ LOOK AT THE PIC
Answer:
The red line is g(x)
Step-by-step explanation:
* To solve this problem you must to know some fact about
transformation
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
- A vertical stretching is the stretching of the graph away from
the x-axis
• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically
stretched by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed
by multiplying each of its y-coordinates by k.
• if k should be negative, the vertical stretch or compress is
followed by a reflection across the x-axis.
* Now lets solve the problem
- g(x) = -1/2f(x + 2)
# x + 2 ⇒ means the graph moved 2 units to the left
# -1/2 ⇒ means the graph has vertical compressed followed
by a reflection across the x-axis, then multiply
each y-coordinate by -1/2
- The graph of f(x) intersects x-axis at point (3 , 0)
∴ The point will be (1 , 0) on g(x)
- The graph of f(x) intersects y-axis at point (0 , -6)
∴ The point will be (-2 , 3) on g(x)
* Look to the graph
# The red line is g(x)
# The blue line is f(x)
- To check your answer
# The equation of f(x) is f(x) = 2x - 6
∵ g(x) = -1/2f(x + 2)
∴ g(x) = -1/2[2(x + 2) - 6] = -1/2[2x + 4 - 6] = -1/2[2x - 2] = -x + 1
* g(x) intersect x-axis at point (1 , 0) and y-axis at point (0 , 1)
what is 22 * 19 + area model
Answer:
(20+2)(10+9)
Step-by-step explanation:
The area model is written as (a+b)(c+d). To write a multiplication problem into an area model, split it into numbers which add to it. Multiples of 10 are most commonly used.
For example 22*19 becomes (20+2)(10+9).
simplify the expression for the length? A) x + 6 B)x – 6 C)x + 2 D)x – 2
Answer:
A on edge
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
how wide can a 5 m load be to fit under a parabolic underpass that is 7 m wide and 7 m at its highest point
Answer:
[tex]\boxed{\text{3.74 m}}[/tex]
Step-by-step explanation:
This is equivalent to finding the equation of a parabola from three points.
Let's call the ground-level points (-3.5, 0) and (3.5, 0).
The axis of symmetry will be the y-axis, so the vertex is at (0, 7).
Part 1. Find the equation of the parabola
The vertex form of the equation for a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
If the vertex is at (0, 7),
h = 0 and k = 7
The equation is
y = ax² + 7
Insert the point (0, -3.5)
0 = a(0 + 3.5)² + 7
0 = a(3.5)² + 7
0 = 12.25a + 7
-7 = 12.25a
a = -0.5714
The equation in vertex form is
y = -0.5714x² + 7
Part 2. Calculate the width when y = 5
5 = -0.5714x² + 7
-2 = -0.5714x²
x² = 2/0.5714
x² = 3.5
x = ±√3.5 = ±1.87
So, on the graph, the coordinates of the truck at ground level are x = -1.87 and x = +1.87.
The maximum width of the load is 1.87 – (-1.87) =[tex]\boxed{\textbf{3.74 m}}[/tex]
In the diagram below, the red parabola represents the underpass, and the blue box is the truck going through it.
Find the distance from the origin to the graph of 4x-y+8=0
Answer:
[tex]x=\frac{1}{4}y-2[/tex]
Step-by-step explanation:
x= 1 over 4y-2
Answer:
B. 1.94
Step-by-step explanation:
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Anne bought 3 hats for $19.50. which equation could be used to find the cost of each equation?
Answer:
19.50x 3 or 19.50+19.50+19.50
Step-by-step explanation:
You could either multiply it or divide!
Hope I helped!!
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yo I need this as soon as possible
Answer:
Step-by-step explanation:
So, if we know that 25 is the area of the square, that means that each side is 5. That also means the diameter of the circle is 5, so the radius is 2.5. Now, we can input the radius into the circumference formula for a circle, which is 2πradius. So, 2π2.5 which equals 5π, or about 15.71
Which statistical question could the data below answer ? Cost of toys
The statistical question that could be answered by the data is "maximum cost of toys".
The graph shown is a line graph which is a type of chart that displays data points connected by a line. It's a common way to visualize how a particular quantity changes over time or across different categories.
Line graphs makes it easy to determine statistical measures including minimum and maximum values of a category or data.
Here, the maximum cost of toys is 10 and the minimum is 5.
Jasmine wants to make a path from one corner of her yard to the other as shown. The path will be 3 feet wide. What is the area of the path?
Answer:
The answer is 90.
Step-by-step explanation:
Area of the path will be 90 square feet.
How to find the area of the path?The yard is rectangular in shape.In the figure, there are two right angles triangles on two sides of the pathArea of the path = (Area of the rectangular yard) - (Area of two right angled triangles)The width of the path is 3 feet. So, the base of the right angled triangle = (12-3) feet = 9 feet Area of the right angled triangle = base x height/2
= (9 x 30/2) square feet = 135 square feet
Area of the yard = ( length x breadth)= ( 30 x 12) square feet = 360 square feet
Area of the part = {360 - 2(135)} square feet= 90 square feet
Area of the path will be 90 square feet.
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How to simplify 11/3
3 2/3 the answer because....
11 cant fit into three so, if you divide 11%3 = 3 2/3 now let’s see, how much times can you multiply 3 into 11 only 3 times 3,6 and 9 (things) then the 2/3 is there because, if add 1 more 0.1 you get 12/3 but it’s not it’s 2/3 of the value
11/3 is already in its simplest fractional form as there are no common factors between 11 and 3. However, it can be expressed as a mixed number, which is 3 2/3 in this case.
Explanation:To simplify 11/3, you must first understand what it means to simplify a fraction. Simplifying a fraction means to reduce it to its simplest form, or to a form that can no longer be reduced. However, 11/3 is a fraction that cannot be simplified any further as there are no common factors between the numerator (11) and the denominator (3). It is in its simplest form. But, if we're looking to express this as a mixed number, we would divide 11 by 3. The result is 3 with a remainder of 2. Hence, 11/3 can be expressed as the mixed number 3 2/3
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