The greatest number of sets of pens and pencils that can be made, using all of the given 28 pens and 80 pencils in each set, is 4. Each set would contain 7 pens and 20 pencils.
Explanation:In the problem, we are looking to find the Greatest Common Divisor (GCD), which is the greatest number that can evenly divide both the number of pens (28) and the number of pencils (80). The GCD between 28 and 80 is 4.
Thus, the most sets of pens and pencils you can make would be equal to the GCD, which in this case is 4.
This means you can put together 4 sets with an equal number of pens and pencils in each set. In each of these sets, there would be 7 pens (28 pens ÷ 4 sets) and 20 pencils (80 pencils ÷ 4 sets).
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Final answer:
To maximize the number of sets with 28 pens and 80 pencils, find the greatest common divisor and divide the total by it. You can create 27 sets of 4 pens and 10 pencils each.
Explanation:
To find the greatest number of sets you can make with 28 pens and 80 pencils, you need to determine the highest common factor of the two quantities.
Calculate the greatest common divisor (GCD) of 28 and 80, which is 4.
Divide the total number of pens and pencils by the GCD: (28 + 80) ÷ 4 = 27.
You can make 27 sets, each consisting of 4 pens and 10 pencils.
Forrest Lumber purchased a table saw for $735. After 2 years the saw had a depreciated value of $525. What is the amount of yearly depreciation? A. $105 B. $210 C. $90 D. $120
Final answer:
The amount of yearly depreciation for the table saw is calculated by subtracting the depreciated value from the original cost and dividing by the number of years, resulting in an amount of $105 per year.
Explanation:
The question involves calculating yearly depreciation of an asset, which is a common topic in accounting and finance sections of high school mathematics or business studies.
To find the amount of yearly depreciation, we subtract the end value of the asset after depreciation from its original cost and then divide by the number of years over which the depreciation occurred. In this case, we have:
Original cost of the saw = $735
Depreciated value after 2 years = $525
Depreciation over 2 years = Original cost - Depreciated value
Depreciation over 2 years = $735 - $525 = $210
Yearly depreciation = Depreciation over 2 years ÷ Number of years
Yearly depreciation = $210 ÷ 2 = $105
Therefore, the yearly depreciation of the table saw is $105, which corresponds to option A.
Write the arithmetic sequence 17,20,23,26... in standard form
Answer:
an=3n+14
Step-by-step explanation:
Use the formula
an=a1+d(n−1) to identify the arithmetic sequence.
an=3n+14
The standard form of the
Explanation:An arithmetic sequence is formed by adding a constant value to each term. In this case, the first term is 17 and the common difference is 3 (since we add 3 to each term to get the next term).
The standard form of an arithmetic sequence is:
an = a1 + (n-1)d
Where:
an represents the n-th term of the sequencea1 represents the first term of the sequenced represents the common differenceLet's calculate the standard form for the given arithmetic sequence:
an = 17 + (n-1)3
So, the standard form of the arithmetic sequence 17, 20, 23, 26... is an = 17 + 3(n-1).
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to the nearest tenth, what is the length in units of MN?
Answer:
10
Step-by-step explanation:
Answer:
b) 6.7
Step-by-step explanation:
Point M has the coordinates (2, -3)
Point N has the coordinates (8, -6)
The length of the segment MN is computed as follows:
L =√[ (xN - xM)² + (yN - yM)² ]
L =√[ (8 - 2)² + (-6 - (-3))² ]
L =√[ 36 + 9 ]
L = 6.7
keith and michelle went out to dinner. the total cost of the meal,including the tip,came to $53.70. if the combined tip came out yo 9.60,and each friend spent and equal amouny,how much did each friend pay not including the tip?
Answer:
23.45
5
Step-by-step explanation:
53.70-9.60 is 46.90
46.90 divided by 2 is 23.45
Each friend paid $22.05 before the tip.
Keith and Michelle's dinner bill is a mathematics problem that can be solved by subtracting the tip from the total bill to find the cost of the meal alone and then dividing that amount by two to find out how much each friend has to pay without the tip.
First, we subtract the combined tip of $9.60 from the total cost of the meal, which was $53.70. This gives us the cost of the meal before the tip was added:
$53.70 - $9.60 = $44.10
Next, since Keith and Michelle spent an equal amount, we divide the cost of the meal by 2 to find out how much each friend pays:
$44.10 / 2 = $22.05
So, each friend paid $22.05 for the meal before adding in the tip.
The U.S. has about 190 million acres of national forest. One square mile is the same as 640 acres. How many states the size of Wyoming will cover the same area as all the national forests in the U.S.? Wyoming is shaped much like a rectangle. It is about 352 miles long and 278 miles wide:
Answer:
Around 3
Step-by-step explanation:
It is given that 1 sq. mile is equal to 640 acres.
Let's convert 190 million acres to sq. miles.
[tex]190,000,000*\frac{1Sq.Mi.}{640Acres}=296,875Sq.Mi.[/tex]
Taking Wyoming as a rectangle, we can find the area of Wyoming by multiplying length (352 miles) with width (278 miles).
Area of Wyoming is [tex]352*278=97,856[/tex]
To find the number of Whyoming's in total area of national forests, we divide the area of national forests (in sq. mi.) by the area of Wyoming ( in sq. mi.):
[tex]\frac{296,875}{97,856}=3.03[/tex]
So, around 3 Wyoming states' area will cover the area of national forests in US.
2. A forest preserve rents canoes for $18 per hour. Corey has $90 to spend. Write and solve an equation to find how many hours he can rent a canoe
Answer:
5 hours
Step-by-step explanation:
Let x be the number of hours.
18x=90
Divide by 18 on each side
x=5
Final answer:
Corey can rent the canoe for 5 hours with his $90 by setting up and solving the linear equation 18x = 90.
Explanation:
To determine how many hours Corey can rent a canoe, given that he has $90 to spend and the rental cost is $18 per hour, we can set up a linear equation. We let x represent the number of hours Corey can rent the canoe for.
The equation is simply 18x = 90, where 18 represents the hourly rental rate of the canoe and 90 represents the total amount Corey has to spend.
To solve for x, we divide both sides of the equation by 18:
18x / 18 = 90 / 18
x = 5
So, Corey can rent the canoe for 5 hours with his $90.
10p - (3p - 4) = 4(p + 1) + 9
Answer:
p = 3
Step-by-step explanation:
distribute parenthesis on both sides of the equation
10p - 3p + 4 = 4p + 4 + 9 ( simplify both sides )
7p + 4 = 4p + 13 ( subtract 4p from both sides )
3p + 4 = 13 ( subtract 4 from both sides )
3p = 9 ( divide both sides by 3 )
p = 3
Mrs. Rios puts tape around the section of wall shown to indicate the area of the mural she will paint. What is the area of the section she wants to paint?
The area of the section she wants to paint is 48 square feet.
In Euclidean Geometry, the area of a rectangle can be calculated by using this formula;
Area of rectangle = length × width
Area of rectangle 1 = 4 × 9
Area of rectangle 1 = 36 square feet.
For the area of rectangle 2, we have;
Area of rectangle 2 = 4 × 3
Area of rectangle 2 = 12 square feet.
Now, we can find the area of the figure;
Area of figure = 36 + 12
Area of figure = 48 square feet.
Complete Question:
Mrs. Rios puts tape around the section of wall shown to indicate the area of the mural she will paint. What is the area of the section she wants to paint?
On average a cow produces 7 gallons of milk per day on average how many cups of milk will a cow produce in a week
Nathan has two parents, four grandparents, and so on. Explain how you can write both an explicit formula and a recursive formula that represents the number of ancestors Nathan has if we go back n generations.
Answer:
Explicit formula
f(n) = 2*2⁽ⁿ⁻¹⁾
Recursive formula
f(n) = aₙ₋₁ * r
Step-by-step explanation:
Since, Nathan has two parents, four grandparents, and so on, it would form a Geometric Progression (GP) series for the number of Nathan's ancestors as below:-
2, 4, 8, 16, 32, ....
First term (a₁) = 2
Common Ratio (r) = [tex]\frac{a_{2} }{a_1}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
So,
Number of ancestors of Nathan if we go back n generations = a₁r⁽ⁿ⁻¹⁾
Plugging in the values of a₁ and r, we get
f(n) = 2*2⁽ⁿ⁻¹⁾ [Explicit formula]
Now,
A geometric progression (GP) series is of the form,
a, ar, ar², ar³, ar⁴, ar⁵........
in which the first term a₁=a and other the terms are obtained by multiplying with r.
Observe that each term is r times the previous term. So, to get the [tex]n_{th}[/tex] term, we multiply [tex](n-1)_{th}[/tex] term by r.
i.e. aₙ = aₙ₋₁ * r
=> f(n) = aₙ₋₁ * r [Recursive formula]
Which sequence of transformation will not result in a figure that is congruent to the original figure?
A) a rotation of 270° counter clockwise about the origin followed by translation of eight units to the right
B) A reflection over the Y axis followed by a rotation of 180° about the origin
C) a dilation with a scale factor of four followed by reflection over the x-axis
D) A reflection over the Y axis followed by a translation of 3 units to the left and 2 units to the right
Answer:
The correct option is C.
Step-by-step explanation:
Two figures are congruent if their corresponding sides are congruent.
We know that, reflection, rotation and translation are rigid transformation. It means the size and shape of image and preimage are same. We can say that in rigid transformation, the image and preimage are congruent.
Dilation is not a rigid transformation. It represents enlargement and compression.
If scale factor |k|>1, then it represent enlargement. If scale factor |k|<1, then it represent compression.
In option C, the scale factor is 4. It means the sides of image are 4 times of the preimage.
Therefore option C is correct and the resultant figure of option C is not congruent to the original figure.
Gretchen makes pillows using 1 5/8 yards of fabric per pillow. She has 8 1/4 yards of fabric. What is the greatest number of pillows Gretchen can make?
a( 4 , b(5 , c(6 , or d(8
Gretchen can make 5 pillows with the fabric she has.
Define fractionA fraction is a numerical quantity that represents a part of a whole. It consists of two numbers separated by a line, with the number on top called the numerator and the number on the bottom called the denominator
1 5/8 yards of fabric = 13/8 yards of fabric
8 1/4 yards of fabric = 33/4 yards of fabric
Number of pillows = (Total fabric) ÷ (Fabric per pillow)
Number of pillows = (33/4 yards of fabric) ÷ (13/8 yards of fabric per pillow)
Number of pillows = (33/4 yards of fabric) × (8/13 pillows per yard of fabric)
Number of pillows =5.076≈5
Hence, the greatest number of pillows she can make is 5, which corresponds to option (a) in the multiple choice list.
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The square of the sum of a number and 9 is ??????
[tex]n-a\ number\\\\(n+9)^2=n^2+2(n)(9)+9^2=n^2+18n+81\\\\Used\ (a+b)^2=a^2+2ab+b^2[/tex]
Answer:
(x+9)²
Step-by-step explanation:
The square of the sum of a number and 9 is in terms of x, is (x+9)²
WILL GIVE BRAINLIEST
Which of the following is true about the decimal form of the number? 892/16
A.
It is a terminating decimal.
B.
It is neither a terminating decimal nor a repeating decimal.
C.
It is both a terminating decimal and a repeating decimal.
D.
It is a repeating decimal.
Answer:
The answer is A.
Step-by-step explanation:
When 892/16 was put into decimal form I ended up with 55.75.
That is a terminating decimal.
Terminating decimal ends after a few number of digits.
Answer:
A
Step-by-step explanation:
April has 3 pounds of trail mix she put it on mountain each of eight bags how much trail mix is in each bag
A) 8/3 lb
B)3/8lb
C)1/5lb
D)1/24 lb
If possible please explain why.... THANKS in advance
Answer:
B)3/8lb
Step-by-step explanation:
We have 3 lbs or trail mix. We need to put it in 8 bags.
Take the pounds and divide by the bags.
3 lbs / 8 bags
Each bag will have 3/8 of a pound
Answer:
Pounds / bag = 3/8 = 3/8 of a pound per bag.
Step-by-step explanation:
What you are doing is saying that the total number of bags is 8
Each bag must contain the same amount of trail mix. So your units are pounds per bag. That is a very handy thing to know. It means that pounds is the numerator and bags is the denominator.
pounds = 3bags = 8pounds / bag = 3/8 Conclusion: each bag contains 3/8 pounds.Answer B
which graph has a coefficient correlation r closeest to -0.95
Answer:
Graph has a coefficient correlation r closest to -0.95 is the b).
Step-by-step explanation:
The correlation refers to the slope of a function and the sign indicates the direction to be linear the correlation informs us that it is inversely proportional
Taking some number to realice
Y axis maximum 5
X axis maximum 5
Notice 5 is where cut axis y so b=5
Equation:
[tex]y=mx+b\\y=-0.95x + 5[/tex]
Replacing:
x1=1.25; x2=2.5; x3=3.8;
So:
(1.25, 3.8); (2.5, 2.625); (3.8, 1.39)
The length of the base and the height of a triangle are numerically equal. Their sum is 6 less than the number of units in the area of the triangle. Find the area of the triangle.
Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?
5x + 3y = 18
5x - 3y = 30
5x - y = 30
5x + y = 18
The equation of line CD in standard form is;
B: 5x - 3y = 30
Equation of a lineFormula for slope of line between two coordinates is;
m = (y2 - y1)/(x2 - x1)
Thus, slope of line CD is;
m = (0 - (-5))/(6 - 3)
m = 5/3
Now, equation of a line in slope intercept form is; y = mx + cc is y - intercept which is when x = 0.
Point D gives us the x-intercept because y is zero.
Thus;
0 = (5/3)(6) + c
c = -10
Thus, the equation of the line CD is;
y = (5/3)x - 10
Multiply through by 3 to get;
3y = 5x - 30
>> 5x - 3y = 30
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John is twice as old as Bill. Greg is 7 years older than Bill. Four years ago, the sum of their ages was 55. How old is Greg?
Answer:
Greg is 67 years old.
Step-by-step explanation:
John = 2 * B
G = 7 + B
J - 4 + B - 4 + G - 4 = 55
J + B + G = 67
2B + B + 7 + B = 67
4B = 60
B = 15
J = 30
G = 22
30 + 15 + 22 = 67
67 = 67
- I.A -
The age of Greg is 31 years.
What is a linear equation?A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c.When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y if x is given.
Calculation:-
⇒let the actual age of Bill is X years.
four years ago the age Bill = X-4
⇒ then, the age of John is twice of Bill = 2X
four years ago age John = 2X-4
⇒Greg is 7 years older than Bill
Age of Greg = 2X+7
four years ago age Gerg = 2X+7-4
Four years ago Sum of their ages = 55
⇒ ( X-4)+(2X-4)+(2X+7-4)=55
⇒X-4+2x-4+2x+7-4=55
⇒5X=60
⇒X=12
∴age of Gerg is 2X+7
⇒2(12)+7
⇒31 years
age of bill=12 years
age of John 24 years.
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Select the two pairs of figures are similar
Answer:
1st and last group represent similar figures.
Step-by-step explanation:
We have been given a graph. We are asked to find the similar figures.
We can see that triangles in the 1st group are similar triangles as the measure of their corresponding angles are equal.
We can see that rectangle in the last group are also similar as the sides of the yellow rectangle is 2 times the sides of smaller rectangle, therefore, last pair is also similar.
Therefore, 1st and last group represent similar figures.
At lunch, $60\%$ of the students selected soda while $20\%$ selected milk. If 72 students selected soda, how many students selected milk?
Answer:
24 students
Step-by-step explanation:
If 60% equals 72, then 20% would be 1/3 of 72 which is 24.
Answer:
24 students selected milk
Step-by-step explanation:
Let x be the total number of students,
Since, 60% of students selected soda,
⇒ Number of students who selected soda = 60% of x = 0.6x
According to the question,
0.6x = 72
Divide both sides by 0.6,
⇒ x = 120
Now, 20% students selected milk
Hence, the number of student who selected milk = 20% of 120 = 0.20 × 120 = 24
Barry Olson just purchased 800 shares of an electronics corporation stock at $42.17 per share. His online broker charged him $10.00 commission. What was the total cost of the stock? Show work.
A) 22,489
B) 33, 579
C) 42, 458
D) 33, 746
Answer:
Option D) 33746
Step-by-step explanation:
Total shares: 800
Share price: $42.17
Commission charged: $10
Total price of shares: Total shares × share price
= 800 × 42.17 = 33736
Total Cost: Total price of shares + Total Commission charged
= 33736 + 10 = $33746
i need help, i dont like math
Answer:
#1 is -1
Step-by-step explanation:
The answer to Problem 1 is the number -1. You use PEMDAS to evaluate division first, then you subtract later.
For problem 2, we combine like terms to get this answer: -4a+b. You only add the 'a' terms together, same with the 'b' terms. Think of it like having 2 books and add on 3 more books. We can write that as 2b+3b = 5b. So we have 5 books total.
Problem 3) The answer here is 1.2n after adding n to 0.2n. Think of the first n as 1n or 1.0n
Problem 4) Divide both sides by 15 and you end up with the answer a = 2
Problem 5) Answer: 31.4 This answer is found by multiplying the diameter (10) by the approximate value for pi (3.14). The formula is C = pi*d
Which ordered pairs are on the line 3x−4y=9 ?
Select each correct answer.
(1,−32)
(−1,3)
(−5,−6)
(23,−74)
Answer:
The ordered pair that is on the line is (−5,−6)
Step-by-step explanation: You have to substitute...
Soooo....
(1,-32):
3x − 4y = 9
3(1) - 4(-32) = 9
3 + 128 = 9
131 = 9
NO
Remember, a negative times a negative becomes positive.(-1,3):
3x − 4y = 9
3(-1) - 4(3) = 9
-3 - 12 = 9
-15 = 9
NO
Remember, a negative times a positive becomes a negative.Remember, a negative plus a negative becomes a negative.(-5, -6)
3x − 4y = 9
3(-5) - 4(-6) = 9
-15 + 24 = 9
9 = 9
YES
(23, -74)
3x − 4y = 9
3(23) - 4(-74) = 9
69 + 296 = 9
365 = 9
NO
By substituting the x and y values from the given ordered pairs into the equation, we find that the only ordered pair on the line represented by the equation 3x−4y=9 is (-5,-6).
Explanation:The equation 3x−4y=9 represents a line on a coordinate plane, and ordered pairs (x, y) are points on this plane. To determine which given ordered pairs are on the line, we substitute each x and y value into the equation.
For (1,-32), the equation becomes: 3*1 - 4*(-32) = 9. This simplifies to 3 + 128, which does not equal 9, therefore (1,-32) is not on the line. For (-1,3), the equation becomes: 3*(-1) - 4*3 = 9. This simplifies to -3 - 12, which also does not equal 9, therefore (-1,3) is not on the line. For (-5,-6), the equation becomes: 3*(-5) - 4*(-6) = 9. This simplifies to -15 + 24, which equals 9. So, the ordered pair (-5,-6) is on the line. For (23,-74), the equation becomes: 3*23 - 4*(-74) = 9. This simplifies to 69 + 296, which does not equal 9, therefore (23,-74) is not on the line.
The only correct ordered pair on the line 3x−4y=9 is (-5,-6).
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What’s the rate of change described in the table
Rate of change:
Answer:
(x+4,y+5)
Step-by-step explanation:
If you look at the differences in the x and y rows t=you can see that x is added 4 each time and y is add 5 each time.
please help immediately
Answer:
Look Below
Step-by-step explanation:
I'm not going to do any of these, i'll just set up the equation for you to find x.
9. 75+x=90
10. x+22=180
11. x=84
12. 82+78+x=180
13. (4x+3)+(x-8)=90
14. (8x+9)+(5x+15)=180 (This was hard to read, check to see if I typed it right.)
15. 2x+4+140=180
16. 4x-13=67+2x
17. 9x+7=115
18. 12x=60
19. 4x=x+21
20. 5x+12+73=180
Simplify the expression by combining like terms. 23+6c+8d−7d−6
Answer:
17 + 6c +d
Step-by-step explanation:
To simplify the expression, we need to combine like terms
23+6c+8d−7d−6
I like to put like terms next to each other
23-6+6c+8d−7d
17 + 6c +d
23 + 6c + 8d - 7d - 6
combine like terms
= 6c + (8d - 7d) +(23 - 6)
= 6c + d + 17Can someone help me & explain, please?
Put the numbers in the data set in order from smallest to largest:
44, 45, 45, 47, 49, 50, 50, 51, 55, 55, 55, 56
The smallest number is 44, the largest is 56, so the outside lines need to be above those numbers.
Both A and B have that.
Now find the median ( the average of the middle two numbers)
The middle two numbers from the list are 50 and 50 so the median would be (50 +50) /2 = 100/2 = 50
The middle line inside the rectangle needs to be above 50.
This makes the answer A.
Can someone please help me??
You didn't specify which problems you needed and you are only allowed to submit three questions in one posting so I chose to solve 1, 3, and 5.
NOTES:
Inverse means to swap the x's and y's and solve for "y"
*********************************************************************
1. Answer: y = [tex]\frac{2x+4}{3}[/tex]
Step-by-step explanation:
y = [tex]\frac{-4+3x}{2}[/tex]
swap: x = [tex]\frac{-4+3y}{2}[/tex]
2x = -4 + 3y
2x + 4 = 3y
[tex]\frac{2x+4}{3}[/tex] = y
3. Answer: y = -3(x - 1)
Step-by-step explanation:
y = [tex]-\frac{1}{3}x[/tex] + 1
swap: x = [tex]-\frac{1}{3}y[/tex] + 1
x - 1 = [tex]-\frac{1}{3}y[/tex]
-3(x - 1) = y
5. Answer: y = [tex]-\frac{4}{9}[/tex](x - 4)
Step-by-step explanation:
y = 4 - [tex]\frac{9}{4}x[/tex]
swap: x = 4 - [tex]\frac{9}{4}y[/tex]
x - 4 = [tex]-\frac{9}{4}y[/tex]
[tex]-\frac{4}{9}[/tex](x - 4) = y
x/2+3=-5
solve step by step
Answer:
x=-16
Step-by-step explanation:
x/2+3=-5
Subtract 3 from each side
x/2+3-3=-5-3
x/2 = -8
Multiply each side by 2
x/2*2 = -8*2
x = -16