The most appropriate choice for LCM will be given by
Smallest number of gift boxes Katy can fill is 56
What is LCM?
Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.
Here,
Katy buys toys in bags of 8.
Katy buys keyrings in bags of 14.
Each gift box will contain one toy and one keyring.
Number of gift boxes Katy can fill has to be a common multiple of 8 and 14
Smallest number of gift boxes Katy can fill is the least common multiple of 8 and 14
Now,
8 = 2 x 2 x 2
14 = 2 x 7
LCM of 8 and 14 = 2 x 2 x 2 x 7
= 56
Smallest number of gift boxes Katy can fill is 56
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6. A solid wooden cylinder of height 8 cm and radius 3 cm is cut in two along a vertical axis of symmetry. Calculate the total surface area of the two pieces.
Total surface area of cylinder is 303.34 [tex]cm^{2}[/tex]
What is cylinder ?A cylinder is a 3D solid shape made up of two bases that are parallel and identical and are connected by a curved surface. These bases resemble spherical disks. The axis of the cylinder shape is a line drawn through the center or connecting the centers of two circular bases.
The surface area of a cylinder is
SA = [tex]2\pi r^{2}[/tex] + 2πrh
where:
r = radius
h = height
This formula comes from adding the areas of the surfaces of the cylinder. It has two flat circular faces and a rounded face.
If we cut the cylinder from the circular face symmetrically, the surface area for one piece will be
SA = 2[[tex]\frac{\pi r^{2} }{2}[/tex]] + ([tex]\frac{2\pi r}{2}[/tex])h + 2rh
We will have 2-half flat circular faces, a flat rectangular surface, and half of the rounded surface.
Simplify the SA formula.
SA = [tex]\pi r^{2}[/tex] + πrh + 2rh
SA = r(πr + πh + 2h)
Substitute the values into this formula.
SA = 3(3π + 8π + (2×8))
SA = 3(11π + 16)
SA = 33π + 48
SA = 151.67[tex]cm^{2}[/tex]
Since we have 2 pieces, multiply this result by 2.
2(151.67[tex]cm^{2}[/tex]) = 303.34[tex]cm^{2}[/tex]
Total surface area is 303.34[tex]cm^{2}[/tex]
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plsssss help meeeeeeeeeeeeeee
Answer:
136 ,24 ,180 ,34
Step-by-step explanation:
Find the equation of a line that passes through the point (1,-3) and has a gradient of 3.
Leave your answer in the form
a
x
+
b
y
=
c
Where
a
,
b
and
c
are integers.
Answer:
3x+1y=0
Step-by-step explanation:
the equation of a straight line on a graph is y= mx+c
where m is the gradient and c is the y intercept.
we know that the line passes through (1,-3) and has a gradient of 3, therefore we can substitute these values into the equation.
-3 = 3*1 +c
3 = 3+c
c = 3-3 = 0
therefore the equation of this line is y = 3x+0
now we have to write this in the form ax+by=c
3x+1y=0
Aviv and Marco were trying to describe the parts of the expression 5a/2a+3.
- Aviv said, "The entire expression is the quotient of 5a and 2a+3"
- Marco said, "On it's own, 2a+3 is a sum with 2 terms."
Who is correct?
Choose one answer:
A: Only Aviv
B: Only Marco
C: Neither student is correct
D: Both students are correct
After evaluating the algebraic expression we can infer that both students were correct.
An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .
If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).
The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).
Again the expression 2a +3 is a sum with only two terms.
Hence both students were correct.
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After evaluating the algebraic expression we can infer that both students were correct.
An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .
If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).
The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).
Again the expression 2a +3 is a sum with only two terms.
Hence both students were correct.
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Apply Laws of Exponents to write an equivalent expression.
(3y)-4. (2z)-4
After Applying Laws of Exponents we can write as [tex](6yz)^{-4}[/tex]
What is law of exponents ?The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.
How are powers of powers multiplied?Exponents with distinct bases and the same powers can be multiplied by multiplying the bases and writing the power outside of the brackets.
[tex]a^{n}[/tex] .[tex]b^{n}[/tex] =[tex](a.b)^{n}[/tex]
=[tex]3y^{-4}[/tex] . [tex]2z^{-4}[/tex]
=[tex]3y^{-4}[/tex] . [tex]2z^{-4}[/tex]
= [tex](6yz)^{-4}[/tex]
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In the following equation, what would be the most logical first step when solving for z.
Answer:
Multiply 5/2 to both sides
Step-by-step explanation:
Doing so 'cancels' out the coefficient of (z+1) on the left-hand side.
HELP thanks and 5 stars to the best answer. Enter the value of the smiley face?
The value of the smiley face given the values of the rectangle, triangle and star is 908.
What is the value of the smiley face ?In order to solve this question, take note of the BODMAS rule. The BODMAS rule gives the order in which mathematical operations should be solved.
B - bracket O - of D - division M - multiplication A - addition S - subtractionThe value of the rectangle would be determined first using the third equation provided in the question. let a represent the value of a rectangle.
(4 x a) + (2 x a) - (3 x a) = 15
4a + 2a - 3a = 15
3a = 15
a = 15 / 3
a = 5
The next step is to determine the value of the triangle. The second equation would be used. Let b represent the value of the triangle.
(3 x 5) + (4 x b) = 47
15 + 4b = 47
4b = 47 - 15
4b = 32
b = 32 / 4
b= 8
Now, determine the value of the star using the first equation. Let the value of the star be represented with c.
5 + (3 x 8) - c = 17
5 + 24 - c = 17
29 - c = 17
c = 29 - 17
c = 12
Now, the value of the smiley face can be determined using the last equation:
12 x (8 + 12 - 5) + 8(8 . 12 - 5)
12 x (15) + 8(91)
180 + 728 = 908
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2(3x +4) -(x-2)
expand and simplify
5x + 10 is the simplified form of the expression 2( 3x + 4 ) - ( x - 2 ).
What is the simplified form of the given expression?Given the expression in question;
2( 3x + 4 ) - ( x - 2 )
To expand and simplify, get rid of the first parenthesis using distributive property.
2( 3x + 4 ) - ( x - 2 )
3x( 2 ) + 4 ( 2 ) - ( x - 2 )
6x + 8 - ( x - 2 )
For the second parenthesis, the negative sign before it affects everything inside it, hence;
6x + 8 - ( x ) - ( - 2 )
6x + 8 - x + 2
Collect like terms
6x - x + 8 + 2
Add 6x and -x
5x + 8 + 2
Add 8 and 2
5x + 10
Therefore, the simplified form of the expression is 5x + 10.
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identify 5/6 as irational number
If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the
square?
Answer:
approximately 31.96 m (you can round to 32m)
Step-by-step explanation:
If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the
square?
find the area with the formula ½ × d ^ 2 Square units, take the square root of the result and find the side, multiply by 4 and you have the perimeter.
AREA1/2 11.3^2 =
1/2 127,69 =
63.845 m²
SIDE√63.845 =
7.99 m
Perimeter7.99 * 4 =
31.96 m
Use the point and the slope to graph each line. Write the equation of the line. The line contains point (1,-1) and is perpendicular to a line with slope 1
ANSWER ASAP
20 POINTS AND BRAINLIEST IF FIRST
the equation of the line will be x + y = 0 and it is being graphed.
Point on the line = (1, -1)
Slope of the perpendicular line = 1
So, the slope of the line will be
m × 1 = - 1
m = - 1
Equation of the line will be given by:
y - y₁ = m (x - x₁)
y - (- 1) = (- 1) (x - 1)
y + 1 = - x + 1
x + y = 0
We have graphed the equation.
Therefore, we get that, the equation of the line will be x + y = 0 and it is being graphed.
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michael is one-third of keanus age if the sum of their ages is 52 how old is michael
Answer:
Michael age is 13 and keanus age is 39
Step-by-step explanation:
Michael is 1/3 of keanus age
so Michael is 1 and keanus is 3 so if u add them all up it's 4 so 52 divide by 4 it's 13 so Michael is 13 and if you times three it will be 39, and if u add their age together it adds up to 52 so it's 13
Margie has 15 feet of ribbon. It takes 7/8 of a foot of ribbon to make a bow for a bouquet. How many bows can Margie make with her ribbon?
Margie can make 13 bows with her ribbon.
In the US, a foot is used to measure length or distance. "Feet" is the plural form of the single unit of measurement known as "foot." Foot or feet are denoted by the letter ft.
Margie has 15 feet of ribbon.
To make a bow for a bouquet, it takes 7/8 of a foot of ribbon for a bouquet.
1 bow = 7/8 × 1 foot
Therefore, the number of bows Margie can make with the ribbon will be:
Number of bows = 7/8 × 15 feet
Number of bows = 13.125 ≈ 13
Hence, Margie can make 13 bows with her ribbon.
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If you have $1400 ).and you spend 1/8of it on school supplies and 1/4 of it on groceries and 5/16 of it on clothes what is the total fraction spent
Answer: 11/16
Step-by-step explanation:
1/8=2/16
1/4=4/16
5/16=5/16
add it all together
find the sum of 6 terms in the sequence 3,6,12, ...
If the area of a square shaped rug is 81 in², what is the
measurement
of ONE SIDE of the rug?
Answer: 9 inches
Step-by-step explanation:
We know that the area of a square can be solved with the following formula when s is the length of one side. We will plug in our known values and solve:
a = s²
(81) = s²
[tex]\sqrt{81}[/tex] = s
9 in = s
One side of the rug is equal to 9 inches.
30 Points!!!
AOC and BOD are diameters of a circle, centre O.
Prove that triangle ABD and triangle DCA are congruent by RHS.
Answer:
Answer:
SAS postulate
Step-by-step explanation:
AD (common)
AC = BD (both are diameters)
Angle COD = Ange AOD (vertically opposite angles)
Angle CAD = Angle BAD (angle on the circumference is half the angle at the centre)
Therefore, ABD and DCA are congruent by SAS postulate
Step-by-step explanation:
not even 30 points lol it says 18 ANYWAYS hope this helps
A group of friends decided to buy bulk chocolate from a candy store. If some friends
each want 1/7 of a kilogram of chocolate of the 10 kilograms of chocolate
purchased, then how many people can get a share of chocolate?
70 people can get share from the chocolate.
What is share?Real estate investment trusts, limited partnerships, and mutual funds all employ shares as a sort of unit. A share is an immovable unit of capital that symbolizes the ownership connection between the company and the shareholder. The denominated value of a share is its face value, which could not be the same as the share's market value.
The capital of a firm consists of the whole face value of its issued shares.
Total amount of chocolate purchased = 10 kg
Amount of chocolate each friend want =1/7 kg
So, number of people who can get share = 10 / (1/7)
= (10×7)/1
= 70 people
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Maran is selling candy apples at a fund-raiser for a charity. She made 160 candy apples and spent $120 on ingredients and supplies. She sold all the candy apples for $480.
Select TWO statements that are true.
A.Maran spent $3 on each candy apple.
B.Maran spent $0.75 on each candy apple.
C.Maran sold each candy apple for $4.
D.Maran earned a profit of $3 on each candy apple sold.
E.Maran sold each candy apple for $3.
If Maran made 160 candy apples, spending $120 on ingredients and supplies while selling all the candy apples for $480, then the two statements that are true are:
B. Maran spent $0.75 on each candy apple (Cost Price), and
E. Maran sold each candy apple for $3 (Selling Price).
As per the question statement, Maran made 160 candy apples, spending $120 on ingredients and supplies while selling all the candy apples for $480.
We are required to identify the two true statements from a the set of 5 statements, provided in the question itself, related to the per candy cost price, sell price and profit of Maran.
Since he made 160 candy apples, spending $120 on ingredients and supplies, therefore, the cost price of per candy will be $(120/160) = $0.75, i.e., Statement B that Maran spent $0.75 on each candy apple is True.
Also, he sold all 160 candies for a total of $480, therefore, the sell price of each candy is $(480/160) = $3. Hence, Statement E that Maran sold each candy apple for $3., is also true.
Now, since the cost price of each candy is $0.75 and the sell price of the same is $3, then Maran made a profit of $(3 - 0.75) = $2.25 per candy. But statement D mentions that Maran earned a profit of $3 on each candy sold, which is false.
Cost Price: It is the price at which, an object or commodity is manufactured or bought at, by the retailer.Selling Price: It is the price at which, the commodity is sold by the retailer, and if the selling price is higher than the cost price, the retailer is said to earn a profit, while in the opposite case, the retailer is said to incur a loss.To learn more about Cost Prices & Selling Prices, click on the link below.
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You earn $100 per month and want to save 10% in a savings account.
How much will your monthly contribution be? (Do not include the $ sign in your
response) PLEASE HELPP
A rental company rents a luxury car at a daily rate of $38.48 plus $.50 per mile. Paul is allotted $110 for car rental each day. Write an equation to represent the cost C of renting a car and driving x miles.
How many miles can Paul travel on the $110?
Answer:
C=38.48+0.5x
about 143 miles
Step-by-step explanation:
$38.48 base cost plus $.50 per mile, so after x miles, it would be 0.5x
so C=38.48+0.5x
to find how many miles Paul can travel
we set 110=38.48+0.5x
then solve
x=143.04
so Paul can travel about 143 miles
Write an equation in point-slope form form for the lines that passes through the given point and has the given slope. (3, 2); m = 5
Answer:
y=5x-13
Step-by-step explanation:
1. (3,2) = x,y
2. substitute each x and y digit into y=mx+b format
3. 2=5(3)+b
4. solve for 2=5(3)+b which equals b=-13
5. ANSWER IS SOLVED WHEN ANSWERED IN y=mx+b FORMAT
5. y=5x-13
Does anyone know how to do this? Or tell me how you do these questions?
The equation of line in slope intercept form can be written as y = mx + c where m is the slope of line and c is the y intercept.
We are given three equations namely y = 2x -2, y = -x + 1 and y = x - 4 and we need to determine the description of equation, slope and y intercept. The equation y = 2x - 2 is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = 2 and c = -2. Thus, slope is 2 and y intercept is -2. The equation y = -x +1 is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = -1 and c = 1. Thus, slope is -1 and y intercept is 1. This equation y = x - 4is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = 1 and c = -4. Thus, slope is 1 and y intercept is -4. The graphs of the equation are attached below.
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which equation represents the lines through (2, -4) and (0, 4)?
The equation that represents the lines through (2, -4) and (0, 4) is y = -4x + 4
How to determine the equation of the lineIt is crucial to note that the equation of a line is expressed as;
y = mx+ c
Where;
y is a point of the distance on the y-axisx is a point of the distance on the x-axism is the slope or gradient of the linec is the intercept of the line on the y-axisFrom the information given, we have the point as;
(2, -4) and (0, 4)
Now, let's determine the slope
The formula for determining the slope or gradient of a line is expressed as;
Slope, m = y2 - y1/x2 - y1
Now, substitute the values into the formula
Slope, m = 4 -(-4)/0 -2
expand the bracket
Slope, m = 4 + 4/-2
Add the values
Slope, m = 8/-2
Slope, m = -4
To determine the intercept, use the points of x and y
-4 = -4(2) + c
expand the bracket
-4 = -8 + c
c = -4 + 8
c = 8
The equation of the line is;
y = -4x + 4
Thus, the equation of the line is y = -4x + 4
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16
Adrian, Bhamini and Chas share a sum of money.
1
Adrian gets
6
Bhamini gets
of the money.
1
3
Chas gets the rest of the money.
Adrian gets £42
(a) Work out how much money Bhamini gets.
of the money.
Answer: 84
Step-by-step explanation:
Bhamini =
42 x 6 = 25.2
25.2 x 1/3 = 84
Chas =
252.84 - 42 = 126
Bhamini gets £84!
Hope this answered your question, don't ell Mr Gohil I helped you lol.
Answer provided by Zack.
A carpenter has a 15 foot ladder. For safety, the bottom of his ladder must be placed 5 feet from the wall. In order to complete his work, the ladder must reach 14.5 feet up the wall. Under these conditions, can the carpenter complete his work? Rounded to the nearest tenth, how far up the wall does the ladder reach?
The carpenter will not be able to complete his work because the ladder reach 14.1 ft up the wall.
In this question, we have been given a carpenter has a 15 foot ladder. For safety, the bottom of his ladder must be placed 5 feet from the wall.
Consider the following diagram.
In right triangle ABC, AC represents the length of the ladder, CB is the distance between wall and the bottom of the ladder.
Using Pythagoras theorem,
AC² = AB² + BC²
15² = 5² + AB²
225 - 25 = AB²
AB = √200
AB = 14.1 ft ............(1)
We have been given that in order to complete his work, the ladder must reach 14.5 feet up the wall.
From (1), we can see that the ladder will reach 14.1 ft up the wall.
This means, under these conditions, the carpenter will not be able to complete his work.
Therefore, the carpenter will not be able to complete his work because the ladder reach 14.1 ft up the wall.
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Need help on finding the domain and range
The domain and the range of the graph are x >= 1 and -∝ < y < ∝, respectively
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 1 and it extends indefinitely to the right
This means that the domain is x >= 1
The range
On the graph of the function, we can see that:
The y values extend indefinitely on all sides of the coordinate plane
This means that the range is -∝ < y < ∝
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f(x) =square root of x -6. find the inverse of f(x) and it’s domain
The equation of the inverse function is f'1(x) = x^2 + 6 and the domain is all set of real numbers
How to determine the inverse functions?The function f(x) is given as
f(x) = √x -6
Rewrite as
y = √x -6
Switch/swap the positions of x and y in the above equation
The equation becomes
x = √y -6
Make y the subject of the formula in the above equation
The equation becomes
y - 6 = x^2
Add 6 to both sides
y = x^2 + 6
Rewrite as an inverse function
f'1(x) = x^2 + 6
Hence, the inverse function is f'1(x) = x^2 + 6
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Answer:
f(×)=(×+6)^2;×>-6 there we go..
The amount of time Demi spends studying and her test scores have a proportional relationship. Complete the table. __________ Complete the table.
Both of the blanks given in the table can be filled in by the ratio 18/1.
Here, we are given a table as shown in the image given above.
There is a proportional relationship given between Demi's test scores and her studying time.
When she studies for 3 hours, her test score is 54.
Thus, the ratio of her test score to hours studying is - 54/3
= 18/1
Similarly, when she studies for 4 hours, her test score is 72.
Thus, the ratio of her test score to hours studying is - 72/4
= 18/1
Thus, both of the blanks given in the table can be filled in by the ratio 18/1.
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What is the solution to the inequality |2x – 3| > 5?
A) x < –1 or x > 4
B)x < 0 or x > 8
C)0 < x < 8
D)–1 < x < 4
The solution to the inequality |2x - 3| > 5 is: x < -1 or x > 4
Therefore, the correct option is A) x < -1 or x > 4.
Given that we need to find the solution to the inequality |2x – 3| > 5
To solve the inequality |2x - 3| > 5, we can break it down into two cases:
Case 1: 2x - 3 > 5
In this case, we have:
2x - 3 > 5
2x > 5 + 3
2x > 8
x > 4
Case 2: -(2x - 3) > 5
In this case, we have:
-(2x - 3) > 5
-2x + 3 > 5
-2x > 5 - 3
-2x > 2
x < -1 (remember to reverse the inequality when multiplying or dividing by a negative number)
Combining the solutions from both cases, we find that the solution to the inequality |2x - 3| > 5 is:
x < -1 or x > 4
Therefore, the correct option is A) x < -1 or x > 4.
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