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Related Questions
are the fractions 1/2 and 1/8 equivalent fractions
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1/2 and 1/8 are not equivalent, meaning they are not valued as the same.
1/2 is larger than 1/8 because 1/2 is pretty much half of 1 whole, while 1/8 is smaller than half of 1 whole.
Hope this helps you.
Have a great day! (:
The denominator of the fraction number is different. Then the fraction numbers are not equivalent fractions.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
The fraction numbers are given below.
1/2 and 1/8
In the fraction numbers, the numerator is the same. If the denominator is the same, then the numbers will be equal.
The denominator of the fraction number is different. Then the fraction numbers are not equivalent fractions.
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The diagram represents the floor of a museum. The figure is made up of a rectangle and a triangle.
What is the area of the floor?
Enter your answer in the box.
______ ft2 I'll but the link for the pic
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The figure is formed of a rectangle and a triangle
The rectangle has dimensions:length=38ft and width=20ft
The triangle has dimensions:base=33ft and height=9ft
Area of rectangle=length*width of rectangle
Area of triangle=[tex] \frac{1}{2} [/tex]*base*height
Area of figure= area of rectangle + area of triangle
Area=length*width+[tex] \frac{1}{2} [/tex]*base*height
Area=38*20 + [tex] \frac{1}{2} [/tex]*33*9
Area=760+[tex] \frac{1}{2} [/tex]*297
So we have, Area=760+[tex] \frac{297}{2} [/tex]
Or, Area=760+148.5
Area=908.5
Area of the floor=908.5[tex] ft^{2} [/tex]
Describe how dividing by 2 is the same as finding 1/2 of 1/4
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1/4:1/2=1/4•2/1=2/4=1/2
To understand 1/4 dividend by 1/2 lets start with understanding what division does;
1/4 dividend by any number greater than 1 will make smaller quantities than 1/4 because you cut that 1/4 to make out of it 2 or 3 or 4...etc. equal groups
1/4 : 2 = 1/8
1/4 cut to make 2 groups =2 groups of 1/8
1/4 dividend by a number smaller than 1 like 1/2 will make you bigger quantity than 1/4 because because you don’t make not even a whole group yet a half (1/2) a group.
1/4: 1/2= 1/4 •2= 1/2
One angle is eight times it’s supplement increased by 45 degrees. What is the measures of the two supplementary angles?
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Angle 2 = x
x + 8x + 45 = 180
combine like terms
9x + 45 = 180
subtract 45 from both sides
9x = 135
divide both sides by 9 to isolate x
x = 15
Angle 1 = 8(15) + 45 = 165 degrees
Angle 2 = 15 degrees
A retired couple invested $6000 in bonds at a simple interest rate of 5.1%. At the end of one year, how much interest did they receive on their investment? Please show your work.
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[tex] \frac{5.1}{100} \times 6000 \\ = 0.051 \times 6000 \\ = 306 \\ 306 + 6000 = 6306[/tex]
they have received $306
The retired couple received $306 in simple interest on their investment of $6000 at a rate of 5.1% for one year.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the simple interest earned by the retired couple on their investment of $6000 at a rate of 5.1% for one year
we can use the formula: I = P × r × t
where I is the simple interest,
P is the principal (the amount invested),
r is the interest rate (as a decimal), and
t is the time period (in years).
Plugging in the given values, we get:
I = 6000 × 0.051 × 1
I = 306
Therefore, the retired couple received $306 in simple interest on their investment of $6000 at a rate of 5.1% for one year.
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Which pair of expressions is equivalent using the Associative Property of Multiplication? (3 points) 5(3a ⋅ 4) = 15a ⋅ 20 5(3a ⋅ 4) = (3a ⋅ 4) ⋅ 5 5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4 5(3a ⋅ 4) = 5 ⋅ 3a ⋅ 4 6
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Answer:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
Step-by-step explanation:
The Associative Property is applied to two types of operations: addition and multiplication. This property indicates that, when there are three or more terms in these operations, the result does not depend on the way in which the terms are grouped.
In this sense, the associative property for the sum is mathematically given by:
[tex](x+y)+z=x+(y+z)[/tex]
and for the multiplication by:
[tex](xy)z=x(yz)[/tex]
Now, let:
[tex]x=5\\y=3a\\z=4[/tex]
Using the Associative Property of Multiplication:
[tex](xy)z=x(yz)\\\\Replacing\hspace{3}the\hspace{3}values\\\\(5\cdot 3a)\cdot4=5(3a\cdot 4)[/tex]
Therefore the equivalent expressions are:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
Answer: C
Step-by-step explanation: Sorry If I am wrong, ty!!
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a copper alloy that is 40% copper is to be combined with a copper alloy that is 80% copper to produce 120 kilograms of an alloy that is 70% copper. how many kilograms of each alloy must be used? please work it out
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1. note, that in such tasks mass of pure copper before merging and after merging is the same (this is the base);
2. If the mass of pure copper in alloy with 40% solution is 'x' and the mass of pure copper in alloy with 80% solution is 'y', then It means before merging was x/0.4 and y/0.8, after merging was (x+y)/0.7. It is one equation of the future system.
3. Using 120 kg. of 70% solution, it is possible to define mass of pure copper after merging, 120*0.7(=84 kg.). And before merging it was 'x+y' kg. of pure copper. It is the second equation of the future system.
4. according to the items no.2&3 (to make up the system of two equations and solve it). All the details are in the attached picture.
5. pure copper in 40% solution is 12 kg., pure copper in 80% solution is 72 kg. It means, that the copper alloy with 40% solution is x:0.4=12/0.4=30 kg., and the copper alloy with 80% solution is y:0.8=72/0.8=90 kg.
After setting up and correcting a system of equations, the student needs to use 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy to create 120 kg of a 70% copper alloy.
To solve this problem, we need to set up a system of equations. Let x be the amount of 40% copper alloy needed, and y be the amount of 80% copper alloy needed.
First, we have the total weight equation:
x + y = 120 kg (the final alloy's total weight)
Next, we have the copper content equation:
0.40x + 0.80y = 0.70 × 120 kg (the final alloy's copper content)
Now, let's solve this system of equations:
Address the second equation: 40x + 80y = 8400
Express x in terms of y: 40x = 8400 - 80y
Divide by 40: x = 210 - 2y
Substitute x in the first equation: (210 - 2y) + y = 120
Solve: 210 - y = 120, y = 90 kg
Finally, substitute the value of y back into x = 210 - 2y: x = 210 - 2 imes 90 = 210 - 180 = 30 kg
So, we need 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy.
solve and write multiplication equations
72=0.6r
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72/0.6 = 0.6r/0.6
r = 120
what is the missing reason in the proof?
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Answer:
Perpendicular bisector theorem
Step-by-step explanation:
Perpendicular bisector theorem: if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.
So, if segment ST is the perpendicular bisector of segment RV, then, by perpendicular bisector theorem, any point in segment ST (like S) is equidistant from points R and V, in consequence, segments RS and SV are equal.
For which of these does correlation most likely imply causation?
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Correlation most likely implies causation in the following case: As rainfall increases, the number of umbrellas sold increases.
"Correlation doesn't always imply causation" is a common saying in statistics. Sometimes when there's a high correlation coefficient between two variables, that doesn't always mean that one is the cause for the other.
When rainfall increases, people are in need of umbrellas and often buy new ones, so for this pair of variables, the correlation most likely implies causation.
Have a nice day!
Answer:
As the use of a condition that increases the electricity bill increases as well
Step-by-step explanation:
What is the period of y = 3cot(4x - 3pi)
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The period is π/2.
The period of y = 3cot(4x - 3pi) is π/2 units.
The period of the function y = 3cot(4x - 3π) is calculated as the reciprocal of the absolute value of the parameter in front of x.
To find the period, identify the coefficient of x, which is 4 in this case. The period is then given by 2π/|4| = π/2.
Therefore, the period of the given function y = 3cot(4x - 3π) is π/2 units.
Keith had 694 green, yellow and blue marbles altogether. he had 3 times as many blue marbles as yellow marbles. there were 90 fewer green than blue marbles. how many blue marbles did Keith have?
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number of yellow marbles = x/3
number of green = x- 90
ATQ
x + x/3 + x - 90 = 694
2x + x/3 = 784
(6x + x)/3 = 784
7x/3 = 784
x = 784 x 3/7
x = 112 x 3
x = 336
number of blue marbles = 336
We have
[tex]g + y + b = 694[/tex] (we will call this equation 1)
Also, [tex]b = 3*y[/tex] (yellow marbles are three times as many as blue marbles), so equation 1 becomes
[tex]g + y + 3y = 694[/tex]
But, [tex]g = b - 90[/tex] (green marbles are as many as blue marbles - 90)
and because [tex]b = 3*y[/tex], we have that [tex]g = 3*y - 90[/tex]
So, equation 1 is now
[tex]3y - 90 + y + 3y = 694[/tex]
[tex]7y - 90 = 694[/tex]
We add 90 to both sides so
[tex]7y = 694 + 90 = 784[/tex]
We divide each side by 7, so finally
[tex]y = 112[/tex]
and we have
[tex]b = 3*y = 3*112 = 336[/tex]
and
[tex]g = b - 90 = 336 - 90 = 246[/tex]
To check if our results are correct, we can see that
[tex]g + b + y = 246 + 336 + 112 = 694[/tex],
so we are indeed correct.
Find the area of a parallelogram with base b and height h. B= 74cm H=14.8 cm
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General Idea:
The formula to find the area of parallelogram is given below:
[tex] Area \; of\; the\; parallelogram=BASE \times HEIGHT\\ \\ [/tex]
Applying the concept:
Given, [tex] BASE\; (B)= \; 74\; cm\\ HEIGHT \;(H)=14.8 \;cm\\\\ Area \; of \; the \; Parallelogram = 74 \; cm \times 14.8 \; cm = 1095.2 \; cm^{2} [/tex]
Can someone help with this question please?
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Multiply the number bagged by the number of pounds of each bag.
x= (5 * 1/4 lb) + (2 * 1/2 lb)
x= [(5*1)/4] + [(2*1)/2]
x= 5/4 + 1
convert fraction to mixed number
x= 1 1/4 + 1
x= 2 1/4 total pounds bagged
ANSWER: Libby bagged 2 1/4 pounds of crackers.
Hope this helps! :)
Prove that the angle bisector of the angle opposite to the base of an isosceles triangle is also the altitude to the base
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.. apex angle is divided into 2 equal parts
.. base angles are equal
.. side lengths are equal
1. The triangles are congruent by ASA
2. The angles where the bisector meets the base add to 180°. (They are linear angles formed by the bisector and the base.)
3. The angles where the bisector meets the base are congruent. (The are corresponding angles of congruent triangles.
4. The angles where the bisector meets the base are 90°. (Congruent angles that add to 180° must be 90°.)
5. The bisector is a line from the apex meets the base at a right angle, so is an altitude. (Definition of altitude.)
what direction is 45 degrees in clockwise from due east?
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45° clockwise from due east is just 45° from the east. Moving clockwise, which is the direction the hands of a clock move, you're going to the south, and since it's by 45°, you're halfway between east and south, so you're southeast.
A direction of 45 degrees clockwise from due east would put you in the South-East quadrant of a compass or geometric plane.
Explanation:When discussing directions in terms of degrees, it's commonly understood with the idea of a compass rose or a unit circle in mind. Here, 'Due East' is represented as 0 or 360 degrees. A clockwise rotation would mean we are moving in a positive direction.
Therefore, if you start from Due East which is 0 degrees and rotate 45 degrees in the clockwise direction, you would end up in the south-east direction. This is because in the coordinate system, the +x direction is East and moving in the clockwise direction, the next quadrant would be the South-East quadrant. So, 45 degrees clockwise from due east would be considered as South-East direction on a compass rose or geometrically on a plane if you are looking at it in terms of degrees on a circle.
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Suppose that m∠A = m∠D. Which other fact would guarantee that the triangles are SIMILAR? A) AB DE = CB FE B) m∠C = m∠F C) m∠A + m∠B + m∠C = 180° D) 180° - m∠D = m∠E + m∠F
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The ratio of corresponding sides are similar, that it:
AB/DE=CB/FE=CA/FD
also the corresponding angles should be equal.
hence the answer is:
A] AB/DE=CB/FE and m∠C=m∠F
A truck has a full 50-gallon gas tank. It uses 7 1/4 gallons on the first part of its journey, 13 1/2 gallons on the second part of its journey, and 15 1/4 gallons on the third part of its journey. How many gallons of gas remain in the gas tank?
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find the area of an equilateral triangle (regular 3-gon) with the given measurement
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The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. between what two values do the middle 95% of the lengths of all pregnancies fall?
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a rectangular prism has a volume of 144 cm3. the base is a square with a length of 4 cm. what is the height of the prism
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Answer:
9 cm
Step-by-step explanation:
The volume is given by the formula ...
V = LWH
Filling in the given numbers, you have ...
144 cm^3 = (4 cm)(4 cm)H
H = (144 cm^3)/(16 cm^2) = 9 cm
The height of the prism is 9 cm.
Find the complete factorization of the expression. 32xy − 56xyz
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8xy(4 - 7z)
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <1, -2>, v = <-4, 8>
A) Orthogonal
B) Neither
C) Parallel
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u dot v = 1*(-4) + (-2)*8
u dot v = -4 - 16
u dot v = -20
The nonzero dot product tells us that u and v are not orthogonal
u = k*v
<1,-2> = k*<-4,8>
<1,-2> = <-4k, 8k>
1 = -4k implies that k = -0.25
-2 = 8k implies that k = -0.25
The fact we get the same k value each time tells us the two vectors are parallel (they point in the same direction on the compass). One vector is a scaled version of the other.
Answer: C) Parallel
There are 80 sixth grade students at Howard elementary school.If 25% of the students have green eyes how many sixth grade students have green eyes
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Solve the equation on the interval (0,2pi )
2 Sin Θ cos Θ = -1
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To solve the trigonometric equation 2sin(θ)cos(θ) = -1 on the interval (0,2π), use the double angle identity and find the solutions to be θ = π/4 and θ = 3π/4.
Solve the trigonometric equation:
2sin(θ)cos(θ) = -1
Use the double angle identity: sin(2θ) = 2sin(θ)cos(θ)
Substitute and solve to get sin(2θ) = -1
Find the solutions within the given interval (0,2π) which are θ = π/4 and θ = 3π/4.
Marianne has been collecting donations for her biscuit stall at the school summer fayre. There are some luxury gift tins of biscuits to be sold at £5 each, normal packets at £1 each, and mini- packs of 2 biscuits at 10p each. She tells Amy that she has received exactly 100 donations in total, with a collective value of £100, and that her stock of £1 packets is very low compared with the other items. Amy wants to work out how many of each item Marianne has. Show how she can do it.
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Number of luxury gift tins of biscuits sold at £5 each: 18
Number of normal packets sold at £1 each: 2
Number of mini- packs of 2 biscuits sold at 10p each: 80
Solution:
Number of luxury gift tins of biscuits sold at £5 each: x
Amount received by the number of luxury gift tins of biscuits sold: £5 x Number of normal packets sold at £1 each: y
Amount received by the number of normal packets sold: £1 y
Number of mini- packs of 2 biscuits sold at 10p each: z
Amount received by the number of 2 biscuists sold: 10p z =£0.1z
She tells Amy that she has received exactly 100 donations in total:
(1) x+y+z=100
A collective value of £100:
Total amount receibed: £5 x + £1 y+ £0.1z= £100 → £ (5x+1y+0.1z)= £100 → 5x+y+0.1z=100 (2)
Her stock of £1 packets is very low compared with the other items:
y<<x
y<<z
Then we can despice the value of "y" and solve for "x" and "z":
y=0:
(1) x+y+z=100→x+0+z=100→x+z=100 (3)
(2) 5x+y+0.1z=100→5x+0+0.1z=100→5x+0.1z=100 (4)
Solving the system of equations (3) and (4) using the substitution method:
Isolating z in equation (3): Subtrating x from both sides of the equation:
(3) x+z-z=100-x→z=100-x
Replacing z by 100-x in the equation (4):
(4) 5x+0.1z=100→5x+0.1(100-x)=100
Eliminating the parentheses:
5x+0.1(100)-0.1x=100→5x+10-0.1x=100
Adding similar terms on the left side of the equation:
4.9x+10=100
Solving for x: Subtrating 10 from both sides of the equation:
4.9x+10-10=100-10→4.9x=90
Dividing both sides of the equation by 4.9:
4.9x/4.9=90/4.9→x=18.36734693
Replacing x=18.36734693 in the equation:
z=100-x→z=100-18.36734693→z=81.63265306
We can round x and z: x=18 and z=81 and solve for y in equations (1) and (2):
(1) x+y+z=100→18+y+81=100
Adding similar terms on the left side of the equation:
99+y=100
Subtracting 99 from both sides of the equation:
99+y-99=100-99→y=1
(2) 5x+y+0.1z=100→5(18)+y+0.1(81)=100→90+y+8.1=100→98.1+y=100→98.1+y-98.1=100-98.1→y=1.9→y=2 different to 1
Suppose y=1. Replacing y=2 in equations (1) and (2):
(1) x+y+z=100→x+1+z=100→x+1+z-1=100-1→x+z=99
(2) 5x+y+0.1z=100→5x+1+0.1z=100→5x+1+0.1z-1=100-1→5x+0.1z=99
Repeating the process:
z=99-x
5x+0.1z=99→5x+0.1(99-x)=99→5x+9.9-0.1x=99→4.9x+9.9=99→4.9x+9.9-9.9=99-9.9→4.9x=89.1→4.9x/4.9=89.1/4.9→x=18.18367346
z=99-18.18367346→z=80.81632653
x=18 and z=80
(1) x+y+z=100→18+y+80=100→y+98=100→y+98-98=100-98→y=2
(2) 5x+y+0.1z=100→5(18)+y+0.1(80)=100→90+y+8=100→y+98=100→y+98-98=100-98→y=2
Answer:
Number of luxury gift tins of biscuits sold at £5 each: 18
Number of normal packets sold at £1 each: 2
Number of mini- packs of 2 biscuits sold at 10p each: 80
Number of luxury gift tins of biscuits L sold is 18.
Number of mini- packs of 2 biscuits M sold is 80.
Number of normal packets N sold is 2.
Step-by-step explanation:Let L, M, N represent the number of Luxury, Mini, and Normal packets sold.
Total earned by selling luxury gift tins of biscuits = 5L
Total earned by selling normal packets = £1N
Total earned by selling 2 biscuits at 10p = 0.1M
Marianne tells Amy that she has received exactly 100 donations in total:
Equation becomes:
[tex]L+N+M=100[/tex] .... (1)
total earning is £100, so another equation becomes:
[tex]5L+N+0.1M=100[/tex] .......(2)
Given is that stock of £1 packets is very low compared with the other items:
so, N<L and N<M
Putting y = 0 in equation 1 and 2
[tex]L+M=100[/tex] or [tex]L=100-M[/tex] .....(3)
[tex]5L+0.1M=100[/tex] ......(4)
Replacing L by 100-M in the equation 4
[tex]5(100-M)+0.1M=100[/tex]
[tex]500-5M+0.1M=100[/tex]
4.9M=400
M=81.63
As, L=100-M
[tex]L=100-81.63=18.37[/tex]
L=18.37
We can round L and M to 18 and 81 respectively and solve for N from 1 and 2 equations.
[tex]L+M+N=100[/tex]
=>[tex]18+N+81=100[/tex]
=>[tex]N=1[/tex]
[tex]5(18)+N+0.1(81)=100[/tex]
[tex]90+N+8.1=100[/tex]
=> N=1.9
We will repeat the same process with N = 2 and get the following result.
Number of luxury gift tins of biscuits L sold is 18
Number of mini- packs of 2 biscuits M sold is 80
Number of normal packets N sold is 2
Determine the distance between point (x1, y1) and point (x2, y2), and assign the result to pointsdistance. the calculation is: distance=(x2−x1)2+(y2−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√distance=(x2−x1)2+(y2−y1)2 you may declare additional variables. ex: for points (1.0, 2.0) and (1.0, 5.0), pointsdistance is 3.0.
Answers
d: √ [(x2 - x1) ^ 2 + (y2 - y1) ^ 2]
Example,
for points (1.0, 2.0) and (1.0, 5.0):
d: √ [(1 - 1) ^ 2 + (5 - 2) ^ 2]
d: 3.0
Answer:
the distance between point (x1, y1) and point (x2, y2) is:
d: √ [(x2 - x1) ^ 2 + (y2 - y1) ^ 2]
An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered?
Answers
.. A = π*r^2 = π*(25 ft)^2 = 625π ft^2
The area of 3 such circles will be
.. 3A = 3*625π ft^2 = 1875π ft^2
.. ≈ 5890 ft^2
What is the distance between (-6,8) and (-3,9)
Answers
Answer:10
Step-by-step explanation:I seen the answer
Write2/3and3/4 as a pair of fractions with a common denominator
Answers
[tex] \dfrac{2}{3} \times \dfrac{4}{4} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12} [/tex]
[tex] \dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{3 \times 3}{4 \times 3} = \dfrac{9}{12} [/tex]
Answer: 8/12 and 9/12, respectively.