In an arithmetic sequence, the first term is 8, the common difference is 3 and the last term is 68.
a How many terms are there in this sequence?
b Find the sum of all the terms of the sequence.
Answer: a. 21 terms
b. 798
Step-by-step explanation:
a. 68-8=60 ==> difference between 1st and last term
60/3=20 ==> number of terms after the first term
20+1=21 terms ==> total number of terms
b. Find the mean of the terms first:
(68+8)/2= ==> the mean of all terms in a sequence is equal to the mean of the first and last term
76/2=38
38*21=798 ==> add the mean 21 times to get the total sum since there are 21 terms in the sequence.
I need help asap!! (Fractions)
Answer:
b 2 2/9
Step-by-step explanation:
As we know
6×2/3 = {6×3+2}/3
=> 20/3
20/3 is the walk for 3 days
by unitary method
Walk of one day should be
20/3×3
20/9 = 2×2/9 miles per day
Answer:
2 2/9 miles per day
Step-by-step explanation:
If she walked 6 2/3 miles in 3 days, then she walked 1/3 of 6 2/3 miles in 1 days.
We need to find 1/3 of 6 2/3 miles.
1/3 of 6 2/3 =
= 1/3 × 6 2/3
= 1/3 × (6 + 2/3)
= 1/3 × 6 + 1/3 × 2/3
= 2 + 2/9
= 2 2/9
What is the answer to this problem?
Answer: 3
Step-by-step explanation:
A/B
30/10 = 3
A jug of juice has 8 cups of pineapple juice and 3 cups of orange juice. Write the ratio of number of cups of pineapple juice to total number of cups of juice in three different ways.
Answer:
8 : 3, 8/3, and "8 to 3"
Think About the Process At a te-known vacation spot, taxi fares are a bargain. A 12-mile taxi ride takes 18 minutes and costs $7.20. You want to find the cost of a 33-minute taxi ride. What unit price
do you need?
We need to find out unit price per minute and the unit price is $0.4 per minute.
According to the question we have been given that
12 mile taxi rides takes = 18 minutes
cost of 12 mile taxi ride = $7.20
Thus we need to find the mile and the cost covered in 33 minutes which will be find out by unitary method.
Thus,
18 minutes taxi ride will cover = 12 mile
33 minutes taxi ride will cover = 12/18*33
= 22 miles
cost of 12 mile taxi ride = $7.20
then, cost of 22 miles taxi ride = 7.20/12 * 22
= $ 13.2
Now we need to find out the unit price which is unit price per minute.
Thus unit price is = $13.2/33
= $ 0.4
Hence we need to find out unit price per minute and the unit price is $0.4 per minute.
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What is the result of adding these two equations can you please answer
describe the given set with a single equation or with a pair of equations. the plane through the point parallel to a. the xy-plane b. the yz-plane c. the xz-plane
Equations for the set of the plane through the point [tex](x_0,y_0,z_0)[/tex] and parallel to:
a. xy-plane is [tex]z=z_0[/tex] b. yz-plane is [tex]x=x_0[/tex] c. xz-plane is [tex]y=y_0[/tex]
The given set is the plane through the point [tex](x_0,y_0,z_0)[/tex] parallel to:
a. xy-plane b. yz-plane c. xz-plane
Equation of the plane parallel to a plane containing a vector [tex]\vec r[/tex] through the point [tex](x_0,y_0,z_0)[/tex] is [tex](\vec r-(x_0,y_0,z_0)) .\vec n=0[/tex] ,where [tex]\vec n[/tex] is the normal to the plane and [tex]\vec r =x\vec i +y\vec j +z\vec k[/tex].
a. Plane through [tex](x_0,y_0,z_0)[/tex] and parallel to the xy-plane is,
[tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec k[/tex] = 0
⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec k=0[/tex]
⇒ [tex]z-z_0 =0[/tex]
⇒ [tex]z=z_0[/tex] is the equation of the plane through [tex](x_0,y_0,z_0)[/tex] and parallel to xy-plane.
b. Plane through [tex](x_0,y_0,z_0)[/tex] and parallel to the yz-plane is,
[tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec i[/tex] = 0
⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec i=0[/tex]
⇒ [tex]x-x_0 =0[/tex]
⇒ [tex]x=x_0[/tex] is the equation of the plane through [tex](x_0,y_0,z_0)[/tex] and parallel to yz-plane.
c. Plane through [tex](x_0,y_0,z_0)[/tex] and parallel to the xz-plane is,
[tex](x\vec i +y\vec j+z\vec k) - (x_0+y_0+z_0) . \vec j[/tex] = 0
⇒ [tex](x-x_0)\vec i +(y-y_0)\vec j+(z-z_0)\vec k) . \vec j=0[/tex]
⇒ [tex]y-y_0 =0[/tex]
⇒ [tex]y=y_0[/tex] is the equation of the plane through [tex](x_0,y_0,z_0)[/tex] and parallel to xz-plane.
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walter, agnes, and holly are making beaded lizards. walter has 476 green beads and 32 red beads. agnes has 104 green beads and 16 red beads. holly has 281 green beads and 80 red beads. they all share their beads so as to make the largest possible number of lizards. if a beaded lizard requires 94 green beads and 16 red beads, what is the number of green beads left over?
The number of green beads left over = 15
Walter:
Number of green beads = 476
Number of red beads = 32
Agnes:
Number of green beads = 104
Number of red beads = 16
Holly:
Number of green beads = 281
Number of red beads = 80
Total number of red beads = 32+16+80 = 128 beads
Number of red beads required for making one lizard = 16
Since 128/16 = 8 , there will be no red beads left after making 8 lizards.
Total number of green beads = 476+104+281 = 861 beads
Number of green beads required for making one lizard = 94
Now 861/94 = [tex]9\frac{15}{94}[/tex]
That is , 15 is the remainder when 861 is divided by 94
So there will be 15 green beads left after making 9 lizards.
Therefore, the number of green beads left over = 15
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23. SALES TAX You buy a jacket, and the sales tax is 6%. The total cost is $79.49.
Find the cost of the jacket before the tax.
The Cost of jacket before tax is 74.73.
According to the statement
We have to find that the cost of jacket.
So, For this purpose, we know that the
The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.
From the given information:
the sales tax is 6%. The total cost is $79.49.
Then the real cost is :
Real cost = 6% of the $79.49
Then
solve it
tax amount applied on the jacket = 6/100*79.49
tax amount applied on the jacket = 0.06*79.49
tax amount applied on the jacket = 6/100*79.49
tax amount applied on the jacket = 4.76
Then
Cost of jacket before tax = 79.49 -4.76
Cost of jacket before tax = 74.73.
So, The Cost of jacket before tax is 74.73.
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What is the
y-value of the
of the
solution
system?
y = 5x + 3
y = 7x-3
Answer:
y is about equal to -4.692
Step-by-step explanation:
Identify all the possible proper subset relationships that
occur among the following sets.
the subsets in this case are:
C ⊆ BC ⊆ AB ⊆ AHow to identify the subsets?Remember that for two sets A and B, we say that A is a subset of B if and only if all the elements of A also are elements of B.
In this case, we have 3 sets:
A = {3n| n ∈ N}B = {6n| n ∈ N}C = {12n| n ∈ N}We can rewrite these ones as:
A = {3n| n ∈ N} = {3, 6, 9, 12, 15, 18, ...}B = {6n| n ∈ N} = {6, 12, 18, ...}C = {12n| n ∈ N} = {12, 24, 36, ...}Here we can see that all the elements in C also belong in B and also belong in A, and all the elements in B also belong to A, then the subsets are:
C ⊆ B
C ⊆ A
B ⊆ A
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the length of a rectangle is 2 feet less than the three times length express the area of the rectangle as a function of its width, using correct function notation
The area of the rectangle as a function of its width is a=3b-2.
[tex]s=(3b-2)b\\=3b^{2}-2b[/tex]
[tex]a=3b-2[/tex]
What is the advantages of area ?
Area is significant in contemporary mathematics. Aside from its obvious significance in geometry and calculus, area is also a fundamental characteristic of surfaces in differential geometry and is connected to the definition of determinants in linear algebra. The amount of space within a form is measured by its area.
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PLEASE HELP FAST! 35 PTS!!
Justify each step by identifying the property used.
[tex]t+5(t+1)=t+(5t+5)[/tex]
[tex]=(t+5t)+5[/tex]
[tex]=(1t+5t)+5[/tex]
[tex]=(1+5)t+5[/tex]
[tex]=(6t+5)[/tex]
The algebraic properties used in the steps are the distribution property, the associative property, the identity property, and the distribution property
How to justify each step by identifying the property used?The first step in the equation is given as:
t + 5(t + 1) = t + (5t + 5)
The distribution property states that
a(b + c) = ab + ac
So, the property used in t + 5(t + 1) = t + (5t + 5) is the distribution property
Next, we have:
t + 5(t + 1) = (t + 5t) + 5
The associative property states that
a + (b + c) = (a + b) + c
So, the property used in t + 5(t + 1) = (t + 5t) + 5 is the associative property
Next, we have:
t + 5(t + 1) = (1t + 5t) + 5
The identity property states that
a * 1 = a
So, the property used in t + 5(t + 1) = (1t + 5t) + 5 is the identity property
Next, we have:
t + 5(t + 1) = (1 + 5)t + 5
The distribution property states that
a(b + c) = ab + ac
So, the property used in t + 5(t + 1) = (1 + 5)t + 5 is the distribution property
Lastly, we have the solution
(6t + 5)
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The volume of a prism is given by the formula V=lwh , where l is the length, w is the width, and h is the height of the prism.
a. Solve the formula for h .
Answer:
[tex] \sf \large \: h = \frac{v}{lw} [/tex]
Step-by-step explanation:
Let's solve for h.
v=lwh
Step 1: Flip the equation.
hlw=v
Step 2: Divide both sides by lw.
hlw/lw = v/lw
h= v/lw
There are a children in the class, and b of them are girls. How many boys are in the class?
Number of boys = a - b
Step-by-step explanation:Number of children in the class = a
Number of girls in the class = b
Number of boys = Total - Girls
a - b
A cube-shaped planter has a volume of 729 in.³. What is the length of the planter?
Answer:
9 inches
Step-by-step explanation:
To find the volume of a cube, you could cube the side length, simplified as x³.
x³ = 729
x = 9
9 inches
Hope this helps! :)
Simplify each part of the expression using the laws of exponents.2^7/2^5+(4^5)^0+3^-1
What laws or properties did you use to simplify each part? What is the value of the expression?
Answer:
5.333333333333
Step-by-step explanation:
1. 2^7 &2^7 have the vase, by subtracting their power, the result is 4.
2. (4^5)^0=1
3. 3^-1=0.3333333
4 finally by adding each values in above steps
The lengths of the three sides of a triangle (in feet) are consecutive even integers. If
the perimeter is 96 feet, find the value of the shortest of the three side lengths.
Helpppp I will give 60 points for this one
Answer:
Step-by-step explanation:
A. L+W= 2 in. x 2 in. = 4 in.
the length is 2 in.the width is 2 in. so you multiply 2 in.x 2 in. which = 4 in.Below are some things to help you with perimeter and area(just type it into whatever browser you use, copy and paste)
https://youtu.be/LoaBd-sPzkU
https://th.bing.com/th/id/OIP.Q5D_8qbK_9XGQLj1s0tpbwHaJ3?w=186&h=248&c=7&r=0&o=5&dpr=1.65&pid=1.7
A cartoon of 2 dozen eggs includes 3 with cracks. how many eggs without cracks can be expected in 6 dozen eggs?
If a cartoon of 2 dozen eggs includes 3 with cracks, then the number of eggs without cracks in 6 dozen eggs can be expected to be 63.
A dozen abbreviated as doz is a batch of 12. So in this situation, one dozen refers to 12 eggs. Therefore the number of eggs in 2 dozen will be equal to,
1 dozen = 12 eggs
2 dozen = 12x2= 24 eggs.
Therefore, a cartoon of 24 eggs includes 3 with cracks.
Similarly, 6 dozen is equal to,
1 dozen = 12 eggs
6 dozen = 12 x 6 = 72 eggs
We can determine the number of eggs with cracks by using an algebraic expression,
24 eggs include 3 eggs with cracks
72 eggs include: x eggs with cracks
x = 72×3 ÷ 24
x = 216 ÷ 24 = 9 eggs with cracks.
Therefore the number of eggs without cracks can be calculated by the subtraction of total eggs from the eggs with cracks.
Eggs without cracks= 72 - 9 = 63 eggs.
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Rose has 1 3/4 cups of powdered sugar. she sprinkles 1/3 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies. how much sugar does rose sprinkle on the brownies?
0.58 or more than half of sugar is sprinkled by rose on the brownies.
How much sugar does rose sprinkle on the brownies?
Given,
Rose has 1 3/4 cups of powdered sugar.
1/3 of the sugar sprinkled on lemon cookies
Therefore'
1 3/4 = (4*1+3) / 4
= 7/4
1/3 of the sugar sprinkled on lemon cookies
= 1/3 (7/4)
= 7/12
= 0.58 or more than half of sugar is sprinkled by rose on the brownies.
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(Total 3 marks)
5. Dave and Tanvir each think of a number, where Dave's number is larger,
The difference between their numbers is $. Dave's number plus twice Tanvir's number is 26
By forming simultaneous equations, determine each bloke's number.
Dave and Tanvir each think of a number, where Dave's number is larger,
The difference between their numbers is 5. Dave's number plus twice Tanvir's number is 26. By forming simultaneous equations, determine each bloke's number. The numbers are 12 and 7.
The number of Dave is 12 and the number of Tanvir is 7.
Given that
Dave and Tanvir each think of a number, where Dave's number is larger.
The difference between their numbers is 5.
Dave's number plus twice Tanvir's number is 26.
To find
By forming simultaneous equations, determine each bloke's number.
So, according to the question
Let's assume that numbers are x and y.
So, we can say that
x - y = 5 ------------(1) and
x + 2y = 26 ------------(2)
We have to solve that equations by using forming simultaneous equations.
For forming simultaneous equations, we have multiply equation(1) by 2, then add eq(2) with result.
So, we will get
2x - 2y = 10
(+) x + 2y = 26
---------------------------
3x +0 = 36
3x = 36
x = 36/3
x = 12
Putting the value of x in equation (1),
We will get,
x - y = 5 ------------(1)
12 - y = 5
- y = 5 - 12
- y = -7
y = 7
The numbers are 12 and 7.
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Help, I've been stuck on these questions for an hour!
Explanations would be helpful, please!
Answer:
A. 3005
B. 3110
C. 1016.67
Step-by-step explanation:
A. Inital means occuring at the beginning. So the month they got the account, the value is around 3005. Every tick mark on the y-axis represents 30.
B. Like I said, every tick mark represents 30, so on the x-axis, the line between 6 and 8 is 7. go up towards where the line is, and that equals 3110.
C. I really haven't learned about rate of interest yet, but I tried my best to figure it out. I found out that for every month, you get 1016.67 value of interest.
Ben bowled 128 and 206 in his first two games. What must he bowl in his third game to have an average of at least 190?
Ben must bowl at least
least 190.
in his third game in order to have an average of at
Answer:
236
See the picture below for the work.
Step-by-step explanation:
Lori ran 5 ½ miles Monday, 6 %4 miles Tuesday, 4½ miles Wednesday, and 234 miles on
Thursday. What is the average number of miles Lori ran? Write your answer as an improper
fraction.
19 miles the average number of miles Lori ran.
Miles Lori ran on Monday = 5 ½ = 11/2
Miles Lori ran on Tuesday = 6 ¼ = 25/4
Miles Lori ran on Wednesday = 4½ = 9/2
Miles Lori ran on Thursday = 2¾ = 11/4
Total miles she ran = sum of 4 days runs
= 11/2 + 25/4 + 9/2 + 11/4
= 22/4 + 25/4 + 18/4 + 11/4
= [tex]\frac{22 +25+18+11}{4}[/tex]
= 76/4 miles or 19 miles
How to calculate average number?By combining a set of integers and then dividing by their count, the average number—also known as the arithmetic mean—is created. For instance, the sum of 2, 3, 3, 5, 7, and 10 is equal to 30 divided by 6, which equals 5.
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. determine whether each of the following statement is true or false: a) x ∈ {x} b) {x} ⊆{x} c) {x} ∈{x} d) {x} ∈ {{x}}
(a) True, x is an element of the set {x}
(b) True, the set {x} is a subset of itself.
(c) False, x is an element of {x}, but the set {x} is not an element of {x}.
(d) True, the set {x} is an element of the set {{x}}.
What do you mean by the element of the set?The numbers 1, 2, 3, and 4 are the elements of set A, as indicated by the formula A=1,2,3,4. Subsets of A are collections of components from A, like 1, and 2. Sets may also function as elements.
Consider the set B=1,2,3,4 as an example. B's constituent parts are not 1, 2, 3, or 4. Instead, there are just three components of B: the numbers 1 and 2, as well as the set "3, 4."
A set's components can be anything. For instance, the set "C=red, blue, green" contains the colors red, green, and blue as its constituents.
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Please help!!! I really need this!!! It's piecewise functions......
well, let's take a peek at the graph, hmmm it has a straight line from the origin to (5,10), and then another straight line from (5,10) to (10,5) and then another one from there up to (20,5).
well, let's simply get the equations for each of those lines then
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{2}(x-\stackrel{x_1}{0})\implies \boxed{y = 2x} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{5}}} \implies \cfrac{ -5 }{ 5 }\implies -1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-1}(x-\stackrel{x_1}{5}) \\\\\\ y-10=-x+5\implies \boxed{y=-x+15} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{20}-\underset{x_1}{10}}} \implies \cfrac{ 0 }{ 10 }\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{0}(x-\stackrel{x_1}{10})\implies y-5=0\implies \boxed{y=5}[/tex]
so then hmmm let's use those, we know how f(x) is moving now, so
[tex]\stackrel{y}{f(x)}= \begin{cases} 2x&x\geqslant 0\\\\ -x+15&x\leqslant 10\\\\ 5&x\leqslant 20 \end{cases}[/tex]
[tex]9a-ab+5b if a=2 and b =7[/tex]
Answer:
If you want it graphed the answer is
andb=7
The formula wights are
mass of 1 1 mole of 9 a − a b + 5 b i f a = 2 = 0 g
Step-by-step explanation:
Simplify the expression 4( m - 2 ) + 3m
Answer:
7m-8
Step-by-step explanation:
distribute 4 through the parentheses
4m-8+3m
collect like terms
7m-8
Answer:
7m-8
Step-by-step explanation:
So to simplify this expression, you would need to do distributive property.
4(m-2)
(4*m) + (4*-2)
4m-8+3m
7m-8
So your simplification is 7m-8
K What is 0.288 rounded to the neare hundredth? 0.288 20
Answer: 0.29
Step-by-step explanation:
= 0.288
8>5
= 0.29