Answer
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Hint: We will write the first ten odd natural numbers and then add them to find their sum. We will then substitute the values in the formula of arithmetic mean , a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.
Complete step-by-step answer:
We have to find the arithmetic mean of first ten odd natural numbers .
Natural numbers are counting numbers and starts from 1.
Odd numbers are not multiples of 2.
The first ten odd natural numbers are 1,3,5,7,9,11,13,15,17,19.
Arithmetic mean is calculated by adding all the observations by the total number of observations.
Arithmetic mean is given by a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.
Therefore, we will calculate the sum of the first ten odd natural numbers.
⇒1+3+5+7+9+11+13+15+17+19⇒100
Now, we will divide this by 10 as there are a total 10 numbers.
10010=10
Hence, the arithmetic mean of first ten odd natural numbers is 10.
Note: Arithmetic mean is also known as average or simply mean. Odd numbers are not divisible by 2. The sum of n odd natural numbers is also given by n2
Orion buys 3 books for a total of 25.50. He pays $8 plus sales tax for each book. He wants to know how much the sales tax is for one book.
Let "t" equal the sales tax Orion pays for each book. Write an equation that represents this situation.
The equation that represents this situation is 8 + 3t = 25.50.
How to calculate the value?Let the sales tax for each book be represented as t.
Since Orion buys 3 books for a total of 25.50 and he pays $8 plus sales tax for each book. This will be illustrated as:
Cost of book + Tax = Total amount
8 + (3 × t) = 25.50
8 + 3t = 25.50
Collect like terms
3t = 25.50 - 8.
3t = 17.50
Divide
t = 17.50 / 3
t = 5.83
The sales tax is $5.83.
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PLEASE HELP ASAP
A shop sells a washing machine for £236.25, making a profit of 5%. At what wholesale price did the shop buy the washing machine?
Original price = £
Answer:
£225
Step-by-step explanation:
The relationship between the cost price (cp) and the selling price (sp) is ...
cp + 5% × cp = sp
cp(1.05) = sp . . . . . . collect terms
cp = sp/1.05 . . . . . . divide by 1.05
cp = £236.25/1.05 = £225
The original wholesale price was £225.
Determine the number of solutions you will have for the system: 1/3x+y=2 and 3y=6-x
One solution.
No solutions.
Infinite solutions.
Impossible to determine.
Answer:
infinity solution
solution:
-x-3y=-6
x+3y=6
Which describes the slope of the line that passes through the points (2, 5) and (– 4, 5)?
Answer:
m is the slope of line and x1, y1= 2,5 , and x2, y2= -4, 5
m = 5-2/-4-5 = -1/3
Step-by-step explanation:
What is the slope of the line with equation 2x−5y=52?
Answer:
m = 2/5
Step-by-step explanation:
2x - 5y = 52
-5y = -2x + 52
y = 2/5x - 52/5
The slope of the line with equation 2x−5y=52 is 2/5.
The given equation of line is 2x−5y=52.
What is the slope of a equation?The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis.
The given equation 2x−5y=52 can be rewritten as
2x-52=5y
⇒ y = 2x/5-52/5
Now, compare y = 2x/5-52/5 with the standard form of an equation y=mx+c
So, m=2/5
Therefore, the slope of the line with equation 2x−5y=52 is 2/5.
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A shop sells orange juice in the following ways:
500 ml bottle for £1.25
1.5 litre carton for £2.35 each or 2 cartons for £3.50
2 litre carton for £3.25
What's the cheapest way of buying exactly 8 litres with no extra?
Find the amount of each type of bottle or carton you need and the total cost of buying 8 litres
Answer:
1.
1.5 litre carton for $2.35 is the cheapest way since it's the cheapest out of all the other options.
2.
a. 1.25 / 0.5 = $2.50 per L
2.35 / 1.5 = $1.57 per L
3.25 / 2 = $1.63 per L
b. 2.50 x 8 = $20.00 per 8 L
1.57 x 8 = $12.56 per 8 L
1.63 x 8 = $13.04 per 8 L
Step-by-step explanation:
find unit rate (cost / quantity)
Which sequence is geometric?
Group of answer choices
-2, 1, 6, 13...
-1, 2, 7, 14
-4, 20, -100, 500...
-7, 7, 21, 35...
Hi there! :)
A geometric sequence is a sequence where we use multiplication or division to get to the next term.
We use multiplication in the third sequence (we multiply by -5)
So the answer is Option C
Hope it helps
~Just a gloomy teen who misses her best friend
#CarryOnLearning
[tex]SilentNature[/tex]
i started some of it but i’m really confused with the rest. does anyone know how to do this?
Answer:
see below
Step-by-step explanation:
You're doing well! The parts of the table you've done are correct.
For x = 1, you switch to the second part of the function rule (because that part says to use it if [tex]x \ge 1[/tex].
x =1 : 6 - 2(1) = 4 (1, 4)
x = 2: 6 - 2(2) = 2 (2, 2)
x = 3: 6 - 2(3) = 0 (3, 0)
x = 4: 6 - 2(4) = -2 (4, -2)
Each of the parts of the function rule graph as pieces of straight lines. The first part will be a straight line through points (-4, 1), (-3, 0), (-2, 1), (0, 3) but that part of the graph stops at point (1, 4). Point (1, 4) is on BOTH parts of the graph, so the two lines connect at that point.
Answer:
Step-by-step explanation:
1. A linear function can be represented by the equation y = 7x - 4. Identify the slope and y-intercept.
y-intercept:
Slope:
Hello!
Remember y=mx+b.
m is the slope and b is the y intercept.
So
the slope is 7 and the y intercept is 4.
Hope this helps!
~Just a felicitous teen
#CarryOnLearning
[tex]SIlentNature[/tex]
Answer:
slope: 7
y-intercept:4
Step-by-step explanation:
Х
у
-2
3
2
-9
6
-21
10
-33
Answer:
y = - 3x - 3Step-by-step explanation:
Given table:
x | -2, 2, 6, 10 y | 3, -9, -21, -33Use two pairs of points to work out the equation of the line y = mx + b:
(-2, 3) and (2, - 9)Find the slope:
m = (-9 - 3)/(2 - (-2)) = - 12/4 = - 3Use one pair to find the y-intercept:
3 = - 3*(-2) + b3 = 6 + bb = 3 - 6b = - 3The line is:
y = - 3x - 3m = (-9 - 3)/(2 + 2) = -12/4 = -3 ==> (x)
3 = (-3)•(-2) + b
3 = 3•2 + b
3 = 6 + b
b = -3 ==> (a)
Soo :
y = -3x - 3-3 and -5 what is less, greater than , and or equal
Answer:
-3 is less and -5 is greater
Step-by-step explanation:
Answer:
less than
Step-by-step explanation:
because -5 would be less than -3 because it is bigger
Hello I need plzzzz help
Answer:
The number of hours Jenny babysits
Step-by-step explanation:
Since we know that the 10 is the fixed fee for the babysitting services and 5 represents the amount charged per hour, it is safe to say x represents the number of hours Jenny babysits.
Ex.: Let us say she baby sits for 3 hours. 3 would take the place of the x
5(3)+10. This means Jenny will charge the person she babysat for a total of
$15 just for the hours alone.
Hope this helps! :)
Answer:
x represent the number of hours Jenny Babysits
Step-by-step explanation:
since she charges $5 per hour, then X is always how many hours
To earn an a in mr.whites math class students must score a total of at at least 135 points on three test. On the first two test , kaylees scores were 47 and 48 . What is the minimum score she must get on the third test to earn an a
Answer:
Set an equation x+47+48= 136
solve for x
x+95=136
x= 40
so they need to score a 40
Find two integers whose sum is -3 and product is -18
With this in mind,
x + y = -3
x * y = -18
[] Let's think about the factors of -18Then we will think about which ones could add up to 3
1 & 18, 2 & 9, 3 & 6 are factors of 18 (one being negative results in -18)
Well 1 and 18 cannot make 3, same for 2 and 9, that leaves us with 3 and 6.
[] Last, we will testYou can see our test shows this solution works!
-6 + 3 = -3
-6 * 3 = -18
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
What is the value of the rational expression when x = –3?
-1/12
0
1/6
undefined
Option D is correct, the value of the rational expression when x = –3 is undefined.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is x/x²-9
x divided by x square minus nine.
Now let us find the value of the expression when x is minus three,
Plug in x as -3 in the above expression.
-3/(-3)²-9
-3/9-9
-3/0
Anything divided by zero then the value is undefined.
Hence, Option D is correct, the value of the rational expression when x = –3 is undefined.
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What is the value of the rational expression x/x2-9 when x = –3?
A. -1/12
B. 0
C. 1/6
D. Undefined
what is the common denominator of 6/7 and 3/8(please help i'm failing math)
Answer:
56
Step-by-step explanation:
I need 30 please thank you
Answer:
ok good morning
have a nice day
Step-by-step explanation:
#toxicsquad
Answer:
i think its 7, but you should probably check that...
Please help me! my teacher didn't teach me this!!
Answer:
skew
skew
parallel
parallel
Step-by-step explanation:
First see the below figure to understand parallel and skew lines
As you can see parallel lines lie on the same plane
skew lines lie on different plane and do not intersect
1)AB and GF
AB lies on ABCD plane
GF lies on EFGH plane
and they will never meet / intersect
so skew
2)DH and BF
DH lies on ADHE plane
BF lies on BCGF plane
they seem parallel but they are on different plane, so skew
3)EF and HG
EF and HG both lie on the same plane EFGH
and they both are parallel
4)for this see the second picture
both these planes are parallel
Hope this helps!
If the sum of two consecutive
even integers is - 18, find the
integers.
-10 and -8????
I believe because -10 + -8 = -18 and they are both consecutive
any of these please i don't get this
Answer:
33. $5.75
34. 15 ft
35. 8
36. 32
Step-by-step explanation:
These questions pretty much cover the sorts of things you're supposed to learn in an Algebra course. If you don't get any of it, you may have a problem with follow-on courses.
__
33.You are expected to understand this question gives you two relations in two unknowns. The first step is to assign a variable to each of the unknowns. We can use ...
x = cost of a milk shakey = cost of a sundaeThe given relations have to do with the prices of different quantities of these:
2x +3y = 26.25 . . . . . . cost of 2 shakes and 3 sundaes
4x +2y = 29.50 . . . . . . cost of 4 shakes and 2 sundaes
These two equations in two unknowns can be solved several ways. Here, it is convenient to use the method of "elimination", because the coefficients of x are related by a small integer. Subtracting the second equation from 2 times the first eliminates the x-variable (hence the name of the method).
2(2x +3y) -(4x +2y) = 2(26.25) -(29.50)
4y = 23.00 . . . . . . simplify
y = 5.75 . . . . . . . . . divide both sides by 4
The cost of an ice cream sundae is $5.75.
We can substitute this value into either equation and solve for x. We would find the cost of a shake to be x=4.50. However, the question only asks for the price of a sundae.
__
34.There are formulas for the perimeter, area, and volume of various geometric figures of a generally circular or rectangular shape. You might find it convenient to memorize them. Here, you need the formulas for the volume of a cylinder and of a cone. You also need to know that the diameter of a circle is 2 times the radius of the circle, since most of the circle-related formulas are in terms of the radius.
Volume of a cone of radius r and height h: V = 1/3πr²h
Volume of a cylinder of radius r and height h: V = πr²h
It can be convenient to remember that a cone has 1/3 the volume of a cylinder the same height.
The relation of interest here is the volume of the silo is the sum of the volumes of the bottom cylinder and the top cone.
V = π(20 ft)²(60 ft) + 1/3(20 ft)²(x ft) = 26000π ft³
V = 24000π ft³ +(400/3)x·π ft³ = 26000π ft³ . . . . simplify a bit
400/3·x = 2000 . . . . . . . divide by π ft³, and subtract 24000
x = 2000(3/400) = 15 . . . . multiply by 3/400
The height of the top portion is 15 feet.
__
35.This has to do with understanding the meaning of a table and of an expression relating table values. The expression f(a) = g(b) means you're looking for table entries such that the number in the f(x) column is equal to the number in the g(x) column.
We find the only common function value to be -1, so f(-6) = -1 = g(1). Comparing this to f(a) = g(b), we see that a=-6.
The question asks for |g(a)|. The table tells us g(-6) = -8. Its absolute value will be the value without the negative sign:
|g(-6)| = |-8| = 8 = |g(a)|
__
36.This is a polynomial division problem. It tells you the quotient of the quadratic, divided by (ax +2), is (3x -4) with a remainder of 66. We're concerned with the leading coefficient of the divisor, 'a'.
Polynomial long division is much simpler than numerical long division, because each quotient term is the leading dividend term divided by the leading divisor term. Here, that means ...
96x²/(ax) = 3x
Multiplying by ax gives ...
96x² = 3ax²
Dividing by 3x², we see that ...
(96x²)/(3x²) = (3ax²)/(3x²)
96/3 = a = 32
The value of 'a' is 32.
Part 2
Directions: Use the information in the charts to answer the questions.
Type of Fruit Cost
Estimated
Cost
apple
$1.75/pound
orange
$2.35/pound
banana
$1.50/pound
Answer:
i think you need to add all that up
Step-by-step explanation:
simplify, (xy+yz)² - 2x²y²z² and find the value when x=-1, y=2 and z=1
plz answer this fast plz u will give you brainly plz help me fast only 5min left to answer
We have
(xy + yz)² - 2x²y²zIf,
x = -1, y = 2 and z = 1Putting value:
(xy + yz)² - 2x²y²z➡ (-1×2 + 2×1)² - 2×-1²×2²×1
➡ (-2 + 2)² - 2×1×4×1
➡ (0)² - 8
➡ 0 - 8 = -8,answer
Rewrite 4/6 and 1/3 as a unite rate
Answer: B
Step-by-step explanation: Hope this helps :)
An Earth worm Moves at a
distance of 45cm in 90 secondo
find the speed of the earth
worm
(I need to know how to lay it out as well)
Answer:
if the units is in m/s
Step-by-step explanation:
first work out using this triangle.
distance= speed x by time
so if we're trying to find out the speed we reaarange the triangle to :
distance
---------------------
speed x time
so speed = distance divided by time
distance = 45cm
divided by time = 90 seconds
But the units are cm and should be metres per second
change 45cm to m
that is 45cm = 45/ 100 = 0.45
0.45/ 90= 0.005cm
answer = 0.005 metres per second( m/s)
plz say thanks + rate !
(sinx + cosx)(1 − sinx cosx) ≡ sin3x + cos3x
Step-by-step explanation:
We will use the LHS to find the RHS.
Step 1: Expand the LHS by multiplying through the brackets and simplify
(sinx + cosx)(1 − sinx cosx) ≡ sinx + cosx - (sinx + cosx (sinx cosx))
≡ sinx + cosx - sin²x cosx - sinx cos²x
Step 2: Use the identity sin²x + cos²x = 1, to rewrite the equation
≡ sinx + cosx - cosx (1 - cos²x) - sinx (1 - sin²x)
Step 3: Simplify the equation by adding like terms
≡ sinx + cosx - cosx + cos³x - sinx + sin³x
≡ sin³x + cos³x [QED]
Reminder:
1 - cos²x = sin²x 1 - sin²x = cos²x (cosx)(cosx) = cos²xOwen invested $81,000 in an account paying an interest rate of 3\tfrac{7}{8}3 8 7 % compounded continuously. Zoe invested $81,000 in an account paying an interest rate of 3\tfrac{1}{4}3 4 1 % compounded monthly. After 9 years, how much more money would Owen have in his account than Zoe, to the nearest dollar?
Answer: $6322
114800.8806 - 108478.6929
= 6322.1877
Rounded to the nearest dollar = $6322
Answer:6761
Step-by-step explanation:
There are 16 mangoes in a basket.They are ONLY Julie and east indian.If you take out a Julie and replace it with an east indian ,there will be an equal number of Julie and east indian mangoes.If you take you three east indian mangoes and replace them with Julie,the number of Julie will be three fi me the number of east Indians? At present there are how many east indian and Julie mangoes in the basket?
Answer:
11 Julie's and 5 East Indians
6 * 2 /( -1)4* 5-(8+3)
Answer:
-251
Step-by-step explanation:
Following BEDMAS/PEMDAS
6*2/(-1)4*5-(8+3); first simplify the brackets/parenthesis
= 6*2/(-1)4*5-11; now do divisons and multiplications going from left to right
= 12/(-1)4*5-11 = -12*4*5-11 = -48*5-11 = -240-11
= -251
what is the equation in slope intercept form of the line that has a slope of -7 and y intercept of 3/11
Answer:
y = -7x + 3/11
Step-by-step explanation:
the diameter of a circle is 8 centimeters