Answers
3349/1260 is the amount, according to the provided document.
What does an sum total mean?The outcome of an addition is a total. For instance, adding 1, 2, 3, and 4 results in the printed number 10. (1) Addends—also known as summands—are the integers that are being added together.
(a)
[tex]\begin{aligned}& \text { D) } \sum_{j=1}^7 \frac{2}{j+2} \\& j=1 ; \frac{2}{1+2}=\frac{2}{3} \\& j=2 ; \frac{2}{2+2}=\frac{2}{4}=\frac{1}{2} \\& j=3 ; \frac{2}{3+2}=\frac{2}{5} \\& j=4 ; \frac{2}{4+2}=\frac{2}{6}=\frac{1}{3} \\& j=5 ; \frac{2}{5+2}=\frac{2}{7} \\& j=6 ; \frac{2}{6+2}=\frac{2}{8}=\frac{1}{4} . \\& j=7 ; \frac{2}{7+2}=\frac{2}{9} \\& \sum_{j=1}^7 \frac{2}{j+2}=\frac{2}{3}+\frac{1}{2}+\frac{2}{5}+\frac{1}{3}+\frac{2}{7}+\frac{1}{4}+\frac{2}{9} \\& =\frac{3349}{1260}\end{aligned}[/tex]
(b)
[tex]\begin{aligned}\frac{7}{2} \frac{8+0}{2} & =\frac{840}{1}+\frac{840}{2}+\frac{840}{3}+\frac{840}{4}+\frac{840}{5}+\frac{840}{6}+\frac{840}{7} \\& =840+420+280+210+168+140+120\end{aligned}[/tex]
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Related Questions
the radius of the sphere is 10 units. what is the approximate volume of the sphere? use and round to the nearest whole cubic unit. 42 cubic units 126
Answers
The volume of a sphere with radius 10 units was found to be approximately 42 cubic units.
The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
Where, r is the radius of the sphere. In this case, the radius is 10 units, so we can plug in the values and calculate the volume:
V = (4/3) * π * 10^3 = 4184 cubic units
So, the approximate volume of the sphere with a radius of 10 units is 4184 cubic units.
Rounding off to the nearest whole cubic unit, 4184 cubic units becomes 42 cubic units.
Volume of a sphere is the amount of space inside a sphere.
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Find 2 numbers whose product is 57, and one of the numbers is 5 less than eight times the other number
Answers
One of the numbers is 21, and the other number is 2.5
What is an algebraic expression?
An algebraic expression is when we combine numbers and words to solve a mathematical problem.
Let's call one of the numbers "x". We know that x is 8 times greater than the other number, which we'll call "y". So we have:
y = x / 8
The product of x and y is 57, so:
x * y = 57
Substituting y = x / 8 into the equation above:
x * (x / 8) = 57
Expanding the right side of the equation:
[tex]x^2 / 8 = 57[/tex]
Multiplying both sides by 8:
[tex]x^2 = 8 * 57[/tex]
Solving for [tex]x^2[/tex]:
[tex]x^2 = 456[/tex]
Taking the square root of both sides:
[tex]x =\sqrt{456}[/tex]
x = 21
So, One of the numbers is 21, and the other number is 21 / 8 = 2.5.
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Find a solution to this system of equations:
5x-3y=20
15x+6y=60
Write your solution in (x,y) form.
Please help!!!!!
Answers
Answer:
(x, y) = (4, 0)
Step-by-step explanation:
You want the solution to the system of equations ...
5x -3y = 2015x +6y = 60Standard formIt often works well to start the solution process by putting both equations into standard form. We do that by removing any common factors from the coefficients. Here, we see that the second equation's coefficients each have a factor of 3, so we can remove that and rewrite the system as ...
5x -3y = 205x +2y = 20ObservationChanging the coefficient of the y-term has no effect, telling us that y=0, and the equation reduces to ...
5x = 20
x = 4
More formally, if we subtract the first equation from the second, we get ...
(5x +2y) -(5x -3y) = (20) -(20)
5y = 0 . . . . . . simplify
y = 0 . . . . . . . divide by 5
The solution is (x, y) = (4, 0).
In a bag of 10 marbles, there are 4 blue, 3 red, 2 green, and 1 yellow. What is the probability that you draw one marble that is blue, replace it, and draw another marble that is green? Enter your answer as a fraction in lowest terms. Do not add spaces to your answer. (EX: 1/2)
Answers
Work Shown:
A = the 1st marble is blue
B = the 2nd marble is green
Replacement is applied. This makes A and B independent.
P(A) = (4 blue)/(10 total) = 4/10 = 2/5
P(B) = (2 green)/(10 total) = 2/10 = 1/5
P(A and B) = P(A)*P(B) ... see note below
P(A and B) = (2/5)*(1/5)
P(A and B) = 2/25
Note: The equation is valid because events A and B are independent.
Answer. please.........
Answers
The area of the given parallelogram is 6.6 square units.
What is the area of the parallelogram?The region or space occupied by a parallelogram in a two-dimensional plane is referred to as the area of a parallelogram. A unique category of a quadrilateral is a parallelogram.
A quadrilateral is referred to as a parallelogram if it has two sets of parallel opposite sides. A parallelogram can be anything from a rectangle to a square to a rhombus.
The area of the partogram is calculated as:-
Area = Base x Height
Area = 2.2 x 3
Area = 6.6 square units
Therefore, the parallelogram will have an area of 6.6 square units.
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Which expressions are equivalent to 7^{-2} times 7^{6}
Answers
Answer:
(7^2)^2
Step-by-step explanation:
(7^-2)*(7^6)=7^-2+6
......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2
I have $10,000 to invest for my daughter's car. I earned $215.04 when splitting the money into a
3% interest account and a 1.1% interest account. How much did I invest at each? (1 = prt; 1= interest
earned, p = principle (the amount invested), r = rate as a decimal, t = time in years)
Answers
The amount invested in the 3% interest account is $11,342.11, and the amount invested in the 1.1% interest account is $10,000 - $11,342.11 = $-342.11.
What is the interest?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
Let's call the amount invested in the 3% interest account x. Then, the amount invested in the 1.1% interest account is $10,000 - x.
The interest earned in the 3% interest account is 0.03x, and the interest earned in the 1.1% interest account is 0.011($10,000 - x).
The total interest earned is equal to the sum of the interest earned in each account:
0.03x + 0.011($10,000 - x) = $215.04
Expanding and solving for x:
0.03x + 0.011 * $10,000 - 0.011x = $215.04
0.019x = $215.04 + 0.011 * $10,000 - 0.011 * $10,000
0.019x = $215.04
x = $215.04 / 0.019
x = $11,342.11
Hence, the amount invested in the 3% interest account is $11,342.11, and the amount invested in the 1.1% interest account is $10,000 - $11,342.11 = $-342.11.
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while on a walk in the country, you pass a field full of horses and geese. after a quick count, you determine there are 33 heads and 102 feet in the field. how many of each animal are there?
Answers
The field is full of 18 horses and 15 geese.
Let's assume that there are x horses and y geese in the field. The number of heads can be represented as x + y = 33. The number of feet can be represented as 4x + 2y = 102.
We can use substitution to solve for one variable in terms of the other. From the first equation, we can solve for y in terms of x:
y = 33 - x
Substituting this expression for y into the second equation, we get:
4x + 2(33 - x) = 102
Expanding and simplifying the expression, we get:
4x + 66 - 2x = 102
Solving for x, we get:
2x = 36
And x = 18
So there are 18 horses in the field. Substituting this value for x into the expression for y, we get:
y = 33 - x = 33 - 18 = 15
So there are 15 geese in the field. Thus, the field is full of 18 horses and 15 geese.
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A ball is thrown from the top of a building with an initial velocity of 10 m/s and a height of 100 m. The ball makes an angle of 30 degrees with the horizontal and reaches a maximum height of 80 m. Calculate the potential energy of the ball at its highest point.
Answers
Step-by-step explanation:
To calculate the potential energy of the ball at its highest point, we first need to find the gravitational potential energy of the ball. Gravitational potential energy is given by the equation:
PE = mgh
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2 on the surface of the earth), and h is the height of the ball above the ground.
At its highest point, the height of the ball is 80 m, so the gravitational potential energy can be calculated as:
PE = m * g * h = m * 9.8 * 80
where m is the mass of the ball.
Since the ball was thrown at an angle of 30 degrees with the horizontal, its initial velocity can be broken down into horizontal and vertical components:
v0x = v0 * cos(30) = 10 * cos(30) = 10 * sqrt(3)/2 m/s
v0y = v0 * sin(30) = 10 * sin(30) = 10/2 m/s
The potential energy of the ball at its highest point can be found by adding the initial kinetic energy of the ball to its gravitational potential energy. The kinetic energy of the ball can be calculated as:
KE = 1/2 * m * v0y^2
where m is the mass of the ball and v0y is the vertical component of its initial velocity.
The total potential energy of the ball at its highest point is given by:
PE = KE + mgh = 1/2 * m * v0y^2 + m * g * h
Substituting in the given values, we find:
PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80
Note: The mass of the ball (m) is not given, so the answer is given in terms of m.
Answer:
Step-by-step explanation:
PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80
Choose whether the representation is or is not a function for the problem and select the
reasoning for the answer.
30
8
18
28
38
Y
77
77
77
- 77
Answers
To verify if the representation is a function for this problem, we should verify if each input is mapped to a single output. If there is an input that is mapped to more than one output, then the relation is not a function.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.
With arrows, only one arrow can depart from each value of x, or more than one arrow departing from the same value of x but necessarily arriving at the same value of y.
Missing InformationThe problem is incomplete, hence the general procedure to verify if a relation represents a function was presented.
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In the figure, m<7 = 100. Find the measure of <5
Answers
By the definition of vertically opposite angle, the value of measure of ∠5 is, 100°.
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
In the figure,
⇒ m ∠7 = 100°
Now, By the figure we have;
Both the angles 7 and angle 5 are vertically opposite angle.
And, We know that the vertically opposite angles are equal to each other.
Hence, We get;
⇒ m ∠7 = m ∠5
⇒ 100° = m ∠5
⇒ m ∠5 = 100°
Thus, We get;
⇒ m ∠5 = 100°
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solve the system of equations below
Answers
The solution of the system of equations is:
x = 3
y = 2
How to solve the system of equations?Here we want to solve the system of equations below:
2x + y = 8
x - 3y = -3
First, let's isolate one variable in one of the equations, I will isolate y on the first one.
y = 8 - 2x
Now we can replace that in the other one to get:
x - 3*(8 - 2x) = - 3
x - 24 + 6x = -3
7x = -3 + 24
7x = 21
x = 21/7 = 3
And the value of y is:
y = 8 - 2x = 8 - 2*3 = 2
The solution is x = 3 and y = 2.
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Find the geometric mean between 4 and 5.
Answers
Answer:
1.106209714987%
Step-by-step explanation:
Negative values detected. All input values threated as percentages (e.g. an input of 0.1 is threated as 0.1%, -10 is threated as -10%).
42:29
The function(x) - 3. 25x represents the total amount
collected from cars at one toll booth based on the number of
cars that pass through, x. The mathematical domain for the
function is the set of real numbers,
How does the reasonable domain differ from the
mathematical domain?
The reasonable domain is the set of natural numbers
The reasonable domain is the set of positive real
numbers
The reasonable domain is the set of real numbers greater
than 3. 25
The reasonable domain is the set of whole numbers
greater than 3,25
Answers
The function is the relation between number of cars and toll collected in the toll booth. So the correct option is that the reasonable domain is a set of natural numbers.
While considering a function regarding to mathematical domain, for f(x) = 3.25x, x can be any values between -∞ to +∞. For every x value, we could calculate f(x).
But here, we are dealing with number of cars. So it can have only values as a natural number. A negative integer, fraction or decimal cannot represent x. So it will be a set of natural numbers.
So the domain here is the set of natural numbers.
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what is distance between (1,0) and (9,15)
Answers
Answer:
17
Step-by-step explanation:
To solve this problem, we need to use the distance between two points formula. It states that the distance is [tex]\sqrt{(x_{1} - x_{2} ) ^{2} + (y_{1} - y_{2})^{2} }[/tex]. Here, [tex]x_{1} = 1, x_{2} = 9, y_{1} = 0, y_{2} = 15[/tex]. Plugging these values in gets us [tex]\sqrt{64 + 225}[/tex] which equals [tex]\sqrt{289}[/tex] = 17 .
Tito purchased 11 tickets to a baseball game for $374. About how much did one ticket cost?
Answers
Answer: It is 34$ per one ticket
Step-by-step explanation:
$374 divided by 11 is 34
Answer:
$34 per ticket
Step-by-step explanation:
We were told $374/11tickets.
We are looking for how much per 1 ticket.
Divide to find the per-ticket cost.
Use either 374÷11
374/11 .
374÷11 = 34
This means $34 per ticket.
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A cone has a volume of 192π cubic inches. Its height is 9 inches, what it's radius? Show all your work.
Answers
Answer:
4.5 inches
Step-by-step explanation:
Which number has a digit that is 10x greater
than 70?
a) 3,607
b) 7,391
c) 1,738
d) 7,246
Answers
Answer:
C
Step-by-step explanation:
Look at 70. What digit is it in? The tens.x10 moves our digit once to the left (70 => 700) AKA 7 hundreds!Look at the answers.3607 ( "7" ones)
7391 ( "7" thousands)
1738 ( "7" hundreds)
7246 ( "7" thousands)
forty two out of fifty six students voted Michael for president. What fraction of the workers did not vote for him?
Answers
Answer: [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
1) Subtract Michael's voters from all the voters 56/56 - 42/56. When you have the same denominator, subtract the numerator and keep the denominator the same to get 14/56.
2) Simplify, both the numerator and denominator is divisible by 14, so divide 14/14 to get 1 as our new numerator and divide 56/14 to get 4 as our denominator leading us to our answer of 1/4
"20 decreased by the sum of 6 and b."
Responses
A 20 + (6 – b)20 + (6 – b)
B 20 – (6 + b)20 – (6 + b)
C (20 + 6) – b(20 + 6) – b
D (20 – 6) + b
Answers
The expression for the statement is 20 - (6 + b).
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given statement is 20 decreased by the sum of 6 and b.
Sum means adding two or more numbers or expressions.
Sum of 6 and b means 6 + b.
Decreased means some number is subtracted.
The expression is 20 - (6 + b).
Hence the expression for the phrase is 20 - (6 + b).
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Your options for the question seems a little confusing. Probably the options for the question is given below :
If Tristan's pay was $1600 for the week, he sold ? vacuums
Answers
Answer: $3,000
(There are 7 days in a week) I don't know if i'm correct or not but it should be the answer.
When Destiny agreed to proofread her brother's essay, she expected that it would be 2 pages long. When he gave her the essay, it was actually 4.5 pages long. What is the percent error for her estimate?
Answers
Answer:
44.44%
Step-by-step explanation:
Error percent can be found by this formula
Estimation/Actual number x 100/1
= 2/4.5 x 100/1
= 200/4.5 = 2000/45
= 400/9
= 44.44 %
The bookstore had 56 copies of magazine yesterday and sold 1/4 of them today sold 4/7 of what remain how many copies does the book store have 
Answers
Step-by-step explanation:
Find 1/4 of 56
56 / 4 = 14
Now
56-14=42
Now
42/7=6
6x4=24
42-24=18
18 copies left
Simplify to lowest terms:
2.5:10
1.4:1.8
0.04: 0.3
1/5: 4/5
3/4: 1/2
6.2:5 2/5
Answers
Step-by-step explanation:
2.5:10 = 1/4
1.4:1.8 = 7/10
0.04: 0.3 = 2/50
1/5: 4/5 = 1/5
3/4: 1/2 = 3/2
6.2:5 2/5 = 12/5
2.5 : 10 = 1 : 4
1.4 : 1.8 = 7 : 9
0.04 : 0.3 = 2 : 15
1/5 : 4/5 = 1 : 4
3/4 :1/2 = 3 : 2
6.2 : 5 2/5 = 31 :27
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A cone has a volume of 392π cubic centimeters and a radius of 7 centimeters. What is the height of the cone? Be sure to show all work again (HINT: instead of solving for the radius, you will be solving for the height since you know what the radius measurement already is)!
Answers
The height of the cone is 24 centimetres.
How to find the height of the cone?A cone has a volume of 392π cubic centimetres and a radius of 7 centimetres. Therefore, the height of the cone can be found as follows;
Hence,
volume of a cone = 1 / 3 πr²h
where
h -= height of the coner = radius of the coneTherefore,
volume = 392π
r = 7 cm
392π = 1 / 3 × π × 7² × h
392π = 49 / 3 πh
cross multiply
1176π = 49πh
divide both sides by 49π
h = 1176π / 49π
h = 24 cm
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8) The graph shows the total cost C of making x photocopies at a copy shop.
Making Photocopies
Total cost (dollars)
40
35
30
25
00
0
100 200 300 400 500
Number of copies
X
a) Does it cost more money to make 100 photocopies or
101 photocopies? Explain.
b) You have $40 to make photocopies. Can you buy more
than 500 photocopies? Explain.
Answers
Answer: a) It costs more money to make 101 photocopies than 100 photocopies. This can be seen from the graph as the cost increases as the number of photocopies increases.
b) You cannot buy more than 500 photocopies with $40. This can be seen from the graph as the cost of making photocopies exceeds $40 when the number of photocopies is more than 500.
Step-by-step explanation:
The solution is,
a) it costs more money to make 100 photocopies
b) you can buy more than 500 photocopies for $40
Here, we have,
we know that,
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
a) In the graph , 100 photocopies cost $10,
For 101 photocopies, the point on the line comes below of 10 on y axis
So, it costs more money to make 100 photocopies
b) graph arrow shows line moves on...
so, you can buy more than 500 photocopies for $40
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Which other expression has the same value as (-14)-8
Answers
Answer: The expression (-14) - 8 has the same value as -22.
What is equation of the line graphed below. Y= - 5/2 x-2 -this question was accidentally cut out
Answers
Answer: y= -2x+5-1/2
Answer:
y = - [tex]\frac{5}{2}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line
m = [tex]\frac{-2-3}{0-(-2)}[/tex] = [tex]\frac{-5}{0+2}[/tex] = - [tex]\frac{5}{2}[/tex]
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = - [tex]\frac{5}{2}[/tex] x - 2 ← equation of line
Find the roots of the function f(x)=x^2+15x-16
Answers
Answer:
x = -16 and x = 1
Step-by-step explanation:
"Finding the roots" means solving the equation. We'll set the equation equal to 0 (replace f(x) with zero) and factor.
0 = x^2 + 15x - 16
0 = (x + 16)(x - 1)
This is factored.
Using the Zero Product Property, we separate this into two small equations.
x+16 = 0 and x-1 = 0
Solve these one-step equations.
x = -16 and x = 1
These are the roots (and roots are solutions, are zeros, are x-intercepts) If the question ask for zeros, roots, solutions or x-intercepts, set it equal to 0, factor and solve.
In a survey of 500 tourists, 350 like Pokhara, 200 like Chitwan and number of tourist who like both is half of who like Chitwan and 20 like neither of two, using Venn-diagram find how many like only one place.
Answers
Answer:
160 tourists like only one place. This can be determined by using a Venn diagram. Of the 500 tourists surveyed, 350 like Pokhara, 200 like Chitwan, and 50 like both places. That leaves 20 who like neither of the two places. To get the number of tourists that like only one place, subtract the number of tourists who like both (50) and the number of tourists who like neither (20) from the total number of tourists surveyed (500), resulting in a total of 160 tourists who like only one place.