Answer:
To find the equivalent of 2 4/5 + 4/6, we first need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number part of the mixed number by the denominator of the fraction part, and add the result to the numerator of the fraction part. So 2 4/5 becomes 2 * 5 + 4 = 14/5. Similarly, 4/6 becomes 4 * 1 + 6 = 10/6.
Next, we need to find a common denominator for the two fractions so that we can add them. A common denominator for 14/5 and 10/6 is 30, so we convert both fractions to have a denominator of 30. To convert 14/5 to have a denominator of 30, we multiply the numerator and denominator by 6, which gives us 14 * 6 / 5 * 6 = 84/30. Similarly, we multiply the numerator and denominator of 10/6 by 5 to get 10 * 5 / 6 * 5 = 50/30.
Now that both fractions have a denominator of 30, we can add them to get the equivalent of 2 4/5 + 4/6. This gives us 84/30 + 50/30 = 134/30. Finally, we simplify the fraction to get the final answer, which is 134/30 = 4 8/30 = 4 4/15. So, the equivalent of 2 4/5 + 4/6 is 4 4/15.
Write a numerical expression to represent the phrase "the sum of 25 and the cube of 9." Do not evaluate the expression.
Answer:
25 + 9^3
Step-by-step explanation:
In how many ways can the letters of the word ‘CAR’ be reordered to produce distinct ‘words’?
Answer:2
Step-by-step explanation:
car, and arc, however ar is also a word, not distinctly though.
If tan t = 4/3 in quadrant 3, find the remaining trig functions.
sin t:
cos t:
csc t:
sec t:
cot t:
Answer:
Below
Step-by-step explanation:
edited: FOR QIII (I didn't see that part)
Remember for a right triangle S-O-H-C-A-H-T-O-A
Tan is OPPOSITE LEG / ADJACENT LEG
make the right triangle with legs 3 and 4 ( in quadrant III)
then the hypotenuse is 5
sin = opp/ hyp = - 3/5
cos = - 4/5
csc = 1/sin = - 5/3
sec = 1/cos = - 5/4
cot = 1/tan = 3/4
A milkman had 3 1 litres of milk in the can. He sold 1 1 litres to a customer and 2 litres 423
to a hotel. How much milk is left in the can?
The amount of milk remaining after the milk is sold to the customer and hotel is 18 liters.
What is a mathematical equation and expression?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that a milkman had 31 liters of milk in the can. He sold 11 liters to a customer and 2 liters to a hotel.
Assume that the remaining milk in the container is denoted by [x]. Then, we can write -
[x] = Total milk - {milk sold to customer + milk sold to can}
[x] = 31 - {11 + 2}
[x] = 31 - 13
[x] = 18
Therefore, the amount of milk remaining in the can is 18 liters.
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1. The graph below shows the number of children's and adult tickets sold each day of a performance.
(a) What is the slope of the line? Show your work.
(b) What is the equation of the line in point-slope form?
(c) What is the equation of the line in slope-intercept form?
(d) What is the equation of the line in standard form? Show your steps in converting to standard form.
Answer:
(a) -2
(b) y -120 = -2(x -10)
(c) y = -2x +140
(d) 2x +y = 140
Step-by-step explanation:
Given a graph with y-intercept 140 and x-intercept 70, you want the slope and various equations describing the graph.
(a) SlopeThe line drops from a y-value of 140 to 0 as x increases from 0 to 70. The slope is ...
m = rise/run = -140/70 = -2
The slope of the line is -2.
(b) Point-slope equationThe point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
We have a line with slope -2 that goes through the point (10, 120), so we can write the equation as ...
y -120 = -2(x -10)
(c) Slope-intercept formIn part (a) we identified the y-intercept as 140, so we can write the equation as ...
y = mx + b . . . . . line with slope m and y-intercept b
y = -2x +140 . . . . . . line with slope -2 and y-intercept 140
(d) Standard formThe slope-intercept equation can be converted to standard form by adding the opposite of the x-term to both sides.
y +2x = -2x +2x +140 . . . . . 2x added to both sides
2x +y = 140 . . . . . . . . . standard form equation of the line
2) Explain how graphing these equations can help find the solution to the system.
Graphing these equations can help find the solution to the system by unique solution, no solution and infinite number of solution.
Define equation.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given
Graphing these equations can help find the solution to the system by,
There are three possible outcomes when two equations with two variables are considered in a two-dimensional plane.
1.Unique solution: A point will be where the graphs of the two lines connect.
The One equation's coefficient of variation and constant will not be proportionate to another equation's coefficient of variation and constant.
2. No Solution: The two lines run parallel to one another.
While constants are not proportional, the coefficient of variables of one equation will be related to the coefficient of variables of another equation.
3, Infinite number of Solution: The two lines will coincide.
One equation's coefficient of variation and constant will be proportional to another equation's coefficient of variation and constant.
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question in the photo
The compositions of the functions are given as follows:
(f ∘ g)(0) = 0.(g ∘ f)(1) = -2.The domain and the range of the functions are given as follows:
Domain of g(x) = {-4, -3, 0, 1}.Range of f(x) = {0, 1, 2}.How to obtain the composite functions?The representation of the composite function is that the output of the inner function works as the input to the outer function, as follows:
(f ∘ g)(x) = f(g(x)).
Hence, at x = 0, the composite function is given as follows:
(f ∘ g)(0) = f(g(0)) = f(1) = 0.
At x = 1, the composite function is given as follows:
(g ∘ f)(0) = g(f(0)) = g(1) = -2.
How to obtain the domain and the range?The definitions of the domain and of the range of a function are given as follows:
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Robert had 362 in his bank account. He first spent 54 and then 82 how much money does Robert have left
If Robert had 362 in his bank account. If he first spent 54 and then 82 then the amount left in Robert bank account is $226.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the amount in Roberts bank account is $362.
He first spent 54 and then 82
We need to find the amount left in Robert account.
This we can find by finding the total amount he spent and removing total amount spent from the total amount he has in his account.
The total amount he spend=54+82
Fifty four plus eighty two
136
One hundred thirty six.
The amount left we calculate by subtracting 136 from 362.
362-136
We get 226.
Hence, the amount left in Robert bank account is $226.
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The sum of two numbers is 43 . One number is 19 more than the other.find the numbers
Line d has a slope of 6/7. line e is parallel to line d. what is the slope of line e?
Parallel lines have the same slope.
If one line has a slope of 6/7, then the other line also has a slope of 6/7.
The height of a cell phone tower is 200 ft tall. The tower is secured by 3 wires, stretching from the top of the tower to spots on the ground 50 ft away from the base of the tower. Each wire creates a right triangle with the tower and the ground. What is the length of each wire to the nearest foot?
Question 14 options:
42,500 ft
354 ft
3,704 ft
206 ft
Answer:
206 ft
Step-by-step explanation:
Each wire is a hypotenuse of a right triangle in which the height of the tower is one leg and the distance from the anchor of the wire to the base of the tower is the other leg.
Leg 1: 200 ft
Leg 2: 50 ft
Hypotenuse: x
200² + 50² = x²
x² = 40,000 + 2,500
x² = 42,500
x = √42,500
x = 206
Answer: 206 ft
I need help in stuck on this
Answer:
-22
Step-by-step explanation:
f(4) = [tex]2^{4}[/tex] + 8 = 24
f(-2) = [tex](-2)^{2}[/tex]-48 = -46
24 + -46 = -22
Solve for w |w|=6 I have HW and I need help
[tex]w=\sqrt{6},\sqrt{-6}[/tex]
What is modulus ?
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the output is always favourable. The equation is y = |x|.
Given:
[tex]w|w|=6\\w(-w)=6[/tex]
or
[tex]w(w)=6[/tex]
solving both one by one,
[tex]w(-w)=6\\-w^{2} =6\\w=\sqrt{-6}[/tex]
and,
[tex]w(w)=6\\w^{2} =6\\w=\sqrt{6}[/tex]
[tex]w=\sqrt{6},\sqrt{-6}[/tex]
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Y varies directly as x. If x=6 when y=36 find x when y=72
Answer:
x= 12
Step-by-step explanation:
Y[tex]\alpha[/tex] X
Let the constant be k
For the proportionality sign to be gone,a constant has to be introduced.
Since y varies directly,the constant ( k) will multiply x
Y= kx
Substitute for x=6 and y=36 to find k
36=6x
x = 36/6 = 6
To find the value of x,substitute for k = 6 and y = 72
72= 6x
x = 72/6
x=12
aisha estimated that she has 10 books in her library she actually has 8 books what is the percentage error?
The percentage is the indicating hundredth thus percentage error will be 20%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
Estimated books = 10
Actually number = 8
% error = (10 - 8)/10 x 100 = 20%
Hence "Since the percentage is one-hundredth of a percent, the mistake will be twenty percent.".
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NO LINKS!! Please help me with the Domain and Range and Functions Part 3bb
Domain - the set of possible x-coordinates of a function.
Range - the set of possible y-coordinates of a function.
Question 30
Domain is:
x ∈ [- 6, 6], both ends included as part of graph.Range is:
y ∈ [-3, 7], both ends included as part of graph..This is not a function as it fails the vertical line test.
Question 31Domain is:
x ∈ [- 2, 2], one end is is part of the graph and the other is closed circle.Range is:
y ∈ [-6, 6], both ends included as closed circles.This is not a function as it fails the vertical line test.
Answer:
30.a) Domain: [-6, 6]
30.b) Range: [-3, 7]
30.c) Function: No
31.a) Domain: [-2, 2]
31.b) Range: [-6, 6]
31.c) Function: No
Step-by-step explanation:
Definitions
An open circle indicates the value is not included in the interval.A closed circle indicates the value is included in the interval.An arrow shows that the function continues indefinitely in that direction.Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 30The graph is a conic section (ellipse) and therefore it is not a function.
The smallest x-value is x = -6 and the greatest x-value is x = 6.
The smallest y-value is y = -3 and the greatest y-value is y = 7.
Therefore, the domain and range in interval notation are:
Domain: [-6, 6]Range: [-3, 7]The graph is a not a function as almost all the inputs (x-values) are related to more than one output (y-value).
Question 31From inspection of the graph, the endpoints of the continuous line are:
(-6, 0) and (2, 6)Both endpoints are closed circles, so the values are included in the domain and range.
The smallest x-value is x = -2 and the greatest x-value is x = 2.
Therefore, the domain in interval notation is:
Domain: [-2, 2]The smallest y-value is y = -6 and the greatest y-value is y = 6.
Therefore, the range in interval notation is:
Range: [-6, 6]The graph is a not a function as not all inputs (x-values) are related to one output (y-value).
When ordering the Kids' Lunch at Burger Universe, the customer must choose a size, whether or not to have cheese, a side order, and a type of fruit drink. Here are the possibilities for each choice. Choice Possibilities Size Small, Large Cheese? With cheese, Without cheese Side order Fries, Onion rings Fruit drink Orange, Grape, Cherry, Lemonade How many Kids' Lunches are possible?
The possible Kids' lunches are 32.
What is a permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Using permutations:
you have
- 2 possible choices for the size (small and large),
- 2 possible choices for the cheese (with and without),
- 2 possible choices for the side order (fries and onion rings)
- 4 possible choices for the fruit drink (orange, grape, cherry and lemonade)
The total Kids' lunches possible, are the total combinations you can get, therefore:
2 × 2 × 2 × 4 = 32
There are 32 possible Kids' lunches.
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what is the slope?
Simplify Your answer and write it as a proper fraction, improper fraction, or integer
Answer: 1/2
Step-by-step explanation:
Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact answer. Do not round.)f(x) = x^2 + 5; g(x) = −x^2; x = 0; x = 3
The equations whose graphs encompass a region are thus provided. when the region's area is 301.5
Define area.The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies. The simplest technique is to multiply the room's length and width. The floor surface area for a rectangular room is equal to the length times the width. The formula for this is area = length x width (A = lw).
Given
g(x) = x²
x = 0
x = 3
We must determine the area using the functions f(x) and g(x), which are provided.
ₐ∫ᵇ (f(x) + g(x)) dx
₀∫³ (x² + 15(x + 5)) dx
₀∫³ (x²dx + ₀∫³15(x + 5)) dx
(x³/3) + 15x²/2 + 75x
₀[x³/3]³ + ₀[15x²/2 + 75x]³
[(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]
27/3 + 15(9/2) + 75(3)
9 + 15(4.5) + 7
76.5 + 225
301.5
The equations whose graphs encompass a region are thus provided. when the region's area is 301.5
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Bryan was selling tickets for a school play. Adult tickets cost $10 and children's tickets cost $5. If Bryan madea total of $310 in one day of sales write an equation that could represent the number of adult's
(a) tickets and children's tickets sold.
Answer:
Step-by-step explanation:
10(a)+5(c)=310
a= number of adult
c= number children
Write an equation whose solution is the number of months, x it takes for the account
balance to reach $2000.
An equation whose solution is the number of months, m, it takes for the account balance to reach $2000 would be the initial balance minus the monthly rent times the number of months equals $2000.
$4800-$400m=$2000
Given:
initial balance : $4800
removed from the account each month for rent : $400
Since the account starts with $4,800 and decreases by $400 each month, there will be 4800−400m dollars left in the account after m months have passed.
The question asks us to set up an equation representing the number of months that pass before this quantity equals 2,000, and so the desired equation is
4800−400m=2000.
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Which point could be removed in order to make the relation a function , (0,2) (3,8) (-4,-2) (3,-6) (-1,8) (8,3)
A:(8,3)
B:(3,-6)
C:(-1,8)
D:(-4,-2)
Answer: B
Step-by-step explanation:
(3,8) and (3,-6) both have an x of 3, but a different y, so the list is not a function. If you remove (3,-6), it is a function because the 3 no longer repeats.
A salesperson's weekly paycheck is 15% less than a second salesperson's paycheck. The two paychecks total $1675. Find the amount of each paycheck. (Round your answers to the nearest cent.)
The amount of paycheck of Salesperson 1 and Salesperson 2 is $770 and $905 respectively.
What is Percentage?
The percentage is one of the most used methods to portray statistics. Percentage simply means "per hundred," and the sign for percentage is%. One percent (or 1%) is one hundredth of a total or whole number and is computed by dividing the whole or entire number by 100.
Solution:
Given: Paycheck of Salesperson 1 = 85% of Salesperson 2
Let, Paycheck of Salesperson 2 = x
So, paycheck of Salesperson 1 = 85/100 x
According to the question,
85/100 x + x = 1675
185/100x = 1675
x = 167500 / 185
x = 905.4$ = 905$
Salesperson 1 = 770$
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PLEASE HELP IM GIVING BRAINLIEST AND ITS 15 POINTS
By solving the given expression we get sinα as a final result.
What is tanx in terms of sinx and cosx ?
Tanx can be defined as the ratio of sinx and cosx and tanx can be defined by ratio of opposite side and adjacent side also.
Given expression,
secα / (cotα+tanα)
secα can be written as 1/cosα
cotα = cosα/sinα
tanα = sinα/cosα
so,
by substituting we get,
(1/cosα ) / ((cosα/sinα) + (sinα/cosα) )
(1/cosα ) / (cos2α+sin2α)/sinαcosα
(cos square x + sin square x = 1 )
(1/cosα ) /(1/sinαcosα)
= sinα
Hence , By solving the given expression we get sinα as a final result.
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PLEASE HURRY
Solve the following equation:
5- (4x+3)= 1/2 (8x - 12)
Please solve for x
Answer:
x=1
Step-by-step explanation:
---------- -----------
x =1
Isolate the variable by dividing each side by factors that don't contain the variable.
AreaABC Corp bought a production machine on January 1, 2019 for $31,250. The company did not elect Section 179 expensing and elected out of claiming bonus depreciation in 2019, and is depreciating the machine using the MACRS accelerated depreciation tables for 5-year property, half-year convention. What is the 2021 depreciation (Year 3) deduction for the machine?
2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.
Given that,
ABC Corp spent $31,250 on a production machine on January 1, 2019. The corporation is depreciating the equipment using the MACRS accelerated depreciation tables for 5-year property, half-year convention, and has chosen not to exercise Section 179 expensing or to claim bonus depreciation in 2019.
We have to find what is the machine's Year 3 depreciation deduction for 2021.
We know that,
Computation of 2018 depreciation (year 3) deduction for the machine using MACRS accelerated depreciation table for 5 year property.
Name of the asset is production machine
Basis of machine is $31,250
MACRS Percentage from MACRS Percentage Table A-1 by IRS Publication 946 for 5 year property using half year convention for 3rd year is 19.20%
2018 depreciation (year 3) deduction for the machine is
$31,250×19.20%=$6,000
Therefore, 2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.
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evaluate x 3 + (5x + y)2 if x= -1 and y=4
Answer:
-3
Step-by-step explanation
x^3+(5x+y)2
-1^3=-1
-1 x -1 x -1 = -1
(5x+y)2
(5(-1)+(4)2
(-5+(4))2
(-1)2 = -2
Bring -1 down from -1^3
-1-2=-3
You answer is -3
Help me please it’s due tomorrow!!!!!
Answer:
130 more dollars.
Answer:
130
Step-by-step explanation:
Find the Area of the figure below, composed of an isosceles trapezoid and one semicircle. Rounded to the nearest tenths place
The Area of given figure is 48.28 unit² (Approx.)
How to calculate the surface area of a composite figure?Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
We are Given Length of parallel lines are 13 , 6 respectively
Diameter of semi-circle = 6
Height of parallelogram = 8
Area of given figure
Radius of semi-circle = Diameter of semi-circle / 2
Radius of semi-circle = 6 / 2
Radius of semi-circle = 3
Area of given figure = [1/2][Sum of parallel line][Height] + [πr² / 2]
Area of given figure = [1/2][13 + 6][8] + [(3.14)(3)² / 2]
Area of given figure = 42 + 6.28
Area of given figure = 48.28 unit² (Approx.)
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Samuel wants to deposit $4,000 and keep that money in the bank without deposits or withdrawals for three years. He compares two different options. Option 1 will
pay 1.8% interest, compounded quarterly. Option 2 will pay 1.5% interest, compounded continuously.
How much interest does Option pay?
b. How much interest does Option 2 pay
Part (a)
The compound interest formula is
A = P*(1+r/n)^(n*t)
where,
A = account balance after t yearsP = deposit amountr = annual interest rate in decimal formn = number of times the money is compounded per yeart = number of yearsFor option 1, we have these values:
P = 4000r = 0.018n = 4t = 3Plug them into the formula to get:
A = P*(1+r/n)^(n*t)
A = 4000*(1+0.018/4)^(4*3)
A = 4221.4270078004
A = 4221.43
The account balance after three years is $4221.43
Then subtract off the deposit to find the interest made.
i = A - P
i = 4221.43 - 4000
i = 221.43
Answer: Option 1 pays $221.43 in interest.
====================================================
Part (b)
If n heads to infinity, then the compound interest formula is replaced with the continuously compounded interest formula.
That formula is
A = P*e^(r*t)
where the new item 'e' is a special constant.
e = 2.718...
It's similar to how pi = 3.14...
Most calculators have an "e" button, so it's best to let the calculator handle the decimal digits of "e".
For option 2, we have:
P = 4000r = 0.015t = 3So,
A = P*e^(r*t)
A = 4000*e^(0.015*3)
A = 4184.11143963493
A = 4184.11
and,
i = A - P
i = 4184.11 - 4000
i = 184.11
Answer: Option 2 pays $184.11 in interest.
Option 1 is the better choice.