If a back-to-school sale offered a laptop for $379 and this sale price reflected a 15% discount, after using the equation the cost of the computer before the reduction in price is, $446.47.
What is percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Let's call the original cost of the laptop "x".
The equation to find the cost after a discount is:
x - x * (discount rate) = sale price
In this case, the discount rate is 15%, or 0.15. Plugging in the given values:
x - x * 0.15 = 379
Expanding the equation:
x - 0.15x = 379
0.85x = 379
Dividing both sides by 0.85:
x = 379 / 0.85
x = 446.47
So, the cost of the laptop before the reduction in price was $446.47.
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find end behavior of f(x)=2^x-5
The end behavior of the function f(x) = 2ˣ - 5 will be increasing only.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The function is given below.
f(x) = 2ˣ - 5
We know that the function is an exponential function. And the exponential function is always inceasing.
Thus, the end behavior of the function f(x) = 2ˣ - 5 will be increasing only.
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Find the sum of the squares of the solutions of $x^2-13x+4=0$.
The equation [tex]$x^2-13x+4=0$[/tex] is a quadratic equation and can be solved using the quadratic formula.
The sum of the squares of the solutions of the equation [tex]$x^2-13x+4=0$[/tex]can be found in the following steps:
Solve for the solutions: The equation can be solved using the quadratic formula. The solutions are given by
[tex]$x = \frac{13 \pm \sqrt{13^2 - 4 \cdot 4}}{2 \cdot 1} = \frac{13 \pm \sqrt{169 - 16}}{2} = \frac{13 \pm \sqrt{153}}{2} = \frac{13 \pm 9}{2} = 11$ or $-6$.[/tex]
Square the solutions: Find the square of each solution by raising it to the power of 2.
[tex]$11^2 = 121$ and $(-6)^2 = 36$.[/tex]
Sum the squares: Add the squares of the solutions together to get the final answer: 121 + 36 = 157.
Therefore, the sum of the squares of the solutions of
[tex]$x^2-13x+4=0$[/tex] is 157.
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An employee receives a 2% raise once per year. If the employee's initial salary is $ 77,000.00, what will the employee's salary be after 8 years?
Answer:
90,217.77
Step-by-step explanation:
We can use the equation S+RS=M to figure this out where S is the initial salary before the raise, R being the rate at which the salary is increased, and M being the Salary after the raise.
By plugging it in for the first year we get
77,000+2%*77,000=M
Solving it, we get 78,540 and since there is a new salary increase 78,540 is the new starting salary
78,540+78,540*2%=80,110.8
80,110.8+80,110.8*2%=81,713.016
83,347.27632
85,014.2218464
86,714.506283328
88,448.796408995
90,217.772337175
Or rounded up
90,217.77
Two triangles are considered the same if they have the same three side lengths. Find all possible values of P such that there is only 1 possible triangle with integer side lengths and perimeter P.
Answer:
P ∈ {3, 5, 6, 8}
Step-by-step explanation:
You want the possible perimeter values such that there can only be one triangle with that perimeter and integer side lengths.
ConditionsThe requirement that the triangle satisfies the triangle inequality means the longest side must be shorter than P/2.
TrialsThe smallest triangle with integer side lengths is the {1, 1, 1} equilateral triangle.
P=3, {1, 1, 1}
For P=4, the longest side can be neither 1 nor 2, so P=4 is not an option.
For P=5, the longest side can be 2, requiring the other sides to be 2 and 1:
P = 5, {2, 2, 1}
For P=6, the longest side must be less than 3, so all sides must be 2.
P = 6, {2, 2, 2}
For P=7, two triangles are possible: {3, 3, 1} and {3, 2, 2}.
For P = 8, the longest side must be less than 4, so will be 3. The other two sides must be 3 and 2.
P = 8, {3, 3, 2}
For all values of P above 8, there are at least two possible triangles.
Possible values of P are 3, 5, 6, 8.
8 chicken will lay 20 eggs in 3 days
how many days will it take 12 chickens to lay 100 eggs?
Answer:
it will take approximately 3 and 1/3 days for 12 chickens to lay 100 eggs.
44. 4, 43. 8, 45. 6, 45. 9, 44. 1, 45. 6, 44. 0, 44. 9, 45. 8 mean and MAD answer
For the values 44. 4, 43. 8, 45. 6, 45. 9, 44. 1, 45. 6, 44. 0, 44. 9, 45. 8, the mean of the data set is 49.52. The Mean Absolute Deviation (MAD) of the data set is 4.83.
To find the mean of the given data set, we add up all the values and divide by the number of values:
Mean = (44.4 + 43.8 + 45.6 + 45.9 + 44.1 + 45.6 + 44.0 + 44.9 + 45.8) / 9 = 445.7 / 9 = 49.52
So, the mean of the data set is 49.52.
To find the Mean Absolute Deviation (MAD), we first find the absolute difference between each value and the mean, and then find the mean of these absolute differences:
Absolute Difference = |44.4 - 49.52|, |43.8 - 49.52|, ..., |45.8 - 49.52|
MAD = (Absolute Difference1 + Absolute Difference2 + ... + Absolute Difference9) / 9
Calculating the MAD gives:
MAD = (5.12 + 5.72 + 3.92 + 3.62 + 5.42 + 3.92 + 5.52 + 4.62 + 5.32) / 9 = 43.5 / 9 = 4.83
So, the Mean Absolute Deviation (MAD) of the data set is 4.83.
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Find a increased by 25% pls help ASAP.
Answer:
1.25a
Step-by-step explanation:
Original value = a
An increase of 25% can be found by a x 25/100 = 0.25a
The resulting increased value = Original value + Increase in value
= a + 0.25a
= 1.25a
Sometimes it is a more direct approach to use the final value as original value(1 + increase%/100) in which case it would be a(1+25/100) = a(1 + 0.25) = a(1.25) = 1.25a
find three consective integers if the sum of the first two is 51 more than the third integer
The first of the three consecutive integers is 52. The next two are 53 and 54. These are three consecutive integers such that the sum of the first two is 51 more than the third integer.
Let's call the first of the three consecutive integers "x". The next two would then be "x + 1" and "x + 2".
According to the problem, the sum of the first two integers (x + (x + 1)) is 51 more than the third integer (x + 2), so we can write an equation:
x + (x + 1) = (x + 2) + 51
Expanding the left side and solving for x:
2x + 1 = x + 53
x = 52
So, the first of the three consecutive integers is 52. The next two are 53 and 54. These are three consecutive integers such that the sum of the first two is 51 more than the third integer.
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Carina hiked at Yosemite National Park for 1.75 hours. Her average
speed was 3.5 mi/h. How many miles did she hike?
O 20 mi
O 6.125 mi
O 2 mi
O 61.25 mi
help please. i don’t understand this question and i’ve been stuck for ages
Answer: The perfect answer is 270x
Step-by-step explanation: I don’t really know but if I’d try I will say it’s:
For A: 10 x 12 x 9 x 6 x 15 = 97200
For B: 15 x 18 x ? x ? x X= 270x
97200 divided by 270x = 360x
Find the value of x that makes this a true statement (1/3)^x=27
Answer:
x= -3
Hope this helped
Kim used sticks to make a pattern of squares. Number of squares: 1, 3, 6, 10, 15. Number of sticks: 4, 10, 18, 28, 40. When a shape consists of 28 squares, how many sticks will the shape have?
Answer:
70
Step-by-step explanation:
Find the number pattern (check image)
The shape consisting of 28 squares will have 812 sticks.
Determining the number of sticks the shape will haveFrom the given data, we can see that the number of squares is increasing by consecutive odd numbers, starting from 1:
1, 3, 6, 10, 15, ...
Also, the number of sticks is increasing by consecutive even numbers, starting from 4:
4, 10, 18, 28, 40, ...
This suggests that the number of sticks required to make a pattern of n squares can be found using the formula:
sticks = 2n + (n-2) + (n-4) + ... + 4
This formula represents the sum of the first n even numbers, which can be simplified to:
sticks = n(n+1)
Using this formula, find the number of sticks required to make a pattern of 28 squares:
sticks = 28(28+1) = 28(29) = 812
Therefore, a shape consisting of 28 squares will have 812 sticks.
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Help, Find the expression of the nth term of the sequence.
WILL MARK BRANLIEST!
The expression of the nth term of the sequence is 1/n
How to determine the expression of the nth term of the sequence.From the question, we have the following parameters that can be used in our computation:
The sequence definition
From the sequence, we can see that only the denominator increaes by 1
The numerator is constant at 1
Using the above as a guide, we have the following:
Tn = 1/n
Hence, the expression is 1/n
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Find three consecutive positive odd integers such
that the square of the smallest exceeds twice the
largest by 7.
Answer:
5, 7, 9
Step-by-step explanation:
You want three consecutive positive odd integers such that the square of the smallest exceeds twice the largest by 7.
SetupLet x represent the middle of the integers. Then x-2 is the smallest, and x+2 is the largest. The given relation is ...
(x -2)² -2(x +2) = 7
SolutionEliminating parentheses gives ...
x² -4x +4 -2x -4 = 7
x² -6x -7 = 0 . . . . . . . . . subtract 7, simplify
(x -7)(x +1) = 0 . . . . . . . factor
Values of x that make the factors zero are solutions to this equation:
x -7 = 0 ⇒ x = 7
x +1 = 0 ⇒ x = -1
The positive odd numbers are 5, 7, 9.
__
Check
5² -2(9) = 25 -18 = 7 . . . . as required
which of the examples below represent the importance of determining the number of bacteria in a sample? multiple select question. identifying the type of bacteria present in a sample. determining the quality of milk. assessing the purity of food or water. testing to see if a patient has a bladder infection.
The examples that represent the importance of determining the number of bacteria in a sample are determining the quality of milk, assessing the purity of food or water , testing to see if a patient has a bladder infection.
It is necessary to count the number of organisms present in a sample of a material, such as water, food, or a bacterial culture. Bacterial pathogens, for instance, can enter food at any point, including during growth/production at the farm, processing, handling, and packaging, as well as when the food is prepared in the kitchen . While pathogenic bacteria in tiny quantities are typically not harmful, poor storage and/or cooking practices can cause these germs to grow to dangerously high concentrations .Another method bacteria can be introduced into water is by faecal contamination . Gram-negative, non-spore-forming bacteria called coliforms can ferment lactose to create acid and gas. Fecal coliforms are a subset of these bacteria that are prevalent in both human and animal intestines. Other fecal coliform bacteria are frequently utilized as indicator species since they are rarely observed thriving in nature when there is no fecal pollution. The presence of E. coli signals the presence of feces, which raises the possibility of the presence of dangerous pathogens including Salmonella species and Campylobacter species.
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A ball is dropped from 10 feet above the ground. The function h (t) = -16 t² + 10, where t represents the time
in seconds, h gives the height, in feet, of the ball above the ground. When will the ball be 4 feet above the ground? Use
the given quadratic function model to answer questions about the situation it models.
Answer: The equation to find the time when the ball is 4 feet above the ground is:
-16t^2 + 10 = 4
We can solve for t by subtracting 4 from both sides:
-16t^2 + 6 = 0
And then dividing both sides by -16:
t^2 = -6 / -16
t^2 = 3/8
Taking the square root of both sides:
t = ±√(3/8)
Since time cannot be negative, we choose the positive solution:
t = √(3/8)
So the ball will be 4 feet above the ground after √(3/8) seconds.
Step-by-step explanation:
Asking for help: does anyone have the answer?
Answer:
D
Step-by-step explanation:
AD≅AB because they are tangent segments from the same point, A
x² + 2 = 11
x² = 9
x = √9 = 3, -3 (two solutions of [tex]\sqrt{9}[/tex])
Help!!!!!!!!!!!!!!!!!!!!!!
Answer:
the second option
Step-by-step explanation:
the limit coming to x = 4 from the left (the '-' side) is -4.
the limit coming to x = 4 from the right (the '+' side) is 2.
it does not matter that the point itself is excluded. but the tendency of the function coming from the right is clear and defined.
the one-sided limit would not exist, if the function violently oscillates at the limit point.
or if the limit is infinite. then officially it does not exist, but we can write ±infinite.
for the case of the violent oscillation there is nothing else we can write but DNE.
Suppose that you are given the following expression: -(-20). Which of the following is NOT equivalent to ?-(-20)
A. 20
B.-20
C.[20}
D.{-20}
E.-(-(-(-20)))
The expression that will be not equal to -{-20} are -20,{-20}. The correct options are B and D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is -(-20). The not equivalent expressions are written below,
-(-20) ≠ 20
-(-20) ≠ {-20}
Therefore, expressions like -20, and -20 will not be equal to —20. B and D are the appropriate choices.
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a floor plan is given for the first floor of a new house. one inch represents 10 feet. if the walk-in closet is 2/5. in. by 2/3 in. on the floor plan, what are the actual dimensions? (round to the nearest hundredth).
The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.
Finding actual dimensions:To find actual dimensions multiply the given measurement with the measurement given in scale.
In the given problem, given that 1 in = 10 feet which is the scale given, we need to multiply the given measurements that are in the plan with the scale measurement 10 feet.
Here we have
A floor plan is given for the first floor of a new house.
One inch represents 10 feet.
The walk-in closet is 2/5 in. × 2/3 in. on the floor plan
As we know 1 inch = 10 feet
=> 2/5 in = (2/5) × 10 feet = 4 feet
=> 2/3 in = (2/3) × 10 feet = 6.67 feet
Therefore,
The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.
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uppose that a college has 1000 professors. in how many ways can the board of trustees pick a president? the president should be one of the 1000 professors.
There is only one way to pick a president from 1000 number of professors, and that is to select one of the professors.
1. There are 1000 number of professors to choose from
2. The board of trustees can only pick one of the 1000 professors
3. Therefore, there is only one way to pick a president - select one of the professors.
The board of trustees can pick a president from the 1000 professors by considering their qualifications, experience, and other criteria. They can also take into account the opinion of the faculty and students of the college. If applicable, the board may also take into account any applicable legal requirements. Finally, they can make their selection by majority vote.
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Which soup has more sodium per cup
Answer:
Soup B
Step-by-step explanation:
Soup A = 5 grams sodium = 12 cups
Soup B = 8 grams of sodium = 13 cups
Find the unit rate, so, soup B has more sodium.
I hope this helps.
Also, next time can you write the question entirely?
Determine whether VY//ZW. Justify your answer. ZX = 18, ZV = 6, WX = 24, and YX = 16
Answer:
Step-by-step explanation:
To determine whether VY is parallel to ZW, we need to see if the ratio of their corresponding sides is equal.
The ratio of corresponding sides of two parallel lines is constant, so we can set up an equation to compare the ratios:
ZV/ZX = WX/YX
6/18 = 24/16
Simplifying the fractions, we get:
1/3 = 3/2
Since the two sides of the equation are not equal, VY is not parallel to ZW.
25 points
Matthew is planning a party and found pizzas for $5 each and drinks for $1 each.
Write an expression that represents how much he will spend. (p = pizza, d = drinks)
The expression that represents how much he will spend would be = y ( 5p + 1d)
How to derive the expression that shows how much he will spend?The amount of money that each pizza(p) is sold = $5 each.
The amount of money that each drink(d) is sold = $1.
The total money that Matthew may spend on the party is represented by = y.
Therefore the expression that will show how much he will spend would be = y ( 5p + 1d).
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Finish the patterns
12, _ , _ , _ , 60
1, 3, 5 , 7, _
9, _, _ ,_, 81
_,_,15,_.20
Answer:
Step-by-step explanation:
12, 28, 44, 60
1, 3, 5, 7, 11
9, 25, 49, 81
4, 8, 15, 16, 20
Answer:
1. 12 , 24 , 36 , 48 , 60
2. 1, 3, 5, 7, 9
3. 9, 27, 45, 63, 81
4. 1, 2, 15, 16, 20
Step-by-step explanation:
1. The rule is +12, or add 12.
2. The rule is +2, or add 2.
3. The rule is +18, or add 18.
4. The rule is +1, +13, +1, +4, or add 1, add 13, add 1, add 4.
I need to prove that AC bisects BD. Can anyone help?
Answer:
let the position vector of A,B,C,D and E be OA,OB,OC,OD andOE respectively.
IN triangle OBD , OE = OD+OB/2
OE=OA+AB+OD/2. (in triangle,OB=OA+AB)
OE=OA+OD+DC/2
OE=OA+OC/2. (in triangle ODC,OD+DC=OC)
proved....
a cylindrical can with an open top is to be constructed so that its volume is 167 cubic inches. what height will minimize the amount of tin that will be required to construct the can?
The minimum height of the cone is 17.87 in (approx)
What is the Cylinder:In geometry, the cylinder is a fundamental 3 dimension shape that has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center.
Total surface area, A = 2πr²+ 2πrh square units
The volume of the Cylinder, V = πr²h cubic units
Here we have
A cylindrical can with an open top is to be constructed so that
The volume of the cone is 167 in³
As we know volume of cone = (1/3) πr²h
=> (1/3) πr²h = 167
=> h = 501/πr²
As we know Surface Area of the cone = 2πrh + 2πr²
Substitute h = 501/πr² in Surface Area of cone
=> SA = 2πr(501)/πr² + 2πr²
=> SA = 1002r⁻¹+ 2πr²
Differentiate SA with respect to r
=> SA' = (-1) 1002r⁻²+ 4πr
=> SA' = - 1002r⁻² + 4πr
Here - 1002r⁻² + 4πr = 0
=> - 501r⁻² + 2πr = 0
=> - 501/r² + 2πr = 0
=> [-501 + 2πr³ ]/r² = 0
=> [-501 + 2πr³ ] = 0
=> 2πr³ = 501
=> πr³ = 250.5
=> r³ = 79.70
=> r = 8.92 (approx)
Hence the height of the cone, h = 501/πr²
= 501/π(8.92)
= 17.87 (approx)
Therefore,
The minimum height of the cone is 17.87 in (approx)
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Ethan starts an IRA (Individual Retirement Account) at the age of 34 to save for retirement. He deposits $400 each month. Upon retirement at the age of 65, his retirement savings is $709,165.25. Determine the amount of money Ethan deposited over the length of the investment and how much he made in interest upon retirement.
Ethan deposited 400 each month into his IRA for 31 years.
This totals 148,800 (400 x 31 years = 12,400 x 12 months = 148,800). Upon retirement, Ethan's total savings was 709,165.25. To determine the amount of interest he made, we subtract the total deposits from the total savings: 709,165.25 - 148,800 = 560,365.25. This shows that Ethan made 560,365.25 in interest on his retirement savings over the 31 years. The formula used to calculate the amount of interest Ethan made is: Interest = Total Savings - Total Deposits.Ethan deposited $400 each month into his IRA for 31 years.
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in this article fogel only looks at data from one year (1890). how does he justify drawing conclusions about a much longer time period (1850-1890) from data from just one year?
Robert W. Fogel, in his famous article, used data from one year, 1890, to make inferences about a longer time period, 1850-1890. He did so through the use of statistical methods, including regression analysis and comparative economic growth analysis.
The basic idea behind this approach is to use the data from 1890 as a snapshot of the state of the economy at that time and to use this information to make inferences about the longer time period. The assumption behind this approach is that the data from 1890 is representative of the economy over the entire period 1850-1890, and that the underlying trends and patterns that existed in 1890 were also present in the earlier period.
Fogel used a combination of economic theory, demographic data, and historical information to validate his assumptions and to support his conclusions. He also conducted extensive sensitivity analysis to ensure that his results were robust to different assumptions and data sources.
In conclusion, while using data from one year to draw conclusions about a much longer time period might seem unconventional, it was a valid approach used by Robert W. Fogel in his research and allowed him to make important contributions to our understanding of the economic history of the United States.
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Sam wants to enlarge a triangle with sides of 3 cm, 6 cm, and 9 cm. If the shortest side of the new triangle is 13 cm, what are the measurements of the two longer sides? Do not include units in your answer.