The perimeter of the parallelogram is greater than the perimeter of the square.
What is a perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is obtained by adding up the length of all the sides and edges of the shape. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
Now, let's assume a geometric system of a square and a parallelogram having the same base and equivalent side of the square " a ".
Therefore, the respective two parallel sides of the Parallelogram will also be equal to " a ".
Now, let's rotate the one of the parallel lines with angle Φ clockwise then, the side lengths which aren't equal and parallel to the first set will get increased and it's incremental rate will be responsible for the increase in perimeter of the figures aslike , perimeter is the sum of the sides of the figure.
Now let's rotate alternate side length at maximum at angle θ , aslike it should touch the square at diagonally opposite angles ,
Now, let's calculate perimeters of both the figures -
Square of side length " a " = a + a + a + a = 4a
Parallelogram of two base side length " a " and two parallel set lines of length √2a
= a + a + √2a + √2a
= 2a + 2√2a
= 2a [ 1 + √2 ]
Hence, the acquired perimeter of Parallelogram is greater than that of square
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How many square feet of outdoor carpet will we need for this hole?
Answer:30
Step-by-step explanation:2*5 + 2*4 + 2*2 + 2*4
=10+8+8+4
=30
A train was scheduled to reach the Mumbai Central railway station
1435 hours. It reached the station at 8:15 pm. How late was the train
Answer:
5 hours and 40 minutes late
Step-by-step explanation:
I am assuming by 1435 hours you meant 14:35 -- 2:35 pm.
Hence you subtract 8:15 by 2:35 as the two times you're subtracting should always be the same time format (12 or 24-hour) which is 12 hours in this case.
08:15
- 02:35
Since the minutes of the time above (:15) is higher than 35, we need to add 60 to 15 minutes and at the same time, reduce 8 hours by 1 hour to 7 hours since we are adding 60 minutes (1 hour) to :15:
07:75 (15+60)
- 02:35
and answer will be 5 hours and 40 minutes
Tom makes 298.50 $ in 6 days. How much does he make in 3 days?
Answer:
in 3 days Tom made $149.25
Step-by-step explanation:
If Tom made 298.50 in 6 days, you can find the amount made in 3 days by dividing that number in half.
298.5 / 2 = 149.25
Please help thank you!
Factorise the following
a. x square - 16
b. 8m square - 50n square.
Answer:
(i) (x+4)(x-4)
Step-by-step explanation:
(ii)64m² - 800mn +2500n²
Calculate each year-end balance using the simple
interest rates listed.
Principal
$100.00
$550.00
$1,200.00
$5,000.00
Annual interest
rate
5%
2%
7%
11%
End of year
balance
The year-end balance interest rate for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00.
What is the interest rate?Interest is the cost of borrowing money or the amount of money that is earned on an investment. It is the amount of money paid by a borrower to a lender or earned by an investment, in exchange for the use of the lender's or investor's money.
Here,
To calculate the year-end balance for each principal using the given annual interest rates, we can use the formula:
End of year balance = Principal + (Principal x Interest rate x Number of years)
For a principal of $100.00, the annual interest rate is 5%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $100.00 + ($100.00 x 0.05 x 1) = $100.00 + $5.00 = $105.00
For a principal of $550.00, the annual interest rate is 2%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $550.00 + ($550.00 x 0.02 x 1) = $550.00 + $11.00 = $561.00
For a principal of $1,200.00, the annual interest rate is 7%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $1,200.00 + ($1,200.00 x 0.07 x 1) = $1,200.00 + $84.00 = $1,284.00
For a principal of $5,000.00, the annual interest rate is 11%, and the number of years is 1. So, the end-of-year balance is:
End of year balance = $5,000.00 + ($5,000.00 x 0.11 x 1) = $5,000.00 + $550.00 = $5,550.00
Hence, the year-end balance for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00, and for a principal of $5,000.00 is $5,550.00
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Add one-fourth of two subtracted from thrice a number to twice the same number.
The expression in the mathematical form will be (1/4)( 2 - 3x ) / ( 2x ).
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.
The word form of the expression is given as adding one-fourth of two subtracted from thrice a number to twice the same number.
The expression can be written as,
E = (1/4)( 2 - 3x ) / ( 2x ).
Hence, the expression will be (1/4)( 2 - 3x ) / ( 2x ).
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Convert the following [ Use exchange rate 1CAD 0.82 USD]
1.45 CAD = ? USD
45.50 USD = ? CAD
2.50 CAD = ? USD
1,500 CAD = ? USD
Answer: For converting Canadian Dollars to US Dollars divide 1 by 0.82 to give you an answer of around 1.2195(repeating). Then multiply that number by each of the Canadian Dollar amounts. US Dollars to Canadian Dollars is much simpler, as you just multiply the amount by 0.82 to find the answer.
$1.45 CAD x 1.2195 = $1.77 USD
$45.5 USD x 0.82 = $38.31 CAD
$2.50 CAD x 1.2195 = $3.05 USD
$1,500 CAD x 1.2195 = $1,829.27 USD
Hope this helped, and have a great day!
Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis.
y=x2, y=5−4x, x=0 for x≥0
The volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis is 8.90 unit³.
How do you find the volume of a solid?Since the region is the one for then the intersection we are interested on is x=1 as it can also be seen in the graph.
Where h(x) is the height of the shell which here is the distance between the parabola and the line, so (since the line is on the top we subtract from it the parabola
Notice the limits of the integral are the x-axis (x=0) and the intersection of the parabola and the line that we found before (x=1)
We want the volume generated when the area bounded by the curves :
v = x2 v = 8 —7x , and
x = 0 for x > 0 is revolved about the y axis using the cylindrical shell method .
The intersection of y = x2 and y = 8 —7x is :
y= x2 = 8 — 7x x2 + 7x —8 = 0
(x + 8)(x — 1) = 0 x = —8 or
x = 1 .
We thus have for x > 0 the two curves intersect at x = 1 and y = 12 = 1 .
The limits for integration are --- 0 <x < 1 .
The upper curve is --- y2 = 8 —7x ,
and the lower curve is --- yi = x2 .
The height of the shell is --- h = y2 -yi = 8 —7x — x2 •
The radius of the shell is --- R = x •
[tex]$$The surface area of the shell is :$$A=2 \pi \mathrm{Rh}=2 \pi x\left(8-7 x-x^2\right)=2 \pi\left(8 x-7 x^2-x^3\right) .$$The differential of volume which is the cylindrical shell is :$$\mathrm{dv}=\mathrm{Adx}=2 \pi\left(8 x-7 x^2-x^3\right) \mathrm{dx}$$[/tex]
[tex]$$We then have the volume of revolution is :$$\begin{aligned}v & =2 \pi \int_0^1\left(8 x-7 x^2-x^3\right) \mathrm{d} x \\& =2 \pi\left(4 x^2-\frac{7}{3} x^3-\frac{1}{4} x^4\right)_0^1 \\& =2 \pi\left[4\left(1^2-0^2\right)-\frac{7}{3}\left(1^3-0^3\right)-\frac{1}{4}\left(1^4-0^4\right)\right] \\& =2 \pi\left(4-\frac{7}{3}-\frac{1}{4}\right) \\& =2 \pi\left(\frac{48-28-3}{12}\right) \\& =2 \pi\left(\frac{17}{12}\right) ; \text { or, we have : } \\v & =\frac{17 \pi}{6} .\end{aligned}$$[/tex]
17π/6 = 8.90 unit³
Thus, The volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis is 8.90 unit³.
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find the present value of 2400 due in 4months at 4.5% simple interest
Answer:
Step-by-step explanation:
Interest per annum - 4.5
Interest per 1/3 of an annum - 4.5 x 1/3 = 1.5%
Use the S.I formula,
2400 x (100 + interest)/100
= 2400 x (100 + 1.5)/100
= 24 x 101.5
= 12 x 203
= 2436.
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How would you solve question 12b?
The line y = 3 is shown in the diagram of the graph of y = (x + 1)² for -4 ≤ x ≤ 2.
By using the graph, the solutions of (x + 1)² = 3 to 1 decimal place include the following:
x = -2.7 or x = 0.7.
What is a graph?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.
Next, we would use an online graphing calculator to plot the above quadratic equation with points of intersection at (-2.732, 3) and (0.732, 3) as shown in the graph attached below.
By critically observing graph of the given quadratic equation, we can logically deduce that the solutions of (x + 1)² = 3 on the x-coordinate are x is equal to -2.7 or x is equal to 0.7.
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Help pleaseeee I can’t figure this out
Answer: B. Exponential decay
Step-by-step explanation:
An exponential function is a function of the form f(x) = ab^x where a and b are constants, x is the independent variable, and b is a positive number not equal to 1. In this case, f(x) = -3(4^x). The base of the exponential function is 4, and it is a common base of exponential decay, because the base is less than 1, and the exponent is positive, this means that the output of the function will decrease as the input increases. Therefore, the function represented by f(x) = -3(4^x) is an exponential decay function.
Answer:
Exponential Decay
Step-by-step explanation:
In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed
Substitute the given value into the function and evaluate.
f(x)= -3⋅4^x/8
Math expression work
The given expression is equivalent to the expression -x² + x + 30.
What is the expression?The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given expression,
= (5 + x)(6 - x)
Simplifying the expression using distributive property,
= 5 [6 - x] + x [6 - x]
= 30 - 5x + 6x - x²
= -x² + x + 30
Thus, the given expression is equivalent to the expression -x² + x + 30.
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Topic - n-th term
If x + 1 and -x + 17 are the second and sixth terms of a sequence with a common difference
of 5, find the value of x.
Answer: -2
Step-by-step explanation:
So, the arithmetic sequence formula for the nth term is as follows.
Tₙ = a + (n-1)d
So,
2nd term or (x + 1) = a + d
x + 1 = a + 5 (d = 5). - 1
6th term or (-x + 17) = a + 5d
- x + 17 = a + 25. - 2
Subtract 2 from 1, we get,
2x - 16 = -20
2x = -4
x = -2
You can check it if you want,
Second term = - 1
Sixth term will be - 1 + 5 + 5 + 5 + 5 = 19
There you go.
Select the correct answer from each drop-down menu.
Identify the type of chart described and complete the sentence.
A
chart shows open and close prices and highs and lows, but over a long time period it can also show pricing
.
A particular sort of bar chart known as an OHLC chart displays the open, high, low, and final prices with each period.
What does "open-high-low-close chart" mean?It is obvious from the information provided that the chart being discussed is the Continuously compounded chart.It should be mentioned that an expansive chart (OHLC) is just a term used to describe a sort of chart that is used to depict price changes in a financial instrument over a specific time period.
Here,
The chart's vertical line depicts the price range as a function of time. Since it displays the entire price range for the time period, it is helpful in gauging volatility.
The four main data points throughout a period are displayed on OHLC charts, which are helpful since many traders believe the closing price to be the most significant of the four.
In addition to displaying the opening and closing values of the market for the same time period, open-high-low-close charts also display the high and low price that a stock achieved during that time.
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please help meeee :)
Answer:
9 students
Step-by-step explanation:
34 -25
Kimi Skuban deposits $2,000 at the beginning of each year into an Individual Retirement Account at
Boise Bank. The account pays 7% compounded annually. How much will be in the account in 25 years?
Total amount in the account after 25 years is, $5,500.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
We have to given that;
Kimi Skuban deposits $2,000 at the beginning of each year.
The account pays 7% compounded annually.
Now, We know that;
⇒ Interest = PRT / 100
Where, P is principal amount, R is interest rate and T is time in years.
Substitute all the values, we get;
⇒ Interest = PRT / 100
⇒ Interest = 2000 × 7 × 25/ 100
⇒ Interest = $3,500
Hence, Total amount in the account after 25 years is,
⇒ $2,000 + $3,500
⇒ $5,500
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2 Mark this and return
The following equations which are equivalent are:
2 + x = 5 x + 1 = 4 Negative 5 + x = negative 2How to determine equivalent equation?2 + x = 5
collect like terms
x = 5 - 2
x = 3
x + 1 = 4
Subtract 1 from both sides
x = 4 - 1
x = 3
9 + x = 6
Subtract 9 from both sides
x = 6 - 9
x = -3
x + (negative 4) = 7
x +(-4) = 7
Open parenthesis
x - 4 = 7
x = 7 + 4
x = 11
Negative 5 + x = negative 2
-5 + x = - 2
x = -2 + 5
x = 3
Therefore, 2 + x = 5; x + 1 = 4; Negative 5 + x = negative 2 are equivalent to each other.
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ON = MN, find MN.
A.4
B.5
C. 4// 2
D.4 // 30
The value of x for the given figure is 4√2.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
ΔMNO is a right triangle.
Applying the Pythagorean theorem.
MO² = ON² + MN²
8² = x² + x²
64 = 2x²
2x² = 64
x² = 32
x = √32
x = √(16 x 2)
x = √(4² x 2)
x = 4√2
Thus,
The value of x is 4√2.
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Please please look at the picture and answer the question thank you so much
Answer:
t = I/(Pr)
Step-by-step explanation:
We divide P*r on both sides to isolate t and we get t=I/(P*r)
Help me with this question please!
Answer:
Line B slope = 9
Step-by-step explanation:
When dealing with perpendicular lines, we can let the slope we know represent m1, while the slope we don't know represents m2.
Thus, to find m2, we use the formula:
[tex]m_{2}=\frac{-1}{m_{1} }[/tex]
If we plug in -1/9 for m1, we have:
[tex]m_{2}=-\frac{1}{(-1/9)} \\m_{2}=9[/tex]
If f(x)= |a³-31 |. then f(-1) is equivalent to
The value of f(-1) is either a³ - 31 or the absolute value of a³ - 31, depending on the value of a³ - 31.
We substitute -1 for x in the function: f(-1) = |a³ - 31| To find the value of f(-1), we need to find the value of a³ - 31. If a³ - 31 is positive, then |a³ - 31| will be equal to a³ - 31. If a³ - 31 is negative, then |a³ - 31| will be equal to the absolute value of a³ - 31 (which is the positive value of a³ - 31).So, the value of f(-1) is either a³ - 31 or the absolute value of a³ - 31, depending on the value of a³ - 31.It is not possible to find the exact value of f(-1) without knowing the value of a.
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Geneva treated her parents to dinner at their favorite restaurant. The bill was $73.25. She wants to leave 24% of the total bill as a tip. How much should the tip be, in dollars?
Answer:
To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).
Tip = 0.24 * 73.25
= 17.58
Therefore, the tip should be $17.58 in dollars.
Help with question please
Answer:
b.
Step-by-step explanation:
the result is created :
first result row first result element =
= first A row × first B column
first result row second result element =
= first A row × second B column
...
third result row second result element =
= third A row × second B column
third result row third result element =
= third A row × third B column
the multiplication of a row and a column is done by :
left row element × top column element +
middle row element × middle column element +
right row element × bottom column element
AB =
-4×3 + -3×-5 + 5×-1 -4×-4 + -3×-5 + 5×-3 -4×-1 + -3×1 + 5×2
-5×3 + -4×-5 + -2×-1 -5×-4 + -4×-5 + -2×-3 -5×-1 + -4×1 + -2×2
-1×3 + -2×-5 + -4×-1 -1×-4 + -2×-5 + -4×-3 -1×-1 + -2×1 + -4×2
=
-2 16 11
7 46 -3
11 26 -9
so, b is correct.
g(0)=-4x^2-3x+2
g(2)=-4^2-3x+2
The simplified value for the function at g(0) and g(2) are 2 and -20 respectively.
What is simplification?To simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
Given a function g(x) = -4x² - 3x + 2
to find the values of g(0)
and g(2)
for g(0)
substitute x = 0 in the equation,
g(x) = -4x² - 3x + 2
g(0) = -4(0)² - 3(0) + 2
g(0) = 2
for g(2), substitute x = 2 in the equation,
g(x) = -4x² - 3x + 2
g(2) = -4(2)² -3(2) + 2
g(2) = -4(4) - 6 + 2
g(2) = -16 - 6 +2
g(2) = -20
Hence the values for g(0) is 2 and for g(2) is -20.
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Seats for Sale
State's football program has risen to the ranks of the elite with postseason bowl games in each of the past 10 years, including a national championship game. The Bruins (as the fans are called) fill the stadium each game. Season tickets are increasingly difficult to find. In response to the outstanding fan support, State has decided to use its bowl revenues to expand the stadium to 75,000 seats.
The administration is confident that all 75,000 seats can be sold at the normal price of $40 per game ticket; however, Frank Pinto's job, as athletic director, is to get as much revenue out of the stadium expansion as possible. In addition to stadium boxes for wealthy alums, Frank would like to take this opportunity to repurpose existing seats. A certain number of seats (yet to be determined) would be set aside for premium ticket holders who would pay $200 per ticket for the privilege of 50-yard line seats with chair backs and access to indoor concessions. The question is, how many fans would be willing to pay such a premium? If too many seats are designated in the premium sections, they could remain vacant. Too few premium seats would lose potential revenue for the program.
Frank has decided that if the plan has any chance of success, unsold premium seats should not be sold at reduced rates. It would be better to donate them to local charities instead. Gathering data from his cohorts at peer institutions, Frank has put together the following probability distribution of premium ticket holders. The data begin with 1000 tickets since Frank already has requests for 999 tickets from alumni donors. He is asking for your help in performing the analysis.
No. of Premium Tickets Probability
1,000 0.10
5,000 0.30
10,000 0.24
15,000 0.15
20,000 0.10
25,000 0.06
30,000 0.05
a. Using revenue management, determine how many seats should be reserved for premium ticket holders.
b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?
c. The administration is unsure about Frank's plan. The VP of finance thinks an expected value of the number of premium seats would produce better results. How would the number of premium seats change using expected value? Considering the possible outcomes, which approach yields the most potential revenue?
Answer:
a. To determine how many seats should be reserved for premium ticket holders, Frank can use revenue management techniques. One common method is to use the expected revenue per seat, which is calculated by multiplying the number of seats by the expected price per seat and then multiplying that by the probability of that number of seats being sold. Frank can then compare the expected revenues for different numbers of premium seats and choose the number of seats that maximizes the expected revenue.
b. If the number of premium seats is 1,000, then the expected revenue is:
(1,000 x $200 x 0.10) + (75,000 - 1,000) x $40 x 1 = $200,000 + $3,000,000 = $3,200,000
If the number of premium seats is 5,000, then the expected revenue is:
(5,000 x $200 x 0.30) + (75,000 - 5,000) x $40 x 0.7 = $3,000,000 + $2,330,000 = $5,330,000
If the number of premium seats is 10,000, then the expected revenue is:
(10,000 x $200 x 0.24) + (75,000 - 10,000) x $40 x 0.76 = $4,800,000 + $3,768,000 = $8,568,000
and so on for the rest of the numbers.
From the above calculations, we see that the expected revenue is maximized at 10,000 premium seats, which is expected to generate $8,568,000.
c. Using the expected value of the number of premium seats would be calculated by multiplying the number of seats by its probability. The expected value of the number of premium seats is:
1,000 x 0.10 + 5,000 x 0.30 + 10,000 x 0.24 + 15,000 x 0.15 + 20,000 x 0.10 + 25,000 x 0.06 + 30,000 x 0.05 = 10,000.
Comparing this with the number of seats obtained by maximizing the expected revenue (10,000), we see that both approaches yield the same number of premium seats. This means that both approaches would yield the same potential revenue.
Tell whether b = 12 is a solution of b - 7 = 5
Answer:
Yeah, [tex] \sf b = 12 [/tex]
Step-by-step explanation:
Given equation,
→ b - 7 = 5
Now the value of b will be,
→ b - 7 = 5
→ b = 7 + 5
→ [ b = 12 ]
Hence, the value of b is 12.
Answer: Yes
Step-by-step explanation: If you plug 12 into b, you will get the equation 12 - 7 = 5.
Try solving 12-7. It is 5.
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19. The speed, s, in feet per second, of an object dropped from a
height, h, in feet, is given by the formula s (h) = √64h. Evaluate
the function for heights of 0 feet to 25 feet by calculating points
every 5 feet.
The plotted graph is shown below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
s (h) = √64h
now, when h=0
s(0) = √64h = 0
and, when h= 5
s(5) = √64h
= √64 x 5
= 8 x 2.25
= 17.88
and, when h= 10
s(25) = √64h
= √64 x 10
= 8 x 3.162
= 25.29
and, when h= 15
s(25) = √64h
= √64 x 15
= 30.98
and, when h= 20
s(25) = √64h
= √64 x 20
= 35.77
and, when h= 25
s(25) = √64h
= √64 x 25
= 8 x 5
= 40
The plotted graph is shown below.
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Question 2
For this problem, let's assume the Earth is a perfect sphere of radius 6371 km. Calculate the
volume of the Earth in cubic kilometers (km³). Which of these comes closest to your answer?
Hint: the volume of a sphere is given by (4/3) π R³, where R is the radius. If you specify the radius
in km, the volume will come out in km³. You can use the approximate value π = 3.14.
A 6371
B 27,000
C 170 million
D 1 trilion
Volume of earth in shape of a sphere is 1 Trillion km^3 i.e. D.
What is a sphere?
A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.
The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere. Examples of spheres are a ball, a globe, the planets, etc.
Volume of sphere=4/3πr^3. where r=radius.
Surface area=4πr^2.
Now,
Given radius for earth=6371 km
so, Volume of earth=4/3*3.14*6371^3≈1Trillion km^3.
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Select all of the expressions equivalent to (0.5p + 7) + (0.3p-6).
A.1 +0.8p
B.-6.5p+7.3
C.7.5p - 5.7
D.0.8p + 1
E.7.3 -6.5p
