Answer:
Step-by-step explanation:
just do how tall times the diamiter divided by the
You put $200 per month in an investment plan that pays an APR of 4.5%. How much money will you have after 23 years?
Compare this amount to the total deposits made over the time period.
After 23 years the investment plan will contain
The amount after 23 years on the investment plan is A = $358.20
Given data ,
$200 per month under a 4.5% annual percentage rate investing plan.
Now , A = P(1 + r/n)^(nt)
Where:
A is the total sum.
P stands for the initial deposit's principal.
The yearly interest rate is represented by the decimal r.
The yearly compounding rate of interest is determined by the number n.
The number of years is t.
A = 200(1 + 0.045/1)¹ˣ²³
A = 200(1.045)²³
A ≈ 200(1.791)
A ≈ $358.20
After 23 years, the investment plan will contain approximately $358.20
Total deposits = Monthly deposit amount x Number of months
Total deposits = $200 x (12 months/year) x 23 years
Total deposits = $200 x 12 x 23
Total deposits = $55,200
Consequently, $55,200 would be the total amount of deposits made during the 23-year period.
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You just purchased a house for $100,000 at a local county auction. You spent $50,000 to
renovate the house and netted $160,000 after sale expenses. What is your ROI?
The ROI (Return on Investment) for the above investment is 106.67%.
What is the Return on Investment?
ROI (Return on Investment) is one that is seen as a financial metric used to know the profitability of an investment relative to its cost.
The formula for ROI is:
ROI = (Net Profit / Cost of Investment) x 100%
Hence, the cost of investment is the sum of the price as well as the renovation cost, will be:
Cost of Investment = $100,000 + $50,000
= $150,000
Note that the The net profit from the sale of the house is $160,000.
So, the ROI can be calculated as:
ROI = (Net Profit / Cost of Investment) x 100%
= ($160,000 / $150,000) x 100%
= 106.67%
So, the ROI for the above investment is 106.67%.
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A student is graduating from college in 12 months but will need a loan in the amount of $11,650 for the last two semesters. The student may receive either an unsubsidized Stafford Loan
or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 5.95%, compounded monthly, and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $12,436.41 at graduation
Which loan will have a lower balance, and by how much, at the time of repayment?
O The PLUS loan will have a lower balance by $298.35 at the time of repayment.
O The Stafford loan will have a lower balance by $298.35 at the time of repayment.
O The PLUS loan will have a lower balance by $527.14 at the time of repayment.
O The Stafford loan will have a lower balance by $527.14 at the time of repayment
Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment
How to calculate the loanUsing the formula for compound interest, the total cost of the loan can be calculated as follows:
Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14
Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28
Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).
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can someone help me with this
The sine equation for the object's height is given as follows:
d = -5sin(0.24t).
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The amplitude for this problem is of 5 inches, hence:
A = 5.
The period is of 1.5 seconds, hence the coefficient B is given as follows:
2π/B = 1.5
B = 1.5/2π
B = 0.24.
The function starts moving down, hence it is negative, so:
d = -5sin(0.24t).
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tuesday follows monday in a week express the probability as percent
The probability that Tuesday follows Monday in a week is 100%, or 1/1, since it is always true that Tuesday comes after Monday in a week. Expressed as a percentage, the probability is 100%.
Answer:
100%
Step-by-step explanation:
because according to our calendars, Tuesday is always after monday so the probability as percent is 100%.
A construction company will be penalized each day of delay in construction for bridge. The penalty will be $4000 for the first day and will increase by $10000 for each following day. Based on its budget, the company can afford to pay a maximum of $ 165000 toward penalty. Find the maximum number of days by which the completion of work can be delayed.
Answer:
The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.
Step-by-step explanation:
We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is
[tex]S_{n}[/tex] = 165000.
Let us find the amount as arithmetic series as follows:
4000 + 5000 + 6000
The arithmetic series being, first term is [tex]a_{1}[/tex] = 4000, second term is [tex]a_{2}[/tex] = 5000.
We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:
[tex]d = a_{2} - a_{1} = 5000 - 4000 = 1000[/tex]
The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] ( ‘ d ‘ being the difference. )
Next we can substitute a = 4000, d = 1000 and [tex]S_{n}[/tex] = 165000 in “ [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] “ which can be represented as:
Determining, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex]
⇒ 165000 = [tex]\frac{n}{2}[/tex] [( 2 x 4000 ) + ( n - 1 ) 1000 ]
⇒ 2 x 165000 = n(8000 + 1000n - 1000 )
⇒ 330000 = n(7000 + 1000n)
⇒ 330000 = 7000n + [tex]1000n^2[/tex]
⇒ [tex]1000n^2[/tex] + 7000n - 330000 = 0
⇒ [tex]1000n^2[/tex] ( [tex]n^2[/tex] + 7n - 330 ) = 0
⇒ [tex]n^2[/tex] + 7n - 330 = 0
⇒ [tex]n^2[/tex] + 22n - 15n - 330 = 0
⇒ n( n + 22 ) - 15 ( n + 22 ) = 0
⇒ ( n + 22 )( n - 15 ) = 0
⇒ n = -22, n = 15
We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.
Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.
What is the surface area of the figure for #11?
*with work on how to solve please!
The surface areas of the figures are:
10. 1,376 ft² or F 1,344 ft²11. B. 1,058.4 in².How to determine surface area?10.To find the surface area of this rectangular prism, find the area of each face and then add them together.
Face 1: The front and back faces both have dimensions of 12 ft by 14 ft, so the area of each is:
12 ft × 14 ft = 168 ft²
Two of these faces, so the total area is:
2 × 168 ft² = 336 ft²
Face 2: The top and bottom faces both have dimensions of 20 ft by 14 ft, so the area of each is:
20 ft × 14 ft = 280 ft²
Two of these faces, so the total area is:
2 × 280 ft² = 560 ft²
Face 3: The left and right faces both have dimensions of 12 ft by 20 ft, so the area of each is:
12 ft × 20 ft = 240 ft²
Two of these faces, so the total area is:
2 × 240 ft² = 480 ft²
Now add up the areas of all the faces:
336 ft² + 560 ft² + 480 ft² = 1,376 ft²
11. To find the surface area of the figure, add the areas of all six faces.
Find the area of the rectangular faces:
The front and back faces both have dimensions of 14 in by 14 in, so each has an area of 14 in x 14 in = 196 in².
The top and bottom faces both have dimensions of 13 in by 8.9 in, so each has an area of 13 in x 8.9 in = 115.7 in².
Find the area of the triangular faces. Use the Pythagorean theorem to find the length of the third side of each triangle:
The two side faces are congruent triangles with legs of 14 in and 13 in.
Using the Pythagorean theorem, find the length of the hypotenuse to be √(14² + 13²) ≈ 19.14 in. The area of each triangle is then 1/2 base x height = 1/2 x 19.14 in x 8.9 in ≈ 85.3 in².
Using the Pythagorean theorem, find the length of the hypotenuse to be √(8.9² + 13²) ≈ 15.8 in. The area of each triangle is then 1/2 base x height = 1/2 x 15.8 in x 14 in ≈ 110.6 in².
Finally, add up the areas of all six faces:
Front and back faces: 2 x 196 in² = 392 in²
Top and bottom faces: 2 x 115.7 in² = 231.4 in²
Side faces: 2 x 85.3 in² = 170.6 in²
End faces: 2 x 110.6 in² = 221.2 in²
The total surface area is the sum of these areas:
392 in² + 231.4 in² + 170.6 in² + 221.2 in² ≈ 1,015.2 in²
Therefore, the answer is B. 1,058.4 in².
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Find a function of the form
or (picture) whose graph matches the function shown below:
The sinusoidal function of the form y = A·sin(k·x) + C that matches the function in the graph is; y = 4·sin((π/5)·x) - 1
What is a sinusoidal function?A sinusoidal function is a periodic function based on the sine or cosine functions.
The form of the function is y = A·sin(k·x)
The peak and trough of the graph are; (-7.5, 3), (-2.5, -5)
The amplitude of the function is therefore; A = (3 - (-5))/2 = 4
The vertical shift of the function is; C = (3 + (-5))/2 = -1
The period of the graph (Number of input x-values required to complete a cycle) = 2.5 - (-7.5) = 10 = 2·π/k
Therefore; k = 2·π/10 = π/5
The horizontal shift can be found as follows;
When x = 0, y = -1, therefore;
-1 = 4 × sin(π/5 × (0 - θ)) - 1
arcsin(0/4) = π/5 × (- θ)
θ = 0
The sinusoidal function is therefore;
y = 4·sin((π/5)·x) - 1
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Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.
x2 + 14x − 2 = 0
2x2 + 10x − 7 = 0
3x2 + 12x − 7 = 0
4x2 + 10x − 1 = 0
Answer:
[tex](3 + 2x)(2 + 2x) = 7[/tex]
[tex]6 + 10x + 4{x}^{2} = 7[/tex]
[tex]4 {x}^{2} + 10x - 1 = 0[/tex]
Answer:
4x2 + 10x − 1 = 0
Step-by-step explanation:
Is the factions are proportional 1/2 and 2/4?
Yes, the fractions 1/2 and 2/4 are proportional
What is a fraction?A fraction can simply be defined as an expression that is used in the representation of the part of a whole.
This could be a whole number, a whole element, a whole material or a whole elemeent.
In mathematics, there are different types of fractions.
These fractions are enumerates thus;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractionsFrom the information given, we have that;
If 1/2 and 2/4 are proportional, that is, if equal
2/4 = 1/2
Cross multiply the values
4 = 4
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Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of A′ if the preimage is rotated 270° counterclockwise.
A′(−1, −5)
A′(−1, 5)
A′(−5, 1)
A′(5, −1
Answer:
(d) A'(5, -1)
Step-by-step explanation:
You want the coordinates of A(1, 5) after it has been rotated 270° CCW about the origin.
RotationThe transformation for rotation 270° CCW is the same as that for rotation 90° CW:
(x, y) ⇒ (y, -x)
For the given point, this is ...
A(1, 5) ⇒ A'(5, -1)
The image of A is A'(5, -1), choice D.
ap calculus problem
no need full detail solution
The Taylor series for f(x) = e^2x at x = 1 is option D. Σ2ⁿ e²ˣ/n! (x - 1)ⁿ
How did we get the value?The Taylor series for a function f(x) centered at x = a is given by:
f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...
f'(a), f''(a), f'''(a), ... depict the first, second, third, and higher derivatives of f(x) evaluated at x = a.
In this case:
f(x) = e^(2x)
The first derivative is:
f'(x) = 2e^(2x)
The second derivative is:
f''(x) = 4e^(2x)
The third derivative is:
f'''(x) = 8e^(2x) etc.
Finding the Taylor series for f(x) = e^(2x) at x = 1, evaluate each derivative at x = 1:
f(1) = e^(2)
f'(1) = 2e^(2)
f''(1) = 4e^(2)
f'''(1) = 8e^(2) etc.
Plug these values into the Taylor series formula:
f(x) = f(1) + f'(1)(x-1)/1! + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...
f(x) = e^(2) + 2e^(2)(x-1)/1! + 4e^(2)(x-1)^2/2! + 8e^(2)(x-1)^3/3! + ...
Simplify:
f(x) = e^(2) + 2e^(2)(x-1) + 2e^(2)(x-1)^2 + 4e^(2)(x-1)^3/3 + ...
Therefore, the Taylor series for f(x) = e^(2x) at x = 1 is: Σ2ⁿ e²ˣ/n! (x - 1)ⁿ which is option D.
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Find two numbers such that their sum is 12 and their product is 23.
Let's call the two numbers we're trying to find x and y. We know that x + y = 12 and xy = 23. From the first equation, we can solve for one of the variables in terms of the other. So if we subtract x from both sides, we get y = 12 - x. Now we can substitute this expression for y into the second equation to get x(12 - x) = 23. Expanding this out, we get 12x - x^2 = 23. Rearranging, we get x^2 - 12x + 23 = 0. This quadratic equation can be factored as (x - 2)(x - 10) = 0. So either x = 2 and y = 10, or x = 10 and y = 2.
Answer:
The two numbers are 2 and 10.
Two step for T+4=-7 ?
Answer:
Step-by-step explanation:
T+4 = -7
T = -7 -4
T = -11
Sally owns a restaurant in Wooville. The city is trying to get a minor league team to move there in 2021, either to location A (near her restaurant) or location B. The team might stay in location C in another city. The probability of these events, and her estimated annual profit in 2021 are shown in the table below.
The standard deviation of the restaurant profits in 2021 is given by $71181.
Restaurant profit for outcome 'move to A' = $ 260000
Restaurant profit for outcome 'move to B' = $ 120000
Restaurant profit for outcome 'stay in C' = $ 100000
The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.
Standard deviation of the restaurant profits in 2021 is given by
= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)
= $ √(((100000)² + (40000)² + (60000)²)/3)
= $ √(15200000000/3)
= $ √5066666667
= $ 71181 (rounded to the nearest dollar)
Hence standard deviation of the restaurant profits in 2021 is given by $71181.
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The question is incomplete. The complete question will be -
10^-x-1=36 solve for x
The solution to the exponential equation 10^(-x - 1) = 36 is given as follows:
x = -2.5563.
How to solve the exponential equation?The exponential equation in the context of this problem is defined as follows:
10^(-x - 1) = 36
The log10 operation is the inverse of the power of 10 operation, hence we can isolate the variable x as follows:
-x - 1 = log10(36)
-x - 1 = 1.5563
x = -1.5563 - 1
x = -2.5563.
Which is the solution to the exponential equation in the context of the problem.
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A sample of bacteria is decaying according to a half-life model. If the sample begins with 500 bacteria, and after 20 minutes there are 100 bacteria, after how many minutes will there be 20 bacteria remaining? When solving this problem, round the value of k to four decimal places and round your final answer to the nearest whole number.
The constant k is 0.08
The time taken is 40 minutes
What is the half life?The half-life of a specific radioactive substance is determined by its decay constant, which is a measure of how quickly the substance decays.
Given that;
P= Poe^-kt
P = population at time t
Po = initial population
k = rate of decay
t = time taken
Then;
100 = 500e^-k20
100/500 = e^-k20
0.2 = e^-k20
ln0.2 = e^-k20
k = ln0.2/-20
k = 0.08
We know that;
20 = 500e^-0.08t
20/500 = e^-0.08t
0.04 = e^-0.08t
ln 0.04 = e^-0.08t
ln0.04 = -0.08t
t = ln0.04/-0.08
t = 40 minutes
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Consider the equation that gives the volume of a square pyramid, where
• V represents the volume in cubic feet,
• b represents the length of each side of the pyramid's base in feet, and
• h represents the height of the pyramid in feet.
V= 1²
3
Enter an equation for which the solution is the height of a pyramid, in feet, when its volume is 48 cubic feet and the
length of each side of its base is 4 feet.
An equation for which the solution is the height of a pyramid, in feet, when its volume is 48 cubic feet and the length of each side of its base is 4 feet is h = 3(48)/4².
How to calculate the volume of a square pyramid?In Mathematics and Geometry, the volume of a square pyramid can be calculated by using the following formula:
Volume of a square pyramid, V = 1/3 × a² × h
Where:
h represent the height of a square pyramid.a represent the side length of the base of a square pyramid.By making "h" the subject of formula, the side length of the base of a square pyramid can be determined as follows;
V = 1/3 × a² × h
3V = a²h
Height, h = 3V/a²
Height, h = 3(48)/4²
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Find the partial sum for the sequence.
{2, 3, 5, 8, 13, ...}; S8
S8=
The partial sum of the sequence {2, 3, 5, 8, 13, ...} for the first 8 terms is 761/2.
The sequence given is a Fibonacci sequence, where each term is the sum of the previous two terms. To find the partial sum for the first 8 terms, we can use the formula for the sum of a finite geometric series:
Sₙ = a(1 - rⁿ)/(1 - r),
where Sₙ is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 2, r = 3/2 (since each term is 1.5 times the previous term), and n = 8. Plugging these values into the formula, we get:
S₈ = 2(1 - (3/2)⁸)/(1 - (3/2))
Simplifying the expression, we get:
S₈ = 761/2
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120 students
and 8 teachers go on a school trip.
The recommended ratio of adults to students is 1:15.
Is the ratio of adults to students correct?
Answer:
Yes.
Step-by-step explanation:
8:120 = 4:60 = 2:30 = 1:15
You divide by two each time to simplify.
PLEASE HELP ITS DUE TODAY
For the quadratic equations shown here, which statement is true?
Question 2 options:
The graphs open downward.
The graphs open upward.
The graphs are listed from narrowest to widest.
The graphs are symmetric about the x-axis.
Answer:
The graphs open downward.
If a fair coin is tossed twice the possible outcomes are HH, HT, TH or TT, where HH means both tosses are heads and HT means that the first toss is a head and the second toss is a tail, etc. Since the coin is fair, a 50-50 chance of getting a head or a tail, we assign a probability of 1/4 to each of the four outcomes. Assuming that a fair coin was tossed twice, find the probability that exactly one of the tosses is a head and the other toss is a tail.
Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.
The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.
There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:
P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2
In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.
To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.
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Brooke believes she's getting a great deal on a car - zero down and
payments of only $260 per month for 6 years (72 months). She estimates
the additional costs of owning a car: insurance - $960 per year, registration
- $240 per year, and gas and maintenance of $175 per month.
How much will this car cost her over the life of the loan?
Answer:
First, you need to calculate the total cost of the loan. The monthly payment is $260, and there are 72 payments over 6 years. The total cost of the loan is 72 months * $260/month = $18,720
Next, you calculate the total cost of owning the car for 6 years. The insurance will cost $960 per year, so over 6 years it will cost $960/year * 6 years = $5,760
The registration will cost $240 per year, so over 6 years it will cost $240/year * 6 years = $1,440
The gas and maintenance will cost $175 per month, so over 6 years it will cost $175/month * 72 months = $12,600
Now you can add up all the costs to find the total cost of owning the car over the life of the loan:
Loan cost + insurance cost + registration cost + gas/maintenance cost
= $18,720 + $5,760 + $1,440 + $12,600
= $38,520
Therefore, the car will cost Brooke $38,520 over the life of the loan, including all additional costs of owning the car.
Answer:
$38,520
Step-by-step explanation:
To calculate the total cost of the car, we need to consider the following expenses:
Monthly payments:
$260/month x 72 months = $18,720
Insurance:
$960/year x 6 years = $5,760
Registration:
$240/year x 6 years = $1,440
Gas and maintenance:
$175/month x 12 months/year x 6 years = $12,600
Therefore, the total cost of the car over the life of the loan is:
$18,720 (monthly payments) + $5,760 (insurance) + $1,440 (registration) + $12,600 (gas and maintenance) = $38,520
So, while Brooke may think she's getting a good deal with zero down and low monthly payments, the total cost of the car over the life of the loan is quite high. It's important to consider all the additional costs associated with owning a car before making a decision to purchase one.
Five friends order food and want to split the bill. They order two large cheese pizzas
for $10 each, wings for $18.99, and breadsticks for $5.59. Determine how much each
person owes.
Answer:
$8.92 each
Step-by-step explanation:
The pizzas cost $10 x 2 = $20The wings cost $18.99The breadsticks cost $5.59When you add all of these together, you get $20 + $18.99 + $5.59 = $44.58.To spilt the bill, you need to divide the cost equally between the 5 friends which is $8.916. You cannot pay 0.916 of a dollar so you round the bill to the nearest two decimal places.Use one of the triangles to approximate
�
�
EFE, F in the triangle below.
Triangle D E F has a height of six units, which is side DF. Both the base, side EF, and the hypotenuse, side DE, are unknown. Angle D F E is a right angle and angle F D E measures twenty degrees.
Basd on the information about the triangle, DF is approximately 5.68 units long.
How to calculate the valueFirst, let's find the length of EF using the sine function:
sin 20° = EF / DE
cos 20° = 6 / DE
DE = 6 / cos 20°
Now that we know DE, we can solve for EF:
sin 20° = EF / DE
EF = DE * sin 20°
EF = (6 / cos 20°) * sin 20°
EF ≈ 1.95
DF^2 = DE^2 - EF^2
DF^2 = (6 / cos 20°)^2 - (1.95)^2
DF ≈ 5.68
DF is approximately 5.68 units long.
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Find the volume of the shape below. Round to the nearest tenth. Use
the pi button on the calculator.
Volume =
12 cm
cm³
The volume of the sphere as shown in the diagram is 904.3 cm³.
What is a sphere?A sphere is a three-dimensional round-shaped object.
To calculate the volume of the sphere, we use the formula below
Formula:
V = 4πr³/3...................... Equation 1Where:
V = Volume of the spherer = Radius of the sphereπ = PieFrom the question,
Given:
r = 12/2 = 6 cmπ = 3.14Substitute these values into equation 1
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ABCD is a parallelogram. P is a point on AB such that LPAD = 110° and PC = BC. Calculate (a) LABC, LDCP
please do it with explanation.
The value of the angles in the parallelogram are:
∠ABC = 70°
∠DCP =70°
How to calculate the angles in the parallelogram?Recall that two adjacent angles in a parallelogram add up to 180 degrees. We can say:
∠BAD + ∠ABC = 180° (Where ∠BAD = 110°)
∠ABC = 180 - 110 = 70°
Since PC = BC, ∠BPC = 70°
Also, ∠BCP = 180 - 70 - 70 = 40° (Sum of angles in a triangle)
∠ACB = ∠BAD (opposite angles of parallelogram are equal)
Where ∠BAD = 110°
Thus, ∠ACB = 110°
∠ACB = ∠DCP + ∠BCP
110 = ∠DCP + 40
∠DCP = 110 - 40
∠DCP =70°
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Find the polar coordinates of a point with Cartesian coordinates (x,y)=(2√3,2).Select the correct answer below:
(4,π/6)
(2,2π/3)
(4,2π/3)
(2,7π/6)
(4,7π/6)
(2,π/6)
Answer:
(4,π/6)
Step-by-step explanation:
The correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((2√3)^2 + 2^2)
= √(12 + 4)
= √16
= 4
θ = atan2(2, 2√3)
≈ 0.5236 radians
However, in the polar coordinate system, angles are typically expressed in radians between 0 and 2π. The angle π/6 is equivalent to 0.5236 radians, so the correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).
hi can someone help with this question
Based on the information, we can infer that the investment was made 11.53 years ago.
How to calculate how many years ago was the investment made?To calculate how many years ago was the investment mafe we have to can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount invested)
r = the interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Let's start by finding the initial principal (P) by working backwards from the final amount (A):
A = P(1 + r/n)^(nt)
31372.0 = P(1 + 0.022/1)^(14)(1 + 0.022+0.007/1)^(1(t-4))
Simplifying, we get:
31372.0 = P(1.093248)(1.029)^(t-4)
P = 27500 euros (initial investment)
Now we can solve for t:
31372.0 = 27500(1.093248)(1.029)^(t-4)
1.1412 = (1.029)^(t-4)
log(1.1412) = log(1.029)^(t-4)
t - 4 = log(1.1412)/log(1.029)
t = log(1.1412)/log(1.029) + 4
t = 11.53
Therefore, the investment was made about 11.53 years ago.
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Find a quadratic equation which has solutions x=4/9 and x=9/2. Write the quadratic form in the simplest standard form x^2+bx+c
Answer:
[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]
[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]
