The maximum height of the ball can reach is 49 feet high.
Which is the greatest height?We know that the height is modeled by the quadratic equation:
h(t) = -16t² + 56t
Remember that for the general quadratic equation is written as:
y = ax² + bx +c
The vertex is at the value x of:
x = -b/2a
The maximum height is at the vertex, which in this case is at the value:
t = -56/(2*-16)
t = 1.75
Evaluating the height equation in that time, we get:
h = -16*(1.75)² + 56*1.75
h = 49
The maximum height that the ball can reach is 49ft
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if parallel lines are but by a transversal, then alternate interior angles are congruent and (I have four choices here - alternate interior, complimentary, consecutive interior and exterior) angles are supplementary. can you help me pick the correct choice?
Answer:
When two parallel lines are intersected by a transversal, the alternate interior angles are the pairs of non-adjacent angles that are located between the two parallel lines and on opposite sides of the transversal. These angles are congruent, which means they have the same measure. The other type of angles mentioned in the statement, which are supplementary, are the pairs of adjacent angles that are located on the same side of the transversal and outside the parallel lines. These angles add up to 180 degrees.
The correct choice is "consecutive interior angles are supplementary."
It would really help
Reflecting a point across the x-axis changes the sign of its y-coordinate while keeping the x-coordinate intact. As such, Z' can be rewritten in terms of (x, -y).
If a rectangle shifts downward by five units and rightward by three units, the transformation rule can be expressed as: (x, y) → (x + 3, y - 5).
How to explain the informationConversely, the given equation for this specified action is: (x, y) → (x - 3, y - 4).
Similar but reversed in reflection across the y-axis, where instead it is the x-coordinate that sees its sign changed, given the conditions that the y-coordinate stays constant. Hence, the transformation can be stated as: (x, y) → (-x, y).
The same applies for a mathematical exchange when it comes to reflecting about the x-axis; here the y-coordinate has its signs reversed with no transition in the x-coordinate – simply put, we have as follows: (x, y) → (x, -y).
Finally, observing what occurs when rototating clockwise 270° around the origin reveals each point experiencing an equal shift from said anchor point; permitting us to formalize the related rule accurately as: (x, y) → (y, -x).
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Petra has 126 pounds of apples to sell. She has 39 bags in all. Some are 2-pound bags and some are 5-pound bags. How many of each does petra have?
There are 7.8 pounds per bag of apples
Since unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that ;
Petra has 126 pounds of apples to sell. She has 39 bags in all.
126 total pounds = 39pounds of apples . since there are 5 bags of apples ,
We would divide 5 by 39.
39/5= 7.8 pounds per bag of apples .
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Use normal approximation to estimate the probability of passing a true/false test of 70 questions if the minimum passing grade is 80% and all responses are random guesses.
The probability of passing the test by random guessing is 0.003%.
To estimate the probability of passing a true/false test of 70 questions, we can use the normal approximation to the binomial distribution. Since each question has only two possible outcomes (true or false), the binomial distribution can be used to calculate the probability of getting a certain number of correct answers out of 70.
The mean of the binomial distribution can be calculated as np, where n is the number of trials (70) and p is the probability of success (0.5, since the responses are random guesses). The standard deviation of the binomial distribution can be calculated as the square root of np*(1-p).
To find the probability of passing the test, we need to find the number of correct answers required to achieve a score of 80% or higher. Since 80% of 70 is 56, we need to get at least 56 questions correct.
Using the normal approximation, we can approximate the binomial distribution with a normal distribution with mean 35 and standard deviation 4.79. To find the probability of getting at least 56 questions correct, we can standardize the value (56-35)/4.79 = 4.02 and look up the probability in a standard normal table. The probability of getting at least 56 questions correct is approximately 0.00003.
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The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at the point (10,0). Express the bearing using both methods.
The angle in the rectangular coordinate system is 0 degrees, the compass bearing of the airplane is N (north).
The slope of the line can be found using the formula:
slope = (change in y-coordinate) / (change in x-coordinate)
In this case, the change in the y-coordinate is 0, and the change in the x-coordinate is 10. Therefore, the slope of the line is:
slope = (0 - 0) / (10 - 0) = 0
Since the slope of the line is 0, the line is horizontal, and the angle it makes with the x-axis is 0 degrees or 180 degrees. However, we need to determine which of these angles is the correct bearing of the airplane relative to the observer.
Since the airplane is in the positive x-axis, it lies in Quadrant I. In this quadrant, the angle that a line makes with the positive x-axis is measured counterclockwise from the positive x-axis.
Therefore, the angle that the line connecting the observer to the airplane makes with the positive x-axis is 0 degrees. This is the bearing of the airplane relative to the observer.
To express the bearing using the compass bearing method, we need to convert the angle from the rectangular coordinate system to the angle measured in degrees clockwise from the north direction.
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PLS ANSWER WILL GIVE BRAINLIEST IF ANSWER IS RIGHT(NO LINKS)
Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.
A. LH ≈ 45.68; m∠K ≈ 55°; m∠L ≈ 35°
B. LH ≈ 64.7; m∠K ≈ 53°; m∠L ≈ 34°
C. LH ≈ 10.52; m∠K ≈ 11°; m∠L≈ 79°
D. LH ≈ 45.68; m∠K ≈ 35°; m∠L ≈ 55°
The unknown measures and angle measures are:
A. LH ≈ 45.68; m∠K ≈ 55°; m∠L ≈ 35°
How to find the unknown measures of the triangle?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The unknown measures of the triangle can be founding as follow:
LH² = 56² - 32.4² (Pythagoras Theorem)
LH = √(56²- 32.4²)
LH = 45.68 units
sin K = 45.68/56
K = sin⁻¹(45.68/56)
K ≈ 55°
Thus, m∠K ≈ 55°
sin L = 32.4/56
L = sin⁻¹( 32.4/56)
L ≈ 35°
Thus, m∠L ≈ 35°
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Write an equation you can use to solve for x. I need 1-7 answered. I don't understand this
The sides of the figure is solved to obtain
1. 3x - 8 = 2x - 3
2. x = 5
3. 5y = 3y + 2
4. y = 1
5. BE = 12
6. GH = 5
7. HF = 5
How to write the equation to solve for xThe equation to solve for x is written knowing that the tangents CH and BH are equal
1. CH = BH
3x - 8 = 2x - 3
2. solving for x
3x - 2x = -3 + 8
x = 5
3. HG = HF
5y = 3y + 2
4. solving for y
5y - 3y = 2
2y = 2
y = 1
5. BE = BH + HF
BE = 2x - 3 + 3y + 2
BF = 2 * 5 - 3 + 3 * 1 + 2
BE = 10 - 3 + 3 + 2
BE = 12
6. GH = 5y = 5 * 1 = 5
7. HF = 3y + 2
HF = 3 * 1 + 2
HF = 5
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18 divided by 5.5
PLEASE ANSWER FULL INSTRUCTIONS
Answer:
Step-by-step explanation:
To divide 18 by 5.5, we can use long division method as follows:
_________
5.5 | 18.0000
-16.5
------
1.5
We first divide 5.5 into the first digit of 18, which is 1. This gives us 0 as the whole number part of the quotient. We then multiply 0 by 5.5 to get 0, and subtract it from 1, which gives us 1.
We then bring down the next digit 0 and get 10. We then divide 5.5 into 15, which gives us 2 as the whole number part of the quotient. We then multiply 2 by 5.5 to get 11, and subtract it from 15, which gives us 4.
We then bring down the next digit 0 and get 40. We then divide 5.5 into 40, which gives us 7 as the whole number part of the quotient. We then multiply 7 by 5.5 to get 38.5, and subtract it from 40, which gives us 1.5.
Since there are no more digits to bring down and the remainder is less than the divisor 5.5, we can stop here. Therefore, the result of 18 divided by 5.5 is approximately 3.27, which we get from the quotient of 0.327 rounded to two decimal places.
So 18 divided by 5.5 is approximately 3.27 or 3.27 to two decimal places.
Answer:
3.27 to 2dp
Step-by-step explanation:
18÷5.5
18/1×11/2
X+X+X+Y=4,2
X+X+Y=3,0
X+Y=?
Step-by-step explanation:
it says here "college".
well ...
X + X + X + Y = 4.2
3X + Y = 4.2
X + X + Y = 3.0
2X + Y = 3.0
what is the difference ?
one X (from 3X to 2X) on the left, and 1.2 (from 4.2 to 3.0) on the right.
so, X = 1.2
therefore,
X + Y = 1.8
why ?
because another X (= 1.2) was removed.
and 3.0 - 1.2 = 1.8
On Friday, three friends shared how much they read during the week
Barbara read the first 100 pages from a 320-page in the last 4 days
Judy read the first 54 pages from a 260-page book in the last 3 days.
Nancy read the first 160 pages from a 480-page book in the last 5 days
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)
Answer:
Step-by-step explanation:
Barbara read the first 100 pages from a 320-page in the last four days
Judy read the first 54 pages of a 260-page book in the previous three days.
Nancy read the first 160 pages from a 480-page book in the previous five days
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)
What is the formula for calculating the surface area of a sphere?
Answer:
Please give brainliest
Step-by-step explanation:
c
If is invested $9000 in an account earning 7.5% interest compounded continuously, determine how long it will take the money to triple. Round up to the nearest year.
The time to take the money to triple is, 15.2 years
We have to given that;
It is invested $9000 in an account earning 7.5% interest compounded continuously.
Hence, We can formulate;
27,000 = 9000 (1 + 7.5/100)ⁿ
3 = (1 + 0.075)ⁿ
3 = (1.075)ⁿ
log 3 = n log (1.075)
0.477 = n x 0.0314
n = 0.477 / 0.0314
n = 15.2 years
Thus, The time to take the money to triple is, 15.2 years
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A recent market survey indicated that 37% of the citizens in town would support a new coffee shop. The survey has a margin of error of
1.7%, and the population of the town is 36,170. Based on the survey, which statement about the number of people who would support for
a new coffee shop is true?
Based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.
The margin of error is a measure of the uncertainty in the survey results. It is based on the sample size and the level of confidence desired. In this case, the margin of error is 1.7%.
This means that the actual percentage of citizens in the town who would support a new coffee shop could be as much as 1.7% higher or lower than the survey result of 37%.
To calculate the range of possible values for the percentage of citizens who would support a new coffee shop, we add and subtract the margin of error from the survey result:
37% + 1.7% = 38.7%
37% - 1.7% = 35.3%
Therefore, based on the survey, we can say that between 35.3% and 38.7% of the citizens in the town would support a new coffee shop.
To determine the number of people who would support a new coffee shop, we need to multiply the percentage by the population of the town:
35.3% of 36,170 = 12,776
38.7% of 36,170 = 14,000
Therefore, based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.
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1. A limit imposed by the government on the quantity of a good or product that can be brought into the
country is called a
a. tariff
b. quota
c. foreign bill of exchange
d. value added tax
2. Which of the following would not be an effective argument for the U.S. to enact trade restrictions?
a. they shield U. S. workers from competition by cheap foreign labor
b. they may benefit the security and defense of the nation
c. they help the U.S. maintain diverse industries
d. they make foreign products cheaper to U.S. shoppers
OO
3. What does it mean if a country is on the gold standard?
DO
a. it sets the value of its currency in relation to a specific amount of gold
b. it creates specific standards by which gold is made into jewelry
O c.
O d. none of these
4. Economists tend to classify a country as less developed if the country's average level of Income is less
than
it uses gold instead of paper currency
a. $9,500 per person
b. the average per-person-income of neighboring countries
c. $3.040 per person
gen
d. a U.S. welfare recipient's income
5. Which of the following would not be considered a barrier to economic development?
O
a. high levels of political corruption
b. low population growth
c. low human capital
d. shortage of investment capital
37-09-71.AK
1. A limit imposed by the government on the quantity of a good or product that can be brought into the country is called a quota. The Option B.
2. An option that is not be an effective argument for the U.S. to enact trade restrictions is hey make foreign products cheaper to U.S. shoppers. The Option D is correct.
3. If a country is on the gold standard, this means that it sets the value of its currency in relation to a specific amount of gold. The Option A is correct.
4. An economists tend to classify a country as less developed if the country's average level of Income is less than $3.040 per person. The Option C is correct.
5. The option that would not be considered a barrier to economic development is low population growth. The Option B is correct.
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z varies directly as x^2. When z = 96 when x = 4, find z when x = 3
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"z" varies directly with }x^2}{z = k(x^2)}\hspace{5em}\textit{we also know that} \begin{cases} z=96\\ x=4 \end{cases} \\\\\\ 96=k(4^2)\implies \cfrac{96}{4^2}=k\implies 6=k\hspace{8em}\boxed{z=6x^2} \\\\\\ \textit{when x = 3, what's "z"?}\qquad z=6(3^2)\implies z=54[/tex]
need ASAP! please help with this.
According to the information, the ball returns to the ground about 13.6 feet away.
How to calculate how many feet away the ball returns to the ground?To calculate how many feet away the ball returns to the ground we have to consider that the ball starts 0 feet above the ground (assuming the ground level is the reference point, where h(x) = 0).
To find the maximum height, we need to find the vertex of the parabola, which occurs at
x = -b/2a
where,
a = -0.25
b = 3.4.
x = -3.4 / (2 * (-0.25)) = 6.8
So, the ball reaches a max height of h(6.8) = -0.25(6.8)^2 + 3.4(6.8) = 8.2 feet at a horizontal distance of 6.8 feet away from the club it was hit with.
To find when the ball returns to the ground, we set h(x) = 0 and solve for x:
0 = -0.25x^2 + 3.4x
0.25x(13.6 - x) = 0
x = 0 or x = 13.6
Since x = 0 is the starting point, the ball returns to the ground at x = 13.6 feet away from the club it was hit with.
Therefore, the ball returns to the ground about 13.6 feet away.
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Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 17%
C. 13%
D. 26%
The percentage of the new mixture of peanuts will be 13%. Then the correct option is C.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.
The percentage of the new mixture of peanuts will be given as,
P = [(4 x 0.16) / (12 x 0.40)] x 100
P = [0.64 / 4.80] x 100
P = 0.1333 x 100
P = 13.33%
P ≈ 13%
Thus, the correct option is C.
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For each of the following equations, determine whether its graph is parallel, perpendicular or neither to the given line:
The parallel lines are
a) y = ( 4/7 )x + 6/7
b) 7y = 4x - 18
The perpendicular lines are
a) y = - ( 7/4 )x - 7/4
b) y = - ( 7/4 )x + 2
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = ( 4/7 )x - 3
where the slope of the line is m = 4/7 and y-intercept is b = -3
The parallel lines have the same slope and the perpendicular lines have the negative reciprocal slope
So , the equation of lines are
The parallel lines are
a) y = ( 4/7 )x + 6/7
b) 7y = 4x - 18
And , the perpendicular lines are
a) y = - ( 7/4 )x - 7/4
b) y = - ( 7/4 )x + 2
The lines which are neither parallel not perpendicular are y = 2/3x - 3 and y = -4/7x + 7
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Which of the following is the graph of the function shown below?
W.
X.
Y.
Z.
A.
X
B.
Y
C.
W
Answer:
Cannot be drawn directly.
Step-by-step explanation:
The graph of every function w = f (x, y, z) will be a surface in R 4, though it can't be drawn directly; however, slicing horizontally by w = c produces relations c = f (x, y, z) in x, y, and z whose graphs will be surfaces in 3-space which can be drawn. Therefore, the graph of the function shown above cannot be drawn directly.
The volume of the rectangular prism is given by V(X)=3x^3+x^2-2x+3. Find the missing measures if you know the length is given by (x+1). Find the height and width.
The height and width of the prism are x and 3x - 2
Finding the height and width of the prismFrom the question, we have the following parameters that can be used in our computation:
V(x) = 3x^3 + x^2 - 2x + 3
Length = x + 1
This means that
Side area = Volume/Length
So, we have
Side area = (3x^3 + x^2 - 2x + 3)/(x + 1)
When evaluated, we have
Side area = 3x^2 - 2x + 3/(x + 1)
Ignoring the remainder, we have
Side area = 3x^2 - 2x
Factorize
Side area = x(3x - 2)
This means that
height = x and width = 3x - 2
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Please explain the answer and why for this question
Answer:
Figure A is greater.
Step-by-step explanation:
Figure A has 60 cubic units in volume, if you do length x width x height you get 60. And for figure B the volume is 40 because of again l x w x h.
2. Andrew filled 5 boxes in 35 minutes.
Paige worked for 75 minutes at a
faster rate than Andrew. Select all the
rates that could be Paige's.
A15 boxes in 75 minutes
B10 boxes in 75 minutes
C12 boxes in 75 minutes
D1 box in 6 minutes
E1 box in 9 minutes
The rates that would fill Paige's boxes per minute is
15 boxes in 75 minutes
12 boxes in 75 minutes
1 box in 6 minutes
Given data ,
The rate at which Paige worked can be calculated by comparing the number of boxes filled by Paige with the time Paige worked.
Now , Andrew filled 5 boxes in 35 minutes,
So , The rate of Andrew = Number of boxes filled / Time taken = 5 boxes / 35 minutes = 1/7 boxes per minute
And , Paige worked for 75 minutes at a faster rate than Andrew, so Paige's rate must be greater than 1/7 boxes per minute
A. 15 boxes in 75 minutes:
Rate of Paige = Number of boxes filled / Time taken = 15 boxes / 75 minutes = 1/5 boxes per minute
B. 10 boxes in 75 minutes
Rate of Paige = Number of boxes filled / Time taken = 10 boxes / 75 minutes = 2/15 boxes per minute
C. 12 boxes in 75 minutes
Rate of Paige = Number of boxes filled / Time taken = 12 boxes / 75 minutes = 4/25 boxes per minute
D. 1 box in 6 minutes
Rate of Paige = Number of boxes filled / Time taken = 1 box / 6 minutes = 1/6 boxes per minute
E. 1 box in 9 minutes
Rate of Paige = Number of boxes filled / Time taken = 1 box / 9 minutes = 1/9 boxes per minute
Based on the calculations, options A, C, and D could be Paige's rates, as they are greater than 1/7 boxes per minute
Hence , the equations are solved
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FIRST TO ANSWER GETS BRAINLESS AND NEEDS EXPLANATION
Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Answer:
D is correctStep-by-step explanation:
(4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
Answer: (d)Answer:
ye D is correctStep-by-step explanation:
To combine the terms 12a + 26b - 4b - 16a, you first simplify the like terms. Add the coefficients of a terms and add the coefficients of b terms separately. You get 12a - 16a + 26b - 4b which results in -4a + 22b. Therefore, the correct answer is (c) -4a + 22b.
how to solve 156 x 6=
938 But how did you get 938
156
X 6
____________
The parallelogram is reflected across the line y = x. Which of the following are coordinates of a vertex of the image?
D'(1, 3)
B'(-3, -4)
A'(1, -5)
C'(-1, -2)
The coordinates of a vertex of the image of D are (3, 1)
Which are coordinates of a vertex of the image?From the question, we have the following parameters that can be used in our computation:
The coordinates of point D is
D = (1, 3)
The transformation rule is given as
y = x
Mathematically, this is represented as
(x, y) = (y, x)
Substitute the known values in the above equation, so, we have the following representation
D' = (3, 1)
Hence, the image of point D is D' = (3, 1)
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I need help with this please
U.S. or federal income taxes became public policy in 1913 with the ratification of the 16th Amendment of the U.S. Constitution that gave the Congress the right to charge and collect taxes. Over 41 U.S. states also levy and collect state income taxes. Even local governments may collect local taxes.
How to explain the taxThe 16th Amendment to the much-vaulted United States Constitution was officially ratified in the year 1913. This momentous action has allowed Congress to successfully levy and accumulate income taxes from both individuals and businesses nationwide.
Not only does the federal government take part in the process of collecting taxation by means of earnings, but its 41 associated states have also implemented their own income taxes against citizens living within. Rates remain distinctive between each region; with additional brackets for those with higher incomes who must pay accordingly.
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A composite figure is composed of a semicircle whose radius measures 5 inches added to a square whose side measures 10 inches.
A point within the figure is randomly chosen.
What is the probability that the randomly selected point is in the semicircular region?
Enter your answer rounded to the nearest tenth in the box.
The probability that the point that is selected randomly would be in the semicircular region would be = 0.28.
How to calculate the probability of a selected point in the composite figure?To calculate the probability of a selected point, the formula for probability should be chosen. That is;
Probably = possible outcome/sample space
Possible outcome is the area of the semicircle = πr²/2
where r = 5 in
Area of semicircle = 3.14×5×5/2
=78.5/2 = 39.25 in²
The sample space = area of semicircle+area of square.
But Area of the square;
= length×width
= 10×10 = 100in²
sample space = 100+39.25 =139.25
Probability = 39.25/139.25 = 0.28
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What is the equation of the line shown in this graph?
PLEASEEE help
Answer:
Y=1
Step-by-step explanation:
find the principal needed now to get the given amount; that is, find the present value. To get "$700" after 4 years at 11% compounded monthly.
The present value of $700 is $___
(Round to the nearest cent as needed)
The requreid present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.
To find the present value of $700 after 4 years at 11% compounded monthly, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt}[/tex]
Substituting the given values, we get:
[tex]700 = P(1 + 0.11/12)^{12*4}[/tex]
Simplifying this equation, we get:
[tex]P = 700 / (1 + 0.11/12)^{12*4}\\P = 700 / (1.00917)^{48}[/tex]
P = 700 / 1.487
P = 451.73
Therefore, the present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.
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What is the area of this figure?
The area of the composite figure is equal to 89.5 square yards
How to calculate for the area of the figureThe composite figure can be observed to be made up of a large rectangle at the center with a smaller rectangle and a triangle by the sides, so we shall calculate for the area of the three shape and sum the results to get the total area of the composite figure as follows:
area of the larger rectangle = 14 yd × 5 yd = 70yd²
area of the smaller rectangle = 5 yd × 3 yd = 15 yd²
area of the triangle = 1/2 × 3 yd × 3 yd= 4.5 yd²
total area of the composite figure = 70yd² + 15 yd² + 4.5 yd²
total area of the composite figure = 89.5 yd²
Therefore, the area of the composite figure is equal to 89.5 square yards
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