The total value of $6800 compounded quarterly at 6% for 3 years is $8,123
How to determine the total valueFrom the question, we have
A = final amount
P = principal amount (initial investment) = $6800
r = annual interest rate = 0.06 ie. 6%
n = number of times interest is compounded per year = 4
t = time (in years) = 3
The total value is calculated as:
A = P(1 + r/n)^(nt)
substitute the known values in the above equation, so, we have the following representation
A = 6800(1 + 0.06/4)^(4*3)
Evaluate
A = 8130.2
Hence,, the value is $8130.2
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How do you solve this equation 4(x+3)= -8
Answer:
x= -5
Step-by-step explanation:
4(x + 3) = -8
4x + 12 = -8
4x = -20
x = -5
For time 0≤t≤10 , water is flowing into a small tub at a rate given by the function F defined by F(t)=arctan(π/2−t/10). For time 5≤t≤10 , water is leaking from the tub at a rate given by the function L defined by L(t)=0. 03(20t−t^2−75). Both F(t) and L(t) are measured in cubic feet per minute, and t is measured in minutes. The volume of water in the tub, in cubic feet, at time t minutes is given by W(t).
(a) At time t=3 , there are 2. 5 cubic feet of water in the tub. Write an equation for the locally linear approximation of W at t=3 , and use it to approximate the volume of water in the tub at time t=3. 5.
(b) Find W′′(8). Using correct units, interpret the meaning of W′′(8) in the context of the problem.
(c) Is there a time t , for 5
(d) The tub is in the shape of a rectangular box that is 0. 5 foot wide, 4 feet long, and 3 feet deep. What is the rate of change of the depth of the water in the tub at time t=6 ?
(a) W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.
(b) W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.
(c) We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5
What is the quadratic equation?
The quadratic equation is a formula used to solve quadratic equations of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable.
(a) To find the locally linear approximation of W at t=3, we first need to find W(3) and W'(3).
We know that at time t=3, the volume of water in the tub is 2.5 cubic feet. Therefore, W(3) = 2.5.
To find W'(3), we need to use the fact that the rate of change of the volume of water in the tub is equal to the rate of water flowing in minus the rate of water leaking out.
So, W'(t) = F(t) - L(t).
At time t=3, we have F(3) = arctan(π/2 - 3/10) ≈ 1.383 cubic feet per minute, and L(3) = 0.03(20*3 - 3² - 75) = 0.9 cubic feet per minute. Therefore, W'(3) = 1.383 - 0.9 = 0.483 cubic feet per minute.
The locally linear approximation of W at t=3 is given by:
W(t) ≈ W(3) + W'(3)(t-3)
W(t) ≈ 2.5 + 0.483(t-3)
To approximate the volume of water in the tub at time t=3.5, we plug in t=3.5 into the above equation:
W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.
(b) To find W''(8), we first need to find an expression for W'(t). We know that:
W'(t) = F(t) - L(t)
Taking the derivative with respect to t:
W''(t) = F'(t) - L'(t)
We know that F(t) = arctan(π/2 - t/10), so F'(t) = -1/(10π/4 - t²/100 + t/5²) * (1/5), where we used the chain rule and the derivative of arctan(x) = 1/(1+x²). Evaluating this expression at t=8, we get F'(8) ≈ -0.0397 cubic feet per minute.
We also know that L(t) = 0.03(20t - t²- 75), so L'(t) = 0.03(20 - 2t). Evaluating this expression at t=8, we get L'(8) = -0.6 cubic feet per minute.
Therefore, W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.
Interpreting the meaning of W''(8), we see that it represents the rate of change of the rate of change of the volume of water in the tub at time t=8. Specifically, W''(8) tells us how quickly the volume of water in the tub is changing with respect to time at time t=8 is changing.
(c) Yes, there is a time t for which the volume of water in the tub is neither increasing nor decreasing. This occurs when the rate of water flowing into the tub is equal to the rate of water leaking out. That is, we need to find a value of t such that F(t) = L(t).
We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5
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a company must stretch a caple from the top of tower that is 25 cm high to a point 50 cm away from the base of the tower . what is the length of the caple ?
A/ 625
B/ 2500
C/ 3125
D/ 25√5
The length of the caple is √3125 cm. (option C)
What is the length of the caple?The caple and the tower would form a right triangle. The caple would be the hypotenuse. The tower would be the length and the distance from the base of the tower would be the base.
In order to determine the length of the caple, Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenusec² = 25² + 50 ²
c² = 625 + 2500
c² = 3125
c= √3125 cm
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The ratio of horizontal distance to height of the ramp is 15:1. A builder has a roll of nonslip rubber mat that is 15 feet long. Does he have enough forever to cover the Ramp completely?
Answer:
No. The length of the ramp is [tex]\sqrt{226[/tex] The rubber mat will be too short
Step-by-step explanation:
Out of 1000 students who appeared for C.A. Intermediate Examination, 750 failed in Math, 600 failed in Accounts and 600 failed in Costing, 450 failed in both Math & Accounts, 400 failed in both Math & Costing, 150 failed in both Accounts & Costing. The Students who failed in all the three Subjects were 75. Prove that the above data is not correct.
Yes, the data provided is not correct. This can be proven using the principle of inclusion-exclusion.
According to the given data, the total number of students who failed in Math is 750, the total number of students who failed in Accounts is 600, and the total number of students who failed in Costing is 600.
However, if we apply the principle of inclusion-exclusion, the total number of students who failed in at least one of the three subjects should be equal to the sum of the number of students who failed in each subject, minus the number of students who failed in two subjects, plus the number of students who failed in all three subjects.
Therefore, using this principle, we have:
750 + 600 + 600 - 450 - 400 + 75 = 975
This result shows that the number of students who failed in at least one of the three subjects is 975, which is greater than the total number of students who appeared for the examination (1000), which is not possible.
Therefore, the given data is not correct.
write the sentence as an equation
n and 328 more is the same as 13
The equation which correctly represents the sentence in discuss as required is; n + 328 = 13.
Which sentence correctly represents the equation?It follows from the task content that the equation which correctly represents the sentence given in the task content is to be determined.
The word phrase; n and 328 more can be represented as; n + 328.
Therefore, n and 328 more is the same as 13 can be represented as; n + 328 = 13.
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Jesus believes in looking his best when searching for a job. He wants to save $435 for a new suit for his interviews. He currently has $65.00 and he can save $18.00 per week from his work.
How many weeks in total will it take him to save for the suit, assuming he puts the $65.00 into an account on week 1 and starts saving each week thereafter?
Answer:
6.7 weeks.
Step-by-step explanation:
65.00 x 6.7 = 435.50
Answer:
Step-by-step explanation:
He has $65 on the first week. He’s missing $370. If he can save $18 a week. 370/18 = 20.5. But they’re asking for the total weeks it’ll take. So add the first week. 20.5 + 1 = 21.5
not mine but he did he get it right
The area of Rhode Island is about 1000
square miles. The area of Alaska is about
5.7 x 105 square miles.
Complete the statement based on the
information above:
Alaska's area is ___ times the area of rhode island
Answer:
57
Step-by-step explanation:
To find the ratio of the area of Alaska to the area of Rhode Island, we need to divide the area of Alaska by the area of Rhode Island.
The area of Rhode Island is 1000 square miles and the area of Alaska is 5.7 x 10^5 square miles.
So, the ratio is: 5.7 x 10^5 / 1000 = 57
Therefore, Alaska's area is 57 times the area of Rhode Island.
5.7 x 10^5 divided by 1000 = 57.
Graph the image of square CDEF after a dilation with a scale factor of
1
2
, centered at the origin.
Answer:
Step-by-step explanation:
To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin, you would need to double the x and y-coordinates of each vertex of the square.
Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:
(2a, 2b)
(2a, 2b + 2)
(2a + 2, 2b + 2)
(2a + 2, 2b)
So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.
To graph the image, you would plot each of the new vertices and connect them to form the image square.
The solution is given below.
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
here, we have,
To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin,
we would need to double the x and y-coordinates of each vertex of the square.
Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:
(2a, 2b)
(2a, 2b + 2)
(2a + 2, 2b + 2)
(2a + 2, 2b)
So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.
To graph the image, we would plot each of the new vertices and connect them to form the image square.
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The American flag has 50 stars, 7 red stripes, and 6 white stripes. Write a ratio to represent the ratio of stars to red stripes.
The ratio of stars to red stripes is 50 to 7
How to write a ratio to represent the ratio of stars to red stripes.from the question, we have the following parameters that can be used in our computation:
Number of stars = 50
Red stripes = 7
White stripes = 6
Using the above as a guide, we have the following:
Ratio = Stars : Red stripes
substitute the known values in the above equation, so, we have the following representation
Stars : Red stripes = 50 : 7
Hence, the ratio is 50 : 7
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Match each polynomial on the left with its two factors on the right.
x³-27
x² +27
x+3
x-3
x² + 3x +9
x² + 3x-9
x²-3x+9
x²-3x-9
Answer:
hi
Step-by-step explanation:
[tex]x {}^{3} - 27 = {x}^{3} - {3}^{3} \\ = (x - 3)( {x}^{2} + 3x + 9) \\ {x}^{3} + 27 = {x}^{3} + {3}^{3} \\ = (x + 3)( {x}^{2} - 3x + 9)[/tex]
The inside diameter of a randomly selected piston ring is a random variable with mean value 11 cm and standard deviation 0.02 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.)
(a) Calculate P(10.99 ? X ? 11.01) when n = 16.
(b) How likely is it that the sample mean diameter exceeds 11.01 when n = 25?
a) P(10.99 ≤ X ≤ 11.01) = 0.9544
b) Probability that the sample mean diameter exceeds 11.01 when n = 25 is 0.0062.
We are given the following in the question:
Mean, μ = 11 cm
Standard Deviation, σ = 0.02 cm
We are given that the distribution of diameter is a bell-shaped distribution that is a normal distribution.
Formula: z = (x - μ)/σ
a) P(10.99 ≤ X ≤ 11.01 when n = 16)
Standard error due to sampling = σ/n = 0.02/√16 = 0.005
P(10.99 ≤ X ≤ 11.01) = P((10.99 - 11)/0.005 ≤ z ≤ (11.01 - 11)/0.005)
= P(-2 ≤ z ≤ 2) = 0.9772-0.0228
= 0.9544 = 95.44%
b) P(sample mean diameter exceeds 11.01 when n = 25)
Standard error due to sampling = σ/n = 0.02/√25 = 0.004
P(x > 11.01) = P(z > (11.01 - 11)/0.004) = P(z > 2.5)
= 1 - P(z ≤ 1) = 1 - 0.9938 = 0.0062 = 0.62%
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I will give brainliest and ratings if you get this correct
find derivative of e^(e^x)
use chain rule to find d/dx of e^x is e^x.
so chain rule finds the value e^(e^x) d/dx = e^(e^x) x e^x
simplify to e^[(e^x)+x]
The PTO has 1,932 tickets to sell for the school carnival. They want to split the tickets equally into at least 3, but less than 10 ticket booths. How many ticket booths could they split them into without having any left over? Please explain your answer.
The PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths, without having any tickets left over.
How many ticket booths could they split?We need to find a number that is divisible by at least 3, but less than 10.
We can start by listing out the multiples of 3 and see which one is closest to 1,932:
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15
3 × 6 = 18
3 × 7 = 21
3 × 8 = 24
3 × 9 = 27
We can see that the closest multiple of 3 to 1,932 is 1,932 ÷ 3 = 644. This means that if the PTO split the tickets into 644-ticket batches, they would have 3 equal booths of 644 tickets each.
We can check whether 644 is also divisible by 4, 5, 6, 7, 8, or 9, as those numbers are less than 10. We can see that 644 is not divisible by 4 or 5, but it is divisible by 6, 7, 8, and 9. This means that the PTO could also split the tickets into 6, 7, 8, or 9 ticket booths, with each booth having an equal number of tickets.
Therefore, the PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths.
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The Tour de France is a 2,235 mile long distance bicycle
race that goes through all of France. So far, Haley has
ridden fifteen miles of one mostly uphill stage of the Tour
de France. She rides thirteen miles per hour during this
stage.
Define units for the additional time Haley rides and
the distance Haley rides.
1. How far will Haley have ridden after an additional 120
minutes?
2. Haley grabs a new water bottle from volunteers after six
hours. How far has she traveled?
Enter a variable for the additional time Haley rides and
use this variable to write an expression for the
distance Haley rides.
Quantity Name
Unit
Question 1
Question 2
Expression
Additional Time Distance Haley
Haley Rides
Rides
hours.
miles
2
6
Answer:
Step-by-step explanation:
Isosceles trapezoid KRWT is shown
Given KRWT is an isosceles trapezoid with KR and TW
Prove: WK = TR
An incomplete two-column proof is shown
Answer Choices:
-
-
-
-
What is the missing statement in step 3
More info is in the picture
Thank you for any help!
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In isosceles trapezoid KRWT, the trianngles are ΔKTW and ΔRWT are formed.
In trianngles ΔKTW and ΔRWT, then we have
KW = TR {Given}
∠W = ∠T {Isosceles angles}
WT = WT {Common side}
Then the trianngles ΔKTW and ΔRWT are congruent to each other.
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
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Graph the linear inequality.
x < 2
Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.95. The
number of nickels is 2 less than 5 times the number of dimes. How many nickels and how many dimes are in the coin
purse?
Let's represent the number of dimes in the coin purse as d. Then, the number of nickels in the coin purse can be represented as 5d - 2.
The total value of the coins can be expressed as:
0.05 * (5d - 2) + 0.10 * d = 0.95
Expanding and simplifying the equation, we get:
0.05 * 5d - 0.05 * 2 + 0.10 * d = 0.95
0.50d - 0.10 = 0.95
0.50d = 1.05
d = 2.10
Since the number of dimes must be a whole number, we round d down to 2. So, there are 2 dimes in the coin purse and 5 * 2 - 2 = 6 nickels in the coin purse.
The perimeter of a triangle is 39 inches. If the length of the shortest side is 1/2 the length of the longest side, and the length of the third side is 1 less than the length of the longest side, what is the length of each side?
You estimate that there are 76 marbles in a jar. The actual amount is 59 marbles. Find the percent error. Round to the nearest tenth of a percent if necessary.
Answer: To find the percent error, we can use the formula:
percent error = (estimated value - actual value) / actual value * 100
Plugging in the values:
percent error = (76 - 59) / 59 * 100 = 29.49%
Rounding to the nearest tenth of a percent:
percent error = 29.5%
So the percent error is 29.5%.
Step-by-step explanation:
Can someone pls help me?
What is the initial value of the function?
The initial value of the function is 1.
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
A relationship in which one input value exactly equals one output value is known as a function. A function's initial value is a crucial component. A starting value or starting point is exactly what it sounds like: It is an initial value.
The line intersects the y-axis at (0,1).
The initial value of the function is 1.
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1. The equation 24x² + 2x = 15 has 2 solutions. What is
the greater of the 2 solutions?
A. 3/
B.
M + NO
C.
D. 1/1
E.
Answer:
Step-by-step explanation:
To find the solutions of the equation 24x² + 2x - 15 = 0, you can use the quadratic formula.
The quadratic formula states that given a quadratic equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0, the solutions are given by:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 24, b = 2, and c = -15, so:
x = (-2 ± √(2² - 4 * 24 * -15)) / 2 * 24
x = (-2 ± √(4 + 1440)) / 48
x = (-2 ± √(1444)) / 48
Taking the square root of both sides, we have:
x = (-2 ± 38.2) / 48
Therefore, the solutions are:
x = (-2 + 38.2) / 48 = 36.2 / 48 = 0.75
x = (-2 - 38.2) / 48 = -40.2 / 48 = -0.84
Since 0.75 > -0.84, the greater of the two solutions is 0.75.
Answer:
the answers are: 36/48
-40/48
PLEASE HELP MISSING
WORK
Jonathan wants to save up enough money so that he can buy a new sports equipment set that includes a
football, baseball, soccer ball, and basketball. This complete boxed set costs $85.50. Jonathan has $22.00 he
saved from his birthday. In order to make more money, he plans to wash neighbors' windows. He plans to
charge $4 for each window he washes
Part A
Write and solve an inequality that represents the number of windows Jonathan can wash in order to save at
least the minimum amount he needs to buy the boxed set.
Inequality:_______
PART B
GRAPH THE SOLUTION ON A NUMBER LINE
Explain the meaning of your inequality from Part A based on the context of the problem
The inequality that shows the least amount he needs is 4x + 22 ≥ 85.50 which shows he needs at least $15.875
What is the inequality that show the least amount he needs to buy boxed setThe Inequality that will represent this problem is 4x + 22 ≥ 85.50, where x is the number of windows Jonathan washes.
To solve the inequality, we'll start by subtracting 22 from both sides:
4x ≥ 63.50
And finally, dividing both sides by 4:
x ≥ 15.875
So, Jonathan needs to wash at least 15 windows in order to save up enough money to buy the boxed set.
b.
The graph on the number line showing x ≥ 15.875 is attached below
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The value of a machine, V , at the end of t years
The value of machine after 2 years is $346.4.3
What is Rate of Depreciation?Subtract the asset's cost from its salvage value (what you anticipate it to be worth at the end of its useful life) to determine depreciation using the straight-line technique. The amount that can be depreciated, or the depreciable basis, is the outcome. Subtract this sum from the asset's useful life, which is measured in years.
Given:
C = $707 (the original cost),
r = 0.3 (the rate of depreciation),
and t = 2 (years that have gone by)
Using the Formula
V = C [tex](1-r)^t[/tex]
V = (707)(1 - 0.3)²
V = (707)(0.7)²
V = (707)(0.49)
V = 346.43
Thus, the value of machine is $346.43
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someone help me please and thank you
Ordinal data can be ordered, as the naming implies. Both have "ord" to help remember the connection. An example of this would be something like small, medium, large. The items do not have to be numeric in nature.
Nominal data is any category or name. Order isn't present here. For example, if a survey asked about a person's favorite color, then there isn't any inherent order here.
Solve x - 5 = 8 - 4x
Answer:
Step-by-step explanation:
x - 5 = 8 - 4x
rearrange
x - 5 = -4x + 8
x + 4x - 5 = -4x + 4x + 8
5x - 5 = 8
5x - 5 + 5 = 8 + 5
5x = 13
Divide by 5
5x/5 = 13/5
x = 13/5 or 2 [tex]\frac{3}{5}[/tex]
or 2.6 as a decimal
Find the equation of the line with slope 7 which goes through the point (−2,−9).
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ 7}(x-\stackrel{x_1}{(-2)}) \implies y +9= 7 (x +2) \\\\\\ y+9=7x+14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]
Color the rational numbers blue
Leave the irrational numbers alone
Answer:
The answer is provided in the image below.
PLS HELPP
louise has planted 96 shrubs. the garden centre guaranteed her that at least 7/8 of the shrubs would survive. What is the minimum number od shrubs that should survive?
Answer:
84
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
We can first convert 96 into a fraction.
96 = [tex]\frac{96}{1}[/tex]Now that we know this, we can solve for the number of shrubs. If we know that at least [tex]\frac{7}{8}[/tex] of the shrubs should survive, we can use an equation that looks like this:
([tex]\frac{7}{8}[/tex]) × ([tex]\frac{96}{1}[/tex]) =?Solving the equation:
([tex]\frac{7}{8}[/tex]) × ([tex]\frac{96}{1}[/tex]) = 84Therefore, the minimum number of shrubs that should survive is 84.
The graph above is a transformation of the function X^2
Write an equation for the function graphed above
The equation for the function graphed is g(x) = -1/4(x + 2)^2 - 1
How to determine the equation for the function graphedFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^2
First the function is reflected across the x-axis
This gives
f'(x) = -x^2
Next, the function is stretched vertically by 4
Using the above as a guide, we have the following:
f'(x) = -1/4(x)^2
Lastly the function is translated 2 units left and 1 units dows
This is represented as
g(x) = -1/4(x + 2)^2 - 1
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