The the function to estimate the average age of employee of a company is A(s)=0.285s + 59 , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98
To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22 ;
because the number of years between 2003 and 1981 is = 22 years ;
So , A(22) = 0.285×22 + 59 = 65.27 ;
The average age of an employee in 2003 is approximately 65.27.
To estimate the average age of an employee in 2009,
we need to find the value of A(s) when s = 28
because the number of years between 2009 and 1981 is = 28 years ;
So , A(28) = 0.285×28 + 59 = 66.98 ;
The Average age of employee in 2009 is approximately 71.48.
The given question is incomplete , the complete question is
The function A(s) given by A(s)=0.285s + 59 can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let A(s) be the average age of an employee, and "s" be the number of year since 1981; that is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in 2009 ?
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Triangle ABC i an iocele triangle. AB = BC
mB = 34°
What i mA?
A. 34°
B. 56°
C. 73°
D. 112°
In Triangle ABC which is an Isosceles triangle. AB = BC where mLB = 34° so mLA = 73°
Triangles that have at least two sides of equal length are said to be isosceles.
Sum of all angle of a traingle is 180°
So mLA + mLB +mLC = 180
2(mLA) + mLB = 180
2(mLA ) = 180 - 34
2(mLA ) = 146
mLA = 73°
An isosceles triangle has three angles, which, like other triangles, sum up to 180 degrees. The angles other than the apex angle among the three inner angles are identical in size. According to the isosceles triangle theorem, an isosceles triangle has equal-sized angles on either side of its equal sides. As a result, we have B = C in the isosceles triangle ABC where AB = AC.
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-10(2m+1)=-50
solve for m
Answer:
Step-by-step explanation: Distributing the -10 to the parentheses, we get:
-20m -10 = -50
Adding 10 to both sides:
-20m = -40
dividing both sides by -20:
m = 2
So the solution for m is 2.
Answer:
-7
Step-by-step explanation:
Distribute the -10: -20-10m=50
Add 20 to both sides: -10m=70
Divide by -10 to isolate 70
m = -7
to avoid a possible collision with a manned airplane, you estimate that your small ua climbed to an altitude greater than 600 feet agl. to whom must you report the deviation?
If you operate a small unmanned aircraft (UA) and deviate from your approved flight plan greater than 600 feet agl to avoid a possible collision with a manned airplane, you may need to report the deviation to;
the Federal Aviation Administration (FAA).
The FAA requires all small UAs to comply with certain regulations and guidelines, including the requirement to maintain an altitude of no more than 400 feet above ground level (AGL) unless otherwise authorized.
If you deviate from your approved flight plan, such as by climbing to an altitude greater than 600 feet AGL to avoid a possible collision with a manned airplane, you may need to report the deviation to the FAA.
It is important to follow all FAA regulations and guidelines for small UAs to ensure the safety of other aircraft and people on the ground. If you are unsure about how to report a deviation or what regulations apply to your specific UA, you can contact the FAA for guidance.
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Heyo, help a person out? :)
Answer:
n = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
for the equation to be true for all values of x , then both sides have to be the same.
expand both sides and equate like terms
left side
12(3n - [tex]\frac{1}{2}[/tex] x) ← distribute each term in the parenthesis by 12
= 36n - 6x
right side
- [tex]\frac{2}{3}[/tex] (9x - 18) ← distribute each term in the parenthesis by - [tex]\frac{2}{3}[/tex]
= - 6x + 12
we require
36n - 6x = - 6x + 12
that is
36n = 12 ( divide both sides by 36 )
n = [tex]\frac{12}{36}[/tex] = [tex]\frac{1}{3}[/tex]
for the equation to be true for all x then n = [tex]\frac{1}{3}[/tex]
a group of 14 babies contains 6 boys and 8 girls, including evie and ben. in how many ways can i select 6 of the babies if i want to choose
There are ${14 \choose 6}$ ways to select 6 of the babies from the group of 14, including Evie and Ben.
The question is asking how many ways there are to select 6 of the 14 babies from the group if Evie and Ben are included. This can be solved using the formula for combinations, which is ${n \choose r}$, where n is the total number of items and r is the number of items being selected. In this case, n = 14 and r = 6. Therefore, the answer is ${14 \choose 6}$. This means that there are 1001 ways to select 6 of the 14 babies, including Evie and Ben. To solve this, first the formula is used. Then, the total number of items, 14, is plugged into the formula. Finally, the number of items being selected, 6, is plugged into the formula. This yields the final answer of ${14 \choose 6}$.
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This seems a bit long, but it's not really. I will be very grateful if you can help me ( ____'s need to be filled in )You go to the health center where both Doctor A and Doctor B independently (i.e. you have separate appointments with each of them) consider the possibility that you have cogscitis, a brain condition caused by a virus. Doctor A gives the hypothesis that you do have cogscitis a prior probability of 0.70 (so, the prior probability of the not-cogscitis hypothesis is 0.3). Doctor B gives the cogscitis hypothesis a prior probability of 0.20.The doctors each order three tests, and the results come back sequentially: the results of test 1 come back first, the results of test 2 come back second, and the test 3 results come back third. The Doctors both engage in Bayesian updating after seeing the results of each test.What is Doctor B's prior probability for the hypothesis that you do not have cogscitis? ___Test 1 comes back first, and it is positive. Here are the likelihoods for the positive result for Test 1:Hypothesis Probability of positive test result given hypothesiscogscitis 0.70not cogscitis 0.10After getting the results from Test 1, what is Doctor A's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.____After getting the results from Test 1, what is Doctor B's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.____After observing the positive result for Test 1, what best explains the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis?a) Doctor B thought the false positive rate for test 1 was higher than Doctor A.b) Doctor A thought a positive test result was more likely, given the cogscitis hypothesis, than Doctor B.c) Doctor A thought the hypothesis that you have cogscitis was more probable than Doctor B before either of them saw the results from Test 1.d) Doctor B's prior prior probability for the cogscitis hypothesis was higher than Doctor A's.
The best explanation for the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis is that Doctor A thought the hypothesis that you have cogscitis was more likely than Doctor B before either of them saw the results from Test 1.
After getting the results from Test 1, Doctor A's posterior probability for the hypothesis that you have cogscitis can be calculated as follows:
P(cogscitis|test 1 positive) = (P(test 1 positive|cogscitis) × P(cogscitis)) / P(test 1 positive)
where P(cogscitis) = 0.70 (Doctor A's prior probability) and P(test 1 positive|cogscitis) = 0.70 (probability of positive test result given cogscitis).
P(test 1 positive) can be calculated as the sum of probabilities of getting a positive result for both hypotheses:
P(test 1 positive) = P(test 1 positive|cogscitis) × P(cogscitis) + P(test 1 positive|not cogscitis) × P(not cogscitis)
where P(not cogscitis) = 0.3 (Doctor A's prior probability for not cogscitis).
Substituting the values, we get:
P(cogscitis|test 1 positive) = (0.70 × 0.70) / (0.70 × 0.70 + 0.10 × 0.30) = 0.87 (rounded to two decimal places).
So, Doctor A's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 is 0.87.
Similarly, Doctor B's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 can be calculated as follows:
P(cogscitis|test 1 positive) = (P(test 1 positive|cogscitis) × P(cogscitis)) / P(test 1 positive)
where P(cogscitis) = 0.20 (Doctor B's prior probability) and P(test 1 positive|cogscitis) = 0.70 (probability of positive test result given cogscitis).
P(test 1 positive) can be calculated as the sum of probabilities of getting a positive result for both hypotheses:
P(test 1 positive) = P(test 1 positive|cogscitis) * P(cogscitis) + P(test 1 positive|not cogscitis) × P(not cogscitis)
where P(not cogscitis) = 0.8 (Doctor B's prior probability for not cogscitis).
Substituting the values, we get:
P(cogscitis|test 1 positive) = (0.70 × 0.20) / (0.70 × 0.20 + 0.10 × 0.80) = 0.15 (rounded to two decimal places).
So, Doctor B's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 is 0.15.
The best explanation for the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis is c) Doctor A thought the hypothesis that you have cogscitis was more likely than Doctor B before either of them saw the results from Test 1.
Hence, the correct answer is c.
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Please please help
Engineers have determined that the strengths of a rectangular beam varies as
the product of the width w and the square of the depth d of the beam, that is,
S = kwd2 for some constant k > 0.
a A particular cylindrical log has a diameter of 48 cm. Use Pythagoras' theorem
to show that s = kw (2304 - w²).
b Hence find the dimensions of the strongest rectangular beam that can be cut from
the log.
Answer:
The dimensions of the strongest rectangular beam that can be cut from the log are:
depth d = 16√6 cmwidth w = 16√3 cmStep-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Part (a)From observation of the given diagram, the diameter of the circle is the hypotenuse of a right triangle (with legs w and d). Given that the diameter is 48 cm, substitute the values into Pythagoras' Theorem and rearrange to create an expression for d²:
[tex]\begin{aligned}w^2+d^2&=48^2\\w^2+d^2&=2304\\d^2&=2304-w^2\end{aligned}[/tex]
Substitute the found expression for d² into the given strength equation:
[tex]\begin{aligned}s&=kwd^2\\s&=kw(2304-w^2)\end{aligned}[/tex]
Hence showing that s = kw (2304 - w²).
Part (b)To find the value of w that will maximise the strength of the rectangular beam, first differentiate the equation for s in terms of w:
[tex]\begin{aligned}s&=kw(2304-w^2)\\s&=2304kw-kw^3\\\implies \dfrac{\text{d}s}{\text{d}w}&=2304k-3kw^2\\&=3k(768-w^2)\end{aligned}[/tex]
Set the differentiated equation to zero and solve for w:
[tex]\begin{aligned}3k(768-w^2)&=0\\ 768-w^2&=0\\w^2&=768\\w&=\sqrt{768}\\w&=\sqrt{256 \cdot 3}\\w&=\sqrt{256}\sqrt{3}\\w&=16\sqrt{3}\\\end{aligned}[/tex]
Substitute the value of w that maximises the strength of the beam, together with the given hypotenuse of 48 cm, into Pythagoras' Theorem and solve for d:
[tex]\begin{aligned}w^2+d^2&=48^2\\768+d^2&=2304\\d^2&=2304-768\\d^2&=1536\\d&=\sqrt{1536}\\d&=\sqrt{256 \cdot 6}\\d&=\sqrt{256}\sqrt{6}\\d&=16\sqrt{6}\end{aligned}[/tex]
Therefore, the dimensions of the strongest rectangular beam that can be cut from the log are:
depth d = 16√6 cmwidth w = 16√3 cmSpecial right triangles pls help
Answer:
Step-by-step explanation:
4. short leg= 4
hyp= 8
5. leg 2= 5
hypotenuse= 5√2
6. both legs = 2√2
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0
2000
2%
2001 - 9000
5%
9001 and
up
5.4%
Calculate the state income tax owed on a $60,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
The amount of state income tax owed on a $60,000 per year salary is $3,000.
What should we know about Progressive tax?A progressive tax is one in which the tax rate rises in proportion to the taxable amount. The term progressive refers to the manner in which the tax rate rises from low to high, resulting in a taxpayer's average tax rate being less than the person's marginal tax rate.
We are given that the income is $60,000. The applicable Progressive tax for this income range is 5%.
The state income tax owed on a $60,000 per year salary goes as follows:
= $60,000 * 5%
= $3,000
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The graph below describes the journey of a train between two cities. a) Work out the acceleration, in km/h², in the first 15 mins. 1201 100 Velocity (in km/h) 80 b) Work out the distance between the two cities. 60 40 c) Work out the average speed of the train during 20 the journey. 0 9am 10am Time 11am
The motion of the train, obtained from the velocity time graph, can be described as follows;
a) In the first 15 minutes, the train is accelerating at 200 km/h²
b) The distance between the two cities is 125 kilometers
c) The average speed is 62.5 km/h
What is the velocity of the train?The velocity of the train is the rate at which the displacement of the train changes with time of motion.
The graph indicates that 8 units = 1 hour
1 hour = 60 minutes
Therefore; 8 units = 60 minutes
1 unit = 60/8 minute/unit = 7.5 minutes
a) Acceleration = Change in velocity/Time = Δv/Δt
Therefore, acceleration of the train in the first 15 minutes = The change in the velocity in the first 15 minutes, divided by the time
The velocity of the train after 15 minutes = 50 km/h
The initial velocity of the train = 0 km/h
The change in time, Δt = 15 minutes = 0.25 hours, therefore;
Acceleration = (50 - 0)/0.25 = 200
The acceleration of the train in the first 15 minutes = 200 km/h²(b) The distance is the area under the velocity time graph, therefore, the distance between the two cities is found as follows;
d = 0.5 × 0.25 × 50 + 6 × 0.25 × 50 + (1 + 0.5) × 0.5 × 50 + 0.5 × 0.25 × 50 = 125
The distance between the two cities is 125 kilometers(c) The average speed = Total distance ÷ Time
The time it takes the train to complete the journey = 2 hours
The average speed = 125 km/(2 hrs) = 62.5 km/h
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Violet invested $5,900 in an account paying an interest rate of 7\tfrac{1}{2}% compounded quarterly. Nachelle invested $5,900 in an account paying an interest rate of 6\tfrac{7}{8}% compounded continuously. After 10 years, how much more money would Violet have in her account than Nachelle, to the nearest dollar?
The difference between the amounts of Nachelle and violet is $670.31
What is compound interest?Starting young lets the students take advantage of the magic of "compound interest." Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
Given here: Violet invested $5900 at 7.5% interest and Nachelle invested the same amount but at 6.875 %
After 10 years Violets Amount when compounded quarterly we get
A= 5900×(1+7.5%)⁴⁰
=$12,403.86
Similarly after 10 years Nachelle's amount if it is compounded contionously we get
[tex]P(t)=P_{0}e^{rt}[/tex]
[tex]P(10)=5900e^{0.06875*10}\\ =11733.55[/tex]
∴The difference between their amounts is$12,403.86-11733.55=$670.31
Hence, The difference between the amounts of Nachelle and violet is $670.31
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Answer:670
Step-by-step explanation:
REGAN SOLD 14 NECKLACES AND MADE A TOTAL 210 IF EACH NECKLACE COST THE SAME COUNT HOW MUCH DID ONE NECKLACE COST
Answer: £15
Step-by-step explanation:
210/14 = 15
to check :14x15=210
Answer: One necklace costs $15
Step-by-step explanation:
We know Regan sold 14 necklaces but we do not know how many, we can use "x" to represent the amount of necklaces sold.
We will use the equation 14(x)=210 to represent our word problem
Use PEMDAS and divide both sides by 14, this will give you x=15
$15 per necklace is the answer
A triangle has a 6 cm side, a 7 cm side, and a 45°.
• The 6 cm side is adjacent to the 45° angle.
• The 7 cm side is opposite the 45° angle.
How many triangles can be made with these conditions?
One
No
One
Two
More than 2
?triangle(s) can be made.
K
One triangles can be made with these conditions.
What is the 45 degree triangle's formula?Pythagorean theorem application The Pythagorean Theorem makes it simple to determine the length of the sides of a 45 45 90 triangle as it is a right angle triangle. The Pythagorean Theorem's formula is as follows: A 2 + B 2 = C 2 A2 + B 2 = C 2When the two legs of an isosceles right triangle are congruent to one another and the non-right angles are both 45 degrees, the triangle is known as a 45 45 90 triangle. The Pythagorean theorem may frequently be used to locate the missing legs or hypotenuse of 45 45 90 triangles.To learn more about triangle refer to:
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the linear regression coefficient of x on y is beta. what is the range of regression coefficient of y on x?
The range of the regression coefficient of y on x is (-∞, ∞).
The parameter β (the regression coefficient) represents the amount by which change in x must be multiplied to give the interconnected average change in y or the amount y changes for a unit increase in x. In this manner, it represents the degree to which the line slopes upwards or downwards.
The regression coefficient of x on y, β, represents the change in y per unit change in x. The regression coefficient of y on x, β', represents the change in x per unit change in y.
The range of the regression coefficient of y on x is (-∞, ∞). This is because the relationship between x and y can be positive, negative, or zero, leading to positive, negative, or zero regression coefficients.
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Are these equivalent? Please help!
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
Solution:
We need to simplify the following expression: (5-7y+10)1/5
[tex]\frac{(5-7y+10)*1}{5}[/tex]
Grouping together numerical values
[tex]\frac{(-7y+5+10)*1}{5}[/tex]
We reduce the integers that can be added together: 5+10=15
= [tex]\frac{(-7y+5+10)*1}{5}[/tex]
By reorganizing/simplifying/expanding the terms that are amenable to
[tex]3 -\frac{7}{5}y[/tex]
Answer:
Yes they are in fact equivalent.
(Hope this helped!)
set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan2 x, y = 3, and x = 0 about the line y = 3.
An integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan² x, y = 3, and x = 0 about the line y = 3 is V = ∫[0, arctan(√3)] 2πx(3 - tan²(x)) dx.
The method of cylindrical shells can be used to set up the integral for the solid's volume after rotating the first quarter region defined by the curves y = tan² x, y = 3, and x = 0 about the line y = 3.
We must take into account an infinitesimally thin strip of width dx at a distance x from the y-axis in order to set up the integral.
This cylindrical shell's volume can be estimated by multiplying its height, radius, and thickness (dx) together. Consequently, each shell's volume is as follows:
dV = 2πx(3 - tan²(x)) dx
Setting 3 = tan²(x), we have:
tan²(x) = 3
tan(x) = √3
x = arctan(√3)
Thus, the integral for the volume of the solid is: V = ∫[0, arctan(√3)] 2πx(3 - tan²(x)) dx
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Let y be the percent increase in annual US national production during a year when the unemployment rate changes by u percent. (For example, u = 2 if unemployment increases from 4% to 6%.) Okun's law states that
y=3.5-2u
(a) What is the meaning of the number 3.5 in Okun's law?
(b) What is the effect on national production of a year when unemployment rises from 5% to 8%?
(c) What change in the unemployment rate corresponds to a year when production is the same as the year before?
(d) What is the meaning of the coefficient -2 in Okun's law?
Okun's law states that changes in unemployment and production are inversely related, with a coordinate of -2.
(a) When the unemployment rate stays the same in a given year, Okun's law's number 3.5 indicates the anticipated percent rise in yearly US national production.
(b) In accordance with Okun's law, a year in which unemployment increases from 5% to 8% results in a 1% decrease in national production.
(c) In accordance with Okun's law, a year in which production is equal to the previous year results in a decline of 1.75% in the unemployment rate.
(d) The inverse link between the unemployment rate and national output is represented by the coefficient -2 in Okun's law, which states that a rise in the unemployment rate would result in a fall in national production.
According to Okun's Law, the annual US national production's percent change (y) and the unemployment rate's percent change are connected (u). When the unemployment rate stays constant in a given year, the projected percent increase in national production is represented by the constant 3.5 in Okun's law. The inverse link between the unemployment rate and national output, represented by the coefficient -2 in Okun's law, states that a rise in the unemployment rate will result in a fall in national production. As a result, if unemployment increases from 5% to 8%, national production will decline by 1%. The change in the unemployment rate would need to be a decrease of 1.75 percent for national production to be the same as it was the previous year.
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Express each ratio in simplest form. 10 : 25 : 35
Answer: 2:5:7
Step-by-step explanation:
You need to find the greatest common factor of all three of them which is 5. Then, you divide each number by 5
the table below displays some of the results of last summer's frostbite falls fishing festival, showing how many contestants caught fish for various values of . in the newspaper story covering the event, it was reported that (a) the winner caught fish; (b) those who caught or more fish averaged fish each; (c) those who caught or fewer fish averaged fish each. what was the total number of fish caught during the festival?
The total number of fish caught during the festival can be calculated by adding the number of fish caught for each value of n.
For example, if 10 contestants caught 4 fish, 5 caught 8 fish, 7 caught 10 fish, and 8 caught 7 fish, the total number of fish caught would be 104 + 58 + 710 + 87 = 330.
The argument states that the total number of fish caught during the Frostbite Falls Fishing Festival can be determined by adding the number of fish caught by each contestant.
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HELP!!!!!!! PLS!!!!!! WHERE DO I PUT THE DOTS ON THE GRAPH?!?!?!?!?!?! SCREENSHOT* 18 points!!!!!!!! I DON'T UNDERSTAND THIS!!!!!
Answer:
Use the scale, 400:100
Step-by-step explanation:
400 on x axis, 100 on y axis
800 on x axis, 200 on y axis
Join the points with a line, extend it
That's it!
The bar diagram shows how the circumference C of a circle relates to its diameter d. How does the bar diagram connect to the formula C = πd?
The bar diagram connect to the formula C = πd by taking π as 3
How to determine teh connection between the bar diagram and the formulaFrom the question, we have the following parameters that can be used in our computation:
C = πd
Also from the bar diagram, we have
C = 3d
When the equations are compared, we have
C = πd = 3d
This gives
π = 3
Hence, the value of π is 3
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using a discount rate of 6.5 percent, calculate the present value of a $1,000 profit payment to be received at the end of a. one year b. two years c. three years
Future Value received at the end of one year is 1065
Future Value received at the end of two year is 1134.225
Future Value received at the end of three year is 1207.949
discount rate of 6.5 percent
present value of a $1,000
Present Value= [tex]\frac{FV}{(1+r)^{n} }[/tex]
where:
FV=Future Value
r=Rate of return
n=Number of periods
Future Value received at the end of one year
Future Value= Present Value * [tex](1+r)^{n}[/tex]
= 1000 * (1+ 6.5%)^1
= 1000* 1.065
= 1065
Future Value received at the end of two year
Future Value= Present Value * [tex](1+r)^{n}[/tex]
= 1000 * (1+ 6.5%)^2
= 1000* 1.065^2
= 1000 * 1.134225
= 1134.225
Future Value received at the end of three year
Future Value= Present Value * [tex](1+r)^{n}[/tex]
= 1000 * (1+ 6.5%)^3
= 1000* 1.065^3
= 1000 * 1.207949
= 1207.949
Future Value received at the end of one year is 1065
Future Value received at the end of two year is 1134.225
Future Value received at the end of three year is 1207.949
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someone help please. i need to turn this in tomorrow. Question is in the picture!
write quadratic equation in standard form given vertex (-1, -6) (1 , 2)
The quadratic function with vertex (-1,-6), that passes through (1,2), is given as follows:
y = 2x² + 4x - 4.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.Considering the vertex at x = -1, y = -6, the parameters h and k are given as follows:
h = -1, k = -6.
Hence:
y = a(x + 1)² - 6.
When x = 1, y = 2, hence the leading coefficient a is obtained as follows:
2 = a(2)² - 6
4a = 8
a = 2.
Hence:
y = 2(x + 1)² - 6.
In standard form, we have that:
y = 2x² + 4x + 2 - 6
y = 2x² + 4x - 4.
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192. ∭ e ⎛ ⎝y ln x z ⎞ ⎠dv, where e = ⎧ ⎩ ⎨(x, y, z)|1 ≤ x ≤ e, 0 ≤ y ≤ ln x, 0 ≤ z ≤ 1⎫ ⎭
The calculation is performed in three stages, and the result represents the volume of the object in cubic units.
The expression ∭ e ⎛ ⎝y ln x z ⎞ ⎠dv represents a triple integral, which is a type of mathematical operation that calculates the volume of a 3-dimensional object bounded by certain conditions.
In this particular case, the volume is defined by the limits of integration (1 ≤ x ≤ e, 0 ≤ y ≤ ln x, 0 ≤ z ≤ 1), meaning that it considers only the points in the space that satisfy these conditions.
To understand the triple integral, it is important to understand the concept of single and double integrals.
The calculation of a triple integral is performed in three stages.
First, the integral with respect to x is calculated, then the integral with respect to y, and finally the integral with respect to z.
The expression e ⎛ ⎝y ln x z ⎞ ⎠ represents the integrand, or the function that we are integrating. In this case, it is a product of three functions of x, y, and z.
The ∭ symbol represents the triple integral and the dv represents the differential of the volume, which is used to calculate the volume in small increments.
In conclusion, the triple integral
=> ∭ e ⎛ ⎝y ln x z ⎞ ⎠dv
calculates the volume of a 3-dimensional object defined by the limits of integration.
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Please help precal problem!
Find the value of side a.
A) 2.770
B) 3.516
C) 5.760
D) 7.309
E) None of these
Therefore , the solution of the given problem of triangle comes out to be a value is 3.5154 unit.
What does a triangle actually mean?Triangles are polygons because they have four sides or more. Its form is simple and geometric. An angle square with the letters ABC is known as a triangle. When the sides remain not collinear, Euclidean geometry generates a singular plane or square. Having three parts and three corners makes a triangle a polygon. The corners of a triangle are where the three sides meet. Angles in a triangle add up at 180 °.
Here,
Given :
=> Tan 38° = a/4.5
=> 0.7812 = a /4.5
=> a = 4.5 * 0.7812
=> a = 3.5154 unit
Therefore , the solution of the given problem of triangle comes out to be
a value is 3.5154 unit.
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Witch expression means 9 more than a number help
The imaginary part of [tex]\frac{1}{1+i}[/tex] is ?
The imaginary part of the given expression 1/ ( 1+i ) is -i / 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 1 / ( 1 + i). The imaginary part will be calculated as:-
E = 1 / ( 1 + i)
Rationalize the numbers,
E = 1 / ( 1 + i)
E = [ 1 / ( 1 + i) ] [ ( 1 - i ) / ( 1 - i ) ]
E = ( 1 - i ) / ( 1² +1 )
E = ( 1 - i ) / 2
E = ( 1 / 2 ) - ( i / 2 )
The imaginary part will be -( i / 2 ).
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Rewrite 12-(5+6m) without parenthesizes
7 + 6m is solution of parenthesizes equation .
What is parentheses in maths ?
These are also referred to as round brackets and are represented by the following symbols: ( ). The most typical brackets are those mentioned above.
They are utilized to combine several numbers and formulae. In an equation, terms are grouped together or the order of operations is stated using parentheses or "round brackets."
Rewrite 12-(5+6m)
= 12 - 5 + 6m
= 7 + 6m
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The perimeter of the rectangle below is 76 units. Find the length of side AD.
Write your answer without variables.
Answer: 17 units
Step-by-step explanation: A perimeter of a rectangle can be represented by the equation:
2(L)+2(W) = P
L represents length, W represents width and P represents perimeter
Lets say DC is width so AB has to be width aswell and then AD and BC are length.
We are given width and length as equations and P as 76 so we can substitute it into our equation to get:
2(3x-1) + 2(4x-3) = 76
We are trying to solve x so distributing would make it easy to obtain and we get:
6x - 2 + 8x - 6 = 76
Simplifying and solving for x gives us:
6x - 2 + 8x - 6 = 76
14x - 8 = 76
14x = 84
x = 6
Finally, we know AD represents our Width and AD = BC since we know BC is 3x-1, we can plug x in to get BC which is equal to AD to get:
3x - 1 = BC
3(6) - 1 = BC
17 = BC
since BC = AD
17 = AD
