Answer:
[tex]\large \boxed{\sf \ \ 9\text{ years} \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all, a few remarks:
>>> 1 year is 12 months, right?
>>> Monthly compounding means that each month we compute the interest and they will be included in the investment for the next month.
>>> 6% is an interest per year, it means that to compute the interest for 1 month we need to compute by 6% multiplied by [tex]\dfrac{1}{12}[/tex]
Let's do it !
At the beginning, we have:
$8,000
After 1 month, we will have:
[tex]8000 + 8000\cdot \dfrac{6\%}{12}=8000\cdot (1+ \dfrac{6}{1200})= 8000\cdot (1+ \dfrac{1}{200})[/tex]
After 2 months, we will have:
[tex]8000\cdot (1+ \dfrac{1}{200})\cdot (1+ \dfrac{1}{200})=8000\cdot \left(1+ \dfrac{1}{200}\right)^2[/tex]
After n months, we will have
[tex]8000\cdot \left(1+ \dfrac{1}{200}\right)^n=8000\cdot \left(1.005\right)^n[/tex]
We are looking for n such that
[tex]8000\cdot \left(1.005\right)^n=13709.60\\\\ln(8000)+ n\cdot ln(1.005)=ln(13709.60)\\\\\\n = \dfrac{ln(13709.60)-ln(8000)}{ln(1.005)}=108[/tex]
So, we need 108 months to reach this amount, which means 108/12=9 years.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Write each ratio as a fraction in simplest form.
a) 9 miles to 15 miles
b) 6 1/3 ounces to 9 1/2 ounces
in the diagram ,a and 46° are complementary angles. It is given that a and b are supplementary angles and the angle conjugate to c is 283°. Calculate the values of a,b,c and d. pleaseeeee answer soonn
Answer:
[tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Step-by-step explanation:
It is given that a and 46° are complementary angles.
[tex]a+46^{\circ}=90^{\circ}[/tex]
[tex]a=90^{\circ}-46^{\circ}[/tex]
[tex]a=44^{\circ}[/tex]
It is given that a and b are supplementary angles.
[tex]a+b=180^{\circ}[/tex]
[tex]44^{\circ}+b=180^{\circ}[/tex]
[tex]b=180^{\circ}-44^{\circ}[/tex]
[tex]b=136^{\circ}[/tex]
Angle conjugate to c is 283°.
[tex]c+283^{\circ}=360^{\circ}[/tex]
[tex]c=360^{\circ}-283^{\circ}[/tex]
[tex]c=77^{\circ}[/tex]
Sum of all angles at a point is 360 degrees.
[tex]a+b+c+d+46^{\circ}=360^{\circ}[/tex]
[tex]44^{\circ}+136^{\circ}+77^{\circ}+d+46^{\circ}=360^{\circ}[/tex]
[tex]d+303^{\circ}=360^{\circ}[/tex]
[tex]d=360^{\circ}-303^{\circ}[/tex]
[tex]d=57^{\circ}[/tex]
Therefore, [tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
A manufacturing company has an old machine which produces 25 components per hour. The company has recently installed a new machine which produces 35 components per hour. Yesterday, both machines were in operation for different periods of time. If 430 components were produced when the total number of hours of operation was 14 hours, determine for how many hours each machine was in operation
Answer: old machine 150, new machine 280
Step-by-step explanation:
given data:
Old machine = 25t
New machine = 35t
where t = hrs
we dont know the time for old machine so we assume it to be ( t ),
while that of the new machine is ( 14-t ) hours for new machine, and sum of 430 components.
therefore;
25t +490 - 35t = 430
-10t = -60
divide both sides by -10
t = 6 hours for the first machine.
6hrs * 25 components /hr
= 150 component parts For old machine.
for new machine
= 14 - t ........... eq1.
where ( t = 6 ), substitute t into the equation
= 14 - 6
= 8 hours for the second machine
= 8 * 35
= 280 components parts
Explain how estimating the quotient helps you place the first
digit in the quotient of a division problem.
Step-by-step explanation:
look at the picture and if you still need help let me know or if this doenst help then well im sorry lol
Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2
pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per
pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate
the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?
Answer:
price per pound of apple = $1.25
price per pound of banana = $0.75
Step-by-step explanation:
Your first question is what value should you multiply the second equation by in order to eliminate the y terms.
The number should be 3. Let us multiply the first equation by 2 and the second equation by 3 and see how y will be eliminated.
10x + 6y = 17...............(i)
9x + 6y = 15.75...........(ii)
10x - 9x = x
6y - 6y = 0
17 - 15.75 = 1.25
x = 1.25
let us find y
10x + 6y = 17...............(i)
10(1.25) + 6y = 17
12.5 + 6y = 17
6y = 17 - 12.5
6y = 4.5
divide both sides by 6
y = 4.5/6
y = 0.75
In order to eliminate y term from the system of equations we multiply equation 2 by -3.
The price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
Given equations,
[tex]5x + 3y = 8.5[/tex].........(1)
[tex]3x + 2y = 5.25[/tex].......(2)
Here x is the cost per pound of apples, and y is the cost per pound of bananas.
According to the question, multiply the first equation by 2, we get
[tex]10x+6y=17[/tex].....(3)
So, in order to eliminate y term from the system of equations we multiply equation 2 by -3, we get
[tex]-9x-6y=15.75[/tex].....(4)
Now Adding (3) and (4) equation, we get
[tex]x=1.25[/tex]
Putting the above value of x in equation 3 we get,
[tex]10\times1.25+6y=17\\12.5+6y=17\\6y=17-12.5\\6y=4.5\\y=\frac{4.5}{6} \\y=0.75[/tex]
Hence the price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
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By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
What is the range of the function f(x)=3/4|x|-3
Range is [tex]y\in[-3,+\infty)[/tex].
Hope this helps.
im not sure what it is asking me to do
Answer:
0.79Step-by-step explanation:
[tex]p(x \leqslant 0) = p( - 5) + p( - 3) + p( - 2) + p(0)[/tex]
[tex] = 0.17 + 0.13 + 0.33 + 0.16 [/tex]
[tex] = 0.79[/tex]
Hope this helps...
Best regards!!
Searches related to Searches related to A motorboat travels 135 kilometers in 3 hours going upstream. It travels 183 kilometers going downstream in the same amount of time. What is the rate of the boat in still water? what is the rate of the current?
Answer:
[tex]\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }[/tex]
Step-by-step explanation:
Hello, let's note v the rate of the boat and r the rate of the current. We can write the following
[tex]\dfrac{135}{v-r}=3=\dfrac{183}{v+r}[/tex]
It means that
[tex]135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}[/tex]
But we can as well use the second equation:
[tex]3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}[/tex]
and then
[tex]\boxed{v=\dfrac{159*8}{24}=53}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Determine the domain of the function. f as a function of x is equal to the square root of two minus x.
x ≤ 2
All real numbers
x > 2
All real numbers except 2
Answer:
A. x <= 2
Step-by-step explanation:
The domain of a real function should be all real numbers. In
f(x) = sqrt(2-x)
we need 2-x to be non-negative, therefore
2-x >= 0
which implies
x <= 2
Answer:
[tex]\Huge \boxed{{x\leq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=\sqrt{2-x}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.
[tex]2-x\geq 0[/tex]
[tex]-x\geq -2[/tex]
[tex]x\leq 2[/tex]
The domain of the function is x ≤ 2.
The function y = sin^?1(3x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative. d dx [f(g(x))] = f '(g(x))g'(x) For the given function sin^?1(3x + 1), the "inside" function is 3x + 1 and the "outside" function is f(x) = arcsin(x).
Recall that the derivative of y = sin?1(x) is y' =__________?
Answer:
dy/dx = 3/√1-(3x+1)²
Step-by-step exxplanation:
Given the inverse function y = sin^-1(3x+1), to find the derivative of the expression, we will use the chain rule as shown;
Let u = 3x+1 ...1
y = sin⁻¹u ...2
From equation 1, du/dx = 3
from equation 2;
Taking the sin of both sides;
siny = sin(sin⁻¹u)
siny = u
u = siny
du/dy = cosy
dy/du = 1/cosy
from trig identity, cos y = √1-sin²y
dy/du = 1/√1-sin²y
Ssince u = siny
dy/du = 1/√1-u²
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/√1-u² * 3
dy/dx = 3/√1-u²
Substituting u = 3x+1 into the final equation, we will have;
dy/dx = 3/√1-(3x+1)²
Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known. The data obtained are as follows:
n_1 = 10
x_1 = 87.6
σ_1 = 1
n_2 = 12
x^2 = 74.5
σ_2 = 1.5.
Required:
If μ _1 and μ _2 denote the true mean tensile strengths for the two grades of spars. Construct a 90 percentage confidence interval on the difference in mean strength.
Answer:
(12.141, 14.059)
Step-by-step explanation:
Explanation is provided in the attached document.
Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours
Answer:
3.27 hours
Step-by-step explanation:
Calculate the difference in speed and distance between the trains.
The relative speed:
101 - 90 = 11 mph
Difference in distance:
42 - 6 = 36 miles
[tex]time=\frac{distance}{speed}[/tex]
[tex]t=\frac{36}{11}[/tex]
[tex]t = 3.27[/tex]
Answer:
yeah she is correct
Step-by-step explanation:
YOU WILL GET 30 POINTS AND BRAINLIEST IF YOU GET THIS CORRECT AND ANSWER THIS IN 5 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 3x + 400 f(x) = 3x + 391 f(x) = −3x + 391 f(x) = −3x + 400
Answer:
f(x)= -3x + 400
Step-by-step explanation:
[tex]\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }[/tex]
[tex]\frac{x-3}{13-3} =\frac{y-391}{361-391}[/tex]
-3 ( x-3 ) = (y - 391 )
-3x + 400
Answer:
he is correct
Step-by-step explanation:
Change Y - 4X = 0 to the slope-intercept form of the equation of a line.
Answer:
y=4x
Step-by-step explanation:
Add 4x to both sides to get y=mx+b
0 is y-intercept.
4x is the slope.
Limit of f(t) as t approaches 0. f(t) = (t sin(t)) ÷ (1-cos(t))
Recall the Pythagorean identity,
[tex]1-\cos^2t=\sin^2t[/tex]
To get this expression in the fraction, multiply the numerator and denominator by [tex]1+\cos t[/tex]:
[tex]\dfrac{t\sin t}{1-\cos t}\cdot\dfrac{1+\cos t}{1+\cos t}=\dfrac{t\sin t(1+\cos t)}{\sin^2t}=\dfrac{t(1+\cos t)}{\sin t}[/tex]
Now,
[tex]\displaystyle\lim_{t\to0}\frac{t\sin t}{1-\cos t}=\lim_{t\to0}\frac t{\sin t}\cdot\lim_{t\to0}(1+\cos t)[/tex]
The first limit is well-known and equal to 1, leaving us with
[tex]\displaystyle\lim_{t\to0}(1+\cos t)=1+\cos0=\boxed{2}[/tex]
A group of children is trying to share a pile of stickers. If every
child gets two stickers, there will be 7 stickers left over. If two
children do not get any stickers, then each of the remaining
children will get exactly 3 stickers.
How many children are in the group?
Answer:
7 children
Step-by-step explanation:
Answer:
7 children is the correct answer
and you follow me if you can't I will unfollow you
A local orchestra is holding a charity concert concert at the community center. Each adult ticket $12, and child ticket costs $8. The organizers of the event hope to raise no less than $2,500, and the community center can seat up to 280 people. This graph and system in inequalities represent this situation, where x represents the number of adult tickets and y represents the number of child tickets. 12x + 8y> 2,500. X + y < 280
The answer is (180,80)
To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.
InequalityThe given question is an inequality situation where we are asked to use graph to solve.
The data given are
adult ticket = $12child ticket = $8Total amount raised = $2500Total number of people = 280The inequality for this problem is given is as
[tex]12x + 8y > 2500\\x + y < 280[/tex]
Kindly find the attached image as the graph and solution to this problem.
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A line passes through the points ( – 4, – 2) and ( - 1, - 2). Determine the slope of the line.
Answer: -4/3
Step-by-step explanation:
Formula to find a slope of two given points is
y(sub2) - y(sub1) / x(sub2) - x(sub1)
Plug the values in to get the answer.
-2 - 2 / -1 - (-4)
-4/3
please please please help me. i need to pass, will do anything. ANYTHING!
Answer:
[tex]d \approx 5.8[/tex]
Step-by-step explanation:
Just use the distance formula.
[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]
[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]
[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]
[tex]d=\sqrt{9+25}[/tex]
[tex]d=\sqrt{34[/tex]
[tex]d \approx 5.8[/tex]
Explain the connection between the chain rule for differentiation and the method of u-substitution for integration.
Answer:
Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
Step-by-step explanation:
Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:
[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]
Let integrate both sides in terms of x:
[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]
[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.
Find the unknown side length, x. Write your answer in simplest radical form.
Answer:
Correct option: D
Step-by-step explanation:
In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:
[tex]a^2 = b^2 + c^2[/tex]
Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).
So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:
[tex]x^2 = 40^2 + 42^2[/tex]
[tex]x^2 = 1600 + 1764[/tex]
[tex]x^2 = 3364[/tex]
[tex]x = 58[/tex]
So the correct option is D.
Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
what is the constant of proportionality for 4y=16
Answer:
Step-by-step explanation:
y=4x
1). f(x) = 3x + 15 then what's f^-1(x)?
Answer:
Step-by-step explanation:
f(x)=3x+15
let f(x)=y
y=3x+15
flip x and y
x=3y+15
3y=x-15
y=1/3 x-5
or f^{-1}x=1/3 x-5
Please explain this to me If f(x)=4x-2 than f(x-1)= A. 4x^2-6x+2 B. 4x^2+2x+2 C. 4x+2 D. 4x-6 E. 4x-1
Answer:
D. 4x − 6
Step-by-step explanation:
f(x) = 4x − 2
f(x−1) = 4(x−1) − 2
f(x−1) = 4x − 4 − 2
f(x−1) = 4x − 6
Find the 12th term of the following geometric sequence.
10, 30, 90, 270, ...
Answer:
r = 90/30
r = 3
T12 = 10 × 3¹¹
T12 = 1771470
Which of the following can be calculated using the formula c=2r ?
A.
Area of a circle
B.
Circumference of a circle
C.
Arc length of a circle
D.
Diameter of a circle
Answer:
B. Circumference of a circle
Step-by-step explanation:
The circumference of a circle can be found using formula 2πr where r is the radius of circle.
What is the circumference of a circle?A circle's or an ellipse's circumference is its perimeter. The circumference would be the length of the circle's arc, if the circle were opened up and straightened out to a line segment, in other words.
Here, we have,
Suppose the radius of a circle is 5cm
So, we can find the circumference by using formula 2πr
Circumference = 2 × π × 5 = 10π cm.
Hence, The circumference of a circle can be found using formula 2πr where r is the radius of circle.
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complete question;
The circumference of a circle can be found using the formula c 2r
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year. P = $7000, r = 0.2%, t = 6months
Answer:
$7
Step-by-step explanation:
Simple interest formula:
I = Prt
6 months = 6 * 30 days = 180 days
1 year = 360 days
t = (180 days)/(360 days) = 0.5
I = $7000 * 0.002 * 0.5
I = $7
Answer:
$7
Step-by-step explanation:
Recall that simple interest is given by
I = Prt,
Where :
I = interest (we are asked to find this)
P = principal amount = given as $7000
r = rate = given as 0.2% = 0.002
t = time in years = given as 6 months = 0.5 years
SImply substitute the known values into the equation above:
I = Prt
= (7000)(0.002)(0.5)
= $7
VW=40in. The radius of the circle is 25 inches. Find the length of CT.
Answer:
The answer is B. 40 inches.
Step-by-step explanation:
The question starts by telling you that line VW is equal to 40 in. If you look at the picture you can see it is divided into 2 equal parts of 20 in each. If you look at line CT, you can see that there are the same marks meaning that those segments are also 20 in. That means that line CT and line VW are equal and that line CT is equal to 40 in.