27. How long will it take to double an investment at 4.9% compounded continuously? Round your answer to the nearest tenth of a year.
Answers
Recall that to calculate the amount after t years that is compounded continously at a intereset rate r of an investment of a principal P is given by the formula
\(A=Pe^{rt}\)In this case, the initial amount is P. Since we want to calculate the value of t for which A is exactly 2*P we have the equation
\(2P=Pe^{rt}\)we know that r=0.049 and we want to solve this equation for t. WE start by dividing both sides by P. So we get
\(2=e^{0.049t}\)If we apply the natural logarithm on both sides, we get
\(0.049t=\ln (2)\)so if we divide both sides by 0.049, we get
\(t=\frac{\ln (2)}{0.049}=14.14145860\)which rounded to the nearest tenth of a year is 14.1 years
Related Questions
I'll Give brainliest to whoever answers is correct
Answers
Answer:
52
Step-by-step explanation:
RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.
Answer:
52 degrees
Step-by-step explanation:
right angle = 90
90-38=52
So RTQ = 52 degrees
what is the nth term in a cube number sequence
Answers
Answer:
cube numbers: 1, 8, 27, 64, 125, ... - the nth term is. triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots).Step-by-step explanation:
IF IT HELPED UH PLEASE MARK ME A BRAINLIEST :-)please please help last text then finals l give brainliest
Answers
1. The x - intercepts of the parabola are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex of the parabola is at (5, 80).
What is a parabola?A parabola is a curved shape
1. Given the parabola above, to find the x - intercepts, we proceed as follows.
The x-intercepts are the points at which the graph cuts the x-axis.
They are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.
The plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex is the maximum point on the graph.
So, we see that the vertex is at x = 5 s and y = 80 ft
So, the vertex is at (5, 80).
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Which function below is the inverse of f(x) = The quantity of four x minus three, over two. ? (1 point)
Answers
Answer:
The inverse of f(x) is
\(f^{-1} (x) = \frac{2 x+3}{4}\)
Step-by-step explanation:
Explanation:-
Given \(f(x) = \frac{4 x-3}{2}\)
Inverse of f(x)
f(x) is a one-one function
let f(x₁) and f(x₂) be two functions are
\(f(x_{1} ) = \frac{4 x_{1} -3}{2}\)
\(f(x_{2} ) = \frac{4 x_{2} -3}{2}\)
⇒ \(\frac{4 x_{1} -3}{2} = \frac{4 x_{2} -3}{2}\)
⇒ 4 x₁ - 3 = 4 x₂ - 3
⇒ 4 x₁ = 4 x₂
⇒ x₁ = x₂
Given function is one-one function
y = f(x) = \(\frac{4 x-3}{2}\)
⇒ 2 y = 4 x - 3
⇒ 4 x = 2 y + 3
⇒ \(x = \frac{2 y + 3}{4}\)
⇒ f⁻¹(x) \(= \frac{2 y + 3}{4}\)
Given function f(x) is onto function
Therefore f(x) is one-one and onto function
\(f^{-1} (x) = \frac{2 x+3}{4}\)
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
Answers
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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i get a 25% discount (means decrease) at macys store. if i find a dress i like for $80, how much will i have to pay for it?
Answers
Answer:
you will pay $60
Step-by-step explanation:
25% (1/4) of 80 is 20
subtract 20 from the total (80)
80 - 20 = 60
$60
Answer:
60
Step-by-step explanation:
So if you get 25% off, you're basically paying 75%.
So first, convert the percentage to a decimal:
75% = 75/100 = 0.75
Now just multiply the decimal by the total cost:
80$ (0.75) = $60
Pleasee helpppl
Find the most important variable in the problem.
A rower of a canoe can row at a rate of 5 miles per hour in calm water. With
the current, she can row 14 miles in the same time it takes her to row 6 miles
against the current. What is the rate of the current?
A. the rowing rate in calm water
B. the rate of the current
c. the time it takes to row upstream
Answers
Answer:
B
Step-by-step explanation:
The only reason she can go faster is because of the rate of the current.
Answer: B
Step-by-step explanation: I just did the quiz
In a School sports day, the number of points the 8th grade team scores is given by 3x + 2y + z,
is the red team; y is yellow team, and z is the blue team. What is the total number of points scored by 10* graders when red scores 3 three points, yellow 5 points, and blue 2 points?
Answers
The total number of points scored is given by the equation A = 23 points
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total points scored be represented as A
Now , the equation will be
Substituting the values in the equation , we get
A = 3x + 2y + z be equation (1)
where x = red team = 3 points
y = yellow team = 5 points
z = blue team = 2 points
So , A = 3 ( 3 ) + 2 ( 5 ) + 2
A = 9 + 10 + 2
A = 21 points
Hence , the equation is A = 21 points
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question included as a photo
Answers
a. The linear Equations :
3x + (x+42)= 90
⇒4x +42 =90
b. ∠ 1 = 36° and ∠2 =54°
How do you find the solution to a linear equation?In one of the equations, separate one of the two variables.In the other equation, substitute the expression that is equal to the isolated variable from Step 1.For the final variable, solve the linear equation.Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the coordinate of this point.
here
4x+42 = 90 ⇒ x=12
∠1 =4 x 12=36 and ∠2 = 12+42=54
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at a baseball game a vender sold a combined total of 141 sodas and hot dogs. the number of sodas was 51 more than the number of hotdogs sold. Find the number of sodas sold and the number of hot dogs sold
Answers
Hot Dogs: 45
HELP ASAP LOTS OF POINTS AND BRIANLY
Answers
Answer: Sorry doesn't really show anything of pdf...
Step-by-step explanation: I will help but it's not showing or it's just me!?
Which of the following is the absolute value parent function?
O A. F(x) = 1/x
O B. F(x) = [X]
O C. F(x) = x
O D. Rx) = (x1 - 1
Answers
Answer:
Answer c is the correct one
The absolute value parent function is typically denoted as f(x) = |x|.
None of the given options matches the absolute value parent function.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The absolute value parent function is typically denoted as f(x) = |x|. Therefore, none of the given options matches the absolute value parent function exactly.
f(x) = [x], represents the greatest integer function, also known as the floor function, which returns the largest integer less than or equal to x.
f(x) = 1/x, is a rational function, which has a horizontal asymptote at y=0 and a vertical asymptote at x=0.
f(x) = x, is a linear function, which has a constant slope of 1.
f(x) = (x-1), is a linear function with a slope of 1, but it is shifted to the right by 1 unit.
Therefore,
The absolute value parent function is f(x) = |x|.
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‼️PLEASE HELP MY FINAL IS TODAY‼️‼️‼️
9. Determine mzB. Round to the nearest degree.
35
C
B
a.
34°
43°
C. 47°
d. 56°
b.
24
Answers
Answer:
The answer is 56°. Angle B is an exterior angle of triangle ABC, which means it is equal to the sum of the two remote interior angles (angles A and C). Angle A is 35°, angle C is 121°, so angle B is 56°.
Help Pleasee!!! I’ll make you the brainlyest!!!! Pleaseee
Answers
Answer:
theta = 210°
Step-by-step explanation:
To convert we radians to degrees all we have to do is multiply the radians by π/180:
radians * (180 / π) = degrees
((7π) / 6) * (180 / π) = 210°
What is the equivalent to the product below when x>_0?
√5x² •√15x²
Answers
√(5x²) • √(15x²) = √(5x² * 15x²)
Using the property of square roots that √(a * b) = √a * √b, we can simplify further:
√(5x² * 15x²) = √(5 * 15 * x² * x²)
Next, we simplify the numerical part:
√(5 * 15 * x² * x²) = √(75 * x² * x²)
Since x ≥ 0, x² is always non-negative, so we can remove the square root:
√(75 * x² * x²) = x * x * √75
Finally, we simplify the square root of 75:
x * x * √75 = x² * √75
Therefore, the equivalent expression is x² * √75 when x ≥ 0.
Let h(x) = x² - 8x.
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
Answers
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
your avatar
(a) The average rate of change from 3 to 9 can be found by calculating the slope of the secant line connecting the points (3, h(3)) and (9, h(9)).
The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Applying this formula, we have:
m = (h(9) - h(3)) / (9 - 3)
To find the values of h(9) and h(3), we need to substitute 9 and 3 into the function h:
h(9) = 9² - 8(9) = -27 h(3) = 3² - 8(3) = -9
Substituting into the formula for slope, we have:
m = (-27 - (-9)) / (9 - 3) = -18 / 6 = -3
Therefore, the average rate of change from 3 to 9 is -3.
(b) To find the equation of the secant line containing (3, h(3)) and (9, h(9)), we need to find the slope of the line and its y-intercept.
We've already calculated the slope in part (a) as -3. To find the y-intercept, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope, (x1, y1) is a point on the line, and (x, y) are any other points on the line. We can choose either (3, h(3)) or (9, h(9)) as our point.
Let's use (3, h(3)):
y - h(3) = -3(x - 3)
Simplifying, we get:
y = -3x + 18 - 9 y = -3x + 9
Therefore, the equation of the secant line is y = -3x + 9.
Bandhan Bank employee salary after 10 years
Answers
Answer:
- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries
Quadrilateral ABCD shown below, is translated 3 units to the left to create quadrilateral A'BCD
B
D
Which statement is true?
Answers
are these two line parallel to each other??
Answers
Answer:
No
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 1 ← is in slope- intercept form
with slope m = 3
Calculate the slope using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (2,4) and (x₂, y₂ ) = (4, 12) ← 2 ordered pairs from the table
m = \(\frac{12-4}{4-2}\) = \(\frac{8}{2}\) = 4
Parallel lines have equal slopes
The slope of these 2 lines are not equal , thus not parallel
What is the slope of the line shown below?
Answers
Answer:
D
Step-by-step explanation:
The difference in the x coordinate is 10 and the difference in y is 12
12/10 = 6/5
Answer:
It's D. Rise over run is another option to double check.
Step-by-step explanation:
e
3. If y varies inversely as the square of x and x = 6 when y = -18
find y when x = 8
Answers
The calculated value of y when x = 8 is 10.125
Finding the value of y when x = 8From the question, we have the following parameters that can be used in our computation:
y varies inversely as the square of x
Mathematically, this can be expressed as
y = k/x²
So, we have
k = x²y
Given that x = 6 when y = -18, we have
k = 6² * -18
So, we have
k = -648
When x = 8, we have
y = -648/8²
Evaluate
y = -10.125
Hence, the value of y is 10.125
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How much usable meat is a 28-1b raw turkey likely to yield, if it has a41% waste factor? How many 3-oz servings will that give you if youhave no further losses?
Answers
A 28 pound turkey with a 41% waste factor will yield the following usable meat;
\(\begin{gathered} \text{Waste}=28\times\frac{41}{100} \\ \text{Waste}=\frac{1148}{100} \\ \text{Waste=11.48 lb} \end{gathered}\)If the waste factor is now calculated as 11.48 lb, then the amount of usable meat is derived as;
Usable = Total amount - Waste
Usable = 28 - 11.48
Usable = 16.52 lb
Since we already know that one pound
Easy math help picture below problem 4
Answers
Answer: is 126 degrees
Step-by-step explanation:
The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 andz. They are given by the area of the gray region under the curve in the figure. TABLET NORMAL-CURVE AREAS 2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.0160 0.0557 0.0948 0.1331 0.1700 0.2054 0.2389 0.2704 0.2995 0.3264 0.3508 0.0199 0.0596 0.0987 0.1368 0.1736 0.2088 0.0239 0.0636 0.1026 0.1406 0.1772 0.2123 0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.0319 0.0714 0.1103 0.1480 0.1844 0.2190 0.0359 0.0753 0.1141 0.1517 0.1879 0.2224 0.2549 0.2852 0.3133 0.3389 0.3621 0.2257 0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4648 0.4719 0.4778 0.6 0.7 0.8 0.9 1.0 0.2580 0.2881 0.3159 0.3413 0.2324 0.2642 0.2939 0.3212 0.3461 0.2422 0.2734 0.3023 0.3289 0.3531 0.2454 0.2764 0.3051 0.3315 0.3554 0.2517 0.2823 0.3106 0.3365 0.3599 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 1.1 1.2 1.3 1.4 1.5 0.3749 0.3944 0.4113 0.4265 0.4394 0.3770 0.3962 0.4131 0.4279 0.4406 0.3810 0.3997 0.4162 0.4306 0.4429 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4725 0.4783 0.3708 0.3907 0.4082 0.4236 0.4370 0.4484 0.4582 0.4664 0.4732 0.4788 0.3729 0.3925 0.4099 0.4251 0.4382 0.4495 0.4591 0.4671 0.4738 0.4793 0.3830 0.4015 0.4177 0.4319 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 1.6 1.7 1.8 1.9 2.0 0.450S 0.4599 0.4678 0.4744 0.4798 0.4515 0.4608 0.4685 0.4750 0.4803 0.4525 0.4616 0.4692 0.4756 0.4808 0.4535 0.4625 0.4699 0.4761 0.4812 2.1 2.2 2.3 2.4 2.5 0.4826 0.4864 0.4896 0.4920 0.4940 0.4830 0.4868 0.4898 0.4922 0.4941 0.4834 0.4871 0.4901 0.4925 0.4943 0.4850 0.4884 0.4911 0.4932 0.4949 0.4854 0.4887 0.4913 0.4934 0.4951 0.4857 0.4890 0.4916 0.4936 0.4952 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987 0.4838 0.4875 0.4904 0.4927 0.4945 0.4959 0.4969 0.4977 0.4984 0.4988 0.4842 0.4846 0.4878 0.4881 0.4906 0.4909 0.4929 0.4931 0.4946 0.4948 0.4960 0.4961 0.4970 0.4971 0.4978 0.4979 0.4984 0.4985 0.4989 0.4989 2.6 2.7 2.8 2.9 3.0 0.4955 0.4966 0.4975 0.4982 0.4987 0.4956 0.4967 0.4976 0.4982 0.4987 0.4957 0.4968 0.4977 0.4983 0.4988 0.4962 0.4972 0.4979 0.4985 0.4989 0.4963 0.4973 0.4980 0.4986 0.4990 0.4964 0.4974 0.4981 0.4986 0.4990 Also, for 3 - 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999. ^ The entries in Table II are values for which the area to their right under the 1 distribution with given degrees of freedom (the gray area in the figure) is equal toa. TABLE II VALUE OF d.f. Fo.050 os 0.005 d.. 63.657 9.925 1 2 3 4 6.314 2.920 2.353 2.132 2.015 12.706 4.303 3.182 2.776 2.571 0.010 31.821 6.965 4.541 3.747 3.365 1 2 3 4 5.841 4.604 4.032 S S 6 7 6 7 8 1.943 1.895 1.860 1.833 1.812 2.447 2.365 2.306 2.262 2.228 3.143 2.998 2.896 2.821 2.764 3.707 3.499 3.355 3.250 3.169 8 9 9 10 10 11 12 1.796 1.782 1.771 1.761 1.753 13 14 15 2.201 2.179 2.160 2.145 2.131 2.718 2.681 2.650 2.624 2.602 3.106 3.055 3.012 2.977 2.947 11 12 13 15 16 16 17 18 19 20 1.746 1.740 1.734 1.729 1.725 2.120 2.110 2.101 2.093 2.086 2.583 2.567 2.552 2.921 2.898 2.878 2.861 2.845 17 18 19 2.539 2.528 20 21 22 23 24 25 1.721 1.717 1.714 1.711 1.708 2.080 2.074 2.069 2.064 2.060 2.518 2.508 2.500 2.831 2.819 2.807 2.797 2.787 21 22 23 24 25 2.492 2.485 2.056 2.052 26 27 28 29 Inf. 1.706 1.703 1.701 1.699 1.645 2.479 2.473 2.467 2.462 2.326 2.779 2.771 2.763 2.048 26 27 28 29 Inf. 2.045 2.756 2.576 1.960 Question 2 (20 marks) A tutorial school has been running IELTS mock examination for many years. Below is the summary presented by the tutorial school related to the IELTS mock examination in one of the many online classes selected randomly in year 2022. IELTS score in mock examination Number of students <4 0 5 2 6 7 5 15 8 10 3 9 A report presented by this tutorial school 5 years ago indi that the population mean score of IELTS mock examination was 7.05 points and the population proportion of students got 7 points or above was 0.67. (a) Construct a 95% confidence interval estimate of population mean score a student get in the IELTS mock examination in 2022. (b) Test, at 1% level of significance, if the population proportion of students get 7 points or above in 2022 is higher than that in year 2017. (The report must include the (i) null hypothesis and alternative hypothesis, (ii) rejection region(s), (iii) calculation of test statistics, and (iv) conclusion.) (c) If the confidence interval estimate in part (a) is constructed at 99% instead of 95%, would the interval be (1) wider, (II) narrower, or (III) no change in width? (State your answer, no explanation is needed in part (C).)
Answers
From the table, the area between 0 and 2 under the standard normal distribution curve is 0.4772. Therefore, the probability that a random variable having the standard normal distribution will take on a value between 0 and 2 is 0.4772.
16. What product is represented with the following Algebra Tiles?
(2x²+6) (4x+6)
(4x + 4) (6x + 6)
(2x + 2)(2x + 3)
4x+10
Answers
The product that is represented with the algebra tiles is (2x + 2)(2x + 3)
Finding the product that is represented with the algebra tiles?From the question, we have the following parameters that can be used in our computation:
The algebra tiles
Representing the red tile with digit 1
So, we have
Vertical = 2x + 1 + 1 = 2x + 2
Horizontal = 2x + 1 + 1 + 1 = 2x + 3
The product that is represented with the algebra tiles is then calculated as
Product = Vertical * Horizontal
So, we have
Product = (2x + 2)(2x + 3)
Hence, the product is (2x + 2)(2x + 3)
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Find the product 5 x (-10)
Answers
Answer:
-50
Step-by-step explanation:
Answer : 5x (-10) = -50x
Step-by-step explanation: Mutiply 5x10 to get 50
and make sure to at the negative sign because or the negative 10
and add the letter x because of 5x
Then Find The Value Of X
Answers
Answer:
15
Step-by-step explanation:
The given is a right triangle divided into two parts by a sector
so 3x + 45 = 90 subtract 45 from both sides
3x = 45 divide both sides by 3
x = 15
Ben tiene 3 veces la edad de Daniel y es 4 años mayor que él.
¿Cuántos años tiene Ben?
Answers
Answer:
Ben es 6, Daniel es 2
Step-by-step explanation:
No hablo mucho español, ¡pero intentaré dar una respuesta!
In a standard deck of cards (NOT including jokers), there are:
4 suits (diamonds, hearts, clubs, spades)
13 number and face cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King)
2 colors (red, black)
Face cards are Jack, Queen, King
a) What is the probability of drawing a red or black card?
b) What is the probability of drawing a 7 of spades?
c) What is the probability of NOT drawing a Diamond?
d) What is the probability of drawing a black 2?
Answers
hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((
Graph the function. Identify whether or not the graph is a function
Answers
Answer:
No
Step-by-step explanation:
Because a vertical line can intersect the curve more than once, the graph does not represent a function.