Answer: When r= 9.5% , time = 7.3 years
When r= 2.5% , time = 27.7 years
Step-by-step explanation:
Exponential equation for compounded continuously:
[tex]A=Pe^{rx}[/tex] , where P= Principal value invested , r= rate of interest, x= time
Given : P= $6,000
A = 2P= 2 ($6,000) = $12,000 (i)
When r= 9.5%= 0.095
[tex]A= 6000e^{0.095x}[/tex] (ii)
From (i) and (ii)
[tex]6000e^{0.095x}=12000\\\\\Rightarrow\ e^{0.095x}=2\\\\\Rightarrow\ \ln e^{0.095x} =\ln 2\\\\\Rightarrow\ 0.095x=0.693147\\\\\Rightarrow\ x=\dfrac{0.693147}{0.095}=7.296284210\approx7.3 \text{ years}[/tex]
For r= 2.5% = 0.025
[tex]6000e^{0.025x}=12000\\\\\Rightarrow\ e^{0.025}=2\\\\\Rightarrow\ \ln e^{0.025x} =\ln 2\\\\\Rightarrow\ 0.025x=0.693147\\\\\Rightarrow\ x=\dfrac{0.693147}{0.025}=27.72588\approx27.7 \text{ years}[/tex]
HELPPPPPPPPP!!!
What is z/
W
0-4 + 16i
O 6 + 10i
O 7+11i
O 8+2i
The value of z/w is, (8 + 2i)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The graph is shown in figure.
And, The point z = (6 + 10i)
The point w = (1 + i)
Now,
We can find the value of z/w is,
⇒ z/w = (6 + 10i) / (1 + i)
= (6 + 10i) (1 - i) / (1 + i) (1 - i)
= (6 - 6i + 10i - 10i²) / (1 - i²)
= (6 + 4i + 10) / (1 + 1)
= (4i + 16) / 2
= (8 + 2i)
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Write a polynomial function in factored form of least that the given zeros and a leading coefficient of 1.
1. -6, 3, 5
2. 2, -2, -6i
Write a polynomial function in standard form of least degree that have real coefficients, the given zeros, and a leading coefficient of 1.
3. -1, 1, 7
4. 3, -3, -2i
9514 1404 393
Answer:
p(x) = (x+6)(x-3)(x-5)p(x) = (x-2)(x+2)(x^2 +36)p(x) = x^3 -7x^2 -x +7p(x) = x^4 -5x^2 -36Step-by-step explanation:
Each root r gives rise to a binomial factor (x-r). Each complex root also has a conjugate root, so roots ±ri give rise to a binomial factor (x^2 +r^2).
__
1. p(x) = (x -(-6))(x -3)(x -5)
p(x) = (x+6)(x-3)(x-5)
__
2. p(x) = (x -2)(x -(-2))(x^2 +6^2)
p(x) = (x -2)(x +2)(x^2 +36)
__
If you want standard form, you can start with factored form, then multiply it out.
3. p(x) = (x -1)(x +1)(x -7) = (x^2 -1)(x -7) = (x^2 -1)x +(x^2 -1)(-7)
p(x) = x^3 -7x^2 -x +7
__
4. p(x) = (x -3)(x +3)(x^2 +2^2) = (x^2 -9)(x^2 +4)
p(x) = x^4 -5x^2 -36
Now given a rope hanging from the top of a pole. The end lying on the ground is 3 chi long. When tightly stretchedit is 8 chi from the bottom of the pole. Let x represent the height of the pole. Tell: how long is the rope and how high is the pole
Answer:
Height of the pole = 9.17 chi.
Length of the rope = 12.17 chi.
Step-by-step explanation:
Given that the rope is hanging from the top of a pole having height x chi and the portion of the rope lying on the ground is 3 chi.
So, the length of the rope= x + 3 chi.
Let AB represents the pole in the figure, and one end of the rope is at point A.
When the rope is tightly stretched, let C be the other end of the rope as shown in the triangle.
The length of the rope = AC.
\Rightarrow AC=x+3 chi.
Distance from the bottom of the pole, point A, to the other end of the pole, point B, is 8 chi.
So, BC=8 chi.
As the triangle ABC is a right-angled triangle, so by using Pythagoras theorem,
[tex]AC^2= AB^2+BC^2[/tex]
[tex]\Rightarrow (x+3)^2=x^2+8^2[/tex]
[tex]\Rightarrow x^2+6x+9=x^2+64[/tex]
[tex]\Rightarrow 6x=64-9=55[/tex]
[tex]\Rightarrow x=55/6=9.17[/tex] chi.
Hence, the height of the pole, [tex]AB=x=9.17[/tex] chi,
and the length of the rope, [tex]x+3=9.17+3=12.17[/tex] chi.
Suppose a stock drops in value by 60% one week, then increases in value the next week by 75%. Is the value higher or lower than where it started
Answer:
Lower
Step-by-step explanation:
Use the number 100 to see how the value changes:
First, calculate the 60% drop:
100(0.4)
= 40
Then, calculate the 75% increase:
40(1.75)
= 70
So, since 70 is smaller than 100, the value is lower than where it started.
Gina wants to make
hamburgers for 12 people.
Her recipe serves 8 people
and calls for 4.5 pounds of
ground beef. How much
ground beef should
Gia purchase?
h
Answer:
6.75 pounds
Step-by-step explanation:
This question is of direct variation. We will use x as our answer. 8 is 2/3 of 12, so 4.5 should be 2/3 of x. We can now make an equation.
[tex]4.5=\frac{2}{3} x\\4.5*\frac{3}{2} =\frac{2}{3} x*\frac{3}{2} \\6.75=x[/tex]
In order to solve the equation, we multiply both sides by the reciprocal of 2/3, which is 3/2.
* stands for multiplication
From solving our equation, we get 6.75. We can't forget the units, so the answer is 6.75 pounds.
1/4 es un decimal exacto
Answer:
0.25
Step-by-step explanation:
Decimal exacto
La parte decimal de un número decimal exacto está compuesta por una cantidad finita de términos.
Ejemplos:
15.125
0.1
3.0000001
Si en sus factores sólo aparecen 2, 5 o ambos, la fracción es decimal exacta.
Help please! I’ll give brainliest!
Answer:
i think the answer is B
i am sorry if this is wrong
Step-by-step explanation:
25 miles/hour =_meters/minute
What are steps I need to take to find a? Please include working out ❤️❤️
A bike travels 24 miles in 3 hours. How many miles will the bike travel in 12 hours?
Answer:
72
Step-by-step explanation:
24 / 3 = 8
so
8*7 = 72
Answer:
72
Step-by-step explanation
24 / 3 = 8
so
8*7 = 72
Plz answer quick I need to get it bc it’s a quiz
Answer:
slope equals 2
Step-by-step explanation:
graph points and calculate rise over run
Gavin has a box of crayons. There are four purple crayons, three black crayons, three blue crayons, and two red crayons. What is the probability Gavin will draw a purple crayon put it on the table and then draw another purple
Answer:
4/12
Step-by-step explanation:
classify the triangle based off of the measurements of its sides 30m, 30m
Answer:
i got it
its an isosceles triangle bc two sides are equal.
the cube_____of 27 is 3.
Answer:
3
Step-by-step explanation:
Answer:
the cube ROOT of 27 is 3.
Step-by-step explanation:
Find the product
(3x+4y)(x+y)
Answer:
Step-by-step explanation:
(3x+4y)(x+y)
Solution=3x^2+4xy+3xy+4y^2
=3x^2+7xy+4y^2
PLS answer fast!!!! I am literally in tears. Brainliest to the first person to answer it correctly
Answer:
-682
Step-by-step explanation:
I worked it out and got -682
What additional information could be used to prove that triangle XYZ is congruent to triangle Fe.g. using asa or aas check all that apply
Answer:
its the first one and the last one ..that's the answer.
Find the value of the missing angle
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of 28
stores this year shows mean sales of 64 units of a small appliance, with a standard deviation of 13.8 units. During the same point in time last year, an SRS of 28 stores had mean sales of 48.958 units, with standard deviation 15.4 units. An increase from 48.958 to 64 is a rise of about 24%.
1. Construct a 99% confidence interval estimate of the difference μ1−μ2
μ1−μ2, where μ1 is the mean of this year's sales and μ2 is the mean of last year's sales.
(b) The margin of error is
2. At a 0.01 significance level, is there sufficient evidence to show that sales this year are different from last year?
Answer:
Confidence interval = (4.61972, 25.46428)
Margin of Error = 3.9078675
Step-by-step explanation:
Given that :
This year:
Mean (μ1) = 64
Standard deviation (s1) = 13.8
Sample size (n1) = 28
Last year:
Mean (μ2) = 48.958
Standard deviation (s2) = 15.4
Sample size (n2) = 28
99% confidence interval estimate of the difference μ1−μ2
α = 1 - 99% = 0.01
(μ1−μ2) ± t0.01,27 * (√s1²/n1 + s2²/n2)
t0.01, 27 = 2.770683 (t value calculator)
√s1²/n1 + s2²/n2 = √13.8^2/28 + 15.4^2/28 = 3.9078675
(64 - 48.958) ± 2.667(3.9078675)
15.042 ± 10.42228
(15.042 - 10.42228), (15.042 + 10.42228)
(4.61972, 25.46428)
The margin of error :
√(s1²/n1) + (s2²/n2)
√(13.8^2/28) + (15.4^2/28)
√(6.8014285 + 8.47)
√15.2714285
= 3.9078675
Tiffany took her friends out to dinner. If the dinner was $29.53 and she gave a 20% tip, how much money did she spend on dinner?
Answer: The answer is 35.43 because 29.53 times 20% is 5.90, so you add 5.90 to 29.53 to get 35.43.
I need help with Kumon math level I 187 B
Answer:
attached is the answer :)
Step-by-step explanation:
The length of the tangent AB is [tex]\sqrt{2a^{2}+2b^{2} }[/tex] if the radii of the largest circle is a and the radii of the smallest one is b.
What is the tangent?It is a line that touches a single point on the circle.
How to determine the length of that tangent?Firstly we have to draw a perpendicular from O to the radii of the smallest circle. In this way AOLB becomes a rectangle. We let the point where the bisector intersect the radii as L.
OA=a
Lb=a also
O'L=b-a
In triangle OLO' we use pythagoras to calculate the value of OL which wil then equal to AB so,
OL=[tex]\sqrt{(b-a)^{2}+(a+b)^{2} }[/tex]
=[tex]\sqrt{2a^{2}+2b^{2} }[/tex]
It will be the length of AB also.
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can you help me with it please
Answer:
[tex] \frac{20}{29}[/tex]
Step-by-step explanation:
Equation of unit circle is:
[tex] x^2 + y^2 = 1[/tex]
Plug [tex] y = \frac{-21}{29}[/tex] in above equation.
[tex] x^2 + \bigg( \frac{-21}{29}\bigg)^2 = 1\\\\
x^2 + \frac{441}{841} = 1\\\\
x^2 = 1-\frac{441}{841}\\\\
x^2 = \frac{841-441}{841}\\\\
x^2 = \frac{400}{841}\\\\
x =\pm\sqrt{ \frac{400}{841}}\\\\
x =\pm\frac{20}{29}\\\\
[/tex]
Since, point P is in the fourth quadrant.
Therefore, x - coordinate should be positive.
[tex] \huge \red {\boxed {\therefore x =\frac{20}{29}}} \\\\
[/tex]
What is the value of the expression when x = 4 and y = 3?
3x² + 5y
A.27
B.38
C.63
D.159
Answer:
63
Step-by-step explanation:
3x^2+5y
Where X=4,Y=3
So
=3×4×4+5×3
=48+15
=63
So 63 is the answer
Answer:
C.63
Step-by-step explanation:
3x4²+5x3
4² = 16
3x16+5x3
Then
3x16 = 48
5x3 =15
48+15 equals 63
The answer is 63
Have a Good Day!!!!
Simplify: 5 -3 • 5 5
25 8
25 -15
5 -3
5 2
Does -3 and -2 make a right triangle
Answer:
There is no such thing as negative distances. In order to do Pythagoras theorem you need to know which one is the hypotenuse
Daniel has 1615 Skittles stored in boxes. If there are 85 boxes, how many Skittles must go in each box?
Answer:
19
Step-by-step explanation:
While it's really easy to just divide, I'm sure your teacher wants an equation so:
1615=85x here x= skittle boxes
1615/85=x In this line you can use divide to cancel out the multiplication, giving you
x=19
Select the correct answer. Given:In quadrilateral WXYZ , and bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram. Statement Reason 1. and bisect each other. given 2. WA = YA XA = ZA definition of bisection 3. m∠YAZ = m∠XAW Vertical Angles Theorem 4. SAS criterion for congruence 5. ∠ YWX ≅ ∠WYZ Corresponding angles of congruent triangles are congruent. 6. || converse of Alternate Interior Angles Theorem 7. m∠XAY = m∠ZAW Vertical Angles Theorem 8. ∆XAY ≅ ∆ZAW SAS criterion for congruence 9. ∠XZW ≅ ∠ZXY Corresponding angles of congruent triangles are congruent. 10. || converse of Alternate Interior Angles Theorem 11. Quadrilateral WXYZ is a parallelogram. definition of parallelogram What is the missing statement in this proof? A. ∆XWY ≅ ∆ZYW B. ∆YAZ ≅ ∆WAX C. WY = XZ D. ||
Answer:
YAZ WAX is the answer...i couldn't put it as its shown on the problem but its the same letters
Step-by-step explanation:
i took the test and got 5/5....this answer was correct
WILL GIVE BRAINLIEST 20 POINTS!!! PLS HELP!!!?!?!?!?! DO NOT COPY AND PASTE FROM OTHER QUESTIONS OR I WILL REPORT U AND DELETE UR ANSWER!!!!
The functions f(x) and g(x) in the table below show Jane's and Mariah's savings respectively, in dollars, after x days. Some values are missing in the table.
x(years) 1 2 3
g(x) = 3x
Jane's savings in dollars 3 9
f(x) = 3x + 3
Mariah's savings in dollars 6 9
Which statement best describes Jane's and Mariah's savings in the long run?
Jane will save more than Mariah.
Mariah will save more than Jane.
The savings will increase by the same factor for both.
The savings will increase by the same percentage for both.
Answer:
Mariah will save more than Jane.
Step-by-step explanation:
i think
Which equation represents the number of points in the problem below?
A test is worth 60 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 5 points. If the test has 15 questions, how
many multiple-choice questions are there?
O A. 2m+ 5s = 60
B. m + s = 60
O C. 2m + 5s +15 = 60
O D. 2m + 5s = 15
Answer:
Step-by-step explanation:
Let the number of MC questions = x
Let the number of SA questions = y
x + y = 15
2x + 5y = 60
Multiply the top equation by 2
2x + 2y = 30
Put this underneath the second equation and subtract
2x + 5y = 60
2x + 2y = 30 Subtract
3y = 30
y = 10 Subtract
2y = 20
y = 10
x + y = 15
x + 10 = 15
x = 5
Is this relation a function?
Answer:
yes though i am not completely sure
Step-by-step explanation: