Hector invests $10,000 at age 21. He hopes the investments will be worth $150,000 when he turns 50. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Write your answer as a percentage rounded to one decimal place.
Answer:
9.33%
Step-by-step explanation:
Step one:
given
Principal= $10,000
Final amount = $150,000
time = 50-21= 29 years
Required
The rate
Step two:
to solve for the rate we can apply the formula for rate as
r = ln(A/P) /t
r= ln(150000/10000)/29
r= ln(15)/29
r=2.7080502011/29
r=0.0933
r= 0.0933*100
r= 9.33%
The terminal side of Ø is in quadrant II and sin ø = 5/13 What is cos ø?
A. 5/12
B. -12/13
C. -5/12
D. 12/13
Step-by-step explanation:
In Quadrant II, cosine is negative.
We know that sin²x + cos²x = 1, so:
cosx = sqrt[1 - sin²x]
= sqrt[1 - (5/13)²]
= sqrt(144/169)
= -12/13 (since cosx is negative here)
The answer is -12/13. (B)
Option B is correct.
Quadrants and the "cast" Rule:In the first quadrant, the values for sin, cos, and tan are positive.In the second quadrant, the values for sin are positive only.In the third quadrant, the values for tan are positive only.In the fourth quadrant, the values for cos are positive only.
According to the given question
We have, sin ∅ = 5/13
From the trigonometric identities we know that
[tex]sin^{2}[/tex]∅ + [tex]cos^{2}[/tex]∅ =1
substitute the value of sin∅ in the above identity
[tex](\frac{5}{13} )^{2} + cos^{2}[/tex]∅ =1
⇒ [tex]\frac{25}{69} +cos^{2}[/tex]∅ =1
⇒ [tex]cos^{2}[/tex]∅ = 1 - [tex]\frac{25}{169}[/tex]
⇒ [tex]cos^{2}[/tex]∅ = [tex]\frac{169-25}{69} =\frac{144}{169}[/tex]
⇒[tex]cos[/tex]∅ = [tex]\sqrt{\frac{144}{169} }[/tex]
⇒cos∅ = ±[tex]\frac{12}{13}[/tex]
Since, ∅ is in quadrant II, then cos<0
⇒ cos∅ = -[tex]\frac{12}{13}[/tex]
Hence, option B is correct.
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Snare Drum
Backbeats
Bass Guitar
Notes
3
2
90
60
120
80
Part A. Are the two quantities proportional? Justify your answer.
Yes they because they have the same constant proportionality.
Part B. What is the constant of proportionality? *
0.77
Answer : what do i answer
Step-by-step explanation:
Find the zeros of the function.
Enter the solutions from least to greatest.
f(x) = 5x^2 – 20
Answer:
x=-2, 2.
Step-by-step explanation:
5x^2-20=0
factor out the 5
5(x^2-4)=0
5(x+2)(x-2)=0
(x+2)(x-2)=0/5
(x+2)(x-2)=0
x+2=0, x-2=0
x=0-2=-2,
x=0+2=2.
The rectangle shown
I need help with this equation. I'm not that smart so I can't figure it out-
Answer:
x = 0
Step-by-step explanation:
In order to solve for x, first combine both fractions on the left
To add 4x-2/8 + 3+x/4 first find the least common denominator of 8 and 4
It's 8 so multiply the numerator and denominator of 3+x/4 by 8, you would get:
8x+24/32
Multiply 4x-2/8 by 4, you will get:
16x-8/32
Now you can add 16x-8/32 + 8x+24/32, you would get:
24x+16/32
Now you can start to solve for x
Your new equation is 24x+16/32 = 1/2
To solve for x, first multiply diagonally, then solve like a regular equation.
Multiply 24x+16 by 2 to get 48x+32
Then multiply 32 by 1 to get 32
Your new equation is 48x+32=32
Now subtract 32 by 32 to get 48x=0
Now divide 48 by 0 to get x=0
Identify a pair of perpendicular lines in the given figure.
Question 1 options:
p and t
q and t
s and t
p and q
EF is the midsegment of trapezoid ABCD. Determine the value of x. 12.6 F E
The value of x is 5, the correct option is B
What is a Trapezoid?A quadrilateral with one side parallel to the other is a Trapezoid.
The midline in a trapezoid is parallel to its bases and the length is equal to half the sum of the bases.
In the figure attached the length of one of the parallel sides and the midline is given, the other base length has to be determined.
The length of AB = 12.6
The length of the midline EF = 8.8
The value of x =?
From the definition,
8.8 = (12.6 + x) /2
8.8 * 2 = 12.6 +x
x = 5
Therefore,the correct option is B.
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15. Write the first four terms of the sequence:
a. f(n) = −2[tex]n^{2}[/tex] + 4
b. f (1) = 7, f(n)= −4 ∙ f(n-1) − 1 + 15
Answer:
16 17
Step-by-step explanation:
please help me !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
20
Step-by-step explanation:
15 is the mid so +5 is 20 thus 20 is the anser
Please help!!! Thank you!!!
Answer:
1. 180° ∑triangle angles=180°
2. 2x
3. 52°
xx squared - XY + x squared - xy
Answer and Step-by-step explanation:
[tex]x^{2} - xy + x^{2} -xy\\\\2x^{2} -2xy[/tex]
This is the answer.
In case your expression is:
[tex]x^2\:-\:xy\:+\:x^2\:-\:xy[/tex]
Solution:
Given the expression
[tex]x^2\:-\:xy\:+\:x^2\:-\:xy[/tex]
Group like terms
[tex]x^2\:-\:xy\:+\:x^2\:-\:xy=x^2+x^2-xy-xy[/tex]
Add similar elements: x²+x² = 2x²
[tex]=2x^2-xy-xy[/tex]
Add similar elements: -xy-xy = -2xy
[tex]=2x^2-2xy[/tex]
Thus,
[tex]x^2-xy+x^2-xy=2x^2-2xy[/tex]
In case your expression is:
[tex]\left(xx\right)^2\:-\:xy\:+\:x^2\:-\:xy[/tex]
Solution:
Given the expression
[tex]\left(xx\right)^2\:-\:xy\:+\:x^2\:-\:xy[/tex]
Group like terms
[tex]\left(xx\right)^2\:-\:xy\:+\:x^2\:-\:xy=x^2-xy-xy+\left(xx\right)^2[/tex]
Add similar elements: -xy-xy = -2xy
[tex]=x^2-2xy+\left(xx\right)^2[/tex]
as (xx)² = x⁴
so [tex]=x^2-2xy+x^4[/tex]
Therefore, we conclude that:
[tex]\left(xx\right)^2\:-\:xy\:+\:x^2\:-\:xy=x^2-2xy+x^4[/tex]Pls help really fast I don't know this!!!!!
I think it's (3,4) but I am not confident so please be understanding
Answer:
(3, 1 )
Step-by-step explanation:
The centre of the circle is at the midpoint of the diameter.
Given endpoint (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (9, 7) and (x₂, y₂ ) = (- 3, - 5 ) , then
midpoint = ( [tex]\frac{9-3}{2}[/tex], [tex]\frac{7-5}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex], [tex]\frac{2}{2}[/tex] ) = (3, 1 )
Thus centre of circle = (3, 1 )
will give brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:
x=15
Step-by-step explanation:
NEED ASAPPPP
The linear equation below describes the graph of a line.
4x – 3y = -12 Which of these is a point on the graph of the line?
Answer:
(-3,4)
Step-by-step explanation:
to solve for x, make y=0
to solve for y, make x=0
Well, you didnt give answer choices, BUT go onto desmos and use the graphing calculator to figure it out :)
8
9
10
3
4
5
A box contains 7 plain pencils and 3 pens. A second box contains 5 color pencils and 5 crayons. One item from each box is chosen at random. What is the
probability that a plain pencil from the first box and a color pencil from the second box are selected?
form
Answer:
60%
Step-by-step explanation:
add them all to 20
add 7 and 5 to get 12
12 over 20 is 60 percent
i need an opinion, my other note is in anouther question. what do y'all think.
Dear Chelsea
I'm tierd of you scraching me
I mean I love you can't you see
You may not see it but your rude to Sue
you tell me a secret like the one about you know who
Do you like to hurt Sue and me
Dose it make very you happy
I'm done with all the disrespect
I always helped you last I checked
I'm always there for you
I have fun doing all the things we do
I love you like my own child
Evan though you're a little wild
Your pretty and strong
Your hair is not so long
But what do I care
I mean it's your hair
I geuss what I'm trying to say
Is that no matter what you do ill still love you anyway
You are my little cousin more like a sister
And I hope to be there when you get your mister
I may not always be there
But I want you to know I still care
So as I look up at the sky
I write this not to say goodbye
Answer:
good job its very good
Step-by-step explanation:
A baker made 36 blueberry muffins on Monday. what percent of the total number of muffins were blueberry if the baker made 90 muffins?
_% of the total muffins were blueberry
Answer:
32%
Step-by-step explanation:
Find the equation of the line that is parallel to the given line and passes through the given point.
y=-6x + 9; (8,9)
The equation is y =
Answer:
y = -6x - 39
Step-by-step explanation:
A parallel line will have the same slope so m= -6, but it will have different points.
So we have y= -6x + b and the points are (8,9)
Substitute that in
9 = -6*-8 + b
9 = 48 + b
subtract 48 on both sides
9-48 = 48 - 48 + b
-39 = b
so equation is
y = -6x -39
click the red heart button to give thanks :) happy holidays
Answer:
y=-6x+9
0=-6x+9
6x=9
x=9/3
x=3/2
what is the slope intercept form of a linear function
Answer:
In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function. ... y=mx+b. Where m is the slope and b is the y-intercept.
Step-by-step explanation: I hope this helps
Answer:
y=mx + b
Step-by-step explanation:
Find the coefficient of correlation between and X and Y if covariance between X and Y is 15 and the variance of X and Y are respectively 10 and 25
Answer:
0.95
Step-by-step explanation:
[tex]Correlation \ coefficient \ (r) = \dfrac{covaraince \ between \ X \ and \ Y }{SD_X \times SD_Y }[/tex]
[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{10^{1/2} \times 25^{1/2} }[/tex]
[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{3.162 \times 5 }[/tex]
[tex]Correlation \ coefficient \ (r) = \dfrac{15 }{15.81 }[/tex]
[tex]Correlation \ coefficient \ (r) \simeq 0.95[/tex]
There are 35 people who have
entered the sled race. If 60% of
them are over the age of 15, how
many participants are over 15?
33-(2c + 4) = 2(c + 7) +C
Answer:
c=3
Step-by-step explanation:
Find the slope of the graph
Answer:Pick two points on the line and determine their coordinates.
Determine the difference in y-coordinates of these two points (rise).
Determine the difference in x-coordinates for these two points (run).
Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Step-by-step explanation:
A cylindrical tank has a radius of 5.5 ft and an altitude of 16 ft. If a gallon of paint will cover 130ft^2 of surface, how much paint is needed to put two coats of paint on the entire surface of the tank?
Answer:
Approximately 11 gallons of paintStep-by-step explanation:
First we need to calculate the Total surface area of the cylindrical tank as shown;
TSA of the tank = 2πr² + 2πrh
TSA of the tank = 2πr(r+ h) where;
r is the radius of the tank
h is the height
Given
radius = 5.5ft
height = 16ft
Get the surface area;
TSA = 2π(5.5)(5.5+ 16)
TSA = 2π(5.5)(21.5)
TSA = 2π(118.25)
TSA = 2(3.14)(118.25)
TSA = 742.61ft²
If a gallon of paint will cover 130ft^2 of surface, then the total number of paint needed will be;
Total number of paint needed = 742.61/130
Total number of paint needed = 5.7
For one coat we will need 5.7gallons of paint
For two coats we will need 2 * 5.7gallons = 11.4
Hence approximately 11 gallons of paints will be needed for the two coats
Dorian buys 2 pound's of almond's for 21.98 and 3 pound's of dried apricots for 26.25 which is less expensive per pound how much less expensive
Answer: Dried apricots are less expensive they are $8.75
Step-by-step explanation: I divided 21.98 by 2 and got 10.99 then I divided 26.25 by 3 and 8.75 which makes dried apricots less expensive
Abby spent 22 minutes working on her science project yesterday 34 minutes working on today. how many minutes did Abby spend working on her science project altogether
The number of minutes that Abby spend working on her science project altogether is 56 minutes.
How to calculate the value?From the information, Abby spent 22 minutes working on her science project yesterday and 34 minutes working on today.
Therefore, the time used altogether will be the addition of the time used for both occasions
= 22 minutes + 34 minutes
= 56 minutes
This illustrates addition.
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1/2% of 412
with work
Answer:
1.5% x 412 = 618?
Step-by-step explanation:
Answer:
103/50
Step-by-step explanation:
Simplify
1/2
100
(412)
(-2,6) and (1,-1) whats the slope
Please help ASAP 15 points
Answer:
B
Step-by-step explanation:
The answer is B because it tells you the letter atound triangle.
Answer:
b
Step-by-step explanation: