If a certain stock has grown continuously from 1980 to 2015, for this period of time its average annual growth rate is 18%.
It is given that A certain stock has grown continuously from 1980 to 2015.
Stock's initial value in 1980 (I) = $10,000
Stock's final value in 2015 (F) = $3,500,000
time period t = 2015-1980 = 35 years.
Since, the stock has grown continuously, it should have grown compounded annually.
Stock's average annual growth rate (r) is calculated as:
[tex]\text{r} = {(\dfrac{F}{I})^{\frac{1}{t}}-1[/tex]
Substitute all the given values in the above formula:
[tex]\text{r} ={ (\dfrac{3500000}{10000})^{\frac{1}{35}}-1[/tex]
[tex]\text{r} = {(350})^{\frac{1}{35}}-1[/tex]
[tex]r = (350)^{0.02857142857}-1[/tex]
[tex]r=1.18219102629-1[/tex]
[tex]r=0.18219102629[/tex]
[tex]r=0.18[/tex]
[tex]r\approx 18\%[/tex]
Hence, stock's average annual growth rate during the period of 35 years is 18%.
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NEED HELP ASAP! Question in the photo.
Answer:
SAS Postulate
Step-by-step explanation:
You can use the SAS (side, angle, side) postulate that says "if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent"
Side AB is proportionate to DE and
Side AC is proportionate to DF.
Angle A and Angle D are the same; and is between the two sides
I hope this helps.
12)
A hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services. Write a function to
model the cost of services there and then determine how many services you had if you were charged $115
A)
f(x) = 15x + 25; f(6) = 115
B)
f(x) = 25x + 15; f(6) = 165
f(x) = 15x + 25; f(0) = 125
D)
f(x) = 15x + 25; f(115) - 1750
Answer:
25+15x=115
Step-by-step explanation:
25+15x=115 115-25= 90 90/15=6
x=6
Which ratio is equivalent to 10:2
Answer:
5:1
Step-by-step explanation:
The ratio 10: 2 will be equivalent to ratios 20:4, 30:6, 40:8, and 50:10. Then all the options are correct.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The equivalent is the expression that is in different forms but is equal to the same value.
The ratio is given below.
Ratio = 10 / 2
Multiply and divide the ratio by 2. Then we have
Ratio = 10 x 2 / 2 x 2
Ratio = 20 / 4
Multiply and divide the ratio by 3. Then we have
Ratio = 10 x 3 / 2 x 3
Ratio = 30 / 6
Multiply and divide the ratio by 4. Then we have
Ratio = 10 x 4 / 2 x 4
Ratio = 40 / 8
Multiply and divide the ratio by 5. Then we have
Ratio = 10 x 5 / 2 x 5
Ratio = 50 / 10
The ratio 10: 2 will be equivalent to ratios 20:4, 30:6, 40:8, and 50:10. Then all the options are correct.
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The missing options are given below.
20:4
30:6
40:8
50:10
simplify the square root of 4x^6
Answer:
2x^3
Solution
You simplify to the lowest value possible 4x^6
2x^3
(-55 +94i) + (13 – 12i) =
Express your answer in the form (a + bi).
Answer:
(−55+94i) + (13−12i) = (−42+82i)
Step-by-step explanation:
The sum of the two complex numbers, (a+bi) and (c+di), is ((a+c) + (b+d)i)
( - 55 + 94i) + ( 13 - 12i) =
( - 42 + 82i)
PLS HELP
Determine the intercepts of the line. y=11x+6 (x and y intercept)
Answer:
Step-by-step explanation:
the xintercept is (-6/11,0)
y intercept is (0,6)
what is the value of this expression below when x=10
6x-5
Answer:
55
Step-by-step explanation:
6(10)-5
=60-5
=55
PLS GIVE BRAINLIEST
Answer:
55
Step-by-step explanation:
for this problem, you would use substitution. What you do is replace the x in the 6x-5 expression with 10 (since x is already solved for 10).
6x-5 and x=10
substitute x for 10
6(10)-5
simplify
60-5
answer
55
What does y and x equals using elimination
Answer:
I got x = -3/7, y = 20/7. Hope this helps :)
Guess this equation for brainliest
1 + 1 =?
2 X 4 = ?
2xy - y)/(x - 1) = ?
5 X 1
Answer:
1 plus 1= 2
2 × 4 = 8
5 × 1 =5
Step-by-step explanation:
IM SO SORRY IF IM WRONG! I just multiplied and added...
Answer:
1+1=2
2x4=8
?
5x1=5
Step-by-step explanation:
M divided by n times x , x ≠
A proportional relationship exists between x and y. When x=8 the value of y is 14.
(a) Write an equation for y in terms of x.
Answer:
Equation of y in terms of x is: [tex]y = \frac{7}{4}x[/tex]
Step-by-step explanation:
Proportion means that the change in one quantity causes change in other quantity.
Given that A proportional relationship exists between x and y.
It can be expressed mathematically as:
y ∝ x
When the proportionality symbol is removed, constant of proportionality is introduced which is usually denoted as k
[tex]y = kx[/tex]
Given that y=14 when x=8
Putting in equation
[tex]14 = k * 8\\k =\frac{14}{8}\\k = \frac{7}{4}[/tex]
Putting the value of k in equation
[tex]y = \frac{7}{4}x[/tex]
Hence,
Equation of y in terms of x is: [tex]y = \frac{7}{4}x[/tex]
Helps me solve this problem please
Answer:
Option 1: -2
Step-by-step explanation:
Take the rise over the run, where rise is the number of units vertically up the graph and run is the number of units horizontally across the graph
This is a topic on coordinate geometry. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary). I'll be uploading notes on this topic soon. At the meantime, you can take a look at other topics or some tips as well!
Mr. Fink's economy car can travel 420 miles on a 12-gallon tank of gas. Determine how many miles he can travel on 8 gallons.
Answer:
280 miles
Step-by-step explanation:
So, 420 miles=12 gallons
That means that for 1 gallon you would be able to go 35 miles.
Just multiply that by 8. 35*8=280
PLEASE!! For 22 points!!
Write the equation of the line that passes through the points (-4,-4) and (6,3).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
y = 3/5x + 3/5.
Step-by-step explanation:
the /'s are division symbols. 3 3
y = _ + _
5 5
Given ΔDEF : ΔRST, find x. 12 15 16 64
Answer:
12
Step-by-step explanation:
For ΔDEF similar to ΔRST, the value of x is 12. So, option a) is correct.
Two triangles are said to be similar if corresponding angles are equal or corresponding sides are in the same proportion.
Given triangles are similar:
ΔDEF ~ ΔRST
Therefore, using the property of similar triangle that corresponding sides of a similar triangle are in same proportion.
[tex]\dfrac{EF}{ST}=\dfrac{ED}{SR}\\\\\dfrac{x}{16}=\dfrac{3}{4}\\\\x=\dfrac{3}{4}\times 16\\\\x=12[/tex]
Thus, the value of x is 12. So, option a) is correct.
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which equation represents the vertical line passing through (7,-3)
A. x=-3
B. y=-3
C. x=7
D. y=7
Answer:
B- y=-3
Step-by-step explanation:
When Adrian runs the 400 meter dash, his finishing times are normally distributed with a mean of 77 seconds and a standard deviation of 3 seconds. What is the probability that in a given race, his finishing time will be faster than 75 seconds, to the nearest thousandth?
Answer:
0.749
Step-by-step explanation:
We start by calculating the z-score
Mathematically:
z-score = (x-mean)/SD
z-score = (75-77)/3 = -2/3 = -0.67
The probability we want to calculate is;
P( X > -0.67)
we can use the standard normal distribution table for this
Using this table, the probability has a value 0.74857 which is 0.749 to the nearest thousandth
Can someone help me with the questions in the picture?
26 - 20f = 6 please help me
CAN U GUYS HELP ME WITH THIS?!!! I WILL GIVE BRAINLY AND 15 POINTS!!??? THANKSKSKS!
Answer:
3n - 7 = 2n + 5
Step-by-step explanation:
n=12
that is the answer
The pencils , p, we're divided into 6 groups of 2
⚠️⚠️Write an equation PLEASEE I’m almost done ⚠️⚠️
Answer:
6 divided by 2 =p (a made a little graph at the bottom to demonstrate)
Step-by-step explanation:
. . . . . . Graph←
. . . . . .
Find the sum (2x−6)+4(x−3) =
Answer: x=-2
Step-by-step explanation: First we can multiply 4 times anything in the parantheses to get rid of it.
(2x-6)+4(x-3)
(2x-6)+4x-12
Then we combine like terms.
(2x-6)+4x-12
6x-6-12
6x-18
Finally we divide both sides 6.
6x-18
6x/6-18/6
x=-2
The final answer is x=-2
Hope this helps!
Btw this is a backup account
Answer:
6x - 18
Step-by-step explanation:
Distribute: 2x − 6 + 4x − 12
Group Common Factors: 2x + 4x - 6 -12
Solve: 6x - 18
I hope this helped, please mark Brainliest, thank you!
Monique said the equation y=8.5x represents her summer babysitting earnings where x is the number of hours worked and y is the amount of money earned. What is Monique’s hourly pay?
Answer:
8.5
Step-by-step explanation:
8.5 is the coefficient in front of x
50 = 2x + 12
Solve step by step.
Answer:
x=19
Step-by-step explanation:
subtract 12 from each side: 50-12=2x+12-12
38=2x
divide by 2
38/2=2x/2
19=x
Answer:
x=19
Step-by-step explanation:
50=2x+12
50-12=2x+12-12
38=2x
38/2=2x/2
x=19
A store sells bracelets that cost x dollars and necklaces that cost y dollars. Jessica bought 4 bracelets and 7 necklaces for $18. Brianna bought 5 bracelets and 4 necklaces for $13. Gabby bought 3 bracelets and 2 necklaces. How much money did Gabby spend on bracelets and necklaces?https://brainly.com/app/ask?q=A store sells bracelets that cost x dollars and necklaces that cost y dollars. Jessica bought 4 bracelets and 7 necklaces for $18. Brianna bought 5 bracelets and 4 necklaces for $13. Gabby bought 3 bracelets and 2 necklaces. How much money did Gabby spend on bracelets and necklaces?https://brainly.com/app/ask?q=A store sells bracelets that cost x dollars and necklaces that cost y dollars. Jessica bought 4 bracelets and 7 necklaces for $18. Brianna bought 5 bracelets and 4 necklaces for $13. Gabby bought 3 bracelets and 2 necklaces. How much money did Gabby spend on bracelets and necklaces?
Answer:
X=$7
Step-by-step explanation:
WHAT IS A TAPE DIAGRAM AND WHAT DOES IT LOOK LIKE?
Answer:
A rectangular visual model resembling a piece of tape with divisions used to assist mathematical calculations. Also known as a divided bar model, fraction strip, length model or strip diagram. In mathematics education, it is used to solve word problems.
Step-by-step explanation:
Answer:
Tape diagrams are visual models that use rectangles to represent the parts of a ratio.
Here's what it looks like
CL 2-125.
Explain what you are doing when you find the perimeter of a flat shape. How is that different than finding
its area?
Answer:
It is different because perimeter is the outside and area is the inside.
Step-by-step explanation:
Una escalera de 131313 metros está recargada contra una pared cuando su base empieza a resbalar. Cuando la base está a 121212 metros de la pared, se mueve a una razón de 5\text{ m/s}5 m/s5, start text, space, m, slash, s, end text. En ese momento, ¿a qué razón está cambiando el ángulo \thetaθtheta entre el piso y la escalera?
Answer:
El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.
Step-by-step explanation:
Sea [tex]x[/tex] la distancia horizontal entre la pared y la base de la escalera y [tex]l[/tex] la longitud de la escalera, medidas en metros. Además, tenemos que [tex]\theta[/tex] es el ángulo entre la escalera y el piso, medido en radianes.
Si la pared y el piso son ortogonales entre sí, entonces podemos utilizar la siguiente relación trigonométrica que relaciona las variables anteriores:
[tex]\cos \theta = \frac{x}{l}[/tex] (1)
Por diferenciación implícita y la definición de razón de cambio tenemos que:
[tex]-\sin \theta \,\dot \theta = \frac{\dot x}{l}[/tex] (2)
Donde:
[tex]\dot x[/tex] - Razón de cambio de la distancia horizontal entre la pared y la base de la escalera, medida en metros por segundo.
[tex]\dot \theta[/tex] - Razón de cambio del ángulo entre el piso y la escalera, medida en radianes por segundo.
Pero tenemos que el seno del ángulo está definido por:
[tex]\sin \theta = \frac{\sqrt{l^{2}-x^{2}}}{l}[/tex] (3)
Si aplicamos (3) en (2), expandimos la ecuación como sigue:
[tex]-\frac{\sqrt{l^{2}-x^{2}}}{l}\,\dot \theta = \frac{\dot x}{l}[/tex]
[tex]\dot \theta = - \frac{\dot x}{\sqrt{l^{2}-x^{2}}}[/tex] (4)
Si tenemos que [tex]\dot x = 5\,\frac{m}{s}[/tex], [tex]l = 13\,m[/tex] y [tex]x = 12\,m[/tex], entonces la razón de cambio del ángulo es:
[tex]\dot \theta = -\frac{\left(5\,\frac{m}{s} \right)}{\sqrt{(13\,m)^{2}-(12\,m)^{2}}}[/tex]
[tex]\dot \theta \approx -1\,\frac{rad}{s}[/tex]
El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.
Jasmine found a wooden jewellery box shaped like a right rectangular prism. What is the volume of the jewellery box? MY TEACHER DIDNT TEACH US VOLUME. Ugh. ♀️
Answer:
Volume = Length × Width × Height
Step-by-step explanation:
A right rectangular prism is a three-dimensional object like the one shown in the attachment. It has dimensions: Length, Width and Height. All the angles between the sides are 90°. In order to calculate the volume of an object shaped like a right rectangular prism, we use the following expression.
Volume = Length × Width × Height
the sum of two numbers is 21 . 3/4 of one of the numbers added to 2/3 of the other numbers added to 2/3 of the other gives a sum of 15. find the two numbers
The numbers are 15 and 9 .
Numbers are the basic foundation of mathematics. Numbers are used to represent quantity and used is basic arithmetic operations. Numbers can be categorized into a lot of different types such as real or imaginary. Real numbers can be divided into integers , irrational numbers , whole numbers .The four basic arithmetic operations are multiplication , sum , division and subtraction.
Let us consider one of the given numbers be x .
Given the sum of the numbers is 21
therefore the other number = 21 - x
Now it is given that [tex]\frac{3}{4}[/tex] of 1 number and [tex]\frac{2}{3}[/tex] of another number adds up to 15 .
∴ [tex]\frac{3}{4}[/tex] of x = [tex]\frac{3}{4}x[/tex] and [tex]\frac{2}{3}[/tex] of another number = [tex]\frac{2}{3}\times(21-x)[/tex]
Now the sum of the two new numbers is given as 15.
∴ [tex]\frac{2}{3}\times(21-x) +\frac{3}{4}x =15[/tex]
[tex]or, 14-\frac{2}{3}x +\frac{3}{4}x =15\\\\or, -\frac{2}{3}x +\frac{3}{4}x =15-14\\\\or, \frac{-8+9}{12} x=1\\\\or, \frac{1}{12}x = 1\\\\or, x=12[/tex]
So the other number is 21-12 = 9 .
Hence the two numbers are 15 and 9 .
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