Answer:
[tex]N(t) = 37.1(1.38)^t[/tex]
Step-by-step explanation:
Exponential function:
An exponential function has the following format:
[tex]N(t) = N(0)(1+r)^t[/tex]
In which N(0) is the initial value and r is the rate of change, as a decimal.
37.1 million in July 1998
This means that [tex]N(0) = 37.1[/tex]
So
[tex]N(t) = 37.1(1+r)^t[/tex]
In July 2005, the internet was linked by a global network of about 353 million host computers.
This is 2005 - 1998 = 7 years, so [tex]N(7) = 353[/tex]. We use this to find r.
[tex]N(t) = 37.1(1+r)^t[/tex]
[tex]353 = 37.1(1+r)^7[/tex]
[tex](1+r)^7 = \frac{353}{37.1}[/tex]
[tex]\sqrt[7]{(1+r)^7} = \sqrt[7]{\frac{353}{37.1}}[/tex]
[tex]1 + r = (\frac{353}{37.1})^{\frac{1}{7}}[/tex]
[tex]1 + r = 1.38[/tex]
The formula is:
[tex]N(t) = 37.1(1.38)^t[/tex]
Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $49. At another store she can borrow the tile saw for free if she buys tiles there for $1.29 per tile. How many tiles must she buy for the cost to be the same at both stores?
Margo must buy
tiles for the cost to be the same at both stores.
Answer:
Also need help
Rotation 180° about the origin
Answer:
Step-by-step explanation:
to rotate about origin by 180 ° also means to change ( x, y) ⇔( -x,-y)
the double arrows just mean to change into.. or "transform" ( I think that there might have even been a movie about this, called "transformers" :D JK)
T=( -2, 1)
S = ( -4, 3)
R = ( -5, -2)
use the transform ( x, y) ⇔( -x,-y)
T' = (2,-1)
S' = ( 4, -3 )
R' = (5 , 2 )
if you draw this on a piece of graph paper, you'll see it's the triangle spun 180 ° around the origin :)
may kapangyarihan bilang pinakamataas na hukuman sa kolonya
Answer:
which language is this .
Write an emergency that could happen that would have a financial cost
Answer:
Your house burning down.
Step-by-step explanation:
You would have to pay to repair it.
Answer:
Earthquake will make the building crash and people will lost their things and money. And the building need to rebuild.
The building fire will make people lost their things and the building need to rebuild.
Tsunami will make the things near beach all destroy, all the things will lost and more people will die in disaster. All the building need to rebuild in this disaster.
Bank robbery will lost money, sometimes people will kill by the gun of the thief, and the building do not need to rebuild, maybe the window need to rebuild.
Rob the shop will make the boss of the shop lose all the money in the store, the door or window might need to rebuild.
Blasting vehicle will make the things in the car lose. the car need to put the windows on again.
Terrorist attacks will lost lives more than lost money or other things.
Volcanic eruptions will make the building near burn, and so plant and many other things. The building might need to rebuild.
That is all I can think of.
Item 5
Which measure of central tendency best describes the data?
47, 47, 48, 54, 102, 45, 100, 48, 83
either mean or median
median only
mean only
Answer:
the answer is either mean or median because you can find both of them given the data
A bucket has 16 tennis balls and 10 ping pong balls . What is the probability of selecting a ping pong ball , replacing it and then selecting a tennis ball
Answer:
40/169
Step-by-step explanation:
P(pp,tennis) = [tex]\frac{10}{26}[/tex] × [tex]\frac{16}{26}[/tex] = 40/169 in simplified form
The probability of selecting a ping pong ball, replacing it and then selecting a tennis ball is 40/169.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Tennis ball = 16
Ping pong balls = 10
So, probability of selecting a ping pong ball, replacing it and then selecting a tennis ball
= 10/ 26 x 16/26
= 40/169
Learn more about Probability here:
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um what do i do here
Answer:
you add and subtract
Step-by-step explanation:
You need to match the sum/difference with the expression
Example -
A. 5x+2x 15x+2y (B)
B. 7x+8x+2y. 7x (A)
That's how you match it
2.75 round to the nearest hundreth
Answer:
Its already rounded. Rounded to tenths place would be 2.8
Step-by-step explanation:
5 or higher makes you round up. if its a 4 or lower it would stay the same.
Which graph best represents the equation -4x + 5y = 8? A. B. C. D.
Answer:
It will look like this
Step-by-step explanation:
The equation of line y = 4 / 5x + 8 / 5 can be represented on the basis of coordinates (0, 8/5), (1, 12/5), and (10, 48/5) in the graph attached below.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
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.
Given:
-4x + 5y = 8
Write the line in slope intercept form as shown below,
5y = 4x + 8
y = 4 / 5x + 8 / 5
Put the random values of x and find y,
y = 4 / 5 × 0 + 8 / 5 (when x = 0)
y = 8 / 5
y = 4 / 5 × 1 + 8 / 5 (When x = 1)
y = 12 / 5
y = 4 / 5 × 10 + 8 / 5 (When x = 10)
y = 48 / 5
Plot the coordinates (0, 8/5), (1, 12/5), and (10, 48/5) in the graph and mark the points, joining all the points to get the line.
To know more about equation:
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Find y' if y= In (x2 +6)^3/2
y'=
Answer:
[tex]\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
ln Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = ln(x^2 + 6)^{\frac{3}{2}}[/tex]
Step 2: Differentiate
[Derivative] Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[ln(x^2 + 6)^{\frac{3}{2}}] \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{3}{2} - 1} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] ln Derivative: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Basic Power Rule: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2 \cdot x^{2 - 1} + 0)[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2} \cdot \frac{1}{x^2 + 6} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3(2x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{6xln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Factor: [tex]\displaystyle y' = \frac{2(3x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
A bag of 4 balls weighs 6 pounds. Each ball weighs the same amount. What is the weight of each ball?
Determine whether the equation is true or false.
Answer:
False
Step-by-step explanation:
Hope I helped :)
Out of all of the topics covered so far in the course (whole numbers, fraction notation: multiplication, division, and mixed numerals), which did you enjoy the most? Which do you enjoy the least? Why?
Answer: I would say I've liked multiplication the most and division the least! I have always gotten multiplication because.. I don't really know. It's just easy for me. I can't really explain. For multiplication though.. I have never gotten it. It is the exact opposite. I've never understand how you have to skip a digit because you can't divide it to the other number.
Step-by-step explanation:
Hope this helps! This is my opinion.
I made this don't copy my answer
Calculate the volume of this triangular prism?
Answer:
960 sq cm
Step-by-step explanation:
(16*12*10)/2
Fill in the blank so that the ordered pair is a solution of y = 22 – 9x.
( ,4)
Which statement best describes the function?
O A. The function is increasing when x < 0.
B. The function is decreasing when x > 0.
C. The function is never increasing.
D. The function is always increasing.
Answer:
D. The function is always ingcreasing
Solve for x if 26 = x/2
Answer:
x=52
Step-by-step explanation:
abc~def what sequence of transformation will move ABC onto def
Answer:
c
Step-by-step explanation:
Answer:
is C guys
Step-by-step explanation:
Show that sin( + 180°) + 2 cos( − 360°) − sin( − 180°) = 2x
Answer:
Example 1: Change sin 80° cos 130° + cos 80° sin 130° into a trigonometric function in ... Example 2: Verify that cos (180° − x) = − cos x ... Example 7: Verify that sin (360° − x) = − sin x.
Find the length of the third side. If necessary,
round
to
the nearest tenth.
4
7
Answer:
The answer would be 8.1
Step-by-step explanation:
At art class, Mr. Gibson spends 5 minutes giving instructions, 35 minutes working on the project, and 15 minutes cleaning up. If class starts at 1:15 PM, what time will it end? PM
Answer:
2:10 PM
Step-by-step explanation:
5+35+15=55 mins
1:15+55 mins=2:10PM
Assume v is a vector in R^5. You wish to compute a vector w such that the th entry of w, denoted wi, is the sum of vi-1,vi, vi+1. For example wi is the sum of ,vo,v1 and v2. For elements at the endpoints of w, you will only account for two elements in your sum. For example wo, (assuming zero-based indexing) is the sum of vo and v1. Construct a matrix A such that Av=w.
Answer:
Use the drawing tools to form the correct answer on the graph.
Graph the line that represents this equation:
Step-by-step explanation:
IS THIS IN SIMPLIST FORM? PLEASE HELP! TY!
2( x - 3 + 2 )
Answer:
2x - 2
Step-by-step explanation:
There are two steps to take here. First add together the -3 + 2 in the brackets:
2(x - 3 + 2)
= 2(x - 1)
Now use the distributive property and multiply each term in the brackets by two:
2(x - 1)
= 2x - 2
And you now have it in simplest form.
ASAP I WILL GIVE 100 POINTS AND BRAINIEST ASAP
Find the length of the model train.
Answer:
It would be 7.5 inches.
Hope this helped!!
A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.
Exercise (a)
How much work W is done in pulling the rope to the top of the building?
Exercise (b)
How much work W is done in pulling half the rope to the top of the building?
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]
The work done in pulling half the rope, W₂ = 562.5 lb·ft
Can Someone please help me !!! ( you have to fill out the blanks )
Answer:
1. 5(a-6) = 5a-30
2. 2(3a-b) = 6a-2b
3. 5(-5x+3) = -25x+15
4. -(2c+3) = -2c-3
Both of their first step are correct (Show your calculations to explain)
x-9 = 5
x = 14
2x-18 = 10
2x = 28
x = 14
Step-by-step explanation:
All Above
Function Notation
If f(x) = -3x2 + 2x - 8, find each of the following:
f(-1)
f(0)
f(3)
f(1/3)
State if the triangles in each pair of similar. If so, state how you know they are similar and complete the similarity statement.
triangle UTS~ ____
a. similar, AA, UED
b. similar, SSS, UDE
c. similar, SAS, UDE
d. not similar
Answer:
triangle UTS~∆UED by AAA axiom
(1 point)
Only answer if you know!!! Meg was deep-sea diving at 15 feet below sea level. She dove another 7 feet below sea level. How far
below sea level was Meg?
O 8 ft below sea level
O 12 ft below sea level
O 22 ft below sea level
Answer:
22 feet below sea level
Step-by-step explanation:
she kept going down, basically in a negative way. adding to the already below sea level
Which fraction is marked by the point on the number line?
Answer:
where is the numer line?
Step-by-step explanation: