[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\stackrel{40\%~of~P}{0.4P~~~~}\\ P=\textit{initial amount}\dotfill &P\\ r=rate\to 22.5\%\to \frac{22.5}{100}\dotfill &0.225\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ 0.4P=P(1-0.225)^t\implies \cfrac{0.4P}{P}=(1-0.225)^t\implies 0.4=0.775^t[/tex]
[tex]\log(0.4)=\log(0.775^t)\implies \log(0.4)=t\log(0.775) \\\\\\ \cfrac{\log(0.4)}{\log(0.775)}=t\implies \stackrel{\textit{about 3years, 215days and 8hrs}}{3.59\approx t}[/tex]
so at that time the value is 40% of its original value, I guess is less than that a minute or an hour later.
A bicycle wheel has a circumference of 62 inches. Find the diameter of the wheel. If necessary, round to the tenths place. 39. 5 inches 19. 7 inches 15. 5 inches 9. 9 inches.
Answer:
19.7 inches
Step-by-step explanation:
circumference of a circle = 2πr
62 = 2*22/7 *r
r = 62 * 7 / 44 = 9.86
diameter = 2* r
= 2* 9.86
= 19.7 inches
Please help! Image attached!!!!!
Answer:
x = ln (y)
Step-by-step explanation:
There's two main ways to solve this. When there is no logarithm in the equation you can either take the log of both sides OR change an exponential equation to logarithmic form.
See image.
note: log_2 (2) = 1
log_3 (3) = 1
log_4 (4) = 1
log_5 (5) = 1
if the base and the article are the same then it equals 1
ln e = 1
because ln e means the same thing as log_e
log_e (e) = 1
e is just a number!
If you are changing exponential form to logarithmic form, the base is the same in both forms. The base is the base. The base in exponential form is the base in logarithmic form. The base is the base. The exponent and article basically switch places to change forms.
see image.
An angle measures 52.8 degrees more than the measure of its supplementary angle. what is the measure of each angle?
Answer: 116.4 and 63.6 degrees
Step-by-step explanation:
Let the angle be x, so supplement is 180-x.
This means x - 52.8 = 180 - x
2x = 232.8
x = 116.4
So the angle measures are 116.4 and 63.6 degrees
2. One bag of fertilizer will cover 400 square feet. Find how many bags should be purchased to cover a garden that is
35 feet by 75 feet.
35*75 is
2625
2625/400 is
6.5625
Since you cannot have a decimal amount of a bag, you should purchase
(rounding)
7 bags of fertilizer
Answer:
7 bags
Step-by-step explanation:
First thing you need to do is figure out the area of the garden. Area=length×width, so just put in your numbers, 35×75=2625 square feet. One bag covers 400 feet, so you divide the area by 400, 2625÷400=6.5625. You can't buys 6.5625 bags of fertilizer, so you have to go up to the next whole number which is 7.
Multiply. Express your answer in simplest form.
11 1/7 × 4 2/7
There are 56 female performers in a dance recital. The ratio of men to women is 6:7. How many men are in the dance recital?
A square room contains 1000 m3 of air. If the cost of painting its four walls at Rs. 16 per square meter be Rs. 3200, find the height of the room. (Ans: 2.5 m)
a graphing calculator costs $85. the sales tax on the calculator is 8% . what is the total cost of the calculator
Answer:
The calculator costs $91.80 in total.
Step-by-step explanation:
85*8% = 6.80
85+6.80 = 91.80
probability (a) = 25%
probability (b) = 60%
determine probability (a and b)
Answer:
85%
Step-by-step explanation:
P(a) = 25%=1/4
P(b) = 60%=3/5
P(a and b) = 1/4 + 3/5 = 5+12/20 = 17/20 = 85%
Answer:
The probability of A and B is 85%
Step-by-step explanation:
It is 85% because 25% is 0.25 or 25/100(1/4), and 60% is 0.6 or 6/10(3/5). 0.6+0.25=0.85 and to convert it back to a percentage you need to times 100%. 0.85x100%=0.85x100 with a percentage symbol =85%.
please help me with this word problem for math class.
9 dollars
288/32=9
310.50/34.5=9
360÷4=9
a b
36 9
72 18
80 20
Find the constant of proportionality from a to b. Express
your answer as a fraction in reduced terms.
PLEASE HELP! I cant figure these out!
What is the sum of (−4x2+6x) and (7x2−12) ?
Answer:
3x^2+6x-12
Step-by-step explanation:
Jiiiii
Nunnujjjggynhhhhhhhhhhhh
Answer: I do not understand
Step-by-step explanation:
What is done wrong in this question please answer it ASAP!!!! Need to submit in 30 min please some one please answer!!!!!
Answer:
They flipped the wrong fraction it should have been 2/3 as the fraction you divide by is the fraction you flip
What is the slope of the line that passes through the points (6, 7) and (16,22)??? i have been
Answer:
1.5
Step-by-step explanation:
picture
math the answer i chose was a guess and i need to work it out
A 440 wire is cut into three pieces the second piece is two times as long as the first the third piece is four times as long as the second how long is each piece
Step-by-step explanation:
[tex]x \: as \: the \: first \: piece \\ 2x \: as \: the \: second \: piece \\ 4(2x) = 8x \: as \: the \: third \: piece[/tex]
[tex]x + 2x + 8x = 440 \\ 11x = 440 \\ x = \frac{440}{11} \\ x = 40 \\ 2x = 2 \times 40 = 80 \\ 8x = 8 \times 40 = 320 [/tex]
What fraction of the model is shaded?
Answer:
3/10
Step-by-step explanation:
total boxes = 100
shaded boxes = 30
fraction =30/100
= 3/10
a^2 - ba +ac -cb factorize
Answer:
[tex](a-b)(a+c)[/tex]
Step-by-step explanation:
Factor each half of the expression separately:
[tex]a^2-ba+ac-cb\\a(a-b)+c(a-b)[/tex]
Since both a and c are being multiplied by a-b, we can combine them to get:
[tex](a-b)(a+c)[/tex]
A total of 100 students were surveyed
and asked which color they would like
in the school flag.
5 checked only green.
8 checked only red.
12 checked only blue.
19 checked red and green,
22 checked blue and greer!.
13 checked red and blue.
How many checked all 3 colors?
Answer:
21
Step-by-step explanation:
5+8+12+19+22+13= 79 , 100 students - 79 checked students = 21
Alice brought 6 container of lemonade each container had 1 1/2 of a cup lemonade how many cups of lemonade did she have in all
Find an expression which represents the sum of (6x – 4) and (-2x + 5) in simplest terms.
Answer:
4x+1
Step-by-step explanation:
6x-4-2x+5
4x-4+5
4x+1
please solve the question in the below image.
Answer:
Use the given functions to set up and simplify x^2+1/x^2.
x+1/x=6=x=1/6
x^2+1/x^2=1/x^2
PLEASE Please help meeeeee!!
Question in image*
how does the graph of g(x) = (x - 3)^3 - 2 differ from the group of f(x) = x^3?
A. g is shifted 3 units right and 2 units up.
B. g is shifted 3 units right and 2 units down.
C. g is reflected across the y-axis.
D. g is rotated 90* clockwise.
Answer:
B
Step-by-step explanation:
f(x) = x³
g(x) = (x - 3)³ - 2
The inside of the parenthesis represents a horizontal shift
If the number operation being done to x inside of the parenthesis is adding ( or if the number is positive ) then the graph will shift to the left. If the operation being done inside of the parenthesis to x is subtraction ( or if the number is negative ) then the graph will shift to the right.
The operation being done is subtraction therefore it will shift to the right. So it will go 3 units to the right.
the number on the outside works like a y intercept. if it's positive it goes up, if it's negative it goes down. the number is -2 so it will go down 2 units
we can conclude that g is shifted 3 units right and 2 units down
the answer is B
Pankaj borrows rupees 57,000 to buy a used car and is charged the rate of interest 6% per annum. if the term of his borrowing is 4 years, how much interest does he pay?
Rs.13680 is the answer.
Step-by-step explanation:-
Given-
• Principal (P) = Rs.57,000
• Rate (r%) = 6%
[tex]→ \frac{6}{100} [/tex]
[tex]→ 0.06[/tex]
• Time (n) = 4 years
Applying Interest formula,
[tex]→In=P \times R \times T[/tex]
[tex]→57,000 \times 0.06 \times 4[/tex]
[tex]→Rs.13680[/tex]
Hence, the interest is Rs.13680
Arrange them from highest to lowest, need help asap Ty
181,233,255,251,232,167,207,206,256,248,151,118,113,233,253,247,276,162,228,232
Answer:
113, 118, 151, 162, 167, 181, 206, 207, 228, 232, 232, 233, 233, 247, 248, 251, 253, 255, 256, 276
Step-by-step explanation:
Good luck man :)
Complete the parametric equations for the given rectangular equation
Answer:
a) y = 7
b) y =5 sin t
Step-by-step explanation:
Can someone please help me with this square root problem?
Answer:
x=14.87
Step-by-step explanation:
What we want to use is pythagoras theorem:
a^2+b^2=c^2, where c is the hypotenuse
10^2+11^2=x^2
221=x^2
x=[tex]\sqrt{221}[/tex]
x=14.866...
x=14.87