Answer:
As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.
Step-by-step explanation:
The amount of money in the account after t years is given by:
[tex]A(t) = Pe^{rt}[/tex]
In which P is the initial amount deposited and r is the interest rate, as a decimal.
Michelle deposited $1,600 into an account that is compounded continuously with an annual interest rate of 8%.
This means that [tex]P = 1600, r = 0.08[/tex]
After t years, there was $3,200 in the account. How many years had the money been in the account?
This is t for which [tex]P(t) = 3200[/tex]. So
[tex]A(t) = Pe^{rt}[/tex]
[tex]3200 = 1600e^{0.08t}[/tex]
[tex]e^{0.08t} = \frac{3200}{1600}[/tex]
[tex]e^{0.08t} = 2[/tex]
[tex]\ln{e^{0.08t}} = \ln{2}[/tex]
[tex]0.08t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.08}[/tex]
[tex]t = 8.67[/tex]
As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.
The value of time t is [tex]\frac{ln(2)}{0.08}[/tex].
Given: P=1600
r=8%=0.08
t = ?
A=3200
Using the given compound interest formula we get:
[tex]A=Pe^{rt}\\3200=1600e^{0.08t}\\2=e^{0.08t}\\[/tex]
Take ln on both sides,
[tex]ln(2)=ln(e^{0.08t})\\ln(2)=0.08t\\t=\frac{ln(2)}{0.08}[/tex]
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a department store sells a pair of shoes with an 87% markup, if the store bought the pair of shoes for 55.25, what is the selling price to the nearest dollar?
Answer:
$103
so 87% of $55.25 is 48.0675
48.0675+55.25 is 103.3175
103.3175 rounded to the nearest dollar is 103.
f(x)=-12x^3-14x^2+6x
a) Simplify
X - 2 / 7(x - 2)2
Answer:
3x/7 + 8/7
Step-by-step explanation:
Please help ASAP!
Thank you
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Decide whether the following statement makes sense or does not make sense. Explain your reasoning.
I drove at a speed of 35 miles for the entire trip.
Answer:
It doesn't make sense
Step-by-step explanation:
Given
Statement: .... at a speed of 35 miles .....
Required
Does it make sense?
In motion, speed is measured in km/h, m/s, miles per hour (depending on context) while distance is measured in km, m or miles.
However, the given statement mention the unit of speed to be miles which is incorrect.
Hence, we can conclude that the statement does not make sense.
A correct statement would be: I drove at a speed of 35 miles per hour .......
Pleas e help me 100 points and brainliest
Answer:
this is your answer. I think it is right.
Answer:
see the answersStep-by-step explanation:
to understand thisyou need to know about:factoringlCDPEMDAStips and formulas:L.C.D=lowest common denominatorlet's solve:[tex]1) \sf\frac{7}{m - 6} \: , \frac{1}{m} \\ [/tex]
denominators are m-6,m
therefore
the lowest common denominator is
(m-6)(m)[tex] \sf\frac{1}{n - 1} \: , \frac{1}{ {n}^{2} - 2n + 1 } [/tex]
denominators n-1,n²-2n+1
step-1
factor n²-2n+1 to find the lowest common denominator
use (a-b)²=a²-2ab+b to factor n²-2n+1therefore
(n)²-2.n.1+(1)²(n-1)²therefore
the L.C.D of the second expression is
(n-1)² alternative form(n-1)(n-1)[tex]3) \tt\frac{k}{ {h }^{2} - 5h + 6} \: , \frac{3}{h -3 } [/tex]
step-1
factor out h²-5h+6 to find L.C.D
rewrite -5h as -2h-3h: h²-2h-3h+6factor out h: h(h-2)-3h+6factor out -3: h(h-2)-3(h-2)group: (h-3)(h-2)therefore
the L.C.D of the third expression is
(h-3)(h-2)Write a rule for a function with a parabolic graph that contains the x-intercepts (-20,0) and (40,0) and a maximum point whose y-coordinate is 30.
Step-by-step explanation:
Since the x-intercepts are -20 and 40, the line of symmetry is x = (-20 + 40)/2 = 10.
Now we have y = a(x - 10)² + 30, where a is an unknown constant. We can find a by using an x-intercept point.
=> (0) = a[(40) - 10]² + 30
=> 900a + 30 = 0, a = -1/30.
Hence the rule is y = -(x - 10)²/30 + 30.
Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 4(m∠Y) − 210°. Find m∠Y.
Answer:
angle Y= 60 degrees
Step-by-step explanation:
angle S + angle Y = 90 degrees because they are complementary
Y = 90 - S
angle S = 4(Y)-210
substitute for Y
S = 4(90 - S) - 210
S = 360 - 4S - 210
reduce
5S = 150
S = 30
Y = 90 - 30 = 60
Simplify completely*****
Answer:
[tex]\displaystyle \frac{2(x + 4)}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{4x + 16}{6}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{4(x + 4)}{6}[/tex][Fraction] Reduce: [tex]\displaystyle \frac{2(x + 4)}{3}[/tex]One winter day, the temperature in Houston is 8 Celsius. Find the temperatures in these other cities. Explain or show your reasoning.
In Orlando, it is 17 warmer than it is in Houston
In Salt Lake City, it is 18 colder than it is in Houston
In Minneapolis, it is 25 colder than it is in Houston
In Fairbanks, it is 12 colder than it is in Minneapolis
Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks.
Hence, the temperatures in these other cities are
Orlando is [tex]25[/tex] degree
Salt Lake is [tex]-10[/tex] degree
Minneapolis is [tex]-17[/tex] degree
Fairbanks is [tex]-29[/tex] degree
What is the degree?
A degree, usually denoted by °, is a measurement of a plane angle in which one full rotation is [tex]360[/tex] degrees.
Here given that,
One winter day, the temperature in Houston is [tex]8[/tex] Celsius.
In Orlando, it is [tex]17[/tex] warmer than it is in Houston.
In Salt Lake City, it is [tex]18[/tex] colder than it is in Houston.
In Minneapolis, it is [tex]25[/tex] colder than it is in Houston.
In Fairbanks, it is [tex]12[/tex] colder than it is in Minneapolis.
So, it would be
Orlando = [tex]25[/tex] degree
because [tex]17+8=25[/tex] degree
Salt Lake city [tex]= -10[/tex] degree
because [tex]8-18=-10[/tex] degree
Minneapolis [tex]= -17[/tex] degree
because [tex]8-25=-17[/tex] degree
Fairbanks [tex]= -29[/tex] degree
because [tex]-17-12=-29[/tex] degree
Hence, the temperatures in these other cities are
Orlando is [tex]25[/tex] degree
Salt Lake is [tex]-10[/tex] degree
Minneapolis is [tex]-17[/tex] degree
Fairbanks is [tex]-29[/tex] degree
To know more about the degree
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how many inches is 2 1/6 ft
Answer:
26 inches
Step-by-step explanation:
whats 8 x 2 40 points
Answer:
Error hehehheheheh
Step-by-step explanation:
crown me please hehehhhe hahahahahh hohohoohoho points more more more more points
Help me please!!
15 points!
Answer:
Hi Hi really sorry may i get some points i need them to give it to other people cuz some people want points, ik its not the answer u wanted sorry but hope u get the answer soon!
Step-by-step explanation:
Lillian wants to give 1/3 of a pizza to each of six girls at her party. Dragon drop the correct equation an answer to find how many pizzas Lillian needs
Answer:
2 pizza
Step-by-step explanation:
Given
[tex]Pizza = \frac{1}{3}[/tex]
[tex]Girls = 6[/tex]
Required
Amount of Pizza needed
To do this, we simply multiply the fraction of pizza by the number of girls i.e.
[tex]Amount = Pizza * Girls[/tex]
[tex]Amount = \frac{1}{3} * 6[/tex]
[tex]Amount = 2[/tex]
Hence, Lilian needs 2 pizza
Jeff had 20 $ he spent 1/8 on his money on lunch and 2/5 of his money at the movies. How much money does Jeff have left
Answer:
9.50$
Step-by-step explanation:
First, multiply 20 by the given fractions
20*1/8=2.5
20*2/5=8
Add the two together to get the total amount of money Jeff spent, 10.5, then subtract 10.5 from 20 to get the total amount he has left, 9.5
Answer:
$9.50
I did a test with this question and the correct answer was 9.50
ou intend to draw a random sample in order to test a hypothesis about an unknown population mean. You will use a hypothesis test. A description of each of the steps of a hypothesis test follows, but they may be specified in the incorrect order. Specify the correct order of the steps. Determine the null and alternative hypotheses. Draw a conclusion about the unknown population using what is known about the sample. Determine the probability at which you will conclude that the sample outcome is very unlikely. Draw a random sample, and calculate the sample statistic.
Answer:
Determine the null and alternative hypotheses : STEP 1
Draw a conclusion about the unknown population using what is known about the sample : STEP 4
Determine the probability at which you will conclude that the sample outcome is very unlikely : STEP 2
Draw a random sample and calculate the sample statistic : STEP 3
Step-by-step explanation:
The correct order of the steps are :
Determine the null and alternative hypotheses : STEP 1
Draw a conclusion about the unknown population using what is known about the sample : STEP 4
Determine the probability at which you will conclude that the sample outcome is very unlikely : STEP 2
Draw a random sample and calculate the sample statistic : STEP 3
2 and 1/8 + 1 and 3/4
Pleeeeeeease help me! However helps me first gets brainliest points!
Simplify the following algebraic expressions:
a. - 6x + 5 + 12x -6
b. 2(x - 9) + 6(-x + 2) + 4x
c. 3x2 + 12 + 9x - 20 + 6x2 - x
d. (x + 2)(x + 4) + (x + 5)(-x - 1)
e. (x+8)(x+9)+(x+1)(-x-6)
Answer:
A) 6x-1
B) -6
C) 9x2+8x-8
D) 3
E) 10x+66
Step-by-step explanation:
There are 30 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in the dance recital?
What is the surface area of the cylinder with height 8 ft and radius 5 ft? Round your answer to the nearest thousandth.
What is the volume of a cube with edge lengths of 2/3 units
Answer:
Step-by-step explanation:
8/27 because if you think about it 2/3 x 2/3 x 2/3 x 2/3 = 8/27
how much did he spend on the cookir
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A circles radius is 13 meters what is the circles area using 3.14 rounded to the nearest tenth
Answer:
530.7
Step-by-step explanation:
A circle's area is defined as πr²
You would substitute 13 in for r (the radius) and use 3.14 as your given value for pi, leaving you with this:
3.14×13²
When you calculate this, it should return a value of 530.66, which rounded to the nearest tenth is 530.7
Hope this helps!
If an interest rate of 5% results in interest of $50,
what is the principal amount of the loan?
Answer:
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Help&EXPLAIN
==============
Answer:
A = 108 in.²
Step-by-step explanation:
The figure can be decomposed into 3 rectangles.
✔️Area of rectangle 1 = L*W
L = 8 in.
W = 6 in.
Area = 8*6 = 48 in.²
✔️Area of rectangle 2 = L*W
L = 10 in.
W = 4 in.
Area = 10*4 = 40 in.²
✔️Area of rectangle 3 = L*W
L = 5 in.
W = 4 in.
Area = 5*4 = 20 in.
✔️Area of the irregular figure = 48 + 40 + 20 = 108 in.²
Help it’s due today plz
plz help with 24-28!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
Find The values of ( d ,f ,e ) angles
Answer:
angle d =35, e=55, f=55.............
(9, 19) (2, 16)
Write the coordinates as decimals or integers.
Answer:
In decimal 0.428571428
Step-by-step explanation:
The slope = (y2 - y1)/(x2 - x1) y2 = 16, y1 = 19x2=2 and x1=9
The slope = (16 - 19)/(2 -9)
The slope = (-3)/(-7)
The slope = 0.428571428
So in decimal form the coordinates are going to be written as 0.428571428
Slope is the steepness of a line, it is the difference between the y coordinates divided by the difference in x coordinates.
To go on a summer trip, Felipe borrows $200. He makes no payments until the end of 3 years, when he pays off the entire loan. The lender charges sim
Interest at an annual rate of 2%.
Answer:
Step-by-step explanation:
A=P(1+rt)
A=200(1+.02(3))
A=200(1.06)
A=$212