Answer:3888
Step-by-step explanation:
144= 1 hours
432=2 hours
1296=3 hours
3888=4 hours
A and b are positive integers and a-b=2 ... Evaluate the following:
27^1/3 b / 9^1/2 a
There is an image attached of the problem
Answer:
Step-by-step explanation:
a-b=2
[tex]\frac{27^{\frac{1}{3} b} }{9^{\frac{1}{2}a } } \\=\frac{(3^{3}) ^{\frac{1}{3} b} }{(3^{2} )^{\frac{1}{2} a} } \\=\frac{3^b}{3^a} \\=3^{b-a} \\=3^{-(-b+a)} \\=3^{-2}\\=\frac{1}{3^2} \\=\frac{1}{9}[/tex]
19. “40 of what number is 34” i need work
Answer:
85%
40% × ? = 34
? =
34 ÷ 40% =
34 ÷ (40 ÷ 100) =
(100 × 34) ÷ 40 =
3,400 ÷ 40 =
85
In a parenting magazine, Mrs. Smith read an advertisement about all the different ways that bleach can be used to kill bacteria. The advertisement claimed that some forms of bacteria triple in amount after each hour. Consider the situation where one bacterium is found on Mrs. Smith's countertop at home.
Question:
(a) How many bacteria would be found in 24 hours
(b) How many bacteria would be found in 2 days
(c) How long for 1000 bacteria to be found
Answer:
(a) 282429536481 bacteria
(b) [tex]7.97*10^{22[/tex] bacteria
(c) 6 days
Step-by-step explanation:
The question illustrates an exponential function
[tex]y = ab^x[/tex]
Where
[tex]a = Initial\ Value = 1[/tex]
[tex]b=Rate = 3[/tex] --- i.e. triples
[tex]x = number\ of\ hours[/tex]
Solving (a): Bacteria in 24 hours
In this case:
[tex]x = 24[/tex]
Substitute [tex]x = 24[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]y = 1 * 3^{24[/tex]
[tex]y = 1 * 282429536481[/tex]
[tex]y = 282429536481[/tex] bacteria
Solving (b): Bacteria in 2 days
[tex]2\ days =48\ hours[/tex]
So:
[tex]x = 48[/tex]
Substitute [tex]x = 48[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]y = 1 * 3^{48[/tex]
[tex]y =7.97*10^{22[/tex] bacteria
Solving (c): How long for 1000 bacteria
In this case:
[tex]y = 1000[/tex]
Substitute [tex]y = 1000[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]1000 = 1 *3^x[/tex]
[tex]1000 = 3^x[/tex]
Take Log of both sides
[tex]Log1000 = Log3^x[/tex]
This gives:
[tex]Log1000 = xLog3[/tex]
Make x the subject
[tex]x = \frac{Log1000}{Log3}[/tex]
[tex]x \approx 6[/tex]
Hence: It takes 6 days
Factor Completely
5xz + 2xy - 3yz
Answer:
Your answer is 5xz + 2xy - 3yz
Step-by-step explanation:
The expression is not factorable with rational numbers.
Therefore, You cannot factor the equation.
~Hoped this helped!~
~Brainiliest, please~
Help If don't know do not answer(if link will report)
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsGeometry
Supplementary Angles: Angles that add up to 180°Step-by-step explanation:
Step 1: Define
We can see from the diagram that the 2 angles are supplementary
(6x - 10)° + (7x + 8)° = 180°
Step 2: Solve for x
Combine like terms: 13x - 2 = 180[Addition Property of Equality] Add 2 on both sides: 13x = 182[Division Property of Equality] Divide 13 on both sides: x = 14wich mathematical expression represent this statement?the sqaure of a number times 3
1. 7n
2. 3n^2
3.2n + 8
4. n^3/ 2
Answer:
2
Step-by-step explanation:
( n^2)×3 can be written as 3(n^2)
Keith bought 5 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 40 cards left. How many cards did Keith
start with?
Answer:
85 cards
Step-by-step explanation:
A train leaves at 08:36 and arrives at 10:57. It travelled at an average speed of 85 km/h.
How far did it travel? Give your answer in km to 1DP.
Answer:
199.8 km to the 1 decimal point
Step-by-step explanation:
8:36 to 9:00 is 24 min
9:00 to 10:00 is 60 min
10:00 to 10:57 is 57 min
That's a total of 24 + 60 + 57 = 141 min = 141/60 hr.
d = rt = 141/60(85) = 199.8 km to the 1 decimal point
Triangle ABC has side lengths 8 inches, 17 inches, and 15 inches. Sofia uses the following steps to conclude that triangle ABC is not a right triangle.
a2+b2=c282+172=15264+289=225353 ≠ 225
What mistake did Sofia make?
Sofia made a calculation error.
Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Sofia does not know if triangle ABC is a right triangle, so she cannot use the Pythagorean Theorem or its converse.
Sofia’s conclusion is incorrect. When the sides of a triangle do not satisfy a2+b2=c2, you cannot conclude that the triangle is a right triangle.
Answer: Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Step-by-step explanation: The leg is the smallest number and the hypothenuse is the biggest nunber.
Answer:
Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Step-by-step explanation:
You are a packer for Acme Bottling Company.
You fill cartons with bottles,
seal the cartons, and stack them on pallets.
Monday through Friday you are paid $0.78 for each carton you fill.
On Saturday you are paid an additional$0.38 for each carton you fill.
What is your total pay for a week in which you
filled the following number of cartons?
Mon-210
Tues-175
Wed-224
Thurs-160
Fri-216
Sat-90
Answer:
$872.70
Step-by-step explanation:
Add all numbers from Mon-Fri.
So 985.
Multiply it by 0.78
So $768.30
Add 0.78 and 0.38
So 1.16
Then multiply 90 by 1.16
So $104.40
Then add the two numbers.
768.30+104.40
So $872.70
Hope this helps
The Sanchez family had dinner at their favorite restaurant. A 9% sales tax was added to their bill. Amy paid the bill with a $10 gift certificate plus $30.60. How much did the family's dinner cost before tax? Round your answer to the nearest penny.
Answer:
The bill was $36.95 without tax.
The price before tax was the amount of $37.25 which is before a 9% sales tax was added to their bill.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Their bill was charged a 9% sales tax.
Amy paid the bill with a $10 gift certificate plus $30.60
Use the equation P + rP =T,
where P is the price before tax, r is the sales tax rate, and T is the total price, including tax.
The price before tax (P) is unknown.
The total price(T) = 30.60 + 10 = 40.60
The sales tax rate (r) = 9% = 9/100 = 0.09
⇒ P + rP = T
Substitute the values in the above equation, and we get
⇒ P + (0.09)P = 40.60
⇒ P(1 + 0.09) = 40.60
⇒ P(1.09) = 40.60
⇒ P = 30.60/(1.09)
Apply the Division operation, and we get
⇒ P = 37.247706
Rounded to the nearest hundredth
⇒ P = 37.25
Therefore, the price before tax was the amount of $37.25.
Learn more about Arithmetic operations here:
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I really need help with these, if you know any it would help so much
1 - 53 is 45% of what number?
2 - if you got scored 20 out of 24 what percentage would that be?
3 - 80 is 55% of what number?
Answer:
1: 23.85
2: 83%
3: 44
Step-by-step explanation:
1 - do 53x0.45 (23.85)
2 - Divide 20 by 24, which you get 0.833333333 and move the decimal 2x to the right. You get 83.3333333, but round. So 83%
3 - do 80x0.55 (44)
Find the slope and this line.
Show that (16 1/4)3 and (16 3)1/4 are equivalent
Answer:
They are both 12
Change 16 1/4 into 4.
4 • 3
12
16 • 3 is 48
1/4 of 48 is 12
Hope this helps
HELP ASAP PLAESE HELPP
Answer:
Ur right it's C.448
Step-by-step explanation:
I did it on goo.gle lol
hope this helps luv
Please can someone help I don’t understand the question if it’s right I’ll give more plsssssesssssssssssddsd
Answer:
x = 33°
Step-by-step explanation:
From the figure attached,
FB and FC are two secants intersecting each other at point F outside the circle.
Measure of angles between the secants measures half of the difference between the intercepted arcs.
x° = [tex]\frac{1}{2}(\text{arc BC}-\text{arc DE})[/tex]
x° = [tex]\frac{1}{2}(108-42)[/tex]
x = 33°
Even more trig ratios see attachment
Step-by-step explanation:
1. Use the Pythagorean theorem to solve for side KM:
16^2+KM^2=34^2256+KM^2=1156KM^2=900KM=302. Cosine is adjacent over hypotenuse, so cosine of M would be KM/34, or 30/34
3. Tangent is opposite over adjacent, so tangent of L will be KM/16, or 30/16
4. Sine is opposite over hypotenuse, so sine of M will be 16/34
5. KM=30, solved for in step 1.
hope this helps!!
x
−
3
4
=
8
Which value of
x
satisfies this equation?
what is the distance between -3,500 and 2,000 feet
Answer: if you take 2,000- (-3,500) you get 5,500 ft, making this the distance. Also, think about it this way 2,000 is 2,000 ft from 0, and then there is another 3,500 past zero, putting these together makes the amount of space they are away from each other in total.
Note that when subtracting a negative it becomes positive, using the keep change change rule 2,000 - (-3,500) becomes 2,000 + 3,500
A magician performing a magic act has asked for 2 volunteers from the audience to help with his routine. If there are
250 people in the audience, which of the following expressions represents the number of possible pairs of volunteers ?
.
Answer:
The answer is 125. If you were to pair 250 people in 2, that would be 250 divided by 2. And 250 divided by 2 is 125.
Step-by-step explanation:
Tyler invested $350 in an account paying an interest rate of 4.5% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $700?
Answer:
15.4 I did this on delta math
It would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
How to calculate compounding time?The formula for calculating the future value (FV) of an investment with continuous compounding is:
[tex]FV = Pe^{rt}[/tex]
Where P is the initial principal, r is the annual interest rate (expressed as a decimal), t is the time period (in years), and e is the mathematical constant e (approximately 2.71828).
In this case, we have P = $350, r = 4.5% = 0.045, and we want to find the time t when the FV is $700. Substituting these values into the formula, we get:
[tex]700 = 350e^{0.045t}[/tex]
Dividing both sides by $350, we get:
[tex]2 = e^{0.045t}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) = ln\times e^{0.045t}[/tex]
Using the properties of logarithms, we can simplify this to:
ln(2) = 0.045t ln(e)
Since ln(e) = 1, we can simplify further to:
ln(2) = 0.045t
Finally, solving for t, we get:
t = ln(2) / 0.045 ≈ 15.4
Therefore, it would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
To know more about continuous compounding follow
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2 ways the akkadian and assyria empire are the same
Answer:
The Akkadian and Assyrian empires were two of the world’s first empires. Their conquests reshaped Mesopotamia. The many empires that would follow, worldwide,
Step-by-step explanation:
Write an equation in point-slope form of the line that passes through (-1, – 4) with slope -2.
Answer:
y+4=-2(x+1)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=-2(x-(-1))
y+4=-2(x+1)
A person in an apartment
building sights the top and bottom of an office
building 500 ft. away. The angle of elevation
for the top of the office building is 23° and the
angle of depression for the base of the building
is 50º. How tall is the office building?
Answer:
Step-by-step explanation:
tan23=h1/500
h1=500tan23
tan50=h2/500
h2=500tan50
The height of the building is h1+h2 so
H=500(tan23+tan50)ft (exact)
H=808.1 ft (rounded to nearest tenth of a foot)
Find the future amount at the end of two years for a $7000 investment that earns 7% at the end of each year
Answer:
$8,014.30
Step-by-step explanation:
* This is the correct answer, I have taken the test and am posting the answers in hopes of helping other people :] *
What is the value of y?
Triangle A B C has right angle C with side A C labeled 5. Angle A is 60 degrees and its opposite side B C is labeled y.
Enter your answer, as an exact value, in the box.
y =
Answer:
OMG THANK YOU-
You are putting money into a bank account. You start with $100 and add $12 every month. The total amount of money in your account can be represented by the following equation. (where T is total amount and M is the number of months):
T = 100 + 12 M
If you have $208, how many months have passed?
Show the equation and how you got the answer.
Answer:
9 months
Step-by-step explanation:
Answer:
it will be 9 months like the first person said
Please help me I don’t understand
Answer:
C
Step-by-step explanation:
tan α=opposite side /adjacent side
tan P=16/12=4/3
tanQ=12/16=3/4
Dilate Point B by a scale factor of 1/2
a (1.5,-4)
b (-1.5,1)
c (-1,-1.5)
d (-2,-2)
PLEASE HELP
Answer:
B
Step-by-step explanation:
Divide each coordinate by 2
3/2=1.5
2/2=1
Alejandra plans to sew fringe on a scarf. The scarf is shaped like a rectangle. The length of the scarf is 44 inches. The width is one half the length.
Answer:
Total fringe needed = 132 inches
Step-by-step explanation:
P.S - The exact question is -
Given - Alejandra plans to sew fringe on a scarf. The scarf is shaped like a rectangle. The length of the scarf is 44 inches. The width is one half the length.
To find - How much fringe does Alejandra need?
Proof -
Total fringe needed = Perimeter of the rectangle.
Now,
We know that,
Perimeter of the Rectangle = 2(Length + Width)
Now,
Given that,
Length = 44 inches
Width = one half the length
= [tex]\frac{1}{2}[/tex] × 44 = 22 inches
⇒Width = 22 inches
∴ we get
Perimeter of the Rectangle = 2(44 + 22)
= 2(66) = 132 inches
⇒Perimeter of Rectangle = 132 inches
∴ we get
Total fringe needed = Perimeter of the rectangle = 132 inches
⇒Total fringe needed = 132 inches