Answer:
[tex]\frac{dV}{dt} = 360 \ cm^3/h[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
Volume of a Rectangular Prism: V = lwhCalculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h[/tex]
Step 2: Differentiate
Rewrite [VRP]: [tex]V = l^2h[/tex]Differentiate [Basic Power Rule]: [tex]\frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}[/tex]Step 3: Solve for Rate
Substitute: [tex]\frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)[/tex]Multiply: [tex]\frac{dV}{dt} = 360 \ cm^3/h[/tex]Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.
The lines A and B are parallel. Identify a pair of corresponding angles?
Answer:
2 and 5............................
Answer:
Yes. 2 & 5 / 4 & 8 / 1 & 6 / 3 & 7 (Choose one yourself)
Step-by-step explanation:
Corresponding angles are angles that have one angle outside a pair of parallel lines and one angle within it and they are equal to each other.
what 1+1
duwjus
w7wjqiw
Answer:
hmm.......i think it's 11
it might be 2
no 11
ehh maybe 11
oh my god
so uhmmmmmm
it's either 11
or it's 2
im having a mental crisis
How can this expression be written another way?
Apply the distributive property and the greatest common factor to write an equivalent expression.
Enter your answer by filling in the boxes.
105 + 35m = __ (__)
Answer:
(105 x 30) + (105 x 5) + m
Step-by-step explanation:
Answer:
(105 x 30) + (105 x 5) + m
Step-by-step explanation:
Hope this helped have an amazing day!
A utility company estimates that a power line repair job will take a total of 24 person-hours. If 3 workers are assigned to the job, how long will it take them to complete the job according to this estimate?
Answer:
8hrs
Step-by-step explanation:
[tex] \frac{24}{3} \\ \\ [/tex]
Based on the information given, the number of hours that will be used will be 8 hours.
From the information given, the company estimates that a power line repair job will take a total of 24 person-hours and 3 workers are assigned to the job.
Therefore, the number of hours that will be used will be:
= 24 hours / 3
= 8 hours
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The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?
Answer
a. 0.856
b. 0.78071
c. It is not unusual
d. 13.65 years old
Step-by-step explanation:
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.
We solve this question using z score formula:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Find the probability that a cat will live to be older than 14 years.
For x > 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x<14) = 0.144
P(x>14) = 1 - P(x<14) = 0.856
b. Find the probability that a cat will live between 14 and 18 years.
For x = 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x = 14) = 0.144
For x = 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x = 18) = 0.92471
The probability that a cat will live between 14 and 18 years is calculated as:
P(x = 18) - P(x = 14)
0.92471 - 0.144
= 0.78071
c. If a cat lives to be over 18 years, would that be unusual? Why or why not?
For x > 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x<18) = 0.92471
P(x>18) = 1 - P(x<18) = 0.075288
Converting this to percentage:
0.075288 × 100 = 7.5288%
Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.
d. How old would a cat have to be to be older than 90% of other cats?
From the question above, 10% of the cats would be older than 90% of other cats.
Hence, we find the z score of the 10th percentile
= -1.282
Hence,
-1.282 = x - 15.7/1.6
Cross Multiply
-1.282 × 1.6 = x - 15.7
- 2.0512 = x - 15.7
x = 15.7 -2.0512
x = 13.6488 years old
Approximately = 13.65 years old
write an equation of the line y=5x+8 that passes through the point (4,-3)
The price of admission to the Everglades Historical Museum is $11 more for non-members than for members of the museum’s Friends of the Museum program.
If a group of 3 members and 4 non-members pays a total of $79 to visit the Museum, what is the cost, in dollars, of the ticket for one non-member?
Select one:
A. $9.00
B. $11.00
C. $15.00
D. $16.00
Answer:
d. $16.
Step-by-step explanation:
3 members (m) + 4 nonmembers (n) = $79
nonmembers = $11 more or n=m+11 so...
3m + 4(m+11)=79 [replace "n" with "m+11"]
3m + 4m + 44=79
7m + 44 = 79
7m=35 and reduced m=5 so members pay $5 and nonmembers pay 5+11=$16
Evaluate 5x - 9y if x = 8 and y=-3
Plz help like soon
Solve the following system of equations using the elimination method. 8x – 5y = 5 –8x – 6y = 6
A)
(2,–3)
B)
(0,1)
C)
(–2,3)
D)
(0,–1)
Answer:
x = 0, y = -1
Step-by-step explanation:
Slope and y intercept of y=2.7x+8
Answer:
slope: 2.7
y-intercept: (0,8)
Step-by-step explanation:
In the form y = mx + b, m is the slope and b is the y-intercept.
Can you please help me with the question.
Answer:
Step-by-step explanation:
A. 40:80
B: 80/40
C; 40: 120
D: 80:120 ;)
Solve for x:abx²-(a⁴+b⁴)x+a³b³=0
Step-by-step explanation:
abx² - (a⁴ + b⁴)x + (a³b³) = 0
(ax - b³)(bx - a³) = 0
Therefore x = b³/a or x = a³/b.
I really need help with -8 - 4(5m + 9)
he;ppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
y = 64
Step-by-step explanation:
The angles are supplementary, that is sum to 180° , thus
2(x + 6) + y = 180 ← substitute x = 52
2(52 + 6) + y = 180
2(58) + y = 180
116 + y = 180 ( subtract 116 from both sides )
y = 64
How much simple interest does $5,000 earn in 4 years at an interest rate of 5%. Round to
the nearest cent.
Answer:
1000
Step-by-step explanation:
If A = (2, 4, 6, 8, 10) and B = {4, 8, 10), then which of the following statements is false?
Answer:
A⊂B is the false
Step-by-step explanation:
because there are elements in A not exist in B
Answer:
A is the subset of B
is the false statement.
Please help me answer this :)
I will give braisnlt
Answer:
y = -1/2x + 4
Step-by-step explanation:
I got -1/2x because for every 2 spaces, the line goes down 1 (rise/run)
I got +4 because 4 is where x = 0, or the y intercept
Find 83 1/3 % of 384
Answer:
319.872
Step-by-step explanation:
319.872 / 384 = 83 1/3 / 100
Final Answer: [tex]320[/tex]
Steps/Reasons/Explanation:
Question: Find [tex]83\frac{1}{3}[/tex]% of [tex]384[/tex].
Step 1: Convert mixed fraction into improper fraction.
[tex]\frac{250}{3}[/tex]
Step 2: Multiply [tex]\frac{250}{3 * 100}[/tex] with [tex]384[/tex].
[tex]\frac{96000}{300}[/tex]
Step 3: Simplify
[tex]320[/tex]
~I hope I helped you :)~
Express the percent as a decimal 6.4%
Answer:
0.064
Step-by-step explanation:
Hope this helps!
This my homework and I'm bad at math if you can take the time please help me out f(x)= (x-5)to the power of 2 +12
I need the vertex
Axis of symmetry
Domain
Range
Answer:
Vertex: (5,12)
Axis of Symmetry: x=5
Domain: (-infinity, +infinity)
Range: [12, +infinity)
Step-by-step explanation:
What is the area of a hexagon with a side length of 10? it also has a rectangle in it with other measurements but the question is asking for the area of the hectagon.
Answer:
there is a formula for a hexagon .. it's
Area = 3[tex]\sqrt{3\\}[/tex]/2 * [tex]length^{2}[/tex]
where length is the length of one side, assuming all sides are equal
Step-by-step explanation:
3*[tex]\sqrt{3}[/tex]/2= 7.348469228.........
since the length is 10... the length squared is 100
then the total area of the hexagon is 734.8469228...... [tex]units^{2}[/tex].. what ever they are
if you want to work with some concepts.. you could also say that a hexagon is just a box with the corners cut off and the triangles that are missing are the equilateral right triangles with a hypotenuse of 10 . and since 2 pieces of those triangles make a square.. you can subtract two squares of that size from the bigger box that the hexagon fits into. this is a long way to figure this out but might be good for trigonometry practice :)
it will also be 734.8463288..... see if you can work that out :)
what is the slope, m, and the y-intercept of the line that is graphed below?
Answer:
m= 1; (0, 3)
Step-by-step explanation:
jus bc
Convert 5700 milligrams into pounds. Round your answer to the nearest hundredth.
The value of the 5,700 milligrams in pounds is approximately 0.01 lb
What is a unit of measurement?A unit of measurement is a specified magnitude of a quantity that is accepted and adopted by convention or backed by law, and used as a measurement standard.
In other to successfully convert a quantity in one unit to another unit, both units (initial and destination unit) should refer to the same characteristics of the object being measured.
Once both units are confirmed to refer to the same quantity, conversion factors are used to multiply the quantity in the first unit in order to express it in the other unit.
The given parameters are;
The quantity to be converted to pounds = 5,700 milligrams
The factor of conversion is 1,000 mg ≈ [tex]2.205 \times 10^{-6}[/tex] lb
Therefore;
[tex]5,700\: mg = 5,700 \times 2.205 \times 10^(-3) ≈ 0.0126[/tex]
Therefore, to the nearest hundredth, we have;
5,700 mg ≈ 0.01 lb
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The clothing store marked down all their shirts by 30%. If a shirt originally cost $24, what is the sale price of the shirt?
Answer:
$16.80
Step-by-step explanation:
Since the shirts are marked down by 30%, you need to multiply the cost of the shirt by the percentage.
$24 × 0.3 = $7.20
Next, subtract the discount from the original price to find the discounted price.
$24 - $7.20 = $16.80
Express 236% as a mixed number in simplest form
Answer:
2[tex]\frac{9}{25}[/tex]
Step-by-step explanation:
Patricia added 1 1/4 of salsa to a pot of her homemade chili. With the salsa the pot held 2 1/2 quarts of chili how many cups of salsa are in on quart of chili
A 1/2
B 2
C 5/8
D 1 & 1/4
A math club receives a 120 discount on calculators. If each
calculator costs S15 before the discount, how much will the
club spend on 60 calculators after the discount?
Answer:
$780
Step-by-step explanation:
15x60 = 900 900 - 120 = $780
The area of a square shaped park measures 16900 square feet. How many feet of fencing would be needed to enclose that park?
Answer:
520 feet
Step-by-step explanation:
The area=16900
Area formula=b^2
b^2=16900
square root of 16900=130
130*4=520
is Water is stored in response to changing demand a cause or effect
the answer is effect
Answer:
this a effect you can change the change the water
can you guys help me pls this is my final :(
Answer:
look up on math..way:)
Step-by-step explanation: