Logan has two aquariums. One aquarium contains 1. 3 cubic feet of water and the other contains 1. 9 cubic feet of water. The water in the larger aquarium weighs 37. 44 pounds more than the water in the smaller aquarium. Write an equation with a variable on both sides to represent the situation. Then find the weight of 1 cubic foot of water
Answers
The weight of 1 cubic foot of water is 56.16 pounds.
The equation to represent the situation is w_1 + 37.44 = w_2, where w_1 is the weight of 1 cubic foot of water in the smaller aquarium and w_2 is the weight of 1 cubic foot of water in the larger aquarium.
To find the weight of 1 cubic foot of water, we need to solve for w_1. We know that 1.3 cubic feet of water in the smaller aquarium weighs 1.3w_1 pounds, and 1.9 cubic feet of water in the larger aquarium weighs 1.9w_2 pounds. Using the equation above, we can set up the following equation:
1.3w_1 + 37.44 = 1.9w_2
Substituting w_2 = w_1 + 37.44 into the equation above, we get:
1.3w_1 + 37.44 = 1.9(w_1 + 37.44)
Simplifying, we get:
1.3w_1 + 37.44 = 1.9w_1 + 71.136
0.6w_1 = 33.696
w_1 = 56.16
Therefore, the weight of 1 cubic foot of water is 56.16 pounds.
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Related Questions
11. The sum of proper subsets and subsets of a set is
127. How many elements are there in this set?
Answers
Elements in set A is 7.
How do you calculate the number of items in a correct subset?Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.
RECALL: The number of proper subsets of a set with nn elements is 2^n-12
N
−1.
Let n = number of elements of the set.$
Then,Then, 2^n-1 = 127
2^n = 127+1
2^n=128
2^n = 2^7
N=7
$The set has 7 elements.
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According to the given information in the question the element in set A is 7.
How do you calculate the number of items in a correct subset?Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.
RECALL: The number of proper subsets of a set with nn elements is 2^n-12
N
−1.
Let n = number of elements of the set.$
Then, Then, 2^n-1 = 127
2^n = 127+1
2^n=128
2^n = 2^7
N=7
$The set has 7 elements.
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which of the following quantitative research methods uses a relatively small group of people for testing and is most helpful in obtaining data that are representative of the whole population? a.) in-depth interviews b.) secondary data analysis c.) natural experiments d.) random sampling
Answers
In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.
Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.
An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.
Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.
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Parallel lines r and s are intersected by a transversal line m.
Label a pair of corresponding angle measures (6x +11) and (3y+8)°.
The angle labeled (3y + 8)° is a linear pair with an angle measure of (10x - 13)°.
Set up algebra equations and solve for x and y.
Answers
Answer: x= 8 y= 17
Step-by-step explanation: 6*8 = 48+11=59
3*17=51+8=59
Answer:
x = 11.375
y = 23.75
Step-by-step explanation:
Corresponding angles: A pair of angles that are in the same relative position at each point where a straight line intersects two other straight lines.
If the two lines are parallel, the corresponding angles are equal.
Therefore:
⇒ (6x + 11)° = (3y + 8)°
⇒ 6x + 11 = 3y + 8
⇒ 6x + 3 = 3y
⇒ 3y = 6x + 3
Angles on a line sum to 180°.
Therefore:
⇒ (3y + 8)° + (10x - 13)° = 180°
⇒ 3y + 8 + 10x - 13 = 180
⇒ 3y + 10x = 185
⇒ 3y = 185 - 10x
Substitute the first equation into the second equation and solve for x:
⇒ 6x + 3 = 185 - 10x
⇒ 16x = 182
⇒ 16x = 182
⇒ x = 11.375
Substitute the found value of x into one of the equations and solve for y:
⇒ 3y = 6(11.375) + 3
⇒ 3y = 68.25 + 3
⇒ 3y = 71.25
⇒ y = 23.75
Which expression is equivalent to 5^6?
Answers
Answer:
Option 4
125 × 125
Step-by-step explanation:
5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 125 × 125
Thus, 5⁶ = 125 × 125
-TheUnknownScientist
What are the disadvantages of using manipulatuves when teaching Mathematics?
Answers
Answer:
anything that gets students touching, moving, and experiencing math concepts. The drawbacks of using these physical math manipulatives in the classroom? The teacher needs to be available to give informative feedback. It can take a long time to set up and solve a problem with large numbers or exponential concepts.
Step-by-step explanation:
PLease use a taylor polynomial to solve this one. We want to use the following equation to evaluate π : π=4arctan(1). The Taylor series of arctan(x) is arctan(x)=x−
3
x
3
+
5
x
5
−
7
x
7
+⋯=∑
k=1
[infinity]
(−1)
k+1
⋅
2k−1
x
2k−1
Let p
2n
1(x) be the Taylor polynomial of degree 2n−1 for arctan( x) and the point of approximation 0 . 3. Can we evaluate π more efficiently (that is, using polynomials of lower degrees)? Consider the following equality:
4
π
=4arctan(
5
1
)−arctan(
239
1
)
Answers
Using the Taylor polynomial approximation, 4/π = 4 * arctan(5/1) - arctan(239/1).
To evaluate π more efficiently using polynomials of lower degrees, we can use the Taylor polynomial approximation of arctan(x) to approximate the values of arctan(5/1) and arctan(239/1).
The Taylor polynomial of degree 2n-1 for arctan(x) centered at x = 0 is given by:
p2n-1(x) = x - (1/3)\(x^3\) + (1/5)\(x^5\) - (1/7)\(x^7\) + ... + \((-1)^{n+1\) * (2n-1) * \(x^{2n-1\)
To evaluate arctan(5/1) and arctan(239/1) using the Taylor polynomial approximation, we substitute x = 5/1 and x = 239/1 into the polynomial expression and perform the calculations.
For arctan(5/1):
p2n-1(5/1) = (5/1) - (1/3)\((5/1)^3\) + (1/5)\((5/1)^5\) - (1/7)\((5/1)^7\) + ...
For arctan(239/1):
p2n-1(239/1) = (239/1) - (1/3)\((239/1)^3\) + (1/5)\((239/1)^5\) - (1/7)\((239/1)^7\) + ...
By evaluating these polynomial expressions, we can obtain approximations for arctan(5/1) and arctan(239/1), which can be used to compute a more efficient approximation of π using the given equality:
4/π = 4 * arctan(5/1) - arctan(239/1)
Therefore, we can evaluate π more efficiently by using the Taylor polynomial approximation and substituting the appropriate values into the polynomial expression.
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heyy could you help me out?
Answers
Answer:
Step-by-step explanation:
Well so it is asking you the statements and reasons and there is a select button it would be..... Hold on think about the letter formation. Just choose your best answer you think it is because if we are telling you thats cheating. But look above what I said. Think of the letter formation and quardinate with the question. I am speeding and yes I know I spelt it wrong.
Which integer is NOT less than -21?
A. -30
B. -100
C -19
D -25
Answers
Answer:
Well -19 is less than -21 so it's the other three.
So it's -30, -100 and -25
Anyways the answer is 19!
Hope this helps!
HELP NOW IT IS 6th GRADE MATH HELPPPPPP
Answers
Answer:
S=2t
or
T=1/2 S
What is 7/3 times 5/3 times 11/3 simplified?????
Answers
Answer:
14.26
Step-by-step explanation:
7/3 x 5/3 x 11/3 = 7(5)11/(3³)
35 x 11 = 385/27
385 / 27 = 14.26
a rectangular parking lot has a perimiter of 500 feet and a width of 100 feet. find the lenght of the parking lot be sure to show all four steps
Answers
Answer:
50,0
Step-by-step explanation:
So we know 500×100=50,000
So it's 50,000
i was gone most of this school week and now i’m behind :( can you please help me out
You need to draw up a floor plan of your kitchen so that you can complete a
remodel. The kitchen is 25 ft by 15 feet. You kid sister says that your scale drawing
should be 10 inches by 5 inches. You think she is incorrect. Explain why and give a
better set of measurements for the scale drawing.
please give me the answer and explain it so i can understand it i would greatly appreciate it i turned this up to 35 pts :(
Answers
Answer:
first, not much up because the room is by feat, and hers is by inches, I don't really know the rest
would it br no solution bc the lines are parallel?
Answers
Answer:
Yes
Step-by-step explanation:
The solution to the system of equations shown with a graph is the point where the two lines intersect. Because the lines are parallel they do not intersect, meaning there is no solution.
Christopher is choosing between two cell phone plans that offer the
same number of free minutes. T-Mobile's plan is $39.99 with additional
minutes costing $0.45 each. Verizon's plan is $44.99 with additional
minutes costing $0.40 each. Which equation will let you know how many
additional minutes, a, it will take for the two plans to cost the same? *
39.99a +0.45 = 44.99a + 0.40
39.99 a + 0.45 = 44.99a -0.40
39.99 +0.45a = 44.99 + 0.40a
39.99 + 0.45a = 44.99a +0.40
Answers
Answer:
39.99 + 0.45a = 44.99 + 0.40a you're welcome (:
If there are 3 apples for every 4 oranges, how many apples would you have if you had 20 oranges?
Answers
Answer:
6 Apples
Step-by-step explanation:
There would be six apples and 2 oranges left over.
Hope this Helps!
:D
Answer:
I was kind of confused on this one but is it 15 apples?
Step-by-step explanation:
3, 6, 9, 12, 15
4, 8, 12, 16, 20
I think the answer is 15 apples.
someone please help.
Answers
The completed table with regards to terms of an expression are presented as follows;
Condition \({}\) (6·x + 3) + (5·x - 4) (-4·y - 16) - 8·y + 10 + 2·y
Exactly 3 terms N/A \({}\) N/A
Exactly 5 terms N/A \({}\) N/A
Includes a zero pair No \({}\) No
Uses distributive property No No
Includes a negative factor No
Has no like terms False False
Condition \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\) 0.25·(8·m - 12) - 0.5·(-4·m + 2)
Exactly 3 terms No \({}\) No
Exactly 5 terms Yes \({}\) \({}\) No
Includes a zero pair No \({}\) \({}\) Yes
Uses the distributive property Yes \({}\) Yes
Includes a negative factor Yes \({}\) Yes
Has no like terms No \({}\) No
What is a mathematical expression?A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.
The details of the conditions in the question are as follows;
Terms of an expression
A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction
Zero pair
A zero pair are two numbers that when added together have a zero result
Distributive property
The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend
Negative factor
A negative factor is a factor that has a negative sign prefix
Like terms
Like terms are terms consisting of identical variables with the same powers of the variable
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Find (h . g) (x) h (x) = 3x - 3 and g (x) = x2 + 3 A. 3x3 - 9 B. 3x3 - 3x2 + 9x C. 3x3 - 3x2 + 9x - 9 D. 3x3 + 3x2 + 9x - 9
Answers
Answer:
Step-by-step explanation:
(3x - 3)(x^2 + 3) = 3x^3 + 9x - 3x^2 - 9
3x^3 = 3x^2 + 9x - 9
answer is C
please help! show work if possible
Answers
Answer:
its 2=2=1
Step-by-step explanation:
3-3=0
the least-squares solution of a x = b is the vector in the column space of a closest to b. true or false?
Answers
the least-squares solution of a x = b is the vector in the column space of a closest to b. then the statement is true
Aleast- squares solution of is a vector such that for all in .
The statement is true because the general least-squares problem attempts to find an that maximizes .
The above statement is actually the one that validates the least-square solution statement.
Hence , the least-squares solution of a x = b is the vector in the column space of a closest to b .then the statement is true
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Can you help me with this question Name the Domain.
Answers
Solution:
Given:
\(f(x)=\frac{x+1}{x^2-6x+8}\)The domain is the set of all possible x-values (inputs) that will make the function (output) to be real and defined.
To get the domain of the function given, we need to get the undefined or singularity points.
\(\begin{gathered} f(x)\text{ will be defined only when the denominator is equal to 0.} \\ \text{Hence, singularity or undefined points will occur when,} \\ x^2-6x+8=0 \\ \text{Solving to get these points,} \\ x^2-4x-2x+8=0 \\ x(x-4)-2(x-4)=0 \\ (x-2)(x-4)=0 \\ x-2=0 \\ x=0+2 \\ x=2 \\ \\ OR \\ x-4=0 \\ x=0+4 \\ x=4 \\ \\ \text{Hence, singularity occurs at;} \\ x=2,x=4 \end{gathered}\)
The domain of the function will exist when;
\(\begin{gathered} x\ne2,x\ne4 \\ \\ \text{Hence, the solution to the domain of the function is;} \\ x<2\text{ OR }24 \end{gathered}\)Hence, the solution to the domain is;
\(x<2\text{ OR }24\)In interval notation, the domain is;
\((-\infty,2)\cup(2,4)\cup(4,\infty)\)Therefore, the final answer is;
All real numbers except 2 and 4.
A cat adoption facility takes in an average of 4 cats per day. The facility has to keep their cat occupancy below 300. Currently, the facility has 264 cats.
If none of their cats get adopted, how many more days, x, can the facility continue to take in cats? Select the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit.
A.
x < 9
B.
x < 3
C.
x < 32
Answers
The inequality that includes the largest integer is:
x < 32
So the answer is C.
What is inequality?An inequality is a mathematical statement that compares two values or expressions and shows the relationship between them, using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Inequalities are used to express that one value is less than or greater than another value or that the values are not equal. For example, the inequality "x > 5" means that x is greater than 5. The inequality "y ≤ 10" means that y is less than or equal to 10.
To calculate the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit:
Number of cats the facility can take in before reaching the occupancy limit = 300 - 264 = 36
Number of days the facility can continue to take in cats before reaching the occupancy limit = (Number of cats the facility can take in) / (Average number of cats taken in per day) = 36/4 = 9
So the inequality that includes the largest integer for x is:
x < 32
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A researcher collects data on the outcomes when a fair 6-sided die is rolled. unfortunately, she has forgotten her die at home and needs to submit her results to her teacher. which statistical design would be best utilized to approximate the results of rolling a 6-sided die?
Answers
She could make her approximation in the multiples of 1/6.
Whats is Statistic and probability ?Probability is the chance of happening a certain event of all the possible events that can occur.
Statistics is a branch of mathematics where organising and interpretation of data analysing is needed.
A fair 6 sided dice has 6 sides having numbers from 1 to 6 and for a fair dice each side has a probability of 1/6. So she could make her approximation in the multiples of 1/6 for example 6/36 and the numerator she can vary by ±10 % for approximation.
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Write the equation in slope intercept form y - 4=10(x-5)
Answers
Answer:
y = 10x - 46
Step-by-step explanation:
slope intercept form: y = mx + b
m is slope and b is y-intercept
given: y - 4 = 10(x-5)
1. distibute 10
y - 4 = 10x - 50
2. we need to get y by itself so bring -4 to other side
y = 10x - 50 + 4
y = 10x - 46
slope-intercept form is \(y=mx+b\)
\(y=10(x-5)+4\) ↣ We move -4 to another side and become positive number.
\(y=(10x-50)+4\) ↣ Distribute 10 inside the brackets.
\(y=10x-50+4\\y=10x-46\) ↣ Then we get the slope-intercept form.
Thus, the answer is \(y=10x-46\)
To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 3%. The first credit card compounds interest semi-annually, while the second credit card compounds monthly. The homeowner plans to pay off the loan in 10 years.
Part A: Determine the total value of the loan with the semi-annually compounded interest. Show all work and round your answer to the nearest hundredth.
Part B: Determine the total value of the loan with the monthly compounded interest. Show all work and round your answer to the nearest hundredth.
Part C: What is the difference between the total interest accrued on each loan? Explain your answer in complete sentences.
Answers
The total interest paid on each loan is different by about $34.75.
To calculate the total value of the loan with different compounding frequencies, we can use the formula for compound interest:
\(A = P(1 + r/n)^{(nt)\)
Where:
A = Total value of the loan (including principal and interest)
P = Principal amount (initial loan)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Part A: Semi-annually compounded interest,
Given:
Principal amount (P) = $20,000
Annual interest rate (r) = 3% = 0.03
Number of times compounded per year (n) = 2 (semi-annually)
Number of years (t) = 10
Using the formula, we can calculate the total value of the loan:
\(A = 20000(1 + 0.03/2)^{(2\times10)\)
\(A = 20000(1.015)^{20\)
A ≈ 20000(1.34812141)
A ≈ $26,962.43
Therefore, the total value of the loan with semi-annually compounded interest is approximately $26,962.43.
Part B: Monthly compounded interest
Given:
Principal amount (P) = $20,000
Annual interest rate (r) = 3% = 0.03
Number of times compounded per year (n) = 12 (monthly)
Number of years (t) = 10
Using the formula, we can calculate the total value of the loan:
\(A = 20000(1 + 0.03/12)^{(12\times10)\)
\(A = 20000(1.0025)^{120\)
A ≈ 20000(1.34985881)
A ≈ $26,997.18
Therefore, the total value of the loan with monthly compounded interest is approximately $26,997.18.
Part C: Difference in total interest accrued =
To find the difference in total interest accrued, we subtract the principal amount from the total value of the loan for each case:
For semi-annually compounded interest:
Total interest accrued = Total value of the loan - Principal amount
Total interest accrued = $26,962.43 - $20,000
Total interest accrued ≈ $6,962.43
For monthly compounded interest:
Total interest accrued = Total value of the loan - Principal amount
Total interest accrued = $26,997.18 - $20,000
Total interest accrued ≈ $6,997.18
The difference between the total interest accrued on each loan is approximately $34.75 ($6,997.18 - $6,962.43).
The loan with monthly compounded interest accrues slightly more interest over the 10-year period compared to the loan with semi-annually compounded interest.
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Math help 60!!!!!!!!!!!!!
Answers
Answer:
perimeter is 36 and area I think is 72
Step-by-step explanation:
A rectangular prism is shown below.
What is the volume of the rectangular prism?
A. 260 cm
B. 240 cm
C. 220 cm
D. 200 cm
Answers
200 sq. cm. or 200^3
10x5=50
50x4=200
a circular reception tent has a center pole 25 feet high, and the poles along the outside are 10 feet high. assume that the distance from the outside poles to the center pole is 30 feet. a.what is the slope of the line that follows the roof of the reception tent?b.how high is the tent 5 feet in from the outside poles?c.ropes are used to stabilize the tent following the line of the roof of the tent to the ground. how far away from the outside poles are the ropes at-tached to the ground?
Answers
The slope of the line which follows is 0.50 and height of the tent 5 feet from the outside pole will be 12.5.
The rise to run ratio is known as the slope. From 10 feet to 25 feet, there is a 15-foot increase. The run is 30 feet from the edge to the center.
slope = rise/run
= 15 /30 = 1/2
= 0.50
25 feet from the center pole is equivalent to 5 feet from the outer pole.
The rise at 25 feet from the central pole is now determined by
rise = m*run
=-12.5
As a result, the height of the pole decreases by 12.5 feet as one moves 25 feet from the central pole to the outside pole.
Consequently, the tent's height at 5 feet from the outside pole would be 25 - 12.5 = 12.5 feet.
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Classify each number according to its value. 3. 2 × 105 1. 9 × 10-1 2. 2 × 103 2. 4 × 103 5. 9 × 102 6. 1 × 101 2. 5 × 104
Answers
3.2 x 10^5 goes in greater than 2.4 x 10^4
1.9 x 10^-1 goes in less than 1.2 x 10^2
2.2 x 10 goes in less than 1.2 x 10^2
2.4 x 10^3 goes in between 1.2 x 10^2 and 2.4 x 10^4
5.9 x 10^2 goes in between 1.2 x 10^2 and 2.4 x 10^4
6.1 x 10 goes in less than 1.2 x 10^2
2.5 x 10^4 goes in greater than 2.4 x 10^4
What is a place value?
The foundation of our entire number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number. The digits in the numbers 42,316 and 61,432 are distinct from one another.
Here, we
First, let's find out what 2.4 x 10^4 and 1.2 x 10^2 are.
2.4 x 10^4 = 24000
1.2 x 10^2 = 120
3.2 x 10^5 is obviously greater than 2.4 x 10^4 because the exponent of ten in 3.2 x 10^5 is one more value than the exponent in 2.4 x 10^4. The decimal is also greater.
1.9 x 10^-1 = .19, which is less than 1.2 x 10^2
2.2 x 10 = 22, less than 1.2 x 10^2
2.4 x 10^3 = 2400, in between 1.2 x 10^2 and 2.4 x 10^4
5.9 x 10^2 = 590, in between 1.2 x 10^2 and 2.4 x 10^4
6.1 x 10 = 61, less than 1.2 x 10^2
2.5 x 10^4 we can solve this without explanation, 2.5 is greater than 2.4 meaning the product will be greater,
to check 2.5 x 10^4 = 25000, greater than 2.4 x 10^4
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A bag contains 20 counters. 16 of the counters are green. A counter is picked at random. What is the probability that it is green? Give your answer as a fraction. pls help urgent
Answers
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
3/4
Step-by-step explanation:
We need two points to find the slope
( 20,20) and (60,50)
m = (y2-y1)/(x2-x1)
= (50-20)/(60-20)
= 30/40
= 3/4