the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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What is the area of the real object that the scale drawing models? Scale factor. 1:5 Area = 10 square cm Scale drawing Real object
Answer:
D. 50 square centimeters
A young sumo wrestler decided to go on a special diet to gain weight rapidly. He gained weight at a constant rate.
The table compares the wrestler's weight (in kilograms) and the time since he started his diet (in months).
Time (months) Weight (kilograms)
1.5
1.51, point, 5
85.8
85.885, point, 8
3.0
3.03, point, 0
93.6
93.693, point, 6
4.5
4.54, point, 5
101.4
101.4101, point, 4
What was the wrestler's weight before he went on his diet?
The wrestler's weight before he went on his diet was 78.0 kilograms.
What is y-intercept?
In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.
To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.
We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:
(1.5, 85.8) and (3.0, 93.6)
The change in weight over the time interval of 1.5 to 3.0 months is:
93.6 - 85.8 = 7.8
The change in time over that interval is:
3.0 - 1.5 = 1.5
So the slope of the linear function is:
7.8 / 1.5 = 5.2
Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:
y - 85.8 = 5.2(x - 1.5)
where y represents the wrestler's weight and x represents the time in months.
To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:
y - 85.8 = 5.2(0 - 1.5)
y - 85.8 = -7.8
y = 78.0
Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.
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The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
A. Reflective property
B. Symmetric property
C. Transitive property
D. Addition property
The correct answer is B. Symmetric property.
The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.
The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.
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Each year, the school has a goal to have a third as many students in remedial mathematics courses as the year before. Currently the school has 1,200 students in remedial math. Approximately how many students will be enrolled in four years?
(a) 44 (b)15 (c) 32,400 (d) 1
Answer:
44 students
Step-by-step explanation:
1200 for the first year
a third of that is 400
400 for the second year
a third of that is 133.4
133.4 for the third year
a third of that is 44
- 1 and combining like terms
(x² - 4x+9)-(3x² - 6x-9)
Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36
What are algebraic expressions?Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.
Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;
SubtractionBracketDivisionParenthesesMultiplicationAdditionFrom the information given, we have;
(x² - 4x+9)-(3x² - 6x-9)
First, expand the bracket
x² - 4x + 9 - 3x² + 6x + 27
Now, collect the like terms
x²- 3x² - 4x + 6x + 9 + 27
Add or subtract
-2x² + 2x + 36
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A bank account gathers compound interest at a rate of 5% each year. Another bank account gathers the same amount of money in interest by the end of each year, but gathers compound interest each month. If Abraham puts £4300 into the account which gathers interest each month, how much money would be in his account after 2 years and 5 months? Give your answer in pounds to the nearest 1p.
Answer:
$6235 1
' 1 . ' 8
Answer:
Step-by-step explanation:
Simplify 1/cos x + 1/cos x -1
Answer:
-2cotxcscx
Step-by-step explanation:
Step 1: Find a common denominator
Step 2: Simplify
Which two statements best describe Michael’s height while on the two roller coasters?
It switches between negative and positive every 40 seconds. it switches between positive and negative every 80 seconds. So correct statements are B and E.
Describe Algebra?Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.
Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.
As a result, every 40 seconds it alternates between negative and positive.
B is accurate.
We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.
As a result, every 80 seconds it alternates between positive and negative.
E is accurate.
The complete question is:
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Nine friends share 4 sandwiches equally what fraction of a sandwich does each friend get
Answer:
4/9
Step-by-step explanation:
4 sandwiches in between 9 friends
4 sandwiches must be divided in between 9 people
- > [tex]\frac{4 sandwiches}{9 people}[/tex] = [tex]\frac{4}{9}[/tex]
Answer:
Step-by-step explanation:
2/3
I need this done in 10 mins or less!!!
Answer:
To find the volume of Leah's new planter, we need to multiply the length, width, and height of the container:
V = 15 m x 4 m x 8 m x 11 m x 3 m
V = 11,880 cubic meters
Therefore, the total volume of Leah's new planter is 11,880 cubic meters.
Let's represent the volume of the large box as x cubic inches. Since the total volume of both boxes is 212 cubic inches, we can set up the following equation:
8 x 4 x 2 + x = 212
Simplifying the left side, we get:
64 + x = 212
Subtracting 64 from both sides, we get:
x = 148
Therefore, the volume of the large box is 148 cubic inches.
The surface area of a cylinder is given by the formula SA = 2r2 + 2rh. A cylinder has a radius of 12 cm and a surface area of 1,632 cm^2 . Find the height of the cylinder.
A. 52 cm
B. 56 cm
C. 59 cm
D. 34 cm
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
Using trigonometric functions, we can find that the value of the angle N is 3°.
What are trigonometric functions?The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.
Here, using the cosine theorem:
CosM = n² + l² - m²/2nl
⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70
⇒ -0.981 = 729 + 4900 - m²/3780
⇒ 5629 - m² = -3708
⇒ m² = 9337.
Now Cos N = m² + l² - n²/2ml
= (9337 + 4900 - 729) / (2 × √9337 × 70)
= 0.9985
Cos N = 0.9985
Putting [tex]Cos^{-1}[/tex] on both sides:
[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985
⇒ N ≈ 3°
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The complete question is:
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
Someone please help me answer this question
The two statements that are both true are as follows: line
AC is perpendicular to line HB and line AC is parallel to FG. That is option A.
What is a perpendicular line?A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.
A line is said to be parallel to each other when they do not intercept as they are both on the same plane.
From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.
Also, line AC is parallel to FG, because they can never intersect till infinity.
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At age 25 , someone sets up an IRA (individual retirement account) with an APR of 4 %. At the end of each month he deposits $95 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
Question content area bottom
Part 1
After retirement the IRA will contain $
enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.
How will you calculate the balance of the IRA?To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:
FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)
Where:
Pmt = $95 (the monthly deposit amount)
r = 4% / 12 = 0.003333 (the monthly interest rate)
n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)
Plugging in these values, we get:
FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)
FV = $98,052.52
Therefore, the IRA will contain $98,052.52 at age 65.
Part 2
To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:
Total Deposits = Pmt * n
Plugging in the values, we get:
Total Deposits = 95 * 480
Total Deposits = $45,600
Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.
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75909931 rounded to the nearest hundred thousand
Answer:
the answer is supposably 75900000
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
A 2.25 inches
B 4.5 inches
C 6.75 inches
D 12.75 inches
Answer:
6.75 inches.
Step-by-step explanation:
[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]
[tex]= 56.52 + 18.84h[/tex]
[tex]183.69 - 56.52 = 18.84h[/tex]
[tex]127.17 = 18.84h[/tex]
[tex]=\frac{127.17}{18.84}[/tex]
[tex]=6.75[/tex]
Rachel ran 3 miles when she was training for a race. How many feet did she run?
15,840 feet
5,280 feet
10,560 feet
14,840 feet
To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:
3 miles x 5,280 feet/mile = 15,840 feet
Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.
please please please help i’ll give brainlist
The scale factor of PQRS to JKLM is 4/5.
The scale factor of JKLM to PQRS is 5/4.
The value of w, x, and y are 20, 12.5, and 20 respectively.
The perimeter ratio is 4:5.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor of PQRS to JKLM = 15/12
Scale factor of PQRS to JKLM = 5/4 or 1.25.
Scale factor of JKLM to PQRS = 12/15
Scale factor of JKLM to PQRS = 4/5 or 0.8.
For the value of w;
15/12 = 25/w
15w = 12 × 25
w = 20
For the value of x;
15/12 = x/10.
12x = 150
x = 12.5
For the value of y:
15/12 = y/16
12y = 15 × 16
y = 20
Perimeter ratio = 12 : 15 = 4:5
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I need help with a problem on my test.
Write an exponential function to model the situation. Tell what each variable represents. A price of $115 increases 9% each month.
Please help
Answer: 1050$
Step-by-step explanation:
im a math teacher
The function S=m^(2)+6m+8 models the growth of book sales in m months, where S is an amount in thousands of dollars. In how many months do book sales reach $80,000 ?
Answer:
We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.
We can set up an equation as follows:
S = m^2 + 6m + 8 = 80
Subtracting 80 from both sides, we get:
m^2 + 6m - 72 = 0
We can factor this quadratic equation as:
(m + 12)(m - 6) = 0
This gives us two possible solutions:
m + 12 = 0 or m - 6 = 0
Solving for m in each case, we get:
m = -12 or m = 6
Since we are looking for a number of months, we can discard the negative solution.
Therefore, book sales reach $80,000 in 6 months.
So, the answer is: 6 months.
To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Reflect on why you think guitar tabs are easier or harder to read than regular musical notation.
This will have to be in paragraph form. :)
Guitar tabs are generally considered easier to read than regular musical notation because they are written in a language that most guitarists are familiar with.
What is Guitar?Guitar is a stringed musical instrument played with the fingers or a pick. It is one of the most popular instruments in the world and is widely used in genres such as rock, jazz, blues, country, folk, and classical.
Unlike traditional notation, guitar tabs do not require any knowledge of music theory to understand. Instead, they are laid out in a straightforward format that conveys the pitch of a note and the timing of when it should be played. This makes it easier for most guitarists to quickly learn a new piece of music without having to spend time studying the complexities of traditional notation. Additionally, guitar tabs also offer an easy way to determine the fingering of certain chords or techniques.
While guitar tabs are easier to read than traditional notation, they do have some drawbacks. For one, guitar tabs cannot convey the same level of detail about a piece of music as traditional notation can. Additionally, it can be difficult for some to distinguish between rhythm and lead parts when reading guitar tabs. Finally, guitar tabs do not easily convey the dynamics or expression of a piece of music, which are important to consider when playing music.
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88.128 x 0.5 Multiplication question
Answer:
44.064x
Step-by-step explanation:
Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064
Hope this helps :)
I will mark you brainiest!
The value of M is
A) 14
B) 18
C) 20
D) 28
Answer:
I got 28
Step-by-step explanation:
use the formula k=y/x. 6/8=0.75
21/0.75=
Need help pls
geometry
#23
Answer: I think its C
Answer:
Step-by-step explanation:
C is false. [tex]\angle BEC = \angle AED=126[/tex] (vertically opposite).
The rest are correct.
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
If you place a 26-foot ladder against the top of a building and the bottom of the ladder is 20 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. help please now.
Answer: The building is approximately 16.6 feet tall.
Step-by-step explanation:
Use Pythagorean theorem (a²+b²=c²) to solve this.
We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.
Your equation would be: 20²+x²=26²
subtract 20² from 26² --> 276=x²
then take the square root --> 16.6=x
What is the fourth term of the sequence:
Write the number in the blank only.
a_1 = 5
a_n = 2a_n-1 + 3
The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.
Calculating the fourth term of the sequenceGiven the following definition of functions
a₁ = 5
aₙ = 2aₙ₋₁ + 3
To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:
a₂ = 2a₁ + 3 = 2(5) + 3 = 13
a₃ = 2a₂ + 3 = 2(13) + 3 = 29
a₄ = 2a₃ + 3 = 2(29) + 3 = 61
Therefore, the fourth term of the sequence is 61.
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The sum of twice a number,n, and 14 is 30. Write an equation that models this statement.Then explain how you might use reasoning to find the value of n.
Answer:
2n + 14 = 30
Step-by-step explanation:
Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.
This model represents the total on the top and the 2 parts on the bottom.