Oil leaks from a tank. At hour t = 0 there are 360 gallons of oil in the tank. Each hour after that, 3% of the oil leaks out.
(a) What percent of the original 360 gallons has leaked out after 8 hours?
%
(b) if Q(t) = Q0e^kt the quantity of oil remaining after t hours, find the value of k.
k=
(c) What does k tell you about the leaking oil? Select all that apply if more than one statement is true
A. It tells what percent of oil remains after each hour.
B. It is the amount that the oil that leaks out each second.
C. Because it is less than one, we know the amount of oil in the tank is decreasing,
D. It tells by what percent of oil decays each hour.
E. Because it is negative, we know the amount of oil in the tank is decreasing.
F. It gives the continuous hourly rate at which oil is leaking.
G. None of the above
I struggled with this !
Answer:
1 gallon = 2.85
Step-by-step explanation:
22.80-14.25=8.55
8.55/3=2.85
1 gallon cost 2.85
an academic department has just completed voting by secret ballot for a department head. the ballot box contains four slips with votes for candidate a and three slips with votes for candidate (a) List all possible outcomes. This answer has not been graded yet. (b) Suppose a running tally is kept as slips are removed.
Therefore , the solution of the given problem of probability comes out to be AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)
What is probability?The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.
Here,
(a) The voting box contains a total of seven slips, four of which are for candidate A and three for candidate B. Thus, there are 35 events that can occur from 7 choose 4 (or 7 choose 3) options.
Each vote can be represented by a letter, with A standing for a vote for candidate A and B for candidate B, so that all outcomes can be listed. These are the potential results:
AAAA
AAAB
AABA
ABAA
BAAA
AABB
ABAB
BABA
BBAA
ABBB
BABB
BBAB
BBBA
(b)
For instance, the following results could occur if the slips were removed in the following order:
A (1 vote for contender A) (1 vote for candidate A)
AA (2 ballots for candidate A) (2 votes for candidate A)
AAB (2 ballots for candidate A, 1 vote for candidate B) (2 votes for candidate A, 1 vote for candidate B)
AAAB (3 ballots for candidate A, 1 vote for candidate B) (3 votes for candidate A, 1 vote for candidate B)
AAAAB (4 ballots for candidate A, 1 vote for candidate B) (4 votes for candidate A, 1 vote for candidate B)
AAAABB (4 ballots for candidate A, 2 votes for candidate B) (4 votes for candidate A, 2 votes for candidate B)
AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)
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ASAP NEED ANSWER !! Thank You! :>
The size of angle y in the quadrilateral is 130 degrees.
How to find the angle of a quadrilateral?A quadrilateral is a polygon with 4 sides and angles. The quadrilateral above is a kite. The sum of angles in a quadrilateral is 360 degrees.
Therefore, let's find the angles in the quadrilaterals as follows:
y + y + 70 + 30 = 360(sum of angles in a quadrilateral)
2y + 100 = 360
2y = 360 - 100
2y = 260
divide both sides by 2
y = 260 / 2
y = 130 degrees
Therefore, the size of y is 130 degrees.
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Dana saved 450 for food for her upcoming vacation. The breakfast was included with their hotel, but lunch and dinner are not. When Dana cooks lunch or dinner it costs on average 10 . When the family goes to a restaurant for lunch or dinner it costs on average 40 . Let c represent meals that Dana cooks and let r represent meals the family goes to restaurants for. Write an inequality to represent the situation.
Answer:
\(10d + 40r \leq 450\)
Step-by-step explanation:
Given
\(Savings = 450\)
\(Dana\ Cooks, d = 10\)
\(Restaurant, r = 40\)
Required
Represent this as an inequality
When Dana cooks;
\(Cost\ per\ meal = 10\)
\(Cost\ per\ d\ meals = d * 10\)
\(Cost\ per\ d\ meals = 10d\)
At Restaurant
\(Cost\ per\ meal = 40\)
\(Cost\ per\ r\ meals = 40 * r\)
\(Cost\ per\ r\ meals = 40 r\)
Add these two results:
\(Result = 10d + 40r\)
To represent as an inequality, the above result must be less than or equal to Dana's total savings
i.e.
\(10d + 40r \leq 450\)
A square lawn has area 242 ft squared. A sprinkler placed at the center of the lawn sprays water in a circular pattern as shown in the figure. What is the
radius of the circle?
Answer:
see below
Step-by-step explanation:
There is no picture attached, but assuming that the circle fits inside the square:
Area of square lawn = 242 ft²
Therefore, length of each side = \(\sqrt{242} \) = \(11\sqrt{2} \) ft
Therefore, the radius of the circle will be half of this = \(\frac{11\sqrt{2} }{2} \) = 7.78 ft = 93.34 in
Which expression is the same as 7 × 7 × 7? A. 7×3 B. 7 + 7 + 7 C. 2⁷ D. 7³
The answer is D
7 x 7 x 7
Answer:
7³Step-by-step explanation:
Hi! The expression that is the same as 7*7*7 is 7³.
Problem solved! It's been a pleasure helping you.
PLEASSS HELPPPP
Rewrite the following expression using addition.
-11 – (-4)
OPTIONS
-11 + (-4)
-11 + 4
11 + (-4)
11 + 4
Answer:
-11 + 4
Step-by-step explanation:
When you subtract a negative the sign will switch to plus, so it this case you would switch the - (-4) to a + 4 but you don't change the -11 at the front.
We can write the given expression using addition as -
- 11 + 4.
What is Addition?
Addition is a mathematical operation in which two or more numbers are combined to equal a greater number.
Given is the following expression -
- 11 - (- 4)
The given expression is -
- 11 - (- 4)
In terms of addition, we can write the given expression as -
- 11 + 4
In this way, we can write the expression using addition.
Therefore, we can write the given expression using addition as -
- 11 + 4
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PLEASE HELP SOLVE FOR X
the answer for x in the question is 6.
Answer:
In the equation the value
x = 6
Step-by-step explanation:
Have a good day
#Nova
NO LINKS!! Please assist me with this problem Part 1m
Answer:
(x + 8)² + (y - 8)² = 64=======================
Given ConditionsTangent to x-axis,Tangent to y-axis,In the second quadrant,Radius is 8 units.SolutionEquation of circle:
(x - h)² + (y - k)² = r², where (h, k) is center and r - radiusThe center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.
So the coordinates of the center are:
x = - 8, y = 8The equation is:
(x - (-8))² + (y - 8)² = 8²(x + 8)² + (y - 8)² = 64
Answer:
\((x+8)^2+(y-8)^2=64\)
Step-by-step explanation:
Required conditions:
Tangent to both axes.Center in the second quadrant.Radius = 8 units.If the circle is tangent to both axes, its center will be the same distance from both axes. That distance is its radius.
If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).
Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.
If the radius is 8 units, then the center is (-8, 8).
\(\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)
Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:
\(\implies (x-(-8))^2+(y-8)^2=8^2\)
\(\implies (x+8)^2+(y-8)^2=64\)
Neil eats 1/2 of an apple in 1/6 of a minute. How much time, in minutes, does it take him to eat a full apple? Type your answer as a fraction. If it is improper, change it to a mixed number. Do not include "minutes" in your answer.
Answer:
20 seconds
Step-by-step explanation:
He eats 1/2 of the apple in 10 seconds, meaning he eats the whole apple in 20 seconds.
I need helppppppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple
Answer:
Step-by-step explanation:
Hello, by definition a perfect square can be written as \(a^2\) where a in a positive integer.
So, to answer the first question, \(6^2\) is a perfect square.
(a,b,c) is a Pythagorean triple means the following
\(a^2+b^2=c^2\)
Here, it means that
\(x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29\)
Thank you.
Answer:
Its B
Step-by-step explanation:
Solve the system. Check the solution.x + y = 8(x=y-3
Answer:
\(\begin{gathered} \text{Solution:} \\ (2.5,5.5) \end{gathered}\)Step-by-step explanation:
Given the following system of equations:
\(\begin{gathered} x+y=8\text{ (1)} \\ x=y-3\text{ (2)} \end{gathered}\)Since on equation 2, x is already isolated, substitute it into equation 1:
\(\begin{gathered} (y-3)+y=8 \\ \end{gathered}\)Solve for y.
\(\begin{gathered} 2y=8+3 \\ y=\frac{11}{2}=5.5 \end{gathered}\)Knowing the value of y, plug it into equation (2) and solve for x:
\(\begin{gathered} x=y-3 \\ x=5.5-3 \\ x=2.5 \end{gathered}\)Tahir is twice as old as Faheem now. In 5 years, Faheem will be 10 years old. What is Tahir's age now? 15 25 10 20
Answer:
10
Step-by-step explanation:
10-5= 5
5*2=10
tahir is 10
Math problem pls help I will give brainiest
Answer:
y=5
Step-by-step explanation:
125 +125+13y+9y=360
punch it into math-way.
250+22y=360
22y= 110
y=5
Please answer see the image
Answer:
39 km²Step-by-step explanation:
surface area of a square pyramid
= Area of base + 1/2 base perimeter * slant height
= (3 x 3) + (1/2 x (3*4) x 5)
= 9 + 30
= 39 km²
Why is choosing a smaller unit of measure is more meaningful?
Pls explain due tomorrow!!!
Answer: Choosing a smaller unit of measure is more meaningful because it allows for more precise measurements. When using a smaller unit of measure, such as millimeters instead of centimeters, or seconds instead of minutes, you are able to capture more detailed information about the measurement. For example, measuring something in centimeters may give you a rough idea of the size, but measuring it in millimeters will give you more detailed information, which can be especially important in scientific or technical fields. Additionally, choosing a smaller unit of measure can be more meaningful when making comparisons or performing calculations, as it allows for greater accuracy.
Step-by-step explanation:
Hopes this helps you for Tomorrow!!
Determine whether each statement is always true, sometimes true, or
never true.
1. Every square is a rhombus.
2. Every rhombus is a parallelogram.
3. Every rectangle is a parallelogram.
4. The diagonals of a square are perpendicular.
5. If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a square.
6. If the diagonals of a quadrilateral are perpendicular, then the
quadrilateral is a rhombus.
7. The diagonals of a rectangle are congruent.
8. The diagonals of a rhombus bisect the vertex angles.
9. Some rectangles are rhombi.
10. Some rhombi are squares.
Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.
1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.
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You want to estimate the mean amount of time college students spend on the Internet each month. How many college students must you survey to be 95% confident that your sample mean
Answer:
752.95
Step-by-step explanation:
Data provided in the question
The standard deviation of population = 210
The Margin of error = 15
The confidence level is 75%, so the z value is 1.96
Now the required sample size is
\(= 1.96^2\times \frac{210^2}{15^2}\)
= 752.95
Hence, the number of college students spends on the internet each month is 752.95
Simply we considered the above values so that the n could come
Rachael gets 94 marks in her exams.these are 47% of the total marks.find the maximum number of mark
Answer:
200 is the maximum amount
Step-by-step explanation:
94x100=9400
9400/47=200
can i have brainliest?
Try Again19Writeas a decimal. If necessary, use a bar to indicate which digit or gri63.16Х5?
ANSWER
6 - 9y - 12v
STEP-BY-STEP EXPLANATION
Given information
\((-2\text{ + 3y}+\text{ 4v) (-3)}\)Expand the parentheses by multiplying through by -3
\(\begin{gathered} (-3\times-2)\text{ + (-3}\times3y)\text{ + (-3}\times4v) \\ =\text{ 6 - 9y - 12v} \\ \end{gathered}\)Please help with this math question!
Answer:
5. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Please help me to figure out this math graph problem.
Answer:
Step-by-step explanation:
someone help please with b (the slope is 5)
the company bought $15000 worth of equipment beginnning of year 2018 the equipment is est. to increase in value at a rate of 15.9% per year how many yers, t , after which the value of the company's new equipment will be less than 7500
The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years
How to determine the valueTo solve this problem, we can use the formula for exponential growth:
V(t) = V₀ * (1 + r)^t
Given that the parameters are;
V(t) is the value of the equipment at a time tV₀ is the initial value of the equipment ($15,000)r is the growth rate (15.9% or 0.159)t is the time in yearsTo determine time t when the value of the equipment will be less than $7500.
Let's set up an inequality;
V(t) < 7500
Substituting the formula for V(t), we get:
V₀ * (1 + r)^t < 7500
Substitute the values
(1 + 0.159)^t < 0.5
t * log(1 + 0.159) < log(0.5)
t > log(0.5) / log(1 + 0.159)
Using a calculator, we get:
t > 2.64
Hence, the value is 2.64 years.
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Solve Linear Equation.
Px + q = r
Answer:
In both equations, the p, q, and r represent rational numbers, either integers or fractions. ... Subtract q from both sides if positive or add q to both sides if negative. This gives you px + q - q = r - q, which simplifies to px = r - q.
Step-by-step explanation:
Evaluate the expression for the given value. πr^2, r=17
type answer in terms of pi
πr^2=
Step-by-step explanation:
r=17
pi=22/7
22/7×14×2
22×2×2=88
so i cancelled out 7 cuz 7×2 is 14 and so i made 14 as 2
4) An arithmetic sequence has a 7th term of 54 and a 13th term of 94. Find the common difference
Please answer!!
Answer:
20/3
Step-by-step explanation:
Every nth term takes the form of a + n*d, where a is the first term.
So 7th term = (54 = a + 7d), 13th term = (94 = a + 13d).
equate them both:
94 - 13d = 54 - 7d
40 = 6d
d = 40/6
Find the common ratio r of the geometric series an that satisfies the following conditions: C = 4, S
= 16.
The common ratio of the geometric series which satisfies the condition given is; 4.
Common ratio of geometric seriesThe given Geometric series has successive terms;
C = 4 and S = 16.Hence, the common ratio of the geometric series is the quotient of S and C;
Common ratio, r = S/C = 16/4 = 4.Read more on geometric series;
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