The rain barrel, losing water at a rate of 2.5 gallons per minute, started with a volume of 55 gallons. It will take a total of 22 minutes to completely empty the barrel.
To calculate the total number of minutes it will take to completely empty the rain barrel, we must first establish how much water is being lost per minute and use that rate to determine how long it will take to empty the current amount of water in the rain barrel.
We know that the rain barrel loses water at a rate of 2.5 gallons per minute and after seven minutes, it contains 37.5 gallons. To determine the starting volume (V0) when the barrel was full, we can add the amount of water already used in seven minutes back to the current volume:
V0 = current volume + (rate of loss x time)V0 = 37.5 gallons + (2.5 gallons/minute x 7 minutes)V0 = 37.5 gallons + 17.5 gallonsV0 = 55 gallonsWith a starting volume of 55 gallons and a loss rate of 2.5 gallons per minute, we can calculate the total time (T) to empty the barrel:
T = Total volume / Rate of lossT = 55 gallons / 2.5 gallons/minuteT = 22 minutesTherefore, it will take a total of 22 minutes to empty the rain barrel completely.
Every 6 months Reuben lopez puts 420$ into an account paying 10% compounded semiannually. Find the account balance after 15 years.
The above question is related to the future value of an amount saved at regular intervals.
We need to find the future value of the $ 420 saved every six month which are compounded semi-annually.
When the compounding is semi-annually, the same is divided by 2 and the time is multiplied by 2.
The future value will be calculated as -
Future value = $ 420 × FVIFA for 30 years @ 5 %
Here, the annual rate was 10 % but since compounding is semi-annually, thus it is divided by 2. Similarly, time is multiplied by 2 i.e 15 years X 2 = 30 periods
Referring the FVIFA table, we got -
FVIFA for 30 years @ 5 % = 66.4388
Future value = $ 420 × 66.4388 = $ 27,904.30
Credit card A offers an APR of 27.29%, compounded monthly, while credit card B offers an APR of 27.12%, compounded daily. All else being equal, which card offers the better deal for the consumer?
The effective interest rate, also known as the effective annual interest rate, annual equivalent rate, or simply effective rate. The card which offers a better deal to the customer is Credit card A.
What is an effective rate of interest?
The effective interest rate, also known as the effective annual interest rate, annual equivalent rate, or simply effective rate, is the interest rate on a loan or financial product that is restated from the nominal interest rate and expressed as the equivalent interest rate if compound interest was payable annually in arrears. It is calculated by the formula,
EIR = [1+(i/n)]ⁿ - 1
The effective rate of interest on Credit Card A is,
Effective rate = [1+(i/n)]ⁿ - 1 = [1+(0.2729/12)]¹² - 1 = 30.97%
The effective rate of interest on Credit Card B is,
Effective rate = [1+(i/n)]ⁿ - 1 = [1+(0.2712/365)]³⁶⁵ - 1 = 31.14%
Since the effective rate of Credit card A is less than credit card B, therefore, the card which offers a better deal to the customer is Credit card A.
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Find the critical value za/2 that corresponds to a 82% confidence level.
The critical value (or z-score) that corresponds to a 82% confidence level is approximately ±1.34, which is determined using a standard normal distribution table related to the value calculated from α/2 = 0.09.
Explanation:To find the critical value za/2 that corresponds to a 82% confidence level, we start by knowing that confidence level (CL) is the area in the middle of the standard normal distribution. We know that CL = 1 - α, hence for this particular question, α = 1 - 0.82 = 0.18, and α/2 = 0.09. The Z score associated with α/2 = 0.09 in the standard normal distribution table, which represents the critical value za/2, is approximately ±1.34.
So for an 82% confidence level, the critical value za/2 is roughly ±1.34.
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Mario cut a circular pizza into 9 equal slices. he put a slice of pizza on each of 5 plates. what is the measure
for the angle of the slices that are left
The measure for the angle of the slices that are left is 160°.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Mario cut a circular pizza into 9 equal slices.
Angle of a circle = 360°
If Mario cut into 9 pieces.
360° / 9 = 40°
That means, the angle measure of each slice is 40°.
And he put a slice of pizza on each of 5 plates.
That means, he left 9 - 5 = 4 slice on the plate.
So, the angle measure;
4 x 40° = 160°
Therefore, the angle measure of the 4 slices are 160°
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Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5 . . . ? Check all that apply.
f(n) = –6.5n + 14.5
f(n) = –1.5n + 9.5
f(n) = 6.5n + 1.5
f(1) = 8, f(n + 1) = f(n) – 6.5
f(1) = 8, f(n + 1) = f(n) – 1.5
f(1) = 8, f(n + 1) = f(n) + 6.5
Answer:
f(n) = –6.5n + 14.5
f(1) = 8, f(n + 1) = f(n) – 6.5
Step-by-step explanation:
The nth term of an arithmetic sequence is given as
Tn = a + (n-1)d
where a is the first term and d is the common difference between two consecutive terms
From the given sequence,
a = 8, d = 1.5 - 8
d = -6.5
As such, Tn = f(n) = 8 + (n-1)-6.5
= 8 - 6.5n + 6.5
= 14.5 - 6.5n
f(1) = 8
f(n + 1) - f(n) = – 6.5
f(n + 1) = f(n) – 6.5
Someone help I don't understand this.
If a 10-pound sack of potatoes costs $6.55, how much would 1 pound cost? Round your answer to the nearest cent.
The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground
Answer:
3 seconds is the time when the object hits the ground.
Step-by-step explanation:
Given the height of a free falling object at time t can be found using the function is given by:
[tex]h(t)=-12t^2+36t[/tex] ....[1]
where,
h(t) is the height in feet
t is the in seconds.
We have to find the time when the object hits the ground.
⇒h(t) = 0
Substitute this in [1] we have;
[tex]-12t^2+36t =0[/tex]
⇒[tex]12t^2-36t = 0[/tex]
⇒[tex]12t(t-3) = 0[/tex]
⇒t = 0 and t = 3
Since, time cannot be 0.
⇒t = 3 seconds
Therefore, the time when the object hits the ground is, 3 seconds
PLEASE HELP ME OUT ASAP! I WOULD REALLY APPRECIATE IT AND GOD BLESS
2. A,B,C,D ?
3. A,B,C,D ?
find the area of the regular decagon if the apothem is 2.8ft and a side is 1.8ft
Domingo works 40 hours per week as a tire store manager. If he made $29,640 last year, how much was he paid per hour? A. $14.25 B. $16.50 C. $12.25 D. $11.00
By dividing Domingo's annual salary of $29,640 by the total number of hours worked in a year (2080 hours), we find that his hourly rate is $14.25.
To determine how much Domingo was paid per hour, we need to follow these steps:
Find the total number of hours Domingo worked in the year. He works 40 hours per week for 52 weeks, so the total is 40 hours/week × 52 weeks/year = 2080 hours/year.Calculate the hourly wage by dividing his total annual salary by the total number of hours worked. He made $29,640 last year, so we do the following calculation: $29,640 / 2080 hours = $14.25/hour.Therefore, Domingo was paid $14.25 per hour.
Answer: A. $14.25A single fair die is tossed. find the probability of rolling a number greater than 55.
I need help on this question
Which set of coordinates, when paired with (3, −3) and (10, −3), result in a square? (−3, −3) and (−10, −3) (3, 10) and (10, 3) (−3, 4) and (−10 , 4) (3, 4) and (10, 4)
Which expression is equivalent to 24 - (-6), minus, left parenthesis, minus, 6, right parenthesis?
Select the best answer for the question.
2. Express the fractions 3/4, 7/16, and 5/8 with the LCD.
A. 9/16, 49/16, 36/16
B. 3/4, 2/4, 3/4
C. 12/16, 7/16, 10/16
D. 24/32, 14/32, 24/32
The Volume of the cone shown is 6 cubic inches. What is the height of a cone with the same base diameter but a volume of only 3 cubic inches?
Answer:
3 cubic inches
Step-by-step explanation:
Using the formula, volume of the cone.
Subst. the known value of into the equation.
Thus, the volume of cone= 1(3)= 3 cubic inches.
The amount after 8years will be what
Your principal surprises you by buying your class a turtle. He brings the turtle to your class along with a sheet from the pet store titled "Turtle Tank Rule."
*Tank walls must be at least 1 foot tall so the turtle can't climb out.
*There must be at least 400 square inches of floor space for the turtle to walk around on.
Your teacher says the volume of the tank must be smaller than 5000 cubic inches so it doesn't take up too much room in the classroom.
Give the dimensions of a tank that would work for your new turtle. Use words and numbers to explain how your tank satisfies the "Turtle Tank Rules" and your teacher requirements.
Volume of a rectangular prism= length X width X height
To satisfy the 'Turtle Tank Rules' and your teacher's requirements, the tank dimensions must meet certain criteria. You can use the formula for the volume of a rectangular prism to find the dimensions.
Explanation:To satisfy the 'Turtle Tank Rules' and your teacher's requirements, the tank dimensions must meet the following criteria:
The tank walls must be at least 1 foot tall.The tank floor must have a minimum of 400 square inches of space.The volume of the tank must be smaller than 5000 cubic inches.Let's assume the tank has length, width, and height as its dimensions. By using the formula for the volume of a rectangular prism (Volume = length * width * height), we can manipulate it to find the dimensions:
Choose a reasonable value for the height (for example, 6 inches).Calculate the area of the tank floor by dividing 400 square inches by the chosen height.Find the length and width that multiply to give this area while satisfying the volume requirement of less than 5000 cubic inches.pls help soon:)
James threw a flying disc from a height of 4 feet above the ground. The disc travels a horizontal distance of 30 feet before falling to the ground. The height of the disc, in feet, at a distance of t feet from James, is modeled on the graph below.
FILL IN BLANK
The domain represents the A. horizontal distance covered by B. maximum height of C. possible heights of the flying disc. The range of this function is [A. 1 B. 0 C. 2, A. 7 B. 6 C. 5 ]. For this function, the range represents the flying disc's A. possible heights B. maximum heights C. horizontal distance covered
evaluate the following algebraic expression if a equals 3 and b equals 4 2a^+5b
HELP ASAP!!!!!!
Solve and graph the inequalities below.
Describe your graphs using words as illustrated in the sample below.
SAMPLE: Part 1: The solution is x > 5 and x<=9.
Part 2: There would be an open circle on 5 and a closed circle on 9.
Part 3: The shading is between the two numbers.
Be sure that you have included all three parts when answering each question. "Greater than or equal to" would be typed >=. "Less than or equal to" would be typed <=.
1.) d - 1 > -3 and d + 2 < 5
2.) -3k + 7 > -5 and -7k + 5 < -2
3.)-5 < 2y - 3 < 23 (Hint: refer to example 2 in the lesson.)
4.)x - 4 < 5 or x + 2 > 15
5.) 5x - 4 > 6 or -4x + 5 > 1
Write 760% as a decimal and as a simplified fraction
7.6
760/100
76/10
7 6/10
760% can be expressed as a decimal by simply dividing by 100, resulting in 7.6. The same percent can be expressed as a simplified fraction by writing it over 100 and simplifying, resulting in 38/5.
Explanation:To convert 760% into a decimal and a simplified fraction, we follow the process of converting percents. First, to convert a percent to a decimal, we need to divide the percent by 100. So 760% becomes 7.6 when expressed as a decimal.
Then, to convert the percent to a simplified fraction, we write the percent as a fraction over 100. So, 760% would be written as 760/100. But it can be simplified. Both 760 and 100 can be divided by 20, so when simplified the fraction becomes 38/5.
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Find the length of the arc shown in red. Leave your answer in terms of Pi
The calculated length of the red arc is 4.71 units
Finding the length of arc DF
From the question, we have the following parameters that can be used in our computation:
Central angle = 30 degrees
Radius = 9 meters
Using the above as a guide, we have the following:
Arc length = central angle/180 * 3.14 * Radius
Substitute the known values in the above equation, so, we have the following representation
Arc length = 30/180 * 3.14 * 9
Evaluate
Arc length = 4.71
Hence, the length of the arc is 4.71 meters
hey can you please help me posted picture of question
100 POINTS
What is the area of the figure:
Answer:
144 ft²
Step-by-step explanation:
There are a number of ways you can solve this problem. One is to figure the leg lengths, and use those to compute the area of the triangle in the usual way.
AC = (24 ft)·sin(45°) = 12√2 ft
BC = (24 ft)·cos(45°) = 12√2 ft
Area = 1/2·AC·BC = (1/2)·(12√2 ft)·(12√2 ft) = 144 ft²
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Another is to recognize that the altitude from the hypotenuse of this isosceles right triangle is half the length of the hypotenuse, or 12 ft. Then the triangle area formula gives the area as ...
Area = (1/2)·AB·(AB/2) = (1/2)·(24 ft)·(12 ft) = 144 ft²
___
Along the same lines, the triangle is half a square whose diagonals are both 24 ft. The area of the square is half the product of those diagonals:
square area = (1/2)·(24 ft)² = 288 ft²
The triangle area is half of that, or
Area = (1/2)(288 ft²) = 144 ft²
Answer:
144 ft²
Step-by-step explanation:
AC = (24 ft)·sin(45°) = 12√2 ft
BC = (24 ft)·cos(45°) = 12√2 ft
Area = 1/2·AC·BC = (1/2)·(12√2 ft)·(12√2 ft) = 144 ft²
A Japanese garden has a circular koi pond in the middle that has a radius of 3 feet. What is the area of the Japanese garden around the koi pond? Use 3.14 for pi. 195.74 ft2 224.00 ft2 252.26 ft2 337.04 ft2
Answer: [tex]195.74\ ft^2[/tex]
Step-by-step explanation:
From the given picture, the length of the garden = 16 ft
The width of the garden = 14 ft
Now, the area of the whole garden is given by :-
[tex]\text{Area of whole garden}=length\times width\\\\\Rightarrow\text{Area of whole garden}=16\times14=224\ ft^2[/tex]
Also, the radius of the circular pond (r)= 3 ft
The area of the circular pond is given by :-
[tex]\text{Area of pond}=\pi r^2\\\\\Rightarrow\text{Area of pond}=(3.14)(3)^2\\\\\Rightarrow\text{Area of pond}=28.26\ ft^2[/tex]
Now, the area of the Japanese garden around the koi pond
= Area of the whole garden - Area of the Koi pond
=[tex]224-28.26=195.74\ ft^2[/tex]
Hence, the area of the Japanese garden around the koi pond is [tex]195.74\ ft^2[/tex]
Jeff put a small box that is 12 inches long, 8inches wide, and 4 inches tall inside a box that is 20 inches long, 15 inches wide and 9 inches high. How much space is left in the larger box?
What is the solution to the expression –2 – 3 – (–4)?