Chang added some chlorine to the water in the pool . The chlorine evaporated at a fixed rate every week. The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks
Answers
The function that best shows the relationship between n and f(n) is;
f(n) = 24(0.5)ⁿ⁻¹
How to solve function tables?The function table that shows the amount of chlorine is given as;
n 1 2 3 5
f(n) 24 12 6 3
Where;
f(n) is the amount of chlorine in ounces, that was left in the pool after n weeks:
We can see that the value of f(n) is decreasing as n increases from the table.
Due to the fact that f(n) does not have common difference. Let us attempt tp see if it has a common ratio;
12/24 = 0.5
6/12 = 0.5
3/6 = 0.5
Using the formula for the nth term of a geometric progression is;
aₙ = arⁿ⁻¹
Where;
a represents the first term = 24
r represents the common ratio = 0.5
Thus, the equation of the function is;
f(n) = 24(0.5)ⁿ⁻¹
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Related Questions
Victor biked from his hometown to a neighboring city in 6 hours. He biked back to his hometown in 4 hours. His speed on the return trip was 4 mph faster than his speed on the first trip. How far apart are the two cities?
Answers
We will have the following:
His speed on the return (r) trio was 4mph faster than his speed in the first trip (o), so:
\(r=o+4\)Then, we have that speed times distance equals time, and distance is equal to time over speed. Thus:
\(6h(\frac{x}{\text{hours}})=4h(\frac{x+4}{\text{hours}})\)Then, we have:
\(6x=4x+16\Rightarrow2x=16\)\(\Rightarrow x=8\)So, the initial speed was of 8mph.
Then we deternine the distance:
\(d=(8mi/h)(6h)\Rightarrow d=48mi\)So, the two cities are 48 miles apart.
Convert 10 pounds and 12 ounces to ounces.
Answers
Answer: 172 ounces
Step-by-step explanation:
We are given 10 pounds and 12 ounces to convert to ounces.
There are 16 ounces in 1 pound.
We can create a proportion to find out how much ounces 10 pounds is.
10 pounds / x ounces = 1 pound / 16 ounces
We need to solve for x by isolating the variable x.
10/x = 1/16
10 = x/16
10 * 16 = x
160 ounces = x
so 10 pounds is equivalent to 160 ounces. But we are not done yet.
We were asked to convert 10 pounds and 12 ounces.
So add together the ounces to find the total ounces:
160 ounces + 12 ounces = 172 ounces.
will give brainlist if u help
explain how 1 is likely
Answers
Answer:
A probability of one is equal to 100%, which means it is likely to happen as there is no way it cannot happen.
Step-by-step explanation:
See Above
Please give me right answer i mark you brainliest if you answer fast , At a stationery sale, pencils were sold in packets of 4 and erasers were sold in packets of 6. The cost of a packet of pencils was the same as the cost of a packet of erasers. Mrs Tan bought 12 pencils for $6. What was the cost of a packet o erasers?
Answers
Answer:
The answer is $2
I packet has 4 pencils so 12 pencils is 3 packets
if 3 packets cost $6 1 packet costs $2 and since 1 packet of pencils is the same price as one packet of erasers 1 packet of erasers cost $2
Question 3 A 44-metres long fire-fighting ladder is leaned against a building, as shown in the diagram. The base of the ladder is 7 metres from the building and 3 metres above the ground. How high on the building will the ladder reach?
Answers
The ladder will reach a Height of approximately 43.46 meters on the building.
To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.
Using the Pythagorean theorem, we can set up the equation:
(Height of the building)^2 + 7^2 = 44^2
Simplifying the equation, we have:
(Height of the building)^2 + 49 = 1936
Subtracting 49 from both sides, we get:
(Height of the building)^2 = 1887
To find the height of the building, we take the square root of both sides:
Height of the building = √1887
Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.
Therefore, the ladder will reach a height of approximately 43.46 meters on the building.
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Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
Answers
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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write as power of 2 or 3
a. 2187
b. 1 / 256
d. 8 / 52488
Answers
Answer:
a. \(3^{7}\)
b. \(2^{-8}\)
c. \(3^{-8}\)
Step-by-step explanation:
It's pretty simple. Just keep dividing till you get your answer (which is above)
one side of a rectangle is 12 feet shorter than seven times another side. find the length of the shorter side if we also know that the perimeter of the rectangle is 168 feet.
Answers
As per the perimeter the length of the shorter side is 10.5 feet and the length of the longer side is 73.5 feet.
The perimeter of a rectangle is the sum of the lengths of all its sides. If we know the perimeter of a rectangle and some information about the relationship between its sides, we can use that information to find the lengths of the sides.
Let's call the length of the shorter side "x".
The other side is seven times as long, so it is 7x.
The perimeter of the rectangle is 168 feet, so we have
=> 2x + 14x = 168.
Simplifying the equation, we have
=> 16x = 168.
Dividing both sides of the equation by 16, we find
=> x = 10.5.
So, the length of the shorter side is 10.5 feet and the length of the longer side is
=> 7x = 7 * 10.5 = 73.5 feet.
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There is a 30 percent chance that A can fix her busted computer. If A cannot, then there is a 40 percent chance that her friend B can fix it.
a) Find the probability it will be fixed by either A or B.
b) If it is fixed, what is the probability it will be fixed by B.
Answers
a) The probability that the computer will be fixed by either A or B is 58%.
b) The probability that it was fixed by B is 57.14%
Given data:
a)
To find the probability that the computer will be fixed by either A or B, we can use the principle of addition for probabilities.
The probability that A can fix the computer is 30% or 0.30, and the probability that B can fix the computer if A cannot is 40% or 0.40.
Therefore, the probability that either A or B can fix the computer is the sum of these probabilities:
P(A or B) = P(A) + P(B if A cannot) = 0.30 + (0.70 * 0.40) = 0.30 + 0.28 = 0.58
Therefore, there is a 58% probability that the computer will be fixed by either A or B.
b)
Let's denote event A as A fixing the computer and event B as B fixing the computer.
P(A) = 0.30 (probability A can fix the computer)
P(B|A') = 0.40 (probability B can fix the computer given that A cannot)
To find P(B|A), the probability that B fixes the computer given that it was fixed, use Bayes' theorem:
P(B|A) = (P(A|B) * P(B)) / P(A)
Since the computer is fixed, P(A) + P(A') = 1, so P(A) = 1 - P(A') = 1 - 0.30 = 0.70
P(B|A) = (P(A|B) * P(B)) / P(A)
P(B|A) = (1 * 0.40) / 0.70
P(B|A) = 0.40 / 0.70
P(B|A) ≈ 0.5714
Hence, if the computer is fixed, there is a 57.14% probability that it was fixed by B.
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Seventy homes that were for sale in Tampa, Florida in Spring of 2019 were randomly selected. A regression model to predict house price was run based on first floor square footage and the indicator variable for Beach (1 if the house was within 1 mile of the beach, 0 if not). There was also an interaction term for firstfloorsquarefootage*Beach.
Term Estimate Std. Error
Intercept -93.4 214.5
Beach 782.5 31.45
firstfloorsquarefootage 0.412 0.120
firstfloorsquarefootage*Beach 0.004 0.012
How would you interpret the slope coefficient for firstfloorsquarefootage*Beach?
A. Homes near the Beach are less expensive than elsewhere for a given size.
B. The slope of the relationship between firstfloorsquarefootage and price is lesssteep for homes near the beach than elsewhere in Tampa
C. Homes near the Beach are more expensive than elsewhere for a given size.
D. The slope of the relationship between firstfloorsquarefootage and price is moresteep for homes near the beach than elsewhere in Tampa
Answers
Answer:
D.The slope of the relationship between first floor square footage and price is more steep for homes near the beach than elsewhere in Tampa
Step-by-step explanation:
We can see from the output that was run in this regression that this variable has a positive coefficient. So the result is going to be interpreted to show an increase. Therefore d is the answer as it shows that these homes which are closer to the beach are steeper compared to those that are in other areas of tampa. It's necessary to always look out for the signs of the coefficient when interpreting a regression result
classify the following differential equation s given in both standard and differential form. Q5 only
Answers
y' = 2xy + x
Rewriting it in differential form, we get:
(2xy + x)dx - dy = 0
This is a first-order linear differential equation, which can be written in the form:
y' + P(x)y = Q(x)
where P(x) = -2x and Q(x) = x.
Therefore, the differential equation is a first-order linear differential equation.
how are 2-D and 3-D objects related to each other in real world
Answers
Answer:
You can see 2-D flat shapes on the faces of 3-D objects.
For example: You go to the store and you see a box,
the box has 6 faces. The bottom of the box is one of It's faces which is 2-D.
Step-by-step explanation:
There are 6 acts in a talent show.
An acrobat, a dancer, a guitarist, a singer, a violinist, and a whistler.
A talent show host randomly schedules the 6 acts.
Compute the probability of each of the following events.
Event A: The acrobat is first, the singer is second, the violinist is third, and the whistler is fourth.
Event B: The first four acts are the whistler, the acrobat, the guitarist, and the dancer, In any order.
Write your answers as fractions in simplest form.
P(A) =
P (B) =
Answers
The probability of Event A is 1/360 and the probability of Event B is 1/15.
For Event A, we can calculate the probability by considering the order in which the acts are scheduled.
There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.
Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.
Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.
Therefore, the total number of possible ways to schedule all 6 acts is:
6 x 5 x 4 x 3 x 2 x 1 = 720
Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.
There are 2 remaining acts, so there are 2 possible choices for the fifth act.
Only one act remains for the last slot.
Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:
1 x 1 x 1 x 1 x 2 x 1 = 2
Thus, the probability of Event A is:
P(A) = 2/720 = 1/360
For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.
There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.
Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.
Therefore, the total number of possible ways to schedule the first four acts is:
4 x 3 x 2 x 1 = 24
Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.
Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:
24 x 2 = 48
Thus, the probability of Event B is:
P(B) = 48/720 = 1/15
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Select the correct answer.
Which graph represents the solutions to this equation?
x2 + 8x = -20
(as a graph pls!)
Answers
Answer:
Step-by-step explanation:
-4 is greater than of equal to x - 11
Answers
Using the inequality rule we know that 11 is greater than -11, (11 > -11).
What is an Inequality Equation?Mathematical expressions with inequalities are those in which the two sides are not equal.
Contrary to equations, we compare two values in inequality.
Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.
So, let's say the inequality equation looks like this: A
Right now, A is valued at
Let p be used to representing the initial number.
P equals 11, so
Let q be used to representing the second number.
Q has a value of -11.
-11 and 11 are both numbers that are greater than zero.
Then, 11 > -11 ... (1)
A has a value of 11 > -11.
Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).
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Correct question:
Is 11 greater than, equal to, or less than -11?
A rectangular park is 4a m and 3a m broad, find it's area in m2
Answers
Answer:
Area = 12a m²
Step-by-step explanation:
Given information,
→ Length = 4a m
→ Width = 3a m
Now we have to,
→ find the area of rectangular park.
Formula we use,
→ Area = L × W
Then the area of rectangle is,
→ L × W
→ 4a × 3a
→ (4 × 3)a
→ 12a m²
Therefore, the area is 12a m².
Arrange the steps in order to simplify the expression
Answers
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
rewrite 25/99 into a decimal
Answers
Answer:it’s 25:99
Step-by-step explanation:
parallelogram s and t are each labeled with a base and corresponding height . Find the area of each one
Answers
Parallelogram S:
By looking at the graph:
b= 7 units
h=6 units
Paralellogram T
b= 3 units
h=6 units
Area of a parallelogram : b x h
S Area = 7 x 6 = 42 square units
T area = 3 x6 = 18 square units
can someone solve these for me?? URGENT
Answers
Solve the inequality for x.
4 − 4x < 16
x < −3
x > −3
x > 3
x < 3
Answers
Answer:
x > -3
Step-by-step explanation:
4 - 4x < 16
- 4x < 16 - 4
- 4x < 12 (note that both can be divided by -4)
x > -3
That's the final answer.
AND if you're co fused about why the sign changed, you should always remember this
• ALWAYS change the inequality sign when you divide (÷) or multiply (×) by a negative numberBy negative num I mean any number that starts with a minus for example -2, -3, -5, -100
In 2 + In 8 - In 4
In 4
In 6
In 64
DONE
Answers
Answer:
ln 4
Step-by-step explanation:
plus(+) will become times and minus(-)will become divide. Combine all together as all are in terms of ln
ln (2x8)/4
=ln 4
Answer: In 4
Step-by-step explanation: edge 2021
evaluate the expression
when a=4 and b = -4
2b-a
Answers
2(-4) - (4)
=-12
:)
Answer:
- 12
Step-by-step explanation:
a = 4
b = - 4
2(- 4) - 4
- 8 - 4
Subtract 4 is the dame as adding its opposite which is - 4.
- 8 + (- 4)
= - 12
Hope this helps :)
Carry is a real estate agent. She earns 8.15% commission on each sale she makes. After working with a potential buyer for 3½ months, she finally sold a house for $877,000.
a.) What did Carry earn in commissions for this sale?
$
71475.50
b.) This was her only sale for the entire 3½ month period. What was her average salary per month for this period?
Round to the nearest hundred dollars.
$
c.) For the next four months, Carry is not able to sell a house due to a faltering economy. What is her average monthly salary for the past 7½ months?
Round to the nearest hundred dollars.
Answers
The amount that Carry earn in commissions for this sale is: $71,475.5. The average salary per month for this period is $20,421.57 and the average monthly salary for the past 7½ months is:$9,530.07 per month.
CommissionA. Commission:
Commission=8.15%($877,000)
Commission=$71,475.50
b. Average salary:
Average salary=$71,475.5/3.5 months
Average salary=$20,421.57 per month
c. Average monthly salary:
Average monthly salary=$71,475.5/7.5 months
Average monthly salary=$9,530.07 per month
Therefore the amount that Carry earn in commissions for this sale is: $71,475.5. The average salary per month for this period is $20,421.57 and the average monthly salary for the past 7½ months is:$9,530.07 per month.
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You are the owner of four Taco Bell restaurant locations. You have a business loan with Citizens Bank taken out 60 days ago that is due in 90 days. The amount of the loan is $50,000, and the rate is 9.5% using ordinary interest.
You currently have some excess cash: $35,000. Due to situations beyond your control, you, as the owner, must make an immediate business decision now to pursue only one of these two choices:
1) sending all of the $35,000 to Citizens Bank as a partial payment on your loan, or
2) using the $35,000 to purchase serving supplies such as food containers, cups, and plastic dinnerware for your inventory. This is the last day to take advantage of the opportunity to save some money due to a special discount price that is "10% off" the normal cost of $35,000 for these items.
Consider these calculations:
(a)
How much interest (in $) will you save on this loan if you make the partial payment and don't purchase the additional serving supplies? (Round your answer to two decimal places.)
$
Incorrect: Your answer is incorrect.
(b)
How much money (in $) will you save if you purchase the serving supplies with the discount and don't make a partial payment on the loan? (Round your answer to two decimal places.)
$
(c)
How much (in $) will you save by purchasing the discounted serving supplies rather than making the partial payment? (Hint: Find the difference between the savings on the supplies found in part (b) and the savings on the loan interest found in part (a). Round your answer to two decimal places.)
$
(d)
What other factors should you consider before making this decision?
Answers
The amount saved by repaying the loan early is $831.25
The amount of discount received by purchasing supplies is $3,500
The net amount saved by purchasing supplies rather than repaying loan is $2,668.75
What is ordinary interest?
Ordinary interest is the interest computation that is based on 360-day a year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.
Amount saved in interest=$35,000*9.5%*90/360
Amount saved in interest=$831.25
Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000
Amount saved with discount=10%*$35,000
Amount saved with discount=$3,500
The difference between discount on supplies and interest saved=$3,500-$831.25
The difference between discount on supplies and interest saved=$ 2,668.75
The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies
Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates
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please very soon I offer the crown !!! + 10 points urgently !!!
Answers
b- 11
c- 7
d- 4
e- 10
f- 1
Write the equation of the line in slope intercept form that goes through (5,4) and is
parallel to −4x + y = 5
Answers
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
Here we go ~
First, let's find slope of line parallel to required line by converting the equation into slope intercept form :
\(\qquad \sf \dashrightarrow \: - 4x + y = 5\)
\(\qquad \sf \dashrightarrow \: y = 4x + 5\)
So, it's slope is 4 ( Coefficient of x )
Slope of required line is equal to the line parallel to it, so slope of required line is 4 as well.
Now, we have slope : m = 4, and it passes through point (5 , 4) so let's write it's equation in point slope form ~
\(\qquad \sf \dashrightarrow \: y - y _ 1 = m(x - x _ 1)\)
\(\qquad \sf \dashrightarrow \: (y -4) = 4(x - 5)\)
\(\qquad \sf \dashrightarrow \: y - 4 = 4x - 20\)
\(\qquad \sf \dashrightarrow \: y = 4x - 20 + 4\)
\(\qquad \sf \dashrightarrow \: y = 4x - 16\)
Find the area of the shape
Answers
Hello!
area
= 2*25 + (20 - 2)*(25-8)
= 50cm² + 306cm²
= 356cm²
Maria has 12 bags of chocolate chips in her pantry. A batch of cupcakes requires og legs of chocolate chips, and a batch of cookies requires or bags
chocolate chips. If none of the chocolate chips are wasted and she makes 8 complete batches of cookies, what is the maximum number of complete
batches of cupcakes that she can make?
Answers
Answer:
10
Step-by-step explanation:
Maria has 12 bags of chocolate chips, and each batch of cookies requires 1/2 bag of chocolate chips, and she makes 8 complete batches of cookies. So we can calculate the number of bags of chocolate chips used by:
1/2 * 8 = 4 bags
The number of bags of chocolate chips left after making the cookies is:
12 - 4 = 8 bags
A batch of cupcakes requires 3/4 of a bag of chocolate chips, and Maria has 8 bags of chocolate chips left. So we can calculate the maximum number of complete batches of cupcakes that she can make by:
8 / (3/4) = 8 * (4/3) = 32/3 = 10.67
Maria can make a maximum of 10 complete batches of cupcakes. Since a batch of cupcakes cannot be fractional, it means Maria can't make any more cupcakes after using all the chocolate chips.
this is one of my homework questions and if possible please help, I do some of it to a certain point but then get stuck. if im correct, the right choice is sin with a degree but I need some guidance. Thank you!
Answers
Given the expression:
\(2\sin 67.5\degree\cos 67.5\degree\)The angle of the sine and the cosine is the same angle = 67.5°
The given expression is the same as the rule of the sine of the double angle
Where:
\(2\sin \theta\cos \theta=\sin (2\theta)\)so, we will use the sine double-angle to solve the question
So, the answer will be:
\(\sin (2\cdot67.5\degree)=\sin 135\degree\)So, the answer will be option B) sin 135°