Let f(n) represent the number of bottles in the store on n-th week.
When n=0, f(n)=250.
Then 40% of the bottles were sold, this means that were sold 250·0.4=f(n)·0.4. The amount of bottles left is 250-250·0.4=f(n)-f(n)·0.4=f(n)·0.6.
If 48 new bottles arrived in shipments, then the amount of bottles became
f(n)·0.6+48=f(n+1).
Since n>0, then
f(n)=f(n-1)·0.6+48.
Answer: correct choice is A.
Option: A is the correct answer.
A: f(n) = f(n − 1) ⋅ 0.6 + 48, n > 0
Step-by-step explanation:It is given that:
A store had 250 bottles of water.
Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments.
This means that the number of bottles that will be present in the store after 40% of the bottles will be sold at a particular week= 100%-40%=60% plus 48 new arrival
This means that each time the number of bottles in the store will be 60% of the bottles that were sold previous week plus 48.
Hence, if f(n-1) represent the number of bottle in the (n-1)th week then the number of bottles in the nth week will be represented by:
[tex]f(n)=60\%\ of\ f(n-1)+48\\\\i.e.\\\\f(n)=0.6\cdot f(n-1)+48[/tex]
80 POINTS!! PLEASE HELP ME OUT!!!
It is non-proportional. The graph is in a straight line but doesn't cross the origin!
Unproportional. For it to be proportional, the line should go through the origin (0,0).
When 8668/25+4141/9-5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of that mixed number?
Answer:
Fractional part of the mixed number is [tex]\frac{23}{45}[/tex].
Step-by-step explanation:
First we have to simplify the given expression,
[tex]\frac{8668}{25} +\frac{4141}{9} -\frac{5533}{25}[/tex]
=[tex]\frac{(8668*9)+(4141*25)-(5533*9)}{25*9}[/tex]
=[tex]\frac{(8668-5533)*9+(4141*25)}{25*9}[/tex]
=[tex]\frac{(3135*9)+(4141*25)}{25*9}[/tex]
=[tex]\frac{28,215+103,525}{225}[/tex]
=[tex]\frac{131,740}{225}[/tex]
=[tex]\frac{26,348}{45}[/tex]
=[tex]585.51111[/tex]
Now we have to take the whole number that we get by dividing numerator by denominator,
It is 585
Now we have to find the remainder after taking the numerator,
[tex]26,348-(585*45)=23[/tex]
Now we represent the whole number and the fraction of remainder together as a mixed number.
[tex]585\frac{23}{45}[/tex]
Therefore, fractional part of the mixed number is [tex]\frac{23}{45}[/tex].
Find the range of the function for the given domain. f(x) = 2x - 7 ; {-2, -1, 0, 1, 2}
The domain is a discrete set. So we will have a discrete range.
The range is a set containing:
f(-2)=-11
f(-1)=-9
f(0) = -7
f(1) = -5
f(2) = -3
Range = {-11,-9,-7,-5,-3}
Final answer:
The range of the function f(x) = 2x - 7 for the domain {-2, -1, 0, 1, 2} is found by substituting the domain values into the function, resulting in the range {-11, -9, -7, -5, -3}.
Explanation:
The student is asking to find the range of a given function f(x) = 2x - 7 for a specific domain. The domain provided is {-2, -1, 0, 1, 2}. To find the range, we substitute each value from the domain into the function and calculate the corresponding output values.
For x = -2, f(x) = 2(-2) - 7 = -4 - 7 = -11For x = -1, f(x) = 2(-1) - 7 = -2 - 7 = -9For x = 0, f(x) = 2(0) - 7 = 0 - 7 = -7For x = 1, f(x) = 2(1) - 7 = 2 - 7 = -5For x = 2, f(x) = 2(2) - 7 = 4 - 7 = -3Therefore, the range for the given domain is {-11, -9, -7, -5, -3}.
Why is a coordinate plane useful for graphing locations? Why is it useful as a map?
800,00 rounded to the nearest hundred thousand
It is 80,000 im not sure what you meant by "800,00"
Find f'(x)
f(x)=(1-2x^2)^3
Answer: f'(x) = 12x + 48x³ - 48x⁵
Step-by-step explanation:
f(x) = (1 - 2x²)³
= (1 - 2x²)(1 - 4x² + 4x⁴)
1 - 4x² + 4x⁴
-2x² + 8x⁴ - 8x⁶
= 1 - 6x² + 12x⁴ - 8x⁶
f'(x) = 0 -2(6)x²⁻¹ + 4(12)x⁴⁻¹ - 6(8)x⁶⁻¹
= 12x + 48x³ - 48x⁵
Ms. Edwards is redecorating her office. She has a choice of 8 colors of paint, 5 kinds of curtains, and 6 colors of carpet. How many different ways are there to redecorate? A.240 B.19 C.297 D.357
Please hurry
Mrs.Magdalino kept records on how much she spent on gasoline and the maintenance of her car. She found that it cost $485 to drive 500 miles in a month. Find the cost per month.Write a rule to describe the cost c for gasoline and the maintnance of a car as a function the number of miles m the car is driven.
Cost per mile = [tex]\frac{cost}{number of miles}[/tex]
[tex]= \frac{485}{500}[/tex]
= 0.97
Now,
c - cost for gasoline and maintenance and
m - number of miles traveled
Hence, the required expression is c = 0.97m.
use the fact that 147*16=2352 to write two different multiplication facts that have a product of 2352
Two different facts using the original fact of 147 multiplied by 16 to reach the product of 2352 are 73.5 multiplied by 32 and 147 multiplied by 16.
To find two different multiplication facts that have a product of 2352, using the fact that 147 multiplied by 16 equals 2352, we can manipulate the factors in various ways. One way is to halve one of the factors and double the other. If we take half of 147, we get 73.5, and doubling 16 gives us 32. Therefore, 73.5 multiplied by 32 is one multiplication fact that equals 2352. Another way is to multiply both factors by the same number. If we multiply both 147 and 16 by 1, technically we get a different multiplication expression with the same product. This means 147 multiplied by 16 is still valid since we have applied the identity operation (multiplying by 1).
In summary, two different facts using the original fact of 147 multiplied by 16 to reach the product of 2352 are 73.5 multiplied by 32 and 147 multiplied by 16.
Need help with Foundation of Mathematics 11, Question is attached
Here's another picture of the same thing. There is one in Saskatchewan (I live in Alberta, so that is my next door neighbor). I was wondering if this faced essentially east west.
If it did, then it likely had some sort of religious significance having to do with sun worship. Since the labeling is so carefully done, I think the bisector is probably pointing very near due east and is in the fall solstice. All of this could be coincidental or it could mean something more serious (like sun worship). Man is very ingenious where his religious expressions are concerned.
In which number is the digit 7 ten time larger than it is in the number 794
7,381 is the answer.
I need help plzz!! Just box number 4, TY
12.36% I think sorry if its wrong ;-;
Find the slope of the line. A.-4, B.4, C. 1/4, D. -1/4
The slope of a line passing through two points is found by taking the change in y-coordinates divided by the change in x-coordinates. For the given points (1, 0.1) and (7, 26.8), the slope is approximately 4.45.
Explanation:The slope of a line passing through two points can be found using the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
Given the points (1, 0.1) and (7, 26.8), the change in y-coordinates is 26.8 - 0.1 = 26.7 and the change in x-coordinates is 7 - 1 = 6. Substituting these values into the formula, we get:
slope = 26.7/6
slope ≈ 4.45
What is 24:4 in lowest terms
24:4 in lowest terms would be 6:1
Answer,
6:1
Hope this helps :-)
Divide. 1.74÷(−0.06)
Answer:
- 29
Step-by-step explanation:
Multiply numerator and denominator by 100. It isn't necessary, but it makes the problem easier to see.
174 / (-6)
Put into your calculator like this
174
÷
(-)
6
=
And the answer comes out as - 29
Solve for x.
x+15.09=−2.57
x+15.09= -2.57
x= -17.66
If you want the value of x: you would have to subtract -15.09 on both sides.
x+15.09-15.09=-2.57-15.09
x=-17.66
Solve the compound inequality. Graph your solution using a number line. Please help.
4+k>3 or 6k<-30
Thanks!
Answer:
(-∞,-5)∪(-1,∞)
Step-by-step explanation:
1. You have the compound inequality given in the problem above:
[tex]4+k>3[/tex] or [tex]6k<-30[/tex]
2. First, you must solve for [tex]k[/tex], as following:
[tex]4+k>3\\k>3-4\\k>-1[/tex]
[tex]6k<-30\\k<\frac{-30}{6}\\k<-5[/tex]
3. Then, the solution is:
(-∞,-5)∪(-1,∞)
5. You can pose the solution in the number line, as it is shown in the graph attached.
PLZ HELP 90 PTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Graph f(x)=−0.25x+4. Use the line tool and select two points to graph the line.
We need to graph ⇒⇒⇒ f(x) = - 0.25 x + 4
the given equation represents a linear equation, we need just 2 points to graph it
At x = 0 ⇒⇒⇒ f(x) = -0.25 * 0 + 4 = 4
At x = 4 ⇒⇒⇒ f(x) = -0.25 * 4 + 4 = 3
The attached figure represents the table and the graph of the given function.
Answer:
this equation represents a linear equation, you just need 2 points to graph it
At x = 0 to f(x) = -0.25 * 0 + 4 = 4
At x = 4 to f(x) = -0.25 * 4 + 4 = 3
Hope this helps. :)
Round 32,879 to the nearest thousand and use a number line to model your thinking
Solution
The given number is 32, 897
Here we need to round the thousand place.
Find the number in the thousands place.
We have 2 in the thousands place.
Look for digit which is right to 2.
We have 8, which is greater than 5, if we have the number greater than 5 we have to add 1 with thousands place and make the other numbers zeros.
Since we have 8 right to the number 2, so we add 1 with 2.
2 + 1 = 3
Now thousands place became 3 and make other digits zero.
32, 879 = 33, 000
The answer is 33,000
Note: Here I have attached the place value chart.
The ratio of the length to the height of the American flag is 3:2. If the length of the American flag is 1.8 yards, what is the height?
27:10
1/8 equals 9/5
3/2*9/5=27/10
To find the height of the American flag, convert the known length from yards to feet, use the given ratio to set up a proportion, solve it to find the height in feet, and then convert it back to yards, resulting in a height of 1.2 yards.
The ratio of the length to the height of the American flag is given as 3:2. Knowing that the length of the flag is 1.8 yards, we can set up a proportion to find the height. Since we know that 1 yard equals 3 feet, we first convert the length into feet. 1.8 yards is equivalent to [tex]1.8 imes 3 = 5.4 feet[/tex]. Using the ratio 3:2, we can write the proportion as 3/2 = 5.4/height in feet. To solve for the height, we cross-multiply and [tex]get 2 imes 5.4 = 3 imes height,[/tex] yielding 10.8 = 3 imes height. Dividing both sides by 3 gives us the height as 3.6 feet. To convert feet back to yards, we recall that 3 feet equal 1 yard, and hence, 3.6 feet is 1.2 yards. Therefore, the height of the American flag is 1.2 yards.
Plzzzz I NEED help with 9 and 10 plzzzzz
Question 9:
[tex]\frac{20*(5)}{50}[/tex] Simplify what is in the parenthesis
[tex]\frac{100}{50}[/tex] Multiply 20 to 5
[tex]2[/tex] Divide 50 to 100
*(Answer)*= [tex]2[/tex]
Question 10:
[tex]5+(18)[/tex] ÷ [tex]6[/tex] Simplify what is in the parenthesis
[tex]5+3[/tex] Divide 6 to 18
[tex]8[/tex] Add 5 to 3
*(Answer)*= 8
Hope this helps
User who answered: BangtanBoyScouts
a number is multiplied by 4. Next, 3 is added to the product, ans then 11 is substracted. If the result is 24, what is the number
Answer:
8
Step-by-step explanation:
work backward
24+11=35
35-3=32
32/4=8
John wants to buy a new bike That cost $337 and he already has saved $103 estimate to find about how much more Johnny’s to see if to buy the bike
estimate......
340 - 100 = 240
337 -> 340
103 -> 100
340-100
= 240 left to save
Which of the following is an adjustment allowed by the IRS?
A.) Dental Expenses
B.) Medical Expenses
C.) Work Expenses
D.) Moving Expenses
Answer: moving expenses apx xx
Step-by-step explanation: apix approveddfmdo
The correct answer is moving expenses which are allowed by the IRS option (D) is correct.
What are moving expenses?The reasonable costs of moving home goods and personal possessions to a new residence are characterized as moving expenses. These expenditures also include the employee's and his or her immediate family's journey to the new location.
You can deduct charges for transporting a trailer, packing, crating, in-transit storage, and insurance when relocating your household items and personal effects.
The moving expenses adjustment is allowed by IRS.
Thus, the correct answer is moving expenses which are allowed by the IRS option (D) is correct.
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Which of the following equations represents the line that passes throught the points (2, -6) and (-4,3)?
First, find the slope of the line that goes through the 2 given points, which you should know how to do. Call it m. Then a perpendicular line must have a slope of -1/m. The slope-intercept form of the equation you seek is
y = (-1/m)x + b,
where b is any real number. Examine the list of choices, and pick any that have a slope of -1/m.
The equation that represents the line that passes through the points (2, -6) and (-4,3) is 2y + 3x = -6.
How to find the equations represent the line that passes through the points (2, -6) and (-4,3)?The equation of the line that passes through the points (x1,y1) and (x2,y2) can be obtained with the formula:
[tex]y-y_1 = m (x-x_1)[/tex]
The slope of the points are
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We need to find the equation that represents the line that passes through the points (2, -6) and (-4,3)
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
[tex]m=\dfrac{3+6}{-4-2}\\\\\\ m = 9/-6 = -3/2\\[/tex]
So, the equation is:
[tex]y-y_1 = m (x-x_1)\\\\y +6 = -3/2(x -2)\\\\2y +12 = -3x +6\\\\2y + 3x = -6[/tex]
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A washer and a dryer cost $800 combined. The washer costs $50 less than the dryer. What is the cost of the dryer?
800-50=750 so 750+50=800 the dryer maybe go be 750
When a washer and a dryer cost $800 combined. The washer costs $50 less than the dryer the cost of the dryer is $425.
Let's assume the cost of the dryer is "D" dollars.
According to the given information, the washer costs $50 less than the dryer, so the cost of the washer would be "D - $50" dollars.
Now, we know that the combined cost of the washer and dryer is $800, so we can set up an equation:
Cost of washer + Cost of dryer = $800
(D - $50) + D = $800
Now, let's solve for the cost of the dryer (D):
2D - $50 = $800
Add $50 to both sides:
2D = $850
Now, divide by 2 to solve for D:
D = $850 / 2
D = $425
So, the cost of the dryer is $425.
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Grandview Golf makes wooden golf tees. in 2010 they made 380,285 tees. in 2011 they made 513,525 tees. to the nearest ten thousand how many tees did they make in the two years
Answer:
They made 890,000 tees.
Step-by-step explanation:
You have the following information given in the problem above:
- In 2010 they made 380,285 tees.
- In 2011 they made 513,525 tees.
2. Therefore, to calculate the amount of tees made by them in the two years, you only need to add the amount of tees they made in 2010 and 2011, as following:
[tex]380,285+513,525=893,810[/tex] tees
3. To the nearest ten thousand: 890,000 tees.
Help quickly limited time 20 points!!!!!!!!!
Which of the following equations has the given solution set?
Solution set: Ø
-2m + 5 = 2m + 5
-2m + 5 = -2m + 5
-2m + 5 = -2m - 5
So,
-2m+5=-2m-5
-2m + 2m = -5 - 5
0 = -10
which is no solution.
Therefore, the required equation is -2m + 5 = -2m - 5.
Frank drove 320 km in 4 hours. What was his average speed?
Answer: 80
Step-by-step explanation:
You know frank drove 320 in 4hr so you do 320 divide by 4 and u get 80
f=1/6(g+h-k) solve for g
The value of g will be as g = 6f - h + k.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given equation is
f=1/6(g+h-k)
WE have to solve the equation for g;
f = 1/6(g+h-k)
By cross multiplication;
6f = g + h - k
g = 6f - h + k
Thus, the value of g will be as g = 6f - h + k.
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