An air freshener starts with 33 grams and evaporates. In each of the following situations define a function that gives the remaining mass of the air freshener (in grams) in terms of the number of days, t t, since the air freshener was first used.

Answers

Answer 1

Hello!

A) The mass of the air freshener A decreases by 3.2 grams each day. Define a function, f, to represent this situation.

In this function, the mass of the air freshener A (m) is the dependent variable and the days (t) and the initial amount of the air freshener A (mi) are the independent variables. If the mass decreases by a fixed amount each day, you only have to multiply this amount by the number of days:

[tex]m=mi-(3,2*t)[/tex]

B) The mass of the air freshener B decreases by 3.2% each day. Define a function, g, to represent this situation.

This function is trickier since there isn't a fixed amount of decreasing. Instead, the rate of decreasing depends on the initial amount of the freshener (mi). You have to include this initial amount in the equation to correctly model it. This is how you do it:

[tex]m=mi-(mi* \frac{3,2}{100}*t) [/tex]

Have a nice day!

Related Questions

What is the GCF of 95,42 and 97?

Answers

the greatest common factor is 1

Final answer:

The GCF of 95, 42, and 97 is 1 because the prime factorizations of these numbers do not share any common factors other than 1.

Explanation:

To find the Greatest Common Factor (GCF) of the numbers 95, 42, and 97, we need to look for the highest number that can divide all three numbers without leaving any remainder. When considering 95, 42, and 97, we notice that:

95 is a product of the prime numbers 5 and 19,42 is a product of the prime numbers 2, 3, and 7,97 is a prime number itself, hence it only has 1 and 97 as its factors.

Since the prime factorization of these numbers does not share any common factors other than 1, the GCF of 95, 42, and 97 is 1.

What is the Value of:

Answers

1/2^3 = 1/2 x 1/2 x 1/2 = 1/8

Answer is C

Ken is a tour guide at an art museum. He earns $11 an hour regular pay and receives time-and-a-half for overtime. Last week he worked 40 hours plus overtime. If he made $66.00 in overtime, how many overtime time hours did he work?

Answers

He earns $16.50 for one hour of overtime.
He worked 4 hour of overtime.
I figured this out by first finding out how much he earns in one overtime so that equals $16.50. Then you need to divide $66.00 by $16.50 to get 4.

Answer:

Ken worked 4 hours overtime.

Step-by-step explanation:

Ken earns $11 for an hour in his regular pay.

He receives time-and-a-half for overtime = $11 + (11/2) = 11 + 5.50 = $16.50

Ken worked 40 hours plus overtime and he made $66.00 in his overtime.

So he worked overtime = $66.00 ÷ 16.50 = 4 hours

Ken worked 4 hours overtime.

how many ways can you arange the letters in the word cube

Answers

You could four times because there are four letters in the word cube, so there are only four possible ways you could spell it.

Hope this helps:)
Plz rate branliest

An artist is deciding between two different triangular shapes to use for a sculpture. The first triangle has a base of 20 feet and a height of 5 feet. The second triangle has a base of 25 feet. If the two triangles have the same area, what is the height of the second triangle?

Answers

4 i belive altho i could be way wrong

The height of the second triangle is 4 feet, which is found by using the formula for the area of a triangle (A = bh/2) and equating the area of the first triangle to that of the second.

To find the height of the second triangle with the same area as the first, we use the formula for the area of a triangle, A = bh/2, where b is the base and h is the height. The area of the first triangle with a base of 20 feet and height of 5 feet is:

A1 = (20 feet * 5 feet) / 2 = 50 [tex]feet^2[/tex]

Since the second triangle must have the same area, we can set up the equation:

50 feet2 = (25 feet * h2) / 2

Solving for the height (h2) of the second triangle:

100 feet2 = 25 feet * h2h2 = 100 [tex]feet^2[/tex] / 25 feeth2 = 4 feet

Therefore, the height of the second triangle is 4 feet.

What is the approximate volume of the cone that is 8 cm in height and 12 cm as a radius use 3.14 for pi

Answers

1206.37 will be your answer!

The volume is 1206.37
π144(8/3)
452.16×2.6666(repeating)
1205.76 cubic cm
It is off since you are using 3.14 as a substitute for pi, but using the full number (or close to it) it is 1206.37

draw a polygon that has 2 pairs of parallel sides, 2 pairs of sides equal in length 2 acute and 2 obtuse angles

Answers

I don't think that I could show you on this website. Sorry.

the polygon is called a rhombus

What is the area of the shape?

Answers

A = (14)(18) + 1/2(18)(13)
A = 252 + 117
A = 369

answer
369 m^2

a candy machine contains 120 spherical kids each candy is solid and has diameter of 0.25 in what is the total volume of the candies in the machine

Answers

Final answer:

The total volume of the candies in the machine is approximately 0.981 cubic inches.

Explanation:

To find the total volume of the candies in the machine, we first need to calculate the volume of one candy. The diameter of each candy is 0.25 inches, so the radius is half of the diameter, which is 0.125 inches. The formula for the volume of a sphere is V = (4/3)πr³. Plugging in the values, we get V = (4/3)π(0.125)³ = 0.0081777 cubic inches.

Since there are 120 candies in the machine, we can multiply the volume of one candy by the number of candies to get the total volume. Total Volume = 120 * 0.0081777 = 0.981324 cubic inches.

Starting at home, Ishaan traveled uphill to the gift store for 18 minutes at just 10 mph. He then traveled back home along the same path downhill at a speed of 30 mph.

What is his average speed for the entire trip from home to the gift store and back?

Answers

D=TxR
D=18 minutes x 10 miles/hr
D= 180 minutes miles / hr 1 hr/60 minutes
D= 3 miles

T= D/R T= 3 miles/ 30 miles/ hr T= 1/10/hr 6 minutes

It took Ishaan 24 minutes to go 6 miles so his average speed is D/T=R
6miles/24minutes=miles/hr 1 miles/4 minutes x 60 minutes/hr = 15 miles/hr
Ishaan's average speed was 15 mph.

50 POINT QUESTION. ANSWER AND EXPLAIN HOW YOU GOT THE ANSWER. IF NOT, YOU GET REPORTED. THANK YOU VERY MUCH !
In the morning, a farm worker packed 3 pints of strawberries every 4 minutes. In the afternoon, she packed 2 pints of strawberries every 3 minutes. What was the difference between her morning and afternoon packing rates, in pints per hour?

A. 5
B. 10
C. 40
D. 45

Answers

A. 5
her morning packing rate was 45 pints per hour.
her afternoon packing rate was 40 pints per hour.

Edit:
By dividing 60 by 4, you get 15, so multiply 15 by 3, this gives you 45.
By dividing 60 by 3, you get 20, so multiply 20 by 2, this gives you 40

3 pints every 4 minutes = ? pints every 60 minutes.
2 pints every 3 minutes = ? pints every 60 minutes.

For the first one, just divide 60/4. That is 15. 15*3 = 45, so 45 pints every hour.

Do the same process for the second equation. (60/3) * 2 = 40

Finally, 45-40=5.

The answer is A.

Hope that helps!

What fraction is equivalent to 4/10

Answers

To get equivalent fraction, we multiply or divide the numerator and denominator by the same number

[tex] \dfrac{4}{10} = \dfrac{4 \div 2}{10 \div 2} = \dfrac{2}{5}[/tex]

[tex]\text {So } \dfrac{4}{10} \text { is equivalent to } \dfrac{2}{5}[/tex]

4 / 10 = 2 / 5

The fraction equivalent to 4 /10 can be gotten by reducing the actual fraction to it lowest term.

Therefore, let's divide the numerator and denominator by 2.

4 / 10 ÷ 2 / 2 = 2 / 5

The fraction equivalent to 4 / 10 is 2 /5 .

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What is the measure of angle x?

Enter your answer in the box.
x = ( )°

Answers

90 - 47 = 43

x = 43
vertical angles are equal

hope it helps

We know that angles on a straight line sum to 180°, and we can see that 90° has already been defined on the left top left hand, leaving us with 90° on the top right hand. We are given 47°, so that must mean that the angle between the right angle and the 47° angle is:
90-47= 43°
Opposite angles around a 360° point are equal, and we see that angle x is opposite the 43° that we just found out. Therefore, x= 43°

15 points just please help and dont guess

Answers

The answer is the first one, because the number of tires properly installed on Monday will not be the same as everyday.

The answer is A
Hope I helped!

The Daily Focus newspaper has a circulation of 382 198. Round this number to the nearest 100 000.

Answers

390000 because the 82 rounds up to a nine

Rewrite the following equation in slope-intercept form. 6x − 14y = -3 Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:
y = (3/7) x + (3/14)

Explanation:
The slope-intercept form has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept

The given is:
6x - 14y = -3

To get in the slope-intercept form, we need to isolate the y as follows:
6x - 14y = -3
14y = 6x + 3
y = (6/14)x + (3/14)
y = (3/7) x + (3/14)

Hope this helps :)

Y=0
6x = -3
X= -2

X=0
-14y=-3
Y= 3/14

Two supplementary angles have the same measurements of 2x - 8 and 8x - 12. What is the measurement of the largest angle?

Answers

Supplementary angles add up to 180 degrees.
2x - 8 + 8x - 12 = 180
10x - 20 = 180
10x = 200
x = 20

Angle 1 = 32
Angle 2 = 148
The measure of the largest angle is 148

Hope this helps =)

PLEASE HELP! What is the value of x?

Answers

It is a rectangle so its opposite sides are congruent. Because they are congruent we can set them equal to each other and solve for x.

40 = 5x + 10
30 = 5x
6 = x

So the value of x is 6.

The two sides are congruent so the value of x can be found with the equation 5x+10=40.

5x+10-10=40-10

5x=30

5x/5=30/5

x=6

There are 254 212 610 registered cars in the United States.
What is this number rounded to nearest million?

Answers

Answer:

254,000,000

Step-by-step explanation:

As it's 212,610 you round it down

The value of number rounded to nearest million is,

⇒ 254,000,000

What is rounding off?

Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.

Given that;

There are 254 212 610 registered cars in the United States.

Hence, The value of number rounded to nearest million is,

⇒ 254,000,000

Learn more about the rounding number visit:

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Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this problem.

Brittany is painting a mural on one of the walls in her room. The mural is in a parallelogram-shaped frame. The area of the mural is 1056 in² and the base is 32 inches.

What is the height of the mural?

Enter your answer in the box.

[___] in

Answers

33 in because 1056 divided by 32 is 33
hope you pass your test

The area of the mural is 1056 in² and the base is 32 inches. We have to determine the height of the mural.

Area of parallelogram = [tex] b \times h [/tex]

where 'b' is the base and 'h' is the height.

1056 [tex] in^{2} [/tex] = 32 [tex] \times h [/tex]

[tex] h=\frac{1056}{32} [/tex] in

Therefore, the height of the mural is 33 inch.

use the formula for the ares of a trapezoid A=h (b^2+b^2/2)= where A is area b1 and b2 are the length of the bases and h is the height to answer the question how many square fet of grass and there on a trapezoidal field with a height of 75 ft bases of 125 ft and 81 ft?

A. 725 ft^2
B. 1025 ft^2
C. 7725 ft^2
D. 15,450 ft^2

Answers

The answer is C. 7725ft^2

during a festive season a shop offered a discount of 20 percent on the marked price of all items find the SP of 3 trousers mardep at rs 1800 each and two t shirts marked at rs 550 each

Answers

Think of the retail price as the whole price or 100%. Since the items are discounted 20% you end up paying 80% of the retail price for each item. 80% of the retail price is the sale price.

TROUSERS
We need to find 80% of 1800. Percent means out of 100 so we can represent it using [tex] \frac{80}{100} [/tex] or .80 whichever is easier for you to work with. Multiply this by 1800 and you have your sales price for 1 trouser. That is, the sales price for a trouser is (1800)(.8) = 1440.

SHIRTS
Same as we did for trousers we multiply the price of a shirt (550) by (.8) to get the sale price. It is 440.

3 TROUSERS AND 2 SHIRTS
The sales price for 3 trousers and 2 shirts is (3)(1440) + (440)(2) = 5200

NOTE
I noticed that you didn't include currency (dollars, pounds, euros, for example). If these are dollars then the price of a trouser might be $18.00 as opposed to 1800 which seems really high. Similarly I would expect 18,00 Euros as opposed to 1800 Euros for a pair of pants. If this is the case take the answers given above and merely insert a decimal point to spaces from the left (or in Europe and other parts of the world a comma).

12+18n+7-14n write an equivalent expression using like terms

Answers

You can get a similar expression with the same value by simplifying the expression.

19 + 4n

Hope this helps!

what is the greatest common factor (GCF) OF 88 and 72?

Answers

The Greates Common Factor (GCF) is: 2 x 2 x 2 = 8

The GCF of 72 and 88 is 8. 8 is the highest number that both of these numbers are divisible by.
Answer: 8

What is 4 1/3 times 18

Answers

Change 4 1/3 to improper fraction: 13/3

13/3 * 18/1 = 234/3

234/3 = 78.

Hope this helped☺☺♥♥

Well, 4 1/3 is equal to 13/3

So you have 13/3 times 18/1,
Which equals 234/3, or 78

I BEG YOU MY FRIENDS HELP ME!

Answers

The maximum point is (3,4) so a<0.The axis of synmentry is x=3.The maximum value is 4.

Kyle and his brother have a marble set. Of the marbles, 12 are blue. This represents 50/100 of all the marbles. What decimal is equivalent to 50/100

Answers

The decimal equivalent to 50/100 is 0.50, which is found by dividing 50 by 100.

The decimal equivalent to 50/100 is 0.50. This is because 50/100 is the same as dividing 50 by 100, which gives you 0.50.

This conversion is a standard way of expressing fractions where the denominator is 100, and it's commonly used to convert fractions into percentages or decimals.

For example, to convert 1/4 to a percent, you multiply by 25 (since 4 times 25 equals 100) to get 25 percent, which is equivalent to the decimal 0.25.

So, 50/100 is equivalent to 0.5 as a decimal.

The Marriott family bought a new apartment three years ago for $65,000. The apartment is now worth $86,515. Assuming a steady rate of growth, what was the yearly rate of appreciation?

Answers

Final answer:

The annual appreciation rate for the Marriott family's apartment they bought three years ago for $65,000, now worth $86,515, is 10%.

Explanation:

The subject matter of this question is the calculation of the appreciated rate of the Marriott family's apartment. They bought this apartment three years ago for $65,000, and now it is worth $86,515. We want to find a constant rate of growth over these three years.

To determine the annual rate of appreciation, we need to use the formula for exponential growth: final value = initial value × (1 + annual growth rate) ^ number of years.

Let's plug in the given values: $86,515 = $65,000 × (1 + growth rate)³.

First, we divide the final value by the initial value: $86,515/$65,000 = 1.33177.

Second, we must calculate the cubic root of 1.33177 (since we have three years), which is 1.1. Therefore, the annual growth rate is 1.1 - 1 = 0.1 or 10%.

Hence, the yearly rate of appreciation for the apartment is 10%.

Learn more about annual rate of appreciation here:

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at a local gas station, regular gasoline sells for $2.899 per gallon, while premium gasoline sells for $3.379 per gallon. how much does a person save on 15.25 gallons of gas by buying regular instead of premium?

Answers

the person saved $7.32

We first need to find what each type of gasoline equals at 15.25 gallons.
Regular Gasoline:
2.899•15.25
44.20975
Premium Gasoline:
3.379•15.25
51.52975
Let’s subtract regular from premium to see how much you would save.
51.52975-44.20975
7.31975
So you would save $7.31975 when buying regular gas instead of premium.

Rewrite the following equation in slope-intercept form. 5x + 7y = 7 Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:
y = (-5/7) x + 1

Explanation:
The slope-intercept form of the line has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept

The given is:
5x + 7y = 7

To put this in slope-intercept form, we will need to isolate the y as follows:
5x + 7y = 7
7y = -5x + 7
y = (-5/7) x + (7/7)
y = (-5/7) x + 1
where:
m is the slope = -5/7
c is the y-intercept = 1

Hope this helps :)

Y=0
5x= 7
X= 7/5

X=0
7y=7
Y=1

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