Jake forgot to replace the cap on a bottle of deodorant. The deodorant began to evaporate at the rate of 12% per day. If the original amount of deodorant in the bottle was 30 grams, which of the following graphs best represents the amount of deodorant f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
Answers
f(x) = 30(0.88)^x
Answer:
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
Step-by-step explanation:
We are given that,
Original amount of deodorant in the bottle = 30 grams
The rate of evaporation = 12% = 0.12
That is, we see that the deodorant is decreasing as the number of days increases.
So, the function form of the decrease in the amount of deodorant is given by,
[tex]f(x)=30(1-0.12)^x[/tex], where x is the number of days.
i.e. [tex]f(x)=30(0.88)^x[/tex], where x is the number of days.
Hence, the graph representing the amount of deodorant after x number of days is,
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
Related Questions
Express the ratio of a's to n's in the word banana, in simplest form.
Answers
The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word. Therefore, the correct answer is D: 2:1.
To find the ratio of A's to N's in the word BANANA, we need to count the number of A's and N's in the word.
1. Count the occurrences of A and N:
In the word BANANA, there are 3 A's and 1 N.
2. Express the ratio:
The ratio of A's to N's is 3:1.
3. Simplify the ratio:
To simplify the ratio, we can divide both parts by their greatest common divisor (GCD), which is 1 in this case, because 3 and 1 have no common divisor other than 1.
[tex]\[ \text{Ratio} = \frac{3}{1} = 3:1 \][/tex]
4. Check the given options:
Now, let's compare the simplified ratio 3:1 with the given options.
A. 2:3 - This doesn't match the simplified ratio.
B. 3:2 - This doesn't match the simplified ratio.
C. 1:2 - This doesn't match the simplified ratio.
D. 2:1 - This matches the simplified ratio.
Therefore, the correct answer is D: 2:1.
The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word.
The complete question is:
Express the ratio of A's to N's in the word BANANA, in simplest form.
A: 2:3
B: 3:2
C: 1:2
D: 2:1
HOLA FELLOW AMERICANS I AWAIT YOUR ASSISTANCE
Answers
Answer:
2
Step-by-step explanation:
the sum of two fractions is three times their difference.six times the smaller fraction exceeds the larger fraction by 3/2.find the fractions
Answers
.. a +b = 3(b -a)
.. 6a -b = 3/2
Rewriting the first equation, we have
.. 4a -2b = 0
or
.. 2a -b = 0
Subtracting this from the second equation gives
.. 4a = 3/2
.. a = 3/8
.. b = 2a = 3/4
The two fractions are 3/8 and 3/4.
In your math class there are 15 boys and 21 girls. 12 of the boys and 15 of the girls are freshmen. if you randomly choose a student in your class, what is the probability that you'll choose a girl or a freshman?
Answers
Final answer:
The probability of randomly choosing a girl or a freshman from the class is 0.916 or 91.6%. This is calculated by considering the total number of girls and freshmen in the class, while avoiding double-counting freshman girls in the calculation.
Explanation:
To calculate the probability that a randomly chosen student from the class is either a girl or a freshman, we need to consider the total number of students in the class, as well as the number of girls and the number of freshmen. The class consists of 15 boys and 21 girls, totaling 36 students. Out of these, 12 boys are freshmen and 15 girls are freshmen, but we must avoid double-counting the girls who are also freshmen.
First, we calculate the total number of freshmen: 12 boys + 15 girls = 27 freshmen. Next, we calculate the probability of picking a girl: 21 girls / 36 total students = 0.583 (to three decimal places). We then calculate the probability of picking a freshman: 27 freshmen / 36 total students = 0.750. However, since the freshmen include both boys and girls, we must subtract the probability of picking a freshman girl to avoid double-counting: 15 girls who are freshmen / 36 total students = 0.417.
Finally, we add the probability of picking a girl and the probability of picking a freshman, and subtract the probability of picking a freshman girl to obtain the inclusive probability: 0.583 (girl) + 0.750 (freshman) - 0.417 (freshman girl) = 0.916.
Therefore, the probability that a randomly chosen student is either a girl or a freshman is 0.916, or 91.6%.
If it takes bottling machine to fill 150 bottles per minute, how many minutes will it take the machine to bottle 4500 bottles
Answers
How do I solve this?
Answers
I find it convenient to draw a graph of a line that represents the ladder. I choose to have the y-intercept be where the ladder touches Catie's head (5.5 feet above the ground), and the x-intercept to be where the ladder touches the ground, 16 inches away from Catie.
Then the wall is 4.5 feet (54 inches) from the ladder's base, or 38 inches in the other direction from Catie. The graph shows the ladder hits the wall at a height of about 18.6 feet.
The graph shows the calculations for the position of the wall and for the equation of the line. (The line is written in "intercept form.") The graphing calculator shows the intercept points, so no "work" is required except to highlight them.
Please help me asap!!!
Answers
-x - 2y = - 9
multiply the (1st) equation by 3
-3x - 6y = -27
now you have
-3x - 6y = -27
3x - 6y = -15
-----------------------add
-12y = -42
y = 3.5
2(3.5) = -x + 9
7 = - x + 9
x = 2
answer
(2 , 3.5)
#16 ) BRAINLIEST + POINTS !!!!!
Answers
Answer:
b is correct
Step-by-step explanation:
Convert 4 miles to feet.
20,210 feet
21,000 feet
21,120 feet
22,000 feet
Answers
A jar made of 3/16-inch-thick glass has an inside radius of 3.00 inches and a total height of 6.00 inches (including the bottom thickness of glass). The glass has a density of 165 lb/ft3. The jar is placed in water with a density of 62.5 lb/ft3.
Assume the jar sits upright in the water without tipping over. How far will the empty jar sink into the water?
What is the volume of the glass shell of the jar? Precision 0.00
What is the weight of the jar? Precision 0.00
What is the weight of water the empty jar will displace? Precision 0.00
What is the volume of water the empty jar will displace? Precision 0.00
How far will the empty jar sink?
Answers
The total volume of the jar is:
[tex]V_t=Bh=\pi h(r+a)^2[/tex]
Where h is the height of the jar, a is the thickness and r is the inner radius.
The volume of empty space, bounded by the jar, is:
[tex]V_e=B(h-a)=\pi r^2(h-a)[/tex]
The volume of a jar shell is the difference between these two:
[tex]V_s=V_t-V_e=\pi h(r+a)^2-\pi r^2(h-a)[/tex]
When we plug in all the number we get:
[tex]V_s=27.17 {$in}^3[/tex]
The weight of the jar is simply its volume times its density. We have to convert density of the glass:
[tex]165 \frac{lb}{ft^3}=\frac{165}{1728}\frac{lb}{in^3}=0.0949\frac{lb}{in^3}[/tex]
Now we can find the mass:
[tex]m_j=V_s\rho_j=27.17\cdot 0.0949=2.58 $lb[/tex]
The volume of water jar would displace depends how far the jar would sink.
There two forces acting on the jar when you put in the water. The first one is gravity and it's pulling the jar down. The second force is the buoyancy the and this force pushes the jar upward. In order for that jar to be stable, these two forces must be the same.
The buoyancy is given with this formula:
[tex]B=\rho gV_{disp}[/tex]
The volume of water that would be displaced by the jar can be expressed by this formula:
[tex]V_{disp}=\pi h'(r+a)^2[/tex]
Where h' is the height of the jar that is submerged in the water.
So the buoyancy force is:
[tex]B=\rho_w g\pi h'(r+a)^2[/tex]
This force must be equal to the force of gravity acting on the jar:
[tex]F_g=B\\ m_jg=\rho_w g\pi h'(r+a)^2\\ m_j=\rho_w \pi h'(r+a)^2\\[/tex]
We solve for h':
[tex] h'=\frac{m_j}{\rho_w \pi(r+a)^2}[/tex]
If we plug in the number we get:
[tex]h'=2.24 $in[/tex]
Now we can calcuate the amount of water discplaced and its mas(keep in mind that we also converted density of water into lb/in^3):
[tex]V_{disp}=\pi h'(r+a)^2=71.50${in}^3\\ m_v=\rho_w\cdot V_{disp}=2.58$lb[/tex]
We get the same mass as the mass of the jar, which makes perfect sense:
[tex]m_jg=\rho_w V_{disp}g\\ m_j=m_{wdisp}[/tex]
The volume of the glass shell of the jar is 0.0136 ft³ and its weight is 2.24 lbs. The weight and volume of the water it will displace amounts to 2.24 lbs and 0.036 ft³ respectively. Consequently, the jar will sink approximately 2.2 inches into the water.
Explanation:To begin, the volume of the glass shell of the jar will first need to be established. Given that the thickness of the glass is 3/16 inches, the outer radius of the jar is 3 inches + 3/16 inches = 3.1875 inches. To get the volume, utilise the formula for the volume of a cylinder, which is πr²h. Thus, with measurements converted to feet for the calculations (1 inch = 0.08333 foot), we have an external volume of π(0.265625 ft)² * 0.5 ft = 0.1118 ft³ and an internal volume of π(0.25 ft)² * 0.5 ft = 0.0982 ft³. Hence, the volume of glass is 0.1118 ft³ - 0.0982 ft³ = 0.0136 ft³
Next, the weight of the jar is determined by the formula mass = volume * density, so mass = 0.0136 ft³ * 165 lb/ft³ = 2.24 lbs.
To ascertain the weight of water the jar will displace, we consider the principle of buoyancy, which suggests that an object will displace a volume of fluid with a weight equal to its own weight. Thus, the weight of the water displaced is 2.24 lbs.
Then, the volume of this water is found with the formula volume = weight/density -> volume = 2.24 lbs / 62.5 lb/ft³ = 0.036 ft³.
Lastly, considering the jar will sink until the weight of the water being moved equals the weight of the jar. The volume of the water displaced equates to the submerged volume of the jar. Its depth in feet is then the volume divided by the cross-sectional area of the jar (internal radius), so the distance the jar sinks is roughly 0.036 ft³ / π(0.25 ft)² = 0.18 ft -> convert to inches = 2.2 inches.
Learn more about Buoyancy here:https://brainly.com/question/36883204
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***WILL GIVE MEDAL TO WHOEVER HELPS***
Question:
Sherri has 23 pieces of jewelry to sell. She sells the bracelets for $2 and the necklaces for $3, and earns a total of $55. If the bracelets are represented by x and the necklaces are represented by y, which of the following systems of equations can be used to calculate the number of bracelets and necklaces sold?
Answer choices:
x + y = 23, 3x + 2y = 55
x + y = 55, 3x + 2y = 23
x + y = 23, 2x + 3y = 55
x + y = 55, 2x + 3y = 23,
Answers
Choose the polynomial that is written in standard form. (1 point)
−3x5y2 + 4x3y + 10x2
−8xy2 + 4x4y2 + 3x3
x4y2 + 4x3y5 + 10x4
x6y2 + 4x3y8 + 10x7
Answers
The only one where this is true is the first one.
The degree goes from 7 to 4 to 2
Answer:
[tex]-3x^5y^2+4x^3y+10x^2[/tex]
Step-by-step explanation:
A polynomial in two variables is in standard form if its monomial from left to right are arrangerd in descending order. We say that a monomial [tex]x^ay^b[/tex] is greater than a monomial [tex]x^{a^{\prime}}y^{b^{\prime}}[/tex] if [tex]a+b > a^{\prime} + b^{\prime}[/tex] or [tex]a+b=a^{\prime}+b^{\prime} \quad \text{and} \quad (a,b)>(a^{\prime},b^{\prime}})[/tex] in the alphabetical order.
For example
[tex]x^2y>xy \quad \text{since} \quad 2+1>1+1 \\\\x^2y>xy^2 \quad \text{since} \quad 2+1=1+2 \quad \text{and} \quad 2>1[/tex]
The polynomial [tex]-3x^5y^2+4x^3y+10x^2[/tex] is in standard form, since [tex]x^5y^2 > x^3y >x^2[/tex]. On the other hand, the polynomial [tex]-8xy^2+4x^4y^2+3x^3[/tex] is not in standard form since [tex]x^4y^2>xy^2.[/tex]
How do you find the x intercept, y intercept, and M
Answers
.. (2x/12) + (-3y)/12) = 1
.. x/6 + y/-4 = 1
The x-intercept is 6
The y-intercept is -4
The "slope triangle" is 4 units high and 6 units wide, so ...
.. the slope is m = 4/6 = 2/3.
Please help asap!!! 16 points ):
Answers
ANSWER: D) x=3
Hope this helps! :)
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
V(t)=24,500(0.95^t)
Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.
Answers
The value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
The dollar value v(t) of a certain car model that is t years old is given by the exponential function.
[tex]\rm V(t)=24,500(0.95^t)[/tex]
The initial value plug t = 0 in the above function:
V(0) = $24500
Plug t = 13 years in the above exponential function
[tex]\rm V(13)=24,500(0.95^1^3)[/tex]
After calculating, we get:
V(13) = 12576.88
V(13) = 12576.9 dollars
Thus, the value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
Learn more about the exponential function here:
brainly.com/question/11487261
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PLEASE HELP ME ASAP
PLEASE
Answers
Choice D
Company 2 is greater in avg rate of change by $750
=======================================
Explanation:
Average rate of change is the same as slope through two points. The two points are the endpoints of the interval.
The x values we'll use is x = 0 and x = 12 since it constitutes the first 12 years (12-0 = 12)
For company 1, if x = 0 and x = 12, then y = 12000 and y = 30000 respectively. The two points (0,12000) and (12,30000) are on the graph for company 1
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (30000-12000)/(12-0)
m = 18000/12
m = 1500
Over the first twelve years, the average rate of change for company 1 is 1500
For company 2, the points (0,15000) and (12,42000) are on the graph
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (42000-15000)/(12-0)
m = (27000)/(12)
m = 2250
Over the first twelve years, the average rate of change for company 2 is 2250
Now find the difference in the slopes
2250-1500 = 750
Company 2's rate of change is larger by $750
So that's why the answer is choice D. Over this timespan, company 2 is growing faster on average compared to company 1
Andy is trying to determine the correlation between the number of math homework assignments he completes and his test score. Which is the BEST estimate for the correlation coefficient of the data? A) r = 1.5 B) r = 0.5 C) r = 0.96 D) r = −0.90
Answers
The model is close to being linear. Therefore, there is a strong positive correlation.
Answer:
Option C
Step-by-step explanation:
It is really obvious that whenever the number of homework assignments he completes increases, his knowledge in the subject increases. This will increase automatically his test score in Maths.
Thus we can expect a perfect linear association between number of assignments done and his test score.
The correlation coefficient which is a measure of linear association between two variables always lies between -1 and +1.
Hence Option a cannot be correct since the value is greater than 1.
b) r=0.5 gives a positive but not very strong association. This is wrong as there is a strong association between the two variables
c) r=0.96 seems to be a correct answer as the positive and near to 1 r value confirms the linear strong positive association between the two variables.
D) r =-0.90 is wrong since there cannot be a negative association.
So only option right is option C
If x and y are positive integers, what is the value of x + y ? x+y=15 xy=6
Answers
The width of Zorn’s patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?
Answers
4th option is the correct answer
Solution:
The shape of Zorn's Patio is rectangular, as shown in the given image/ The perimeter of rectangle is calculated as:
Perimeter = 2 (Length + Width)
Width is given to be = (7x+4) feet
Perimeter is given to be = (30x+26) feet
Using the formula of perimeter we can write:
30x+26 = 2(Length + 7x+4)
Taking out 2 common from left hand side, we get:
2(15x+13) = 2(Length + 7x + 4)
Cancelling the common 2 from both sides, we get:
15x + 13 = Length + 7x + 4
⇒
Length = 15x + 13 - 7x -4
Length = 8x + 9
Therefore, the length of Zorn's Patio is (8x+9) feet
Perimeter = (30x + 26)
Perimeter = 2( Length + Width)
30x + 26 = 2(Length + 7x + 4)
[Divide by 2 through]
15x + 13 = Length + 7x + 4
[Minus 7x on both sides]
15x + 13 - 7x = Length + 7x + 4 - 7x
8x + 3 = Length + 4
[Minus 4 on both sides]
8x + 13 - 4 = Length + 4 - 4
8x - 1 = Length
Length = 8x + 9 (Answer D)
10 POINTS + BRAINLIEST ANSWER!!
Let the function f be defined by f(x) = (x - 1)(x + 7). Which of the following is an equivalent form of f in which the minimum value of f appears as either a coefficient or a constant?
A. f(x) = x^2 - 7
B. f(x) = x^2 + 6x - 7
C. f(x) = (x + 3)^2 - 16
D. f(x) = (x - 3)^2 - 20
Answers
All you have to do is foil
Sandra can type 180 words in 3 minutes. At this rate, how many words can she type in 5 minutes?
_____MInutes
(FREE ANSWER> I WILL MARK BRAINLIEST AND RATE AND SAY THANKS)
Answers
60 x 5 = 300
she can type 300 words in 5 minutes
What equation results from completing the square and then factoring x^2-12x=58
Answers
The correct answer is (x - 6)2 = 94
Answer:
A for me
Step-by-step explanation:
Can Someone Please Help Me Factor (x^(2)+6x+58)
Answers
1*58 = 58
2*29 = 58
(-1)*(-58) = 58
(-2)*(-29) =58
Then go through those factors and see which two values add to 6 (which is the middle number in the given expression)
1+58 = 59
2+29 = 31
-1+(-58) = -59
-2+(-29) = -31
None of those sums are 6, so the original expression cannot be factored. It is said to be prime.
The following is an idealized equation representing the world population of Leatherback turtles, where t represents time in years since 1970.
f(t) = 50,000(.92)^t
How would you determine the population in the year 2000?
Is this a growth or a decay function?
How can you tell a growth or decay function just by looking at it?
Answers
so population in 2000 = 50,000 * (0.92)^30 = 4098 Asawer
This is a function of decay.
The function is decay because the number in the parentheses is < 1.
How do you find a scale factor?
Answers
Determine the ratio of corresponding linear dimensions of geometrically similar figures.
Read the problem statement.
___
The method is determined by the nature of the information you are given to work from.
Jensen wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.75 square feet. The mirror is 4 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (2 points)
2x2 + 6x − 19.25 = 0
3x2 + 5x − 19.25 = 0
4x2 + 18x + 0.25 = 0
4x2 + 18x + 20 = 0
Answers
The frame will have the same thickness on both sides of the mirror. Therefore we add 5+x+x to get the total length, and we have 4+x+x to get the total width.
The area is found by multiplying the total width and total length:
A=(5+x+x)(4+x+x)
A=(5+2x)(4+2x)
Multiplying the binomials, we have:
A=5*4+5*2x+2x*4+2x*2x
A=20+10x+8x+4x²
A=20+18x+4x²
We know that the area is 19.75:
19.75=20+18x+4x²
We need quadratics set equal to 0, so subtract 19.75 from each side:
19.75-19.75 = 20+18x+4x²-19.75
0=0.25+18x+4x²
In standard form, it will be:
4x²+18x+0.25=0
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
Answers
then y+(x+2)+(x-2)+(x-10) = y +3x -10 =360 (by adding both sides by 10)
y + 3x =370 ;.... eq 1
the sum of each two opposite sides in a quad inscribed in a circle =180
then (x+2)+(x-2)=180
therefore 2x =180
therefore x=90 (sub in eq 1)
y+3*90 =y +270 = 370 (subtracting both sides by 270)
therefore y=100
then measure angle B=100 degrees
A=92 degrees
C=88 degrees
D=80 degrees
Taylor is competing in a 30 km race. She has already run 12.35 km through a park and swam 3.75 km. She will bike the rest of the way. Round each distance to the nearest km. About how far does Taylor need to bike to finish the race? A. about 12 km B. about 13 km C. about 14 km D. about 23 km
Answers
12km + 4km = 16km
30km - 16km = 14km
I will give brainliest.
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y + 5 = x + 2 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)
Answers
Answer:
You are requested to kindly provide the equation of line to which our to be found line is perpendicular.
Step-by-step explanation:
Molly can either take her lunch or buy it at school. It cost $1.95 to buy lunch. If she wants to spend no more than $30 each month, how many lunches can she buy at most?
Answers
Final answer:
Molly can purchase a maximum of 15 school lunches per month with a budget of $30, considering each lunch costs $1.95.
Explanation:
The question asks how many school lunches Molly can buy if each lunch costs $1.95 and she wants to spend no more than $30 each month. To find out how many lunches Molly can buy, we divide her monthly budget by the cost of one lunch.
So, we perform the calculation: $30 ÷ $1.95 ≈ 15.38. Since Molly cannot buy a fraction of a lunch, we round down to the nearest whole number, which means Molly can buy 15 lunches at most in a month without exceeding her budget.