An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = eˣ
Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 - r)^t
Where:
P(t ) represents the volume of water in gallons.t represents the time or number of years.I represents the initial volume of water.r represents the decay rate.Substituting the given parameters into the formula, we have;
P(t) = I(1 - r)^t
P(50) = 1500 × (1 - 0.3)^0.2{50}
P(50) = 1500 × (0.97)^10
P(50) = 1,106 gallons.
Therefore, there would be 1,106 gallons of water left in the pool after 50 minutes.
Next, we would determine the amount of time it would take to have less than 1000 gallons in the pool:
P(t) = I(1 - r)^t
1000 = 1500 × (1 - 0.3)^0.2t
1000 = 1500 × (0.97)^0.2t
1000/1500 = (0.97)^0.2t
2/3 = (0.97)^0.2t
Taking the log of both sides, we have:
log0.97(0.2t) = log(2/3)
t = log(2/3)/(0.27log0.97)
Time, t = 66.6 minutes.
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Complete Question:
A pool drains at a rate of 3% every 5 minutes. If it starts with 1500 gallons, how many gallons are left in the pool after 50 minutes? About how many minutes will it take to have less than 1000 gallons in the pool? Justify your answer with a mathematical model of the problem situation.
10) Your friend has a play tepee. The tepee
has a radius of 4 feet and a height of 6
feet. What is the volume of the tepee?
The volume of the tepee is 100.48 feet³
The formula for the volume of tepee is same as the volume of cone which is given as :
V = 1/3 πr²h (1)
where V = volume
r = radius of the tepee
h = height of the tepee
According to the question we have been given that
radius = 4 feet
height = 6 feet
Putting the required values in equation (1) we get
V = 1/3 π (4)²(6)
= 1/3 (3.14)(96)
= 301.44/3
= 100.48 feet³
Hence the volume of the tepee is 100.48 feet³
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Graham drove 423 miles in 13 hours.
a. How many miles did he drive in one hour?
Bron
b. How many hours did he take to drive one mile?
Graham drove 32.58 miles in one hour and it took 1.84 minutes to drive a mile
Miles Graham drove in 13 hours = 423 miles
Unitary method: A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. It is a technique that we employ for the majority of math calculations.
Part a:
Miles driven in one hour = Total miles driven/Total no. of hours taken
= 423/13 = 32.58 miles
Part b:
Hours took to drive a mile = Total no. of hours taken/ Total miles driven
= 13/423 = 0.030 hours or 1.84 minutes
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Find the length
Of the three line segments that form the triangle pictured below. The units of the grid each represent one centimeter.
4. Show your work or discribe how you found the length of the diagonal segment AB
5. Give the x-coordinate of the midpoint of AC. X=?
6.( same thing as 5 just with BC)
7.(same thing as 6,and 5 just with AB)
Step-by-step explanation:
for the lengths of BC and AC we can count the squares, because the lengths of these lines are the sum of the side lengths of each inducing square.
1.
BC = 7 - -2 = 7 + 2 = 9 cm
2.
AC = 13 - 1 = 12 cm
3.
but for AB we cannot do that, because AB consists of the lengths of all the diagonals of the squares. and a diagonal must always be longer than any side.
just look at the triangle : it is clear that AB must be longer than AC.
no, for a line that goes across the grid squares we need other methods.
in our case, we have a right-angled triangle and can use Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs of the triangle (enclosing the 90° angle).
AB is in our case the Hypotenuse, and we get
AB² = 12² + 9² = 144 + 81 = 225
AB = sqrt(225) = 15 cm
4.
as explained, we used Pythagoras.
5.
the coordinates for a midpoint between 2 points (x1, y1) and (x2, y2) are simply
((x1+x2)/2, (y1+y2)/2)
A = (13, -2)
B = (1, 7)
C = (1, -2)
midpoint AC = ((13+1)/2, (-2 + -2)/2) = (14/2, -4/2) =
= (7, -2)
the x coordinate is 7.
6.
midpoint BC = ((1+1)/2, (7+ -2)/2) = (2/2, 5/2) = (1, 2.5)
the y coordinate is 2.5
7.
midpoint AB = ((13+1)/2, (-2+7)/2) = (14/2, 5/2) =
= (7, 2.5)
Y=-4x-2 fill in the table using this function rule
what 30x30x1,000 bydb3yuehwu
HELP HELP HELPP i'll mark brainliest
Solve for x: 3( + 1) − 7( − 1) = 3(2 − 4)
Answer:
10 = -6
Step-by-step explanation:
Answer:
X = - 39
Step-by-step explanation:
x divided by 3x 1 - 7(-1)=3(2-4)X(1/3)+7-3(-2)X times 1/3 +7+-3 x2x/3+7-6x+21/ 3 = -6x+21 + (-3)6X +21 = -3x6x+21 = - 18(x+21) + (-21)= -18 +(-21)X+21-21= - 18-12ANSWER: x+3x7/3 = - 6
Hope this helps u : )
A charge of $8.99 is automatically deducted from Ari's bank account each
month for a live TV streaming service. What is the change in Ari's bank
account after 6 months for this service?
Ari loss 53.94% of his account balance for this live tv streaming service.
Given,
The charge for a live tv streaming service that is automatically deducted from Ari's bank account each month = $8.99
This deduction continues for 6 months.
We have to find the change in Ari's bank account after 6 months for this service.
Charge for 1 month = 8.99
Charge for 6 months = 6 × 8.99 = 53.94
That is if Ari had $100 in his account, now after 6 months 53.94% deducted for the tv streaming service charge.
Now, he has an account balance:
100 - 53.94 = 46.06
In terms of amount, he has an account balance of $46.06.
In terms of percentage,
Ari lost 53.94% from his account balance and now he has 46.06% account balance.
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The endpoints of CD are C(-8, -1) and D(2,4). Find the coordinates of midpoint M
Answer:
M(-3;3/2)
Step-by-step explanation:
substitute in this formula of finding midpoint coordinate:M(x1+x2÷2;y1+y2÷2)
need help with this question, pls
How long would it take to double your principal in an account that pavs 6.5 % annual interest compounded continuously?
It will take 4.63 years to double the principal.
The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously after t years is-
A = P[tex]e^{rt}[/tex]
Here r = 6.5%
= 0.065
Let the principal amount be P,
then the amount after t years = 2P
A = P[tex]e^{rt}[/tex]
2P = P[tex]e^{rt}[/tex]
2P/P = [tex]e^{rt}[/tex]
2 = [tex]e^{0.065t}[/tex]
Taking log on both sides-
Log 2 = log [tex]e^{0.065t}[/tex]
Log 2 = 0.065t log e
Log 2 = 0.065t
0.65t = Log 2t
= log 2/ 0.065t
= 0.301/ 0.065 t
= 4.63
Thus, it will take 4.63 years to double the principal.
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The following data shows the scores Gina obtained on 12 IQ tests:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
The box plot represents the data:
box plot has minimum value equal to 74, lower quartile equal to 83, median equal to 86.5, upper quartile equal to 92.75 and maximum value equal to 99
Which of the following is shown incorrectly in the box plot?
Median
Lower quartile
Upper quartile
Maximum value
The maximum value of the data is being incorrectly shown by the box plot diagram.
We are given the data:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
We are also given the box plot diagram of the data which shows that:
Minimum value of the data = 74
Lower quartile = 83
Median quartile = 86.5
Upper quartile = 92.75
Maximum value = 99
We need to tell which is the wrong interpretation among these.
We can see that, the maximum value of the data is only 93 and not 99.
So, that is the wrong representation by the box plot.
Therefore, we get that, the maximum value of the data is being incorrectly shown by the box plot diagram.
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The dot plot shows predictions for the winning time in the 200 meter sprint. the winner finished the race in 22.2 seconds. what is the greatest percent error among the predictions?
The greatest percent error among the predictions time of the race is: 3.15 %
Although part of your question is missing, you might be referring to this dot plot that shows the predictions for the winning time (see image attached)
To solve this exercise, we have to apply the percentage formula:
Error (%) = [(prediction time – real time) / real time] * 100
Information about the problem:
Prediction time= 22.9 secondsreal time =22.2 secondsError (%) =?Applying the percentage formula, we have:
Error (%) = [(prediction time – real time) / real time] * 100
Error (%) = [(22.9 seconds – 22.2 seconds) / 22.2 seconds] * 100
Error (%) = [(0.7 seconds) / 22.2 seconds] * 100
Error (%) = 0.0315 * 100
Error (%) = 3.15 %
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
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Three orders are placed at a sandwich shop. Four sandwiches, two beverages, and
one salad costs $40; two sandwiches, one beverage, and two salads costs $26; and
three sandwiches, three beverages, and two salads costs $38. How much does each
item cost?
The respective prices are given below as
The price of the sandwich is 20/3 dollars.
The salad may be purchased for a price of $16/3.
There is a fee of $2 for the drinks.
How can you build equations that are simultaneous?Let's say that the price of the sandwich is x.
Allow the price of salad to equal y.
Allow the price of drinks to equal z.
The new total for this meal is $46. It includes three sandwiches, three beers, and two salads. Thus;
3x + 3y + 2z = 40 ——- (eq 1)
The price of $29 covers two sandwiches, two drinks, and one salad.
Thus;
2x + 2y + z = 26 ——-(eq 2)
It will cost you $54 for four sandwiches, one drinks, and three salads. Thus;
4x + y + 3z = 38 ———-(eq 3)
The following are the results of concurrently solving the three equations:
x = 20/3
y = 16/3
z = 2
Therefore, the following is how much each item costs:
There is a charge of $20/3 for the sandwich.
The salad may be purchased for a price of $ 16/3.
There is a fee of $2 for the drinks.
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a book weighs 4 3/8 pounds. a store needs to mail 5 copies of the book.
create an equation to find how many pounds the books weigh in all.
The question is 0.65 into a fraction can anyone help me figure this out?
Answer:
If 0.65 is a decimal, then as a fraction it would be 65/100. This can be simplified though. 65 and 100 are both divisble by 5.
100 divided by 5 is 20 and 65 divided by 5 is 13. This is as simplified as it can go, so the answer is 13/20.
For clarification the answer is
13/20
Step-by-step explanation:
1/4(4)-5(6)-2 solve step by step.
Answer:
[tex] \rightarrow \sf \: −31[/tex]
Step-by-step explanation:
[tex] \rightarrow \sf \frac{1}{4} (4)-5(6)-2[/tex]
[tex] \rightarrow \sf \: \frac{1}{4} \times \frac{4}{1} - 30 - 2[/tex]
[tex] \rightarrow \sf \: 1 - 30 - 2[/tex]
[tex] \rightarrow \sf \: - 31[/tex]
-64-32+83-13???!!!!
Answer:20
Step-by-step explanation:
Seven times the sum of 23 and a number
Answer: 161+7n
Explanation: Let the number be n.
7(23+n)
=161+7n
Hope this helps you! Have a great day!!!!! :) :D
The Cohen family desperately needs to catch up on doing laundry. Over the weekend, Mr. and Mrs. Cohen got 3 loads done. Now, during the week, they plan to do 1 load per day.
Write an equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x.
y =
The equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x will be y = 3 + x.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
In this case, Cohen family desperately needs to catch up on doing laundry. Over the weekend, Mr. and Mrs. Cohen got 3 loads done. Now, during the week, they plan to do 1 load per day.
The equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x will be:
y = 3 + 1(x)
y = 3 + x
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What is the value of the expression 8^2+3\times78
2
+3×7 ?
The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ 8² + 3 × 78² + 3 × 7
Simplify the expression, then we have
⇒ 8² + 3 × 78² + 3 × 7
⇒ 64 + 3 × 6084 + 21
⇒ 85 + 18252
⇒ 18337
The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
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Find the amount in a continuously compounded account for the given conditions.
principal: $ 6000 ; annual interest rate: 6.8 % ; time: 10 years
The amount after 10 years is $11,842.43
In continuous compounding the number of times by which compounding occurs tends to infinity.
In order to calculate the amount use the following formula
A= Pe^rt
where P represents the initial amount, e is the mathematical constant having value 2.7182, r is the rate of interest and t is the time period
Here the principal amount is $6000, r is 6.8 and time period t is 10 years
A = $6000 x 2.718⁽¹⁰ ˣ ⁶·⁸ %⁾
A = 6000 x 2.718⁽¹⁰ ˣ ⁶·⁸÷¹⁰⁰⁾
A = 6000 x 2.718 x 0.68
A = $ 11,842.43
Therefore the total amount calculated after 10 years is $ 11,842.43
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what is 3 (3/8) * -7/3
Answer:
-21/8
Step-by-step explanation:
3 (3/8) * -7/3
= 9/8 * -7/3
= 3/8 * -7
= -21/8
HELP HELP HELP HELP HELPPPPPPPPPPPPPPPP!!!!!!!!!!
x=3.4
Im writing this bc the app says the answer is too short
The duck pond game at the capital has a pool whit 75 toy ducks twenti-five of these duck are marked undemeant
Let us organize the information first. The game consists in picking up a numbered duck. Let us denote the number of the duck as xx. The possible prizes are
1≤ x≤ 60 consolation prize
60 ≤ x ≤ 70 stuffed duck
70≤ x ≤ banana
We have 75 possible numbers equally likely to select, and 1111 outcomes where we win the stuffed duck
60, 61, 62, 63, 64, 65, 66, 67, 68, 69 and 70
Therefore, the probability of winning a stuffed duck is
p(60 ≤ x ≤ 70) = 11/75= 0.146
The event of not winning a duck or a banana is that of winning the consolation prize, that is, picking a number 1 ≤x ≤ 60.
Those are 59 equally likely to occur outcomes. Then we have
c= 59/75= 0.786
To check whether this result is right, we can use the complementary events law. That is, the probability of not winning a duck or a banana is 11 minus the sum of the probabilities of winning a duck or a banana. Mathematically this is
p (1 ≤ x ≤ 60) = 1-(p (60≤x≤70)+p(70≤x≤75)
p (1≤ x ≤ 60) = 0.786
which is a desired result.
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Select the expression that matches the scenario correctly. On January 1, the high temperature was 81 F in Kona, Hawaii the low temperature was -29 F in Barrow, Alaska. What was the difference between the two temperatures?
A. -29 + 81
B. |89 - 21|
C. |81 - (-29)|
D. 36 divided 6
Option c is correct i.e., |81 - ( -29)|
On January 1, the high temperature was 81 F in Kona and the low temperature was - 29 F in Barrow.
We have to find the difference between the two temperatures.
So the difference between is
= 81 - (- 29)
= 81 + 29
= 110
Therefore the difference the two temperatures is 110.
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fill in the boxes please (gradients)
pls help giving brainliest answers!! :)
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
y = 7x , that is y = 7x + 0 ← in slope-intercept form
with gradient 7 and y- intercept (0, 0 )
--------------------------------------------------------------
y = 6x - 8 ← is in slope- intercept form
with gradient 6 and y- intercept (0, - 8 )
the height of a triangle is twice its base the area is 144cm³ find the base
Answer:
12
Step-by-step explanation:
Area of a triangle = 1/2*b*h
[tex]144=(\frac{1}{2})*(2x)*(x)\\12=x[/tex]
Find the greatest integer that is less than the value of the logarithm. Use your calculator to check your answers.
log 5
We need to know about logarithm to solve this problem. The greatest integer that is less than the value of log 5 is 0.
Logarithm is the exponent that is raised to a base to get a certain number. There are a few rules of algorithm, log a+ log b can be written as log ab, log a -log b can be written as log a/b, when a number whose logarithm is being calculated is raised to a certain power then the power can be directly multiplied to the log itself. Logarithm when written as log has a base of 10, the logarithm of a number that is same as it's base is always 1, the log of 1 is always zero, because any nonzero number raised to 0 is 1.We will find the value of log 5 first and then choose the nearest integer that is less than log 5.
log 5=log 10/2 =log 10-log 2=1-0.30=0.7
Therefore the greatest integer that is less than the value of log 5 is 0.
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Me ayudan urgente por favor y gracias
The result of the linear expression [tex]5-\frac{t}{3}[/tex] is 1.
What is linear expression?
An algebraic expression that uses either a constant or a variable raised to the first power for each term is known as a linear expression. This means that none of the exponents can be greater than 1.
Given [tex]5-\frac{t}{3}[/tex]
Also given that t = 12
Substitute the value of t and we get
[tex]5-\frac{12}{3}\\=5-4\\=1[/tex]
Therefore, the result of the linear expression [tex]5-\frac{t}{3}[/tex] is 1.
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Pls help me ASAP. NO ignoring, just give me the answer to my first question.
Unit rate is a rate for one of something. True or false? (NO IGNORING PLEASE)
Answer:
Step-by-step explanation:
True
TRUE AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH