Using the exponential function T = 18 + 68e^(-t/8), the initial temperature is 86°C, the time the temperature will reach 35°C is 11.1 minutes
Exponential FunctionAn exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form f(x) = aˣ
In the question given, the exponential function given shows an exponential decay
T = 18 + 68e^(-t/8)
a) The initial temperature when the tea was poured would be (t = 0)
T = 18 + 68e^(-0/8)
T = 16 + 68 = 86°C
b) The temperature of the tea at 35°C
35 = 18 + 68e^(-t / 8)
T = 11.1
c) The reason why the the tea will never reach 15°C is because there's no solution for the expression.
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Sydney’s fitness app says she has completed `70\%` of her goal for the week. Her goal is `50` miles. How far has she biked?
Sydney has biked `35` miles.
Malik spent $7.00 for a drink and a sandwich. His drink cost $ 2.00. Did he have a ham sandwich for $ 3.00, a tuna sandwich for $ 5.00, or a turkey sandwich for $ 4.00 Use the equation s + 2.00 = 7.00 to justify your answer.
Answer: tuna sandwich
Step-by-step explanation: 2+5=7
Explain why the slope(m) of this line is
2/6
The slope is 2/6 because the rise is 2 while the run is 6
rise 2
------- = -------
run 6
The length of a rectangle is 3ft longer than its width.
If the perimeter of the rectangle is,58ft find its length and width.
The length and width of the rectangle is 16 ft and 13 ft respectively.
What is the dimensions of the rectangle?The perimeter of a rectangle = 2(length + width)
Perimeter of the rectangle = 58 ftWidth of the rectangle = w ftLength of the rectangle = (w + 3) ftThe perimeter of a rectangle = 2(length + width)
58 = 2{(w + 3) + w}
58 = 2(w + 3 + w)
58 = 2(3 + 2w)
open parenthesis
58 = 6 + 4w
subtract 6 from both sides
58 - 6 = 4w
52 = 4w
divide both sides by 4
w = 52/4
w = 13
Hence,
Width of the rectangle = w ft
= 13 ft
Length of the rectangle = (w + 3) ft
= 13 + 3
= 16 ft
Therefore, the dimensions of the rectangle is given by 16 ft and 13 ft respectively
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Find the present value (the amount that should be invested now to accumulate the following amount) if the money is compounded as indicated.
$6800 at 4% compounded quarterly for 3 years
The present value the amount that should be invested now to accumulate is $7662.24.
What is meant by compound interest?Compound interest is the adding of interest to the principal amount of a loan or deposit, or interest on interest + principal. It is the outcome of reinvesting interest, or adding it to lent capital, rather than paying it out or requesting payment from the borrower, so that interest is received on the principle sum plus previously accumulated interest in the next month. In finance and economics, compound interest is common.
Compound interest differs from simple interest in that previously collected interest is not added to the current period's main amount, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods in a year.
Given,
Principle P=$6800
T=3 years
And also given that the money is compounded quarterly.
Present value=P[tex](1+(R/4)^{4t}[/tex]
=6800[tex](1+(4/400)^{12}[/tex])
=6800[tex](1+(1/100))^{12}[/tex]
=6800[tex](101/100)^{12}[/tex]
=6800[tex](1.01)^{12}[/tex]
=6800×1.1268
=$7662.24
The present value the amount that should be invested now to accumulate is $7662.24
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Assume gas cost $3.70 a gallon. Write an equation representing the total amount you need to spend on the car for the trip, after paying for a one time tune-up of $100.
The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Also an equation is a set of variables that are constrained through a situation or case.
Given that the 1 gallon is $3.70
x gallons = $3.70x
So, C = 3.70x
This will be the cost of x gallons
Hence "The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x".
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during basketball season josh made 3 out of every 7 free throw attempts in the last game josh attempted 28 free throws how many free throws would he have been expected to make
There are 12 free throws would he have been expected to make.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities.
Given that;
During basketball season josh made 3 out of every 7 free throw attempts in the last game.
Now,
Since, During basketball season josh made 3 out of every 7 free throw attempts in the last game.
Hence, Let number of free throws would he have been expected to make for attempted 28 free throws = x
So, We can formulate;
⇒ 3/7 = x/28
Solve for x as;
⇒ 3 × 28 / 7 = x
⇒ x = 3 × 4
⇒ x = 12
Thus, There are 12 free throws would he have been expected to make.
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question below answer quick
The x-intercept is (5,0)
The y-intercept is (0,10)
What is intercept ?
A y-intercept, also known as a vertical intercept, is the point where the graph of a function or relation intersects the y-axis of the coordinate system in analytical geometry, using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. As a result, x = 0 is satisfied at these sites.
A line's x-intercept and y-intercept are the points at which the x- and y-axes cross, respectively.
To find x-intercept we put y = 0 to the equation
4x + 2y = 20
4x = 20
x = 5
To find y-intercept we put x = 0 to the equation
4x + 2y = 20
2y = 20
y = 10
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Susan has a collection of 60 nickels and dimes. If the number of nickels is four times the number of dimes, how many nickels and how many dimes does she have?
Answer: 12 dimes, 48 nickles.
Step-by-step explanation:
Let x = the number of dimes
Let 4x = the number of nickels
x + 4x = 60
5x = 60
x = 12 dimes
4x = 48 nickles
She has 48 nickels and 12 dimes.
Equation
At first, we have to express the sentence into equation:
Given:
x = nickels
y = dimes
Susan has a collection of 60 nickels and dimes --> x + y = 60 ............. (1)
the number of nickels is four times the number of dimes --> x = 4y ......(2)
then we must input the equation (2) into the equation (1):
x + y = 60
4y + y = 60
5y = 60
y = 60/5
y = 12
As we know the value of y, we can calculate the value of x from the equation (2):
x = 4y
x = 4 * 12
x = 48
Thus, Susan has 48 nickels and 12 dimes
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Julie likes to make bead necklaces. She has 296 beads altogether, but has 32 more round beads than square beads. How much of each bead does she have?
Jordan is helping his dad build a doghouse. The floor is rectangle-shaped with a width of 5 feet and an area of 36.25 ft2. What is the length of the rectangular floor?
The length is 7.25 feet
Here the detail
The formula for rectangled-shaped area is multiply length and width
Area = Length x Width
In this case, we know that the area is 36.25 ft2 and the width is 5 feet
so we can divided the area and the width to solve the length
Area = Length x Width
36.25 = Length x 5
Length = 36.25 : 5
Length = 7.25 feet
Hence the length of the rectangular floor is 7.25 feet
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Jason uses his car for business. he must keep accurate records so his company will reimburse him for his car expenses. when he started his trip, the odometer read 43,156.1. Jason's car gets 35 miles per gallon. his tank was full at the beginning of the trip. when he filled the tank, it cost $34.24. what price did he pay per gallon of gas on this fill-up?
The price Jason paid per gallon of gas on this fill-up is $0.03 per gallon
What is the price per gallon?Based on the given task content; this can be solved using the division method.
Total miles = 43,156.1Jason's miles per gallon = 35 miles per gallonTotal cost to fill Jason's car = $34.24Total 35 miles in Jason's odometer = Total miles / 35
= 43,156.1 / 35
= 1233.031428571428
Approximately,
1,233.03 of 35 miles per gallon
Amount Jason paid per gallon of gas on this fill-up = 1,233.03 / $34.24
= 0.027768991833126
Approximately,
$0.03 per gallon
In conclusion, the amount Jason paid per gallon of gas is $0.03 per gallon
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15 points!! Is the triangle a right triangle?
Answer: Yes.
Step-by-step explanation:
Answer:
yes, it is because the right side is the bigger side.
Step-by-step explanation:
See in a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse.
Your car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol. How much of 69% percent ethanol fuel should you use so
that your tank is 40 percent ethanol?
Answer: 7.5
Step-by-step explanation:
the tank is 15 gallons and you can get 13 percent ethanol or 69 percent ethanol, so you simply just get 7.5gallons of 69 percent and then 7.5 gallons of 13 percent
.69 divided by 15 is .046
.13 divided by 15 is .008
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
What is mixture?A mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids.Given is that a car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol.
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is given by -
{x} = 69% of 15 - {40% of 15}
{x} = (69/100 x 15) - (40/100 x 15)
{x} = 10.35 - 6
{x} = 4.35
Therefore, the amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
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A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $54 . The total cost to rent 5 chairs and 3 tables is $36 . What is the cost to rent each chair and each table?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The cost of each chair is $2.25.
The cost of each table is $8.25.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x + 4 = 5 is an equation.
We have,
Cost of each chair = x
Cost of each table = y
Now,
2x + 6y = 54 _____(1)
5x + 3y = 36 ______(2)
From (1) we get,
2x = 54 - 6y
x = (54 - 6y)/2 ______(3)
Now,
Putting (3) in (2) we get,
5(54 - 6y)/2 + 3y = 36
270/2 - 30y/2 + 3y = 36
135 - 15y + 3y = 36
99 = 12y
y = 99/12
y = 8.25 ______(4)
Now,
Putting 4 in (3) we get,
x = (54 - 6 x 8.25) / 2
x = 4.5/2
x = 2.25
Thus,
The cost of each chair is $2.25.
The cost of each table is $8.25.
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A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built
The dimensions of the rectangle for the most economical fence are length, L = 50 feet and width, W = 25 feet
How to find the dimensions of the rectangle for the most economical fence?Given: Area = 1250 square feet, , cost of material along three sides = $6 per foot, cost of material for fourth sides = $18 per foot
In order to calculate the dimension of the fence
Let L and W represent the length and width of the fence respectively
Thus, the area of the fence can be represented as:
A = L × W = 1250 ---- (1)
L = 1250/W
Let the total cost to construct the fence be 'C' can be obtained if we construct the shorter side with material with a cost of $18 per foot
C = 6×(2W + L) + 18×L
C = 12W + 24L ---- (2)
Substituting the value of L from equation 1 into equation 2 we have:
C = 12W + 24×(1250/W)
To minimize the cost we differentiate both sides with respect to W and equate the result to zero:
C = 12W + 24×(1250/W)
dC/dW = d/dW (12W + 30000/W)
0 = 12 - 30000/W²
12W² = 30000
W² = 2500
W = 50 feet
Since L = 1250/W
L = 1250/50
L = 25 feet
Therefore, the dimensions of the rectangle are length of 25 feet and width of 50 feet
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Can somebody help me with this please?
Answer: -16.66
Reason: 10*-5/3=−16.66666667 or −50/3
I’m certain year, there were 86 female officials in congress, which comprised of the House of Representatives and the senate. If there were 58 more female me members of the House of Representatives than female senators, find the number of females in each house of congress
Answer:
58 members of the House of Representatives, and 28 members of the senate.
Step-by-step explanation:
We can find the answer to this by simply subtracting:
86 - 58 = 28
So, there are 58 members of the House of Representatives, and 28 members of the senate.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
If the variance of the data values in a sample is 289, what is the standard
deviation of the data values?
O A. 17
OB. 19
OC. 18
O D. 16
Answer:
17
Step-by-step explanation: ..
The power P (in W) generated by a particular windmill is given by P=0.015V where V is the velocity of the wind (in
mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 5.9 mph. Round
your answer to the nearest tenth.
OA. 0.3 W/mph
OB. 3.5 W/mph
OC. 1.6 W/mph
D. 6.2 W/mph
The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.
What is the rate of change function?
The pace at which one quantity changes in relation to another is known as the rate of change function.
Given, P = 0.015[tex]V^{3}[/tex]
Differentiating P with respect to V:
P′=(0.015)(3)[tex]V^{2}[/tex]
At V = 5.9 mph, then
P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph
Hence, the instantaneous rate of change of power is 1.6 W/mph.
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A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the following grouped frequency distribution. What is
the class width?
The class width is
The class width of the distribution is 4
What is class width?Class width is the difference between the Upper class limit and the Lower class limit of a class interval.
Class Width = Upper Class Limit − Lower Class Limit. For example: For a class interval, 163−175, Class Width =175−163=12.
Similarly for a class interval of 75-79, the class width is 79-75= 4.
The upper class limit is 79 and the lower class limit is 75.
The class limit for all the frequency distribution is constant.
Therefore the class width of the distribution is 4
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What does absolute value represent?
Step-by-step explanation:
The distance from zero that a number is on the number line without considering Direction
two packages of cookies cost $9.50. How much do seven packages cost?Try using a proportion to solve or finding unit rate?
Answer:
$33.25
1 package is $4.75
Step-by-step explanation:
9.5 divided by 2 is 4.75, that is how much one package costs.
4.75 times 7 is 33.25, that's seven packages worth.
a group of four numbers has an average of 15. The first three numbers are 12,19 and 7. What is the other number
Answer:
22
Step-by-step explanation:
12 + 19 + 7 + _?_ = 15
38 + _?_ = 15
-38 -38
-----------------------
? = 23
12 + 19 + 7 + 23 = 61
-1
12 + 19 + 7 + 22 = 60
60 ÷ 4 = 15
I hope this helps!
A canoe rental service charges a $20 transportation fee and $30 dollars an hour to
rent a canoe. Write and graph an equation representing the cost, y, of renting a canoe
for x hours. What is the cost of renting a canoe for twelve hours?
The graph of the equation y = 30x + 20 is shown below.
It would cost $380 for 12 hours.
How to Write and Graph an Equation?The equation of a graph can be written as y = mx + b, if we know the slope of the graph (m) and the y-intercept (b) which is the point on the y-axis that the line will intercept.
Therefore:
Slope/unit rate (m) = $30 per hour
Rental service charges is the y-intercept (b) = $20
To write the equation, substitute m = 30 and b = 20 into y = mx + b:
y = 30x + 20
See the attachment below for the graph of the equation.
Substitute x = 12 into the equation y = 30x + 20 to find the cost of renting canoe for 12 hours:
y = 30(12) + 20
y = $380
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The weather report suggested that your city’s temperature increased from -10 degree celsius to 20 degree celsius. What is the rise in temperature?
Answer:
The temperature increased in 30 degrees Celsius
Step-by-step explanation:
Jaxon goes to a restaurant and the subtotal on the bill was x dollars. A tax of 8% is applied to the bill. Jaxon decides to leave a tip of 23% on the entire bill (including the tax). Write an expression in terms of x that represents the total amount that Jaxon paid.
Answer:
Step-by-step explanation:
If the equation is going off of what is the traditional, and correct way to tip, the tip would be based off the total BEFORE tax.
Therefore, the expression for the total cost would be: x + .23x +.08x, which, simplified, would be 1.33x.
what is the slope of a line that is parallel to the line connecting point O (-5,1) and point P (2,3)?
Answer:
2/7
Step-by-step explanation:
2 parallel lines have the same slope
we just need to find the slope of the line with the point’s connecting O and P
We use y2-y1/x2-x1 to find slope
3-1/2-(-5)
2/7
2/7 is the slope
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide. 7 and 2
24 units is the area of the shaded region if the "frame" is 2 units wide.
What is Area of Rectangle?The area of Rectangle is length times of width
We know that the frame is 2 units wide, and the measure of the rectangle and the frame are:
width = 7 units
length = 12 units
Now, if we remove the frame, we will remove 2×2 units = 4 units for each measure (because for each measure we have the frame in both sides).
So the measures for the shaded rectangle are:
width = 7 units - 4 units = 3 units
length = 12 units - 4 units = 8 units.
And the area of a rectangle is given by the product between the width and length, then we have:
A = (3 units)*(8 units) = 24 square units.
Hence, 24 units is the area of the shaded region if the "frame" is 2 units wide.
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In your own words, tell me the difference between a geometric and an arithmetic sequence.
As several differences are there between them and is differentiated below.
What is Sequence?
A list of numbers in a specific order is called a sequence. The terms of the sequence are the various numbers that appear in it.
Let a sequence's terms be a1, a2, a3,..., an,..., etc.
The term's position is indicated by the subscripts. That implies,
Initial phrase = a1
term two = a2
term three Equals a3
….
The nth term, indicated by an, is the number that appears in the sequence at the nth place. This phrase is also known as the sequence's general phrase.
Geometric Sequence:
It is a sequence of numbers in which each new term is calculated by multiplying by a non-zero and fixed number.Multiplication or Division is done in every step.A common ratio between 2 successive terms is the common ratio.It is of the Exponential Form.Arithmetic Sequence:
It is a list of numbers, in which every new term alters from another preceding term by a definite quantity.Addition or Subtraction is done in every step.A common ratio between 2 successive terms.It is of the Linear Form,To learn more about Sequence, visit:
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