Answer:
88 days
Step-by-step explanation:
inversely proportional means for a response y and input x, we have the formula
y = k/x
10 days = k/44 workers
multiply both sides by 44 to find k
44 workers * 10 days = k
k = 440 workers * days
y = k/x
x = 5 workers
440 workers * days / 5 workers = y
88 days = y
Solve for x. Round all intermediate values and answers to the nearest tenth . 19 70 61
12.6 is the measure of the value of x
Solving the sides of a right triangleThe given diagram is a right triangle and we need to determine the measure of value of 'x'.
First, we need to determine the measure of the height using the trigonometry identity;
cos55 = h/45
h = 45cos55
h = 25.81
Determine the measure of 'x'
tan 64 = h/x
x = h/tan64
x = 25.81/tan64
x = 12.6
Hence the measure of the value of x from the fiigure is 12.6
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use transformations of f(x)=[tex]x^{2}[/tex] to graph g(x)=[tex]x^{2}[/tex] -3 select all the transformations that are needed to graph the given function
Select all the transformations that are needed to graph the given function using .
A.
Shift the graph to the left.
B.
Stretch the graph vertically by a factor of .
C.
Shift the graph .
D.
Reflect the graph about the y-axis.
E.
Reflect the graph about the x-axis.
F.
Shift the graph to the right.
G.
Stretch the graph horizontally by a factor of .
H.
Shift the graph .
I.
Shrink the graph horizontally by a factor of .
J.
Shrink the graph vertically by a factor of .
The transformations that are needed to graph the given function is
Shrink the graph vertically by a factor of 3.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
f(x) = x²
g(x) = x² - 3
We see that,
f(x) → g(x)
There is a vertical shrink by a factor of 3.
Thus,
There is a shrinking vertically of f(x) by a factor of 3.
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1. The tiles shown are placed in a bag. You randomly select one of the tiles,
return it to the bag, and then randomly select another tile. What is the
probability that the first number divided by the second number is greater
than zero?
the numbers:
-2
-1
2
1
Therefore, the probability that the first number divided by the second number is greater than zero is 1/3.
What is probability?In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.
Here,
Since we are returning the first tile to the bag before selecting the second one, the two selections are independent of each other.
There are two cases to consider:
Case 1: We select a positive number on the first draw.
The probability of selecting a positive number on the first draw is 2/3, since there are two positive numbers (-12 and 1) out of a total of three tiles.
Regardless of what number we select on the first draw, there is only one negative number (-2) in the bag, so the probability of selecting a negative number on the second draw is 1/3.
Therefore, the probability of selecting a positive number on the first draw and a negative number on the second draw (which results in a quotient greater than zero) is:
(2/3) x (1/3) = 2/9
Case 2: We select the negative number (-2) on the first draw.
The probability of selecting the negative number (-2) on the first draw is 1/3.
In this case, we must select the positive number on the second draw in order for the quotient to be greater than zero. There is only one positive number (1) in the bag, so the probability of selecting it on the second draw is 1/3.
Therefore, the probability of selecting the negative number (-2) on the first draw and the positive number on the second draw (which results in a quotient greater than zero) is:
(1/3) x (1/3) = 1/9
Since these are the only two cases that satisfy the condition, the overall probability is the sum of the probabilities of these two cases:
2/9 + 1/9 = 3/9 = 1/3
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What does the index value of 99.2 in 1980 mean? Explain your reasoning.
The index value of 99.2 in 1980 mean Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992, the correct option is D.
What is the ratio?
Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
Years, prices, prices as a percentage of 1990 price, price index 1990=100
Now,
The given table shows the average gasoline prices per gallon for various years, as well as the price index for each year, with 1990 being the reference year with a price index of 100. The price index measures the change in the price of gasoline relative to the price in 1990. Therefore, the price index value of 99.2 for 1980 means that the average gasoline price in 1980 was 0.992 times the price of gasoline in 1990.
It is important to note that the gas price index does not directly measure the cost per gallon of gas. Rather, it is a measure of the change in gasoline prices over time, with a reference year (in this case, 1990) used as a baseline.
Therefore, by ratio the answer will be Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992.
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Consider the following points.
(−2,−3),(3,3)
and (3,−3)
Step 1 of 2 : Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene.
The perimeter of a triangle is the sum of the lengths of its three sides.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
In the case of triangle HGI, the perimeter is calculated by adding the three side lengths together. For example, if the three sides are labeled a, b, and c, the perimeter would be calculated as a + b + c.
The perimeter of triangle HGI can be calculated by knowing the lengths of its three sides. If the lengths of the three sides are 7, 8, and 9 units respectively, the perimeter of triangle HGI is 7 + 8 + 9 = 24 units.
The perimeter of triangle HGI can also be calculated using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. Using this theorem, the lengths of the other two sides can be calculated if the length of one side and the measure of the included angle is known.
In summary, the perimeter of triangle HGI can be calculated by adding the lengths of its three sides or by using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known.
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difference of cubes
Formula for the difference of cubes are,
⇒ x³ - y³ = (x - y) (x² + xy + y²)
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
To find the difference of cubes of two numbers.
Now, Let two numbers are x and y.
Hence, Formula for the difference of cubes of numbers x and y are,
⇒ x³ - y³ = (x - y) (x² + xy + y²)
Thus, Formula for the difference of cubes are,
⇒ x³ - y³ = (x - y) (x² + xy + y²)
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Bethany is driving from her house to her parents’ house. After driving 127.56 miles, her GPS says she is 397.24 miles away from her parents’ house. What was the total distance, in miles, from Bethany’s house to her parents’ house?
The total distance from Bethany’s house to her parents’ house would be = 524.8 miles
How to calculate the total distance covered by Bethany?The first distance covered by Bethany towards the parents house = 127.56 miles.
The distance remaining for her to arrive to ab destination = 397.24 miles
The total distance covered
= 127.56 miles + 397.24 miles
= 524.8 miles.
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The total distance, in miles, from Bethany's house to her parents' house is 524.8 miles.
How is the total distance determined?The total distance is determined using the mathematical operation of addition.
Addition is one of the four mathematical operations, including subtraction, division, and multiplication.
The distance already covered after driving from her house = 127.56 miles
The distance remaining = 397.24 miles
The total distance from Bethany's house to her parents' = 524.8 miles (127.56 + 397.24)
Thus, the total distance is 524.8 miles.
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3 three sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 5?
The probability that the sum of numbers we will get will be 6 is 7/27.
What is probability?Probability is simply the possibility that something will happen.
Since we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.
The study of events that fit into a probability distribution is known as statistics.
Probability, or the likelihood that an event will occur, is calculated by dividing the number of favorable outcomes by the total number of potential possibilities.
A coin toss serves as the most simple illustration.
When you flip a coin, there are only two possible outcomes: heads or tails.
So, the probability formula:
P(E) = Favourable events/Total events
We need to get the probability of getting the sum of 6.
Then, calculate as follows:
P(E) = Favourable events/Total events
P(E) = 7/27
Therefore, the probability that the sum of numbers we will get will be 6 is 7/27.
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Correct question:
3 three-sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 6?
7. Alexis has 145 stickers. She wants to divide the stickers evenly among 5 of her friends. How
many stickers will each friend get?
Write your answer in the box.
stickers.
8. There are 2,472 seats in the school auditorium. The seats are divided into 6 equal sections.
How many seats are in each section? Write your answer in the box.
seats
Explain how you found your answer. Show your work.
Answer: 7: 29 stickers for each friend
8: 412 seats in each section
Step-by-step explanation:
We will have to divide 145 (stickers) by 5 (friends) to get 29
We will have to divide 2472 by 6 to get 412
7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers
8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.
I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.
A regular deck of playing cards is well shuffled. Please answer the following questions. All answers should be in fraction form.
On a single draw, what would be the probability of drawing the Ace of Hearts?
On a single draw, what would be the probability of drawing an Ace?
On a single draw, what would be the probability of drawing a red card?
On a single draw, what would be the probability of drawing a face card? A face card is a Jack, Queen or King.
What would be the probability of not drawing an Ace?
On the first draw, the Ace of Hearts is removed and not replaced. What would the probability be that on the next draw you draw another Ace?
Answer:
1/52
4/52 == 1/13
13/52 == 1/4
12/52 == 6/26 == 3/13
48/52 == 12/13
3/51
I Really Need Help ASAP!!!
To draw the inequality on a number line first select an open point and mark at 3 and then click on ray and draw a ray from point 3 to the right side of the number line.
What is inequality?
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have an inequality:
0.3(x - 4) > -0.3
After simplifying:
0.3x - 1.2 > -0.3
0.3x > -0.3 + 1.2
0.3x > 0.9
x > 3
Select open point and mark at 3.
Click on ray and draw a ray from point 3 to the right side of the number line.
Thus, to draw the inequality on a number line first select an open point and mark at 3 and then click on ray and draw a ray from point 3 to the right side of the number line.
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Find and interpret the average rate of change illustrated in the following graph
Answer:
Step-by-step explanation:
Average rate of change is the same thing as the slope. Ours here is negative. Our rate of change then goes down $5000 per year, so it is -5 per year. That means that the value of the machine decreases $5000 for every year that goes by.
Macy has 27 red stickers and 33 blue stickers. She gives away 50
stickers. How many stickers does she have left? Choose the two
operations needed to solve the problem.
First add, then subtract
First add, then divide
First multiply, then subtract
Answer:
First add, then subtract
10
Step-by-step explanation:
First subtract, then determine the result:
27 + 33 = 60
60 - 50 = 10
Macy has 10 stickers left.
The operations needed to solve the problem are:
First add, then subtract.
A card is drawn at random from a standard deck. What is the probability that it is a black card and a king?
Answer: 1/52 or 1.923%
Step-by-step explanation:
Due to the fact that the standard deck of 52 cards has 4 Kings then out of 52 is 1 that is going to be a black card. Hence the 1/52 as for the 1.923% is the percentage form of 1/52 for either or you need.
Equivalent function for .5=2^-1
The equivalent function for .5=2⁻¹ is: 2x = 1 or log2(0.5) = -1 These are alternative ways of expressing the same relationship between 0.5 and 2⁻¹.
Understanding the Exponential Function
In mathematics, the exponential function is a function that is defined as f(x) = a^x, where 'a' is a constant called the base of the exponential function, and 'x' is the exponent. The exponential function is an important function in mathematics and is used in many different fields, such as finance, physics, and engineering.
To understand the relationship between an exponential function and a power of a number, we can consider the example of 0.5 = 2⁻¹ This means that 2 raised to the power of -1 is equal to 0.5.
To prove this, we can use the definition of the exponential function as f(x) = a^x. In this case, a = 2 and x = -1. So, we have:
f(-1) = 2⁻¹
We can simplify this expression using the property of negative exponents that states that a^-n = 1/a^n. Therefore:
f(-1) = 1/2¹
Simplifying further, we get:
f(-1) = 1/2
So, we see that 2 raised to the power of -1 is indeed equal to 0.5.
In conclusion, understanding the exponential function is important in mathematics and many other fields. The example of 0.5 = 2⁻¹ helps to illustrate the relationship between an exponential function and a power of a number, and how we can use the properties of exponents to simplify expressions involving exponential functions.
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Desmond is curious about how many hours of TV his family watches each week. Upon asking his family members, he found that they watched 30 hours of TV last week versus 17.7 hours of TV this week.
12.3 hours or 12 hours and 18 minutes.
This suggests that Desmond's family has decreased their TV-watching time by 12.3 hours in the past week.
This can be expressed numerically as 12.3 hours, or 12 hours and 18 minutes.
To calculate this, we can subtract 17.7 hours from 30 hours:
Last week: 30 hours of TV
This week: 17.7 hours of TV
30 hours - 17.7 hours = 12.3 hours
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During the summer, Curran and AJ
started their own business mowing
lawns. Before starting any work, Curran
spent $20 to ! ll up the gas tank for the
lawnmower. The boys agreed that each
person would earn the same amount
after Curran was reimbursed the money
he spent for gas. After a week of work,
the boys were paid a total of $177.
Curran ! lled up the gas tank just once.
How much did each boy earn?
The boys agreed that each person would earn the same amount after Curran was reimbursed the money he spent on gas. After a week of work, the boys were paid a total of $177. thus each boy earned $88.50.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
Let's denote the amount each boy earns by x.
According to the given information, Curran spent $20 for gas, which he should be reimbursed for. This means that the total revenue of the business was $177 + $20 = $197.
Since each person earns the same amount, we can set up an equation:
2x + $20 = $197
Simplifying and solving for x, we get:
2x = $177
x = $88.50
Therefore, each boy earned $88.50.
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There were 28 students in the RSM Math Challenge class. Over the year, eight students were late to class 12 times, 9 students were late 10 times, and the rest of the students were late
heeeeeeeelp
Answer:
3 students
Step-by-step explanation:
Now for RSM Olympiad are 8 math kangaroo are 7 studs that did both are 4
Total number of studs that participated are
(8-4) + 4 + (7-4)
4+4+3=11
those who didn't participate are
11-14-13
All 155 students in the math club went on a field trip some students rode in cars which hold five students each and some students wrote in buses which holds 30 students each how many of each type of vehicle do they use if there were only 11 vehicles total
7 cars and 4 buses were used on the trip
How to find how many of each type of vehicle do they use if there were only 11 vehicles total
Let's start by defining some variables to represent the unknowns in the problem:
Let x be the number of cars used.
Let y be the number of buses used.
We know that there were a total of 11 vehicles used, so we can write an equation based on that:
x + y = 11
We also know that the total number of students who went on the trip is 155.
We can use this information to set up another equation:
5x + 30y = 155
This equation represents the fact that the total number of students in cars (5x) plus the total number of students in buses (30y) equals the total number of students (155).
Now we have two equations with two unknowns. We can solve for x and y using a method like substitution or elimination.
Let's use substitution. Solve the first equation for x in terms of y:
x + y = 11
x = 11 - y
Substitute this expression for x into the second equation:
5x + 30y = 155
5(11 - y) + 30y = 155
Simplify and solve for y:
55 - 5y + 30y = 155
25y = 100
y = 4
Now that we know y, we can use the first equation to find x:
x + y = 11
x + 4 = 11
x = 7
Therefore, there were 7 cars and 4 buses used on the trip.
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PLS ANSWER MY QUESTION QUICKLY
Answer:
The answer is D.
Step-by-step explanation:
Solve each of the following system of linear equations
x_1+〖3x〗_2=1
2x_1+〖5x〗_2=3
Answer:
To solve the system of linear equations:
x_1 + 3x_2 = 1 ...(1)
2x_1 + 5x_2 = 3 ...(2)
We can use the method of elimination to eliminate one of the variables. To do this, we multiply equation (1) by 2, and subtract it from equation (2), as follows:
2(x_1 + 3x_2 = 1) => 2x_1 + 6x_2 = 2 ...(3)
2x_1 + 5x_2 = 3 ...(2)
(2x_1 + 6x_2 = 2) ...(3)
-x_2 = 1
Thus, we have found that x_2 = -1.
We can substitute this value of x_2 into either equation (1) or (2) to solve for x_1. Let's use equation (1):
x_1 + 3(-1) = 1
x_1 - 3 = 1
x_1 = 4
Therefore, the solution to the system of linear equations is x_1 = 4, x_2 = -1.
So the solution set is {(4, -1)}.
Find answers to 6,7,8
The solution is, the length of MP = 9.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
from the given figure we get,
MPN is a right angled triangle,
by using Pythagorean theorem, we get,
here, height = 12
hypotenuse = 15
so, base = MP
= √15² - 12²
=√81
=9
Hence, The solution is, the length of MP = 9.
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pls help i need the answer
Answer:
6
Step-by-step explanation:
to be very honest I'm not very good at mathematics but Im here to learn
The way entertainment is sold and viewed has changed drastically in the past decade. In the year
2011, there were 6.1 billion DVDs sold worldwide. In the year 2021, the number had declined to
1.2 billion.
a. What is the average rate of change in DVD sales during this period?
b. Using the numbers in 2011 as an initial value, write a linear model that models the
number of DVD sales worldwide. Make sure to define the variables.
c. If the rate stays the same, predict the number of DVD sales in the
year 2023.
Answer:
Step-by-step explanation:
a. The average rate of change in DVD sales during this period can be calculated as:
average rate of change = (change in DVDs sold) / (change in years)
We are given that in 2011, 6.1 billion DVDs were sold, and in 2021, 1.2 billion DVDs were sold. The change in DVDs sold is:
change in DVDs sold = 1.2 billion - 6.1 billion = -4.9 billion
The change in years is:
change in years = 2021 - 2011 = 10
So the average rate of change in DVD sales during this period is:
average rate of change = (-4.9 billion) / 10 = -0.49 billion DVDs per year
Therefore, DVD sales declined by an average of 0.49 billion per year during this period.
b. Using the numbers in 2011 as an initial value, we can write a linear model that models the number of DVD sales worldwide as:
DVD sales = -0.49(t - 2011) + 6.1
where t is the year and DVD sales are measured in billions.
c. If the rate stays the same, we can predict the number of DVD sales in the year 2023 by substituting t = 2023 into the linear model and solving for DVD sales:
DVD sales = -0.49(2023 - 2011) + 6.1 ≈ 0.5 billion DVDs
Therefore, if the rate of decline in DVD sales stays the same, we can predict that there will be about 0.5 billion DVDs sold worldwide in 2023.
A carver begins work on a block of material that has a mass of 1250 g. The block's dimensions are 5 cm by 14 cm by 7 cm. What is the density of the material?
Answer:
Below
Step-by-step explanation:
Definition of density is mass / volume = 1250 g / (5 x14x7) = 2.55 gm/cm^3
FIND THE PRODUCT
(x - y)(8x + y)
Answer:
Step-by-step explanation:
8x^2 + xy - 8xy - y^2
8x^2 - 7xy - y^2
Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x) = 6/x, c = 1 Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x) = ln(x), c = 1 Find the Maclaurin series for the function. (Use the table of power series for elementary functions.) f(x) = ex9/9
Answer:
Step-by-step explanation: sometimes it is hard to do in school because I'M and 15th-grade class and i got to take my time
gage stocks two ponds with bass and blue hill. he stocks pond a with 60 fish and pond b with 300 fish. gage stocks pond b with twice the amount of bass and six times the amount of bluegills as pond a. how many bass and bluegills does gage stock in pond w
Finally, we can use the earlier equations to find the number of bass and bluegills in pond B:
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
What is a math equation, exactly?In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.
Let's denote the number of bass in pond A as "x" and the number of bluegills in pond A as "y".
According to the problem, Gage stocks pond B with twice the amount of bass as pond A, so the number of bass in pond B is 2x. He also stocks pond B with six times the amount of bluegills as pond A, so the number of bluegills in pond B is 6y.
We know that Gage stocks pond A with a total of 60 fish, so:
x + y = 60
We also know that Gage stocks pond B with a total of 300 fish, so:
2x + 6y = 300
x + 3y = 150
Now we have two equations:
x + y = 60
x + 3y = 150
We can solve for x in the first equation:
x = 60 - y
Substitute this expression for x into the second equation:
(60 - y) + 3y = 150
2y = 90
y = 45
Now that we know that pond A has 45 bluegills, we can use the equation x + y = 60 to find that pond A has 15 bass (since 45 + 15 = 60).
2x + 6y = 300
2(15) + 6(45) = 300
30 + 270 = 300
Therefore, pond B has 30 bass and 270 bluegills.
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PLEASE HELP!
Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
Answer:
Step-by-step explanation:
A possible trigonometric function that would model the tide situation for this beach is:
h(t) = -2 + 3sin(πt/12)
where h(t) represents the height of the tide at time t in hours, and πt/12 represents the angle (in radians) corresponding to the time t on a unit circle with a period of 24 hours.
The constant -2 represents the lowest point of the tide (2 feet below sea level), and the coefficient of 3 in front of the sine function determines the amplitude of the tide, which is 3 feet (half the difference between the highest and lowest points of the tide, which is 4 - (-2) = 6 feet). The sine function oscillates between -1 and 1, so the range of the function h(t) is between -2 - 3 = -5 feet (when the sine function takes on its minimum value of -1) and 4 - 2 = 2 feet (when the sine function takes on its maximum value of 1), as expected for the given tidal range.
Because the Earth rotates through two tidal “bulges” every lunar day, coastal areas experience two high and two low tides every 24 hours and 50 minutes. High tides occur 12 hours and 25 minutes apart. It takes six hours and 12.5 minutes for the water at the shore to go from high to low, or from low to high.
A nurse administers 25 milligrams of a drug to a patient. The amount of the drug, A, in milligrams, left in the patient after t hours can be modeled by the function A(t) = 25e 0.354 How many hours will it take for the amount of the drug left in the patient to drop to 0.25 milligrams? Round your answer to the nearest tenth of an hour.
As a result, it will take around 4.9 hours for the quantity of medicine remaining in the body to decline to 0.25 milligrams.
What is exponent?In mathematics, an exponent (also known as power or index) is a number that indicates how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number. For example, in the expression 2³, 2 is the base number and 3 is the exponent. The exponent 3 indicates that the base number 2 is multiplied by itself 3 times, resulting in the value 8. Exponents are a shorthand notation for repeated multiplication and are used in many areas of mathematics and science.
Here,
The given model for the amount of the drug left in the patient after t hours is:
A(t) = 25e*(0.354t)
We need to find the time t when the amount of the drug left in the patient is 0.25 milligrams. So we can set A(t) = 0.25 and solve for t:
0.25 = 25e*(0.354t)
Dividing both sides by 25, we get:
0.01 = e*(0.354t)
Taking the natural logarithm of both sides, we get:
ln(0.01) = 0.354t
Simplifying, we get:
t = ln(0.01)/0.354 ≈ 4.9 hours
Therefore, it will take about 4.9 hours for the amount of the drug left in the patient to drop to 0.25 milligrams.
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