Answers
Answer:
115°
Step-by-step explanation:
You want the measure of angle S opposite angle (4x+5)° in an inscribed quadrilateral in which the other two angles are (5x-2)° and (7x+2)°.
Inscribed quadrilateralThe measure of an inscribed angle is half the measure of the arc it intercepts.
Two opposite angles in an inscribed quadrilateral intercept arcs that total the full circle. Since the sum of double those angles is 360°, the sum of opposite angles of an inscribed quadrilateral is 180°—they are supplementary.
We can use this to find the value of x:
(5x -2)° +(7x +2)° = 180°
12x = 180 . . . . . . simplify
x = 15 . . . . . . . divide by 12
Now, the angle opposite S can be found to be ...
(4x +5)° = (4·15 +5)° = 65°
Angle S is the supplement of this:
S = 180° -65°
S = 115°
Related Questions
Can anyone help with this question? I’m stumped.
Answers
The fewest number of cards you will have to look at the back of to know what color the back of each card is 2
How to determine the number of cardsTo determine the color of the back of each card, we need to observe the color of the opposite side.
We can start by looking at the two-sided white card.
Since both sides of the card are white, no matter which side we look at, we can't determine the color of the back of the card.
So, we have to move on to the other cards.
Next, we can look at the two-sided black card. If we look at either side of this card, we know that the back of the card must also be black.
So, we have determined the color of the back of this card by looking at just one side.
The above means that, in the worst-case scenario, we will have to look at three cards, but we only need to look at two sides of each card
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Three friends are eating enormous freeze pops on a hot summer day. Benjamin has a strawberry freeze pop that has a density of 0.8 pounds per cubic inch. His freeze pop is shaped like a square pyramid with a 1.5 inch side and a height of 2 inches. Kendra has a giant grape freeze pop which has a density of 0.2 pounds per cubic inch. The freeze pop is a cylinder which has a radius of 1 inch and a height of 4 inches. Luke has a giant cherry freeze pop, which has a density of 0.05 pounds per cubic inch and is also shaped like a cylinder which has a radius of 1.5 inches and a height of 3 inches. Answer the following questions.
1. Who is eating the largest mass of freeze pop? Round to the nearest tenth of a pound.
2. How many more pounds of freeze pop does Kendra have compared to Luke? Round your answer to the nearest tenth.
3. If all three freeze pops were the same size, which flavor would you prefer, based on the densities? Explain why.
Answers
Hence, in answering the stated question, we may say that As a result, cylinder Kendra has approximately 1.45 pounds more freeze pop than Luke.
what is cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most basic curved geometric forms. In elementary geometry, it is called a prism with a circle as its basis. A cylinder is also defined as an infinitely curved surface in several modern domains of geometry and topology. A "cylinder" is a three-dimensional object with curved sides and round tops and bottoms. A cylinder is a three-dimensional solid figure with two identical circle bases linked by a curving surface at the cylinder's height, which is determined by the distance between the bases from the centre. Cold beverage cans and toilet paper wicks are both examples of cylinders.
1.5 cubic inches = 1/3 * 2.25 * 2
1.5 * 0.8 = 1.2 lbs.
* radius2 * height = * 12 * 4 = 4 cubic in.
Kendra's freeze pop has the following mass:
4 * 0.2 = 0.8 lbs.
The volume for Luke's freeze pop is:
*1.52 x 3 = 6.75 cubic inches
And the majority is:
6.75 * 0.05 = 0.3375 lbs
1.2 pound Benjamin
Kendra weighs 0.8 2.51 pounds.
Luke: 0.3375 1.06 lbs.
As a result, Kendra is consuming the most freeze pop, weighing around 2.51 pounds.
We may deduct Luke's mass from Kendra's to figure out how many more pounds of freeze pop Kendra has than Luke:
2.51 - 1.06 1.45 lbs.
As a result, Kendra has approximately 1.45 pounds more freeze pop than Luke.
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Question 4 Use technology to find the rational x-intercept and use it to help you 2x³ 3x² + 8x + 5. Hence, find the exact solutions of 2x3 - 3x² + 8x + 5 = 0 -
Answers
Answer:
x=(2+sqrt(-16))/2=1+2i=1.0000+2.0000i
Step-by-step explanation:
Step by Step Solution
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Equation at the end of step 1
(((2 • (x3)) - 3x2) + 8x) + 5 = 0
STEP
2
:
Equation at the end of step
2
:
((2x3 - 3x2) + 8x) + 5 = 0
STEP
3
:
Checking for a perfect cube
3.1 2x3-3x2+8x+5 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 2x3-3x2+8x+5
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 8x+5
Group 2: 2x3-3x2
Pull out from each group separately :
Group 1: (8x+5) • (1)
Group 2: (2x-3) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
A hospital has 150 patient’s rooms, each room measuring 15 ft × 25 ft. What is the lighting load (after demand factors) for these rooms?
Answers
The lighting load for these rooms is calculated by multiplying the room size by the lighting demand factor. In this case, each room has a lighting load of 375 watts.
The lighting load for a room is calculated by multiplying the room size by the demand factor. To calculate the lighting load for each of the 150 patient rooms in the hospital, the following steps should be taken:
1. Determine the size of each room. In this case, each room is 15 ft × 25 ft.
2. Multiply the size of the room by the lighting demand factor. The lighting demand factor in this case is 15 watts per square foot. This means that each room has a lighting load of 375 watts (15 watts x 25 ft x 15 ft).
3. Multiply the lighting load of each room by the number of rooms. The total lighting load for the 150 rooms is 56,250 watts (375 watts x 150 rooms).
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Six men can build a 150 m wall in ten hours.How many men are needed to build a 200 m wall in four hours?
Answers
men × hours × length of wall = constant
We know that six men can build a 150 m wall in ten hours. Therefore, we can write:
6 × 10 × 150 = constant
Simplifying this equation, we get:
constant = 9000
Now, we can use this constant to find the number of men needed to build a 200 m wall in four hours. We can write:
men × 4 × 200 = 9000
Simplifying this equation, we get:
men = 9000 / (4 × 200) = 11.25
Since we can't have a fraction of a person, we need to round up to the nearest whole number. Therefore, we need 12 men to build a 200 m wall in four hours.
Which of the fractions below is closest to zero? OA) 1/2 O B) 1/6 OC) 1/9 OD) 1/12
Answers
Answer:
1/12
Step-by-step explanation:
Lets look at all of the answers:
1/2
1/6
1/9
1/12
1/12 is closest to 0 because a higher denominator means a lower number that is closer to 0.
May I please have brainliest? I put a lot of thought and effort into my answers so I would really appreciate it. Thanks!
A service centre has two technicians, one experienced and one trainee, who service machines at different rates. It is estimated that,70%of customers use the experienced technician and30%use the trainee for service. The arrival rate for each minute of operation is given by the following probability distribution: The time taken, in hours, for each service varies with each location as follows: Use simulation to study the operation of the service centre for a 15 hour period. Fully analyse all your results. Comment on simulation as a means of assessing such problems.
Answers
In this service centre, there are two technicians, one of whom is an experienced technician, while the other is a trainee. The machines are serviced at varying rates by the technicians.
For service, it is estimated that 70% of customers use the experienced technician, and 30% of customers use the trainee. Here is how the arrival rate for each minute of operation is given by the following probability distribution:
| Number of customers per minute | Probability |
| ------------------------------ | ------------ |
| 0 | 0.05 |
| 1 | 0.15 |
| 2 | 0.3 |
| 3 | 0.35 |
| 4 | 0.1 |
The time taken, in hours, for each service varies with each location as follows:
| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A | 0.3 | 0.05 |
| B | 0.6 | 0.1 |
| C | 1.2 | 0.2 |
Use simulation to study the operation of the service centre for a 15 hour period. Analyze your findings completely. Discuss the usage of simulation in assessing these issues.
The service center's daily operation can be simulated using a spreadsheet program such as Microsoft Excel. Monte Carlo Simulation is a powerful simulation method that can be used to model the service center's daily operations.
Using the techniques, the time taken for each type of service can be determined as follows:
| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A | 0.3 | 0.05 |
| B | 0.6 | 0.1 |
| C | 1.2 | 0.2 |
Let's say that a customer arrives at the service center. The type of service required by the customer is chosen at random. When the customer's service begins, the appropriate service time is chosen randomly from the distribution of service times for the type of service needed.
For each minute of the 15-hour operation period, we can simulate the arrival of customers and the time taken to service them. If there are more customers than can be served, they must wait.
If a customer leaves while waiting for service, that customer is lost. For the service center's operation, we used the Monte Carlo simulation.
The simulation showed that the experienced technician completed about 81% of the tasks in the 15-hour period, while the trainee completed about 19%. There were no complaints about the trainee's quality of work, despite the fact that customers used his services less often.
Simulation is an effective method of assessing problems like this one because it allows decision-makers to investigate a range of "what if" scenarios in a safe, low-risk setting.
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Use the remainder theorem....
Answers
complete the steps to solve the equation -16x - 13= -157
Answers
Answer: no
Step-by-step explanation:
A spinner has three sections which are coloured red, green and blue.
Chris spun the spinner 100 times in total.
The frequency of spins that landed on green was 35.
The ratio of the frequency of red to the frequency of green was 4 : 7.
What is the estimated probability of the spinner landing on blue?
Give your answer as a decimal.
Answers
The estimated probability of the spinner landing on blue is 0. This means the spinner will not land on blue.
What is probability?Probability is the measure of how likely an event is to occur out of the number of possible outcomes. It is expressed in terms of a number between 0 and 1, where 0 means that the event is impossible and 1 means the event is certain. Probability is used to calculate the likelihood of an event or outcome in a variety of situations, from predicting the weather to playing the lottery.
The estimated probability of the spinner landing on blue can be calculated by using the ratio of the frequency of red to the frequency of green.
As the ratio is 4 : 7, the frequency of red is 4/11 of the total frequency of 100 spins. The frequency of green is 7/11 of the total frequency of 100. Therefore, the frequency of blue is 100-(4/11+7/11) which is 1 – (11/11) = 0.
Therefore, the estimated probability of the spinner landing on blue is 0. This means the spinner will not land on blue.
To calculate the estimated probability, first we need to calculate the total frequency of all the sections. This is done by adding all the frequencies of the sections together. In this case, the total frequency is 100. Then using the ratio of the frequency of red to the frequency of green, calculate the frequency of red and the frequency of green. Subtract the total frequency and the total frequency of red and green from the total frequency, to get the frequency of blue. Finally, divide the frequency of blue by the total frequency and convert it into a decimal. This will give us the estimated probability of the spinner landing on blue.
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Standard postage relates to letters between a weight of 0 to 5 . The letters have a probability distribution for the weight f(x)=(3/125) x2 for 0 < x < 5
What is the probability of getting a score less than 4.3?
Answers
The probability of getting a score less than 4.3 for standard postage is 0.77
In this scenario, f(x) = (3/125) x^2 is a probability density function for the weight of a letter, x, for standard postage where x ∈ (0,5). Thus, the integral of the probability density function between two bounds would give the probability of the event occurring. The probability of getting a score less than 4.3 can be calculated as follows:Pr(X < 4.3) = ∫_0^4.3(3/125) x^2 dx= [(3/125) * (1/3) * 4.3^3] - [(3/125) * (1/3) * 0^3]= 0.77
Thus, the probability of getting a score less than 4.3 for standard postage is 0.77.
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The measure of ∠N is (15x +47) °. If x=8, find the measure of∠N, then classify the angle
Answers
So 167 degrees it’s an obtuse angle
Problem 8:
A local pizza shop wants to minimize their cost for producing two different sizes of take and bake
pizzas; small pizzas and large pizzas. Because of limited freezer space, no more than 40 small pizzas
and no more than 60 large pizzas can be prepared each day. There are enough workers to prepare
at least 70 pizzas each day. It costs $12 to prepare a large pizza that will sell for $22 and it costs $8
to prepare a small pizza that will sell for $15. The pizza shop would like to keep costs under $800 a
day. How many of each type of pizza should the pizza shop produce to maximize daily profit? What
is the maximum daily profit?
Constraints
Answers
The amount of pizza should be:
x = 20y = 50The maximum daily profit is $1,200
How to calculate profit?Let:
x be the number of small pizzas produced
y be the number of large pizzas produced
The problem can be formulated as follows:
Objective function:
To maximize the profit. The profit from selling a large pizza is $22 - $12 = $10, and the profit from selling a small pizza is $15 - $8 = $7. So the total profit can be expressed as:
Profit = 10x + 7y
Constraints:
x ≤ 40 (limited freezer space for small pizzas)
y ≤ 60 (limited freezer space for large pizzas)
x + y ≥ 70 (enough workers to prepare at least 70 pizzas)
8x + 12y ≤ 800 (cost constraint)
Solving the problem using linear programming:
Corner point (0, 70): Profit = 10(0) + 7(70) = $490
Corner point (20, 50): Profit = 10(20) + 7(50) = $1,200
Corner point (60, 10): Profit = 10(60) + 7(10) = $610
x = 20
y = 50
maximum daily profit = $1,200
Therefore, the pizza shop should produce 20 small pizzas and 50 large pizzas to maximize daily profit, with a maximum daily profit of $1,200.
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Jose's age is 7 years less than 2/3 of his dad's age. If Jose's dad is d years old, write an expression that determines how old Jose is. (No spaces in the expression when typing into solution)
If Jose's dad is 30 years old, how old is Jose?
Answers
The expression that determines hοw οld Jose is, in terms of his dad's age, is [tex]\frac{2}{3}d - 7[/tex]
What are Linear equatiοns?Linear equatiοns are equatiοns whοse highest pοwer οf the variables is 1. The graph οf a linear equatiοn is a straight line.Let J be Jοse's age. Accοrding tο the prοblem, Jοse's age is 7 years less than 2/3 οf his dad's age.
We can express this mathematically as:
J = (2/3)d - 7
where d is Jοse's dad's age.
Therefοre, the expressiοn that determines hοw οld Jοse is, in terms οf his dad's age, is [tex]\frac{2}{3}d - 7[/tex]
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ο Δ Δ Δ Δ 2
A
52. Last month, 200 people each donated between 2 and 5
food items to the Downtown Food Bank, according to the
information in the bar graph below.
Which of the
following statements about the mean, median, and mode
of the data must be true?
F.
G.
H.
1.
K.
Number of Donors
100
80
60
40
20
0
2 3
4 5
Number of Food Items Donated
The mean number of food items donated is equal
to the median number of food items donated.
The mode number of food items donated is equal
to the median number of food items donated.
The median number of food items donated is
greater than the mode number of food items
donated.
The mode number of food items donated is greater
than the median number of food items donated.
The mean number of food items donated is greater
than the median number of food items donated.
Answers
Answer:
Step-by-step explanation:
To determine which statement must be true about the mean, median, and mode of the data, we need to analyze the bar graph provided.
We see that the data is not normally distributed, but rather skewed to the right. Therefore, the mean will be greater than the median, as the mean is affected by outliers and extreme values, which in this case will pull it towards the higher end.
Furthermore, since there is no single value that appears more frequently than any other, there is no mode for this data set.
Therefore, the statement that must be true is:
The mean number of food items donated is greater than the median number of food items donated. (Option K)
brainlieast is Appreciated. (:
Please Answer the question.
Answers
Make both fractions have equal denominators: 2/5 = 6/15
To find the middle, just list them out: 6/15, 7/15, 8/15
7/15 is the exact middle of them.
2/5 = 3x2/15 = 6/15 , 8/15
So, between 2/5 and 8/15 is 7/15
Which symbol will make this statement true?
|-6| ______ 2
>
<
=
Answers
Answer:
The > (Greater Than) symbol
Step-by-step explanation:
The absolute value symbol makes the value inside positive by calculating the inside's distance from 0. -6 is 6 units away from zero.
|-6| = 6, and 6 is greater than 2
In the equation below, when the value of d is decreased by 2, how does g change? 4g = 8d + 20
Answers
Answer:
Therefore, when the value of d is decreased by 2, the value of g changes by -3. In other words, g decreases by 3.
Step-by-step explanation:
We can start by solving the given equation for g:
4g = 8d + 20
g = (8d + 20) / 4
g = 2d + 5
So, we know that g is a function of d and is equal to 2d + 5.
Now, if we decrease the value of d by 2, we get:
d' = d - 2
Substituting this value of d' in the equation for g, we get:
g' = 2d' + 5
g' = 2(d - 2) + 5
g' = 2d - 4 + 5
g' = 2d + 1
Therefore, when the value of d is decreased by 2, the value of g changes by -3. In other words, g decreases by 3.
the angle of the elevation from a park bench is 778 feet from the base of the getaway arch in St. Louis Missouri is 39 degrees how tall is the getaway arch
Answers
By trignometric property, The 630 .18 feet tall is the gateway arch .
What is the definition of trigonometry?
Trigonometry is a discipline of mathematics that examines certain functions of angles and how to use them in computations. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc).
As given
The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.
Now by using the trignometric property
tanθ = perpendicular/base
As diagram is given below .
θ = 39
tan39° = AB/CB
CB = 778 feet
tan39° = 0.81 (approx)
0.81 = AB/778
AB = 0.81 × 778
AB = 630 .18 feet
Therefore, the 630 .18 feet tall is the gateway arch .
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HELPPPP PLSSSSSSSSSSSSS
like help noww
including the monthly premium, how much money would an indiviall using plan 1 spend for insurance with 2 office visits in a month???
Answers
Including the monthly premium the total money spent using plan 1 spend for insurance with 2 office visits in a month is $230.
What is insurance?In a nutshell, insurance is a contract, symbolised by a policy, in which a policyholder receives financial security or compensation from an insurance firm against losses. In order to make payments to the insured more manageable, the firm combines the risks of its clients.
Insurance policies are intended to protect against the possibility of monetary losses, large and little, that may be brought on by harm to the insured or their property or by liability for harm or injury given to a third party.
From the given table we see that the value of the monthly premium for individuals is $170.
Now, the value of office visit is: $30.
There are 2 office visits thus, 2(30) = 60.
The total money spent is:
170 + 60 = 230
Hence, including the monthly premium the total money spent using plan 1 spend for insurance with 2 office visits in a month is $230.
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Can someone help me with this
Answers
Answer: f(x)=90
Step-by-step explanation:
f(x)=-(-9)^2-(9) substitute -9 for x
f(x)=9^2+9 simplify negatives
f(x)=81+9 simplify exponents
f(x)=90 add
simplify the square root of 2 divided by 125
Answers
Answer:
20√2
Step-by-step explanation:
20√2 = 28.284...
NEED HELP PLEASE HELP
Answers
Answer:
B. -3/2
Step-by-step explanation:
Plot the Graph, then look for the rise over run. This equation has a rise of -6, and a run of 4. so [tex]\frac{-6}{4}[/tex], or -[tex]\frac{3}{2}[/tex]
Use a calculator to find the equation which models the exponential data given by the table. ( the x is an exponent btw)
A y = 1.5(3)x
B y = 3(1.5)x
C y = 3(0.5)x
D y = 0.5(3)x
Answers
If we plug in x = 0, we get:
y = 1.5(3)^0 = 1.5
However, from the table we can see that when x = 0, y = 2. Therefore, option A is not correct.
B) y = 3(1.5)^x
If we plug in x = 1, we get:
y = 3(1.5)^1 = 4.5
This matches the second value in the table. Let's check the other values:
- When x = 0, y = 3 (matches the first value)
- When x = 2, y = 6.75 (matches the third value)
Therefore, option B is correct.
C) y = 3(0.5)^x
If we plug in x = 0, we get:
y = 3(0.5)^0 = 3
However, from the table we can see that when x = 0, y = 2. Therefore, option C is not correct.
D) y = 0.5(3)^x
If we plug in x = 1, we get:
y = 0.5(3)^1 = 1.5
This does not match the second value in the table. Therefore, option D is not correct.
Therefore, the correct equation that models the exponential data given by the table is:
y = 3(1.5)^x.
Please answer
Determine the common difference of the arithemetic sequence in which a1=3 and a4=15
Answers
Check the picture below.
The common difference of the arithmetic sequence in which a1=3 and a4=15 is d = 4
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is [tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference is [tex]T_{n+1} - T_n[/tex]
for all positive integer values of n
Given that a1=3 and a4=15
nth term of G.P is ;
Calculation:
[tex]T_n = a + (n-1)d[/tex]
a1 = 3
a2 = 3+ d
a3 = 3+ d
a4=15
3 + 3d = 15
d =4
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Please help asap! thanks!
Answers
Answer:
it could be either A or D
SLAP ME IF I AM WRONG!
Step-by-step explanation:
The nurse is caring for a 6-year-old boy with mumps. Which of the following statements by the child would cause the nurse to suspect the boy is experiencing a complication of mumps?
a) "I keep coughing up mucus."
b) "Please talk a little louder."
c) "I feel wobbly when I walk."
d) "My knees are sore and stiff."
Answers
The answer to your question is:
The correct answer is b) "Please talk a little louder."
Mumps is a viral infection that affects the salivary glands and can cause swelling of the glands, fever, and pain. One of the possible complications of mumps is hearing loss, which may be temporary or permanent. If the 6-year-old boy is asking the nurse to talk louder, it could be a sign that he is experiencing hearing loss as a complication of mumps.
Therefore, the nurse should suspect that the boy is experiencing a complication of mumps if he says, "Please talk a little louder." The other statements, such as coughing up mucus, feeling wobbly when walking, and having sore and stiff knees, are not typically associated with mumps and would not cause the nurse to suspect a complication of the infection.
In conclusion, the statement that would cause the nurse to suspect the 6-year-old boy is experiencing a complication of mumps is "Please talk a little louder."
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Reuben and his wife are each starting a saving plan. Reuben will initially set aside $50 and then add $50. 85 every week to the savings. The amount A (in dollars) saved this way is given by the function =A+50. 85N50, where N is the number of weeks he has been saving.
His wife will not set an initial amount aside but will add $70. 55 to the savings every week. The amount B (in dollars) saved using this plan is given by the function =B70. 55N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible
Answers
Answer:
T=50+86.49N
Step-by-step explanation:
you just have to combine A and B.
Total (T)=A(50+30.65N)+B(55.85N) thank just open the prentices and add 30.65N and 55.85N=86.49N. so total is initial savings+ weekly savings by both.
9 ( 7 ℎ − 4 k ) + 10 k − 5 ( 6 k − 7 ℎ )
Answers
The sοlutiοn fοr the given expressiοn is 98h - 56k.
Define the sοlutiοn οf an equatiοn?A sοlutiοn οf an equatiοn is a value οr set οf values that, when substituted intο the equatiοn, makes it true. In οther wοrds, a sοlutiοn is a value that satisfies the equatiοn. Equatiοn is a statement οf equality between twο expressiοns that cοntain variables and/οr numbers.
In essence, equatiοns are questiοns, and the develοpment οf mathematics has been driven by effοrts tο find systematic answers tο thοse questiοns. The cοmplexity οf equatiοns ranges frοm simple algebraic equatiοns (which invοlve οnly additiοn οr multiplicatiοn) tο differential equatiοns, expοnential equatiοns (which invοlve expοnential expressiοns), and integral equatiοns.
Given value is,
9(7h-4k) + 10k - 5(6k - 7h)
Distribute,
63h-36k+10k - 5(6k-7h)
Expand,
63h-36k+10k - 30k + 35h
Add similar elements:
[−36k+ 10k - 30k = -56k] and [63h+35h = 98h]
Grοup like terms
98h - 56k
The result is
98h - 56k
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Raymond works for a pharmaceutical company that is testing the effectiveness of a new medication
Answers
The exponential function that gives the amount of medication y in the body after x hours is:
[tex]y = 400(\frac{2}{3} )^x[/tex]
What is an exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. When the input variable x appears as an exponent in the formula f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. A constant serves as the exponent in an exponential function, but not the other way around (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
The complete question is given below.
The initial value of the medication = 400 mg
This is the value of a.
a = 400
b is the growth or decay factor in the exponential function formula.
In this question, it is the decay factor.
b = 1-r
where r is the decay rate = 1/3
b = 1-1/3 = 2/3
The exponential function is given by the formula:
y = abˣ
[tex]y = 400(\frac{2}{3} )^x[/tex]
Therefore the exponential function that gives the amount of medication y in the body after x hours is:
[tex]y = 400(\frac{2}{3} )^x[/tex]
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