The function f(x) = 6log₂x - 3 increasing at the greatest rate in the interval [1/8, 1/2].
What are maxima and minima?The maxima and minima of a function are the extreme values within the range; in other words, they are the maximum and minimum values of a function, respectively, at a given position.
Let the function be f(x) = 6log₂x - 3
For the interval x ∈ [2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased most rapidly in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
Therefore, the range [1/8, 1/2] is where the function f(x) = 6log₂x - 3 increases at the fastest pace.
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person a starts walking north at 4 ft/s from a point p. five minutes later, person b starts walking south at 5 ft/s from a point 500 feet due east of p. at what rate are the people moving apart 15 minutes after person b starts walking?
The rate at which the people are moving apart 15 minutes after person B starts walking is √2660 feet per second. To the nearest tenth of a foot per second, this is 51.3 feet per second.
Let's call the rate at which the people are moving apart "d".
15 minutes after person B starts walking, person A has been walking for 15 + 5 = 20 minutes, for a total distance of 20 * 4 = 80 feet north from point P.
At the same time, person B has been walking for 15 minutes, for a total distance of 15 * 5 = 75 feet south from point 500 feet due east of P.
The distance between the two people is the square root of the sum of the squares of their north-south and east-west separations, or:
d = √(80^2 + (500)^2) = √(80^2 + 250000) = √250100 = 500
Since the rate at which they are moving apart is the derivative of their separation with respect to time, we can find it by taking the derivative of the above equation with respect to time:
d/dt = √(2 * 80 * 4dt / dt + 2 * 500 * 5dt / dt) = √(160 + 2500) = √2660
To the nearest tenth of a foot per second, this is 51.3 feet per second.
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The height, h, of the triangle is 11 cm greater than its corresponding base.
What is the area of the triangle?
A=
cm²
33 cm
10 cm
Answer:
If the height of the triangle is 11 cm greater than its corresponding base, we can represent the base as b and the height as h = b + 11.
Using the formula for the area of a triangle, A = (1/2) bh, we can substitute the values of b and h:
A = (1/2) (b)(b + 11)
A = (1/2) b^2 + (1/2) 11b
If the base of the triangle is 10 cm, then we can substitute b = 10 into the equation:
A = (1/2) (10^2) + (1/2) 11 * 10
A = 50 + 55
A = 105 cm^2
So, the area of the triangle is 105 cm^2.
Step-by-step explanation:
When the data is asymmetrical, you use _ (IQR/SD) to measure the spread.
Fοr distributions with a nοrmal shape or symmetry, the mean and standard deviation are emplοyed; for asymmetrical distributiοns, the median and interquartile range are used.
Do you calculate spread using IQR or standard deviation?Because it is unaffected by οutliers, the IQR is frequently regarded as a mοre accurate measure of spread than the range. The variance and standard deviatiοn are indicators of hοw widely the data are dispersed from the mean. Each οbserved data value's prοximity to the mean is summarised.
Why are skewed data sets used for IQR?The strοngest indicator of variability in data sets with οutliers or skewed distributions is the interquartile range. It's unlikely to be impacted by οutliers because it's based οn numbers that come frοm the centre half of the distribution.
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working alone, Ted can install a new deck in 15 hours. Jimmy can install the same deck in 16 hours. How long would it take them to install the deck if they worked together
The time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
What is the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.
Let W be the total work to be done, which is installing a new deck.
Given Ted alone can complete the work W in 15 hours.
Using unitary method,
So in one hour, work done by Ted = W/15
Also given Jimmy alone can complete the work W in 16 hours.
So in one hour, work done by Jimmy = W/16
Using unitary method,
In one hour the work done by Jimmy and Ted together = W/15 + W/16 = 31W/240
ie 31W/240 = 1 hour
So W = 240/31 = 7.7 hours
Therefore the time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
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assume that there are 60 students in a class and they will be seated in a classroom where there are 62 seats. in how many different ways this can be done?
There are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.
If there are 60 students and 62 seats, then there will be 2 empty seats in the classroom. We need to find out the number of ways to seat the 60 students in these 62 seats.
To solve this problem, we can use the permutation formula:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects we want to arrange.
In this case, we want to arrange 60 students in 62 seats, so we can use the formula as follows:
62P60 = 62! / (62 - 60)!
= 62! / 2!
= 62 x 61 x 60 x ... x 3 x 2 x 1
= 4,431,621,036,503,680
Therefore, there are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.
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Evaluate: -2[-4+3(2-32+4⋅2-3)-3]
Answer:
68
Step-by-step explanation:
-2[-4+ 3(2 - 32 + 4 · 2 -3) - 3] Start in the center and work your way out.
-2[-4 + 3(2 - 32 + 8 -3) - 3]
-2[-4 + 3(-30 + 8 - 3) -3]
-2[-4 + 3(-22 -3) -3]
-2[-4 + 3(-25)-3]
-2[-4 -27 -3}
-2[-31 - 3]
-2(-34)
68
this is just for fun I already know the answer but I will give branly and a lot of points to who ever answers
2+2
Answer:
4
Step-by-step explanation:
Answer: 4
Step-by-step explanation: Because 1+1=2
2+2=4 therefore 2*2 also equal 4 and 2^2= 4
A water bottle holds 72 ounces of water. How many cups does the water bottle hold? (1 cup = 8 fluid ounces) 4 cups 8 cups 9 cups 64 cups
Answer:
9 cups
Step-by-step explanation:
1 cup is 8 ounces
72/8 is 9
Jemma filled one-fourth of a barrel with compost on Saturday. Then she filled the remaining space with 4,200 g4,200 g4, comma, 200, start text, space, g, end text of compost on Sunday.
How many kilograms of compost are in the barrel?
.....kilograms?
The kilograms of compost in the barrel is 5.6 kg
How to determine the kilograms of compost in the barrel?From the question, we have the following parameters that can be used in our computation:
Amount filled on day 1 = 1/4
Remaining space = 4200 grams
The number of kilograms in the barrel is calculated as
Remaining space = (1 - 1/4) * Original space
Substitute the known values in the above equation, so, we have the following representation
(1 - 1/4) * Original space = 4200 grams
Convert to kg
(1 - 1/4) * Original space = 4.2 kg
So, we have
Original space = 4.2 kg/(1 - 1/4)
Evaluate
Original space = 5.6 kg
Hence, the original space is 5.6 kg
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in a board of directors composed of people, how many ways can one chief executive officer, one director, and one treasurer be selected?
A chairman and vice chairman are to be selected from a committee of eight people in such a way that no one treasurer individual can hold more than one position. The permutation of 8 different objects, chosen two at a time, results in the number of possible chairman selections in this situation.
[tex]^{8} P_{2} =[/tex][tex]8/8-2=8/6=8*7*6/6=8*7=56[/tex]
Cash and liquidity management, risk management, and corporate finance are among the important basic responsibilities of a corporate treasurer. The division in charge of a nation's finances, economy, and revenue is known as the treasury. Although in certain nations the treasury answers to a Secretary of the Treasury or Chancellor of the Exchequer, the treasurer is often in charge of the department. After the Prime Minister and Deputy Prime Minister, the Treasurer is a senior minister in Australia and frequently the second or third most significant member of the cabinet. Additionally, each Australian state and autonomous territory has its own treasurer.
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En una empresa líder en investigación se quiere estimar la proporción de personas a favor de una nueva reforma política en el distrito A. ¿A cuántas personas se necesitará para la estimación, si de una muestra piloto se obtuvo que el 64. 1% de las personas están a favor de la reforma política, se desea estar seguro con un 97% de confianza y tener a lo más 4. 7% de error de estimación?
A sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%
To estimate the sample size, we can use the following formula:
n = (Z^2 * p * (1-p)) / E^2
where:
n = sample size
Z = the Z-score for a given confidence level (for 97% confidence, Z = 2.33)
p = the proportion in the pilot sample (0.641)
E = the maximum allowed error of estimation (0.047)
Plugging in the values, we get:
n = (2.33^2 * 0.641 * (1 - 0.641)) / 0.047^2
n = (5.3929 * 0.359) / 0.00222009
n = 1.928 / 0.00222009
n = 869.75
Since the sample size must be a whole number, we round up to the nearest whole number.
n = 870
Therefore, a sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%
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Jessica said that the equation 2.5 + 4y =10 is in standard form but her friend Frankie says it is not. Who do you agree with? Explain your reasoning.
Answer: no. it is not in standard form
We cannot find the x-intercept of this equation by substituting 0 for y and solving for the x.
Step-by-step explanation:
alyssa likes to play roulette, but she doesn't like the low probability of betting on a single number. therefore, she bets on a block of 4 numbers, increasing her probability of winning to 438. she generally places a $5chip on her block of 4. if one her 4 numbers come up, she wins $40 (and gets to keep her bet!). what is the expected value for alyssa playing roulette? round to the nearest cent. do not round until your final calculation.
If one her 4 numbers come up, she wins $40 (and gets to keep her bet!). Alyssa can expect to lose 47 cents per bet over the long run.
The expected value of a game is the average amount that a player can expect to win or lose per bet, taking into account both the probabilities and the payouts of each possible outcome. To find the expected value, we multiply the probability of each outcome by the amount won or lost for that outcome, and then sum up these products.
In this case, Alyssa bets $5 on a block of 4 numbers, which gives her a probability of winning of 4/38, or approximately 0.1053. If one of her 4 numbers comes up, she wins $40, for a net gain of $35 (since she gets to keep her $5 bet as well). If none of her 4 numbers comes up, she loses her $5 bet.
Therefore, the expected value for each bet is:
(0.1053 × $35) + (0.8947 × -$5) = -$0.47
So if she plays many times, she can expect to lose money overall. It's important to keep in mind that expected value is not a guarantee of what will happen on any particular bet, but rather a long-term average based on probabilities.
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A2=6. R=1/2 use the given term and common ratio to write the explicit formula and recursive formula of the geometric sequence
The explicit formula and recursive formula of the geometric sequence is Aₙ = 12(R)ⁿ⁻¹ where n is an integer.
It is given that in a geometric sequence, the second term and the common ratio are 6 and /2 respectively.
Now, we have to write the standard formula that can be further formulated as the explicit formula and recursive formula of the geometric sequence, The formula goes as,
Aₙ = A₁(R)ⁿ⁻¹
Here,
Aₙ is the nth term of the sequence. So, if we want the first term then will put n = 1, n= 2 for second term and so on.
Now, putting n = 2,
A₂ = A₁(R)²⁻¹
A₂ = A₁(R)
6 = A₁(1/2)
A₁ = 12
So, the explicit and recursive formula will be Aₙ = 12(R)ⁿ⁻¹.
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The distance to the nearest exit door is at most 100 feet. Write an inequality
Answer:
The distance to the nearest exit door is at most 100 feet can be written as an inequality as:
d ≤ 100
George ate a meal that included a steak, a loaded baked potato, and coleslaw. The coleslaw had 50 fewer calories than the baked potato. The steak had twice as many calories as the baked potato. The total number of calories in the meal was 1550 calories. Write an equation that could be used to find the number of calories in the loaded baked potato (where P presents the calories in the loaded baked potato). Then, SOLVE the equation.
Answer:
400 calories
Step-by-step explanation:
Let's call the number of calories in the loaded baked potato as P. Then the coleslaw had P-50 calories and the steak had 2P calories.
So the equation for the total number of calories in the meal is:
P + (P-50) + 2P = 1550
4P = 1600
P = 400
Therefore, the loaded baked potato had 400 calories.
Answer:
Below
Step-by-step explanation:
c oleslaw = p - 50
p = potato
s = 2 p Summed these = 1550
p-50 + p + 2p = 1550 Gather 'like' terms
4p - 50 = 1550 add 50 to both sides of the equation
4p = 1600 divide both sides by 4
p = 400 calories
I need help with this
Answer:
10) m∠2 = 139°
11) m∠3 = 139°
12) m∠4 = 41°
Step-by-step explanation:
Question 10
∠2 and the adjacent angle of 41° are supplementary angles since they lie on opposite sides of the same line; they must add up to 180°
m∠2 + 41° = 180°
m∠2 = 180-41 =139°
Question 11
∠2 and ∠3 are formed by the intersection of two rays. They are vertically opposite angles and therefore they must be equal
m∠3 = m∠2 = 139°
Question 12
Angles ∠3 and ∠4 are supplementary angles (same reasoning as q 10)
Therefore m∠4 = 180° - m∠3
= 180° - 139° = 41°
Note that there are many ways to arrive at the answers for m∠4
angles 4 and 41° are opposite vertical angles so they must be equal and m∠4 = 41°angles 2 and 4 are supplementary and therefore m∠2 + m∠4 = 180° => 139 + m∠4 = 180° or m∠4 = 180 - 139 = 41°Madison took a taxi from her house to the airport. The taxi company charged a pick-up fee of $3.20 plus $5 per mile. The total fare was $98.20, not including the tip. Write and solve an equation which can be used to determine
m, the number of miles in the taxi ride.
Answer:
19 miles
Step-by-step explanation:
hope this helps!!
what is the van't hoff factor for a solution of (nh4)3po4? write your answer in number format such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.
In this solution, each molecule of (NH₄)₃PO₄ dissociates into three ammonium ions (NH₄₊) and one phosphate ion (PO4₃₋), resulting in a total of 4 ions per molecule. Hence, the Van 't Hoff factor for this solution is 4.
The Van 't Hoff factor (i) is a measure of the degree to which a substance ionizes in a solution, and is defined as the ratio of the number of ions formed to the number of molecules (or formula units) dissolved. For the case of a solution of (NH₄)₃PO₄, the Van 't Hoff factor is 4. The Van 't Hoff factor is a measure of the extent to which an ionic substance dissociates into individual ions when dissolved in water. It is defined as the ratio of the number of ions formed to the number of formula units or molecules of the substance that are dissolved. For a solution of (NH₄)₃PO₄, the Van 't Hoff factor is 4 because each molecule dissociates into 3 ammonium ions (NH₄₊) and 1 phosphate ion (PO4₃₋), resulting in a total of 4 ions per molecule. The Van 't Hoff factor is important in determining the colligative properties of solutions, such as boiling point elevation and freezing point depression.
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Which equations are correct? select each correct answer. 8x3(3x2)=24x6 4x3(6x2)=24x6 6b3(−2b3)=−12b6 3a3(−3a4)=−9a7?
The correct equations are:8x^3 * (3x^2) = 24x^5, 6b^3 * (-2b^3) = -12b^6, 3a^3 * (-3a^4) = -9a^7. The equations are correct because they follow the rules of algebra. The equation 4x^3 * (6x^2) = 24x^5 is not correct.
The distributive property of multiplication over addition allows us to multiply a factor by each term inside a set of parentheses. In the equation 8x^3 * (3x^2), we can use the distributive property to multiply 8x^3 by each term inside the parentheses, giving us 24x^5.
Similarly, the product of two negative numbers is positive, which explains why the equation 6b^3 * (-2b^3) equals -12b^6.
Finally, multiplying two terms with the same base means we add the exponents, so in the equation 3a^3 * (-3a^4), we get -9a^7.
Therefore, these equations are correct and follow the rules of algebra.
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What is the length of the radius of the above sphere if the volume is 14,130 in3?
Solve this equation and you will have the solution:
4 • 3.14 • r3 ÷ 3 = 14,130
Your last step when solving this equation is to find the cube root of a both sides!
The length of the radius of the sphere is 15 in.
What is a sphere?It is a three-dimensional figure and has a diameter and a radius and the volume of a sphere is 4/3πr³.
We have,
Volume of the sphere = 14130 in³
So,
4/3πr³ = 14130 _____(1)
Solve for r.
4/3 x 3.14 x r³ = 14130
keep r on one side and the rest on the other side.
r³ = 14130 x 3 / 4 x 3.14
Cube root on both sides.
r³ = 3375
∛r³ = ∛3375
[ 15 x 15 x 15 = 3375 ]
So,
r = 15
Thus,
The radius of the sphere is 15 in.
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What is the kinetic energy of a 3 kg ball that is rolling at 2 m/s
The kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules. The kinetic energy of an object is the energy it possesses due to its motion.
The kinetic energy of an object is the energy it possesses due to its motion. The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
In this case, the mass of the ball is 3 kg and its velocity is 2 m/s, so we can plug these values into the formula:
Kinetic Energy = [tex](1/2) * 3 kg * (2 m/s)^2[/tex]
Kinetic Energy = [tex](1/2) * 3 kg * 4 m^2/s^2[/tex]
Kinetic Energy = 6 J
So the kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules.
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1. suppose that the students in your class want to have a party at which they will serve punch to drink. the punch the students want to serve is sold in half-gallon containers. if 25 students attend the party and if each student drinks 8 fluid ounces of punch, then how many containers of punch will you need? describe two different ways students could correctly solve this problem. for each method of solving the problem, explain simply and clearly why the method makes sense.
As per the volume, we need to to purchase 4 containers of punch.
To calculate the amount of punch required, we need to find the total volume of punch needed, which can be calculated as follows:
Total volume of punch = number of students * volume of punch per student
= 25 * 8 fluid ounces
= 200 fluid ounces
Now, we know that the punch is sold in half-gallon containers. One gallon is equal to 128 fluid ounces. Therefore, a half-gallon container is equal to 64 fluid ounces. We can use this information to find out how many containers of punch are needed:
Number of containers of punch = Total volume of punch / Volume of punch per container
= 200 / 64
= 3.125
Since we cannot purchase a fractional number of containers, we need to round up to the nearest whole number. Therefore, we need to purchase 4 containers of punch.
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Need help with this question urgent please
The equation y < - 4 · x - 1 represents the inequality seen in the figure.
How to determine an inequality
According to analytic geometry, we can derive the equation of a line from the knowledge of two points along the line. In this problem we must determine an inequality of the form:
y < m · x - b
m = Δx / Δb
Where:
m - Slopeb - InterceptWe know that points (x, y) = (- 1, 3) and (x, y) = (0, - 1) are points of the line. Now we proceed to determine the equation of the line:
m = (- 1 - 3) / [0 - (- 1)]
m = - 4
b = - 1
y < - 4 · x - 1
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Choose a method that can be used to solve this system of equations by elimination 2x – 2y = 24 4x + 7y = –40
Answer: x = 4, y = -8
Step-by-step explanation:
Because 2 is a multiple of four, multiply the first equation by two to eliminate the x value and effectively isolate y.
4x - 4y = 48
4x + 7x = -40
If we were to subtract the x values, that gives us -11y = 88, or y = -8.
Then, just plug y into your equation of choice.
2x - 2(-8) = 24
2x + 16 = 24
2x = 8
x = 4
One way you can check whether the values is right is plug the y value into the other equation and see if you receive the same answer.
4x + 7(-8) = -40
4x = -40 + 56
4x = 16
x = 4
over the course of a year, malachi gets 2 haircuts at a price of $12.00 each, 3 haircuts at a price of $15.00 each, and 1 haircut at a price of $25.00. for malachi,what is the weighted mean cost of a haircut?
The weighted mean cost of a haircut for Malachi is $15.67, divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.
We must compute the total cost of all haircuts and divide it by the total number of haircuts in order to determine the weighted mean price of a haircut for Malachi. The expense of each haircut must be weighed according to the frequency with which it occurred, though, because they varied in price.
To begin, let's figure out how much each haircut will cost overall:
2 haircuts at $12.00 each = $24.00
3 haircuts at $15.00 each = $45.00
1 haircut at $25.00 = $25.00
Total cost = $24.00 + $45.00 + $25.00 = $94.00
Next, We must determine the total number of cuts:
2 haircuts + 3 haircuts + 1 haircut = 6 haircuts
Finally, The weighted mean cost of a haircut can be determined by dividing the total cost by the total number of haircuts:
The weighted mean cost of a haircut = Total cost / Total number of haircuts
= $94.00 / 6 haircuts
= $15.67 per haircut (rounded to the nearest cent)
Therefore, Malachi's weighted mean haircut expense is $ 15.67 , divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.
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Clarice has animated a 3D airplane with visible passengers in the windows. She wants the plane to move on a predetermined path across the screen. What form of animation should she use?
4 Natasha is foot taller than her little
brother. Natasha is no more than 5-½ feet
tall. Which inequality can be used to
find the possible height of her little
brother, b?
The possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as: b ≤ 4.5
How to find the inequalityLet's denote the height of Natasha as "n" and the height of her little brother as "b".
We know that Natasha is one foot taller than her little brother, so we can write:
n = b + 1
We also know that Natasha's height is no more than 5-1/2 feet, so we can write:
n ≤ 5.5
Now we can substitute the first equation into the second equation and get:
b + 1 ≤ 5.5
Simplifying this inequality, we get:
b ≤ 4.5
Therefore, the possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as:
b ≤ 4.5
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Your Assignment
Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
2. Simplify both sides. Show your work.
3. Is x = 6 a solution to the equation? Why or why not? (3 points
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
please help me!
Answer:
5(x – 3) = x + 13 with x = 6 substituted: 5(6 – 3) = 6 + 13
Simplifying both sides: 5(3) = 6 + 13
15 = 19
x = 6 is not a solution to the equation because when you substitute it, the left side of the equation (15) does not equal the right side of the equation (19).
To find a value of x that is a solution to the equation, we can start by solving for x:
5(x – 3) = x + 13
5x – 15 = x + 13
4x = 28
x = 7
So, x = 7 is a solution to the equation 5(x – 3) = x + 13. To find this solution, we first substituted x = 7 into the equation and simplified both sides to see if they were equal.
Step-by-step explanation:
The number of bacteria in a lab experiment can be modeled by the function y(t)=270(1.129)^4t. Write an equivalent function of the form y(t)=ab^t. Round your final values to 4 decimal places.
