Answer:
a).[tex]P_{t}=\frac{5}{3}P_{t-1}[/tex]
b).[tex]A_{t}=300e^{0.1277\times t}[/tex]
c). 6429 bacteria
Step-by-step explanation:
Population of the bacteria grows exponentially.
Therefore, growth of the bacteria will be represented by the formula
[tex]P_{t}=P_{0}e^{kt}[/tex]
Where [tex]P_{t}[/tex] = Population of the bacteria after time t
[tex]P_{0}[/tex] = Initial population of the bacteria
k = growth constant
t = time taken for growth
Now we plug in the values in the formula
[tex]P_{t}[/tex] = 500
[tex]P_{0}[/tex] = 300
Time t = 4 hours
[tex]500=300e^{4k}[/tex]
[tex]e^{4k}=\frac{500}{300}[/tex]
Now we take the natural log (ln) on both the sides
[tex]ln(e^{4k})=ln(\frac{500}{300})[/tex]
4k(lne) = ln(500) - ln(300)
4k = 6.2146 - 5.7038
4k = 0.5108
k = [tex]k=\frac{0.5108}{4}=0.1277[/tex]
a). Recursive formula for the sequence formed by the bacterial growth
Since [tex]P_{t}=(1+r)P_{t-1}[/tex]
500 = (1 + r)300
[tex](1+r)=\frac{5}{3}[/tex]
r = [tex]\frac{5}{3}-1=\frac{2}{3}[/tex]
Therefore, the recursive formula will be
[tex]P_{t}=\frac{5}{3}P_{t-1}[/tex]
b). Explicit formula for the number of the bacteria will be
[tex]A_{t}=300e^{0.1277\times t}[/tex]
c). We have to calculate the number of bacteria after 24 hours
[tex]A_{t}=300e^{0.1277\times 24}[/tex]
[tex]A_{t}=300e^{3.0648}[/tex]
[tex]A_{t}=300\times 21.43[/tex]
[tex]A_{t}=6429[/tex] bacteria
12+5x-8=2(6X-5)
show all work plz
Estimate the product of 75x5
Answer:
375
Step-by-step explanation:
Simplify. 14.2 • (–6) ÷ 15 • (–4) ÷ 0.4 A. –56.8 B. –3.55 C. 56.8 D. 3.55
In a lottery game you pick ine number from 000 to 999. If you pick one such number, what is the probability that you will win the lottery
Find the slope of the line containing the points (3,8) (1,8)
What's the correct name for the polygon below?

A. Octagon B. Nonagon C. Pentagon D. Heptagon
An object is launched vertically in the air at 24.5 meters per second from a 11-meter-tall platform. Using the projectile motion model h(t)=-4.9t^2+v0t+h0, where h(t) is the height of the projectile t seconds after it’s departure, v0 is the initial velocity in meters per second, and h0 is the initial height in meters, determine how long it will take for the object to reach its maximum height. What is the maximum height?
The object will take 2.5 seconds to reach its maximum height. The maximum height attained by the object will be 42.375 meters.
To find how long it takes for the object to reach its maximum height, we can use the projectile motion formula
h(t) = -4.9t² + v0t + h0.
The maximum height is achieved when the vertical velocity component is zero. This happens midway through the flight.
The time to reach maximum height can be found using the formula
t = v0 / g,
where v0 is the initial velocity and
g is the acceleration due to gravity (9.8 m/s²).
In this case, v0 = 24.5 m/s and g = 9.8 m/s², so the time (t) to reach maximum height is
t = 24.5 m/s / 9.8 m/s² = 2.5 s.
The maximum height (H) can be calculated as the initial height plus the displacement due to the initial velocity upwards before it starts coming down.
Since we know the time to reach the maximum height, we can plug it into the original equation h(t) to find the maximum height:
H = -4.9(2.5)² + 24.5(2.5) + 11
We then find that
H = 42.375 m.
The perimeter of a rectangular field is 380yd. The length is 50 yd longer than the width. Find the dimensions.
The length of the given rectangular field is 120 yd while the width is 70 yd.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the length of a rectangle is L while the width is W
So,
Perimeter 2(L + W) = 380
And,
L = W + 50
By substitution,
W + 50 + W = 190
2W + 50 = 190
2W = 140
W = 70
And
L = 70 + 50 = 120
Hence "The length of the given rectangular field is 120 yd while the width is 70 yd.
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4 different math books, 6 different physics books and 2 different chemistry books are to be arranged on a shelf. how many different arrangements are possible if
Show how to equate
- 15 + 12.8
how to equate: to add 12.8 to -15 subtract 12.8 from 15
15-12.8 =2.2
since 15 is negative and is larger than 12.8 the answer would be negative so 2.2 becomes -2.2
-15 + 12.8 = -2.2
-15 + 12.8 equates to -2.2 by subtracting the smaller absolute value from the larger one and considering the sign of the number with the larger absolute value. The solution involves basic arithmetic with negative and positive numbers.
Solving the Equation -15 + 12.8
To solve the equation -15 + 12.8, follow these steps:
Consider the two numbers: -15 (a negative integer) and 12.8 (a positive decimal).When adding a positive number to a negative number, subtract the smaller absolute value from the larger absolute value.The absolute values are: |12.8| = 12.8 and |-15| = 15. So, subtract 12.8 from 15.15 - 12.8 = 2.2Since the larger absolute value is from the negative number (-15), the result will be negative.Therefore, the solution is -2.2.So, -15 + 12.8 equates to -2.2.
What is 2 2/5 x 1/4=
A baseball used in major league games weighs at least 5 oz and not more than 5.25 oz.About what is that range measured in grams?Explain your reasoning.
630 meters in 18 seconds write this ratio as a unit rate
divide 630 by 18
630/18 = 35
so unit rate would be 35 meters per second
Compare and Contrast: Below are two equations. Solve each equation and compare the two solutions. Choose the statement that is true about each solution. (3 points)
Equation #1
|2x - 3| = -17
Equation #2
|5x + 3| = 12
a-Equation #1 and Equation #2 have the same number of solutions.
b-Equation #1 has more solutions than equation #2.
c-Equation #1 has fewer solutions than equation #2.
d-None of the statements above describe the number of solutions to equations shown.
Jill wants to put 45 sunflower seeds, 81 corn plants, and
63 tomato plants in her garden. If she puts the same
number of plants in each row and if each row as only
one type of plant, what is the greatest number of plants
that Jill can put in one row?
Listed below are four different cases in which a comparison of means was conducted. match the case to the appropriate set of equations needed to compare the means.
The cases can be categorized by comparing the means as follows: 'B. Two proportions' apply to situations like income bracket and voter likelihood comparison, 'C. Matched pairs, dependent groups' apply to dependent groups like a math test given to third graders, 'D. exclusive groups' represent separate unaffected and experimental groups, and 'A. Two independent means, normal distribution' refers to situations where two separate groups are compared.
Explanation:From the details given, we can classify the cases by comparing the means as follows:
B. Two proportions: This would apply to the question of politicians comparing the proportion of individuals from different income brackets who might vote for them. It implies two independent groups and hence a comparison of two population proportions. C. Matched pairs, dependent groups: This could describe a scenario like a math exam given to the third-grade children attending ABC school. Two random samples of scores were taken. This represents a dependent groups design in which two means are compared, for instance before and after a treatment. D. exclusive groups: These likely represent two independent means involving separate unaffected (control) groups and experimental groups. An example of this is studies that compare various diet and exercise programs. A. Two independent means, normal distribution: This refers to a situation where two separate groups are compared, such as studies involving independent samples where the sample values selected from one population are not related in any way to the sample values selected from the other population. Learn more about Comparison of Means here:
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y=-3/8x-7 in standard form
To convert the slope-intercept form equation y = -3/8x - 7 into standard form, mulitply by 8 to remove the fraction, then rearrange to form 3x + 8y = -56, making sure the 'A' coefficient is positive.
The student's question asks about rewriting the slope-intercept form equation y = -3/8x - 7 into standard form. To do so, we need to rearrange the equation so that all variables and constants are on one side and the equation is set equal to zero. In standard form, the equation should be written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.
Let's convert the given equation to standard form step by step:
Multiply both sides of the equation by 8 to clear the fraction: 8y = -3x - 56.
Move the 'x' term to the left side by adding 3x to both sides: 3x + 8y = -56.The equation now is in standard form; however, typically, we want A to be positive. Since our A is already positive, we are done.The tax rate is 8.5% what is the tax on $95? Rounded to the nearest hundredth.
The tax on $95 will be equal to $8.08 at the rate of 8.5%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the tax rate is 8.5% the tax on $95 will be calculated as,
Sales tax = 8.5% of 95
Sales tax = 0.085 x 95
Sales tax = $8.08
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In a group of 48 children there are twice as many boys as girls how many girls are they
How many integers between 14 and 3,452 can be divided by 42 with a remainder of zero?
Find the equation, (f(x) = a(x-h)2+ k), for a parabola containing point (-1,0) and having (-3, 4) as a vertex. What is the standard form of the equation?
Answer:
D.The vertex form is f(x) = −(x +3)^2 + 4. The standard form is f(x) = −x2−6x−5.
Step-by-step explanation:
usatestprep
A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
Convert 95 pints to gallons. Round to one decimal point. Please show your work
how many twelfths are in 3?
Answer:
36 twelfths.
Step-by-step explanation:
We are asked to find number of twelfths are in 3.
We can write 3 as a fraction as:
[tex]\frac{3}{1}[/tex]
To convert our given number to twelfths, we will multiply numerator and denominator of our fraction by 12 as:
[tex]\frac{3}{1}\times \frac{12}{12}[/tex]
[tex]\frac{3\times 12}{1\times12}[/tex]
[tex]\frac{36}{12}[/tex]
Therefore, there are 36 twelfths in 3.
A fair die will be rolled 11 times. what is the probability that 1, 2, or 3 is rolled exactly 4 times? round your answer to four decimal places.
The probability of a 1, 2, or 3 is 3/6 = 1/2. There are C(11,4) = 11!/(4!(11-4)!) = 330 ways the desired outcome can show up in the 11 rolls. The probability is
... 330×(1/2)⁴(1/2)⁷ = 330/2048 ≈ 0.1611
In a standard normal curve, what percentile corresponds to a z score of 1.0?
The bottom floor of a parking garage has an elevation of -36 feet. The top floor is 124 feet higher. What is the elevation of the top floor
The set of possible values of m is {5,7,9}. What is the set of possible values of k if 2k=m+3?
Dakota runs a half-marathon every 6 weeks, and Madison runs a half-marathon every 15 weeks. If they start now, in how many weeks will they again be running a half marathon at the same time?
Answer:
30 weeks
Step-by-step explanation:
Given : Dakota runs a half-marathon every 6 weeks,
Madison runs a half-marathon every 15 weeks
To Find : . If they start now, in how many weeks will they again be running a half marathon at the same time?
Solution :
Since Dakota runs a half-marathon every 6 weeks, Madison runs a half-marathon every 15 weeks
So, to calculate If they start now, in how many weeks will they again be running a half marathon at the same time
We will take the LCM (lowest common factor) of 6 and 15
3 | 6,15
2 | 2,5
5 | 1,5
| 1,1
LCM = 3*2*5 =30
The LCM of 6 and 15 is 30
So, If they start now, in 30 weeks they will again be running a half marathon at the same time
how would a weather reporter say 0.103 meters of snow