does someone mind helping me with this question? Thank you!

Answer:

4860 bacteria

Step-by-step explanation:

The given scenario can be modelled using an exponential function with base e.

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$y=Ae^{kx}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $k$ is some constant.\\\end{minipage}}[/tex]

Define the variables:

Given the initial number of bacteria is 20, then A = 20.

[tex]\implies y=20e^{kx}[/tex]

If the bacteria triples its number in 16 hours, then when x = 16:

[tex]\implies y=3 \times 20= 60[/tex]

Substitute x = 16 and y = 60 into the equation and solve for k:

[tex]\begin{aligned}y&=20e^{kx}\\\implies 60&=20e^{16k}\\\dfrac{60}{20}&=e^{16k}\\3&=e^{16k}\\\ln 3&=\ln e^{16k}\\ \ln3&=16k \ln e\\\ln3&=16k\\k&=\dfrac{1}{16} \ln 3\end{aligned}[/tex]

Therefore, the equation that models the given scenario is:

[tex]\large\boxed{y=20e^{\left(\frac{1}{16}x \ln 3\right)}}[/tex]

To find how many bacteria there are after 80 hours, substitute x = 80 into the equation and solve for y:

[tex]\implies y=20e^{\left(\frac{1}{16}(80) \ln 3\right)}[/tex]

[tex]\implies y=20e^{\left(5 \ln 3\right)}[/tex]

[tex]\implies y=20e^{\left(\ln 3^5\right)}[/tex]

[tex]\implies y=20e^{\left(\ln 243\right)}[/tex]

[tex]\implies y=20 \cdot 243[/tex]

[tex]\implies y=4860[/tex]

Therefore, there are 4860 bacteria after 80 hours.

-----------------------------------------------------------------------------------------------

Please note that I have solved this question so that you can calculate the number of bacteria for any number of hours, part hours, etc.

However, there is a much simpler way of solving this particular question.

If the number of bacteria triples every 16 hours, then it will triple 5 times within 80 hours since 80 ÷ 16 = 5.

Therefore:

As you can see, the result is the same as the previous method.

Answer:

y = 5/6x+11/12

Step-by-step explanation:

divide by -1 on both sides to get 10x+11=12y

divide by 12 on both sides

Answer:

c) 4/3

Step-by-step explanation:

Answer:

-4t ≥ -2/5

Step-by-step explanation:

t≥0.1

The total number of students participating in a school club or sport is 105.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Given that three out of 5 students at Maria's school participate in a school club or sport and there are 175 students at the school.

In this situation, the number of people that participate will be:

= Fraction utilized × Total number of students

= 3/5 × 175

= 105

The number of people is 105.

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3+4=7 is the total of all possible integer values of n.

Integers include zero, a positive natural number, and a negative integer represented by a minus sign.

The negative numbers are the inverse additions of the comparable positive numbers.

In mathematical notation, the letter Z is widely used to denote a set of numbers.

An integer is a whole number that can be positive, negative, or zero and is not a fraction.

Integer examples include -5, 1, 5, 8, 97, and 3,043.

So, the two inequalities are resolved independently. We add 3n to both sides of the first inequality, -3n7n-20, to find the solution:

Then, we add 20 to both sides to get 010n-20:

20<10n.

Lastly, multiplying both sides by 10 yields 2n, indicating that n must be bigger than 2.

We deduct 3n from both sides of the second inequality, 7n-203n:

Add 20 on both sides of 4n-200 to obtain:

4n<20.

Lastly, n must be less than 5 since the result of dividing both sides by 4 is n5.

Only the numbers 3 and 4 are greater than 2 and less than 5.

Therefore, 3+4=7 is the total of all possible integer values of n.

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Answer:

y=5x+53

Step-by-step explanation:so all i did was go into the demos app and typed in y=5x-7 and then i entered y=5x+30 and i kept going up until i found the right answer

Gambler A loses his comparative advantage the more coins that are tossed for both Gamblers. But Gambler A will always maintain the advantage and has quite a heavy advantage when a few coins are tossed.

What is the binomial distribution?

The discrete probability distribution of the number of successes in a series of n independent experiments is called the binomial distribution with parameters n and p in probability theory and statistics.

Let X be the count of successes in the first n flips by A, Y the indicator that the last flip by A is also a success, and Z the count of successes in n flips by B.

Because Y is independent of X and Z, then:

P(X + Y > Z) = P(Y = 1) P(X ≥ Z) + P(Y = 0) P(X > Z)

= 1/2(P(X = Z) + 2P(X > Z))

P(X > Z) = P(Z > X)

Gambler A loses his comparative advantage the more coins that are tossed for both Gamblers. But Gambler A will always maintain the advantage and has quite a heavy advantage when a few coins are tossed.

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The height of the triangle is 32 mm

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The area of a triangle can be represented as follows:

area of a triangle = 1 / 2 bh

where

Therefore, the triangle has an area of 32 mm² and base of 8 mm. Let's find the height of the triangle as follows:

area of a triangle = 1 / 2 bh

32 = 1 / 2 × 8 × h

4h = 32

divide both sides by 4

h = 32 / 4

h = 8 mm

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Answer:

0 , All real numbers are solutions.

Step-by-step explanation:

Let's solve your equation step-by-step.

−4(v+1)+6v=2(v+2)−8

Step 1: Simplify both sides of the equation.

−4(v+1)+6v=2(v+2)−8

(−4)(v)+(−4)(1)+6v=(2)(v)+(2)(2)+−8(Distribute)

−4v+−4+6v=2v+4+−8

(−4v+6v)+(−4)=(2v)+(4+−8)(Combine Like Terms)

2v+−4=2v+−4

2v−4=2v−4

Step 2: Subtract 2v from both sides.

2v−4−2v=2v−4−2v

−4=−4

Step 3: Add 4 to both sides.

−4+4=−4+4

0=0

Answer:

no solution

Step-by-step explanation:

-4(v + 1) + 6v = 2(v + 2) - 8

-4v - 4 + 6v = 2v + 4 - 8

2v - 4 = 2v - 4

0 = 0

no solution

Answer: 2n!

Step-by-step explanation:

6N -4 N =2N

Answer:

22.5

Step-by-step explanation

22.5 is the correct answer because 4.50 times 5 is 22.5 :))))

Answer:

22.5

if one baseball cost $ 4.50 , we multiply it by 5 , or add 4.50+4.50+4

.50+4.50+4.50 same thing.

The value of the function f(x) = -3x+4 is -3x+5

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given a function, f(x) = -3x+4

g(x) is described as f(x) +1

g(x) = -3x+4+1

g(x) = -3x+5

The graph of f(x) will move 1 unit farther when transformed into g(x).

Hence, The value of the function f(x) = -3x+4 is -3x+5

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Answer:

y = -5x -8

Step-by-step explanation:

The slope must be the negative reciprocal(-5). So we have y = -5x + b, where we need to find b. To do that, we will plug in the known point. This gives us [tex]-3 = -1 * -5 + b[/tex], or[tex]-3 = 5 + b[/tex]. We subtract 5 from both sides to get b = -8.

The nth partial sum of an infinite sequence is the sum of first n terms starting from the first one. The partial sum of the sequence is given as 280.

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

Given that,

The sequence is  13,22,31,40....

The first term of the sequence is a₁ = -13.

The  difference between consecutive terms is,

22 - 13 = 9

31 - 22 = 9

And, 40 - 31 = 9

Since, the difference between two consecutive terms are same, the given sequence is arithmetic.

The sum of first n terms of an arithmetic sequence is given as,

Sₙ = n/2(2a₁ + (n - 1)d)

Substitute n = 7 to obtain,

S₇ = 7/2(2 × 13 + (7 - 1) × 9)

    = 7/2 × 80

    = 280

Hence, the seventh partial sum of the given sequence is 280.

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Answer:

m > -20

Step-by-step explanation:

Multiply the 5 on both sides. Now you have 3m > -60. Divide both sides by 3. Now you have m > -20.

Voila

Distinct value of x, y, z are will be 3

Consider the function will be f(x) = x3 - x2 - 2x +2 = ( x - 1 ) (x2 - 2 )

we have three real roots and ,

x + y + z = - 1/ (-1)

= 1 ,

1/x + 1/y + 1/z = -2 /(-2)

= 1

Consider the function

f(x) = x3 - x2 - 40 + 20.

Set the derivation equal 0 we get x = 4 and x = -10/3

are two local extrema. When x= 4 , f(x)<0,when x = -10/3 . f(x) >0 there are three real roots . we have x + y + z = 1 and 1/x + 1/y + 1/z = - (-40)/ 20 = 2

consider the function

f(x) = x3 - x2- 40x + 40/3 .

we still have same local extrema as (2) and we have x= 4 , f(x) < 0 and we

x= -10/3 , f(x) > 0 so there are three real roots. We have x+ y + z = 1 and 1/x + 1/y + 1/z = -(-40)/40/3 = 3

So, there are 3 distinct values

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Answer:

20/50

Step-by-step explanation:

40% is equal to 40/100

40/100 is equal to 20/50

The minimum value within a 1 sd range of the average as calculated from the given data is  1.84 ml.

standard deviation range = [average - SD, average + SD]

Here ,

the maximum value =

average - SD = 2.5 - 0.66 = 1.84  ml

and the maximum value =

average + SD = 2.5+ 0.66 = 3.16 ml

Both the standard deviation and range are indicators of how widely distributed a set of data is. Given that they are both measures of variance, each number conveys to us in its own particular way how dispersed the data are.

Although the range and standard deviation do not directly correlate, there is a general method that can be used to connect these two statistics. The range rule for standard deviation is another name for this connection.

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After covering 194 miles, Mr. Etrada's car can go a maximum of 316 miles with the gas still in the tank and the inequality that represents the given situation is x + m ≤ 510.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign.

It is an illustration of inequity.

This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

Finding the x numbers for which the inequality holds true is what we are most interested in.

So, the inequality that can represent the given situation is:
x = total distance traveled

m = miles that the gas will allow you to go

The maximum number of miles per full tank is 510.

Then,

x + m ≤ 510

194 + m ≤ 510

m ≤ 510 - 194

m ≤ 316

Therefore, after covering 194 miles, Mr. Etrada's car can go a maximum of 316 miles with the gas still in the tank and the inequality that represents the given situation is x + m ≤ 510.

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109.5° is the bond angle between two nearby hybrid orbitals. sp3 will be the hybridization.

The hybridization would be sp3. This is because the bond angle of 109.5° is characteristic of hybridized orbitals with four sp3 orbitals, which form an angle of 109.5°. sp3 hybridization occurs when one s orbital and three p orbitals mix to form four sp3 hybrid orbitals.

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Answer:

7/3 or 3

Step-by-step explanation:

Step by step explanation is shown in the picture attached.

Hope it helps

Mary Beth Mars, develops a Pareto chart using the information. The recommendations that you would make is as follows:

A graph containing both bars and a line, the bars representing individual values in descending order and the line representing the cumulative total, is known as a Pareto chart. The Pareto chart allows us to concentrate on it when we need to. The Pareto chart is built upon the 80%-20% run of the show. The Pareto chart states that 20% of arrangements assist in resolving 80% of issues. The complex manager, Mary Beth Marrs, must concentrate on issues with the pool, the ground, and the stopping part in order to satisfy the majority of residents and reduce complaints.

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The margin of error that corresponds to a 95 % confidence interval for the proportion of residents that are opposed to the use of photo - cops for issuing traffic tickets is 0.04.

Given:

in a survey of 500 residents, 300 were opposed to the use of photo-cops for issuing traffic tickets.

Sample size n = 500

Number of success X = 300

Sample proportion p = X/n

= 300/500

= 30/50

= 3/5

= 0.6

z score at 95% = 1.96

Margin of error = z * [tex]\sqrt{p(1-p)/n}[/tex]

= 1.96 * [tex]\sqrt{0.6(1-0.6)/500}[/tex]

= 0.04

Therefore the margin of error that corresponds to a 95 % confidence interval is 0.04.

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The equation of the perpendicular line to x + 6y = 42 is: y = 6x + 1.

The lines that are perpendicular to each other will have slope values that have a product of -1, which means one is a negative reciprocal of the other.

Given the equation, x + 6y = 42, it can rewritten in slope-intercept form as shown below:

6y = -x + 42

6y/6 = -x/6 + 42/6

y = -1/6x + 7

The slope of the line is -1/6. The negative reciprocal of -1/6 is 6. Therefore, the slope of the line that is perpendicular to x + 6y = 42 is 6.

Substitute m = 6 and (x, y) = (1, 7) into y = mx + b to find the y-intercept (b):

7 = 6(1) + b

7 = 6 + b

7 - 6 = b

b = 1

Tp write the equation of the perpendicular line, substitute m = 6 and b = 1 into y = mx + b:

y = 6x + 1

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The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;

a. Interest for the first quarter = $8.125

b. First quarter ending balance = $6,508.125

c. Interest for the second quarter = $8.13515625

d. Second quarter ending balance = $6,516.26015625

e. Interest for the third quarter = $8.1432520325

f. Third quarter closing balance = $6,524.40548145

g. Interest for the fourth quarter = $8.15550685975

h. The amount of interest earned in a year is about $32.56

An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.

The amount Fred deposited, P = $6,500

The interest paid by the account, r = 0.5% compounded quarterly

a. The first quarter interest can be found by the formula;

[tex]C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times \dfrac{1}{4} }- P[/tex]

Therefore;

[tex]C.I. = 6500\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6500 = 8.125[/tex]

The interest after the first period is $8.125

b. The first quarter ending balance is therefore;

A = P + C.I.

A = $6,500 + $8.125 = $6,508.125

c. The second quarter's interest can be found from the formula;

[tex]C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times t} - P[/tex]

Here, P = The balance from the first quarter = $6,508.125

t = 1/4 for one quarter

Therefore;

[tex]C.I. = 6508.125\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6508.125 = 8.13515625[/tex]

The second quarter's interest is $8.13515625

d. The second quarter ending balance is therefore;

A = $6,508.125 + $8.13515625 = $6,516.26015625

The second quarter ending balance is $6,516.26015625

e. The third quarters interest is therefore;

[tex]C.I. = 6516.26015625\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6516.26015625 = 8.1432520325[/tex]

The third quarter's interest is about $8.1433

f. The third quarter's ending balance is therefore;

A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145

The third quarter's ending balance is $6,524.40548145

g. The fourth quarter's interest can be found as follows;

[tex]C.I. = 6,524.40548145 \times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6524.40548145 = 8.15550685975[/tex]

The fourth quarter's interest is; $8.15550685975

h. The balance at the end of one year is therefore;

Balance = C.I. fourth quarter + Principal for the fourth quarter

Therefore;

Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831

i. The interest the account earns in a year is therefore;

$6,532.56098831 - $6,500 = $32.5609883

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Answer:

The 4th scatter plot indicates a linear relationship

Step-by-step explanation:

The first and third scatter plot graphs are too noisy to indicate a proper trend. The second scatter plot is quadratic and the fourth one is linear.

The distance from Lakewood than to Bluepoint is 17.98 miles.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Distance between Bluepoint to Arcadia = 5.38 miles.

Distance between Arcadia to Lakewood= 12.6 miles.

Distance between Lakewood to Dayton = 12.88 miles.

So, the distance from Lakewood than to Bluepoint

= 12.6 +5 .38

= 17.98 miles

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