Number 1 please answer need help

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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(A) stamped envelope will cost 5+s pence

6 stamped envelopes will cost 6(5+s) pence

n stamped envelopes will cost n(5+s) pence

(B) expanded form of the ii part is 30+6s pence

and expanded form of the iii part is 5n+ns pence

As an envelope cost 5 pence and stamp cost s pence

(I) to get an stamped envelope we need to buy an envelope and the we have to get a stamp so the collective sum will be the cost that is

5+s pence

(II)to get 6 stamped envelope we need to buy 6 envelopes and the we have to get 6 stamps so the collective sum will be the cost that is

6(5+s) pence

(III))to get n stamped envelope we need to buy n envelopes and the we have to get n stamps so the collective sum will be the cost that is

n(5+s) pence

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Answer:

Step-by-step explanation:

There are 5 cans left over after painting the walls.

Let x represent the maximum number of trims that can be painted

Since each trim requires 1/2 a can, x trims will take x/2 cans

This cannot exceed 5 cans so we get the inequality:
x/2 ≤  5

Multiplying by 2 both sides of inequality:
x  ≤ 10

In words:
Maximum number of trims that can be painted with 5 cans is 10

Number line attached

There are 495 different possible orders for the group to choose from

To determine the number of different possible orders for the group, we can use the combination formula, which is:
C(n, k) = n! / (k!(n-k)!)
In this student question, there are 12 different main dishes (n = 12), and the group collectively orders 4 different dishes to share (k = 4).

So, we can plug these values into the formula:
C(12, 4) = 12! / (4!(12-4)!)
C(12, 4) = 12! / (4! * 8!)
C(12, 4) = (12 * 11 * 10 * 9 * 8!)/(4 * 3 * 2 * 1 * 8!)
The 8! terms cancel out, leaving:
C(12, 4) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
C(12, 4) = 11,880 / 24
C(12, 4) = 495
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Always choose the alpha level as 0.05.

The given statement;

When conducting a significance test in practice, how should you choose the alpha( α ) level,

→ When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a greater alpha. Since it's the most appropriate in every case, choose alpha ( α ) = 0.05 always. When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha.

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The given "proof" is incomplete and does not prove the reflexivity of the relation R.

A reflexive relation is one in which each element maps to itself in terms of relationships and functions. Consider a set A = 1, 2, for instance. R = (1, 1), (2, 2), (1, 2), (2, 1) will now be the reflexive relation.

The given "proof" is indeed invalid. Let's examine the steps to identify the flaw:

i. Suppose a ∈ A.

ii. Take an element b ∈ A such that (a, b) ∈ R.

iii. Because R is symmetric, we also have (b, a) ∈ R.

iv. Because R is transitive, (a, b) ∈ R and (b, a) ∈ R, we have (a, a) ∈ R, as desired.

The flaw in this proof is that it assumes the existence of an element b such that (a, b) ∈ R. However, there is no guarantee that such an element exists for every element a ∈ A.

To show that R is reflexive, we need to demonstrate that for every element a ∈ A, (a, a) ∈ R. This requires examining all possible pairs of the form (a, a) and checking if they are in R.

Therefore, the given "proof" is incomplete and does not prove the reflexivity of the relation R.

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Answer:

150cm²

Step-by-step explanation:

In a trapezoid, the length of one base is equal to its height and the length of the other base is twice its height. If the height is 10 centimeters, what is the area of the trapezoid?

The formula for the area of a trapezoid = 1/2(a + b) h

Where a = Length of the first base

b = Length of the second base

h= height of the trapezoid

h = 10cm

The length of one base is equal to its height

Hence:

a = h = 10cm

The length of the other base is twice its height.

b = 2h

h = 10cm

b = 10 × 2 = 20cm

Therefore, the Area of the Trapezoid =

1/2 (20 + 10)10

1/2 × 30 × 10

= 150cm²

Answer:

Yes, the runners number of strides will fit evenly into the length of the race.

Step-by-step explanation:

The bridge is 138,435 feet. You would divide this to get 46,145 as a whole number.

Answer:

Step-by-step explanation:

You are dividing 138435 by 3.

The quotient would be 46145 with no remainder. So the answer would be yes.

A 2nd way to do this is to see if 183435 is a multiple of 3.

Hope this helps!

Have a great day!

As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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We need to know simple division to solve the problem. The maximum number of men in the lift is 8 and the maximum number of women in the lift is 10.

We will be using the simple concept of division to find the number of people that the lift can carry. The average weight of a man is given to be 84 kg and the average weight of  a woman is given to be 70kg. The lift can carry 720 kg, we will find separately the number of men and women that can be carried in the lift. Inorder to find the maximum number of men we divide the total weight the lift can carry by the average weight of a man, we will similarly calculate the maximum number of women.

number of men= 720/84=8.57 which means that the number of men is 8

number of women =720/70=10.28 which means that number of women is 10.

Therefore the lift can carry at most 8 men and at most 10 women.

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The correct statements are:

1. If the product AB = 0 (zero matrix), then either A = 0 or B = 0.

4. BC = CB.

Explanation:

1. If the product of two matrices AB equals the zero matrix, it implies that at least one of the matrices A or B (or both) must be the zero matrix for the product to result in zero.

4. The statement BC = CB states that the order of multiplication of matrices B and C does not affect the resulting matrix. This property holds true for matrices of any size as long as the dimensions are compatible for matrix multiplication.

The other statements are not necessarily true in general:

2. Both BC and CB being square matrices is not guaranteed. The product of two matrices can result in a square matrix only if the number of columns of the first matrix is equal to the number of rows of the second matrix. In this case, B has 3 columns and C has 2 rows, so BC and CB are not square matrices.

3. The matrix A + BC is not defined since the addition of matrices requires them to have the same dimensions. In this case, A is a 2×2 matrix, while BC is a 2×3 matrix, so they cannot be added together.

5. The statement A = A12​ = I2​ implies that matrix A is equal to the 2×2 identity matrix I2​. However, this is not necessarily true as the given information does not provide any details about the values or properties of matrix A.

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Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Standard deviation = √ {(xi – x)^2 / (n-1)}

here (xi – x)^ 2 means variance and n is sample size .

so we can say

Standard deviation = √{ (variance / sample size – 1 )}

here variance is 64.58 and sample size is 26 is given.

So stand deviation = √{64.58 / (26-1)}

standard deviation =0.32144673

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the standard deviation will be 0.32144673 for the data having variance as 64.58 and sample size as 26.

Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Standard deviation = √ {(xi – x)^2 / (n-1)}

here (xi – x)^ 2 means variance and n is sample size .

so we can say

Standard deviation = √{ (variance / sample size – 1 )}

here variance is 64.58 and sample size is 26 is given.

So standard deviation = √{64.58 / (26-1)}

standard deviation = 0.32144673

Therefore, the standard deviation will be 0.32144673 for the data having variance as 64.58 and sample size as 26.

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At the end of the year, Achley Company's owner's equity is $4,685,000 and can be calculated by starting with the beginning owner's equity, adding the revenues, subtracting the expenses, and subtracting the owner's withdrawals.

To calculate Achley Company's owner's equity at the end of the year, we start with the beginning owner's equity of $5,175,000. We then add the revenues of $225,000 and subtract the expenses of $165,000. This gives us the net income, which is the difference between revenues and expenses, and represents the increase in owner's equity.

So, net income = revenues - expenses = $225,000 - $165,000 = $60,000. Next, we subtract the owner's withdrawals of $550,000 from the net income. Owner's withdrawals are personal expenses or cash withdrawals made by the owner and reduce the owner's equity.

Owner's equity at the end of the year = Beginning owner's equity + Net income - Owner's withdrawals.Owner's equity at the end of the year = $5,175,000 + $60,000 - $550,000. Calculating the above expression, we find that Achley Company's owner's equity at the end of the year is $4,685,000.

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Answer:

b

Step-by-step explanation:

Each value inside the parenthesis is raised to the exponent outside , then

\(abc)^{4}\)

= \(a^{4}\)\(b^{4}\)\(c^{4}\) → b

The truth value of the conditional statement is false, and the counterexample of this statement is corresponding angles

The conditional statement is given as:

If two angles are congruent, then they are vertical angles.

The above statement is false because not all congruent angles are vertical angles

A counterexample of this statement is a corresponding angle

i.e. corresponding angles are congruent angles, but they are not vertical angles

Hence, the truth value of the conditional statement is false, and the counterexample of this statement is a corresponding angle

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\(\tt Step-by-step~explanation:\)

To solve, we need to write this in slope-intercept form.

\(\tt Step~1:\)

Slope: 3

Point: (1,2)

Slope-intercept form:

y = mx + b (y = y value, m = slope, x = x value, b = y-intercept)

y = 2, m = 3, x = 2, b = ?

We have to solve for b. To do so, we plug in all these values into our formula. Move all values not equal to b to the left of the equation.

\(\tt 2 = 3(1)+b\\2=3+b\\2-3=3-3+b\\-1=b\)

\(\tt Step~2:\)

Now that we know what b is, we can plug it into our equation. Plug in only the value of the slope and the y intercept.

y = mx + b

y = 3x - 1

\(\large\boxed{\tt Our~final~answer:~y=3x-1}\)

To solve the given linear programming problem using the graphical method, we can plot the constraints and then find the feasible region.

Then we can find the optimal solution by plotting the objective function and finding the minimum value within the feasible region. So, the given LP problem is:\(Min Z = 25A + 25Bsubject to:4A + 3B ≥ 245A + 27B ≥ 24A, B ≥ 0\)Let's plot the constraints one by one:\(4A + 3B ≥ 24On plotting 4A + 3B = 24,\) we get a straight line passing through the points (0, 8) and (6, 0) as shown below:\(5A + 27B ≥ 24On plotting 5A + 27B = 24\), we get a straight line passing through the points (4.8, 0) and (0, 0.89) as shown below:

The optimal solution is the point where the objective function intersects the feasible region. This occurs at the point (4, 4) with \(Z = 25(4) + 25(4) = 200\).Hence, the optimal solution of the given LP problem is \(A = 4, B = 4 and Z = 200.\)

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The equation of the line is (y + x = 0).

The slope of a line indicates its steepness in addition to its direction.

m = Δy/Δx

where, m is the slope

And, tan θ = Δy/Δx

The above tan is also known as the line's slope.

The slope of a line can also be calculated just using two straight line points. The slope of line formula could then be used with two point coordinates.

Now, in response to the question;

P₁ = (x₁, y₁)

P₂ = (x₂, y₂)

Then slope will be;

Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)

Consider the values given in the question;

(x₁, y₁) = (-1,-3) and,

(x₂, y₂) = (1,-5).

Put the values in the formula of the slope;

Slope = m = (-5 + 3)/(1 + 1)

m = -2/2

m = -1

Thus, the slope of the line is -4.

Now, the formula for finding the equation of line using the two points system.

(y - y₁) = m(x - x₁)

(y + 3) = (-1)(x + 1)

y + 3 = -x - 1

y + x + 4 = 0.

Therefore, the equation of the line using two point system is calculated as (y + x = 0).

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Answer: y = -5

Here you go

Explanation:

The graph of the linear equation y = -1/3x, aka y = -x/3, goes through the points (0,0) and (3,-1). To generate any point, plug in a value for x to get its paired value of y.

Another way to graph this line is to start at (0,0). Then move down 1 and over to the right 3 units to arrive at (3,-1). Draw a straight line through those points.

The graph is shown in the diagram below. Points B, C, F, H, J are all below that red line.

Therefore, the average value of f(x) on the closed interval [2, 6] is:-1.848

To find the average value of f(x) on the interval [2, 6], you need to use the formula for the average value of a function. That formula is given as:

average value of f(x) = (1/(b-a)) * ∫[a,b] f(x)dx

Here, a = 2 and b = 6. So, we have:

average value of f(x) = (1/(6-2)) * ∫[2,6] f(x)dx

Now, f(x) = (x² + x)cos(5x).

Therefore,∫[2,6] f(x)dx = ∫[2,6] (x² + x)cos(5x) dx

This integral can be evaluated using integration by parts.

Let u = (x² + x) and dv = cos(5x)dx.

Then, du/dx = 2x + 1 and v = (1/5)sin(5x).

Using the integration by parts formula, we have:

∫(x² + x)cos(5x)dx = uv - ∫vdu= (x² + x)(1/5)sin(5x) - ∫[(1/5)sin(5x)][(2x + 1)dx]= (x² + x)(1/5)sin(5x) - (2/25)cos(5x) - (2/25)xsin(5x) + C

Putting the limits of integration, we get:

∫[2,6] f(x)dx = [(6² + 6)(1/5)sin(5(6)) - (2/25)cos(5(6)) - (2/25)6sin(5(6))] - [(2² + 2)(1/5)sin(5(2)) - (2/25)cos(5(2)) - (2/25)2sin(5(2))]≈ -1.848

Therefore, the average value of f(x) on the closed interval [2, 6] is:-1.848

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We can see that there are 6 sections and three of them are yellow. So, the theoretical probability of the spinner landing on the yellow section is:

3 ( yellow sections)/ 6 (Total number of sections)

3/6 = 1/2 (Simplifying)

The answer is 1/2.

\(\huge\underline{\frak{ \: \: \: \: \: \: Solution : \: \: \: \: \: \: }} \\ \\ \)

\(\frak {\pink{Let}}\begin{cases} \sf{\red{Breadth \: be \: x}}\\ \sf{\orange{The \: Length = x + 9}}\end{cases} \\ \)

\(\bigstar \: \underline{\textsf{According to the given Question :} }\\ \\\)

\(:\implies \sf Area = Length \times Breadth \\ \\ \\ \)

\(:\implies \sf 360=(x + 9 ) x \\ \\ \\ \)

\(:\implies \sf 360= {x}^{2} + 9x \\ \\ \\ \)

\(:\implies \sf {x}^{2} + 9x - 360 = 0\\ \\ \\ \)

\(:\implies \sf {x}^{2} + 24x - 15x - 360 = 0\\ \\ \\ \)

\(:\implies \sf x(x + 24) - 15(x + 24) = 0\\ \\ \\ \)

\(:\implies \sf (x + 24) \: (x - 15) = 0\\ \\ \\ \)

\(:\implies \underline{ \boxed{ \sf x = - 24 \: or \: x = 15}}\\ \\ \\ \)

\(\therefore\:\underline{\textsf{Ignoring the negative value, the Breadth of rectangular garden is \textbf{15 ft}}}. \\ \\ \\ \)

\(\bigstar \: \underline{\textsf{Dimensions of rectangular garden :}} \\ \\ \)

\(\bullet\:\:\textsf{The Breadth of rectangular garden = x = \textbf{15 ft.}} \\ \\ \)

\(\bullet\:\:\textsf{The Length of rectangular garden = x + 9 = 15 + 9 = \textbf{24 ft.}} \\ \\ \)

Answer:

Step-by-step explanation:

18 -> 1,2,3,6,9,18

12 -> 1,2,3,4,6,12

heighest common factor is 6.

It will be nice if you give me brainliest. Good luck!

Answer:

prime numbers

Step-by-step explanation:

2 3 7 9 11 13 are set of prime numbers

(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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Answer:

Division problem - 2/5

Fraction - 2/5

Step-by-step explanation:

The answer is the same because in mathematical situations, division and fraction is considered same.

It is not rational to predict that the first ticket will not win in a fair lottery.

In a fair lottery where there are 1000 tickets and only one winning ticket, each ticket has an equal chance of winning. Therefore, the probability of winning for any individual ticket is 1/1000. The fact that the lottery is fair means that there is no inherent bias or pattern that would make one ticket more likely to win over another.

Predicting that the first ticket will not win based on the assumption that the lottery is fair is not a rational prediction. The order in which the tickets are drawn does not affect the probability of any specific ticket winning. Each ticket has an independent and equal chance of being drawn as the winning ticket, regardless of its position in the sequence.

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Answer:

Step-by-step explanation:

First calculate the total number of students in all the schools:

= 618 + 378 + 204  

= 1,200 students

Use this number to calculate the proportion of the total population that a school so that this can then be used to determine the proportion of the 20 delegates they should sent.

North Middle school:  

= 618/1,200 * 20  

= 10 students

Central Middle School:  

= 378 / 1,200 * 20  

= 6 students

South Middle School:  

= 204/1,200 * 20  

= 4 students