the initial number of bacteria in a culture is 12,000. the culture doubles each day. how many bacteria are there after 6 days​

Answer:

a) 1 : 4

b) 60 : 180 or 1 : 3

Step-by-step explanation:

Answer:

a. 1:4

b. 1:3

Step-by-step explanation:

Let’s start with a.

So the ratio 14:56 can be divided in two to 7:28 and they are both divisible by 7 we its most simplified form is 1:4 because 28/7 is 4 and 7/7 is 1.

Now for b.

So if 240 were sold in total and 180 of them were online them doing 240-180, 60 of them were sold in person so the ratio is 60:180 which can be simplified to 30:90 to 15:45 to 3:9 to 1:3.

The gradient of the function f(x, y) = 5xy + 8x^2 at point P = (-1, 1) is ∇f(-1, 1) = (18, -5). The directional derivative  D_u f(x, y) at P = (-1, 1) in the direction from P = (-1, 1) to Q = (1, 2) is D_u f(-1, 1) = -29/√5.


To find the gradient ∇f(-1, 1), we take the partial derivative with respect to x and y. ∂f/∂x = 5y + 16x, and ∂f/∂y = 5x. Evaluating these partial derivatives at (-1, 1) gives ∇f(-1, 1) = (18, -5).

To find the directional derivative D_u f(-1, 1), we use the formula D_u f = ∇f · u, where u is the unit vector in the direction from P to Q. The direction from P = (-1, 1) to Q = (1, 2) is given by u = (1-(-1), 2-1)/√((1-(-1))^2 + (2-1)^2) = (2/√5, 1/√5). Taking the dot product of ∇f(-1, 1) and u gives D_u f(-1, 1) = (18, -5) · (2/√5, 1/√5) = (36/√5) + (-5/√5) = -29/√5. Therefore, the directional derivative is -29/√5.

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Answer:

20,000

Step-by-step explanation:

The current value of Certificate A is approximately $4322.41, and the current value of Certificate B is approximately $4319.03.

For Certificate A the first payment of $2200 is received in three months. The second payment of $2200 is received in six months.

PV = CF / (1 + r)ⁿ

PV = Present Value

CF = Cash Flow

r = Rate of return

n = Number of periods

n = 3/12

n = 0.25

PV₁ = \(\frac{2200}{(1+0.455)^{0.25}}\)

PV₁= 2200 / 1.011349

PV₁ = 2174.24

n = 6/12

n = 0.5

PV₂ =  \(\frac{2200}{(1+0.455)^{0.5}}\)

PV₂ = 2200 / 1.022595

PV₂ = 2148.17

Therefore, the current value of Certificate A is approximately $2174.24 + $2148.17 = $4322.41.

For Certificate B the first payment of $2200 is received in four months. The second payment of $2200 is received in seven months.

PV₁ =  \(\frac{2200}{(1+0.455)^{\frac{6}{12} } }\)

PV₁ = 2200 / 1.014674

PV₁ = 2161.40

PV₂ = \(\frac{2200}{(1+0.455)^{\frac{7}{12} } }\)

PV₂ = 2200 / 1.018202

PV₂ = 2158.63

Therefore, the current value of Certificate B is approximately $2161.40 + $2158.63 = $4319.03.

The current value of Certificate A is approximately $4322.41, and the current value of Certificate B is approximately $4319.03.

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To show that both the sequences {a} and {bn} converge, it is necessary to confirm that an is bounded from below while bn is bounded from above.

In order for a sequence to converge, it must be both monotonic (either increasing or decreasing) and bounded. In this case, we are given that {an} is monotonically decreasing and {b} is monotonically increasing.

To prove that {an} converges, we need to show that it is bounded from below. This means that there exists a value M such that an ≥ M for all n. Since {an} is monotonically decreasing, it implies that the sequence is bounded from above as well. Therefore, an is both bounded from above and below.

Similarly, to prove that {bn} converges, we need to show that it is bounded from above. This means that there exists a value N such that bn ≤ N for all n. Since {bn} is monotonically increasing, it implies that the sequence is bounded from below as well. Therefore, bn is both bounded from below and above.

In conclusion, to establish the convergence of both {a} and {bn}, it is necessary to confirm that an is bounded from below while bn is bounded from above.

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Answer:

40%

Step-by-step explanation:

Investment in automation cost = $8,750,000 when there

no further change in capacity.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Following are the informations of Cent:

Current automation = 7%

Capacity of next round = 1,100

New automation = 7 + 2 = 9

Investment in automation cost = Capacity * (4 * (New automation - previous automation)) * 1000

= 1,100 * (4 * (9 - 7)) * 1,000

= 1,100 * (4 * 2) * 1000

= 1,100 * 8 * 1,000

= $8,800,000.

Investment in automation cost = $8,800,000.

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The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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The given equation is$\frac{5}{7}=\frac{a_2}{a_3}\times \frac{a_4}{a_5}\times \frac{a_6}{a_7}$Now, let us take $a_2=5$ and $a_4=1$. Thus, we get, $\frac{5}{7}=\frac{5}{a_3}\times \frac{1}{a_5}\times \frac{a_6}{a_7}$To simplify, we get, $\frac{5a_5a_6}{7a_3a_7}=1$

Hence\(, $5a_5a_6=7a_3a_7$Now, let us take $a_5=7$, $a_6=1$, $a_3=5$ and $a_7=1$.\)Putting the values, we get, $5\times7\times1=7\times5\times1$.Thus,\($a_2=5$, $a_3=5$, $a_4=1$, $a_5=7$, $a_6=1$ and $a_7=1$\) satisfies the given equation $\frac{5}{7}=\frac{a_2}{a_3}\times \frac{a_4}{a_5}\times \frac{a_6}{a_7}$.

Therefore, there is a single sequence of integers \($a_2$, $a_3$, $a_4$, $a_5$, $a_6$, $a_7$\)such that $\frac{5}{7}=\frac{a_2}{a_3}\times \frac{a_4}{a_5}\times \frac{a_6}{a_7}$ and the values are: \($a_2=5$, $a_3=5$, $a_4=1$, $a_5=7$, $a_6=1$ and $a_7=1$.\)

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Step-by-step explanation:

x + y = 25

x = y + 9

so, using the second equation in the first :

y + 9 + y = 25

2y = 16

y = 8

x = y + 9 = 8 + 9 = 17

Answer:

Step-by-step explanation:

probability ∈[0,1]

or probability ≥0

and ≤1

so a,b,g cannot be the probability of an event.

Answer:

See Explanation

Step-by-step explanation:

The probability of an event ranges from 0 to 1.

So, the options c. 0.6, d. 0.888, e. 0 and f. 0.39 represents the probability of an event.

Probability of an event cannot be negative number or more than 1.

Hence, options a. - 1, b. 4.2, g. - 0.5 does not represent the probability of an event.

To find the length of the base of the triangle, we can use the formula for the area of a triangle:

Area = (base * height) / 2

We know that the area of the triangle is 25.8 square meters and the height is 8.6 meters, so we can plug in these values and solve for the base:

25.8 = (base * 8.6) / 2

Multiplying both sides by 2:

51.6 = base * 8.6

Dividing both sides by 8.6:

base = 6

Therefore, the length of the base of the triangle is 6 meters.

Answer:

6 meters

Step-by-step explanation:

Formula for area of a triangle is 1/2 base x height

Since we are looking for base length, we have to work in reverse.

25.8 / 8.6 = 3 meters (half of the base)

To find whole base, times by 2

3 meters x 2 = 6 meters (base length)

The metal in the frame weighs 70.5 kg in total. If a rectangular frame measuring 5 metres in length and 12 metres in width is constructed from five straight pieces of metal.

Get the diagonal

d² = 52 + 122

d² = 25+ 144

d² = 169

d = 13m

Get the perimeter of the rectangular frame:

Perimeter of the frame = 2(5+12) + 13

Perimeter of the frame = 2(17) + 13

Perimeter of the frame = 34 + 13

Perimeter of the frame = 47m

If the weight of the metal is 1.5 kg per metre, the total weight will be expressed as:

Total weight = 47×1.5

Total weight = 70.5kg

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The complete question is

This rectangular frame is made from 5 straight pieces of metal.

5 m

12 m

The weight of the metal is 1.5 kg per metre.

Work out the total weight of the metal in the frame.

Step-by-step explanation:

so, from year 0 to year 1 after arrival the population grows by 5% (= factor 1.05).

as growth means the number of people before plus the additional 5%.

so, we multiply 15,400 by (1 + 0.05) or simply by 1.05.

and in year 2 after arrival we multiply that result again by 1.05.

which is the year 0 number multiplied by 1.05 × 1.05 or simply 1.05².

in year 3 after arrival that result gets multiplied by 1.05. or year 0 multiplied by 1.05×1.05×1.05 or simply 1.05³.

and so on, and so on.

so, we get an exponential function with starting value of 15,400 :

y = 15,400 × (1.05)^x

to calculate the local population x years after the arrival of the large company.

for x = 0 we get the starting value of 15,400.

The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)

The points that are on the line are given below.

(-9, -10), (-3, -1), and (3, 8)

The inequality of the line is given as,

(y - 8) ≥ [(8 + 1) / (3 + 3)] (x - 3)

y - 8 ≥ (3/2)(x - 3)

2y - 16 ≥ 3x - 9

2y - 3x ≥ 7

The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

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Answer: c

Step-by-step explanation:

The probability of a car rolling over in a crash is approximately 0.016, or 1.6%, indicating that it is unlikely for a car to roll over in a crash.

We have,

To find the probability that a randomly selected passenger car crash results in a rollover, we divide the number of rollovers by the total number of crashes:

Probability of a rollover = Number of rollovers / Total number of crashes

Probability of a rollover = 83,600 / (83,600 + 5,127,400) ≈ 0.016

The probability of a rollover is approximately 0.016, or 1.6%.

Since the probability is relatively low, it can be considered unlikely for a car to roll over in a crash.

Thus,

The probability of a car rolling over in a crash is approximately 0.016, or 1.6%, indicating that it is unlikely for a car to roll over in a crash.

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Answer:

62 degrees

Step-by-step explanation:

Points (12,440 and (20,20)

Slope = -3

Equation of line: y - 44 = -3(x - 12)

Plug in x = 6 to get y = 62.

Answer:

Step-by-step explanation:

The given y=x²+4x+3 should be re-written in "vertex form," which is

y = a(x - h) + k, where (h, k) is the vertex.

Here y=x²+4x+3 = y=x²+4x + 4 - 4 +3 (completing the square), or

y = x^2 + 4x + 4 - 1. which condenses to   y = (x + 2)^2 - 1

Thus, h = -2 and k = 1, and so the vertex is at (h, k), or (-2, 1).  This parabola opens up.  The axis of symmetry is the vertical line  x = -2.

An alternative equation for a vertical parabola that opens up is:

y - k = 4p(x - h)^2.  Rewriting y = (x + 2)^2 - 1 to fit this form leads to:

y + 1 = 4p(x + 2)^2.  We must find the value of p that makes this equation true at any (x, y) on the graph.  Suppose we arbitrarily choose x = 1.  Then, according to y=x²+4x+3, y = 1^2 + 4(1) + 3, or y = 8 when x = 1.

Then y - k = 4p(x - h)^2 becomes 8 - 1 = 4p(1 + 2)^2, or

7 = 4p(9), or p = 7/36

The focus is thus 7/36 units above the vertex:  (-2 + 7/36), and the directrix is the horizontal line which is 7/36 units below the vertex:  y = -2 - 7/36.

Vertex:  (-2, 1)

Focus:  (-2, 2 7/36)

Directrix:  y = -2 7/36

Answer:

\(5A + 4P = 10\)

\(5A + 5P = 11\)

1 apple costs $1.2

1 pear costs $1

Step-by-step explanation:

Represent Apples with A and Pears with P

For the person in my front, the expression is:

\(5A + 4P = 10\)

For me, the expression is

\(5A + 5P = 11\)

Hence, the system of equation is:

\(5A + 4P = 10\)

\(5A + 5P = 11\)

Solving for the values of A and P.

Substract equation (2) from (1)

\(5A - 5A + 4P - 5P = 10 - 11\)

\(-P = -1\)

\(P = 1\)

Hence, 1 pear costs $1

Substitute 1 for P in \(5A + 4P = 10\)

\(5A + 4 * 1 = 10\)

\(5A + 4 = 10\)

\(5A = 10 - 4\)

\(5A = 6\)

\(A = \frac{6}{5}\)

\(A = \$1.2\)

Hence, 1 apple costs $1.2

The measure of angle B on the straight line is 22 degrees

When two angles lie along a straight line, they form a straight angle which measures 180 degrees.

The statement from the question can be represented as

m∠A = 4(m∠B + 17.5°)

But we know that the sum of the measures of angles A and B is 180 degrees, since they form a straight angle.

m∠A + m∠B = 180°

Substitute the known values in the above equation, so, we have the following representation

4(m∠B + 17.5°) + m∠B = 180°

Simplifying this equation, we get:

5m∠B + 70° = 180°

Subtracting 70 degrees from both sides, we get:

5m∠B = 110°

Dividing both sides by 5, we get:

m∠B = 22°

Therefore, the measure of angle B is 22 degrees.

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Step-by-step explanation:

5×a×5×a

collect like terms

5×5×a×a

25×a^2

25a^2

To meet her daily goal, Ling need to pedal approximately 1,008 revolutions each day.

To find the number of revolutions Ling will need to pedal each day to meet her daily goal, we need to first find the circumference of her unicycle tire.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since the diameter of Ling's unicycle tire is 20 inches, the radius is 10 inches. Therefore, the circumference of her unicycle tire:

C = 2π(10) = 20π inches.

Next, we need to convert Ling's daily goal of one mile, or 5280 feet, to inches. There are 12 inches in a foot, so 5280 feet is equal to 5280 * 12 = 63360 inches.

Finally, we can find the number of revolutions Ling will need to pedal each day by dividing her daily goal in inches by the circumference of her unicycle tire in inches:

Number of revolutions = 63360 inches / 20π inches = 20,160π / 20π = 1,008

Therefore, Ling will need to pedal approximately 1,008 revolutions each day to meet her daily goal.

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Open questions:

Closed questions:

Open questions allow individuals to express their thoughts, feelings, and opinions freely. These questions promote exploration and encourage the respondent to provide unique and personal insights.

Closed questions provide limited options for responses and are useful when seeking specific information or clarifying details. They are used in surveys, assessments etc.

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Since McKenzie fills the 2-quart pitcher 2 times, there are a total of 4 quarts.

2 quarts × 2 times filled = 4 quarts

Recall that

1 quart = 4 cups

Since each quart is 4 cups, having 4 quarts is equivalent to

4 quarts × 4 = 16 cups

Therefore, there are a total of 16 cups of juice that was made.

Yes, this relationship is a Funtion.

The relationship between the no of gallons of milk purchased and the total cost can be represented by this equation:
y = 3.5x

where y is the total cost  and x represents the number of gallons of milk purchased. A function is a collection of ordered pairs (x, y) with exactly one value of y for each value of x. for each input (x), just one output (y) is created.

In this situation, there is only one equivalent value of y for each value of x .We may see this by putting different value of x into the equation and get ing a different result for y.
For example, when x = 1, y = 3.5 ×1 = 3.5
when x = 2, y = 3.5 × 2 = 7
when x = 3, y = 3.5 × 3 = 10.5
and so on.

So, the relationship between the number of gallons of milk purchased and the total cost is a Funtion.

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Step-by-step explanation:

Hope this helps, and sorry for the image, my phone is glitchy.

cheers!!!