Suppose that the number P(t) of bacteria in a culture after t days is given by the formula
P(t) = 95 (1.53)^t
How long does it take for the population to triple in size?

Answer: It could be 7 or 10 or 113

Step-by-step explanation:  Just to make sure that you don't think it's only for 5. If I just get something, that something is equal to itself, which is just going to be true no matter what x you pick.

Number of the 61 days in 2009 the Dow decreased by more than 1% is 0.514.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Given:

61 days in 2009 the Dow decreased by more than 1%.

In 2009

z = (1- (-0.198))/2.331

z = 0.514

In 2010

z = (1-0.078)/0.821

z = 1.123

Thus, number of the 61 days in 2009 the Dow decreased by more than 1% is 0.514.

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Using simultaneous equations, the investor invested $7,560 in the 2% term, if the total investment averaged 3.75% for the year.

Simultaneous equations are a system of equations solved concurrently.

The solutions to a system of equations are found at the same time.

The total investment in the portfolio = $42,000

Investment in a 2% term for one year = a

Investment in 4.5% mortgage for one year = b

The average earnings from the investment = 3.75%

a + b = 42,000... Equation 1

(0.02a + 0.045b) ÷ 2 = 0.0375

0.01a + 0.0225b = 0.0375... Equation 2

Multiply Equation 1 by 0.0225:

0.0225a + 0.0225b = 945 ... Equation 3

Subtract Equation 2 from Equation 3:

0.0225a + 0.0225b = 945

-

0.01a + 0.0225b = 0.0375

0.0125a = 944.9625

a = 7,560

= $7,560

b = 42,000 - 7,560

b = 34,440

= $34,440

Thus, the investor invested $7,560 in the 2% term and $34,440 in the mortgage.

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According to the information, the possible combinations that Jane can have are: Coffee and waffle, Coffee and pancakes, coffee and toast, mocha and waffle, mocha and pancakes, mocha and toast, latte and waffles, latte and coffee, and latte and toasts. In total there are 9 options.

To identify the possible options that Jane has, we must identify the products that are available and the combination that she wants. In this case, it is a hot drink and a bakery product.

According to the above, the possible options would be:

In total there are 9 options.

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The weight of the draft horse is [tex]10^6[/tex] times the weight of the paper clip.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Weight of the paper clip = [tex]10^{-3}[/tex]

Weight of the draft horse = 10³

Now,

Weight of the draft horse.
= [tex]10^6[/tex] x Weight of the paper clip

= [tex]10^6[/tex] x [tex]10^{-3}[/tex]

= [tex]10^6[/tex]  x 1/10³

= 10³

Thus,

The weight of the draft horse is [tex]10^6[/tex] times the weight of the paper clip.

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Answer:

the answer is 6

Step-by-step explanation: 1 kilometer is equal to 0.621371 miles. To convert 13 kilometers to miles, you can multiply 13 by 0.621371.

13 kilometers * 0.621371 miles/kilometer = 8.042443 miles

So 13 kilometers is equal to 8.042443 miles.

The total number of people are 1064 to whom the single cell phone towers are assigned in a particular city.

In a graphical or tabular format, a frequency distribution displays the frequency of repeated entries. It provides a visual representation of the frequency of various items or counts their occurrences.

There are total of 44,700 people in the city and total of 42 cell ,

so to find out the number of people using single cell tower is,

Number of people on single cell tower = 44700/42

=1064.285 ≈ 1064 people

The gathered information is arranged in tables using the frequency distribution method. The information might include student grades, local weather information, volleyball match point totals, etc. We must provide data in a relevant way for improved understanding after data gathering. Create a table that contains a summary of all the data's characteristics. The term "frequency distribution" refers to this.

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The value of tanФ = -1/4 in the III quadrant is -14⁰:

A trigonometric ratio is a ratio between two sides of a right triangle. The tangent ratio is just one of these ratios. In this tutorial, you'll see how to find the tangent of a particular angle in a right triangle.

Tangent = opposite /Adjacent

Tan ∅ = -1/4

Tan ∅= -0.25

Taking the tangent inverse to get ∅

∅=Tan⁻0.25

∅=-14

This is to say that in the III quadrant, Tan ∅=-1/4 is -14⁰

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The system of equations has an infinite number of solutions. The correct answer would be an option (D).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The system of equations is given in the question, as follows:

-5.9x - 3.7y = -2.1     .....(i)

5.9x + 3.7y =  2.1     .....(ii)

As we know that when a solution set of infinite points exists, a system of linear equations has an infinite number of solutions.

Here the system of equations has an infinite number of solutions because both equations are identical.

Hence, the correct answer would be an option (D).

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If the Heptagon  has been dissected into five triangle , the the proof that sum of the interior angle of any heptagon is always 900° is shown below .

To prove that the sum of the interior angles of a heptagon is 900°, we can use the five triangles that have been dissected from the Heptagon, as follows: let the 5 triangles be A , B , C , D and E .

we know that the sum of interior angle of triangle is always 180° ;

Triangle A: The sum of the angles of triangle A is 180°.

Triangle B: The sum of the angles of triangle B is 180°.

Triangle C: The sum of the angles of triangle C is 180°.

Triangle D: The sum of the angles of triangle D is 180°.

Triangle E: The sum of the angles of triangle E is 180°.

So , the sum of all the angles in the five triangles is 180°×5 = 900°, which is also equal to the sum of the interior angles of the heptagon.

Therefore , we can conclude that the sum of the interior angles of any heptagon is always 900°.

The given question is incomplete , the complete question is

The Heptagon  has been dissected into five triangle with angle labeled , use the five triangle to prove that the sum of the interior angle of any heptagon is always 900° .

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Answer:

(12,7) and (16,7)

There is no slope as both points are on the same line. So the equation would be:

y=7

Step-by-step explanation:

The radius of each sphere is 0.63 cm.

What is Sphere?

It is given that 15 solid spheres are made by melting a solid metallic cone.

The base diameter (D) of  solid metallic cone is 2 cm and its height (H) is 15 cm.

So, the radius (R) of the solid metallic cone is 1 cm.

Now, volume of the cone (V) can be given as,

[tex]V = \frac{1}{3} \pi R^{2} H\\\implies V = \frac{1}{3} \pi \times 1^{2} \times 15[/tex]

Let the radius of the solid sphere be r.

Then, the volume of one sphere (V') can be given as,

[tex]V'=\frac{4}{3}\pi r^{3}[/tex]

The volume of 15 spheres can be given as,

[tex]V' \times 15=\frac{4}{3}\pi r^{3} \times 15[/tex]

Here, Volume of solid metallic cone = Volume of 15 solid spheres

[tex]\implies V = 15 \times V'\\\implies \frac{1}{3} \pi \times 1^{2} \times 15 = 15 \times \frac{4}{3}\pi r^{3}[/tex]

Solving for r, we get

[tex]r^{3} =\frac{1}{4}\\ \implies r=\sqrt[3]{\frac{1}{4}} \\\implies r= 0.63[/tex]

Therefore, the radius of each sphere is 0.63 cm.

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Answer:31.5

Step-by-step explanation: Since we are decreasing 90 by 65%, we want to find 35% of 90. To do this, simply multiply 90 by 0.35 to get 31.5.

1. 9 cans of white paint will she need to mix with 6 cans of blue

2. The rate of white to blue is 9 : 6.

3. The unit rate is 3/2.

Given:

Anne must add 3 cans of white paint to every 2 cans of blue paint.

So, the ratio of white to blue = 3:2

and, for 6 cans of blue paint the white paint needed

= 6 x 3/2

= 3x 3

= 9 cans

2. The rate of white to blue is 9 : 6.

3. The unit rate is 3/2.

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The solution to sin(t) is sin(t) = -√[1 -  cos²(t)]

From the question, we have the following parameters that can be used in our computation:

The angle t is the quadrant IV

This means that

sin²(t) + cos²(t) = 1

Subtract cos²(t) from both sides of the equation

So, we have the following representation

sin²(t) = 1 -  cos²(t)

Take the square root of both sides

sin(t) = ±√[1 -  cos²(t)]

sin(t) is negative in quadrant IV

So, we have

sin(t) = -√[1 -  cos²(t)]

Hence, the solution is sin(t) = -√[1 -  cos²(t)]

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The value of x, obtained using the condition of proportional ratio of the lengths of the sides of similar triangles, is x = 11

Similar triangles are triangles that have the same interior angles, such that the three interior angles of one triangle are congruent to the three interior angles of the other, similar triangles, but the lengths of the sides of the triangles may vary.

The triangles ΔQRS and ΔTUV are similar. Based on the location of the obtuse angle ∠R and ∠T, and the longest sides, RS and UV, we get;

[tex]\frac{RS}{UV} = \frac{RQ}{UT}[/tex]

Therefore, we get;

[tex]\frac{54}{36} = \frac{24}{x+5}[/tex]

54 × (x + 5) = 24 × 36

54·x + 54 × 5 = 24 × 36

54·x = 24 × 36 - 54 × 5 = 594

x = 594 ÷ 54 = 11

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It will take 70 days for the population of bacteria to reach 10,000 from 1000, if it is growing according to the Malthusian model and doubling itself in 10 days.

This can be calculated using the exponential growth formula: N(t) = N0 * (1 + r)^t, where N0 is the initial population size (1000), r is the growth rate (2/10 = 0.2), and t is the time in days (70).

The Malthusian model of population growth is an exponential growth model developed by Thomas Robert Malthus in 1798. It states that the population of a species increases exponentially, doubling every generation, and is limited only by the available resources.

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Answer:

8-15

8-23

and

15+23

15+8

Step-by-step explanation:

(E) 7/6 π-√3/2

We divided the white region into 5/6 of a circle with radius $1$ and two equilateral triangles with side length $1$ by drawing four lines from the intersection of the semicircles to their centers. This gives the white region a size of 5/6 π+2. √3/4=5/6π+√3/2. The area of the shaded region is equal to the area of the white region minus the area of the large semicircle. This is equal to 2 π-(5/6 π+√3/2)=7/6 π-√3/2.

 

Note

First, it is 5/6 of a circle because the middle sector has a degree of 180-2.60=60, resulting in 60/360=1/6 of a circle.

The other two each have an area of 180-60/360=1/3 of a triangle

Therefore, the total fraction of the circle IS 1/6+2.1/3=1/6+4/6=5/6


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Answer:

The solution is w ≤ 18

The series is the converge series and the sum of the converges is 55/16

The term converge series in math is defined as a series is the sum of the terms of an infinite sequence of numbers

Here we have know that the series 20/8 + 80/64 − 320/512 + 1280/4096.

When we simplify this series the  we get,

=> 20/8 + 80/64 − 320/512 + 1280/4096

=> 5/2 + 5/4 - 5/8 + 5/16

As per the following rule If ∑an is conditionally convergent and r is any real number then there is a rearrangement of ∑an whose value will be r.

Based on these we have to simplify then we get, here with unlike denominators find the Least Common Denominator (LCD)

=> LCD = 16

Multiplying numerators and denominators to get the LCD in all fraction denominators

Then we get,

=> 40/16 + 20/16 - 10/16 + 5/16

=> 55/16

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The length of the other side of the triangle is 30 cm. Thus, option b is correct.

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given that  hypotenuse = 32 and one side = 16

Using Pythagoras theorem

32² = 16² + x²

x = [tex]\sqrt{32^2 - 16^2}[/tex]

x = 30

Hence, the length of the other side of the triangle is 30 cm.

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The true statement of the inequality is that g is greater than 9 and as a false statement, g is less than 9.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality of 5g > 45.

Dividing both sides by 5 we have (5/5)g > 45/5.

g > 9.

Now, The true statement is 'g' is greater than 9 and as a false statement 'g' is less than 9.

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A perfectly competitive firm will produce 10 units of output at a market price of $50 by setting its marginal cost (SRMC) equal to the market price: 2q + 30 = 50. The short-run supply function of this firm is q = 10 when p = $50.

a. If the market price is $50, this firm will produce the output level at which the marginal cost (SRMC) equals the market price. To find this output level, we set the marginal cost equal to the market price:

2q + 30 = 50

2q = 20

q = 10

So the firm will produce 10 units of output at a market price of $50.

It is not necessarily true that $50 is a long-run equilibrium price. In the long run, a perfectly competitive firm will exit the market if the market price is lower than its average total cost, and it will enter the market if the market price is higher than its average total cost. Therefore, to determine if $50 is a long-run equilibrium price, we need to know the firm's average total cost.

b. The short-run supply function of a perfectly competitive firm is the relationship between the market price and the quantity of output that the firm is willing and able to produce. It is found by combining the cost function (SRTC) and the profit-maximizing rule (producing at the level where marginal cost equals the market price).

The equation of the short-run supply function is:

q = (50 - 30)/2 = 10 units of output at a market price of $50

So the short-run supply function of this firm is:

q = 10 when p = $50

Complete Question:

A perfectly competitive firm has the following short-run cost function: SRTC = q2+30q+400

The corresponding short-run marginal cost function is given by: SRMC = 2q + 30

a. If the market price is $50, how much output will this firm produce? Is $50 a long-run equlibrium price? Explain your reasoning.

b. Find the equation of this firm's short-run supply function.

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Check the picture below.

so if we pluck the cylinder from the inside, what's leftover is that cyan ring with a height of 10, well, let's get the area of the ring and simply multiply it by its height.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=15\\ r=11 \end{cases}\implies A=\pi (15^2-11^2)\implies A=104\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of a hollow cylinder}}{104\pi }\cdot 10 ~~ \approx ~~ \text{\LARGE 3267.26}~in^3 ~~ \approx 3266~in^3[/tex]

[tex] \frac{3}{1} = \frac{d}{9} \\ [/tex]

cross multiply...

[tex]d = 27[/tex]

For the given Poison variables, the probability that X = 2 is 0.22.

Poisson variables are used to model count data, such as the number of customers arriving at a store in an hour, or the number of goals scored in a soccer match. The mean and variance of a Poisson variable are equal.

In this problem, you are given two independent Poisson variables, X and Y, where X has a mean of 3 and Y has a mean of 4. The sum of these two variables is 7. Your goal is to find the probability that X = 2.

Here we need to solve this problem, we can use the formula for the Poisson distribution. The probability of X = k is given by:

=>[tex]P(X = k) = \frac{(e^{-\mu}) * (\mu^k)}{k!}[/tex]

where μ is the mean of the Poisson variable, and e is the mathematical constant approximately equal to 2.718.

Now by substituting the values for X, we have:

=> [tex]P(X = 2) = \frac{(e^{-3}) * (3^2)}{2!}[/tex]

=> P(X = 2) =  (0.0498) * (9) / 2

=> 0.224

Therefore the correct option is D) 0.22.

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Value of the following expressions for a = 3 + 4j and b  = 3 - 4j , where      j = √−1 are as follow :

1. a + b = 6

2.  a × b = 25

Calculation of the value for the required expression by substituting the given values are:

1. a + b

= ( 3 + 4 j ) + ( 3 - 4j )

Take like terms together we get,

= ( 3 + 3 ) + (  4j - 4j )

= 6 + 0j

= 6

To get the value of second expression substitute the value of 'a' and 'b' we get :

2. a × b

= ( 3 + 4 j ) × ( 3 - 4j )

Apply the formula : ( x + y ) (x - y ) = x ² - y²

= ( 3 )² - ( 4j )²

= 9 - 16j²

Here j = √-1 ⇒ j² = -1

= 9 - 16 (-1 )

= 9 + 16

= 25

Therefore, the value of 1. a + b = 6 and 2. a × b = 25.

The above question is incomplete, the complete question is:

Given a = 3 + 4j and b  = 3 - 4j , where j = √−1 , find (use just pencil and paper, not software or calculators) Find the value of the following :

1. a + b    2. a × b

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well, we know there are 60 minutes in 1 degree, so in 40 minutes that'll be 40/60 degrees or namely 2/3 of a degree.

We know that 180° is π radians, so let's find 43 ⅔ degrees

[tex]\stackrel{mixed}{43\frac{2}{3}}\implies \cfrac{43\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{131}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\\\ \frac{131}{3}&x \end{array}\implies \cfrac{180}{~~ \frac{ 131}{3 } ~~} = \cfrac{\pi }{x}\implies \cfrac{\frac{180}{1}}{~~ \frac{ 131}{3 } ~~} = \cfrac{\pi }{x} \implies \cfrac{180}{1}\cdot \cfrac{3}{131}=\cfrac{\pi }{x} \\\\\\ \cfrac{540}{131}=\cfrac{\pi }{x}\implies 540x=131\pi \implies x=\cfrac{131\pi }{540}\implies x\approx 0.762~radians[/tex]