A fisherman illegally drops some fish into a pond, and they quickly propagate (reproduce). The population growth of the new specifies is modeled by P(x) = 6∙2x, where x is the time in weeks following the moment he dropped the fish into the pond. How many fish are in the pond after 3 months? (assume there are four weeks in a month) a. 48 b. 8, 916 c. 24,576 d. 72

Answer:

(4^6)^-3 = 1/4^18(4^0)^-9 = 4^0(4^-3)^-3 = 4^9(-4^9)^2= (-4)^18Step-by-step explanation:(4^6)^-3 = 1/4^18(4^6)^-3= 4^(6*-3)(4^6)^-3= 1/4^18(4^0)^-9 = 4^0(4^0)^-9 = 4^(0*-9)(4^0)^-9= 4^0(4^-3)^-3 = 4^9(4^-3)^-3= 4 ^ (-3*-3)(4^-3)^-3 = 4^(9)(-4^9)^2= (-4)^18(-4^9)^2= -4^(9*2)(-4^9)^2=(-4)^18

Step-by-step explanation:

Answer:

[tex](4^{-3})^{-3}=4^9[/tex]

[tex](4^6)^{-3}=\dfrac{1}{4^{18}}[/tex]

[tex](4^0)^{-9}=4^0[/tex]

[tex](-4^9)^2=(-4)^{18}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$(a^b)^c=a^{bc}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]

Apply the above exponent rules to simplify each expression.

[tex]\begin{aligned}\implies (4^{-3})^{-3}&=4^{-3 \times -3}\\&=4^9\end{aligned}[/tex]

[tex]\begin{aligned}\implies (4^6)^{-3}&=4^{6 \times -3}\\&=4^{-18}\\&=\dfrac{1}{4^{18}}\end{aligned}[/tex]

[tex]\begin{aligned}\implies (4^0)^{-9}&=4^{0 \times -9}\\&=4^0\end{aligned}[/tex]

[tex]\begin{aligned}\implies (-4^9)^2&=(-4)^{9 \times 2}\\&=(-4)^{18}\end{aligned}[/tex]

Answer:

The numbers are being divided by 2 each time.

240/2 = 120

120/2 = 60

So the next set of numbers would be:

30, 15 because

60/2 = 30

30/2 = 15

Step-by-step explanation:

Hope it helps!

Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.

An equation is an expression that shows the relationship between two or more numbers.

From the line plot shown:

Total number of students = 3 + 4 + 2 + 2 + 8 + 4 + 6 + 9 = 38

Students who ran more than 3 laps = 2 + 8 + 4 + 6 + 9 = 29

Students who ran more than 2 1/2 laps = 2 + 2 + 8 + 4 + 6 + 9 = 31

Students who ran more than 3 1/2 laps = 2 + 8 + 4 + 6 + 9 = 29

Hence:

Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.

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The expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

What is the probability distribution?

A probability distribution is a mathematical function that describes the probability of different possible values of a variable.

The probability of winning on a $5 bet on a specific number in chuck-a-luck is determined by the number of ways that the number can appear on the three dice and the total number of possible outcomes.

If the number appears on exactly one die, there are 3 ways that this can happen out of a total of 6^3 = 216 possible outcomes, giving a probability of 3/216 or 1/72.

If the number appears on exactly two dice, there are 3 ways to choose the two dice on which it appears, and 3 ways to choose the third die, giving a total of 33 = 9 ways out of 216 possible outcomes, giving a probability of 9/216 or 1/24.

If the number appears on all three dice, there is only 1 way this can happen out of 216 possible outcomes, giving a probability of 1/216.

If it appears on none of the dice, there are (543) ways this can happen, giving a probability of (54*3)/216 = 20/216.

We can use this information to construct the probability distribution for chuck-a-luck:

x P(x)

-5 (losing the bet) 20/216

5 (winning the bet for one appearance) 1/72

10 (winning the bet for two appearances) 1/24

15 (winning the bet for three appearances) 1/216

To find the expected winnings on a $5 bet, we can multiply the value of each outcome by its corresponding probability, and sum the results:

E(X) = (-5)(20/216) + (5)(1/72) + (10)(1/24) + (15)(1/216)

E(X) = -5/43.2 + 5/72 + 5/12 + 15/216

E(X) = -0.1157

Hence, the expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

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Answer:

See picture below

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

You multiply 23×2 and that is how I got my answer.

Answer:

5.369 x 105

Step-by-step explanation:

Answer:

5.369 x 105

Cause in scientific notation, the decimal point is always after the first number from the left.

The prices where the quantity demanded is greater than quantity supplied are :

Quantity demanded refers to the amount of goods and services that people and businesses in an economy demand.

This amount of goods and services demanded will be more than the quantity supplied when the price of the good or service is less than the equilibrium price.

The equilibrium price here is $ 3 and so the prices less than $ 3 are $2, $1, and $ 0.

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A. Commutative property of addition

B. Distributive property

C. Commutative property of addition

D. Associative property of multiplication

                                    a + b =b + a

        Here, a and b is whole numbers, integers or decimals, or even fractions.

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The complete question is:

Name the property that is shown by each equation.

A. 6a + 4 = 4 + 6a

B. 30 + 60 = 15(2 + 4)

C. 3(8x + 4) = 3(4 + 8x)

D. 4(6a) = (4 · 6)a

The decimal that is represented by the shaded portion of the model is 0.45

Suppose that the number is abcd.efg and belongs to the decimal numerical system.

Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.

Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.

We are given In the model, a hundreds grid represents 1 whole.

Since 45 out of the 100 squares are shaded,

This means the fraction would be 45/100

45/100 = 0.45.

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Answer:

y = -8/3x + 73/4

Step-by-step explanation:

A line perpendicular to the 3rd equation has a slope that is the negative inverse of the other line. It also has the same y-intercept (b) because it is forming a square.

Therefore, the equation of the 4th line is:

y = -8/3x + 73/4

Answer: 256b

Step-by-step explanation: So, first we need to find the square root of 16b.

That'd be 4b, because a square root is when a number can be divided by a number, such as 4 can go into 16 4 times, and like 5 can go into 25 5 times. So, we got 4b

So, 4 to the power of 4 (ignore the b right now) is the same as 4 x 4 x 4 x 4.

So simplified, that'd be 16 x 4 (64). So, 64 x 4 = 256.

So, I'd be 256b

actual measures : model measures = 12 : 1 .

In mathematics, a ratio shows how many times one number contains another. The comparison or simplified form of two quantities of the same kind is referred to as a ratio. This relation gives us how many times one quantity is equal to the other quantity. In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones.

The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’.

A ratio can be written as a fraction, say 2/5. We happen to see various comparisons or say ratios in our daily life.

Given,

Actual sign measures 12 inches on each side

Jason's model sign measures 1 inch on each side.

Ration between actual to model sign measurement=

Measurement of actual sign / Measurement of model sign

= 12/1

Ratio = 12:1

Hence, the ratio between actual to model sign measurement is 12:1.

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Answer:

it is a rational number already

Step-by-step explanation:

201.06 square units (rounded to 2 decimal places) is the area of the given circle.

The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).

Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:

r = d/2

= 16/2

= 8

A=πr2

AND HALF THE DIAMETER IS THE RADIUS (r)

r=8

A= πr2 = π (8) squared = 64 * π = 200.96

or,

Now, substituting the values of r and π into the formula for the area of a circle, we get

A = πr²

= (3.14159)(8²)

= (3.14159)(64)

= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.

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Answer:

Step-by-step explanation:

from the figure we kown the speed is 9/3=15/5=21/7=3 km per minute

the distance in 8 minute is 3 ×8=24 km

For Quadratic equation, It is possible to know if there are 2 real solutions by examining the discriminant that is [tex]b^2-4ac[/tex] of the equation [tex]ax^2+bx+c[/tex].

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

discriminant : [tex]b^2-4ac[/tex]

if [tex]b^2-4ac[/tex] is positive, Both solutions are real.

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Step-by-step explanation:

For Pythagoras' Theorem to be valid, the triangle must be a right-angled one.

The formula is:

c^2 = a^2 + b^2

Where c is the longest side. While a,b are the side lengths.

Using the above formula and the measurements given in the question, we can find the value of x.

By Pythagoras' Theorem,

26^2 = (5x)^2 + (12x)^2

676 = 25x^2 + 144x^2

169x^2 = 676

x^2 = 676 ÷ 169

x^2 = 4

x = 2

The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Now, According to the question:

Solving Two Step Equations:

Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:

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Let x be the coefficient of y^2 in the expression 2x^2y+15xy^2-7y. So x=0.

What is co-efficient?

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.

Write an example of co-efficient.

As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.

The given algebraic expression is 2yx^2+15xy^2-7y.

The terms are xy^2, yx^2 any y^2

So the co-efficient of y^2 is 0

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The required inequality expression for the third side is 1 < m < 25. The correct option is (B).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The sides of the triangle are given as 12 and 13 units respectively.

As per the rule for sides of a triangle, the third side is always less than the sum and greater than the difference of two sides.

Then, the inequality can be written as,

13 - 12 < m < 13 + 12

⇒ 1 < m < 25

Hence, the measure of third side can be written in inequality as 1 < m < 25.

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The average speed of the falcon to 3 significant figures will be 107.526 m/s

Distance travelled by falcon = 100 meters

Time taken by falcon to travel the distance = 0.93 seconds

As we have the formula for finding the average speed:

Average speed is a pace defined as a quantity divided by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t is used to compute average speed, where S is the average speed, d is total distance, and t is total time.

Average speed can be find by simply dividing the total distance covered by falcon by the total time taken by him to cover the distance.

So, the value of the average speed will be = (100 m/0.93 sec) =107.526 m/s

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Answer:

The answer is $4.50.

Step-by-step explanation:

To solve this problem, divide the result ($6.75) by the percentage (150%). This gives you the original number which was multiplied by the percentage. So,

$6.75 / 150% = $4.50.

Answer:

$4.50

Step-by-step explanation:

150% × □ = $6.75

First, we can rewrite 150% as the fraction 3/2.

[tex]\dfrac{3}{2} \times \square = \$ 6.75[/tex]

Then, we can also rewrite 6.75 as the fraction 27/4.

[tex]\dfrac{3}{2} \times \square = \$ \, \dfrac{27}{4}[/tex]

Next, we can isolate the unknown by multiplying both sides by 2/3 (the reciprocal of 3/2).

[tex]\left(\dfrac{2}{3} \right)\left(\dfrac{3}{2} \times \square \right) = \left(\$ \, \dfrac{27}{4}\right)\left(\dfrac{2}{3} \right)[/tex]

After that, simplify by multiplying out the numerators and denominators on the right side of the equation.

[tex]\square = \$ \, \dfrac{27 \times 2}{4 \times 3}[/tex]

[tex]\square = \$ \, \dfrac{54}{12}[/tex]

Finally, simplify the expression on the right side to a decimal form.

[tex]\square = \$ \, \dfrac{54 \div 2}{12 \div 2}[/tex]

[tex]\square = \$ \, \dfrac{27 \div 3}{6 \div 3}[/tex]

[tex]\square = \$ \, \dfrac{9}{2}[/tex]

[tex]\square = \$ 4.50[/tex]

The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² = [tex](10 \sqrt{34})^2 \\[/tex]

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

When two or more lines in a plane cross one another, they are referred to as intersecting lines. The common point shared by all intersecting lines is the point of intersection, which can be found on all of them.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² =

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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Answer: A ratio is a comparison of two or more values. To compare the ratios of orange juice to yogurt, we want to ensure that the proportion of orange juice to yogurt is the same in each ratio.

Option A is 40:30. To compare this ratio to the original ratio, we can convert the amounts in cups to tablespoons. 40 cups is equal to 320 tablespoons and 30 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 320 is not equivalent to 3.

Option B is 19:9. To compare this ratio, we convert the amount in cups to tablespoons. 19 cups is equal to 152 tablespoons of orange juice and 9 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 19 cups.

Option C is 15:20. To compare this ratio, we convert the amount in cups to tablespoons. 15 cups is equal to 120 tablespoons of orange juice and 20 tablespoons of yogurt. The proportion of orange juice to yogurt is not the same as the original ratio since 4 cups of orange juice is not equal to 15 cups.

Option D is 8:6. To compare this ratio, we convert the amount in cups to tablespoons. 8 cups is equal to 64

Step-by-step explanation:

The sample size needed for a margin of error of 1%, for a confidence level of 90%, is of:

6,766.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error of the interval is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

We have no prior estimate, hence the proportion is given as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of M = 0.01, the needed sample size n is obtained as follows:

[tex]0.01 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.645 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 0.5}{0.01}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 0.5}{0.01}\right)^2[/tex]

n = 6,766.

(rounding up, as for a sample size of 6,765 the margin of error would be slightly above 0.01).

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The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.

Let's write the terms in the order x, y therefore,

y - 2x + 5 = 0

- 2x + y = - 5.

2x - y = 5.

And

y + 4x + 1 = 0.

4x + y = - 1.

The graph of the system of equations is attached in the image.

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The function which has greater slope is Function 2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Function 1:

y = -2x + 10

and Function 2:

Slope = (5-10)/( 2-0) = -5/2

So, the Equation of line

(y - 10) = -5/2 (x -0)

y - 10 = -5/2x

y = -5/2x + 10

y= -2.5x +10

So, the slope of Function 1 is greater than slope of function 2.

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