Solve each of the following problems and show ALL STEPS. Q-7: Solve the given equation for x. X2/3 + x1/3 - 6 = 0 Hint: The equation is quadratic in form

The initial population at time t = 0 was approximately 234. The size of the bacterial population after 5 hours is approximately 2,464,154.

For the initial population at time t = 0, we can use the concept of doubling time. The doubling period of 15 minutes means that the population doubles every 15 minutes.

So, if the population was 60000 at time t = 120 minutes, we can work backwards to find the initial population.

Since the doubling period is 15 minutes, we can calculate the number of doubling periods that have occurred from time t = 0 to t = 120 minutes. In this case, 120 minutes divided by 15 minutes equals 8 doubling periods.

Since the population doubles with each doubling period, we can divide the population at t = 120 minutes by 2 raised to the power of the number of doubling periods.

In this case, the initial population would be 60000 divided by 2 raised to the power of 8, which is 60000 / (2^8) = 234.375.

Therefore, the initial population at time t = 0 was approximately 234.

For the size of the bacterial population after 5 hours (300 minutes), we can calculate the number of doubling periods that occur in 300 minutes. 300 minutes divided by 15 minutes equals 20 doubling periods.

Using the formula for exponential growth, we can find the population after 20 doubling periods.

The population after 20 doubling periods would be the initial population multiplied by 2 raised to the power of 20. In this case, the population after 5 hours would be 234 * (2^20) = 2464153.6.

Therefore, the size of the bacterial population after 5 hours is approximately 2,464,154.

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The fraction of the money that Sam receives is \(\frac{7}{16}\) of the money they share.

To solve this problem, we need to first understand what the ratio 7:9 means. It means that for every 7 parts that Sam receives, Adam receives 9 parts.
Let's say the sum of money they are sharing is $100. To find out how much Sam receives, we need to divide the total amount into 16 parts (7 + 9).
Each part would then be worth $6.25 ($100 ÷ 16).
To find out how much Sam receives, we need to multiply the number of parts he receives by the value of each part.
Sam receives 7 parts out of 16, so his share would be 7 x $6.25 = $43.75.
To express this as a fraction, we can put Sam's share over the total amount:
\(\frac{43.75}{100}\)
We can simplify this fraction by dividing both the numerator and denominator by 25:
\(\frac{1.75}{4}\)
Therefore, the fraction of the money that Sam receives is \(\frac{1.75}{4}\) or \(\frac{7}{16}\).
In summary, Sam receives \(\frac{7}{16}\) of the money they share, which is equivalent to $43.75 if the total amount they are sharing is $100.

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Answer:

one

Step-by-step explanation:

Answer:

I'll help you tomorrow ok

Answer:

2.20

Step-by-step explanation:

First, change 42° to radian

42/180 * π = 0.733 rad

The length of the arc = 3 * 0.733 = 2.20

The required measure of the arc RT is given as 2.512 units.

Given that,
In circle S with m RST = 42 and

RS = 3 units,

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Arc = radius  × angle
Arc = 3 × 42 × π/180

The length of the arc = 2.512

Thus, the required measure of the arc ET is given as 2.512 units.

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The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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Answer:

sorry where is figure.

Step-by-step explanation:

area of triangle ABE=area of triangle BE3

The two consecutive integers that will make the inequality true are 13 and 14.

inequality, is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

If you check for the square root of 181 \(\sqrt{181}\) is 13.453

And the two consecutive integers smaller than 13.45 and greater than 13.45 are 13 and 14 respectively.

In conclusion, the two consecutive integers for the expression are 13 and 14.

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Answer:

To tell if a polynomial is constant, linear, quadratic, cubic or quartic, you must first look at the highest power of the variable in the polynomial. If the highest power is 0, then the polynomial is a constant. If the highest power is 1, then it is a linear polynomial. If the highest power is 2, then it is a quadratic. If the highest power is 3, then it is a cubic and finally, if the highest power of the variable is 4, then the polynomial is a quartic.

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

2 pounds divided by 4 days

Answer: 1/2

Step-by-step explanation:

2 pounds in 4 days so, 2 divided by 4 is 1/2

The area of the figure can be obtained by splitting the figure into smaller components

The area of the irregular figure = Area of A + Area of B + Area of C

Area of A = L X B = 12 x 7 = 84 sq meters

Area of B = L X B = 5 X 8 = 40 sq meters

Area of C = L X B = 5 x 8 = 40 sq meters

Total area = 84 + 40 + 40 = 164 sq meters

The Simplest form of the square root of 1,764 is 42. This means that the square root cannot be simplified any further, since 42 is already an integer and cannot be expressed as a fraction or a decimal.

The simplest form of the square root of 1,764 is 42.

To understand why, it's helpful to know what a square root is. A square root is a mathematical operation that finds the number which, when multiplied by itself, gives a certain number. For example, the square root of 25 is 5, because 5 multiplied by itself equals 25.

In the case of the square root of 1,764, we want to find the number that, when multiplied by itself, equals 1,764. To do this, we can use a calculator or do it manually by trial and error. One way to do it manually is to start with a number and square it until we get 1,764.

For example, we could start with 10 and square it to get 100. Then we could try 20, which gives us 400. Continuing in this way, we eventually find that 42 multiplied by itself equals 1,764.

So, the simplest form of the square root of 1,764 is 42. This means that the square root cannot be simplified any further, since 42 is already an integer and cannot be expressed as a fraction or a decimal.

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Answer:

504

Step-by-step explanation:

14x18x2=

(14x18)x2=

252x2=

504

Answer:

rise: 1

run: 2

rise over run 1/2

Step-by-step explanation:

to find slope move up one over 2 to the left

Throwing a dart at a stationary dart board can be classified as a projectile motion.

:

When a dart is thrown at a stationary dartboard, it follows a curved path known as projectile motion. Projectile motion occurs when an object is launched into the air and moves along a curved trajectory under the influence of gravity, with no other external forces acting on it. In this case, the dart is subjected to the force of gravity but doesn't experience any significant air resistance or external forces once it leaves the hand of the thrower.

The motion of the dart can be described using principles of kinematics. The dart moves in two dimensions: horizontally and vertically. The horizontal motion is uniform and unaffected by gravity, while the vertical motion is influenced by the force of gravity acting in the downward direction. The dart follows a parabolic path, with its maximum height reached at the peak of the trajectory.

To determine the distance and accuracy of the dart throw, various factors need to be considered, such as the initial velocity, launch angle, and the height of the dartboard. These factors can be used to calculate the range, time of flight, and maximum height of the dart.

Throwing a dart at a stationary dartboard involves projectile motion, where the dart follows a curved path influenced by gravity. Understanding the principles of projectile motion can help improve accuracy and distance in dart throwing by considering factors like initial velocity and launch angle. By mastering the art of projectile motion, dart players can enhance their skills and aim for higher scores on the dartboard.

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At 2.5 and 5.4 seconds, the ball will be 213 feet from the ground

A function is defined as a relation between a set of inputs having one output each.

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and codomain or range.

In this case, we simply input the value of s = 213 and solve the quadratic equation

s(t) = -16t² + 126t

So, we have

213 = -16t² + 126t

Collect the like terms

-16t² + 126t - 213 = 0

Using a graphing tool, we have

t = 5.4s and t = 2.5s

This means that the ball will be 213 ft from the ground at 5.4 seconds and 2.5 seconds

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The approximation or the rounding off number is A = 840,000

Given data ,

Let the number be represented as n

Now , let the rounded number be represented as A

where n = 837,796

And , number 837,796 can be approximated to the nearest ten thousand, which is 840,000

Hence , the rounded number is A = 840,000

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Answer:

(-4,-8)

Step-by-step explanation:

The solution to the system of equations is,

⇒ (- 4, - 8)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expressions are,

⇒ y = 1/2x - 6

⇒ x = - 4

Now, We can simplify the expression for y as;

⇒ y = 1/2x - 6

Put x = - 4;

⇒ y = 1/2 × - 4 - 6

⇒y = - 2 - 6

⇒ y = - 8

Thus, The solution to the system of equations is,

⇒ (- 4, - 8)

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A. We can solve this system of equations to determine if it has a solution for any (x, y, z)ᵀ in ℝ³. If it does, then the given set is a spanning set.

B. 4a + 3b + 0c = x

3a + b + 2c = y

5a - c - 4c = z

C. We can determine if the vectors span ℝ³.

To determine whether a set of vectors is a spanning set in ℝ³, we need to check if any vector in ℝ³ can be expressed as a linear combination of the given vectors.

(a) {(4,3,0)ᵀ, (3,1,2)ᵀ, (5,-1,-4)ᵀ}

To check if this set is a spanning set, we need to determine if any vector (x, y, z)ᵀ in ℝ³ can be expressed as a linear combination of these vectors:

(x, y, z)ᵀ = a(4,3,0)ᵀ + b(3,1,2)ᵀ + c(5,-1,-4)ᵀ

Expanding this equation, we get the following system of equations:

4a + 3b + 5c = x

3a + b - c = y

2b - 4c = z

We can solve this system of equations to determine if it has a solution for any (x, y, z)ᵀ in ℝ³. If it does, then the given set is a spanning set.

(b) {(4,3,5)ᵀ, (3,1,-1)ᵀ, (0,2,-4)ᵀ}

To check if this set is a spanning set, we set up a similar system of equations:

4a + 3b + 0c = x

3a + b + 2c = y

5a - c - 4c = z

(c) {(3,1,2)ᵀ, (2,4,5)ᵀ, (2,4,5)ᵀ}

Again, we set up the system of equations:

3a + 2b + 2c = x

a + 4b + 4c = y

2a + 5b + 5c = z

Now, we can solve each system of equations to determine if they have solutions for any (x, y, z)ᵀ in ℝ³. If they do, then the corresponding sets are spanning sets in ℝ³.

By solving each system, we can determine if the vectors span ℝ³.

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Answer 2019 /0.0047   /2014/  0.493

Step-by-step explanation:

The percent change in average full-time worker in the U.S from 2014 to 2019 is 4.93%.

A percentage is a portion of a whole that is stated as a number between 0 and 100 as opposed to being expressed as a fraction.

The percentages of everything are 100%, nothing is 0%, 50% of something is 50%, and nothing is 0%.

Given:

In 2019, the average full-time worker in the U.S. spent `8.5` hours working each workday.

This is an increase on the average of `8.1` hours per workday in 2014.

So, Percent change =  (Final value - initial value) / initial value x 100

Percent change = 8.5 - 8.1 / 8.1 x 100

Percent change = 4.93%

Thus, the percent change in average full-time worker in the U.S from 2014 to 2019 is 4.93%.

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Answer:

10

Step-by-step explanation:

The lower the number is, the higher the amount that the quotient will be

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE

The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.

ANOVA basically stands for analysis of the variance.

Hence, according to above statements, given fact is true.

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Answer:

Step-by-step explanation:

-9 + b/4 >= -4

b/4 >= 5

b >= 20

the solution is d

a) The probability that at most one is a six is 5/6.

b) The probability that at most one is a six is 2/3.

In the question two dice are rolled in a random experiment and we have to find what is the probability that at most one is a six and if the two faces are different, what is the probability that at most one is a six.

a) The probability that at most one is a six is 5/6. There are only 6 possible outcomes when rolling two dice, and 5 of those outcomes involve at most one six: (1,2), (1,3), (1,4), (1,5), (2,5).

b) The probability that at most one is a six is 2/3. If the two faces are different, there are only 3 possible outcomes: (1,2), (2,3), (3,4). 2 of those outcomes involve at most one six: (1,2), (2,3). Thus, the probability is 2/3.

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Answer:

130 students do not ride the bus to school.

Step-by-step explanation:

520 * .75 = 390

390 students ride the bus to school.

520-390=130

130 students do NOT ride the bus to school.

Hope this helps! :)

Answer:

Step-by-step explanation:

When James is twice as old as John, the difference in their ages will be John's age: 10. That is 5 years from now, so John's age now is 10 -5 = 5.

John is 5 years old.

__

3 years ago, John was 2 and James was 12. Their total age at that time was 14.

I apologize, I am unable to create tables or upload scanned documents. However, I can assist you in calculating the amount each investor will receive in each year based on the given information.

To calculate the amount received by each investor in each year, we need to follow these steps:

Calculate the total profit earned by the bank in each year by subtracting the loss values from zero.

Year 1: 0 - (-78,000) = 78,000

Year 2: 0 - (-23,000) = 23,000

Year 3: 29,000

Year 4: 63,000

Year 5: 103,500

Calculate the total profit to be distributed among the investors in each year, which is 60% of the total profit earned by the bank.

Year 1: 0.6 * 78,000 = 46,800

Year 2: 0.6 * 23,000 = 13,800

Year 3: 0.6 * 29,000 = 17,400

Year 4: 0.6 * 63,000 = 37,800

Year 5: 0.6 * 103,500 = 62,100

Calculate the profit share for each investor based on their respective share of the investment.

Year 1:

Fahad: (30/100) * 46,800

Yashara: (50/100) * 46,800

Saud: (20/100) * 46,800

Fariha: (40/100) * 46,800

Younus: (25/100) * 46,800

Asif: (35/100) * 46,800

Similarly, calculate the profit share for each investor in the remaining years using the same formula.

By following the calculations above, you can determine the amount each investor will receive in each year based on their share of the investment.

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Answer:

(2,2) is the solution of the given lines.

Step-by-step explanation:

Given that,

y = x ..(1)

y = 3x-4 ...(2)

We need to find the coordinates of the point of intersection.

From equation (1) and (2).

x=3x-4

4 = 3x-x

4 = 2x

x = 2

Also,

y = 2