truth table for (P^Q)​

The population in the year 2000 is 1230  students.

The equation for the population, P, of the school t years after 2000 is P = 53t + 1389.

The population of the school in 2015 in 2025 students

The starting population in 2003 is 1389.

average population growth per year = 53

The population in the year 2000 will be:

number of year = 2000 - 2003 = -3  (3 years back)

population in the year 2000 = 1389 -3(53) = 1230

To find an equation for the population, P, of the school t years after 2000. We can write:

P = 53t + 1389

Using your equation, predict the population of the school in 2015:

t = 2015 - 2003 = 12

P = 53t + 1389

P = 53(12) + 1389

P = 2025 students

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114.9 feet did Adam run more than Julie.

Two or more expressions with an Equal sign is called as Equation.

To compare the distances run by Adam and Julie, we need to convert both distances to feet.

Given Adam ran 2/5 mile and Julie ran 3/8 mile.

2/5 of a mile is equal to 2/5 * 5780 = 2312.4 feet

3/8 of a mile is equal to 3/8 × 5780 = 2167.5 feet.

Now let us find the difference between two persons.

So, Adam ran 2312.4 - 2167.5 = 114.9 feet.

Hence, 114.9 feet did Adam run more than Julie.

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An expression that calculates the time in hours a person takes to walk 35 miles at a speed of 5 miles/hour is: T = 35/5 = 7 hours.

In Mathematics, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Making time the subject of formula, we have:

Time = distance/speed

Time = 35/5

Time = 7 hours.

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The best description for this distribution is bimodal.

What is the Bimodal ?

Bimodal is a term used in statistics to describe a distribution with two modes, or peaks, in the frequency of occurrence of the values.

The distribution of the values: 3, 3, 5, 4, 3, 2, 5, 6, 5, 1 is best described as:

c. Bimodal

Bimodal means that the distribution has two modes, or peaks, in the frequency of occurrence of the values. In this case, the values 3 and 5 both have a high frequency of occurrence, forming two distinct modes in the distribution.

Therefore, the best description for this distribution is bimodal.

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Step-by-step explanation:

14/16 = 7/8

3/12 = 1/4

16/28 = 4/7

The number of adults who attended the concert is 824.

Linear Equation:

The equation is said to be linear if the greatest power of a variable always equals 1. It is also known as a one-degree equation. The usual form of a linear equation with one variable is Ax + B = 0. In this case, the variables x and A are variables while the variable B is a constant.

It is given in the question that the number of adults are twice the number of children.

then,

Suppose there were x children present at the concert.

Then number of adults will be 2x.

According to the given question,

x + 2x = 1236

3x = 1236

dividing both sides by 3, we get

x= 412

therefore, number of children who attended the concert is 412.

Then the number of adults will be,

2x = 2 x 412 = 824

therefore, the number of adults who attended the concert is 824.

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The number of values greater than 10.5 and less than 12.5 is 5. By adding the frequencies between these quantities, we could get the number.

A histogram is a graph representing frequency distribution of data points in a dataset. In one axis the data points are given, and the other axis is the frequency. It can be used in both discrete and continuous dataset. In discrete data, there will be individual data points and for continuous it will be a range.

Here the given dataset is a continuous dataset. The frequency of datapoints between 10.5 and 11.5 is 2 and frequency between 11.5 and 12.5 is 3. So the total will be 2+3 = 5.

So the frequency or values between 10.5 and 12.5 is 5

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The complete question is in the image.

The surface area ranges from 0 to 1, and is equal to the integral of the circumference of a circle with a radius of x2x5 times.

An integral can be used to define the surface area gained by rotating the curve y2=x2x5 around the x-axis for y0 and 0x1. This integral represents the circumference, from 0 to 1, of a circle with radius x2x5 multiplied by. This can be expressed as x25x624x3+8 times the integral of from 0 to 1 for. When the given curve is rotated about the x-axis over the specified range of y and x, this integral will evaluate to the surface area achieved. This integral can be expressed in the simplest possible form as 01 x25x624x3+8 dx.

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The fraction of the original surface area to the new surface area is 1/100.

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

Since the ratio of the new side to original length is 1/10.

Thus, the fraction of the original surface area to the new surface area will be the square of the ratio of the length. That is:

fraction of length = new length/ original = 1/10

fraction of area = (1/10)² = 1/100

fraction of area = new area/original area

1/100 = new area/original area

new area = 1/100 * original area

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The required ATP singles rankings for tennis players rank is false.

An interval scale is a type of measurement scale that has equal units of measurement and a zero point, meaning that differences between scale values can be meaningfully compared, but there is no meaningful interpretation of the zero point.

In tennis, ranking points are assigned based on a player's performance in a set number of tournaments over a rolling 52-week period, but the actual number of points assigned to a player is not an interval scale.

Thus, it is incorrect to say that the ATP singles rankings for tennis players are an example of an interval scale.

The given statement is false.

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The ratio completes the equivalent proportion a/b is 16/30.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

The given proportion is a/b = 8/15.

To get the equivalent proportion multiply both the numerator and denominator by 2 we get

16/30

Multiply both the numerator and denominator by 3 we get

24/45

Therefore, the ratio completes the equivalent proportion a/b is 16/30.

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The fair price to pay to play the game of rolling a colored die with three green sides, two red sides, and one blue side is; $2

How to Fair Price?

We are told that in the game of rolling the colored die;

- A roll of a red loses.

- A roll of blue pays 6.00.

- A roll of green pays 2.00.

Now, the best game to get the fairest price is to play; GGGRRB

Fair price = 2(3/6) + 6(1/6) + 0(2/6)

Fair price = $2

The child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.

A differential equation is an equation that contains one or more functions with its derivatives.

The distance between the kite and the child's hand level "d". Then, using the Pythagorean theorem, we can write:

d² + 105²= (165)²

d² = 165² - 105²

d = 129.1 ft

The length of the cord is increasing at a rate of 6 feet per second

Let us consider the length of the cord "L".

d² + L² = (165)²

Differentiating both sides with respect to time (t), we get:

2d(dd/dt) + 2L (dL/dt) = 0

We want to find (dL/dt) when L = 165 and d = 129.1.

(dL/dt) = -d × (dd/dt) / L

Substituting in the values we found for d and L, we get:

(dL/dt) = -(129.1 ft) × (0 ft/s) / (165 ft) = 0 ft/s

Therefore, the child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.

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The required, we have strong evidence to suggest that the population means is not equal to zero.

The null hypothesis, denoted as H0, is a statistical hypothesis that assumes that there is no significant difference between a population parameter and a hypothesized value or between two or more population parameters.

Here,
If we choose a 5% significance level, this means that we are willing to reject the null hypothesis (Hop=0) if the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis is less than 5%.

The observed value of the test statistic is z = -3.38. This means that the observed value is 3.38 standard deviations below the mean under the null hypothesis.

We can use a standard normal distribution table or calculator to find the probability of obtaining a z-score as extreme as -3.38 or less. The probability is approximately 0.0004, or 0.04%.

In other words, we have strong evidence to suggest that the population means is not equal to zero, and we can be 95% confident that the true population means falls within a certain range of values (based on the confidence interval).

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The required example of a function with a minimum at a value where its derivative is undefined is f(x) = |x|.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

A function that has a minimum at a point where its derivative is undefined is the absolute value function. The absolute value function is defined as:

f(x) = |x|

At x = 0, the absolute value function has a minimum value of 0. However, the derivative of the absolute value function is undefined at x = 0, because the function is not differentiable there.

At x < 0, the absolute value function is decreasing and therefore has a negative derivative. At x > 0, the absolute value function is increasing and therefore has a positive derivative. At x = 0, the behavior of the function changes abruptly from decreasing to increasing, which makes the derivative undefined. Despite this, the absolute value function still has a minimum value of 0 at x = 0.

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The area of figure above is a) 6cm²

In addition to the circumference, a square shape also has an area, where the area of a square is calculated by squaring the length of its side.

Formula: Area of square= s²

The question above, the side of square is 1 cm.

so the area of one small square is 1×1= 1cm²

Because the shape is contain of 6 small square, therefore the total area is 6×1cm²=6cm²

A square has the following properties

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Years: 2.455 years

Amounts: $843 billions

This can be solved by using equation solving method.

An expense classified as personal is one that is not related to a trade or enterprise, a passive activity, or an investment. Personal consumption spending is often divided into two categories: goods and services. Groceries, automobiles, and fuel are a few examples of products. Rent, medical treatment, and insurance are a few examples of services.

f(x) = 40.74x + 742.65

h(x) = 47.93x +725

For f(x) = h(x),

40.74x + 742.65 = 47.93x +725

47.93x - 40.74x = 742.65 - 725

x (47.93-40.74) = 17.65

x = 17.65 /7.19 = 2.455 years.

2.455 years after 1995, that is in 1998, these expenditures would be equal to each other.

The amount spent on each would be :-

40.74(2.455) + 742.65 = $842.667

= $843 billions.

Years: 2.455 years

Amounts: $843 billions

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Answer: A person who is eligible to use a 1040EZ form when filing a federal income tax return must meet certain criteria:

Must have taxable income of less than $100,000

Must not claim any dependents

Must only have wages, salaries, tips, taxable scholarship or fellowship grants, unemployment compensation, or Alaska Permanent Fund dividends, and your taxable interest is less than $1,500

Given these criteria, the correct answer is:

D. Single person, with no dependents, who made $49,000 last year.

Step-by-step explanation:

The total cost to purchase a tarp that is the same size as Keith's tent is given as follows:

$24.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

The dimensions for the tarp in this problem are given as follows:

Hence the area is given as follows:

A = 3 x 8 = 24 square feet.

As the cost is $1.00 per square feet and there are 24 square feet, the total cost is given as follows:

$24.00.

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c² + 9 + 6c is the solution by distributive property .

What in mathematics is a distributive property?

This characteristic states that multiplying the total of two or more addends by a number will produce the same result as multiplying each addend separately by the number and then combining the products collectively.

                                       When you multiply one value by another, you are using the distributive property of multiplication over addition. When multiplying 5 by the sum of 10 plus 3, for instance, add 3. We typically add the numbers first, then multiply the result by 5, since the terms are similar. However, in accordance with the property, you can first multiply each addend by 5.

= (c+3)^2

= c² + 9 +  2 * c * 3

= c² + 9 + 6c

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Drawing the histogram helps in guessing the average by allowing us to visually see the distribution of the data.

It is used to show the frequency of occurrence of different values within a set of data. In a histogram, the data is divided into a set of intervals or "bins," and the height of each bar represents the number of data points that fall within that bin.

The x-axis of a histogram typically represents the range of values in the data, while the y-axis represents the frequency of occurrence of those values. The bars are positioned so that they touch each other, indicating that the data is continuous and that there are no gaps between the bins.

Discrete data refers to data that can only take certain values within a defined range, such as the number of candies sold. Continuous data refers to data that can take any value within a defined range, such as swimming time.

To create a histogram for the swimming times, we first need to determine the range of the data and choose an appropriate interval width. In this case, the lowest value is 87 and the highest value is 136, so the range is 87 to 136. A suitable interval width could be 5. This would give us 11 intervals, from 85 to 90, 90 to 95, and so on, up to 135 to 140.

Next, we would tally the number of swimming times that fall into each interval and plot this information as bars on the histogram. The height of each bar represents the frequency of the interval.

Drawing the histogram helps in guessing the average by allowing us to visually see the distribution of the data. Based on the shape of the histogram, we can make a guess as to where the average is likely to fall. If the histogram is symmetrical, the average is likely to be in the middle. If it is skewed, the average will be closer to the side with the longer bar. By drawing a vertical line labeled "My Guess" on the histogram, we can see how close our guess was to the actual average.

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Answer: 10 M

Step-by-step explanation:

Answer:

Correct option is C)

Given s= 7m, h=9 m

Lateral surface area = Area of the curved surface =2πrh=2×

7

22

×7m×9m=396m

2

Total surface area = Area of curved surface + Area of two circular surfaces

=2πrh+2πr

2

=396m

2

+2×

7

22

×7m×7m=(396+308)m

2

=704m

2

The surface area of cylinder B is 548 square km.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, cylinder B is the image of cylinder A after dilation by a scale factor of 4.

The surface area of cylinder A is 137 km².

Then the surface area of cylinder B is 4×137

= 548 square km.

Therefore, the surface area of cylinder B is 548 square km.

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The amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

A cuboid is a three dimensional shape , with 6 faces , each face is a rectangle.

The concrete can be considered as in the shape of a cuboid.

Length = 18

Breadth = 24'

Height = 4"

Volume of Cuboid = Length * Breadth * Height

Volume of the cuboid = 18 * 24 * 4 *12*12 *(0.0278)³

=5.34 cu.yard.

Therefore the amount of concrete required to pour a floor slab of the following dimensions: 18′ × 24′ × 4′′ is 5.34 cu.yard.

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Triangle OGD and triangle ATC are similar triangles by the criteria of Side - Angle - Sides.

The set of triangles with the same shape but different sizes are known as similar triangles. For example, all the equilateral triangles are similar triangles.

We can determine similar triangles by using the following conditions

Angle-Angle Similarity condition

Side-Angle-Side Similarity condition

Side-Side-Side Similarity condition

Here we have

Triangle OGD and triangle ATC  

From the given triangles

=> Side OD = Side AC   [ Equal sides ]

=> m ∠O = m ∠ A         [ Equal angles ]

=> m ∠G = m ∠T          [ Equal angles  ]

Hence, By the criteria of Side - Angle - Side given triangles are similar triangles.

Therefore,

Triangle OGD and triangle ATC are similar triangles by the criteria of Side - Angle - Sides.

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The measure of trapezoid's opposite angle is 135°. The solution has been obtained by using properties of trapezoid.

What is a trapezoid?

Four sides make up the quadrilateral of a trapezoid, two of which are parallel while the other two are not. It is also referred to as a trapezium. A closed, four-sided form or figure known as a trapezoid has its own perimeter and can enclose an area.

We are given that one base angle is equal to 45°

We know that in a trapezoid

Base angle + Opposite angle = 180°

Using this, we get

⇒45° + Opposite angle = 180°

⇒Opposite angle = 180° - 45°

⇒Opposite angle = 135°

Hence, the measure of trapezoid's opposite angle is 135°.

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Answer: 396

Step-by-step explanation:

length- x+4

width - x

perimeter = 40

40 = x+4+x

40-4=2x

36=2x

x=18

length - 18+4=22

width - 18

area = 22*18 = 396