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A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers but a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers

Continuous and discrete variables are two types of quantitative variables in statistics.

A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers. Examples of continuous variables include height, weight, time, temperature, and distance. These variables can be measured using instruments with varying degrees of precision, but they can theoretically take on an infinite number of values.

On the other hand, a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers. Examples of discrete variables include the number of siblings a person has, the number of cars in a parking lot, and the number of points a basketball team scores in a game. These variables can only take on a limited number of values, and often represent counts or whole numbers.

The main difference between continuous and discrete variables is the way they can be measured and the number of possible values they can take. Continuous variables can take on an infinite number of values and can be measured with varying degrees of precision, while discrete variables can only take on specific values and are often measured with exact precision.

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The conversion value of the given quantity 58 percentage in decimals is equal to 0.58.

One percentage converted to decimals is written as :

1 percentage = ( 1 / 100 )

                      =  ( 0.01 )

Now Get the value in decimals for 58 percentage using conversion factor we have ,

= 58 percentage

= ( 58 / 100 )

= ( 0.58 ) in decimal form

Therefore, the value which we get after conversion of percentage to decimals is equal to 58 percentage = 0.58 in decimals.

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As a result, the island's population will be about 1397.33 persons in 6 years.

An exponent, also called a power or index, is a mathematical operation that indicates the number of times a base number is multiplied by itself. Exponents are written as a superscript number to the right of the base number. Exponents can be positive or negative, and they can be whole numbers or fractions. A positive exponent tells us to multiply the base number by itself, while a negative exponent tells us to divide the base number into 1. Exponents can be used to simplify and solve many mathematical problems, and they are an important part of many areas of mathematics, including algebra, calculus, and geometry.

Here,

If the population of the island doubles every 34 years, we can use the exponential growth formula to determine the population after a certain period of time:

P = P0 * 2ⁿ÷³⁴

where P is the population after time t, P0 is the initial population, and t is the time elapsed in years.

We know that the current population is 1233, so P0 = 1233. We want to find the population 6 years from now, so t = 6. Plugging these values into the formula, we get:

P = 1233 * 2⁶÷³⁴

P ≈ 1397.33

Therefore, the population of the island will be approximately 1397.33 people 6 years from now.

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The integral for the mass of a thin wire in the shape of a parabola density is [tex]\int[-1,1]\int[0,x^2] x^2 y^2 dy dx[/tex]

To find the mass of the thin wire in the shape of a parabola with density function ρ(x, y) = [tex]x^2 y^2[/tex],

we can set up a double integral over the region that describes the parabola. The mass M is given by the following integral:

M = ∬ρ(x,y) dA

where dA represents the area element in the xy-plane. To set up this integral, we need to first determine the limits of integration for x and y.

The parabola can be described by the equation y =[tex]x^2[/tex], where x ranges from -1 to 1. Therefore, the limits of integration for x are -1 to 1.

For each value of x, the y-values range from the parabola to the x-axis, which is the region between y = 0 and y = [tex]x^2[/tex]. Therefore, the limits of integration for y are 0 to[tex]x^2[/tex].

Using these limits of integration, the integral for the mass of the thin wire is:

M = ∫∫ρ(x,y) dA

=[tex]\int[-1,1]\int[0,x^2] x^2 y^2 dy dx[/tex]

This integral can be evaluated using standard integration techniques.

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The solution to the differential equation is:

[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]

What is a differential equation?

Any equation involving the derivatives of one dependent variable with respect to another independent variable is referred to as a differential equation. Differential equations are widely used in mathematics, but they also play an important role in the sciences of medicine, chemistry, physics, and engineering.

To solve this differential equation, we need to find a function y(x) that satisfies the equation. Here's how to do it:

First, we can divide both sides of the equation by D³ + 1 to get:

y = (eˣ+1)² / (D³+1)

Next, we can take the derivative of both sides with respect to x:

dy/dx = d/dx[(eˣ+1)² / (D³+1)]

Using the quotient rule of differentiation, we get:

dy/dx = [(D³+1)(2eˣ)(eˣ+1) - (eˣ+1)²(3D²)] / (D³+1)²

Simplifying the numerator, we get:

[tex]dy/dx = [2e^{(2x)} + 2e^x - 3D^{2}(e^x+1)^2] / (D^3+1)^2[/tex]

Therefore, the solution to the differential equation is:

[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]

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Answer:

0.06

Step-by-step explanation:

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle either is in the hexagon or in the circle

Area of rectangle = 26.2 * 13 =  340.6 sq inch

Area of Hexagon  = 3√3(side)²/2 = 3√3 (1.8)²/2 = 8.42 sq inch

Area of circle = π(radius)² = 3.14 * (2)² = 12.56 sq inch

Area of hexagon + area of circle = 12.56 + 8.42 = 20.98 sq inch

Probability of selecting point inside the hexagon or in the circle  = 20.98/340.6

= 0.06

The limit definition of the derivative is written as [tex]f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]. Here, h is defined as (x₂ – x₁) or ∆x or the change in x.

The limit definition of the derivative is also known as the difference quotient or increment definition of the derivative.  This is a product of the input value difference, (x + h) - x, and the function value difference, f(x + h) - f(x). This can be calculated using the difference quotient formula as follows,

[tex]\begin{aligned}f '(x) &= \lim_{h \to 0}\;\text{(difference quotient)}\\f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\end{aligned}[/tex].

Here, f(x) represents (y₁), f(x+h) represents (y₂), x represents x₁, x+h represents x₂, h represents (x₂ – x₁) or ∆x or the change in x, Lim represents the slope M as h→0, and f (x+h) – f (x) – represents (y₂ – y₁).

This provides a measurement of the function's average rate of change over an interval. In other words, this provides the current rate of change.

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The radius of the cone in terms of x is: r = √(x² + 14x + 49). This can be solved by using volume of cone formula.

Volume of cone (V) = 1/3πr²h, where r is the radius and h is the height of the cone.

Given:

h = 9 in.

V = 3πx² + 42πx + 147π

r = ?

Substitute

3πx² + 42πx + 147π = 1/3(π)(r²)(9)

3π(x² + 14x + 49) = (π)(r²)(3)

Divide both sides by 3π

x² + 14x + 49 = r²

Square on both sides

√(x² + 14x + 49) = r

r = √(x² + 14x + 49)

Therefore, the radius of the cone in terms of x is: r = √(x² + 14x + 49).

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The required, measure of QK is approximately 10.82.

In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.

First, we can use the Pythagorean theorem to find the length of side XZ:

[tex]XZ^2 = XY^2 - YZ^2[/tex]

[tex]YZ = \sqrt{(XY^2 - XZ^2) }[/tex]
[tex]= \sqrt(24^2 - 22^2) = 10[/tex]

The length of the perpendicular bisector of XY is half the distance between points A and the midpoint of XY. The midpoint of XY can be found by dividing the length of XY by 2:

midpoint of XY = (X + Y)/2

Since we are given the length of XY, we can find the coordinates of its endpoints X and Y. Let X be the origin (0,0) and let Y have coordinates (24,0) (since XY = 24). Then the midpoint of XY is the midpoint of XY
= (X + Y)/2
= (0 + 24)/2
= (12,0)

Now we can use the distance formula to find the distance between A and the midpoint of XY distance between A and the midpoint of XY
= [tex]= \sqrt((12 - 0)^2 + (0 - 15)^2)[/tex]
= [tex]\sqrt(12^2 + 15^2)[/tex]
=[tex]3 \sqrt(29)[/tex]

This is the length of the perpendicular bisector of XY, which passes through the center of the circumscribed circle. So the distance from Q to the center of the circle is the distance from Q to center = 15 - 9 = 6

Finally, we can use the Pythagorean theorem to find QK:

[tex]QK^2 = QJ^2 + JK^2 = QJ^2 + (distance \ from \ Q \ to\ center)^2[/tex]

[tex]QK^2 = 9^2 + 6^2 = 81 + 36 = 117[/tex]

[tex]QK = \sqrt(117)\\ = 10.82[/tex]

Therefore, QK is approximately 10.82.

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Answer:

pair c has the inverse functions

The yield of 5x2 is 10

Yield is a term used in mathematics to describe the output or result of a calculation or operation. In this case, we are looking at the yield of 5 multiplied by 2 (5x2).

When we multiply two numbers together, we are finding the yield or product of those numbers. In this case, 5 multiplied by 2 gives us a yield of 10. So, the yield of 5x2 is 10.

It's important to note that yield can be used in different contexts in mathematics, such as in finance to describe the return on an investment or in chemistry to describe the amount of product obtained from a chemical reaction. But in this case, we are simply looking at the yield of a multiplication operation.

In summary, which means that when we multiply 5 and 2 together, we get a result or output of 10.

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If the  fruit seller threw some rotten apples away and the ratio of apples to oranges became 1 : 4. The fruit seller threw away 630 rotten apples.

To find the number of rotten apples that the fruit seller threw away, we will need to use the given information and set up equations to solve for the unknown variable.

Let's start by using the given information that there were 2/3 as many apples as oranges. We can set up an equation to represent this relationship:

2/3 O = A

Where O is the number of oranges and A is the number of apples.

We are also given that the fruit seller had 2520 apples and oranges in total. We can set up another equation to represent this relationship:

O + A = 2520

Now, we can use the first equation to solve for one of the variables in terms of the other. Let's solve for A in terms of O:

A = (2/3)O

Now we can substitute this expression for A into the second equation:

O + (2/3)O = 2520

Simplifying this equation gives us:

(5/3)O = 2520

Now we can solve for O:

O = (3/5)(2520) = 1512

Now that we know the number of oranges, we can use the first equation to solve for the number of apples:

A = (2/3)(1512) = 1008

So the fruit seller originally had 1008 apples and 1512 oranges.

We are also given that after throwing away some rotten apples, the ratio of apples to oranges became 1:4. We can set up an equation to represent this relationship:

(A - X)/O = 1/4

Where X is the number of rotten apples that were thrown away.

Substituting the values we found for A and O into this equation gives us:

(1008 - X)/1512 = 1/4

Cross-multiplying and simplifying gives us:

4(1008 - X) = 1512

4032 - 4X = 1512

4X = 2520

X = 630


Therefore, the answer to the question is 630.

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20 centimeter is approximately equal to 7.8740 inches ( rounded to four decimal places )

To convert 20 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

20 cm = 20 x 0.393701

Multiply the numbers

= 7.8740 inches ( rounded to four decimal places )

Therefore, 20 centimeter is 7.8740 inches

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The minimum value of the bacterial population on the interval [2, 6] is 4, and the maximum value is 64.

To find the minimum and maximum values of the bacterial population along the interval [2, 6], we need to evaluate the function b(t) at t = 2 and t = 6, respectively, and then compare the results.

at t = 2

b(2) = 2^2 = 4, which means that after 2 days, the sample has 4 bacteria.

at t = 6

b(6) = 2^6 = 64, which means that after 6 days, the sample has 64 bacteria.

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Answer:

Ms. Perry needs to make an additional 1/24 kg of fudge.

Step-by-step explanation:

Ms. Perry has a total of 8/8 + 1/6 = 13/6 kg of fudge. She needs 1 1/8 kg of fudge for the brownies, which is equivalent to 9/8 kg. To find how much more fudge she needs to make, we can subtract the amount of fudge she already has from the amount she needs:

9/8 - 13/6 = 27/24 - 26/24 = 1/24

Therefore, Ms. Perry needs to make an additional 1/24 kg of fudge.

Answer:

Step-by-step explanation:

Decimals are out of 100.

7/10 = 70/100

Which equals to 0.70 or 0.7

So your answer is 0.70 (0.7)

Answer:

The exact decimal equivalent of 7/10 is 0.7

Step-by-step explanation:

The reason for this is because when you divide something by ten you move the decimal place one place to the left.

So then 7.0 becomes 0.7 because the decimal place is moved once divided by ten.

The mean of the data is 16.5 and the standard deviation is 7.28

The given data set is a small sample of 12 observations.

To determine the type of distribution, we can first create a histogram or a boxplot of the data.

A histogram of the data shows that the distribution is unimodal and slightly right-skewed.

Alternatively, we can calculate the skewness of the data. If the skewness is close to zero, then the data is approximately symmetric. If the skewness is positive, then the data is right-skewed. If the skewness is negative, then the data is left-skewed.

Calculating the skewness of the data set, we get:

skewness = (n / ((n - 1) * (n - 2))) * Sum[(xi - x-bar)^3 / s^3]

where n is the sample size, x-bar is the sample mean, s is the sample standard deviation, and Sum is the sum of the values in the data set.

Using this formula, we get a skewness of approximately 0.456, which indicates that the distribution is slightly right-skewed.

Based on these findings, we can conclude that the distribution of the data set is approximately normal, but slightly right-skewed.

To find the best measure of center and spread, we can calculate the sample mean and sample standard deviation, respectively.

Sample mean:

mean = (1 + 7 + 11 + 14 + 17 + 17 + 17 + 21 + 21 + 23 + 23 + 26) / 12 = 16.5

Sample standard deviation:

s = sqrt((1/11) * [(1 - 16.5)^2 + (7 - 16.5)^2 + ... + (26 - 16.5)^2]) = 7.28

Therefore, the best measure of center for this data set is the sample mean of 16.5, and the best measure of spread is the sample standard deviation of 7.28.

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Answer:

Inscribed angle

Step-by-step explanation:

Central angles have the vertex as the center of the circle, and chords are not angles

Answer:

$129,870.13 AUD

Step-by-step explanation:

To find out what we need to solve, we can use these exchange rates:

Now, we need to divide 100,000 by 0.77.

We do this because we need to figure out how many times 0.77 must be multiplied to get 100,000. Then, we take that amount, and multiply that by however many AUD's you have.

Therefore, for every $100,000 USD, there is $129,870.13 AUD.

a) 30 minutes are taken to have the same amount of water.

b) Both pools have an amount of 1372.5 liters when 30 minutes have passed.

A linear function is one that produces a straight line when plotted. Generally, it is a polynomial function with a maximum degree of 1 or 0. 

Now in the given question ,

a) Physically speaking, the capacity (Q) of each pool, in liters, is equal to the product of flow rate , in liters per minute, and time (t), in minutes. Hence, we derive the following functions :

First pool,

[tex]Q_1=915+15.25t\\[/tex]           ...... (1)

Second pool,

[tex]Q_2=45.75t[/tex]                   ....... (2)

The following expression can be used to calculate how long it will take to find two pools with the same amount of water:

[tex]Q_1=Q_2[/tex]                       ........ (3)

By putting value of (1) and (2) in (3),

915 + 15.25 t = 45.75 t

30.5 t = 915

t = 915 ÷ 30.5

t = 30 minutes

30 minutes are taken to have the same amount of water.

b) By (2) and knowing that t = 30 , then we have the corresponding amount:

[tex]Q_2=45.75t\\\\Q_2=45.75*30\\\\Q_2=1372.5L[/tex]

Both pools have an amount of 1372.5 liters when 30 minutes have passed.

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Answer:2/8 + 2/8

Step-by-step explanation:

so, you start at 2/8

then, you add the extra 2/8

then, you add them together ( don’t forget: when the bottom numbers of the fraction are the same the stay at the same number ex: 3/8 + 3/8 = 6/8)

then after adding them up you get 4/8 which could also mean 1/2

Answer:

2

Step-by-step explanation:

The seventh root of a number is the number that would have to be multiplied by itself 7 times to get the original number so if you multiply 2 by itself 7 times you'd get 128

The length of each side of the square by factoring the area expression are  (4x+3).

A square's area is equal to the square of each side since all of its sides are the same length.

The following is the formula for determining a square's area:

A = L²

where L is the length of each side of square.

Given the area of a square expressed as 16x² + 24x + 9

Factorize 16x² + 24x + 9

16x² + 24x + 9

=  16x² + 12x + 12x + 9

= 4x(4x+3) + 3(4x+3)

= (4x+3)²

Hence the length of each side of the square is (4x+3).

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Answer:

[tex]a = \frac{5 \sqrt{2} }{2} [/tex]

[tex]c = \frac{3 \sqrt{3} }{2} [/tex]

Step-by-step explanation:

The first triangle is an isoceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. So we have:

[tex]a \sqrt{2} = 5[/tex]

[tex]a = \frac{5}{ \sqrt{2} } = \frac{5 \sqrt{2} }{2} [/tex]

The second right triangle is a 30°-60°-90° triangle, so the length of the shorter leg is one-half the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. Here, the length of the shorter leg is 3/2, or 1.5, and so we have:

[tex] {( \frac{3}{2}) }^{2} + {c}^{2} = {3}^{2} [/tex]

[tex] {c}^{2} = \frac{27}{4} [/tex]

[tex]c = \frac{3 \sqrt{3} }{2} [/tex]

Answer: a) To find the height of the pyramid, we can use the Pythagorean theorem. Let H be the height of the pyramid, and let M be the midpoint of QR. Then, PM is half of PQ, which is 15 cm. We can use the Pythagorean theorem to find H:

H^2 = PQ^2 - PM^2

H^2 = 30^2 - 15^2

H^2 = 675

H = sqrt(675) = 5 sqrt(3) cm

b) To find the angle that PS makes with the base QRST, we can use trigonometry. Let A be the foot of the perpendicular from P to the base QRST, and let B be the midpoint of PS. Then, we have:

tan(angle PSB) = AB / PB

Since triangle PAB is a right triangle, we can use the Pythagorean theorem to find AB:

AB^2 = AP^2 - PB^2

AB^2 = H^2 + (PQ/2)^2 - PB^2

AB^2 = (5 sqrt(3))^2 + (15/2)^2 - PB^2

AB^2 = 225/4 + 75 - PB^2

AB^2 = 375/4 - PB^2

Since triangle PBS is also a right triangle, we can use the Pythagorean theorem to find PB:

PB^2 = PS^2 - BS^2

PB^2 = (2 H)^2 - (PQ/2)^2

PB^2 = 4 (5 sqrt(3))^2 - (15/2)^2

PB^2 = 500 - 56.25

PB^2 = 443.75

Substituting these values into the equation for tan(angle PSB), we get:

tan(angle PSB) = sqrt(375/4 - 443.75) / sqrt(443.75)

tan(angle PSB) = -0.4385

Since angle PSB is in the second quadrant, we have:

angle PSB = 180 degrees + arctan(-0.4385) = 152.4 degrees (rounded to one decimal place)

c) To find the total surface area of the pyramid, including the base, we can divide the pyramid into four triangular faces and a square base. The area of each triangular face can be found using the formula:

area = (1/2) base * height

where the base is the length of one edge of the square base, and the height is the height of the pyramid. The area of the base is simply the area of the square QRST, which is (20 cm)^2 = 400 cm^2. Therefore, we have:

area of each triangular face = (1/2) (20 cm) (5 sqrt(3) cm) = 50 sqrt(3) cm^2

total surface area = 4 (50 sqrt(3) cm^2) + 400 cm^2 = 200 sqrt(3) cm^2 + 400 cm^2

total surface area = (200 + 200 sqrt(3)) cm^2 ≈ 532.4 cm^2 (rounded to one decimal place)

Step-by-step explanation:

The probability that the sample average exceeded 5100 is given as follows:

0%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 250, \sigma = 5000, n = 64, s = \frac{5000}{\sqrt{64}} = 625[/tex]

The probability that a sample average exceeds $5,100 is one subtracted by the p-value of Z when X = 5100, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (5100 - 250)/625

Z = 7.76

Z = 7.76 has a p-value of 1.

1 - 1 = 0.

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The volume of the rectangular prism in the image is 480 cubic units.

What is volume ?

Volume is a measurement of the amount of space occupied by a three-dimensional object. It is a physical quantity that is measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

The image shows a rectangular prism with a length of 12 units, a width of 8 units, and a height of 5 units.

To find the volume of a rectangular prism, you need to multiply its length, width, and height.

So, the volume of the rectangular prism in the image is:

Volume = length x width x height

Volume = 12 units x 8 units x 5 units

Volume = 480 cubic units

Therefore, the volume of the rectangular prism in the image is 480 cubic units.

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In the given homogeneous system in parametric vector form, where the solution set is x = x₁ x₂ x₃, x = x₃. where the value of x₁ = 5k, x₂ = 5k and x₃ = 10k.

The system is

x₁ + x₂ - 15x₃ = 0 .......(1)

2x₁ + x₂ - 15x₃ = 0 .......(2)

-x₁ + x₂ = 0

We write the system in the matrix form or AX = 0

Where A = ( 1   2   -15)                 and X = ( x₁)

                 ( 2   1    -15)                               (x₂)

                 ( -1   1      0)                               (x₃)

Now, | A | = [15] -2 [-15] -15 [2+1]

= 15 + 30 - 45

= 0

∴ Since, | A | = 0, ∴ Given system has non-trivial solution.

Let x₃ = k

∴ From equation (1), x₁ + x₂ = 15k

from equation (2), 2x₁ + x₂ = 15k × 2

4x₁ + 2x₃ = 30k - x₁  + 2x₂ = 15k

= 3x₁ = 15k

∴ x₁ = 5k

and x₂ = 15k - 2x₁ = 15k - 10k

∴ x₂ = 5k.

To find x₃ = x₁ + x₂

x₃ = 5k + 5k

∴ x₃ = 10k.

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