Stanley left his home at 8:00 a. M. And went to Peter's house. For the first 48 minutes of his trip, his average driving speed was 50 km/h. (a) Find the distance travelled (in km) for the first 48 minutes of his trip. (b) For the remaining journey, Stanley drove at a speed of 90 km/h for 1 minutes. It is given that his average driving speed for the whole journey is 70 km/h. Hours if he -Example 73) (i) Express, in terms of 1, the distance travelled (in km) for the remaining journey. (ii) Did Stanley arrive at Peter's house before 9:30 a. M. ? Explain your answer

Point KLMN in the quadrilateral has coordinates that are [tex]N' (-3, 2)[/tex].

The enclosed figure of a quadrilateral has four sides. Raphael created the quadrilaterals in these geometric forms. a shape in quadrilaterals. The shape contains no right angles and just single set of parallel sides.

A closed form noted for having sides with various widths and lengths is a quadrilateral. It is a closed, two-dimensional polygon with four sides, four angles, and four vertices. The trapezium, parallelogram, rectangular, square, rhombus, and kite are just a few examples of quadrilaterals.

When a point is reflected across the [tex]y-axis[/tex], its [tex]x[/tex]-coordinate becomes its opposite while its [tex]y[/tex]-coordinate remains the same.

So to find the coordinates of [tex]N[/tex]', we need to reflect the point [tex]N(3, 2)[/tex]across the y-axis, which means we change the sign of its x-coordinate:

[tex]N' = (-3, 2)[/tex]

Therefore, the coordinates of point [tex]N'[/tex] are [tex](-3, 2)[/tex].

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Answer: [tex]c-34=21[/tex]; 55 cups of lemonade.

Step-by-step explanation:

We are given the amount sold and the amount leftover so we need to figure out how many cups were there at the start. Since you are subtracting the amount of cups you sold from the amount you start with and it equals an end amount, the cups can be modeled by the equation [tex]c-34=21[/tex] rather than [tex]21+c=34[/tex].

Now to solve for c

[tex]c-34=21\\[/tex]

add 34 to both sides

[tex]c=55[/tex]

False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B).

Probability refers to the measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 indicates a certain event.

This formula is known as the Addition Rule for Probability and states that to calculate the probability of either event A or event B occurring (or both), we add the probability of A happening to the probability of B happening, but then we need to subtract the probability of both A and B happening at the same time to avoid double counting.

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The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.

The formula for the probability that a truck drives between 99 and 128 miles in a day is:

[tex]Z = (X - \mu) /\sigma[/tex]

where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:

[tex]Z = (99 - 120) / 11 = -1.91[/tex]

The value of Z for 128 miles driven per day is:

[tex]Z = (128 - 120) / 11 = 0.73[/tex]

Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:

[tex]P(-1.91 < Z < 0.73) = 0.7734[/tex]

Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

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The contrapositive of the given statement is "If it is not a cat, then it is a lion."

The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).

The contrapositive takes the form:

"If it is not a cat, then it is a lion."

So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."

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Answer:

Step-by-step explanation:\Write an expression for the sequence of operations describe below Add C and the quotient of 2 and D do not simplify any part of the expression

Answer:

  (A)  10e^(i7π/4)

Step-by-step explanation:

You want the exponential form of 5√2 -5i√2.

There are numerous ways a complex number can be written in "polar form".

The usual choices are ...

  a +bi . . . . . . . . . . . . . rectangular form

  A(cos(θ) +i·sin(θ)) . . . . a sort of hybrid form

  A·cis(θ) . . . . . . . . . . an abbreviation of the above

  A∠θ . . . . . . . . . . . . polar form

  A·e^(iθ) . . . . . . . . . using Euler's formula

The conversion from rectangular form to any of the others makes use of trig identities and the Pythagorean theorem.

  A = √(a² +b²)

  θ = arctan(b/a) . . . . . with attention to quadrant

For the given number, ...

  A = √((5√2)² +(-5√2)²) = (5√2)√(1 +1) = 5·2

  A = 10

  θ = arctan(-5√2/(5√2)) = -1 . . . in the 4th quadrant

  θ = 7π/4

Then the desired exponential form of the complex number is ...

  10e^(i7π/4)

__

Additional comment

Spreadsheets and some calculators have an ATAN2(x, y) function that performs a quadrant-sensitive angle conversion.

a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%.

Human blood is categorized into four types which are A, B, AB, and O. The percentages of Americans who have each of the four types are given below:

O - 43% A - 40% B - 12% AB - 5%

To calculate probabilities for various scenarios, we can use these percentages as follows.

a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%. The combined percentage of O and AB blood types is 48%. We can therefore say that the probability of an American having O or AB blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%. The percentage of Americans who don't have type O blood is the sum of percentages of A, B, and AB blood types, which is  Hence, the probability of not having O blood is lower than 57%. Therefore, the probability of a randomly selected American not having type O blood is 57%.

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Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P[tex](1-r)^{n}[/tex] = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320[tex](1-0.07)^{n}[/tex] = 100

Simplifying the equation, we get:

[tex]0.93^{n}[/tex] = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:

One solution

Step-by-step explanation:

I added a photo of my solution

Answer:

The system has one solution: (0, 4).

The solution to the system of equations is (x, y) = (1, -1) where the given equations are 11x+9y=-20 and x=-5y-6.

The substitution method is a technique used in algebra to solve systems of equations by replacing one variable with an expression containing another variable. The goal is to eliminate one of the variables so that we can solve for the other one.

We are given the following system of two equations with two variables:

11x + 9y = -20 (equation 1)

x = -5y - 6 (equation 2)

To solve the system using the substitution method, we need to solve one of the equations for one of the variables, and then substitute the expression for that variable into the other equation. Let's solve equation 2 for x:

x = -5y - 6

Now we can substitute this expression for x into equation 1, and solve for y:

11x + 9y = -20

11(-5y - 6) + 9y = -20 (substituting x = -5y - 6)

-55y - 66 + 9y = -20

-46y = 46

y = -1

Now that we have found y = -1, we can substitute this value back into equation 2 and solve for x:

x = -5y - 6

x = -5(-1) - 6

x = 1

Therefore, the solution to the system of equations is (x, y) = (1, -1).

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If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.

Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.

It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.

If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:

If x=4, (4×4)^1/2 = 4

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The value of the given expressions are as follows: a. 25 b. 4 c. 1/4 d. 1/3.

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical object or quantity. Expressions can be written using variables, operations, functions, and mathematical symbols such as parentheses, exponents, and radicals. An expression can represent a value, an equation, or a formula, and can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 2x + 5, sin(θ), and (a + b)².

Here,

a. [tex]125^{2/3}[/tex]

radical form:

[tex]\sqrt{ (125^2)} = 125^{1/2}[/tex]

[tex]125^{1/2}[/tex] = √125

= 5√5

Therefore, [tex]125^{2/3} = (125x^{1/3})^{2}[/tex]

= [tex](5^3)x^{2/3}[/tex]

= [tex]5x^{3*2/3}[/tex]

= 5²

= 25

b. √16

In radical form:

√16 = 4

Therefore, [tex]16x^{-1/2} = \sqrt{16}[/tex]

= 4

c. [tex]16^{1/2}[/tex]

In radical form:

1/√16 = 1/4

Therefore, [tex]16^{-1/2} = 1/\sqrt{16}[/tex]

= 1/4

d.[tex]\sqrt[4]{81}[/tex]

In radical form:

[tex]\sqrt[4]{81}[/tex] = √(√81)

= √9

= 3

Therefore, [tex]\sqrt[4]{81} = 1/\sqrt[4]{81}[/tex]

= 1/3

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a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.

ii. For mothers who smoke is 6.82 pounds.

iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:

Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.

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In response to the stated question, we may state that The scatter plot indicates a clustering pattern in the data, and as elevation increases, temperature drops.

"Scatter plots are graphs that show the association of two variables in a data collection. It is a two-dimensional plane or a Cartesian system that represents data points. The X-axis represents the independent variable or characteristic, while the Y-axis represents the dependent variable. These plots are sometimes referred to as scatter graphs or scatter diagrams."

"A scatter plot is also known as a scatter chart, scattergram, or XY graph. The scatter diagram plots numerical data pairings, one variable on each axis, to demonstrate their connection."

Because the graph is a scatter plot, the data displays a clustering pattern.

We may deduce from the figure that as height increases, temperature falls.

As a result, C and E are the proper choices.

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The correct question is -

The scatter plot shows the relationship between elevation and temperature on a certain mountain peak in North America. Which statements are correct?

A. The data shows one potential outlier

B. The data shows a linear association

C. The data shows a clustering pattern

D. The data shows a negative association

E. As elevation increases, temperature decreases

The theorem is Every nonzero element in the ring has an inverse, hence we deduce that Z[i]/(p) is a field. For any prime number p that is irreducible in Z[i], as asserted, Z[i]/(p) is a field.

         Proof of Theorem is Let p be a prime number that is irreducible in Z[i]. We want to show that Z[i]/(p) is a field, where (p) denotes the ideal generated by p.

Suppose that [c] + [d]i is a nonzero element of [tex]Z[i]/(p)[/tex], where [c] and [d] are congruence classes in Zp.

If one of [c] and [d] is [0], then [c] + [d]i is a unit, since the other element is nonzero. So, suppose that [c] and [d] are both nonzero in Zp.

We observe that p cannot divide c + di in Z[i] since p is irreducible in Z[i] and it cannot divide both c and d. Therefore, p and c + di are relatively prime in Z[i].

            By Theorem 16.7, there exist Gaussian integers r and s such that [tex](c + di)r = 1 + ps.[/tex]

Now, suppose that [e] + [f]i is another nonzero element of Z[i]/(p), where [e] and [f] are congruence classes in Zp. We want to show that [e] + [f]i is also a unit.

Since p and c + di are relatively prime, there exist integers u and v such that [tex]pu + (c + di)v = 1[/tex] , by Bezout's identity.

Multiplying both sides by e + fi, we get:

          [tex]pue + (c + di)ve + (ce - df) + (cf + de)i = e + fi[/tex]

Therefore, [tex](e + fi)(ue + vi(c + di)) = (e + fi)(1 - (cf + de)i)[/tex]

Multiplying both sides by the conjugate of (e + fi), we get:

           [tex](e + fi)(e - fi)(ue + vi(c + di)) = (e^2 + f^2)[/tex]

Since p is irreducible in Z[i], it is also prime. Thus, Z[i]/(p) is an integral domain, which means that the product of two nonzero elements is nonzero. Therefore, [tex]e^2 + f^2[/tex] is nonzero in Zp, and

so    [tex](e + fi) (ue + vi(c + di))[/tex] is a unit in Z[i]/(p).

             We conclude that Z[i]/(p) is a field since every nonzero element has an inverse in the ring.

            Therefore, Z[i]/(p) is a field for any prime number p that is irreducible in Z[i], as claimed

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For a bounded region, R between the curves y = 4x² and y = 4 and the volume of a solid has base R, and cross sections perpendicular to the y-axis is equals to the π square units.

We have a region R is bounded by the curves y = 4x² and y = 4. Solid has base R and cross sections perpendicular to the y-axis are semicircles with the diameter lying in region R. When solving the volume using slicing method we use the basic formula which is the area times the length V = A×l, where A is the area of the cross-section. Also, the formula for the area of cross section for semicircle

= (1/2)π(d/2)²

= (π/8)d², where d is the diameter

Based on the graph the volume of a single semicircle strip is, dV = (π/8)x²dy

=> dV = (π/8) (y/4) dy ( since, y = 4x² , x²

= y/4 )

=> dV = (π/32)4y dy

=> dV = (π/8)ydy --(1)

Now, the limits are, y = 0, 4

Integrating equation (1), with limits 0 to 4.

[tex]∫dV = \frac{π}{8} ∫_{0}^{4}y dy[/tex]

[tex]V= \frac{π}{8} [ \frac{y^{2} }{2} ]_{0}^{4} [/tex]

[tex]V = \frac{π}{8} [ \frac{16}{2} - 0] = 8(\frac{π}{8}) = π[/tex]

Hence, the required volume is π square units.

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The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.

The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.

Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.

Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.

Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.

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The correct answer is graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9.

Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph. In a line graph, the x-axis is the horizontal line and the y-axis is the vertical line.

The first graph shows a relationship between the number of side dishes and the total cost of the special that does not match the data given in the table.

The second graph does not reflect the data given in the table, as the total cost of the special increases from $5.25 to $9.00 when the number of side dishes increases from 0 to 5.

The third graph also does not reflect the data given in the table, as the total cost of the special increases from $6.75 to $8.25 when the number of side dishes increases from 0 to 4.

The fourth graph also does not reflect the data given in the table, as the total cost of the special increases from $5.75 to $7.25 when the number of side dishes increases from 0 to 1.

Therefore, the correct answer is mentioned above. This graph accurately reflects the relationship between the number of side dishes and the total cost of the special.

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The correct answer is "graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0,6 and 75 hundredths through the point 3,9".

Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph.

This graph correctly illustrates the relationship between the number of side dishes and the total cost of the special as shown in the table.

The line starts at 0 side dishes and $6.75

and ends at 4 side dishes and $8.25, both of which are in the table.

The graph accurately reflects this by having a line that starts at 2 side dishes and $6.75 and ends at 5 side dishes and $9.00.

This shows that as the number of side dishes increases, the cost also increases.

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By using addition calculation, we determine that Angela will end up making 42 cards in total.

Angela made 23 cards for her friends, but she wants to make even more to share with others. To determine how many cards she will make in total, we need to add the number of cards she has already made with the number of cards she plans to make.

So, we add 23 (the number of cards she has made) and 19 (the number of cards she plans to make) so in total, she will make:

23 + 19 = 42

Therefore, Angela will make 42 cards in all.

By using simple arithmetic calculation of basic addition, we find that  Angela will make 42 cards in all.

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Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

The missing area or side length in the triangles are:

1: Area = 145 units²

2: Area =  17 units²

3: Area  = 29 units²

4: Area= 27 units²

5: length = √37 units

6: length = 2√26 units

7: length = 3√11 units

8: length  = 5√3 units

Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. That is:

c² = a² + b²

Where  a and b are the lengths of the legs, and c is the length of the hypotenuse

No. 1

Area (hypotenuse)  = 81 + 64 = 145 units²

No. 2

Area (hypotenuse)  = 16 + 1 = 17 units²

No. 3

Area (hypotenuse)  = 5² + 2² = 29 units²

No. 4

Area (leg)  = 36 - 9 = 27 units²

No. 5

length (hypotenuse)  = √(6² + 1²) = √37 units

No. 6

length (hypotenuse)  = √(10² + 2²) = 2√26 units

No. 7

length (leg)  = √(10² - 1²) = 3√11 units

No. 8

length (leg)  = √(10² - 5²) = 5√3 units

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The vertices of the resulting image, quadrilateral H’ I’ J’ K’ include the following:

H' (4, -1).

I' (2, -3).

J' (-4, 1).

K' (-2, 3).

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).

By applying a rotation of 270° about the origin to quadrilateral HIJK, the location of its vertices is given by:

(x, y)                                   →         (y, -x)

Ordered pair H (1, 4)        →    Ordered pair H' (4, -(1)) =  (4, -1).

Ordered pair I (3, 2)        →    Ordered pair I' (2, -(3)) =  (2, -3).

Ordered pair J (-1, -4)        →    Ordered pair J' (-4, -(-1)) =  (-4, 1).

Ordered pair K (-3, -2)        →    Ordered pair K' (-2, -(-3)) =  (-2, 3).

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The number which, when subtracted from 80, results in -30 is equal to 110.

To solve this problem, we can use algebraic equations to represent the given information. Let x be the number that we want to find.

According to the problem, when we subtract x from 80, we get -30:

80 - x = -30

To solve for x, we can isolate it on one side of the equation by adding x to both sides, and then simplify:

80 - x + x = -30 + x

80 = -30 + x

Next, we can isolate x by subtracting -30 from both sides:

80 - (-30) = x

Simplifying the right-hand side:

80 + 30 = x

110 = x

Therefore, the number that was subtracted from 80 and gave -30 as the result is 110.

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The city had 20,000 residents. The next year, it went up by 2%. The new population of the city after a 2% increase is 20400.

To find the new population of the city after a 2% increase from 20000, we need to use the following formula:

New population = Old population + (Percentage increase x Old population)

Substituting the given values into the formula, we get:

New population = 20000 + (2/100 x 20000)

New population = 20000 + 400

New population = 20400

It is important to note that this calculation assumes that the increase in population is the only factor affecting the total population. In reality, there may be other factors that affect the population, such as migration, birth rates, and mortality rates.

Additionally, this calculation only gives the estimated population based on the percentage increase, and the actual population may differ due to various factors.

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By answering the presented question, we may conclude that As a result, expressions Ivanna's average speed is approximately 2.311 miles per hour.

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

We can use the formula:

rate = distance / time

Let's calculate Ivanna's rate for the first part of her journey:

rate = distance divided by time = 12 miles divided by 5 hours = 2.4 miles per hour

Let us now compute Ivanna's rate for the second leg of her journey:

rate = distance divided by time = 20 miles divided by 9 hours = 2.222... miles per hour

As a result, Ivanna's overall rate is the average of these two rates:

rate = (2.4 miles per hour + 2.222... miles per hour) / 2 = 2.311... miles per hour

As a result, Ivanna's average speed is approximately 2.311 miles per hour.

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The Z-score of the interval within standard deviations of the mean for a normal distribution contains 87% of the probability is 1.11 (rounded to two decimal places).

To find the z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we need to use the standard normal distribution table (Z-table) or a calculator that has the inverse normal function.

The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of 1. It is denoted by the letter Z. Z-scores measure the number of standard deviations a data point is from the mean of the data set. A positive Z-score indicates a data point is above the mean, while a negative Z-score indicates a data point is below the mean.

To find the Z-score such that the interval within standard deviations of the mean for a normal distribution contains 87% of the probability, we first need to find the probability that is outside the interval. Since the interval is within standard deviations of the mean, we can use the empirical rule or the 68-95-99.7 rule to find the probability that is outside the interval.

The 68-95-99.7 rule states that 68% of the probability lies within 1 standard deviation of the mean 95% of the probability lies within 2 standard deviations of the mean 99.7% of the probability lies within 3 standard deviations of the mean. Since we are interested in the interval within standard deviations of the mean that contains 87% of the probability, we can assume that the interval is 1 standard deviation away from the mean.

Using the 68-95-99.7 rule, we can find the probability that is outside the interval:

100% - 68% = 32%

Since the probability that is outside the interval is 32%, we want to find the Z-score that corresponds to the probability of 16% on either side of the mean. We use the Z-table or a calculator that has the inverse normal function to find the Z-score that corresponds to a probability of 0.16.

From the Z-table, the Z-score that corresponds to a probability of 0.16 is 1.11 (rounded to two decimal places).

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Answer:

(a - 1)(3p - 2)

Step-by-step explanation:

3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term

= (a - 1)(3p - 2)

Answer:

Step-by-step explanation:

is 8,15,24

The required perimeter is 25+√61 units.

We can find the distance between each pair of consecutive points and then add them up to get the perimeter of the polygon.

Using the distance formula, the distance between points A and B is:

[tex]$$AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(-4 - 4)^2 + (8 - 2)^2} = \sqrt{100} = 10$$[/tex]

Similarly, the distances between the other pairs of points are:

[tex]$$BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(-7 + 4)^2 + (4 - 8)^2} = 5$$[/tex]

[tex]$$CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(-1 + 7)^2 + (-4 - 4)^2} = 10$$[/tex]

[tex]$$DA = \sqrt{(x_A - x_D)^2 + (y_A - y_D)^2} = \sqrt{(4 + 1)^2 + (2 + 4)^2} = \sqrt{61}$$[/tex]

Therefore, the perimeter of the polygon is:

[tex]$$AB + BC + CD + DA = 10 + 5 + 10 + \sqrt{61}$$[/tex]

= 25+√61

Thus, required perimeter is 25+√61.

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