Figure 1 and Figure 2 below are similar. Which point corresponds to point V?

The dimensions of this rectangular swimming pool include the following:

Width = 10 meters.

Length = 21 meters.

Mathematically, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

From the information about the width, we have:

Width, W = L - 11

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

62 = 2(L + L - 11)

62 = 4L - 22

4L = 84

Length, L = 21 meters.

For the width, we have:

Width, W = L - 11

Width, W = 21 - 11

Width, W = 10 meters.

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1. The probability the project will be finished in 62 weeks or less is 0.6915. 2.The probability the project will be finished in longer than 65 days is 0.8944.

The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalising is the process of transforming a raw score into a standard score.

Given that,

mean = 60 weeks

SD = 4 weeks

1. P (p ≤ 62) = P(z ≤ 62)

The z-score is given by:

z-score = x - mean / SD

Substituting the values we have:

z-score = 62 - 60/4 = 2/4 = 0.5

P(z ≤ 0.5) = 0.6915 (Using the z -table)

Hence, the probability the project will be finished in 62 weeks or less is 0.6915.

Similarly,

2. P(z > 65) = P(z > 1.25) = 0.8944

Hence, the probability the project will be finished in longer than 65 days is 0.8944.

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The slope of this graph​ is equal to 0.375 or 3/8.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (35 - 20)/(40 - 0)

Slope, m = 15/40

Slope, m = 0.375 or 3/8.

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Answer:

Second inequality is
12x + 16y ≥ 460

We also have implied inequalities x ≥ 0, y ≥ 0 meaning hours cannot be negative

Step-by-step explanation:

The other equality refers to the earnings

Let x be the hours worked in the first job
Earnings at $12 per hour = 12x

Let y be the hours worked in the second job
Earnings at $16 per hour = 16y

Total earnings = 12x + 16y
This must be at least $460
"at least" means ≥

So second inequality is
12x + 16y ≥ 460

The equation has no real solution.

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

Given that;

The function is,

⇒ y = 4 (x + 1)³ + 8

Now, All the zeroes are find by substitute y = 0,

⇒ y = 4 (x + 1)³ + 8

⇒ 0 = 4 (x + 1)³ + 8

⇒ 4 (x + 1)³ = - 8

⇒ (x + 1)³ = - 8

⇒ x + 1 = ∛- 8

⇒ x + 1 = ∛8i²

⇒ [tex]x + 1 = 2i^{2/3}[/tex]

⇒ [tex]x = 2i^{2/3} - 1[/tex]

Hence, It has no real solution.

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The domain where fx) is 1-to-1 is x ≥1 , and the inverse there is:

f⁻¹(x) =  √x + 1

Here we have the quadratic function:

f(x) = (x - 1)^2

If we look from the vertex to the right (or the left, is the same) we will have an one to one function.

Here the vertex is at x = 1

f(1) = (1 - 1)^2 = 0

Then for x ≥1 we have an one to one function.

Noe let's find the inverse, if the inverse is f⁻¹(x), then we must have that:

f( f⁻¹(x) ) = x

Solving that:

(f⁻¹(x)  - 1)^2 = x

(f⁻¹(x)  - 1) = √x    (here we only take the positive square root)

f⁻¹(x) =  √x + 1

That is the inverse.

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Answer: i think its 20

Answer:

1 2/3 x 12 = 20

Step-by-step explanation:

1 2/3 x 12  = 5/3 x 12

5x12/ 3 x 1

60/3

60/3 / 3/3

= 20

A function that represents the height of Elmer's carriage is,

h(x) = 52cosx + 77.

The adjacent side to hypotenuse ratio is known as the cos function. It aids in determining the triangle's side lengths regardless of the provided angle. If the angle between the adjacent side and the hypotenuse of a right triangle is, we may write this using the cosine function. Adjacent Side/Hypotenuse = Cos.

Given:
Elmer is on a Ferris wheel which has a diameter of 104 ft and whose center is 129 ft off the ground.

That means the radius of the Ferris wheel is r = 104/2 = 52 feet.

The wheel is 129 - 52 = 77 feet off the ground.

Elmer's carriage makes an angle of x radians in a horizontal way.

So, the height of Elmer's carriage is,

= rcosx + a

Here, r = 52 and a = 77

So, we get,

h(x) = 52cosx + 77.

Therefore, the function is h(x) = 52cosx + 77.

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The mean and the variance of the poisson distribution are;

Mean = 2.66

Variance = 1.277

The formula for the PMF of a Poisson distribution is;

p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......

Thus;

p(x = 0) =  [e^(-λ) * λ^(0)]/0!

e^(-λ) = 0.07

λ = - In 0.07

λ = 2.66

That is the mean

Variance is square root of standard deviation;

Variance = √√(2.66)

Variance = 1.277

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Answer:

2.65926003693 for mean and variance.

Step-by-step explanation:

First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.

Answer:

{x = -1, 3}

Step-by-step explanation:

See picture below :)

The total earnings for the first month are given as follows:

R370,256.

The series in this problem is a geometric sequence, as there is a common ratio between consecutive terms.

Each day, the amount paid to you by the company is doubled, hence the common ratio of the geometric sequence is given as follows:

r = 2.

The amount paid on the first day is given as follows:

a(1) = 0.01.

The sum of the first n terms of a geometric sequence is given as follows:

S = [a1(1 - r^n)]/(1 - r).

Hence the sum for the first 30 days is given as follows:

S = [0.01(1 - 2^30)]/(1 - 30)

S = 370,256.

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Step-by-step explanation:

x - y = 16 ---eq(1)

x - y = 16 ---eq(2)

From eq(1)

x - y = 16

x = 16 + y ---eq(3)

Substituting the value of eq(3) into eq(2)

(16 + y) - y = 16

16 = 16

We can't get a proper value for this pair of linear Equations

But, Since both the equations are the same, the lines formed by them will be coincident and therefore they will have infinitely many solutions

Mr. Finn's rent in the next 3 years will be £ 833.49

To find the rent, calculate how much it will increase in the first and in the second year by using calculating percentages individually or using the compound interest formula. From the find total rent for next years. Using the total rent in the second year find the rent in 3rd year.

Here we have

The rent paid by Mr. Finn is £700 per month in rent.

His landlord informed him that rent will increase by 5% for the next two years and by 8% after that.

The rent in the 1st year = 700 + 5% of 700

= 700 + (5/100) 700

= 700 + 35 = 735  

In the second year again the rent will increase by 5%

The total rent in the second year = 735 + 5% of 735

= 735 + 36.75 = 771.75

After 2 years, the increment will be 8%

So, The total rent in the 3rd year year = 771.75 + 8% of 771.75

= 771.75 + (8/100) 771.75

= 833.49

Therefore,

Mr. Finn's rent in the next 3 years will be £ 833.49

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We have discussed what is skewed distribution and how to deal with skewed data as mentioned below.

What is a skewed distribution?

When one tail is longer than the other, the distribution is said to be skewed. The asymmetry of a distribution is defined by skewness. These distributions are asymmetric, in contrast to the well-known normal distribution and its bell-shaped curve. Because the data are not equally distributed on both sides of the distribution peak, the two parts of the distribution are not mirror images.

A) The direction of outliers is revealed by skewness. A distribution curve's tail is longer on the right side when there is a positive skew. As a result, the distribution curve's outliers are more extreme to the right and closer to the mean to the left. Skewness simply conveys the direction of outliers; it does not convey the number of outliers.

B) Lower or upper boundaries on the data frequently cause skewed data. In other words, data with a lower bound are frequently skewed right, whereas data with an upper bound are typically skewed left.

C) One popular method for handling skewed outcome data is to logarithmically transform each observation before conducting the analysis with the resulting values.

D) It is likely that the income distribution curve you plot on a graph will be positively skewed to the right. If the majority of people earn normal earnings and a smaller proportion earn high incomes, then this would happen.

Therefore this is what skewed distribution is and the above mentioned ways are how one deals with skewed data in research.

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Answer:6

Step-by-step explanation: because the 2 feet already has four pieces and if you add two more pieces to it there will be six in total.

Reflection across x=3 is a transformation that involves reflecting a figure across a vertical line of symmetry at x=3.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.


This transformation produces a mirror image of the original figure. Reflection across x=3 can be represented in the form of a matrix equation,

A= [[-1, 0],
   [ 0, 1]]

This matrix equation demonstrates that the x coordinates of a point will be multiplied by -1, while the y coordinates will remain unchanged. This transformation is also known as a reflection over the y-axis.

Reflection across x=3 can be used to change the orientation of a figure in a 2-dimensional coordinate plane. For example, if a triangle is located at the position (2,4) and the coordinates need to be changed so the triangle is reflected across x=3, the coordinates would be transformed to (-2,4).

Reflection across x=3 can also be used to solve various types of mathematical problems. For example, if a problem asks for the coordinates of a point that is the reflection of a point across x=3, the coordinates of the reflected point can be calculated by multiplying the original x coordinate by -1 and leaving the y coordinate unchanged.

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The value of the integral is π(540)^2.

We can change the order of integration as follows:

∫^(∞)(0)∫540∫9y6e−x2+zdxdydz = ∫^(540)(0)∫^∞_0∫^√(9y^6)_(−∞)e−x^2dzdxdy

The limits of z are from −∞ to ∞, but the integrand is an even function of z, so we can simplify the integral by taking the absolute value of the integrand and multiplying it by 2:

∫^(540)(0)∫^∞_0∫^√(9y^6)(−∞)e−x^2dzdxdy = 2∫^(540)_(0)∫^∞_0∫^√(9y^6)_0 e−x^2dzdxdy

We can now evaluate the integral with respect to z:

2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−√x^2+z)/2]|^√(9y^6)_0 dxdy

where erf is the error function.

Substituting the limits of integration and simplifying, we get:

2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−3y^3/√2x)/2]dxdy

Next, we can evaluate the integral with respect to x:

2∫^(540)_(0)[√π/2(x - √2/3y^3erf(−3y^3/√2x))]|^∞_0 dy

Since the limits of integration with respect to x are from 0 to ∞, the first term in the square brackets evaluates to ∞, and the second term evaluates to √π/2. Therefore, the integral reduces to:

2∫^(540)_(0)√π/2 dy = π(540)^2

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The statement A and statement B are supported by the data in the table. The solution has been obtained by studying the bar graph.

What is a bar graph?

Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.

We are given a graph showing grasshopper numbers before and after blue jays preyed on them.

From the graph, we can observe that there is no change in the number of green grasshoppers. This means that blue jays did not prey them.

Also, there is a great fall in the brown grasshoppers which means that they are most visible to the blue jays.

Hence, the statement A and statement B are supported by the data in the table.

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The complete question has been attached below

Answer:

Please Mark Brainlaiest Answer

Step-by-step explanation:

The best linear approximation for f(x) = cos(x) near x = pi/2 is given by the equation:

y = -(x - pi/2) + 1

This is because the linear approximation should have the same value and slope as the original function at x = pi/2.

At x = pi/2, the value of f(x) = cos(pi/2) = 0. The value of the linear approximation at x = pi/2 is:

y = -(pi/2 - pi/2) + 1 = 1

So, the value of the linear approximation matches the value of the original function at x = pi/2.

The slope of the original function at x = pi/2 is -sin(pi/2) = -1. The slope of the linear approximation is:

y' = -1

So, the slope of the linear approximation also matches the slope of the original function at x = pi/2.

Therefore, the best linear approximation for f(x) = cos(x) near x = pi/2 is:

y = -(x - pi/2) + 1

Hence, the correct option is "y equals negative x plus pi over 2 plus 1".

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Verified Answer ✅

Answer:

Step-by-step explanation:

To determine which pairs satisfy the equation 2y - 8x = 6, we need to find values of x and y that make the equation true. One way to do this is to solve for y in terms of x:

2y - 8x = 6

2y = 8x + 6

y = 4x + 3

Now we can substitute different values of x into this equation and see what values of y we get. For example:

When x = 0, y = 3

When x = 1, y = 7

When x = -1, y = -1

When x = 2, y = 11/2

When x = -2, y = -5

So the pairs that satisfy the equation 2y - 8x = 6 are:

(0, 3), (1, 7), (-1, -1), (2, 11/2), (-2, -5)

In each of these pairs, when we substitute the values of x and y into the equation, we get a true statement

The proportion of people with IQs above 140 is 2.5% of a mean of 100 and standard deviation of 20.

Comparative magnitude or extent; ratio; the relationship between several entities or components in terms of relative size, number, or degree. the right or ideal relationship between components of a whole; symmetry or balance. If a change in one variable can be expected from a change in the other, two variables are said to be in proportion. For secondary school chemists, there are two separate sorts of proportional relationships: direct proportion and inverse proportion.

When we find the proportion , we obtain:

P(y > 140) = 1 - P(y< 140)

               = 1 - P[(x - α) / β < (140 - 100) / 20]  

               = 1 - P(z < 2)                                  

               = 1 - 0.9772

               = 0.0228

               = 2.5%.

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Answer:

19. x = 60

20. x= 27

Step-by-step explanation:

19. Given 2 triangles are congruent

so BQ/BC = BR/BD

30/84 = x/168

84x = 30(168)

84x = 5040

x = 5040/84 = 60

20. Given 2 triangles are congruent

QS/QP = ST/PR

18/x = 10/15

10x = 18(15)

10x = 270

x = 270/10 = 27

The solution is, the required z-score is, 0.25.

In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.

here, we have,

Given that :

Mean score, μ = 69

Standard deviation, σ = 4

Score, x = 64

The standardized score, Zscore can be obtained using the formular :

Zscore = (x - μ) / σ

Zscore = (69 - 68) / 4

Zscore = 1 / 4

Zscore = 0.25

Hence, The solution is, the required z-score is, 0.25.

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Answer:

Angle 1= 45°

Angle 2= 90°

Step-by-step explanation:

Angle is found when you divide 90 by 2

We do this because all edges of a square add up to 90 and this angle is split in half, which is why we divided by 2

The to find angle 2 you get 45 for the left side of the triangle, 45 on the right side add them, which will give you 90, then subtract from 180 because angles in triangle equals 180 when you do this you get 90.

The investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method.

The process through which an investment earns returns on both the principal and the accrued interest over time is known as compounding. To put it another way, it is the reinvestment of interest income into an investment that enables the investment to increase exponentially over time.

Compounding works on the basic premise that interest earned on an investment is added to the principal amount. The interest is then calculated using the new, higher principal amount during the subsequent interest period, yielding even more interest. When the money generated is reinvested and grows over time, this cycle keeps repeating, increasing the investment's value more swiftly.

The investment given has a principal of $1,000, an annual interest rate of 3%, and interest periods of 4 per year. The investment is held for 15 years. To compare this investment to one with the same principal and annual interest rate compounded annually, we need to calculate the future value of the investment using both methods and compare the results.

Using the given investment method, we can calculate the future value as follows:

FV = P(1 + r/n)^(nt)

FV = 1000(1 + 0.03/4)^(4*15)

FV = $1,489.36

Using annual compounding, we can calculate the future value as:

FV = P(1 + r)^t

FV = 1000(1 + 0.03)^15

FV = $1,520.10

So, the investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method. This difference occurs because compounding more frequently leads to more frequent accumulation of interest, resulting in a higher final amount.

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The probability of spinning a blue is is 1/4.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1. Probability is applied in many areas, including finance, statistics, weather forecasting, and gambling.


The probability of spinning a blued, then blue is 1/4. The numerator of this fraction is 1.

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On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Use the variables a and y to represent the number of student and adult tickets sold, respectively.

Then write the following system of inequalities -

a ≥ 10 (they must sell a minimum of 10 student tickets)

y ≥ 55 (they must sell at least 55 adult tickets)

7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)

The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.

To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.

Alternatively, solve the system of inequalities using algebra.

First, simplify the third inequality by subtracting 7a from both sides -

10y ≥ 690 - 7a

Then, divide both sides by 10 -

y ≥ (690 - 7a)/10

This inequality represents the revenue constraint in terms of the number of student tickets sold.

Now combine the revenue constraint with the other two constraints -

a ≥ 10

y ≥ 55

y ≥ (690 - 7a)/10

Use substitution to solve for a in terms of y -

y ≥ (690 - 7a)/10

10y ≥ 690 - 7a

7a ≥ 690 - 10y

a ≥ (690 - 10y)/7

To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -

(690 - 10y)/7 ≥ 10

y ≥ 55

These inequalities can be simplified -

690 - 10y ≥ 70

y ≥ 55

The first inequality can be solved for y -

-10y ≥ -620

y ≤ 62

Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -

55 ≤ y ≤ 62

Now use the expression for a in terms of y to find the corresponding values of a -

a = (690 - 10y)/7

For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -

a ≥ 10

y ≥ 55

7a + 10y ≥ 690

For example, when y = 55 -

a = (690 - 10(55))/7 = 20

7a + 10y = 7(20) + 10(55) = 690

Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.

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Answer:

Step-by-step explanation:

Answer:21 dimes and 28 quarters

Step-by-step explanation:

In order to run a successful charity event for 6 people, it is important to ensure that everyone has something to enjoy.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


One way to do this is to provide cupcakes to one out of every three people. This will ensure that some people get a special treat while the others still have a chance to get one if they come to the event again. It also allows for a sense of fairness and equality, as everyone has an equal chance of receiving a cupcake. Additionally, it helps to build a sense of community and fellowship among the participants, as they can share the cupcakes and enjoy the experience together. It is also a great way to raise awareness about the charity and its cause, as people can talk about it while enjoying the cupcakes. To make sure that the event runs smoothly, it is important to have plenty of cupcakes on hand and to make sure that everyone is aware of the rules for receiving one.

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Answer:

Step-by-step explanation:

No.