Use class intervals 10- <20, 20- <30, ... to construct a histogram of the original data. Use intervals 1.1- <1.2, 1.2- <1.3, ... to do the same for the transformed data. What is the effect of the transformation?

The given information is, Find the z-score that has 73.6% of the distribution's area to its right. the z-score that has 73.6% of the distribution's area to its right is 0.63.

The total area under the standard normal distribution is 1. To find the z-score that has 73.6% of the distribution's area to its right, first, we have to find the area to the left of the z-score by using the standard normal distribution table.

Here, the area to the right of the z-score will be 1 - area to the left of the z-score (by the complement rule).So, the area to the left of the z-score is 1 - 0.736 = 0.264.To find the z-score, we will need to look up the area of 0.264 in the standard normal distribution table.

We can use a standard normal distribution table or calculator to find that the z-score that has an area of 0.264 to its left is approximately -0.63 (rounded to two decimal places).

Therefore, the z-score that has 73.6% of the distribution's area to its right is 0.63.

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Answer:

√25 =5

√4=2

Step-by-step explanation:

5×5 =25

√25=5

2×2=4

√4=2

Answer:

12barras

Step-by-step explanation:

Hoy vamos a hacer una excursión con la escuela y tuvimos que hacer sándwiches para toda la clase. Si gastamos 2 hogazas de pan para hacer sándwiches para mis 4 hermanos, ¿cuántas hogazas de pan necesitaremos para hacer sándwiches para los 24 estudiantes de la clase?

De la pregunta anterior:

4 personas = 2 barras de pan

24 personas = x

Multiplicar cruzada

4 × x = 24 × 2 barras de pan

x = 24 × 2 barras de pan / 4

x = 12 barras de pan

The given sequence is geometric because common ratio is constant that is 5.

Given,

The sequence ; 4, 20, 100 .....

We have to find whether;

Geometric Sequence;-

Every term in a geometric series is obtained by multiplying the term before it by the same number.

Here,

= 2nd term / 1st term

= 20/4

= 5

Next,

Using the 3rd and 2nd term gives:

= 100/20

= 5

= 2nd term - 1st term

= 20 - 4

= 16

Using the 3rd and 2nd term gives:

= 100 - 20

= 80

Here,

The given sequence is geometric because common ratio is constant that is 5.

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The generating function for the sequence 1, 0, 1, 0, 1, 0, ... is\(f(x) = 1 + x^2/(1 - x^2)\). The generating function for the sequence -1, 1, 0, -1, 1, 0, ... is \(f(x) = (-x + x^2)/(1 - x^3)\). The generating function for the sequence 1, 0, 1, 1, 0, 2, 1, 0, 4, 1, 0, 8, 1, 0, 16, ... is  \(f(x) = 1 + x^2 + x^3/(1 - 2x^2)\).

(a) The generating function for the sequence 1, 0, 1, 0, 1, 0, ... can be expressed as: \(f(x) = 1 + x^2 + x^4 + x^6 + ...\)

Notice that the sequence alternates between 1 and 0, which corresponds to the powers of x being even or odd. We can rewrite the generating function as: \(f(x) = 1 + x^2(1 + x^2 + x^4 + ...)\). The term in the parentheses is a geometric series with a common ratio of \(x^2\). Using the formula for the sum of an infinite geometric series, we have: \(f(x) = 1 + x^2(1/(1 - x^2))\)

Simplifying further: \(f(x) = 1 + x^2/(1 - x^2)\)

(b) The generating function for the sequence -1, 1, 0, -1, 1, 0, ... can be expressed as: \(f(x) = -x + x^2 - x^4 + x^5 - x^7 + x^8 - ...\)

Notice that the sequence follows a repeating pattern of -x, \(x^2\), 0, -x, \(x^2\), 0, ... We can rewrite the generating function as:

\(f(x) = (-x + x^2) + (-x^4 + x^5) + (-x^7 + x^8) + ...\)

We can observe that the terms in parentheses form separate geometric series with different starting terms and common ratios. Using the formula for the sum of an infinite geometric series, we have:

\(f(x) = (-x + x^2)/(1 - x^3)\)

(c) The generating function for the sequence 1, 0, 1, 1, 0, 2, 1, 0, 4, 1, 0, 8, 1, 0, 16, ... can be expressed as:

\(f(x) = 1 + x^2 + x^3 + 2x^4 + x^5 + 4x^6 + x^7 + 8x^8 + ...\)

The terms in the sequence can be seen as a combination of powers of 2 and a repeating pattern of 1, 0, 1, 0, ... We can rewrite the generating function as: \(f(x) = 1 + x^2 + x^3(1 + 2x^2 + 4x^4 + 8x^6 + ...)\)

The term in the parentheses is a geometric series with a common ratio of \(2x^2.\) Using the formula for the sum of an infinite geometric series, we have: \(f(x) = 1 + x^2 + x^3(1/(1 - 2x^2))\)

Simplifying further: \(f(x) = 1 + x^2 + x^3/(1 - 2x^2)\).

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Answer:

D

Step-by-step explanation:

We have to find the vertex of m(t) = t² - 4t + 25

a = 1

b = 4

c = 25

To do that we first need to move the 25 to the other side by subtracting 25 from both sides

m(t) = t² - 4t + 25

- 25              - 25

m(t) - 25 = t² - 4t

To continue completing the square, we have to add 4 to both sides since it is the square of half of b.

m(t) - 25 + 4 = t² - 4t + 4

m(t) - 21 = t² - 4t + 4

Now, we already found the minimum amount of members, but let's finish the square completion to find the vertex.

m(t) - 21 = t² - 4t + 4

Factor the right side

m(t) - 21 = (t-2)(t-2)

m(t) - 21 = (t-2)²

Finish it by adding 21 to both sides

m(t) - 21 = (t-2)²

      + 21         +21

m(t) = (t-2)² + 21

With this vertex form equation, we can tell that the vertex is (2,21)

Meaning 21 is the lowest number for m(t) for this equation.

Multiple Regression is the regression analysis involving one dependent variable and more than one independent variable.

A regression is a technique that relates a dependent variable [response]  to one or more independent (explanatory) variables.

The linear regression equation is in the form, y = mx + b ., where X is an Independent variable and Y is a Dependent variable.

Multiple regression is a  technique that can be used to analyze the relationship between a single dependent variable and several independent variables.

The objective of multiple regression analysis is to use the independent variables whose values are known to predict the value of the single dependent value.

Y = a + b₁X₁+ b₂X₂ + .........+ bₙXₙ

Hence, Multiple Regression analysis involving one dependent variable and more than one independent variable.

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We have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

To prove that there exists a value of x such that tan(x) = x for each whole number n, we can use the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a continuous function takes on two different values at two different points in an interval, then it must also take on every value between those two points at some point within the interval.

In this case, we consider the function f(x) = tan(x) - x. We want to show that there exists a value of x in the [(2n-1)π/2, (2n+1)π/2] where f(x) = 0, which means tan(x) = x.

First, we note that f(x) is continuous within the given interval since both tan(x) and x are continuous functions.

Next, we evaluate f((2n-1)π/2) and f((2n+1)π/2):
f((2n-1)π/2) = tan((2n-1)π/2) - (2n-1)π/2 = -∞ - (2n-1)π/2 < 0
f((2n+1)π/2) = tan((2n+1)π/2) - (2n+1)π/2 = ∞ - (2n+1)π/2 > 0

Since f((2n-1)π/2) < 0 and f((2n+1)π/2) > 0, by the Intermediate Value Theorem, there must exist a value of x in the integral  [(2n-1)π/2, (2n+1)π/2] such that f(x) = 0. This means there exists an x such that tan(x) = x for each whole number n.

Therefore, we have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

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The simple conditions for introducing basic ideas about inference for µ do not include C) a known value of the population mean µ.

In statistical inference, the goal is to make inferences or draw conclusions about population parameters, such as the population mean (µ), based on sample data. The conditions necessary for making these inferences typically involve assumptions about the sample and population.

The simple conditions for introducing basic ideas about inference for µ include:

A) A simple random sample: This condition ensures that each individual in the population has an equal chance of being selected for the sample. It helps to minimize bias and allow for generalization from the sample to the population.

B) A measure of interest that follows a Normal distribution exactly: Many statistical inference procedures, such as confidence intervals and hypothesis tests, rely on the assumption that the sample mean or the sampling distribution of the mean follows a Normal distribution, particularly for large sample sizes.

D) A known value of the population standard deviation σ: This condition refers to cases where the population standard deviation is known and can be used in the inference procedures. However, in practice, the population standard deviation is often unknown, and estimation methods are employed.

C) A known value of the population mean µ: This condition is not included in the simple conditions for introducing inference for µ. In most cases, the population mean is unknown and is the parameter of interest that we want to estimate using the sample data.

Therefore, the correct answer is C) a known value of the population mean µ.

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John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

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To find the product of 16 and 214 using the Distributive Property, we break down 214 into its place value components (200 + 10 + 4). Then, we apply the Distributive Property to each component, multiplying them individually by 16. Finally, we add up the results to find the final product of 16·214.

To use the Distributive Property to multiply 16 and 214, we break down 214 into its place value components: 200, 10, and 4. Then, we apply the Distributive Property to each component.

16 multiplied by 200 equals 3200.

16 multiplied by 10 equals 160.

16 multiplied by 4 equals 64.

Finally, we add up the results: 3200 + 160 + 64 = 3424.

Therefore, using the Distributive Property, the product of 16 and 214 is 3424.

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Answer:

2.99805126668

Step-by-step explanation:

I got this by doing $20/6.71, since the way to find anything per, is doing

(total amount of money/amount of product given by that amount)

Answer:

10,8,12

Step-by-step explanation:

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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Answer:

Step-by-step explanation:

I can only tell you that 4x-y=6 is parallel to y=4x-6. Do u mind sort out the rest of the variables and the numbers on your own?

The lines parallel to given line are y + 1 = 4(x - 2) and y = 4x + 11. Therefore, option C and D are the correct answers.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, the equation of a line is 4x-y=6.

Now, y=4x-6

Here, the slope of the equation is 4.

The slope of a line parallel to given line is m1=m2

So, here the slope of a parallel line is 4.

y + 1 = 4(x - 2) and y = 4x + 11 have same slope, then they are parallel to given line.

Therefore, option C and D are the correct answers.

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The behavior sees the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

The behavior of the graph of the polynomial function f(x) as the variable x approaches either positive or negative infinity represents the end behavior of the function. The final behavior of a polynomial function's graph is determined by the degree of the function as well as the leading coefficient.

Generally, the equation for is zeros  mathematically given as

y=x^4−2x^3−11x^2+12x+36

Therefore

(x+2)^2(x-3)^2=0

x=-2

x=3

since the graph attached has a positive leading coefficient and a positive degree

In conclusion, If the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

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The expression (a+b+c)(d+e+f) consists of six terms, and each term contains three factors.

To understand the number of terms and factors in this expression, we need to expand it using the distributive property. The distributive property states that each term in the first expression is multiplied by each term in the second expression.

(a+b+c)(d+e+f): ad + ae + a f + bd + be + bf + cd + ce + cf

From the above, we can see that there are six terms, which are ad, ae, a f, bd, be, and bf.

Each term contains three factors: a factor from the first parentheses (a, b, or c), a factor from the second parentheses (d, e, or f), and a multiplication sign connecting them.

Therefore, the expression (a+b+c)(d+e+f) consists of six terms and each term contains three factors.

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The Hermite curve with four control points P0(0,0), P1(1,1), P2(2,-1), and P3(3,0) has tangent vectors P0'(1,1) and P3'(1,1) at the endpoints. To determine the intermediate points on the curve at t = 1/3 and t = 2/3, we can use the Hermite interpolation formula.

The Hermite interpolation formula allows us to construct a curve based on given control points and tangent vectors. In this case, we have four control points P0, P1, P2, and P3, and tangent vectors P0' and P3'.

To find the intermediate point at t = 1/3, we use the Hermite interpolation formula:

P(t) = \((2t^3 - 3t^2 + 1)P0 + (-2t^3 + 3t^2)P3 + (t^3 - 2t^2 + t)P0' + (t^3 - t^2)P3'\)

Substituting the given values:

\(P(1/3) = (2(1/3)^3 - 3(1/3)^2 + 1)(0,0) + (-2(1/3)^3 + 3(1/3)^2)(3,0) + ((1/3)^3 - 2(1/3)^2 + (1/3))(1,1) + ((1/3)^3 - (1/3)^2)(1,1)\)

Simplifying the equation, we can find the coordinates of the intermediate point at t = 1/3.

Similarly, for t = 2/3, we use the same formula:

\(P(2/3) = (2(2/3)^3 - 3(2/3)^2 + 1)(0,0) + (-2(2/3)^3 + 3(2/3)^2)(3,0) + ((2/3)^3 - 2(2/3)^2 + (2/3))(1,1) + ((2/3)^3 - (2/3)^2)(1,1)\)

Calculating the equation yields the coordinates of the intermediate point at t = 2/3.

In this way, we can use the Hermite interpolation formula to determine the intermediate points on the Hermite curve at t = 1/3 and t = 2/3 based on the given control points and tangent vectors.

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Answer:

B

Step-by-step explanation:

On a coordinate plane, parallel lines have the same slope as geometric figures are true. Thus option B is correct.

Marks, splines, spheres, and curved are used to build enclosed geometric shapes. We can see these shapes all around us. Illustrations of geometric shapes include circles, rectangles, triangles, and others. Any configuration of points, columns, or angles is a geometry figure.

A point is the most fundamental algebraic concept because it has no boundaries. Simply put, a point upon that plane is a location. A dot is used to symbolize it. A plane can be identified by three non-straight-line points.

As two or much more vectors seldom cross each other and are located on the same dimension, these are said to be parallel. The slope of these lines is constant. Coplanar lines that seem to be parallel are the ones that don't cross. Therefore, option B is the correct option.

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The reasonable solutions to the equation 11.5 = 2.925 sin(27d) + 12.18, within the interval [0°, 720°), are d ≈ 0.496° and d ≈ 6.16°.

To solve the equation 11.5 = 2.925 sin(27d) + 12.18, we can start by isolating the sin(27d) term:

11.5 - 12.18 = 2.925 sin(27d)

-0.68 = 2.925 sin(27d)

Next, divide both sides by 2.925:

-0.68 / 2.925 = sin(27d)

-0.2323 ≈ sin(27d)

To find a solution within the interval [0°, 720°), we can use the inverse sine (arcsine) function. However, it's important to note that the inverse sine function only returns values between -90° and 90°. We'll need to find an angle that satisfies the equation within this restricted range.

Let's find the reference angle by taking the arcsine of the absolute value of -0.2323:

θ = arcsin(|-0.2323|)

θ ≈ 13.38°

Since the sine function is negative in the 3rd and 4th quadrants, we can add or subtract multiples of 180° to find other solutions. We're interested in finding solutions within the interval [0°, 720°), so let's consider two cases:

First solution:

27d = θ

27d = 13.38°

d ≈ 0.496° (approximately)

Second solution:

27d = 180° - θ

27d = 180° - 13.38°

27d ≈ 166.62°

d ≈ 6.16° (approximately)

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The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.

In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:

f(x) = 1 / (b - a)

where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.

To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.

Therefore, the probability that the commuting time will be between 50 and 60 minutes is:

P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.

Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.

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The rate of interest is 10% and the sum is Rs 10,1000.

The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.

The compound interest formula is given by

Compound Interest = Amount – Principal

Here, the amount is

\(A=P(1+\frac{r}{100} )^{n}\)  where,

A = amount

P = principal

r = rate of interest

n = time (in years)

Given:

C.I. of a sum of money in 3 years = Rs 13310

C.I. of a sum of money in 4 years = Rs 14641

Let the principal be P and the rate of interest be r%

Then, according to the question,

For 3 years:

\(13310=P(1+\frac{r}{100} )^{3}\)       ..... (1)

For 4 years:

\(14641=P(1+\frac{r}{100} )^{4}\)       ..... (2)

Dividing equation (2) by (1), we obtain

\(\frac{14641}{13310} =(1+\frac{r}{100} )\)

⇒\(\frac{14641-13310}{13310} =\frac{r}{100}\)

⇒\(\frac{1331}{13310} =\frac{r}{100}\)

⇒\(r=\frac{100}{10}\)

⇒ r = 10%

Now, substituting r in equation (1),

\(13310=P(1+\frac{10}{100} )^{3}\)

⇒\(13310=P(\frac{1331}{1000} )\)

⇒P = Rs 10,000

Therefore, the rate of interest is 10% and the sum is Rs 10,1000.

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This student performed better than 68% of the other test-takers in the verbal part and better than 27% in the quantitative part.

Given,

Test-taker scored at the 68th percentile for their verbal grade and at the 27th percentile for their quantitative grade .

Now,

68% percentile : 68% scores equal or less .

27% percentile : 27^ scored equal or less .

Thus option D

This student performed better than 68% of other test taker in verbal and better than 27% in quantitative part .

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∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.

Triangle is a polygon that has three sides and three angles and the sum of the angle of the triangle is 180 degrees.

The figure is attached in the picture, please refer to the attached picture.

Given that:

An Angle in the figure is a right angle.

Its measure = 90°

So,∠2 = 90° ( vertically opposite angles are equal )

∠1 + ∠2 = 180° ( Linear Pair )

∠1 = 180 - 90

∠1 = 90°

∠1 = ∠2 = 90°

So, ∠1 and ∠2 are right angles because measure of both angles is 90°.

Adjacent angles because both a common arm and a common vertex.

Thus, ∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.

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Answer:

it is used for univariate data

Step-by-step explanation:

Answer:

univariate data

Step-by-step explanation:

data that is not the average, but something like the height, or age of the people in your class.

Answer:

p > 31

Step-by-step explanation:

If their record is 31, and they need to beat it, then it would mean his score needs to be greater than 31, which is written as:

p > 31

Hope this helps

The critical point of f at z = 1 is a local minimum.

To find the critical points of the function f(z, 3) = 4z^2 - 8z + 1, we need to find the values of z where the first partial derivatives with respect to z are equal to zero. Let's solve it step by step.

Take the partial derivative of f with respect to z:

∂f/∂z = 8z - 8

Set the derivative equal to zero and solve for z:

8z - 8 = 0

8z = 8

z = 1

The critical point of f occurs when z = 1.

To determine whether the critical point is a local minimum, local maximum, or a saddle point, we can use the second partial derivative test. We need to calculate the second partial derivative ∂²f/∂z² and evaluate it at the critical point (z = 1).

Taking the second partial derivative of f with respect to z:

∂²f/∂z² = 8

Evaluate the second derivative at the critical point:

∂²f/∂z² at z = 1 is 8.

Analyzing the second derivative:

Since the second derivative ∂²f/∂z² = 8 is positive, the critical point (z = 1) corresponds to a local minimum.

Therefore, the critical point of f at z = 1 is a local minimum.

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Answer:

77

Step-by-step explanation:

Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.