1. A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about the
drought's effect on the size of his trees. To decide whether the growth of the trees has been re tard ed, the farmer
decides to take a sample of the heights of 25 trees and obtains the following results (recorded in inches).
60 57 62 69 46 54 64 60 59 58 75 51 49
67 65 44 58 55 48 62 63 73 52 55 50
a. Find the average tree height. _______________ Round your answer to one decimal place. You can use
software for this if desired.
b. Find the median tree height. __________________
c. Find the mode tree height. _____________
d. Find the range of this data _____________
e. Find the standard deviation for this sample. ______________ Round your answer to one decimal place.
You can use software for this if desired.
f. The tree farmer feels the normal height of a tree that was unaffected by the drought would be 65 inches.
Using the information you previously found, find the z-score for a tree that is 65 inches tall, rounding to
two decimal places.

Answer: The correct answer is D, X^2 - 1.

A prime polynomial is a polynomial that has no real or complex roots (i.e., no solutions), except for 0. X^2 - 1 has two roots, -1 and 1, both of which are not 0. Hence, it is a prime polynomial.

Step-by-step explanation:

The required slope of the line is -1/4 which passes through points (1,-1) and (5,-2).

The slope of the line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

Given,

Let

x₁ = 1 , y₁ = -1

x₂ = 5, y₂ = -2

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula, and we get

m = (-2 - (-1))/(5 - 1)

m = (-2 + 1)/(4)

m = -1/4

Thus, the required slope of the line is -1/4.

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The number of 1/5 in a cube required to fill a prism which is 2 2/5 inches x 3 1/5 inches x 2 inches is,  2000 1/5 inch cubes

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

Given that,

The dimensions of a prism  2 2/5 inches by 3 1/5 inches by 2 inches

The volume of the prism = 2 2/5 inches x 3 1/5 inches x 2 inches

                                         = 16  inches³

To find the number of 1/5 inch cubes required to fill the prism,

we need to find the volume of one cube

and then divide the volume of the prism by the volume of one cube:

Volume of one cube = (1/5 inch)³

                                  = (1/5)³ inch³

                                  = 1/125 inch³

Volume of the prism / Volume of one cube = 16 / (1/125)

                                                                        = 16 x 125

                                                                        = 2000 cubes

So, it will take 2000, 1/5 inch cubes to fill the prism.

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There are 15 packages in the pile after 30 minutes.

From the question, we have the following parameters that can be used in our computation:

Rate = 2 + 8t packages per hour

To find the number of packages after t minutes, we need to integrate the rate of growth of the pile over time.

We can use the formula:

p(t) = p(0) + ∫_0^t (2 + 8t) dt

where p(0) = 13 is the number of packages in the pile at t = 0.

Evaluate

P(t) = 13 + 2t + 4t^2

For t = 30 minutes, which is equal to 0.5 hours, we have:

P(30) = 13 + 2 * 0.5 + 4 * 0.5^2

P(30) = 15

So, approximately there are 15 packages in the pile after 30 minutes.

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The correct measure of variation for best to describe this distribution is,

⇒ interquartile range

Option B is true.

For a data set has outliers and variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.

Given that;

The dot plot shows the ages of the 20 people currently in Ms. Jens classroom.

Hence, To describe this distribution we can use the interquartile range.

Thus, The correct measure of variation for best to describe this distribution is,

⇒ interquartile range

Option B is true.

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Answer:

x=4

Step-by-step explanation:

12x+20-4=64

12x+16=64

12x=64-64

12x=48

x=4

Answer:

you are right

Step-by-step explanation:

Nixon's visit to China was intended to advance their relationship and create new trade opportunities.

The President stated on live television that he would visit the PRC in 1972 on July 15, 1971. The American public was able to see photos of mainland China for the first time in more than 20 years during the week-long tour, which took place from February 21 to 28, 1972.

Nixon intended to protect the global populace, which meant he wanted to improve relations amongst the world's superpowers. Nixon's visit to China was intended to advance their relationship and create new trade opportunities.

A significant step in normalizing diplomatic ties with China, Nixon's visit was a big success. The following year, American tourists began to travel there, and American business organizations established a booming trade with China. The United States and China achieved complete diplomatic ties by the year 1979.

Therefore, the correct answer is option B. The Soviet Union was close to falling apart and communism would leave Eastern Europe.

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The measure of ZPQR is approximately 113°. This can be solved usiing the concept of geometry.

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry.

Therefore, to find the measure of ZPQR, we would follow the following steps:

Let x= measure of <PQR

Hence, the measure of <PQR

296 = x/360 x 3.14 x 2 x 150

Hence, x = 113.12 °

Approximately, the measure of ZPQR is 113 °

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Answer:

Step-by-step explanation:

0

As a result, there is a 52% chance that a pupil chosen at random will be doing homework or playing an activity after school.

By reducing the number of positive outcomes by the overall number of potential outcomes, probability—the chance that a will occur—is determined. The most basic illustration is a coin toss. There are just two results when users flip a coin: either it shows up heads or tails.

We need to discover the sum of the percentage of students who plan to do homework and the percentage of students who plan to engage in a sport in order to calculate the likelihood that a student chosen at random will be doing homework or playing a sport after school.

Therefore, the likelihood that a pupil chosen at random will be working on homework or playing an activity after school is:

24% + 28% = 52%

This is because the two events are not mutually exclusive, and a student may plan to do both activities after school.

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The unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.

What is a unit vector?

A measurement that combines magnitude and direction is called a vector. A vector having magnitude 1 is referred to as a unit vector.

We are given three points P, Q and R.

The two vectors PQ and PR will lie on the plane through the three given points P(3, 0, 1), Q(4, -2, 1) & R(5, 3,-1).

The vector PQ = (9, 9, 9) and PR = (9, 9, 16) .

Therefore, the required vector is

N = PQ × PR

N = 63i - 63j + 0k

Hence, the unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.

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a) From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

b) From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

c) From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

What is Chi-square distribution?

Chi-square distribution with k degrees of freedom is defined as the sum of the k standard normal variables. This is also defined as the square of the deviations taken from the mean. Chi-square distribution is used for testing goodness of fit and independence in contingency tables.

• If  [tex]z_{1}, z_{2},...........z_{k}[/tex]

are independent standard normal variables, then

[tex]\sum_{i=1}^k z_{i}^2\sim X_{k}^2[/tex]

• If   [tex]X\sim X_{m}^2[/tex]

and   [tex]Y\sim X_{n}^2[/tex]

, then

[tex](X+Y)\sim X_{m+n}^2[/tex]

Step: 1

(a)

The distribution of    [tex]\sum_{i=1}^5 Y_{i}^2[/tex]

is obtained below:

From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

The random variable,  [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

representing the sum of squares of standard normal variables and hence, the distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is identified as chi-square distribution.

Hint:

Use chi-square distribution to find the distribution of

.[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

Step: 2

(b)

From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

The random variable    [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

representing the sum of squares of deviations taken from the mean for 5 standard normal variables and hence, the distribution of
[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

is chi-square distribution with 5 degrees of freedom.

Hint:

Use       [tex](X+Y)\sim X_{m+n}^2[/tex]  

to find the distribution of

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

Step: 3

(c)

From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

Therefore,

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2\sim X_{5+1}^2[/tex]

[tex]\sim X_{6}^2[/tex]

The distribution of    [tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

is identified as chi-square distribution with degrees of freedom is obtained by adding the degrees of freedom of[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and the degrees of freedom of   [tex]Y_{6}^2[/tex].

The distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is chi-square distribution with 5 degrees of freedom.

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Answer: 6.3%

Step-by-step explanation:

The probability that the same song is played twice = Number of favourite outcomes / Total outcomes.

= 1 / 6

= 0.0625

in per cent = 6.25%

Probability to the nearest tenth of % = 6.3%

.: Probability - Probability is a number that reflects the chance or likelihood that a particular event will occur.
Probability can be expressed as proportional that ranging from 0 to 1.

They can also be expressed as percentages ranging from 0% to 100%.

As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.

In terms of the geometry, a quadrilateral is really a four-sided polygon with four corners and four corners. Its origins originate from the Latin terms tetra and latus (meaning "side"). A rectangle is a this double form with four sides, 4 vertices, with four corners. Two main types of convex and convex exist. Convex bedbugs or bed bug also have a number of subclasses, such as trapezoids, parallelograms, quarters, rhombuses, and squares. Corresponding points come in many irregular configurations, such as quadrilaterals, trapezoids, rectangles, kites, square, and rhombuses.

given

The vertices of the quadrilateral ABCD are A(-4, -5), B(-3, 0), C(0, 2), and D. (5, 1).

We need to determine whether ABCD is a trapezoidal shape or not.

We are known that a trapezoid has one set of parallel opposed sides, making it a quadrilateral. Moreover, the slopes of two parallel lines are equal.

To start, the slopes of sides AB, BC, CD, and DA will be calculated.

It has

The incline for

AB =0+5/ -3+4

5. In the first step.

Step 2: The slope in BC is

=> 2-0 / 0+3

=> 2/3.

Step 3: The CD's gradient is

1-2/5-0 is equivalent to -1/5.

The gradient of DA is equal to in step four.

=>-5.1/-4.4/2.3

=>2/3.

As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.

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The smallest integer is 10, the middle integer is 11, and the largest integer is 12.

What is the consecutive integers in algebra?

In algebra, consecutive integers are a sequence of numbers that follow each other in order, where each number is one more than the previous number.

Let's call the smallest integer "x". Then, the middle integer is "x + 1" and the largest integer is "x + 2".

Now, using the given information, we can set up an equation:

x + 2(x + 1) = 56 - 3(x + 2)

Expanding the equation and simplifying:

3x + 2 = 56 - 3x - 6

6x = 62

x = 10

So, the three consecutive integers are 10, 11, and 12.

Hence, The smallest integer is 10, the middle integer is 11, and the largest integer is 12.

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The equation for w(width of rectangle) is: W = (P - 2L)/2

The correct answer is an option (c)

We know that the formula for the perimeter of the rectangle is:

P = 2L + 2W

where P is the perimeter of the rectangle,

L is the length of the rectangle,

and W is the width of the rectangle.

We need to rearrange this equation for w.

Consider equation,

P = 2L + 2W

P - 2L = 2L + 2W - 2L      ......(subtract 2L from each side of equation)

P - 2L = 2W

(P - 2L)/2 = 2W/2             .....(divide each side by 2)

W = (P - 2L)/2

Therefore, the correct answer is  W equals the quantity P minus 2 times L all over 2

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The complete question is:

Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle. P = 2L + 2W.

a) W = 2P − 2L

b) W = P/ 2-2 times L

c) W equals the quantity P minus 2 times L all over 2

d) W = 2P + 2L

Answer:

c) W equals the quantity P minus 2 times L all over 2

Step-by-step explanation:i just took the test

Note that:
a) This is a cross-sectional observational study because the data was collected from a single point in time and the observations were made without any manipulation of the variables by the researchers.

b) The explanatory variable in the study is the method of delivery (Caseload midwifery, Standard hospital care, Private obstetric care).

c) The two response variables in the study are the rate of vaginal deliveries (58.5%, 48.2%, 30.8%) and the cost of delivery ($3903.78, $5279.23, $5413.69). The rate of vaginal deliveries is a qualitative variable as it is a categorization of the type of delivery, while the cost of delivery is a quantitative variable as it is a measure of the amount of money spent on delivery.

It is to be noted that a cross-sectional observational study is a type of study in which data is collected from a single point in time without any manipulation of variables by the researchers.

The data collected provides a snapshot of the variables at that point in time.

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In the polynomial f(x) = 3x² - 2x + 5, f(0) is solved to get -2

From the equation of the tangent line

m= -2

b = 5

The derivative of the polynomial f(x) = 3x² - 2x + 5 is solved to be

f'(x) = 2(3)x - 1(2)

f'(x) = 6x - 2

f(0) = -2

Equation of the tangent to the parabola f(x) = 3x² - 2x + 5

f'(x) = 6x - 2 at x = 0, f'(x) = -2 hence the slope, m is -2

Using the point slope formula for (0, 5)

(y - 5) = m (x - 0)

y - 5 = -2x - 0

y = -2x + 5

comparing with y = mx + b

m = -2 and b = 5

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Sorina's chronological age is 8.

What is Intelligence Quotient?

The Intelligence Quotient (IQ) is an intelligence test that measures the intellectual abilities that a person has, that is to say, that it measures intelligence. To obtain a person's IQ, we divide the mental age by the chronological age and multiply the result by 100.

In this case, we have the IQ score, which is 125, and the mental age, which is 10, so we have to clear C (chronological age) to find the chronological age.

(mental age)/( chronological age) X 100 = IQ .  

(10/C) X100 =125

10 X100 =125 X C

1000 = 125C

1000125 = C

8=C

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Sorina's chronological age is 8.

What is Intelligence Quotient?

The Intelligence Quotient (IQ) is an intelligence test that measures the intellectual abilities that a person has, that is to say, that it measures intelligence. To obtain a person's IQ, we divide the mental age by the chronological age and multiply the result by 100.

In this case, we have the IQ score, which is 125, and the mental age, which is 10, so we have to clear C (chronological age) to find the chronological age.

(mental age)/( chronological age) X 100 = IQ .  

(10/C) X100 =125

10 X100 =125 X C

1000 = 125C

1000125 = C

8=C

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Step-by-step explanation:

Ted is correct

When you multiply exponents, they actually add.

Note**

[tex]4x = {4x}^{1} [/tex]

Looking at pearl, when she did

[tex] {2x}^{2} \times 4 {x}^{1} [/tex]

It should have equaled

[tex]8 {x}^{3} [/tex]

Pearl's did not, but Ted's did

Answer:

C

Step-by-step explanation:

The shorter the angle, the shorter the side that lies across from it

In angle order it's 33, 71, 76

The lines across in that order are LK, LJ, JK

The triangles are similar to the AA property.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are items that feature more than two figures that are the same shape but different sizes.

Given triangles ANF and HES

for ΔANF,

∠A = 29°, ∠N = 106°, and ∠F = 45°(from angle sum property)

for ΔHES

∠H = 45°, ∠S = 29° and ∠E = 106°(from angle sum property)

so ∠A  = ∠S

∠N = ∠E

and ∠F = ∠H

so ΔANF ≈ ΔHES

by AA similarity.

Hence option A is correct.

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Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).

It is permissible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, term, and mathematical operator Three components of a numerical method include numbers, variable, and processes (such as addition, subtraction, multiplication or division etc.) It is possible to oppose expressions and words. An expression, often known as an analytical form, is any mathematics statement that contains variables, values, and an arithmetic procedure between them. For instance, the word m in the balanced formula is separated from the terms 4m and 5 by that of the arithmetic symbol +, as is the term m in the expression 4m + 5.

given

Given expression  is (4x⁴-7x³+7x²-12x+15)/(x-1)

then dividing this

=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

=4x³-3x²+4x-8+7/x-1  in form of  q(x)+r(x)/b(x)

= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

= -7x² + 4 + 19/(x-1)

Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).

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Answer:

35

Step-by-step explanation:

The formula for the variance of a sample is:

Variance = Σ (x - average)^2 / (n - 1)

Where n is the sample size and x is each data point.

We are given the variance as 544 and the standard deviation as 4, and we know that:

Standard deviation = sqrt(Variance)

So,

Variance = Standard deviation^2

Variance = 4^2

Variance = 16

Now we have the variance and can find the sample size:

544 = 16 * (n - 1)

n - 1 = 544 / 16

n - 1 = 34

The sample size is n = 35.

The measure of the angle that ladder makes with the ground 41.8°.

Given the data in the question;

This forms a right triangle.

To find the angle, we use trigonometric ratio.

Sine = Opposite / Hypotenuse

sinθ = 20ft / 30ft

sinθ = 2/3

θ = sin⁻¹( 2/3 )

θ = 41.8°

Therefore, the measure of the angle is 41.8°.

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The required answers are

i) -65.6

ii) -64.8

iii) -64

iv) -64

The pace at which an object's position changes in relation to a frame of reference and time is known as its velocity.

Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

Its SI equivalent is the metre per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.

Now in the given question,

1. Average velocity

When t=2

i. [2, 2.1]

= y(2.1) - y(2) / 2.1 - 2

= 205 - 16(2.1)^2 - 205 + 16(2)^2 / 0.1

= 205 - 16*4.41 - 205 +16(4) / 0.1

= -70.56 +64 / 0.1

= -6.56 /0.1

= -65.6

ii. [2, 2.05]

= y(2.05) - y(4) / 4.05 - 4

= 205 - 16(2.05)^2 - 205 +16(2)^2 / 0.05

= 205 - 16*4.2025 - 205 + 16(4) / 0.05

= -3.24 / 0.05

= -64.8

iii. [2, 2.01]

= y(2.01) - y(2) / 2.01 - 2

= 205 - 16(2.01)^2 - 205 + 16(2)^2 / 0.01

= 205 - 16*4.0401 - 205 + 16(4) / 0.01

= -64.64 + 64 / 0.01

= -0.64 / 0.01

= -64

iv. Instantaneous velocity

y = 205 - 16t^2

dy/dx = -32t

Considering t = 2

Instantaneous velocity after 2 seconds = -32(2)

Instantaneous velocity after 2 seconds = -64

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Answer: Para encontrar el denominador que falta, podemos utilizar una regla de tres simple. En este caso, queremos encontrar el valor de la segunda fracción, por lo que podemos escribir:

2/7 = 10/x

Para despejar x, podemos multiplicar ambos lados de la ecuación por x y luego dividir por 2:

2/7 * x = 10

x = 10 * 7 / 2

x = 35

Por lo tanto, el denominador que falta en la segunda fracción es 35. La fracción completa es:

2/7 = 10/35