Let x and y be independent each uniformly distributed on {1,2,...,n} find p(x < y )

The required p'(t) = 0.90t − 12 is and the value of p'(25) is 10.5.

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Now the given function is,

p(t) = 0.45t² − 12t + 105

where t is time in years

Taking first derivative we get,

p'(t) = 0.90t − 12

which is the required expression for p'(t)

Now for p'(25), put p = 25 in p'(t) we get,

p'(25) = 0.90*25 − 12

Solving,

p'(25) = 22.5 − 12

⇒ p'(25) = 10.5

which is the required value of p'(25).

Thus, the required p'(t) = 0.90t − 12 is and the value of p'(25) is 10.5.

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Final answer:

To find the derivative of the price function with respect to time and the value of the derivative at a specific time, follow the steps provided using the given function p(t).

Explanation:

The derivative of the price function with respect to time, p'(t), can be found by taking the derivative of the given function, which is  p'(t) = 0.90t - 12. The value of p'(25) can be calculated by substituting t = 25 into the derivative function, giving p'(25) = 0.90(25) - 12 = 22.5 dollars per year.

Final answer:

The polynomial in standard form is z⁴ + 3z₂ which is a univariate quartic polynomial since the highest power of z is 4.

Explanation:

Expressing the Polynomial in Standard Form

To express the polynomial z² - z⁴ + 2z² in standard form, we combine like terms. The terms z² and 2z² are like terms, which means they can be added together. So, the polynomial in standard form is z⁴ + 3z².

Classification of the Polynomial

This is a quartic polynomial because the highest degree of the variable z is 4. In addition, there is only one variable, z, which makes it a univariate polynomial. Therefore, the correct classification of the polynomial is a univariate quartic polynomial.

Answer: Yes, the quadrilateral ABCD is a trapezoid.

Step-by-step explanation: Given that the vertices of the quadrilateral ABCD are A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

We are to determine whether ABCD is a trapezoid or not.

We know that a trapezoid is a quadrilateral with one pair of opposite sides parallel. Also, the slopes of two parallel lines are equal.

First, we will find the slopes of the sides AB, BC, CD and DA.

We have

[tex]\textup{Step 1: The slope of AB}=\dfrac{0+5}{-3+4}=\dfrac{5}{1}=5,\\\\\textup{Step 2: The slope of BC}=\dfrac{2-0}{0+3}=\dfrac{2}{3},\\\\\textup{Step 3: The slope of CD}=\dfrac{1-2}{5-0}=-\dfrac{1}{5},\\\\\textup{Step 4: The slope of DA}=\dfrac{-5-1}{-4-5}=\dfrac{2}{3}.[/tex]

Since the slopes of the sides BC and DA are equal, so BC an DA are the parallel sides of the quadrilateral ABCD.

Thus, the quadrilateral is a trapezoid because it has a pair of opposite sides parallel.

The quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.

It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.

We have:

Quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1)

To identify the quadrilateral is a trapezoid we must find the slopes of the lines AB, BC, Cd, and AD

For slope m the formula is given by:

[tex]\rm m = \frac{y_2-y_1}{x_2-x_1}[/tex]

For slope of AB:

[tex]=\rm \frac{0-(-5)}{-3-(-4)}[/tex]

[tex]=\rm \frac{0+5}{-3+4}[/tex]

= 5

For slope of BC:

[tex]=\rm \frac{2-0}{0-(-3)}[/tex]

[tex]=\rm \frac{2}{3}[/tex]

For slope of CD:

[tex]=\rm \frac{1-2}{5-0}[/tex]

= -1/5

For slope of AD:

[tex]=\rm \frac{-5-1}{-4-5}[/tex]

= 2/3

Because the slopes of the sides BC and DA are equivalent, BC and DA are the quadrilateral ABCD's parallel sides.

Thus, the quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.

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A rotation by 360° about the origin will always carry an image onto the original figure.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

A rotation by 360° about the origin will always carry an image onto the original figure.

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The segment HJ is the secant line of the circle. Then the correct option B.

If a line intersect the circle at two point, then the line is known as a secant line.

If the line intersect at a single point on the circle, then the line is known as a tangent line.

The segment HJ is the secant line of the circle.

Then the correct option B.

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Answer:

Meters

Step-by-step explanation:

Reason:

Usually, bench length is bigger than then length of the chair and the table.

So it will be measured using meters. If we use meter it will easy to measure  and accurate because it somewhat bigger length than chair and table.

1 meter = 100 centimeters.

The standard length of a bench will 1.5 meters to 2 meters. Usually 3 to 4 people will sit on the bench.

Solution:

The given equation of line is :

→  y- 5 = 43 (x -5)

= y -5 = 43 x - 43 × 5 → [Using distributive property]

= y- 5 = 43 x - 215

→ 43 x - y - 215 +5 =0

→ 43 x - y -210 =0

→ y = 43 x - 210

As the slope of line→y = m x + c is ,43.

Or , tan A = 43, where A is the angle made by line in positive direction of X axis.

And Y intercept = -210

Michael's family ate all of the sweet potato pie (8 slices) and 2 slices of the chocolate pie, making it a total of 10 slices eaten. Each pie has 8 slices, so they consumed 1 and 1/4 pies in total, which corresponds to answer choice C) 1 1/4 pie.

To find out how much pie Michael's family ate on Thanksgiving, we need to consider that the sweet potato pie had 8 slices and the chocolate pie also had 8 slices. All of the sweet potato pie was eaten, this means 8 slices of pie were consumed. From the chocolate pie, only 2 slices were eaten. To get the total number of slices eaten, we add the slices of sweet potato pie to the slices of chocolate pie that were eaten.

Total slices eaten = Slices of sweet potato pie + Slices of chocolate pie eaten
= 8 slices + 2 slices
= 10 slices

Since each pie was divided into 8 slices, we can see that the total pie eaten in terms of whole pies is:

Total pie eaten = 10 slices \/ 8 (slices per pie)
1 and 2 \/ 8
Since 2 \/ 8 can be simplified to 1 \/ 4, we get:

Total pie eaten = 1 and 1 \/ 4 pies

Therefore, the correct answer is C) 1 1 \/ 4 pie.

Answer:

As, there are 595 students in the school.

To find the mean number of books, read by student in the school during summer

If he will survey all the students in the school that will give the exact mean , but that will be little lengthy and tedious.

As, well as larger the number of students surveyed , the better the mean is.

But option A, is true as, select randomly few students , find the mean number of books read by them , that will be less time consuming and gives the mean of population also.

Option A:

To estimate the mean using sample,Terrance will need to randomly select students, he will survey and that represents population as well.

Apart from option A,option B is also true.

Answer:

(0,3)

(1,6)

(2,12)

(3,24)

(4,48)

(5,96)

(6,192)

This is a function.  For each input, there is only one y value.

Step-by-step explanation:

x = number of folds

y = thickness of paper

(0,3)

fold it once, the thickness is doubled (times 2)

Multiply the y coordinate times 2 each time you increase x by 1

(1,6)

(2,12)

(3,24)

(4,48)

(5,96)

(6,192)

This is a function.  For each input, there is only one y value.

Answer:

(0,3)

(1,6)

(2,12)

(3,24)

(4,48)

(5,96)

(6,192)

all of those are a function.

Step-by-step explanation:

B) decreases is the answer

Answer: (-30 , 10)   Option C

In given question, some information is missing.

Complete question is :

Which ordered pair would form a proportional relationship with the point graphed below?

(–10, 30)

(30, –15)

(–30, 10)

(80, –30)

Explanation:

In graph, given point's coordinate is (60 , -20)

We need to find the proportion of the given point (60 , -20)

Proportion is number considered in comparative relation.

So,

[tex] \frac{60}{(-20)}  [/tex]

= [tex] -\frac{60}{20}  [/tex]

Divide by common factor 2 both numerator & denominator.

= [tex] -\frac{30}{10}  [/tex]

So, proportion poit's coordinate is (-30 , 10)  Option C

That's the final answer.

I hope it will help you.

Answer:

[tex]6.36\times 10^7[/tex]  

Step-by-step explanation:

We are asked to represent 63,600,000 in scientific notation.

To express our given number in scientific notation, we need factors such that first factor is a number between 1 ans 10 and second factor will be power of 10.

[tex]63,600,000=6.36\times 10000000[/tex]  

[tex]63,600,000=6.36\times 10^7[/tex]  

Therefore, our number in scientific notation would be [tex]6.36\times 10^7[/tex].

75 +40 = 115

Answer is A 115 degrees

The stack is now 119 cm high.

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics.

Given that, A stack of 20 identical boxes the stack is 140 cm take 3 of the top

20 boxes makes 140 cm

Therefore, 1 box height = 140/20 = 7 cm

Since, 3 boxes are removes, so the left boxes = 20-3 = 17

The height of stack = 17x7 = 119 cm

Hence, the new height of the stack is 119 cm

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