An arithmetic sequence has first term 13 and common difference 6. Find the 25th term
of the sequence.

The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution.

A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.

The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution. Because sample size is used to assess this degree of freedom, degrees of freedom are dependent on sample size.

The t distribution tends to follow a normal distribution as sample size rises. The degree of freedom is ultimately determined by the sample size, so as the degree of freedom rises, the t distribution tends to be a normal distribution.

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All rectangles are square is a false statement

The given statement is false statement.

What is a rectangle and square?

A rectangle is a quadrilateral with opposite sides parallel and equal and each angle is a right angle, where as a square is quadrilateral with opposite sides parallel and each side is equal. and every angle is a right angle.

We are given a statement All rectangle are squares.

As every side of a square is of equal length And only opposite sides are of equal length in rectangle

All rectangles are not square

Hence the statement is not true

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Answer:

? = 6

Step-by-step explanation:

given a line parallel to a side of a triangle and intersecting the other 2 sides , then it divides those sides proportionally , that is

[tex]\frac{?}{15}[/tex] = [tex]\frac{4}{14-4}[/tex] = [tex]\frac{4}{10}[/tex] ( cross- multiply )

10? = 15 × 4 = 60 ( divide both sides by 10 )

? = 6

Under coverage of the population will be the most noticeable bias in distributing the survey at his point in time.

Undercoverage bias happens when segments of the target population are entirely executed or loses represented in the sample than they are in the population. This means that these segments are executes from the sampling process. Non response bias occurs when parts of the sampled population are unable or refuse to respond.

Undercoverage occurs when an element of the target population is not represented on the survey frame and therefore not given any chance of selection in the survey sample; that is the element has zero probability of selection into the sample. It refers to a type of sampling bias that occurs when a piece of information from your sample responses goes missing or uncovered in the results. This significant entity goes unselected or has zero chance of getting in your representing sample.

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The height of the flagpole is 16.96 ft or 17 ft using the angle of elevation .

What is angle of elevation ?

The angle of elevation is the angle between the horizontal line of sight and the line of sight up to an object.

Here ,

angle of elevation is 58 degree.

And distance of Myleen from base of flagpole = 20 ft.

So, the height of flagpole = 20*sin(58°)

                                           = 20 * .8480

                                           = 16.96

                                           ≈ 17 ft.

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Answer:

box plot becauase wire width is numerical :)

Step-by-step explanation:

Answer:

$27.35

Step-by-step explanation:

To solve this, we just set up an equation based on the situation given:

2 candles for 5.95 each would be (2 x 5.95)

3 cans of candy for 2.50 each would be (3 x 2.50)

1 ornament for 7.95 would just be 7.95

(2 x 5.95) + (3 x 2.50) + 7.95 = total cost

   11.90     +     7.50     + 7.95 = total cost

                $27.35 = total cost

The slope of as per the given points will be equal to 3/2. Hence, option B is correct.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the information given in the table,

The points are (-14, -18) and (-10, -12)

Use the equation given below to find the slope,

m = (y₂ - y₁)/(x₂ - x₁)

Substitute values in above equation,

m = (-12 - (-18))/(-10 - (-14))

m = (-12 + 18)/(-10 + 14)

m = 6/4

m = 3/2

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By completing squares in the quadratic equation, we can see that the values of p and q are:

p = -10

q = 40

Here we want to complete squares for the following quadratic equation:

x^2+20x+60=0

Remember that the perfect square trinomial is:

(a + b)^2 = a^2 + 2ab + b^2

So we can rewrite our equation as:

x^2 + 2*10*x + 60 = 0

If we add and subtract 10^2 = 100 we will get:

x^2 + 2*10*x + 10^2 - 10^2 + 60 = 0

(x^2 + 2*10*x + 100) - 100 + 60 = 0

(x + 10)^2 - 40 = 0

(x + 10)^2 = 40

So the value of p is p = -10 (the negative sign comes because in the given equation p is being subtracted) adnt he value of q is q = 40.

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Here each tea mug has 60 milliliters of tea.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

2.4 liters of tea were equally distributed to 40 mugs.

2400 milliliter of tea.

So each tea mug has = 2400/40 = 60 milliliters of tea.

Hence, each tea mug has 60 milliliters of tea.

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A ∝ 1/M

A = K/M

A is the acceleration and M is the mass of the object.

The object's acceleration for an object of mass 13 kg is 4 m/s²

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass.

This means,

A ∝ 1/M

A is the acceleration and M is the mass of the object.

Now,

A = K/M

26 = K / 2

K = 26 x 2

k = 52

Now,

M = 13

A = K/M

A = 52/13

A = 4 m/s²

Thus,

The object's acceleration for an object of mass 13 kg is 4 m/s²

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The required absolute value of the given complex number is |-3 + 2i| = √13.

Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.  

The complex number is given in the question as:

-3 + 2i

We have to determine the absolute value of the given complex number.

The absolute value of a complex number a+ib is denoted as |a+ib| and is given by √(a²+b²)

As per the given question, we have

⇒ |-3 + 2i| = √((-3)²+2²)

⇒ |-3 + 2i| = √(9 +4)

⇒ |-3 + 2i| = √13

Therefore, the required absolute value of the given complex number is |-3 + 2i| = √13.

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Answer:

The length of the wire is 24 ft long.

Step-by-step explanation:

The increase in the orbital period is by a factor of k^3/2. Option D

From the Kepler's laws, we know that the square of the period of the planet is directly proportional to the cube of the distance of the planet from the sun. We can see that this has been typified by the expression; T^2 =A^3 where T is the period of the planet and A is the distance between the planet and the sun.

Now, we can see that from the relationship, If planet Y is k times the mean distance from the sun as a planet X then the orbital period would be increased by a factor of about k^3/2.

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Answer:

D

Step-by-step explanation:

A Hyperbola looks like a Parabola and its reflection, each Parabola curving opposite directions.

Answer:

D.  Hyperbola

Step-by-step explanation:

A conic is the intersection of a plane and a right circular cone.

Formed when a cone is intersected by a plane so that the plane is parallel to the circular base.

Formed when a cone is intersected by a plane so that the plane is at an angle with respect to the circular base.

Formed when a cone is intersected by a plane so that the plane is parallel to an edge.

Formed when a double-cone is intersected by a plane so that the plane is perpendicular to the circular bases.

The value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6

What is the interquartile range (IQR) of the data?

The interquartile range (IQR) of the data is the middle half of the data, which contains 2nd and 3rd quartiles.

Interquartile range is the difference of third quartile and first quartile.

IQR = Q₃ - Q₁

According to the given question:

In the dot plot below, the data is given as,

0 2 4 6 8 10 12

The first quartile is the medium of the lower half, while the third quartile is the medium of the upper half. For the above data,

Q1 = 3

Q3 = 9

Thus, Interquartile range is,

IQR = Q₃ - Q₁

IQR = 9 - 3

IQR = 6

Hence, the value of interquartile range (IQR) of the data set which is plotted in the dot plot 0 2 4 6 8 10 12 is 6

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Base (cube): [tex]V=s^3[/tex]

   [tex]V=9\cdot9\cdot9=729[/tex]

Top (triangular prism): [tex]V=\frac{1}{2}bhl[/tex]

   [tex]V = \frac{1}{2}(9\cdot7)\cdot9=283.5[/tex]

Together:

   [tex]V = 729+283.5 =1012.5[/tex]

C.

1012.5 cubic units.

On solving the provided question, we got to know that - they are perpendicular, they are perpendicular and they are intersecting lines

A straight line that intersects another straight line at a 90° angle is said to be perpendicular. A little square is placed in the middle of two vertical lines to represent a 90° angle, often known as a right angle, as illustrated. The two straight lines in this instance are perpendicular to one another since they connect at a right angle.

1) For this case, we have to define perpendicular lines:

[tex]m1 * m2 = -1[/tex]

[tex]m1 = 1/5\\m2 = -5\\so, m1*m2 = -1\\[/tex]

they are perpendicular

2) they are perpendicular

3)  they are intersecting lines

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Answer:

1.   d = 40; 2 irrational

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions.\\\end{minipage}}[/tex]

Given quadratic equation:

[tex]3x^2+4x-2=0[/tex]

Therefore:

Substitute the values of a, b and c into the discriminant formula:

[tex]\begin{aligned}\implies b^2-4ac&=(4)^2-4(3)(-2)\\&=16-12(-2)\\&=16+24\\&=40\end{aligned}[/tex]

Therefore, as d = 40 and 40 > 0:

[tex]\implies b^2 - 4ac > 0 \implies \text{two real solutions}.[/tex]

To determine if the solutions are irrational or rational, simply square root the discriminant.

[tex]\implies \sqrt{d}=\sqrt{40}=2 \sqrt{10}[/tex]

As the discriminant is not a perfect square, then its square root is irrational and so the solutions of the quadratic equation are irrational.

The time it takes for the cannonball to strike the ground if a certain cannon is fired from a height of 8.1 meters above the​ ground, at a certain​ angle, the height of the cannonball above the​ ground, h, in​ meters, at​ the time, t, in​ seconds, is found by the function h(t) =-4.9 t² + 27.5t + 8.1 is 5.612 seconds.

A vector measure of movement's speed and direction is called velocity. Simply described, velocity is the rate of movement in a specific direction.

Given:

The height of the cannon = 8.1 m

The height equation, h  = -4.9 t² + 27.5t + 8.1

Calculate the time by putting the value of  height in the equation as shown below,

h = (-4.9 t² + 27.5t + 8.1)

8.1 = (-4.9 t² + 27.5t + 8.1)

-4.9 t² + 27.5t = 0

Solve the quadratic equation,

t = 5.61224 sec

Therefore, the time it takes for the cannonball to strike the ground if a certain cannon is fired from a height of 8.1 meters above the​ ground, at a certain​ angle, the height of the cannonball above the​ ground, h, in​ meters, at​ the time, t, in​ seconds, is found by the function h(t) =-4.9 t² + 27.5t + 8.1 is 5.612 seconds.

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The points of intersection of the system formed by the circle (x - 2)² + (y - 3)² = 16 and the ellipse (x - 2)² / 16 + (y - 3)² / 64 = 1 are (x₁, y₁) = (- 2, 3) and (x₂, y₂) = (6, 3).

Herein we get a system formed by two conics, the former represents a circle and the latter represents an ellipse. There are different methods to solve the system, the use of graphing tools offers a quick though reasonable approach to find that. First, write the equations corresponding to the conics:

Circle

(x - 2)² + (y - 3)² = 16

Ellipse

(x - 2)² / 16 + (y - 3)² / 64 = 1

Second, plot the two graphs of the functions. (Please see the image attached below)

Third, write the points of intersection:

(x₁, y₁) = (- 2, 3), (x₂, y₂) = (6, 3)

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Answer:

2, 3, 4

Step-by-step explanation:

The term "at least" interprets as "greater than or equal to".

Because George has a Maximum of 300 hours left to complete sculptures and paintings, the Sum of the Hours (30x and 15y) must be Less Than, or can be Equal to 300.

The area of the resulting square is 3600 in²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a square has area 1600 in² whose length has been increased by 20 in each side.

Area of the square = side²

Let the original side length be x, then,

x² = 1600

x = 40 (neglecting -40, because length of anything can not be negative)

After 20 in increase, the side is (40+20) = 60 in

Area of new square = 60x60 = 3600 in²

Hence, The area of the resulting square is 3600 in²

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Answer:

D) 22

i hope it's correct

The requried sum of all nine numbers would be equal to 22. Option B is correct.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
For 3 x 3 tables,
Emily already wrote two numbers one is 2 in the 1 cell of the table and 3 in the 6th cell of the table.
For the given conditions for each side of cells in the table, the sum of the two adjacent cells must be equal.
So, If two is located at 1st cell, we put 3 on both the adjacent sides of 2 and 2 on both adjacent sides of 3 so that the sum equal to 5,
And the whole 3x3 table is given as,

2  3  2
3  2  3
2  3  2

Now, sum of all the digits, = 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 = 22

Thus, the requried sum of all nine numbers would be equal to 22. Option B is correct.

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I have earned 10 college credit hours before end of my high school graduation date.

A credit hour is an approach to estimating how much credit an understudy gets for going to a course which relates to the hours out of each week spent in that course. Dissimilar to numerous conventional secondary school courses that expect understudies to go to class consistently, school courses may just meet a few times each week.

Each hour that an understudy spends in the class regularly compares to a credit hour. For instance, on the off chance that an understudy signs up for a class that meets for one hour on Monday, Wednesday, and Friday, that course would be worth three credit hours, which is normal of numerous school courses.

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Answer:

The following statements are true:

A) The equation |-x - 4| = 8 will have two solutions.

D) The equation |2x - 10| = -20 will have two solutions.

E) The equation |0.5x - 0.75| + 4.6 = 0.25 will have no solutions.

The other statements are not true. The equation 3.4|0.5x - 42.1| = -20.6 will not have one solution, as the absolute value of a number cannot be negative. The equation |1/2x - 3/4| = 0 will not have no solutions, as the absolute value of a number cannot be zero. The equation |1/8x - 1| = 5 will not have infinitely many solutions, as the absolute value of a number cannot be negative.

Step-by-step explanation:

Answer:

d = 9.43398113206

Step-by-step explanation:

d=√((x2 – x1)² + (y2 – y1)²)

d = √((-4-1)² + (5+3)²)

d = √((-5)² + (8)²)

d = √(25 + 64)

d = √89

d = 9.43398113206

In the Algebra prompt above, If f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions.

We are given the following:

f(n)=1/2f(n-1) + 2; and

f(1) = 8

Thus,

f(2) = 1/2 x 8 + 2

= 4 + 2

f(2 )=  6

Hence,

f(3) = 1/2 x 6 + 2

= 3 + 2; thus,

f(3) = 5

Therefore,  it is correct to state that if f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

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The number of seconds the ball has gone by when the ball is at its highest point is 1 second

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

The graph

On the graph, we have the following axis label

The highest point on the graph is the vertex of the graph

In this case, the point is

(t, h) = (1, 4.9)

Remove the h-coordinate

t = 1

This means that the time is 1 second

Hence, the ball has gone by 1 second when the ball is at its highest point

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Answer:

B

Step-by-step explanation:

The function is increasing anywhere the slope is positive.  This corresponds to the intervals -4<x<-2 and 0<x<2.  So, answer B is correct.