7) Given the geometric sequence
9, 3, 1, 1/3, ...
What is the sum of the first 8 terms?

Answer:

12756pi km

Step-by-step explanation:

Circumference = pi * diameter

Diameter = radius * 2

kilometer = meter/1000

6378000*2= 12756000

diamter = 12756000 meters

12756000/1000 = 12756 kilometers

diameter = 12756 kilometers

12756pi km= circumference

The expression can be simplified to: [tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

We can simplify the expression as follows:

tan(x) + cot(x)/sec(x) = tan(x) + 1/tan(x) / 1/cos(x) = tan(x) + cos(x) / tan(x) * cos(x) = tan(x) + cos^2(x) / tan(x)

Using the identity: tan(x)^2 + 1 = sec^2(x), we can simplify further:

tan(x) + cos^2(x) / tan(x) = tan(x) + cos^2(x) / (sqrt(sec^2(x) - 1)) = tan(x) + cos^2(x) / sqrt(tan^2(x) + 1 - 1) = tan(x) + cos^2(x) / sqrt(tan^2(x))

Using the identity sin^2(x) + cos^2(x) = 1, we can simplify further:

[tex]tan(x) + cos^2(x) / \sqrt(tan^2(x)) = tan(x) + (1 - sin^2(x)) / \sqrt(tan^2(x)) = tan(x) + \sqrt(1 - sin^2(x)) / \sqrt(tan^2(x)) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

Therefore, the expression can be simplified to:

[tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]

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There are no shared functions between the cardiovascular system and the endoplasmic reticulum of the cell.

The endoplasmic reticulum is an organelle within cells that plays a role in protein synthesis, lipid metabolism, and other cellular processes. It does not transport materials around the body or filter wastes.

The endoplasmic reticulum is equipped with a complex network of pathways designed to meet the needs of the cell's secretory and integral membrane protein manufacturing processes. It also has adaptive responses prepared for the endoplasmic reticulum to rely on under stressful situations.

Because to the complexity and necessity of these pathways, a variety of conditions can result in a defective endoplasmic reticulum and a dysfunctional cell, which may advance disease.

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The number of combinations of different engineers is found to form a 7 member committee according to the given conditions.

What is meant by combination?

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. It is described as an arrangement of items where the order in which they are chosen is irrelevant.

Given,

Number of engineers in the faculty = 20

Number of engineers required to form a committee = 20

1) Number of ways when either engr. Marzo or engr. William is only present.

   Excluding Marzo and William, we have 18 engineers.

So we can select 6 engineers from these 18 = 18C6 =  [tex]\frac{18!}{6!12!}[/tex] = 18564

Number of ways we can select only one from Marzo and William = 2C1 = 2

So the total number of combinations for forming a committee = 18564 + 2 = 18566

2) Engr. Cara and Eng. Danny are present.

   Engr. Hillary is not considered.

So we have to select 5 members from the rest of the 15 people

Number of combinations are = 15C5 = 3003

3) Engineers Gilliam, Fernando and Ophelia are selected.

    Now we have to select the rest of the 4 members from the remaining 15 people

Number of combinations = 15C4 = 1365

Therefore the number of combinations of different engineers are found to form a 7 member committee.

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a. There were 126 people who voted for Goron.

b. There were 144 people who voted for Fishman.

The percentage is defined as a ratio expressed as a fraction of 100.

The given circle graph shows the results.

There were 360 people who voted in the election.

According to the question, the required solution would be as:

number of people who voted for Goron = 35% of 360

15%  is expressed as 15/100 in fractional form

number of people who voted for Goron = (35/100) × 360

number of people who voted for Goron = 126

number of people who voted for Fishman = 40% of 360

number of people who voted for Fishman = (40/100) × 360

number of people who voted for Fishman = 144

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The missing figure has been attached below

The probability distribution does not add up to 1.0, in other words.

The complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

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Answer:

It is not accurate

Step-by-step explanation:

If the complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

THEN:

To determine whether the probability distribution is accurate, we need to check two conditions:

The sum of the probabilities should be equal to 1.

All probabilities should be between 0 and 1.

Let's check these conditions:

Sum of probabilities:

p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05

The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.

All probabilities should be between 0 and 1:

The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.

However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.

Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.

The volume of the cylinder is 72π cubic centimeters.

Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.

The formula for the volume of a cylinder is:

V = Bh

where B is the area of the base of the cylinder, and h is the height of the cylinder.

In this problem, the cylinder has a diameter of 6 centimeters, which means the radius is 3 centimeters. The area of the base of the cylinder is therefore:

B = πr²

B = π(3 cm)²

B = 9π cm²

The height of the cylinder is given as 8 centimeters. Therefore, we can use the formula for the volume of a cylinder to find the volume V:

V = Bh

V = (9π cm²)(8 cm)

V = 72π cubic centimeters

Therefore, The volume of the cylinder is 72π cubic centimeters.

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Luego de el 15% de iva, el precio será 9001.51

Si le aplicamos un incremento de un porcentaje x a un precio P, entonces el nuevo precio será:

P' = P*(1 + x)

Donde x es el porcentaje en forma decimal.

En este caso tenemos un 15% de IVA, entonces x = 0.15

Y el precio original es 7827.40

Entonces el nuevo precio será:

P' = 7827.40*(1 + 0.15) = 9001.51

Esa es la cantidad que Luis pago.

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The largest angle of the triangle is ∠C = 66°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Now , the measure of ∠A = measure of ∠B = x

And , the measure of ∠C = measure of ∠A + 9°

Substituting the values in the equation , we get

x + x + ( x + 9 ) = 180

On simplifying the equation , we get

3x + 9 = 180

Subtracting 9 on both sides of the equation , we get

3x = 171

Divide by 3 on both sides of the equation , we get

x = 57°

So , the measure of ∠A = 57°

Now , the measure of ∠C = 57 + 9 = 66°

Hence , the measure of ∠C of triangle is 66°

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The length of x is 6 in the given triangle.

The branch of Mathematics which studies relationships between side lengths and angles of triangles.

We have to find the value of x in the given triangle.

We know that tan theta is the ratio of opposite side by adjacent side.

The opposite side is x and the adjacent side has √12

tan60=x/√12

√3=x/√12

x=√12√3

x=√36

x=6

Hence, the length of x is 6.

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The height of the object at a time of 2 seconds is given as follows:

1106 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

h(t) = -16t² + 1170.

At a time of 2 seconds, the height is found replacing the lone instance of t by two, hence:

h(2) = -16(2)² + 1170

h(2) = 1106 feet.

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The slope of the graph of this function is 1/2, the correct option is C.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We are given that;

The x input and y output of function.

Input x -2 -1 0 1 2

Output y -3 -1 1 3 5

Now

m=y2-y1/x2-x1

m= 2-1/5-3

m=1/2

Also, m=-1+2/-1+3

m=1/2

Therefore, the slope of the function will be 1/2

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The surface area of cube will be 600 square units.

What exactly is a cube?

A Cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges in geometry. It is also described as a regular hexahedron. You've probably seen the 3 3 Rubik's cube, which is the most prevalent example in real life and is useful for improving brain capacity. Similarly, you will come across several real-life instances, such as 6 sided dice, etc. Solid geometry is concerned with three-dimensional objects and figures with surface areas and volumes. Other solid forms include cuboid, cylinder, cone, and sphere.

Surface area of cube=6*side²

Volume of cube=side³

Now,

As Side of cube=10 units

and Surface area of cube=6*side²

=6*10*10

=600 square units.

Hence,

           The surface area of cube will be 600 square units.

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The two integers that are between -83 and +83 are -82 and +82.

What is integers ?

In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.

There are multiple pairs of integers that are between -83 and 83.

Here are two examples:

-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -50 0 50 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -75 0 75 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.

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Step-by-step explanation:

[tex] \frac{1}{ \sin(x ) } - \frac{1}{ \csc(x) } = \csc(x) - \sin(x) [/tex]

[tex] \frac{ \csc(x) - \sin(x) }{ \csc(x) \sin(x) } [/tex]

[tex] \csc(x) - \sin(x) = \csc(x) - \sin(x) [/tex]

Answer:

[tex]\frac{8}{5}[/tex] and - [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

8x - 5y = 1 ( subtract 8x from both sides )

- 5y = - 8x + 1 ( divide through by - 5 )

y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{1}{5}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{8}{5}[/tex]

• Parallel lines have equal slopes

then the slope of a parallel line is m = [tex]\frac{8}{5}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{8}{5} }[/tex] = - [tex]\frac{5}{8}[/tex]

Joel be not able to make a right triangle with his fence because the given dimensions are not satisfying for Pythagoras theorem.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Dimensions of triangle he has to use for fencing are

15 feet, 8 feet, and 20 feet.

For making it a right triangle it must satisfy the "Pythagoras theorem" which states that

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

H²=B²+P²

20²=15²+18²

400=225+64

400≠289

No, it will not be able to make a right triangle.

Hence, Joel will be not able to make a right triangle with his fence because the given dimensions are not satisfying for pythagoras theorem.

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The complete question is given below:

Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.

1. Will he be able to make a right triangle out of his fence? Why or why not?

In the given triangle, ∠F=29°, d>15 and e<15.

What exactly is a triangle?

Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorised into three categories based on its sides, namely:

Scalene Triangle - Each side has a distinct length.

Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.

Equilateral Triangle - A triangle has three sides that are of the same length.

A triangle is categorised into three categories based on its angles, namely:

Acute Angle Triangle - A triangle with all of its angles smaller than 90°.

Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.

Triangle with a Right Angle - A triangle with one of its angles equal to 90°.

Now

As sum of all angles of triangle=180°

∠F+127°+24°=180°

∠F=180-151

∠F=29°

and In a triangle Largest angle is opposite to largest side and smallest angle is opposite to smallest side.

Then the sides e and d will be as following d>15 and e<15.

hence,

          In the given triangle, ∠F=29°, d>15 and e<15.

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The two ways of writing the number 6000 will be 10 x 600 and 100 x 60.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Multiplication is the process of determining the product of two or more numbers in mathematics.

Given that Hassan discovers that the result of two multiples of 10 is 6000.

The two ways can be calculated as:-

10 x 600 = 6000

100 x 60 = 6000

Hence, the two ways are 10 x 600 = 6000 and 100 x 60 = 6000.

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The predicted number of principals in attendance at the conference can be 161

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

A recent conference had 850 people in attendance.

In one exhibit room of 60 people, there were 46 teachers and 14 principals.

The predicated number of principals = ?

The ratio of teachers to principals  = 60/14

                                                          = 30/7

In the same ratio there will be total teachers and principals:

Suppose, the number of teachers = x

the number of principals = y

x + y = 850

x/y = 30/7

x = (30/7)y

(30/7)y + y = 850

37y = 850 x 7

y  = 161 (approx)

Hence, the number of principals cab be 161

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Answer:

D

Step-by-step explanation:

There were about 198 principals in attendance. EZ

(a) The mathematical notations is (xₙ, yₙ)

(b) The alternative hypotheses using the notations defined in the previous question is t = (Xₙ - Yₙ) / SE

(c) The assumptions making is variances of the two populations are equal.

A hypothesis is a tentative explanation or prediction of a phenomenon, and it is essential in scientific research. In this study, we have two hypotheses:

Null Hypothesis: There is no significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.

Alternative Hypothesis: There is a significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.

Model:

A model is a mathematical representation of a phenomenon, and it is used to make predictions or explanations. In this experiment, we can create two simple models:

Model for Neutral pH Snowmelt:

Let Yₙ be the number of Copepod in a microcosm treated with neutral pH snowmelt. Then, Yₙ follows a normal distribution with mean µn and standard deviation σn.

Model for Reduced pH Snowmelt:

Let Yₙ be the number of Copepod in a microcosm treated with reduced pH snowmelt. Then, Yₙ follows a normal distribution with mean µr and standard deviation σr.

Assumptions:

Before conducting a t-test, we must ensure that the data satisfies the following assumptions:

The sample is a random and representative sample of the population.

The data is normally distributed.

The variances of the two populations are equal.

The test statistic for the t-test is:

t = (Xₙ - Yₙ) / SE

where Xₙ is the sample mean of neutral pH snowmelt, Yₙ is the sample mean of reduced pH snowmelt, and SE is the standard error.

Assuming a level of significance v = 0.05, we have a critical value of t = 2.306 for a two-tailed test with 4 degrees of freedom. If our calculated t-value is greater than 2.306 or less than -2.306, we reject the null hypothesis.

We can perform a randomization test as follows:

If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the average number of Cope pod between the reduced pH and neutral pH snowmelt treatments. If the p-value is greater than 0.05, we fail to reject the null hypothesis.

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Answer: x=4, AB=19, ED=57

Step-by-step explanation:

Trapezoid midsegment formula: [tex]\frac{b1+b2}{2}[/tex]=Midsegment

Therefore, (4x+3+18x-15)/2=38

Multiply both sides by 2 in order to get rid of the fraction. (Multiplication property of equality)

4x+3+18x-15=76

Combine like terms.

22x-12=76

Add 12 to both sides. (Addition property of equality)

22x = 88

Solve for x

x = 4

Now, substitute x in for segment AB and ED

AB = 4(4)+3

AB= 16+3

AB= 19

ED=18(4) -15

ED=72-15

ED=57

Check your work:

(ED+AB)/2 = 38

(57+19)/2 = 38

76/2 = 38

38 = 38

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{v = \dfrac{1}{3}(3.14) (5^2) \times 10}\\\\\mathsf{v = \dfrac{1}{3}(\dfrac{3.14}{1})(5\times5)(10)}\\\\\mathsf{v = \dfrac{1\times3.14}{3\times1}(25)(10)}\\\\\mathsf{v = \dfrac{3.14}{3}(25)(10)}\\\\\mathsf{v = 1.046667(25)(10)}\\\\\mathsf{v = 26.166667(10)}\\\\\mathsf{v = \dfrac{785}{3}}\\\\\mathsf{v = 261 \dfrac{2}{3}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{v = \dfrac{785}{3} \ or \ v = 261 \dfrac{2}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

  1 1/6 cups

Step-by-step explanation:

You want to know the amount of bleach to use with 3 1/2 gallons of water to obtain the same strength as 1 2/3 cups of bleach in 5 gallons of water.

The quantities are proportional, so the amount of bleach (b) will need to be ...

  b/(3 1/2 gal) = (1 2/3 cups)/(5 gal)

Multiplying by 3 1/2 gal, we get ...

  b = (3 1/2)(1 2/3)/5 cups = 1 1/6 cups

Mrs. Hanson should use 1 1/6 cups of bleach in 3 1/2 gallons of water.

Answer:15n + 3 = 153

Step-by-step explanation:

15n + 3 = 153

product of 15 and a number n is 15n, and 3 more gets the plus 3, and it said all of this is 153

n=10 also as subtract 3 both sides then get 15n=150 get n by itself by dividing both sides by 15 and get n=10

m∠K = 59.09°. This can be solved by using the concept of SAS theorem.

Triangles are congruent if their two sides and included angles are equivalent to those of another triangle's two sides and included angle. The SAS Theorem states that two triangles are congruent if their included angle and two of their sides are the same.

Here, ∠B = m∠K (consider it)

sin B /b = Sin A /a

sin B / 15 = sin 31° / 9

sin B / 15 = 0.5150 / 9

sin B / 15 = 0.057

sin B = 0.858

B = 59.09°

Thus, m∠K = 59.09°

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The system of equation is written as follows

y = 90 + x

y = 40 + 6x

With regards to cost the choices will be equivalent in 10 day

Assuming additional day is x

Felipe's Moving, they would pay $90 for the first day plus $1 per additional day:

= 90 + x

Rent-a-Truck, the family would pay $40 for the first day plus $6 per additional day.

= 40 + 6x

Equating both costs gives

90 + x = 40 + 6x

90 - 40 = 6x - x

50 = 5x

x = 10

in 10 days the cost will be same

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On solving the provided question we can say that here, trigonometry, f(x) = -7cos(1x) + -3 => f(1) = -7

Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.

Trigonometry is used here.

f(x) = -7cos(1x) plus -3

f(1) = -7

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