Write a function of the geometric sequence with a starting term of 8 and a common ratio of 2. Find the fourth term.

The sum height of men and women is 139600 and 161000 inches respectively. Their mean height is 66.8 inches and the average of their mean is 67.1 inches.

Number of women =2500

Mean height of women = 64.4 inches

So, the total height of 2500 women = 64.4*2500 = 161000 inches

Number of men=2000

Mean height of men = 69.8 inches

So, the total height of 2000 men = 69.8*2000 = 139600 inches

Therefore, the sum height of all 4500 people = 161000+139600 =b

So, their mean height = 300600/ 4500 = 66.8 inches

The sum of mean height of men and women = 64.4 + 69.8 = 134.2 inches

Hence, The average of their mean = 134.2/ 2= 67.1 inches.

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The solutions of the given quadratic equation is;  (1/4) + √7i/4 and  (1/4) - √7i/4

We are given the quadratic equation as;

2x² - x + 1 = 0

To solve this to find the root, we will use the quadratic formula which is given by;

x = [-b ± √(b² - 4ac)]/2a

Now, from the given quadratic equation, we can say that the values of a, b and c are;

a = 2; b = -1 and c = 1

Thus;

x = [-(-1) ± √((-1)² - 4(2 * 1))]/2(2)

x =  [1 ± √(1 - 8)]/4

x = [1 ± √(-7)]/4

x = (1/4) ± √7i/4

Thus;

x = (1/4) + √7i/4 and  (1/4) - √7i/4

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The value of x when y =4 is 2

An inverse proportion is represented as:

k = yx

Where

k represents the constant of proportion

When y = 2, x = 4.

So, we have:

k =2 * 4

k = 8

Substitute k = 8 in k = yx

So, we have:

yx = 8

When y = 4, we have:

4x = 8

Divide by 4

x = 2

Hence, the value of x when y =4 is 2

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The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;

(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

(2) The longest installable sprinkler system is approximately 172.4 feet

1. The slope of the sewer line is found as follows;

The equation of the sewer line can be expressed in point and slope form as follows;

y = 0.3•x - 0.6 + 3

y = 0.3•x + 2.4

The equation of the circumference of the sprinkler can be expressed as follows;

Therefore;

(x - 8)² + (0.3•x + 2.4 - 3)² = 2²

Solving gives;

x= 6.53, or x = 8.48

y = 0.3×6.53 + 2.4 = 4.36

y = 0.3×8.48 + 2.4 = 4.9

Therefore;

2. When the farmland does not cross the sewer line, we have;

sewer line is tangent to circumference of farmland

Slope of radial line from center of the land is therefore;

m1 = -1/0.3

Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;

y - 3 = (-1/0.3)×(x - 8)

Which gives;

y = (-1/0.3)×(x - 8) + 3

The x-coordinate is therefore;

0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3

The longest sprinkler system is therefore;

d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724

Which gives;

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Answer:

20 units

Step-by-step explanation:

Answer:

50 in²

Step-by-step explanation:

→ Find the area of the square

5 × 5 = 25

→ Find the area of the triangle

( 0.5 × 5 × 5 ) = 12.5

→ Double the answer as there is 2 triangles

12.5 × 2 = 25

→ Add the areas together

25 + 25 = 50 in²

The explicit formula for the sequence is an = 14-6(n-1)

This are sequence that has. a common difference that is the difference between the preceding and sthe explicit formula for the sequence is an = 14-6(n-1) is equal.

Given the following

a1 = 14

an = an-1 - 6

The nth term of the sequence is expressed as:

An = a+(n-1)d

an = 14+(n-1)(-6)

an = 14 -6n + 6

an = 14-6(n-1)

Hence the explicit formula for the sequence is an = 14-6(n-1)

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The value of expression is 18.

A modulus function is a function that determines a number or variable's absolute value.  A function with absolute values is another name for it. This function's result is always positive. let's suppose if you want to find modulus of -2 then you will get 2 as the answer.

now according to question

4|a|+8-a at a=-2

here a is negative that means modulus will give us positive value.

put a =-2 in the expression and get the answer. modulus of -2 will give us +2

so

=4(2)+8-(-2)

=8+8-(-2)

=8+8+2

=18

hence the answer is 18.

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Answer:

x = 3

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

Since we know triangles ABC and DEC are similar, we can use the ratio method to find x.

[tex] \frac{ec}{bc} = \frac{ed}{ba} \\ \frac{25}{5} = \frac{18 - x}{x} \\ \frac{18 - x}{x} = 5 \\ 18 - x = 5x \\ 18 = 5x + x \\ 6x = 18 \\ x = \frac{18}{6} \\ = 3[/tex]

Hyperkalemia is what is more likely to occur due to the results of the conditions.

This is used to refer to the condition where there is too much of potassium in the blood of a person.

The side effects is that the person would feel tiredness, weakness and he would feel abnormal heart beat.

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The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

The given parameters are:

Initial = 5200

Rate = 5%

Because the population by 5% every year, then the situation is a geometric sequence.

The common ratio is then calculated as:

Ratio = 1 + Rate

This gives

Ratio = 1 + 5%

Evaluate

Ratio = 1.05

Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

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Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

[tex]S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23[/tex]

It states that for distribution of sample means of size n:

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

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P(blue) = 1/3  

Step-by-step explanation:

Probability for any event A is given by

p(A) = no of times of happening of event A/ total no of occurrence of all the events given under the situation.

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles

So, total no of occurrences of all the events given under the situation

one can either pick blue, red, or 4 green marbles

Total no. of occurrence of all the event = 5 + 6 + 4 = 15

Now, no occurrence of selecting blue.

since there are 5 blue marbles, there is a chance of selecting blue as 5.

no occurrence of selecting blue = 5

Therefore,

P(blue) = no of occurrence of selecting blue /total no of occurrence of picking any color ball

P(blue) = 5/15 = 1/3.

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Answer: [tex]y+4=-\frac{1}{3}(x+6)[/tex]

Step-by-step explanation:

The slope of the given line is 3, so the slope of the line we want to find is -1/3.

Substituting into point-slope form, we get the equation of the line to be

[tex]y+4=-\frac{1}{3}(x+6)[/tex].

A square is a plane shape that has an equal length of sides. The required answers to the questions are;

i. Yes, the area of a square and its length of sides are directly proportional.

ii. Yes, the perimeter and length of the side of a square are directly proportional.

A square is a plane shape that has an equal length of sides, with four internal right angles. The area of a square can be determined as:

Area = length x length

        = [tex](length)^{2}[/tex]

This implies that the value of area of a given square depends on the value of its length. So that the area and length of sides of a square are directly proportional.

If the value of its length increases, then the value of its area increases, viz-a-viz. Then the area and length of the sides of a square are directly proportional.

The perimeter of a square is the sum of the length of its individual sides. Thus, the perimeter of a square can be determined by:

perimeter = 4 x length

Thus the value of the length determines the value of its perimeter. If the length of its sides increases, so is that of the perimeter. Therefore, the length and perimeter of a square are directly proportional.

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The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.

Mathematically, the standard form of an exponential function is given by:

F(x) = ab^x

Where:

As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)

By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).

F(x) = 3.(1.2)^x

Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.

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Answer:

7/15

Step-by-step explanation:

To find the probability the student is a senior

P( senior) = number of seniors / total students

                = 14 / ( 14+7+4+5)

               = 14/30

               = 7/15

Answer:

14/30 or 7/15

Step-by-step explanation:

probability = no. of senior students / total no. of students

probability = 14 / (14+7+4+5)

probability = 14/30

This can be simplified to 7/15.

Hope this helps!

Answer:

3. increasing

4. decreasing

Step-by-step explanation:

well for graph 3 the values are increasing

and for graph 4 the values are decreasing

Answer:

22 cm.

Step-by-step explanation:

Volume =  πr^2 h  =  π 6^2 * 11

So to double the volume

Height will be 2*11 = 22 cm.

Answer:

[tex]\huge\boxed{\sf x = -2.5}[/tex]

Step-by-step explanation:

4x + 2 = -8

Subtract 2 to both sides

4x = -8 - 2

4x = -10

Divide 4 to both sides

x = -10/4

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

4x + 2 = - 8

Subtract 2 from both sides,

Subtract 2 from - 8 = - 10,

Divide both sides by 4,

____________________

Answer:

75

Step-by-step explanation:

Use PEMDAS (Perenthesis, Exponents, Multiply, Divide, Add, Subract)

45/5-6+24*3

9-6+24*3

9-6+72

3+72

75

Answer:

75

Step-by-step explanation:

PEMDAS:

45/5=9

24*3=72

9-6+72=75

Answer: [tex]y+4=\frac{7}{3}(x+8)[/tex]

Step-by-step explanation:

See attached image.

Answer:

11.281

Step-by-step explanation:

For this question, since we see a right angle triangle, we know that we can use Pythagoras' Theorem to solve for this question.

By Pythagoras' Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {x}^{2} = {4.6}^{2} + {10.3}^{2} \\ \\ {x}^{2} = 127.25 \\ x = \sqrt{127.25} \\ = 11.281 \: or \: \frac{ \sqrt{509} }{2} [/tex]

Answer: The triangles are not similar.

Step-by-step explanation:

Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.

For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.

Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.

[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]

Since we matched corresponding sides, we can now check whether they have the same ratio).

[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]

[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]

Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their

The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

The formula for calculating the slope of a line is expressed as

slope = y2-y1/x2-x1

Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:

Slope = 1-0/-2-0

Slope = 1/-2

Slope = -1/2

Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

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The slope of the line m is - 1 / 2.

The slope a line can be found as follows:

slope = m = y₂ - y₁ / x₂ - x₁

using (0, 0)(2, -1)

hence,

slope = - 1 - 0 / 2 - 0

slope = - 1 / 2

hence,

slope = - 1 / 2

Therefore, the slope of the line m is - 1 / 2.

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The area of the shaded region is 502.4 ft^2

The area of a circle is the space occupied by a circle in a two-dimensional plane. Alternatively, the space taken up inside the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, etc. Area of a circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. It is a special mathematical constant.

It is given that inner diameter is 36 ft and width of the ring is 4 ft

We need to find the area of the shaded region

diameter of outer ring= d1=36+4+4 = 44 ft ,

diameter of inner ring= d2=36 ft,

r1=d1/2= 44/2 = 22 ft , r2=d2/2 = 36/2 = 18 ft

Area of shaded region = Area of Outer circle - Area of inner circle

= π r1^2 - π r2^2

= π ( 22^2 - 18^2 )

= 3.14 * 160

= 502.4 ft^2

Hence the area of the shaded region is 502.4 ft^2

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The area of the shaded region is 502.4 sq. ft.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space.

According to the question,

Diameter of inner circle = 36 ft.

Radius of inner circle = 36/2 ft. =18 ft.

As the width of the ring is 4 ft. , the diameter of the outer circle = 36+4+4= 44 ft.

Radius of outer circle = 22 ft.

Area of the shaded region = Area of outer circle - Area of inner circle

                                              = π(22)(22) - π(18)(18)

                                              = π(484 - 324)

                                              = 3.14 * 160

                                              = 502.4 sq. ft.

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The complete question:

A baby's t-shirt requires 4/5 yards of fabric. How many t-shirts can be made from 48 yards? A book is on sale at a 30% discount. If the sales price is $28, what was the original price?

Charles is going to buy 3 computer tables for $390. If he pays the same rate, how much would it cost for 8 computer tables?

If your cell phone bill was $67.82 and you were charged a 7.5% late fee, how much will your total bill be?

Mrs. Margulis paid $125 to have her hair colored and cut. If she tips her hairdresser 15%, what is her total bill?

Macy's is having a one-day 35% off special. If Sara bought $124.50 worth of items, what would the final bill total be after applying the discount of 35%?

Sara's total bill exists the cost of the items bought smaller the amount of the 35% is $143.75.

The number of t-shirts that can be created from 48 yards exists at 60 yards.

The original price of the book exists $40.

The cost of 8 computer tables exists $1040.

My total bill would be $72.91.

Mrs. Margulis's total bill is $143.75

My total bill after involving the discount of 35% would be $80.93.

If one t-shirt requires 4/5 yards. The number of t-shirts that can be created with 48 yards can be specified by dividing 48 yards by 4/5 yards

48 yards ÷ 4/5 yards

48 x 5 / 4 = 60 shirts

The cost of the book existed decreased by 30%. This indicates that the sales price exists 70%(100 - 30%) of the original price.

Let p denote the original price. This equation can be utilized to describe the information in the question:

70% [tex]*[/tex] p = $28

0.7p = $28

p = $28 / 0.7

p = $40

To define the cost of 8 computer tables, the cost of one computer table contains to be decided first.

Cost of one computer table = cost of three tables / 3

$390 / 3 = $130

The cost of 8 computer tables = Cost of one computer table [tex]*[/tex] 8

$130 x 8 = $1040

The total bill exists as the sum of the cell phone bill and the late phone charge

$67.82 + ( 7.5% [tex]*[/tex] $67.82)

$67.82 + (0.075 [tex]*[/tex] $67.82 )

$67.82 + 5.09

= $72.91

Mrs. Margulis's total bill exists the sum of the amount she paid and the cost of her tip.

$125 + ( 15% [tex]*[/tex] $125)

$125 + (0.15 [tex]*[/tex] $125)

$125 + $18.75

= $143.75

Sara's total bill exists the cost of the items bought smaller the amount of the 35%

$124.50 - (35% [tex]*[/tex] $124.50)

$124.50 - (0.35 [tex]*[/tex] $124.50)

$124.50 - $43.58

= $80.93

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