Find the sum if it exists of the infinite geometric series related to the infinite geometric sequence described by an=12(0.2)^n-1

The measure of each of the missing angles is m<1 = 40°, m<2 = 61°, m<3 = 119°, m<4 = 61°, m<5 = 58°, m<6 = 122°, m<7 = 58°, m<8 = 82° and m<9 = 98°

To solve this problem, we need some angle geometry knowledge:

Since the sum of angles on a straight is 180°. Thus:

m<1 + 82° + 58° = 180°

m<1 = 180° -82° - 58° = 40°

The sum of angles on a triangle is 180°:

m<2 + 58° + 61° = 180°

m<2 = 180° - 58° - 61° = 61°

m<2 + m<3 = 180° (angles on a straight )

61°+ m<3 = 180°

m<3 = 180°-61° = 119°

m<4 = m<2 = 61° (alternate angles)

m<5 + m<4 + 61 = 180° (angles on a straight )

m<5 + 61° + 61 = 180°

m<5 = 180°- 61°-61° = 58°

m<5 + m<6 =  180° (angles on a straight )

58°+ m<6 =  180°

m<6 =  180°-58° = 122°

m<7 =  58°  (alternate angles)

m<1 + m<7 +m<8 = 180° (angles on a triangle )

40+58°+m<8 = 180°

m<8 = 180°-40-58° = 82°

m<8+m<9 = 180° (angles on a straight )

82+m<9 = 180°

m<9 = 180°-82° = 98°

The measure of the missing angles m<1, m<2, m<3, m<4, m<5°, m<6, m<7, m<8 and m<9 are 40°, 61°, 119°, 61°, 58°, 122°, 58°, 82° and 98° respectively

Learn more about angle geometry on:

https://brainly.com/question/24775470

#SPJ1

By using the equation of the line and the perpendicular line relationship, the equation of the perpendicular line y = (8 / 3) · x - 5

Mathematically speaking, lines are represented by equations of the form:

y = m · x + b

Where:

And two lines perpendicular to each other observe the following relationship:

m · m' = - 1

Where:

First, determine the slope of the perpendicular line by perpendicular line relationship:

m = - 3 / 8

m' = - 1 / (- 3 / 8)

m' = 8 / 3

Second, calculate the intercept of perpendicular line by the equation of the line:

b = y - m · x

b = 3 - (8 / 3) · 3

b = 3 - 8

b = - 5

Third, write the equation of the perpendicular line:

y = (8 / 3) · x - 5

To learn more on equations of perpendicular lines: https://brainly.com/question/25790244

#SPJ1

Answer:

Below

Step-by-step explanation:

See diagram below....you are looking for 'x' in the right triangle

Use Pythagorean Theorem :

5^2 + x^2 = 13 ^2

x ^2 = 13^2 - 5^2

x ^2 = 144

x = 12 m

To write our number as a fraction, the order of the steps is:

First, we define our number:

x = 0.1717...

So we start with the step 3.

Now notice that there are two repeating decimals, so we need to multiply both sides by 100 (as many zeros as repeating decimals)

100*x = 10*0.1717... = 17.1717...

This is step 5.

Now we can subtract the original number in both sides so we remove the repeating decimals:

100*x - 0.1717... = 17.1717... - 0.1717...

99*x = 17

These are steps 4 and 2.

Finally, we divide both sides by 99 to get:

x = 17/99

Which is step 1.

And that is our number written as a fraction.

Learn more about repeating decimals:

https://brainly.com/question/22063097

#SPJ1

Answer:

Both are correct. Gavin just took more steps to get his answer.

Step-by-step explanation:

Briana's work:

20x23=460

522-460=92

4x23=92

92-92=0

24x23=552

Gavin's work:

10 x 23=230

552-230=322

10x23=230

322-230=92

2x23=46

92-46=46

46-46=0

24x23=552.

Hope this helps :)

Answer:

k = 5

Step-by-step explanation:

substitute the values of x into 3x + k and equate with the corresponding value, that is

x = 1

3(1) + k = 8

3 + k = 8 ( subtract 3 from both sides )

k = 5

x = 3

3(3) + k = 14

9 + k = 14 ( subtract 9 from both sides )

k = 5

x = 5

3(5) + k = 20

15 + k = 20 ( subtract 15 from both sides )

k = 5

the value of k is therefore 5

Answer:

i believe its 1.2

Step-by-step explanation:

hopethishelpsya:)

The answer is 6/5.

When the numerator is always higher than or equal to the denominator, the fraction is said to be an improper fraction.  When a fraction contains a whole number and a proper fraction is said to be a mixed fraction.

Write the given equation with mixed fraction to an improper fraction,

[tex]2\frac{1}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}=\frac{9}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}[/tex]

When we divide a fraction, we convert division into multiplication by turning the fraction upside down. Here, we convert the division sign before (-1/2) into multiplication by changing this fraction upside down as (-2/1).

Therefore,

[tex]2\frac{1}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}=\frac{9}{4}+\left(\frac{2}{5}\times\left(\frac{-2}{1}\right)\right)-\frac{1}{4}[/tex]

Now using the BODMAS rule, solve the bracket first. Followed by multiplication, addition, and subtraction.

[tex]\begin{aligned}2\frac{1}{4}+\frac{2}{5}\div \left(\frac{-1}{2}\right)-\frac{1}{4}&=\frac{9}{4}-{\frac{4}{5}-\frac{1}{4}\\&=\frac{8}{4}-\frac{4}{5}\\&=\frac{40-16}{20}\\&=\frac{24}{20}\\&=\frac{6}{5}\end{aligned}[/tex]

Therefore, the answer is 6/5.

To know more about the BODMAS rule:

https://brainly.com/question/17103671

The complete question is -

Simply the given expression 2 1/4+2/5÷(−1/2)−1/4

The relative humidity is a measure the average amount of vapor in the air and the random sample of 100 days refers the distribution displays a gap with a potential outlier located between 40% and 45%.

Average:

Basically, the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set is known as an average.

Given

Relative humidity is a measure, expressed as a percentage, of the amount of water vapor present in air. the following histogram summarizes the relative humidity, at noon, for a random sample of 100 days for a certain city.

Here we need to find the best description of the distribution

Basically, the relative humidity is a variable expressed as a percentage that represents the amount of water vapor present in air. It can be  is used to monitor and predict weather conditions, and it is calculated based on the temperature of the air.

And it is also independent of temperature because a high temperature can have low relative humidity and vice-versa.

While we looking into the given question, there are no observed data values between 45% relative humidity and 55% relative humidity, so there is a gap displayed in the distribution.

Therefore, the value located between 40% and 45% is unusually small when compared with the other data values. And this point are known as outliers that are used to test that it is an outlier would require using the 1.5×IQR rule or using the two standard deviations rule.

To know more about Average here.

https://brainly.com/question/16956746

#SPJ4

a) Domain={2,3,4,5,6}, Range={0,1,2,3,4}

b)Domain={-3,-1,1,3,4}, Range={1,3,-2,2,6}

What are the domain and range of a function?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

a) Domain is the set of x values:

 x={2,3,4,5,6}

 The range is the set of y values:

  y={0,1,2,3,4}

b) Domain is the set of x values:

 x={-3,-1,1,3,4}

 The range is the set of y values:

  y={1,3,-2,2,6}

To learn more about the domain and range from the given link

https://brainly.com/question/28801359

#SPJ1

In the simplified expression, the coefficient of the term b² is -1.

When you solve any Math Operations, it is necessary to be attentive to the order of the operations.

First, you should solve the operation insides of Parentheses. After that priority is given to Exponents. Thereon,  you can solve multiplication or division operations from left to right. Finally, addition or subtraction  from left to right

See the order below

The question gives the expression (4a² +2ab) - (2a² -ab + b²). Therefore, for solving the expression you should follow the order of the math operations.

       4a² +2ab -2a² +ab - b²

       2a²+3ab-b²

Like, there are no more similar terms. Therefore, you can represent the expression (4a² +2ab) - (2a² -ab + b²) by  the expression  2a²+3ab-b².

Learn more about the algebraic expression here:

brainly.com/question/2164351

#SPJ1

The vectors combined sum is equal to (-1, 1)

Given data;

Let 'w' be the vector with an initial point (2,0) and terminal point (3,2).

Let 'v' be the vector with the initial point (2,2) and terminal point (0,1).

To find the sum of two vectors, firstly;

For 'w';

w = (3 - 2)i + (2 - 0)j

w = i + 2j → (I)

For 'v';

v = (0 - 2)i + (1 - 2)j

v = -2i + j → (II)

Now,

From (I) & (II);

w + v = (i + 2j) + (-2i + j)

        = -1, 1

Hence, the sum of the vectors w + v = (-1, 1)

To learn more about vectors click here:

brainly.com/question/13322477

#SPJ4

Answer:

10.49

Step-by-step explanation:

We should solve this by subtracting the total amount of fuel minus the gallons left to find the gallons used.

In other words:

Subtract the total amount of fuel minus the gallons left

[tex]15.04 -4.9[/tex]

Answer:

[tex]10.49[/tex]

I hope this answers your question :)

Note: Make sure you line up the decimal places!!

the park is open for 8 hours.

Answer:

0.31

Step-by-step explanation:

1 1/4 - 1/3 - 3/5 = 19/60

≅ 0.3166667

Runs scored by Willie Mays is given by the linear equation y = 2x+58.

A linear equation is an algebraic equation which is in the form y=mx+b, where m is said to be the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

The variables in the preceding equation are x and y, and it is commonly referred to as a "linear equation of two variables."

Let the runs scored by Roger be x.

According to the question, Willie Mays hit 58 more than double the number of home runs Roger hit.

Runs scored by Willie Mays = 2x+58

Let the runs scored by Willie May be y.

Then, y = 2x+58.

Hence, the runs scored by Willie Mays is given by the linear equation
y = 2x+58.

To find similar questions on 'linear equation'

visit- https://brainly.com/question/12032643

#SPJ9

Answer:

No

Step-by-step explanation:

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third ...

18 + 21   = 38   are not more than 39  

Answer:No,the side of lengths 18m,21m and 39m could not form a

Step-by-step explanation:

To form a triangle, the sum of any two sides must be greater than the third side.

here,

18m + 21m = 39m

the sum to two side is equal to third side that is 39m

that's why these three sides cannot form any triangle

Answer: 4.4

Step-by-step explanation:

First, know that 10% is equal to 0.1. Calculate 10% of 4 and add that to 4 to find the final value:

[tex]4+4*0.1=4+0.4=4.4[/tex]

Answer: 14

Step-by-step explanation:

What is 10 more than 4 We are looking for a new number which is 10 more than 4 We will get the new number by adding 10 to 4 We write it down as: 4+10=14

Normal Distribution or central tendency is a bell-shaped curve that is produced by many measurements.

The graphical representation of a normal probability distribution, whose underlying standard deviations from the mean form the curved bell shape, is referred to as having a "bell curve." The variability of data dispersion, in a set of provided values around the mean, is measured using a standard deviation. The highest point on the bell curve is the mean, which is the average of all the data points in the data set or sequence.

A bell-shaped normal distribution graph is referred to as a bell curve.

At the peak of the curve, the mean, mode, and median of the collected data are shown.

The standard deviation of the bell curve reveals how pronounced the bell curve is around the mean.

Bell curves (normal distributions) are extensively used in statistics, particularly when analyzing financial and economic data.

Hence Normal Distribution is the basic concept of bell shaped curve.

To learn more about Bell Shaped Curved click on the link https://brainly.com/question/24182600

#SPJ4

I think it is 2/9ths? Look it up on a calculator to check

For the quadratic equation other solution is given by :

x = 4-5i  other solution is x = 4 + 5i

x= 5 + 4i other solution is x = 5 -4i

x = -5 -4i other solution is x = -5 + 4i

x = -4 + 5i other solution is x = -4 -5i

As given in the question,

Number of quadratic equations mentioned = 4

Given one solution for each quadratic equation is given by:

x = 4-5i

x= 5 + 4i

x = -5 -4i

x = -4 + 5i

In standard form:

if the one of the solution of quadratic equation is in complex form x + iy then other solution is given by its conjugate x - iy.

Hence,

Other solution are given by :

x = 4-5i  other solution is given by its conjugate x = 4 + 5i

x= 5 + 4i other solution is given by its conjugate x = 5 -4i

x = -5 -4i other solution is given by its conjugate x = -5 + 4i

x = -4 + 5i other solution is given by its conjugate x = -4 -5i

Therefore, for the quadratic equation other solution is given by :

x = 4-5i  other solution is x = 4 + 5i

x= 5 + 4i other solution is x = 5 -4i

x = -5 -4i other solution is x = -5 + 4i

x = -4 + 5i other solution is x = -4 -5i

The complete question is:

One solution each is given for four quadratic equations. Assuming that each quadratic equation has two solutions, what is the second solution for each equation?.

x = 4-5i

x= 5 + 4i

x = -5 -4i

x = -4 + 5i

Learn more about quadratic equation here

brainly.com/question/17177510

#SPJ4

The exact value of CSC(COS^-1(-5/8)) is 8/[tex]\sqrt{39}[/tex].

Given:

= CSC(COS^-1(-5/8))

= 1/sin(cos^-1(-5/8)

we know identity sin(cos^-1(x)) = [tex]\sqrt{1-x^{2} }[/tex]

= 1/[tex]\sqrt{1-(-5/8)^{2} }[/tex]

= 1/[tex]\sqrt{64-25/64 }[/tex]

= 1/[tex]\sqrt{39}[/tex]/8

= 8/[tex]\sqrt{39}[/tex].

Therefore the value of CSC(COS^-1(-5/8)) is 8/[tex]\sqrt{39}[/tex].

Learn more about the exact value here:

https://brainly.com/question/17123024

#SPJ1

Answer:

319 would be the sum

Step-by-step explanation:

(E) None of these equations of a line is parallel to the equation [-2y = 4 - 2x] and passes through the point (-5. 9).

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

On the y-axis, this value c is referred to as the intercept.

Y = MX + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

So, first plot the equation [-2y = 4 - 2x] on the graph:

Now, plot all the equations on the graph.

We can now check which equation is parallel to [-2y = 4 - 2x] and passing through the point (-5. 9).

According to the plotting, we can say that no equation is parallel to the equation [-2y = 4 - 2x] and passes through the point (-5. 9).

Therefore, (E) none of these equations of a line is parallel to the equation [-2y = 4 - 2x] and passes through the point (-5. 9).

Know more about the equation of lines here:

https://brainly.com/question/13763238

#SPJ1

Complete question:

Find the equation of a line parallel to -2y = 4 - 2x that passes through the point.

(-5,9).

A. y=x-2

B. y=-x+14

C. 2x + 2y = 8

D. 2x - 2y = -28

E. None of these

The minimum unit cost of the car is $12232.1

Given: cost function C(x)=0.9x² - 414x + 59,366

In order to find the minimum point, take the derivative of the cost function:

dC/dx = 2x - 414          (equate to zero and solve for x)

2x - 414 = 0                

2x = 414

x = 414/2 = 207

Thus, the minimum point is at x =207

The minimum unit cost can be obtained by substituting x = 207 into the cost equation:

C(x) = 0.9x² - 414x + 59,366

C(207) = 0.9(207)² - 414(207) +  59,366

          = 38564.1 - 85698 + 59,366

           = $12232.1

Therefore, the minimum unit cost is $12232.1

Learn more about cost function on:

https://brainly.com/question/2292799

#SPJ1

The factorization of the expression is -3(1+3z+7y+0.8)

Factorisation of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.

To the factor a number means to break it up into numbers that can be multiplied to get the original number.

in the expression, -3 −9z−21y−2.4, it is discovered that -3 is a common factor in all the terms.

Therefore dividing all the terms by -3 and bring -3 out of parentheses we have -3(1+3z+7y+0.8)

learn more about factorization from

https://brainly.com/question/22048677

#SPJ1

Yusuf remaining observations, considering the statistical measures, are given as follows:

64, 73, 80.

There are four statistical measures used in this problem, which are:

The mode is the observation that appears the most times, hence one of the remaining observations is of 80.

The median is the middle value of the data-set, which is the value of which 50% of the measures are less than and 50% of the measures are greater than.

In this problem, the data-set has an even cardinality, hence the median is the mean of the 4th and of the 5th element, hence, considering the median of 74, the missing element is given as follows:

(x + 75)/2 = 74.

x + 75 = 148

x = 73.

The range is the difference between the largest value and the smallest value in the data-set.

Considering the range of 16 and the highest value of 80, the remaining value is given as follows:

80 - x = 16

x = 80 - 16

x = 64.

More can be learned about statistical measures at https://brainly.com/question/19243813

#SPJ1

Answer:

should be
38 = 9x

Step-by-step explanation

multiply both sides with the least common denominator of the denominator of the fraction (the number below the line).
of the numbers 4 and 6, the least common denominator is 12.
so multiply both sides of the equation by 12.
you will have
12 * (4 - 3/4 x) = 12 * 5/6
simplify and you will get
48 - 9 x = 10

and you can even more simplify it to 9x = 38 or 38 = 9x