the geometric series $a ar ar^2 \cdots$ has a sum of $12$, and the terms involving odd powers of $r$ have a sum of $5.$ what is $r$?

The high temperature is a linear function of the number of days after the new year.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

Three points on the graph are given as follows:

(1, -3), (3,1) and (10,15).

The slopes, calculated as the change in y divided by the change in x, for each of the intervals is given as follows:

Due to the constant slopes, the relationship is in fact a linear function.

The problem asks if the high temperature in this city a linear function of the number of days after the new year.

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a) If two points on a line are A(-5,7) and B(-2,1), the rise -6, the run is of 3, and then the slope is of -2.

b) If two points on a line are A(10,-3) and B(12,9), the rise 12, the run is of 2, and then the slope is of 6.

c) If two points on a line are A(4,6) and B(8,-8), the rise -14, the run is of 4, and then the slope is of -3.5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

As the slope represents the rate of change of the output relative to the input, it is calculated as the change in the output y divided by the change in the input x, that is, the rise divided by the run.

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Answer:

-10

Step-by-step explanation:

-8 + n/2 = -13

n/2 = -13 + 8

n/2 = -5

n = -5 * 2

n = -10

Hope it helps!

The solution of the graph are x=1 and y=11.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

In the first graph the one line is passing through points (-1, -3) and (0,4)

m=4+3/0+1=7

4=7(0)+b

b=4

y=7x+4..(1)

Now other line passing through points (-4, 0) and (0, -4)

m=-4/4=-1

0=-1(-4)+b

b=-4

y=-x-4..(2)

-x-4=7x+4

Take all the variables on one side.

-x-7x=8

-8x=8

x=1

Now let us find y value

y=7+4=11

Hence, the solution of the graph are x=1 and y=11.

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Michael is 3 33 times as old as brandon. 18 1818 years ago, michael was 9 99 times as old as brandon so michael is 272454 years old.

Since we have given that

Michael is 3 times as old as Brandon .

Let the age of Brandon be 'x'.

Let the age of Michael be 333x

According to question, 181818 years ago, Michael was 999 times as old as Brandon.

181818 years ago,

Age of Brandon was x-181818

Age of Michael was 333x-181818

So, our equation becomes,

999( x- 181818) = 333x - 181818

999x - 181636182 = 333x - 181818

666x = 181454364

x = 272454

Hence, Age of Brandon is 272454 years.

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Answer:

A. 11.025

Step-by-step explanation:

1 Kilogram equals exactly 2.20462 pounds.

2.20462 multiplied by 5 is 11.025

Step-by-step explanation:

（3*10＾9）（2.3*10＾7）

＝

[tex]6.9 \times {10}^{16 \\} [/tex]

Answer:

Larger number will be 33

Smaller number will be 24

Step-by-step explanation:

So the easiest way to go about this is to divide the each of numbers by two

57/2 = 28.5

9/2 = 4.5

so now we have two 28.5's we will add 4.5 to one and subtract 4.5 from one

28.5 + 4.5 = 33

28.5 - 4.5 = 24

Proof:

33 + 24 = 57

33 - 24 = 9

Answer:

Smaller number = 24, Larger number = 33

Step-by-step explanation:

x + (x+9) = 57 Set up equation x is the smallest number and (x+9) is he larger number

2x+9 = 57

2x = 48

x = 24

Smaller number = 24, Larger number = 33

x>-9 is the solution of the inequality 5x + 30 > - 15

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 5x+30>-15

Five times of x plus thirty greater than minus fifteen.

Subtract 30 on both sides

5x>-45

Divide both sides by 5

x>-9

Hence, x>-9 is the solution of the inequality 5x + 30 > - 15

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Answer:

-10v([tex]v^{2}[/tex] - 5v - 4)

Step-by-step explanation:

First, we have to find the GCF

The GCF is: -10v

We factor the GCF outside, and what is left we put in the ( )

-10v([tex]v^{2}[/tex] - 5v - 4)

a) When x = 4, the function y = 4 has the greater numeric value.

b) The two equations have the same value for x = 6.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

From graph, when x = 0, y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by two, y increases by one, hence the slope m is given as follows:

m = 1/2

m = 0.5.

Meaning that the function is given as follows:

y = 0.5x + 1.

When x = 4, the value is given as follows:

y = 0.5(4) + 1

y = 3 < 4.

The two functions will have the same value when:

0.5x + 1 = 4

0.5x = 3

x = 3/0.5

x = 6.

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The slant height of the right cone is 24.2 units, rounded to the nearest tenth.

A right triangle's hypotenuse, or side opposite the right angle, has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean Theorem can be used to determine the slant height of a right cone. The circular base's radius is equal to its diameter times half, or 6/2 = 3 units.

The volume of the cone can be found using the formula:

V = (π/3)r²h

Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:

72π = (π/3)r²h

72π = (π/3)3²h

72π = (π/3)9h

72π = 3πh

24 = h

Using the Pythagorean Theorem, we can find the slant height as follows:

c² = a² + b²

Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:

c² = 24² + 3²

c² = 576 + 9

c² = 585

c = 24.2

Hence, the slant height of the right cone is 24.2 units, rounded to the nearest tenth.

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The table can be completed including the Elapsed Time and Average Speed, with the assumption that the length of the entire track is 1 meters as follows;

[tex]{}[/tex]                       Time (Initial)(s)   (Final)(s)    Elapsed(s)    Average Speed (m/s

1st 1/4 of the Track  [tex]{}[/tex]  0.74           2.07        1.33               0.19

2nd 1/4 of the Track  1.40 [tex]{}[/tex]          1.09         0.31               0.81

3rd 1/4 of the Track[tex]{}[/tex]   1.60           0.95        0.65             0.38

Final 1/4 of the Track [tex]{}[/tex]1.88           0.81          1.07             0.23

Average speed is the ratio of the distance an object travels to the duration the object takes to travel.

The data in the table can be completed by plugging in the values in the following equations.

Elapsed Time = Time (Final) - Time (initial)

Average Speed = Distance traveled in the time interval/(Elapsed Time)

The values of the 1st 1/4 of the track, indicates that we get;

Elapsed Time = 2.07 - 0.74 = 1.33

The elapsed time is 1.33 seconds

Average Speed = (1/4)/1.33 = 25/133 ≈ 0.19

The Average Speed is about 0.19 m/s

The values for the 2nd 1/4 of the Track, we get;

Elapsed Time = 1.40 - 1.09 = 0.31

Elapsed Time = 0.31 s

Average Speed = (1/4)/(0.31)  = 25/31 ≈ 0.81

The Average Speed for the 2nd 1/4 is about 0.81 m/s

The 3rd 1/4 of the Track indicates;

Elapsed Time = 1.60 - 0.95 = 0.65

The Elapsed Time = 0.65 s

Average Speed = (1/4)/0.65 = 5/13 ≈ 0,38

The Average Speed ≈ 0.38 m/s

The Final 1/4 of the Track indicates;

Elapsed Time = 1.88 - 0.81 = 1.07

The Elapsed Time is 1.07 s

The Average Speed = (1/4)/1.07 = 25/107 ≈ 0.23

The Average Speed for the Final 1/4 of the Track is about 0.23 m/s

The table can be completed with the above calculated values

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The diameter of the cone is 18 in.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is

We have,

Volume = 1040 in³

Height = 12 in

The volume of a cone is (1/3)πr²h.

So,

1040 = (1/3)πr²h

3 x 1040 = πr² x 12

3120/12 = πr²

260 = 3.14 x r²

260/3.14 = r²

r² = 82.80

r = √(82.80)

r = 9.099

r = 9 in

Now,

Diameter = 2r

So,

= 2 x 9

= 18 in

Thus,

The diameter is 18 in.

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The values of the indicated measures are:

i. EF = 44 units

ii. FG = 36 units

iii. DF = 62 units

A straight line that divides a given line into two equal parts and which is at right angle is called a perpendicular bisector of a line segment.

So that to determine the values of indicated measures, we have:

FE = ED

7x + 9 = 9x - 1

collect like terms

1 + 9 = 9x - 7x

10 = 2x

x = 10/ 2

x = 5

Also,

FG = GD

7y + 8 = 10y - 4

collect like terms,

4 + 8 = 10y - 7y

12 = 3y

y = 12/ 3

y = 4

Therefore;

i. EF = 7x + 9

       = 7(5) + 9

       = 35 + 9

EF = 44 units

ii. FG = 7y + 8

        = 7(4) + 8

        = 28 + 8

FG = 36 units

iii. DF = 2(3x + 4y)

         = 2(3*5 + 4*4)

         = 2(15 + 16)

         = 2(31)

DF = 62 units

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The probability that the three friends are seated next to each other is 1/420

The total number of ways to seat the 7 people is 7! To find the number of ways to seat the three friends next to each other, we need to consider the number of ways to seat the other 4 people around them. So the number of favorable outcomes is 4!

The probability that the three friends are next to each other is then given by the ratio of the number of favorable outcomes to the total number of outcomes: (4!)/(7!) = 4!/5040 = 1/420.

So the probability that the three friends are seated next to each other is 1/420.

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Check the picture below.

The probability that the average height of Canadians is less than 157 cm is 0.337.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score. A value that is one standard deviation from the mean would have a Z-score of 1.0. Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean.

Given that the standard deviation = 7cm and the mean = 160cm.

The z -score is given as:

z = x - mean / SD

z = 157 - 160/ 7

z = -3/7

z = - 0. 428

z = 0.337

P (X < 157) = P (z < -0.428)

P(X < 157) = 0.337

Hence, the probability that the average height of Canadians is less than 157 cm is 0.337.

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Answer: B. 2 quarts

Step-by-step explanation: 16 divided by 8 is 2 so you multiply 2 by 1 and you get 2. :)

Based on the data provided, the probability that one student studied for exactly one hour is 0.22.

When it comes to calculating the probability, we need to identify the frequency of a specific outcome (the probability a student studied for one hour) and compare it to the total outcome (total of students) as follows:

Total of students who studied for one hour: 8

Total of students: 1+8+2+5+9+7+3 = 35

Total of students who studied for one hour / total students

8/35 = 0.228 which can be rounded as 0.23 or 23% if expressed as a percentage.

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The formula a(7) * 1.01 represents an exponential growth model, where a(7) is the area covered by mold at week 7, and 1.01 represents a growth rate of 1% per week.

The exponential growth model is represented by the formula a(7) * 1.01, where a(7) is the area covered by mould at week 7, and 1.01 indicates a weekly growth rate of 1%.

By multiplying the area at week 7 by 1.01, we can approximate the area covered by mold at week 8.

However, it's important to note that this model assumes that the growth rate remains constant and does not account for any limiting factors such as availability of food or changes in environmental conditions.

Additionally, this model may not accurately represent the actual growth of mold, as mold growth can be complex and affected by many variables.

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A, B, and D are some advantages of online surveys.

The advantages of online surveys are:

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The time it takes a 100g sample of woosterium-21 to decay to 1/3rd of its original amount is 3.002 hours.

The initial amount of woosterium-21 (Ni) that is provided is 100g

The half life of woosterium-21 (t1/2) is given as 3 hours

The final time (t) is provided as 10 hours

The equation for half life is given by the equation:

Nt =  Ni * (1/2)^(t/t₁/₂)

Where, Nt = the final amount of woosterium-21 after 10 hours.

Therefore, Nt = 100 * (1/2)^(10/3) = 100 * 0.5^3.33 = 100 * 0.09944 = 9.944g

Let third life of woosterium-21 be t₁/₃

Substituting values in equation Nt =  Ni * (1/2)^(t/t₁/₂)

9.944 = 100 * (1/2)^(10/t₁/₃)

0.9944 = (1/2)^(10/t₁/₃)

Taking log on both sides,

log 0.9944 = 10/(t₁/₃) log 0.5

-1.0026 = 10/(t₁/₃) * (-0.301)

1.0026 = 3.01/(t₁/₃)

t₁/₃ = 3.002 hours

Therefore, the third life of woosterium-21 was found to be 3.002 hours.

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Complete Question: Suppose that Woosterium-21 is a radioactive substance that has a half-life of 3 hours. (Woosterium-21 does not, as far as I know, exist in real life.) Suppose the initial amount of Woosterium-21 is 100 mg. How much Woosterium-21 remains after 10 hours? Round your answer to three decimal places. (Enter only a number. Do not include units.) |What is the third-life of Woosterium-21? That is, find the time it takes a sample of Woosterium-21 to decay to 1/3 of its original amount. Round your answer to three decimal places. (Enter only a number. Do not include units.

The slope of the perpendicular line is the inverse reciprocal of the line on which the line is perpendicular.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x can be used to express the change in the y coordinate with regard to the change in the x coordinate.

The slope of two parallel lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other. The relationship between the slope of perpendicular lines can be represented by the formula m1 if the slopes of the two perpendicular lines are m1, m2.

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Answer:

Step-by-step explanation:

you get 5000 and divide 21and it equals 238 people

The original fraction is 3/12.

The original fraction is 5/12. This can be determined by solving the equation provided. The equation states that the denominator of a fraction is 9 more than the numerator and that if the numerator is decreased by 3 and the denominator is increased by 3, the value of the fraction is 1/4. To solve, we can set up an equation, where x is the numerator and (x+9) is the denominator.

Let the original fraction be x/y

According to the given information,

y = x + 9

After making the changes,

x - 3 = 1

and

y + 3 = 4

Now, substituting the value of y from the first equation in the second equation,

x - 3 = 1

and

x + 6 = 4

Solving the above equations,

x = 3

and

y = 12

Therefore, the original fraction is 3/12.

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The probability mass function of x is p(x) = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.

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

x denote the number of cards removed

This means that

x = 1, 2, ..., 52

The probability of selecting an ace is

P(Ace) = 4/52

This means that

P(Ace') = 48/51 ----- the card is selected without replacement

When x Aces are selected, the remaining cards is 52 - x

Using the above as a guide, we have the following:

PMF = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.

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Answer:

3x - 6

Step-by-step explanation:

Let's call the number of coins Karen has "x".

According to the information given, Bill has 6 coins fewer than two times the number of coins Karen has, so we can write the following expression for the number of coins Bill has:

Bill: 2x - 6

To find the total number of coins Karen and Bill have, we simply add the number of coins each person has:

Karen + Bill: x + (2x - 6) = 3x - 6

So the total number of coins Karen and Bill have is 3x - 6.

Answer:  the total amount of coins Bill and Karen have can be found with the following equation: 3x-6

Step-by-step explanation:

Karen has x coins

Bill's coins are twice the x, so 2x, and he has 6 fewer than that.

The equation becomes x+2x-6 which can be simplified to 3x-6.

Answer:

56.27⁰

Step-by-step explanation:

a/sinA =b/sinB

35/sin 50⁰ = 38/sin B

cross multiply

35sinB = 38sin50⁰

sin B=29.1096/35

sinB=0.8317 find the inverse sine

angle BCA= 56.27⁰

Only one student is expected receive an A for the exam.

The 68-95-99.7 rule states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean is 70 and the standard deviation is 10, so the range of scores that would be considered an "A" would be between 90 and 100.

We can calculate the number of standard deviations from the mean that the range 90 to 100 covers and use the 68-95-99.7 rule to estimate the percentage of students who would receive an "A".

For a score of 90, the number of standard deviations from the mean is (90 - 70) / 10 = 2.

For a score of 100, the number of standard deviations from the mean is (100 - 70) / 10 = 3.

So, the range of scores between 50 and 90 covers two standard deviations from the mean and between 40 and 100 covers three standard deviations from the mean. According to the 68-95-99.7 rule, 99.7% of the data falls within three standard deviations of the mean and 95% of the data falls within two standard deviations of the mean, so we would expect about (99.7% - 95%)/2 = 2.35% of the students to receive an "A".

With 50 students, we would expect approximately 50 * 0.0235 = 1.175 ≈ ` student to receive an "A". We can round up to the nearest whole number to get an estimate of 50 students.

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