The first term of a geometric sequence is -2100. The common ratio of the sequence is -0.1.
What is the 7th term of the sequence?
Enter your answer in the box.

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 equation of the line graph is y = -3/8x + 5/2

A line is defined as the shortest distance between two points. The equation of a line in slope intercept form is expressed as:"

y = mx + b where:

m is the slope

b is the intercept

Using the coordinate points (-4, 4) and (4, 1)

Slope = 1-4/4-(-4)
Slope = -3/8

Determine the y-intercept

1 = -3/8(4) + b

1 = -3/2 + b

b = 1 + 3/2

b = 5/2

The required equation of the graph is y= -3/8x + 5/2

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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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The required probability for the parts which are examined for defects are ;

1. Probability of both the parts are good is equal to 0.375.

2. Probability represents exactly one part has major defect is 0.2333.

Total number of parts to be examined for defects = 16

Number of good parts = 10

Number of parts with minor defects = 4

Number of parts with major defects = 2

Number of parts to be chosen at random without replacement = 2

Total number of outcomes = ¹⁶C₂

                                             = (16!) / ( 16 - 2 )!2!

                                             = 120

1. Probability of both the parts to be good

Number of favourable outcomes = ¹⁰C₂

                                                        = 10! / (8!)(2!)

                                                        = 45

Required Probability = 45 / 120

                                   = 0.375

2. Probability of exactly one major defect

Number of favourable outcomes= ²C₁ × ¹⁴C₁

                                                      = 2 × 14

                                                      = 28

Required Probability = 28/ 120

                                   = 0.2333

Therefore, the probability of both are good is 0.375 and probability of exactly one major defect is 0.2333.

The above question is incomplete, the complete question is:

'16 parts are examined for defects. It is found that 10 are good, 4 have minor defects, and 2 have major defects. Two parts are chosen at random from the 16 without replacement; that is; the first part chosen is not returned to the mix before the second part is chosen:

1. What is the probability that both parts are good?

2. What is the probability that exactly one part has major defect?'

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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. :)

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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The measure of the angle opposite to the side 'x' is 49.6177°. Then the value of the variable 'x' will be 6.856 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The measure of the hypotenuse of the upper triangle is given as,

h² = 5² + 3²

h² = 25 + 9

h² = 34

h = 5.8309

Then the measure of the angle opposite to the side 'x' is given as,

cos ∅ = 5.8309 / 9

cos ∅ = 0.64788

      ∅ = 49.6177°

Then the value of the variable 'x' is given as,

sin 49.6177° = x / 9

0.7617 = x / 9

x = 6.856 units

The measure of the angle opposite to the side 'x' is 49.6177°. Then the value of the variable 'x' will be 6.856 units.

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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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There's no guaranteed way to make someone fall in love with you.

Love is a complex and deeply personal emotion that is influenced by a wide range of factors, including a person's upbringing, life experiences, and individual preferences and values.

The best approach is to simply be yourself, be kind and respectful, and let the relationship develop naturally over time. It's important to understand that you cannot control someone else's feelings, and trying to force or manipulate someone into falling in love with you is unlikely to result in a healthy and happy relationship.

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Answer: 20% would be the answer

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 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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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

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)

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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Approximately 68% of the area under the normal distribution curve falls within 1 standard deviation above and below the mean. This is known as the empirical rule, also called the 68-95-99.7 rule.

Approximately 95% of the area under the normal distribution curve falls within 2 standard deviations above and below the mean.

Approximately 99.7% of the area under the normal distribution curve falls within 3 standard deviations above and below the mean.

It's important to note that these values apply to a standard normal distribution (mean = 0, standard deviation = 1). For any normal distribution with a different mean and standard deviation, you can use the standard score (z-score) to transform the data into the standard normal distribution, and then use the standard normal distribution to find probabilities.

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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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The correct response is b. 47.06 minutes. the shortest wait time that would still be in the longest 15% of wait times is 47.06 minutes.

A minute is a unit of time equal to 60 seconds and one-sixtieth of an hour. (See leap second; certain uncommon minutes have 59 or 61 seconds.) The minute is acceptable for use with SI units even though it is not a SI unit. In mathematics, time is defined as a continuous and ongoing sequence of events that occur one after another in the past, present, and future. Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. When you say something has to be done, you are emphatically stating that it should happen or be done right away.

Mean, μ[tex]=38.12[/tex]

Standard deviation,σ[tex]=8.63[/tex]

Waiting times that are longer are worse than those that are shorter. Therefore, the 15% of wait times that are the worst fall into this category. The inferred level of confidence is 0.85.

The z value corresponding to the right tail probability of 0.15 is

[tex]z=1.03[/tex]

But

Z= x−μ/σ

x=Z∗σ+μ

[tex]=1.03∗8.63+38.12=47.06[/tex]

The quickest waiting period that would still fall into the worst 15% of waiting periods is 47.06 minutes.

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By increasing his speed to 10.4 km/h, he saves 0.175 - 0.16875 = 0.00625 hours or 0.375 minutes.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

If a man runs at the speed of 10 km/h, it will take him 1.75 / 10 = 0.175 hours or 10.5 minutes to cover 1.75 km.

If he increases his speed to 10.4 km/h, it will take him 1.75 / 10.4 = 0.16875 hours or 10.13 minutes to cover the same distance.

So, by increasing his speed to 10.4 km/h, he saves 0.175 - 0.16875 = 0.00625 hours or 0.375 minutes.

Hence, by increasing his speed to 10.4 km/h, he saves 0.175 - 0.16875 = 0.00625 hours or 0.375 minutes.

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The alumni giving rates would represent a nominal variable, as it is a categorical variable representing donors and non-donors.

An appropriate graph to depict these data would be a bar graph. The bar graph would show the number of alumni who donated (the numerator) and the number of alumni who did not donate (the denominator) in a given year. The formula for this calculation would be,

Alumni Giving Rate = (Number of Alumni Donors / Total Number of Alumni) x 100

For example, if 10 alumni donors out of 100 total alumni donated, the alumni giving rate would be 10%. The graph would show the percentage of alumni that donated in a given year.given year. The formula for this calculation would be,

Alumni Giving Rate = (Number of Alumni Donors / Total Number of Alumni) x 100

For example, if 10 alumni donors out of 100 total alumni donated, the alumni giving rate would be 10%. The graph would show the percentage

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Answer:

Step-by-step explanation:

you get 5000 and divide 21and it equals 238 people

The frequency distribution looks to have a normal distribution because (A) the frequencies start off low, rise to one or two high frequencies, then fall to a low frequency, and the distribution is fairly symmetric.

Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range.

The distribution is known as a relative frequency distribution in the latter case.

Frequency distribution that is cumulative.

Frequency distribution relative. distribution of the relative cumulative frequency.

Measurements of position and central tendency (mean, median, mode) Dispersion metrics (range, variance, standard deviation) How much symmetry or asymmetry there is (skewness) The peakedness or flatness (kurtosis).

Because the frequencies begin low, rise to one or two high frequencies, then fall to a low frequency, and the distribution is roughly symmetric, the frequency distribution appears to have a normal distribution.

Therefore, the frequency distribution looks to have a normal distribution because (A) the frequencies start off low, rise to one or two high frequencies, then fall to a low frequency, and the distribution is fairly symmetric.

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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

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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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Answer:

The ratio to represent the relationship between Hallie's donation of blue jeans and Mattie's donation of blue jeans is 4 : 6, or 2 : 3.

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.

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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Write an equation using x to represent the cost of socks and y to represent the cost of shoes is 5x+2y=100.

As according algebra, an equations is a statement that illustrates the equivalence of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. a formula that illustrates the relationship between the two expressions on either side of a sign. Every equation is a formula. Not all equations have formulas. It is the purpose of equations to be solved for a variable. We analyze formulas. An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions are combined into one equation by using the equal symbol.

Let the cost of sock be $x.

Let the cost of shoes be $y.

According to question

[tex]5x+2y=100[/tex]

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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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Step-by-step explanation:

（3*10＾9）（2.3*10＾7）

＝

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