the three consecutive term of geometric series be increased by their middle term, then prove that the resulting term will be in Harmonic series.

​

Yes, because it is practical to obtain that many aspirin because the number is relatively small. The correct option is B.

The minimum sample size required to be 99% confident that the sample standard deviation (s) is within 10% of the population standard deviation (σ) is 336, according to the table provided.

This means that in order to have a high level of confidence (99%) that the sample standard deviation is within a reasonable range of the population standard deviation, a minimum sample size of 336 is needed.

In this case, the sample size requirement is met with a relatively small number, 336, compared to the larger values provided in the table for higher levels of confidence.

Therefore, it can be considered practical to obtain that many aspirin tablets for the purposes of this study.

Thus, the correct option is B.

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Answer:

Para encontrar el valor de la expresión 6 - (3x + 1) + 2x^2 cuando x = 4, sustituimos el valor de x en la expresión y evaluamos:

6 - (3x + 1) + 2x^2

= 6 - (3 * 4 + 1) + 2 * 4^2

= 6 - (12 + 1) + 2 * 16

= 6 - 13 + 32

= -7 + 32

= 25

Por lo tanto, cuando x = 4, el valor de la expresión 6 - (3x + 1) + 2x^2 es igual a 25.

Step-by-step explanation:

Answer: The pair of equations required this the given question is x+y=100 and 3x+6y=396

Step-by-step explanation:

If x denotes the number of burritos and y denotes the number of salads sold. then,

1. x+y =100 (as there are a total of 100 meals sold)

2. 3x+6y=396(as the cost of each burrito is $3 and cost of each salad is $6, the total cost of the meal is $396)

Hence, The pair of equations required this the given question is x+y=100 and 3x+6y=396

Answer:

The length of a side of the base of the box is 13 cm.

Step-by-step explanation:

To find the length of a side of the base of the box, we need to use the formula for the volume of a box.

The volume of a box is given by the formula:

V = l^2 * h

Where:

V is the volume,

l is the length of a side of the base, and

h is the height of the box.

Substituting the given values:

V = 1352 cm^3

h = 8 cm

1352 = l^2 * 8

Dividing both sides by 8:

l^2 = 169

Taking the square root of both sides:

l = √169

Calculating the length of a side of the base:

l = 13 cm

Therefore, the length of a side of the base of the box is 13 cm.

A graph of this quadratic equation x² + x - 6 = 0 is shown below.

The solutions to the equation x² + x - 6 = 0 are (-3, 0) and (2, 0).

In Mathematics, the graph of a quadratic function always form a parabolic curve or arc because it is u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive one (1) and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function x² + x - 6 = 0 is positive one (1), we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts (-3, 0) and (2, 0). Also, the value of the quadratic function f(x) would be minimum at -6.25.

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Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

Answer:

6

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the missing number in the given sequence, let's analyze the pattern:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, ???

Looking at the sequence, we can identify a few patterns:

The sequence alternates between increasing and decreasing numbers.

The first two numbers, 2 and 4, are increasing.

The next two numbers, 4 and 3, are decreasing.

The following two numbers, 3 and 6, are increasing.

The subsequent two numbers, 6 and 3, are decreasing.

The next two numbers, 3 and 8, are increasing.

The subsequent two numbers, 8 and 9, are increasing.

Based on these observations, it appears that the sequence is following a pattern where it alternates between increasing and decreasing numbers, but the specific values being added or subtracted are not consistent.

Now let's determine the missing number:

From the pattern, the next two numbers should be decreasing. Following the pattern of alternating between increasing and decreasing numbers, the missing number after the last given number (8) should be less than 9.

Let's assume the missing number is x:

8 - x

Since the previous decreasing sequence was 6 - 3, we can assume that x is 1 less than the previous number (3):

8 - (3 - 1) = 8 - 2 = 6

Therefore, the missing number in the sequence is 6.

The complete sequence is:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, 6

To determine the annual interest rate paid, we need to calculate the simple interest for one month and then convert it to an annual rate.

The formula for simple interest is:

Simple Interest = Principal × Rate × Time

In this case, the principal amount is $720, and after one month, you pay back a total of $1272. Therefore, the interest paid is:

Interest = $1272 - $720 = $552

We can now calculate the monthly interest rate:

Rate = Interest / Principal = $552 / $720 ≈ 0.7667

To convert the monthly interest rate to an annual rate, we multiply it by 12:

Annual Rate = Monthly Rate × 12 = 0.7667 × 12 ≈ 9.20

Therefore, you paid an annual interest rate of approximately 9.20%.

The distance from X to Z will be 386 km when rounded to 3 significant figures.

The distance from Y to XZ will be 141 km when rounded to 3 significant figures.

To obtain the distances, we need to extend the distances traveled by the airplane and this yields another triangular form. Angle Y = 105°, z = 200 km, and Z = 30°.

y/Sine Y = z/Sine Z

y/Sine 105° = 200/Sine 30°

y = 200 × 0.966/0.5

386 km to 3 significant figures

Also for the distance from Y to XZ,

We assume that the distance from Y to XZ is d

Sine 45°/1 = d/200

d = 200 sine 45°

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Step-by-step explanation:

A LOT of different outfits !
8  x  5  x  4  x  2   = 320 outfit possibilities

The solution to the compound inequality -28 < -4r < 16 is 7 > r > -4

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

-28 < -4r < 16

Divide through the inequality by -4

so, we have the following representation

-28/-4 < -4r/-4 < 16/-4

When the quotients are evaluated, we have

7 > r > -4

Hence, the solution to the compound inequality is 7 > r > -4

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Answer:

Step-by-step explanation:

3.14 . 11= 150/360

The angles supplementary to ∠EOF are ∠FOB and ∠COE.

Supplementary angles are those angles that sum up to 180 degrees. In

other words, two angles are called supplementary when their measures

add up to 180 degrees.

Therefore, let's find the angles that are supplementary angles to ∠EOF.

Therefore, let's use the angle relationships in the line intersection to find

the angles that are supplementary to ∠EOF.

Hence, the angles supplementary to  ∠EOF are ∠FOB and ∠COE

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The area of the shaded region is equal to 45 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 8 × 6

Area of rectangle = 48 square units.

Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;

L₁ = 8 - 5 = 3 units.

L₂ = 6 - 4 = 2 units.

Area of right triangle = 1/2 × 3 × 2

Area of right triangle = 3 square units.

For the area of the shaded region, we have:

Area of the shaded region = 48 square units - 3 square units.

Area of the shaded region = 45 square units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probabilities of getting eagles in different quantities, given the number of coins would be:

There are 8 possible outcomes when tossing 3 coins: HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.

The probability of getting 2 eagles is 3/8 because the ways of getting eagles HHH, HHT, and HTH.

The probability of getting at least 1 eagle is 7 / 8. There are 7 ways to get at least 1 eagle: HHH, HHT, HTH, THH, TTH, THT, and HTT.

The probability of getting no eagles is 1/8 / . There is only 1 way to get no eagles: TTT.

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Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

The ordered pair that is a solution of the system is (-3, -3), the second option.

There are two ways of finding this.

You can use your graph and identify which of the given pointes lies in the region where the two shaded areas intersect.

Another way, is replacing the values of the coordinate points in both inequalities and checking that both are true when evaluated in the point.

Here we will use the graph, because you already had it (and you can see a more precise graph in the image at the end).

We can see that the region os solutions is on the left side of the graph, and the only point that lies on there is (-3, -3)

So that point is the solution.

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The rationalized form of the expression √(3/5) is √15/5.

To rationalize the denominator of the expression √(3/5), we need to eliminate the square root in the denominator.

We can achieve this by multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of √5 is also √5, so we can multiply the expression by (√5)/(√5):

√(3/5)×(√5)/(√5)

Multiplying the numerator and denominator, we have:

√(3 × 5)/(√(5×5))

Which simplifies to:

√15/√25

√15/5

Therefore, the rationalized form of √(3/5) is √15/5.

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Answer:

x = 36.1°

Step-by-step explanation:

In the Right-angled triangle, opposite side of angle x and adjacent side of angle x is given, and we have to find the angle x. To find angle x, we can use the trigonometry ratio 'tan x'.

           [tex]\sf Tan \ x = \dfrac{opposite \ side \ of \ \angle X}{adjacent \ side \ of \ \angle x}[/tex]

                     [tex]\sf = \dfrac{22}{30}\\\\ = 0.73[/tex]

                  [tex]x = arctan \ (0.73)[/tex]

                      = 36.13

                  x = 36.1°

Answer:

The optimal size of each production run is 180 pounds, and the total annual inventory cost is $832,825.

Step-by-step explanation:

To determine the optimal size and total annual inventory cost, we need to consider the production capacity, demand, setup costs, and carrying costs.

Given:

Production capacity per day = 250 pounds

Demand per day = 180 pounds

Setup cost = $125

Carrying cost per pound per year = $12

First, let's calculate the optimal production size. We want to produce enough cheese to meet the demand without exceeding the production capacity.

Optimal production size per day = Minimum(Production capacity, Demand)

Optimal production size per day = Minimum(250 pounds, 180 pounds) = 180 pounds

Next, let's calculate the total annual inventory cost. This cost includes both the setup cost and the carrying cost.

Total annual inventory cost = (Setup cost * Number of setups per year) + (Carrying cost per pound * Optimal production size * Number of days in a year)

Number of setups per year = Number of production runs per year

Number of production runs per year = Total days in a year / Days per production run

Assuming a year has 365 days and each production run takes one day:

Number of production runs per year = 365 days / 1 day = 365 runs

Total annual inventory cost = ($125 * 365) + ($12 * 180 pounds * 365)

Total annual inventory cost = $45,625 + $787,200

Total annual inventory cost = $832,825

Answer: 97 degrees

Step-by-step explanation: 180-83=97

The height of the cylinder is 25.

Option C is the correct answer.

We have,

To find the height of the right cylinder, we need to use the given information of the diagonal length and the total surface area.

The diagonal length of a right cylinder can be found using the formula:

diagonal = √(height² + radius²)

Given that the diagonal length is 37, we can set up the equation:

37 = √(height² + radius²)

We also know that the total surface area of a right cylinder is given by:

surface area = 2πrh + 2πr²

Given that the total surface area is 492π, we can set up the equation:

492π = 2πrh + 2πr²

Simplifying the surface area equation, we have:

246 = rh + r²

Now we have a system of equations:

37 = √(height² + radius²)

246 = rh + r²

Since we only need to find the height of the cylinder, we can focus on the first equation:

37 = √(height² + radius²)

Squaring both sides of the equation, we get:

37² = height² + radius²

1369 = height² + radius²

Substituting the second equation (246 = rh + r²) into the equation above, we have:

1369 = height² + (246 - rh)

Simplifying further, we get:

1369 = height² + 246 - rh

Now, let's analyze the answer options:

a. 35

b. 42

c. 25

d. 17

e. 32

We need to substitute each value into the equation and check if it satisfies the equation.

After checking each option, we find that the height that satisfies the equation is:

c. 25

Therefore,

The height of the cylinder is 25.

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In my community, there are several situations where hypothesis testing can be applied. Here are three examples: Traffic Flow Optimization, Recycling Program Assessment, and Crime Prevention Strategy Evaluation

For the purpose of this response, let's choose Situation 1 (Traffic Flow Optimization) and go through the four steps.

1. Problem Statement: The local authorities want to determine if implementing a new traffic signal timing system will significantly reduce the average travel time for commuters passing through a busy intersection during peak hours.

2. Null Hypothesis (H0): The new traffic signal timing system has no effect on the average travel time for commuters passing through the intersection.

Alternative Hypothesis (H1): The new traffic signal timing system significantly reduces the average travel time for commuters passing through the intersection.

3. Level of Significance: α = 0.05

4. Rejection Region: The rejection region will depend on the specific test statistic used. Let's assume we are using a t-test to compare the mean travel time before and after implementing the new traffic signal timing system. In this case, we would calculate the t-statistic and determine the critical value(s) based on the degrees of freedom and the chosen level of significance. The rejection region would be in the tails of the t-distribution corresponding to the critical value(s).

Possible Type I Error: Rejecting the null hypothesis when it is actually true, indicating that the new traffic signal timing system is effective when it is not. In this case, it would mean concluding that the new system significantly reduces travel time when, in reality, it has no effect.

Possible Type II Error: Failing to reject the null hypothesis when it is actually false, indicating that the new traffic signal timing system is ineffective when it is actually effective. In this case, it would mean not detecting a significant reduction in travel time when the new system does indeed have a positive impact.

It's worthy of note that the specific test statistic and rejection region may vary depending on the nature of the data and the chosen statistical test. The above steps provide a general framework for conducting hypothesis testing in the given situation.

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The statement that correctly compares the centers of the distributions is this:

D. The mean of East Hills HS is greater than the mean of Southview HS.

Since, The statement that correctly describes the centers of the distributions is option D. To find out, we will calculate the mean of the two distributions as follows:

For East Hills HS

25 * 1 + 29 * 1 + 31 * 2 + 33 * 4 + 35 * 5 + 37 * 8 + 39 * 4

= 875

And, Frequency = 1 + 1 + 2 + 4 + 5 + 8 + 4 = 25

Hence,

Mean = 875/25

Mean = 35

For Southview

25 * 2 + 27 * 6 + 29 * 9 + 31 * 6 + 33 * 2

= 725

Frequency = 2 + 6 + 9 + 6 + 2 =25

Hence, Mean = 29

So, from our calculation, the mean of East Hills HS is greater than the mean of Southview HS.

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Answer:

1) 5/6
2) 19/30
3) They are mutually exclusive.

Step-by-step explanation:

Let's break the diagram down.
We have four types of smoothies:

Contains apple but not blueberry - 12
Contains blueberry but not apple - 7
Contains both blueberry and apple - 3
Doesn't contain either - 8

From here, we find that there are 30 smoothies in total.

In addition, we know that the number of smoothies containing an apple is 15, and the number of smoothies containing blueberry is 10.

Therefore,

[tex]P(\text{contains apple}) = \frac{\text{contains apple}}{\text{total}} = \frac{15}{30} = \frac12\\\\P(\text{contains blueberry}) = \frac{\text{contains blueberry}}{\text{total}} = \frac{10}{30} = \frac13\\\\\text{a) } P(\text{contains apple}) + P(\text{contains blueberry}) = \frac12 + \frac13 = \frac36 + \frac26 = \frac56[/tex]

Now, the probability of getting apple OR strawberry is given by adding the probabilities of getting one of the flavors but not the other.

[tex]P(\text{apple, no blueberry}) = \frac{12}{30}\\\\P(\text{blueberry, no apple}) = \frac{7}{30}\\\\P(\text{apple or blueberry}) = \frac{12}{30} + \frac7{30} = \frac{19}{30}[/tex]

We can check if the events are mutually exclusive using the formula:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In our case, A means contains apple, and B means contains blueberry.
[tex]P(A \cup B)[/tex] resembles the case for exclusively apple or exclusively blueberry (AKA our answer for b).

[tex]P(A \cap B)[/tex] resembles the case for both apple and blueberry (AKA the intersection), which is equal to 3/30 = 1/10.

If the two sides are equal, the cases are not mutually exclusive.

[tex]\frac{19}{30} = \frac{15}{30} + \frac{10}{30} - \frac{3}{30}\\\\\frac{19}{30} \ne \frac{22}{30}[/tex]

Therefore, the events are mutually exclusive.

The solution of the System of equation are,

⇒ x = 1

⇒ y = 5

We have to given that;

System of equation are,

⇒ 3x - 5y = - 22

⇒ 4x + 2y = 14

Now, We can simplify as;

From (ii);

2x + y = 7

y = 7 - 2x

Put above value in (i);

3x - 5 (7 - 2x) = - 22

3x - 35 + 10x = - 22

13x = - 22 + 35

13x = 13

x = 1

From (i);

⇒ 3x - 5y = - 22

⇒ 3 - 5y = - 22

⇒ 3 + 22 = 5y

⇒ 25 = 5y

⇒ y = 5

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The expression that can be used to find the amount of oatmeal in the container, obtained from the formula for the volume of a cylinder is π · 2² · 8. The correct option is therefore, the option C.

C. π · 2² · 8

The volume of a cylinder is; V = π × Radius² × Height

The part of the question that appear missing, obtained from a similar question on the internet, includes;

The radius of the can = 2 inches

The height to which the can was filled = 8 inches

The volume of oatmeal in the can is therefore;

V = π·r²·h

Where;

r = The radius of the can = 2 inches

h = The height to which the oatmeal is filled = 9 - 1 = 8 inches

Therefore;

V = π × 2² × 8

The expression that can be used to find the amount of oatmeal in the can is therefore;

C. π · 2² · 8

The possible question options, obtained from the online question are;

A. (4·π·9) - 1

B. 2·π·8

C. π·2²·8

D. (4·π·9)/3

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The job A is the best job based on pay scale

Given data ,

a) Job A:

Hours per week: 40

Hourly rate: $15

On simplifying the equation , we get

Gross pay per week: 40 hours * $15/hour = $600

b) Job B:

Hours per week: 30

Hourly rate: $5

On simplifying the equation , we get

Gross pay per week: 30 hours * $5/hour = $150

In addition to the base pay, Job B also offers tips averaging $350 per week.

Considering the total compensation for each job:

Total compensation for Job A: $600 per week (base pay)

Total compensation for Job B: $150 per week (base pay) + $350 per week (tips) = $500 per week

Based on the total compensation, Job A offers a higher gross pay of $600 per week, while Job B offers a total compensation of $500 per week.

Hence , if the decision is solely based on pay, Job A would be the better choice.

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