Please help!!! basic algebra. Find the value of x

the size of the union of the three sets is: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 3  × 24 million - 3 × 1.4 million + 1.2 million ≈ 69 million

A combination is a way of selecting a subset of objects from a larger set without regard to their order. The formula for the number of combinations of n objects taken r at a time is:
C(n, r) = n! / (r! ×  (n - r)!)
where n! means the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 ×  4 ×  3 ×  2 ×  1 = 120.
To apply this formula to our problem, we first need to count the total number of coins in the pile. Since there are at least 16 of each type, the minimum total is:
16 + 16 + 16 + 16 = 64
But there could be more coins of each type, so the total could be larger than 64. However, we don't need to know the exact number, only that it is large enough to allow us to choose 16 coins from it.
Using the formula for combinations, we can calculate the number of different collections of 16 coins that can be chosen from the pile:
C(64, 16) = 64! / (16! × (64 - 16)!) ≈ 1.1 billion
That's a very large number! It means there are over a billion ways to choose 16 coins from a pile that contains at least 16 of each type.
To answer the second part of the question, we need to count the number of collections that contain at least 3 coins of each type. One way to do this is to use the inclusion-exclusion principle, which says that the number of elements in the union of two or more sets is equal to the sum of their individual sizes minus the sizes of their intersections, plus the sizes of the intersections of all possible pairs, minus the size of the intersection of all three sets, and so on.
In this case, we can consider three sets:
- A: collections with at least 3 pennies
- B: collections with at least 3 nickels
- C: collections with at least 3 dimes
- D: collections with at least 3 quarters
The size of each set can be calculated using combinations:
|A| = C(48, 13) ≈ 24 million
|B| = C(48, 13) ≈ 24 million
|C| = C(48, 13) ≈ 24 million
|D| = C(48, 13) ≈ 24 million
Note that we have to choose 3 coins of each type first, leaving 4 coins to be chosen from the remaining 48 coins.
The size of the intersection of any two sets can be calculated similarly:
|A ∩ B| = C(43, 10) ≈ 1.4 million
|A ∩ C| = C(43, 10) ≈ 1.4 million
|A ∩ D| = C(43, 10) ≈ 1.4 million
|B ∩ C| = C(43, 10) ≈ 1.4 million
|B ∩ D| = C(43, 10) ≈ 1.4 million
|C ∩ D| = C(43, 10) ≈ 1.4 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 43 coins.
The size of the intersection of all three sets can also be calculated:
|A ∩ B ∩ C| = C(38, 7) ≈ 1.2 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 38 coins.

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Answer:

After 12 days both bamboo plants were 9ft tall

Answer:

122.5 units

Step-by-step explanation:

The proportion would be between the perimeters and the given ratio:

7/2 = p/p

Where P is the perimeter of the bigger figure and p is the perimeter of the smaller figure.

Remember that the perimeter is the sum of all sides, using all given values and solving for P, we have

7/2=P/9+5+9+12

7/2=P/35

7(35)/2=P

P=245/2=122.5

Therefore, the perimeter of Figure A is 122.5 units.

Answer:

I think the sum of the first 10terms of each geometric series is

4x3=12

= 4+12

12x3=36

=4+12+36

36x3=108

=4+12+36+108

108x3=324

=4+12+36+108+324

324x3=972

=4+12+36+108+324+972

972x3=2916

= 4+12+36+108+324+972+2916

2916x3=8748

=4+12+36+108+324+972+2916+8748

8748x3=26244

=4+12+36+108+324+972+2916+8748+26244

26244x3=78732

=4+12+36+108+324+972+2916+8748+26244+78732=the sum of the geometric series which is = 118,096.

hope this helps I am not sure of the answer but I tried my best.

The top priority during physical activity in the classroom is the safety and well-being of the students.

Ensuring a safe environment for physical activity helps prevent injuries and promotes the overall health and engagement of the students.

1. Supervision: Adequate adult supervision should be provided to monitor the students' activities, ensuring they are engaged in safe and appropriate physical exercises.

2. Proper Warm-up and Cool-down: Encouraging students to perform warm-up exercises before engaging in more vigorous activities and cool-down exercises afterward helps prevent injuries and promotes proper muscle recovery.

3. Suitable Physical Activities: The chosen physical activities should be age-appropriate, taking into account the students' physical abilities and limitations. Activities should be designed to minimize risks and promote participation for all students.

4. Clear Instructions and Demonstration: Teachers should provide clear instructions and demonstrate proper techniques for exercises or activities to ensure students understand how to perform them safely and effectively.

5. Equipment and Environment Safety: Regular inspection of equipment and ensuring the physical environment is free from hazards (such as tripping hazards or obstacles) is essential for maintaining a safe setting.

6. Individual Needs and Modifications: Teachers should consider any individual needs or limitations of students, such as physical disabilities or health conditions, and make necessary modifications or adaptations to ensure their safety and inclusion.

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the top priority during physical activity in the classroom is?

Answer:

y = -1/7x + 4

Step-by-step explanation:

(3-5)/(7-(-7)) = -2/14 = -1/7

3 = -1/7(7) + b

3 = -1 + b

b = 4

The average distance of electric cars is 275.

The range of the data set is 300.

Given:

To find: Average distance of electric cars

Solution:

The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:

250, 250, 250, 400, 300, 300, 350, 100

To find the average distance of electric cars, we can use the formula:

Average = (Sum of all the data points) / (Number of data points)

Substituting the given values, we get:

Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8

Average = 2200 / 8

Average = 275

Therefore, the average distance of electric cars is 275.

Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.

Range = Maximum value - Minimum value

Range = 400 - 100

Range = 300

Therefore, the range of the data set is 300.

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Answer:

\(a=x\\\\b = 0\)

Step by step explanation:

\(x = a - \sqrt b~~~~~~~~~~...(i)\\\\x = a + \sqrt b ~~~~~~~~~~...(ii)\\\\\text{From eq (i) and eq (ii),}\\\\~~~~a - \sqrt b = a+ \sqrt b\\\\\implies \sqrt b + \sqrt b = a-a \\\\\implies 2 \sqrt b = 0\\\\\implies \sqrt b = 0\\\\\implies b = 0\\\\\text{Substitute b = 0 in eq (i):}\\\\~~~~~~x = a- \sqrt {0}\\\\\implies x = a -0\\\\\implies x = a\\\\\implies a = x\\\)

In linear equation, $ 1300 is the cost for 80 employees.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.      

                             The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Given that cost of a company picnic varies directly as the number of employees attending the picnic

Let "c" be the company picnic cost

Let "n" be the number of employees attending the picnic

Therefore,

 cost ∝ number of employee attending picnic

       c ∝ n

   c = kn

Where "k" is the constant of proportionality

c = kn ---------- eqn 1

Given that company picnic costs $487.50 for 30 employees

Therefore substitute c = 487.50 and n = 30

   487.50 = k(30)

  k =   487.50/30

   k = 16.25

Substitute n = 80 and k = 16.25 in eqn 1

    c = 16.25(80)

    c = 1300

Thus $ 1300 is the cost for 80 employees.

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Answer: 9

Step-by-step explanation: sorry I don’t know

If Art makes 12 cookies with the same amount of dough and sells each cookie for 60 cents, then Roger needs to sell each cookie for 70 cents in order to earn the same amount from a single batch.

To explain how this is determined, we can use a basic equation. We know that Art made 12 cookies with the same amount of dough. If Art sells each cookie for 60 cents, then the total amount of money they earn from a single batch is 12 x 60 = 720 cents. We also know that Roger is trying to earn the same amount from a single batch of cookies.

To calculate how much each of Roger's cookies should cost, we need to divide the total amount of money, 720 cents, by the number of cookies, 12. Therefore, the cost of each of Roger's cookies is 720 / 12 = 70 cents.

To summarize, if Art makes 12 cookies with the same amount of dough and sells each cookie for 60 cents, then Roger needs to sell each cookie for 70 cents in order to earn the same amount from a single batch.

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Answer:

nearest percentage=64%

Step-by-step explanation:

math

Answer:

12

Step-by-step explanation:

There are 8 one-eighths in one inch

You have 1.5 inches

This means to find the number of one eighths all you need to do is multiply 8 by 1.5 and your answer is 12.

There are 3/2 of 1/8ths  inch in 1 ½ inches.

To solve this problem, convert 1 ½ inches to a fraction with a denominator of 8 (since we are looking for the number of 1/8ths of an inch in 1 ½ inches).

Note: 1 inch is equal to 8/8 or 1 whole inch,

so 1 ½ inches is equal to:

1 ½ = 1 + ½ = 8/8 + 4/8 = 12/8

Thus, there are 12/8 of an inch in 1 ½ inches.

To simplify this fraction,  divide both the numerator and denominator by their greatest common factor, which is 4:

(12/4) / (8/4) = 3/2

Therefore, there are 3/2 of 1/8ths  inch in 1 ½ inches.

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The double dot plot shows the quiz scores for two different class periods, represented by the two sets of data points. Each data point represents the score of a single student on the quiz.

The first population, represented by the data points on the left side of the plot, appears to have a center at around 16-18 points and a variation that is more spread out. This suggests that the students in this class period had a wider range of quiz scores, with some students scoring higher and some scoring lower.

The second population, represented by the data points on the right side of the plot, appears to have a center at around 8-10 points and a variation that is more tightly clustered. This suggests that the students in this class period had a narrower range of quiz scores, with fewer students scoring higher and fewer scoring lower.

 Based on these observations, an inference that can be drawn about the two populations is that the class period with higher quiz scores had more students who performed well on the quiz, while the class period with lower quiz scores had fewer students who performed well on the quiz. This suggests that the level of student proficiency in the subject may vary across class periods, and that it may be important to consider this variability when designing instructional strategies.

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Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)

Answer:

13

Step-by-step explanation:

The common difference is 13 I

12 + 13 = 25

25 + 13 = 38

And so on.....

Answer:

Step-by-step explanation:

Given,

Number of words Lucy can type in 5 minutes

= 300 words

So,

Number of words Lucy can type in 1 minute

\( = \frac{300}{5} \: words\)

= 60 words

Therefore,

Number of words Lucy can type in 27 minutes

= (60 × 27) words

= 1,620 words

Hence, Lucy can type 1620 words in 27 minutes.

Answer: 114

Step-by-step explanation:

To find the perimeter, you will find the distance around the shape by adding the numbers.

The is one missing side  and to find that side you will subtract  10 from 38.

38 - 10 = 28

Now add the them.

28 + 5 +  10 + 26 + 10 + 35 = 114

Step-by-step explanation:

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Answer:

800g gives a better value for money

Step-by-step explanation:

To find which box which gives you better value for money

Divide the gram by the cost of the cereal

1st calculations

--› 500g ÷ $2.5

=> 200

2nd calculations

--› 800g ÷ $3.95

=> 202.5316455696202

so the question that the value is bigger which is 800g= 202.5316455696202 gives you more money value

The unit tangent and unit normal vectors t(t) = (3/√(34), -5sin(t)/√(34), 5cos(t)/√(34)) and n(t) = (0, -cos(t), -sin(t)).

We'll start by determining the derivative of the vector function r(t) in order to determine the unit tangent and unit normal vectors.

r(t) = 3t, 5cos(t), 5sin(t)

Taking each component's derivative with respect to t, we obtain:

r'(t) = 3, -5sin(t), 5cos(t)

We must divide the derivative vector r'(t) by its magnitude in order to normalize it and obtain the unit tangent vector t(t). Calculating the size of r'(t) is as follows:

|r'(t)| = √((3)² + (-5sint)² + (5cost)²)

|r'(t)| = √(9 + 25sin²t + 25cos²t)

|r'(t)| = √(9 + 25(sin²t + cos²t))

|r'(t)| = √(9 + 25)

|r'(t)| = √34

By dividing the derivative vector r'(t) by its magnitude, we can now get the unit tangent vector t(t):

t(t) = r'(t)/|r'(t)|

t(t) = (3/√(34), -5sint/√(34), 5cost/√(34))

The unit tangent vector's derivative with respect to t can then be used to find the unit normal vector n(t), which is then normalised.

Taking t(t)'s derivative with regard to t, we get the following:

t'(t) = (0, -5cost/√(34), -5sin(t)/√(34))

The magnitude of t'(t) is:

|t'(t)| = √(0² + (-5cost/√(34))² + (-5sint/√(34))²)

|t'(t)| = √(0 + 25cos²t/34 + 25sin²t/34)

|t'(t)| = √(25/34)

|t'(t)| = 5/√(34)

By dividing the derivative vector t'(t) by its magnitude, we may finally determine the unit normal vector n(t):

n(t) = t'(t)/|t'(t)|

n(t) = (0, -5cos(t)/√(34), -5sin(t)/√(34))/(5/√(34))

n(t) = (0, -cos(t), -sin(t))

Therefore, the unit tangent vector is t(t) = (3/√(34), -5sin(t)/√(34), 5cos(t)/√(34)), and the unit normal vector is n(t) = (0, -cos(t), -sin(t)).

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Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.  

A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.

Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.

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Answer:

750

Step-by-step explanation:

3000 divided by 4 =

750

Answer:

750 boxes

Step-by-step explanation:

Yes, it would be unusual to get a score of 0 on a binomial distribution with a mean of 2.5 and a standard deviation of 1.4. This is because the expected value of such a distribution is much higher than 0.

Yes, it would be unusual to get a score of 0 on a binomial distribution with a mean of 2.5 and a standard deviation of 1.4. This is because the expected value of such a distribution is much higher than 0. The binomial distribution is a type of probability distribution which is used to describe the probability of a discrete event occurring a certain number of times in a given number of trials. The mean of the binomial distribution is the expected value of the events, while the standard deviation is a measure of how much the values of the events vary from the expected value. In this case, the expected value is 2.5, and the standard deviation is 1.4. This means that the probability of getting a score of 0 is quite low, since the expected value is so much higher than 0. Therefore, it would be considered unusual to get a score of 0 on this binomial distribution.

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Answer:

x+2y=-3

x+2(-1)=-3

x-2=-3

x=-3+2

x=-1

Step-by-step explanation:

9+b>-3

b>-3-9

b>-12

any number greater than -12 will result in an answer greater than -3

The volume of dirt needed for the flower garden is 452.5 cubic units.

Volume of cylinder is given as ,

pi*r²h

here , r =6

and h = 4

therefore , volume will  be

22/7 * 36 * 4

=452.5

A volume is just the amount of space taken up by any three-dimensional solid. A cube, a cuboid, a cone, a cylinder, or a sphere are examples of solids.

Volumes differ depending on the shape. In 3D geometry, we examined numerous three-dimensional shapes and solids such as cubes, cuboids, cylinders, cones, and so on.

A solid's volume is measured in cubic units. If the dimensions are supplied in meters, the volume will be given in cubic meters. This is the International System of Units' standard volume unit (SI).

Other volume units include cubic cm, cubic feet, and cubic inches.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

36 boards

Step-by-step explanation:

The boards are as long as the room, so I only had to worry about the width. If the boards were 1/2 ft wide, I would need 2 boards for every foot of width. For 16 ft, I would need 32 boards.

Instead of dividing, I wrote the equivalent multiplication by multiplying by the reciprocal of 11/24 (the reciprocal of 11/24 is 24/11)

I simplified by dividing both 2 and 24 by 2, and both 11 and 33 by 11.

Therefore he needs 36 boards

The  statements regarding the implications of the central limit theorem that are true are;

The Theorem shows that even when the original variables are not normally distributed, the standardized sample mean frequently trends towards the standard normal distribution for identically distributed independent samples.

It should be noted that the central limit theorem stressed that a distribution of the sample means can be distributed  in the presence of population with mean and standard deviation .

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Which statements regarding the implications of the central limit theorem are true?

As the number of sample means decreases, the means get closer to a standard normal distribution.

For an infinite number of samples, 99.7% of the sample means would fall within the interval .

The central limit theorem holds true only for populations that are normally distributed.

For an infinite number of samples, 95% of the sample means would fall within the interval .

The mean of the population is the same as the mean of any sample taken from the population.

If the population is normally distributed, then the mean of a sample from that population will be normally distributed.