Element X has 25 protons and is known to exist as 3 isotopes.
One isotope is 56.5% abundance and has 38 neutrons. Another
isotope is 23.4% and has 39 neutrons. The other isotope is
20.1% and contains 40 neutrons. What is the average atomic
mass?

the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that the numerator or denominator doesn't have commonly divisible.

As a small addition, you get 4+12+20+…+76, which is an arithmetic sequence. There are ten terms, so you can use

So the sum will be 10(4+76)/2 = 400

Hence the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.

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The probability that the events do not occur is 0.6778`.

The probability that the events do not occur is given by `P(Ac)=1-P(A)` and `P(Bc)=1-P(B)`.

The given probabilities are `P(A)=0.2272` and `P(B)=0.4506`.

Using the formula `P(A∪B)=P(A)+P(B)-P(A∩B)`, we have `P(A∩B) = P(A) + P(B) - P(A∪B)`

Using the fact that the two events are mutually exclusive, we get `P(A∩B) = 0`.

Thus, `P(A∪B) = P(A) + P(B) = 0.2272 + 0.4506 = 0.6778`.

The probability that either A or B but not both occurs is given by `P(AΔB) = P(A∪B) - P(A∩B) = 0.6778 - 0 = 0.6778`.

Hence, the required probability is `P(AΔB) = 0.6778`.

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Answer:

488000

(real number)

= 4.88 × 105

(scientific notation)

= 4.88e5

(scientific e notation)

number of significant figures: 3

It will take 13 weeks to gather funds that sum up to $4500.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given: I have $2485 and I save $155 weekly

Thus amount left to be gathered is $4500-$2485=2015

If I save $155 weekly then we get = $2015/$155

                                                        =13 weeks

Hence, It will take 13 weeks to gather funds that sum up to $4500.

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Answer:

x=14

Step-by-step explanation:

g(x) = 2(x − 4)

Let g(x) = 20

20 = 2(x − 4)

Divide each side by 2

20/2 = 2(x-4)/2

10 = x-4

Add 4 to each side

10+4 = x-4+4

14 =x

Answer:

6070m^2

Step-by-step explanation:

Finding the Area of the house: 50*35 = 1250m^2
Finding the area of driveway = 9*20 = 180m^2

The total Area of the trapesium = \(\frac{1}{2} (a+b)h\)

= A = ½ (80 + 120) * 75

= A = ½ * 200 * 75 = 7500 m^2

Add the area of house and driveway and subtract it from the total area of the plot :

7500 - ( 1250 + 180)

= 7500 - 1430 = 6070m^2 is covered in grass

In physics, if quantity "s" represents a length and quantity "t" represents a time, then the quantities "v" and "a" can be defined as follows:

- Quantity "v" represents velocity, which is the rate of change of length with respect to time. It can be calculated by dividing the change in length (Δs) by the change in time (Δt): v = Δs/Δt. Velocity measures how fast an object's position changes over time.

- Quantity "a" represents acceleration, which is the rate of change of velocity with respect to time. It can be calculated by dividing the change in velocity (Δv) by the change in time (Δt): a = Δv/Δt. Acceleration measures how quickly an object's velocity changes over time.

In summary, velocity (v) is the rate of change of length with respect to time, while acceleration (a) is the rate of change of velocity with respect to time. These quantities are fundamental in describing the motion of objects and play a crucial role in physics and engineering.

Velocity (v) and acceleration (a) are important concepts in physics that describe the motion of objects. Velocity measures the rate at which an object's position changes over time, while acceleration measures the rate at which an object's velocity changes over time.

To understand these concepts better, let's delve deeper into the definitions of velocity and acceleration. Velocity is the ratio of the change in position (Δs) to the change in time (Δt): v = Δs/Δt. It tells us how far an object moves in a given amount of time. For example, if a car travels 100 meters in 10 seconds, its velocity would be 10 meters per second.

Acceleration, on the other hand, is the ratio of the change in velocity (Δv) to the change in time (Δt): a = Δv/Δt. It describes how quickly an object's velocity is changing. If a car accelerates from rest to a speed of 20 meters per second in 5 seconds, its acceleration would be 4 meters per second squared.

Both velocity and acceleration are vector quantities, meaning they have both magnitude and direction. The direction of velocity indicates the object's motion (e.g., forward or backward), while the direction of acceleration tells us whether the object is speeding up or slowing down.

These quantities are fundamental in analyzing the motion of objects in various fields such as physics, engineering, and sports. They help us understand how objects move, predict their future positions, and design systems to optimize performance. Whether it's the motion of a ball, a car, or a planet, velocity and acceleration provide essential insights into the behavior of physical systems.

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Answer:

B

Step-by-step explanation:

their is 5 different colors and they look the about the same and you spin it 100 times so

5 divided by 100 you would get 20

Answer:

f(x) = [x] - 2 + 8

[x] is the notation for 'greatest integer function'

f(-1.8) = [-1.8] - 2 + 8 = -2 -2 + 8 = 4

The answer is 4

Step-by-step explanation:

The value of the function  f(x) = [x] - 2 + 8 when x = -1.8 is 12

Given the function f(x) =[x] - 2 + 8, we need to find f(-1.8)

To get the value of f(-1.8), we will simply substitute x = -1.8 into the function to have:

f(-1.8) = -1.8 - 2 + 8

f(-1.8) = -3.8 + 8

f(-1.8) = 11.8

Since x is in a square bracket, we will round the value up to the nearest whole number, hence;

f(-1.8) = 12

Therefore the value of the function  f(x) = [x] - 2 + 8 when x = -1.8 is 12

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Answer:Good luck bro

Step-by-step explanation:

10. Variable : x = 4.78

60(x)=287

11. x = 94

$6.90 - $1.25 = $5.65

6(x) = 5.65

Sorry I couldn't do all someone else can do the 2 others

To find the values of "a" and "b" in the equation y = a * xᵇ + 4, we can use the given information when x = 1 and y = 9, and when x = 2 and y = 44.

When x = 1 and y = 9, we substitute these values into the equation:
9 = a * 1ᵇ + 4
Simplifying the equation:
9 - 4 = a * 1ᵇ
5 = a
When x = 2 and y = 44, we substitute these values into the equation:
44 = a * 2ᵇ + 4
Simplifying the equation:
44 - 4 = a * 2ᵇ
40 = 2ᵇ
To solve for "b", we can rewrite 40 as 2³ * 5:
2³ * 5 = 2ᵇ
Since the bases are the same, the exponents must be equal:
3 = b
Therefore, the value of "a" is 5, and the value of "b" is 3.

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a) a minimum of 3 doctors required so that at least 70% of the arriving patients.

b) a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes

a) Minimum number of doctors required so that at least 70% of the arriving patients can receive treatment immediately

Formula used:

The number of patients arriving in an hour: λ = 9

Treatment time: μ = 6 minutes

Per the Little’s law, the waiting time is proportional to the average number of patients present at any given time.

λ/μ is the average number of patients present at any given time.

If there are k servers present in the ER, the number of patients they can serve is given by kμ.

Hence, the percentage of patients who have to wait is given by:

Percentage of patients waiting = λ / (kμ + λ)

Percentage of patients receiving treatment immediately = kμ / (kμ + λ)

Thus, we can now form an equation as:

kμ / (kμ + λ) ≥ 0.7

=> kμ / (kμ + 9) ≥ 0.7

=> k ≥ 3 doctors (Approximately)

Therefore, a minimum of 3 doctors required so that at least 70% of the arriving patients can receive treatment immediately.

b) Minimum number of doctors required so that the average time a patient waits for treatment is no more than 30 minutes as advertised

The percentage of patients who have to wait = λ / (kμ + λ)

Again, let us use the Little's law to find the average time patients spend waiting in the queue, which is equal to

λ / (k(μ - λ/k)).

We are given that the waiting time should not be more than 30 minutes, which can be converted to 0.5 hours.

Thus:

λ / (k(μ - λ/k)) ≤ 0.5

=> 9 / (k(0.1 - 1/k)) ≤ 0.5

=> 18 ≤ k(0.1 - 1/k)

=> 0.1k - 1 ≤ 18/k

=> 0.1k² - k - 18 ≥ 0

Using the quadratic formula, the solution is k = 6.66, which is rounded up to 7, and k = 2.5, which is rounded up to 3.

Therefore, a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes as advertised and a minimum of 3 doctors are required so that the average time a patient waits for treatment is no more than 15 minutes.

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We can see here that the equation that represents the situation is:

d. 4 ÷ 1 = 4 (The customer bought 4 kg of tangerines, which is equivalent to 4 bags, each weighing 1 kg).

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts that two expressions are equal, usually represented by a "=" sign. Equations can take many forms and can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

In order to draw the diagram, you need to get the equations correct.

The others equations a, b, c and e doesn't represent the situation, they are not mathematical equations and they are not related to the problem.

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Hence, the deal of  $\(479\) is best unit price per blender.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Oliver is buying equipment for his restaurant. He can buy two blenders for $\(396\) or three blenders for $\(479\).

So,

Oliver buying two blenders at  $\(396\) so the cost of one blender is

i.e., \(\frac{396}{2}=198\)$

Oliver buying two blenders at  $\(479\)  so the cost of three blenders is

i.e., \(\frac{479}{3}=159\)$

Hence, the deal of  $\(479\) is best unit price per blender.

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This means that the weight of the ear of corn is 0.55 standard deviations below the mean weight of the distribution for the Ohio farm's corn.

To determine how many standard deviations an observation is from the mean of a distribution, we need to calculate its z-score. The z-score measures the number of standard deviations an observation is above or below the mean.

Let's assume we know the mean and standard deviation of the distribution of weights for the Ohio farm's corn. For example, let's say that the mean weight is 1.5 pounds and the standard deviation is 0.2 pounds.

Then, we can calculate the z-score for an ear of corn that weighs 1.39 pounds using the formula:

z = (x - μ) / σ

where x is the weight of the ear of corn, μ is the mean weight of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have:

z = (1.39 - 1.5) / 0.2

z = -0.55

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Vertical angles are two non-adjacent angles formed by intersecting two lines. The intersection forms two pair of vertical angles. And it is true that:

For the green triangle, we can use the triangle sum theorem, which states that the sum of the internal angles of a triangle is equal to 180, so:

Using the same theorem for the blue triangle:

? = w, therefore, ? = 26

Check the picture below.

Where k is a constant

When y = 36 , x = 3 , z=3

The value of y is 40

Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

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Answer:

$74.00

Step-by-step explanation:

multiply 40 by 0.83=34 add to 40=74

The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and  X and Y are not independent because the value of X affects the possible range of values for Y.



a. To compute the conditional probability mass function (PMF) of Y=i given X=1, we need to find the probability of Y=i when X=1. Since X=1, the only possible outcome is (1,1), and Y can only be 1. Hence, the conditional PMF of Y=i given X=1 is:

P(Y=i | X=1) = 1, if i=1; 0, otherwise.

b. X and Y are not independent. If they were independent, the outcome of one die roll would not provide any information about the other die roll. However, given that X is the largest value and Y is the smallest value, we can see that X directly affects the possible range of values for Y. If X is 6, then Y cannot be greater than 6. Therefore, the values of X and Y are dependent on each other, and they are not independent.



Therefore, The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and  X and Y are not independent because the value of X affects the possible range of values for Y.

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Answer:

m = -4/3

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-2,2) (1,-2)

We see the y decrease by 4 and the x increase by 3, so the slope is

m = -4/3

A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

45 lb is about 20.412; rounding it would be 20.4

Step-by-step explanation:

1 kg is about 2 pounds. (Used a conversion thing).

Answer:

Step-by-step explanation:

 nn, ,b,,566666666666666666665

We can see here that using the converse of  the Triangle Proportionality Theorem to verify if line MQ || line PR, we see that they are actually parallel. Thus, 6/8 = 12/16 = 3/4.

The Triangle Proportionality Theorem (also known as the Side Splitter Theorem) is a theorem in geometry that relates the proportions of the sides of two triangles that are formed when a line is drawn parallel to one side of a triangle.

The theorem states that if a line is drawn parallel to one side of a triangle, then it divides the other two sides into proportional segments.

That is, if a line is drawn parallel to side AB of triangle ABC, intersecting sides AC and BC at points D and E respectively, then:

AD/DC = BE/EC

We see here that taking the ratio of the sides, we have:

6/8 = 3/4

12/18 = 3/4

Thus, since their ratios are equal, they are parallel.

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The 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

The following formula is used to calculate a confidence interval for the proportion of all American adults who support same-sex marriage

KI = p ± z*(√(p*(1-p)/n))

where:

p = percentage of respondents who support same-sex marriage

n = sample size (total number of respondents)

z = z-score for the desired confidence level

substitute all the values in the above formula,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/n))

To compute confidence intervals, we need to know the sample size (n). the sample size is large, so we can use the normal distribution.

the random sample size of 1000 is taken as no sample size is specified.

For n = 1000,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/1000))

= 0.517 ± 0.032

Therefore, the 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

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1. Congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD

2. Triangle EAB ≅ Triangle ECD and Triangle EAC ≅ Triangle EBD by ASA Congruence Postulate.

In this scenario, we have two concentric circles and four tangents drawn from point E to these circles, creating points of tangency A, B, C, and D.

1. Pairs of congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD

2. Showing congruence for each pair:

a) To show that Triangle EAB and Triangle ECD are congruent, we can use the following information:
- EA and EC are both radii of the larger circle, so EA = EC (congruent radii).
- AB and CD are tangents to the smaller circle, so the segments are parallel and form corresponding angles at points A and C. Thus, Angle EAB and Angle ECD are congruent (alternate interior angles).
- EB and ED are both radii of the smaller circle, so EB = ED (congruent radii).
With this information, we can prove Triangle EAB ≅ Triangle ECD using the Angle-Side-Angle (ASA) Congruence Postulate.

b) To show that Triangle EAC and Triangle EBD are congruent, we can use the following information:
- EA and EB are both radii of the larger circle, so EA = EB (congruent radii).
- AC and BD are tangents to the larger circle, so the segments are parallel and form corresponding angles at points A and B. Thus, Angle EAC and Angle EBD are congruent (alternate interior angles).
- EC and ED are both radii of the smaller circle, so EC = ED (congruent radii).
With this information, we can prove Triangle EAC ≅ Triangle EBD using the Angle-Side-Angle (ASA) Congruence Postulate.

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The standard deviation of security B, the answer is option D, 18.75%.

Given that Security A and B have a covariance of 450%2,

Security A is estimated to have a variance of 900%2,

and the correlation between the two securities is 0.8.

We know that the covariance between Security A and B is given as;

Cov(A,B) = p(A,B)σAσB, where p(A,B)

is the correlation between A and B, σA is the standard deviation of A, and σB is the standard deviation of B.

Therefore, the standard deviation of Security B is given by;

σB = Cov(A,B)/[p(A,B)σA]

= (450%2)/[0.8 × (900%2)1/2]

= (450%2)/[0.8 × (900)1/2]%

≈ 18.75%.

Therefore, the answer is option D, 18.75%.

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