x(3 + y) - z if x=6, y=4, and z=5

The number 48,000,000,000 can be written in scientific notation as:

4.8 × 1010 or 48 × 109

Scientific notation is a way of expressing numbers in a concise form. It is typically used when dealing with very large or very small numbers. In scientific notation, a number is written as the product of two factors: a number between 1 and 10, and a power of 10.

For example, to express the number 48,000,000,000 in scientific notation we must first determine the two factors.

First factor: This is the number between 1 and 10. To determine this factor, we must count the number of places to the right of the decimal point (in this case, 0 places) and then move the decimal point that many places to the left.

48,000,000,000 → 4.8

Second factor: This is the power of 10. To determine this factor, we must count the number of places we moved the decimal point and then express this number as a power of 10.

In this example, we moved the decimal point 10 places to the left. Therefore, our power of 10 is 10.

Therefore, the number 48,000,000,000 can be written in scientific notation as:

4.8 × 1010 or 48 × 109

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Answer: A, A

Explanation:

48,000,000,000 g = 4.8 × 1010 g

0.000000655 mL = 6.55 × 10-7 mL

Equal arcs have equal angles measure.

In a circle, angles that intercept the same arc are equal to each other. This property can be used to find the value of m∠FEH if we assume that segment FH intersects segment GE and creates an arc that includes angle m∠FGH and angle m∠FEH. If m∠FGH is given as 50°, then we know that m∠FEH is also 50° since they intercept the same arc.

This is because angles that intercept the same arc are said to be subtended by that arc, and so their measures are equal. It is important to note that this property only holds true for angles that intercept the same arc.

If the arc intercepted by angle m∠FEH and angle m∠FGH is different, then we cannot assume that they have the same measure. In summary, the value of m∠FEH is equal to 50° if it intercepts the same arc as angle m∠FGH.

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a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

Huhhhhhhhhhhhh 4x and 5x

The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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'dz' because d and z are different values.

Answer:

t-t

Step-by-step explanation:

One example of an experiment that utilizes qualitative data is a study examining the experiences and perceptions of individuals who have undergone a specific medical procedure, such as organ transplantation.

In this experiment, researchers could conduct in-depth interviews with participants to explore their emotional reactions, coping mechanisms, and overall quality of life post-transplantation.

The qualitative data collected from these interviews would provide rich insights into the lived experiences of the participants, allowing researchers to gain a deeper understanding of the psychological and social impact of the procedure.

By analyzing the participants' narratives, themes and patterns could emerge, shedding light on the complex nature of organ transplantation beyond quantitative measures like survival rates or medical outcomes.

This qualitative approach helps capture the subjective experiences of individuals and provides valuable context for improving patient care and support in the medical field.

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So, the coach could have participated in at least 14 handshakes.

The total number of handshakes is the sum of the handshakes between gymnasts from different teams and the handshakes between gymnasts from the same team and the coach.

The coach shakes hands with each gymnast from her own team, so the number of handshakes between the coach and gymnasts is equal to the number of gymnasts on the team.

Let's assume the number of gymnasts on a team is x. And the number of teams is y. So the number of handshakes between gymnasts from different teams is x*(x-1)*y/2.

Given the total number of handshakes is 281, we know that:

x*(x-1)*y/2 + x = 281

In order to get the minimum number of handshakes the coach could have participated in, we can assume the maximum number of gymnasts on a team, which is x = 14.

So the equation becomes:

1413y/2 + 14 = 281

So we can find the value of y by solving this equation:

y = (281-14)/(13/2) = 17

Therefore, with x = 14 and y = 17, the minimum number of handshakes the coach could have participated in is 14, which is the number of gymnasts on the team.

So the coach could have participated in at least 14 handshakes.

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Answer:

Step-by-step explanation:

First order these into the correct order, I believe central tendency is similar to median. (from lowest to highest)

14,16,17,19,20

then choose the middle one, the middle one is 17

Thus your correct answer I believe is 17. Be sure to double check my work I may be wrong, make sure to rate five stars thank and mark brainlist

Answer:

23

Step-by-step explanation:

If Damon needs a mean of 21, he must score 23 on his seventh test. Just add up all the numbers you listed (21 + 20 + 24 + 19 + 20 + 24) and divide by 6 (the number of tests). That gives us a sum of 128. Then divide that number by 7 (the total number of tests, including the 7th one), which gives you an answer of 18.3. Since Damon needs to have an average of exactly 21, he must score a 23 on his seventh test in order to make it possible!

The value of the middle of the three is 25.

Let x be the first odd integer, then the next two consecutive odd integers are x+2 and x+4. The sum of these three consecutive odd integers is given as 75, so we can write the equation:

x + (x+2) + (x+4) = 75

Simplifying the left side of this equation gives:

3x + 6 = 75

Subtracting 6 from both sides gives:

3x = 69

Dividing by 3 gives:

x = 23

So the first odd integer is 23, and the next two consecutive odd integers are 25 and 27. The middle of these three is the second consecutive odd integer, which is 25. Therefore, the value of the middle of the three is 25.

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Sabella flew at a rate of 7 miles per minute.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

The table below provides the speed formula:

s = d/f

To find the miles per minute, we can divide the total distance by the total time:

Miles per minute = Total distance / Total time

Miles per minute = 840 miles / 120 minutes

Miles per minute = 7 miles/minute

Therefore, Sabella was moving at a speed of 7 miles per hour.

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This is an incomplete question, the correct question is given below.

Find the missing number of each unit rate \(\frac{15}{5}=\frac{?}{1}\) and \(\frac{24}{6}=\frac{?}{1}\)

Answer : The missing number of each unit rate of \(\frac{15}{5}=\frac{?}{1}\) and \(\frac{24}{6}=\frac{?}{1}\) are, 3 and 4 respectively.

Step-by-step explanation :

As we know that a unit rate is a rate in which 1 is present in denominator.

Or we can say that,

A unit rate is also called a single unit rate that means it will compare 1 unit of some quantity to a different units of a different quantity.

As we are given that that unit rates:

\(\frac{15}{5}=\frac{?}{1}\) and \(\frac{24}{6}=\frac{?}{1}\)

Now we have to determine the missing number of each unit rates.

So, we can write the given expression as:

\(\frac{15}{5}=\frac{?}{1}\)

When are dividing 15 by 5, we get:

\(\frac{15}{5}=\frac{3}{1}\)

Thus, the missing number is, 3

And

\(\frac{24}{6}=\frac{?}{1}\)

When are dividing 24 by 6, we get:

\(\frac{24}{6}=\frac{4}{1}\)

Thus, the missing number is, 4

Answer:

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Step-by-step explanation:

Given

\(y=c_1e^x +c_2e^{-x\)

\(y(1) = 0\)

\(y'(1) =e\)

Required

The solution

Differentiate \(y=c_1e^x +c_2e^{-x\)

\(y' = c_1e^x - c_2e^{-x}\)

Next, we solve for c1 and c2

\(y(1) = 0\) implies that; x = 1 and y = 0

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(0 = c_1 * e^1 + c_2 * e^{-1}\)

\(0 = c_1 e + \frac{1}{e}c_2\) --- (1)

\(y'(1) =e\) implies that: x = 1 and y' = e

So, we have:

\(y' = c_1e^x - c_2e^{-x}\)

\(e = c_1 * e^1 - c_2 * e^{-1}\)

\(e = c_1 e - \frac{1}{e}c_2\) --- (2)

Add (1) and (2)

\(0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2\)

\(e = 2c_1e\)

Divide both sided by e

\(1 = 2c_1\)

Divide both sides by 2

\(c_1 = \frac{1}{2}\)

Substitute \(c_1 = \frac{1}{2}\) in \(0 = c_1 e + \frac{1}{e}c_2\)

\(0 = \frac{1}{2} e+ \frac{1}{e}c_2\)

Rewrite as:

\(\frac{1}{e}c_2 = -\frac{1}{2} e\)

Multiply both sides by e

\(c_2 = -\frac{1}{2} e^2\)

So, we have:

\(y=c_1e^x +c_2e^{-x\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}\)

\(y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}\)

Answer:

612 I think well how this helps

The value of dI/da can be obtained by using the chain rule, which states that dI/da = (dI/dt) / (da/dt).

Given that I_dt = Floo and y = cos(4t^2) and y_dt = -8t*sin(4t^2), we can solve for dI/da by finding da/dt when t = 5 and substituting the values in the formula.

Let's first apply the chain rule to the equation y = cos(4t^2) to find dy/dt:

dy/dt = -sin(4t^2) * d/dt (4t^2) = -8t*sin(4t^2)

Next, we can use the given value I_dt = Floo, which means that dI/dt = 1.

To find da/dt, we need to differentiate a with respect to t. However, the value of a is not given explicitly in the equation. Therefore, we need to use the given information that when t = 5, a = -7. This means that we can write the equation for a as follows:

a = 5t - 42

Taking the derivative of both sides with respect to t, we get:

da/dt = 5

Now we can substitute the values we have found into the formula for dI/da:

dI/da = (dI/dt) / (da/dt) = 1 / 5 = 1/5

Therefore, the exact value of dI/da is 1/5.

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The probability that a randomly selected adult female's pulse rate is less than 83 beats per minute is approximately 0.7257.

To calculate the probability, we need to standardize the value using the z-score formula and then find the corresponding area under the standard normal distribution curve.

First, we calculate the z-score using the formula:

z = (x - μ) / σ

where x is the given value (83 beats per minute), μ is the mean (76.0 beats per minute), and σ is the standard deviation (12.5 beats per minute).

z = (83 - 76.0) / 12.5

z = 0.56

Next, we find the area to the left of the z-score using a standard normal distribution table or a calculator. The area represents the probability of a randomly selected adult female having a pulse rate less than 83 beats per minute.

Using the standard normal distribution table or a calculator, we find that the area to the left of the z-score 0.56 is approximately 0.7257.

The probability that a randomly selected adult female's pulse rate is less than 83 beats per minute is approximately 0.7257. This means that there is a 72.57% chance of selecting an adult female with a pulse rate lower than 83 beats per minute from the given normal distribution.

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Answer:

the answer is C .  (y-5)(y-5)

Step-by-step explanation:

i just did it in edge

Answer:

10.5

Step-by-step explanation:

Plug in 2 1/4

10.5 or 10 1/2

Answer:

21/2 in fractions or 10.5 in decimals

Step-by-step explanation:

6(2 1/4)-3            multiply the denominator with the whole number 2 and add 1

6x 9/4-3         reduce the number with the gratest common factor 2

3 x 9/2-3             when dealing with fraction just multiply denominator

27/2-3                 the denominator will stay the same always

21/2                        Calculate the difference

Answer:

100 ft

Step-by-step explanation:

We need to find the diagonal ( or hypotenuse)

We can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

80^2 + 60^2 = c^2

6400+3600 = c^2

10000 = c^2

Taking the square root of each side

sqrt(10000) = sqrt(c^2)

100 = c

Answer:

x=3

Step-by-step explanation:

the second-highest coefficient of the chromatic polynomial is an-1 = |E|.

assume that for any graph with k vertices, the degree of its chromatic polynomial is k. Let's consider a graph with k+1 vertices. We can remove one vertex from this graph, resulting in a graph with k vertices. By the induction hypothesis, the degree of the chromatic polynomial of the reduced graph is k. Adding back the removed vertex, it can be colored in k+1 ways since it is adjacent to at most k vertices. Therefore, the degree of the chromatic polynomial of the graph with k+1 vertices is also k+1.

Hence, we can conclude that if n is the degree of PG(x), then n = |V|.

(b) The leading coefficient of the chromatic polynomial PG(x) is always 1, meaning the coefficient of the highest degree term is 1. This can be proven by induction on the number of vertices in the graph.

For the base case, when the graph has only one vertex, the chromatic polynomial is P1(x) = x, and the leading coefficient is 1.

Now, assume that for any graph with k vertices, the leading coefficient of its chromatic polynomial is 1. Let's consider a graph with k+1 vertices. We can remove one vertex from this graph, resulting in a graph with k vertices. By the induction hypothesis, the leading coefficient of the chromatic polynomial of the reduced graph is 1. Adding back the removed vertex, it can be colored in k+1 ways since it is adjacent to at most k vertices. Therefore, the leading coefficient of the chromatic polynomial of the graph with k+1 vertices is also 1.

Hence, we can conclude that PG(r) is monic, meaning an = 1.

(c) The second-highest coefficient of the chromatic polynomial PG(x) is equal to the number of edges in the graph, |E|. This can be observed from the expansion of the chromatic polynomial.

The chromatic polynomial PG(x) is defined as the sum of products of terms of the form a(ix^i), where i ranges from 1 to n, and a(i) represents the number of proper colorings of the graph with i colors. The coefficient of x^(n-1) in PG(x) is equal to a(n-1), which represents the number of proper colorings of the graph with n-1 colors.

The number of proper colorings of the graph with n-1 colors is equal to the number of edges in the graph, |E|. This is because in any proper coloring, each edge must have endpoints with different colors. Therefore, the number of ways to color the edges is equal to the number of edges.

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Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

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Answer:

76

Step-by-step explanation:

Answer:

Step-by-step explanation:

Your input: find the z-score of x=2 with μ=32 and σ=25.

Z-score is calculated according to the following formula:

z=x−μσ=2−3225=54.

Answer: the z-score is z=54.

The values of k for which the augmented matrix follows the consistent  linear system are all the real numbers except 2 i.e. R- {2}

The linear equations become consistent when it has unique or infinitely many solutions. We have to find k according to the linear system which is consistent.

Consider the given matrix,

\(\left[\begin{array}{ccc}1&k&-4\\4&8&2\end{array}\right]\)

After dividing R2 by 2,

\(\left[\begin{array}{ccc}1&k&-4\\2&4&1\end{array}\right]\)

Now the linear equations will be,

x+ky = -4

2x+4y = 1

For infinitely many solutions it should be coincident lines so a1/a2=b1/b2=c1/c2 which is not going to happen for any value of k.

Therefore it should follow the condition of a unique solution i.e.

a1/a2\(\neq\)b1/b2

1/2\(\neq\)k/4

k\(\neq\)2

Therefore the value of k other than 2  i.e R-{2} will satisfy the linear equations.

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-4

15+-19

15 to 19 is 4

19 is the larger than 15 so since 19 is negative your answer will also be negative

Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

In summary, fy(a,b) is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

The given expression represents the partial derivative of f(x, y) with respect to y, evaluated at (a, b):

fy(a,b) = lim┬(y→b)⁡〖[f(a,y) - f(a,b)]/(y - b)〗

Geometrically, this partial derivative represents the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

To see why this is the case, consider the following argument:

Let L be the limit in the expression given above.

Let h = y - b be the change in the y-coordinate from b to y.

Then, we can rewrite the limit as:

fy(a,b) = lim┬(h→0)⁡〖[f(a,b + h) - f(a,b)]/h〗

This expression represents the average rate of change of f(x, y) with respect to y over the interval [b, b + h].

As h approaches 0, this average rate of change approaches the instantaneous rate of change, which is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

Therefore, fy(a,b) is the partial derivative of f(x, y) with respect to y, evaluated at (a, b).

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