find the particular solution that satisfies the differential equation and the initial condition. f ''(x) = ex, f '(0) = 4, f(0) = 7

Answer:

B

Step-by-step explanation:

vertical angles from two parallel lines and a transverse line

Given:

Consider the given function is:

\(f(x)=5^x+1\)

To find:

The average rate of change between x = 0 and x = 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

\(m=\dfrac{f(b)-f(a)}{b-a}\)

We have,

\(f(x)=5^x+1\)

At \(x=0\),

\(f(0)=5^0+1\)

\(f(0)=1+1\)

\(f(0)=2\)

At \(x=0\),

\(f(4)=5^4+1\)

\(f(4)=625+1\)

\(f(4)=626\)

Now, the average rate of change between x = 0 and x = 4 is:

\(m=\dfrac{f(4)-f(0)}{4-0}\)

\(m=\dfrac{626-2}{4}\)

\(m=\dfrac{624}{4}\)

\(m=156\)

Hence, the average rate of change between x = 0 and x = 4 is 156.

Answer:

Angle A= 120⁰.. Angle B=60⁰

Step-by-step explanation:

To find angle A, you subtract 60 from 180, which would be 120. Angle A and 60⁰ are supplementary angles, meaning they have to add up to 180.

To find angle B, you take 360, since all the interior angles of that shape add up to 360.

360-90-90-120=60

9514 1404 393

Answer:

  $125

Step-by-step explanation:

For x = 140, the function definition for x ≥ 100 is used.

p(140) = 95 +0.75(140 -100) = 95 +30 = 125

The customer will owe $125 for items with a value of $140.

Answer:

$9.10

Step-by-step explanation:

Answer:

9.10

Step-by-step explanation:

1.95/3=0.65

0.65x14=9.10

Volatile organic compounds (d) evaporate easily and contribute to ozone formation.

The Volatile-organic-compounds (VOCs) are "organic-chemicals" which have high "vapor-pressure" and evaporate readily into atmosphere. They come from various sources, including industrial processes, vehicle emissions, solvents, and household products.

When VOCs are released into the air, they can contribute to the formation of ground-level ozone through complex chemical reactions involving sunlight and other pollutants. Ground-level ozone is a harmful air pollutant and a primary-component of smog.

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

Volatile organic compounds

(a) are considered a secondary criteria pollutant,

(b) are often odorless and therefore present a great danger to humans,

(c) are responsible for increasing greenhouse gas concentrations,  

(d) evaporate easily and contribute to ozone formation.

Andre travelled distance in one hour is 38 miles.

Define the relationship between Speed, Distance and Time

Given,

Distance travelled  of Andre is = 228 miles

Time taken to cover 228 miles = 6 hours

Then speed will be = Distance / time

speed = 228 / 6

          = 38 miles/hour

It means in 1 hour Andre covers a distance = 38 miles with a speed of 38 miles/hour

Hence, Andre travelled distance in one hour is 38 miles.

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Answer:

the closest estimate would be 300 boxes

the actual answer is closer to 322 boxes

Step-by-step explanation:

7715/24=321.458

hope this helps have a great day :)

Answer:

\(\mathsf{\cos T=\dfrac{28}{53}}\)

Step-by-step explanation:

\(\mathsf{\cos(\theta)=\dfrac{adjacent\ side}{hypotenuse}}\)

\(\implies \mathsf{\cos T=\dfrac{28}{53}}\)

Step-by-step explanation:

The angles on the same side of the parallel lines and the transversal are called corresponding angles.

Corresponding angles are congruent

So 11x+1 = 10x+10

x = 10-1 = 9

11*9+1 = 100

So both are 100 degrees

Answer:

2:3 I think

Step-by-step explanation:

The statement "There is a strong positive correlation between studying and grades" best describes the meaning of a correlation coefficient of 0.93. The correct answer is A.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of 0.93 indicates a strong positive correlation between studying and grades.

A positive correlation means that as the value of one variable (study time) increases, the value of the other variable (grades) also tends to increase. A correlation coefficient close to +1 indicates a strong positive relationship, suggesting that an increase in study time is associated with higher grades. e correct answer is A.

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Answer: the graph is decreasing everywhere

Answer:

The solution set is {4, -1}

Step-by-step explanation:

6x²- 18x -18 = 6

6x²- 18x -18 - 6 = 0

6x²- 18x -24 = 0

6(x² - 3x - 4) = 0

6(x - 4)(x + 1) = 0

6 = 0 not true

x - 4 = 0 ;   x + 1 = 0

x = 4           x = - 1

The solution set is {4, -1}

Answer:

(2, -1)

(10, 15)

Step-by-step explanation:

Subtract the second equation from the first

  y = x² – 10x + 15

- (y =           2x – 5)

————————————

 0 = x² - 12x + 20

Factor

(x  - 2)(x - 10) = 0

x = {2, 10}

-------------------

For x = 2

y = 2(2) - 5

y = -1

Solution 1

(2, -1)

----------------------

For x = 10

y = 2(10) - 5

y = 15

Solution 2

(10, 15)

Answer:not sure but x>-9

Step-by-step explanation:

Someone double check me

so I think the answers ~ Garrett finishes his homework at 6:05.

only thats not an option so choose E because its the closest

hopefully this helps!!!

Answer:210 because 150 divided by 25 is 6 and 35 times 6 is 210

Step-by-step explanation:hope this helps : )

The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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Is it multiple choice?

Answer:(it might be)

y=5/3x+1/3

Step-by-step explanation:

Answer:

I believe the answer is = 6,-6

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\( - \frac{1}{2} {n}^{2} + 18 = 0 \\ \)

Subtract sides 18

\( - \frac{1}{2} {n}^{2} + 18 - 18 = - 18 \\ \)

\( - \frac{1}{2} {n}^{2} = - 18 \\ \)

Negatives simplifies

\( \frac{1}{2} {n}^{2} = 18 \\ \)

Multiply sides by 2

\(2 \times \frac{1}{2} {n}^{2} = 2 \times 18 \\ \)

\( {n}^{2} = 36\)

Take √ of the sides

\( \sqrt{ {n}^{2} } = \sqrt{36} \\ \)

\( |n| = 6\)

\(n = ± \: 6\)

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1. The official lines of authority. 2. The formal lines of communication. 3. The base level of the organization.

Organizational structure box-and-lines diagrams show at least three things:

1. The official lines of authority: These diagrams illustrate the formal hierarchy within an organization, indicating the chain of command and reporting relationships. The lines represent the flow of authority and communication, highlighting who reports to whom. For example, a manager may have multiple employees reporting to them, and those employees may further have their own subordinates.

2. The formal lines of communication: These diagrams also depict the formal channels through which information flows within the organization. They show how information is passed between different levels and departments. For instance, a diagram may show that information flows vertically from top management to lower-level employees or horizontally between departments.

3. The base level of the organization: These diagrams display the entry-level positions within the organizational structure. This helps to understand the foundational roles that exist and how they fit into the larger structure. For instance, the diagram may indicate positions such as interns, junior associates, or entry-level staff.

In summary, organizational structure box-and-lines diagrams provide a visual representation of the official lines of authority, the formal lines of communication, and the base level of the organization. These diagrams help individuals understand the hierarchy, communication flow, and entry-level positions within an organization.

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Answer:

Danny

Step-by-step explanation:

Danny charges 44/4 = 11 dollars an hour

Martin charges 60/5 = 12 dollars an hour

Danny is the better deal.

In the given scenario, where there is one infinitely long track and overtaking is impossible, the initial situation consists of three equally spaced trains, each moving at a different speed. The trains have the capability to link up when one catches up to the other, resulting in a single train moving at the speed of the slower train.

As the trains move, they will eventually reach a configuration where the fastest train catches up to the middle train. At this point, the fastest train will link up with the middle train, forming a single train moving at the speed of the middle train. The remaining train, which was initially the slowest, continues to move independently at its original speed. Over time, the process continues as the new single train formed by the fastest and middle trains catches up to the remaining train. Once again, they link up, forming a single train moving at the speed of the remaining train. This process repeats until all the trains eventually merge into a single train moving at the speed of the initially slowest train. In summary, on this strange railway line, where trains can only link up and cannot overtake, the initial configuration of three equally spaced trains results in a sequence of mergers where the trains progressively combine to form a single train moving at the speed of the initially slowest train.

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The first term (a) of the arithmetic sequence is 17, and the common difference (d) is 6.

To determine the first term (a) and the common difference (d) of an arithmetic sequence, we can use the formulas:

a + (n - 1) * d = Tn

where a is the first term, n is the term number, d is the common difference, and Tn is the nth term of the sequence.

Given that T5 = 41 and T32 = 203, we can set up two equations using the formula above:

a + (5 - 1) * d = 41 (equation 1)

a + (32 - 1) * d = 203 (equation 2)

Simplifying equation 1, we have:

a + 4d = 41

Simplifying equation 2, we have:

a + 31d = 203

Now we have a system of two equations. We can solve this system of equations to find the values of a and d.

Subtracting equation 1 from equation 2, we get:

(a + 31d) - (a + 4d) = 203 - 41

27d = 162

d = 162 / 27

d = 6

Substituting the value of d into equation 1:

a + 4(6) = 41

a + 24 = 41

a = 41 - 24

a = 17

Therefore, the first term (a) of the arithmetic sequence is 17, and the common difference (d) is 6.

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Answer:

Find the roots of

x (2 − 24x) = 0 by solving for x.

x = 0 , 1/12

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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We need to find the probability of a randomly selected bolt having thread length (a) within 1.9 SDs of its mean value, (b) farther than 2.4 SDs from its mean value, and (c) between 1 and 2 SDs from its mean value.

(a) To find the probability that the thread length of a randomly selected bolt is within 1.9 SDs of its mean value, we can use the empirical rule or the 68-95-99.7 rule. According to this rule, approximately 68% of the values fall within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. Therefore, the probability of the thread length being within 1.9 SDs of the mean is approximately (0.5 + 0.45) = 0.95 or 95%.

(b) The probability of a bolt's thread length being farther than 2.4 SDs from its mean value is the same as the probability of a value being beyond 2 SDs plus the probability of a value being beyond 3 SDs. The probability of a value being beyond 2 SDs is approximately 0.05, and the probability of a value being beyond 3 SDs is approximately 0.003. Therefore, the total probability is (0.05 + 0.003) = 0.053 or 5.3%.

(c) To find the probability of the thread length being between 1 and 2 SDs from the mean, we can subtract the probability of values beyond 2 SDs from the probability of values beyond 1 SD. Using the empirical rule, we know that the probability of a value being beyond 1 SD is approximately 0.32, and the probability of a value being beyond 2 SDs is approximately 0.05. Therefore, the probability of the thread length being between 1 and 2 SDs from the mean is approximately (0.5 - 0.32 - 0.05) = 0.13 or 13%.

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By applying the binomial distribution formula, it can be concluded that the probability that more than 6 will say yes is 0.423 (option B).

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

C(n,r) = n! / (r! (n-r)!) where

n = number of samples

r = number of selected samples

The binomial distribution formula is used to find the probability of the specific outcome in a discrete distribution.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\) where:

C = combination value

p = probability of success on a single trial

q = probability of failure on a single trial

n = 22

p = 28% = 0.28

q = 1 - 0.28 = 0.72

The probability that r adults will say yes is given by the binomial distribution:

P(X=r) = C(n,r) * \(p^{r}\) * \(q^{n-r}\)

= C(22,r) * \(0.28^{r}\) * \(0.72^{22-r}\)

P(X≤6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

Now we calculate for each probability:

P(X=0) = C(22,0) * 0.28⁰ * 0.98²² = 0.000726633

P(X=1) = C(22,1) * 0.28¹ * 0.98²¹ = 0.00621676

P(X=2) = C(22,2) * 0.28² * 0.98²⁰ = 0.025385

P(X=3) = C(22,3) * 0.28³ * 0.98¹⁹ = 0.0658131

P(X=4) = C(22,4) * 0.28⁴ * 0.98¹⁸ = 0.121571

P(X=5) = C(22,5) * 0.28⁵ * 0.98¹⁷ = 0.1702

P(X=6) = C(22,6) * 0.28⁶ * 0.98¹⁶ = 0.187535

If we sum up the results, we get P(X≤6) = 0.577447493

P(X>6) = 1 - P(X≤6)

           = 1 - 0.577447493

           = 0.422552507

           ≈ 0.423

Thus the probability that more than 6 will say yes is 0.423.

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Answer:

Step-by-step explanation: