Find the general solution of the differential equation dby day +14 = 0. dxb +49 dr4 O A. None of these. OB. y=x+(C, +C_x) cos( V7x)+(C3+ C4) sin(-V7x) OC. y = (C, + C2x) cos(17x)+(C3 +Cq2) sin(17x) D.

Answer:

Step-by-step explanation:

3.6

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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Answer:

A_el hijo vio 20 películas la hija vio 16 películas el padre vio 16 películas la madre vio 12 películas y los abuelos familiares vieron 6 películas

B_el hijo vio más películas y los abuelos vieron menos que todos

C_el padre y la madre vieron más películas dramáticas,y la madre y los abuelos familiares vieron menos películas comicas

Answer:

y=-0.5ˣ

Step-by-step explanation:

each time the x-value is increased by one, the y-value is cut in half compared to the previous point

Answer:

y=-0.5ˣ

Step-by-step explanation:

each time the x-value is increased by one, the y-value is cut in half compared to the previous

Answer:

5 batches

Step-by-step explanation:

Step-by-step explanation:

sin/cos=tan theta.It is the value of the safety angle

Answer:

4) The ball has fallen 10 units after 1 second

5) The depth of the will is 157.84 units

Step-by-step explanation:

We have

h = -16t² + 6

4) t = 1

h = -16(1²) + 6

= -16 + 6

= - 10

The ball has fallen 10 units down after 1 second

5) t = 3.2 seconds

h = -16(3.2²) + 6

= -16(10.24) + 6

= -163.84 + 6

= -157.84

The depth of the will is 157.84 units

To determine the number of rectangles in a Mondrian painting with red, blue, and yellow colors, we need to analyze the painting and identify the rectangular shapes formed by the intersecting lines.

Examine the Mondrian painting with red, blue, and yellow colors.

Identify the straight lines in the painting that form the boundaries of rectangles. These lines can be vertical, horizontal, or diagonal.

Count the number of rectangles formed by the intersecting lines. Each rectangle should have four sides formed by the lines.

To ensure accuracy, pay attention to rectangles of varying sizes and orientations within the painting.

Sum up the total number of rectangles in the Mondrian painting with red, blue, and yellow colors.

Please note that the specific number of rectangles may vary depending on the Mondrian painting being referenced.

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Answer:

Step-by-step explanation:

b. 1/2n-4

The expression  \(\frac{1}{2} n-4\) represents four less than half a number, n. The correct option is b.

The concept of an algebraic expression (or) a variable expression is considered as a set of terms that have been combined using operations like addition, subtraction, multiplication, and division.

The half a number, \(n\) means \(\frac{1}{2}n\) .

As we know four less than \(x\) is \(x-4\).

Then, four less than half a number will be \(\frac{1}{2} n-4\).

So, the expression represents four less than half a number, \(n\) is \(\frac{1}{2} n-4\).

This means the correct option is b. \(\frac{1}{2} n-4\).

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The price elasticity of the supply is 0.43.

The relationship between the percentage change in a product's quantity demanded and the percentage change in price is known as price elasticity of demand. It helps economists comprehend how supply and demand shift in response to changes in a product's price.

Price Elasticity of Demand =\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)=\(\frac{\Delta Q}{\Delta P}\)

Further, the equation for price elasticity of demand can be elaborated into

Percentage change in quantity=ΔQ=\(\frac{(q_{2}-q_{1})}{(q_{2}+q_{1})}}\)

Percentage change in quantity=ΔP=\(\frac{(p_{2}-p_{1})}{(p_{2}+p_{1})}}\)

Where, \(q_{1}\)= Initial quantity, \(q_{2}\)= Final quantity,\(p_{1}\)= Initial price and \(p_{2}\) = Final price

Here,  \(q_{1}\)=10000,\(q_{2}\)=5000

Percentage change in quantity=ΔQ

=\(\frac{10000-5000}{10000+5000}\)

=\(\frac{5000}{15000}\)

=0.333

Here,  \(p_{1}\)=20 and \(p_{2}\)=15

Percentage change in quantity=ΔP

= \(\frac{20-15}{20+15}\)

=\(\frac{5}{35}\)

=0.143

Price Elasticity of Demand

=\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)

=\(\frac{0.333}{0.143}\)

=2.33

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Answer:

15

Step-by-step explanation:

5x3 = 15 It's Simple Hope it helps

It will take 3.2 hours to travel 385.00 kilometers at 75.00 miles per hour

From the question, the speed at which you are traveling is 75.00 miles per hour. To determine how long it will take you to travel 385.00 kilometers,

First, we will convert 385.00 kilometers to miles

1 kilometer = 0.621371 miles

∴ 385.00 kilometer = 385 × 0.621371 miles

385.00 kilometer ≅ 239.228 miles

Now, to determine how long it will take to travel a distance of 239.228 miles at a speed of 75.00 miles per hour

From the formula

\(Speed = \frac{Distance }{Time}\)

∴ \(Time = \frac{Distance}{Speed}\)

But, Distance = 239.228 miles and Speed = 75.00 miles per hour

∴ \(Time = \frac{239.228}{75.00}\)

Time = 3.2 hours

Hence, it will take 3.2 hours to travel 385.00 kilometers at 75.00 miles per hour

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Each friend will receive "x/5" antique letters, where "x" represents the total number of antique letters in the box.

Sasha wants to give an equal number of letters to each of her five friends. The box of antique letters contains the letters that she wants to distribute among her friends. The question is to determine how many antique letters each friend will receive.

The total number of antique letters in the box is unknown. Let's assume that there are "x" antique letters in the box. If Sasha wants to distribute "x" letters among five friends equally, she can find out how many letters each friend will receive by dividing the total number of antique letters by the number of friends. Hence, each friend will receive x/5 letters.

To summarize, each friend will receive "x/5" antique letters.

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Answer:

For something to be perpendicular, it must intersect at a right angle.

Step-by-step explanation:

When we are young we learn in geometry that two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians).

The map visually represents the spatial distribution of the Hispanic population across U.S. counties, allowing for the identification of patterns and clusters. On the other hand, the histogram provides a quantitative representation of the distribution, illustrating the frequency or density of Hispanic population within specific ranges or categories.

The map reveals certain features that may not be apparent in the histogram. For instance, it allows us to observe spatial concentrations or clusters of Hispanic population, such as regions with high densities of Hispanic residents or areas where the Hispanic population is more dispersed. These spatial patterns can provide insights into factors like immigration patterns, cultural heritage, or historical settlement patterns that influence the distribution of the Hispanic population in the United States.

Conversely, the histogram highlights features that may not be readily visible in the map. The histogram enables a more detailed examination of the distribution within specific population ranges or categories. It can reveal the frequency or density of the Hispanic population within each range, allowing for comparisons across different counties or regions. By examining the histogram, one can identify variations in the size or proportion of the Hispanic population in different areas, potentially indicating demographic disparities or variations in population growth rates.

In summary, the map provides a visual understanding of the spatial distribution of the Hispanic population, highlighting clusters and patterns, while the histogram offers a quantitative representation, revealing variations in population density within specific ranges or categories. Both tools are valuable for analyzing and interpreting the distribution of the Hispanic population in U.S. counties, providing complementary perspectives for understanding demographic trends and patterns.

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Answer: 32.6%

Step-by-step explanation:

percentage is whatever number you have x100 which would move the decimal point right 2 points and in this case would move the decimal from .326 to 32.6

The magnitude (numerical value) of the z-score provides information about how many standard deviations a data point is from the mean.

z score or standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is observed or measured.

It tells us how many standard deviations a data point from the mean.

A z-score of 0 means that the data point is exactly at the mean, while a z-score of 1 means that the data point is one standard deviation above the mean.

A negative z-score indicates that the data point is below the mean.

The larger the magnitude of the z-score, the further away the data point is from the mean.

This information can be used to determine how unusual or typical a data point is in relation to the rest of the data set.

For example, a z-score of 2.5 would indicate that the data point is 2.5 standard deviations above the mean, and is therefore relatively unusual compared to the rest of the data.

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Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

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Answer: 105

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the sum of all angles in a triangle is always 180°.

the combination of an inner and an outer angle towards a flat line is always 180°. simply because that line simulates a diameter of a circle with the vertex being the center. and half a circle has 180°.

so,

180 = angle 3 + angle 4 = angle 3 + 120°

angle 3 = 60°

180 = angle 1 + angle 2 + angle 3 = angle 1 + 35 + 60

angle 1 = 180 - 35 - 60 = 85°

180 = angle 1 + angle 5 = 85 + angle 5

angle 5 = 95°

The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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The most reasonable prediction for the number of times two odd numbers will occur when two number cubes are rolled 2,000 times is 480.

Option D is the correct answer.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of times the dice were rolled = 50

The number of times two odd numbers occur = 12

The percentage of two odd numbers occurs.

= 12/50 x 100

= 12 x 2

= 24%

Now,

Number of times the dice were rolled = 2000

The most reasonable prediction for the number of times two odd numbers will occur.

= 24% of 2000

= 24/100 x 2000

= 24 x 20

= 480

Thus,

The most reasonable prediction for the number of times two odd numbers will occur is 480.

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Value of x corresponding to P81 is 59.06.

A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3.

The task is to find P81, which separates the bottom 81% from the top 19%.

For any normally distributed variable z with mean u and standard deviation o, the cumulative distribution function is defined as the probability of a standard normal variable being less than or equal to z.

A standard normal distribution has a mean of 0 and a standard deviation of 1.

That is, the variable z can be calculated as: z = (x - u) / o

The value P(z < z0) can be read off a standard normal table for any value z0.

As the normal distribution is symmetric, we can use the fact that P(z < -z0) = 1 - P(z < z0).

We now calculate z as follows: z0 = (P81 + 1) / 2 = 0.9051

From a standard normal table, we can see that P(z < 0.9051) = 0.8186.

Therefore, P(z < -0.9051) = 1 - P(z < 0.9051) = 0.1814.

Now we calculate the corresponding value of x:

z = (x - u) / o-0.9051 = (x - 67.3) / 9.3x = 59.06

Therefore, P81 corresponds to the value x = 59.06.

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The conditional statement p: 10 > 7, q: 10 > 5, p → q is True. It affirms that if 10 is greater than 7 (which is true), then 10 is also greater than 5 (which is also true).

Let's break down the conditional statement "p → q" and explain it step by step.

The statement "p: 10 > 7" states that 10 is greater than 7. This is a true statement because 10 is indeed greater than 7.

Similarly, the statement "q: 10 > 5" states that 10 is greater than 5. This is also a true statement because 10 is indeed greater than 5.

Now, let's examine the conditional statement "p → q". This statement is read as "p implies q" or "if p, then q". It expresses a relationship between the truth values of p and q.

To determine the truth value of the conditional statement, we evaluate whether p being true guarantees that q is also true. In other words, if p is true, can we say with certainty that q is also true.

In this case, since p is true (10 is greater than 7) and q is also true (10 is greater than 5), we can conclude that p being true guarantees that q is true.

Therefore, the conditional statement "p → q" is true. It affirms that if 10 is greater than 7 (which is true), then 10 is also greater than 5 (which is also true).

The missed conditional statement in the question should be:

p: 10 > 7

q: 10 > 5

p → q

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Answer:

A complementary angle are angles that add up to 90 degrees.  For example, a 30 degree angle and a 60 degree angle are complementary angles because 30+60=90

Step-by-step explanation:

Answer:

Complementary angles are angles that add to a total of 90 degrees. An example of complementary angles are 44 and 46 degrees, because they sum to 90! Hope this helps you out!

The larger cup holds 15.71 cubic inches more than the smaller cup.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Volume of cone=π/3r²h

Now let us find volume of small cone with radius 1.5 in and height 4 inches.

Volume of small cone=3.14/3×(1.5)²×4

=9.42 cubic inches.

Volume of cone with 2 inches radius and 6 inches height.

Volume of larger cone=3.14/3×(2)²×6

=25.13 cubic inches

Now let us find how much more water can the larger cup hold than than the smaller cup.

25.13-9.42

15.71 cubic inches.

Hence, the larger cup holds 15.71 cubic inches more than the smaller cup.

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About 95.44% of the cockroaches have weights between 76 grams and 84 grams.

we can use the properties of the normal distribution. We know that the weights of dormitory cockroaches follow a normal distribution with a mean of 80 grams and a standard deviation of 2 grams.
To find the percent of cockroaches with weights between 76 grams and 84 grams, we need to calculate the area under the normal curve between these two values.

First, let's standardize the values of 76 grams and 84 grams using the z-score formula:
Z = (X - μ) / σ

where X is the given value, μ is the mean, and σ is the standard deviation.
For 76 grams:
Z1 = (76 - 80) / 2 = -2

For 84 grams:
Z2 = (84 - 80) / 2 = 2

Now we can use a standard normal distribution table or a calculator to find the area under the curve between -2 and 2.
From the standard normal distribution table, we can find that the area to the left of -2 is approximately 0.0228, and the area to the left of 2 is approximately 0.9772.

To find the area between -2 and 2, we subtract the smaller area from the larger area:
0.9772 - 0.0228 = 0.9544

So, approximately 95.44% of the cockroaches have weights between 76 grams and 84 grams.

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