David is preparing for a dance competition. He needs to practice for 14 hours in 4 days. Which of the following statements show that David is practicing according to the required unit ratio? A. 44 hours in 8 days B. 21 hours in 12 days C. 53 hours in 9 days D. 28 hours in 8 days

The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

a. The extreme points of the feasible region are the vertices of the polygon formed by the intersection of the constraint lines. In this case, the extreme points are (0,0), (5,0), (3.75, 3.75), (3.5,4.5), and (0,8).

b. To find the optimal solution and the objective function value, we evaluate the objective function at each extreme point and choose the point that maximizes the objective function. In this case, the point (3.5, 4.5) maximizes the objective function with a value of 59.5. Therefore, the optimal solution is x = 3.5 and y = 4.5, and the objective function value is 59.5.

c. The slack variables represent the surplus or slack in each constraint. We calculate the slack variables by subtracting the actual value of the left-hand side of each constraint from the right-hand side. In this case, the values of the slack variables are s1 = 0 (indicating no slack in the first constraint), s2 = 2 (indicating a surplus of 2 in the second constraint), and s3 = 0 (indicating no slack in the third constraint).

Therefore, the correct option is:

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

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Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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Answer:

48

Step-by-step explanation:

The best prediction for the number of times both coins will land on tails if you flip a coin 96 times is 48. This is because if each coin flip is independent, the probability of getting tails on a single flip is 0.5. Therefore, the probability of getting tails on both flips is 0.5 * 0.5 = 0.25. So, if you flip a coin 96 times, the expected number of times both coins will land on tails is 96 * 0.25 = 24.

Answer:

x = 20

Step-by-step explanation:

I don't see a y in the diagram.

The 3 angles x, 90 and (4x - 10) lie on the line EF and sum to 180°, so

x + 90 + 4x - 10 = 180, that is

5x + 80 = 180 ( subtract 80 from both sides )

5x = 100 ( divide both sides by 5 )

x = 20

The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

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Answer:

  200 +4c -6b

Step-by-step explanation:

Your ending balance is the sum of your beginning balance plus sales, less your purchases. If each sale nets $4, then c sales will increase your balance by 4c. If each purchase costs $6, then b purchases will reduce your balance by 6b.

Your ending balance is ...

  200 +4c -6b

In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

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The assessed value of the property with a market value of $60,000 and an assessment rate of 45% is $27,000. T

To compute the assessed value of a property, you'll need to consider both the market value and the assessment rate. In this case, the market value is $60,000, and the assessment rate is 45%.

To find the assessed value, you can multiply the market value by the assessment rate. Using the provided values, you can calculate the assessed value as follows:

Assessed Value = Market Value x Assessment Rate
Assessed Value = $60,000 x 0.45

Assessed Value = $27,000

In this case, the assessed value of the property with a market value of $60,000 and an assessment rate of 45% is $27,000. This value represents the taxable amount on which property taxes will be calculated and is an essential factor for both property owners and tax authorities.

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Answer: B.) -54

Step-by-step explanation: view screenshot

Answer:

x = 101

Step-by-step explanation:

\(x+(-21)=21-(-59)\\x-21=21+59\\x-21=80\\x=101\)

The final cost be $27.

Given that,

Based on the above information, the calculation is as follows:

\(= \$60 \times (1-0.40) \times (1-0.25)\)

= $27

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The big-o time analysis for the combined time of attaching all n numbers i O(n).

The big-O running time gives the relationship between the steps taken for the algorithm and its running time. it is denoted by O(.), where . refers to the some f(n). f(n) is determined by the way of the algorithm in each step.

Here, we attach 1, then 2,then 3 and so on up to n to make a sequence of numbers. So at a time, only 1 number is attached and therefore one step of the algorithm is working. So we can say that the big-O time analysis for the combined time of attaching all n numbers is O(n).

This means that at n = 1, only 1 step is taken by the algorithm .At n=2, two steps and continued like this up to n steps.

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CosA is negative for the largest angle in an obtuse triangle. Using the law of cosines, a²>b²+c², a>b, and a>c are derived.

Step 1: As the obtuse triangle has the largest angle A (more than 90 degrees), the cosine function's value is negative.

Step 2: By applying the Law of Cosines in the triangle, a²>b²+c², which is derived from a²=b²+c²-2bccosA, and hence a>b and a>c can be derived.

Step 3: From the previously derived inequality a²>b²+c², we can conclude that a>b and a>c as a²-b²>c². The value of a² is greater than both b² and c² when a>b and a>c.

Therefore, the largest angle of an obtuse triangle is opposite the longest side.

Step 4: In triangle ABC, A=103°, a=25, and c=30.

a² = b² + c² - 2bccos(A),

a² = b² + 900 - 900 cos(103),

a² = b² + 900 + 900 cos(77),

a² > b² + 900, so a > b.

Similarly, a² > c² + 900, so a > c.

Therefore, triangle ABC satisfies a>b and a>c.

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Answer:

The function f of x equals 6 x + 2. First, replace the function notation f of x with y. y equals 6 x plus 2. Reverse the x and y variables. x equals 6 y plus 2. Solve for y by isolating it on one side of the equal sign. First subtract 2 from both sides of the equation. x minus 2 equals 6 y. Divide both sides by 6. The quantity of x minus 2 divided by 6 equals 6 y over 6. The quantity x minus 2 over 6 equals y. Replace y with the inverse function notation. The quantity of x minus 2 divided by 6 equals the inverse function of x. Now solve for the inverse function when x equals two. Substitute 2 for each x. The quantity of 2 minus 2 divided by 6 equals the inverse function of 2. Simplify. 0 divided by 6 equals the inverse function of 2. When x equals two, the corresponding y value on the inverse function is zero. 0 equals the inverse function of 2.

Answer:

105/9

Step-by-step explanation:

180 - 132 = 48 degrees

180 - 48 - 45

= 180 - 93

= 87 degrees

<2 = 180 - 87

= 93 degrees

=> 9x - 12 = 93

=> 9x = 105

=> x = 105/9

Answer:

x = 12°

m∠2 = 96°

Find the missing inside angle for right triangle:

180° - 132°

48°

Find the missing angle for left triangle:

90° - 48°

42°

As it is an isosceles triangle, the angles will be similar.

Thus solve:

9x - 12 + 42° + 42° = 180°

9x + 72° = 180°

9x = 180° - 72°

9x = 108°

x = 108°/9

x = 12°

Therefore m∠2 :

m∠2 = 9x - 12

m∠2 = 9(12) - 12

m∠2 = 96°

P(X = 2) is not equal to P(X = 3)

To show that P(X = 2) = P(X = 3) in a binomial distribution with n = 5 and p = 0.5, we need to use the formula for the probability mass function (PMF) of a binomial distribution.

The PMF of a binomial distribution is given by the formula:

P(X = k) = C(n, k) *\(p^k * (1-p)^{(n-k)}\)

where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) represents the binomial coefficient.

In our case, n = 5 and p = 0.5. Let's calculate P(X = 2) and P(X = 3) using the formula:

P(X = 2) = \(C(5, 2) * (0.5)^2 * (1-0.5)^{(5-2)}\)

        = 10 * 0.25 * 0.125

        = 0.3125

P(X = 3) = C(5, 3) * \((0.5)^3 * (1-0.5)^{(5-3)}\)

        = 10 * 0.125 * 0.125

        = 0.125

As we can see, P(X = 2) = 0.3125 and P(X = 3) = 0.125.

Therefore, P(X = 2) is not equal to P(X = 3) in this specific case of a binomial distribution with n = 5 and p = 0.5.

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Answer:

The value of x is i√21/5−2/5,−i√21/5−2/5

Step-by-step explanation:

Hope this helps!

Don't mind the loading lol.

The number of people prefer comedy movie be 34 then 75 persons will prefer comedy movies.

A ratio that compares a part to a whole is known as a percentage. Two integers that each represent a component of a whole are compared to determine their proportion. In essence, a proportion asserts the equality of two fractions, despite the difference in magnitude.

The difference between a % and a proportion is that a percentage always has 100 as the denominator and is defined as the relationship or equivalence between two ratios or fractions. Fractions can be used to express proportions and percentages. It's a percentage out of 100.

The given table : super hero sci fi comedy drama romance

\($$\begin{array}{lllll}63 & 24 & 34 & 20 & 17\end{array}$$\)

From the table, the number of people prefer comedy movie = 34

The total number of people surveyed: 63+24+34+20+17=158

Now, the probability of people preferring comedy movie is given by :-

Number of comedy movies \($=\frac{34}{158}$$\)

Based on these findings, it is estimated that, out of 350 respondents, the following number would prefer comedy films:

\($\frac{34}{158} \times 350=75.3164556962 \approx 75$$\)

Therefore, 75 persons will prefer comedy movies.

The complete question is:

The table shows the results of a random survey of people about their favorite movie genres.

super hero sci fi comedy drama romance

63 24 34 20 17

Based on these results, if 350 people are asked about their favorite movie genres, how many people will prefer comedy movies?

Enter your answer to the nearest whole number in the box.

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Answer:

kkffkyeurkyerkurkurumeukulruor

The sum of the digits of the number which when added to 2000 makes the resulting number divisible by 12,16,18 and 21 is 7

The smallest number which when added to 2000 makes the resulting number divisible by 12, 16, 18, and 21 is 312. The sum of the digits of x is 3 + 1 + 2 = 6.

To find the smallest number x that can be added to 2000 to make the resulting number divisible by 12, 16, 18, and 21, we need to find the least common multiple (LCM) of these numbers.

The LCM of 12, 16, 18, and 21 is 1008. Then we need to find the smallest multiple of 1008 that is greater than 2000. This is 1008 * 3 = 3024. The difference between 3024 and 2000 is 1024, so x = 1024.The sum of the digits of x is 1 + 0 + 2 + 4 = 7. Therefore, the sum of the digits of x is 7.

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Answer:

(B)

The elevation of the chameleon

Step-by-step explanation:

the fly is above the chameleon, so it's elevation should be represented by a positive number

Answer:

============================

Proportional relationship has the form of:

The value of k should be same for any pair of coordinates:

Answer: 3

Step-by-step explanation:

Given

The period of the function is \(4\pi\) i.e. function completes a full cycle in this zone.

For a horizontal length of \(12\pi\)

Number of cycles is

\(\Rightarrow \dfrac{12\pi }{4\pi }=3\)

So, there are 3 ycles of the function in length of \(12\pi\).

Answer:

3

Step-by-step explanation:

I just did it and it was correct.

Answer:

Step-by-step explanation: (x,y) (4,2)

Using the normal distribution, we know that the likelihood of a lizard living longer than 2.5 years is 16%.

The normal distribution is the correct name for a probability bell curve alone.

A normal distribution has a mean of zero and a standard deviation of one. Its kurtosis is 3, and its skew is 0.

Not all normal distributions are symmetrical, despite the fact that all symmetrical distributions are normal.

So, a lizard's average lifespan is 3.1 years, with a 0.6-year standard deviation.

Lizard u = 3.1 on average.

0.6 is the standard deviation.

To determine the probability that a lizard would live longer than 2.5 years:

p(X<2.5)

μ + aσ = 2.5

3.1 + a(0.6) = 2.5

a(0.6) = −0.6

a = −1

Use the empirical rule to calculate the probability.

100% of the total area (since total probability always is 1)

The area from p(X > p) = 50% from to area between () and (+) equals 68%.

Area between (μ−σ) and μ is p((μ−σ) < X < μ) =34%

Hence,

p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))

p(X< (μ−σ)) = 1 − (0.34 + 0.5)

p(X< (μ−σ)) = 0.16  

Therefore, using the normal distribution, we know that the likelihood of a lizard living longer than 2.5 years is 16%.

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Answer:

angle 1 and angle 7 are alternate exterior angles.

angle 1 and angle 5 are corresponding angles.

angle 3 and angle 8 are same side interior angles.

angle 2 and angle 8 are alternate interior angles.

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

your equation can be written as: x + 3 = 11

subtract 3 from both sides to isolate x: x = 8

your answer is 8

Answer:

40 degrees

Step-by-step explanation:

The value of angle x is 40 degrees. Since we know PA is parallel to BC, PAB should parallel CBA. B is 40 degrees so therefore A is as well.