Help someone please I need this one correct to get a good grade

The missing side of the triangle, B, is approximately 13.86 units long.

Let's denote the missing side as B. According to the Pythagorean Theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, which is the hypotenuse. Mathematically, this can be represented as:

A² + B² = C²

In our case, we are given the lengths of sides A and C, which are 8 and 16 respectively. Substituting these values into the equation, we get:

8² + B² = 16²

Simplifying this equation gives:

64 + B² = 256

To isolate B², we subtract 64 from both sides of the equation:

B² = 256 - 64

B² = 192

Now, to find the value of B, we take the square root of both sides of the equation:

√(B²) = √192

B = √192

B ≈ 13.86 (rounded to two decimal places)

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Complete Question:

How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 8, C= 16?

Research Question: CSU is doing saliva screenings for COVID-19 that involve spitting into a tube. You've heard that if you need to make a lot of saliva quickly, you should think about salty foods (like dill pickles or salt and vinegar chips).

Population and Sample: The population of interest would be individuals who are undergoing saliva screenings for COVID-19 at CSU. The sample could be a random selection of individuals from this population who are willing to participate in the study.

Paired Data Design: To obtain paired data, the study could be designed as follows: The same individual is tested twice, once with exposure to talking about salty foods (experimental condition) and once without exposure to talking about salty foods (control condition).

Not Paired Data Design: To obtain not paired data, the study could be designed as follows: Two separate groups of individuals are tested - one group exposed to talking about salty foods (experimental group) and another group not exposed to talking about salty foods (control group).

Advantages of Paired Data Design: One advantage of using a paired data design is that it controls for individual differences, as the same individual serves as their own control. This helps to minimize confounding variables and increases the internal validity of the study. One disadvantage is that there may be order effects, where the order of conditions can influence the results.

Advantages of Not Paired Data Design: One advantage of using a not paired data design is that it allows for comparison between two separate groups, which can help to establish cause-and-effect relationships. Another advantage is that it may be logistically simpler and quicker to conduct.

Study Design Choice: If I were to choose between a paired data design and a not paired data design for this research question, I would choose the paired data design. This is because using a paired design would allow for better control of individual differences and increase the internal validity of the study.

Example of Impossible Paired Study: An example where a paired study would be impossible is when the research question involves comparing two unrelated and distinct groups, such as comparing the effects of a new drug on two different populations.

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Answer:

.1

Step-by-step explanation:

There are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

To determine the number of ways to award first, second, and third prizes in a contest with 950 contestants, we can use the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of contestants and r is the number of prizes to be awarded (in this case, 3).

Using this formula, we get:

P(950, 3) = 950! / (950 - 3)!

= 950! / 947!

= 950 × 949 × 948

= 853,818,600

Therefore, there are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

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The distribution of the total resistance of the two components in series for a randomly selected toaster is also normal, with a mean equal to the sum of the means of the two components, and a standard deviation equal to the square root of the sum of the variances of the two components.

Let's accept that the resistance of each component is regularly conveyed, with implies of μ1 and μ2, and standard deviations of σ1 and σ2, separately. We also assume that the two components are free of each other.

Add up to resistance = R1 + R2

where R1 and R2 are the resistances of the two components.

Concurring to the properties of ordinary dispersions, the entirety of two autonomous ordinary factors is additionally regularly dispersed, with a cruel rise to the entirety of the implies and a change rise to the whole of the changes. Hence, the cruelty of the overall resistance is:

Cruel = μ1 + μ2

and the change is:

Fluctuation = σ1\(^{2}\)+ σ2\(^{2}\)

The standard deviation of the full resistance is at that point the square root of the change:

Standard deviation = sqrt(σ1\(^{2}\) + σ2\(^{2}\))

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The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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The low value is 2.

The Q1 value is 5.

The median value is 7.

The Q3 value is 9.

The high value is 10.

To find the mean weight of the people in the elevator, we divide the total weight by the number of people. The total weight is 16 multiplied by the mean weight:

Mean weight = Total weight / Number of people

Since we are given the load limit of the elevator is 2500 pounds, we know that the total weight must be equal to the load limit. So:

Total weight = 2500 pounds

Therefore, the mean weight is:

Mean weight = 2500 pounds / 16 = 156.25 pounds

Rounded to two decimal places, the mean weight is approximately 156.25 pounds.

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The range of the distribution is the parameter that is required to convert a computer-generated random variable into a uniform random variable. Below are more than 100 words explaining this in detail:A uniform random variable is a random variable with a probability distribution function that is uniform across all possible values.

The probability density function of a uniform distribution is constant over the range of values of the variable. Therefore, it has equal probability of taking any value within the range of values that it is defined.The process of converting a computer-generated random variable into a uniform random variable is known as uniform random number generation. The process of uniform random number generation is an important aspect of computer simulation and statistical analysis of data.

It is used to generate random numbers that follow a uniform distribution, which is a common distribution in many applications.The range of the distribution is the parameter that is required to convert a computer-generated random variable into a uniform random variable. This is because the range of the distribution defines the possible values that the variable can take. By mapping the computer-generated random variable to the range of the uniform distribution, we can convert it into a uniform random variable.

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52 tiles are there in the 25th figure in this pattern.

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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Answer:

\(m\angle F\approx 100^{\circ}\)

Step-by-step explanation:

For any triangle, the Law of Cosines is given by \(c^2=a^2+b^2-2ab\cos C\), where all three variables are interchangeable.

Therefore, we have:

\(f^2=g^2+h^2-2gh\cos F,\\960^2=380^2+820^2-2(380)(820)\cos F,\\\cos F=-\frac{131}{779},\\F=\arccos(-\frac{131}{779})\approx \boxed{100^{\circ}}\)

Answer:

B(7 , -2)

Step-by-step explanation:

A(-9 , 6)

Midpoint = (-1 , 2 )

\(Midpoint = (\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2}) = (-1 , 2)\\\)

                   \((\frac{-9+x_{2}}{2},\frac{6+y_{2}}{2}) = (-1 , 2)\\\)

Compare the x co ordinates and y co ordinates,

\(\frac{-9+x_{2}}{2}= - 1\)               &    \(\frac{6+y_{2}}{2}=2\)

-9 + x₂ = -1*2            & 6 + y₂ = 2*2

-9 + x₂ = -2               & 6 + y₂ = 4

      x₂ = -2 +9          &       y₂  = 4 - 6

      x₂ = 7                 &       y₂   = -2

B(7 , -2)  

The normal distribution have an importance in statistics of whether or not out appears in nature, because it fits several natural phenomena.

For exa. measurement error, heights, IQ scores, and physical activity measures all follow the normal distribution.

In this question we need to describe why does the normal distribution have an importance in statistics of whether or not out appears in nature.

We know that if we plot the probability distribution and it forms a bell-shaped curve. If the mean, mode, and median of the sample are equal then the variable has normal distribution.

A normal distribution is dependent on two parameters of the data set: mean and the standard deviation of the sample.

This characteristic of the normal distribution makes it extremely simple.

Also, the normal distribution is important because of the Central limit theorem.

It makes math easy - like calculating moments, correlations between variables, and other calculations that are domain specific.

So, the normal distribution have an importance in statistics of whether or not out appears in nature.

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If you choose the lottery, you would be considered a risk taker.

By opting for the lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing, you are demonstrating a willingness to take a chance and accept the uncertainty associated with the potential outcomes. A risk taker is someone who is willing to engage in risky or uncertain situations for the possibility of gaining a favorable outcome. In this case, you are accepting the risk of potentially winning nothing in exchange for the chance to win a larger amount.

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Answer:

The answer is 37.6 degrees

Step-by-step explanation:

Since a right angle is 90 degrees in total, to find the missing degree subtract 52.4 from 90 to find the value of x.

90-52.4= 37.6 degrees

37.6 degrees is your answer  

Hope this helps

Answer:

31.1

Step-by-step explanation:

Answer:

31.1

Step-by-step explanation:

124.4 / 4

= 0.1 * (1244/4)

= 0.1 * 311

= 31.1.

Answer:

°F = 356

Step-by-step explanation:

°C = (°F - 32) ÷ 1.8

180 = (°F - 32) ÷ 1.8

180×1.8 = °F - 32

324 = °F - 32

°F = 324 + 32

°F = 356

Answer:

About 29%

Step-by-step explanation:

Square Perimeter = 4(4x-1)

Rectangle Perimeter = 2(2x+1) + 2(x+2)

Square Perimeter = Rectangle Perimeter

4(4x-1) = 2(2x+1) + 2(x+2)

16x - 4 = 4x + 2 + 2x + 4

16x - 4 = 6x + 6

-6x +4 -6x +4

10x = 10

x = 1

The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.

The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.

Given, the double integral ∫∫yA and the region y = x-6 and x = y²

y = x-6

x = y²

y² = y +6

y² - y - 6 = 0

y² - 3y +2y - 6 = 0

(y-3) (y+2) = 0

y = 3 and y = -2

\(\int\int\limits_\triangle {y} \, dA\\ \\\)

= \(\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}\)

The value for the double integral is 125/12.

Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.

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»»————-　★　————-««

I believe your answer is:  

\(g(3) = -8\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Evaluating the function...}}\\\\g(x)=-4x+4; g(3)\\\\--------------\\\rightarrow g(3)=-4(3)+4\\\\\rightarrow g(3) = -12 + 4\\\\\rightarrow \boxed{g(3)=-8}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Thus, the Laplace transform of y′′+16y=0 is Y(s)=7s/(s²+16) of this function and the final answer is y(t) = 7δ(t) + y′(0)u(t) + 7cos(4t).

Given a differential equation:

y′′+16y=0y(0)=7y′(0)=___To find:

Laplace transform and final answer of the differential equation.

Solution: The Laplace transform of a function f(t) is given by:

L{f(t)}=F(s)=∫0∞e−stdf(t)ds

Let's find the Laplace transform of given differential equation.

L{y′′+16y}=0L{y′′}+L{16y}=0s²Y(s)-sy(0)-y′(0)+16Y(s)=0s²Y(s)-7s+16Y(s)=0(s²+16)Y(s)=7sY(s)=7s/(s²+16)

Therefore, the Laplace transform of y′′+16y=0 is Y(s)=7s/(s²+16)

To find the value of y′(0), differentiate the given function y(t).

y(t) = 7 cos(0) + [y′(0)/s] + [s Y(s)]

y(t) = 7 + [y′(0)/s] + (7s²/(s²+16))

Taking Laplace inverse of the function y(t), we get;

y(t) = L⁻¹ [7 + (y′(0)/s) + (7s²/(s²+16))]

y(t) = 7L⁻¹[1] + y′(0)L⁻¹[1/s] + 7L⁻¹[s/(s²+16)]y(t) = 7δ(t) + y′(0)u(t) + 7cos(4t)

Hence, the solution to the given differential equation with the given initial conditions is: y(t) = 7δ(t) + y′(0)u(t) + 7cos(4t).

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Answer:

\(y = 9\)

Step-by-step explanation:

1) Add 3 to both sides.

\(3y = 2y + 6 + 3\)

2) Simplify 2y + 6 + 3 to 2y + 9.

\(3y = 2y + 9\)

3) Subtract 2y from both sides.

\(3y - 2y = 9\)

4) Simplify 3y - 2y to y.

\(y = 9\)

Therefor, the answer is y = 9.

Answer:

3y-3=2y+6

3y-2y=3+6 (You will group like terms)

therefore,y=9

Answer:

The answer is 1760

Step-by-step explanation:

I=Prt

P=??

I=22

r=2.5%

t=6 months which is half a year

22=P×2.5%×1/2

22=0.0125P

P=1760

Answer:x+8=2x-2

Step-by-step explanation:

Se considera x la edad de Ana, entonces se le suman 8, ya que dice que será dentro de 8 años. eso tiene que ser igual al doble de su edad (2x)-2 que son los años que hace de eso.

De eso puedes sacar--> x+8=2x-2

                                       x=6

The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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Answer:

180

Step-by-step explanation:

A 3-digit number cannot start with 0, so the leftmost digit is a choice of 6 digits out of the 7. The middle digit can be chosen from all 7 digits minus the one already used, so there are 6 choices. The right digit can be chosen from 5.

6 × 6 × 5 = .180

The number of three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 is 180.

This can be calculated by finding the number of element availabe at first place which is 6 excluding 0 than for second position 6 as first number is excluded and 0 is added and for the last positon the number of possibe combination is 5 as 2 digits are already used.

The final answer is 6*6*5 = 180

so count of 3 digit numbers that can be formed by the given set of digit without repetetion allowed is  180

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5 x 5 = 25 possible pairings. The five boys can be paired with any of the five girls, and the five girls can be paired with any of the five boys, creating 25 possible pairings. To explain this mathematically, we can use permutations.  

A permutation is an arrangement of objects or symbols in which the order of the arrangement matters. In this case, the order of the arrangement matters because the pairings have to be specific boy-girl pairs.  We can also use factorials to explain the answer. Factorials are used to calculate the number of possible arrangements for a given set.

In this case, the set consists of five boys and five girls, and the factorial calculation would be 5! x 5! = 5 x 4 x 3 x 2 x 1 x 5 x 4 x 3 x 2 x 1 = 25, which is the same answer as the permutation calculation.  The final answer of 25 possible pairings can be explained using both permutations and factorials. Both methods of calculation show that there are 25 possible pairings, with each pairing consisting of one boy and one girl.

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Answer:

Convergent

Step-by-step explanation:

One method to determine if  \(\displaystyle \sum^\infty_{k=1}ke^{-k^2}\)is convergent or divergent is the Integral Test.

Suppose that the function we use is \(f(x)=xe^{-x^2}\). Over the interval \([1,\infty)\), the function is always positive and continuous, but we also need to make sure it is decreasing before we can proceed with the Integral Test.

The derivative of this function is \(f'(x) = e^{-x^2}(1-2x^2)\), so our critical points will be \(\displaystyle x=\pm\frac{1}{\sqrt{2}}\), but we can drop the negative critical point as we are starting at \(k=1\). Using some test points, we can see that the function increases on the interval \(\bigr[0,\frac{1}{\sqrt{2}}\bigr]\) and decreases on the interval \(\bigr[\frac{1}{\sqrt{2}},\infty\bigr)\). Since the function will eventually decrease, we can go ahead with the Integral Test:

\(\displaystyle \int_{{\,1}}^{{\,\infty }}{{x{{{e}}^{ - {x^2}}}\,dx}} & = \mathop {\lim }\limits_{t \to \infty } \int_{{\,1}}^{{\,t}}{{x{{{e}}^{ - {x^2}}}\,dx}}\hspace{0.5in}u = - {x^2}\\ & = \mathop {\lim }\limits_{t \to \infty } \left. {\left( { - \frac{1}{2}{{{e}}^{ - {x^2}}}} \right)} \right|_1^t\\ & = \mathop {\lim }\limits_{t \to \infty } \left( {-\frac{1}{2}{{e}}^{ - {t^2}}-\biggr(-\frac{1}{2e}\biggr)}} \right) = \frac{1}{2e}\)

Therefore, since the integral is convergent, the series must also be convergent by the Integral Test.

Functions which are polynomials are y=\(5x^{4} +x^{2} -8\) ,y=\(7x^{3}\) and y=\(6^{x}\)

Given Functions : 1) y=\(-x^{2} +1/1-2x\) 2)y=\(5x^{4} +x^{2} -8\). 3) y=\(7x^{3}\)and g(x)=\(6^{x}\).

We need to find which functions are polynomials. We know that polynomials is an expression consisting of indeterminates and coefficients that involves only the operations of addition, subtraction, multiplication and non negative integers .

First function is y=\(-x^{2} +1/1-2x\)

The above function is not a polynomial because it has not a variable containing power in whole number and it is in fraction form. Two different polynomials can form numerator and denominator in a fraction.

Second function is y=\(5x^{4} +x^{2} -8\)

The above function is a polynomial as it has a variable having power and it is not in fraction also.

Third function is  y=\(7x^{3}\)

The above function is also a polynomial for the same reason.

Fourth function is g(x)=\(6^{x}\).

The above function is also a polynomial.

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After the formation of the European Union (EU), it eliminated all tariffs among its member countries. This means that there are no import taxes or duties imposed on goods traded between EU member countries.

One of the key objectives of the European Union is to create a single market among its member countries, fostering economic integration and facilitating the free movement of goods, services, capital, and people. As part of this goal, the EU implemented the elimination of tariffs among its member countries. Tariffs are taxes or duties imposed on imported goods, which can increase their cost and hinder trade.

By removing tariffs, the EU promotes the free flow of goods within its borders. This has significant benefits for businesses and consumers within the EU, as it allows for increased trade, competition, and access to a wider range of products. Eliminating tariffs encourages economic cooperation and integration among EU member countries, creating a more seamless and efficient trading environment.

Option a is incorrect because the EU does not bar imports of specific products or favor domestic companies. Option c is incorrect because the EU aims to promote trade and economic activity among its member countries rather than decreasing imports and exports. Option d is incorrect because the North American Free Trade Agreement (NAFTA) is a trade agreement between the United States, Canada, and Mexico and is not directly related to the European Union.

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