Can a triangle have sides with the given lengths? Explain.
11. 2 in., 3 in., 6 in.
12. ll cm, 12 cm, 15 cm
13. 2 yd, 9 yd, 10 yd

The length of YV is equivalent to 7.

Given is that UV = x + 6 and UY = x - 1. Also, WY intersects UV at Y.

We can write that -

UV = UY + YV

YV = UV - UY

YV = (x + 6) - (x - 1)

YV = x + 6 - x + 1

YV = 7

Therefore, the length of YV is equivalent to 7.

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To construct a 3×3 matrix, not in echelon form, whose columns span ℝ³, we can choose three linearly independent vectors as the columns of the matrix.

To demonstrate that the constructed matrix has the desired property of spanning ℝ³, we can construct a specific example. Let's consider the matrix A:

A = [[1, 0, 0],

[0, 1, 0],

[0, 0, 1]]

In this case, A is a 3×3 matrix with three columns [1, 0, 0], [0, 1, 0], and [0, 0, 1]. Each column represents a standard basis vector in ℝ³.

To show that the columns of A span ℝ³, we need to demonstrate that any vector in ℝ³ can be expressed as a linear combination of the columns of A.

Let's consider an arbitrary vector x = [x₁, x₂, x₃]ᵀ in ℝ³. We can express x as a linear combination of the columns of A:

x = x₁[1, 0, 0] + x₂[0, 1, 0] + x₃[0, 0, 1]

Simplifying this expression, we get:

x = [x₁, x₂, x₃]ᵀ

Thus, we have shown that any vector x in ℝ³ can be expressed as a linear combination of the columns of the matrix A. Therefore, the columns of A span ℝ³.

Note: It is important to emphasize that there are many possible matrices that can be constructed to satisfy the given condition. The example provided here is just one of the many valid choices

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Answer:

f(f(x)) = \(x^{4}\) + 2x² + 2

Step-by-step explanation:

to evaluate f(f(x)), substitute x = f(x) into f(x)

f(f(x))

= f(x² + 1)

= (x² + 1)² + 1 ← expand factor using FOIL

= \(x^{4}\) + 2x² + 1 + 1

= \(x^{4}\) + 2x² + 2

Answer:

\(f[f(x)]=x^4+2x^2+2\)

Step-by-step explanation:

Given function:

\(f(x)=x^2+1\)

To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):

\(\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}\)

Answer:

Step-by-step explanation:

To find the value of x, solve the equation. Do this by rearranging the equation to make x the subject.

Answer:

x=32761 /4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x+7=32768

Step 2: Subtract 7 from both sides.

4x+7−7=32768−7

4x=32761

Step 3: Divide both sides by 4.

The mean square errors for the three-month and four-month moving average forecasts shown below.

How closely a regression line resembles a set of data points is determined by the Mean Squared Error. It is a risk function that corresponds to the squared error loss's expected value. The average, more particularly the mean, of errors squared from data related to a function is used to determine mean square error.

Given:

According to the Given data we construct a table as

Month   Sales   3- month           4- month      3- month     4- month      

                         moving             moving         squared       squared

                        averages            averages      error           error

1             9.6      

2             9.2

3             9.3

4             9.2     9.367                                        0.111            

5             9.2     9.400                   9.450           0.160        0.123    

6             9.2     9.500                  9.500            0.010        0.140    

7             9.2     9.733                   9.625            0.001         0.006  

8             9.2     9.733                   9.725            0.751          0.776  

9             9.2     10.000                 9.950           0.010           0.002  

10            9.2     10.067                  9.975            0.218          0.141  

11             9.2     10.033                   9.950          0.401           0.322

12            9.2     9.633                   9.975             0.004          0.031

13                       9.567                 9.650    

                                                        MSE             0.185            0.176

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The solution to the equation cos θ = 7/16, rounded to the nearest tenth, is θ = 64.05 degrees.

Equations with trigonometric functions that hold true for all of the variables in the equation are known as trigonometric identities.
These identities are used to solve trigonometric equations and simplify trigonometric expressions.

To solve for θ when cos θ = 7/16, we need to use the inverse cosine function (also called the arc-cosine function), which is denoted as cos⁻¹

Using this function, we can write:

cos θ = 7/16

θ = cos⁻¹(7/16)

To find the value of θ in degrees, we can use a calculator or a table of trigonometric values. Using a calculator, we get:

θ = 64.05°

Therefore, the solution to the equation cos θ = 7/16, rounded to the nearest tenth, is θ = 64.05 degrees.

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Answer:

p= 4s

40 m

Step-by-step explanation:

Answer:

You would multiply 10 by 4 or add 10 4 times. A square has 4 sides and if each side is 10 meters, the answer would be

40 meters

:)

The value of x at which f(x) is a minimum is 3/2.

To find the minimum value of f(x), we need to calculate its derivative and set it equal to zero.

So,

\(f(x) = ∫(x^2 - 3x - 2) e^(t^2) dt\)

Taking the derivative of f(x) with respect to x, we get:

\(f'(x) = 2x e^(x^2 - 3x - 2) - 3 e^(x^2 - 3x - 2)\)

Setting f'(x) equal to zero:

\(2x e^(x^2 - 3x - 2) - 3 e^(x^2 - 3x - 2) = 0\)

Factorizing, we get:

\(e^(x^2 - 3x - 2) (2x - 3) = 0\)

So, either e\(^(x^2 - 3x - 2)\)= 0 (which is not possible), or

2x - 3 = 0

Solving for x, we get:

x = 3/2

Therefore, the value of x at which f(x) is a minimum is 3/2.

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f'(x) changes from negative to positive at x = 2.105, we know that f(x) has a local minimum at x = 2.105.
Therefore, the answer is c. 2.

To find the value of x at which f(x) is a minimum, we need to find the critical points of f(x) and then determine whether each critical point is a minimum or maximum using the first derivative test.

To find the critical points of f(x), we need to find where f'(x) = 0. Using the Fundamental Theorem of Calculus and the Chain Rule, we can find that:

\(f'(x) = 2x - 3 - 2xe^{(x^2-3x-2t^2)}\)

To find where f'(x) = 0, we need to solve the equation\(2x - 3 - 2xe^{x^2-3x-2t^2} = 0\) for x. Unfortunately, this equation cannot be solved algebraically, so we need to use numerical methods. One way to do this is to use a graphing calculator or computer program to graph y = 2x - 3 and\(y = 2xe^{x^2-3x-2t^2)\)and find their intersection(s).

Using this method, we can find that there is only one critical point, which is approximately x = 2.105. To determine whether this critical point is a minimum or maximum, we need to use the first derivative test. Since f'(x) changes from negative to positive at x = 2.105, we know that f(x) has a local minimum at x = 2.105.

Therefore, the answer is c. 2.

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There are two factors.

The design described in this scenario has two factors: advertisement and price point. Each factor has multiple levels: there are four advertisements and five price points.

In experimental design terminology, a factor is an independent variable that is manipulated by the experimenter, and a level is a specific value or category of that factor. The goal of the experiment is to determine how each factor and its levels affect the response variable (e.g., the number of product purchases).

Therefore, in this experiment, the factor of advertisement has four levels (the four advertisements) and the factor of price point has five levels (the five distinct price points). Overall, there are two factors (advertisement and price point)

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Answer:

41cm^2×11cm=451cm^3

Step-by-step explanation:

You need to multiply the surface of the 'base' with height

Answer: 451 cm³

Step-by-step explanation: the rule of the volume is base times height so multiply 41

times 11 so the answer is 451 . The units is to the power of 3 in finding volume of figures . The hexagon is the base and the rectangle is the height so multiply their lengths and don't forget the units . Hope this helps .

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

F = 5.67503704

Step-by-step explanation:

K=5/9(F+459.67)   K = 5/9F / 5/9  =  255.376667 / 5/9 = F = 5.67503704

The given equation is solved for F in terms of K is F= 9/5 K-459.67.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is K=5/9(F+459.67)

9K=5(F+459.67)

9/5 K=(F+459.67)

F= 9/5 K-459.67

Therefore, the given equation is solved for F in terms of K is F= 9/5 K-459.67.

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Answer:

(Choice A) A Yes

Step-by-step explanation:

Answer:

16 + 9 = 25

Step-by-step explanation:

For each term in the sequence, we can see that the second number being added increases by 2 each time (3, 5, 7)

And that the first number of each term increases by the value of the second term

(1 increases by 3; 4 increases by 5)

we can follow out these two observations to find T4

the first term (9) will increase by the value of the second term (7)

{the sum of the previous term is the first number}

so the first number of T4 will be 16.

Because we left off on +7, we are now on +9

so, T4 is

16 + 9 {and then do the math accordingly}

16 + 9 = 25

So, T4 is

16 + 9 = 25

hope this helps!! have a lovely day!! :)

Answer:

Step-by-step explanation:

The largest three-digit multiple of 33 * 30 is 990, which uses only two different digits. Now we work backwards: Subtracting 33 once gives 990-33=957, which has three different digits. Therefore, our answer is 957

957 is the greatest three-digit number which is multiplied by 33.

A numerical digit is a single sign that can be used alone or in combination to denote a number in a positional numeral system.

A digit is a component of a set that, when put together, forms a numerical system.

Examples of digits include 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

If we multiply 33 by 31

It gives 1023 which is a four-digit number.

Now trying to multiply less than 31

By 30

33 × 30 = 990 but here two digits are the same.

By 29

33 × 29 = 957 and all three are different.

Hence "957 is the greatest three-digit number which is multiplied by 33".

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Answer:

a) 15.52mm

b) 25.8275mm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X, or the area to the left side of the curve. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, that is, the area to the right side of the curve.

A) What wing-span has an area of 0.1005 on it left side under the standard normal curve?

This is X when Z has a pvalue of 0.1005. So it is X when Z = -1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.28 = \frac{X - 20}{3.5}\)

\(X - 20 = -1.28*3.5\)

\(X = 15.52\)

This wing-span is 15.52mm.

B) What wing-span has an area of 0.0480 on it right side under the standard normal curve?

This is X when Z has a pvalue of 1 - 0.0480 = 0.9520. So this is X when Z = 1.665.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.665 = \frac{X - 20}{3.5}\)

\(X - 20 = 1.665*3.5\)

\(X = 25.8275\)

This wing-span is 25.8275mm.

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Answer:

8 CDs for $14.50

Step-by-step explanation:

We have to divide both of the numbers by the number of CDs. Our formula is:

(price) ÷ (number of CDs) = price per CD

When we divide both of the prices by the number of CDs, we see that 6 CDs for 12.00 is worse because it is 2.00, whereas the inflation is lower when you compare to the other rate. You get $1.81.

2 is 4/6, 8/12

3 is 2/4, 4/8

4 is 8/10, 16/20

5 is =

6 is >

7 is >

8 is =

9 is =

10 is <

11 is =

12 is >

Answer:

y = -9 or y = -4

Step-by-step explanation:

y^2 + 13y = -36

y^2 + 13y + 36 = 0

(y + 9)(y + 4)

y + 9 = 0

y = -9

y + 4 = 0

y = -4

Best of Luck!

Answer:

n = 0

Step-by-step explanation:

1.2n + 1 = 1 - n

Add n and - 1 on both sides.

1.2n + n = 1 - 1

Combine like terms.

2.2n = 0

Divide both sides by 2.2.

n = 0

Answer:

the answer without a doubt it b B B

Step-by-step explanation:

Answer:

46\(\sqrt{2}\)

Step-by-step explanation:

4\(\sqrt{16} \sqrt{2} =4\sqrt{32}\)

\(\sqrt{16} =4\)

4x4=16

16\(\sqrt{2}\)

\(6\sqrt{25} \sqrt{2} =6\sqrt{50}\)

\(\sqrt{25} =5\)

6x5=30

30\(\sqrt{2}\)+16\(\sqrt{2}\)

=\(46\sqrt{2}\)

A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.

The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.

This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.

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Answer:

2:00 PM

Step-by-step explanation:

time per student = 60 mins = 1 hr

number of student = 4

time of break = 10 mins

hr : mins

start: 9:30 AM

student 1: 1

break: 10

student 2: 1

break: 10

student 3: 1

break: 10

student 4: 1

\( - - - - - - \)

13:60 --> 1 hr

= 14:00

2:00 PM (ANS)

Answer:

9 Hours

Step-by-step explanation:

290 divided by 5 = 58MPH

^  miles divided by hours

522 divided by 58 = 9 Hours

^ miles divided by the MPH

Answer:

9 hours

Step-by-step explanation:

290 miles-->  5 hours

1 miles--> 5/290 hours

522 miles --> (5/290)*522 = 9 hours

Answer:From the given information, we know that after sailing for 2 hours, Alvin and his friends are 10 miles from shore. This can be written as y = 10 when x = 2.

Since there is a proportional relationship between x and y, we can write an equation using this information: y = kx, where k is the proportionality constant.

Substituting the known values, we get: 10 = k * 2

Solving for k, we get: k = 10/2 = 5

So, the equation relating x and y is: y = 5x

To find their distance from shore after sailing for 3 hours, we can plug in x = 3 into the equation:

y = 5x

y = 5 * 3

y = 15

So, after sailing for 3 hours, Alvin and his friends are 15 miles from shore.

Step-by-step explanation:

Answer:

What is it you need help with?

Step-by-step explanation:

Which one