What is the measure of angle abd in trapezoid abcd? 24° 40° 64° 92°

Answer:

x=5

Step-by-step explanation:

isolate the x on one side of the equal sign so move the 2 over by adding 2

4x=x+15 ( add 2 to both sides )

then move the x over

3x=15 ( subtract x from both sides )

then divide by 3

x=5

Answer: Hope it helps, have a nice day :)

x=5

Step-by-step explanation:

So you can only have x on one side, so first you move an x to the other side of the equal sign.

so, 4x-2=x+13, you can move either x, but I'm moving x instead of 4x

    -x      -x

Your new equation is 3x-2=13, because the x's cancel out

Then you add 2 on both sides 3x-2=13

                                                       +2  +2

                                                 ___________

                                                    3x=15

then you divide by 3 on both sides

3x divided by three leaves x by itself, and 15 divided by three is 5.

3x=15

3    3

x=5

a) Alternatives:

1. Build a distribution center near Fresno

2. Build a distribution center near Henderson

States of nature:

1. Earthquake occurs near Fresno in the next 3 years

2. Earthquake does not occur near Fresno in the next 3 years

Payoff table:

                                     |Earthquake occurs | Earthquake does not occur |

Build near Fresno        | -$20 million            | $0 million                              |

Build near Henderson | -$40 million            | -$20 million                           |

b) Expected value calculation without hiring the geologist:

Probability of earthquake occurring near Fresno = 0.20

Expected value of building near Fresno = (0.20) x (-$20 million) + (0.80) x ($0 million) = -$4 million

Expected value of building near Henderson = (0.20) x (-$40 million) + (0.80) x (-$20 million) = -$28 million

Since the expected value of building near Fresno is higher, the optimal alternative is to build near Fresno.

c) Expected value of perfect information (EVPI):

The EVPI is the difference between the expected value with perfect information and the expected value without perfect information.

Without perfect information, the expected value of building near Fresno is -$4 million. With perfect information, Amazon would know whether an earthquake will occur or not and make the decision accordingly.

If an earthquake is predicted, Amazon will choose to build near Henderson and the expected value will be -$20 million.

If an earthquake is not predicted, Amazon will choose to build near Fresno and the expected value will be $0 million.

The probabilities of these two outcomes depend on the accuracy of the geologist's prediction.

If the geologist predicts an earthquake, the probability of an earthquake occurring is 0.90, and the probability of an earthquake not occurring is 0.10.

If the geologist predicts no earthquake, the probability of an earthquake occurring is 0.10, and the probability of an earthquake not occurring is 0.90.

Therefore, the EVPI can be calculated as follows:

EVPI = (0.10 x (-$20 million)) + (0.90 x $0 million) = -$2 million

This means that the maximum Amazon should pay for the geologist's prediction is $2 million.

d) Posterior probabilities:

If the geologist predicts an earthquake:

Probability of an earthquake occurring = 0.90 x 0.20 = 0.18

Probability of no earthquake occurring = 0.10 x 0.80 = 0.08

Normalization factor = 0.18 + 0.08 = 0.26

Posterior probability of an earthquake occurring = 0.18 / 0.26 = 0.6923

Posterior probability of no earthquake occurring = 0.08 / 0.26 = 0.3077

If the geologist predicts no earthquake:

Probability of an earthquake occurring = 0.10 x 0.20 = 0.02

Probability of no earthquake occurring = 0.90 x 0.80 = 0.72

Normalization factor = 0.02 + 0.72 = 0.74

Posterior probability of an earthquake occurring = 0.02 / 0.74 = 0.027

Posterior probability of no earthquake occurring = 0.72 / 0.74 = 0.973

e) Using the calculations from above, the expected value of sample information (EVSI) can be calculated as follows:

EVSI = E(EVSI | E)P(E) + E(EVSI | ¬E)P(¬E)

where E represents the event that an earthquake will occur and ¬E represents the event that an earthquake will not occur.

From the calculations in part (d), the posterior probabilities are P(E) = 0.144 and P(¬E) = 0.856.

If the geologist predicts an earthquake, then the expected value of perfect information (EVPI) is $8 million (calculated in part c).

If the geologist predicts no earthquake, then Amazon will build the distribution center near Fresno without hiring the geologist, so the expected value of sample information is simply the expected value without the geologist, which is $56 million.

Therefore, the EVSI can be calculated as follows:

EVSI = E(EVSI | E)P(E) + E(EVSI | ¬E)P(¬E)

    = ($8 million - $5.5 million) x 0.144 + ($56 million - $5.5 million) x 0.856

    = $44.896 million

Since the EVSI is positive and substantial, Amazon should hire the geologist to reduce uncertainty and improve the decision-making process.

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The perimeter measures around 36 metre.

The perimeter refers to the area surrounding an object. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.

While 12.74 rounds up to 13, 5.45 rounds down to 5. Recatangle created a total of four sides, two of which are identical in length to the other two (which is a poor way to explain it). There are two sides that are 13 inches long and two sides that are 5 inches long, which is the solution to this question. When added together, the perimeter would be 13+13+5+5.

As an expression,

2(13)+2(5)

=26+10

=36.

The perimeter is approximately 36 meters.

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The value of the given integral is \((-1/18)ln|x| - (1/36)ln|6x^2-1|\)+ C, where C is the constant of integration.

To evaluate the integral, we can use integration by substitution. Let u = x² - x, then \(\frac{du}{dx}\) = 2x - 1 and dx = \(\frac{du}{(2x-1)}\). Substituting this in the integral, we get:

We can further simplify this by breaking the integral into partial fractions:

\(\frac{u}{(18x(2x-1))}\) = A/x + B/(2x-1)

u = A(2x-1) + Bx

Equating coefficients, we get A = -1/18 and B = 1/18. Substituting these values, we get:

∫ \(\frac{(x^2 - x)}{(36x^3 - 6x)}\) dx = (-1/18)∫ \(\frac{dx}{x}\) + (1/18)∫ dx/(2x-1)

= \((-1/18)ln|x|\) - (1/36)ln|2x-1| + C

Since the natural logarithm function is only defined for positive values, we need to use absolute values in the final answer to account for negative values of x. Therefore, the answer is  

\((-1/18)ln|x| - (1/36)ln|6x^2-1|\) + C.

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To determine the probability that the man would have done at least as well if he had no ESP, we can use the concept of the binomial distribution.Sum of P(X = 7), P(X = 8), P(X = 9), and P(X = 10) is solution..

In this case, the probability of getting a correct prediction for each flip is 0.5, as it is a fair coin. The man made 10 predictions, and he got 7 correct.To calculate the probability, we need to consider all possible outcomes that would result in 7 or more correct predictions out of 10 flips. This includes getting 7, 8, 9, or 10 correct predictions.

Using the binomial probability formula, we can calculate the probability for each outcome and then sum them up.The probability of getting exactly k successes out of n trials is given by the formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the binomial coefficient.

In this case, the probability of getting 7 or more correct predictions is the sum of P(X = 7), P(X = 8), P(X = 9), and P(X = 10).Calculating these probabilities and summing them up will give us the probability that the man would have done at least as well if he had no ESP.

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Answer:

Please elaborate more your question so I can actually give you a more accurate answer.

Step-by-step explanation:

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

a+b+c=anser

Step-by-step explanation:

Answer:

indicates the relationship of two variables whenever one variable changes.

Step-by-step explanation:

Step-by-step explanation:

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.

this is also called the slope of the line.

based on our equation y = 5.5x

y/x = 5.5

so, C is the right answer.

Answer:

total = $477.36

Step-by-step explanation:

459 x 1.04 = $477.35

a) \(Calculation of 5 point DFT of x(n) is: X(k) = [28, -2 - 16j, -8, -2 + 16j, -2]\)On squaring the values of X(k),\(we getY(k) = X(k)²= [784, 68 - 80j, 64, 68 + 80j, 4]\)

Now we need to compute the inverse DFT of Y(k) which is given below:

\(Let us calculate the 5-point IFFT by using the circular convolution approach as: Y(k) = X(k)²[784, 68 - 80j, 64, 68 + 80j, 4] = x²(k)By using 5-point IFFT\),

\(we can obtain the values of y(n) as below:y(n) = [1960, -360 + 168j, 256, -360 - 168j, 16]b) Given x(n) = ejwon, 0≤n≤N - 1\)and zero otherwise.

We need to find the Fourier Transform X(w) of x(n) and N-point DFT X(k) of x(n).

\(The Fourier Transform X(w) of x(n) is:X(w) = Σx(n)ejwn = Σejwon ejwn = N∑(k=0) ej2πkn/N\)

The above expression is a Geometric series.

\(When the common ratio is |r|<1, the sum of the geometric series becomes:S = a(1 - r^n)/(1 - r)\)

\(Substituting r = ej2π/N and a=1, we get:S = 1(1 - ej2πn/N)/(1 - ej2π/N)\)

\(Hence, the Fourier Transform X(w) of x(n) is:X(w) = N(1 - ej2πn/N)/(1 - ej2π/N)\)

The N-point DFT of the finite length sequence x(n) is given by:\(X(k) = Σx(n)ej2πkn/N  , for 0 ≤ k ≤ N - 1\)

\(Here, the given sequence x(n) is:x(n) = ejwon, 0≤n≤N - 1\) and zero otherwise.

\(Substituting the given sequence in the above equation, we get:X(k) = Σej2πkn/Nfor 0 ≤ k ≤ N - 1 = Σcos(2πkn/N) + jsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

\(Here, let us separate the real and imaginary parts as below:X(k) = Σcos(2πkn/N) + jsin(2πkn/N) for 0 ≤ k ≤ N - 1= Σcos(2πkn/N) + Σjsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

\(On substituting the values of cos and sin in the above equation, we get: X(k) = Re(X(k)) + jIm(X(k)), for 0 ≤ k ≤ N - 1where, Re(X(k)) = Σcos(2πkn/N) for 0 ≤ k ≤ N - 1Im(X(k)) = Σsin(2πkn/N) for 0 ≤ k ≤ N - 1\)

Therefore, we can calculate the N-point DFT X(k) of x(n) by using the above expression.

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Answer: $190=£131.1

Step-by-step explanation:

190x0.69=

131.1

Answer:

£131.1

Step-by-step explanation:

0.69 x 190 = 131.1

I searched your question and here is what I found:

Step-by-step explanation:

L = 4 + 3W  (from the second condition)

L2 = 66 + LW (combining the first and third condition)

L2 = 66 + L(L-4)/3

3L2 = 198 + L2 -4L

2L2 + 4L -198 = 0

(2L - 18)(L + 11) = 0; discarding the negative root for lack of practicality , L = 9

from the first equation W = (L - 4)/3 = 5/3 = 1 2/3; 1.67

Hence the length of the rectangle is 9 cm and the width is 1.67 cm

check;        

2nd condition; L = 4 + 3*1.67 = 9 (proven)

1st and 3rd condition; 92 = 66 + 9*1.67 = 81 (proven)

The length of the rectangle is 9 cm.

The width of the rectangle is 5/3 cm.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Length = 3w + 4

Width = w

Area = (3w + 4)w

Square:

Side = 3w + 4

Area = (3w + 4)²

Now,

The area of the square is 66 more than the area of the rectangle.

This means,

(3w + 4)² =  (3w + 4)w + 66

9w² + 16 + 24w = 3w² + 4w + 66

9w² - 3w² + 24w - 4w + 16 - 66 = 0

6w² + 20w - 50 = 0

2 (3w² + 10w - 25) = 0

3w² + 10w - 25 = 0

3w² + (15 - 5)w - 25 = 0

3w² + 15w - 5w - 25 = 0

3w(w + 5) - 5(w + 5) = 0

(3w - 5)(w + 5) = 0

w + 5 = 0 and 3w - 5 = 0

w + 5 = 0

w = -5 (rejected since its negative)

3w - 5 = 0

3w = 5

w = 5/3

Now,

Length.

= 3w + 4
= 3 x 5/3 + 4

= 5 + 4

= 9

Width = 5/3

Thus,

The length and width of the rectangle are 9 and 5/3.

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The probability that exactly 5 out of 10 graduates become vice presidents is 0.2007 or 0.201 (rounded to three decimal places).

We can use the binomial distribution to solve this problem.

Let X be the number of graduates who become vice presidents out of the 10 selected.

Then X follows a binomial distribution with parameters n = 10 and p = 0.4. We want to find the probability that exactly 5 become vice presidents, i.e., P(X = 5).

Using the formula for the binomial probability mass function, we have:

P(X = 5) = (10 choose 5) *\((0.4)^5 * (0.6)^5\)

P(X = 5) = (252) * (0.01024) * (0.07776)

P(X = 5) = 0.2007

Therefore,

The probability that exactly 5 out of 10 graduates become vice presidents is 0.2007 or 0.201 (rounded to three decimal places).

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a) The values in the F(x) column represent the cumulative probabilities for X. For example, F(0) = 0.10 means that the probability of X being less than or equal to 0 is 0.10, F(1) = 0.30 means that the probability of X being less than or equal to 1 is 0.30, and so on.

To answer the given question, let's first write down the cumulative distribution function (CDF) values for the random variable X based on the provided probability mass function (PMF) table:

(a) Table of F(x) - Cumulative Distribution Function (CDF) for X:

x   |  P(X=x)  |  F(x)

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

0   |   0.10   |  0.10

1   |   0.20   |  0.30

2   |   0.35   |  0.65

3   |   0.25   |  0.90

4   |   0.10   |  1.00

(b) To calculate the probability P(X < 2), we need to find the cumulative probability up to x = 1:

P(X < 2) = F(1)

From the table above, F(1) is 0.30.

the probability P(X < 2) is 0.30.

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If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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let p (t) = 600(0.974)^t be the population of a good place in the year 1900. a) rewrite this equation in the form p(t) = ae^(kt)

The final form of the given exponential function p(t) = 600(0.974)^t is p(t) = 600e^(-0.0264t).

The exponential function is a mathematical function where an independent variable is raised to a constant, and it is always found in the form y = ab^x. Here, we need to rewrite the given equation p(t) = 600(0.974)^t in the form p(t) = ae^(kt)Round k to at least 4 decimal places.

We know that exponential function is in the form p(t) = ae^(kt)

Here, the given equation p(t) = 600(0.974)^t ... equation (1)

The given equation can be written as:

p(t) = ae^(kt) ... equation (2)

Where,p(t) is the population of a good place in the year 1900

ae^(kt) is the form of the exponential function

600(0.974)^t can be written as 600(e^(ln 0.974))^t

p(t) = 600(e^(ln 0.974))^t

p(t) = 600(e^(ln0.974t) ... equation (3)

Comparing equations (2) and (3), we get: a = 600

k = ln 0.974

Rounding k to at least 4 decimal places, we get k = -0.0264

Therefore, the final form of the given exponential function p(t) = 600(0.974)^t is p(t) = 600e^(-0.0264t)

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Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the function is not given. However, the following explanation will guide you.

The average rate of change is calculated using;

\(A = \frac{f(b) - f(a)}{b - a}\)

Where

\((a,b) = (-1,5)\)

Take for instance;

The function is:

\(f(x) = 2x\)

We have to solve for f(-1) and f(5);

i.e.

\(f(-1) = 2 * -1 -2\)

\(f(5) = 2 * 5 = 10\)

Substitute -1 for a and 5 for b

\(A = \frac{f(b) - f(a)}{b - a}\)

\(A = \frac{f(5) - f(-1)}{5 - (-1)}\)

\(A = \frac{f(5) - f(-1)}{5 +1)}\)

\(A = \frac{f(5) - f(-1)}{6}\)

Substitute values for f(5) and f(-1)

\(A = \frac{10 - (-2)}{6}\)

\(A = \frac{10 +2}{6}\)

\(A = \frac{12}{6}\)

\(A = 2\)

Apply this steps in your work

The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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Answer:

Step-by-step explanation:

to find the inverse of an equation

1. substitute x=y and y=x

y = (x-3)³ is the initial equation

x= (y-3)³

2. write the new equation as y= something

∛x= ∛(y-3)³, cube root both sides

∛x = y-3 , add 3 to both sides

y = ∛x +3

the inverse equation of y = (x-3)³ is y = ∛x +3

Answer:

Step-by-step explanation:

For the first question the answer is 50(0.2 + 1)^2 = 72

For the second question it is y = 32

Step-by-step explanation:

In case you need to see how i got it...it's below

For number 1, y is proportional to (x + 1)^2

The equation would be y(x +1)^2 = k(the constant). Then I substituted numbers you gave me in the equation which was : 50(0.2 + 1)^2 = k(72)

For number 2 I used this equation: y (x + 1)^2 = 72. I substituted x for 0.5. The equation will be: y(0.5 + 1)^2 = 72. Then I got 32 for y.

Hope this helps:) i am the best lil kissman

Answer:

4/9

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

Answer:

the question is not correct. please rewrite the question.

Answer:

239y

Step-by-step explanation:

956/4  

The equation of a line is y = -1/3x - 4

The general formula for the equation of a line is expressed as;

y = mx + c

Given that the parameters are;

From the information given, we have that;

Slope, m = -1/3

Substitute the values

-1 = -1/3(-9) + c

expand the bracket

-1 = 3 + c

collect like terms

= -4

Hence, the equation is y = -1/3x - 4

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Answer:

-2 floor so underground

The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

Answer:

The length of the box is 6 cm. The width of the box is 3 cm. The height of the box is 2 cm.

Step-by-step explanation:

volume = length x width x height In this instance volume = 36 m³. I will let “b” be the length of the box. “w’ will be the width of the box. And “h” will be the height of the box. Therefore we know that b = 2w and b=3h. So: w= b /2 and h=b /3.

36 m³= b(b/2)(b/3)

36 = b³/6

b ³ = 216

b = 6

w = 6/2 = 3

h = 6/3 = 2