For what values of a are the following expressions true?

1) |a-5|=5-a

2) |a|=-a

Write in inequality format!

PLS HELP

Ak is the event that the sum of the dots facing up is k, Bk is the event that the sum is greater than or equal to k, E is the event that the sum is even, and O is the event that the sum is odd. The total number of outcomes, which is 36.

a) To find P[Ak], we need to count the number of ways we can obtain a sum of k and divide by the total number of possible outcomes. This gives P[Ak] = (number of ways to obtain k)/(total number of outcomes) = (number of ways to obtain k)/36. Similarly, P[BX] is the probability of obtaining a sum greater than or equal to X, which is the same as the probability of obtaining a sum of X or more, so we can use the same approach as for P[Ak].

b) P[O|B8] is the probability that the sum is odd given that it is greater than or equal to 8. To find this, we can use Bayes' theorem: P[O|B8] = P[O and B8]/P[B8]. We can calculate P[O and B8] by counting the number of outcomes where the sum is odd and greater than or equal to 8, which is 10 (9, 11, ..., 19), and divide by the total number of outcomes that satisfy B8, which is 25 (8, 9, ..., 12). Therefore, P[O and B8] = 10/36 and P[B8] = 25/36, so P[O|B8] = (10/36)/(25/36) = 2/5.

c) P[A U A11\B8] is the probability that the sum is either 2, 3, ..., 11 or 12, but not 8. To find this, we can add the probabilities of the individual events and subtract the probability of their intersection: P[A U A11\B8] = P[A2] + P[A3] + ... + P[A11] + P[A12] - P[B8]. Note that P[B8] is the probability that the sum is 8 or more, so we can use our previous calculation to find this.

d) P[B80] is the probability that the sum is 8 or more. We can count the number of outcomes where the sum is 8 or more, which is 25 (8, 9, ..., 12), and divide by the total number of outcomes, which is 36.

e) P[B:|B-] is the probability that the sum is even given that it is odd. To find this, we can use Bayes' theorem: P[B:|B-] = P[B: and B-]/P[B-]. We can count the number of outcomes where the sum is even and odd, which is 18, and divide by the total number of outcomes where the sum is odd, which is 18 (1, 3, ..., 11), so P[B: and B-] = 18/36 = 1/2. We can also count the number of outcomes where the sum is odd, which is 18, and divide by the total number of outcomes, which is 36, to find P[B-].

f) P[E|B8] is the probability that the sum is even given that it is greater than or equal to 8. To find this, we can use Bayes' theorem: P[E|B8] = P[E and B.

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Answer:

$3.60

Step-by-step explanation:

Hope this helped

The approximate directional derivative of f at point p in the direction of q is 0.

To approximate the directional derivative of f at point p in the direction of q, we can use the formula:

Df(p;q) ≈ ∇f(p) · u

where ∇f(p) represents the gradient of f at point p, and u is the unit vector in the direction of q.

First, let's compute the gradient ∇f(p) at point p:

∇f(p) = (∂f/∂x, ∂f/∂y)

Since f(p) = 15, the function f is constant, and the partial derivatives are both zero:

∂f/∂x = 0

∂f/∂y = 0

Therefore, ∇f(p) = (0, 0).

Next, let's calculate the unit vector u in the direction of q:

u = q - p / ||q - p||

Substituting the given values:

u = (3.03, 3.96) - (3, 4) / ||(3.03, 3.96) - (3, 4)||

Performing the calculations:

u = (0.03, -0.04) / ||(0.03, -0.04)||

To find ||(0.03, -0.04)||, we calculate the Euclidean norm (magnitude) of the vector:

||(0.03, -0.04)|| = sqrt((0.03)^2 + (-0.04)^2) = sqrt(0.0009 + 0.0016) = sqrt(0.0025) = 0.05

Therefore, the unit vector u is:

u = (0.03, -0.04) / 0.05 = (0.6, -0.8)

Finally, we can approximate the directional derivative of f at point p in the direction of q using the formula:

Df(p;q) ≈ ∇f(p) · u

Substituting the values:

Df(p;q) ≈ (0, 0) · (0.6, -0.8) = 0

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Answer:

4 plates with 2 apples and 5 apricots per plate

Step-by-step explanation:

you are welcome

The Critical value to be used to gain the 98 confidence interval for the population mean is2.508 and can be determined using the t- distribution table.

critical value is the value of a test statistic that defines the upper and lower bounds of the confidence interval or determines the position of statistical significance in a statistical test.

Given

The following way can be carried out to determine the critical value

Step 1-First determine the degrees of freedom using the following formula

degrees of freedom = n- 1

where n is the sample size.

Step 2- Replace" n" in the below formula.

degrees of freedom = 23- 1

= 22

Step 3- Now you can use the t- distribution table to determine the critical value to get a 98 confidence interval.

critical value = 2.508

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Logistic Regression is preferred over Linear Regression for classification problems for several reasons.

Firstly, the predicted values in Logistic Regression are much more interpretable as they lie in the range of 0 to 1, which represents the probability of a certain outcome occurring. In contrast, Linear Regression predicts continuous values which are difficult to interpret as probabilities.
Secondly, the sigmoid curve used in Logistic Regression fits the data better than a straight line used in Linear Regression. This is because the sigmoid curve captures the non-linear relationships between the input variables and the output variable, which is often the case in classification problems.
Lastly, Logistic Regression uses maximum likelihood estimation to estimate parameters, whereas Linear Regression minimizes the mean squared error. Maximum likelihood estimation is a more appropriate method for estimating parameters in classification problems as it takes into account the binary nature of the output variable. Linear Regression, on the other hand, does not consider this binary nature and may not produce accurate results in classification problems.

In summary, Logistic Regression is preferred over Linear Regression for classification problems because of its interpretable predicted values, better fit to non-linear relationships, and appropriate method of estimating parameters using maximum likelihood estimation.

We prefer Logistic Regression over Linear Regression for classification problems for the following reasons:

1) Predicted values in Logistic Regression are more interpretable as they lie in the range of 0 to 1, representing probabilities of class membership, while Linear Regression predicts continuous values which may not directly indicate class membership.

2) The sigmoid curve in Logistic Regression fits the data better for classification problems, as it represents a natural threshold between classes, while a straight line from Linear Regression may not provide clear separation between classes.

3) Logistic Regression uses maximum likelihood estimation to estimate parameters, which makes it more suitable for classification problems as it finds the best fit for the probability of class membership. Linear Regression minimizes the mean squared error, which focuses on minimizing the distance between predicted and actual values, but does not directly optimize for class membership probabilities.

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Step-by-step explanation:

a+b+c=78

b=10+a

c=2b

then, we back the first

a+10+a+2b=78

2a+2b=78- 10

2a+2(10+a)=68

2a+2a=48

4a=48

a=12

b=22

c=44

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

18

Step-by-step explanation:

Let x be the smaller number. The larger number would be...

x+7 as the question states their difference is 7.

We can use this to set up an equation:

x+x+7=43

Combine like terms

2x+7=43

Subtract 7 from both sides

2x=36

Divide both sides by 2

x=18

The smaller number is 18

The roots of the equation x⁴ - 2 = 0 are ±√2 and ±i√2.

To find the roots of the given equation x⁴ - 2 = 0, we need to solve for x. By rearranging the equation, we have x⁴= 2. To isolate x, we take the fourth root of both sides of the equation.

The fourth root of 2 can be expressed as two sets of roots: ±√2 and ±i√2. The symbol "±" indicates that there are two possible values for each set of roots. The first set of roots, ±√2, represents the real solutions to the equation, while the second set of roots, ±i√2, represents the complex solutions. The letter "i" represents the imaginary unit, which is defined as the square root of -1.

When we substitute these roots back into the original equation, we find that each root satisfies the equation x⁴ - 2 = 0. For example, if we substitute √2 into the equation, we get (√2)⁴ - 2 = 0, which simplifies to 2 - 2 = 0.

In summary, the roots of the equation x⁴ - 2 = 0 are ±√2 and ±i√2, encompassing both real and complex solutions.

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The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is

||A - A1||₂=0 where A is 2×2 matrix.

We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]

note here that C₂= 3C₁

where Cᵢ --> iᵗʰ column

v = [ 5 ; 6 ; -1 ; -4 ; 2]

||v||² = 82 => ||v|| = √82

and A At v = 820 v

and A At = [ 82 246 ; 246 738]

AAt [1;3] = 820[1;3]

=> v1 = 1/√10(1,3)^t

Then the best rank of 1 approx

= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]

= A

Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0

Hence, the minimal Approx. ||A - A1||2 = 0 .

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Complete question:

Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?

Answer:

Step-by-step explanation:

P(t) = K / (1 + (K/P0 - 1) * e^(-rt))

In this equation, P(t) is the population at time t, P0 is the initial population at time t=0, K is the carrying capacity, r is the intrinsic growth rate, and e is the base of the natural logarithm ( approximately 2.71828).

To find the carrying capacity, you can set P(t) equal to K and solve for t. This will give you the time at which the population reaches its carrying capacity.

To find the value of k, you can plug in the values for P(t), P0, and r and solve for K.

To write the solution of the equation, you can solve for t by rearranging the equation and taking the natural logarithm of both sides.

To find the population after 10 weeks, you can plug in the values for P0, K, r, and t=10 into the equation and solve for P(t).

I hope this helps! Let me know if you have any further questions.

According to the information, it can be inferred that the bees must travel a distance of 4,803,620.82 km to complete the 30 kg of honey that a hive produces.

To calculate the distance that bees register to produce honey we must perform the following operation.

1. Calculate how many kilometers are equal to the circumference of the earth with the following formula 2*pi*R. In this case we replace the R, by the radius of the earth and we will obtain the distance of the circumference of the earth.

\(2\pi r\)

\(2\pi 6,371 km = 40,030.1736\)

2. Once we have identified the circumference of the earth, we must multiply it by four to know how much distance the bee will recover to produce one kg of honey.

40,030.1736 * 4 = 160,120.694

3. Finally we must multiply the distance it takes to produce 1kg by 30 to find the distance it takes to produce 30kg of honey.

160,120,694 * 30 = 4,803,620.82

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Answer:

28

Step-by-step explanation:

20 x 1.4 = 28

An increase of 40% is the same as multiplying by the multiplier 1.4

the value of c that makes the function f(x, y) = ce^−2x−3y a joint probability density function over the given range is:
\(c = -6 / (e^−5-1)\)

To determine the value of c that makes the function f(x, y) = \(ce^−2x−3y\) a joint probability density function over the range 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, we need to make sure that the function integrates to 1 over this range. This is because the total probability over the entire range should equal 1.

Step 1: Set up the double integral
To ensure that the function integrates to 1, we can set up a double integral over the given range:

∫∫ f(x, y) dx dy = 1

Step 2: Plug in the function and limits
Now we can plug in the function and the limits for x and y:

∫₀¹ ∫₀¹ ce^−2x−3y dx dy = 1

Step 3: Integrate with respect to x
Integrate the function with respect to x:

∫₀¹ [(-c/2)e^−2x−3y]₀¹ dy = 1

Evaluate the integral at the limits:

∫₀¹ [-c/2(e^−2−3y - e^−3y)] dy = 1

Step 4: Integrate with respect to y
Now integrate with respect to y:

[-c/6(e^−5 - 1)]₀¹ = 1

Evaluate the integral at the limits:

- c/6(e^−5 - 1) = 1

Step 5: Solve for c
Finally, solve for c:

c = -6 / (e^−5 - 1)

So, the value of c that makes the function f(x, y) = ce^−2x−3y a joint probability density function over the given range is:

c = -6 / (e^−5 - 1)

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Answer:

x^2+7x+6

Step-by-step explanation:

Answer:

a = 20

b = 10

Or if in coordinate format, (20,10)

Step-by-step explanation:

\(\left \{ {{4a-3b=50} \atop {5a-2b=80}} \right.\)

Solve the system using elimination:

In elimination, you want to eliminate a term. I want to eliminate b, so what I would do is to get it the same coefficient (LCM)

Now, plug in 20 for an into any of the original equations

The solution of the system is written as a coordinate, in alphabetical order. Since the variables are a and b, you write it as (a,b).

The solution is \(\boxed{(20,10)}\)

-Chetan K

We were given that:

The iguana is 42cm at birth

It increases by 12% every week; r = 12% = 0.12

The number of weeks is represented by ''x'' & the length of the Iguana is represented by ''y''

This function is represented by the expression below:

Answer:

6.5m/sec

Step-by-step explanation:

speed = distance

time

= 1500 1 min = 60 seconds

230 3 min = 180 seconds

180 + 50

= 6.5217391304 = 230

Round off to 1 decimal place = 6.5

Answer:

2(4a+b-2)

Step-by-step explanation:

All you need to do is factor out 2 from the expression. (sorry if this is wrong)

The angle can be described by plotting a terminal side of the angle on a

graph that is rotated clockwise from the horizontal axis.

Reasons:

The angle which shares the same sine value with the required angle = \(\displaystyle \frac{5 \cdot \pi}{4}\)

Let θ represent the angle, we have;

\(\displaystyle sin(\theta) = \mathbf{ sin\left( \frac{5 \cdot \pi}{4}\right)} = -\frac{\sqrt{2} }{2}\)

Given that the sine of the angle is negative and that the sine of angles in

Quadrant I and Quadrant II are positive, we have that the location of the

angle is in Quadrant III or Quadrant IV.

Therefore, the best option for the location of the angle is; Quadrant IV

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Answer: c Quadrant IV

Step-by-step explanation: edge

Answer:

23446

76532

12839

09192

29292

Answer:

A) only figure 1 and figure 2

Step-by-step explanation:

Answer: Choice A) only figure 1 and figure 2

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

Explanation:

Let's assume that figure 2 is similar to figure 3.

If this is the case, then the horizontal portions would divide to 30/15 = 2, showing that figure 3 has sides that are twice as long compared to figure 2. But then notice that the vertical sides divide to 36/24 = 1.5, which doesn't match with the previous result of 2.

Figures 2 and 3 cannot be similar for that reason.

Also, figures 1 and 3 are not similar either. Note the horizontal portions divide to 30/10 = 3 while the vertical portions divide to 36/16 = 2.25; the results 3 and 2.25 don't match.

We eliminate answers B, C and D. The only thing left is choice A.

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

To verify choice A is true, we divide each corresponding piece like so

Each division leads to the same result of 1.5, meaning that figure 2's side lengths are 1.5 times longer than the corresponding side lengths of figure 1. So this confirms that figure 1 is similar to figure 2.

The density function of √u, where u is uniformly distributed on [0,1], is f(v) = 2√v for 0 ≤ v ≤ 1.

To find the density function of √u, where u is uniformly distributed on the interval [0,1], we can use the transformation method.

Let's denote the random variable √u as v = √u. We want to find the probability density function (PDF) of v.

First, we find the cumulative distribution function (CDF) of v:

F(v) = P(v ≤ x) = P(√u ≤ x) = P(u ≤ x²) = x², for 0 ≤ x ≤ 1.

Next, we differentiate the CDF to obtain the PDF of v:

\(\begin{equation}f(v) = \frac{d}{dv} F(v) = \frac{d}{dv} (x^2) = 2x, \quad 0 \leq x \leq 1\)

However, we need to express the PDF in terms of v, not x. Since v = √u, we can substitute x = √v into the PDF:

f(v) = 2√v, for 0 ≤ v ≤ 1.

Therefore, the density function of √u is f(v) = 2√v, for 0 ≤ v ≤ 1.

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Answer:

c

Step-by-step explanation:

the parabola crosses the x axis at (0,0) and (4,0)

Based on the price of the cell phone in November and December, the price of the cell phone in March was $39

To find the price of the cell phone in March, you need to first find the price of the cell phone in November.

The price of the cell phone in November was $25 more than the price in December:

= 25 + 53

= $78

The price in November was double the price in March so the price in March was:

= 78 / 2

= $39

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Answer:

x= 23780. 6. An airplane climbs at an angle of 18° with the ground. Find the ground distance the plane travels as it moves 2500 m through the air.' 2378m. 1. lighthouse .

Step-by-step explanation:

Answer:

Approximately 6.3405 feet

Step-by-step explanation:

Our trigonometric ratio will be tangent in this case, since we are working with the opposite and adjacent sides.

Our equation that we set up will end up being \(tan\theta=o/a\)

\(tan(26)=x/13\)

\(13tan(26)=x\)

\(13(0.4877) = x\)

\(x=6.3405\)