Rosalind Franklin played an important role in the discovery of DNA's structure. Her data was used to support Watson's and Crick's hypothesis that DNA had the structure of a double helix. Even with this data and support from other scientists, the structure of DNA was not a widely accepted theory. Select all of the reasons why was their discovery was not considered a theory at the time of the paper's publication? 1. A newly released hypothesis must wait a least a year before the scientific community can vote for it to become a theory. 2. Theories are never developed by three people. 3. Theories need to undergo peer-review. 4.The hypothesis wasn't supported by their own data.

The given statement "If f(x) has roots over R, then f(x) is reducible over R" is a True statement.

The degree of f(x) is greater than one and it has roots over R, then we need to know about the basic theorem which is "If f(x) is a polynomial over a field K and f(a) = 0, then (x-a) divides f(x)".Hence, we can say that "If f(x) has degree greater than one and it has a root over a field R, then f(x) is reducible over R."

Hence, the given statement "If f(x) has roots over R, then f(x) is reducible over R" is a True statement.

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Answer:

mDE⌢=129°, and mBC⌢=65°. Find m∠A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

If x - 2 is a factor it means that the whole equation will return 0 when x = 2. That's because x - 2 will go to 0. It doesn't matter what the rest of the equation factors into. The x - 2 is enough to make it all go to 0.

Equation

y = x^4 - 3x^3 +2x - 8

Substitute and Solve

x = 2

y = 2^4 - 3*2^3 + 2(3) - 8

y = 16 - 24 + 6 - 8

y = - 8 - 2

y = - 10

Conclusion

x - 2 is not a factor of this equation.

Answer:

Simplifying

an = 8n + -7

Reorder the terms:

an = -7 + 8n

Solving

an = -7 + 8n

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Divide each side by 'n'.

a = -7n-1 + 8

Simplifying

a = -7n-1 + 8

Reorder the terms:

a = 8 + -7n-1

The functions are differentiable at all the z-plane is f'(z) = 2x when function is f(z) = x² + y² + i2xy.

Given that,

The function is f(z) = x² + y² + i2xy

We have to determine if the functions are differentiable throughout the z-plane or only a portion of it, and then we must assess any derivatives that may exist.

We know that,

Take the function,

f(z) = x² + y² + i2xy

f(x + iy)  = x² + y² + i2xy

f(x + iy)  = u + iv

We can say, u =x² + y², v= 2xy

Differentiate u with respect to x

uₓ = 2x

Differentiate v with respect to y

[tex]v_y[/tex] = 2x

So,

uₓ = 2x = [tex]v_y[/tex]

uₓ = [tex]v_y[/tex]

Differentiate u with respect to y

[tex]u_y[/tex] = 2y

Differentiate v with respect to x

[tex]v_x[/tex] = 2y

So,

[tex]u_y[/tex] = -[tex]v_x[/tex] = -2y ⇒ y = 0

Let D = {z : x | x, y∈R}

f is differentiable on D.

The derivative is f'(z) = [tex]u_x + iv_x[/tex] = 2x

Therefore, the functions are differentiable at all the z-plane is f'(z) = 2x.

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Let the each angle be x , 2x and 3x.

→ x + 2x + 3x = 5600

→ 8x = 5600

→ x = 5600/8

→ x = 700

the value of x is Rs.700.

Now, 2x = 2×700 = 1400

, 3x = 3×700 = 2100

Each one will get Rs.700 , Rs.1400 and Rs. 2100.

With 90% confidence, the lower confidence limit (LCL) for the mean winnings is approximately $34,955.09 and the upper confidence limit (UCL) is approximately $40,485.31.

The mean winnings for all the show's players with a 90% confidence level, we can use the formula for a confidence interval for the population mean.

The sample of winnings:

30,692, 43,231, 48,269, 28,592, 28,453, 36,309, 45,318, 36,362, 42,871, 39,592, 35,456, 40,775, 36,466, 36,287, 38,956

We can calculate the sample mean (x(bar)) and the sample standard deviation (s) from the given data.

Sample mean

(x(bar)) = (30,692 + 43,231 + 48,269 + 28,592 + 28,453 + 36,309 + 45,318 + 36,362 + 42,871 + 39,592 + 35,456 + 40,775 + 36,466 + 36,287 + 38,956) / 15

≈ 37,720.2

Sample standard deviation

s = √[((30,692 - 37,720.2)² + (43,231 - 37,720.2)² + ... + (38,956 - 37,720.2)²) / (15 - 1)]

≈ 6,522.45

The standard error (SE) of the mean is calculated as SE = s /√n, where n is the sample size.

Standard error (SE) = 6,522.45 / √15 ≈ 1,682.12

To calculate the confidence interval, we need to find the critical value corresponding to a 90% confidence level. For a 90% confidence level, the critical value is approximately 1.645.

Margin of error = Critical value × Standard error

= 1.645 × 1,682.12

≈ 2,765.11

Lower confidence limit (LCL) = Sample mean - Margin of error

= 37,720.2 - 2,765.11

≈ 34,955.09

Upper confidence limit (UCL) = Sample mean + Margin of error

= 37,720.2 + 2,765.11

≈ 40,485.31

Therefore, with 90% confidence, the lower confidence limit (LCL) for the mean winnings is approximately $34,955.09 and the upper confidence limit (UCL) is approximately $40,485.31.

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The question is incomplete the complete question is :

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 90% confidence the mean winning's for all the show's players. 30692 43231 48269 28592 28453 36309 45318 36362 42871 39592 35456 40775 36466 36287 38956 Lower confidence level (LCL) = ? Upper confidence level (UCL) = ?

The solution to a system of the type x2=A+f(t) must be 22 and is given in:

(a) Eigenvalues: λ = -2, 11. Eigenvectors: (1, 1), (-1, 1).

(b) Particular solution: [tex]\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)[/tex]

(c) General solution: [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex]

(d) Second linearly independent solution: x = 22t - 23.

Here is the explanation :

(a) The system is of the form x' = Ax + f(t), where A is a 2x2 matrix and f(t) is a 2x1 vector-valued function. The characteristic equation of A is |A - λI| = 0, which in this case gives us λ² + λ - 22 = 0. The eigenvalues are λ = -2 and λ = 11. The eigenvectors corresponding to these eigenvalues are (1, 1) and (-1, 1), respectively.

(b) The particular solution to the system in (a) is given by [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + f(t)[/tex].

The function f(t) must satisfy the initial conditions x(0) = (1, -6) and x'(0) = (-2, 1). Using these initial conditions, we can find [tex]c_1[/tex] and [tex]c_2[/tex] as follows:

[tex]\begin{equation}c_1 = \frac{1 - 6}{-2 - 11} = -\frac{1}{13}[/tex]

[tex]\begin{equation}c_2 = \frac{-2 + 1}{-2 - 11} = \frac{1}{13}[/tex]

Therefore, the particular solution to the system is

[tex]\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)[/tex]

(c) The general solution to the system is given by [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + u[/tex], where u is a particular solution to the system. In this case, we have already found [tex]\begin{equation}u = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex].

Therefore, the general solution to the system is [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex].

(d) The system has a repeated eigenvalue of -1, and Fire is one solution to the system. The second linearly independent solution can be found using the method of variation of parameters. In this method, we assume that the second solution is of the form x = vt + w, where v and w are constants to be determined. Substituting this into the system gives us the following equations:

-2v + w = -21

v + 11w = -1

Solving these equations gives us v = 22 and w = -23. Therefore, the second linearly independent solution is x = 22t - 23.

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Answer:

Step-by-step explanation:

Answer:

Answer is linked

Step-by-step explanation:

The equation is in slope-intercept form, which is y = mx + b.

To graph the line, first we have to find the slope, m, and the y- intercept, b.

So, the slope is 2 and the y- intercept is 1.

We can graph this, beginning with the y- intercept, 1. The y- intercept is always on the y axis, so the (x) value will always be zero.

Plot a point at (0, 1).

Next, add more points using the slope. The slope is 2, or [tex]\frac{2}{1}[/tex]. Start at the point we have made on the y axis. The slope equals the [tex]\frac{rise}{run}[/tex]. We can rise 2 units, then run one more unit to the right. If the slope is negative, the run goes to the left. However, in this case, the slope is positive, to it slants to the right.

We end on point (1, 3). We can continue this path infinitely, some other points on the graph could be (2, 5), (3, 7), (4, 9) and (5, 11).

Connect these points to make a line.

The finished line is linked below as well.

I hope this helps :] Good luck ^^

Answer:

28.14

Step-by-step explanation:

Answer:

2/12

Step-by-step explanation:

since there are six sides, rolling twice will give you a total of 12 possibilities, each time, you have 1 chance out of 6 each time to roll 3

1/6 + 1/6 = 2/12

If you want to, or need to reduce 2/12, divide both the numerator and denominator by two, and you will get 1/6 again.

Answer:

J

Step-by-step explanation:

Given

5(y + 2) + 4 ← note 4 is outside the parenthesis

Each term in the parenthesis is multiplied by 5, that is

5 • y + 5 • 2 + 4 → J

The solution to f(x) = g(x) can be found by looking at the point where the graphs of the two functions intersect.

The given functions are: f(x) = 73x - 3g(x) = 2x - 4. To find the solution, we need to set f(x) = g(x) and solve for x.73x - 3 = 2x - 4. Simplifying the above expression, we get: 71x = 1x = 1/71.Therefore, the solution to f(x) = g(x) is x = 1/71. Now let's look at the given graph: From the graph, we can see that the solution x = 1/71 is not listed as one of the answer choices.

However, we can see that the point of intersection of the two lines is at approximately x = 0.02. Therefore, the correct answers are: 0 (since x = 0.02 is rounded to the nearest whole number, which is 0) and2 (since the point of intersection has an x-coordinate of approximately 0.02, which is between 0 and 3).Therefore, the correct answers are:0 and 2.

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Answer:

1. (1/4 x 5/4 x 5/4) = 25/64

2. (2/4 x 2/4 x 6/4) = 3/8

3. (1/4 x 1/4 x 4/2) 1/8

Step-by-step explanation:

Thank me later.

The variance is the average squared deviation of each value from the mean. It calculates how far each value in a group is from the mean, and then it squares the result of each of those calculations. Finally, it averages the sum of the squares to produce a figure that represents how varied the data is from the mean.

The variance formula is as follows:

Var(X) = (Σ (Xi - μ)^2) / (n - 1)

Where, X is a random variable representing the group data, μ is the mean of the group data, Xi is each value in the group data, Σ is the sum of all Xi values, and n is the number of values in the group data.

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According to given information, the probability that a contract will last between 15 and 35 weeks is `0.905`.

To compute the probability that a contract will last between 15 and 35 weeks, we must utilize the standard deviation for the normal distribution.

To solve for the probability of a normal distribution, we use the formula `z = (x - μ) / σ`, where `x` is the value we are looking for, `μ` is the mean, and `σ` is the standard deviation.

We can compute the standard deviation using the variance, which is the square of the standard deviation, which is `σ^2`.

To begin, we first find the standard deviation.  `σ = sqrt(36) = 6`.

Next, we will calculate the `z-scores` for 15 and 35.

[tex]`z1 = (15 - 25) / 6 = -10 / 6 = -1.67`[/tex]

and [tex]`z2 = (35 - 25) / 6 = 10 / 6 = 1.67`[/tex].

Now we can use the `Z-table` to find the probabilities that correspond to `z1` and `z2`. We can see that the probability of `z1` is `0.0475` and the probability of `z2` is `0.9525`.

Finally, to obtain the probability that a contract will last between 15 and 35 weeks, we must subtract the probabilities corresponding to `z1` from `z2`.

[tex]`P(15 ≤ X ≤ 35) = P(Z ≤ 1.67) − P(Z ≤ −1.67) = 0.9525 − 0.0475 = 0.905`[/tex].

Therefore, the probability that a contract will last between 15 and 35 weeks is `0.905`.

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The digit replacements for x in the number 95,768,24x that make it divisible by  4 is either 0, 4, or 8.

To evaluate the digit replacements for x in the number 95,768,24x that make it divisible by 4, we need to determine the possible values for x that satisfy this condition.

For a number to be divisible by 4, the last two digits must be divisible by 4. Therefore, we need to find the values of x that make the number 24x divisible by 4.

The possible values for x that make 24x divisible by 4 are 0, 4, 8. This is because any multiple of 4 ends in 0, 4, 8 when the tens and units place are considered.

Therefore, the possible digit replacements for x are 0, 4, and 8. These values will make the number 95,768,24x divisible by 4.

Hence, the digit that will make the first number divisible by 4 is either 0, 4, or 8.

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Answer:

Value of X=51.43

Step-by-step explanation:

the measure of the central angle of a regular heptagon is about 51.43 degrees which = X

if this helped please leave a rating and mark me brainliest

Answer:

158.35

Step-by-step explanation:

Answer:

Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

Step-by-step explanation:

(0, -6) is the y-intercept, as x = 0.  Moving up 2, and right 1 represents the slope of the function. Going up is positive in the y direction, and going right is positive in the x direction.  

Drawing a line through the 2 points gives a sneak peak on the full function to be graphed

PRO GAMER MOVE: function is y = 2x - 6

Answer:

It's A. (Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.)

Answer:

72.8%

Step-by-step explanation:

Percentage residual value = (residual value / worth of the car) x 100

(44,999 / 61,815) X 100 = 72.8%

Answer:

volume of cylinder=pi×r²×h

volume of cylinder =3.14×(11ft)²×10ft

volume of cylinder=3799.4ft³

Answer:

6 in. per triangle & 24 in total (white squares only)

Step-by-step explanation:

 So, one side is 12 inches and each side is made up of one blue and one white. With this you can just divide each side by 2, getting 6. There are 4 sides so,

4 sides X 6 in. per each square= 24

Therefore, she used 24 in. in total and 6 for each triangle.

Hoped this helped!

Answer:

option 1

Step-by-step explanation:

if it goes up 6 then it means plus 6

Answer:

20 people chosen to March

Step-by-step explanation:

The sample can be explained as a random subset of the population. It is a given number of draws or selection made usually at Random from the entire or larger population set. The sample is usually smaller Than the population and if done randomly will be representative of the population set. The entire spectator attending the baseball game is the population of interest while the 20 selected from the entire pool to March in the victory parade is the sample data obtained from the population set.

P(BA) is the conditional probability of event B given that event A has occurred approximately 0.04

P(BA), we need to know the individual probabilities of events A and B, as well as the probability of the intersection of events A and B.

P(B AND A) = 0.04

P(A) = 0.18

We can use the formula for the intersection of two events:

P(BA) = P(B AND A) = P(A) × P(B | A)

P(B | A) is the conditional probability of event B given that event A has occurred.

To calculate P(B | A), we can rearrange the formula as:

P(B | A) = P(B AND A) / P(A)

Putting in the given values:

P(B | A) = 0.04 / 0.18 ≈ 0.2222

Now we can calculate P(BA) using the formula:

P(BA) = P(A) × P(B | A)

= 0.18 × 0.2222

≈ 0.04

Therefore, P(BA) is approximately 0.04.

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You dont deserve answers if ur gonna do that to other people.

The second derivative of the function r(t) = (118,5t, cos t),

is determine as r''(t) = (0, 0, - cos t).

The second derivative of the function is calculated by applying the following method.

The given function;

r(t) = (118, 5t, cos t)

The first derivative of the function is calculated as;

derivative of 118 = 0

derivative of 5t = 5

derivative of cos t = - sin t

Add the individual derivatives together;

r'(t) = (0, 5, - sin t)

The second derivative of the function is calculated as follows;

derivative of 0 = 0

derivative of 5 = 0

derivative of - sin t = - cos t

Adding all the derivatives together;

r''(t) = (0, 0, - cos t)

Thus, the second derivative of the function is determine as  r''(t) = (0, 0, - cos t).

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Answer:

C

Step-by-step explanation:

Plug in the points to see which equation is true