A circle divided into 4 parts. 2 parts are shaded.
Which fraction is equivalent to One-half? Use the diagram to help answer the question.

One-fourth
Two-fourths
Three-fourths
Four-fourths

Answer:

25/64

Step-by-step explanation:

The length of an alpha helix with 31 amino acids is approximately 50.6 angstroms.

An alpha helix is a common secondary structure in proteins where the polypeptide chain forms a tightly coiled helical structure. The length of an alpha helix can be calculated using the formula:

Length = (3.6 * number of amino acids)^(1/2)

In this case, the number of amino acids is 31. Plugging this value into the formula, we get:

Length = (3.6 * 31)^(1/2)

      = (111.6)^(1/2)

      ≈ 10.56

However, this value is in units of turns, where one turn is equal to 3.6 amino acids. To convert it to length, we need to multiply by the pitch of the helix. The pitch is the vertical distance between one complete turn of the helix.

The average pitch of an alpha helix is approximately 5.4 angstroms per turn. Multiplying the number of turns by the pitch, we get:

Length = 10.56 * 5.4

      ≈ 57.02

Therefore, the length of an alpha helix with 31 amino acids is approximately 57.02 angstroms.

The length of an alpha helix with 31 amino acids is approximately 57.02 angstroms. This calculation takes into account the formula for calculating the length of an alpha helix and the average pitch of the helix. It is important to note that this is an approximation as the actual length can vary depending on factors such as the specific amino acid sequence and the presence of any structural constraints within the protein.

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The standard error of the of the sampling distribution is 0.073.

The standard error of a proportion is given by the formula:

standard error = √[(p * (1 - p)) / n]

where p is the proportion and n is the sample size.

In this case:

p = 20% = 0.2

n = 30

Substituting the given values:

standard error = √[(0.2 * (1 - 0.2)) / 30]

standard error = 0.073

Therefore, the standard error of the sampling distribution of the proportion of employees who are allergic to pets is 0.073.

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Using Pythagoras theorem:-

H²= P²+ B²

Putting the value in equation

\( {x}^{2} = {5}^{2} + {3}^{2} \\ {x}^{2} = 25 + 9 \\ {x}^{2} = 34 \\ x = \sqrt{34} = 5.83\)

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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Answer:

D.

Step-by-step explanation:

\(\frac{\sqrt{a} }{\sqrt{b} } =\sqrt{\frac{a}{b} }\)

There is a rule like this, so answer is D.

Answer:

2

6

9

Step-by-step explanation:

Because if you pay attention to our teacher he told us how to respond it!

\(V=V_1+V_2\\\\V_1=12\cdot9\cdot15=540\\V_2=18\cdot9\cdot15=2430\\\\V=540+2430=2970\)

The indefinite integral, \(\int {sin(9x)} \, dx\) = \(\frac{-1}{9} cos(9x) + C\)

We have to find the indefinite integral,

    \(\int {sin(9x)} \, dx\)

using the substitution 9x = u.

So we need to change the variable of integration from x to u using this substitution.

9x = u ⇒ 9 dx = du

So   \(\int {sin(9x)} \, dx\) = \(\frac{1}{9} \int{sin(u) \ du\)

                          = 1/9 (- cos(u)) + C,   [ Since integral of sin(u) = -cos(u) ]

where C is the integration constant which is often put when evaluating indefinite integrals.

Now replacing u with x to get the final answer,

1/9 (- cos(u)) + C = -1/9 cos(9x) + C

Therefore,   \(\int {sin(9x)} \, dx\) = \(\frac{-1}{9} cos(9x) + C\)

The question is incomplete. Find the complete question below:

Evaluate the indefinite integral by using the given substitution to reduce the integral to standard form.   \(\int {sin(9x)} \, dx\), 9x = u.

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If Rodney traded €228.75 for $314.52 then his exchange was done on Friday, Option B is correct.

Rodney received $314.52 for €228.75, then the exchange rate he received is:

Exchange rate = dollars per euro = $314.52 / €228.75

= 1.3748

Let us compare this exchange rate with the rates given in the table to find the corresponding day:

Monday: 1/0.7102 = 1.4072

Tuesday: 1/0.7053 = 1.4165

Wednesday: 1/0.6869 = 1.4553

Thursday: 1/0.6910 = 1.4465

Friday: 1/0.7273 = 1.3766

Saturday: 1/0.7544 = 1.3253

The exchange rate received by Rodney  matches the rate on Friday

Therefore, if Rodney traded €228.75 for $314.52 then his exchange was done on Friday

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By rearranging the formula, we can express the base area A in terms of the volume V and height h as:

A = (3V) / h

To rearrange the formula to highlight the base area, we start with the given formula:

V = (1/3) × A × h

Let's isolate A, the area of the base, on one side of the equation. We can do this by multiplying both sides of the equation by 3 and dividing by h:

3V = A × h

Now, to highlight the base area A, we divide both sides of the equation by h:

A = (3V) / h

Therefore, by rearranging the formula, we can express the base area A in terms of the volume V and height h as:

A = (3V) / h

This rearranged formula allows us to calculate the base area when the volume and height of the pyramid are known.

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Answer:

The range.

Step-by-step explanation:

It is important to remember that the null hypothesis is only accepted or rejected, not proved or disproved. Therefore, this experiment should be repeated multiple times with different test subjects to get a better sense of the validity of the alternative hypothesis.

The null hypothesis to test your friend's claim is that the average time to walk to class from your dorm is 10 minutes.

This can be tested by having multiple people time themselves walking from the dorm to class and averaging the results. If the average time is greater than 10 minutes, then the null hypothesis is rejected, and the alternative hypothesis is accepted - that the average time is 7 minutes. If the average time is less than 10 minutes, then the null hypothesis is accepted, and the alternative hypothesis is rejected.

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The value of X is 13 .

the measure of RSM is 99°.

the measure of PTU is 99 °.

The angles congruent to∠ RSM are ∠STP , ∠OTU and ∠NST.

The angles congruent to ∠PTU are ∠STQ , ∠RSN and ∠MST.

When two lines do not cross at any point in a plane, they are said to be parallel. A pair of lines that never cross paths and do not have a common junction point are said to be parallel. Parallel lines are represented by the symbol "||".

Any two parallel lines can be separated by a consistent amount of perpendicular space.

Lines that run parallel to one another do not intersect. Parallel lines intersect at infinity is another way of putting it.

Pairs of angles are created when a transversal connects two parallel lines, for example:

Two lines are said to cross at a point in a plane when they do so, which is referred to as an intersection of lines.

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1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).

2. The values of r is A. x=-2 and B. x=0.

Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.

To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).

The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.

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The four Pauli matrices X, Y, Z, and I form an orthonormal basis for the space of 2×2 matrices.

To show that the four Pauli matrices X, Y, Z, and I form an orthonormal basis for the space of 2×2 matrices, we need to demonstrate two properties: linear independence and orthogonality.

1. Linear Independence:

A set of matrices is linearly independent if no matrix in the set can be written as a linear combination of the others. Let's consider the four Pauli matrices:

X = |0  1|      Y = | 0  i|      Z = | 1  0|      I = |1  0|

     |1  0|            |−i  0|            | 0 −1|            |0  1|

To show that these matrices are linearly independent, we'll assume that a linear combination of these matrices equals the zero matrix:

aX + bY + cZ + dI = |0  0|

                               |0  0|

Expanding the left-hand side, we have:

a|0  1| + b| 0  i| + c| 1  0| + d|1  0| = |0  0|

        |1  0|         |−i  0|         |0  1|

This can be rewritten as:

|0   a   c   d|   | 0|   |0|

|1   0   bi  0| * | 1| = |0|

|1  −bi  0   0|   | 0|   |0|

|d   0   0   a|   | 1|   |0|

Now, if we compute the product on the left-hand side, we get:

| c|   |0|

| a| = |0|

|-bi|   |0|

| d|   |0|

From this, we can conclude that a = b = c = d = 0. Therefore, the four Pauli matrices are linearly independent.

2. Orthogonality:

To show that the four Pauli matrices are orthogonal, we need to demonstrate that their inner products are zero. Let's calculate the inner product of each pair:

(X, X) = Tr(X†X) = Tr(|0  1| |0  1|)

                                          |1  0| |1  0|

       = Tr(|0  0|)

                |0  0|

       = 0

(Y, Y) = Tr(Y†Y) = Tr(| 0  i| | 0 −i|)

                                          |−i  0| | i  0|

       = Tr(| 0   1|)

                |−1   0|

       = 0

(Z, Z) = Tr(Z†Z) = Tr(|1  0| |1  0|)

                                          |0 −1| |0 −1|

       = Tr(|1  0|)

                |0  1|

       = 2

(I, I) = Tr(I†I) = Tr(|1  0| |1  0|)

                                          |0  1| |0  1|

       = Tr(|1  0|)

                |0  1|

       = 2

(X, Y) = Tr(X†Y) = Tr(|0  1| | 0  i|)

                                          |1  0| |−i  0|

       = Tr(|−i  0|)

                | 0  i|

       = 0

(X, Z)

= Tr(X†Z) = Tr(|0  1| |1  0|)

                                          |1  0| |0 −1|

       = Tr(|0 −1|)

                |1  0|

       = 0

(X, I) = Tr(X†I) = Tr(|0  1| |1  0|)

                                          |1  0| |0  1|

       = Tr(|0  1|)

                |1  0|

       = 0

(Y, Z) = Tr(Y†Z) = Tr(| 0  i| |1  0|)

                                          |−i  0| |0 −1|

       = Tr(| 0  i|)

                |i  0|

       = 0

(Y, I) = Tr(Y†I) = Tr(| 0  i| |1  0|)

                                          |−i  0| |0  1|

       = Tr(| 0  i|)

                |−i  0|

       = 0

(Z, I) = Tr(Z†I) = Tr(|1  0| |1  0|)

                                          |0 −1| |0  1|

       = Tr(|0  0|)

                |−1  0|

       = 0

From these calculations, we can see that the inner product of any two distinct Pauli matrices is zero, except for (Z, Z) and (I, I), which both equal 2.

Therefore, the four Pauli matrices X, Y, Z, and I form an orthonormal basis for the space of 2×2 matrices.

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Answer:

12

Step-by-step explanation:

sum means to add

8+4=12

Answer: 170

Step-by-step explanation: Like I answered before: Angle G and Angle H are consecutive angles, meaning they both add up to 180 degrees. Thus, if 10 is the value of Angle G, Angle H must be 170.

Answer:

<CDA = 170⁰

Step-by-step explanation:

<A + <D = 180⁰ { Adjacent Angles of an parallelogram are supplementary}

10⁰ + <D = 180⁰

<D = 180⁰ - 10⁰ = 170⁰

<D = x⁰ = 170⁰ = <CDA

Answer:

x=2

Step-by-step explanation:

3x+3+10x-25-2x+4=4

11x-18=4

11x=4+18

11x=22

x=22/11

x=2

Answer:

x = 2

Step-by-step explanation:

3(x + 1) + 5(2x –5)–2(x –2)= 4

First, let's distribute the numbers across the parentheses through multiplication.

3x + 3 + 10x - 25 - 2x + 4 = 4

Combine like terms.

11x - 18 = 4

Add 18 to both sides to isolate x.

11x = 22

Divide both sides by 11 to isolate x further.

x = 2

Check by plugging 2 back into the equation.

3(2 + 1) + 5(2(2) - 5) - 2(2 - 2) = 4

3(3) + 5(4 - 5) - 2(0) = 4

9 + 5(-1) - 0 = 4

9 - 5 = 4

4 = 4

Your answer is correct.

Hope this helps!

Answer:

Step-by-step explanation:

Total surface area:

So

TSA

According to the Federal Emergency Management Agency (F.E.M.A.) , In case of emergency for two people , three days , number of gallons that should be packed is 6 gallons .

During Emergency Situations as we stock food, we need to take into account the family’s unique needs and tastes.

We try to include foods that require no refrigeration, water, special preparation, or cooking are best in case of emergency .

So , by FEMA , it states that we need to store at least one gallon per person per day .

Since there are two people , so , we need 2 gallons per day ;

and for three days , it would requires \(2 \times 3 = 6\) gallons per day .

Therefore , 6 gallons of water should be packed .

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Answer:

V≈8906.42

Step-by-step explanation:

V=πr2h=π·92·35≈8906.41517

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Have a great day!

Answer:

When f(x) = 0, there will be two 'x' values. The point where the graph crosses the positive x-axis represents the point where the cannon hits the earth.

Step-by-step explanation:

The height to the top of the nth story of the building is  ( 24 + 18(n-1) ).

Height of first story of a building = 24 feet

Height of each additional story = 18 feet

Total number of stories in a building = n

The Height of first story of a building is fixed to be 24 feet and Height of each additional story is 18 feet. We first need to calculate total number of additional stories to write an equation.

The total number of additional stories =  ( total number of stories in a building - 1) = (n-1)

The height of total additional stories = 18 (n-1)

Total height of the building = (Height of first story of a building + height of total additional stories) = ( 24 + 18(n-1) ).

The height to the top of the nth story of the building is  ( 24 + 18(n-1) ).

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Answer:

51

Step-by-step explanation:

\(\frac{w-3}{7} + 2w\)

\(\frac{24-3}{7} + 2(24)\)

\(\frac{21}{7} + 48\)

\(3 + 48\)

51

Answer:

51

Step-by-step explanation:

24-3=21; 2x24=48; 21/7+48= 51

I Hope this helps! :D

Answer:

Negative

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

We see that every time our x-value increases, our y-value decreases. Therefore, we know we would have a negative slope.

The coordinates of the vertices of the preimage triangle = (4, 1), (6,1) and (6, -6).

Given the figure of the image triangle.

The coordinates of the image triangle are (-4, 1) , (-6,1) and (-6, -6).

We are asked to find the coordinates of the preimage triangle.

The preimage triangle was reflected over the y-axis .

The image triangle is lying on the 2nd and 3rd quadrants.

So the preimage triangle will lie on the 1st and 4th quadrants.

Then the coordinate (-4,1) will be the image of (4,1).

(-6, 1) will be the image of (6,1) and (-6,-6) will be the image of (6,-6).

Hence the coordinates of the vertices of the preimage triangle = (4, 1), (6,1) and (6, -6).

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Step-by-step explanation:

x = number of games played

c = total cost of game session

x = (c - 5)/1.25

we need to deduct the R 5 entrance fee from the total price (as this has to be paid, even if he did not pay a single game in there).

and for the remaining amount we check how often the price of 1 game fits into this renaming amount. and then we know the number of games he played.

in our specific situation c = 26.25

x = (26.25 - 5)/1.25 = 21.25/1.25 = 17

Melvin played 17 games.

Based on the survey, the estimated proportion (p) of customers planning to purchase Ultra-HD television sets or game consoles in the next five years is approximately 0.1 or 10%.

The estimate of p, the proportion of customers who plan to purchase Ultra-HD television sets or game consoles in the next five years, can be calculated by dividing the number of customers who plan to purchase by the total number of sampled customers.

In this case, the survey found that 50 out of 500 sampled customers plan to purchase. Therefore, the estimate of p is 50/500, which simplifies to 0.1 or 10%.

Hence, the estimate of p, based on this survey, is 0.1 or 10%.

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