5.2.PS-14
Find 3 ratios that are equivalent to the given ratio.
10:16

Two point charges, q1 = 3.99 nC located at x = 0.205 m and q2 = 5.01 nC at x = -0.302 m, are placed on the x-axis. The electric field and direction at a given point can be calculated using the principle of superposition.

The electric field at a point due to a point charge is given by Coulomb's law, E = kq/r^2, where E is the electric field, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the point where the electric field is being measured. To calculate the net electric field at a point due to multiple charges, we use the principle of superposition, which states that the total electric field at a point is the vector sum of the electric fields due to each individual charge.

In this case, we have two charges, q1 = 3.99 nC and q2 = 5.01 nC. The electric field at a point P on the x-axis, due to q1, can be calculated as E1 = kq1/r1^2, where r1 is the distance between q1 and point P. Similarly, the electric field at point P due to q2 can be calculated as E2 = kq2/r2^2, where r2 is the distance between q2 and point P. To find the net electric field at point P, we add the electric fields vectorially, E_net = E1 + E2.

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Answer:

\(\huge\boxed{\sf x = 30}\)

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

According to the statement,

4x - 16 + 2x + 16 = 180

4x + 2x - 16 + 16 = 180

6x = 180

x = 180/6

\(\rule[225]{225}{2}\)

Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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The given partial differential equation is given by; Uz(x, t) + 2xut(x, t) = 2x

The Laplace transform of Uz(x, t) + 2xut(x, t) is given as follows; L[Uz(x,t)] + 2x L[ut(x,t)] = L[2x]sU(x,s) - u(x,0) + 2x[sU(x,s)-u(x,0)] = 2x/sU(x,s) + 2x/s^2 - 1(2x/s)U(x,s) = 2x/s^2 - 1 + sU(x, s)U(x, s) = [2x/s^2 - 1]/[2x/s - s]U(x, s) = s(2x/s^2 - 1)/(2x - s^2) = s/(2x - s^2) - 1/(2(s^2 - 2x))

By using the inverse Laplace transform, we have; u(x, t) = [1/s] * e^(s^2t/2x) - (1/2)sinh(t sqrt(2x)) / sqrt(2x)

Thus, the solution to the given partial differential equation is given as follows; u(x, t) = [1/s] * e^(s^2t/2x) - (1/2)sinh(t sqrt(2x)) / sqrt(2x)Where, u(x,0) = 1 and u(0,t) = 1.

The integral transform known as the Laplace transform is particularly useful for solving ordinary differential equations that are linear. It finds extremely wide applications in var-ious areas of physical science, electrical designing, control engi-neering, optics, math and sign handling.

The mathematician and astronomer Pierre-Simon, marquis de Laplace, gave the Laplace transform its name because he used a similar transform in his work on probability theory.

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Answer:

I think its Your Values, but try and a get a second opinion

Answer:

\(9 - x = 1\)

\(9-x-9=1-9\)

\(-x=-8\)

\(\cfrac{-x}{-1}=\cfrac{-8}{-1}\)

\(\boxed{x=8}\)

\(-252 = 21k\)

\(21k=-252\)

\(\cfrac{21k}{21}=\cfrac{-252}{21}\)

\(\boxed{k=-12}\)

Answer:

x= -6   k=-12

Step-by-step explanation:

15-9 is 6.   9+6=15 9-(-6)=15 because when two negatives are together they make a positive. (--)=+      K=-21 because -252/21 is -12.

A) No, a sample size of 30 or more is not required to obtain a normally distributed sampling distribution of mean loading weights in this problem. According to the Central Limit Theorem, when the sample size is sufficiently large (typically around 30 or more), the sampling distribution of the mean tends to be approximately normally distributed, regardless of the shape of the population distribution. In this case, since the population standard deviation is known (σ = 3 lbs), the sampling distribution of the mean will be normally distributed even with smaller sample sizes.

B) To calculate the probability that 35 boxes chosen at random will have a mean weight less than 44.55 lbs of apples, we need to standardize the mean weight using the Z-score and then find the corresponding probability from the standard normal distribution.

The Z-score is calculated using the formula:

Z = (X - µ) / (σ / √n)

X = 44.55 lbs (mean weight)

µ = 45 lbs (population mean)

σ = 3 lbs (population standard deviation)

n = 35 (sample size)

Substituting the values into the formula:

Z = (44.55 - 45) / (3 / √35)

Calculating Z, we can then find the corresponding probability using a standard normal distribution table or a calculator.

A) The Central Limit Theorem states that with a sufficiently large sample size, the sampling distribution of the mean tends to be normally distributed, regardless of the population distribution. However, in this case, since the population standard deviation is known, the sampling distribution of the mean will be normally distributed even with smaller sample sizes.

B) To calculate the probability, we standardize the mean weight using the Z-score formula and then find the corresponding probability from the standard normal distribution. This allows us to determine the probability of observing a mean weight less than 44.55 lbs of apples.

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Answer:

1/6 +√6 = 2.6162

Step-by-step explanation:

Answer:

B:2.6161564...

Step-by-step explanation:

edge2020

Answer:

a = 20

Step-by-step explanation:

The mean is calculated as

mean = \(\frac{sum}{count}\)

          = \(\frac{25+28+a+30+32}{5}\)  = \(\frac{115+a}{5}\)

Then

\(\frac{115+a}{5}\) = 27 ( multiply both sides by 5 to clear the fraction )

115 + a = 135 ( subtract 115 from both sides )

a = 20

the drop-down boxes to complete the steps of the proof =

1. Tangent Half-angle identity

2. 1 + cos x

3. 1 - cos x

In mathematics, trigonometric functions are real functions that relate the angles of a right triangle to the ratio of the lengths of its two sides. They are widely used in all geometry-related sciences such as navigation, solid mechanics, celestial mechanics, and geodesy.

Trigonometric periodic functions repeat at predictable intervals, but are not a direct result of trigonometric functions. It can be used to accurately predict values ​​outside the original range. Common non-trigonometric functions include: Four corners. triangle.

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The question is incomplete. Please read below to find the missing content.

This proof shows the first five steps for verifying cot^2 (x/2)= cos x+1/cos c-1 use the drop-down boxes to complete the steps of the proof

The correct option is B.

Thus, 68% percentage of the balls weigh within one standard deviation of the mean.

The Empirical Rule indicates that 99.7% of data that are observed to have a normal distribution fall within 3 standard deviations of the mean. According to this formula, 68 percent of the data are within one standard deviation, 95 percent are within two standard deviations, and 99.7 percent are within three standard deviations of the mean.

Because approximately 68% of the data falls within a standard deviation of the mean, according to the empirical rule, 68% of the balls' weights fall within that range.

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I understand that the question you are looking for is:

The weights of tennis balls are normally distributed, with the mean being 5.15 ounces and the standard deviation being 0.10. what percentage of the balls weigh within one standard deviation of the mean

A. 50%

B. 68%

C. 95%

D. 99.7%

The answer is yes, (x + 6) is a possible length of a rectangle with area x² + x − 30.

To determine whether (x + 6) is a possible length of a rectangle with area x^² + x − 30, we can use an area model to visualize the situation.

First, we need to find the width of the rectangle.

The area of a rectangle is given by the formula A = lw,

where A is the area, l is the length, and w is the width.

We are given that the area is x² + x − 30, so we can set this equal to lw and solve for w:

x² + x − 30 = (x + 6)w

w = (x² + x − 30)/(x + 6)

The length of a rectangle must be greater than or equal to its width, so we need to check whether (x + 6) is greater than or equal to (x² + x − 30)/(x + 6). This simplifies to:

(x + 6) ≥ x² + x − 30

Expanding the left side and simplifying, we get:

x² + 12x + 36 ≥ x² + x − 30

11x ≥ -66

x ≥ -6

Since x must be a positive number (since we are dealing with lengths), we can conclude that (x + 6) is the possible length of the rectangle. Therefore, the answer is yes, (x + 6) is a possible length of a rectangle with an area x² + x − 30.

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Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So you need to consider 4 different cases (2 absolute value expressions with 2 possible cases each).

(i) Suppose 2x + 3 < 0 and x - 2 < 0. The first inequality says x < -3/2 and the second says x < 2, so ultimately x < -3/2. Then

|2x + 3| + |x - 2| = 6x

-(2x + 3) - (x - 2) = 6x

-2x - 3 - x + 2 = 6x

-3x - 1 = 6x

9x = -1

x = -1/9

But -1/9 is not smaller than -3/2, so this case provides no valid solution.

(ii) Suppose 2x + 3 ≥ 0 and x - 2 < 0. Then x ≥ -3/2 and x < 2, or -3/2 ≤ x < 2. Under this condition,

|2x + 3| + |x - 2| = 6x

(2x + 3) - (x - 2) = 6x

2x + 3 - x + 2 = 6x

x + 5 = 6x

5x = 5

x = 1

This solution is valid because it does fall in the interval -3/2 ≤ x < 2.

(iii) Suppose 2x + 3 < 0 and x - 2 ≥ 0. Then x < -3/2 or x ≥ 2. So

|2x + 3| + |x - 2| = 6x

-(2x + 3) + (x - 2) = 6x

-2x - 3 + x - 2 = 6x

-x - 5 = 6x

7x = -5

x = -5/7

This isn't a valid solution, because neither -5/7 < -3/2 nor -5/7 ≥ 2 are true.

(iv) Suppose 2x + 3 ≥ 0 and x - 2 ≥ 0. Then x ≥ -3/2 and x ≥ 2, or simply x ≥ 2.

|2x + 3| + |x - 2| = 6x

(2x + 3) + (x - 2) = 6x

2x + 3 + x - 2 = 6x

3x + 1 = 6x

3x = 1

x = 1/3

This is yet another invalid solution since 1/3 is smaller than 2.

So there is one solution at x = 1.

The correct option is b expressed as compound rates of interest. Geometric mean returns are calculated by taking the nth root of the product of (1 + holding period return) for each period, where n is the number of periods.

The result is expressed as a compound rate of return, which reflects the compounding effect over time. Unlike arithmetic mean returns, which are simple averages of holding period returns, geometric mean returns give more weight to the returns in earlier periods and less weight to the returns in later periods. This makes geometric mean returns more applicable when no specific time interval is considered to be any more important than another.

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a. To find the 30th percentile for the standard normal distribution, we first need to locate the z-score that corresponds to this percentile. We can use a standard normal distribution table or a calculator to find this value. From the table, we can see that the z-score that corresponds to the 30th percentile is approximately -0.524. Therefore, the 30th percentile for the standard normal distribution is z = -0.524.

b. To find the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5, we can use the formula for transforming a standard normal distribution to a normal distribution with a given mean and standard deviation. This formula is:
z = (x - μ) / σ
where z is the standard normal score, x is the raw score, μ is the mean, and σ is the standard deviation.
To find the 30th percentile for this distribution, we first need to find the corresponding z-score using the formula above:
-0.524 = (x - 10) / 1.5
Multiplying both sides by 1.5, we get:
-0.786 = x - 10
Adding 10 to both sides, we get:
x = 9.214
Therefore, the 30th percentile for a normal distribution with mean 10 and standard deviation 1.5 is x = 9.214. This means that 30% of the observations in this distribution are below 9.214.

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An inequality that represents the possible dimensions for the garden is ab < 80. And the three different sets of allowable dimensions for the garden are {5, 10}, {10, 5} and {6, 6} and the area  50 square feet,  50 square feet, 36 square feet respectively.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

The maximum area that is available for a rectangular garden is 80 square feet.

Let a and b are the length and width of the rectangular garden.

And A be the area.

(a).

So, A < 80

That means, ab < 80.

(b).

To find the dimension of the rectangle:

We find the numbers whose product is less than 80.

Let the three number sets are,

{5, 10}, {10, 5} and {6, 6}.

(c).

So, the area of the rectangles are:

5 x 10 = 50 square feet,

10 x 5 = 50 square feet,

And 6 x 6 = 36 square feet.

Therefore, the inequality is ab < 80, three number sets are {5, 10}, {10, 5} and {6, 6} and the area  50 square feet,  50 square feet, 36 square feet respectively.

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Answer:

  Eva used a side dimension instead of the height.

Step-by-step explanation:

The base needs to be multiplied by the height, then the result needs to be divided by 2. Eva's mistake is using a side dimension instead of the height. Her approach only works for a right triangle.

Eva multiplied the base by the side height, not the actual height.

Step-by-step explanation:

The area of a triangle is b×h×½, or b×h÷2. Eva multiplied the length times one side, as it says in the problem. The actual height of the triangle we don't know, but we know that Eva multiplied the base, 7.8 cm, by the wrong height.

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The probability that at least three individuals must be typed to obtain the desired type is 1/2 and the probability that the third is of type O is 3/4

Probability is the event of occurances. Many of the events will not be predicted with the total certainty. Four individuals have responded to a request by a blood bank for blood donations. None of them has donated before, so their blood types are unknown.

Suppose only type O is desired and only one of the four actually has this type, and if the potential donors are selected in random order for typing,

The probability that the same as the event that the first and second are not of type O is 2/4 = 1/2

So, the probability that at least three individuals must be typed to obtain the desired type is 1/2

The probability that is, first is not, second is not, and the third is 3/4

So, the  probability that the third is of type O is 3/4

Therefore, the probability that at least three individuals must be typed to obtain the desired type is 1/2 and the probability that the third is of type O is 3/4

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Step-by-step explanation:

1. 3 3/5 × (-8 1/3)

2. 18/5 × -25/3

3. 18/5 × -25/3 = -90/3

Ans. -30

Answer: 1

Step-by-step explanation:

For every three its going down, its going three to the left.

So it's going -3/-3

            OR

-1/-1 = 1/1 = 1

In a Cartesian coordinate system for a three-dimensional space, let the sphere S be represented by the equation:

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

where (a, b, c) are the coordinates of the center of the sphere, and r is the radius.

Let the plane P be represented by the equation:

Ax + By + Cz + D = 0

where (A, B, C) is the normal vector to the plane.

Since the line d is parallel to P and passes through the origin, it can be represented by the equation:

lx + my + nz = 0

where (l, m, n) is a vector parallel to the plane P.

To find the intersection points of the sphere S and the line d, we can substitute the equation of the line into the equation of the sphere, which gives us a quadratic equation in t:

(lt - a)^2 + (mt - b)^2 + (nt - c)^2 = r^2

Expanding this equation and collecting terms, we get:

(l^2 + m^2 + n^2) t^2 - 2(al + bm + cn) t + (a^2 + b^2 + c^2 - r^2) = 0

Since the line d passes through the origin, we have:

l(0 - a) + m(0 - b) + n(0 - c) = 0

which simplifies to:

al + bm + cn = 0

Therefore, the quadratic equation reduces to:

(l^2 + m^2 + n^2) t^2 + (a^2 + b^2 + c^2 - r^2) = 0

This equation has two solutions for t, which correspond to the two intersection points of the line d and the sphere S:

t1 = -(a^2 + b^2 + c^2 - r^2) / (l^2 + m^2 + n^2)

t2 = -t1

The coordinates of the intersection points can be obtained by substituting these values of t into the equation of the line d:

A = lt1, B = mt1, C = nt1

and

D = lt2, E = mt2, F = nt2

To find the distance between A and B, we can use the distance formula:

AB = sqrt((A - D)^2 + (B - E)^2 + (C - F)^2)

To maximize this distance, we can differentiate the distance formula with respect to t1 and set the derivative equal to zero:

d/dt1 (AB)^2 = 2(A - D)l + 2(B - E)m + 2(C - F)n = 0

This equation represents the condition that the direction vector (A - D, B - E, C - F) is orthogonal to the line d. Therefore, the vector (A - D, B - E, C - F) is parallel to the normal vector (l, m, n) of the plane P.

Using this condition, we can find the values of t1 and t2 that correspond to the maximum distance AB. Then we can substitute these values into the distance formula to find the maximum length of AB.

the angle of rotation is 180°. The parallelogram in quadrant I is the image of the parallelogram in quadrant II after a counterclockwise rotation about the origin.

The angle of rotation is 180°.

The parallelogram in quadrant I is the image of the parallelogram in quadrant II after a counterclockwise rotation about the origin. This means that the parallelogram in quadrant I has been rotated 180° (a full circle) relative to the parallelogram in quadrant II. Thus, the angle of rotation is 180°.

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Answer:

61

Step-by-step explanation:

Answer:

2/7 I Don't know the other one

here you go, hope that helps some

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

\(\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6\)

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

If you didn't know what the question was, here is the translation:

The ethanol density is 0.79 gr / ml. Calculate the mass of ethanol 25.7 ml of ethanol.

Answer: B. statistic

Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.

The first law of thermodynamics is a fundamental principle in physics that states energy cannot be created or destroyed, only converted from one form to another. It can be expressed in terms of heat and work through the equation:

ΔU = q - w

where ΔU represents the change in internal energy of a system, q represents the heat added to the system, and w represents the work done on or by the system.

Now, let's address when the quantities q and w would be negative numbers.

1) When q is negative: This occurs when heat is removed from the system, indicating an energy loss. For example, when a substance is cooled, heat is extracted from it, resulting in a negative value for q.

2) When w is negative: This occurs when work is done on the system, decreasing its energy. For instance, when compressing a gas, work is done on it, leading to a negative value for w.

In both cases, the negative sign indicates a reduction in energy or the transfer of energy from the system to its surroundings.

In summary, the first law of thermodynamics can be expressed as ΔU = q - w, and q and w can be negative numbers when energy is lost from the system through the removal of heat or when work is done on the system.

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