a normal distribution has a mean of 61 and a standard deviation of 14. what is the median? (enter an exact number as an integer, fraction, or decimal.)

Answer:

integer

Step-by-step explanation:

the slope looks like it's 4/1 when simplified it's 4. (integer)

Answer:

The slope is the integer 4

Step-by-step explanation:

take the points (-2, -9) (-1, -5) and put them in the formula  y2 - y1 over x2 - x1 and you get m = 4

The surface area (S) can be calculated as follows:

S = 2π ∫[a, b] y(x) √(1 + (dy/dx)^2) dx

  = 2π ∫[0, 10] 2e(et - x) √(1 + (2e(et - x) (et - 1))^2) dx

To find the surface area generated by rotating the curve x = et − t, y = 4et/2 about the y-axis, we can use the formula for the surface area of revolution:

S = 2π ∫[a, b] y(x) √(1 + (dy/dx)^2) dx

In this case, we want to find the surface area between t = 0 and t = 10.

To express the curve in terms of x, we need to solve the equation x = et − t for t in terms of x:

x = et − t

Rearranging the equation, we get:

t = et − x

Substituting this value of t into the equation y = 4et/2, we have:

y = 4e(et - x)/2

  = 2e(et - x)

Now, let's calculate dy/dx:

dy/dx = d(2e(et - x))/dx

      = 2e(et - x) d(et - x)/dx

      = 2e(et - x) (et - 1)

Now, we can calculate the integrand:

Integrand = y(x) √(1 + (dy/dx)^2)

        = 2e(et - x) √(1 + (2e(et - x) (et - 1))^2)

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By solving a quadratic equation, it can be calculated that-

x = 2 or x = \(\frac{1}{2}\) and y = -3

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A two degree equation is known as quadratic equation.

Here, a quadratic equation needs to be solved

The graph of the curve y=2x²-5x -1 and a straight line PQ where drawn, to solve the equation 2x²-5x+2=0

2x²-5x -1 - y =  2x²-5x+2

-1-y = 2

y = -1-2

y = -3

Now, the quadratic equation is

2x²-5x+2 = 0

2x²-4x-x+2 = 0

2x(x - 2) - 1(x - 2) = 0

(x - 2)(2x - 1) = 0

x - 2 = 0 or 2x - 1 = 0

x = 2 or x = \(\frac{1}{2}\)

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Answer:

140 poles

Step-by-step explanation:

1. Convert to the same unit. Either meters to kilometers or kilometers to meters, so you can complete the computation.

2. Divide 0.06 by 8.4 (8.4/0.06 = 140).

3. 140 poles can be placed on the 8.4 km road when separated by 60 m or 0.06 km.

Answer:

Step-by-step explanation:

Choice

Answer:

Can you award me brainest

Answer:

See below.

Step-by-step explanation:

1.)

\(24=-3+3n\\27=3n\\9=n\)

2.)

\(11+4x=x-10\\11+3x=-10\\3x=-21\\x=-7\)

3.)

\(-216=1+7(1+8m)\\-216=1+7+56m\\-216=8+56m\\-224=56m\\-4=m\)

4.)

\(3p-3(2-2p)=34+4p\\3p-6+6p=34+4p\\9p-6=34+4p\\5p=40\\p=8\)

Answer:

96

Step-by-step explanation:

Answer:

1. The relationship is proportional.

2. The cost for 30 roses is 90 dollars.

Step-by-step explanation:

1. The price (y) divided by the number of roses (x) equals 3, no matter what section in the table you try it on; y/x = 3. This means that the relationship is proportional.

Another way to explain this is x * 3 = y. For example, 3 roses * $3 = $9

2. We know that one rose costs $3. So you can multiply:

30 roses * $3 = $90

Answer: 36 quarts

Step-by-step explanation:

pretty much just do 9 * 4 qts

hope this helped!!

Answer: Parker has 36 Quarts of water.

We are given the following:

We are asked to find:

This question strictly revolves the around the conversion of units. In other words, in order to answer this question, we must know how many quarts are in a gallon.

Fortunately, we know that 4 quarts = 1 gallon.

Since Parker possesses 9 gallons of water, we would do \(4*9=36\). Arriving us at our answer of 36 quarts of water.

Parker has 36 quarts of water.

The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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Answer:

the width of the path is 24m²

Step-by-step explanation:

the area of a parallelogram is in general

baseline × height.

the baseline here is 15 m.

and the area is given : 150 m²

15×height = 150

height = 10 m

After 10 minutes, there will be 130 kg of salt in the tank.

The initial amount of salt in the tank is 0.3 kg. We need to find the amount of salt in the tank after 10 minutes of adding and removing brine solution.

During each minute, 5 gallons of brine solution with 0.4 kg of salt per gallon is added to the tank. So, the amount of salt added per minute is:

0.4 kg/gallon x 5 gallons/minute = 2 kg/minute

At the same time, 5 gallons of the mixture containing salt is removed from the tank. So, the amount of salt removed per minute is:

(0.3 kg + amount of salt added) / 200 gallons x 5 gallons/minute = (0.3 + 2t) / 200 kg/minute

where t is the number of minutes.

The change in the amount of salt in the tank after 1 minute is the difference between the amount of salt added and the amount of salt removed:

2 kg/minute - (0.3 + 2t) / 200 kg/minute = (400 - 3 - 4t) / 200 kg/minute

After 10 minutes, the amount of salt in the tank will be:

0.3 kg + integral from t=0 to t=10 of [(400 - 3 - 4t) / 200] dt

= 0.3 kg + [200t - 2\(t^2\) - 3t] evaluated from t=0 to t=10

= 0.3 kg + [200(10) - 2\((10)^2\) - 3(10)] - [200(0) - 2\((0)^2\) - 3(0)]

= 0.3 kg + 160 - 30

= 130 kg

Therefore, after 10 minutes, there will be 130 kg of salt in the tank.

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Given that, the coordinates of the endpoints of ij are i(3,5) and j(17,19). point k is on ij and divides it such that ik:jk is 3:4.

The coordinates of the point k are (9,10)

The concept of section formula asserts that if a line segment is divided into two pieces in a certain ratio, the coordinates at the point of division may be obtained using the formula:

(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = K

where (x1, y1) and (x2, y2) are the line segment's endpoint coordinates, and m:n is the provided ratio by which the line segment is divided.

The ends of the line segment IJ in this example are I(3,5) and J(17,19), and the ratio by which it is divided is 3:4, implying that IK:JK is 3:4.

As a result, m:n = 3:4, implying that m = 3 and n = 4.

When we enter these values into the formula, we get:

K = (3 x 17 + 4 x 3)/(3+4), (3 x 19 + 4 x 5)/(3+4)

When we simplify this expression, we get:

K = ( 51 + 12)/(7), (57 + 20)/(7)

K = (63)/(7),(77)/(7)

K = 9,10

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Thus, the given sequence is arithmetic, and the common difference is -100

The given sequence is: -18, -118, -218, -318,...To determine whether the sequence is arithmetic or not, we need to check whether the difference between consecutive terms is constant or not.If the difference is constant, then the sequence is arithmetic.

The sequence is not arithmetic.Difference between consecutive terms can be found by subtracting the second term from the first term, the third term from the second term, and so on.

Difference between the first two terms: (-118) - (-18) = -118 + 18 = -100Difference between the second two terms: (-218) - (-118) = -218 + 118 = -100Difference between the third two terms: (-318) - (-218) = -318 + 218 = -100The difference between each of the consecutive terms is -100. Thus, the given sequence is arithmetic, and the common difference is -100.

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The unknown angle x in the triangle is 80 degrees

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

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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-1

1/4×-2= -2/4 -2/4×2/1= -1

Answer:

1. 12

2.

a can be a triangle (obtuse)

b can be a triangle (acute)

Step-by-step explanation:

The area of trapezoid ABCD is 50 square units.

The formula for the area of a trapezoid is given by: area = (1/2) \(\times\) (base1 + base2) \(\times\) height.

In this case, base1 is AB and base2 is CD, and the height is given as 5 units.

Substituting the values into the formula, we have:

Area \(= (1/2) \times (8 + 12) \times 5\)

\(= (1/2) \times20 \times 5\)

\(= 10 \times5\)

= 50 square units.

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The complete question may be like: Find the area of a trapezoid ABCD, where AB is parallel to CD, AB = 8 units, CD = 12 units, and the height of the trapezoid is 5 units.

Greetings from Brasil...

For QR: we need to use the Sine Law in Any Triangle....

QS/SEN 72 = QR/SEN 25

6/SEN 72 = QR/SEN 25

6,3 = QR/SEN 25

For PS: we need to use the Cosine Law in Any Triangle....

PS² = PQ² + QS² - 2.PQ.QS.COS Q

PS² = 7,4² + 6² - 2.(7,4).6.COS 34

PS² = 90,76 - 73,61

PS = √17,14

For area we use Heron's Formula 2x.....

for ΔQRS = A1:

A1 = √[P.(P - QR).(P - RS).(P - QS)]

where P = (QR + RS + QS)/2

A1 = √[P.(P - QR).(P - RS).(P - QS)]

     RS = 6,26 (using RS/SEN 97 = QS/SEN 72)

P = (2,66 + 6,26 + 6)/2

P = 14,92/2 ⇒ P = 7,46

A1 = √[7,46.(7,46 - 2,66).(7,46 - 6,26).(7,46 - 6)]

A1 = 7,92

for ΔPQS = A2:

A2 = √[P.(P - PQ).(P - PS).(P - QS)]

P = (7,4 + 4,14 + 6)/2 = 8,77

A2 = √[8,77.(8,77 - 7,4).(8,77 - 4,14).(8,77 - 6)]

A2 = 12,41

Total Area = A1 + A2

Total Area = 7,92 + 12,41

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Answer:

A

Step-by-step explanation:

The three represents the amount it costs for each hour parked, and is continuous, which is a rate.

A vector is in the direction 39.0∘ clockwise from the −y-axis. The x-component of A is Ax = -18.0 m. What is the y-component of A? To determine the y-component of A, we will use the trigonometric ratio.

sinθ = opposite/hypotenuse where θ = 39.0°, hypotenuse = |A|, and opposite = Ay. Therefore, sinθ = opposite/hypotenuse Ay/|A| = sinθ ⟹ Ay = |A| sinθSince A is in the third quadrant, its y-component is negative.

Ay = - |A| sinθWe know the x-component and we know that it is negative, so the vector is in the third quadrant, and the y-component is negative.

Ax = -18.0 m, θ = 39.0°We know that the magnitude of A is:

A = √(Ax² + Ay²)Since Ax = -18.0 m, we can substitute it into the equation:

A = √((-18.0)² + Ay²)B) The magnitude of A is |A| = 19.4 m.

We can conclude that the y-component of A is -11.5 m, and the magnitude of A is 19.4 m.

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The y-component of vector A, given that the vector is pointing 39 degrees clockwise from the -y axis and has an x-component of -18 m, is approximately -14.67 m. The magnitude of this vector is about 23.03 m.

Firstly, since the vector A is pointing 39 degrees clockwise from the -y axis, it means our angle with respect to the standard x-axis is 180-39 = 141 degrees. We use the trigonometric relation cos(α) = Ax/A or Ax = A cos(α) to isolate A in the equation (magnitude of A), we get that A = Ax/cos(α). Substituting given values, we get A approximately equal to 23.03 m.

Then, the y-component can be found using sine relation: Ay = A sin(α). Substituting A=23.03 m and α= 141 degrees gives us Ay approximately equal to -14.67 m. Therefore, the y-component of A is -14.67 m and the magnitude of A is approximately 23.03 m.

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The probability that a randomly selected band member is a senior given that he or she plays the trumpet is 34.78%.

Probability is defined as the likeliness of an event to happen. It can be calculated by dividing the total desired outcomes by the total outcomes.

P = desired outcomes / total outcomes

Of the 108 band members, if 23 play the trumpet, and 8 are seniors who play the trumpet, then the probability that a randomly selected band member is a senior given that he or she plays the trumpet is 8 divided by 23.

P = 8/23 x 100

P = 34.78%

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To determine whether the given series converges or diverges, we use the Alternating Series Test.

This is because the series consists of alternating positive and negative terms whose magnitudes are decreasing. That is:

Σ (-1)"e-n 72=0= 1 - 1/ e^72 + 1/e^144 - 1/e^216 + ...

The sequence {1/e^n} is decreasing and converges to 0 as n → ∞.

Therefore, the series is alternating, decreasing, and converges to 0. Thus, the Alternating Series Test states that the given series converges. Now, we have to determine whether it is absolutely convergent or conditionally convergent. The series is not absolutely convergent because the series of absolute values of terms, Σ |(-1)"e-n| from n = 0 to ∞, is the harmonic series, which diverges. Hence, the series Σ (-1)"e-n 72=0 is conditionally convergent.

To decide whether the given series is convergent or divergent, we use the Alternating Series Test.

This is because the series consists of alternating positive and negative terms whose magnitudes are decreasing.

That is:Σ (-1)"e-n 72=0= 1 - 1/ e^72 + 1/e^144 - 1/e^216 + ...

The sequence {1/e^n} is decreasing and converges to 0 as n → ∞.

Therefore, the series is alternating, decreasing, and converges to 0. Thus, the Alternating Series Test states that the given series converges.Now, we have to determine whether it is absolutely convergent or conditionally convergent. The series is not absolutely convergent because the series of absolute values of terms, Σ |(-1)"e-n| from n = 0 to ∞, is the harmonic series, which diverges.

Hence, the series Σ (-1)"e-n 72=0 is conditionally convergent.

The given series Σ (-1)"e-n 72=0 is convergent, and it is conditionally convergent.

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Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

Answer:

11

Step-by-step explanation:

5 x 2 = 10

10 + 6 = 16

16 - 5 = 11

there u go!

The correct answer is as follows: a) The data set that has the greatest sample standard deviation is Data set (ii).

b) Data set (ii) has the largest mean and mode, but the smallest median and the largest standard deviation.

(a) The data set that has the greatest sample standard deviation is Data set (ii).

The sample standard deviation is a measure of the amount of variation or dispersion of a set of data values.

In this case, Data set (ii) has more entries that are farther away from the mean, which results in a larger standard deviation.

(b) The data sets are the same in terms of containing the same numbers (11, 12, 13, 14, 15, 16, and 17).

However, they differ in terms of the order in which these numbers are arranged.

In addition, they differ in terms of the mean, median, mode, and standard deviation.

For example, Data set (ii) has the largest mean and mode, but the smallest median and the largest standard deviation.

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.Answer:

Step-by-step explanation:

The sum expressed in sigma notation is:

Σ(8n + 5), where n goes from 1 to 5.

1. Identify the pattern in the given sequence:

13, 21, 29, 37, 45.
2. Notice that each term is 8 more than the previous term, so the common difference is 8.
3. Find the general formula for the sequence:

an = a1 + (n-1)d, where an is the nth term, a1 is the first term (13), n is the term's position, and d is the common difference (8).
4. Plug in the values to get the formula:

an = 13 + (n-1)8.
5. Simplify the formula:

an = 8n + 5.
6. Express the sum in sigma notation:

Σ(8n + 5), where n goes from 1 to 5.

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