evaluate the summation of 2n+5 from n=1 to 12

29
36
216
432

The number of ways the first two places can come out is 56.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

[tex]^nP_r = \dfrac{n!}{(n-r)!},\ \ ^nC_r = \dfrac{n!}{(n-r)!\times r!}[/tex]

where,

n is the number of choices available,

r is the choices to be made.

Eight people enter a race, n = 8,

There are no ties, r = 2,

As there is an equal chance of everyone being first and second, but also there will be cases where the first and second positions can be exchanged between the same two people. therefore, there is a particular order in which these 8 people can win. Thus, we will use permutation.

[tex]^8P_2 = \dfrac{8!}{(8-2)!}=\dfrac{8!}{(6)!} = \dfrac{8\times 7\times 6!}{6!} = 8\times 7 = 56[/tex]

Hence, the number of ways the first two places can come out is 56.

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The resulting expression for x when the algebraic expression is simplified is 2.4x - 4.4

The simplification of algebraic expressions follows an approach where we aim to solve for the unknown variables of the algebraic expression.

From the given algebraic expression, we have:

0.3(4x – 8) – 0.5(–2.4x + 4)

1.2x - 2.4 + 1.2x - 2

1.2x + 1.2x = 2.4 + 2

2.4x = 4.4

2.4x - 4.4

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Answer:

simply d

Step-by-step explanation:

Answer:

Third table  represents the second piece of the function f(x)

Step-by-step explanation:

The second piece of the function f(x) is [tex]f(x)=8-2x[/tex]

Now, we substitute some values of x and find the corresponding function values and check which table satisfy the points.

For x = 1

[tex]f(1)=8-2(1)\\f(1)=6[/tex]

For x = 2

[tex]f(2)=8-2(2)\\f(2)=4[/tex]

For x = 3

[tex]f(3)=8-2(3)\\f(3)=6[/tex]

Among the given tables, third tables contains these values.

Third table  represents the second piece of the function f(x)

Answer:

Next letter will be k.

Step-by-step explanation:

we have to find the letter which will come next at the end of the row of letters

a b d g.

First we will write the alphabets as below to understand the sequence

a b c d e f g h i j k

Between a and b alphabet skipped = 0

Between b and  d alphabets skipped = 1 (c)

Between d and g skipped alphabets = 2 (e and f)

Therefore after g number of alphabets skipped will be = 3 (h i j)

Next alphabet will be k.

The probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.

Here's how we can calculate this:

Standardize the values: Convert the heights of 67 inches and 69 inches to z-scores using the formula:

z = (x - mean) / standard deviation.

In this case, z for 67 inches is -0.33 and z for 69 inches is 0.33.

Calculate the area between the z-scores: Using a standard normal distribution table or calculator, find the area between -0.33 and 0.33. This represents the probability of an 18-year-old man having a height within that range.

Round the answer: The calculated area is approximately 0.261, which is the probability of a randomly selected man being between 67 and 69 inches tall.

Therefore, the probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.

The probability that an 18-year-old man selected at random is between 67 and 69 inches tall is approximately 0.259.

To find the probability that an 18-year-old man selected at random is between 67 and 69 inches tall, we first need to standardize the values using the z-score formula:

[tex]\( z = \frac{x - \mu}{\sigma} \)[/tex]

where x is the value

[tex]\( \mu \)[/tex] is the mean, and

[tex]\( \sigma \)[/tex] is the standard deviation.

For x = 67 inches: [tex]\( z = \frac{67 - 68}{3} = -0.333 \)[/tex]

For x = 69 inches: [tex]\( z = \frac{69 - 68}{3} = 0.333 \)[/tex]

Using the standard normal distribution table or calculator, we find the corresponding probabilities:

P(z < -0.333) and P(z < 0.333)

P(z < -0.333) = 0.3707 and P(z < 0.333) = 0.6293

To find the probability between 67 and 69 inches, we subtract the smaller probability from the larger:

0.6293 - 0.3707 = 0.2586

area = l x h

l=4h

area = 4h x h = 4h^2

4h^2 =63

63/4 = 15.75

h^2 = 15.75

sqrt(15.75)=h

h = 3.968cm

rounded to nearest tenth would be 4.0cm

check L=4(4) = 16 x 4 = 64 ( since it was round 64 is pretty close to 63)

Answer with explanation:

Equation of the Parabola is

[tex]f(x)= y=3x^2+9x+12\\\\y=3[x^2+3 x+4]\\\\y=3[(x+\frac{3}{2})^2+4-(\frac{3}{2})^2]\\\\y=3[(x+\frac{3}{2})^2+(\frac{\sqrt 7}{2})^2]\\\\y-\frac{21}{4}=3[(x+\frac{3}{2})^2][/tex]

Vertex of the parabola can be obtained by

   [tex]x+\frac{3}{2}=0\\\\ x=\frac{-3}{2}\\\\ y-\frac{21}{4}=0\\\\y=\frac{21}{4}\\\\ Vertex(\frac{-3}{2},\frac{21}{4})[/tex]

Axis is that line of parabola which divides the parabola into two equal halves.

[tex]x+\frac{3}{2}=0\\\\x=-\frac{3}{2}[/tex]  

The digital monitoring system attached at 6 inch from telescope.

A curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a stationary point is equal to its distance from a fixed line.

Here, we have a parabolic frame with the focus point and on the tip from the stem coming from its center, the digital monitoring system.

So, the equation that in this situation is

x = y² / 12

12x = y²

y= √12x

So, at x= 3 the y will be

y = √12(3)

y = √36

y = 6

Thus, the digital monitoring system attached at 6 inch from telescope.

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The graph of the function g(x) = 2(|x - 2|) represents a translation 2 units to the right followed by a horizontal stretch by a factor of 2 on the graph of f(x) = |x|.

To represent a translation 2 units to the right followed by a horizontal stretch by a factor of 2 on the graph of f(x) = |x|, we can define the function g(x) as g(x) = 2(|x - 2|).

The function |x - 2| represents the translation 2 units to the right, while the factor of 2 in front of the absolute value represents the horizontal stretch by a factor of 2.

For example, when x = 1, g(x) = 2(|1 - 2|) = 2(|-1|) = 2.

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I believe the answer is D.

Answer:

B) Median, because there is one outlier that affects the center

Answer: 8 inches

Step-by-step explanation:

The volume of a cone is given by :-

[tex]\text{Volume}=\dfrac{1}{3}\pi r^2 h[/tex], where r is radius and h is height of the cone.

Given : The volume of cone = 83.74 cubic inches

The height of cone = 5 inches

Then by using the above formula , we have

[tex]83.74=\dfrac{1}{3}(3.14) r^2 5\\\\\Rightarrow\ r^2=\dfrac{3\times83.74}{3.14\times5}\\\\\Rightarrow\ r^2=16.0012738854\approx16\\\\\Righatrrow\ r=\sqrt{16}=4\text{ inches}[/tex]

Diameter of cone = [tex]2r=2(4)=8\text{ inches}[/tex]

Hence, the diameter of cone =  8 inches

Answer:

[tex]arc\ TU=71\°[/tex]

Step-by-step explanation:

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite

In this problem we have that

[tex]63\° =\frac{1}{2}(arc\ SR+arc\ TU)[/tex]

we have

[tex]arc\ SR=55\°[/tex]

substitute and solve for arc TU

[tex]63\° =\frac{1}{2}(55\°+arc\ TU)[/tex]

[tex]126\° =(55\°+arc\ TU)[/tex]

[tex]arc\ TU=126\°-55\°=71\°[/tex]

Answer:10

Step-by-step explanation:

The rate of the increase would be 18.56% to the nearest percent.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Seema obtained a score of 57% on her exam, that corresponds to 67 out of 100.

We have been given 120 bacteria to start, which increases to 200 bacteria in 3 hours.

The population-increasing formula is given by

⇒ P(n) = P₀(1+ r)ⁿ

Here  P(n) = 200,  P₀ = 120, and n = 3

Substitute the values in the above equation,

⇒ 200 = 120(1+ r)³

⇒ 200 / 120 = (1+ r)³

⇒ 5/3 = (1+ r)³

⇒ ∛5/3 = 1+ r

⇒ ∛5/3 - 1 =  r

⇒ r = 0.18563

⇒ % r = 18.56%

Therefore, the rate of the increase would be 18.56% to the nearest percent.

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The rate of increase for a bacteria culture that starts with 120 bacteria and grows to 200 after 3 hours is calculated by dividing the increase in population (80) by the initial population (120) and then multiplying by 100 to get the percentage. The rate of increase is 66.67%, which rounds to 67% to the nearest percent.

To find the rate of increase to the nearest percent for a bacteria culture that starts with 120 bacteria and grows to 200 bacteria after 3 hours, we must calculate the percentage growth over the time period given.

First, we need to find the absolute increase in the number of bacteria:

 Final population - Initial population = Increase in population

 200 - 120 = 80

Next, we calculate the rate of increase based on the initial population:

 (Increase in population / Initial population)

   (80 / 120)

   Multiplying by 100 to get the percentage: (80 / 120) ×100

 Rate of increase = 66.67%

Rounded to the nearest percent, the rate of increase is 67%

Answer:

The purpose of long division with polynomials is similar to long division with integers; to find whether the divisor is a factor of the dividend and, if not, the remainder after the divisor is factored into the dividend. The primary difference here is that you are now dividing with variables.