Need the Answer for this, provide an explanation.

By Logical reasoning, missing tile in the given figure is Option C.

Initially find the similarity in each row or column. Get the logic relation between the blocks/tiles. Then try to apply the same logic on the missing tile/block to get the answer.

In the given question there are 9 tiles with 1 missing tile.

Now Check the first row:(As we go to the right one-by-one)

1) Normal circle is changing its square side in anti clockwise direction and also it goes in and out every time we pass a block/tile.

2)Dark circle is at corners of the squares as we pass the block it goes out or in tile by tile and also it changes the corner every time one corner is visited.

3)Triangle is at corners of the square and always inside the square, it changes the corner tile by tile in anti clockwise direction.

Similarly the same logic applies to remaining two rows.

Now for third row:

1) As the normal circle is at right side of square and inside the square, as we pass the tile it goes up(anti clockwise) and to outside of square.

2)The dark circle changes the corner once it visits a corner as it visited the down corner once it changes the corner to top right of square

3)Triangle just changes the corner as we pass, so it goes to bottom left corner of the square.

By Logical reasoning, missing tile in the given figure is Option C.

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The p-value for the hypothesis test about factor b is greater than 0.05.

What is Hypothesis?

In effect, a theory is a hypothesis or group of hypotheses that refers to a particular issue or problem.

Thus, a hypothesis is a set of possible explanations or resolutions applicable to a situation. In other words, the hypotheses pose different scenarios in which the aim is to explain the origin and eventual resolution of the problem.

The p-value for the hypothesis test about factor b is greater than 0.05.

The p-value is a measure of statistical significance used in hypothesis testing. It represents the probability of obtaining a result at least as extreme as the one observed in the sample, given that the null hypothesis is true.

In general, a p-value less than 0.05 is considered statistically significant and indicates that the observed result is unlikely to have occurred by chance. A p-value between 0.01 and 0.025 is considered moderately significant, while a p-value between 0.025 and 0.05 is considered borderline significant. A p-value greater than 0.05 is not considered statistically significant and indicates that the observed result is likely due to chance.

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Describe hypothesis.

A theory is, in essence, a hypothesis or set of hypotheses pertaining to a certain subject or issue(s).

Consequently, a hypothesis is a group of potential explanations or solutions that could be applied to a situation. In other words, the hypotheses present many possibilities with the intent of illuminating the problem's origin and potential solutions.

The p-value for the factor b hypothesis test is higher than 0.05.

A statistical significance indicator used in hypothesis testing is the p-value. Given that the null hypothesis is true, it represents the likelihood of obtaining a result that is at least as extreme as the one seen in the sample.

A p-value of less than 0.05 is typically regarded as statistically significant and denotes the likelihood that the observed result did not arise by chance. While a p-value between 0.025 and 0.05 is regarded as borderline significant, one between 0.01 and 0.025 is regarded as moderately significant. The observed result is most likely the result of chance if the p-value is greater than 0.05, which is the threshold for statistical significance.

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To graph the triangle AABC, we can plot the coordinates of the three vertices and then connect them to form the triangle. The coordinates of the vertices are (0, 2), (3, 2), and (2, 1), so we can plot these points on a coordinate grid and connect them with line segments to form the triangle:

 |

 |

 |    (2,1)

 |   /

 |  /

 | /

 |/

(0,2) __________ (3,2)

To reflect the triangle in the x-axis, we can multiply the y-coordinate of each vertex by -1. This will cause the triangle to be flipped over the x-axis. The coordinates of the reflected triangle are (0, -2), (3, -2), and (2, -1), so we can plot these points on the same coordinate grid and connect them with line segments to form the reflected triangle:

 |

 |

 |

 |   /\

 |  /  \

 | /    \

 |/      \

(0,2) __________ (3,2)

|

|

| (2,-1)

|

The resulting graph shows the original triangle AABC and its image after reflection in the x-axis.

Answer:

A' = (0, -2)

B' = (3, -2)

C' = (2, -1)

Step-by-step explanation:

Given vertices of triangle ABC:

The mapping rule for a reflection in the x-axis is:

Therefore, the vertices of ΔA'B'C' are:

Answer:6 dollars

Step-by-step explanation:

Cuz u going to need to buy 3 mc flurries :D

Answer:

x > 6. graph this on the number line.

Step-by-step explanation:

-2x-12 > -4x

-12 > -2x

12 < 2x

6 < x

Answer:

x > 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve for x:

3 x^4 - 16 x^3 + 4 x + 363 = 0

Eliminate the cubic term by substituting y = x - 4/3:

363 + 4 (y + 4/3) - 16 (y + 4/3)^3 + 3 (y + 4/3)^4 = 0

Expand out terms of the left-hand side:

3 y^4 - 32 y^2 - (476 y)/9 + 3059/9 = 0

Divide both sides by 3:

y^4 - (32 y^2)/3 - (476 y)/27 + 3059/27 = 0

Add 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27 to both sides:

y^4 + 2/3 sqrt(3059/3) y^2 + 3059/27 = 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27

y^4 + 2/3 sqrt(3059/3) y^2 + 3059/27 = (y^2 + sqrt(3059/3)/3)^2:

(y^2 + sqrt(3059/3)/3)^2 = 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27

Add 2 (y^2 + sqrt(3059/3)/3) λ + λ^2 to both sides:

(y^2 + sqrt(3059/3)/3)^2 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2

(y^2 + sqrt(3059/3)/3)^2 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (y^2 + sqrt(3059/3)/3 + λ)^2:

(y^2 + sqrt(3059/3)/3 + λ)^2 = (476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2

(476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (2 λ + 32/3 + (2 sqrt(3059/3))/3) y^2 + (476 y)/27 + 2/3 sqrt(3059/3) λ + λ^2:

(y^2 + sqrt(3059/3)/3 + λ)^2 = y^2 (2 λ + 32/3 + (2 sqrt(3059/3))/3) + (476 y)/27 + 2/3 sqrt(3059/3) λ + λ^2

Complete the square on the right-hand side:

(y^2 + sqrt(3059/3)/3 + λ)^2 = (y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)))^2 + (4 (2 λ + 32/3 + (2 sqrt(3059/3))/3) (λ^2 + 2/3 sqrt(3059/3) λ) - 226576/729)/(4 (2 λ + 32/3 + (2 sqrt(3059/3))/3))

To express the right-hand side as a square, find a value of λ such that the last term is 0.

This means 4 (2 λ + 32/3 + (2 sqrt(3059/3))/3) (λ^2 + 2/3 sqrt(3059/3) λ) - 226576/729 = 8/729 (729 λ^3 + 243 sqrt(9177) λ^2 + 3888 λ^2 + 864 sqrt(9177) λ + 165186 λ - 28322) = 0.

Thus the root λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3)) allows the right-hand side to be expressed as a square.

(This value will be substituted later):

(y^2 + sqrt(3059/3)/3 + λ)^2 = (y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)))^2

Take the square root of both sides:

y^2 + sqrt(3059/3)/3 + λ = y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)) or y^2 + sqrt(3059/3)/3 + λ = -y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) - 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3))

Solve using the quadratic formula:

y = 1/6 (sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) + sqrt(2) sqrt(48 - sqrt(9177) - 9 λ + 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) or y = 1/6 (sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) - sqrt(2) sqrt(48 - sqrt(9177) - 9 λ + 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) or y = 1/6 (sqrt(2) sqrt(48 - sqrt(9177) - 9 λ - 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177))) - sqrt(2) sqrt(9 λ + 48 + sqrt(9177))) or y = 1/6 (-sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) - sqrt(2) sqrt(48 - sqrt(9177) - 9 λ - 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) where λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3))

Substitute λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3)) and approximate:

y = -2.83639 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i

Substitute back for y = x - 4/3:

x - 4/3 = -2.83639 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i

Add 4/3 to both sides:

x = -1.50306 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i

Substitute back for y = x - 4/3:

x = -1.50306 - 2.06535 i or x - 4/3 = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i

Add 4/3 to both sides:

x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i

Substitute back for y = x - 4/3:

x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x - 4/3 = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i

Add 4/3 to both sides:

x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or y = 2.83639 + 1.07606 i

Substitute back for y = x - 4/3:

x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or x - 4/3 = 2.83639 + 1.07606 i

Add 4/3 to both sides:

Answer:  x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or x = 4.16972 + 1.07606 i

The correct solution to the given inequalities is;

a No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Let the number of child bikes be denoted as c.

Let the number of adult bikes be denoted as a.

For the building time of bikes, the inequality equation would be;

4c + 6a ≤ 120

For the testing time of bikes, the inequality equation would be;

4c + 4a ≤ 100

Checking the equations, for given 60 child bikes and 6 adult bikes in the week.

For the building of bikes,

( 4 × 60) + ( 6 × 6) ≤ 120

240 + 36 ≤ 120

276 ≥ 120 (Inequality not satisfied)

For the testing of bikes,

( 4 × 60 ) + ( 4 × 6 ) ≤ 100

240 + 24 ≤ 100

264 ≥ 100 (Inequality not satisfied)

Hence, the correct option is A.

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The correct statement regarding why f(x) ≠ g(x) is given as follows:

a. f(x) ≠ g(x) because the graphs do not intersect.

Two functions are classified as different when they do not intersect.

The functions in this problem are given as follows:

For them to intersect, it is needed that:

f(x) = g(x).

x² = 2x - 3.

x² - 2x + 3 = 0.

Which is a quadratic function with the coefficients given as follows:

a = 1, b = -2, c = 3.

The number of solutions of the quadratic function depends on the discriminant, given as follows:

Discriminant = b² - 4ac.

Hence the numeric value for the discriminant in this problem is given as follows:

Discriminant = (-2)² - 4 x 1 x 3 = -8.

As the discriminant is negative, the quadratic function has no solutions, meaning that the functions do not intersect and statement a is correct.

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1/6 because $160 as a fraction is 1/6

Step-by-step explanation:

since it is geometric sequence we will use the formula

[tex]tn = {a \times r}^{n - 1} [/tex]

a = 2

[tex]r = - \frac{1}{4} [/tex]

The first term

T1(a) = 2

The second Term

[tex]t2 = {a \times r}^{2 - 1} = {a \times r}^{1} [/tex]

[tex]t2 = {2 \times - \frac{1}{4} }^{1} = - \frac{1}{2} [/tex]

The third term

[tex]t3 = {a \times r}^{3 - 1} = {a \times r}^{2} [/tex]

[tex]t3 = {2 \times - \frac{1}{4} }^{2} = 2 \times - \frac{1}{16} = \frac{1}{8} [/tex]

The fourth term

[tex]t4 = {a \times r}^{4 - 1} = {a \times r}^{3} [/tex]

[tex]t4 = {2 \times - \frac{1}{4} }^{3} = 2 \times - \frac{1}{64} = - \frac{1}{32} [/tex]

The fifth term

[tex]t5 = {a \times r}^{5 - 1} = {a \times r}^{4} [/tex]

[tex]t5 = {2 \times - \frac{1}{4} }^{4} = 2 \times - \frac{1}{256} = - \frac{1}{128} [/tex]

i hope all these helped

Answer:

[tex]2,\; -\dfrac{1}{2},\; \dfrac{1}{8},\; -\dfrac{1}{32},\; \dfrac{1}{128}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the given values of a and r into the formula to create an equation for the nth term:

[tex]a_n=2\left(-\dfrac{1}{4}\right)^{n-1}[/tex]

To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.

[tex]\begin{aligned}\implies a_1 & =2\left(-\dfrac{1}{4}\right)^{1-1}\\& =2\left(-\dfrac{1}{4}\right)^{0}\\& =2\left(1\right)\\&=2\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_2 & =2\left(-\dfrac{1}{4}\right)^{2-1}\\& =2\left(-\dfrac{1}{4}\right)^{1}\\& =2\left(-\dfrac{1}{4}\right)\\&=-\dfrac{1}{2}\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_3 & =2\left(-\dfrac{1}{4}\right)^{3-1}\\& =2\left(-\dfrac{1}{4}\right)^{2}\\& =2\left(\dfrac{1}{16}\right)\\&=\dfrac{1}{8}\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_4 & =2\left(-\dfrac{1}{4}\right)^{4-1}\\& =2\left(-\dfrac{1}{4}\right)^{3}\\& =2\left(-\dfrac{1}{64}\right)\\& =-\dfrac{1}{32}\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_5 & =2\left(-\dfrac{1}{4}\right)^{5-1}\\& =2\left(-\dfrac{1}{4}\right)^{4}\\& =2\left(\dfrac{1}{256}\right)\\& =\dfrac{1}{128}\end{aligned}[/tex]

Therefore, the first 5 terms of the given geometric sequence are:

[tex]2,\; -\dfrac{1}{2},\; \dfrac{1}{8},\; -\dfrac{1}{32},\; \dfrac{1}{128}[/tex]

The ratio in the series is 1.5.

The ratio consists on making the division of a value from a series, divided by its previous value. In this case you have 2 options for finding the ratio, and you will get the same answer:

6/4= 1.5

9/6= 1.5

Hence, the ratio in the series is 1.5.

The area of the triangle is 11.1 square cm

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

Legs = 3cm and h cm

Hypotenuse = 8 cm

The area of the triangle is calculated using

Area = 0.5 * b * h

Where

h = √(8² - 3²) --- this is gotten from the Pythagorean theorem

So, we have

h = 7.4

The area is then calculated as

Area = 0.5 * b * h

So, we have

Area = 0.5 * 3 * 7.4

Evaluate

Area = 11.1

Hence, the area is 11.1 square cm

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Answer: $14 for 1 ticket

Step-by-step explanation: 84 divided by 6 is 14. hope this helps

The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Answer:

  (a)  211,555.72

  (b)  16.64%

Step-by-step explanation:

You want to know the total interest earned on a 200,000 investment at ...

And you want to know the effective rate for the last period.

The multiplier of the investment at rate r compounded n times per year for t years is ...

  k = (1 +r/n)^(nt)

Using this multiplier for the rates and periods given the balance of the account at the end of 6 years will be ...

  200,000(1 +.08/12)^(12·2) × (1 +.12/4)^(4·1.5) × (1 +.16/2)^(2·2.5)

  ≈ 411,555.72

The interest earned is the difference between the account balance and the principal invested:

  411,555.72 -200,000 = 211,555.72 . . . . interest earned in 6 years

The annual multiplier for the last term is ...

  (1 +.16/2)^(2·1) = 1.1664

The effective interest rate is 1 less than this:

  16.64% = effective rate during final year

__

Additional comment

The repetitive math can be less tedious if you let a calculator or spreadsheet do it.

No currency units are given in the problem statement.

Answer:

1/2

Step-by-step explanation:

Let's say the number is 1.5

1.5 = 1 + 0.5

(1.5 = 1 + 0.5)*10 ==> multiply by 10 to remove decimals

15 = 10 + 5

5 is half of 10

Hence, 0.5 is half of 1 ==> 0.5 = 1/2

The inequality that represents the number of minutes Cynthia would need to walk to reach her goal before she gets to school is;

50m + 236 ≥ 950

We are told that;

Cynthia has a watch that counts the number of steps she takes every

day.

She can get 50 steps every minute for a casual walk.

Number of steps she has walked today = 236 steps

Number of steps she wants to get to before going to school = 950 steps

Now, if m represents the number of minutes Cynthia would need to walk to reach her goal before she gets to school, then the inequality equation her is;

50m + 236 ≥ 950

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Answer:

4 hours

Step-by-step explanation:

7h - 5(3h - 8) = -72  Distribute the -5

7h - 5(3h )(-5)(-8) = -72  A negative times a negative is a positive

7h - 15h + 40 = -72  Combine like terms

-8h + 40 = -72  Subtract 40 from both sides

-8h +40 - 40 = -72 - 40

-8h = -32  Divide both sides by -8

[tex]\frac{-8h}{-8}[/tex] = [tex]\frac{-32}{-8}[/tex]

h = 4

The percentage of information that is remembered by a particular person after one year (52 weeks) is 20%

The function f(x)=80e-0.5x+20 describes the percentage of information that a particular person remembers after x weeks.

To find the percentage of information that is remembered by a particular person after one year (52 weeks), we need to substitute x=52 in the given f(x).

f(x)=80[tex]e^{-0.5x}[/tex]+20

x=52, f(52)= 80[tex]e^{(-o.5\times 52)}[/tex]+20

       =80[tex]e^{-26}[/tex]+20

       =80(5.109 [tex]E^{-12[/tex])+20

       = 4.087[tex]E^{-20}[/tex]+20

f(52)= 20

The percentage of information that is remembered by a particular person after one year (52 weeks) is 20%

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The statement that in the Orthogonal Decomposition Theorem, each term in formula (2) for Å, is itself an orthogonal projection of y onto a subspace of W is true .

The orthogonal decomposition of the vector of is the sum of the vectors of the subspaces of and the vectors of the orthogonal complements of . The orthogonal decomposition theorem states that each vector in can be uniquely described in the form , if W is a subspace of V then ecah vector in can be written in uniquely. Therefore z belongs to W⊥ because it is orthogonal to the spanning set of W. To keep the decomposition y = p + z unique, assume another decomposition y = q + w such that q ∈ W and w ∈ W⊥. Both decompositions are equal to y, so we have p − q = w − z. where p − q is in W and w − z is in W⊥.

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One lb = one pound.

and 11 lb is 11 pound

Is 8 oz the same as 1 lb?

Each pound has 16 ounces or oz.

5,44311

What do you mean by pounds?

a unit for measuring weight: One pound is approximately equal to 454 grams. One kilogram is roughly the same as 2.2 lbs. There are 16 ounces in one pound.

What is a pound and examples?

Image result for What do you mean by pounds?

In simpler words, pounds tell us how heavy an object is. For example, the weight of a soccer ball is about one pound. A pound is expressed as lb or lbs, where “lb” stands for libra. It is a Latin word that means “balance” or “scale”.

Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.

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Comparing the ratios in form of fraction, the ratio 1:3 is the largest.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

In the ratios given, we have 2:9, 3:18 and 1:3

Let's write these in form of fraction to the decimal and determine which is the largest.

i)

2:9 = 2/9 = 0.22

ii)

3:18 = 3/18 = 0.1666 ≅ 0.17

iii)

1:3 = 1/3 = 0.33

From the above fractions, the ratio 1:3 is the largest.

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Answer: It is just 4

Step-by-step explanation: That means the absolute value of 4 and it is just 4

Part (a)

There are 18 red slots out of the total 38, so the probability is [tex]18/38=\boxed{9/19}[/tex]. Note that the previous spins don't impact the result.

Part (b)

Similar to part (a), the answer is [tex]\boxed{9/19}[/tex].

On solving the provided question we can say that - probability distribution, E(X)= 47.5, V(X)= 128.75, [tex]E(X^{2})[/tex] = 2605

A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that different possible experiment results will occur. The sample space and event probabilities are used to build a mathematical description of random occurrences.

E(X)= (20 * 0.05) + (30 *0.05)+ (40 * 0.35) + (50 * 0.20) + (60 *0.35)

      = 1+ 1.5 + 14 + 10 + 21

      = 47.5

V(X)= ((20-38)2 * 0.05) + ((30-38)2 *0.05)+ ((40-38)2 * 0.35) + (50-38)2 * 0.20) + ((60-38)2 *0.35)

      = 16.2 + 3.2 + 1.4 + 28.8 +169.4

      = 128.75

[tex]E(X^{2})[/tex]=

              =(202 * 0.05) + (302 *0.05)+ (402 * 0.35) + (502 * 0.20) + (602 *0.35)

             = 20 + 45 + 560 + 500 +1260

            =2605

[tex]V(X^2)[/tex]   =  2605 - ( 47.5)2

               = 2385 - 2256.25

          =128.75

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On solving the provided question, we can say that -  95 confidence interval Z alpha 2 = 1.96, CI = (4.1 , 53.9)

The z critical value is 1.96 for a test with a 95% confidence level (e.g. = 0.05). The z critical value is 5.576 for a test with a 99% confidence level (for instance, with = 0.01).

The two red tails represent the alpha level split by two. Finding the z-score for an alpha level for a two-tailed test is what is meant when a question asks you to determine z alpha/2. The confidence interval may be subtracted from 100% to calculate alpha, which is connected to confidence levels.

for 95% confidence,

[tex]Z_{\frac{\alpha }{2} }[/tex] = 1.96

CI = (5279 - 5250) ± 1.96[tex]\sqrt{\frac{140^2}{395} + \frac{210^2}{395} } \\[/tex]

CI = (4.1 , 53.9)

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The probability that (a and b) or (c and d) or (b and d) are selected is 3/25

To find the probability that a and b or c and d or b and d are selected, we can use the formula for probability:

Probability = Number of favorable outcomes / Total number of outcomes

Probability of a = 1/5

Probability of b = 1/5

Probability of a and b = 1/5 × 1/5 = 1/25

Probability of c = 1/5

Probability of d = 1/5

Probability of c and d = 1/5 × 1/5 = 1/25

Probability of b = 1/5

Probability of d = 1/5

Probability of b and d = 1/5 × 1/5 = 1/25

The probability that (a and b) or (c and d) or (b and d) are selected will be:

Probability of (a and b) or (c and d) or (b and d) = P(a and b) +  P(c and d +  P(b and d)

Probability of (a and b) or  (c and d) or (b and d) = 1/25 + 1/25 + 1/25 = 3/25

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Charles evaluates f(-2) and determines its value to be 30  Charles concludes that is not factor of f(x).

What is Factor theorem?

The factor theorem in algebra establishes a connection between a polynomial's factors and zeros. The polynomial remainder theorem has this particular special instance. A polynomial f(x) has a factor if and only if f=0, according to the factor theorem.

Given : f(x)=2x^4 -3x^3 +5x -16

By Factor theorem, If x+2 is a factor of f(x), then f(-2) should be equal to 0.

So, Charles can use factor theorem to determine whether x + 2 is a factor of f(x) by putting x=-2 in f(x),

f(x) = 2x^4 -3x^3 +5x -16

     = 2×(-2)^4 - 3×(-2)^3 + 5(-2) - 16

     = 2×16 + 3×8 - 10 - 16

     = 32 + 24 -10 -16

     = 56 -26

     = 30.

Since, f(-2) ≠ 0, (x +2) is not a factor of f(x).

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