Let X1, X2, ... are i.i.d. Let Z be the average Z := (X1 + X2 + X3 + X4)/4 Assume that the standard deviation of X1 is equal to 2. What is the standard deviation of Z?

The probability of guessing at least 11 out of 15 questions correctly is 0.059.

The probability of guessing any one question correctly is 1/2, and the probability of guessing any one question incorrectly is also 1/2.

Since each question is an independent trial with only two possible outcomes, this situation can be modeled using a binomial distribution with n = 15 (the number of trials) and p = 1/2 (the probability of success on each trial).

To find the probability of guessing at least 11 out of 15 correctly, we need to calculate the probability of guessing 11, 12, 13, 14, or 15 questions correctly, and then add these probabilities together.

Using the binomial probability formula, we can calculate the probability of guessing exactly k questions correctly as:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

where nCk is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

For k = 11, we get:

P(X = 11) = (15C 11) * (1/2)¹¹ * (1/2)¹⁵⁻¹¹ = 0.042

For k = 12, we get:

P(X = 12) = (15 C 12) * (1/2)¹² * (1/2)¹⁵⁻¹²= 0.014

For k = 13, we get:

P(X = 13) = (15 C 13) * (1/2)¹³ * (1/2)¹⁵⁻¹³ = 0.003

For k = 14, we get:

P(X = 14) = (15C14) * (1/2)¹⁴ * (1/2)¹⁵⁻¹⁴ = 0.000

For k = 15, we get:

P(X = 15) = (15C15) * (1/2)¹⁵ * (1/2)¹⁵⁻¹⁵= 0.000

To find the probability of guessing at least 11 out of 15 correctly, we add these probabilities together:

P(guessing at least 11 out of 15 correctly) = P(X >= 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.059

Therefore, the probability of guessing at least 11 out of 15 questions correctly is 0.059.

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The right answer is SSS since two triangles are said to be congruency when each of their three sides and Mario is correct.

Triangles are said regarded as being congruent if their size and shape actually match exactly. The word "congruent" contains the sign. When a triangle's three sides and three angles match those of a another triangle's three sides and three angles, two triangle are said to be congruent.

Here,

begin by writing the names of the triangles' vertices, beginning with triangles DAB and BCD, as shown below.

AB = CD

DA = BC

In both triangles, side BD is the same, therefore

BD = BD

We can infer that the triangles DAB & BCD are congruent that use the SSS feature of a congruence triangle because they have the same number of sides on each side.

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Answer: Slope: 16

Step-by-step explanation:

Slope Formula:

(y2-y1)/(x2-x1)=m

(8-(-8))/9-8=

(8+8)/1=16

Antonella have a number of coins of quaters and nickels whose total value is 250.

The number of coins of nickel is 10 and the number of coins of quarters is 7.

Nickel and quarters are the coin based form of currency in the United States. The value of one nickel is 5 cents, while that of one quarter is 25 cents. We have given that

Antonella has 3 more quaters than nickles.

Let she has "x" number of quaters and "y" be number of nickels .

According to question,

y = 3+ x ---(1)

Combined value of all is 225 cents .

i.e 25 × x + y× 5 = 225 cents

plug the value of y from equation (1) to equation(2) we get,

25 x + 5(3+x) = 225

solve the equation

=> 25x + 15 + 5x = 225

=> 30x = 210

=> x = 7

put the value of x in equation (1)

y = x + 3 = 10

Hence, the number of nickels coins is 10 and numbers of quaters are 7.

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Answer:

63/100

Step-by-step explanation:

0.63 = 63/100

To find the vector from vertex C to the midpoint of side AB, we first need to find the coordinates of the midpoint of side AB. The midpoint formula states that the coordinates of the midpoint (M) are given by (x, y, z) = [(x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2]. By applying this formula to the coordinates of points A and B, we find the midpoint coordinates to be M(2.5, 4, 3). Next, we subtract the coordinates of C from the coordinates of M to obtain the vector from C to M, which is given by (-0.5, 3, 2).

To find the midpoint of side AB, we use the midpoint formula:

x = (x₁ + x₂)/2,

y = (y₁ + y₂)/2,

z = (z₁ + z₂)/2,

where (x₁, y₁, z₁) are the coordinates of point A and (x₂, y₂, z₂) are the coordinates of point B. Plugging in the values, we have:

x = (3 + 2)/2 = 2.5,

y = (5 + 3)/2 = 4,

z = (4 + 2)/2 = 3.

Therefore, the coordinates of the midpoint M are (2.5, 4, 3).

To find the vector from C to M, we subtract the coordinates of C from the coordinates of M:

x = 2.5 - 1 = 1.5,

y = 4 - 1 = 3,

z = 3 - 1 = 2.

The resulting vector is (-0.5, 3, 2), which represents the displacement from C to the midpoint of side AB.

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Answer:

2x+3x=90

or ,5x=90

or,x=90/5

X=18

Answer:

90/5=18 degrees

Step-by-step explanation:

Step-by-step explanation:

x = -4y + 6

Now,

Substituting the value of x on 2x + 9y = 16, we get -.

2(-4y + 6) + 9y = 16

-8y + 12 + 9y = 16

y = 16 - 12

Now,

Substituting the value of y on 2x + 9y = 16, we get -

2x + 9(4) = 16

2x = 16 - 36

2x = -20

Hence,

The value of x is -10 and y is 4.

Answer:

4 if rong so so sorry

Step-by-step explanation:

No as their no difference in Mr. Goodman's evaluation and the History department

What is Statistics ?

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

descriptive statistics types in mathematics The data in this type of statistics is summarized using the provided observations. Statistics that are inferential. To interpret the meaning of descriptive statistics, this kind of statistics is employed. Example of Statistics.

Seeing the data we can conclude that their no difference in Mr. Goodman's evaluation and the History department

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Answer:

10

Step-by-step explanation:

a1=2

a=2

an=-5an-1+3

plug in

(2)5=10

Answer:

y= -1/3x + 5

Step-by-step explanation:

Answer:

Not function.

Step-by-step explanation:

Because we have more than one output for 1 or 4 input.

Answer:

2sqrt(5)

Step-by-step explanation:

Using Fourmla of distance between two points

Answer:

my answer is 3:5

Step-by-step explanation:

sana makatulong yan

Step-by-step explanation:

Volume (V) = 100 cm³

Mass (M) = 159 g

Density (D) =?

We know density is defined as mass per unit volume so

D = m / v

= 159 / 100

= 1.59 g /cm³

The density of the metal block is 1.59 g/cm³.

Note : If the question is asked to change the units in SI system then u have to write in kg/m³.

Hope it will help :)❤

It is possible to break a clock into 7 pieces so that the sums of the numbers in each piece are consecutive numbers.

To achieve a set of consecutive sums, we can divide the clock numbers into different groups. Here's one possible arrangement:

1. Group the numbers into three pieces: {12, 1, 11, 2}, {10, 3, 9}, and {4, 8, 5, 7, 6}.

2. Calculate the sums of each group: 12+1+11+2=26, 10+3+9=22, and 4+8+5+7+6=30.

3. Verify that the sums are consecutive: 22, 26, 30.

By splitting the clock into these particular groupings, we obtain consecutive sums for each group.

This arrangement meets the given conditions, where each piece has at least two numbers, and no number is damaged or split into separate digits.

Therefore, it is possible to break a clock into 7 pieces so that the sums of the numbers in each piece form a sequence of consecutive numbers.

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Answer:

40

Step-by-step explanation:

Answer:

Opposite

Step-by-step explanation:

The opposite of -6 is 6, because it is 6 units from zero on the number line.

Hope this helped! I would appreciate a Brainliest, or even a thanks, if this was correct or at least made enough sense to understand.

Answer: The lines in the triangle above intersect the angles into halves, splitting each angle into 2 identical angles. As such, this shows that angle bisectors bisect each angle in a triangle.

I got ECHA... hope it's right:)

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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Answer:

The missing measure is 70.

Step-by-step explanation:

Because the two inside angles that arent next to each other on the suppelment add up to the outside angle, 120-50 is the missing angle. Sorry if this explaination is confusing.  

L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

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Answer:

55

Step-by-step explanation:

AB // DC

∠B + ∠C = 2x + 15 + x = 180

3x = 165

x = 55

Answer: B. 55

Step-by-step explanation:

You need to know that within one parallelogram, the same-side interior angles are supplementary angles, meaning that they add up to 180°.

---------------------------------------------------------------------------------------

Given

(2x+15)+x=180

Expand parenthesis

2x+15+x=180

Combine like terms

3x+15=180

Subtract 15 on both sides

3x+15-15=180-15

3x=165

Divide 3 on both sides

3x/3=165/3

x=55

Hope this helps!! :)

Please let me know if you have any questions

No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.

A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.

When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.

However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.

In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.

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Answer:

It will take 60 weeks for Ernesto to save $315

Answer:

60 weeks or 15 months.

Step-by-step explanation:

y = mx + b

315 = 5.25x + 0

Divide 315 by 5.25 and you get 60, so 60 weeks or 15 months. Check by plugging it into the equation.

315 = 5.25(60) + 0

315 = 5.25(60)

315 = 315

When comparing the two numbers we get that 116/9 is greater than square root of 160.

The square root of 160

= √160

= 12.6491...

≈ 12.65

The fraction number is 116/9 , converting to decimal we get:

116/9

= 12.888

≈ 12.89

Now comparing the two numbers we get:

12. 89 > 12.65

hence 116/9 > 12.65

The opposite of squaring an integer is finding its square root. Finding a number that, when squared, yields the original value will reveal the square root of a number, which is found by multiplying it by itself. If "a" is equal to "b" squared, then a = b.

Every number has four roots that are four by four, one of a positive value and one of a negative value, because the square of almost any integer always represents a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of an integer is typically expressed using only the positive value.

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