A mural made of triangular tiles has an area of 1750 square centimeters. Each triangle has a height that is 3 centimeters longer than its base of 2 centimeters. How many triangular tiles are there?

To find the probability distribution of the random variable Y = X^2 + 1, where X is a binomial random variable with parameters n and p = 1/4, we need to determine the probability mass function (PMF) of Y.

The PMF gives the probability of each possible value of the random variable. In this case, Y can take on values of 1, 2, 5, 10, and so on, depending on the values of X. Let's calculate the PMF for Y: P(Y = y) = P(X^2 + 1 = y) = P(X^2 = y - 1). Since X is a binomial random variable, its possible values are 0, 1, 2, ..., n. Therefore, we need to find the values of X that satisfy the equation X^2 = y - 1.

For each value of y, we can find the corresponding values of X and calculate the probability of X taking on those values using the binomial probability formula: P(X = r) = C(n, r) * p^r * (1 - p)^(n - r) where C(n, r) is the binomial coefficient given by C(n, r) = n! / (r! * (n - r)!). Let's calculate the PMF for each possible value of Y: For y = 1: P(Y = 1) = P(X^2 = 1 - 1) = P(X^2 = 0). The only value of X that satisfies X^2 = 0 is X = 0. P(X = 0) = C(n, 0) * p^0 * (1 - p)^(n - 0) = (1 - p)^n. For y = 2: P(Y = 2) = P(X^2 = 2 - 1) = P(X^2 = 1). The values of X that satisfy X^2 = 1 are X = -1 and X = 1. P(X = -1) = C(n, -1) * p^(-1) * (1 - p)^(n - (-1)) = 0 (since n cannot be negative), P(X = 1) = C(n, 1) * p^1 * (1 - p)^(n - 1) = n * p * (1 - p)^(n - 1). For y = 5: P(Y = 5) = P(X^2 = 5 - 1) = P(X^2 = 4).

The values of X that satisfy X^2 = 4 are X = -2 and X = 2. P(X = -2) = C(n, -2) * p^(-2) * (1 - p)^(n - (-2)) = 0 (since n cannot be negative), P(X = 2) = C(n, 2) * p^2 * (1 - p)^(n - 2). Similarly, you can continue this process for other values of y. Please provide the value of n (the number of trials) to calculate the specific probabilities for each value of Y.

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Answer:

7

Step-by-step explanation:

Answer:

f(3)=-11

Step-by-step explanation:

Plug in what you know so: -3(3)-2

Multiply: -9-2

Subtract: -11

a.The statement is True  b.The statement is True

c. The statement is False   d. The statement is False

a. The statement is true. Two matrices are considered equivalent if one can be transformed into the other using a sequence of elementary row operations. These operations include swapping rows, multiplying a row by a non-zero scalar, and adding a multiple of one row to another. These operations preserve the solution set of a system of linear equations.

b. The statement is true. Different sequences of row operations can indeed lead to different echelon forms for the same matrix. The echelon form of a matrix is not unique, and the specific sequence of row operations used determines the resulting echelon form.

c. The statement is false. Different sequences of row operations will always lead to the same reduced echelon form for the same matrix. The reduced echelon form is a unique form obtained through a specific sequence of row operations and is unique for a given matrix.

d. The statement is false. A linear system with more variables than equations, such as four equations and seven variables, can have a unique solution, infinitely many solutions, or no solutions at all. The number of solutions depends on the specific coefficients and constants in the system of equations and cannot be determined solely based on the number of equations and variables.

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Answer:

.............................

The missing vertex is (11, 7) with an area of 128 in2.

The probability she makes at least 65 is 0.0139.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

\(\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}\)

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The correct solution to this problem is option e. 1/e. We can find it in the following manner.

The time constant of an RC circuit is the time in which the current decreases to 1/e (approximately 0.368) of its initial value.

This can be derived from the equation for the current in an RC circuit:

\(I=10 * e^({-t/RC} )\)

where I is current at time t, I0 is the initial current, R is the resistance, C is the capacitance, and e is the mathematical constant approximately equal to 2.71828.

To find the time constant, we set the exponent to -1:

\(e^({-t/RC} ) = 1 /e\)

Solving for t/RC, we get:

t/RC = 1

Therefore, the time constant is equal to RC, and the current decreases to 1/e of its initial value in one time constant.

So the answer is e. 1/e.

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Answer:

A) The volume of the cylinder is 1017.9 in³.

B) The volume of the enlarged cylinder is 27,482.7 in³.

Step-by-step explanation:

The radius of the cylinder is r = 6 in and the height is h = 9 in.

The volume of a cylinder can be found using the formula:

Substitute r = 6 and h = 9 into the formula.

The volume of the cylinder is 1017.876 in³.

If the cylinder is enlarged by a factor of 3, this means that each dimension is getting increased by 3.

Therefore, we need to multiply the original volume by a factor of three cubed; 3³.

The volume of the enlarged cylinder is 27,482.652 in³.

Answer:

The answer is C. 55,000

Step-by-step explanation:

Hope this helps ;)

To find F(x), we integrate the given derivative function. F'(x) = 6 implies that F(x) is the antiderivative of 6 with respect to x, which is 6x + C. To find F"(x), we differentiate F'(x) with respect to x. F"(x) is the derivative of 6x + C, which is simply 6.

To find F(x), we need to integrate the given derivative function F'(x) = 6. Since the derivative of a function gives us the rate of change of the function, integrating F'(x) will give us the original function F(x).

Integrating F'(x) = 6 with respect to x, we obtain:

∫6 dx = 6x + C

Here, C is the constant of integration, which can take any value. So, the antiderivative or the general form of F(x) is 6x + C, where C represents the constant.

To find F"(x), we differentiate F'(x) = 6 with respect to x. Since the derivative of a constant is zero, F"(x) is simply the derivative of 6x, which is 6.

Therefore, the function F(x) is given by F(x) = 6x + C, and its second derivative F"(x) is equal to 6.

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The scale factor of dilation is 3.

What is Dilation of a circle?

Dilation is the process of altering an object's or shape's size by reducing or enlarging its dimensions by a certain amount of scale. A circle with a radius of 10 units, for instance, is reduced to a circle with a radius of 5 units. This technique is applied in art and craft, photography, and logo design, among other fields.

Given : Radius of original circle A = 3

            Radius of Dilation circle B = 9

We know that, Scale factor of dilation =

Dimension of Dilation shape / Dimension of original shape

So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A

                                                      = 9/3

                                                      = 3.

Hence, Scale factor of dilation of circle B on Circle A is 3.

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Distance more for Kiara run than walk is, 2/3 miles.

We have,

Kiara ran 5/6 a mile and walked 1/6 of a mile.

Since, Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Hence, Distance for Kiara run than walk is,

= 5/6 - 1/6

= (5 - 1) / 6

= 4/6

= 2/3 miles

Therefore, Distance more for Kiara run than walk is, 2/3 miles.

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The projection of v along u is ∥=⟨(13/2), (13/2)⟩.

To find the projection ∥=⟨,⟩ of =⟨6,7⟩ along =⟨1,1⟩, we first need to find the unit vector in the direction of =⟨1,1⟩. This can be done by dividing =⟨1,1⟩ by its magnitude:

||⟨1,1⟩|| = √(1^2 + 1^2) = √2
unit vector in the direction of =⟨1,1⟩: =⟨1/√2, 1/√2⟩

Next, we need to find the dot product of =⟨6,7⟩ and the unit vector in the direction of =⟨1,1⟩:

⟨=⟨6,7⟩, =⟨1/√2, 1/√2⟩⟩ = (6/√2) + (7/√2) = 13√2

Finally, we can use the dot product to find the projection ∥=⟨,⟩ of =⟨6,7⟩ along =⟨1,1⟩:

∥=⟨,⟩ = (⟨=⟨6,7⟩, =⟨1/√2, 1/√2⟩⟩ / ||⟨1,1⟩||^2) * =⟨1,1⟩
= (13√2 / 2) * =⟨1,1⟩
= ⟨13√2 / 2, 13√2 / 2⟩

Therefore, the projection ∥=⟨,⟩ of =⟨6,7⟩ along =⟨1,1⟩ is ⟨13√2 / 2, 13√2 / 2⟩.
Hi! I'd be happy to help you find the projection of vector v along vector u. Given the terms "∥=⟨,⟩", "projection", "v=⟨6,7⟩", and "u=⟨1,1⟩", here's the step-by-step explanation to find the projection:

Step 1: Find the dot product of v and u.
v = ⟨6,7⟩
u = ⟨1,1⟩
v∙u = (6*1) + (7*1) = 6 + 7 = 13

Step 2: Find the magnitude of u squared.
|u|^2 = (1^2) + (1^2) = 1 + 1 = 2

Step 3: Calculate the scalar projection.
scalar_proj = (v∙u) / |u|^2 = 13 / 2

Step 4: Multiply the scalar projection by the unit vector u.
proj_v = scalar_proj * u = (13/2) * ⟨1,1⟩ = ⟨(13/2), (13/2)⟩

So, the projection of v along u is ∥=⟨(13/2), (13/2)⟩.

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1, 4, & 5 are quadratic expressions in vertex form

Answer: 60

Step-by-step explanation:

From the question, we are informed that a small box holds 40 stuffed toys and that a large box holds 150% as many stuffed toys as that of a small box.

The number of stuffed toy that the large box hold would be calculated as:

= 150% × 40

= 150/100 × 40

= 1.5 × 40

= 60

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Can I get brainly?

Answer:

c and d

Step-by-step explanation:

ok so i do not know how to explain

The equation of the horizontal parabola with vertex (2, -1) that passes through the point (5, 0) is: y + 1 = (1/9)(x - 2)^2

The equation of a horizontal parabola can be written in the form:

(y - k) = a(x - h)^2

where (h, k) represents the vertex of the parabola.

Given that the vertex is (2, -1), we have h = 2 and k = -1.

Substituting these values into the equation, we have:

(y - (-1)) = a(x - 2)^2

Simplifying, we get:

y + 1 = a(x - 2)^2

To find the value of 'a' and complete the equation, we can use the fact that the parabola passes through the point (5, 0).

Substituting x = 5 and y = 0 into the equation, we have:

0 + 1 = a(5 - 2)^2

1 = 9a

Solving for 'a', we get:

a = 1/9

Substituting this value of 'a' back into the equation, we have:

y + 1 = (1/9)(x - 2)^2

Therefore, the equation of the horizontal parabola with vertex (2, -1) that passes through the point (5, 0) is:

y + 1 = (1/9)(x - 2)^2

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Answer:

The number is  48

Step-by-step explanation:

First, let's call the number we are looking for n.

We can then write "two-thirds of the number" as 2/3n

We can also write "one-half of a number" as 1/2n

Finally, we are told 1/2n is the same as 2/3n −8 or: 1/2n = 23n −8  

We can now solve for n: 1/2n − 2/3n = 2/3n −8 − 2/3n 1/2n − 2/3n = −8We next need to get the fractions over common denominators, in this case, 6 by multiplying each fraction by the necessary for of 1: (3/3) 1/2n − (2/2) 2/3n = −8 3/6n − 4/6n = −8 − 1/6n = −8.  

We can finally solve for n by multiplying by -6 to isolate n −6 ⋅(−1/6)n = −8⋅ − 6  

1n = 48

n =48

Answer:

Common difference = x - 2.

Step-by-step explanation:

Differences:

-2x - 9 - (-3x - 7)

= -2x - 9 + 3x + 7

= x - 2

-x - 11 - (-2x - 9)

= - x - 11 +2x + 9

= x - 2

So, it is Arithmetic.

Answer:

Arithmetic sequence.

Common difference = -x - 11

Step-by-step explanation:

This is an arithmetic sequence.

-3x - 7, -2x - 9,  -x - 11, ...

Find the common difference.

Common difference =second term - first term.

                                 = -2x - 9 - (-3x - 7)

                                = -2x -  9 + 3x  +7

                                = -2x + 3x - 9 + 7      {Combine like terms}

                                = x - 2

If we add the common difference to the second term, we will get the third term.

Third term = second term + common difference

                  = -2x - 9 + x - 2

                  = -2x + x - 9 - 2

                  = -x - 11.

Hence this is an arithmetic sequence.

The solution to the equation is x = -2, -1.46, -1, x = 5.46

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

0 = x^{5}+x^{4}-20x^{3}-68x^{2}-80x-32

Express properly

So, we have

x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0

Next, we plot the graph of x^5 + x^4 - 20x^3 -68x^2 -80x - 32 = 0 to determine the solution graphically

See attachment for graph

From the graph, we have

x = -2, -1.46, -1, x = 5.46

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First is to express all values the same way. For example, convert the fraction and percentage into decimal numbers:

60% → divide it by 100 and you get 0.6

7/11=0.63

Now you can order them

0.6<0.63<0.7

Using the original expressions you get that:

60%<7/11<0.7

Answer:It is not possible

Step-by-step explanation: It is not possible because we need 12 plot to solve for an accurate mean but there is only 11 data which is impossible.

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Good measures are robust, valid, objective, simple, and precisely definable.

In the context of measurement, good measures possess certain qualities that make them reliable and useful. Based on the options provided, the following qualities apply:

Robust: Good measures are robust, meaning they are resistant to outliers or extreme values that may affect the accuracy of the measurement.

Valid: Good measures are valid, meaning they accurately measure what they are intended to measure and provide meaningful information.

Objective: Good measures are objective, meaning they are free from bias or subjective interpretation, ensuring consistency and fairness.

Simple: Good measures are simple, making them easy to understand and apply. They avoid unnecessary complexity and confusion.

Precisely definable: Good measures have clear and precise definitions, ensuring consistent interpretation and allowing for replication in different contexts.

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The geometric mean between 5 and 125 will be 25.

What is geometric mean?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

The Geometric Mean (GM) is the average value or mean that, in mathematics, represents the centre tendency of a group of numbers by calculating the product of their values. In essence, we multiply the numbers collectively and take the nth root of the resulting multiplied numbers, where n is the total number of data values.

The given number is 5, 125.

So the Geometric Mean willl be (5*125)\(.^{1/2}\)

So \((625)^{1/2}\)

= 25

Hence, the geometric mean between 5 and 125 will be 25.

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Answer:

40, leg

Step-by-step explanation:

The triangle has side lengths of 9, 40, and 41.

41 is the hypotenuse, so 40 is a leg.

Answer:

s-2=5

Step-by-step explanation:

Difference of s and 2= (s-2)

" is " means "="

Hence, The difference of s and 2 is 5 can be written as s-2=5

==========================================================

Explanation:

x = number of years

y = height in feet

The equation for the first tree is

y = x+3

The slope is 1 to represent a rate of 1 ft per year of growth. The y intercept of 3 is the starting height. Refer to y = mx+b form.

For the second tree, the equation is:

y = 0.5x+4

This time we have a slope of 0.5 and a y intercept of 4.

Apply substitution to solve for x

y = x+3

0.5x+4 = x+3

0.5x-x = 3-4

-0.5x = -1

x = -1/(-0.5)

x = 2

The trees will be the same height in  2   years.

What will that height be? Plug x = 2 into either equation to find y. We should get the same y value.

y = x+3

y = 2+3

y = 5

Or we could say

y = 0.5x+4

y = 0.5*2+4

y = 1+4

y = 5

We've shown that both equations lead to y = 5 when x = 2. This means that at the 2 year mark, both trees are 5 feet tall. This helps confirm we have the correct x value.