A baseball player has a lifetime batting average of 0.349. If each at bat is independent and he comes to bat 6 times in a given game, what is the probability that the following occur? (Round your answers to five decimal places.) (a) he will get 4 hits (b) he will get more than 4 hits

The value of the account after 15 years will be approximately $5,756.24.

To calculate the future value of the savings account, we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial deposit), r is the interest rate (expressed as a decimal), n is the number of compounding periods per year, and t is the number of years. In this case, the deposit is $3,200, the interest rate is 3.5% (or 0.035), and compounding is done quarterly (n = 4). Substituting these values into the formula with t = 15 years, we can calculate the future value. Therefore, the value of the account after 15 years will be approximately $5,756.24.

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We establish the given binomial expression (x + y)^4 in the following way

The nth power of the sum of two integers a and b may be represented as the sum of n + 1 terms of the form, according to the binomial theorem, which states that for every positive integer n.

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

(x+y) 4=

((x+y)2) 2=

(x2+2xy+y2) 2=

(x2+2xy) 2+2(x2+2xy) (y2)+(y2) 2=

(x4+4x3y+4x2y2)+(2x2y2+4xy3)+(y4)=

x4+4x3y+6x2y2+4xy3+y4

The binomal theorem is a more comprehensive strategy:

(x+y)

n=∑k=0n(nk)

⋅xn−k⋅yk=∑k=0n(nk)

⋅xk⋅yn−k\sWhere\s(nk)=n!((n−k)!)⋅(k!)

n!={1n⋅((n−1)!)

n=0n>0

∑k=0nf(k)=f(0)+f(1)+f(2)+…+f(n)

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Answer:

V = pi * R^2 * h

R = (V / (pi * h))^1/2 = (141.3 / (3.14 * 5))^1/2 = 3 cm

The radius of the cylinder is 3 cm.

Given,

The volume of the cylinder is 141.3 cubic centimeters.

We need to find what is the approximate radius of the cylinder.

Use 3.14 for the approximation of pi.

It is given by:

V = π r² h

h = height of the cylinder

r = radius of the cylinder.

We have,

V = 141.3 cm³

π = 3.14

h = 5 cm

V = π r² h

141.3 = 3.14 x r² x 5

141.3 / 3.14 x 5 = r²

r² = 9 cm²

r = 3 cm

Thus the radius of the cylinder is 3 cm

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Answer: x = 4

Step-by-step explanation:

The formation of a triangle with 15 dots can vary depending on the arrangement of the dots. To form a triangle, we need at least 3 points connected by straight lines.

One possible arrangement is to have 3 dots arranged in a straight line. By connecting these dots, we can form a triangle. Another possibility is to have 4 dots in a square shape, where the diagonals of the square connect to form a triangle.

Additionally, we can arrange the dots in a pattern where the first row has 1 dot, the second row has 2 dots, the third row has 3 dots, and so on, forming a triangular pattern. In this case, we would need a total of 15 dots to complete the triangular pattern.

Overall, there are multiple ways to form a triangle with 15 dots, but we need to ensure that there are at least 3 dots connected by straight lines.

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Answer:

\( \frac{(x - 7)(x + 2)}{x(2 {x}^{2} -13x - 7) } \\ \frac{(x - 7)(x + 2)}{x(x - 7)(2x + 1)} \\ \frac{(x + 2)}{x(2x + 1)} \)

The value of Sally's interest after 4 years is approximately £903.48.

To calculate the interest, we use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. In this case, Sally's principal amount is £8000, the annual interest rate is 2.8% (or 0.028 as a decimal), and the interest is compounded annually (n = 1). Plugging these values into the formula, we get A = 8000(1 + 0.028/1)^(1×4) = £903.48. Therefore, Sally's interest after 4 years is approximately £903.48.

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Answer:

Step-by-step explanation:

b/c this is an isosceles triangle  we know that either leg is the same length.. so we can use many trig functions  :)

SOH CAH TOA to remember how trig functions fit on the triangle...

we know the hypotenuse and the angle and we want to find the adjacent leg ( which for this triangle is also the opposite leg )

use Cos = Adj / Hyp

Hyp*Cos(45) = adj

16* \(\sqrt{2}/2\) = adj

8*\(\sqrt{2}\) = adj

each leg is the same  \(8\sqrt{2}\)

The number of individuals in Chicago that will respond positively to Program 2 is 22 out of 25.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Given that the chances of a positive response from Chicago residents to two government programs are 65.9% for Program 1 and 87.5%  for Program 2, the likelihood of a positive response for Program 2 given that the person is from Los Angeles must be calculated as follows:

87.5 100 = X

43.75 / 50 = X

21.875 / 25 = X

Therefore, 22 out of 25 individuals in Chicago  will respond positively to Program 2.

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Answer:

(12,7) is not a solution

Step-by-step explanation:

Given

\(y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6\)

Required

Point that is not a solution

We have:

\(y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6\)

Substitute \(\frac{2}{3}x + 6\) for y in the first inequality

\(\frac{2}{3}x + 6 \ge x + 5\)

Collect like terms

\(\frac{2}{3}x - x \ge 5-6\)

\(-\frac{1}{3}x \ge -1\)

Solve for x (the inequality will change because we are to divide by a  negative number_

\(x \le -1/-\frac{1}{3}\)

\(x \le 3\)

Without solving further, we can conclude that the first option is not a solution.

Because (12,7) implies that \(x =12\)

Compare \(x =12\) to \(x \le 3\), then \(x \le 3\) is false

Answer:

the thrid one

Step-by-step explanation:

bc its all correct like i went over all of it and its correct glad to help bro!!!!!

Answer:

c

Step-by-step explanation:

Answer:

hello :

Step-by-step explanation:

x(x+3)(x+3)=0  means : x=0 or x+3=0 or x+3=0

x=0 or x=-3 or x=3

Answer: 4.The equation has no solutions.

The equation 2+3x=4x+1-X has no solutions.

To solve for x, we can combine like terms and then factor the equation.

2+3x=4x+1-X

-X+3x=1-2

2x=-1

x=-1/2

However, this value of x does not satisfy the original equation. When we substitute x=-1/2 into the original equation, we get

2+3(-1/2)=4(-1/2)+1-(-1/2)

-1=-3

This is a contradiction, so the equation has no solutions.

Therefore, the correct answer is 4. The equation has no solutions.

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Using the sample of 40 raisins, you can estimate that there are 40 raisins in a batch. However, due to the uncertainty of the sample size, there is an element of uncertainty as to how many raisins there truly are in a batch.

Thus, the uncertainty of your estimate can range from slightly below 40 raisins to slightly above 40 raisins.

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Complete question is;

Tiothy evaluated the expression using x = 3 and y = –4. The expression is (xy^(-2))/(3x²y^(−4))

1. (1/3)x^(−1)(y²) 2. ((1/3)^(3−1))(−4²) 3. (1/3)(1/3)(−4)² 4. (1/3)(1/3)(−16) 5. −16/9 Analyze Timothy's steps. Is he correct? If not, why not?

A) Yes, he is correct.

B) No, he needed to add the exponents when he simplified the powers of the same base.

C) No, he needed to multiply 3 and –1 instead of creating a positive exponent in a fraction.

D) No, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.

Answer:

D) No, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.

Step-by-step explanation:

The expression is;

(xy^(-2))/(3x²y^(−4))

Simplifying this using law of indices gives;

⅓(x^(1 - 2)) × (y^(-2 -(-4))

This gives;

= (⅓x^(-1)) × y²

= ⅓ × (1/x) × y²

We are told that x = 3 and y = –4, thus;

= ⅓ × ⅓ × (-4)²

Square of a negative number is positive, thus (-4)² = 16

Thus;

⅓ × ⅓ × (-4)² = 16/9

Looking at the answer Timothy got, it's clear he made a mistake of not getting a positive number when he squared -4.

Thus,option D is the correct answer.

Answer:

D

Step-by-step explanation:

i got it correct

Answer:

-26

Step-by-step explanation:

I just did it and I got it right

Answer:

64

Step-by-step explanation:

Answer:

80% of the students passed the algebra test

Step-by-step explanation:

So for this question, they want to know the percentage of the people that passed.

20 out of 25 students passed, we could find the percentage using two ways:

-------

1. We can use proportions to figure out the percentage (This can only work if the numbers are factorable by 100 such as 10, 25, 50...)

25 × 4 would equal 100. You must multiply the same number to the top as well.

So 20 × 4 = 80

--------

2. We can divide the two numbers

20 ÷ 25 = 0.8

When changed into a percentage, 0.8 would be 80%

-------

Have a good day :)

Answer:

4.5

Step-by-step explanation:

45/10=4.5

Answer:

it is

Step-by-step explanation:

beacaus in Quadrilateral the opposite sides are equal

A Quadrilateral has 4sides,4angles,2 diagonals and the sum of the interior and exterior of Quadrilateral is equal to 360°

Interior means=inside

Exterior means=outside

The value of the missing value in ? is 12

The diagram given in the question is known as a quadrilateral. A quadrilateral is a two-dimensional plane figure in a closed shape containing:

The shape of the second diagram given in the question is a rhombus. The opposite sides of a rhombus are parallel to each other.

Therefore, we can conclude that the missing value of the shape is 12.

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Answer:

Step-by-step explanation:

8x³ + 2x²  -20x - 5

= (8x³ + 2x²) + (-20x - 5)

= 2x² (4x + 1) + (-5)(4x + 1)

= (2x² - 5)(4x +1 )

The volume of a square pyramid is given by the formula: V = (1/3) * b^2 * h

where b is the base length and h is the height.

In this case, the base is a square with sides of length 2.75 inches, so the base area is:

b^2 = 2.75^2 = 7.5625 square inches

The height of the pyramid is also 2.75 inches.

Therefore, the volume of the ornament is:

V = (1/3) * 7.5625 * 2.75 = 6.5391 cubic inches

Rounding to the nearest hundredth, the approximate volume of the ornament is:

V ≈ 6.54 cubic inches

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Answer: 25 pi

Step-by-step explanation:

Answer:

Step-by-step explanation:

The least common multiple of 126 and 131 is

16,506

The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)

First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).

Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).

\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)

\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)

Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)

Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.

Now, we will write the equations with the coordinates of the basis vectors of \(b'\).

\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)

Now we will write the matrix of \(A\) as follows:

\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)

Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

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Answer:

\(y = - x + 3 \\ 3y + 5x = - 1\)

Step-by-step explanation:

\(3( - x + 3) + 5x = - 1 \\ - 3x + 9 + 5x = - 1 \\ 2x = - 10 \\ x = - 5 \\ y = - x + 3 \\ y = 5 + 3 = 8 \\ y = 8\)

Answer: x = 6

Step-by-step explanation:

9(8 - x) = 3x

72 -9x = 3x

add 9x to both sides

72 = 12x

divide 72 by 12

x = 6

Answer:

x = 18

Step-by-step explanation:

sum of interior angles of a polygon is determined by the formula

(n - 2) · 180° where 'n' is the number of sides the polygon has

there are 5 sides in this problem so the number of degrees is 3 · 180 = 540°

we can get the sum of all 5 angles and set it equal to 540

3x + 23 + 9x - 6 + 7x - 4 + 90 + 95 = 540

19x + 13 + 185 = 540

19x + 198 = 540

19x = 342

x = 342/19 = 18