Which of the following can be used to evaluate the series 8∑k=1 5(2/3)^k-1?

The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.

P(B) = 1/4

P(A and B) = 3/25

The conditional probability is used to find the P(A|B):

P(A|B) = P(A and B) / P(B)

Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.

By substituting the given values in the given probability, we get:

P(A|B) = (3/25) / (1/4)

Divide the fraction and multiply it with its reciprocal:

P(A|B) = (3/25) * (4/1)

P(A|B) = 12/25

Therefore, we can conclude that the missing probability is P(A|B) is 12/25.

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The complete question is:

Find the missing probability.

P(B)=1/4P

(AandB)=3/25P

P(A|B)=?

The sample proportion who said they pray is approximately 0.84, or 84%.

The sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).

Sample proportion = Number of students who said they pray / Total number of students in the sample

Sample proportion = 105 / 125

Sample proportion = 0.84

Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.

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The measurement of DE is 10 inches.

If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.

Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.

Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:

BD = √(L^2 + W^2)

Since we know that the diagonals of a rectangle are equal, we have:

AC = BD

BD = 20

Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.

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The correct matrix representation is;  [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,

Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(1, 3) and P₂(5, 2)

Thus, by the coordinates of the two vectors, we can represent the matrix  ;

[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Hence, Option A) is the correct answer.

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Segment BF is 36 will be the accurate statement.

A triangle known to be similar if the ratio of similar sides of the triangle is equal to a constant.

From the given triangle, the following expression is true:

EC/FC = AC/BF+FC

Substitute the given parameters into the formula to have:

20/30 = 24+20/BF+30

20/30 = 44/BF+30

2/3 = 44/BF + 30

2(BF+30) = 132

2BF + 60 = 132

2BF = 132 - 60

2BF = 72

BF = 36

Hence the correct statement will be that segment BF is 36

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The equation for the distance of the point (x, y), from the center of the circle is; (x - 4)² + (x - 2)² = 5²

The general form of the equation of a circle with center (h, k) is; (x - h)² + (y - k)² = a², where the radius of the circle is; a

The radius of a circle is the distance from the center to a point (x, y) on the circumference, therefore, the equation for the distance of the point (x, y) from the center of the circle, is equivalent to the equation for a circle, where the distance of the point (x, y) from the center is the radius.

The coordinates of the center of the circle, (h, k) = (4, 2)

The radius of the circle, r = a = 5

The equation for the distance (x, y) from the center, which radius of the circle, with center (4, 2), is therefore;

Equation of a circle; (x - h)² + (y - k)² = a²

Equation from the center; (x - 4)² + (y - 2)² = 5²

Where;

5 = The radius, a = The distance from the center of the circle

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The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

We have,

To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:

x² + 12 = x² + (2√3)²

Now we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

In this case, we have a = x and b = 2√3. So we can write:

= x² + 12

= x² + (2√3)²

= (x + 2√3)(x - 2√3)

Therefore,

The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

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[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

is the equation of the given system.

Equation of the line using the coordinates (-3, 0) and (0, 3), we get:

slope = (3 - 0) / (0 - (-3)) = 1

Now we have the slope of the line. Next, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Using the point (-3, 0) and the slope we just found (which is also the slope of the line passing through the point (0, 3)), we get:

y - 0 = 1(x - (-3))

Simplifying, we get:

y = x + 3

Therefore, the equation of the line passing through (-3, 0) and (0, 3) is y=x+3.

Similarly, the equation of the line passing through (1, -1) and (0, -4) is y = -3x + 2.

Thus, from the graph the equation of the system is,

[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

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Answer:

(- 2, 0 ) , (1, - 3 )

Step-by-step explanation:

the solutions to the system of equations are at the points of intersection with the curve and the straight line.

points of intersection are at (- 2, 0 ) and (1, - 3 ) , then

solutions are (- 2, 0 ) , (1, - 3 )

Okay, here are the steps to solve this problem:

1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48

2) We want to find the time (t) when the rocket hits the ground (h = 0)

3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0

4) Factor the left side: - 3(t2 - 0t) + 48 = 0

5) Solve for t2 - 0t: t2 - 0t = 16

6) Add 0t to both sides: t2 = 16 + 0t

7) Take the square root of both sides: t = 4

Therefore, the time for the rocket to hit the ground is 4 seconds.

So in this case, t = 4

Let me know if you have any other questions!

Answer:

4 seconds.

Step-by-step explanation:

When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]

Now set this equal to 0

[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.

[tex]-48 = -3t^2[/tex]

[tex]16 = t^2[/tex]

From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.

Hope this helps

1/4π radians is approximately equal to 45 degrees.

To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.

Degrees = Radians × 180/π.

Therefore, to convert 1/4π radians to degrees, we have:

Degrees = (1/4π) × (180/π) ≈ 45°

Hence, 1/4π radians is approximately equal to 45 degrees.

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After considering the given interval we reach the conclusion that the coefficient of t² is 1/2(3w² - 1), under the condition that the given expression is [tex](1-2 t w+t^{2})^{-1/2}[/tex] with range of (t<<1)

To evaluate the value for the given expression we have to apply the principles of binomial theorem

Then

[tex](1-2 t w+t^{2})^{-1/2} = (1 + (-2 t w + t^{2})/2 + (-2 t w + t^{2})^{2/8} + (-2 t w + t^{2})^{3/16} + ...)[/tex]

= 1 - t w + 3/8 * t² * w² - 5/16 * t³ * w³ +

The coefficient of t is the coefficient of the first term with a power of t.

Therefore, the coefficient of t is 1/2(3w² - 1).

The binomial theorem refers to the statement regarding any positive integer n, the nth power of the sum of two numbers a and b could be expressed as the sum of n + 1 terms of the form. The binomial theorem is applied in algebra and probability theory.

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The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

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The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?

Answer:

74,000

Step-by-step explanation:

use intelligence

The claims are this year some of their clients will have a starting salary of at least $38,500 and last year at least one of their clients had a starting salary of exactly $38,500. Correct options are A and B.

Based on the given information, option A can be true. This is because the average starting salary of the job placement agency's clients was $38,500 last year, which means some clients had a starting salary equal to or greater than that amount.

Option B is also true because the mean includes all values, including the value of $38,500, so it is likely that at least one client had that starting salary.

Option C cannot be determined from the given information as it is unclear what percentage of clients had a starting salary above $38,500. Option D is not necessarily true as there is no information on the starting salary of any client exceeding $42,000.

Option E is also not true as the average salary of $38,500 does not guarantee that all clients had that same starting salary. Therefore, the correct answer is A and B, and the rest cannot be determined from the given information.

Correct options are A and B.

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The volume of the rectangular pyramid is 144.48 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]

[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]

[tex]\sf V = \dfrac{433.44 }{3}[/tex]

[tex]\sf V = 144.48 \ cubic \ feet[/tex].

Hence, the volume of the rectangular pyramid is 144.48 cubic feet.

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The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

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The value of x will be 10.

Given a triangle we need to set a proportion to solve for the value of x,

Therefore, according to the definition of the similar triangles,

x / 5 = 15+5 / x

x² = 5 × 20

x² = 100

x = 10

Hence the value of x will be 10.

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Answer:

20

Step-by-step explanation:

She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.

The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

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Using the first two points we can get an exponential model:

[tex]y = (225/23)*(23/15)^x[/tex]

The general exponential equation can be written as:

[tex]y = A*(b)^x[/tex]

We can replace any two values of the table to get the system of eqautions:

[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]

Taking the quotient between the second and the first equation we get:

[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]

Replacing that on the first equation we will get:

[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]

Then an exponential model is:

[tex]y = (225/23)*(23/15)^x[/tex]

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Answer:

34

Step-by-step explanation:

1. Plug in the week's salary into the formula

S=400+35v

1590=400+35v

2. Solve for v.

1590=400+35v

Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.

1190=35v

Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.

34=v

The length of fencing needed around her triangular garden is 41 feet.

A given shape which has three sides and three measures of internal angles which add up to 180^o is said to be a triangle.

For Mary to build a fence around her triangular garden, the amount of fencing needed can be determined by adding the length of each side of the garden.

So that;

A + B + C = 180^o

A + 49 + 40 = 180

A = 180 - 89

   = 91

A = 91^o

Applying the sine rule, we have;

a/Sin A = b/Sin B = c/Sin C

a/Sin A = b/Sin B

a/Sin 91 = 13/ Sin 49

aSin 49 = 13*Sin 91

             = 12.998

a = 12.998/ 0.7547

  = 17.22

a = 17 ft

Also,

b/Sin B = c/Sin C

13/Sin 49 = c/ Sin 40

cSin 49 = 13*Sin 40

             = 8.3562

c = 8.3562/ 0.7547

  = 11.0722

c = 11 feet

Thus the amount of fencing required = 13 + 17 + 11

                                                    = 41

The fencing required is 41 feet length.

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The values of c  on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].

According to the Mean Value Theorem for Integrals, if f(x) is continuous on the interval [a, b], then there exists a value c in [a, b] such that:

f(c) = 1/(b-a) . ∫(a to b) f(x) dx

For f(x) = x⁴ on the interval [-5, 5], we have:

∫(-5 to 5) x⁴ dx = (1/5) . (5⁵ - (-5)⁵)/5

= (1/5) . (3125 + 3125)

= 1250

So we need to find c such that f(c) = 1250/10 = 125.

f'(x) = 4x³, so we can use the Mean Value Theorem for Derivatives to find a value of c that satisfies the condition.

f'(c) = (1/(5-(-5)))  . ∫(-5 to 5) f'(x) dx

= (1/10)  . [f(5) - f(-5)]

= (1/10) . [(5⁴) - ((-5)⁴)]

= 100

Therefore, by the Mean Value Theorem for Derivatives, there exists a value c in [-5, 5] such that f'(c) = 100.

Now, we need to check if there exists a value c in [-5, 5] such that f(c) = 125.

f(c) = c⁴, so we need to solve the equation c⁴ = 125.

c = ±[tex]5^{1/4[/tex]

Both of these values are in the interval [-5, 5], so they satisfy the Mean Value Theorem for Integrals.

Therefore, the values of c that satisfy the Mean Value Theorem for integrals for f(x) = x⁴ on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].

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Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.

We have,

A postulate is a statement or proposition that is accepted as true without proof.

It is an assumption or starting point in a logical argument that is considered to be self-evident or evident based on previous experience or observation.

In mathematics,

Postulates are used to define the basic concepts and axioms that form the foundation of a particular system of thought.

They are often used as the starting point for deriving other mathematical concepts and theorems.

Postulates are also known as axioms or assumptions.

Thus,

Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.

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Answer:

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Step-by-step explanation:

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The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)