in how many ways can the board of trustees pick a president? the president should be one of the 1000 professors.

The value of VT is 13 units and the value of ST is 23.56 units

Consider the following diagram of rectangle RSTU

We know that the diagonals of rectangle bisect each other, intersect at right angles.

For rectangle RSTU,

2RV = RT

But RT = US

So, 2RV = US

2(x + 6) = 5x - 9

2x + 12 = 5x - 9

12 + 9 = 5x - 2x

3x = 21

x = 7

So, RV = 7 + 6

RV = 13 units

But RV = VT

So, VT = 13

Now we find the value of ST using Pythagoras theorem.

RT² = ST² + RS²

ST = [tex]\sqrt{RT^2 - RS^2}[/tex]

ST = 23.56 units

Thus, VT = 13 and ST = 23.56

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Answer:441

Step-by-step explanation:

Answer:

The answer is C). 4 ÷ one third.

The table with the correct values for A, B and C are,

Black 9 36 63 90

White 13 52 91 130

A proportional relationship is defined as follows:

⇒ y = kx.

In which k is the constant of proportionality.

Here, The input and output variables for this problem are given as follows:

Input:     number of black keys.

Output:  number of white keys.

Hence, The constant k is obtained as follows:

91 = 63k

k = 91/63

k = 13/9.

So, The equation is,

⇒ y = 13x/9.

Hence, the values are given as follows;

For A:

when x = 9,

y = 13 × 9 / 9

y = 13

For B:

when x = 36,

y = 13 x 36/9

y = 52.

For C:

when x = 90,

y = 13 x 90/9 = 130.

Thus, First table is correct.

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The value of x in triangle HJK is 5 √2, So correct option is (A). The value of x in triangle ABC is 25√3, So correct option is (H).

The Pythagorean Theorem is a fundamental theorem in mathematics that relates the lengths of the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, the Pythagorean Theorem can be expressed as:

a² + b² = c²

where "a" and "b" are the lengths of the two sides of the right triangle and "c" is the length of the hypotenuse.

The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It is a widely used theorem in mathematics and has numerous applications in many fields, including geometry, trigonometry, engineering, physics, and computer graphics.

For example, in geometry, the Pythagorean Theorem can be used to find the distance between two points in two-dimensional space. In trigonometry, it can be used to find the sine, cosine, and tangent of an angle. In physics, it can be used to calculate the force required to accelerate an object, or to determine the velocity of an object at a given time.

Overall, the Pythagorean Theorem is an important theorem that provides a simple and elegant solution to many problems involving right triangles and is widely used in mathematics and science.

9. To find the value of x in triangle HJK, we can use the Pythagorean theorem. Let's call JK = x.

HK² + JK² = KH²

Since Angle HKJ is 60 degrees and Angle KHJ is 90 degrees, we can use the trigonometric ratios to find the length of HK:

HK = JK × tan 60 = JK / √3

Substituting this into the equation above, we get:

JK² / 3 + JK² = 5²

Expanding and solving for JK, we find that:

JK = 5 √2

So, the answer is (a) 5√2.

10. To find x in triangle ABC, we can use similar methods as in question 9. Let's call BC = x. Then, by the Pythagorean theorem, we have:

AC² + BC² = AB²

Since Angle BAC is 60 degrees and Angle ABC is 90 degrees, we can use the trigonometric ratios to find the length of AB:

AB = AC / √3

Substituting this into the equation above, we get:

AC² + BC² = (AC / √3)²

Expanding and solving for BC, we find that:

BC = AC * √3 / 2 = 50 × √3 / 2 = 25√3

So, the answer is (H) 25√3

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After answering the provided question, we can conclude that Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).

In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of side lengths. A parallelogram is a type of quadrilateral in which both sets of opposite corners are similar and equal. Parallelograms are classified into four types, three of which are unique. The four different shapes are parallelograms, squares, geometric shapes, and rhombuses. A quadrilateral is a parallelogram when it has two sets of equal spacing. The opposing sides and angles of a parallelogram are both the same length. The interior angles on each side of the solid line are also angles. The total number of interior angles is 360.

Option C: The fact that V is the midpoint of PR suffices to demonstrate that PORS is a parallelogram.

We know that PV = VR because V is the midpoint of PR. Furthermore, because QR = SP (as shown in the drawing), we can conclude that triangles QRP.

We can deduce from this congruence that angle QRP is congruent to angle SPR, which means that angle POR is congruent to angle PSR (because they are corresponding angles). Angle OPS is also congruent with angle ORP (because they are corresponding angles).

Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).

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The length of the tunnel is approximately 205.6 meters to the nearest tenth.

What is Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

       a²+b²=c²

Here's one way to find the length of the tunnel:

1) Draw a diagram to represent the situation

2) Draw the perpendiculars from the surveyor to each entrance, and label the height of the triangle formed by each entrance and the surveyor as h1 and h2, respectively

3) Use trigonometry to find h1 and h2:

h1 = 243 * sin(47) = 160.1

h2 = 186 * sin(27) = 105.8

4) Find the horizontal distance between the two entrances, which is the length of the tunnel, by using the Pythagorean theorem:

[tex]d = \sqrt{(h1^2 + h2^2) }\\\\ d = \sqrt{(160.1^2 + 105.8^2)}\\\\ d = 205.6[/tex]

So, The length of the tunnel is approximately 205.6 meters to the nearest tenth.

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Answer:

Step-by-step explanation:

width is 10 length is 15.

The system of equations to find the number of each type of shot is x + y = 59 and x + 2y = 103

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let x represent the number of 1 point shots and y represent the number of 2 point shot.

The team made 59 successful shots, hence:

x + y = 59      (1)

Also, The team scored 103 points in all, therefore:

x + 2y = 103    (2)

From both equations:

x = 15, y = 44

The team made 15 number of 1 point shots and 44 number of 2 point shot.

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Answer:

there is no question. but these are two of the same lines with different Y-intercepts.

The value of (x + y) in parallelogram ABCD is equal to 150°.

Since ABCD is a parallelogram and ∠ADC is equal to 105°. Additionally, side AB in parallelogram ABCD is produced to point E. This ultimately implies that, angle C (∠C) and angle D (∠D) are adjacent angles of parallelogram ABCD:

∠C + ∠D = 180° (supplementary angles).

x + 105° = 180°

x = 180 - 105

x = 75°

Based on alternate interior angles theorem, ∠y is congruent to ∠x. Therefore, we have the following:

∠y ≅ ∠x

y = 75°

(x + y) = (75 + 75)

(x+ y) = 150°.

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According to square root and multiplication, the simplified answer is 126.54.

Rewriting the equation first to perform multiplication and simplify the equation -

Equation = (5✓3 + ✓15) × (3✓5 + ✓15)

Firstly multiplying the possibile entities in the equation

Equation = 15✓15 + 5✓3×✓15 + 3✓5×✓15 + 15

Keep the value of ✓3 and ✓15 in the equation

✓15 = 3.9

✓3 = 1.7

Equation = 15×3.9 + 5×1.7×3.9 + 3×1.7×3.9 + 15

Performing multiplication on Right Hand Side of the equation

Equation = 58.5 + 33.15 + 19.89 + 15

Performing addition on Right Hand Side of the equation

Equation = 126.54

Thus, the simplified form of equation is 126.54.

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The inverse function of p(x) = 50x - 400 is p⁻¹(x) = x/50 + 8.

Given the function in the question;

p(x) = 50x - 400

To determine the inverse, replace p(x) with y.

p(x) = 50x - 400

y = 50x - 400

Now, interchange the variables y and x.

x = 50y - 400

Solve for y

Add 400 to both sides

x + 400 = 50y - 400 + 400

x + 400 = 50y

Reorder the equation

50y = x + 400

Divide both sides by 50

50y/50 = x/50 + 400/50

y = x/50 + 400/50

y = x/50 + 8

Replace y with p⁻¹(x)

p⁻¹(x) = x/50 + 8.

Therefore, the inverse is  x/50 + 8.

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A. A polynomial function A for the total sales of football and baseball jerseys is 26t^4 + 26t^2 + 760

B. The function A is neither even nor odd

a. To find a polynomial function for the total sales of football and baseball jerseys, we simply add the two functions:

A = G + H = 15t^4 + 13t^3 + 10t^2 - 10t + 750 + 11t^4 - 13t^3 + 9t^2 + 8t + 650 = 26t^4 + 26t^2 + 760

b. The function A is neither even nor odd. An even function is one that is symmetrical around the y-axis and an odd function is one that is symmetrical around the origin. The polynomial function A has no symmetry around either the y-axis or the origin, so it is neither even nor odd.

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For a quadratic equation:

a*x^2 + b*x + c = 0

The quadratic formula is just:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

For a general quadratic equation:

a*x^2 + b*x + c = 0

The quadratic formula is:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

So for example, let's assume that we have the quadratic equation:

3x^2 + 7x - 12 = 0

Here we have the values:

a = 3

b = 7

c = -12

Now you could just replace them in the quadratic formula and you will get:

[tex]x = \frac{-7 \pm \sqrt{7^2 - 4*3*-12} }{2*3}[/tex]

And if you simplify that you will get the two solutions.

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The exact value of the given trigonometry expression is 16/65

Given the following trigonometry expressions

Cos (x + y)

sin x = 5/13 and:

sin y = 4/5

We need to find the exact value of cos(x+y)

According to the trigonometry identity

cos(x+y) = cosxcosy - sinxsiny

If sinx = 5/13, then cosx = 12/13. Also, if siny = 4/5, then cosy = 3/5

Substitute to have:

cos(x+y) = 12/13(3/5) - 5/13(4/5)

cos(x+y) = 36/65 - 20/65

cos(x+y) = 16/65

Hence the exact value of cos(x+y) is 16/65

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Answer:

Step-by-step explanation:

Let's start by calculating the distance traveled in the first scenario:

Distance = Average speed x time

First, we need to convert 2 hours and 45 minutes to hours. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours. Therefore, the total time is:

2 hours and 45 minutes = 2 + 0.75 = 2.75 hours

Now we can calculate the distance:

Distance = 106 km/h x 2.75 hours = 291.5 km

So the car travels 291.5 km in 2 hours and 45 minutes.

To find the constant speed the car must drive to travel the same distance in 2 hours and 35 minutes, we can use the same formula:

Distance = Speed x time

We know the distance is 291.5 km, and the time is 2 hours and 35 minutes. Again, we need to convert the minutes to hours:

2 hours and 35 minutes = 2 + 35/60 = 2.583 hours

Now we can solve for the speed:

Speed = Distance / time = 291.5 km / 2.583 hours ≈ 113 km/h

Therefore, the car must drive at a constant speed of approximately 113 km/h to travel the same distance in 2 hours and 35 minutes.

Answer:

A=50 B=50 too C=180

The radius of the circle is equal to the distance between the two points, or LD and LE.

A circle is a safe consisting of all points in a plane that are given distance from a given point the centre the distance from the centre to any point on the circle is known as the radius is alkal is no slider corners and all points along the circle are equidistant from the centre.


mCB= Circumference of the circle is the distance around the outside of the circle.
m/FOB= The formula for finding the circumference of a circle is C=2πr, where C is the circumference, π is 3.14, and r is the radius of the circle.
m/FIG= The formula for finding the area of a circle is A=πr2, where A is the area of the circle, π is 3.14, and r is the radius of the circle.
MAE= Mean Average Error (MAE) is used to measure the accuracy of a model or an algorithm by calculating the average difference between the predicted values and the actual values.
m/COF= The coefficient of friction (COF) is a measure of the resistance of a surface to sliding. It is usually expressed as a ratio of the force of friction to the normal force.
mZAJC= Distance between O and A is the same as the distance between J and C, or mZAJC.
mFG= The length of the arc FG is equal to the product of the central angle and the radius of the circle, or mFG.
MFI= The length of the arc FI is equal to the product of the central angle and the radius of the circle, or MFI.
m/ELD= The length of the line segment ED is equal to the difference between the lengths of the two arcs, or m/ELD.
mFM= The length of the arc FM is equal to the product of the central angle and the radius of the circle, or mFM.
m/AOC= The length of the line segment OC is equal to the difference between the lengths of the two arcs, or m/AOC.
m/AHF= The length of the line segment HF is equal to the difference between the lengths of the two arcs, or m/AHF.
IF= The length of the arc IF is equal to the product of the central angle and the radius of the circle, or IF.
PC= The length of the line segment PC is equal to the difference between the lengths of the two arcs, or PC.
HM= The length of the line segment HM is equal to the difference between the lengths of the two arcs, or HM.
LD and LE are tangent to the circle. This means that the radius of the circle is equal to the distance between the two points, or LD and LE.

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Answer:20x^8+28

Step-by-step explanation:multiply both terms by 4

The kind of sampling that is being used by the snack food company, which is developing a new flavor for crackers and which asks customers to text their preference between two possibilities, is known as non-probability sampling.

Non-probability sampling refers to a sampling technique where a researcher selects samples that are based on the subjective judgment of the researcher rather than random selection. This kind of sampling is a less stringent method, and the method depends heavily on the expertise of the researchers.

Non-probability sampling is carried out by observation, and it is used widely for qualitative research.

Since the food company selects only samples that the company would like (the samples being the company's own customers), the company uses non-probability sampling.

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The solution of the system of equations include the following:

(0, 2)

(-4, 0).

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the above, we can logically deduce the following system of equations:

y = 1/2(x) + 2     .......equation 1.

2y = x + 4           .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

2(1/2(x) + 2) = x + 4

x + 4 = x + 4

x - x = 4 - 4 (no solution).

However, we would solve the system of equations graphically in order to determine the solutions as shown in the image attached below.

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Answer:

Step-by-step explanation:

$300

For f(x) =4x+1 and g(x) = x²-5, the answer of (f/g) (x) is D) 4x+1/x²-5, x≠±√5

From the question, we have:

f(x) =4x+1

g(x) = x²-5

If what you are looking for is( f/g) (x), then only place the value of f(x) as the quantifier and g(x) as the denominator. Then the function that satisfies is D.

But here there is a condition that (f/g) (x) applies if the value of x is not √5 or -√5. Because if it becomes an x value then the result will be 0.

We can prove this:

With this equation (f/g) (x)=4x+1/x²-5

let's try to use value of x is √5, it will be

(f/g) (x)=4x+1/x²-5

(f/g) (√5) = 4.√5+1/(√5)²-5

=(4√5+1)/5-5

=(4√5+1) /0

=0

Then, try to use value of x is -√5, it will be

(f/g) (x)=4x+1/x²-5

(f/g) (√5) = 4.(-√5)+1/(-√5)²-5

=(-4√5+1)/5-5

=(-4√5+1) /0

=0

From the results above it proves that option D cannot be used if x= ±√5.

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The future value of this one-time investment of $1,000 in 5 years is equal to: A. $1,082.5.

Mathematically, future value can be calculated by using this formula:

F = P(1 + r)

Where:

Substituting the given parameters into the future value formula, we have the following;

Future value, F = 1,000(1 + 8.25/100)

Future value, F = 1,000(1 + 0.0825)

Future value, F = 1,000(1.0825)

Future value, F = $1,082.5.

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Answer: H = -1

Step-by-step explanation:

12 + 7h = 5

7h = -7

H = -1

The algebraic expression for this problem is given as follows:

2C - D = -2x² + 2x + 11.

The definition for C in this problem is given as follows:

C = x + 3.

We applying the distributive property to multiply by 2 as follows:

2C = 2(x + 3) = 2x + 6.

The definition for D in this problem is given as follows:

D = 2x² - 5.

The subtraction is then obtained as follows:

2C - D = 2x + 6 - (2x² - 5)

2C - D = 2x + 6 - 2x² + 5

2C - D = -2x² + 2x + 11.

Meaning that the second option is correct.

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The correct choices are 1) B, 2) G, 3) C, 4) I.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

1) The price paid for $60 jeans after a 35% discount is applied can be found as follows:

Discount Amount = 60 * 35% = $21

Price Paid = 60 - 21 = $39

Correct choice is B.

2) The discount amount on a $55 sweatshirt with a 20% discount can be calculated as follows:

Discount Amount = 55 * 20% = $11

Correct choice is G.

3) The 20% tip on a $73 meal can be calculated as follows:

Tip Amount = 73 * 20% = $14.6

Correct choice is C.

4) The 7% sales tax on a new $32,000 car can be calculated as follows:

Tax Amount = 32000 * 7% = $2,240.

Correct choice is I.

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Answer:

30

Step-by-step explanation:

5 + 5 + 10 + 4 + 6 = 30