a college plans to interview 12 students for possible offer of graduate assistantships. the college has 4 assistantships of different value available. how many ways can the assistantships be awarded

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

To prove that for any two events A and B in a sample space S, P(AUB) ≤ P(A) + P(B), we can use the axioms of probability theory. There are two or more occurrences of the number 4 in a given situation or experiment.

To prove the inequality P(AUB) ≤ P(A) + P(B) using only the axioms of probability, we start with the definition of the union of two events: AUB is the event that either A occurs or B occurs (or both).

Using the axioms, we can express the probability of the union as follows:

P(AUB) = P(A) + P(B) - P(A∩B)

The term P(A∩B) represents the probability of the intersection of events A and B, which is the event where both A and B occur simultaneously.

Since the intersection of two events cannot have a probability greater than or equal to the individual events, we have P(A∩B) ≤ P(A) and P(A∩B) ≤ P(B).

Therefore, by substituting these inequalities into the expression for P(AUB), we have:

P(AUB) ≤ P(A) + P(B) - P(A∩B) ≤ P(A) + P(B)

Thus, we have proven that for any two events A and B in a sample space S, P(AUB) ≤ P(A) + P(B) using only the axioms of probability theory.

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Answer:

64

Step-by-step explanation:

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Answer:

for the second part its d+2.5d+d-4

Step-by-step explanation:

The part of the expression represents the total amount each friend pays is  d+2.5d+d-4.

An expression is combination of variables, numbers and operators.

Each friend pays for the entrance fee, a booklet of ride tickets, and a meal ticket.

The entrance fee costs d dollars.

A booklet of ride tickets costs 2.5 times the entrance fee, which is 2.5d dollars.

A meal ticket costs $4 less than the entrance fee, which is (d - 4) dollars.

Therefore, the total amount each friend pays is:

d + 2.5d + (d - 4)

Simplifying the expression, we get:

4.5d - 4

Hence,  d+2.5d+d-4 is the part of the expression represents the total amount each friend pays.

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Using the properties of Isosceles Triangle we get that When the line containing the vertex of an isosceles triangle is drawn from the vertex angle perpendicular to the base, it bisects the vertex angle and the base.

Based on the length of the sides of the triangle, there are three types of equilateral triangles . , isosceles triangle, unequal triangle. An isosceles triangle is a triangle with two sides of equal length and corresponding angles are equal.

Statement : -

Let ABC be an isosceles triangle such that AB=AC.

Let AD be the bisector of ∠A.

we have to prove:- BD=DC

Proof :-

In △ABD&△ACD

AB=AC(∵△ABC is an isosceles triangle)

∠BAD=∠CAD(∵AD is the bisector of ∠A)

AD=AD (Common)

By S.A.S.(side angle side)

△ABD≅△ACD

By corresponding parts of congruent triangles-

⇒BD=DC

Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.

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Complete question:

Prove that if a line containing a vertex of an isosceles triangle is perpendicular drawn from the vertex angle to the base bisect the vertex angle and the base.

Two sides are congruent to each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.

A triangle with all sides of different lengths. All angles are different, too. So no sides are equal and no angles are equal.

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Answer:

Two sides are congruent to each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry.

A triangle with all sides of different lengths. All angles are different, too. So no sides are equal and no angles are equal.

Step-by-step explanation:

Answer:

0.4231 or 42.31%

Step-by-step explanation:

In a standard 52 card deck there are 13 spade cards (52/4) and there are 12 face cards (4 suits x 3 face cards). Moreover, 3 cards are both face and spade cards.

Therefore, the probability that the card Bashir chooses is either a face card or a spade is given by:

\(P(F\ or\ S)=P(F)+P(S)-P(F\ and\ S)\\P(F\ or\ S)=\frac{13}{52} +\frac{12}{52} -\frac{3}{52}\\P(F\ or\ S)=0.4231\)

The probability is 0.4231 or 42.31%

Answer:

got it on kahn trust

Step-by-step explanation:

Answer:

40°

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

A nonagon has 9 sides , then

divide sum by 9 for measure of one exterior angle

exterior angle = 360° ÷ 9 = 40°

The probability of rolling a number greater than 8 is (a) 0.125

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

Rolling a number cube once

Using the above as a guide, we have the following:

Sample space,  S = {1, 2, 3, 4, 5, 6, 7, 8}

In the above sample space, we have

Outcomes greater than 7 = {8}

So, we have

P(greater than 7) = n(Outcomes greater than 7)/n(Sample space)

Substitute the known values in the above equation, so, we have the following representation

P(greater than 8) = 1/8  = 0.125

Hence, the probability is 0.125

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The percent yield of zinc carbonate is 5.91%.

The chemical reaction is the reaction between two reactants which led to the formation of products.

The products are substances which forms after reaction. The reactants are the substances which are original materials.

Given is a reaction between 1.7 moles of zinc iodide and excess sodium carbonate yields 12.6 grams of zinc carbonate.

The given balanced equation is:  Na₂CO₃ + ZnI₂ → 2NaI + ZnCO₃

From given moles of zinc iodide, the moles of zinc carbonate

1.7 moles of ZnI₂ = 1.7 moles of ZnCO₃

Molar mass of zinc carbonate is 125.38 g/mol

Theoretical yield =  1.7 moles of ZnCO₃ x  125.38 g/mol = 213.15 g  ZnCO₃

Theoretical yield is 213.15 g and the actual yield is given as 12.6 g.

percent yield = [ 12.6 g / 213.15 g  ZnCO₃ ] x 100

percent yield = 5.91%

The percent yield of zinc carbonate is 5.91%.

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The tangent line to the curve y = x√(x - 1) at the point (2, 2√(2 - 1)) is given by the equation y = 4x - 6. This line has a slope of 4 and passes through the point (2, 2√(2 - 1)). The tangent line represents the instantaneous rate of change of the curve at the given point.

To find the equation of the tangent line to a curve at a specific point, we need to determine the slope of the tangent line and the y-intercept.

First, we find the derivative of the given function y = x√(x - 1) using the power rule and the chain rule. Taking the derivative, we get:

dy/dx = (3x^2 - 2x)/(2√(x - 1))

Next, we evaluate the derivative at x = 2 to find the slope of the tangent line at that point:

m = dy/dx | x=2 = (3(2)^2 - 2(2))/(2√(2 - 1))

                 = (12 - 4)/(2√1)

                 = 8/2

                 = 4

Now we have the slope of the tangent line, which is 4.

To find the y-intercept, we substitute the coordinates of the given point (2, 2√(2 - 1)) into the equation y = mx + b and solve for b:

2√(2 - 1) = 4(2) + b

2√1 = 8 + b

2 = 8 + b

b = -6

Therefore, the equation of the tangent line in slope-intercept form is y = 4x - 6.

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The best prediction of the average amount of money spent on groceries for a household that has 7 people can be determined by examining the scatterplot and estimating the corresponding value on the y-axis.

Based on the scatterplot, the best prediction for the average amount of money spent on groceries for a household with 7 people would be around $160.

To arrive at this prediction, we observe the position on the x-axis where the number of people in the household is 7. Then, we look at the corresponding position on the y-axis to determine the average amount of money spent on groceries. In this case, the scatterplot suggests that households with 7 people tend to spend around $160 on groceries.

It's important to note that this prediction is based on the pattern observed in the given scatterplot, and there may be some variability or uncertainty in the actual amount spent on groceries for a specific household with 7 people.

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Answer:

13

Step-by-step explanation:

Correct on edge

The function will be one-to-one only if c = 13.

A function is one-to-one if and only if each value in the range appears only once.

So, the given set will represent a one-to-one function if c takes a value that is not repeated in any of the other coordinate pairs.

We have:

(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)

For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.

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An equation that would describe the line of best fit is

Using the line of best fit, a prediction of Spot's weight after 18 months is 35 pounds.

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the graph, we would use the point-slope equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (20 - 5)/(10 - 2)

Slope (m) = 15/8

Slope (m) = 1.875

At data point (2, 5) and a slope of 1.875, a linear equation for the line of best fit can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1.875(x - 2)  

y = 1.875x + 1.25

When x = 18, the weight is given by:

y = 1.875(18) + 1.25

y = 35 pounds.

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Complete Question:

John recorded the weight of his dog Spot at different ages as shown in the scatter plot below.

Part A:

Write an equation that would describe the line of best fit.

Part B:

Using the line of best fit, make a prediction of Spot's weight after 18 months.

Answer:

(2,0)

Step-by-step explanation:

Plug in 2 for x

y=5(2)-10

y=10-10

y=0

Therefore

x=2, y=0

or

(2,0)

Answer:

(0,-10), (1,-5), (2,0)

Step-by-step explanation:

Sorry if I'm wrong

The probability that the Watson family eats dinner together at least six times during a 7-day period can be calculated using the binomial distribution. The probability is approximately 0.0332 or 3.32%.

Let's define success as the event that the Watson family eats dinner together on a particular day, with a probability of success being 2/5. Since the events of eating dinner together on different days are independent, we can use the binomial distribution to calculate the probability.  

To find the probability of having at least six successful events (eating dinner together) in a 7-day period, we need to sum the probabilities of having exactly 6, 7 successful events, and so on, up to 7.

Using the binomial probability formula, P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials (7 in this case), k is the number of successful events (6 or 7), and p is the probability of success (2/5), we can calculate the probabilities for each k and sum them.

P(X≥6) = P(X=6) + P(X=7) ≈ 0.0332 or 3.32%

Therefore, there is approximately a 3.32% chance that the Watson family will eat dinner together at least six times during any 7-day period.

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The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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Answer:

x=75

Step-by-step explanation:

The total degrees of a pentagon is 540

120+120+2(75)+75+75

120+120=240

2(75)=150

75+75=150

240+150+150=540

Answer:

4

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

LCM of 8 and 12 is 24. please refer the picture for venn diagram

The graph have a negative slope and a positive y intercept. The graph is given by y = -x + 2. The point (2, 1) lies on th line 3y = 2x - 1

An equation is an expression that shows the relationship between two or more numbers and variables.

The graph have a negative slope and a positive y intercept. The graph is given by y = -x + 2

Given the equation:

3y = 2x - 1

When x = 2:

3y = 2(2) - 1

y = 1

The point (2, 1) lies on th line 3y = 2x - 1

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x^2+y^2-12x+6y+36=0

Top Point: (6,0)

Left Point: (3,-3)

Right Point: (9,-3)

Bottom Point: (6,-6)

Answer:

\( x^2 +y^2 -12x +6y +36 =0\)

And we can complete the squares like this:

\( (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2\)

And we got:

\( (x-6)^2 + (y+3)^2 = 9\)

And we have a circle with radius r =3 and the vertex would be;

\( V= (6,-3) \)

The graph is on the figure attached.

Step-by-step explanation:

For this case we have the following expression:

\( x^2 +y^2 -12x +6y +36 =0\)

And we can complete the squares like this:

\( (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2\)

And we got:

\( (x-6)^2 + (y+3)^2 = 9\)

And we have a circle with radius r =3 and the vertex would be;

\( V= (6,-3) \)

The graph is on the figure attached.

The probability of one red sweet and one green sweet is 1/77

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

Red sweet = 11

Green sweet = 7

This means that

P(Red) = 1/11

P(Green) = 1/7

So, the required probability is

P = 1/11 * 1/7

Evaluate

P = 1/77

Hence, the probability is 1/77

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Answer:

y ≤ -x - 4

x > -1

y ≥ 4

Step-by-step explanation:

For the sloped line, we can see that the y-intercept is -4 and the x-intercept is -4.

This means at x = 0, y = - 4 and at y = 0, x = -4. We also see that the bottom of the line is shaded and that the line is not broken.

Thus, the inequality is; y ≤ -x - 4

For the vertical line, we can see it has only an x-intercept at x = - 1. We also see that the line is broken which means the equal to symbol is not part of the inequality. Also, the shaded part is to the right. Thus, the inequality is:

x > -1

For the horizontal line, we see that it has only a y-intercept at y = 4. We also see that the line is not broken which means the equal to symbol is part of the inequality. Also, the shaded part is above. Thus, the inequality is:

y ≥ 4

Therefore, the inequalities that satisfy the region R are:

y ≤ -x - 4

x > -1

y ≥ 4

Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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Answer:

cindy is 51

Step-by-step explanation:

70 divided by 2 is 45

45+ 6 is 51

Answer:

44.8 inches

Step-by-step explanation:

5.6x8

need to write something to let me answer

Answer:

44.8 inches

Step-by-step explanation:

Hope this helps

Answer:

1.176471

Step-by-step explanation:

that is in its simplest form!

Answer:

1 3/17

Step-by-step explanation:

the fraction would be 20 / 17

if you simplify it then it would be 1 3/17

Answer:

2/7 or 29%

Step-by-step explanation:

you add all the numbers than you put the blue marble on top and there it is.

Answer:

2/7

Step-by-step explanation:

Hello there.

1. First, you would add all the numbers up to get the total.

3 + 2 + 2 = 7 total marbles

2. Of those 7 marbles, 2 are blue. This would be 2/7 in fraction form.

Hence, there is a 2 in 7 chance that Sandra will choose a blue marble from the bag.

Hope this helps.

- Angelo