A starting lineup in basketball consists of 2 guards, 2 forwards, and 1 center.
(a) a certain college team has on its roster 5 guards, 4 forwards, 3 centers. how many
different starting lineups can be created?
(b) suppose that mary is listed on the roster as a forward, and alice is listed on the
roaster as a center. assume that, for a given starting lineup, all players are randomly
chosen for each role among qualified players on the roster (guards are chose among
guards only, etc.). what is the probability that mary and alice will get on the
lineup?

Answer:

Mean: 16; Mode: 15

Step-by-step explanation:

I did it.

Answer:

I think the mean is 16.

The mode is 15 because it is the most seen number in the data set.

Step-by-step explanation:

Add then divide for the mean (add all numbers, then divide by how many numbers there are).

The mode is the one that you see the most.

Hope this helps guys!

The expression which is equal to x²+5x+6/x+2 +x+5 is ( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6))

We are given that;

Expression= x²+5x+6/x+2 +x+5

Now,

Step 1: Find the LCD

The LCD is the product of the different factors of the denominators. To find the factors, we need to factor the denominators first.

x + 2 = x + 2 (no change)

x² + 5x + 6 = (x + 2)(x + 3) (by finding two numbers that multiply to 6 and add to 5)

The LCD is (x + 2)(x + 3)

Step 2: Rewrite each expression with the LCD as the denominator

To do this, we multiply each expression by a form of 1 that has the missing factor in both the numerator and denominator.

(x² + 5x + 6) / (x + 2) = ((x² + 5x + 6) / (x + 2)) * ((x + 3) / (x + 3)) = ((x² + 5x + 6)(x + 3)) / ((x + 2)(x + 3))

(x + 5) / (x² + 5x + 6) = ((x + 5) / (x² + 5x + 6)) * ((x + 2) / (x + 2)) = ((x + 5)(x + 2)) / ((x² + 5x + 6)(x + 2))

Step 3: Add or subtract the numerators and write the result over the LCD

(x²+5x+6/x+2) +( x+5) = ((x²+5x+6)( x+3))/(( x+2)( x+3)) +( ( x+5)( x+2))/(( x²+5 x+6)( x+2))

= ((( x²+5 x+6)( x+3))+(( x+5)( x+2)))/(( x+2)( x+3)( x²+5 x+6))

= (( x³+8 x²+23 x+18)+( x²+7 x+10))/(( x+2)( x+3)( x²+5 x+6))

= ( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6))

Step 4: Simplify the result if possible

( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6))

Therefore, by the expression the answer will be ( x³+9 x²+30 x+28)/(( x+2)( x+3)( x²+5 x+6)).

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Answer:

c , 828 on edge

Step-by-step explanation:

happy graduating!

The maximum amount of monthly rent payment he could pay is to be considered as the $828.

Renting is a type of agreement where one party pays for the temporary use of another's good, service, or property. It is also referred to as hiring or letting. In a gross lease, the landlord pays all day-to-day costs while the tenant only has to pay a set monthly rent.

We have,

closing costs = $ 7100

So, the amount before rent payment should be

= closing costs + 36 monthly payments

= $7,100 + ($675 (36)

= $7,100 + $24,300

= $31,400

Now, $750 + 37R = $31,400        

37R = $30,650

R = $828

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Answer:

the s is 4 and r is -3 and the other angle is 2

Step-by-step explanation:

if this right good but if it not i tried

Answer:

The length of RS is 5 units.

Step-by-step explanation:

One ounce of food contains average  about 28 grams of carbs.

One of the three macronutrients that the body needs for energy, carbohydrates can be found in a wide variety of foods. Sugar, starch, and fiber are the three elements that make up carbohydrates. Weight is measured in ounces, which weigh 28.35 grams. As a result, one ounce of food contains about 28 grams of carbs. Carbohydrates are crucial for supplying the body with the 4 calories per gram of energy it needs to function, fuel physical activity, and help with digestion. Foods like fruits, vegetables, grains, nuts, and dairy products all naturally include ounces of carbs. It is crucial to remember that there are several kinds of carbs, some of which are healthier than others.

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The complete question is

How many grams of carbs in an ounce of food ?

The equation as given in the task content above can be said to represent; Choice C; function online.

By definition, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

A relation, on the other hand defines the relationship between sets of values of ordered pairs.

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Answer:

5 cms

Step-by-step explanation:

This is assuming that it is equilateral and that n is the length of one side

Answer:

$1.35

Step-by-step explanation:

8n = 10.80

Divide both sides by 8 to get n alone.

n = 10.80/8 = $1.35

Answer:

The Slope is -1/3

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainliest

The probability that 2 math majors and 2 computer science majors are chosen is 0.3778.

In a class of 18 students, there are 11 math majors and 7 computer science majors. Four students are randomly picked to prepare a demonstration on the use of a graphing calculator. Then the probability that 2 math majors and 2 computer science majors are chosen To solve the problem, we need to use combinations as the order in which the students are selected doesn't matter.                                                                                                                                      

The total number of ways of choosing 4 students out of 18 students is shown by :18C4 = (18 × 17 × 16 × 15) / (4 × 3 × 2 × 1) = 3060 The number of ways of choosing 2 math majors from 11 math majors is shown by :11C2 = (11 × 10) / (2 × 1) = 55 .The number of ways of choosing 2 computer science majors from 7 computer science majors is given by :7C2 = (7 × 6) / (2 × 1) = 21 Thus, the number of ways of choosing 2 math majors and 2 computer science majors out of 11 math majors and 7 computer science majors, respectively, is given by :55 × 21 = 1155 Therefore, the probability that 2 math majors and 2 computer science majors are chosen is :1155 / 3060 = 0.3778 (rounded to four decimal places)Thus, the probability that 2 math majors and 2 computer science majors are chosen is 0.3778.

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3060 possible groups of four students can be formed using a combination of math majors and computer science majors.

In a class of 18 students there are 11 math majors and 7 computer science majors. Four students are randomly picked to prepare a demonstration on the use of a graphing calculator.

We need to find out how many possible groups of four students can be formed using a combination of math majors and computer science majors.

We can apply the combination formula to find the number of possible combinations.

The combination formula is given as: C(n, r) = (n!)/(r!(n-r)!) Where, n is the total number of items available for selection, r is the number of items to be selected at a time C(n, r) is the number of possible combinations.

The number of math majors = 11

The number of computer science majors = 7

The total number of students = 18

We need to select a group of four students, therefore r = 4

The number of possible groups of four students can be formed using a combination of math majors and computer science majors is given by: C(18, 4) = (18!)/(4!(18-4)!)= (18 × 17 × 16 × 15)/(4 × 3 × 2 × 1) = 3060

Therefore, there are 3060 possible groups of four students that can be formed using a combination of math majors and computer science majors.

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On solving the provided question, the equation will be \(y^2 = - 4ax\) and the factors - This cannot be determined from the information given

When points on a curve are equally spaced from a fixed point and line, the curve is said to have a parabola as its equation. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. Remember that the fixed point is not on the fixed line as well. A parabola is the locus of any point that is equidistant from both a focus and a straight line. A conical curve of interest in coordinate geometry is a parabola.

The equation will be

=> \(y^2 = - 4ax\)

=> \(y^2 = -24x\)

Factors - This cannot be determined from the information given

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First, we convert 1/2% to a decimal.

Similarly:

The water output rate for Reed's sprinkler is 25L/hour. We have to find the water output rate for each sprinkler if the sum of the two rates was 45L per hour. We know that the Rogers family sprinkler was used for 15 hours and the Reed family sprinkler was used for 30 hours.

Therefore the combined time the two sprinklers were used for was:15 + 30 = 45 hours

Therefore, The Rogers family's sprinkler output rate: r₁

The Reed family's sprinkler output rate: r₂

Given that the sum of the two rates was 45L per hour: r₁ + r₂  = 45 -----Equation (1)

Now, let's calculate the water output of each sprinkler using their respective times:

Water output of Rogers' sprinkler = r₁ × 15

Water output of Reed's sprinkler = r₂  × 30

The total output was 1050L:

r₁ × 15 + r₂  × 30 = 1050 -----Equation (2)

We have two equations and two variables. We will solve for r₁ and r₂ :

r₁ + r₂ = 45r₂ = 45 - r₁

Substituting the value of r₂ in equation (2), we get:

r₁ × 15 + (45 - r₁) × 30 = 105015r₁ + 1350 - 30r₁

= 1050-15r₁

= -300r₁

= 20r₂

= 45 - r₁

= 45 - 20 = 25

Therefore, The water output rate for Rogers' sprinkler is 20L/hour.

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The graph of the polynomial f(x) is added as an attachment

From the question, the equation of the polynomial is given as

f(x) = x^3 + 3x^2 – 4x – 12

To start with, we need to represent the function of the polynomial properly

So, we have the following representation

f(x) = x³ + 3x² – 4x – 12

Solving further, we need to factorize the function

This gives

f(x) = x²(x + 3) - 4(x + 3)

Factor out x + 3

f(x) = (x² - 4)(x + 3)

Express as difference of two squares

f(x) = (x - 2)(x + 2)(x + 3)

When the above equation is solved, we have

x = 2, x = -2 or  = -3

This means that the intercepts of the function are -3, -2 and 2

Next, we plot the polynomial function using the above intercepts and the end behavior

See attachment for the graph of the function

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Answer:

3 * 20s

Step-by-step explanation:

In order to find out how much Mr. Hartman will spend in total we first need to multiply the price of the keyboard and mouse by the number of computers in a single computer station. Once we have these products we add them together. Finally, we multiply this new value by 3 since there are a total of 3 computer stations. If we turn this into an expression it would be the following...

3 * (13.50s + 6.50s)

We can even simplify this by first adding the cost of the keyboard and mouse and then multiplying by s

3 * 20s

Answer:

Step-by-step explanation:

200 grams is equal to 7 ounces.

Answer:

D)7 ounces

Step-by-step explanation:

     2. It is a proportio

      \(\frac{85}{3} =\frac{200}{x}\)   so,

3. x=200*3/85

4. x is approximately equal to 7 ounces

Answer:

Correct answer is 54.82 ft.

Step-by-step explanation:

First of all, let us label the diagram and do the construction as per the attached answer image.

Let us consider \(\triangle ABC\):

\(\angle B = 90^\circ\\\angle ACB = 180-110 = 70^\circ\)

Let side AB = d ft and let side BC = x ft

We need to find AB to find the shortest distance across the river.

Using trigonometric identity of tangent:

\(tan\theta = \dfrac{Perpendicular}{Base}\)

\(tan 70 = \dfrac{d}{x}\\\Rightarrow x = \dfrac{d}{tan70} = 0.36d ..... (1)\)

Now, let us have a look at another right angled triangle ABD:

Let us consider \(\triangle ABC\):

\(\angle B = 90^\circ\\\angle ADB = 180-150 = 30^\circ\)

side AB = d ft and side BD = x+75 ft

Using trigonometric identity of tangent:

\(tan\theta = \dfrac{Perpendicular}{Base}\)

\(tan 30 = \dfrac{d}{x+75}\\\text{Using equation (1)}:\\0.577 = \dfrac{d}{0.36d+75}\\\Rightarrow 0.207d + 43.27 = d\\\Rightarrow 0.793d = 43.27\\\Rightarrow d \approx 54.82\ ft\)

Correct answer is 54.82 ft.

Answer: B 58.34

Step-by-step explanation: the angle supplementary to the 150 angle = 30

So the remaining angle is 180-110-30= 40

sin40/75 = sin30/x

solve for x = 58.34

Just did the quiz.

The value of the stock can be calculated by using the Gordon Growth Model. Gordon Growth Model The Gordon Growth Model is a technique that is used to value stocks using the present value of future dividend payments.

This model assumes that the dividends of the company will grow at a constant rate, and it takes into consideration the required rate of return of the investors. The formula for the Gordon Growth Model is given as follows: Stock Price = D1/(r-g)Where,D1 = Expected dividend in the next periodr = Required rate of returng = Growth rate in dividends Now, let's use the Gordon Growth Model to find the value of the stock in the given question. Dividend in the next period (D1) = Expected dividend * (1 + growth rate) = $2.48 * (1 + 3.15%) = $2.55Required rate of return (r) = 11.05%Growth rate in dividends (g) = 3.15%Stock price = D1/(r-g)= $2.55/(11.05% - 3.15%)= $30.95Therefore, the value of the stock is $30.95.Answer: The value of the stock is $30.95.

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The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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Answer:

4

Step-by-step explanation:

(x1,y1)(x2,y2)

(2,8)   (0,0)

0-8 / 0-2 = -8/-2

simplify -8/-2 = 4

Answer:

4.

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

-  that is rise / run.

We use the points (2, 8) and (2,0) ( - the last point is vertically below (2,8) and is on the x axis)

Here y2 = 8, y1 = 0, x2 = 2 and x1 = 0.

So the slope = (8-0)/(2-0)

= 4

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Value of sin x is 25/7.

In trigonometry, the hypotenuse, base (which is adjacent), and perpendicular are the three sides that make up a right-angled triangle (opposite). All sciences relating to geometry, physics, and many other fields make extensive use of these trigonometric formulas and identities. We can use trigonometric ratios to locate the missing angles and sides of a triangle. They are utilized in right-angled triangles, or triangles having one angle equal to 90 degrees, to be more precise.

Given

Value of trigonometric ratio

Sin X = Opposite/hypotenuse

Opposite = 50

Hypotenuse = 14

Sin x = 50/14

Sin x = 25/7

Value of sin x is 25/7.

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In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

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Answer:

Step-by-step explanation:

Let

The known number = 12

The unknown number = x

Result = 102

Product of 12 and a number= 12*x

= 12x

Tripled product of 12x= 3(12x)

=36x

36x = 102

Divide both sides by 36

x = 102/36

= 2.833

x=2.833

The 99% confidence interval for how much the drug will lower a typical patient's systolic blood pressure is approximately (40.6, 43.8).

The formula for calculating the confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

we need to find the critical value associated with a 99% confidence level. Since the sample size is large (n = 309), we can use the z-distribution.

The critical value for a 99% confidence level is approximately 2.576.

Next, we need to calculate the standard error using the formula:

Standard Error = Standard Deviation / √(Sample Size)

Standard Error = 10.7 / √309

Now we can calculate the confidence interval:

Confidence Interval = 42.2 ± (2.576 * (10.7 / √309))

Calculating the values:

Confidence Interval = 42.2 ± (2.576 * 0.609)

Confidence Interval ≈ 42.2 ± 1.570

Therefore, the 99% confidence interval for how much the drug will lower a typical patient's systolic blood pressure is approximately (40.6, 43.8).

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The equation of the line is, y = -3x.

What is point slope form of the line?

A line's point slope form equation is y - y1 = m(x – x1). Consequently,

y - 0 = m(x - 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

Let the line passes through the point (1, -3) and having slope of -3.

Consider, the point slope form of the line,

\(y-y_1=m(x-x_1)\)

Plug, \((x_1, y_1) = (1, -3), m = -3\)

So, the above equation becomes

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

Hence, the equation of line that passes through the point (1, -3) and having slope -3 is y = -3x.

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Answer: 8/3

Step-by-step explanation:

Answer: I THINK ITS THE SENCOND ONE

Step-by-step explanation:

Matching the reasons with the statements; we have the following;

CPCTE (Corresponding Parts of Congruent Triangles are Equal)

SAS (Side-Angle-Side) type of congruent triangles.

Reflexive property of equality

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Answer:

The answer is x=4 or x=−10

Solutions:

(x + 3)² = 49

(x+3)(x+3)=49

x²+6x+9=49

x²+6x+9-49=0

(x-4)(x+10)

x-4=0 x+10=0

x=4 x=-10

For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

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