committee of 50 politicians is to be chosen from among the 100 u.s. senators. if the selection is done at random, what is the probability that each state will be represented?

Answer:

The answer is C. (-5, 14)

Answer:

adult $8.00

child $5.50

Step-by-step explanation:

Let the price of 1 adult ticket = x.

Let the price of 1 child ticket = y.

2x + 4y = 38

3x + 3y = 40.5

Multiply the first equation by 3. Multiply the second equation by -2. Then add them.

         6x + 12y = 114

(+)      -6x - 6y = -81

-----------------------------

                  6y = 33

y = 33/6

y = 5.5

2x + 4y = 38

2x + 4(5.5) = 38

2x + 22 = 38

2x = 16

x = 8

Answer:

adult $8.00

child $5.50

Answer:

An adult ticket is $8.00 and a child's ticket is $5.50.

Step-by-step explanation:

We form a system of 2 equations and solve them.

Let a be the price of adult ticket and c the price of a child's.

2a + 4c = 38         (A)

3a + 3c = 40.5      (B)

Multiply equation A by 3 and equation B by -2:

6a + 12c = 114

-6a - 6c = -81        Adding these 2 equations:

0 + 6c = 33

c = 33/6 = 5.5.

Now we substitute for c in equation A:

2a + 4(5.5) = 38

2a = 38 - 22

2a = 16

a = 6.

Let's now check these results by substitution in equation B:

3a + 3c = 40.5

3(8) + 3(5.5) = 24.0 + 16.5 = 40.5

- so it checks out.

Answer:

Step-by-step explanation:

Bonsoir,

63°

The value of external angle x intercepted by two tangents is 63°

We have,

From the given figure,

External  angle = x

From the definition of external angle intercepted by two tangents.

External angle = 1/2 x difference of the intercepted arc length

Now,

Difference of the arc length.

= 243 - (360 - 243)

= 243 - 117

= 126

Now,

Substituting the values.

External angle = 1/2 x difference of the intercepted arc length

= 1/2 x 126

= 63

Thus,

The value of external angle x is 63°

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Answer:

-2x + (-3) = x

x = -1

Step-by-step explanation:

-2x + (-3) = x

add 2x to each side

-3 = 3x

divide each side by 3

-1 = x

The first partial derivatives of the function z = x sin(xy) is x²cos(xy)

The term partial derivatives is defined as the rate of change of a function with respect to a variable and the derivatives are fundamental to the solution of problems in calculus and differential equations.

Here we have given that the function z = x sin(xy).

And as per the definition of partial derivative the value is calculated as,

Here we have given that

=> f(x, y) = x sin(xy)

And then here we need to find fx​ we treat y as constant and differentiate with respect to x, then we get

=> fx = sin(x y) + xy cos(xy)

Similarly now we have to find fy​ we treat x as constant and differentiate with respect to y

=> fy​ = x²cos(xy)

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Answer:

$725

Step-by-step explanation:

First you subtract $600 from $3500 then divide $2900 by 4 which is $725

Answer:

Step-by-step explanation

2=x

Answer:

length = 15x + 6

Step-by-step explanation:

given the length is 3 times the width, then

length = 3(5x + 2) ← distribute parenthesis by 3

          = 15x + 6

Answer:

t(g)= -4g + 20

Step-by-step explanation:

James is playing his favorite game at the arcade. After playing the game 3 times, he has 8 tokens remaining. He initially had 20 tokens, and the game costs the same number of tokens each time. The number tt of tokens James has is a function of gg, the number of games he plays

Solution

Let

g=No. of games James plays

t= No. of tokens James has.

Find the slope using

y=mx + b

Where,

m = Slope of line,

b = y-intercept.

Before James started playing the games, he has a total of 20 tokens.

That is, when g=0, t=20

After James played the games 3 times, he has 8 tokens left

That is, when g=3, t=8

(x,y)

(0,20) (3,8)

m=y2-y1 / x2-x1

=(8-20) / (3-0)

= -12 / 3

m= -4

Slope of the line, m= -4

y=mx + b

No. of tokens left depend on No. of games James plays

t is a function of g.

t(g)

t(g)= -4g + 20

Answer:

-4g + 20

Step-by-step explanation:

I did it on khan and this was right

Answer:

The slope of AB = slope of CD and slope of BC = slope of DA

Hope this helps!

Step-by-step explanation:

(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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Answer:

$5.25

Step-by-step explanation:

Divide 26.25 by 5 and there's your answer.

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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Answer: 3log5(2) - 1 or ~0,29203

Step-by-step explanation:

2log5(4) - log5(10)

log5(4^2) - log5(10)

log5(4^2/10)

log5(16/10)

log5(8/5)

Log5(8) - log5(5)

log5(2^3) - 1

3log5(2) - 1

Answer:

is D

Step-by-step explanation:

The equation that could represent the graph of the parabola is (d) \(y = 2x^2 + 8x + 8\)

From the question, we have the following highlights

The highlights above mean that: the y-coordinate (k) of the vertex is positive.

For a parabola: \(y = ax^2 + bx + c\), the vertex is:

\((h,k) = (-\frac{b}{2a},f(h))\)

Next, we test the options

(a) y = 9x2 + 6x + 4

We have:

\(h = -\frac{6}{2 \times 9}\)

\(h = -\frac{1}{3}\)

Substitute -1/3 for x in the function

\(y = 9x^2 + 6x + 4\)

\(k = 9(1/3)^2 + 6(1/3) + 4\)

\(k = 7\)

The value of k is not zero.

So, this cannot represent the parabola

(b) y = 6x2 – 12x – 6

We have:

\(h = -\frac{-12}{2\times 6}\)

\(h = 1\)

Substitute 1 for x in the function

\(y = 6x^2 - 12x - 6\)

\(k = 6(1)^2 - 12(1) - 6\)

\(k = -12\)

The value of k is not zero.

So, this cannot represent the parabola

(c) y = 3x2 + 7x + 5

We have:

\(h = -\frac{7}{2\times 3}\)

\(h = -\frac{7}{6}\)

Substitute -7/6 for x in the function

\(y = 3x^2 + 7x + 5\)

\(k = 3(-7/6)^2 + 7(-7/6) + 5\)

\(k = 0.92\)

The value of k is not zero.

So, this cannot represent the parabola

(b) y = 2x2 + 8x + 8

We have:

\(h = -\frac{8}{2\times 2}\)

\(h = -2\)

Substitute -2 for x in the function

\(y = 2x^2 + 8x + 8\)

\(k = 2(-2)^2 + 8(-2) + 8\)

\(k = 0\)

The y-coordinate (k) is zero.

Hence, \(y = 2x^2 + 8x + 8\) could represent the parabola

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Answer:

Area≈804.25

Step-by-step explanation:

Answer:

its just 804 when rounded to 3 significant figures :)

Step-by-step explanation:

just completed it

Answer:

2044

Step-by-step explanation:

90,360,000 is each year, and if you multiply that by 10, it is 903,600,000. Do it again to get 1,807,200,000. That would equal the year of 2037, but it isnt enough. Then add 722880000, which would be 2044 and the total would be 7.53 billion + 1807200000 + 722880000 which equals to 10,060,800,000

If row-reducing the augmented matrix does not produce any non-zero entries in the right-hand side, then the columns of A are linearly independent.

To determine if the columns of matrix A form a linearly independent set, we need to check if the equation Ax = 0 has only the trivial solution x = 0.

Let's assume the given matrix A is:

A = [a1, a2, a3, ..., an]

If the columns of A are linearly independent, then the equation Ax = 0 has only the trivial solution.

To solve the equation Ax = 0, we set up the augmented matrix [A | 0] and row-reduce it:

[A | 0] =

[a1, a2, a3, ..., an | 0]

Row-reducing the augmented matrix will help us determine if there are any non-trivial solutions to the equation Ax = 0.

If row-reducing the augmented matrix leads to a row of zeros with a non-zero entry in the corresponding row of the right-hand side (0), then the columns of A are linearly dependent, and there exists a non-trivial solution.

If row-reducing the augmented matrix does not produce any non-zero entries in the right-hand side, then the columns of A are linearly independent.

By performing row operations on the augmented matrix [A | 0] and examining the resulting row echelon form, we can determine if the columns of A are linearly dependent or independent and find the dependence relation if they are dependent.

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Answer:

Step-by-step explanation:

He has $500 to start with, and he takes $25 out of the account each week. But he wants more than 200 in his account by the end of summer. 25 goes into 500 20 times. But if he wanted more than 200 left, like 300-400, he could spend 4 week's worth of money to have 400 left, or 8 weeks to have 300 left. This is the best-case scenario.

Answer:

since the radius is 11 witch the radius is only half so times by 2 witch would be the diamater witch is 22 so the area would be A≈381

Step-by-step explanation:

A=14πd2=14 · π · 222 ≈ 381

i think thats it bc If the object is a circle, and you know its circumference, you would divide the circumference by pi to find the diameter of the circle. Half the diameter is the radius. Square the radius and multiply by pi to find the area of the circle.

Answer:

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

a. 2.25 km

Step-by-step explanation:

the scale on a map means how many units in the mapp corresponds to how many units in reality.

in this case

1 cm on the map = 75000 cm in reality =

= 75000/100 m = 750 m =

= 750/1000 km = 0.75 km

3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km

To find the mean of a probability density function, multiply each value of x by its probability density and integrate over the range of x.

To find the mean of a probability density function (PDF), you can follow these steps:

Start with a continuous probability density function f(x).

Multiply each value of x by its corresponding probability density f(x).

Integrate the product over the entire range of x.

The result of the integration is the mean of the probability density function.

Mathematically, the mean (μ) of a continuous PDF is calculated using the following formula:

μ = ∫(x × f(x)) dx

where the integral (∫) is taken over the entire range of x.

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To find the mean of a probability density function (PDF), you need to integrate the product of the random variable and the PDF over its entire range. The mean is also known as the expected value.

To find the mean of a probability density function (PDF), you need to integrate the product of the random variable and the PDF over its entire range. The mean of a PDF is also known as the expected value.

The formula for finding the mean of a PDF is:

mean = ∫(x * f(x)) dx

Where:

To find the mean, you need to evaluate this integral. The mean represents the average value of the random variable, weighted by the PDF.

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The given expression is 3 x (5-2)-1

From the options

If Orlando has 5 actions figures.

He decides to give 2 of them to his younger brother, then he will have (5-2) action figures left

His parents were happy with him and tripled what he had left

3 x ( 5 -2 ) action figures.

If he had so many actions figures after that and he gave his brother 1 more action figure then he will have

3 x ( 5-2) - 1 action figures left.

The right answer is therefore option B

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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Answer:

1/3x^11

Step-by-step explanation:

1/3x^11 is the answer

Answer:

v = 2034.72 mm³

Step-by-step explanation:

radius = 18mm

height = 6mm

pi = 3.14

v = πr²h/3

v = 3.14 * (18mm)² x 6mm/3

v = 3.14 * 324mm²  x 2mm

v = 2034.72 mm³

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The jar of glitter was used for each poster is 4/3

Given,

In the question:

Brad used 1/3 jar of glitter evenly among 4 posters.

To find the  how much of the jar of glitter was used for each poster?

Now, According to the question;

Based on the given conditions:

Formulate;

Brad used 1/3 jar of glitter

and, evenly among 4 posters.

= \(\frac{1}{\frac{3}{4} }\)

Calculate:

Divide a fraction by multiplying its reciprocal

= 4/3

Hence, The jar of glitter was used for each poster is 4/3

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