{1, 2, 3, 4, 5} {2, 4, 6, 8, 10} Please Help Which of the following shows the union of the sets?

Answer:

25.02% probability that exactly 19 men and 18 women are chosen

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

19 men, from a set of 25

18 women, from a set of 22

[tex]D = C_{25,19}*C_{22,18} = \frac{25!}{19!6!}*\frac{22!}{18!4!} = 1295486500[/tex]

Total outcomes:

37 people from a set of 25 + 22 = 47. So

[tex]T = C_{47,37} = \frac{47!}{37!10!} = 5178066751[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{1295486500}{5178066751} = 0.2502[/tex]

25.02% probability that exactly 19 men and 18 women are chosen

Answer:

  54.8 N·m

Step-by-step explanation:

The horizontal distance from the dumbbell to the elbow is ...

  (0.366 m)cos(15°) ≈ 0.3535 m

Then the torque due to the vertical force is ...

  (155 N)(0.3535 m) = 54.8 N·m

Answer:

8 years old.

(3x+9)

(3(8)+9)=33

Answer:

The real and imaginary parts of the result are [tex]\frac{1441}{1601}[/tex] and [tex]\frac{4}{1601}[/tex], respectively.

Step-by-step explanation:

Let be [tex]f(z) = \frac{z}{z+1}[/tex], the following expression is expanded by algebraic means:

[tex]f(z) = \frac{z\cdot (z-1)}{(z+1)\cdot (z-1)}[/tex]

[tex]f(z) = \frac{z^{2}-z}{z^{2}-1}[/tex]

[tex]f(z) = \frac{z^{2}}{z^{2}-1}-\frac{z}{z^{2}-1}[/tex]

If [tex]z = 4 - i5[/tex], then:

[tex]z^{2} = (4-i5)\cdot (4-i5)[/tex]

[tex]z^{2} = 16-i20-i20-(-1)\cdot (25)[/tex]

[tex]z^{2} = 41 - i40[/tex]

Then, the variable is substituted in the equation and simplified:

[tex]f(z) = \frac{41-i40}{41-i39} -\frac{4-i5}{41-i39}[/tex]

[tex]f(z) = \frac{37-i35}{41-i39}[/tex]

[tex]f(z) = \frac{(37-i35)\cdot (41+i39)}{(41-i39)\cdot (41+i39)}[/tex]

[tex]f(z) = \frac{1517-i1435+i1443+1365}{3202}[/tex]

[tex]f(z) = \frac{2882+i8}{3202}[/tex]

[tex]f(z) = \frac{1441}{1601} + i\frac{4}{1601}[/tex]

The real and imaginary parts of the result are [tex]\frac{1441}{1601}[/tex] and [tex]\frac{4}{1601}[/tex], respectively.

Answer:

[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

4 = [tex]\frac{1}{12}[/tex]

2 = [tex]\frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ equal to 100000

For the alternative hypothesis,

H1: µ greater than 100000

This is a right tailed test

Since the population standard deviation is nit given, the distribution is a student's t.

Since n = 200

Degrees of freedom, df = n - 1 = 200 - 1 = 199

t = (x - µ)/(s/√n)

Where

x = sample mean = 103157

µ = population mean = 100000

s = samples standard deviation = 27498

t = (103157 - 100000)/(27498/√200) = 1.62

We would determine the p value using the t test calculator.

p = 0.053

Alpha = 10% = 0.1

Since alpha, 0.1 > than the p value, 0.053, then

b) At the 10% significant level, the p-value/statistics is 0.053, so we should not reject the null hypothesis.

c) Hence, we may conclude that the average has not increased and the probability that our conclusion is correct is at least 90 percent.

Answer:

pls look at photo attached

Step-by-step explanation:

solution.

if variable d increases then w reduces

w=k.u ×1/d

=ku/d

therefore w=k.u/d

Answer:

The graph g(x) is the graph f(x) vertically stretched by a factor of 7.

Step-by-step explanation:

Quadratic Equation: f(x) = a(bx - h)² + k

Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.

Answer:

The graph g(x) is the graph f(x) vertically stretched by a factor of 7.

Step-by-step explanation:

Quadratic Equation: f(x) = a(bx - h)² + k

Since we are modifying the variable a, we are dealing with vertical stretch (a > 1) or vertical shrink (a < 1). Since a > 1 (7 > 1), we are dealing with a vertical stretch by a factor of 7.

Answer:

7

Step-by-step explanation:

Remove parentheses.

[tex]\frac{-8+4(4.5)}{6.25-8.25} \\[/tex]

Add −8 and 4.5.

[tex]\frac{4(-3.5)}{6.25 - 8.25} \\\\[/tex]

Subtract 8.25 from 6.25.

[tex]\frac{4*-3.5}{-2}[/tex]

Multiply 4 by −3.5.

[tex]\frac{-14}{-2}[/tex]

Divide −14 by −2.

= 7

Answer:

Step-by-step explanation:

the mass is 2000 mg, or 2 g.

the density is 8 g/cm^3

divide 2 by 8

0.25 cm^3

if this helped, mark as brainliest :)

Answer:

Jet= 420 mph     Wind = 10mph

Step-by-step explanation:

The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.

The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.

This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.

So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.

Answer:

5

Step-by-step explanation:

Answer:

-3 , 9

Step-by-step explanation:

Sum = - 6

Product = -27

Factors = 3, -9

x² - 6x-27 = 0

x² + 3x - 9x - 9*3 = 0

x(x + 3) - 9(x + 3)  = 0

(x + 3) (x - 9) = 0

x +3 = 0   ; x - 9 = 0

x = - 3     ; x = 9

Solution: x = -3 , 9

Answer:

  60 miles

Step-by-step explanation:

We assume the trip is "d" miles and that the "extra hour" refers to the additional time that a current of 2 mph would add. That is, we assume the reference time is for a current of 0 mph.

The time with no current is ...

  time1 = distance/speed

  time1 = d/12 . . . . hours

With a current of 2 mph in the opposite direction, the time is ...

  time2 = d/(12 -2) = d/10

The second time is 1 hour longer than the first, so we have ...

  time2 = 1 + time1

  d/10 = 1 + d/12

  6d = 60 + 5d . . . . multiply by 60

  d = 60 . . . . . . . . . subtract 5d

The one-way distance is 60 miles.

Answer:

The answer is: 325 517 424 395 494

Step-by-step explanation:

Hey there!

To find the answer, we just need to see which point falls in this blue, which represents the inequality.

We see that the point (5,-5) is not on the blue.

We see that the point (1,5) is on the blue.

(-3,-3) is on the dotted line but not a solution of the inequality. The dotted line is excluded from the inequality. If it were a bold line, then it would be a solution of the inequality.

(3,-1) is also on the dotted line so it is not a solution.

Therefore, the answer is B. (1,5)

I hope that this helps!

We want to see which point is a solution for the graphed inequality.

We will find that the correct option is B, (1, 5)

Notice that the line that defines the inequality contains the points (-3, -3) and (3, -1)

Then the slope of that line is:

[tex]a = \frac{-1 -(-3)}{3 - (1)} = 1/2[/tex]

Then the line is something like:

y = (1/2)*x + b

To find the value of b, we use the fact that this line passes through the point (3, -1), then we have:

-1 = (1/2)*3 + b

-1 - 3/2 + b

-5/2 = b

So the line is:

y = (1/2)*x - 5/2

And we can see that the line is slashed, and the shaded area is above the line, then we have:

y > (1/2)*x - 5/2

Now that we have the inequality, we can just input the values of the points in the inequality and see if this is true.

First, options C and D can be discarded because these points are on the line, and the points on the line are not solutions.

So we only try with A and B.

A) x = 5

   y = -5

then we have:

-5 > (1/2)*5 - 5/2

-5 > 0

Which clearly is false.

B) x = 1

   y = 5

Then we have:

5 > (1/2)*1 - 5/2 = -4/2

5 > -4/2

This is true, then the point (1, 5) is a solution.

Thus the correct option is B.

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Answer:

a{(1, 3), (2, 3), (4,3), (9,3)}

Step-by-step explanation:

For the relation to be a function, each x can only go to 1 y

a{(1, 3), (2, 3), (4,3), (9,3)}

function

b{(1, 2), (1, 3), (1, 4), (1,5)}

x=1 goes to 4 different y's so not a function

c{(5, 4), (-6, 5), (4, 5), (4, 0)}

x=4 goes to 2 different y's so not a function

d{(6,-1), (1,4), (2, 3), (6, 1)}​

x = 6 goes to 2 different y's so not a function

Answer:

Option A

Step-by-step explanation:

The first thing we want to do here is to rewrite the equation given to us, in standard circle equation -

[tex]x^2+y^2-6x+8y+21=0,\\\left(x-3\right)^2+\left(y-\left(-4\right)\right)^2=2^2[/tex]

The " standard form " of a circle is given to be in the following form,[tex](x-a)^{2} + (y-b)^{2} = r^2[/tex] where r = radius, centered at ( a, b )

Now as you can see, the center ( given by ( a, b ) ) should be ( 3, - 4 ). Respectively the radius is 2, and therefore the circle properties are -

Center [tex]( 3, - 4 )[/tex]; radius [tex]2[/tex]

Hope that helps!

Answer:

0.45 ft/min

Step-by-step explanation:

Given:-

- The flow rate of the gravel, [tex]\frac{dV}{dt} = 35 \frac{ft^3}{min}[/tex]

- The base diameter ( d ) of cone = x

- The height ( h ) of cone = x

Find:-

How fast is the height of the pile increasing when the pile is 10 ft high?

Solution:-

- The constant flow rate of gravel dumped onto the conveyor belt is given to be 35 ft^3 / min.

- The gravel pile up into a heap of a conical shape such that base diameter ( d ) and the height ( h ) always remain the same. That is these parameter increase at the same rate.

- We develop a function of volume ( V ) of the heap piled up on conveyor belt in a conical shape as follows:

                                [tex]V = \frac{\pi }{12}*d^2*h\\\\V = \frac{\pi }{12}*x^3[/tex]

- Now we know that the volume ( V ) is a function of its base diameter and height ( x ). Where x is an implicit function of time ( t ). We will develop a rate of change expression of the volume of gravel piled as follows Use the chain rule of ordinary derivatives:

                               [tex]\frac{dV}{dt} = \frac{dV}{dx} * \frac{dx}{dt}\\\\\frac{dV}{dt} = \frac{\pi }{4} x^2 * \frac{dx}{dt}\\\\\frac{dx}{dt} = \frac{\frac{dV}{dt}}{\frac{\pi }{4} x^2}[/tex]

- Determine the rate of change of height ( h ) using the relation developed above when height is 10 ft:

                              [tex]h = x\\\\\frac{dh}{dt} = \frac{dx}{dt} = \frac{35 \frac{ft^3}{min} }{\frac{\pi }{4}*10^2 ft^2 } \\\\\frac{dh}{dt} = \frac{dx}{dt} = 0.45 \frac{ft}{min}[/tex]

Answer:

x>0

Step-by-step explanation:

The domain are the possible values of x you can use.

For ln functions, x must be positive (the ln of a negative number does not exist).

So, x must be larger than 0. No part of the graph will be left of the y axis.

Answer:

The answer is option A.

Hope this helps you

1) The marginal profit is [tex]4.3 - 0.7 ln(x)[/tex].

2) The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.

Thus, option (A) is correct.

C) To maximize profit 462,481 thousands of candles should be sold.

Given: [tex]P(x) = 5 x - 0.7 x[/tex] [tex]{\text}ln x.[/tex]

1) Take the derivative of the profit function P(x) with respect to x.

P(x) = 5x - 0.7x ln(x)

To find P'(x), differentiate each term separately using the power rule and the derivative of ln(x):

[tex]P'(x) = 5 - 0.7(1 + ln(x))[/tex]

       = [tex]5 - 0.7 - 0.7 ln(x)[/tex]

       = [tex]4.3 - 0.7 ln(x)[/tex]

2) Substitute x = 10 into the derivative:

P'(10) = 4.3 - 0.7 ln(10)

         = 4.3 - 0.7(2.30259)

         = 4.3 - 1.61181

         = 2.68819

Therefore, the additional profit for selling a thousand candles once 10,000 candles have already been sold.

Thus, option (A) is correct.

C) Set P'(x) = 0 and solve for x:

[tex]4.3 - 0.7 ln(x) = 0[/tex]

[tex]0.7 ln(x) = 4.3[/tex]

[tex]{\text} ln(x) = 4.3 / 0.7[/tex]

[tex]{\text} ln(x) = 6.14286[/tex]

[tex]x = e^{6.14286[/tex]

[tex]x = 462.481[/tex]

Therefore, 462,481 thousands of candles should be sold.

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1) The marginal profit, P'(x), is -0.7ln(x) + 4.3.

2) The number of thousands of candles that should be sold to maximize profit is approximately 466.9.

1) To find the marginal profit, P'(x), we need to take the derivative of the profit function, P(x), with respect to x. Using the power rule and the chain rule, we can differentiate the function:

P(x) = 5x - 0.7x ln(x)

Taking the derivative with respect to x:

P'(x) = 5 - 0.7(ln(x) + 1)

Simplifying:

P'(x) = 5 - 0.7ln(x) - 0.7

P'(x) = -0.7ln(x) + 4.3

2) To find P'(10), we substitute x = 10 into the marginal profit function:

P'(10) = -0.7ln(10) + 4.3

Using a calculator, we can evaluate this expression:

P'(10) ≈ -0.7(2.3026) + 4.3 ≈ -1.6118 + 4.3 ≈ 2.6882

The value of P'(10) is approximately 2.6882.

Now, let's interpret what P'(10) represents:

The correct interpretation is A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.

P'(10) represents the rate at which the profit is changing with respect to the number of candles sold when 10,000 candles have already been sold. In other words, it measures the additional profit (in thousands of dollars) for each additional thousand candles sold once 10,000 candles have already been sold.

Lastly, to determine the number of thousands of candles that should be sold to maximize profit, we need to find the critical points of the profit function P(x). This can be done by setting the derivative P'(x) equal to zero and solving for x.

-0.7ln(x) + 4.3 = 0

-0.7ln(x) = -4.3

ln(x) = 4.3 / 0.7

Using properties of logarithms:

x = e^(4.3 / 0.7)

Using a calculator, we can evaluate this expression:

x ≈ e^(6.1429) ≈ 466.9

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Answer:

√6

Step-by-step explanation:

√6 = 2.44948974278...

The number never ends and the values don't repeat therefore, the correct answer is √6.

Hope this helps! :)

Answer:

B. The square root of 5

Step-by-step explanation:

You can only square root a number that can be the answer to an equation like x*x=5, which it is not.

Answer

i think its federal income tax increase. 2nd one i believe

Step-by-step explanation:

The President of the United States proposes a new national plan to reduce water pollution.

Which of these would most likely provide the revenue to pay for this new public service?

Step-by-step explanation:

answer is :

Answer:

11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.

Answer: Ratio is 2:11

Step-by-step explanation:

So your ratio of pirates to non-pirates would be 9:11

So you subtract number of pirates from total trick-or-treaters and get 2.

So the proportion of non-pirates would be 2:11.

Answer:

Total annual inventory cost = $480

c) 480

Step-by-step explanation:

given data

annual demand for the oil filter = 1200 units

ordering cost per order S = $80

holding cost of carrying 1 unit = $1.2 per year

lead time = 12 working days

number of working days = 360 days

solution

we get here economic order quantity that is express as

economic order quantity = [tex]\sqrt{\frac{2DS}{H}}[/tex]    ...............1

here D is annual demand and S is ordering cost and H is per unit cost

so put here value and we get

EOQ = [tex]\sqrt{\frac{2\times 1200 \times 80}{1.2}}[/tex]  

EOQ = 400 units

and

Annual ordering cost = annual demand × ordering cost ÷ order size   .........2

and here

No orders (Q) = annual demand ÷ order size   ...........3

Q =  1200 ÷ 400

Q = 3 orders

so

Annual ordering cost = ordering cost × number of order  ................4

put here value

Annual ordering cost = 80 × 3

Annual ordering cost = $240

and

Annual carrying cost = average inventory × per unit cost    ..........5

and

average inventory = EOQ ÷ 2        ...........6

Annual carrying cost = (EOQ × H) ÷ 2

put here value and we get

Annual carrying cost = 400 × 1.2  ÷ 2

Annual carrying cost = $240

and

so here Total annual inventory cost = Annual ordering cost + Annual carrying cost    .........................7

Total annual inventory cost = $240 + $240)

Total annual inventory cost = $480

Answer:

  sum: 2 6/7

Step-by-step explanation:

The first term is 2, and the common ratio is 0.6/2 = 0.3. This value is less than 1, so the series converges.

The sum is ...

  S = a0/(1 -r) = 2/(1 -0.3) = 2/0.7

  S = 2 6/7

Answer:

See Explanation

Step-by-step explanation:

Given:

Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10).

(a)If we translate  quadrilateral JKLM 3 units down and 3 units left:

(x-3,y-3), we obtain: W(5,1), X(1,7), Y(9,9), and Z(11,7)

Therefore, we match it with: A translation 3 units down and 3 units left

(b)If we translate  quadrilateral JKLM 2 units right and 3 units down:

(x+2,y-3), we obtain: O(10,1), P(6,7), Q(14,9), and R(16,7)

Therefore, we match it with:A translation 2 units right and 3 units down

S(4, 16), T(10, 20), U(12, 12), and V(10, 10)

(c) If we transform quadrilateral JKLM by a sequence of reflections across the x- and y-axes, in any order, we obtain:

A(-8, -4), B(-4, -10), C(-12, -12), and D(-14, -10)

(d)If we translate  quadrilateral JKLM 3 units left and 2 units up:

(x-3,y+2), we obtain:E(5,6), F(1,12), G(9,14), and H(11,12)

Therefore, we match it with: A translation 3 units left and 2 units up

(e)S(4, 16), T(10, 20), U(12, 12), and V(10, 10)

No suitable transformation is found from JKLM to STUV.

Answer:

a translation 3 units down and 3 units left

W(5,1), X(1,7), Y(9,9), and Z(11,7)

a translation 2 units right and 3 units down

O(10,1), P(6,7), Q(14,9), and R(16,7)

a sequence of reflections across the

x- and y-axes, in any order

S(4, 16), T(10, 20), U(12, 12), and V(10, 10)

a translation 3 units left and 2 units up

E(5,6), F(1,12), G(9,14), and H(11,12)

Answer:

0, 10

Step-by-step explanation:

The given function is:

[tex]g(y) = \frac{y-5}{y^2-3y+15}[/tex]

According to the quotient rule:

[tex]d(\frac{f(y)}{h(y)}) = \frac{f(y)*h'(y)-h(y)*f'(y)}{h^2(y)}[/tex]

Applying the quotient rule:

[tex]g(y) = \frac{y-5}{y^2-3y+15}\\g'(y)=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}[/tex]

The values for which g'(y) are zero are the critical points:

[tex]g'(y)=0=\frac{(y-5)*(2y-3)-(y^2-3y+15)*(1)}{(y^2-3y+15)^2}\\(y-5)*(2y-3)-(y^2-3y+15)=0\\2y^2-3y-10y+15-y^2+3y-15\\y^2-10y=0\\y=\frac{10\pm \sqrt 100}{2}\\y_1=\frac{10-10}{2}= 0\\y_2=\frac{10+10}{2}=10[/tex]

The critical values are y = 0 and y = 10.