Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.

Formula for a converging infinite series. a1 is the first term and r is the common ratio.

A. 4
B. 1.33
C. 5.33

Step-by-step explanation:

in total we have 3+4 = 7 balls.

when we draw the first ball, the probability to draw a red ball is 3/7, and a blue ball 4/7.

when we draw the second ball, we have now only 6 balls in total.

the probabilty to draw a red back now depends also on the result of the first draw.

if the first ball was already red, then we have only a chance now of 2 out of 6.

if the first ball was blue, then we have now a chance of 3 out of 6.

so, the probably to draw at least 1 red ball in 2 draws is the probability of drawing one on the first draw plus the probability of drawing one on the second :

1 - probability to see 2 blue balls

1 - 4/7 × 3/6 = 1 - 12/42 = 30/42 = 0.714285714...

the expected number of red balls in 2 draws is

1 red in first red in first red in second

but not second and second but not first

1×(3/7 × 4/6) + 2×(3/7 × 2/6) + 1×(4/7 × 3/6) = 12/42 + 12/42 + 12/42 = 36/42 = 6/7 = 0.857142857 ≈ 0.8571

Answer:

25 and 57.

Step-by-step explanation:

Let the lowest number be x then the other is 2x + 7, So:

x(2x + 7) = 1425

2x^2 + 7x - 1425 = 0

2 * - 1425 = -2850 = -2 * 3 * 5 * 5 * 19

We need 2 numbers whose product is -2850 and whose sum is + 7.

These are 3 * 19 = 57 and -2* 5 * 5 = -50 so we write:

2x^2 - 50x + 57x - 1425 = 0  Now we factor by grouping:

2x(x - 25) + 57( x - 25) = 0)

(2x + 57) ( x - 25) = 0

x = -57, 25.

We ignore the negative as we are given that the number is positive,

x = 25 is one number and the other is 2(25) + 7 = 57.

Answer:

[tex]r \geqslant 10.4[/tex]

The maximum rate at which the diver will descend will be 7 feet per hour.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

Initial depth of scuba diver = 12.8 feet

Let's say the rate of a scuba diver is "r".

Initial depth + depth cover with constant rate ≤ final depth

12.8 + (312/60)r ≤ 49.2

r ≤ 7

Thus, the maximum rate at which a diver can descend is 7 feet per hour.

Hence"The maximum rate at which the diver will descend will be 7 feet per hour".

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Answer:

at least 8

Step-by-step explanation:

Answer:

At least 8

Step-by-step explanation:

I took the test

Using the midpoint formula, the coordinates of endpoint H are (4, -6).

The midpoint formula is given as: [tex](x_m, y_m) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]

Where,

[tex](x_m, y_m)[/tex] = coordinates of the midpoint

[tex](x_1, y_1)[/tex] = coordinates of the first point

[tex](x_2, y_2)[/tex] = coordinates of the second point

Given the following:

[tex](x_m, y_m)[/tex] = M( 6,-4)

[tex](x_1, y_1)[/tex] = G(8,-2)

[tex](x_2, y_2)[/tex] = H(?, ?)

Plug in the values into the midpoint formula

[tex]M(6, -4) = (\frac{8 + x_2}{2}, \frac{-2 + y_2}{2} )[/tex]

Solve for the x-coordinate and y-coordinate separately

[tex]6 = \frac{8 + x_2}{2}[/tex]

[tex]6 \times 2 = 8 + x_2\\\\12 = 8 + x_2\\\\12 - 8 = x_2\\\\4 = x_2\\\\\mathbf{x_2 = 4}[/tex]

[tex]-4 = \frac{-2 + y_2}{2}\\\\-8 = -2 + y_2\\\\-8 + 2 = y_2\\\\-6 = y_2\\\\\mathbf{y_2 = -6}[/tex]

Therefore, using the midpoint formula, the coordinates of endpoint H are (4, -6).

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Work Shown:

1.45*270 = 391.50

The multiplier 1.45 represents a 45% increase

Think of it as 1.45 = 1+0.45 = 100% + 45%

Answer:

391.5

Step-by-step explanation:

the 45% of $270 is $121.5

The vertices of the feasible region of the constraints is (0,2.5)

The constraints are given as:

x + 3y ≤ 6

4x + 6y ≥ 9

x ≥ 0,  y ≥ 0

Express the inequalities as equations

x + 3y = 6

4x + 6y = 9

Make x the subject in x + 3y = 6

x = 6 - 3y

Substitute x = 6 - 3y in 4x + 6y = 9

4(6 - 3y) + 6y = 9

Expand

24 - 12y + 6y = 9

Evaluate the like terms

-6y = -15

Divide by 6

y = 2.5

Substitute y = 2.5 in x = 6 - 3y

x = 6 - 3 * 2.5

Evaluate

x = -1.5

So, we have:

(x,y) = (-1.5, 2.5)

Recall that: x ≥ 0,  y ≥ 0

This means that the feasible region must have positive coordinates or zero

So, we set x = 0

(x,y) = (0, 2.5)

Hence, the vertices of the feasible region of the constraints is (0,2.5)

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Answer:

The price of 1 adult ticket is 12 dollars, and the price of a ticket for one student is 7 dollars

Step-by-step explanation:

Make a system of equations for the two days that the play was shown.

Let x = the price of an adult ticket

Let y = the price of a student ticket

For the first day:

For the second day:

Now, we can solve using the elimination method. Multiply the first equation by 2 and the second equation by 9. Then swap the order of the equations.

Answer: And I don’t know math

Step-by-step explanation:

Answer:

The answer is 9

Explanation:

0.5a+8.75=13.25

We simplify the equation to the form, which is simple to understand

0.5a+8.75=13.25

We move all terms containing a to the left and all other terms to the right.

+ 0.5a=+13.25-8.75

We simplify left and right side of the equation.

+ 0.5a=+4.5

We divide both sides of the equation by 0.5 to get a.

a=9

81°

Step-by-step explanation:

The sum.of the interior angles of a triangle is equal to 180°. Hence, in our triangle, we can see that

[tex]41° + 58° + \angle{3} = 180° \Rightarrow 99°+\angle{3} = 180°[/tex]

We then see that

[tex]\angle{3} = 180° - 99° = 81°[/tex]

Answer: 81 i believe

Step-by-step explanation:

Answer:

L=30 W=15

Step-by-step explanation:

90 divided by 6 is 15. 15 is the Width. Multiply 15 by 2 and you get 30 which is the Length.

Answer:

The second number would be 108.

Step-by-step explanation:

Multiply 70 by 2 and subtract 32 from the product.

Answer:

Step-by-step explanation:

Let the number is x.

Translate the given into equation and solve for x:

Answer:

It is B

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

8x-20=4x+32

start by moving the terms,

8x-4x=32+20

combine

4x=52

divide each side by 4

x=13

Answer:

[tex] \frac{1}{2} \: \: \: \: \: \frac{1}{4 \: } \: \: \: \frac{1}{8} [/tex]

[tex] \frac{4}{8} \: \: \: \frac{2}{8} \: \: \: \frac{1}{8} [/tex]

She ate

[tex] \frac{7}{8} [/tex]

Answer:

A. 30% B. 45%

Step-by-step explanation:

A. 72,000/240,000 = x/100

(72,000)(100) = (240,000)x

7,200,000 = 240,000x

30 = x

B. 108,000/240,000 = x/100

10,800,000 = 240,000x

45 = x

Answer:

[tex]f^{-1} (x) =x-11[/tex]

Step-by-step explanation:

[tex]f(x) = x+11\\\\\text{Write f(x) as y = x+11}\\\\\text{Replace x with y,}\\\\x = y+11\\\\\text{Solve for y}\\\\x=y+11\\\\\implies y= x-11\\\\\implies f^{-1} (x) = x-11[/tex]

Answer:

umm i think its A/B

Step-by-step explanation:

Answer:

√49 < √56 < √64

Step-by-step explanation:

√56 = 7.4833....

7x7 = 49

8x8 = 64

√49 < √56 < √64

Answer:

What supplies?

Step-by-step explanation:

Answer:

for 3, 4 or both?

4. is probably zero

Step-by-step explanation:

Wait is 4 a question?

[tex]cos^2 x + \cos^2 y = \cos(2x + 2y)\\\\\implies \dfrac{d}{dx} (\cos^2 x + \cos^2 y) = \dfrac{d}{dx} \cos(2x+2y)\\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-\sin(2x+2y) \left(2+2\dfrac{dy}{dx} \right) \\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-2\sin(2x+2y) -2\sin(2x+2y)\dfrac{dy}{dx} \right) \\\\\implies 2 \sin(2x+2y) \dfrac{dy}{dx} - 2 \cos y \sin y \dfrac{dy}{dx} = 2 \cos x \sin x-2\sin(2x+2y)[/tex]

[tex]\implies \sin(2x+2y) \dfrac{dy}{dx} - \cos y \sin y \dfrac{dy}{dx} = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}\\\\\implies y'(x) = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}[/tex]

Answer:

The choice 66

Step-by-step explanation:

[tex]6x + 2m \\ 6(14) + 2( - 9) \\ 84 - 18 \\ = 66[/tex]

Answer:

Nick will have to pay $63.56 for the shoes.

Step-by-step explanation:

f the original cost of the shoes is $56.75 and the markup is 12% greater than the original price, the final price would be $63.56.

$56.75 • 0.12 = $6.81

$56.75 + $6.81 = $63.56

$56.75 + 12% = $63.56

Answer:

Nick will have to pay $63.56 for the shoes.

Step-by-step explanation:

An acute triangle is a triangle whose angles are all acute (i.e. less than 90°). In the acute triangle shown below, ∠a, ∠b and ∠c are all acute angles. Example 1: A triangle has angles 46°, 63° and 71°.

Answer:

A

Step-by-step explanation:

You have to move the decimal 5 places to the left to get 2