Express as a fraction 12 1\2%

Answer:

-3901 silver coins (a loss)

Step-by-step explanation:

Probability of surviving the quest = 85.4% (Gain of 5,533 silver coins.)

If the insured were to die, the insurance company would pay a death benefit(incur a loss) of 59,086 silver coins.

Therefore:

The probability of not surviving the quest = 100%-85.4% =14.6%

Therefore, the expected value of this insurance policy to the insurance company

[tex]=(5,533 X 85.4\%)+(-59,086 X 14.6\%)\\=(5,533 X 0.854)+(-59,086 X 0.146)\\=-3901.37\\\approx -3901$ silver coins[/tex]

The expected value of this insurance policy to BIC is -3901 silver coins

The expected value of this insurance policy to BIC is -3901 silver coins (a loss)

Since st to Moria. Based on past experience, the probability of surviving such a quest is 85.4%. If BIC charges a premium of 5,533 silver coins and would pay a death benefit of 59,086 silver coins

So here the expected value is

= 85.4% of 5,533 + (14.6% of -59,086)

= -3901

Hence, The expected value of this insurance policy to BIC is -3901 silver coins (a loss)

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Answer:

Solution,

Let the length and breadth of smaller rectangle be l and b.

Length and breadth of larger rectangle be 3L and 3 b.

Besides, depth is same in both beds.

As area of small rectangle=180

Area of larger rectangle:

[tex]3l \times 3b \\ = 9lb \\ = 9 \times 180 \\ = 1620 \: kg[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

651.

Step-by-step explanation:

Note: In the given series it should be -29 instead of 29 because 29 cannot be a term of AP whose first term is 91 and common difference is -6.

Consider the given series is

[tex]91+85+79+...+(-29)[/tex]

It is the sum of an AP. Here,

First term = 91

Common difference = 85 - 91 = -6

Last term = -29

nth term of an AP is

[tex]a_n=a+(n-1)d[/tex]

where, a is first term and d is common difference.

[tex]-29=91+(n-1)(-6)[/tex]

[tex]-29-91=(n-1)(-6)[/tex]

[tex]\dfrac{-120}{-6}=(n-1)[/tex]

[tex]20=(n-1)[/tex]

[tex]n=20+1=21[/tex]

Sum of AP is

[tex]Sum=\dfrac{n}{2}[\text{First term + Last term}][/tex]

[tex]Sum=\dfrac{21}{2}[91+(-29)][/tex]

[tex]Sum=\dfrac{21}{2}[62][/tex]

[tex]Sum=651[/tex]

Therefore, the sum of given series is 651.

Answer:

32:  median

Step-by-step explanation:

Use the median.  Here the median is the middle value of the data string

8, 29, 32, 31, 33, that is, 32.  

Answer:

( x-2)^2 + ( y+1) ^2 = 25

Step-by-step explanation:

The equation of a circle is

( x-h)^2 + ( y-k) ^2 = r^2  where ( h,k) is the center  and r is the radius

The center is ( 2,-1) and the radius is the difference from the center to a point on the circle

(2,4) and (2,-1)

 since x is the same the radius is (4- -1) = 5

( x-2)^2 + ( y--1) ^2 = 5^2

( x-2)^2 + ( y+1) ^2 = 25

Answer:

B. 642.22 units squared

Step-by-step explanation:

Knowing that QP ║ MN and ∠QLP = ∠MLN, then ΔQLP ~ ΔMLN.

That means corresponding sides and heights have the same ratios.

We know that QP = 25, which corresponds to MN = 34. Also, the height of ΔQLP, LS, corresponds to the height of ΔMLN, LR = LS + SR = LS + 10. Let's say LS = x.

We can now write:

QP / MN = LS / LR

25 / 34 = x / (x + 10)

Cross-multiply:

34 * x = 25 * (x + 10)

34x = 25x + 250

34x - 25x = 250

9x = 250

x = 250/9 ≈ 27.78 units

So, LS = 27.78 units and LR = LS + SR = 27.78 + 10 = 37.78 units.

The area of a triangle is denoted by A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of ΔLMN is MN = 34, and the height is LR = 37.78. Plug these in:

A = (1/2) * b * h

A = (1/2) * 34 * 37.78 ≈ 642.22 units squared

The answer is thus B.

~ an aesthetics lover

Answer:

5/8

Step-by-step explanation:

72 = 16/10 of 45

45 = 10/16 = 5/8 of 72

Answer:

  book 25; pen 8

Step-by-step explanation:

If we let b and p represent the cost of a book and a pen, respectively, then the two purchases can be written as ...

  7b +4p = 207

  5b +5p = 165

Multiply the second equation by 4/5 and subtract the result from the first equation:

  (7b +4p) -4/5(5b +5p) = (207) -4/5(165)

  3b = 75 . . . . simplify

  b = 25 . . . . . divide by 3

Dividing the second equation by 5 gives ...

  b + p = 33

Solving for p, we have ...

  p = 33 -b = 33 -25 = 8

The cost of an exercise book is 25; the cost of a pen is 8.

Answer:

x = 60

Step-by-step explanation:

L // M

Sum of co-interior angles = 180

2x + 5 + x - 5 = 180

Add the like terms

3x + 0 = 180

3x = 180

Divide both sides by 3

3x/3 = 180/3

x = 60

Answer: Water: 120 gallons

Premium Antifreeze: 200 gallons

Step-by-step explanation:

Had to complete the question first.

A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 80% pure antifreeze. The company wants to obtain 320 gallons of a mixture that contains 5% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?

Water: ____ gallons

Premium Antifreeze: _____ gallons

Solution:

Let w = amt of water required

An equation based on the the percent water, an 80% solution is 20% water

Multiply through

= 20% (320 - w) + w = 50% x ( 320)

64 - 0.2w + w = 160

Collecting like times

0.8w = 160 - 64

w = 96%

w = 120 gal of water to produce 320 gal of 50% antifreeze

320 - 120 = 200 gal of 80% solution

Water: 120 gallons

Premium Antifreeze: 200 gallons

Answer:

The altitude is 4√3 units long

Step-by-step explanation:

Since the triangle is equilateral, all the sides will measure 8 units.

Now to find the altitude, we drop a line from the middle vertex to the horizontal line below and this splits the horizontal line into 2 equal parts which measures 4 units exactly.

Now we will be having 2 right-angled triangles, with the hypotenuse of each measuring 8 units and the other side measuring 4 units

Mathematically to find the altitude, we can solve using Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides

Let’s call the altitude h;

8^2 = h^2 + 4^2

64 = h^2 + 16

h^2 = 64-16

h^2 = 48

h= √(48)

h = 4 √3 units

Answer:

THE ANSWER IS B

Step-by-step explanation:

Answer:

Option (C).

Step-by-step explanation:

Graphed function is,

f(x) = x² - 2x - 3

     = x² - 2x + 1 - 1 - 3

     = (x² - 2x + 1) - 4

     = (x - 1)² - 4

f(-2x) = (-2x)² - 2(-2x) - 3

        = 4x² + 4x - 3

        = 4(x² + x) - 3

        = 4[x² + 2(0.5)x + (0.5)²- (0.5)²] -3

        = 4(x + 0.5)² - 1 - 3

        = 4(x + 0.5)² - 4

        = 4[(x - 1) + 1.5]² - 4

Therefore, parent function 'f' will be a horizontal shrink by 4 units and  shifted 1.5 units to the left.

Option (C) will be the answer.

Answer:

i think its -$2

Step-by-step explanation:

The expected value of profit or loss is ZERO

Picker Wheel is a wheel spinner for a random picker. Various functions & customization. Enter choices or names, spin the wheel to decide a random result.

We have

If the wheel lands on win, you win $5;

on lose, you win nothing.

It costs $2 to play.

According to the question

Win written four times and Lose written six times.

P (W) = 4/10 = 0.4

P (L) = 6/10  = 0.6

x                  net                p(x)         xP(x)

Win            5 - 2  = 3         0.4          1.2

Loose        0 - 2  = -2        0.6         -1.2

∑xP(x) = 1.2 - 1.2 = 0

Hence , expected value  of profit or loss is  ZERO

or

You can say expected value is 2  $ against 2$ cost

5(0.4) + 0(0.6) = 2    against 2 $ ticket.

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Answer:

60

Step-by-step explanation:

Tangents to a circle from a common external point are congruent, thus

JA = JB = 6

AL = KC = 11

CK = KB = 13

Thus

perimeter = 2(6) + 2(11) + 2(13) = 12 + 22 + 26 = 60

The perimeter of a triangle JKL is 60 units. Therefore, option D is the correct answer.

A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet. The lengths of tangents drawn from an external point to a circle are equal.

Given that,

Given that, JK, KL and LJ are all tangent to O. JA=6, AL=11 and CK=13.

In the figure,

From the external point J, tangents JA=JB

JB=6

From the external point L, tangents AL=LC

LC=11

From the external point K, tangents KB=KC

BK=13

So, JL=JA+LA

JL=6+11=17

LK=LC+CK

= 11+13

= 24

JK=JB+KB

= 6+13

= 19

Now, the perimeter is JL+LK+JK

= 17+24+19

= 60 units

Therefore, option D is the correct answer.

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Answer:

The comparable tax rate is 3.95%, thus you should choose the 4.5% taxable account option.

Step-by-step explanation:

In order to convert the tax-free interest rate of 3% per year to the comparable taxable interest rate, one should consider that 3% is the interest rate after the marginal tax discount. If you are at the 24% marginal tax bracket, the comparable rate is:

[tex]r*(1-0.24)=0.03\\r=\frac{0.03}{0.76}\\r=0.0395\\r=3.95\%[/tex]

The comparable tax rate is 3.95%, thus you should choose the 4.5% taxable account option.

The comparable tax rate is 3.95%, so you should choose the 4.5% taxable account option.

Since the rate is 3% per annum, the other rate should be 4.5% and there is tax rate of 24%

So,

rate (1 - 24%) = 3%

rate = 3.95%

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Step-by-step explanation:

It's given that <KPL and <JPL are linear pair so when we add both we will get 180° so

<KPL + <JPL = 180° [ Being linear pair ]

2x + 24 + 4x + 36 = 180

6x + 60 = 180

6x = 120

x = 120/ 6

Therefore x = 20

Now

x = 20

m<KPL = 2x + 24 = 2 * 20 + 24 = 64

m<JPL = 4x + 36 = 4 *20 + 36 = 116

1 pound = 16 ounces.

9 pounds of sand x 16 = 144 total ounces of sand.

144 ounces / 6 ounce bottle = 24

He made 24 bottles.

Answer:

24 bottles

Step-by-step explanation:

Trevor bought 9 pounds of sand

He fills 6-ounce bottles

First let's convert pounds to ounces:

Now, number of bottles required:

Answer and Step-by-step explanation:

The domain of a function is the values the invariable can assume to result in a real value for the variable. In other words, it is all the values x can be.

Since it's related to area, the values of x has to be positive. The domain must be, then:

[tex]-6x^{2} + 105x - 294 = 0[/tex]

Solving the second degree equation:

[tex]\frac{-105+\sqrt{105^{2} - 4(-2)(-294)} }{2(-6)}[/tex]

x = 3.5 or x = 14

The domain of this function is 3.5 ≤ x ≤ 14

The maximum area is calculated by taking the first derivative of the function:

[tex]\frac{dA}{dx} = -6x^{2} + 105x - 294[/tex]

A'(x) = -12x + 105

-12x + 105 = 0

-12x = -105

x = 8.75

A(8.75) = [tex]-6.8.75^{2} + 105.8.75 - 294[/tex]

A(8.75) = 165.375

The maximum area of the garden is 165.375 square units.

The Range of a function is all the value the dependent variable can assume. So, the range of this function is: 0 ≤ y ≤ 165.375, since this value is the maximum it will reach.

A(x) = 100

[tex]100 = -6x^{2} + 105x-294[/tex]

[tex]-6x^{2} + 105x - 394 = 0[/tex]

Solving:

[tex]\frac{-105+\sqrt{105^{2}-4(-6)()-394} }{2(-6)}[/tex]

x = 5.45 or x = 12.05

The values of x that produces an area of 100 square units are 5.45 and 12.05

Answer:

The total number of marbles is 3.4*r

Step-by-step explanation:

We have 25% more red than blue, so we can write the equation:

[tex]red = 1.25*blue[/tex]

We have 60% more green than red, so:

[tex]green = 1.6*red[/tex]

In total we have 'r' red marbles, so:

[tex]red = r[/tex]

The total number of marbles in the collection is the sum of all three amount of marbles:

[tex]total = red + blue + green[/tex]

[tex]total = red + (red/1.25) + 1.6*red[/tex]

[tex]total = r + 0.8*r + 1.6*r[/tex]

[tex]total = 3.4*r[/tex]

The total number of marbles is 3.4*r

Answer:

Please post useful questions thanks!

Step-by-step explanation:

Answer:

I believe it's Area = 120cm^2

Step-by-step explanation:

Answer:

solution,

Given: A rhombus

To find: It's area.

Formula to find the area of rhombus:

[tex] = \frac{1}{2} \times d1 \times d2[/tex]

( half of product of diagonals)

Also, in a rhombus ,the diagonals bisects each other.

So,

D1=5*2=10

D2=12*2=24

Area of rhombus:

[tex] \frac{1}{2} \times d1 \times d2 \\ = \frac{1}{2} \times 10 \times 24 \\ = \frac{240}{2} \\ = 120 \: {cm}^{2} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

7 and 6

Step-by-step explanation:

The given expression is

=> [tex]\frac{7m}{9} + 6r - \frac{4}{5}[/tex]

Coefficients are the numbers with variables.

So, here in this expression the coefficients are 7 and 6

Answer:

D. 7/9 and 6

Step-by-step explanation:

Answer:

Length= 58

width= 26

Step-by-step explanation:

Answer:

X=20; pqr = 130°

Step-by-step explanation:

They key here is to notice that the instructions say that qs bisects pqr, meaning that it evenly cuts it into 2 pieces. So, to find x, you just solve for x in the equation 3x+5=2x+25. Then, you plug it back into either side of the equation, at which point, you should get 65. Since it is half of pqr, just double it to get your final answer of 130°

31.7 + 42.8 + 26.4 + x/4 = 39.1

Add up all the plain numbers on the left side:

100.9 + x/4 = 39.1

Subtract 100.9 from each side:

x/4 = 39.1

Multiply each side by 4:

x = 156.4

Answer:

Step-by-step explanation:

To solve this, we have to first find the sum of each of the terms on the numerator of the fraction on the right:

31.7 + 42.8 + 26.4 + x = 100.9 + x

The sum of terms ind the numerator of the fraction on the right.

39.1 + 100.9 + x= 140 + x

Next step is to cancel out the denominators as they are equal.

Now we are left with

100.9+x = 140+x

Rearrange and solve

To get x = 156.4

Answer:I cStep-by-step explanation:

Answer:

C

Step-by-step explanation:

Okay, here we have the equation of the sine wave as;

y = asin(k(x + b))

By definition a represents the amplitude

k represents the frequency

b represents the horizontal shift or phase shift

Now let’s take a look at the graph.

By definition, the amplitude is the distance from crest to trough. It is the maximum displacement

From this particular graph, amplitude is 4

K is the frequency and this is 1/period

The period ;

Firstly we find the distance between two nodes here and that is 1/2 from the graph (3/4 to 1/4)

F = 1/T = 1/1/2 = 1/0.5 = 2

b is pi/4 ( phase is positive as it is increasing rightwards)

So the correct option here is C

Answer: it is

a=4, k=2, and b= pi/4

Step-by-step explanation:

got it right on A P E X

Answer:

D.

Step-by-step explanation:

The formula to find the solutions of a quadratic equation is -b plus or minus the square root of b^2 - 4ac divided by 2a. In this case, a = 2, b = 5, and c = -10.

[tex]\frac{-b +-\sqrt{b^2 - 4ac} }{2a}[/tex]

= [tex]\frac{-5 +-\sqrt{5^2 - 4*2*-10} }{2 * 2}[/tex]

So, the right answer should be the choice on the lower right corner.

Hope this helps!