You are given 12 to 1 odds against drawing two hearts when two cards are selected at random from a standard deck of 52 cards (with replacement of the first card before the second card is drawn). This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Round to the nearest cent.

Answer:

A

Step-by-step explanation:

In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

\(4\frac{2}{4}\) that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

\(4\frac{2}{4} = \frac{16+4}{2}\)

=\(\frac{18}{4}\)

Then \(4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}\)

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that \(\frac{18}{4}\) is less than \(\frac{37}{4}\) Hence, Darren is wrong.

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Given:

75 people to 25 people

To find:

The percentage value.

Explanation:

The percentage is,

Hence, the percentage is 300%.

Final answer:

The percent value is 300%

a. The relation is an equivalence relation, and its corresponding partition has blocks {1, 4}, {2}, and {3}.

b. The relation is not specified.

c. The relation is not an equivalence relation because it is not transitive.

d. The relation is not an equivalence relation because it is not reflexive.

a. The relation is an equivalence relation because it is reflexive, symmetric, and transitive. The blocks of its corresponding partition are {1, 4} and {2} and {3}.

b. The relation is not specified, so it is impossible to determine whether it is an equivalence relation or not.

c. The relation is not an equivalence relation because it is not transitive. Specifically, (3, 1) and (1, 3) are in the relation, but (3, 3) is not.

d. The relation is not an equivalence relation because it is not reflexive (i.e., 1 and 4 are not related to themselves).

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Answer:

Just subtract the area of two triangles from the area of the rectangle

Step-by-step explanation:

Answer:

149 ft^2

Step-by-step explanation:

First, figure out the whole square area.

Which is 9 1/4 x 20 = 185

One triangle is 6 x 6 x .5 because the formula of a triangle is A=bh1/2.

Triangle=18

There are two triangles so its 36.

185-36 = 149

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The ordered pair which is a solution to every linear equation of the form given is; (0, 0).

It follows from the task content that the ordered pair which satisfies the equation of the form y =Mx be determined.

On this note, since the product of any real number, slope in this scenario and 0 is; 0.

Ultimately, it follows that the required ordered pair is; (0, 0) for any real number value of the slope, m.

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Answer:

$54.87

Step-by-step explanation:

The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.

The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.

The total area to be covered with mulch is 108 - 15 = 93 square feet.

The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.

Therefore, the total cost of the mulch will be $54.87.

Answer:

-10

Step-by-step explanation:

Step-by-step explanation:

hope it helps

The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealised relationship between two changing quantities.

We have given function as ,

f(x) = 1/√(x-4)

We have to find f(x) - f(5)/x-5

f(x) = f(5)/x-5 = 1/√(5-4)/(x-5)

= 1/√(5-4)/(x-5)

= (x-5)/√(5-4)

= (x-5)

Therefore, The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

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The height of the object at a time of 2 seconds is given as follows:

1106 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

h(t) = -16t² + 1170.

At a time of 2 seconds, the height is found replacing the lone instance of t by two, hence:

h(2) = -16(2)² + 1170

h(2) = 1106 feet.

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Answer:

the 1 cause it's a 100

Step-by-step explanation:

100 + 80 + 9

Option B, option C, and option E are correct because the equation is Negative 3 less than 4.9 times a number, x, is the same as 12.8.

It is defined as the combination of constants and variables with mathematical operators.

The options are:

A: -3 - 4.9x = 12.8

B: 4.9x - (-3) = 12.8

C: 3+ 4.9x = 12.8

D: (4.9 - 3)x = 12.8

E: 12.8 = 4.9x + 3

We have a statement:

Negative 3 less than 4.9 times a number, x, is the same as 12.8.

We can write in a mathematical form:

4.9x - (-3) = 12.8

or

4.9x + 3 = 12.8

or

12.8 = 4.9x + 3

Thus, option B, option C, and option E are correct because the equation is Negative 3 less than 4.9 times a number, x, is the same as 12.8.

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

The equation shows that x = -1/4 and y = 1/20.

-3x + 5y = 1

12x - 20y = 4

Multiply equation i by 12

Multiply equation ii by -3

-36x + 60y = 13

-36x + 60y = -12

120y = 1

y = 1/20

From equation i, -3x + 5y = 1

-3x + 5(1/20) = 1

-3x + 1/4 = 1

-3x = 3/4.

x = -1/4

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The system of equations has exactly one solution where x = 0 and y = -2. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

-5x + y = -2

y = 5x - 2            .....1

6x - y = 2

y = 6x - 2            .....2

From equations 1 and 2, then we have

6x - 2 = 5x - 2

x = 0

Then the value of y is given as,

y = 6(0) - 2

y = - 2

The system of equations has exactly one solution where x = 0 and y = -2. Then the correct option is C.

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Answer:

111,739 square feet

Step-by-step explanation:

Two adjacent sides of the park say x and y are,

x=533feet

y=525feet

A=53º

area=1/2*b*c*sin(A)

111739 feet^2

Answer:

y = -6x + 2

Step-by-step explanation:

y = mx + b

m = slope

slope = m = -6

y = -6x + b

8 = -6(-1) + b

b = 2

y = -6x + 2

Answer:

y = -6x + 2

Step-by-step explanation:

We can use point slope formula, when we have a point and a slope.

y - 8 = -6(x  + 1)

that's the equation.

If you want it in Slope intercept form, you simply distribute the -6 and move the 8 to the other side

y - 8 = -6x - 6

y = -6x +2

The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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Answer:

\(\pi\)

Step-by-step explanation:

If a number can be written as an integer/integer in a fraction form or in a decimal form as a terminating or repeating decimal, it is rational.  An integer is a set up numbers that fall into this pattern:

...-3,-2,-1,0,1,2,3...

0.16 is a terminating decimal or 16/100 as a fraction.

2.53 is a terminating decimal or 253/100

-1/5 can be written as a decimal at -0.2 and it terminating.

Answer:

\(24\pi \: {cm}^{2} \)

Step-by-step explanation:

Given:

A cone

h (height) = 4 cm

r (radius) = 3 cm

Find: A (surface area) - ?

In order to find the surface area, we have to know the length of the slant height first (use the Pythagorean theorem):

\( {l}^{2} = {r}^{2} + {h}^{2} \)

\( { l}^{2} = {3}^{2} + {4}^{2} = 9 + 16 = 25\)

\(l > 0\)

\(l = \sqrt{25} = 5 \: cm\)

Now, we can find the surface area:

\(a(surface) = \pi {r}^{2} + \pi \times r \times l\)

\(a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 5 = 9\pi + 15\pi = 24\pi \: {cm}^{2} \)

Answer:

Step-by-step explanation:

Answer:

the domain is "the set of all real numbers."

the range of the given function is (5, infinity)

Step-by-step explanation:

This is an exponential function.  For the sake of clarity you must enclose "x - 2" inside parentheses:  f(x) = 2(3)^(x-2).  This function is defined for all real x-values, so the domain is "the set of all real numbers."  

Focusing on  (3)^x:  This has the same shape as the basic exponential y = e^x; the graph starts in Quadrant II and increases with x, more and more rapidly as you pass x = 0.  The functions y = e^x and that of y = 3^x are always positive.  Likewise in the case of f(x) = 2(3)^(x-2):  the function is always positive.  If we look at f(x) = 2(3)^(x-2) alone, we conclude that the domain is (0, infinity).  But that " + 5 " in y=2(3)^(x-2) + 5 translates the entire graph of f(x) = 2(3)^(x-2) upward by 5 units.

Thus, the range of the given function is (5, infinity).

I don't understand what you are talking about, but I can list you the factor pairs of 16!

16=1,16; 2,8; 4,4

Thise are all the factor pairs

Answer:

1 x 16,

2 x 8

4 x 4

Factors of 16: 1, 2, 4, 8, 16

To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:

1. Reflect A over the y-axis to get A': (-2, 2)

2. Reflect A' over the x-axis to get A'': (-2, -2)

Therefore, the new point A'' is (-2, -2).

Answer:

Option C

Step-by-step explanation:

I just graphed on my TI-84

Hope this helps!

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°