Please help — Which ratio represents cos(c)?

The probability that the card will be a spade or a club 50%

Probability in math is referred as  how likely an event is to occur, or how likely it is that a proposition is true.

Here we have given that a card is drawn from a standard deck of 52 playing cards.

And we need to find  the probability that the card will be a spade or a club and we have to express your answer as a fraction or a decimal number rounded to four decimal places.

While we looking into the given question, we have identified the the total number of cards is 52.

And the number of spade cards = 13 and the number of club cards = 13

Therefore, the total number of spade and club cards

=> 13 + 13

=> 26

Therefore, the probability of getting a spade or  a club from a single draw is,

=> 26/52

When we simplified this one, then we get,

=> 0.5

When we convert this into percentage then we get

=> 50%.

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Answer:

I think it is $66 at first sorry if wrong

Answer:

6.4

Step-by-step explanation:

The optimal solution for this LP model is x = 2 and y = 2, with a maximum objective function value of 10

To graph the constraints, we can rewrite each inequality in slope-intercept form:

2x + 2y < 8

y < -x + 4

3x + 2y < 12

y < -1.5x + 6

x + 0.5y < 3

y < -2x + 6

Now we can plot these three lines on a coordinate plane and shade the regions that satisfy each inequality. The feasible region is the region that satisfies all three inequalities.

To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region and choose the point that maximizes the objective function.

The corner points of the feasible region are (0,0), (0,3), (1.5,3), and (2,2).

Objective function at (0,0): 3(0) + 2(0) = 0

Objective function at (0,3): 3(0) + 2(3) = 6

Objective function at (1.5,3): 3(1.5) + 2(3) = 9

Objective function at (2,2): 3(2) + 2(2) = 10

Therefore, the optimal solution is at (2,2), which gives a maximum value of 3(2) + 2(2) = 10.

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The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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The smaller zero of the quadratic function x² - 6x + 8 is 2.

Quadratic expressions are polynomial expressions which has a degree of 2.

The general form of a quadratic expression is ax² + b x + c.

Here given a quadratic expression,

x² - 6x + 8

We have to find the zeroes of the quadratic expression.

Let x² - 6x + 8 = 0

We have to factorize the expression.

We can factorize this as (x + p)(x + q) such that pq = 8 and p + q = -6.

Two such numbers are -4 and -2.

(x - 4) (x - 2) = 0

⇒ (x - 4) = 0 or (x - 2) = 0

⇒ x = 4 and x = 2

Hence the smaller zero is 2.

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Answer:

50 i believe.

Step-by-step explanation:

Answer:

c=4.95+3.99b

Step-by-step explanation:

4.95 is the monthly fee. we do not need a variable for this because we know what it is and it only happens once in the problem. the b is how many movies you purchase times 3.99

The equivalent value of the equation is n = 0.3

Given data ,

Let the equation be represented as A

Now , the value of A is

3.6 = 12n   be equation (1)

On simplifying , we get

Divide by 12 on both sides , we get

n = 3.6 / 12

On further simplification , we get

n = 0.3

Hence , the expression is n = 0.3

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The probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

A financial planner has three portfolios: A, B, and C.

Each portfolio has stocks and Bond

P(stock) = 0.5

P(bond) = 0.5

Customers are equally likely to choose stocks.

P(stock and bond from B) = P(stock, B) + P(bond, B)

= 0.25×0.5 + 0.25×0.5

= 0.25 or

= 25%

Thus, the probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.

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Using operations with functions, we have that:

a) w(t) = -3t + 5.

b) The pool will leak all the water in 1.67 hours.

c) 1.67 hours.

d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

e) The domain of the function is 0 ≤ t ≤ 1.67.

The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.

For this problem, these following functions are given:

Hence the amount of water in the pool is given by:

w(t) = f(t) - d(t)

w(t) = t² + 8t + 9 - t² - 11t - 4

w(t) = -3t + 5.

Hence:

The function is: w(t) = -3t + 5.

The pool will have leaked all the water when:

w(t) = 0.

Hence:

-3t + 5 = 0.

3t = 5

t = 1.67.

The pool will leak all the water in 1.67 hours.

Equaling f(t) and d(t), we have that:

t² + 8t + 9 = t² + 11t + 4.

3t = 5.

t = 1.67.

Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:

Hence:

The domain of the function is 0 ≤ t ≤ 1.67.

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Answer:

1). y= -5+3x

2). y= -2x-13

3). y= -6x+2

4). y= -x+4

5). y≈ 0.57x

6). y=2x-9

7). Equation incomplete

8). y=3x+23

Step-by-step explanation:

1).

3x-y=5

Subtract 3x from both sides

-y=5-3x

Multiply both sides by -1

y= -5+3x

2).

y+7= -2(x+3)

y+7= -2x-6

Subtract 7 from both sides

y= -2x-13

3).

y= -10-6(x-2)

y=  -10-6x+12

y= -6x+2

4).

3x=12-3y

Add 3y to both sides

3x+3y=12

Subtract 3x from both sides

3y=12-3x

Divide both sides by 3

y= -x+4

5).

-4x-7y=0

Add 4x to both sides

-7y= -4x+0

Multiply both sides by -1

7y= 4x

Divide both sides by 7

y≈ 0.57x

6).

4x-2y=18

Subtract 4x from both sides

-2y= -4x+18

Multiply both sides by -1

2y=4x-18

Divide both sides by 2

y=2x-9

7).

y= 5-

Equation is incomplete.

8).

y-2=3(x+7)

y-2=3x+21

Add 2 to both sides

y=3x+23

The ratios are shown equivalent as by simplification done below.

Ratio is the representative of comparison of part of things in a complete thing. Equivalent ratios are collection of ratios that show same comparison. As per the given question, the equivalent ratios are calculated as follows -

First column -

Ratio = 6:2

Dividing both the parts of ratio by 2

Ratio = 3:1

Second column -

Ratio = 9:3

Dividing both the parts of ratio by 3

Ratio = 3:1

Third column -

Ratio = 12:4

Dividing both the parts of ratio by 4

Ratio = 3:1

Fourth column -

Ratio = 15:5

Dividing both the parts of ratio by 5

Ratio = 3:1  

Similarly, for rest of the columns, division by 6, 7 and 8 of both parts of ratio will give the result 3:1. Hence, the given rations are shown as equivalent ratios, by simplifying into 3:1.

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Answer:

Therefore, the only statement that is false is x² + y² > 1. The other two statements are true.

Answer:

1.) y = 2x -2

2.) y = 1/3x + 1

3.) y = 1x - 1

4.) y = -3x - 4

\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)

Answer:

Step-by-step explanation:

Given the equation:

Substitute given values into equation and solve for the missing one:

Sydawna works 9 hours at the gas station

The answer is

\( {x}^{2} {y}^{3} \)

I hope this helps, have a great day!

Answer:

y=4-x/2

Step-by-step explanation:

To find the characteristic equations for the given differential equations, we'll start with each equation separately.

1. For the equation \(\(y'' - 9y' = 0\)\), we assume a solution of the form \(\(y = e^{rt}\)\) and substitute it into the equation:

\(\[y'' - 9y' = 0\]\)

\(\[(e^{rt})'' - 9(e^{rt})' = 0\]\\ \\ \\ \\\\\r^2e^{rt} - 9re^{rt} = 0\]\)

\(\[e^{rt}(r^2 - 9r) = 0\]\)

  Since \(\(e^{rt}\)\)is never zero, we can divide both sides of the equation by \\(\(e^{rt}\):\)

\(\[r^2 - 9r = 0\]\)

  Now, we factor out \(\(r\)\) from the equation:

\(\[r(r - 9) = 0\]\)

  This gives us two possible solutions for \(r\):

\(\(r_1 = 0\) and \(r_2 = 9\)\)

  Therefore, the characteristic equation for \(\(y'' - 9y' = 0\)\) is:

\(\[(r - 0)(r - 9) = 0\]\)

\(\[r(r - 9) = 0\]\)

2. For the equation \(\(t^2y'' + 16y = 0\)\), we assume a solution of the form \(\(y = t^r\)\) and substitute it into the equation:

\(\[t^2y'' + 16y = 0\]\)

\(\[t^2(t^r)'' + 16(t^r) = 0\]\)

\(\[t^2(r(r-1)t^{r-2}) + 16t^r = 0\]\)

  Simplifying the equation, we get:

\(\[r(r-1)t^r + 16t^r = 0\]\)

  Since \(\(t^r\)\) is never zero, we can divide both sides of the equation by \\(\(t^r\):\)

 \(\[r(r-1) + 16 = 0\]\)

  This gives us a quadratic equation for \(r\):

\(\[r^2 - r + 16 = 0\]\)

\(\[(r(r-1) + 16)t^r = 0\]\)

  The solutions for \(r\) can be found using the quadratic formula:

\(\[r = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(16)}}{2(1)}\] \\ \\ \\\\\r = \frac{1 \pm \sqrt{1 - 64}}{2}\]\)

\(\[r = \frac{1 \pm \sqrt{-63}}{2}\] \\ \\\\\r = \frac{1 \pm i\sqrt{63}}{2}\]\)

  Therefore, the characteristic equation for \(\(t^2y'' + 16y = 0\)\) is:

\(\[(r - \frac{1 + i\sqrt{63}}{2})(r - \frac{1 - i\sqrt{63}}{2}) = 0\]\)

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Answer:

D

Step-by-step explanation:

Answer:

$6.48.

Step-by-step explanation:

To calculate the total price of 4½ pounds of apples this week at the grocery store, we need to determine the price per pound after the 10% discount and then multiply it by the weight of the apples.

First, let's calculate the discounted price per pound:

Discounted price = Original price - (Original price * Discount percentage)

= $1.60 - ($1.60 * 0.10)

= $1.60 - $0.16

= $1.44

Therefore, the price per pound of apples this week, after the 10% discount, is $1.44.

Now, let's calculate the total price of 4½ pounds of apples:

Total price = Price per pound * Weight of apples

= $1.44/pound * 4.5 pounds

= $6.48

Therefore, the total price of 4½ pounds of apples this week at the grocery store, considering the 10% discount, is $6.48.

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Answer:

C

Step-by-step explanation:

y=mx+b m=slope b=y-intercept, y-int: 4 slope: 3/1 but can just be put as 3. y=3x+4 bc it's a positive slope with a positive y-int.

Answer:

3:10 bcs 6:20 simplify by 2

Solution:

We know that:

\(\frac{\tex\text{Diamonds}}{\text{Emeralds}} = \frac{3}{4}\)

\(\text{Emeralds} = 16\)

Substitute the amount of emeralds in the ratio to find the amount of diamonds.

\(\dfrac{\tex\text{Diamonds}}{16} = \dfrac{3}{4}\)

\(\tex\text{Diamonds} = \dfrac{3 \times 16}{4}\)

\(\tex\text{Diamonds} = \dfrac{48}{4} = 12\)

Thus, there were 12 diamonds.

(a)

girls to boys → 2 : 1

2 → 24

1 → 12

There are total 12 boys.

(b)

diamonds to emeralds → 3 : 4

4 → 16

1 → 4

3 → 12

There are 12 diamonds.

Answer:

65038.55

Step-by-step explanation:

First, Let's turn 12.3% into a decimal which is 0.123

Then Multiply 57,915 by 0.123

57,915 × 0.123= 7123.545 Round; 7,123.55

Then Add  [Mark up = Add] 57,915 with 7,123.55

57,915 + 7,123.55= 65038.55

Hence, the Answer is 65038.55

The exact value of cos 15° can be found using the half-angle identity. The main answer is that cos 15° = √(2 + √3) / 2.

To explain further, let's consider the half-angle identity for cosine, which states that cos (θ/2) = ±√((1 + cos θ) / 2). We will use the positive root since 15° is in the first quadrant.

We can start by rewriting 15° as the sum of two angles: 15° = 45° / 3. This allows us to express cos 15° as cos (45° / 3).

Applying the half-angle identity, we have cos (45° / 3) = √((1 + cos (45°)) / 2).

Since cos (45°) is known to be √2 / 2, we can substitute it into the equation:

cos (45° / 3) = √((1 + √2 / 2) / 2).

Next, we rationalize the denominator by multiplying both the numerator and denominator by √2:

cos (45° / 3) = √(2 + √2) / 2.

Finally, we simplify the expression by rationalizing the numerator using the conjugate:

cos (45° / 3) = (√(2 + √2) / 2) * (√(2 - √2) / √(2 - √2)).

Expanding and simplifying the numerator yields:

cos (45° / 3) = √((2 + √2)(2 - √2)) / 2.

The product of (2 + √2)(2 - √2) simplifies to 4 - 2 = 2:

cos (45° / 3) = √2 / 2.

Therefore, the exact value of cos 15° is √2 / 2.

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Answer:

Step-by-step explanation:

Add the frations by simplifying then ploy

Answer:

\(10100\)

Step-by-step explanation:

Use this formula,

\( \frac{n}{2} (2 {a} + d(n - 1)\)

where n is the amount of even intergers, a is the starting term, d is the common difference.

\( \frac{100}{2} (4 + 2(99)\)

\(50(4 + 198)\)

\(50(202)\)

\(10100\)

In this scenario, each man shakes hands with all the other men (excluding himself) and with all the women (excluding his spouse). Therefore, each man shakes hands with \($25$\) people in total.

Since there are \($13$\) married couples, there are \($13$\) men and \($13$\) women. Hence, the total number of handshakes involving men is \($13 \times 25 = 325$\).

As for the women, they do not shake hands with each other, so we only need to consider the handshakes involving men. Therefore, the total number of handshakes among these \($26$\) people is \($325$\).

If you would like to represent this solution using LaTeX code, you can use the following snippet:

\(\text{Number of handshakes involving men} \\\\= \text{Number of men} \times \text{Number of handshakes per man} \\\\= 13 \times 25 = 325\)

Therefore, the total number of handshakes among the \($26$\) people is \($325$\).

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