The ratio of boys to girls at a movie is 3:4 . If there are 16 girls ​, how many boys are at the​ movie?

when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

Take the power set. It has 2^(2n+1) members.

Replace any member which has n+1 or more elements with its complements.

Now the power set has members, which have n or fewer elements, and each such member appears twice.

Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

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The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer:

-0.5

Step-by-step explanation:

-0.7 + 0.5 - 0.3 = -0.5

Answer:

2x+6y-4

Step-by-step explanation:

First distribute x and 3y

2 times x is 2x

2 times 3 is 6y

(2x+6y) -4

2x+6y-4

Hope this helps!

Answer:

2(x+3y-2)

Step-by-step explanation:

See the steps below:)

The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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Answer:

1250 g

Step-by-step explanation:

12.5% of 10 kg

12.5% of 10000 g

.125 of 10000 g

.125 * 10000 g

1250 g

Answer:

Step-by-step explanation:

\( \frac{12.5}{100} \times 10kg = x \: grams\)

\(1.25kg = 1250 \: grams\)

P = (3,-4)

M = (1,3)

Q = (Qx,Qy)

Midpoint = (x1+x2)/2 , (y1+y2)/2

Mx = (Px+Qx) /2

1= (3+Qx) /2

Solve for Qx

1 (2) = 3+Qx

2 = 3 +Qx

2-3 = Qx

Qx= -1

My = (y1+y2) /2

3 = (-4+Qy) /2

Solve for QY

3 (2) = -4+Qy

6= -4 + Qy

6+4 = Qy

10 = Qy

Coordinates of the Endpoint Q:

Q = (-1,10)

Answer:

18

Step-by-step explanation:

125 = 7x - 1 ...... because if the two lines are parallel alternate interior angles are congruent

125 + 1 = 7x

126 = 7x

\( \frac{126}{7} = \frac{7x}{7} \)

x = 18

hope it helps

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Anders will have the Amount of $ 16,310.90 in his account after 11 years

Compound Interest:

Compound interest is the interest charged on a loan or deposited amount. The compound interest will depend on both the Principal amount and interest gained over the given time period. The formula for the Amount in compound interest, A = P( 1 + r/n)^tn

From given problem

The principal amount P =  $12,000  

Rate of interest, r = 2.8% = 2.8/100 = 0.028  

Time period, t = 11 years

Number of compounds in a year = 4  [ ∵ interest compounded quarterly ]  

The Amount after 11 years = 12000(1+0.028/4)^(11)(4)  

= 12000(1+0.007)⁴⁴

= 12000(1.007)⁴⁴

= 16,310.90  

Anders will have $ 16,310.90 in his account after 11 years

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Answer: 2,000 milliliters.  

Step-by-step explanation:

Hi, to answer this question we have to add the amount of water and the amount of sports drink that he drank:

1 liter + 1 liter = 2 liters of liquid.

Finally, we have to convert the result into milliliters.

Since 1 liter = 1000 liters

We have to multiply the liters drank by 1000.

2 x 1000 = 2,000 milliliters.  

Feel free to ask for more if needed or if you did not understand something.  

Answer:

The answer is D

Step-by-step explanation:

the standard equation for circle is (x －h)² ＋(y －k)² = r² which h is the x coordinate, k is the y coordinate, r is radius. In this case, both x coordinate and y coordinate are 0, so the left side of the equation is x² + y², since the radius is √249, the r² is 249. So the equation is x² + y² = 249, and the answer is D.

Hope this will help❤️

Answer:

10u

Step-by-step explanation:

Since they all have the same variable you can solve it normally.

8+10= 18

18-1=17

17-7=10

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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D) 2.65 gallons of gas left in his car after taking both friends home when 1.05 gallons of gas is used to take one friend home and three tenths gallon to take the other friend home.

Manny used 1.05 + 0.3 = 1.35 gallons of gas to take his friends home.

Since he originally had 4 gallons of gas, he had 4 - 1.35 = 2.65 gallons of gas left in his car after taking both friends home.

So the answer is D.

Here is the solution in more detail:

Manny started with 4 gallons of gas.

He used 1.05 gallons of gas to take one friend home.

He used 0.3 gallons of gas to take the other friend home.

The total amount of gas he used was 1.05 + 0.3 = 1.35 gallons.

Therefore, he had 4 - 1.35 = 2.65 gallons of gas left in his car.

I hope this helps! Let me know if you have any other questions.

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The situation given in the question occurs due to the lower mortality rate which is seen in women of the age group 50-60.

Discrepancies between men and women's death rates and life expectancy. In general, women live longer than males. This means that, assuming everything else is equal, we should anticipate that women will make up somewhat more than half of the population.

Birth sex ratios are not equal. Males outnumber female births in every country. This means that, assuming everything else is equal, we should anticipate that men will make up somewhat more than half of the population.

The population's gender distribution can be impacted through migration. All other things being equal, we would anticipate that men would make up more than 50% of the population if some countries import a sizable amount of male-dominated labor.

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Answer:

a) The watch is cheaper in Geneva.

b)  The watch is cheaper by £20

Step-by-step explanation:

a) In which city is the watch cheaper?

Step 1. Translate Pounds into Swiss Francs.

£145 * 1.55 = 224.75 CHF

Step 2. Determine which price is higher.

224.75 is greater than 193.75.

Step 3. Always answer a Word problem in complete sentences.

The watch is cheaper in Geneva.

b) By how much is it cheaper?

224.75 - 193.75 = 31

Translate CHF to Pounds.

31 / 1.55 = 20

The watch is cheaper by £20.

12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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The missing values in the triangle are:

∠B = 90°

AB =  20.98

CB = 16.99

First, remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write:

51 + 39 + ∠B = 180

∠B = 180 - 51 - 39 = 90

So we have a right triangle.

Now, to find the values of AB and CB, we can use trigonometric relations, we know that teh hypotenuse is 27 units, then we can use:

cos(51°) = CB/27

27*cos(51°) = CB = 16.99

And:

cos(39°) = AB/27

27*cos(39°) = AB = 20.98

These are the missing values.

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Yes, an exponential function can have 1 as a base.

An exponential function is a function of the form f(x) = a^x, where a is the base and x is the exponent. The base can be any real number, including 1.

When the base is 1, the exponential function is defined as f(x) = 1^x = 1 for any value of x. This function is a constant function that always equals 1.

It is important to note that when the base of an exponential function is less than 0, the domain of the function is all real numbers except for certain values of x.

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The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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distributive property

Answer: The cat drank 7/9 of the milk in the utensil.

Step-by-step explanation:

To find the fraction of milk that the cat drank, we need to divide the amount of milk the cat drank by the total amount of milk in the utensil.

The cat drank 1 3/4 liters of milk, which is the same as 7/4 liters.

The utensil had 2 1/4 liters of milk, which is the same as 9/4 liters.

So, the fraction of milk that the cat drank is:

(7/4) ÷ (9/4) = 7/9

Therefore,

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Answer:

A) \(y = 3x - 4\)

Explanation:

Slope-intercept form is y = mx + b

Answer:kkkkkkk

Step-by-step explanation:

Answer:

y = -4/5x - 2.6

Step-by-step explanation:

First find the slope:

m = y2-y2 / x2-x1

m = 3-(-1) / -3-2

m = 4/-5

m = -4/5

y = -4/5x + b

-1 = -4/5(2) + b

-1 = 1.6 + b

b = -2.6

y = -4/5x - 2.6

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The volume of the cone is 7225.66 m³ and the volume of the hemisphere is 209.44 cubic feet.

From the general formula of the volume of the cone,

Volume = πr²h

in the given case,

Radius (r) = 10 m

Height (h) = 23 m

Thus, Volume = π*10²*23

Volume = 7225.66 m³

The formula for the volume of a hemisphere is:

V = (2/3) * π * r³

where π is pi (approximately 3.14159), and r is the radius of the hemisphere.

Substituting the given value of r = 10 ft, we get:

V = (2/3) * π * (10 ft)³

= (2/3) * π * 1000 ft³

= (2/3) * 314.16 ft³

≈ 209.44 ft³

Therefore, the volume of the hemisphere is approximately 209.44 cubic feet.

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Answer:

the ration to the money spend on ads to website is 4:3

The amount spent on advertising to the amount spent on its website as a ratio in its simplest form is: 4: 3

Given that:

Thus, the ratio of the amount spent on the advertising and the website is computed as:

£1: £ 0.75

Since a ratio can be expressed in a fraction when solving to its simplest form, then we have:

\(\mathbf{\dfrac{1}{0.75}}\)

Let's multiply both the numerator and the denominator by 100 to shift the decimal in two places in 0.75

Then, we have:

\(\mathbf{=\dfrac{1\times 100}{0.75 \times 100}}\)

\(\mathbf{=\dfrac{ 100}{75 }}\)

Divide both sides by 5;

\(\mathbf{=\dfrac{ 20}{15 }}\)

Divide both sides by 5;

\(\mathbf{\dfrac{4}{3}}\)

Therefore, the amount spent on advertising to the amount spent on its website in ratio is 4:3

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In an isosceles triangle, the two https://brainly.com/question/28412104 form the two equal angles opposite those sides.

An isosceles triangle is a type of triangle that has two sides of equal length. The two congruent sides are referred to as the legs of the triangle, while the remaining side is known as the base. The key property of an isosceles triangle is that the angles opposite the congruent sides are also equal. This means that the triangle has two equal angles formed by the congruent sides and a third angle formed by the base.

To understand why the congruent sides form equal angles, consider the following: When two sides of a triangle are equal in length, it implies that the opposite angles they form are also equal. This is known as the Isosceles Triangle Theorem. In an isosceles triangle, the two congruent sides are equal in length, which means the angles opposite those sides must also be equal. Therefore, the two congruent sides of an isosceles triangle form the two equal angles opposite them.

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