Researchers surveyed one hundred students on which superpower they would most like to have. The two-way table below displays data for the sample of students who responded to the survey.
Superpower Male Female TOTAL
Fly 30 10 40
Invisibility 12 32 44
Other 10 6 16
TOTAL 52 48 100
Find the probability that the student was male, given the student chose to fly as their superpower.
P\left( \text{male }| \text{ fly} \right)=P(male ∣ fly)=P, left parenthesis, start text, m, a, l, e, space, end text, vertical bar, start text, space, f, l, y, end text, right parenthesis, equals

Answer:

Step-by-step explanation:

f(x+1) = 2(x+1)^2 + 1

= 2(x^2 + 2x + 1) + 1

= 2x^2 + 4x + 3

Answer:

(5*85)/4-(7-4)

425/4-(7-4)

425/4-3

106.25-3

103.25

It is not 47.

Answer:

-55

Step-by-step explanation:

Given expression:

               [tex]\frac{h}{5}[/tex] - 2  = -11

To solve this problem implies finding the variable h;

            [tex]\frac{h}{5}[/tex] - 2  = -11

Add +2 to both left and right hand side;

          [tex]\frac{h}{5}[/tex] - 2 + 2  = -11 + 2

             [tex]\frac{h}{5}[/tex]  = -9

Now, multiply both sides by 5;

         [tex]\frac{h}{5}[/tex] x 5  = -9 x 5

            h  = -45

Answer:

y=-3x+9

Step-by-step explanation:

Find the change, then plug in the point.

I use complex analysis to compute the integrals in question.

First, notice that the first integrand is even:

[tex]\dfrac{\cos(-x)}{(-x)^2+1}=\dfrac{\cos(x)}{x^2+1}[/tex]

[tex]\implies\displaystyle\int_0^\infty\frac{\cos(x)}{x^2+1}\,dx=\frac12\int_{-\infty}^\infty\frac{\cos(x)}{x^2+1}\,dx[/tex]

Consider a contour C that's the union of

• Γ, a semicircle of radius R in the upper half-plane, and

• the line segment connecting the points (-R, 0) and (R, 0)

On Γ, we have [tex]z=Re^{it}[/tex] with 0 ≤ t ≤ π.

Consider the complex function

[tex]f(z)=\dfrac{e^{iz}}{z^2+1}[/tex]

and notice that our original integrand is the real part of f(z). Then the integral of f(z) over C is

[tex]\displaystyle\int_Cf(z)\,dz=\lim_{R\to\infty}\left(\int_{-R}^Rf(z)\,dz+\int_\Gamma f(z)\,dz\right)[/tex]

As R → ∞, the first integral on the right is exactly twice the one we want. Estimate the second one to be bounded by

[tex]\displaystyle\left|\int_\Gamma f(z)\,dz\right|\le\pi R|f(z)|\le\frac{\pi R}{R^2-1}[/tex]

since

[tex]|z^2+1|\ge\bigg||z^2|-|-1|\bigg|=|R^2-1|[/tex]

and so the integral along Γ vanishes.

f(z) has only one pole in the interior of C at z = i. By the residue theorem,

[tex]\displaystyle\int_Cf(z)\,dz=2\pi i\,\mathrm{Res}\left(f(z),z=i\right)=2\pi i\lim_{z\to i}(z-i)f(z)=\frac\pi e[/tex]

[tex]\implies\displaystyle\int_0^\infty\frac{\cos(x)}{x^2+1}\,dx=\frac12\mathrm{Re}\left(\int_Cf(z)\,dz\right)=\frac\pi{2e}[/tex]

For the second integral, we recall that for complex z,

[tex]\sqrt z=\exp\left(\dfrac12\left(\ln|z|+i\arg(z)\right)\right)[/tex]

Consider a keyhole contour C, the union of

• [tex]\Gamma_R[/tex], the larger circle with radius R and [tex]z=Re^{it}[/tex], with 0 < t < 2π ;

• [tex]\Gamma_\varepsilon[/tex], the smaller circle with radius ε and [tex]z=\varepsilon e^{-it}[/tex], with 0 < t < 2π ;

• [tex]\ell_1[/tex], the line segment above the positive real axis joining [tex]\Gamma_\varepsilon[/tex] to [tex]\Gamma_R[/tex] ; and

• [tex]\ell_2[/tex], the other line segment below the positive real axis joining [tex]\Gamma_R[/tex] to [tex]\Gamma_\varepsilon[/tex]

Then

[tex]\displaystyle\int_Cf(z)\,dz=\int_{\Gamma_R}f(z)\,dz+\int_{\ell_1}f(z)\,dz+\int_{\Gamma_\varepsilon}f(z)\,dz+\int_{\ell_2}f(z)\,dz[/tex]

and in the limit, the integral over [tex]\ell_1[/tex] converges to the one we want.

Estimate the integrals over the circular arcs:

• [tex]\Gamma_R[/tex] :

[tex]\displaystyle\left|\int_{\Gamma_R}f(z)\,dz\right|\le2\pi R|f(Re^{it})|\le\dfrac{2\pi R^{3/2}}{|R-\sqrt5|^2}\to0[/tex]

as R → ∞.

• [tex]\Gamma_\varepsilon[/tex] :

[tex]\displaystyle\left|\int_{\Gamma_\varepsilon}f(z)\,dz\right|\le2\pi \varepsilon|f(\varepsilon e^{-it})|\le\dfrac{2\pi\varepsilon^{3/2}}{|\varepsilon-\sqrt5|^2}\to0[/tex]

as ε → 0.

Consider the integral over [tex]\ell_2[/tex] :

[tex]\displaystyle\int_{\ell_2}f(z)\,dz=\int_R^\varepsilon\frac{\sqrt z}{z^2+2z+5}\,dz\\\\=\int_R^\varepsilon\frac{\exp\left(\dfrac12\left(\ln|z|+2\pi i\right)\right)}{z^2+2z+5}\,dz\\\\=-\int_R^\varepsilon\frac{\exp\left(\dfrac12\ln|z|\right)}{z^2+2z+5}\,dz\\\\=\int_\varepsilon^R\frac{\sqrt z}{z^2+2z+5}\,dz\\\\=\int_{\ell_1}f(z)\,dz[/tex]

so in fact,

[tex]\displaystyle\int_Cf(z)\,dz=2\int_0^\infty\frac{\sqrt x}{x^2+2x+5}\,dx[/tex]

By the residue theorem,

[tex]\displaystyle\int_Cf(z)\,dz=2\pi i\sum_{\rm poles}\mathrm{Res}\,f(z)[/tex]

We have poles at z = -1 + 2i and z = -1 - 2i. On our chosen branch,

[tex]\sqrt{-1+2i}=i\sqrt[4]{5}\exp\left(-\dfrac i2\tan^{-1}(2)\right)[/tex]

[tex]\sqrt{-1-2i}=i\sqrt[4]{5}\exp\left(\dfrac i2\tan^{-1}(2)\right)[/tex]

The residues are

[tex]\mathrm{Res}(f(z),z=-1-2i)=\dfrac{i\sqrt[4]{5}\exp\left(\frac i2\tan^{-1}(2)\right)}{-4i}[/tex]

[tex]\mathrm{Res}(f(z),z=-1+2i)=\dfrac{i\sqrt[4]{5}\exp\left(-\frac i2\tan^{-1}(2)\right)}{4i}[/tex]

Their sum is

[tex]\displaystyle\sum_{\rm poles}\mathrm{Res}\,f(z)=-\frac{\sqrt[4]{5}}2\sin\left(\dfrac12\tan^{-1}(2)\right)=-\frac{\sqrt[4]{5}}2\sqrt{\frac{5-\sqrt5}{10}}=-\frac i2\sqrt{\frac1\phi}[/tex]

where ɸ = (√5 + 1)/2 is the golden ratio, and so the overall integral is

[tex]\displaystyle\int_0^\infty\frac{\sqrt x}{x^2+2x+5}\,dx=\frac\pi2\sqrt{\frac1\phi}[/tex]

Lastly, recall

[tex]\displaystyle\sum_{k=0}^\infty\frac1{k!}=e[/tex]

Then our expression reduces to

[tex]\left(\dfrac{e\times\frac\pi{2e}}{\frac\pi2\sqrt{\frac1\phi}}\right)^2=\boxed{\phi}[/tex]

Answer:

Step-by-step explanation:

Its The last one just took a test

Answer:

D. complementary

Step-by-step explanation:

The two angles a and b add up to 90 degrees, so they are complementary.

Hopefully this helps - let me know if you have any questions!

Answer:

3.6 miles

Step-by-step explanation:

Pythagorean Theorem:

[tex]2^{2}+3^{2} =\\4 + 9 = \sqrt{13}[/tex]

√13 = 3.60555127546

Nearest tenth = 3.6

Answer:

Temperature is the measure of hotness or coldness expressed in terms of any of several scales. An example  would be "The cup of beans are boiling hot and has a temperature of 100 °C, whereas the water in the tub is just comfortably warm, with a temperature of about 38 °C. Although the water in the tub has a much lower temperature, it has greater thermal energy".

Step-by-step explanation:

Answer:

Renewable resources are abundant.

Step-by-step explanation

I have answered this question before

Answer:

A. Renewable resources are abundant.

Step-by-step explanation:

hope this helps

The decimal computed shows that Tracy doesn't have enough for the construction.

From the information given, Tracy has three pieces of wood that are each 8 meters long and one piece that is 7 meters long. Therefore, the addition of the lengths will be:

= (3 × 8) + 7

= 24 + 7.

= 31m

Since Tracy needs 31.5 meters of wood for a porch railing, it shows that she doesn't have enough.

Learn more about decimal on:

https://brainly.com/question/1015576

Answer:

22/35

Step-by-step explanation:

Simplify the following:

((1 + 4/7)×2)/5

((1 + 4/7)×2)/5 = ((1 + 4/7)×2)/5:

((1 + 4/7)×2)/5

Put 1 + 4/7 over the common denominator 7. 1 + 4/7 = 7/7 + 4/7:

((7/7 + 4/7) 2)/5

7/7 + 4/7 = (7 + 4)/7:

(((7 + 4)/7)×2)/5

7 + 4 = 11:

(11/7×2)/5

11/7×2 = (11×2)/7:

((11×2)/7)/5

((11×2)/7)/5 = (11×2)/(7×5):

(11×2)/(7×5)

7×5 = 35:

(11×2)/35

11×2 = 22:

Answer: 22/35

Answer:

First choice.

Step-by-step explanation:

Th first  option.

(x + 1)^2 - 25

The minimum value is -25 because the minimum value of the squared term is 0.   A squared term cannot be negative,

Answer: -9 degrees

Explanartion:

-5+8=3

3-12=-9

Answer:

probably -9 degrees

Step-by-step explanation:

Answer:

Large number: 20

Small number: 12

Step-by-step explanation:

Hello!

This problem is a word problem, and if we assign variables to find each of the numbers, it could help.
A variable is usually an unknown number that stands for that unknown.
Since in this problem we know there is a small and large number, let's assign the large number as the variable x and small number as variable y.

For the first part, it says two numbers whose difference is 8, which means the large number minus the smaller number equals 8.

x-y=8

For the second part is tricky. It's saying that the small number times three is 16 more than the large number itself. When constructing a equation, this is what we get:

x+16=3y   x plus 16 equals 3 times y

To solve this equation together so we can make it super easy, let's do the method of substitution, which is where we make an equation equal to a variable and input that equation into the second equation.
We can use x-y=8 to input, we can rearrange y and plug it to the right side to get x=8+y

Since x equals 8+y, let's input this into the second equation.

(8+y)+16=3y    input the rearranged equation into the second

24+y=3y         combine like terms

    -y   -y

24=2y              divide by two to get y by itself

12=y

We aren't done yet! We have to find x still; let's use the previous first equation to find x. We know y=12, so let's plug it in.

x-y=8    original formula

x-12=8      plug it in

+12  +12

x=20

Therefore, the large number is 20, and smaller number is 12.

Answer:

12 and 20

Step-by-step explanation:

                         small=x

                         big= (x+8)

(x+8) = 3x -16

24 = 2x

x=12 (small)

12+8 = 20(big)

Answer:

ok so scale means that for every 1/2 each is one foot so each inch 2 feet

so lets just multiply each one by 2 and say their feet

5*2=10 feet

11*2=22 feet

22 feet tall

10 feet wide

Hope This Helps!!!

Answer:

4n - 11 = (15 - 2)n

Step-by-step explanation:

Using the keywords;

'Difference of'

'Equal to'

'Less than'

'Times', we can find the equation.

Let's piece it together:

Difference of; 4n(four times n) and 11

Equal to( = )

(15 - 2)n, which is 15 less than 2, multiplied by n

Answer:

26.22 cubed inches

Step-by-step explanation:

V=πr2h

r = radius = diameter/2

h = height

π = pi = 3.14

v = 3.14([tex]1.2^{2}[/tex])5.8

v = 3.14(1.44)5.8

v = 4.52 x 5.8

v = 26.22

Have a great day! :)

PLEASE RATE!!

The volume of the cylindrical can is equal to 26.0 [tex]in^3[/tex].

Given the following data:

Radius = [tex]\frac{diameter}{2} =\frac{2.4}{2} =1.2\;in[/tex]

Mathematically, the volume of a cylinder is given by this formula:

[tex]V = \pi r^2h[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]V = 3.14 \times 1.2^2 \times 5.8\\\\V = 4.5216 \times 5.8[/tex]

V = 26.22 ≈ 26.0 [tex]in^3[/tex].

Read more on volume of a cylinder here: brainly.com/question/21367171

Solution:

Step-1: Find the area of the rectangle.

L = 5/8 foot; B = 4/9 foot

Step-2: Verify all the options.

Looking at all the options, we can see that Option C (1/4 ft²) is the best estimate of the area we obtained as 10/36 and 9/36 are really close fractions.

Thus, Option C is correct.

Answer/Step-by-step explanation:

Explanation for False ( Counterexample)

[2] False. Look at the picture below

[4] False Look at picture below

Answer:

ion know

beyond ma capacity

Answer:

Equiangular triangle

Step-by-step explanation:

"equiangular triangle" means a triangle that has equal sides

knowing that the sum of the angles of a triangle is 180° each angle must be 60° because [tex]\frac{180}{3}=60[/tex]

Answer:

1.  $4200

2. $8000

3. Profit $3800

4. 90.48% (2 d.p.)

Step-by-step explanation:

40 x 105 = 4200

40 x 200 = 8000

8000 - 4200 = 3800

Rate of Return = (Final Value - Initial Value) divided by Initial Value

(8000-4200) divided by 4200 = 19/21 or 0.9047619048

= 90.48%

Answer:

1. $4,200

2. $8,000

3. $3,800 profit

4. 90.48%

Step-by-step explanation:

QUESTION 1:

The cost of one share two years ago was $105. Since you bought 40 shares, you would have to multiply that price by 40:

[tex]$105*40=4,200[/tex]

That means the total cost of purchasing 40 shares two years ago was $4,200.

QUESTION 2:

One share currently costs $200. Just like with problem 1, since they're asking about all 40 shares, you need to multiply that price by 40.

[tex]200*40=8,000[/tex]

That means that 40 shares is currently valued at $8,000.

QUESTION 3:

Profit or loss is calculated by subtracting the final value by the initial value. In this case, subtracting the current price by the price you originally bought the shares for.

[tex]8,000-4,200=3,800[/tex]

Because it's a positive number, you know that you've made a profit of $3,800 off of 40 shares.

QUESTION 4:

Rate of return is calculated by dividing the profit (or loss) by the original cost:

[tex]3,800/4,200=0.9048[/tex]

Of course, since rate of return is expressed in a percentage, you would need to multiply 0.9048 by 100 and tack a percent sign onto the end, giving you 90.48%. (I rounded the number to the nearest hundredth.)

Answer:

x^(2)+(y+3)^(2)=13

Step-by-step explanation:

Answer:

it is D or C

Step-by-step explanation:

Answer:

7) given

8) distributive property

9) subtraction property

10) division property

11) HA = WK

12) segment addition

13) Substitution

14) HW = AK

Answer:

  A.  32 miles

Step-by-step explanation:

The shortest route from the middle school to the airport is via City Hall and the high school. Returning by the same route lets Mary drop her father at City Hall as required. The total map distance is ...

  2(21 cm +12 cm +15 cm) = 2(48 cm) = 96 cm

At a scale of 3 cm per mile, that distance represents ...

  (96 cm)/(3 cm/mi) = 32 mi

Mary traveled 32 miles.

Answer:

A. 32 miles

Step-by-step explanation:

i got it right on edge

Answer:

116

Step-by-step explanation:

$232=$2

if each brick is $2 and you spent $232 divide it

232/2 would be 116 so to check your answer

  116*$2(each brick) it would be 232

Answer:

116 bricks

Step-by-step explanation:

you divide 232 by 2

which will give you 116

and to make sure u got 232 you multiple 116 × 2=232

Answer:

x|x< -2

Step-by-step explanation:

3x < -6

divide each side by 3

x <-2