ten cards are choosen at random, what is the probablitiy that the largest pile has 4 cards

Answer:

45°

Step-by-step explanation:

\(tan^{-1}(1)\) = 45°

Answer:

\(\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}\)

Step-by-step explanation:

\(\tan\theta=1\)

\(\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o\)

The total number of people who answered the survey is 100.

To determine the number of people who answered the survey, we can sum up the individual counts of people who watched each movie type: 32 (romance), 89 (action), and 47 (science fiction). However, simply adding these counts would overcount the people who watched multiple types of movies.

To correct for this, we need to consider the overlapping counts. According to the survey results, 10 people watched both romance and action, 4 people watched both romance and science fiction, and 45 people watched both action and science fiction. Additionally, 2 people watched all three types.

To obtain the total count, we can use the principle of inclusion-exclusion. We start with the sum of the individual counts, then subtract the overlapping counts once, add back the counts of those who watched all three types. Mathematically, this can be expressed as:

32 + 89 + 47 - 10 - 4 - 45 + 2 = 111.

However, we need to consider that 5 people watched none of these types. By subtracting 5 from the previous count, we get the final result:

111 - 5 = 106.

Therefore, the total number of people who answered the survey is 100.

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Answer:

R = 23 ohms

Step-by-step explanation:

Start with V = I*R.  Solve for R:  R = V/I

Here I = 8 amps and V = 184 volts, and so

R  = (184 volts) / (8 amps) = 23 ohms

Answer: sum, multiple

Step-by-step explanation:

A number is divisible by 9 if the sum of digits is a multiple of 9.

Answer:

Step-by-step explanation:

A number is divisible by 9 if the sum of digits is a divisible of 9.

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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Answer:

it is A

Step-by-step explanation:

i had the question on ed

Answer:

y greater - than - or - equal - to StartFraction 2 over 15 EndFraction

Step-by-step explanation:

the volume of the solid obtained by rotating the rectangle with width a and height x about the x-axis is (2π/3) a^3

Assuming you meant "a rectangle with width x", we can find the volume of the solid obtained by rotating this rectangle about the x-axis using the method of cylindrical shells.

Consider a thin vertical strip of width dx at a distance x from the y-axis. The length of this strip is the height of the rectangle, which is x. When this strip is rotated about the x-axis, it sweeps out a cylindrical shell of radius x and thickness dx. The volume of this cylindrical shell is given by 2πx(x dx) = 2πx^2 dx.

To find the total volume of the solid, we integrate the volume of each cylindrical shell from x = 0 to x = a, where a is the width of the rectangle. Therefore, the volume of the solid is given by:

V = ∫ 2πx^2 dx (from x = 0 to x = a)

V = [2π/3 x^3] (from x = 0 to x = a)

V = (2π/3) a^3

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Answer:

\(\bold{\dfrac{6}{7}}\)

Step-by-step explanation:

Given ratio is:

8 gal to \(9\frac{1}3\) gal

To find:

Ratio in Lowest form with whole numbers in numerator and denominator.

Solution:

First of all, let us convert \(9\frac{1}3\) to simple \(\frac{p}{q}\) form:

Formula:

\(a\dfrac{b}{c} = \dfrac{a\times c+b}c\)

Using the formula, we get:

\(9\dfrac{1}{3} = \dfrac{9\times 3+1}{3} = \dfrac{28}{3}\)

Now, let us have a look at the ratio:

\(8 : \dfrac{28}{3}\)

Any ratio, \(p:q\) can be written as \(\frac{p}{q}\).

Writing given ratio as per above:

\(\dfrac{8}{\dfrac{28}{3}}\\\Rightarrow \dfrac{8 \times 3}{28}\\\Rightarrow \dfrac{2\times 3}{7}\\\Rightarrow \bold{\dfrac{6}{7}}\)

Therefore, the answer is

\(\bold{\dfrac{6}{7}}\)

Answer:

16 and 25

Step-by-step explanation:

they are square numbers

1^2 = 1 .. etc.

this is a I

There is an error 2*2 is 4 lol realised I wrote tht whoops

The 24 meters should the fence be cut up in order to minimize the total area enclosed by the fence

Given that,

The length of fence is 288 meters.

Let us take the size of the smallest square is x , middle square is y and the largest square is z.

Length of the fence is equal to sum of the perimeter of the three square.

4x + 4y + 4z = 288

4(x + y +z) = 288

x + y +z = \(\frac{288}{4}\)

x + y +z = 72 --------> equation(1)

The total area A = x² + y² + z²

Put z = 72 - x - y in A

A = x² + y² + (72 - x - y)²  ---------->equation(2)

Now we have to find the x and y values to minimize A.

\(\frac{dA}{dx} = \frac{d}{dx} [x^2 + y^2 + (72 -x - y)^2]\\\)

\(\frac{dA}{dx}= 2x + 0 +2(72-x-y)(-1)\)

\(\frac{dA}{dx}= 2x - 2(72-x-y)\)

Taking \(\frac{dA}{dx}\) = 0

2x - 2(72 - x - y) = 0

x - 72 + x + y = 0

2x + y - 72 = 0

2x + y = 72 ---------> equation(3)

Now, \(\frac{dA}{dy} = \frac{d}{dy} [x^2 + y^2 + (72 -x - y)^2]\\\)

\(\frac{dA}{dy}= 0 + 2y +2(72-x-y)(-1)\)

\(\frac{dA}{dy}= 2y - 2(72-x-y)\)

Taking \(\frac{dA}{dy}\) = 0

2y - 2(72 - x - y) = 0

y - 72 + x + y = 0

x + 2y - 72 = 0

x + 2y = 72 ---------> equation(4)

Now, equation(3) ×2 and subtracted by equation(4)

4x + 2y = 144

x   + 2y  = 72

-------------------(subtraction)

3x = 72

x = 24

Taking x = 24 in equation(3)

2x + y = 72

2(24) + y = 72

48 + y = 72

y = 72 - 48

y = 24

Substituting y and x in equation(1)

x + y + z = 72

24 + 24 + z = 72

48 + z = 72

z = 72 - 48

z = 24

Therefore, The 24 meters should the fence be cut up in order to minimize the total area enclosed by the fence

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Call the number of hours of labor x.

A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)

Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.

We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000

we have that

P+0.50=0.8554

so

P=0.3554

using the tables of z-score

For P=0.3554

the value of z is

a) The interquartile range for the masses of the emperor penguins is 4.5 kg.

b) The median mass of the king penguins is 14 kg.

c) i. The median mass of the emperor penguins is greater than the median mass of the king penguins by 9 kg.

ii. Emperor penguins have a lower range of mass than king penguins.

In Mathematics and Statistics, the interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of data set = Q₃ - Q₁

First quartile (Q₁) = [(n + 1)/4]th term

First quartile (Q₁) = [(40 + 1)/4]th term = 10.25th term

Third quartile (Q₃) = [3(n + 1)/4]th term

Third quartile (Q₃) = [3(40 + 1)/4]th term = 30.75th term

By tracing the line from a cumulative frequency of 10.25 and 30.75, the interquartile range is given by:

Interquartile range of masses = 23 - 19.5

Interquartile range of masses = 4.5 kg.

Part b.

By critically observing the box plot, we can logically deduce that the median mass of the king penguins is equal to 14 kg.

Part c.

Difference in median mass = 23 - 14

Difference in median mass = 9 kg.

Therefore, the median mass of the emperor penguins is greater than the median mass of the king penguins by 9 kg. Additionally, emperor penguins have a lower range of mass than king penguins.

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Answer:

(21, 2)

Step-by-step explanation:

set equations equal to each other because they both equal y.

-1/3x + 9 = 2/3 x - 12

combine like terms by adding 1/3x and 12 to both sides.

21 = x

plug x in.

y = -1/3(21) + 9

y = -7 + 9

y = 2

check with other equation.

y = 2/3(21) - 12

y = 14 - 12

y = 2

solution: (21, 2)

hope this helps :)

Answer:

(21,2)

Step-by-step explanation:

took the quiz on edge

Answer:

56

Step-by-step explanation:

56 would be the arc. reasoning is because line CG form an arch of 56 and Angle A and C also form a angle of 34

The divergence of a vector field F = <P, Q, R> in three-dimensional space (R³) is defined as the scalar function that represents the rate at which the field "spreads out" or "diverges" from a given point.

The divergence of a vector field F = <P, Q, R> is denoted by ∇ · F, where ∇ (del) represents the gradient operator. The divergence is a scalar function that calculates the change in the flux of the vector field across an infinitesimally small volume around a point. It measures how the vector field expands or contracts at each point in space.

Mathematically, the divergence of F is given by the sum of the partial derivatives of its components with respect to their corresponding variables: ∇ · F = (∂P/∂x) + (∂Q/∂y) + (∂R/∂z). Geometrically, the divergence represents the density of the field's source or sink at a particular point. Positive divergence indicates an outward flow, while negative divergence implies an inward flow.

The divergence theorem, also known as Gauss's theorem, establishes a relationship between the divergence and the flux of a vector field through a closed surface. It states that the flux of a vector field across a closed surface is equal to the volume integral of the field's divergence over the region enclosed by the surface.

In summary, the divergence of a vector field in three-dimensional space provides information about the rate at which the field diverges or converges at each point. It is a scalar function obtained by summing the partial derivatives of the field's components. The divergence theorem relates the divergence to the flux of the vector field through a closed surface.

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Answer:

27

Step-by-step explanation:

Since it is addition to make the expression a perfect square, it would not be as direct

√9577 = 97.86214794

we round off to the nearest whole number, since we need a perfect square number

therefore it would be 98

98² = 9604, the perfect square number we'll get after adding to 9577

therefore amount needed to add= 9604-9577= 27

Answer:

Step-by-step explanation:

17

Answer:

500$ is the answer....

Answer:

$60 and $560

Step-by-step explanation:

Prt= Interest

(500)(0.04)(3)= $60

A = P(1 + rt)

A = 500 (1 + 0.04(3))

A= $560

Answer:

v=72 in3

sa=104 in2

Step-by-step explanation:

hope this helps!

Step-by-step explanation:

(5^-4/4^-6) multiplied by 5^3

4⁶×5³/5⁴

4⁶/5

819.2

Answer:

\({ \tt{ (\frac{ {5}^{ - 4} }{ {4}^{ - 6} } ) \times {5}^{3} }} \\ \\ = { \tt{ \frac{ {5}^{ - 4} . {5}^{3} }{ {4}^{ - 6} } }} \\ \\ { \tt{ = \frac{ {5}^{ - 1} }{ {4}^{ - 6} } }} \\ { \tt{ = \frac{ {4}^{6} }{ {5}^{1} } }} \\ = { \tt{ \frac{4096}{5} }} \\ \\ = 819.2\)

Answer:

6250000

Step-by-step explanation:

Answer:6250000

Step-by-step explanation:

The height of the PEMEX tower is  287.6 meters if She walks towards the tower 500m and finds that the angle is 60 degrees.

The angle of elevation = 30 degrees

Walking distance = 500m

The angle of elevation after walking  = 60 degrees

When Pamela is  500 meters away from the tower, the tangent of the angle of elevation is calculated as:

tan(30°) = h / 500

h = 500 * tan(30°)

h = 500 * 0.5774

h = 288.7 meters

After walking 500m,

tan(60°) = h / d

h = d * tan(60°) ---------equation 1

The new distance between her and the tower is:

d = 500 - x

Using the tangent function with an angle of 60 degrees, the equation can be written as:

h = (500 - x) * tan(60°)

500 * tan(30°) = (500 - x) * tan(60°)

288.7 = (500 - x) * 1.732

166.5 = 500 - x

x = 333.5 meters

Substituting this value of x  in equation 1:

h = (500 - 333.5) * tan(60°)

h = 166.5 * 1.732

h = 287.6 meters

Therefore, we can conclude that the height of the tower is 287.6 meters.

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The complete question is-

Pamela wants to calculate the height of a PEMEX tower. She observes that the angle of elevation to the top of the tower is 30 degrees. She walks towards the tower 500m and finds that the angle is now 60 degrees.

The area of the reservoir in standard form is 1.8 × 10⁴ square miles

The volume of the reservoir in scientific notation is 2.8 × 10⁴ cubic miles

From the question, we are to determine the area of the reservoir in standard form and the volume of the reservoir in scientific notation

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form

Thus,

To write a number in standard form, we will write the number as a product of a number between 1.0 and 10.0 and a power of 10

From the given information,

The area of the reservoir is 1.8 × 10⁴ square miles.

The area of the reservoir is already written in standard form

Now,

To write the volume of the reservoir in scientific notation

NOTE: Standard form is the same as scientific notation

From the given information,

The volume of the reservoir is 28000 cubic miles

28000 = 2.8 × 10⁴

Hence, the volume in scientific notation is 2.8 × 10⁴ cubic miles

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Step-by-step explanation:

\(2p + 2p + 2p + 60 = 360 \\ 6p = 360 - 60 \\ 6p = 300 \\ p = \frac{300}{6} \\ p = 50\)