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At the height of the swing forth, the swing seat would be at a maximum height of 2 + (6 * (1 - cos(pi/4))) = 4 feet above the ground.

Cosine is a trigonometric function that relates the length of the adjacent side of a right triangle to the length of the opposite side to the hypotenuse. It is represented by "cos" and its formula is cos(x) = adjacent / hypotenuse. It is commonly used in mathematics, physics, and engineering to solve problems related to angles and vectors.

Cosine is a fundamental trigonometric function that is used in many areas of mathematics, physics, and engineering. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. It can also be defined as the dot product of the unit vector pointing in the direction of the angle and the unit vector pointing in the direction of the adjacent side. Cosine is periodic with a period of 2π and is always between -1 and 1, inclusive. It has many important properties and relationships with other trigonometric functions such as sine, tangent, and cotangent.

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In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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Answer:

Step-by-step explanation:

The domain and range of a linear function is always real numbers (T or F)

It is True. This is because of a couple of reasons.

    1.) You cannot divide by 0.

     2. A negative number cannot have its square root taken.

The range is determined by the domain in a linear function, and thus it must always consist of real numbers.

Answer:

The juice contains 75 mg of Vitamin C

Step-by-step explanation:

We are going to make a proportion

45/x = 60/100

60x=4500

x = 75

Answer:

4.3890563e+45!!

Step-by-step explanation:

Answer:1.4

Step-by-step explanation:

The solution is, the area in terms of pi is 246.49 ft^2.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

we know that,

The area of a circle is π multiplied by the square of the radius.

The area of a circle, (A) when the radius 'r' is given is πr2.

π is approximately  3.142

Given,

Radius of a circle = 10/2 = 5 ft

Therefore,

Area in terms of pi

A = pi(r) ^2

A = 3.14(5) ^2

A = 15.7 ^2

A = 246.49

Hence, The solution is, the area in terms of pi is 246.49 ft^2.

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The  expression represents the total surface area of the prism is

2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

The term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the  sum of the areas of all the faces (including the bases) of the prism.

for the rectangular prism, the Total Surface Area can be calculated using the formula:

TSA = 2lw + 2lh + 2wh

where

l = 5

w = 4

h = 7

plugging in the values gives

TSA = 2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

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The equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Using the coordinates of points A and B, we have:

m = (4 - 9) / (8 - 2) = -5 / 6

The slope of a line perpendicular to this line would be the negative reciprocal of this slope, so:

m= -1 / m = -6 / 5

Next, we can use the point-slope form of a line to find the equation of the line, which is:

y - y1 = m * (x - x1)

Substituting the values for m, x1, and y1 (where x1 and y1 are the coordinates of point C), we have:

y - (-2) = -6/5 * (x + 3)

Simplifying and solving for y, we get:

y = -6/5 * x - 20/5 + 2

So, the equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2

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If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Answer:

a = T - 4

Step-by-step explanation:

Simply just subtract 4 on both sides to get the answer!

Answer:

a=T-4

Step-by-step explanation:

subtract 4

Answer:

1,2,3,4,6,8,12,24 sub set

Answer:

y = \(\sqrt{55}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = \(\sqrt{55}\)

Since both terms are perfect squares, factor using the difference of squares formula,

a² − b² = (a + b) (a − b) where a = 5(x + 5/4) and b = 4 (x (7/4) ).

− (12x + 25/4) (2x + −25/4)

The area that is enclosed by the curve defined by the polar equation r = sin θ sin(4θ). can be solved by using the formula of A=\(\frac{1}{2}\) ∫[f(θ)]²dθ.

Note also that this all given polar function can be evaluated from a limit 0 to  2 π.

First we sketch the polar curve which is r=sin4θ

Then Derive a Polar Curve where:

r = x² + y²

tan⁻¹\(\frac{y}{x}\)

The graph for  r=sin4θ is given in the image attached.

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Answer:

2/10, 0.2, 20%

Step-by-step explanation:

hope this helps

Step-by-step explanation:

a triangle is equal to 180 degrees

180 minus 36 gives us 144

144 divided by 8c equals 18

c equals 18

Answer:

405

Step-by-step explanation:

We can use a ratio to solve

3 infected           x infected

------------------ = ----------------

50 sampled     6750 population

Using cross products

3*6750 = 50x

Divide each side by 50

3*6750/50 = x

405

Answer:

Around 405 elk should be infected with the parasite.

Step-by-step explanation:

6,750/50=135

135 * 3 = 405

hope this helps :)

Answer:

3, 5, 7 are correct

Step-by-step explanation:

the function is linear and continious b/c it is written in the form of ax + b=f(x).

y -intercept is 2.

the slope is -2.

Answer:

B. $7.50

Step-by-step explanation:

We know profit or P-----P(n) where n is the quantity/number of the item) is the difference of the revenue-----R(n)-----and the cost-----C(n)

P(n) = R(n) - C(n)

Revenue is

R(n) = pn

Cost is a combination of

The cost function resembles a linear equation:

C(n) = mn + c

Since we're shown that P = 7.5n - (2.25n + 15), we know that R(n) must be R(n) = 7.5n and C(n) must be C(n) = 2.25n + 15

Thus, we know she charges $7.5 per necklace sold.

The shape that can tessellate without leaving gaps is the hexagon (option A).

The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).

A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.

On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.

A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.

In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).

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The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.

In order for us to find out the total possible combinations, we will use the formula as:

Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons

We are given that;

Number of possible chairpersons = 16

Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)

Thus, we can say that;

Total possible combinations = 16 * 15

Total possible combinations = 240 combinations

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Answer: X = 21/6

Step-by-step explanation:

The angle is a 90 degree angle.

that means we know 21x+6=90

21x = 90-6

21x=84

x = 84/24

x = 21/6

x = 21/6

Answer:

A - 2.25

B - 1 1/3

Step-by-step explanation:

A - Divide the cups of flour given by the number of dozens it makes then multiply it by the cups of flour she has at the moment.

4.5 ÷ 6 = 0.75

0.75 × 3 = 2.25

B - Divide the number of dozens given (6) by the amount of flour (4.5) it makes then multiply it by 1.

6 ÷ 4.5 = 1.333333332

1.333333332 × 1 = 1.333333332

1.333333332 = 1 1/3