Write the six trig functions for the following

SOH CAH TOA

Please and thank you

Answer:

.625

Step-by-step explanation: calculator

Answer:

The volume of the prism is 54 in³.

This can be calculated by multiplying the length by the width by the height.

Which comes out to 9 in x 1 ¹⁄ ³ in x 4 ²⁄ ³ in = 54 in³.

The probability against Brian winning a gift card are approximately 3.118 to 1.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event happening is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields, such as statistics, finance, science, engineering, and gaming, to make predictions and decisions based on uncertain events.

In the given question,

The probability of the arrow stopping on a black slice is 3/10. Therefore, the probability of the arrow stopping on a non-black slice is 7/10.

If the arrow stops on the border of two slices, the wheel is spun again, so Brian has another chance to win. The probability of the arrow stopping on a non-black slice is 7/10, so the probability of the arrow stopping on a black slice on the second spin is 3/7.

To find the odds against Brian winning a gift card, we first find the probability of him not winning a gift card on either spin:

P(not winning) = P(non-black on first spin) + P(black on first spin and non-black on second spin)

P(not winning) = (7/10) + (3/10) × (4/7)

P(not winning) = 0.7571

The probability of not winning is 0.7571, so the odds against winning are:

Odds against winning = P(not winning) / P(winning)

Odds against winning = 0.7571 / 0.2429

Odds against winning = 3.118

Therefore, the odds against Brian winning a gift card are approximately 3.118 to 1.

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A piecewise function is a function that has different definitions, based on the interval of the input values of the function.

A piecewise function is a mathematical function that is defined by different rules over different intervals or subdomains of its domain. These different rules can take on different forms or expressions, allowing the function to behave differently on different parts of its domain.

Hence one example of a piecewise function is the absolute value function, which is defined as follows, depending on the signal of the input:

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The employee must sell $32,000 worth of merchandise in the month to make a total of $4,000.

Let's first find out how much commission an employee would earn if they sold $x in a month,

where x is the amount of sales over $7,000.

The commission earned would be 8% of x, or 0.08x.

To earn a total of $4,000 for the month, the employee would need to earn a base salary of $2,000 plus an additional $2,000 in commission.

So we can set up the following equation:

0.08x + 2000 = 4000

Subtracting 2000 from both sides, we get:

0.08x = 2000

Dividing both sides by 0.08, we get:

x = 25000

Therefore, the employee must sell $25,000 in a month to make a total of $4,000 for the month. Note that this is the amount of sales over $7,000, so the total sales for the month would be $25,000 + $7,000 = $32,000.

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Answer:

C  m∠A + m∠B = 180°

Step-by-step explanation:

Because angle A and angle B are inscribed angles on the diameter they are half of 180° which is 90°

When both of these angles are added they equal 180°

Answer:1:2

Step-by-step explanation:

Answer: The correct solution using the quadratic formula is:

x = (-(-5) ± sqrt((-5)^2 - 4(1)(-2))) / (2(1))

Simplifying:

x = (5 ± sqrt(33)) / 2

Therefore, the exact solutions of x^2 - 5x - 2 = 0 are:

x = (5 + sqrt(33)) / 2 or x = (5 - sqrt(33)) / 2

So the final answers are:

x = 2.79 or x = 2.21 (rounded to two decimal places)

Your welcome (:

Answer:

C

Step-by-step explanation:

It was right for me

The values are, ∠Q = 96°, x = 1, ∠QTR = 47°

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

Given that the diagram QRST is a parallelogram then the parallel sides and angles are equal.

So, ∠Q = ∠S   (Equal angles)

      ∠Q = 96°

and, QT = RS   (Equal parallel sides)

     6x = 6

      x = 1

Co-interior angle of figure, RS║QT and ST is a transversal line,

So, ∠RST + ∠STQ = 180°    

96° + 37° + ∠QTR = 180°                (here ∠STQ = 37° + ∠QTR)

∠QTR = 180° - 133°

∠QTR = 47°

Therefore, The values are, ∠Q = 96°, x = 1, ∠QTR = 47°

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Answer: The point-slope formula is given by:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

We have a point (1,2) and a slope of -5/6. Substituting these values into the point-slope formula, we get:

y - 2 = (-5/6)(x - 1)

Expanding and rearranging this equation gives:

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

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

y = (-5/6)x + (17/6)

This is the equation of the line in slope-intercept form, y = mx + b, where m is the slope (-5/6) and b is the y-intercept (17/6).

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be  BZ = (8/9) * BC = 40/9 as a result.

Due to its two or more extra sections, a trapezoid is a polygon. Its shape is a simple rectangle. Only the three edges A, B, but instead C distinguish a triangle from a regular triangle. Euclidean geometry produces a singular area rather than a cube when the borders are not perfectly collinear. Triangular shapes are defined as having three sides and three angles. Angles are formed by the meeting of a quadrilateral's 3 sides.

Here,

Let D represent the intersection of the angle bisector BY and the side AC, and let E represent the intersection of the angle bisector CZ and the side AB.

=>BC² = AB² + AC² - 2AB * AC * cos(BAC)

However, since BY and CZ are angle bisectors, we can calculate BAC as follows:

=> BC² = 8² + 9² - 2(8)(9)cos[(180° - (ABC + ACB))/2]

If we simplify, we get:

=> BC² = 145 - 144cos[(ABC + ACB)/2]

Using the angle bisector theory once more, we have the following:

=> AD/DC = 8/BC

=> DC = BC(AD/8)

Simplifying and substituting into the Law of Cosines equation yields:

=> BC² = 145 - 144cos[(ABC + ACB)/2]

=>  145 - 144cos[(180° - BAC)/2]

=> 145 - 144cos(B/2)

in which B Equals ABC.

We can now replace the value of BZ that we discovered earlier with:

=> BZ = (8/9) * BC

and solve for BC:

=> BC² = 145 - 144cos(B/2)

=>  (9/8)² * (145 - 144cos(B/2)) + (8/9)² * BZ²

Simplifying and substituting BZ results in:

BC² = 25

Since BC is a length, we obtain: by taking the positive square root.

=> BC = 5

=> BZ = (8/9) * BC = 40/9 as a result.

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the total number of dinosaurs: George has collected 27 dinosaurs.

Multiplication is a mathematical operation that involves combining two or more numbers to find their total or product. It is a way to represent repeated addition. For example, 3 times 4 can be written as 3 x 4, which means adding 3 to itself 4 times to get a total of 12. Multiplication is denoted by the symbol "x" or "·" or "*", and the numbers being multiplied are called factors or multiplicands, while the result is called the product. Multiplication can be done using different methods, such as memorization of multiplication tables, or using algorithms like long multiplication or lattice multiplication. Multiplication is a fundamental operation in mathematics, and it is used in many areas of science, engineering, and economics.

Given by the question.

To find out how many dinosaurs George has collected, we can start by calculating 3/5 of the total number of dinosaurs:

3/5 x 45 = 27

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Answer: 15 Cakes

Step-by-step explanation:

2 slices per person, and 8 slices in 1 cake means that 4 people can share 1 cake.

So, you would do the amount of people (60) divided by the number of people that can eat 1 cake (4) to end up with ordering 15 cakes

The values are, ∠BCA = 65°, ∠B = 72°,  x = 3

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

Given that the diagram ABCD is a parallelogram,

So, BC = AD   (parallel sides are equal)

      2x = 6

       x = 3

BC ║ AD and AC is a transversal line,

then, ∠BCA = ∠DAC    (alternate interior angle)

∠BCA = 65°

Opposite angles are equal for parallelogram then,

∠B = ∠D

∠B = 72°

Therefore, the values are, ∠BCA = 65°, ∠B = 72°,  x = 3

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Answer:

the value of x for which the volume of the box will be as large as possible is approximately 2.67 inches.

Step-by-step explanation:

Let x be the length of the side of the squares that are cut out of the corners of the cardboard. Then the dimensions of the base of the rectangular box will be:

Length = 16 - 2x (since two squares of side x are cut out of each end of the 16-inch length)

Width = 16 - 2x (since two squares of side x are cut out of each end of the 16-inch width)

The height of the box will be x, since that is the height of the squares that were cut out.

The volume of the box can be expressed as:

V = Length × Width × Height

V = (16 - 2x) × (16 - 2x) × x

V = 4x^3 - 64x^2 + 256x

To find the value of x that maximizes the volume of the box, we can take the derivative of V with respect to x and set it equal to zero:

dV/dx = 12x^2 - 128x + 256 = 0

We can solve this quadratic equation for x using the quadratic formula:

x = [128 ± sqrt(128^2 - 4 × 12 × 256)] / (2 × 12)

x = [128 ± sqrt(16384)] / 24

x = [128 ± 128] / 24

x = 10.67 or x = 2.67

Since x represents the length of a side of a square, it must be non-negative. Therefore, the only valid solution is x = 2.67 inches.

So, the value of x for which the volume of the box will be as large as possible is approximately 2.67 inches.

Answer: Let x be the side length of the square corners that are cut out of the cardboard. Then the dimensions of the base of the box (after the corners have been cut out and the flaps folded up) are 16-2x by 16-2x, and the height of the box is x.

The volume V of the box is given by:

V = (16-2x)(16-2x)(x)

Expanding this expression gives:

V = 4x^3 - 64x^2 + 256x

To find the value of x that maximizes V, we can take the derivative of V with respect to x and set it equal to zero:

dV/dx = 12x^2 - 128x + 256 = 0

Dividing both sides by 4 gives:

3x^2 - 32x + 64 = 0

This quadratic equation can be factored as:

(3x - 16)(x - 4) = 0

So the solutions are x = 16/3 and x = 4.

Since x must be less than half of 16 (the side length of the cardboard), we can reject x = 16/3. Therefore, the value of x that maximizes the volume of the box is x = 4 inches.

Step-by-step explanation:

The pair of equations that can be used to find x and y are:

x + y = 62

(1.02)x = 7

The form of the pair of equations would be:

hours worked last week + hours worked this week = total hours worked both weeks equation 1

(1 + percent increase/100) x hours worked last week = hours worked this week equation 2

x + y = 62 equation 1

(1 + 20/100) ×x = y

(1.02)x = 7 equation 2

The two equations can be solved using either of these three methods:

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Answer:If my calculations are right it should be 18

Step-by-step explanation:

The frisbee would spend 2.62 seconds in air before touching ground.

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let h represent the height of the frisbee after t seconds.

h = -16t² + 40t + 5

The time the Frisbee is in air is at h = 0, hence:

-16t² + 40t + 5 = 0

t = 2.62 seconds

The frisbee would spend 2.62 seconds in air

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a) Note that given the above function the height of the Frisbee each second it is in the air are:

b) The frisbee lasts  t [tex]\approx[/tex] 2.6 (s) in the air.

Recall that the function given is -16t² + 40t + 5
t=0; and h = 5

a)
Where t is 1
h = -16t² + 40t + 5

h= -16(1)² + 40(1) + 5

h= -16 + 40 + 5

h= 24 + 5

h= 29, thus, where = 1, h = 29

Using a similar sequence above, where t is
t=2; h = 21 feet; and where

t =3; h = -19

b) in this case, we must set h(t) = 0

⇒ -16t² + 40t + 5 = 0
To solve for t in the equation -16t² + 40t + 5 = 0, we can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -16, b = 40, and c = 5, so substituting these values into the quadratic formula, we get:

t = (-40 ± √(40² - 4(-16)(5))) / 2(-16)

Simplifying:

t = (-40 ± √(1600 + 320)) / (-32)

t = (-40 ± √(1920)) / (-32)

t = (-40 ± 8 √(30)) / (-32)

t = (5/4) ± (√(30)/4)

Thus we have:

t = (5/4) + (√(30)/4) or t = (5/4) - (√(30)/4)

t₁ = 1.25 + (5.477225575051661134569697828008/4) or
t₂ = 1.25 - (5.477225575051661134569697828008/4)

t₁ = 1.25 + 1.369306393762915283642424457002
t₁ [tex]\approx[/tex] 2.6

t₂ = 1.25 - 1.369306393762915283642424457002

t₂ [tex]\approx[/tex] -0.119

Thus the Frisbee lasts approximatley 2.6 seconds in the air.

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Answer:

the total force on the port hole due to liquid pressure is approximately 7400 pounds.

Step-by-step explanation:

The area of the circle is A = πr^2, where r = d/2 = 1 foot is the radius of the circle. So, the area is A = π(1 ft)^2 = π ft^2.

The port hole is submerged in water, with a height of 6 feet. The pressure of water at a depth of h feet is given by the formula P = ρgh, where ρ = 62.4 lb/ft^3 is the density of water, and g = 32.2 ft/s^2 is the acceleration due to gravity.

The total force on the port hole due to liquid pressure is the product of the pressure and the area of the circle, so we have:

F = P × A = ρgh × A = 62.4 lb/ft^3 × 32.2 ft/s^2 × 6 ft × π ft^2 ≈ 7400 lb

Therefore, the total force on the port hole due to liquid pressure is approximately 7400 pounds.

Answer: 578490-=356478e

Step-by-step explanation:

part of a circle is 75849=n so we use all the equations so 56748=4 we know the answer by the book page 356 then on chemestry rules.

Considering the definition of perimeter, the length and width of the rectangle is 85 in and 7 in respectively.

The perimeter of a two-dimensional figure is the distance around the figure. That is, the perimeter of a flat geometric figure is called the length of its contour.

The perimeter is the measurement obtained as a result of the sum of the sides of a flat geometric figure.

A rectangle is a geometric figure that has two pairs of sides of equal length. The expression to calculate the perimeter of a rectangle is:

Perimeter= 2× length + 2× width

In this case, you know

Replacing in the definition of the perimeter of the rectangle:

184= 2× (11×width + 8) + 2× width

Solving:

184= 2×11×width + 2×8 + 2× width

184= 22×width + 16 + 2× width

184 - 16= 22×width + 2× width

168= 24×width

168÷ 24= width

7 in= width

So, the length can be calculated as:

lenght= 11×7 in + 8 in

lenght= 85 in

Finally, the length of the rectangle is 85 in and the width of the rectangle is 7 in.

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Answer: probably a function

Step-by-step explanation:

huh um intentaría ayudar pero no tiene mucho sentido lo siento

The top of the ladder is 15 feet up the wall.

What is right-angle triangle?

If one of the triangle's angles is 90 degrees, the triangle is said to be right-angled. The combined angles of the other two are 90 degrees. The triangle's base and perpendicular sides both include the right angle. The longest side of the three sides, known as the hypotenuse, is the third side.

Given that the height of the ladder is 17 feet. The distance between the base of the ladder and the wall is 8 feet.

It forms a right-angle triangle.

The hypotenuse of the triangle is 17 feet and the base is 8 feet.

Apply Pythagorean theorem:

Altitude² = Hypotenouse² - Base²

Altitude² = 17² - 8²

Altitude² = 289 - 64

Altitude² = 225

Take square root on both sides:

Altitude = ± 15

Since height can't be a negative number, Altitude =  15 feet.

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Answer:

Interest = $530.4

Step-by-step explanation:

We know:

Interest = Principal x Rate x Time

First, put in the numbers:

Interest = $1,300 x 6.8% x 6 years

Interest = $1,300 x [tex]\frac{6.8}{100}[/tex] x 6 years

Interest = $13 x 6.8 x 6 years

Interest = $88.4 x 6

Interest = $530.4

The correct statement regarding the average rate of change of the functions f(x) and g(x) on the interval [-2,2] is given as follows:

Over the interval [-2,2], the function f is increasing at a faster rate than function g is decreasing.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

For the function f(x), the numeric values at x = -2 and x = 2 are given as follows:

Hence the rate is of:

(26 - 14)/(2 - (-2)) = 12/4 = 3. -> positive rate -> increasing.

For function g(x), the rate is given as follows:

(-16 - 4)/4 = -5.

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Answer:

18

Step-by-step explanation:

Counting:

07 17 27 37 47 57 67 70 71 72 73 74 75 76 78 79 87 97

notice we can ALSO use variation with no repetition equation with n=9 (numbers from 0 to 10) and p=1 (two digits) but the value can be in the first position or the second position

[tex]\frac{9!}{(9-8)!}[/tex] +  [tex]\frac{9!}{(9-8)!}[/tex][tex]=9+9=18[/tex]

Answer:

percentage = (part/whole) x 100%

where "part" is the value we are trying to express as a percentage of "whole". In this case, "part" is 3984 and "whole" is 24.9.

So we can substitute these values into the formula:

percentage = (3984/24.9) x 100%

percentage = 159.838% (rounded to three decimal places)

Therefore, 3984 is approximately 159.838% of 24.9.

Answer:

3984 is 16,000% of 24.9

Step-by-step explanation:

percentage = (3984÷24.9) x 100%

percentage = 159.838%

or percentage ≈ 16,000%

Finding the percentage of consumers who bought fewer than six flowers requires figuring out what proportion of the data is below six.  [tex]40[/tex] % of customers purchased fewer than 6 flowers.

Based on the box plot, we can see that the minimum value is 2, and the maximum value is 12. The box plot also shows that the median (50th percentile) is between 6 and 8.

To find the percent of customers who purchased fewer than 6 flowers, we need to determine what percent of the data is below 6.

From the box plot, we can see that the lower quartile (25th percentile) is at 2, and the upper quartile (75th percentile) is at 10.

Therefore, the interquartile range (IQR) is   [tex]10 - 2 = 8.[/tex]

To find the percentage of customers who purchased fewer than 6 flowers, we need to find the percentile rank of 6.

Percentile rank = ((value below target) / (total values)) x 100

Percentile rank of   [tex]6 = ((2 / 5) \times 100) = 40[/tex]%

Therefore,  [tex]40[/tex] % of customers purchased fewer than 6 flowers.

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The given question is incomplete. the complete question is given below.

Rodrigo works at a flower shop. He recorded how many flowers each customer purchased

yesterday. This box plot shows the results.

Flowers purchased

++

2

6

8

10

12

What percent of the customers purchased fewer than 6 flowers?

%