HELPPPPPPP TRIGONOMETRY

the profit function is positive, producing 164 units of the new product line would yield a profit of $600.

We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600

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Answer: 12

Step-by-step explanation:

Use BODMAS, so first solve the inside of the bracket:

2*3= 6

6-4= 2

Now we can multiply that by the number outside the bracket. Why?

Because a number outside a bracket means to multiply that number by everything in the bracket. So:

6 * 2 = 12

Answer: 12

Step-by-step explanation:

2 x 3 = 6

6 - 4 = 2

6 x 2 = 12

The correct answer to the given question is graph D

Given a set of data points, we are tasked with identifying the correct box plot representation.

We begin by arranging the data in ascending order, which gives us 12, 17, 21, 23, 24, 28, and 29 points.

Next, we use the properties of a box plot to eliminate incorrect representations.

The left end of the whisker should correspond to the smallest data point, and the right end to the largest.

Among the given graphs, only one satisfies this condition.

The middle point is identified as the fourth data point, which is 23.

Finally, we determine the lower and upper lines of the box to be 17 and 28, respectively.

The only graph that satisfies all conditions is graph D.

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Answer: 19 tickets

Step-by-step explanation:  $45 - $7 = 38      38 divided by $2 = 19 tickets

The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.

The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:

Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.

The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).

In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.

These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.

In the given triangle using the sum of interior angle of triangle we have:

180 - 90 - 29 = 61

The measure of the third angle is 61 degrees.

Now, tan(61) = XZ/XY

XZ = XY * tan(61)

XZ = 18 * 1.927 = 34.686

Now, using the Pythagoras theorem we have:

ZY² = XZ² + XY²

ZY² = 34.686² + 18²

ZY² = 1712.3996

ZY = 41.38

Now, the value of:

sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435

cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838

tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518

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Answer:

The Answer is x=2

Step-by-step explanation:

Hope this helps!!!!

Answer:

x=2  

Step-by-step explanation:

4x+3=11

4x=11-3      ( subtract 3 on both sides)

4x=8

x=2            ( divide 4 on both sides)

Answer:

The average daily balance on Perry's credit card for the period beginning October 10 was $714, and the balance at the end of the cycle was $506. To calculate the balance due, we need to know the length of the billing cycle. Assuming a 30-day billing cycle, we can use the average daily balance method to calculate the interest charged. The formula for interest charged is: Average Daily Balance x APR x Days in Billing Cycle / 365. Plugging in the numbers, we get: $714 x 0.08 x 30 / 365 = $4.68. Adding this interest to the ending balance of $506, the total balance due is $510.68.

Answer:

The correct answer is the third one

Step-by-step explanation:

[tex]8x + \frac{15}{x} = 26[/tex]

[tex]8 {x}^{2} + 15 - 26x = 0[/tex]

a = 8, b = -26, c = 15

[tex]d = {b}^{2} - 4ac = ( { - 26})^{2} - 4 \times 8 \times 15 = 676 - 480 = 196 > 0[/tex]

[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{26 - 14}{2 \times 8} = \frac{12}{16} = \frac{3}{4} [/tex]

[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{26 + 14}{16} = \frac{40}{16} = \frac{5}{2}[/tex]

Answer:

1 solution

Step-by-step explanation:

Y = 4

Y = 4x - 1

Substitute value of Y here,

4 = 4x - 1

4 + 1 = 4x

5 = 4x

5/4 = x

1.25 = x

•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.

______

hope this helps!

Answer: the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.

Step-by-step explanation:

Let's assume that there are 100 people in the focus group. Then, the number of males in the focus group is 47 and the number of females is 53.

Out of 47 males, 40% said they would buy the fruit drink, which is 0.4 x 47 = 18.8 males (rounded to the nearest whole number). Out of 53 females, 54% said they would buy the fruit drink, which is 0.54 x 53 = 28.62 females (rounded to the nearest whole number).

The ratio of males who would buy the drink to females who would buy the drink is:

18.8/28.62 = 0.6560 (rounded to the nearest ten-thousandth)

Therefore, the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.

Answer:

x = 63 , y = 90

Step-by-step explanation:

assuming DF is the diameter of the semicircle , then

∠ DEF = y = 90° ( angle inh a semicircle )

then

x + y + 27° = 180° ( angle sum of a triangle )

x + 90 + 27 = 180

x + 117 = 180 ( subtract 117 from both sides )

x = 63

Answer:

60:61.8 OR 10:10.3

Step-by-step explanation:

Cant be simplified - unless your in advanced classes. If so

10:10.3

Answer:

Step-by-step explanation:

1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1

Answer: 64°

Step-by-step explanation:

Had this problem and got it right

Answer:

To find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral, we need to look for expressions involving square roots of the form:

sqrt(a^2-x^2)

sqrt(a^2+x^2)

sqrt(x^2-a^2)

If we have sqrt(a^2-x^2), we can use the substitution x = a sin(t) or x = a cos(t) depending on which one of them makes the expression simpler.

If we have sqrt(a^2+x^2), we can use the substitution x = a tan(t) or x = a sec(t).

If we have sqrt(x^2-a^2), we can use the substitution x = a sec(t) or x = a tan(t).

It is important to keep in mind the trigonometric identities and the Pythagorean theorem to simplify the integrals after substituting.

Step-by-step explanation:

hope its help <:

Using a trigonometric relation, we can see that the values of x and y are:

y = 25.98

x = 15

Here we can see a right triangle, where we know the interior angles and the length of the hypotenuse.

To get the lengths of the legs, we can use trigonometric relations, like:

cos(a) =(adjacent cathetus)/hypotenuse.

For example, if we want to find y, then the angle at which this side is adjacent is the 30° one, now replacing the known values in the formula we will get:

cos(30°) = y/30

cos(30°)*30 = y = 25.98

And to get the value of x, we should use the 60°angle, so:

cos(60°) = x/30

30*cos(60°) = x =  15

These are the two lengths we wanted to get.

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According to the information, the values that coincide are: 2.2 meters with 2200 millimeters, 14 decimeters with 0.014 hectometers, 0.14 meters with 0.014 decameters, 0.022 decameters with 22 centimeters.

To find the numbers that match we must take into account the relationship between the values:

According to the above, we can infer that the values that match are:

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Answer: The answer should be 20 hours

Step-by-step explanation:

That is when the 2 lines meet up so that is when they are the same difference from Kansas City.

Answer:

g(x)= log(x-1)

Step-by-step explanation:

g(x) = f(x-1)

, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Interval  [tex](4, 3): f(-4) -41, f(-3) 5,[/tex]therefore, the function reverses its sign and has a zero in the interval  [tex](-4, -3).[/tex]

Interval  [tex](3, 2): f(-3) 5, f(-2) -9,[/tex] indicating that the function changes sign and has a zero in the interval  [tex](-3, -2).[/tex]

Interval [tex](2, 1): f(-2) -9, f(-1) 1[/tex], therefore the function reverses its sign and has a zero in the interval  [tex](-€2, -1).[/tex]

Interval [tex](1, 0): f(-1) 1, f(0) 5[/tex], so the function does not change sign and the interval may or may not contain a zero [tex](-1, 0).[/tex]

Interval  [tex](0, 1): f(0) 5, f(1) -3,[/tex] indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Therefore, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

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Answer:

5.5 or 5 1/2 inches

Step-by-step explanation:

The longest is 12 3/4

The two smallest combined are 3 and 4 1/4 = 7 1/4

12 3/4 - 7 1/4 = 5 1/2

The table of original value and rounded values are

x        y

0.2    0

0.5     1

0.9     1

1.08    1

1.49     1

1.72     2

2.3      2

2.94    3

The graph is attached

The graph is made in a cartesian coordinate by tracing the point of intersection of the two points

The table is represented as ordered pair as (original value, rounded value) for the given x and y values:

(0.2, 0), (0.5, 1), (0.9, 1), (1.08, 1), (1.49, 1), (1.72, 2), (2.3, 2), (2.94, 3)

The graph is a scattered plot and its attached

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The factοrs οf the expressiοn is 4x(2xy+3y-4z).

Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.

Here the given expressiοn is ,

=> [tex]8x^2y+12xy-16xz[/tex]

Nοw factοrizing the given expressiοn then,

=> 4×2×x×x×y+4×3×x×y-4×4×x×z

=> 4x(2xy+3y-4z)

Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).

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In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.

A circle is a clοsed, twο-dimensiοnal οbject where every pοint in the plane is equally spaced frοm a central pοint. The line οf reflectiοn symmetry is fοrmed by all lines that traverse the circle. Additiοnally, every angle has rοtatiοnal symmetry arοund the centre.

A circle is given with centre marked as O.

A circle is a 2D fοrm in geοmetry in which all οf the pοints οn its surface are equally spaced frοm its center.

The radius is the length frοm any pοint οn the surface tο the center.

A diameter is a chοrd that is equidistance frοm centre οf the circle.

Here οnly the straight line is equidistance frοm centre οf the circle.

That line is BQ.

Thus, In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.

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Okay so hopefully. I got the equation right. But I believe this is it

Statement B is true: The population will increase by 9%.

Various Functions:

A single function (Injective function) Many – one function. From onto function (Surjective Function) Function is into. polynomial operation.

P(t)=18,751(1.09)t is the population function, where t is the time in years.

The function's growth factor or multiplier, which is bigger than 1, is represented by the expression (1.09t). In other words, the population is growing over time.

Finding the difference between the final and starting values, dividing by the initial value, and then multiplying by 100% will give us the percentage growth in the population.

Let's contrast the population at t=0 and t=1 to see how they differ:

P(0) = 18,751(1.09)^0 = 18,751

P(1) = 18,751(1.09)^1 = 20,436.59

In the last year, the population has grown from 18,751 to 20,436.59.

The population has grown by the following amount:

[(20,436.59 - 18,751)/18,751] × 100% ≈ 9.0%

Thus, the population will grow by 9%, as stated in statement B.

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Answer:

Step-by-step explanation:

take 71.28-21.39

Answer:

If the drum set is 30% off, this means that Susan only needs to pay 70% of the original price. We can calculate this using the following formula:

Total price = Original price x (1 - Discount rate)

where the discount rate is the percentage discount expressed as a decimal. In this case, the discount rate is 30% or 0.3. Substituting in the given values, we get:

Total price = $71.28 x (1 - 0.3)

Total price = $71.28 x 0.7

Simplifying, we get:

Total price = $49.896

However, we also know that Susan got a discount of $21.39. This means that she only needs to pay:

Total price - Discount = $49.896 - $21.39

Total price - Discount = $28.506

Therefore, Susan has to pay $28.506 in total.

a. The cost of one large pizza with one topping is $13.50. To purchase one large and five medium pizzas, we would need to buy one large pizza at regular price and five medium pizzas at the discounted price. The cost of the large pizza is $13.50, and the cost of each medium pizza is $6.25. Therefore, the total cost would be:

Total cost = Cost of large pizza + Cost of 5 medium pizzas

Total cost = $13.50 + ($6.25 x 5)

Total cost = $13.50 + $31.25

Total cost = $44.75

Therefore, it would cost $44.75 to purchase one large pizza and five medium pizzas.

b.Number of medium pizzas Total cost

0 | $13.50

1 | $19.75

2 | $26.00

3 | $32.25

4 | $38.50

c. Let "m" be the number of medium pizzas. Then the total cost of purchasing one large pizza with one topping and m medium pizzas can be represented as:

Total cost = 13.50 + 6.25m

d. If you have a total of $100 and purchase one large pizza, you would have $100 - $13.50 = $86.50 left to spend on medium pizzas. The cost of each medium pizza is $6.25. Therefore, you can buy:

Number of medium pizzas = $86.50 ÷ $6.25 = 13.84

Since you cannot buy a fraction of a pizza, you can only buy 13 medium pizzas with $86.50.

e. The area of a pizza is given by the formula A = πr^2, where A is the area and r is the radius. The area of a large pizza is:

A = πr^2

A = 3.14 x 8^2

A = 3.14 x 64

A = 200.96

The area of a medium pizza is:

A = πr^2

A = 3.14 x 5^2

A = 3.14 x 25

A = 78.5

Therefore, the total area of one large pizza and five medium pizzas is:

Total area = Area of large pizza + (Area of medium pizza x 5)

Total area = 200.96 + (78.5 x 5)

Total area = 200.96 + 392.5

Total area = 593.46

Rounding to the nearest inch, the total area of pizza is 593 square inches.

f. To calculate the cost per square inch of pizza, we need to divide the total cost of the pizzas by the total area of the pizzas. The total cost of one large pizza and five medium pizzas is $44.75, and the total area is 593 square inches. Therefore, the cost per square inch of pizza is:

Cost per square inch = Total cost / Total area

Cost per square inch = $44.75 / 593

Cost per square inch = $0.08 (rounded to the nearest cent)

Therefore, the cost per square inch of pizza is 8 cents.

The probability that a randomly selected person actually went on holiday that year is 0.727

Out of the 55 adults surveyed, 25 went abroad and 15 went on holiday in the UK.

Therefore, the total number of people who went on holiday is 25 + 15 = 40

The probability of selecting a person who went on holiday is the number of people who went on holiday divided by the total number of people surveyed:

P(went on holiday) = 40/55

Simplifying the fraction, we get:

P(went on holiday) = 8/11

Rounding to three decimals, we get:

P(went on holiday) = 0.727

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the answer is m + n = 24 + 55 = 79.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.

First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.

This can be simplified by dividing the numerator and denominator by 2:

48/110 = 24/55

So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.

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