Find the value of each trigonometric ratio. Express your answer as a fraction in lowest terms.

The function represented by the graph is:

f(x) = |x – 1| + 3

This function takes the absolute value of the difference between x and 1, and then adds 3 to the result. The graph of this function will have a "V" shape centered at x = 1 with the vertex at (1, 3). The left side of the vertex will have a slope of -1, and the right side of the vertex will have a slope of +1. The y-intercept will be 3 units above the x-axis.

Answer:  B

Step-by-step explanation: YES

The equation represents how many grams of the compound will remain after 4 hours m(4) = 0.285m₀

Radiation and decay are important concepts in nuclear physics. The rate at which radioactive compounds decay is measured in terms of half-life and the decay constant.

To solve this problem, we can use the exponential decay equation, which describes the rate of decay of a radioactive substance.

In this scenario, we are interested in finding the remaining mass of the radioactive compound, which can be obtained by multiplying the number of remaining atoms by the atomic mass of the substance. The equation for the remaining mass is:

m(t) = N(t) x m

where:

m(t) represents the mass of the radioactive substance remaining at time t.

N(t) is the number of radioactive atoms remaining at time t.

m is the atomic mass of the substance.

To determine the values of N0 and λ for our radioactive compound, we can use the decay rate given in the problem. If the compound decays at a rate of 27% per hour, it means that the remaining fraction of the substance after each hour is 0.73 (i.e., 100% - 27% = 73%). Therefore, the decay constant can be calculated as follows:

ln(0.73) = -λ

λ = 0.312

Next, we can use the initial mass of the compound (320 grams) and the exponential decay equation to find the remaining number of atoms at 4 hours:

[tex]N(4) = N_0 \times e^{-0.312 x 4}[/tex]

N(4) = N₀ x 0.285

Since we don't know N₀, we can express it in terms of the initial mass and the atomic mass:

N₀ = m₀ / m

where:

m₀ is the initial mass of the radioactive compound.

m is the atomic mass of the substance.

Substituting this into the previous equation, we get:

N(4) = (m₀ / m) x 0.285

Finally, we can use the equation for the remaining mass to find the answer:

m(4) = N(4) x m

m(4) = (m₀ / m) x 0.285 x m

m(4) = 0.285m₀

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The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the sides of a right triangle.

The Pythagoras Theorem states that : in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of squares of lengths of other two sides.

Mathematically, the Pythagoras Theorem is written as:

⇒ c² = a² + b² ;

where c is = length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.

The Converse of Pythagoras Theorem states that : If in a triangle, the square of the length of the longest side is equal to the sum of squares of lengths of other two sides, then triangle is a right triangle.

Both the Pythagorean Theorem and its converse apply only to right triangles, which are triangles that have a right angle .

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Step-by-step explanation:

Let the distance between them be y

sin20° =

=> 0.342 =           [  sin20° = 0.342]

=> y =  33/ 0.342

=> y = 96.5 ft

So, the distance between them is 96.5 ft

Applying the Two Tangents Exterior Angle Theorem, the value of x is: 12.

m(BD) = 120°

If you draw two tangents from a point outside a circle, the size of the angle they form is equal to half of the difference between the sizes of the two arcs they intercept inside the circle, based on the Two Tangents Exterior Angle Theorem.

Therefore, we have:

6x - 12 = 1/2[(-12 + 21x) - (12x - 24)] (according to the Two Tangents Exterior Angle Theorem)

Solve for x:

6x - 12 = 1/2[(-12 + 21x - 12x + 24)

2(6x - 12) = -12 + 21x - 12x + 24

12x - 24 = 9x + 12

12x - 9x = 24 + 12

3x = 36

x = 36/3

x = 12

m(BD) = 12x - 24 = 12(12) - 24

m(BD) = 120°

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Answer: Width = 45 feet; Length = 15 feet;

Step-by-step explanation: Start by substituting 3w for the length because it says that in the problem. We know that 2(L+W) equals the perimeter. Since we substituted 3w for length we get 8w for the perimeter. Divide 120 by 8 to find that the width is 15 feet and plug it into 3w to get the length of 45 feet.

Answer:

45 feet and 15 feet are the length and width

Step-by-step explanation:

P = 120 feet

a (length) = 3 * b (width)

P = 2 * (a + b)

P = 2 * (3b + b)

P = 2 * 4b

P = 8 * b

                           => 8b = 120 feet

P = 120 feet

b = 120 / 8

b = 15 feet

a = 3 * b

a = 3 * 15

a = 45 feet

Answer:

121

Step-by-step explanation:

1242-150=1092/9 = 121 (remainder 3)

Answer: 121

Step-by-step explanation: 1241 - 150 / 9

The length of the segment NT is  4.5  units

What is isosceles triangle?

An isosceles triangle is one that has two sides of equal length.

The angles opposite to equal sides are equal.

Let RM=x, then  MS=RN=NT=x  ( because RS = RT )

RS=RT =2x

RST and RMN are two similar triangles

So, we have

ST/MN = RT/NT

=>  ST/3.5 = 2x/x

=> ST/3.5 = 2

=> ST = 2*3.5 = 7

Given , perimeter = 25

=> RS+ST+RT = 25

=> 2x+ST+ 2x = 25

=>  4x + 7 = 25

=> 4x= 25-7 = 18

=> x=18/4 = 4.5

NT=x= 4.5  units

The length of the segment NT is  4.5  units

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Answer:

180 most likely

On solving the provided question, we can say that the inequality is  y+2> -3x-3, Graph the points (0,-5) and (-2,1)

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

the inequality is

y+2> -3x-3

y > -3x-5

y = -3x-5

x   y = -3x-5

0   -5

-1   -2

-2   1

Graph the points (0,-5) and (-2,1)

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The total number of cows is given by the equation c = 182 cows and the total number of legs of cows is n = 728 legs

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total number of cows and goats = 452

So , c + g = 452   be equation (1)

And , ( 5/7 )c = ( 13/27 )g

On simplifying the equation , we get

c = ( 13 x 7 ) / ( 5 x 27 ) g

c = ( 91/135 )g   be equation (2)

Substituting the value of c in equation (1) , we get

( 91 / 135 ) g + g = 452

On further simplification , we get

( 91 + 135 ) / 135 g = 452

( 226 / 135 ) g = 452

Divide by 226 on both sides of the equation , we get

( 1/135 )g = 2

Multiply by 135 on both sides of the equation , we get

g = 270 goats

Now , the number of cows = 452 - 270 = 182 cows

The number of legs = 182 x 4 = 728 legs

Hence , the number of cows is 182 cows

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The height of the electric pole in order to cast a shadow of 10 m in the same condition as to be 14 m.

The flog poce cast a shadow of 5 metre and itself as a height of 7 m.

Now we have to find the height of an electric pole that will cast the shadow of length 10 m under the same conditions.

The word under the same condition means that the angle of elevation will be same in both the cases, so, we can use the tan theta here,

Tan A = perpendicular/base

Tan A will be equal for both.

Tan A = 7/5

Tan A = H/10

H is the height of the electric pole.

7/5 = H/10

H = 14m

The height of the electric pole will be 14 m.

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Answer: 15%

Step-by-step explanation:

54 divided by 360 = 0.15%

Option (a) The quantity supplied rises by 165. To determine the change in the total supply of meals in your survey when the price increases from $8 per meal to $9 per meal, we need to compare the quantity of meals supplied at the $8 and $9 prices across all food trucks.

From the table, we can see that the quantity of meals supplied at the $8 price per meal is as follows:

Mario's Taco Stand: 140

Curbside Chargrilled Burgers: 210

Chuckin' Clouds BBQ: 175

Burrito Dan's: 240

La Jefa Cubanos: 150

What a Jrk Jamaican Food: 220

The total quantity supplied at $8 per meal is 1,135 meals.

At the $9 price per meal, the quantity of meals supplied is as follows:

Mario's Taco Stand: 160

Curbside Chargrilled Burgers: 240

Chuckin' Clouds BBQ: 200

Burrito Dan's: 260

La Jefa Cubanos: 190

What a Jrk Jamaican Food: 250

The total quantity supplied at $9 per meal is 1,300 meals.

The change in the total supply of meals is the difference between the total quantity supplied at $9 per meal and the total quantity supplied at $8 per meal, which is:

1,300 - 1,135 = 165

Therefore, the answer is (a) The quantity supplied rises by 165.

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Complete question is in the image

Answer:

Since ∠1 and ∠2 are vertical angles, they have equal measure. And since ∠3 and ∠4 are right vertical angles, they have measure 90° each.

Since ∠3 is adjacent to both ∠1 and ∠2, we can say that:

∠1 + ∠3 = 180°

∠2 + ∠3 = 180°

Adding these two equations together:

∠1 + ∠2 + 2∠3 = 360°

Substituting the values we have:

∠1 + ∠2 + 2(90°) = 360°

∠1 + ∠2 + 180° = 360°

Solving for ∠1 + ∠2:

∠1 + ∠2 = 180° - 180° = 0°

Finally, the sum of the measure of ∠4 and the measure of ∠1 minus the measure of ∠2 is:

∠4 + (∠1 - ∠2) = 90° + (∠1 - 0°) = 90° + ∠1

So the answer is 90° + ∠1.

The angle relationship that will fill the correct angle are given below.

An angle is said to be generated when two or more lines intersect at a point. Thus series of angles which have some common relationship on comparison are formed. Some common angle relationships are; supplementary angles, complementary angles, vertical angles, etc.

The angle relationship to fill the correct angle are:

1. <AXE and <CXD are vertical angles.

2. <AXF and <DXF are supplementary angles.

3. <DXC and <BXC are complementary angles.

4. <CXB and <AXB are adjacent angles.

5. <AXC and <CXD are supplementary angles.

6. <DXE and <AXC are vertical angles.

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the unit rate is 6/5 inches per hour, or approximately 1.2 inches per hour.

The unit rate in inches per hour can be found by dividing the amount of rain falling per unit of time by the corresponding unit of time. In this case, we have 4/5 inches falling every 2/3 hours, so we can find the unit rate by dividing 4/5 by 2/3:

(4/5) / (2/3) = (4/5) X (3/2) = 6/5 inches per hour

So the unit rate is 6/5 inches per hour, or approximately 1.2 inches per hour.

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Answer:

24

Step-by-step explanation:

If we convert this problem into "math language", it's basically asking what is 8 divided by 1/3? So, we set this up: [tex]\frac{8}{\frac{1}{3} }[/tex] = 8 * 3 = 24

The required probability of removing a white marble followed by a blue marble is 2/33.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
There are 12 marbles in the bag in total, so the probability of selecting a white marble on the first draw is 4/12 or 1/3.

After the first marble is put aside, there are now 11 marbles in the bag, with 2 of them being blue. Therefore, the probability of selecting a blue marble on the second draw is 2/11.

To find the probability of selecting a white marble followed by a blue marble, we need to multiply the probability of the first event (selecting a white marble) by the probability of the second event (selecting a blue marble):

P(white, then blue) = P(white) x P(blue|white)

P(white, then blue) = (1/3) x (2/11)

Simplifying:

P(white, then blue) = 2/33

Therefore, the probability of removing a white marble followed by a blue marble is 2/33.

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They are skating in the same direction, how long will it take Sam to catch up to tom

will take Sam 2.72 seconds to catch up to Tom.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

To find out how long it will take Sam to catch up to Tom, we can use the following formula:

time = distance / (rate of Sam- the rate of Tom)

In this case, the distance is 120 ft (the distance between Tom and Sam when they start speed skating) and rate of Sam is 50 ft/sec, and the rate of Tom is 44 ft/sec.

Plugging these values into the formula, we get:

time = 120 / (50 - 44) = 120 / 6 = 20

So it will take Sam 20 seconds to catch up to Tom.

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The percent of sales tax that has been applied to the item is 5%.

A sales tax is a consumption tax imposed on the sale of items. It is often applied to the selling price of an item.

Here, the original cost is $90 and the final cost is $94.5.

Let, the sales tax rate is r%.

Calculate the percentage of sales tax.

Final price after sales tax = Selling Price×(1 + Rate of sales tax/100)

94.5 = 90(1+r/100)

94.5 = 90 + 0.9r

0.9r = 4.5

r = 5

Therefore, the obtained answer is 5%.

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The probability that someone is chosen to play in the left-wing position is 9%.

The general formula to calculate the probability or the likelihood of an event happening is the specific or desired outcome/ total possible outcomes.

Based on the above, let's calculate the probability in this case:

Specific outcome: To be chosen to play in the left-wing position = 1 position available

Total of players:  11 players

Now, let's calculate the probability

1/ 11 = 0.09 which is equivalent to 9%

Note: This question is incomplete; here is the missing information:

What is the probability to be chosen to play in the left-wing position?

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Answer: No, because not all of the corresponding sides are proportional

Step-by-step explanation:

If you set up ratios for corresponding sides, you will see they all evaluate to different numerical results. This means that the sides are not in a fixed ratio, which leads us to conclude the the shapes are not scalar multiples of each other. Two of those angles are congruent though!

Using the concept of proportions, the first rate does not form a proportion while the second rate form a proportion and the the cost of 9 pizza is $152.55

Proportion is a mathematical concept that refers to the relationship between two values or sets of values. It expresses the relative sizes of two or more quantities and can be represented as a fraction, decimal, or percentage.

6.

16 players for 24 teams

20 players for 32 teams

Let's find the ratio of player to team if they're consistent.

16 / 24 = 2/3 ≠ 20 / 32 = 5/8

The rates do not form a proportion.

7.

10 inches in 6 hours

80 inches in 2 days

10 / 6 = 5/3  = 80 / 48 = 5/3

The rates form a proportion.

8.

4 pizza = 67.80

9 pizza = x

Cross multiply both sides

4x = 67.80 * 9

4x = 610.2

x = 610.2 / 4

x = 152.55

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The height of the triangular prism will be 100mm.

The three-dimensional object has a base of triangular shape and has some height is called a triangular prism.

Given that the height and the base of the triangular shape of the triangular prism are 8 mm and 6.9 mm respectively. The volume of the prism is V = 2760 cubic mm.

The height of the triangular prism will be calculated as:-

Volume = 1/2 x b x h x H

2760 = 1/2 x 8 x 6.9 x H

H = 100 mm

Therefore, the height of the prism is 100mm.

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A total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.

Let the three-digit number be written as abc, where a, b, and c are the hundreds, tens, and ones digits, respectively. We want b to be the absolute value of half the difference between a and c. In other words, we want b = [tex]\left|\frac{a-c}{2}\right|.[/tex]

Since a, b, and c are digits, we know that [tex]0 \leq a, b, c \leq 9.[/tex] Since b is the absolute value of a number, we know that b is non-negative.

Case 1: [tex]a \geq c[/tex]

If [tex]a \geq c[/tex], then[tex]b = \frac{a-c}{2}[/tex]. Since b must be non-negative, we have two

subcases to consider:

Subcase 1: a=c

In this subcase, b=0, which means that the number abc is of the form a00, where [tex]0 \leq a \leq 9[/tex]. There are 10 such numbers.

Subcase 2: a>c

In this subcase, [tex]b = \frac{a-c}{2}[/tex] is a positive integer. Since a and c must have the same parity (i.e., they are either both even or both odd), we have two

sub-subcases to consider:

Sub-subcase 1: a and c are both even

In this sub-subcase, a and c are both integers between 0 and 8 inclusive (since they are even and cannot be equal to 0 or 9). There are 4 such pairs of values for a and c: (2,0), (4,2), (6,4), and (8,6). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.

Sub-subcase 2: a and c are both odd

In this sub-subcase, a and c are both integers between 1 and 9 inclusive (since they are odd and cannot be equal to 0 or 8). There are 4 such pairs of values for a and c: (9,7), (7,5) , (5,3), and (3,1). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.

Case 2: a < c

If a < c, then[tex]b = \frac{c-a}{2}[/tex]. Since b must be non-negative, we have only one

subcase to consider:

Subcase: c- a is even

In this subcase, c-a is an even integer between 2 and 8 inclusive (since it cannot be equal to 0 or 9). There are 4 such even integers: 2, 4, 6, and 8. For each even integer, the values of a and c that satisfy c-a are uniquely determined, and the value of b is then uniquely determined. So there are 4 corresponding numbers abc.

Putting everything together, we have a total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.

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The student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.

To find the minimum score the student needs on the fourth test, we can use the formula for the average of four numbers:

Average = (sum of the numbers) / 4

We know that the student needs an average of at least 80 to earn a grade of B, and we also have the scores for the first three tests: 77, 77.25, and 81.25. So, we can set up the equation:

80 = (77 + 77.25 + 81.25 + x) / 4

where x is the score the student needs on the fourth test. Solving for x:

80 = (235.5 + x) / 4

320 = 235.5 + x

x = 320 - 235.5

x = 84.5

So, the student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.

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The area of the composite figure is 294 cm square.

The figure above is a composite figure. The figure is formed by combining two trapeziums.

Therefore, the area of the figure is the sum of the whole area of the shape.

Hence,

area of the composite figure = area of the trapezium1 + area of the trapezium2.

area of the trapezium1 = 1  / 2 (a + b)h

hence,

area of the trapezium1 = 1 / 2 (12 + 25)6

area of the trapezium1 = 1 / 2 (37)6

area of the trapezium1 = 111 cm²

area of the trapezium2 = 1 / 2 (24 + 37)6

area of the trapezium2 = 3 × 61

area of the trapezium2 = 183 cm²

Therefore,

area of the composite figure = 111 + 183

area of the composite figure = 294 cm²

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The distance is a function of time and the slope of the distance time graph will give the speed

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the first quantity be represented as Distance D

Let the second quantity be represented as Time T

Now , the function is given as

The distance D is a function of time and the slope of the line between the x and y axis of the distance time graph will give us the speed

Substituting the values in the equation , we get

Let the y axis represent the distance D

And , let the x axis represent the time T

So , Slope m = y / x

On simplifying the equation , we get

Slope m = Distance / Time = Speed

Hence , the distance is a function of time

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Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

Let's call the number of hours Camden works babysitting "x".

We know that x + 9 (hours of lifeguarding) cannot be more than 14 and that his total earnings must be at least $180. So we can write two equations based on these conditions:

x + 9 ≤ 14 (hours worked can't exceed 14)

10x + 18 × 9 ≥ 180 (earnings must be at least $180)

Now we can substitute the first equation into the second:

10x + 18 × 9 ≥ 180

10x + 162 ≥ 180

10x ≥ 18

x ≥ 1.8

Since x has to be a whole number of hours, we round up to find that Camden must work at least 2 hours babysitting.

So, Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.

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