Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression. tan x(cot x - cos x)​

The value of (f o g)(3) using composite function is 35

Composite function refers to the combining of functions in a manner where the output from one function becomes the input for the next function.

To calculate the composite function (f o g)(3), we use the techniques below.

From the question,

Given:

Note that,

Step 1: Find g(3)

Therefore,

Step 2: To find f(g)(3), we subetitute the value of x in f(x) by 12

Hence, (f o g)(3) is 35

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Answer:

y = (-1/3)n + 42

Step-by-step explanation:

We can use the point-slope form of a linear equation to find the slope of the line:

slope = (y2 - y1) / (x2 - x1) = (30 - 32) / (36 - 30) = -1/3

Now we can use one of the points (30, 32) to find the y-intercept:

y = mx + b

32 = (-1/3)(30) + b

b = 42

So the linear relationship between the number of bean stalks and the yield is:

y = (-1/3)n + 42

The equation that demonstrates the distributive property is 36 + 8 = 4(9 + 2), the correct option is C.

The distributive property states that when a number or variable is being multiplied by a sum or difference inside parentheses, the number or variable can be distributed or multiplied to each term inside the parentheses.

The equation that demonstrates the distributive property is C: 36 + 8 = 4(9 + 2). We can verify this by using the distributive property as follows:

4(9 + 2) = 4(11) = 44

Therefore, the equation can be written as:

36 + 8 = 44

This equation is true, which confirms that the distributive property was correctly applied.

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The complete question is:

Which equation demonstrates the distributive property?

Responses

A (9 + 2)4 = 4(9 + 2)

B 36 + 8 = 4

C 36 + 8 = 4(9 + 2)

D 36 x 8 = 8 x 36

The answer of the given question based on graph is Part A: the unit rate of square feet painted per minute is 1.125, so the ordered pair that displays this unit rate is (1, 1.125) and Part B:  the points that lie on the line are (3.5,3.9375), (4,5), and (32,36).

Slope refers to the steepness of a line or a surface. More specifically, slope is defined as the ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two points on a line or a surface. In other words, slope measures how much a line or a surface rises or falls as it moves horizontally.

Since the relationship between the minutes worked and the square feet painted is proportional, we can use the slope-intercept form of a linear equation to represent it:

To find the equation of the line, we can use the given point (16,18) and the fact that the relationship is proportional. If we let the unit rate be r (in square feet per minute), then we have:

18 = r(16)

r = 18/16

r = 1.125

So the equation of the line is:

y = 1.125x

Part A: The unit rate of square feet painted per minute is 1.125, so the ordered pair that displays this unit rate is (1, 1.125), since the slope represents the unit rate in a proportional relationship.

Part B: To determine which of the points lie on the line, we can plug in the x-values into the equation y = 1.125x and see if the resulting y-values match.

(y - 18) / (x - 16) = slope

Using the slope calculated above, we can simplify this equation to:

y = 1.125(x - 16) + 18

Now, we can plug in the x and y values for each point and check if they satisfy this equation:

(2,2.5): 2.5 = 1.125(2 - 16) + 18, not on the line

(3.5,3.9375): 3.9375 = 1.125(3.5 - 16) + 18, on the line

(4,5): 5 = 1.125(4 - 16) + 18, on the line

(32,36): 36 = 1.125(32 - 16) + 18, on the line

(10,11.5): 11.5 = 1.125(10 - 16) + 18, not on the line

(0,0): 0 = 1.125(0 - 16) + 18, not on the line

Therefore, the points that lie on the line are (3.5,3.9375), (4,5), and (32,36).

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Answer 1452

Step-by-step explanation:

n(m n p n c) =n(m) + n(p) + n(c) - n(m n p) - n(m n c) - n(p n c) + n(m n p n c) = 960+ 780 + 572 - 300 - 340 - 260 + 130 = 1452

Answer:

5

Step-by-step explanation:

[tex]\sqrt{(7-2)^2+((-1)-(-1))^2\\[/tex]

subtract 2 from 7

[tex]\sqrt{5^2+((-1)-(-1))^2[/tex]

raise 5 to the power of 2

[tex]\sqrt{25+((-1)-(-1))^2[/tex]

Multiply -1 by -1

[tex]\sqrt{25+(-1+1)^2[/tex]

Add -1 and 1

[tex]\sqrt{25+0^2[/tex]

Add 25 and 0

[tex]\sqrt{25[/tex]

rewrite 25 as 5^2

[tex]\sqrt{5^{2}[/tex]

pull term out from under the radical assuming positive real numbers.

5

Answer:

The slope is [tex]\frac{-1}{3}[/tex]

Step-by-step explanation:

From the two points (0,-1) (3,0). The y values are 0 and -1. The x values are 3 and 0.  The slope is the change in y over the change in x.  You find the change by subtracting.

[tex]\frac{0-1}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex]

Helping in  the name of Jesus.

The conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is 0.6 or 60%.

What is Probability ?

Probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty and provide a basis for making informed decisions in various fields such as science, engineering, economics, and finance.

To find the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, we need to use the formula for conditional probability:

P(A | B) = P(A and B) / P(B)

where A is the event that the contestant played an acoustic guitar, and B is the event that the contestant wore leather pants.

We are not given the total number of contestants in the competition, but we can use the information provided in the table to calculate the probabilities of A and B, as well as the joint probability of A and B.

Let's first calculate the probability of B:

P(B) = number of contestants wearing leather pants / total number of contestants

P(B) = 15 / 45

P(B) = 1/3

Now, let's calculate the joint probability of A and B, i.e., the probability that a randomly selected contestant played an acoustic guitar and wore leather pants:

P(A and B) = number of contestants who played acoustic guitar and wore leather pants / total number of contestants

P(A and B) = 6 / 45

Finally, we can use the formula for conditional probability to find the probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants:

P(A | B) = P(A and B) / P(B)

P(A | B) = (6 / 45) / (1/3)

P(A | B) = 0.6

Therefore, the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants, is 0.6 or 60%.

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The value of j is equal to 9√3 meters.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).

Note: j is the side opposite to the 60° angle.

The side opposite to the 60° angle, j = 9 × √3

The side opposite to the 60° angle, c = 9√3 meters.

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Answer:

Step-by-step explanation:

16

lbozo

Answer:

In-text citations are the short citations you include in the written text that help a reader to understand which sources you are quoting or referring to in your writing example(Field, 2022). Reference is the full details of the source you have cited in your writing.

Answer:

C) neither. Both events are equally likely.

Step-by-step explanation:

Answer: This issue can be resolved by employing trigonometry. Let's say that the surveyor is standing at point A, and the landmark on the other side of the pond is at point B. We can also make the assumption that the distance between points A and B is the width of the pond we need to find. Now, let's draw a line from point A to point B to represent the pond's width. Let's call this distance x. The surveyor's distance from the pond can also be represented by drawing a line 50 feet away from point A to point C.

The tangent of an angle is the opposite side (in this case, x) divided by the adjacent side (in this case, 50 feet), so we can now use the tangent function to determine x. We now have:

Rearranging this equation allows us to solve for x: tan(theta) = x/50, where theta is the angle between the lines from point A to point B and point A to point C.

We do not know the value of theta, but we are aware that the surveyor measured the angle to the landmark. x = 50*tan(theta) We should expect that the assessor estimated the point in degrees. Then, we can multiply the angle's tangent by 50 to get x using a calculator. For instance, if the surveyor measured an angle of 30 degrees, we would have:

The pond's width is therefore approximately 28.85 feet, rounded to the nearest foot, as x = 50tan(30) = 500.577. The response isn't given in the decisions, yet it is nearest to 29 feet

Step-by-step explanation:

Data: John's current pay is $78,000. Annual salary increase rate: 5% Maximum 401k contribution: 15% of pre-tax gross yearly salary Every year, John intends to pay 10% of his current earnings to his 401k.

Annual compounded return on 401k investments is expected to be 8%.

$10,000 wedding money target in 12 months

Short-term CD interest rate: 2%

Goal for house down payment: $40,000 in 5 years

Annual expected return on housing fund investments: 4%

At the age of 60, your 401k balance is $1,000,000.

85 years is the average life expectancy.

0.5% (6%/12) monthly rate of return on retirement investments

To figure out John's 401k balance at age 60, do the following:

Compute John's annual contribution to his 401k: $78,000 x 10% = $7,800

Employ the financial calculator's future value (FV) function:

N (number) = 30  (number of years until retirement)

I/Y = 8% (annual rate of return)

PMT = -$7,800 (negative because it’s a cash outflow)

PV = 0 (no initial balance)

FV = $?

FV = $1,057,323.95

Therefore, John would have saved approximately $1,057,323.95 at age 60.

a) To achieve an age 60 balance of one million dollars:

Use the present value (PV) function on the financial calculator:

N = 30 (number of years until retirement)

I/Y = 8% (annual rate of return)

PMT = -$? (negative because it’s a cash outflow)

PV = 0 (no initial balance)

FV = $1,000,000

PMT = -$9,308.79

Therefore, John would have to save approximately $9,308.79 every year to achieve an age 60 balance of one million dollars.

b) To find the percentage of his current salary that the annual savings amount represents: Divide the annual savings amount by John’s current salary: $9,308.79 / $78,000 = 0.1194

Multiply by 100 to get the percentage: 0.1194 x 100 = 11.94%

Therefore, the annual savings amount represents approximately 11.94% of John’s current salary.

To calculate how much John will have to contribute to the wedding fund every month for the next 12 months:

Use the present value (PV) function on the financial calculator:

N = 12 (number of monthly deposits)

I/Y = 2%/12 = 0.1667% (monthly rate of return)

PMT = -$? (negative because it’s a cash outflow)

PV = 0 (no initial balance)

FV = $10,000

PMT = -$821.47 As a result, John will have to contribute $821.47 to the wedding fund each month for the following 12 months.

To determine how much John must save each month for the next 60 months in order to acquire $40,000:

Employ the financial calculator's future value (FV) function:

N = 60 (number of months) (number of months)

I/Y = 4%/12 = 0.3333% (monthly interest rate)

PMT = -$? (negative since it represents a monetary outflow)

PV = 0 (no starting balance) (no initial balance)

FV = $40,000

PMT = -$603.94

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Answer:

1. Differentiated Instruction: This intervention involves tailoring lessons and activities to meet the individual learning needs and preferences of students. For example, a teacher can design various instructional materials for students with different skill levels to ensure they engage in the lesson and learn effectively.

2. Explicit Instruction: This intervention involves breaking down a complex process or concept into smaller, more manageable parts, and explaining each part clearly and explicitly. The teacher provides ample opportunities for students to practice and apply what they have learned.

3. Formative Assessment: This intervention involves using ongoing, informal assessments to monitor students' progress and provide feedback to both students and teachers to make necessary adjustments. Teachers can use formative assessments to identify areas of difficulty and intervene early.

4. Collaborative Learning: This intervention involves encouraging students to work together in pairs or small groups to complete tasks or solve problems. Within these groups, students share ideas, clarify misunderstandings, and learn from each other.

Differentiated Instruction, Small Group Instruction, Formative Assessment, Peer Tutoring, Real-World Connections and Positive Feedback are the strategies to assist the child.

Teaching can be defined as engagement with learners to enable their understanding and application of knowledge, concepts and processes

Differentiated Instruction, Small Group Instruction, Formative Assessment, Peer Tutoring, Real-World Connections and Positive Feedback:

These strategies are effective because they are research-based and have been shown to support students' learning in mathematics.

By catering to the specific needs of students, providing individualized support, and making connections to the real world, students are more likely to engage in mathematics, understand mathematical concepts, and develop positive attitudes towards mathematics.

Hence, Differentiated Instruction, Small Group Instruction, Formative Assessment, Peer Tutoring, Real-World Connections and Positive Feedback are the strategies to assist the child.

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If the median of the given data is 19, the value of P is 6.

In statistics, the median is a measure of central tendency that represents the middle value of a data set when it is arranged in numerical order. It is the value that separates the upper half of the data set from the lower half. To find the median of a set of data, the data must first be arranged in order from lowest to highest (or highest to lowest). If there is an odd number of data points, the median is simply the middle value.

Here,

To find the value of P, we first need to find the median class interval. We know that the median is 19, which means that half the data is above 19 and half the data is below 19. We can calculate the cumulative frequency of the data by adding up the frequencies of each class interval.

Age  f cf

12-18 10 10

18-24 P 10+P

24-30 4 14+P

30-36 6 20+P

36-42 3 23+P

The total frequency is 23 + P. The median class interval is the interval that contains the 12th value (since we have 23 + P total values). To find the median class interval, we need to find the cumulative frequency that is closest to, but not less than, 12. In this case, the cumulative frequency that is closest to 12 is 10, which corresponds to the first class interval (12-18). Therefore, the median class interval is 12-18. We can use the following formula to find the value of P:

Median = L + (n/2 - F) * w

where L is the lower limit of the median class interval, n is the total frequency, F is the cumulative frequency up to the median class interval, and w is the width of the class interval.

For the median class interval of 12-18:

L = 12

n = 23 + P

F = 10

w = 6

Substituting these values into the formula, we get:

19 = 12 + ((23+P)/2 - 10) * 6

Simplifying the equation:

7 = ((23+P)/2 - 10)

14 = 23+P - 20

P = 6

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Answer:

Step-by-step explanation:

5 + x (where x represents the number)

x / (-2)

2x

x - 7

12x

x - 3

$15h (where h represents the number of hours worked)

C - $5 (where C represents the cost of the ticket)

x + 24

50 / n (where n represents the number of students)

(2/5)x

(1/2)x - 19

-4x - 11

8x + 5

x^2 - 14

(3/4)x + 17

----------------------------------

Five added to a number

The result of dividing a number by -2

Two times a number

A number decreased by 7

The result of multiplying a number by 12

A number decreased by 3

Earning $15 per hour

The cost of the ticket minus $5

The sum of a number and 24

Dividing 50 markers among several students

Two-fifths times a number

Half of a number minus 19

The result of subtracting 11 from the product of a number and -4

The sum of eight times a number and five

The difference between the square of a number and 14

Three-fourths times a number plus 17

The potato hits the ground approximately 0.302 seconds after it has been launched.

It is possible to solve quadratic equations of the type ax2 + bx + c = 0 using the quadratic formula, where a, b, and c are constants and x is the variable. The equation is:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, we can use it to find the time when the potato hits the ground by setting h(t) = 0 and solving for t.

h(t) = -16[tex]t^2[/tex] + 50t + 64 = 0

Using the quadratic formula, we have:

t = (-b ± √(b² - 4ac)) / 2a

where a = -16, b = 50, and c = 64.

Plugging these values into the formula, we get:

t = (-50 ± √(50² - 4(-16)(64))) / 2(-16)

t = (-50 ± √(2500 + 4096)) / (-32)

t = (-50 ± √(6596)) / (-32)

We can simplify the square root:

t = (-50 ± 2√(1649)) / (-32)

We can also simplify the expression by dividing both the numerator and denominator by 2:

t = (25 ± √(1649)) / 16

So the time when the potato hits the ground is approximately:

t ≈ 0.302 seconds or t ≈ 2.095 seconds (rounded to three decimal places)

Note that we have two possible solutions because the quadratic equation has two roots. However, we can discard the negative value since time cannot be negative in this context.

Therefore, the potato hits the ground approximately 0.302 seconds after it has been launched.

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Answer: Let's assume that the width of the rectangular room is "x" meters. Then, according to the problem, the length of the room is 2 times the width, which means the length is "2x" meters.

The perimeter of the room is the sum of all four sides, so we can write:

Perimeter = 2 × (length + width)

Substituting the values, we get:

48 = 2 × (2x + x)

Simplifying the expression, we get:

48 = 2 × 3x

Dividing both sides by 2, we get:

24 = 3x

Solving for "x", we get:

x = 8

Therefore, the width of the room is 8 meters and the length is 2 times the width, which is 2 × 8 = 16 meters.

So the dimensions of the room are 8 meters by 16 meters.

Step-by-step explanation:

The area of a rectangle is given by the formula:

Area = length x width

In this case, the length of the park is x + 5 and the width is x - 2. So, we can substitute these expressions into the formula to get:

Area = (x + 5) x (x - 2)

Expanding the product, we get:

Area = x^2 + 5x - 2x - 10

Simplifying, we have:

Area = x^2 + 3x - 10

Therefore, the area of the rectangular park is given by the expression x^2 + 3x - 10.

Answer:

[tex]\frac{12}{35}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5}[/tex] x [tex]\frac{6}{7}[/tex] = [tex]\frac{12}{35}[/tex]

[tex]\frac{12}{35}[/tex] is already in simplest form, so the answer is [tex]\frac{12}{35}[/tex]

Answer:

x = 4 is a straight, vertical line at 4 on the x axis.

The z-score for an age of 30 years is 0.43.

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level.

To convert an age to a z-score, we use the formula:

z = (x - μ) / σ

where:

x = the age we want to convert to a z-score

μ = the mean age

σ = the standard deviation of the ages

For example, if we want to convert an age of 30 years to a z-score using the given information with μ = 28.5 and σ = 3.5, we have:

z = (30 - 28.5) / 3.5

z = 0.43

So the z-score for an age of 30 years is 0.43.

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Complete question:

The equation that represents the represents the rational function in the graph, based on the asymptotes and the intercepts is; y = ((3/4)·x - 3)/(x + 3)

An asymptote is a line that approaches a curve but at any infinite distance, is still at some distance from the curve.

The asymptotes of the functions are;

Horizontal asymptote;  x = -3

Vertical asymptote; y = 1

The points on the graph are;

y-intercept = (0, -1)

x-intercept = (4, 0)

The function is a rational function of the form f(x) = P(x)/Q(x)

The horizontal asymptote of x = -3 indicates that the denominator has a factor of (x + 3)

The vertical asymptote of y = 1 indicates that the degree of the numerator and the denominator are the same and the leading coefficients are the same

The function is therefore in the form; f(x) = (a·x + c)/(x + 3)

a = 1, therefore;

f(x) = (x + c)/(x + 3)

The y-intercept (0, -1) indicates that when x = 0, y = -1, therefore;

-1 = (0 + c)/(0 + 3)

-3 = c

c = -3

The function is therefore;

f(x) = y = (a·x - 3)/(x + 3)

The x-intercept (4, 0), indicates that when y = 0, x = 4, therefore;

0 = (a·4 - 3)/(4 + 3)

a·4 - 3 = 0

a = 3/4 = 0.75

The function is therefore;

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Answer:

The answer is D. 65

Step-by-step explanation:

The first step is to substitute n as 4 and k as 13. This results in the fraction

[tex]\frac{4}{20}[/tex]= [tex]\frac{13}{x}[/tex].  Since there is an equal sign, this indicates you can cross multiply. That means that you would multiply the 4 with the x and the 20 with the 13. This results in the next step, which is 4x=20(13) ---> 4x=260. Finally, to find the value of x, divide the 4 from the x to isolate it. The reasoning behind this is that you have to do the inverse operation, meaning since 4 is being multiplied by x, the inverse of this is dividing by 4 to get x by itself. Also, whatever you do on one side of the equal sign, you have to do it on the other. Therefore, [tex]\frac{4x}{4}= \frac{260}{4}[/tex] ; x=65.

The random variable x can take on the values of 0, 1, 2, or 3, representing the number of defective items in the sample of 3 items.

The random variable x represents the number of defective items in a sample of 3 items selected at random from the box.

Since there are 3 defective items out of 12 total items, the probability of selecting a defective item on the first draw is 3/12 or 1/4.

After the first draw, there are only 11 items remaining in the box, of which 2 are defective. Therefore, the probability of selecting a defective item on the second draw, given that the first draw was also defective, is 2/11.

Similarly, the probability of selecting a defective item on the third draw, given that the first two draws were also defective, is 1/10.

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Answer:

mp = 37500

Step-by-step explanation:

let mp be x

D.A = 20×x/100

= 20x/100

=x/5

price after discount = mp - DA

= x-x/5 = 4x/5

VAT= 15%of 4x/5

= 15/100 × 4x/5

= 60x/500

sp with vat= 4x/5 +60x/500

= 460x/500

sp with vat - sp after discount = 4500

460x/500-4x/5=4500

60x= 4500×500

x= 37500

Hello!

Lets consider what the question asks for:

 --> graphs of either line intersecting/parallel/identical

 --> # of solutions the system has

The information given:

  6x + y = 25

  x + 3y = 3

Let's solve the FIRST problem

  --> graphs of either line intersecting/parallel/identical

             --> let's put both equations into slope-intercept form, where we

                   isolate the y-variable all by itself to one side

                               [tex]6x+3y=25\\3y=-6x+25\\\\y=-2x+\dfrac{25}{3}[/tex]

                                [tex]x+3y=3\\3y=-x+3\\y=-\dfrac{1}{3}x+1[/tex]

             --> both equations AREN'T parallel as the slope (coefficient of x-

                   variable) aren't equal

             --> both equations AREN'T identical as they don't look the same

              --> both equations ARE INTERSECTING as they have different

                   slopes and aren't identical

Let's solve our second question:

   --> how many solutions does the system have:

       --> both lines intersect

           -->both lines are linear as the highest power that the x-variable

                has are 1

                 --> thus there is only ONE SOLUTION

Answer:

 Intersecting

 Has ONE SOLUTION