The expression 3x-(4-x) is equivalent to 4x-4
The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.
To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:
3x - (4 - x) = 3x - 4 + x
Now we can combine the like terms (3x and x) to get:
3x - 4 + x = 4x - 4
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The given question is incomplete, the complete question is:
Which expression is equivalent to 3x-(4-x)?
At a science exhibition, students learnt that it takes 5 hours for a block of ice to melt at 32° C.
Determine the time taken to melt a similar-sized block of ice at 20° C.
Evaluate f(x)=1/2x-3 for each value of x. Show your work. (a)f(-8)
(b)f(0)
(c)f(3)
(d)f(10)
Answer:
To evaluate f(x)=1/2x-3 for each value of x, we substitute each value into the function and simplify:
(a) f(-8) = (1/2)(-8) - 3 = -4 - 3 = -7
(b) f(0) = (1/2)(0) - 3 = 0 - 3 = -3
(c) f(3) = (1/2)(3) - 3 = 1.5 - 3 = -1.5
(d) f(10) = (1/2)(10) - 3 = 5 - 3 = 2
Therefore, the values of the function for each value of x are:
(a) f(-8) = -7
(b) f(0) = -3
(c) f(3) = -1.5
(d) f(10) = 2
there are 17 students in a kindergarten class. if each kindergartner can have only one task, in how many ways can the teacher assign out the following tasks: line leader, wipe down the tables, pass out papers?
As per the combination method, there are 4,080 ways for the teacher to assign the tasks of line leader, table wiper, and paper passer to three different students in the class of 17 kindergartners.
To start, let's count the number of ways to choose one student to be the line leader. There are 17 students to choose from, so there are 17 possible choices.
Next, let's count the number of ways to choose one student to wipe down the tables.
Finally, let's count the number of ways to choose one student to pass out papers. We've already chosen two students for the other tasks, so there are only 15 students left to choose from. Thus, there are 15 possible choices for the paper passer.
To find the total number of ways to assign the tasks, we need to multiply the number of choices for each task. So the total number of ways to assign the tasks is:
17 x 16 x 15 = 4,080
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As per the combination method, there are 4,080 ways for the teacher to assign the tasks of line leader, table wiper, and paper passer to three different students in the class of 17 kindergartners.
To start, let's count the number of ways to choose one student to be the line leader. There are 17 students to choose from, so there are 17 possible choices.
Next, let's count the number of ways to choose one student to wipe down the tables.
Finally, let's count the number of ways to choose one student to pass out papers. We've already chosen two students for the other tasks, so there are only 15 students left to choose from. Thus, there are 15 possible choices for the paper passer.
To find the total number of ways to assign the tasks, we need to multiply the number of choices for each task. So the total number of ways to assign the tasks is:
17 x 16 x 15 = 4,080
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PLEASE ANSWER ASAP!!
The graph that would have x - intercepts if the functions are graphed on the xy- coordinate plane, is C) y = 3 sec x.
How to find the graph with x - intercepts ?An x-intercept is a point where the graph intersects the x-axis, which means the value of y is 0 at that point.
We can analyze the functions randomly.
y = csc x + 3
The cosecant function is the reciprocal of the sine function, so csc x = 1 / sin x. For this function to have x-intercepts, we need 1 / sin x + 3 = 0. However, this equation cannot be satisfied since the minimum value of 1 / sin x + 3 is greater than 0. Therefore, there are no x-intercepts for this graph.
y = 3 sec x
The secant function is the reciprocal of the cosine function, so sec x = 1 / cos x. For this function to have x-intercepts, we need 3(1 / cos x) = 0. This equation can be satisfied when cos x = 0, which occurs at x = (2n + 1)π/2, where n is an integer. Therefore, this graph has x-intercepts.
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assume that the heights of women in a population follow a normal distribution with a mean of 64.3 and a standard deviation of 2.6. (a) a woman is chosen at random from this population. what is the probability that she is more than 67 inches tall? g
The probability that a woman chosen at random from this population is more than 67 inches tall is approximately 0.1492 or 14.92%.
To find the probability that a woman chosen at random from this population is more than 67 inches tall, we need to calculate the z-score for this height and then find the corresponding probability from the standard normal distribution.
The z-score is calculated as:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation.
In this case, x = 67, μ = 64.3, and σ = 2.6. Substituting these values into the formula, we get:
z = (67 - 64.3) / 2.6
= 1.04
Next, we look up the probability corresponding to a z-score of 1.04 in a standard normal distribution table or using a calculator. The probability of a z-score being less than 1.04 is 0.8508.
Since we are interested in the probability of a woman being more than 67 inches tall, we need to subtract this probability from 1:
P(x > 67) = 1 - P(z < 1.04)
= 1 - 0.8508
≈ 0.1492
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A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Which of the following is the best interpretation of the interval? Five percent of the time, the time for response is less than 2.8 minutes or greater than 12.3 minutes. B The probability is 0.95 that a randomly selected time for response will be between 28 minutes and 12.3 minutes Ninety-five percent of the time the mean time for response is between 2.8 minutes and 12.3 minutes. (D) We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes We are 95% confident that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.
The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct
A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.
Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The statement "The graph cοntains the pοint (0, 0)" is true.
What is a Quadratic Functiοn?Quadratic functiοns are used in different fields οf engineering and science tο οbtain values οf different parameters. Graphically, they are represented by a parabοla.
The statements that are true abοut the functiοn and its graph are:
1.The graph οf the functiοn is a parabοla.
2.The graph οf the functiοn οpens dοwn.
3.The graph cοntains the pοint (0, 0).
The functiοn [tex]f(x) = x^2 - 5x + 12[/tex] is a quadratic functiοn, which means its graph is a parabοla. The leading cοefficient οf the functiοn is pοsitive, which means the parabοla οpens dοwn.
Tο find the value οf f(-10), we can substitute -10 fοr x in the functiοn and evaluate:
[tex]f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162[/tex]
Therefοre, the statement "The value οf f(–10) = 82" is false.
The pοint (20, -8) is nοt οn the graph οf the functiοn, because if we substitute x = 20 in the functiοn, we get:
[tex]f(20) = 20^2 - 5(20) + 12 = 200 - 100 + 12 = 112[/tex]
Therefοre, the statement "The graph cοntains the pοint (20, –8)" is false.
On the οther hand, the pοint (0, 0) is οn the graph οf the functiοn, because if we substitute x = 0 in the functiοn, we get:
[tex]f(0) = 0^2 - 5(0) + 12 = 12[/tex]
Therefοre, the statement "The graph cοntains the pοint (0, 0)" is true.
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the perimeter of an isosceles triangle is 56 in. the ratio of the sides is 5:4. find the lengths of the sides and the base of the triangle
The perimeter of an isosceles triangle is the sum of the length of the sides. In this case, the perimeter is 56 inches. The ratio of the sides is [tex]5:4.[/tex]
To calculate the lengths of the sides and base, we need to first calculate the lengths of the two equal sides. To do this, divide the perimeter (56 inches) by the sum of the ratio (5 + 4) which is 9. This gives us a result of 6.2 inches for the two equal sides.
To calculate the length of the base, multiply the two equal sides by the ratio of 5:4, which gives us a result of 7.5 inches for the base.
Therefore, the lengths of the sides and the base of the triangle are: two equal sides of 6.2 inches, and a base of 7.5 inches.
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The bases of the prism below are right triangles. If the prism's height measures 11 units and its volume is 130.9 units 3 3 , solve for x x.
The value of x is equal to 4.8 units.
How to calculate the volume of a triangular prism?In Mathematics and Geometry, the volume of a triangular prism can be determined or calculated by using the following formula:
Volume = base area × height of the prism.
Assuming the variable x represent the length of one side of its base. Since the height of this triangular prism measures 11 units and its volume measures 130.9 cubic units, the value of x can be determined as follows;
Base area of triangle = 1/2 × x × 5
Base area of triangle = 5x/2 square units.
Volume of triangular prism = base area × height of the prism.
130.9 = 5x/2 × 11
130.9/11 = 5x/2
11.9 = 5x/2
5x = 23.8
x = 4.8 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
philp made tables of values to solve a system of equations first he found that the x-value of the solution was between 0 and 1 then he found that it was between 0.5 and 11 next time he made this table apex btw
The ordered pair is the best approximation of the exact solution is (0.6, 1.9). The correct option is c.
What is a system of equations?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
y = -2x + 3
y = 5x - 1
Equate the right sides of both equations:
-2x + 3 = 5x - 1,
-2x - 5x = -1 -3,
x = 4/7
then
y = -2 x 4/7 + 3 = 8/7 + 3 = 3x7-8 /7 = 13/7 = 1 x 5/7
4/7 = 0.6 and 1 x 5/7 is equal to the ordered pair (0.6, 1.9).
Therefore, the correct option is c, (0.6, 1.9).
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The question is incomplete. The full question is given below:
Which ordered pair is the best approximation of the exact solution?
if 2 chickens can lay 3 eggs in eight days how many days can 5 chickens lay in 6 days?|continental math league ml
Answer:
8
Step-by-step explanation:
2=3
3÷2=1.5
1.5×5=7.5
round up to get 8
the equation y equals 20 times 3 to the power of t shows the number of infected people from an outbreak of whooping cough. the variable y represents the number of infected people, and t represents time in weeks. in how many weeks will the number of infected people reach 1,000?
An exponential equation, y = (20) 3ᵗ, shows the number of infected people from an outbreak of whooping cough. The number of Infected people reach 1000 after 3.56 weeks.
We have an equation that shows the number of people infected from a whooping cough outbreak. This equation is y is equal to 20 times 3 to the power of t, i.e. y = (20) 3ᵗ -- (1)
where y--> number of infected people
t--> time in weeks
An exponential equation is an equation with exponents where either the exponent or part of the exponent is a variable. As we see 't' is variable so, eqution (1) is an exponential equation. We have to determine time in weeks when the number of infected people count reach 1,000. Substitute, y = 1000 in (1)
=> 1000 = (20)3ᵗ
Dividing by 20 both sides
=> 1000/20 = 3ᵗ
=> 50 = 3ᵗ
Taking natural logarithm both sides,
=> ln(50) = ln( 3ᵗ)
=> ln(50) = t ln(3)
=> t = ln(50)/ln(3)
=> t = 3.56
Hence, required value of t is 3.56 weeks.
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In a chemistry lab there are 9. 52 g of powdered substance in a container max needs to place an equal amount of the powdered substance into each of three glass plates the amount of powdered substance he places into each glass glass plate is 1. 98 g
No, the given statement about the lab experiment is not reasonable.
If Max places 1.98 grams of powdered substance into each glass plate and he needs to place the substance into 3 glass plates, then the total amount of the powdered substance he needs is 1.98 x 3 = 5.94 grams. This is greater than the amount Max estimates to be in the container (4.5 grams).
Therefore, it is not reasonable to assume that there are only 4.5 grams of the powdered substance in the container when Max needs to use more than that amount for his experiment.
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Complete Question:
In chemistry lab, there are 9.52 grams of powdered substance in a container. Max needs to place substance into each of 3 glass plates. The amount of powdered substance he places into each glass plate is 1.98 grams. Max estimates that there are 4.5 grams of the powdered substance in the container. Is the statement reasonable?
maple has 4 identical loaves of bread that weigh a total of 6.6 pounds how much does 1 loaf of bread weigh ;show your work:
Answer:
1.45 pounds
Step-by-step explanation:
6.6 divided by 4
Camile walked 1/2 of a mile from school to Tom's house and 2/5 of a mile from Tom's house to her own house how many miles did Camile walk in all
Answer: 0.9 or 9/10
Step-by-step explanation:
The question asks how many miles did Camila walk in all, so we have to add 1/2 mile and 2/5 of a mile.
1/2 + 2/5 = 9/10
Answer:
9/10 of a mile
Step-by-step explanation:
1/2 + 2/5
= 5/10 + 4/10
=9/10
What is an equation of the line that passes through the point (6,6)(6,6) and is parallel to the line 3x-2y=43x−2y=4?
The equation of the line that passes through (6,6) and is parallel to 3x - 2y = 4 is y = (3/2)x - 3.
What is an equation of the line parallel to the given line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
To find the equation of the line passing through (6,6) that is parallel to 3x - 2y = 4.
We need to find the slope of the given line first.
3x - 2y = 4
-2y = -3x + 4
y = (3/2)x - 2
The slope of the given line is 3/2.
Since the line we want to find is parallel to this line, it will have the same slope.
Therefore, we can use the point-slope form of the equation of a line to write the equation:
y - y1 = m( x - x1 )
Plug in m = 3/2 and (x1,y1) : (6,6)
y - 6 = (3/2)(x - 6)
Simplifying:
y - 6 = (3/2)x - 9
y = (3/2)x - 3
Therefore, the equation of the parallel line is y = (3/2)x - 3.
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in the picture .............................................................................................................................................
The graph showing one cycle of the trigonometric function y = 8 cos 8x is plotted and attached
What is trigonometric graph?Trigonometric graphs are graphical representations of trigonometric functions, which are functions that relate the angles of a right triangle to the ratios of its sides. The three most commonly used trigonometric functions are
sine, cosine, and tangent.The graphs of these functions are periodic, meaning they repeat themselves over a regular interval.
In the problem, the graph plotted is that of cosine function and the amplitude of is 8
The 5 points marked are
(-π/16, 0) - the first point
(0, 8) - showing the amplitude and 1/4 cycle
(π/16, 0) - 1/2 cycle
(-π/16, -8) - 3/4 cycle
(3π/16, 0) - one complete cycle
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State the coordinates of the point.
Answer:
Step-by-step explanation:
look get 8 then 7 then you get 5 and luh tyler.
Kathy is adding a new slide to her swing set. The slide is 5 feet long, and the ladder is 4 feet high. How
many feet away is the base of the ladder from the end of the slide, g, as shown below?
5 ft
g
4ft
The number of feet away is the base of the ladder from the end of the slide, g, as shown is 3 ft.
How many feet away is the base of the ladder from the end of the slide?The base of the ladder from the end of the slide forms a right triangle.
Hypotenuse² = opposite² + adjacent²
Hypotenuse = 5 ft
Opposite = 4 ft
Adjacent = g
So,
Hypotenuse² = opposite² + adjacent²
5² = 4² + g²
25 = 16 + g²
subtract 16 from both sides
25 - 16 = g²
9 = g²
find the square root of both sides
√9 = g
g = 3 ft
In conclusion, the base of the ladder is 3 ft away from the end of the slide.
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I've been waiting to order your cupcakes all day!
I'll have 4 Nom-Nom-Nom cupcakes -- that's
80% of my order. The rest of the order are Wow.
Using fraction, the total number of cupcakes is obtained to be 5.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.
Specifically, if x is the total number of cupcakes, then we can write -
4/x = 80/100
where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.
Solving for x, we get -
x = 4 / (80/100) = 5
So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.
Therefore, in total there are 5 cupcakes.
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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.
20 POINTS NEED HELP DUE TODAY HELP!!!!!!
2. Is the point (-0.5, sin(4π/3)) on the unit circle? Explain your reasoning.
3. Is the point (-0.5, sin(5π/6)) on the unit circle? Explain your reasoning.
4. Suppose that sin(Θ) = -0.5 and that Θ is in quadrant 4. What is the exact value of cos(Θ)? Explain your reasoning.
1) The point is on the unit circle.
2) The point is not on the unit circle
3) cos(Θ) = 0.866
Is the point on the unit circle?We know that all the points on the unit circle have a magnitude of 1, then we can write:
√[ (-0.5)² + (sin(4π/3)²) = 1
This means that the point is on the unit circle.
b) Now the point is (-0.5, sin(5π/6))
We need to do the same thing, this time we will get:
√[ (-0.5)² + (sin(5π/6)²) = 0.71
So this point is not on the number line.
c) Here we know that sin(Θ) = -0.5 and the angle is in the quadrant 4.
Then Θ = Asin(-0.5) = -30°
Remember that -30° is on the fourth quadrant, so this is correct, now the cosine of that is:
cos(-30°) = 0.866
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Can anyone help me with this?
The quadrilateral given is a square and the measure of the angles as required are as follows;
m<EFG = 90°.m<GDH = 45°.m<FEG = 45°.m<DHG = 90°.What are the measures of the missing angles as required?It follows from the task content that the given quadrilateral is a square.
Recall, that the four interior angles of a square sum up to 360° in which case, each vertices is a right angle.
Additionally, the diagonals of a square intersect at a point to form right angle at the point.
Also, each diagonals is a bisector of the angles at the vertices.
Therefore, we have that;
m<EFG = right angle = 90°.m<GDH = right angle = 90°.m<FEG = right angle = 90°.m<DHG = right angle = 90°.Read more on interior angles of a square;
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Identify the asymptotes, domain, and range of each function.
The function f(x) = 5/(x+3), vertical asymptote at x = -3, domain of the function is all real numbers except x = -3, range is all real numbers except 0.
Describe Function?A function is a mathematical object that takes one or more inputs (usually represented as variables) and produces a single output. In other words, a function is a relation between sets of inputs and outputs that associates each input value with exactly one output value.
A function can be represented by an equation or a graph. The most common way to write a function is in the form f(x) = y, where x is the input variable and y is the output variable. The function f maps each value of x to a corresponding value of y.
Functions can be classified based on their properties, such as their domain (set of allowable input values), range (set of output values), and behavior (e.g., increasing, decreasing, constant, etc.). Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions.
The function f(x) = 5/(x+3) has a vertical asymptote at x = -3, since the denominator becomes zero at that point.
The domain of the function is all real numbers except x = -3, since division by zero is undefined.
To find the range, we can consider what happens to the function as x approaches -3 from both sides. As x approaches -3 from the left (i.e., as x gets closer and closer to -3 from values less than -3), the function becomes increasingly negative. As x approaches -3 from the right (i.e., as x gets closer and closer to -3 from values greater than -3), the function becomes increasingly positive. This means that the range of the function is all real numbers except 0.
Therefore, the asymptote is x = -3, the domain is all real numbers except x = -3, and the range is all real numbers except 0.
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Rewrite the following equation in slope-intercept form. 16x − 5y = 16
Write your answer using integers, proper fractions, and improper fractions in simplest form
Slope intercept form of the given equation is y=16/5x-16/5
What is a line's Slope Intercept Form?The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. where, m and c are real integers in the slope-intercept form of the linear equation.
The slope, m, refers measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, the y-coordinate of the location where the line's graph crosses the y-axis.
Given equation16x-5y=16
Writing equation in slope intercept form
16-5y=16
-5y=16-16x
y=16/-5 +16/5x
y=16/5x-16/5.
hence, Slope intercept form of the given equation is y=16/5x-16/5
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a normal population with unknown variance has a mean of 20. is one likely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1? if not, what conclusion would you draw?
We can conclude that it is unlikely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1 because the sample mean of 24 is different from the population mean of 20.
To answer this question, we can use a t-test to determine if the sample mean of 24 is significantly different from the population mean of 20.
The t-test formula is:
t = (x' - μ) / (s / √(n))
Where x' is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the values given in the question, we get:
t = (24 - 20) / (4.1 / √(9)) = 2.93
To determine if this t-value is significant, we need to compare it to the critical t-value for a two-tailed test with 8 degrees of freedom (n-1). Using a t-table or calculator, we find the critical t-value to be approximately 2.31 at a 5% significance level.
Since our calculated t-value of 2.93 is greater than the critical t-value of 2.31, we can reject the null hypothesis that the sample mean is equal to the population mean.
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The expression the quantity cosecant squared of theta minus 1 end quantity over cotangent of theta simplifies to which of the following?
The quantity cosecant squared of theta minus 1 can be simplified as 1/(cosecθ)² - 1. So, the correct answer is -1/tanθ.
What is cosecant?Cosecant, denoted as csc, is a trigonometric function that is the reciprocal of the sine function. It is the ratio of the side opposite the angle over the hypotenuse in a right triangle.
This can be further simplified by multiplying the numerator and denominator of the fraction by the cosecant of theta to get the expression 1 - cosec²θ/cosecθ.
Rearranging this expression gives -cosec²θ/cosecθ.
The cosecant of theta can be further simplified by using the identity cosecθ = 1/sinθ.
Substituting this into the expression gives -1/sin2θ.
The sine of theta can then be further simplified by using the identity
sinθ = 1/tanθ.
Substituting this into the expression gives -1/tan²θ.
Finally, using the identity tan²θ = tanθ/1 simplifies the expression to -1/tanθ.
Therefore, the correct answer is -1/tanθ.
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Question:
The expression the quantity cosecant squared of theta minus 1 end quantity over cotangent of theta simplifies to which of the following?
A. 1
B. 0
C. -cotθ
D. -1/tanθ
consider a markov chain with the following probability transition matrix: what is the period of this chain?
The period of the Markov chain is 2.
The period of this Markov chain is determined by the number of times you have to go through the probability transition matrix before you return to the same state. The period for this Markov chain is 2, as you can see from the probability transition matrix below:
P(i,j) State 0 State 1 State 0 0.5 0.5 State 1 0.3 0.7
Starting from State 0, the probability of transitioning to State 0 is 0.5, and the probability of transitioning to State 1 is 0.5. If we start from State 1, the probability of transitioning back to State 0 is 0.3, and the probability of transitioning back to State 1 is 0.7.
Therefore, it takes two steps for the chain to return to its original state and the period of this Markov chain is 2.
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work out the circumference of this circle, and give your answer in terms of pi.
the radius is 6mm
Answer: 37.7mm
Step-by-step explanation:
c = 2πr
c = 2π(6)
c ≈ 37.7
f(x)=x^2
shifted 5 units left
reflect over x-axis
shift 3 down
vertically stretch by a factor of 2
The transformed function is f(x)=(-2*((x+5)²)-3) and green is graph.
The vertical shift depends on the value of k. The vertical shift is described as follows:
g(x) = f (x) + k - The graph is shifted up k units.
g(x) = f (x) − k - The graph shifts down units.
we have,
f(x)=x²
reflected in the x-axis
f(x)=-(x)²
vertically stretched by a factor of 2
f(x)=2*x²
shifted five units to the left
f(x)=(x+5)²
shifted three units to dawn
f(x)=x²-3
we can write all together
f(x)=(-2*((x+5)²)-3)
graphing red original function green is transformed function.
the complete question is-
The graph of f(x) = x^2 is reflected in the x-axis, vertically stretched by a factor of 2, shifted five units to the left, and shifted three units down.
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Find the x- and y-intercepts of the graph of -7x + 3y = 21. State each answer as
an integer or an improper fraction in simplest form.
x-intercept:
Submit Answer
Terms
Use
y-intercept:
The x-intercept and y-intercept of the graph of -7x + 3y = 21 are -3 and 7 respectively.
How to find the x-intercept and y-intercept of a graph?The x-intercept of a graph is the point where a line crosses the x-axis, while the y-intercept of a graph is the point where a line crosses the y-axis.
Therefore, the x-intercept is the value of x when y = 0 while the y-intercept is the value of y when x = 0.
Hence, let's find the x and y-intercept of -7x + 3y = 21
x-intercept
-7x + 3(0) = 21
-7x = 21
x = 21 / -7
x = -3
Y-intercept
-7x + 3y = 21
-7(0) + 3y = 21
3y = 21
y = 21 / 3
y = 7
Therefore,
x-intercept = (-3, 0)
y -intercept = (0, 7)
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