In this question you're given that a coin is flipped 12 times. Now I'll make some assumption here. The first assumption is that the coin is fair. That means the probability of getting ahead in a trial in the toss is the same as probability of getting a deal in the toss and that would be half And second. The all the 12 flips or tosses are independent of each other. And thirdly that the probability of getting ahead, it's the same in each toss and you can see that in each talks there's only two outcomes ahead or not ahead which is a so this is considered a success and this is a failure. It just happened to be the probability of the success and the probability of failure is the same at heart. So this actually follows a binomial distribution model. But in the event that you have not learned by normal distribution we can just go by simple probability multiplication rule. So in probability and it's times or is plus. But the assumption of independent trials and the coin is fair is still the same whether you're using binomial distribution or just simple probability multiplication rule, no Probability of obtaining 12 heads in a row when flipping a coin would be the first pulse, you get a hit. And the second course you also get ahead. And the third toss you get ahead. So on so forth. Up to the last toss, which is the 12th toss, you also get a hit. So it's hit for every toss. So what this means is that probability of first courses ahead is half so that's half now. N and in probability means multiple execution. So just times and second hand is second thoughts is also ahead. So there's a half and so N. S. A. Terms enter is ahead, so that's another half, so so on, so forth. All the way to the last end here. Mr toms And the 12 is also a hit. So this times, how so what we have here is half to the power of 12 since half is multiplying itself 12 times. And so the answer is 1/4 oh 96 Or 0.0002, 44 six, decimal places. Now, if you are using binomial distribution to solve this problem, you will be after this part here. You will be letting X be the number of heads. Oh 12 courses. Right, So X follows the binomial distribution Number of trials is 12, 12 horses. And probability of success in this case is probability of getting ahead in a in a toss is half, so probability of X equals two. R. Where r is the number of heads in 12 courses will be 12, choose our half to the power of our and one minus half is also half To the power of 12 minus are so probability of obtaining 12 heads in a role. So we will be looking at probability of X equals 2, 12. So just suck 12 into the arm. So is this and you will get the same answer of 0.000244
What is the volume 
On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
volume of figure 1 = volume of cuboid = lbh = 8*3*1 = 24 in cubic
volume of figure 2= volume of cuboid = lbh = 6*3*1 = 18 in cubic
total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
What exactly is a cuboid?In geometry, a cuboid is a solid or three-dimensional form. A cuboid is an 8-vertex, 12-sided polyhedron with 6 rectangular faces. A cuboid is another name for a cuboid. A cube is a six-square-faced cuboid. Books and bricks are examples of items found in boxes. The key distinctions between cubic and cubic are as follows: A cube has six equally sized square faces, as opposed to a cube's rectangular faces. Although the cube and cuboid structures appear similar, they differ in terms of side length, diagonal, and area.
Figure 1 volume = cuboid volume = lbh = 8*3*1 = 24 in cubic
Figure 2 volume = cuboid volume = lbh = 6*3*1 = 18
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Homer places a toy rocket on the ground of his backyard, When Homer turns it on, he moves 8 meters away from it. Five seconds after the rocket is launches, Homer can see the rocket from a 75° angle of elevation while he is standing up. If Homer is 1.8 meters tall, how high is the rocket?
Answer:
Step-by-step explanation:
To find the height of the rocket, we can use the tangent function. We know the angle of elevation (75°), the height of Homer's eyes (1.8 meters), and the distance from Homer to the rocket (8 meters), so we can use the formula:
tan(angle) = height / distance
We'll solve for the height:
height = distance * tan(angle)
height = 8 * tan(75°)
However, we need to convert the angle from degrees to radians first, as the tangent function operates in radians. We can use the formula:
radians = degrees * (π / 180)
radians = 75° * (π / 180) = 1.309 radians
Now, we can substitute the value for the angle in radians back into the original equation:
height = 8 * tan(1.309)
Using a calculator, we can find that the height is approximately 15.57 meters.
So, the height of the rocket is approximately 15.57 meters.
Rosa has measured 3 cups of water.Is this enough water for Rosa to make a double recipe of green slime for a class project? Explain
Based on the recipe for making green slime, 3 cups of water is not enough to make a double recipe of green slime.
What is the recipe for making green slime?One recipe of green slime requires 1 pint of water, which is equal to 2 cups.
In order to make a double recipe, you would need to double the amounts of all the ingredients, including the water.
So, for a double recipe of green slime, you would need:
4 cups of water (2 cups per recipe)
1/2 cup of cornstarch (1/4 cup per recipe)
Green food coloring
Therefore, Rosa would need to measure out 4 cups of water to make a double recipe of green slime for the class project.
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The last time it placed an order for ingredients, Sweet Treats Bakery ordered 9,390 kilograms of sugar. This time, the bakery is ordering 7,512 kilograms. What is the percent of decrease in the size of the sugar order?
Answer:A decrease of 20%.
First we must subtract out new total from our old total.
9390 - 7512 is 1878. This means that there is a difference of 1878. Next we must divided both 7512 and 1878 into 9390.
7512/9390 is 0.8 & 1878/9390 is 0.2
As a percentage that is 80% and 20%.
This means that the new amount of sugar only makes up 80% of the old amount. That means that there was a decrease of 20% of kilograms of sugar.
I hope this helped & Good Luck <3 !!!
The figure shows a pair of eyeglasses. The lengths RS and TU of the lenses are equal.
From transitive property of equality, RT = SU.
Given:
RS = TU
What is Segment addition postulate ?
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC
Since , from Segment addition postulate
ST = ST
What is addition property of equality ?
The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation. if a-b=c,then a−b+b=c+b, or a=c+b. The same goes with the subtraction property of equality.
Now , by addition property of equality
SU = ST + TU
Similarly,
RT = RS + ST
Now , Using transitive property of equality,
RT = SU
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Which of the statements is true about the graph for the system of inequalities?
y ≤-2x
y ≥ 3
A The graph of the boundary line for y ≥ 3 should be dashed.
B Area C should be the shaded region.
C Area A should be the shaded region instead of the region shaded on the graph.
D The equations y < -2x should be an uphill line, not a downhill line.
Answer Option C
The point-slope form of the equation of the line is:
Where m is the slope and b is the intersection with the y-axis.
In the line , you can identify that:
The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).
Then the answer is the option C.
please mark me brainliest
Answer:
C
Step-by-step explanation:
Area A should be the shaded region instead of the region shaded on the graph.
Given below are descriptions of two lines.
Line 1: Goes through (-6,-3) and (0,5)
Line 2: Goes through (-6,-5) and (-3,-1)
The slope of Line 1 is m =
The slope of Line 2 is m =
Finally, which of the following is true?
O Line 1 is parallel to Line 2.
O Line 1 is perpendicular to Line 2
O Line 1 is neither parallel nor perpendicular to Line 2
Answer:
The slope of line 1 is -4/3.
The slope of line 2 is 2/3.
Line 1 is neither parallel nor perpendicular to line 2.
Step-by-step explanation:
firstly we find slope using two point formula .
The lines are said to be parallel when their slopes are equal.The lines are said to be perpendicular when the product of their slope is -1. Hence, line 1 is neither parallel nor perpendicular to line 2.
Suppose that Jenny, a college admissions officer for the Department of Mathematics at Smalltown University, is reading applications submitted by prospective students. The president of Smalltown University is weary about admitting too many domestic students and not enough international students. However, the applications are blinded so Jenny cannot see if an applicant is a domestic student or international student. Jenny is instructed by the president to admit exactly 20 applicants to the Department of Mathematics in a given year. Suppose that 38 domestic students and 42 international students applied to the Department of Mathematics at Smalltown University this year, and suppose that there is no difference in the qualifications of domestic and international students applying to Smalltown University.
Let represent the number of domestic applicants that Jenny selects this year. Calculate the mean, , and standard deviation, , of .
Please give the exact value for the mean and round your standard deviation to the nearest three decimal places.
The mean number of domestic applicants that Jenny selects is exactly 9.5, and the standard deviation is approximately 1.932
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
This is a problem involving a hypergeometric distribution since we have a fixed population (all applicants), two groups within the population (domestic and international students), and a fixed number of samples (20 students to be admitted).
Let X be the number of domestic applicants that Jenny selects this year. Then X follows a hypergeometric distribution with parameters N = 80 (total number of applicants), K = 38 (number of domestic applicants), and n = 20 (number of students to be admitted).
The mean of X is given by μ = nK/N, and the standard deviation of X is given by,
σ = √(nK(N-K)/(N²(N-1))).
Substituting the given values, we get:
μ = (20 x 38)/80 = 9.5
σ = √(203842/(80² x 79)) ≈ 1.932
Therefore, the mean number of domestic applicants that Jenny selects is exactly 9.5, and the standard deviation is approximately 1.932.
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A bag of garden soil weighs 40 pounds and holds 5 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:
weight
x = 15bags X 28/1 X 0.453
x = 258.21 kg
volume
x = 15 X 4/27 = 2.222 yd
15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.
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On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.
What is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:
weight
x = 15bags X 28/1 X 0.453
x = 258.21 kg
volume
x = 15 X 4/27 = 2.222 yd
15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.
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There are vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%.
Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
Red
Total
Question content area bottom
Part 1
Complete the table.
Row Relative Frequency Table
Color
Type of Vehicle
Car
Truck
Total
Blue
enter your response here%
enter your response here%
100%
Red
enter your response here%
enter your response here%
100%
Total
enter your response here%
enter your response here%
100%
Answer:
you su ck hah lol
Step-by-step explanation:
ez
f(x) =
-x² + 3x
4(x)³
x+5
x-1
x≤-2
-2 < x < 1
x ≥ 1
The value of the piecewise function f(-2) + 2f(-1) - f(3) is -14
How to determine the value of the piecewise functionFrom the question, we have the following parameters that can be used in our computation:
The definition of a piecewise function
Given that
f(-2) + 2f(-1) - f(3)
Using the definition of the piecewise function and the domain values. we have
f(-2) + 2f(-1) - f(3) = -(-2)^2 + 3(-2) + 2(4(-1)^3) + [(3 + 5)/(3 - 1)]
Evaluate
f(-2) + 2f(-1) - f(3) = -14
Hence, the solution is -14
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Assume that the variables, x and y, have been assigned integer values. Write a boolean expression which evaluates to True if x is non-negative and y is negative. Note that zero is a
non-negative number.
The boolean expression that evaluates to True if "x is non-negative and y is negative" is: (x >= 0) ∧ (y < 0).
A boolean expression is a logical expression that evaluates to either true or false. Boolean expressions can be composed of one or more boolean operators, such as AND, OR, and NOT, and can involve one or more variables.
We need to find boolean expression for: "x is non-negative and y is negative", then output is true.
The boolean expression is:
(x >= 0) ∧ (y < 0), or (x>=0) AND (y<0)
In this expression, the ∧ symbol represents the logical AND operator. The expression (x >= 0) checks if x is greater than or equal to 0 (i.e. non-negative), and the expression (y < 0) checks if y is less than 0 (i.e. negative).
If both conditions are true, the overall expression evaluates to true, indicating that x is non-negative and y is negative.
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What is the vertex for the graph below?
Answer:B
Step-by-step explanation: the graph moves x vertically -1 while y is moved vertically to 4
TO determine which side of a linear inequality to shade in for its graph, you
should pick a point on one side of the dashed or solid line and plug its
coordinates into the original inequality. If the coordinates satisfy the
inequality, you should shade in that half of the plane.
• A. True
• B. False
The given statement about inequality is true.
What is inequality?The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.
The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.
The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.
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what is 4y - 2x= -8 in slope-intercept form
Solve this problem using Rational Zeroes Theorem (but explain it, please).
What are the real zeroes of the polynomial function:
f(x) = 4x^4 - 8x^3 - 19x^2 + 23x - 6?
The real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
What do you mean by Polynomial?In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using the operations of addition, subtraction, and multiplication. A polynomial can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer powers. For example, the polynomial 2x² - 3x + 1 has three terms: 2x², -3x, and 1.
For the given polynomial function, the constant term is -6 and the leading coefficient is 4. Therefore, the possible rational zeroes of the function are of the form p/q, where p is a factor of -6 and q is a factor of 4.
The factors of -6 are ±1, ±2, ±3, and ±6. The factors of 4 are ±1, ±2, and ±4. So the possible rational zeroes are:
±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±3/2
To determine which of these possible rational zeroes are actual zeroes, we can use synthetic division or long division to evaluate the function at each possible zero. Doing so, we find that the actual zeroes of the function are:
x = 1/2, x = 1, x = 3/2, x = 2
Therefore, the real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
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Help me with this question…..
Answer:
In order from least to greatest, the numbers would be organized as such: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex]. So C is the correct answer.
Step-by-step explanation:
At first glance, these numbers are not the simple whole and decimal numbers one might be used to. However, we can find their approximate values and order them correspondingly. [tex]\frac{2}{3}[/tex] is a fraction that is less than one, so on a number line it would be between 0 and 1, making it the smallest number out of the four. [tex]\sqrt{5}[/tex] and [tex]\frac{5}{2}[/tex] are both between 2 and 3, but [tex]\sqrt{5}[/tex] is approximately equal to 2.24, while [tex]\frac{5}{2}[/tex] is equal to 2.5. Therefore, we can conclude that [tex]\frac{5}{2}[/tex] is greater than [tex]\sqrt{5}[/tex]. Lastly, [tex]\pi[/tex] is a constant number that is the ratio of a circle's circumference to its diameter that equals approximately 3.14, so we can conclude that [tex]\pi[/tex] is the greatest number out of the four.
Now that we have the four numbers in an easier and visually more clear way to find their exact values, we know that the order of these numbers from least to greatest would be choice C: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex] .
Have a great day! Feel free to let me know if you have any more questions :)
The polynomial of degree 5,
P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0, and a root of multiplicity 1 at
x = -5 Find a possible formula for P(x).
Answer:
Step-by-step explanation:
Given the information that the polynomial function P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0, and a root of multiplicity 1 at x = -5, we can use this information to find a possible formula for P(x).
A polynomial function's roots are the values of x that make the function equal to zero. If a root has multiplicity n, it means that (x - root) is a factor of the polynomial function n times.
So, based on the given information, we know that P(x) must be divisible by the factors (x - 1)^2, (x - 0)^2, and (x + 5), and that the leading coefficient must be 1.
Putting it all together, a possible formula for P(x) is:
P(x) = (x - 1)^2 (x - 0)^2 (x + 5) = (x^2 - 2x + 1)(x^2)(x + 5) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5
So, the possible formula for P(x) is P(x) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5.
Answer: [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]
Explanation:
If k is a root of P(x), then x-k is a factor. The multiplicity is the exponent for that factor.
For instance, the root x = 1 with multiplicity 2 leads to the factor [tex](\text{x}-1)^2[/tex]
The leading coefficient is the number out front. For example, if the leading coefficient was 8, then we'd have [tex]P(\text{x}) =8\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]
However, we change that "8" to a "1" since the leading coefficient is 1 here.
That's how we get to
[tex]P(\text{x}) = 1\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex] aka [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]
Optionally if you were to expand everything out, combine like terms, and simplify then you'd get
[tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5) = \text{x}^5 + 3\text{x}^4- 9\text{x}^3+5\text{x}^2[/tex]
I don't recommend doing this because you lose the information about the roots along with their corresponding multiplicities. It's better to keep things factored.
You can use a graphing tool like Desmos or GeoGebra to verify the answer.
Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model mathematically his motion and starts her stopwatch. Let t be the number of seconds the stopwatch reads and let y be the number of meters Tarzan is from the riverbank. Assume that y varies sinusoidally with t, and that y is positive when Tarzan is over water and negative when he is over land. Jane finds that when t = 2, Tarzan is at one end of his swing, where y = -23. She finds when t = 5 he reaches the other end of his swing and y = 17.
We can represent the sinusoidal function for Tarzan's motion as given below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model mathematically his motion and starts her stopwatch.
Assume the sinusoidal equation to be -
y = Asin(ωt)
We can represent the coordinates as -
For {t} = 2, {y} = -23. So -
- 23 = Asin(2ω) ... { 1 }
For {t} = 5, {y} = 17. So -
17 = Asin(5ω) ... { 2 }
Therefore, we can represent the sinusoidal function for Tarzan's motion as given above.
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Identify the y- intercept of the graph below
b= -4
b=6
b=4
b= -10
Can somebody help awnser these questions
A. The amount deducted from Frank's bank every years is $59700
B. The salary of the tax will be $99500.
C. Tax deducted from her new pay is $39800
What is simple interest?A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
a. 79600 - (79600 × 25%)
$59700
b. The formula for simple interest is:
S = p*t*r/100
p = 79600
r = 25%
t=1
S = 79600*1*25/100 = 19900
New salary = 79600 + 19900
= $99500
Hence the salary of the tax will be $99500.
c. 99500 - 59700
= $39800
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Find an angle α that is coterminal with an angle measuring 550∘, where 0∘≤α<360∘.
Answer:
190°
Step-by-step explanation:
Subtract 360° (this is one complete rotation)
"coterminal" is the exact same angle, but 360° bigger (or smaller)
550° - 360°
= 190°
Convert 1,2kg to g to two decimal places where applicable
Answer: 1200g
Step-by-step explanation:
1 kilogram is equal to 1000 grams, so since you want 1.2, simply multiply by that quantity. So the answer is 1200 grams.
Identify the graph of f(x) = 4√x.
Answer:
choice B
Step-by-step explanation:
plug in a few test values of x to prove it. The other choice would be a cube root function of x.
Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the Earth. If 7 such locations are generated, what is the probability that the first 5 locations are in water and the last 2 locations are on land?
A. 0.0010
B. 0.0152
C. 0.0910
D. 0.9090
Answer:
0.0152 is the probability that the first 5 locations are in water and the last 2 locations are on land.
please help question below
Answer:
Step-by-step explanation:
22
2. Determine the area of each composite figure below.
Answer:
[tex]6\pi[/tex]
Step-by-step explanation:
There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.
Area of a Circle:The area of a circle can be calculated using the formula: [tex]A=\pi r^2[/tex] where "r" is the radius, equal to half the diameter.
Since we're dealing with the semi-circles, we can just divide this area by two to get: [tex]A=\frac{\pi r^2}{2}[/tex]
Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.
So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: [tex]A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi[/tex]
One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.
So now let's calculate the area of the inner semi-circle: [tex]A=\frac{\pi (2)^2}{2}=2\pi[/tex]
Now let's just subtract the areas: [tex]8\pi - 2\pi = 6\pi[/tex], so the area is 6 pi
Find the perimeter of the large triangle below
The perimeter of the triangle is equal to 28.7 using the trigonometric ratio
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
tan60 = q/4 {opposite/adjacent}
q = 4 × tan60 {cross multiplication}
q = 6.9282
sin60 = q/r {opposite/hypotenuse}
sin60 = 6.9282/r
r = 6.9282/sin60 {cross multiplication}
r = 8
sin45 = q/s {opposite/hypotenuse}
sin45 = 6.9282/s
s = 6.9282/sin45 {cross multiplication}
s = 9.8
cos45 = p/s {adjacent/hypotenuse}
cos45 = p/9.8
p = 6.9282 {cross multiplication}
perimeter of the triangle = 4 + p + s + r
perimeter of the triangle = 4 + 6.9282 + 9.8 + 8
perimeter of the triangle = 28.7282
Therefore, the perimeter of the triangle is equal to 28.7 using the trigonometric ratio.
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EASY POINTS!
Answer from the screenshot :)
Vertex A will be located at (-1, 0) after a rotation of -90°
Vertex B will be located at (-5, 3) after a rotation of 90°
Vertex C will be located at (6, -7) after a -180° rotation
Vertex D will be located at (1, -4) after a 270° rotation
How to find the new locations?The transformation rule for rotation of -90°
(x, y) → (y, -x)
A (0, -1) → (-1, 0)
The transformation rule for rotation of 90°
(x, y) → (-y, x)
B (3, 5) → (-5, 3)
The transformation rule for rotation for -180°
(x, y) → (-x,-y)
C (-6, 7) → (6, -7)
The transformation rule for rotation for 270° rotation
(x, y) → (-y, x)
D (-4, -1) → (1, -4)
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o TP & E Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z. X = y = Z= - 3x + - 2x + y 4y 4y + - 2z = -8 7z = 26 8z = 30 Question Help: Video 1 Video 2 M Message instructor
The system of equations can be written as a matrix and then used to solve for the variables x, y, and z.
The augmented matrix of the system is:
-3 -2 1 | -8
0 4 -2 | -8
0 0 7 | 26
We can use row operations to find the row reduced echelon form of the matrix, which will give us the solutions to the system.
Starting with the first row:
1. Multiply row 1 by -3 to get a leading 1 in the first column:
3 6 -3 | 24
0 4 -2 | -8
0 0 7 | 26
2. Add row 1 to row 2:
3 6 -3 | 24
0 4 0 | 16
0 0 7 | 26
3. Add 3 times row 1 to row 3:
3 6 -3 | 24
0 4 0 | 16
0 0 7 | 26
The row reduced echelon form of the matrix is:
1 2 -1 | 8
0 1 0 | 4
0 0 1 | 9
From this, we can see that the solutions to the system are:
x = 8 - 2y
y = 4
z = 9
So the system has a unique solution: x = 8 - 2y = 8 - 2 * 4 = 0, y = 4, z = 9.
