We can claim that after answering the above question, the As a result, trigonometry the coordinates of the sail's tip after a 270-degree rotation are (3, 2).
what is trigonometry?The study of the relationship between triangle side ed hind angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their potential applications in computations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric shapes.
We may use the following formula for a 2D rotation to calculate the coordinates of the sail's tip after a 270-degree revolution around the origin:
\([x', y'] = [cos(theta) -sin(theta); sin(theta) cos(theta)] * [x; y]\)
where theta is the angle of rotation in radians, [x; y] represents the original point, and [x'; y'] represents the rotated point.
The angle of rotation in this example is 270 degrees, which is equivalent to\(3*\pi/2\) radians. The starting point is (2, -3) and the rotational axis is (0, 0). When we enter these values into the formula, we get:
\([x', y'] = [cos(3*\pi/2) -sin(3*\pi/2); sin(3*\pi/2) cos(3*\pi/2)] * [2; -3]\\ = [0 -(-1); 1 0] * [2; -3]\\ = [3; 2]\)
As a result, the coordinates of the sail's tip after a 270-degree rotation are (3, 2).
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The polynomial 8x + 7y + 4 is prime.
True
or
False
Answer:Is there a picture?
Step-by-step explanation:
Answer:
The WRTX is 8, 8 is not a prime number, so I believe this would be false.
Step-by-step explanation:
solve for x please hurry i will mark brainiest when it shows up if you answer correctly
The value of missing length x in the congruent triangles is determined as 3.6.
option D.
What is the length of segment of x?The length of segment x is calculated by applying congruency theorem as follows;
Consider triangle ABC,
AQ/AT = AB / AC
The given parameters include;
length AQ = 5
length AT = 6
length AB = 5 + 3 = 8
length AC = 6 + x
The value of missing length x is calculated as follows;
5/6 = 8/(6 + x )
5(6 + x) = 6(8)
30 + 5x = 48
5x = 48 - 30
5x = 18
x = 18/5
x = 3.6
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What is the measure of angle Y in this figure
Y=____ degrees
Answer:
163
Step-by-step explanation:
What's great about these problems is that when there is a line that is divided by another line, causing 2 angles, the 2 angles must equal 180 degrees. That means the 163-degree angle + either the x or the z angle would equal 180 degrees. The second best part about this is that if it is separated how yours is, with 2 lines, opposite angles are equal. That means that angle x and angle z are equal, as well as the 163 angle is equal to the y angle. Hope this helps with more than just this problem!
Determine the scale factor for Triangle ABC to Triangle A’B’C
Answer:
C
Step-by-step explanation:
give brainliest
Systolic Blood Pressure (SBP) of 13 workers follows normal distribution with standard deviation 10. SBP are as follows: 129, 134, 142, 114, 120, 116, 133, 142, 138, 148 , 129, 133, 140_ Find the 99%0 confidence interval for the mean SBP level: (124.84 (129.84 (126.84 (125.84 139.16) 139.16) 137.16) 138.16)
Answer:The 99% confidence interval is
To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:
CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)
Where:
Mean is the sample mean of SBP
Z is the Z-score corresponding to the desired confidence level
Standard Deviation is the population standard deviation
Explanation:
Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.
First, we calculate the sample mean:
Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13
= 1724 / 13
≈ 132.62
Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.
Now, we can calculate the confidence interval:
Confidence Interval = 132.62 ± 2.576 * (10 / √13)
132.62 ± 2.576 * (10 / 3.6056)
≈ 132.62 ± 2.576 * 2.771
≈ 132.62 ± 7.147
Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).
What does it mean when you write your measurement as the mean ± standard deviation? (i.e., how much of the data fall within this range?)
When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.
When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. When you add the standard deviation to the mean and also subtract the standard deviation from the mean, you get the upper and lower bounds of the range that contains about 68% of the data. This range is called one standard deviation.The value of the standard deviation indicates how much the data varies around the mean. If the standard deviation is high, then the data is widely spread out and vice versa. Additionally, when you write a measurement as the mean ± standard deviation, it is assumed that the data is normally distributed. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.
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Who here is amazing at math and is willing to help me every time I need help with math?!
Answer:
Me
Step-by-step explanation:
Because I am really good at math
Find the equation of the sphere that passes throught a(1,2,-3), with center b (2,4,0).
The equation of sphere is (x -1 )^{2} + (y - 2 )^{2} + (z+3 )^{2} = 14.
According to the statement
we have to find the equation of the sphere which passes through the a(1,2,-3), with center b (2,4,0).
So, For this purpose, we know that the
Sphere is In analytical geometry, if “r” is the radius, (x, y, z) is the locus of all points and \((x_{0} , y_{0} , z_{0})\)
is the center of a sphere, then the equation of a sphere is given by: \((x -x_{0} )^{2} + (y - y_{0} )^{2} + (z-z_{0} )^{2} = r^{2}\).
So, Here from given equation
The sphere that passes through a(1,2,-3), with center b (2,4,0).
here the locus point is a(1,2,-3).
The radius of sphere is
\(Radius = \sqrt{(1-2)^{2} + (2-4)^{2} + (-3-0)^{2} } \\Radius = \sqrt{(1 + 4 +9 }\)
So, radius is square root 14.
And then the equation of sphere become
\((x -1 )^{2} + (y - 2 )^{2} + (z+3 )^{2} = 14\).
So, The equation of sphere is (x -1 )^{2} + (y - 2 )^{2} + (z+3 )^{2} = 14.
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luisa is building a sand box in her backyard. she places four pieces of wood in a rectangle to form the frame. the rectangle is 4 feet long and 3 feet wide. how can she use a measuring tape to make sure that the corners of the frame will be right angles?
Answer:
As we know rectangles have 90 degree angles at all 4 of its corners.
In this question we know that the length is 4 feet while the bredth is 3 feet.
Therefore to solve this answer we can use the Pythagoras theorm.
By Pythagoras:
\(4^{2} + 3^{2} = diagonal^{2}\)
Therefore the diagonal must be 5 feet
So if Luisa measures the diagonal with a tape and it measures 5
Then it proves that all 4 corners due have 90 degree angles
Please do mark my answer as brainliest. It would really help me answer more of such questions in the future :)
Can someone help me please?
Answer:
No Because the square root of 8 is approximately 2.83
What is the rate of change of the linear function that has a graph that passes through the points (3, 11) and (-1, 3) ?
The rate of change (or slope) of the linear function that passes through the points (3, 11) and (-1, 3) is 2.
The rate of change of a linear function is equal to its slope, which can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
In this case, the given points are (3, 11) and (-1, 3). Substituting these values into the formula, we get:
slope = (3 - 11) / (-1 - 3)
slope = -8 / (-4)
slope = 2
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Plz show how u got the answer
The perimeter of a triangle is 173 - 5 units. One side is 3x + 5
units and another is 82 – 3 units. How many units long is the third side?
A.6x-7
B.6x-13
C.12x-7
D.22x-23
How do I solve this
what is the answer 6u+2(u-8) - 4
Answer:
8u - 20
Step-by-step explanation:
what's the answer? I don't get it
- 1/2 X + 3 = 1/4 (X-12)
Answer:
i think x=8
Step-by-step explanation:
A cinema sells adult tickets and child tickets.
The cost of 2 adult tickets and 2 child tickets is £38.
The cost of 2 adult tickets and 5 child tickets is £59.
Work out how much the following cost:
a) 6 adult tickets and 6 child tickets.
b) 4 adult tickets and 7 child tickets.
c) 3 child tickets.
a) 6 adult tickets and 6 child tickets cost is £102. b) 4 adult tickets and 7 child tickets cost is £77 c) 3 child tickets cost is £21
Describe Elimination Method?The elimination method involves manipulating these equations to eliminate one of the variables. This is done by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations, but with opposite signs. The equations are then added or subtracted, depending on the signs, to eliminate one of the variables.
Let x be the cost of one adult ticket and y be the cost of one child ticket.
From the given information, we can write two equations:
2x + 2y = 38 (equation 1)
2x + 5y = 59 (equation 2)
To solve for x and y, we can use elimination method.
Multiplying equation 1 by 5 and equation 2 by 2, we get:
10x + 10y = 190
4x + 10y = 118
Subtracting equation 2 from equation 1, we get:
6x = 72
x = 12
Substituting x = 12 into equation 1, we get:
2(12) + 2y = 38
2y = 14
y = 7
Therefore, one adult ticket costs £12 and one child ticket costs £7.
a) 6 adult tickets and 6 child tickets:
Cost = 6(£12) + 6(£7) = £102
b) 4 adult tickets and 7 child tickets:
Cost = 4(£12) + 7(£7) = £77
c) 3 child tickets:
Cost = 3(£7) = £21
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Write the equation of the line (in slope-intercept form) that has an x-intercept at -6 and a y-intercept at 2. Provide a rough sketch of the line indicating the given points. [1 mark]. Exercise 2. For the polynomial f(x) = −3x² + 6x, determine the following: (A) State the degree and leading coefficient and use it to determine the graph's end behavior. [2 marks]. (B) State the zeros. [2 marks]. (C) State the x- and y-intercepts as points [3 marks]. (C) Determine algebraically whether the polynomial is even, odd, or neither.
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.
For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.
To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.
The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
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what is the product of 3 1/2 X 3 1/4
Answer:
11 3/8.
Step-by-step explanation:
3 1/2 * 3 1/4
= 7/2 * 13/4
= 91/8
= 11 3/8.
Payton is in charge of the water jugs for the football team. She has 410 ounces of water that she will use to fill plastic cups for the players. If each cup holds 10.25 ounces of water, how many cups can she fill if all are filled completely?
Answer:
40
Step-by-step explanation:
410 divided by 10.25 = 40
The attenuated oral poliovirus vaccine (OVP) is no longer administered in the U.S.A. because it: does not provide good immunity. can occasionally cause poliomyelitis. can be spread to contacts. is very toxic. can be spread to contacts and can occasionally cause poliomyelitis.
The attenuated oral poliovirus vaccine (OPV) is no longer administered in the U.S.A. due to its potential to be spread to contacts and occasionally cause poliomyelitis.
The decision to discontinue the use of the attenuated oral poliovirus vaccine (OPV) in the U.S.A. was primarily based on concerns regarding its safety and efficacy. While the OPV was effective in providing immunity against poliovirus, it had some drawbacks that led to its discontinuation.
One of the major concerns with OPV was its ability to be spread to contacts. OPV contains live but weakened poliovirus strains, which can be shed in the stool of vaccinated individuals. In rare cases, these weakened strains can revert to a virulent form and cause poliomyelitis in contacts who come into contact with the virus through contaminated feces.
Additionally, the OPV has a small risk of causing poliomyelitis itself, although this risk is extremely rare. The weakened strains in the vaccine have a very low potential to cause disease, but in rare instances, they can regain their ability to cause paralysis.
To address these concerns, countries like the U.S.A. have shifted to using the inactivated poliovirus vaccine (IPV), which does not carry the risk of vaccine-derived poliovirus cases or transmission to contacts. IPV is a safer alternative that provides effective protection against poliovirus without the potential risks associated with OPV.
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Steven gets a weekly allowance of $14. He spends $2 each week on treats for his little sister.
He splits the rest of his allowance into equal amounts for savings, charity, and music
downloads.
How much money does Steven save each week?
Answer:
4$
Step-by-step explanation:
First, you have to subtract 2 dollars for his sister.
Then, you are left with 12 dollars. If he splits it equally into three groups, then the answer is 4, as you divide 12/3
Since it arrived at a zoo, a rhinoceros's weight has increased from 1 1/4 tons to 2 1/4 tons. By what percent has the rhinoceros's weight increased?
Answer:
80 percent increase in weight
Step-by-step explanation:
(2 1/4 - 1 1/4)/ 1 1/4 = 1/ (1 1/4) = .8 80 % increase
What is the statement?
Proof:
In △ABC and △DCB,
CB = CB (common)
∠ABC = ∠BCD (each 90°)
and AB = CD (given)
(i) ∴ △ ABC ≅ △DCB (S.A.S. Axiom)
(ii) Hence AC = DB (c.p.c.t.)
Hence proved.
Weights Pounds12.90 $17.1518.20 $23.7720.50 $26.7216.40 $19.8715.40 $23.2210.60 $9.14A. Find the numerical value for correlation between weight and pounds B. Report the equation of the best straight line as predictor (x) and the cost as (y)C. Report the slope and interception of the regression line and explain what it shows. If the intercept is not appropriate, explain D. Report the slope of the regression line and explain what it showsE. Add a new point to your data. A 30 pound turkey is free. Give the new value for R and the new regression equation. What does the negative correlation implies
We have a set of data that relates weights and pounds.
A. We have to find the numerical value for the correlation between weight and pounds.
We can express the correlation coefficient between two samples x and y as:
\(r_{xy}={\frac{\sum_{i}x_{i}y_{i}-n{\bar{x}}{\bar{y}}}{{\sqrt{\sum_{i}x_{i}^{2}-n{\bar{x}}^{2}}} {\sqrt{\sum_{i}y_{i}^{2}-n{\bar{y}}^{2}}}}}.\)biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters. the ecologists will select a random sample of crabs to measure. which of the following is the most appropriate method to use for such an estimate? responses a one-sample z -interval for a population proportion a one-sample z -interval for a population proportion a one-sample z -interval for a sample proportion a one-sample z -interval for a sample proportion a two-sample z -interval for a population proportion a two-sample z -interval for a population proportion a two-sample z -interval for a difference between population proportions a two-sample z -interval for a difference between population proportions a two-sample z -interval for a difference between sample proportions
One-sample z -interval for a population proportion is the most appropriate method to use for estimating the percentage of horseshoe crabs longer than 35 centimeters in a specific area.
What is a one-sample z-interval for a population proportion?In statistical inference, the one-sample z-interval for a population proportion is a method that is employed to estimate population proportions of dichotomous data when a researcher is working with a single sample. It's frequently employed in medical studies to investigate differences in the prevalence of a health issue between two different populations. This is a confidence interval (CI) for the true proportion (or percentage) of a single population that has a particular feature or quality.
What is a population proportion?A proportion refers to the likelihood of a specific trait or behavior in a specific population. It can be defined as the quantity of people who have a certain feature or quality divided by the total number of people in the sample. It's a percentage, usually.
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Identify the property used to the following statements
1. (3)(-5) = (-5)(3)
2. 15+8=23
3. 10(3+2)=10(3)+10(2)
Answer:
co.mutative property
Step-by-step explanation:
you can switch the terms around
two groups of students order cheeseburgers and chicken nuggets at mcdonald’s. one order of 9 cheeseburgers and 4 chicken nuggets cost $22.37. the other order of 3 cheeseburgers and 4 chicken nuggets cost $15.23. find the cost of a cheeseburger
Answer:
$1.19
Step-by-step explanation:
Let the cost of a cheeseburger be $b and that of a chicken nugget be $n.
From the given information, we can form 2 equations.
9b +4n= 22.37 -----(1)
3b +4n= 15.23 -----(2)
Notice that the 2 equations have '4n' in them. I'll be using elimination method to solve the equation by getting rid of the 4n.
(1) -(2):
9b +4n -(3b +4n)= 22.37 -15.23
9b +4n -3b -4n= 7.14
6b= 7.14 (simplify)
b= 7.14 ÷6 (÷6 on both sides)
b= 1.19
Thus, a cheeseburger cost $1.19.
Answer:
Step-by-step explanation
1.19
9.Fred Meyer has cheddar cheese priced at $6.50 for 3 pounds. Costco has 10 pounds of cheddar cheese for $21. Who has the better price? Fred Meyer's unit Rate:
Costco's unit Rate:
Better Price:
Fred Meyer's unit Rate: $2.17 per pound.
Costco's unit Rate: $2.10 per pound.
Better Price: Costco has the better price for cheddar cheese.
To determine who has the better price for cheddar cheese, let's calculate the unit rate for both Fred Meyer and Costco.
Fred Meyer:
Cheddar cheese is priced at $6.50 for 3 pounds. To find the unit rate, we divide the price by the quantity: $6.50 ÷ 3 pounds = $2.17 per pound.
Costco:
Costco offers 10 pounds of cheddar cheese for $21. To find the unit rate, we divide the price by the quantity: $21 ÷ 10 pounds = $2.10 per pound.
Comparing the unit rates, we can see that Fred Meyer's cheddar cheese is priced at $2.17 per pound, while Costco's cheddar cheese is priced at $2.10 per pound.
Therefore, based on the unit rates, Costco has the better price for cheddar cheese. They offer it at a slightly lower price per pound compared to Fred Meyer. Customers can save $0.07 per pound by purchasing cheddar cheese from Costco instead of Fred Meyer.
However, it's important to note that price isn't the only factor to consider when deciding where to purchase cheddar cheese. Other factors such as location, quality, convenience, and personal preferences should also be taken into account.
Additionally, it's always a good idea to compare prices and consider any ongoing promotions or discounts that might affect the final decision.
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use the figure below to find requested values
The measure of angles m∠QTR and m∠PTQ are 98.25° and 81.75° respectively, using the angle N between intersecting tangents.
What is an angle between intersecting tangentsThe angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.
61.5 = 180 - arc PS
arc PS = 180 - 61.5
arc PS = 118.5
m∠QTR = 1/2 × (118.5 + 78) {intersecting chords}
m∠QTR = 196.5/2
m∠QTR = 98.25
m∠PTQ = [360 - 2(98.25)]/2 {one of the angles at a point}
m∠PTQ = 163.5/2
m∠PTQ = 81.75
Therefore, measure of angles m∠QTR and m∠PTQ are 98.25° and 81.75° respectively, using the angle N between intersecting tangents.
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A thrill ride swings passengers back and forth, a little higher each time up to 37 meters. Suppose the height of the swing after 30 seconds is 15 meters. How much higher will the ride swing?