Final answer:
When a transversal intersects parallel lines perpendicularly, all angles formed are right angles (90°). This is due to perpendicular lines creating right angles and the angles at the intersection points being equal in measure because of the corresponding angle postulate.
Explanation:
When a transversal is perpendicular to two parallel lines, all the angles formed measure 90° because of the geometric properties of parallel lines and transversals. A transversal is a line that intersects two or more lines at distinct points. In the case of perpendicular transversals and parallel lines, the angles formed are called right angles.
If we consider two parallel lines, like railway tracks, they never meet and are always the same distance apart, maintaining a 180° straight line angle between them. A transversal that is perpendicular to these lines would intersect at points which lie along the x-axis if we consider the parallel lines to be along this axis. By the definition of perpendicular lines, the angles formed at the intersection points are 90°. As there are two intersection points on each parallel line, and due to the corresponding angle postulate, all four angles formed are equal in measure and hence are all right angles.
This can also be understood by considering vectors in physics, where if two vectors are perpendicular to each other, they form a right triangle, indicating a 90° angle between them. Knowing that parallel lines crossed by a perpendicular transversal produce angles of equal measure, and by the property that perpendicular lines form right angles, we can conclude that all angles formed in the described scenario are indeed 90°.
if d=2, what is the value of 8/(4-d)
The value of the expression 8/(4-d) when d = 2 is 4.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
We have the expression,
8/(4-d)
And here, d = 2.
Substituting the value of d to the expression,
8/(4-d),
= 8/(4-2)
= 8/(2) {using simple division}
= 4
Therefore, 4 is the value of the expression.
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Can you find the measure of angle PVQ for 30 points?
HELP QUICKLY
15 men and 20 women what is the experimental probability that the next person to enter the store will be a man?
Answer: 3/7
Women: 20
Men: 15
Total: 35
15/35 is simplified to 3/7
I need help trying to find the vertex y=2x^2 + 12x +26
Over the last 4 years, Michael has earned $240 interest on an initial investment of $2,000. What simple annual interest rate is the bank paying on this account?
Answer:
3%
Step-by-step explanation:
A simulated game of chess is programmed between two computers. The game is supposed to be biased in favor of player B winning 4 out of 5 times. Which is the most suspicious set of outcomes of 30 games played between the two computers?
AABABBBABBBBBBBBABBBABBBBBBBBA
ABBABBAABBBBBABBBBBBBBBBBBBABB
ABBABABABABBABABABABABABABABAA
ABBABBBABBBBBBBBABBBABBBBBBBBB
Answer:
ABBABABABABBABABABABABABABABAA
Step-by-step explanation:
Player B is supposed to be winning 4 out of 5 times. This means that Player A is supposed to win 1 out of 5 times.
This means out of 30 games, player A should win roughly 1/5(30) = 6 times.
In the first list, player A wins 7.
In the second list, player A wins 6.
In the third list, player A wins 15. This is much different.
In the fourth list, player A wins 5.
What is the angle of rotation of this regular decagon? What is the measure of an interior angle?
A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question.
Confidence Level
90%
95%
99%
z*-score
1.645
1.96
2.58
Remember, the margin of error, ME, can be determined using the formula mc021-1.jpg.
128.75 to 147.25
130.98 to 145.02
132.10 to 143.90
137.38 to 138.62
Using the z-distribution, it is found that the 90% confidence interval for the population mean is: 132.10 to 143.90.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The other parameters are given as follows:
[tex]\mu = 138, \sigma = 34, n = 90[/tex]
Hence, the bounds of the interval are given by:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 138 - 1.645\frac{34}{\sqrt{90}} = 132.1[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 138 + 1.645\frac{34}{\sqrt{90}} = 143.9[/tex]
The 90% confidence interval for the population mean is: 132.10 to 143.90.
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NEED HELP!!!
Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?
A.) How qualified is the trainer at the computer lab?
B.) Where is the computer lab located in the school?
C.) What is the number of learning stations at the computer lab?
D.) How many class projects did you complete using the computer lab?
Answer with explanation:
To know the use of Computer Lab in the School
A Survey has been done.Out of the four Question asked,
The education of the trainer in the computer Lab does not come into consideration,to know the use of computer lab in the school, the use of computer lab can be known only by whether students are getting well versed with Computer and it's applications or not.
Number of Learning Stations in the computer lab, also can't tell the use of computer Lab in the school, because we have to check knowledge of the students about computers to know the better use of the Lab.
So, number of Class projects, or in my own words A test on computer awareness and It's software tools will be a better survey Question.
Option D is the question in the survey is a STATISTICAL QUESTION.
(D) How many class projects did you complete using the computer lab?
solve the equation. choose the answer in simplest form. 4x= 8/7 (A) 1/28 (B) 1/7 (C) 2/7 (D) 7/2
The height h of an arrow in feet is modeled by h(t) = -16t^2 + 63t +4, where t is the time in seconds since the arrow was shot. what is the height of the arrow after 2 seconds?
A ladder is leaning against a building and makes 42° angle with the ground. The top of the ladder reaches 30 feet up on the building. What is the length of the ladder?
The length of the ladder will be 44.8 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
A ladder is leaning against a building and makes a 42° angle with the ground.
The top of the ladder reaches 30 feet up on the building.
Let the length of the ladder be L.
Then the length of the ladder is given by the sine of angle 42°.
sin 42° = 30 / L
L = 30 / sin 42°
L = 30 / 0.699
L = 44.8 feet
The length of the ladder will be 44.8 feet.
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Why is a square a rectangle and a rhombus??
Find two square roots of 36.
The center circle of a soccer field prohibits a defender from being near the ball at the start or restart of a soccer game. On a professional soccer field this circle is 20 yards in diameter. Find the area of this circle. Show work or explain how you found your answer.
The area of the center circle on a professional soccer field, which has a diameter of 20 yards, is calculated using the formula for the area of a circle. The calculated area is approximately 314.16 square yards.
Explanation:To find the area of the center circle on a soccer field, we use the formula for the area of a circle: A = πr^2, where A is the area and r is the radius of the circle. Given that the diameter of the circle is 20 yards, the radius (which is half of the diameter) would be 10 yards. Therefore, substituting 10 for r in the formula gives A = π(10)^2.
Performing the calculations, we find that A = π(100), which equals 314.16 square yards, using 3.1416 as the approximation for σ. Hence, the area of the center circle on a professional soccer field is approximately 314.16 square yards.
a recipe for 2 1/2 dozen whole-wheat muffins require 600 g of flour. How many muffins can be made with 900 g of flour?
With 900 g of flour, you can make 45 muffins.
Explanation:To find out how many muffins can be made with 900 g of flour, we can set up a proportion:
2.5 × 12 = 600
x × 900 = 1
Cross-multiplying gives us:
2.5 × 12 × 900 = 600 × x
30 × 900 = 600 × x
27000 = 600x
x = 27000 / 600
x = 45
Therefore, with 900 g of flour, you can make 45 muffins.
Over the period of one month 159 dogs visited the dog park. Suppose the same number of dogs visited each month for 1 year. How is this total different from the year before 95 dogs visited the dog park every 3 months for the year? Show your work and explain how you got your answer. WILL MARK BRAINLEST!!!!!!
Final answer:
The total number of dogs visiting the park in the current year, assuming 159 dogs visit each month, is 1,908 dogs/year. The previous year, with 95 dogs visiting every 3 months, saw 380 dogs/year. Hence, there are 1,528 more dogs visiting the park in the current year.
Explanation:
Calculating the Total Annual Number of Dogs Visiting the Dog Park
To calculate the total number of dogs visiting the dog park over the course of a year for the current period, we simply multiply the number of dogs that visit each month by the total number of months in a year. For the previous year, we will add up the number of dogs visiting every three months and then determine the difference between the two annual totals.
Current Period Calculation:
Number of dogs visiting each month: 159 dogsNumber of months in a year: 12 monthsTotal dogs visiting in the current year = 159 dogs/month * 12 months/year = 1,908 dogs/yearPrevious Year Calculation:
Number of dogs visiting every 3 months: 95 dogsNumber of 3-month periods in a year: 4Total dogs visiting in the previous year = 95 dogs/3 months * 4 (3-month periods) = 380 dogs/yearNow, we find the difference between the two annual totals:
Difference = Current year total - Previous year totalDifference = 1,908 dogs/year - 380 dogs/yearDifference = 1,528 dogs/yearThe total number of dogs visiting the park in the current year is 1,528 dogs more than the previous year.
Which pair of numbers is an example of opposites? 1/2 and 2 -1/2 and 2 -2 and 1/2 -2 and 2
Answer is : -2 and 2
Step-by-step explanation:
Rhombus WXYZ is graphed on a coordinate plane. What is the area of the rhombus? 24 square units 28 square units 32 square units 48 square units
Rhombus WXYZ is graphed on a coordinate plane.
What is the area of the rhombus?
24 square units
28 square units
32 square units
48 square units
Answer:
24 square units
Step-by-step explanation:
Is 7/8 the right answer
I WILL MARK THE BRAINLIEST! PLZ HELP!
The track-and-field coach wants to know whether the students in the entire school prefer track races or field events. The coach draws a random sample from the following groups:
All students in each grade
All teachers in the school
All boys in each grade in the school
All students on the track-and-field team
Which group best represents the population she should take a random sample from to get the best results for her survey? (5 points)
{A} All students in each grade
{B} All teachers in the school
{C} All boys in each grade in the school
{D} All students on the track-and-field team
The track-and-field coach should select the group which contains all students in each grade to take a random sample to get the best results for her survey.
We have a situation in which track-and-field coach wants to know whether the students in the entire school prefer track races or field events. In order to do so she draws a random sample from the following groups:
• All teachers in the school
• All boys in each grade
• All students in the track-and-field team
• All students in each grade
We have to find the best group from which she should take a random sample of the above mentioned to get the best results for her survey.
What is the condition for Set A to be a Superset of Set B?Set A is superset of Set B if Set A contains all the elements of Set B.
In our question, we have four groups in the form of four sets as -
• Set of all teachers in school (say Set T)
• Set of all boys in each grade (say Set B)
• Set of All students in track-and-field team (Say Set C)
• Set of all students in each grade (Say Set S)
Since the art teacher wants to know the opinion of students, therefore Set T is not correct. Set B contains all boys in each grade, but it would exclude the girls in each grade, therefore it is also not correct. Set C consists of all students in track-and-field team, but it would exclude students who are not in track and field team, therefore incorrect. Set S consist of all Students in each grade, this means that Set S is the superset of Set B and Set C and contains all the students of the school.
Hence, the group that contains all students in each grade should be selected to take a random sample to get the best results for her survey.
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i need your help please!!!
solve using quadratic equations
On a map with a scale of 2 cm = 1km, the distance from Beau's house to the beach is 4.6 centimeters. What is the actual distance?
2.3
since 2 cm=1k you divide by 2
What is the volume of a cube with an edge length of 3.2 meters?
Enter your answer as a decimal
___ cm^3
Find the greatest common factor of 8a 3 b 2 and 12ab 4.
Answer:
4ab²
Step-by-step explanation:
The two expressions are given as 8a³b² and 12ab⁴
Now factors of 8a³b² = 2 × 2 × 2 × a × a × a × b × b
and factors of 12ab⁴ = 2 × 2 × 3 × a × b × b × b × b
Now greatest common factor will be 2 × 2 × a × b × b
= 4ab²
What is the probability that her keys have landed within the forest?
Answer:
0.8
Step-by-step explanation:
egde
Jonathan bought 10lb of flour at 7.50 he had a store cupon for 0.79 what was the final price for flour
the product of two consecutive even integers that are negative is 224. Write an equation and find the two integers.
mrs.beluga is driving on a snow covered road with a drag factor of 0.2. she brakes suddenly for a deer. The tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet. What is the minimum speed she could have been going?
The minimum speed Mrs. Beluga could have been traveling when she braked suddenly on the snow-covered road is approximately 13.68 mph.
To find this, we can use the formula for determining speed from yaw marks: v = √(15 × f × R), where v is the speed in miles per hour, f is the drag factor (0.2 in this case), and R is the radius of the yaw mark.
First, we need to determine the radius of the yaw mark using the given chord length (52 feet) and middle ordinate (6 feet). The formula for R using these values is: R = (C² / 8M) + (M / 2), where C is the chord length and M is the middle ordinate.
Plugging in the values, we get:Therefore, the minimum speed Mrs. Beluga could have been traveling was approximately 13.68 mph.