find the probability that the number of people who say auto racing is their favorite sport is between 46 and 51, inclusive.
Answers
The probability of X being between 46 and 51 will be highest when p is close to 0.5 and n is large.
To find the probability that the number of people who say auto racing is their favorite sport is between 46 and 51, inclusive, we need to know the total number of people surveyed and the percentage of people who said auto racing is their favorite sport.
Assuming we have this information, we can use the normal approximation to the binomial distribution to estimate the probability. Specifically, we can use the following formula:
P(46 ≤ X ≤ 51) ≈ Φ((51 + 0.5 - np) / √(np(1 - p))) - Φ((46 - 0.5 - np) / √(np(1 - p)))
where X is the number of people who say auto racing is their favorite sport, n is the total number of people surveyed, and p is the percentage of people who said auto racing is their favorite sport. Φ(z) is the standard normal cumulative distribution function.
For example, if we surveyed 1000 people and found that 5% of them said auto racing is their favorite sport, then we have n = 1000 and p = 0.05. Plugging these values into the formula, we get:
P(46 ≤ X ≤ 51) ≈ Φ((51 + 0.5 - 1000*0.05) / √(1000*0.05*(1 - 0.05))) - Φ((46 - 0.5 - 1000*0.05) / √(1000*0.05*(1 - 0.05)))
Using a standard normal table or calculator, we can evaluate this expression to find the probability. The result will depend on the values of n and p, but in general, the probability of X being between 46 and 51 will be highest when p is close to 0.5 and n is large.
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Related Questions
A hat company wants to create a cylindrical travel case to protect its beach sun hats using the following pattern.
net drawing of a cylinder is shown as two circles with diameters labeled 15 inches and a rectangle with a height labeled 5 inches
How many square inches of leather will be necessary to create the travel case? Approximate using π = 3.14.
412.13 square inches
588.75 square inches
1,648.5 square inches
1,884 square inches
Answers
The surface area of the cylinder will be 588.75 square inches. Then the correct option is B.
Given that:
Diameter, d = 15 inches
Height, h = 5 inches
The radius of the circle is calculated as,
r = d / 2
r = 15 / 2
r = 7.5
Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,
SA = 2 x 3.14 x 7.5 (5 + 7.5)
SA = 47.1 x 12.5
SA = 588.75 square inches
The surface area of the cylinder will be 588.75 square inches. Then the correct option is B.
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Maria used a number line to find 12 ÷ 4.
Explain how she can use the number line to model the division.
Answers
The way she can use the number line to model the division is; Maria should start at 0 and then make “bounces” of 4 to the right until landing at 12. She will make 3 bounces of 4 because 12 divided by 4 is 3.
How to Model a Number Line?She is using a number line to model division, 12 ÷ 4 = 3
To carry out a division operation using a number line, follow the steps below:
Select the origin (point 0) as the starting pointIdentify the dividend and the divisorUse the divisor as the gap between 0 and subsequent consecutive numbersCount the number of gaps between 0 and the dividendFor the division operation 12 ÷ 4, Maria should:
Make 0 as the starting point on the number lineIdentify the dividend (12) and the divisor(4)Make the gap between 0 and subsequent numbers to be 4(the divisor)Therefore, the points on the number line will be 0, 4, 8, and 12
Count the number of gaps between these points
That is, 0 to 4, 4 to 8, and 8 to 12.
Since there are three gaps between 0 and 12 on the number line, using a gap difference of 4, then 12 ÷ 4 = 3
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The correlation coefficient for blood pressure and amount of vegetables eaten in a group of people is −0. 7. Analyze the following statement: High blood pressure is caused by not eating vegetables. Is this a reasonable conclusion? No; blood pressure and eating vegetables are completely unrelated. No; even though there is a strong negative correlation, not eating vegetables doesn't necessarily cause high blood pressure. Yes; eating vegetables reduces blood pressure, so the opposite is also true. Yes; the correlation coefficient is below −0. 5, so that implies causation.
Answers
Answer:
No, even though there is a strong negative correlation, not eating vegetables doesn’t necessarily cause high blood pressure
Step-by-step explanation:
Brainliest ?
If a is a positive integer and if the unit's digit of a2 is 9 and (a+1)2is 4, what is the unit's digit of (a+2)2?
A
1
B
3
C
5
D
9
Answers
If a is a positive integer and if the unit's digit of a2 is 9 and (a+1)2 is 4, then the unit's digit of (a+2)2 is 1.
We are given that a is a positive integer, and we need to find the unit's digit of (a+2)². To solve this problem, let's first analyze the information provided:
1. The unit's digit of a² is 9.
2. The unit's digit of (a+1)² is 4.
From the first piece of information, we can conclude that the unit's digit a must be either 3 or 7, as 3² = 9 and 7² = 49 (the unit's digit is 9).
Now, let's check the second piece of information. If the unit's digit of a is 3, then the unit's digit of (a+1) would be 4. Since 4² = 16 (unit's digit is 6), this doesn't match the given condition that the unit's digit of (a+1)² is 4.
So, the unit's digit must be 7. In this case, the unit's digit of (a+1) is 8. Since 8² = 64 (unit's digit is 4), this matches the given condition.
Now that we know the unit's digit of a is 7, let's find the unit's digit of (a+2)². If the unit's digit of a is 7, then the unit's digit of (a+2) is 9. Since 9² = 81 (unit's digit is 1), the unit's digit of (a+2)² is 1.
Therefore, the correct answer is:
A) 1
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Which answer choice below is closest to the length of segment DE?
Answers
Answer:
15.71
Step-by-step explanation:
Triangle ABC and triangle ADE are similar triangles so we can find the length of DE using similarity ratio.
\( \frac{14}{22} = \frac{10}{de} \)
Cross multiply fractions14×DE = 220
Divide both sides by 14DE = 15.71 approximately.
Please help! PLEASEEEE
Answers
Determine the complex exponential Fourier series representation for each of the following signals: X(t) = cos wt x(t) = -cos(0.5 * wt) x(t) = cos(2t + 1)
Answers
To determine the complex exponential Fourier series representation for each of the given signals, we can use the formula:
X(t) = ∑[n=-∞ to ∞] Cn * e^(jnω0*t)
where Cn represents the complex Fourier coefficients and ω0 is the fundamental frequency.
X(t) = cos(ωt):
The complex exponential Fourier series representation for X(t) = cos(ωt) is:
X(t) = C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j*(-1)ω0t)
= C0 + C1 * e^(jω0t) + C(-1) * e^(-jω0t)
x(t) = -cos(0.5 * ωt):
The complex exponential Fourier series representation for x(t) = -cos(0.5 * ωt) is:
x(t) = C0 * e^(j0ω0t) + C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j(-1)ω0t)
= C0 + C0 + C1 * e^(j0.5ω0t) + C(-1) * e^(-j0.5ω0t)
x(t) = cos(2t + 1):
The complex exponential Fourier series representation for x(t) = cos(2t + 1) is:
x(t) = C0 * e^(j0ω0t) + C2 * e^(j2ω0t) + C(-2) * e^(j*(-2)ω0t)
= C0 + C2 * e^(j2ω0t) + C(-2) * e^(-j2ω0t)
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In ANOVA, the independent variable is ______ with 2 or more levels and the dependent variable is _______
a. interval/ratio with 2 or more levels; nominal
b. nominal with 2 or more levels; interval/ratio
c. ordinal with 2 or more levels, nominal
d. interval/ratio, nominal with 2 or more levels
Answers
The correct option is (d) interval/ratio, nominal with 2 or more levels.
In ANOVA (Analysis of Variance), the independent variable is interval/ratio with 2 or more levels, and the dependent variable is nominal with 2 or more levels. Here, ANOVA is a statistical tool that is used to analyze the significant differences between two or more group means.
ANOVA is a statistical test that helps to compare the means of three or more samples by analyzing the variance among them. It is used when there are more than two groups to compare. It is an extension of the t-test, which is used for comparing the means of two groups.
The ANOVA test has three types:One-way ANOVA: Compares the means of one independent variable with a single factor.Two-way ANOVA: Compares the means of two independent variables with more than one factor.Multi-way ANOVA: Compares the means of three or more independent variables with more than one factor.
The ANOVA test is based on the F-test, which measures the ratio of the variation between the group means to the variation within the groups. If the calculated F-value is larger than the critical F-value, then the null hypothesis is rejected, which implies that there are significant differences between the group means.
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zero point three divided by zero point 9
Answers
Answer:
0.33333
Step-by-step explanation:
Answer: the answer is 0.3 with a recipricol bar
Step-by-step explanation:
Solve b(x)=16x2−25 to find the zeroes of b(x)
Answers
Answer:
5/4 and -5/4
Step-by-step explanation:
Solve means change b(x) to 0, factor and use zero product property (write two smaller equations)
This equation is a "difference of two squares" or "difference of perfect squares"
b(x) = 16x^2 - 25
0 = (4x - 5)(4x + 5)
Make two smaller equations.
4x-5=0 and 4x+5=0
Solve both of these separately.
4x - 5 = 0
add 5
4x = 5
divide by 4
x = 5/4 and,
4x + 5 = 0
subtract 5
4x = -5
divide by 4
x = -5/4
"zeros" are solutions are roots, are x-intercepts. These are all pretty commonly interchangeable. (Not exactly, technically for a mathematician) But for a student knowing what to do with a question, for all these:
find zeros
find solutions
find roots
find x-intercepts
Set it equal to 0 and solve.
The zeros are 5/4 and -5/4
Answer:
b(x)= (4x)^2-(5)^2
b(x)=(4x-5)(4x+5)
The zeros of b are 5/4 and -5/4
a can of soda is placed inside a cooler. as the soda cools, its temperature in degrees celsius is given by the following function, where is the number of minutes since the can was placed in the cooler. find the temperature of the soda after minutes and after minutes. round your answers to the nearest degree as necessary.
Answers
The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.
Substitute x = 0 into the function T(x):
T(0) = -19 + 39e^(-0.45*0).
Simplify the expression:
T(0) = -19 + 39e^0.
Since e^0 equals 1, the expression simplifies to:
T(0) = -19 + 39.
Calculate the sum:
T(0) = 20.
Therefore, the initial temperature of the soda is 20 degrees Celsius.
To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):
Substitute x = 20 into the function T(x):
T(20) = -19 + 39e^(-0.45*20).
Simplify the expression:
T(20) = -19 + 39e^(-9).
Use a calculator to evaluate the exponential term:
T(20) = -19 + 39 * 0.00012341.
Calculate the sum:
T(20) ≈ -19 + 0.00480599.
Round the answer to the nearest degree:
T(20) ≈ -19 + 1.
Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.
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INCOMPLETE QUESTION
A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.
Two cars are traveling along a straight road. Car A maintains a constant speed of 77.0 km/h. Car B maintains a constant speed of 114 km/h. At t=0, car B is 45.0 km behind car A. How long does it take before car A is overtaken by car B?
Answers
Answer: 72.97 Minutes
Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.
To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.
Relative speed = Speed of car B - Speed of car A
Relative speed = 114 km/h - 77.0 km/h
Relative speed = 37.0 km/h
So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.
To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.
Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours
Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).
Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes
Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.
Hope this helps!
Ex2. Prime Numbers ( 40 points) You will implement in this exercise an ancient Greek algorithm for finding the prime numbers less than a given number. (ask your instructor about the name of the algorithm after class!) Reminder: A prime number is a positive integer greater than 1 that is divisible only by itself and by 1 . Here is how the algorithm works assuming we would like to find the prime numbers ≪=20 : 1. Initially, assume that all the numbers are prime by marking them with 1 (0 means not prime). 2. For each number that is marked as prime, starting at 2, mark all of its multiples as not prime. which marks all the multiples of num in the array (of size n ) as not prime (excluding num). 2. Write a program that prints the prime numbers κ=150 : a) Create and initialize an array for marking the numbers with 0 (not prime) or 1 (prime). b) For every number 2<=i<150, use function cross_multiples_out to mark all of its multiples as not prime. c) Pass through the array and print the numbers marked as prime.
Previous question
Answers
The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.
This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.
It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.
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When reading a word problem, there are clues that will help you to determine whether you need to find the surface area or the volume to solve the problem. Which clues would indicate that you need to find volume? Check all that apply. an object that is filled covering the outside of an object an object that is solid cubic units square units
ANSWER: 1,3,4
Answers
The options are as follows
(1) An object that is filled
(2) Covering the outside of an object
(3) An object that is solid
(4) Cubic units
(5) Square units
Answer:
(1) An object that is filled
(3) An object that is solid
(4) Cubic units
Step-by-step explanation:
Clues that applies
(1) An object that is filled: By filling means that object has that amount of volume that is being filled completely.
(3) An object that is solid is likely a clue to finding the volume of an irregularly shaped solid.
(4) Cubic units, volume is measured in cubic units.
Clues that Doesn't Apply
(2) Covering the outside of an object is a clue to finding the surface area of an object.
(5) Square units is a measure of area not volume.
HELP ASAP PLEASE!!!!!!!!!!!!!
Answers
Step-by-step explanation:
-2=--4(1)+b
I gotchuu
Le regioni italiane bagnate dal mare sono un insieme?
Answers
Answer:
non so cosa intendi per intero
Step-by-step explanation:
Può essere più preciso?
edin has £300 in his saving account.
his bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years.
how much interest will he have earned after 3 years?
Answers
Answer:
$45
Step-by-step explanation:
300/100 = $3 = 1%
$3 x 5 = $15 = 5%
$15 x 3 years = $45
One hundred tomato plants were randomly selected from a large garden, and a 90% confidence interval was computed to determine the true proportion of plants that produce useable tomatoes. The interval is 0.86 to 0.92.
What would happen to the width of the confidence interval if the confidence level increased to 95%?
Answers
Answer:
The width of the interval would increase.
Step-by-step explanation:
The sum of how many terms of the AP 8,15,22,. . is 395
Answers
The sum of approximately 10 terms of the given arithmetic progression is 395.
To find the sum of a certain number of terms in an arithmetic progression (AP), we need to determine the number of terms involved.
Let's denote the number of terms as 'n'.
In an arithmetic progression, each term can be represented by the formula: a + (n-1)d,
where 'a' is the first term and 'd' is the common difference.
Given the AP 8, 15, 22, ..., we can observe that the first term 'a' is 8, and the common difference 'd' is 15 - 8 = 7.
To find the sum of the first 'n' terms, we can use the formula: Sn = (n/2)(2a + (n-1)d), where 'Sn' represents the sum of the first 'n' terms.
We are given that the sum of the terms is 395.
Substituting the values into the formula, we have:
395 = (n/2)(2(8) + (n-1)(7))
Simplifying the equation:
395 = (n/2)(16 + 7n - 7)
395 = (n/2)(7n + 9)
Multiplying through by 2 to eliminate the fraction:
790 = n(7n + 9)
Rearranging the equation:
7n² + 9n - 790 = 0
To solve this quadratic equation, we can either factorize, complete the square, or use the quadratic formula.
By factoring or using the quadratic formula, we find that the positive value of 'n' that satisfies the equation is approximately 10.55.
Since 'n' represents the number of terms, we round it down to the nearest whole number.
Therefore, the sum of approximately 10 terms of the given arithmetic progression is 395.
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i don’t understand how to find x
Answers
1
11+3p-7=6p+5-3p
No Solution
Infinite Many Solutions
p=4
p=5
Answers
Answer:
No Solution
Step-by-step explanation:
Given expression:
11 + 3p - 7 = 6p + 5 - 3p
To solve this problem, we have to collect like terms from both sides.
3p - 6p + 3p = 5 + 7 - 11
0 = 1
This equation has no solution. It is not an equality.
Developers determine the specifics of how to build a system in the _____ phase.
a. analysis
b. design
c. implementation
d. testing
Answers
Developers determine the specifics of how to build a system in the design phase. b
The design phase and its importance:
Define Objectives:
The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.
The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:
During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.
This architectural design provides a high-level view of the system's organization.
Design System Components:
With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:
The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:
The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.
Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.
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A researcher's results should be considered fraudulent if Group of answer choices animals were used while conducting experiments. the researcher used any form of survey to collect the data. participants were not debriefed after completion of the study. data were changed in order to support the hypothesis
Answers
A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.
Explanation:
A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Additionally, if animals were used while conducting experiments, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. If a survey was used to collect data, the researcher should have ensured the survey was properly designed and administered to avoid any biases or errors. Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.
The scientific method requires researchers to conduct experiments in a transparent and objective manner. This means that the researcher should design experiments to test hypotheses, collect data systematically, and analyze data objectively. Any manipulation of data to support a hypothesis undermines the scientific method and is considered unethical. Researchers who intentionally manipulate data can be considered fraudulent and may face disciplinary action.
If animals were used in the experiment, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. Ethical guidelines ensure that animals are treated humanely, minimize their pain and discomfort, and maximize their welfare. Researchers who violate these guidelines can be considered fraudulent and may face disciplinary action.
If a survey was used to collect data, the researcher should have ensured that the survey was properly designed and administered to avoid any biases or errors. Surveys can be susceptible to various sources of error, including sampling errors, measurement errors, and non-response bias. Researchers who fail to address these sources of error can produce biased or invalid results, which can be considered fraudulent.
Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Debriefing allows participants to understand the purpose of the study, ask questions, and voice any concerns they may have. Participants who are not debriefed may feel deceived or harmed by the study, which can damage their trust in research and researchers.
In summary, researchers must adhere to ethical standards and maintain the integrity of their research. This includes avoiding data manipulation, following ethical guidelines for animal welfare, ensuring that surveys are properly designed and administered, and debriefing participants after completion of the study. Failure to do so can result in fraudulent research and harm to participants, animals, and the scientific community as a whole.
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5. What is the largest value of x that is not a
solution to -(9x - 4) + 12 + 18x > 79?
Answers
Answer:
7
Step-by-step explanation:
- 9x + 4 + 12 + 18x > 79
9x+16>79
9x>63
x>7
All numbers greater than7 are solution to -(9x - 4) + 12 + 18x > 79.
So, the largest value of x that is not a
solution to -(9x - 4) + 12 + 18x > 79 is 7.
what is a simpler form for the radical expression 4√2401x^12y^16
Answers
Answer:
\(49x^{6}\)\(y^{8}\)
Step-by-step explanation:
1. Factor 2401 into its prime factors
2401 = 74
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
2401 = 74
No factors remain inside the root!!
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
49 = 72
At the end of this step the partly simplified SQRT looks like this:
49√(x^12y^16)
2. Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) √(x8)=x4
(3.2) √(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) √(x5)=x2•√(x)
(4.2) √(x-7)=x-3•√(x-1)
Applying these rules to our case we find out that
SQRT(x12y16) = x6y8
Combine both simplifications:
sqrt (2401x12y16) =
49x6y8
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Gary, the technology coordinator of a high school, is planning to
purchase one memory stick for each of the teachers. There are 86
teachers at the school. The English teachers requested memory sticks
that have a capacity of 32 gigabytes. Gary determines that $600 is the
maximum amount that can be spent for all of the memory sticks. Gary
finds the following prices for the purchases from Computer City.
Option
Memory Stick
Capacity
Cost Each
A
16 gigabyte
$5. 99
B
32 gigabyte
$9. 99
Free shipping for any order $35 or more.
1
If a represents the number of 16-gigabyte memory sticks
and b represents the number of 32-gigabyte memory sticks,
which equation represents the number of each kind of
memory stick that should be purchased for the teachers?
A a + b = 86
C 16a + 32b = 86
B a + b = 600
D 16a + 32b = 600
Answers
Answer:
D
Step-by-step explanation:
dentify the function shown in this graph
A. y = −x + 3
B. y=-3x-3
C. y = 3x - 3
D. y=-3x+3
Answers
Answer:
B
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line
m = \(\frac{-3-0}{0-(-1)}\) = \(\frac{-3}{0+1}\) = \(\frac{-3}{1}\) = - 3
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - 3x - 3 ← equation of line
ASAP!! If quadrilateral PQRS is a square, what are the coordinates of point E?
Answers
Answer:
E - (28, 25)
Hope this helps!
Which of the following traingles is Cos B = 0.8?
Answers
ANSWER:
EXPLANATION:
Given:
To find:
Which triangle is cos B = 0.8
For the 1st Triangle:
We have to first determine the value of side BC using the Pythagorean theorem as seen below;
\(\begin{gathered} 5^2=4^2+BC^2 \\ 25=16+BC^2 \\ BC=\sqrt{25-16} \\ BC=\sqrt{9} \\ BC=3 \end{gathered}\)So cosine B will be;
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{3}{5} \\ \cos B=0.6 \end{gathered}\)For the 2nd Triangle:
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{5}{8} \\ \cos B=0.625 \end{gathered}\)For the 3rd Triangle:
We have to first determine the value of side AB using the Pythagorean theorem as seen below;
\(\begin{gathered} AB^2=4^2+5^2 \\ AB^2=16+25 \\ AB=\sqrt{41} \end{gathered}\)So cosine B will be;
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{4}{\sqrt{41}} \\ \cos B=0.62 \end{gathered}\)For the 4th Triangle:
\(\begin{gathered} \cos B=\frac{adjacent\text{ }side\text{ }to\text{ }angle\text{ B}}{hypotenuse} \\ \cos B=\frac{4}{5} \\ \cos B=0.8 \end{gathered}\)So in the below triangle cos B = 0.8
With respect to the diagram, which relationship is false if ∠FEA is supplementary to ∠HGD?
Answers
The statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:
A. measure of angle FEB + measure of angle HGD = 180°
What are Supplementary Angles?By definition, supplementary angles are two angles that have a sum of 180 degrees when added together, that is, one is a supplement of the other.
Given the image below, we know the following:
Since angle FEA is supplementary to angle FEA would be congruent to angle HGC, and angle HGD is congruent to angle FEB. This is because, the supplement of angle
angle FEA + angle FEB - angle FEA + angle HGD = 180° - 180°. Therefore,
angle FEB = angle HGD.
In summary, from the options given, the statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:
A. measure of angle FEB + measure of angle HGD = 180°
Learn more about supplementary angles on:
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