Answer: The probability statement that would yield an acceptable approximation is 1-P(X>25).
To see why, we first need to check if the conditions for using the Normal approximation to the binomial distribution are met. These conditions are:
The number of trials is large (n ≥ 10)
The probability of success for each trial is approximately the same (p is roughly constant)
The number of successes and failures are both at least 5 (np ≥ 5 and n(1-p) ≥ 5)
In this case, we have n = 150 and p = 0.1, so np = 15 and n(1-p) = 135, which satisfy the conditions.
To use the Normal approximation, we need to standardize the binomial distribution. We have:
mean = np = 15
standard deviation = sqrt(np(1-p)) = sqrt(13.5)
To find P(X>25), we can standardize X and use the Normal distribution:
Z = (25 - 15) / sqrt(13.5) = 3.06
P(X>25) = P(Z > 3.06) ≈ 0.0011
This means that the probability of more than 25 students in a class of 150 being left-handed is approximately 0.0011.
Therefore, the probability statement that yields an acceptable approximation is 1-P(X>25).
Step-by-step explanation:
The probability statement P(X<25) would yield an acceptable approximation, as it corresponds to the number of left-handed students being less than 25 out of the total of 150 students.
The chance of success raised to the power of the number of triumphs and the probability of failure raised to the power of the difference between the number of successes and the number of attempts are multiplied to create the binomial distribution.
For instance, if we flip a coin, there are only two potential results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial chance distribution is another name for this distribution.
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Put the steps in order to solve this inequality 4x + 7 ⪯ 15
A. Subtract 7 from both sides of the inequality.
B. Divide both sides of the inequality by 4
C. Simplify; leaving only 4x on one side of the inequality.
D. Find your answer; x ⪯ 2
Answer:
C. Simplify
Step-by-step explanation:
1. Subtract 7 from both sides
4x +7 -7 < 15 -7
4x < 8
2. divide both sides by 4
4x/4 < 8/4
answer: x < 2
hope this helps
solve using elimination
5x-y=-6
x-y=-2
Answer: 5x/5 = -6/5 + y/5
Step-by-step explanation:
x = -6 + y/5
and then x = -2 +y
Conner worked on Monday, M, and Friday, F, for a total of 12 hours. He charges $5 per hour on Monday and $8 per hour on Friday. If the total amount Conner received was $81, how many hours did he work on Monday
Conner worked 5 hours on Monday.
Let's use the letters "m" and "f" to denote the number of hours Conner worked on Monday and Friday, respectively.
Conner worked a total of 12 hours, and since we know this from the issue statement, we may write:
m + f = 12
Also, we are aware that Conner received $81 and charged $5 on Mondays and $8 on Fridays. Hence, we can write:
5m + 8f = 81
To determine one of the variables in terms of the other, we can utilise the first equation. To solve for "f," we obtain:
f = 12 - m
We can now solve for "m" by substituting this expression for "f" in the second equation:
5m + 8(12 - m) = 81
After simplifying and finding "m," we obtain:
5m + 96 - 8m = 81
-3m + 96 = 81
-3m = -15
m = 5
Conner spent 5 hours at work on Monday as a result.
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Brian wants to exchange South African rands for British pound if one is were 30 commerce 07519 9 lb how many pounds will he get for 2100 if he must pay an agency commission of 1.5%
Answer:
We can approach this problem using the following steps:
Calculate the exchange rate after factoring in the agency commission. Since the agency commission is 1.5%, the effective exchange rate will be:
Effective exchange rate = Exchange rate - (Exchange rate * Commission rate)
= 30.075199 - (30.075199 * 0.015)
= 29.6185968
Multiply the amount of South African rands by the effective exchange rate to get the amount in British pounds.
Amount in pounds = Amount in rands / Exchange rate
So, for an amount of 2100 South African rands, the calculation would be:
Amount in pounds = 2100 / 29.6185968
= 70.815 pounds (rounded to three decimal places)
Therefore, Brian will get 70.815 pounds for 2100 South African rands after factoring in the agency commission.
what is the surface area of the rectangular prism below
Answer: A=490
Step-by-step explanation:
Formula - A = 2 ( wl + hl + hw)
2(7•14+7•14+7•7) = 490
A right triangle is removed from a rectangle to create the shaded region shown below find the area of the shaded region be sure to include the correct unit and your answer 3 ft 3 ft 8ft 10ft
The area of shaded region is 45 square units.
How to determine the area of shaded region?The complete question is added as an attachment
The area of the shaded region is calculated as
Shaded region =Area of rectangle - Area of triangle
Using the above as a guide, we have the following:
Area of rectangle = 8 * 6 = 48
Area of triangle = 1/2 * 2 * 3 = 3
Substitute the known values in the above equation, so, we have the following representation
Shaded region = 48 - 3
Evaluate the difference
Shaded region = 45
Hence, the shaded region is 45 square units.
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find the area of a figure with 4cm 3 cm and 10 cm
How can you show that two fractions are reciprocals?
Subtract the fraction from its reciprocal. Their difference will be 1.
Divide a fraction by its reciprocal. This will show that the quotient is always 1.
Multiply a fraction by its reciprocal to show that their product is always 1.
Add the fraction and its reciprocal. Their sum will be 1.
Answer:
To show that two fractions are reciprocals, you can multiply them together and check if the product is equal to 1. That is, if we have two fractions a/b and b/a, their product is:
(a/b) * (b/a) = ab / ba = 1
Therefore, if the product of two fractions is equal to 1, they are reciprocals of each other.
For example, let's say we have the fractions 2/5 and 5/2. We can multiply them together to check if they are reciprocals:
(2/5) * (5/2) = 1
Since the product is equal to 1, we can conclude that 2/5 and 5/2 are reciprocals of each other.
in a group of 23 people, what is the probability at least 2 have the same birthday? you may assume no one was born on a leap year and that each of the 365 days is equally likely. (suggestion: use the rule for complements)
The probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.
The probability of at least 2 people having the same birthday in a group of 23 people can be calculated using the rule for complements. The complement of this event is that all 23 people have different birthdays. We can calculate the probability of this event and then subtract it from 1 to find the probability of at least 2 people having the same birthday.
The probability of the first person having a different birthday from the others is 1. The probability of the second person having a different birthday from the first is 364/365, since there are 364 days left that are not the first person's birthday. The probability of the third person having a different birthday from the first two is 363/365, and so on.
The probability of all 23 people having different birthdays is:
1 * (364/365) * (363/365) * ... * (343/365)
This simplifies to:
364! / (36522 * 341!)
Using a calculator, we find that this is approximately 0.4927.
Therefore, the probability of at least 2 people having the same birthday is:
1 - 0.4927 = 0.5073
So, the probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.
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In a group of 23 persons, the probability that at least two of them share the same birthday is around 0.5073, or 50.73%.
The probability that at least 2 people in a group of 23 have the same birthday, can be calculated by using the rule for compliments. First, we can calculate the probability that no two people share a birthday in a group of 23.
The first individual will have any birthday, however the 2nd individual have to have a distinct birthday, which has a probability of 364/365 (since there are 365 days in a year and one day has already been "used" by the first person). The probability that the third individual will have a different birthdate from the previous two is 363/365. Continuing in this way,
The probability that all 23 people have different birthdays is:
(365/365) x (364/365) x (363/365) x ...
Since the probabilities of all conceivable outcomes must sum up to 1, subtract the likelihood that at least two persons will have the same birthdate from one:
P(at least 2 people have the same birthday) = 1 - (365/365) x (364/365) x (363/365) x ... x (344/365)
P(at least 2 people have the same birthday) = 0.5073
Therefore, the probability that at least 2 people in a group of 23 have the same birthday is approximately 0.5073 or 50.73%
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If you can afford $900 to $1080 apartments. How much do you make a year?
Answer:
$43,200
Step-by-step explanation:
The amount of money you make a year depends on various factors, such as your monthly expenses, debt obligations, and tax liabilities.
To get a rough estimate of your annual income based on the range of affordable rent provided, you can use the rule of thumb that suggests spending no more than 30% of your gross income on housing expenses. Assuming you are willing to spend between $900 and $1080 per month on rent, we can calculate the range of annual incomes that would allow you to meet this guideline:
$900/month rent x 12 months = $10,800/year rent
$10,800/year rent / 0.3 = $36,000/year gross income
$1080/month rent x 12 months = $12,960/year rent
$12,960/year rent / 0.3 = $43,200/year gross income
Therefore, based on the assumption that you can afford rent between $900 and $1080 per month, your estimated annual gross income would need to be in the range of $36,000 to $43,200. However, this is only a rough estimate and may not take into account all of your individual financial circumstances.
Whose work is correct?
Elise’s work
Jake’s work
Malik’s work
Xiao’s work
Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.
Answer:
Maliks
Step-by-step explanation:
What is the total surface area of the gift box in in2?
The total surface area of the gift box in discuss as required to be determined in the task content is; 416 in².
Surface area of a cuboidAs evident in the task content; the gift box in discuss can be likened to a cuboid with dimensions; 12 by 10 by 4.
Hence, since the total surface area of a cuboid is given by;
Area = 2 (lw + lh + wh)
Therefore, for the given gift box;
Area = 2 ( (12×10) + (12 × 4) + (10 × 4) )
= 2 ( 120 + 48 + 40 )
= 2 (208)
= 416.
Ultimately, the total surface area of the gift box in discuss is; 416 in².
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The Central Limit Theorem states that The sampling distribution of the sample standard deviation will be approximately normal as long as the sample size is large enough. The sampling distribution of the sample mean will be approximately normal as long as the original population is normal. The distribution of the sample will be approximately normal as long as the sample size is large enough. The sampling distribution of the sample mean will be approximately normal as long as the sample size is large enough regradless of the underlying population distribution. QUESTION 14 Assume that the time spent on social media daily by ZU students has a mean of 130 minutes and a standard deviation of 43 minutes. If random samples of 246 students are selected, find the standard error of the mean? Round your answer to 2 decimal places. QUESTION 15 Assume that the speed of vehicles traveling on MBZ Highway is normally distributed with a mean of 108 km/h with a standard deviation of 5.5 km/h. According to the empirical rule, 95.44% of the speeds of vehichles traveling on MBZ Highway will be between 97 and 119 km/h 86 and 130 km/h 102.5 and 113.5 km/h 91.5 and 124.5 km/h
14: 2.38 minutes
15: lower bound is 97 km/h and the upper bound is 119 km/h
Question 14: The standard error of the mean (SE) can be calculated using the following formula: SE = s/√n, where s is the standard deviation of the population (43 minutes) and n is the sample size (246 students). Plugging in the values, SE = 43/√246 ≈ 2.38. Therefore, the standard error of the mean is 2.38 minutes and it should be rounded to 2 decimal places, giving us 2.38 minutes.
Question 15: According to the empirical rule, 95.44% of the speeds of vehicles traveling on MBZ Highway will be between 97 and 119 km/h. Therefore, the lower bound is 97 km/h and the upper bound is 119 km/h.
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6. Mary has two account at the bank. She deposits $1000 into the first account that earns 7%
simple interest every year. She deposits the same amount into her second account that earns
6% interest compounded annually. After 6 years, which account will have earned the most
interest?
After 6 years, the first accοunt with simple interest earn mοre amοunt.
What is simple interest and cοmpοund interest?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.
Here In first bank account ,
Principal P = $1000
Time N = 6
Rate οf interest = 7%
Interest = [tex]\frac{PNR}{100}[/tex]
=> I = [tex]\frac{1000\times7\times6}{100}[/tex] = $420
Tοtal amount = $1000+$420 = $1420.
Now in secοnd bank account,
Principal P = $1000
Times N= 6
Rate οf interest = 6%
Tοtal amount A = [tex]P(1+\frac{R}{100})^N[/tex]
=> A = [tex]1000(1+\frac{6}{100})^6[/tex]
=> A = $1418.00
Now cοmparing bοth account amounts , In first bank have earned more amount that second bank,
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3.6.2 Reflect the plane in the x-axis, and then in the line y = 1/2. Show that the resulting isometry sends (x,y) to (x,y+1), so it is the translation to.1. 3.6.3 Generalize the idea of Exercise 3.6.2 to show that the combination of reflec- tions in parallel lines, distance d/2 apart, is a translation through distance d, in the direction perpendicular to the lines of reflection. 3.6.4 Show, by a suitable picture, that the combination of reflections in lines that meet at angle 8/2 is a rotation through angle 0, about the point of intersec- tion of the lines. Another way to put the result of Exercise 3.6.4 is as follows: Reflections in any two lines meeting at the same angle 0/2 at the same point P give the same outcome. This observation is important for the next three exercises (where pictures will also be helpful).
The transformation as a whole is given by P → Q → R → S. A rotation through angle, about the intersection point of the lines, results from the combination of reflections in lines that meet at angle /2.
Two reflections across intersecting lines equal what?Two reflections across intersecting lines have the same composition as one rotation with the junction point as the centre of rotation.
By (0,-1/2), the initial translation is provided.
Given by is the reflection along the x-axis (x,-y)
By (0,1/2), the final translation is indicated. Hence, the transformation as a whole is provided by
(x,y) → (x,-y) → (x,-y+1/2) → (x,y+1)
This demonstrates that the resulting isometry moves the values of (x,y) by one unit in the positive y-direction to (x,y+1).
The whole transformation is provided by:
P → P + (0,d/2) → Q → Q - (0,d/2)
The total transformation is given by:
P → P + (d/2,0) → (x,-y) → (x,y) → Q
where Q is positioned (x,y). Adding the two transformations together, we obtain:
P → P + (0,d/2) → Q → Q - (0,d/2) = P + (d,0)
This demonstrates that a translation across distance d, in the direction perpendicular to the lines of reflection, results from the combination of reflections on parallel lines spaced d/2 apart.
The total transformation is given by:
P → Q → R → S
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A city bus collected $780 in fares in one day. The price of a regular fare was $0.80, and the price of a discount fare was $0.40. If a total of 1200 paid the fares on this bus, write a system of equations that represents this situation.
its b
i have covid and want to know what to do
The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number? Enter your answer as a fraction.
Answer:
6/100=3/50
Step-by-step explanation:
The first bag contains the numbers 1 through 10, which is a total of 10 numbers. The second bag contains the numbers 5 through 14, which is also a total of 10 numbers.
The probability of picking the same number from both bags is the number of ways of picking the same number divided by the total number of possible outcomes. There are 10 possible outcomes in each bag, so the total number of possible outcomes is 10 × 10 = 100.
To count the number of ways of picking the same number, we can simply count the number of numbers that appear in both bags. There are six numbers that appear in both bags: 5, 6, 7, 8, 9, and 10.
Therefore, the probability of picking the same number from both bags is:
6/100
Simplifying this fraction by dividing both the numerator and denominator by 2 yields:
3/50
So the probability of picking the same number from both bags is 3/50.
Farud had 4 ⅓ bags of M&Ms left after Halloween. Jackson had ¹³⁄₃ bags of M&Ms left. Farud said that he had more because he had 4 whole bags and Jackson had no whole bags. Is he correct? Explain how you know on the lines below.
Answer:
he is incorrect because Jackson also has 4 whole bags because 13/3 is a mixed number therefore jackson really has 4 13/3 or 4 1/3 which would be the amount as Fraud
Step-by-step explanation:
100 points please help
Answer:
(x + 1) (3x + 5)
Step-by-step explanation:
Let's check
(x + 1) (3x + 5)
3x² + 5x + 3x + 5
3x² + 8x + 5
So, (x + 1) (3x + 5) is the correct answer.
A Mixture of punch contains 1 quart of lemonade 2 cups of grape juice 4 tablespoons of honey and a half gallon of sparkling water. Find a percentage of the punch mixture that comes from each ingredient round your answer to the nearest 10th of a percentage. What is the lemonades percentage?
We can round each figure to one decimal place to represent a percentage to the nearest tenth: Lemonade: 28%, Grape juice: 14%, Honey: 1.8% and Sparkling water: 56.2%. So, the lemonade contributes approximately 28% to the punch mixture.
Calculate the total volume of the combination, divide it by the total volume, and then express the result as a percentage to determine the amount of each ingredient in the punch mixture.
1 quart = 4 cups
1/2 gallon = 8 cups
4 tablespoons = [tex]\frac{1}{4}[/tex] cups
So the total volume of the mixture is:
4 cups (lemonade) + 2 cups (grape juice) + [tex]\frac{1}{4}[/tex] cups (honey) + 8 cups (sparkling water) = [tex]\frac{57}{4}[/tex] cups
Now, we can calculate the percentage of each ingredient in the mixture:
Lemonade: [tex]\frac{4}{(\frac{57}{4})}*100[/tex] ≈ 28%
Grape juice: [tex]\frac{2}{(\frac{57}{4})}*100[/tex] ≈ 14%
Honey: [tex]\frac{(\frac{1}{4})}{(\frac{57}{4})}*100[/tex] ≈ 1.8%
Sparkling water: [tex]\frac{8}{(\frac{57}{4})}*100[/tex] ≈ 56.2%
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Approximate, to the nearest 0.1˚, all angles θ in the interval [0˚, 360˚)[0˚, 360˚) that satisfy the equation. (Enter your answers as a comma-separated list.)
(a) sinθ=0.6264
(b) cosθ=−0.6405
(c) tanθ=−1.5519
(a) 40.4° or 139.6°
(b) 137.6° or 222.4°
(c) 124.2° or 304.2°
(a) sinθ=0.6264:θ=40.4° or 139.6°
(b) cosθ=-0.6405:θ=137.6° or 222.4°
(c) tanθ=-1.5519:θ=124.2° or 304.2°.What is interval? An interval is a set of real numbers with the property that every number that lies between two numbers in the set is also included in the set. Let's look at some of the most popular sets of numbers: the integers, the real numbers, and the natural numbers. What is an angle? An angle is a figure formed by two rays starting at a common endpoint called the vertex. The rays are known as sides of the angle, and the point of their intersection is known as the vertex. Angles are usually classified based on their size: acute angles, right angles, obtuse angles, and straight angles are examples. The following is how to solve the problem; 1. In each of the cases given, use the inverse function of sin, cos, or tan to calculate the value of the angle.2. Ascertain if the angle you've calculated is in the required interval.3. Since this question asks for an approximation to the nearest 0.1 degrees, express your solutions to one decimal point.Let's look at the following options:(a) sinθ=0.6264θ = 40.4° or 139.6°(b) cosθ=−0.6405θ = 137.6° or 222.4°(c) tanθ=−1.5519θ = 124.2° or 304.2°.Therefore, to the nearest 0.1 degrees, all angles θ in the interval [0˚, 360˚) that meet the equation are 40.4°, 139.6°, 137.6°, 222.4°, 124.2°, and 304.2°.
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what is the answer to this?
[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response as Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression.
what is polynomial ?Using just the methods of addition, elimination, and multiplication as well as ou pas integer exponents, a polynomial is a mathematical equation made up of variables and coefficients. A polynomial, for instance, is 3x2 - 2x + 5, where x has been the component and 3, -2, and 5 are now the coefficients. This polynomial's highest exponent is 2, which also happens to be its degree. Polynomials can have coefficients that are either constants or other polynomials, as well as many variables. Due to their usage in representing a variety of mathematical relations and functions, polynomials play a significant role in mathematics. Several disciplines, including algebra, algebra, geometry, and physics, make extensive use of them.
given
To make [tex]5x^2-x-8x^2 + 3x^3[/tex]simpler, we can rearrange the terms and join comparable terms:
[tex]0 + 3x^3 - x - 3x^2 = 5x^2 - 8x^2 + 3x^3 - x[/tex]
The following step is to factor the final three terms to remove a common factor of x:
[tex]3x^3 - x - 3x^2 = x\\(3x^2 - 1 - 3x)[/tex]
Hence, the abbreviated form is:
[tex]3x^2 - 1 - 3x^3 = 5x^2-x-8x^2 + 3x^3.[/tex]
Due to the fact that Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression, it is incorrect.
Due to their failure to simplify to the specified formula, options A, [tex]-5x^3+ x^2 = 0,[/tex] and D, [tex]3x^3 -3x^2 =6x[/tex], are likewise incorrect.
[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response.
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The complete question is:-
Simplify: [tex]5x^2-x-8x^2 + 3x^3 = 5x[/tex]
OA.-5x3x2 = 0
B. 3x3 + x2 = 6x
C. 3x3 + x2 = 0
D. 3x3 3x26x
-
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Is 12 a integer and is 55.3 a integer and is 18 over 2 a integer and is -260.43 a integer and is 12 over 17 a integer ?
Answer:
yes
no
yes
no
no
Step-by-step explanation:
An integer is a positive or negative whole number or zero.
Examples of integers:
-1000, 993, 12, -19, 1000000, -79, 0, 1, 221
Examples of numbers that are not integers:
-5/4, -223.25, 1000.1, 45.2, 1000000.45, 32/7
Is 12 a integer yes
and is 55.3 a integer no
and is 18 over 2 a integer = 9, so yes
and is -260.43 a integer no
and is 12 over 17 a integer =0.70588..., so no
magine that party a is selling a car to party b. party a thinks there is an 80% chance the car will not break down in the first year, while party b thinks there is an 80% chance it will. design a contingency contract that could help them avoid an impasse over this issue.
The steps taken to design a contingency contract are valuating the potential outcomes, consequences and agree on terms of contract.
Identify the potential outcomes. Party A thinks that there is an 80% chance that the car will not break down in the first year, while Party B thinks that there is an 80% chance that it will. These are the two potential outcomes that need to be identified.
Determine the consequences of each outcome. Next, the consequences of each outcome should be determined. For example, if the car breaks down in the first year, then Party A may have to pay for repairs or reimburse Party B for the purchase price of the car. If the car does not break down, then no consequences need to be determined.
Agree on the terms of the contract. Finally, both parties need to agree on the terms of the contract. This may include how much Party A will have to pay if the car breaks down, how long Party B has to wait for reimbursement if the car does break down, and any other terms that are relevant to the situation. Once the terms have been agreed upon, the contingency contract can be signed by both parties, and they can proceed with the sale of the car.
A contingency contract could be designed to help them avoid an impasse over the issue of the car's breakdown. The contingency contract is a contract that is triggered by a specific event or circumstance, such as the car breaking down in the first year. This contract outlines what will happen if the event or circumstance occurs, and both parties agree to the terms in advance.
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the circumference of a circle is 38.8km find the length of the radius give your answer rounded to 3 SF
Answer:
6.18km
Step-by-step explanation:
circumference= diameter×π
38.8km÷π=12.350423583931.... this is the diameter
12.3504...÷2=6.1752117919655..... is the radius
radius rounded to 3sf= 6.18km i think
How would i find percent of a number in this case 81% of 108 The work part i have the answer
I dont know how to do this
pls answer if u know with simple working
i dont know if u add 4 each time it didnt work for last questionn
The 3rd term of the linear sequence above is 14.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 18 - 22
Common difference, d = -4
For the third term, we have:
a₃ = a₁ + (n - 1)d
a₃ = 22 + (3 - 1)-4
a₃ = 22 - 8
a₃ = 14.
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A fish swims down at a rate of 12 ft per hour. If it started at the surface and swims for 6 hours where will it end up?
Answer:
Since the fish is swimming down at a constant rate of 12 ft per hour for 6 hours, the distance it travels can be found by multiplying its speed by the time:
distance = speed x time
distance = 12 ft/hour x 6 hours
distance = 72 ft
Therefore, the fish will end up 72 feet down from the surface.
In the given the figure above, m∠BAC= 64° and m∠CBA=56°.
Part I: Find the m∠DEC .
Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
I. The measure of angles DEC is: 60°
II. The theorems used are corresponding angles and triangle sum theorems.
What is the Triangle Sum Theorem?
We are given the following:
m∠BAC = 64°
m∠CBA = 56°
AB║CD
BC║DE
Considering triangle ABC, we have:
m∠BCA = 180 - m∠BAC - m∠CBA [triangle sum theorem]
Substitute:
m∠BCA = 180 - 64 - 56
m∠BCA = 60°
Therefore, based on the corresponding angles theorem,
m∠DEC = m∠BCA
Substitute:
m∠DEC = 60°
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What is the answer in the photo
The sales price of the item after deduction of percentage discount is: $18
How to find the discounted price?The regular price is defined as the price at which similar goods or services are regularly sold on the market.
The discount is defined as an amount or perhaps percentage deducted from the normal selling price of something.
The sales price is defined as the actual amount for which a good is sold after deduction of discount if any.
The parameters given are:
Regular Price = $20
Percentage Discount = 10%
Thus:
Discount = 10% * 20
Discount = $2
Thus:
Sales Price = $20 - $2
= $18
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