Answer:
To the nearest tenth of a degree
∠E= 47.9°
Step-by-step explanation:
ΔDEF , let's recognize that it's a right angle triangle because of the presence of ∠F=90°.
Other important measurements are
DE = 82 feet, and EF = 55 feet.
We are to find ∠E
Let's find the missing side first
Side DF
DF² = DE² - EF²
DF²= 82²_55²
DF²=6724-3025
DF²= 3699
DF= 60.82 feet
Let's use the sine formula to look for the angle.
DF/sin ∠E= DE/sin 90
Sin 90= 1
DE= 82
DF= 60.82
Sin ∠E= DF/DE
Sin ∠E= 60.82/82
Sin ∠E= 0.7417
∠E= sin^-1 (0.7417)
∠E= 47.8764
To the nearest tenth of a degree
= 47.9°
Darío buys applesauce cups for a family reunion. He needs 23 cups, and he buys them in packs of 6. How many packs does Dario need?
Answer:
He needs four packs.
Step-by-step explanation:
6*4=24 there is 23 so he will need 4 packs in total.
Answer:
4 packs
Step-by-step explanation:
3 packs only gives him 18 and he needs atleast 23. The closest number that meets 23 is 24. It takes 4 packs of 6 to get 24.
Bad gums may mean a bad heart. Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 33% of healthy people have this disease. Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability. A. If someone has periodontal disease, what is the probability that he or she will have a heart attack
Answer:
37.27% probability that he or she will have a heart attack.
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Periodontal disease
Event B: Heart attack
Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums.
This means that [tex]P(A|B) = 0.82[/tex]
Only 33% of healthy people have this disease.
This means that [tex]P(A) = 0.33[/tex]
Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability.
This means that [tex]P(B) = 0.15[/tex]
If someone has periodontal disease, what is the probability that he or she will have a heart attack
[tex]P(B|A) = \frac{0.15*0.82}{0.33} = 0.3727[/tex]
37.27% probability that he or she will have a heart attack.
Which expression is equal to 5y^3÷5y^-2
Answer:
[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]
Step-by-step explanation:
[tex]5y^3/5y^-2[/tex]
as 5 is both in numerator and denominator it will get cancelled so we have now expression
[tex]y^3/y^-2[/tex]
we will use law of indices wherein if there is
[tex]a^x/a^y = a^(x-y)[/tex]
which means that if the base is same in numerator and denominator then we have to subtract the power of denominator from numerator to get the reduced form using this concept
here power in numerator is 3 and power in denominator is -2
hence we will be subtracting -2 from 3
[tex]y^3/y^-2 = y^(3-(-2) = y^(3+2) = y^5[/tex]
Thus,
[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]
A random sample of a specific brand of snack bar is tested for calorie count, with the following results: Assume the population standard deviation is σ and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars.
Answer:
The 95% confidence interval for the population mean (calorie count of the snacks bars) is (130.32, 161.68).
Step-by-step explanation:
The question is incomplete:
"A random sample of a specific brand of snack bar is tested for calorie count, with the following results: 149, 145,140,160,149,153,131,134,153. Assume the population standard deviation is σ=24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars."
We start by calculating the mean of the sample:
[tex]M=\dfrac{1}{9}\sum_{i=1}^{9}(149+145+140+160+149+153+131+134+153)\\\\\\ M=\dfrac{1314}{9}=146[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is know and is σ=24.
The sample mean is M=146.
The sample size is N=9.
As σ is known, the standard error of the mean (σM) is calculated as: [tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{24}{\sqrt{9}}=\dfrac{24}{3}=8[/tex]
The z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_M=1.96 \cdot 8=15.68[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 146-15.68=130.32\\\\UL=M+t \cdot s_M = 146+15.68=161.68[/tex]
The 95% confidence interval for the population mean is (130.32, 161.68).
does anyone know this ?
Answer:
Always
Step-by-step explanation:
If the irrational parts of the numbers have zero sum, the sum is rational. If not, the sum is irrational. It is true, for example, for 2 7, 3. It is false, for example, for3+2 5,−2 5 .
Answer:
always
Step-by-step explanation:
Rational numbers can be expressed as a fraction of two integers. So, adding two rationals is the same as adding two such fractions.
The kitchen-tile installer has 20 green, 14 beige, and 16 white tiles in a box. What is the probability of picking a beige tile from the box without looking?
Answer: P = 0.28
Step-by-step explanation:
If we pick it at random, the probability of selecting each tile must be equal. this means that the probability of picking a tile of a giving color is equal to the number of the tiles of that color divided the total number of tiles.
We have 14 beige tiles and 20 + 14 + 16 = 50 tiles in total.
Then the probability of piking a beige tile is:
P = 14/50 = 0.28
Explain the meaning of the following percentiles in parts (a) and (b). (a) The 10th percentile of the weight of males 36 months of age in a certain city is 11.0 kg. (b) The 90th percentile of the length of newborn females in a certain city is 53.3 cm.
Answer:
a) 10% of the babies with 36 months of age weigh less than 11kg, and 100 - 10 = 90% weigh more.
b) 90% of the newborn females have a lenght of less than 53.3 cm and 100 - 90% = 10% have a length higher than 53.3 cm.
Step-by-step explanation:
Meaning of a percentile:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
(a) The 10th percentile of the weight of males 36 months of age in a certain city is 11.0 kg.
10% of the babies with 36 months of age weigh less than 11kg, and 100 - 10 = 90% weigh more.
(b) The 90th percentile of the length of newborn females in a certain city is 53.3 cm.
90% of the newborn females have a lenght of less than 53.3 cm and 100 - 90% = 10% have a length higher than 53.3 cm.
The dean of the engineering school at a technical university wants to emphasize the importance of having students who are gifted at reading and writing as well as math. She wants to know if she can accurately claim that graduate students in engineering programs at her school have significantly higher scores on the verbal reasoning section of the GRE (a standardized test used in the admissions process for many graduate programs) than the national average for engineering students. The national average for the verbal reasoning GRE score for engineering students was 150 with a standard deviation of 9. A random sample of 49 engineering graduate students at her school were found to have an average verbal reasoning GRE score of 153. After analyzing the data to determine whether the mean verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the national average, the p-value of 0.0099 was obtained. Using a 0.05 significance level, what conclusion can be drawn from the data?
Answer:
Step-by-step explanation:
The null hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is less than or equal to the national average: u ≤ 150
The alternative hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average: u > 150
Since the p-value of 0.0099 was gotten which is less than the significance level of 0.05, we reject the null hypothesis and conclude that actually there is a statistically significant evidence to prove that the mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average
Nathan recently bought a paint sprayer for his painting business. Over the last seven days, he has used 211 gallons of paint to cover
79,125 square feet of wall space. If Nathan uses the sprayer approximately 4 hours each day, how many ounces of paint is the
sprayer dispensing each minute?
Answer: 16.1 ounces per minute
Step-by-step explanation:
in 7 days, he painted by 4 hours each day, so we have a total of 28 hours.
In a hour we have 60 minutes, so we have a total of:
28*60 = 1680 minutes.
He used 211 gallons, and knowing that 1 gallon is 128 ounces, then 211 gallons is:
211*128 ounces = 27,008 ounces.
Then the ounces dispensed each minute are:
R = 27,008/1680 ounces per minute = 16.1 ounces per minute
What are the best data structures to create the following items? And why? Designing a Card Game with 52 cards. Online shopping cart (Amazon, eBay, Walmart, Cosco, Safeway, ...) Online waiting list (De Anza College class waiting list, ...) Online Tickets (Flight tickets, concert tickets, ...)
Answer:
The best data structure in storing card is an array.
The best choice for a shopping cart is hash-maps. the advantage of harsh mark is that they are dynamic in nature.
Waiting lists are managed by a method called the First In First Out. when an individual is waiting for too long, he or she should be given the first chance for service.
Sorted links are a better options for storing tickets.
Step-by-step explanation:
Solution
In other to store the cards the best structure to be applied here is an array.
Now, we are aware the array size, which comprises of 52 items, and hence card vales can be easily stored For standard 52-deck cards, a 2D array of size 4x15 can also be applied, with 4 being color count, and 13 being card in each color.
In this example, the better option for shopping cart is hash-maps, because it is dynamic in nature for instance, when items are removed and more often, and also, there is a need for mapping of item ID or name to its actual database, so these values can be kept or stored as key-value pairs.
Waiting lists are normal managed in a way of First In First Out, since a person is waiting longer should be given the first chance for service. this FIFO method is best used by a Queue. so this online waiting list can best be used by a queue.
For tickets storing, a better option will be the sorted linked lists. because the tickets are to be stored in a large amount, and there will be deletions and insertions in large quantity. so keeping them in a sorted list will reduce the resource usage and the trade-off made as high search time will also have less effect, as there will be a limited number of searches.
What’s the correct answer for this?
Answer:
1/4
Step-by-step explanation:
Let's denote the probabilities as following:
Probability that a teenager has a sister:
P(A) = 12/28
Probability that a teenager has a brother:
P(B) = 7/28
Probability that a teenager has both a sister and a brother:
P(A⋂B) = 3/28
Probability that a selected teenager has a sister also has a brother, or in other words, he/she has a brother, given he/she had a sister:
P(B|A)
Let's apply the formula of conditional probability to work out P(B|A)
P(B|A) = P(A⋂B)/P(A) = (3/28)/(12/28) = (3*28)/(12*28) = 3/12 = 1/4
=> Option C is correct
Hope this helps!
A recent study reported that 73% of Americans could only converse in one language. A random sample of 130 Americans was randomly selected. What is the probability that 100 or fewer of these Americans could only converse in one language?
Answer:
Probability that 100 or fewer of these Americans could only converse in one language is 0.8599.
Step-by-step explanation:
We are given that a recent study reported that 73% of Americans could only converse in one language.
A random sample of 130 Americans was randomly selected.
Let [tex]\hat p[/tex] = sample proportion of Americans who could only converse in one language.
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, p = population proportion of Americans who could only converse in one language = 73%
[tex]\hat p[/tex] = sample proportion = [tex]\frac{100}{130}[/tex] = 0.77
n = sample of Americans = 130
Now, probability that 100 or fewer of these Americans could only converse in one language is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77)
P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.77-0.73}{\sqrt{\frac{0.77(1-0.77)}{130} } }[/tex] ) = P(Z [tex]\leq[/tex] 1.08) = 0.8599
The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.
Write down the 1st term in the sequence given by: T(n) = n2 + 3
Answer:
5
To find the first term
T(1)=(1×2)+3
=2+3
=5
¿Pueden ser complementarios un ángulo agudo y un ángulo obtuso?
Answer:
No porque si sumas los dos el resultado es más de 90 grados.
Step-by-step explanation:
The perimeter of a rectangle is 202. The length is 26 more than 4 times the width. Find the dimensions
Length and width of rectangle is 86 unit and 15 unit
Given that;
Perimeter of a rectangle = 202
Length of rectangle = 26 + 4[Width]
Find:
Dimensions of rectangle
Computation:
Assume;
Width of rectangle = a
So,
Length of rectangle = 4a + 26
Perimeter of a rectangle = 2[l + b]
202 = 2[(4a + 26) + a]
101 = 4a + 26 + a
5a + 26 = 101
5a = 75
a = 15
Width of rectangle = 15 unit
Length of rectangle = 4a + 26
Length of rectangle = 4(15) + 26
Length of rectangle = 60 + 26
Length of rectangle = 86 unit
Learn more:
https://brainly.com/question/16669749?referrer=searchResults
Please answer this correctly without making mistakes
Answer:
1st one, I think so. I'm pretty positive
Answer:
1st Option (4 Blocks)Step-by-step explanation:
So, in this image, there are 6 blocks in total!
The little guy standing in front would only be able to see the bottom two cubes, along with the top two, making 4 blocks in total! :3
#SpreadTheLove <3
Esther, Vida, and Clair were asked to consider two different cash flows: GH¢1000 that they could receive today and GH¢3000 that would be received 3 years from today. Esther wanted the GH¢1000 today, Vida chose to collect GH¢3000 in 3 years, and Clair was indifferent between these two options. Which of the three women made the right choice
Answer:
Step-by-step explanation:
The explanation is given in the attached picture below
"Opportunity" and "Phoenix" are two of the robotic explorers on Mars. Opportunity landed at 2° south latitude, where Mars’ radius is about 2110 miles. Phoenix landed at 68° north latitude, where Mars’ radius is about 790 miles. Mars rotates on its axis once every 24.6 Earth-hours. How far does each explorer travel as Mars rotates by 1 radian? How many hours does it take Mars to rotate 1 radian? Using this answer, how fast is each explorer traveling around Mars’ axis in miles per hour?
Answer:
(a)Distance traveled by each explorer travel as Mars rotates by 1 radian
Opportunity=2108.71 milesPhoenix =295.94 miles(b)Number of hours it takes Mars to rotate 1 radian=3.9152 hours
(c)Speed of each explorer around Mars.
Opportunity=538.59 miles per hourPhoenix =75.59 miles per hourStep-by-step explanation:
Part A
For any given parallel of latitude[tex]\text{Circumference}=2\pi R \cos \beta$ where \beta$ is the angle of latitude.[/tex]
Opportunity landed at 2° south latitude, where Mars’ radius is about 2110 miles.
[tex]\text{Circumference at 2\°S latitude}=2\pi*2110* \cos 2^\circ\\=13249.44$ miles[/tex]
Phoenix landed at 68° north latitude, where Mars’ radius is about 790 miles.
[tex]\text{Circumference at 68\°N latitude}=2\pi*790* \cos 68^\circ\\=1859.44$ miles[/tex]
Part B
Next, we determine the distance (Length of arc) covered by each explorer as Mars rotates by 1 radian.
[tex]\text{Length of arc (in radian)}=\dfrac{\theta}{2\pi} \times $Circumference[/tex]
Opportunity's Distance
[tex]=\dfrac{1}{2\pi} \times 13249.44\\\\ =2108.71$ miles[/tex]
Phoenix's Distance
[tex]=\dfrac{1}{2\pi} \times 1859.44\\\\ =295.94$ miles[/tex]
Part C
Mars rotates on its axis once every 24.6 Earth-hours.
Therefore:
[tex]\dfrac{24.6}{2\pi} \approx $ 3.9152 hour per radian[/tex]
Part D:Speed of each explorer
[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
[tex]\text{Speed of Opportunity = }\dfrac{2108.71}{3.9152}\\$=538.59 miles per hour\\\\Speed of Phoenix =\dfrac{295.94}{3.9154}\\=75.59$ miles per hour[/tex]
a) Lets p, q, r represent the following statements: p: it is hot today. q: it is sunny r: it is raining Express in words the statements using Bicondtional statement represented by the following formulas: i. q ↔ p ii. p ↔ ( q ˄ r ) iii. p ↔ ( q ˅ r) iv. r ↔ ( p ˅ q)
Answer:
Step-by-step explanation:
The arrow with two tips is translated as "if and only if". The symbols [tex]\land, \lor[/tex] and read as "and" and "or"respectively.
If we have the following p: it is hot today. q: it is sunny r: it is raining
Then
i. q ↔ p : It is sunny if and only if it is hot today.
ii. p ↔ ( q ˄ r ) : it is hot today if and only if it is sunny and it is raining
iii. p ↔ ( q ˅ r) : it is hot today if and only if it is sunny or it is raining
iv. r ↔ ( p ˅ q) : it is raining if and only if it is hot today or it is sunny
A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. A new study provides the best evidence yet that this test saves lives. The proportion of people with colon polyps expected to die from colon cancer is 0.01. A sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and 12 of them died from colon cancer. Does this provide evidence that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01?
What are the null and alternative hypotheses?
Answer:
Null hypothesis H0: p = 0.01
Alternative hypothesis Ha: p < 0.01
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above;
The null hypothesis is that the proportion of people with colon polyps expected to die from colon cancer remains 0.01 with or without colonoscopy.
H0: p = 0.01
The alternative hypothesis is that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01.
Ha: p < 0.01
What are the excluded values? x = -3; z = 0 y = -5; z = 0 y = 0; z = -5 none of the above
Answer:
y = 0; z = -5
Step-by-step explanation:
Excluded values are ones that make the fraction "undefined." That will be the case when the denominator is zero.
When y = 0, the denominator is zero.
When z = -5, the denominator is zero.
Excluded values are y = 0; z = -5.
Answer:
-5
Step-by-step explanation:
Rebecca needs a box with a rectangular base of 36 cm2 and a volume of 180 cm3,
What would be the height of this box?
Answer:
Height h = 5 cm
Step-by-step explanation:
Given;
Volume of box V = 180 cm^3
Base area of box A = 36 cm^2
Height = h
Volume = base area × height
height = volume/base area
h = V/A
Substituting the values;
h = (180cm^3)/(36cm^2)
Height h = 5 cm
An economist wants to test if there is any difference in income between Escambia county and Miami-Dade county in Florida. To do this, she collects random samples of residents from both these counties. The information collected from these samples is tabulated below. Assume that both the populations are normally distributed with equal population variances.
Escambia County (Population 1) Miami-Dade County (Population 2)
n 1 = 11 n 2 = 15
x ¯ 1 = 36,700 x ¯ 2 = 34 ,700
s 1 = 7800 s 2 = 7375
Set up the null and alternative hypotheses to test the economist’s claim.
a) H_0 : μ1- μ2 is less than or equal to 0 versus H_a: is μ1- μ2 greater than 0b) H_0 : μ1 <μ2 versus H_a: is μ1 is greater than or equal to μ2c) H_0 : μ1 is not equal to μ2 versus H_a: is μ1 is equal to μ2d) H_0 : μ1- μ2 is greater than or equal to 0 versus H_a: is μ1- μ2 is less than 0e) H_0 : μ1- μ2 = 0 versus H_a: is μ1- μ2 not equal t0 0
Answer:
Yo
Step-by-step explanation:
Ashley and Robbin bought identical backpacks at different stores. Ashley’s backpack originally cost $65 and was discounted 25%. Robbin’s backpack originally cost $75 and was on sale for 30% off of the original price. Which backpack is the better buy? Explain.
Answer:
Ashley’s backpack is the better buy.
Step-by-step explanation:
You have to calculate the price that was paid for each backpack after the discount was applied.
Ashley’s backpack: $65*0.25= $16.25
Final price= $65-$16.25= $48.75
Robbin's backpack: $75*0.3= $22.5
Final price= $75-$22.5= $52.5
According to this, the backpack that is the better buy is the one that Ashley bought because after the discounts were applied it cost $48.75 and Robbin's backpack cost $52.2 which means that Ashley's backpack was cheaper.
If f(x) = 2x2 - 5 and g(x) = 3x + 3, find (f - g)(x).
A. 3x – 2x2 - 2
B. 2x2 – 3x - 2
C. 2x2 – 3x-8
D. - x² – 8
Answer:
2x^2 -3x -8
Step-by-step explanation:
f(x) = 2x^2 - 5
g(x) = 3x + 3,
(f - g)(x)= 2x^2 - 5 -(3x + 3)
Distribute the minus sign
(f - g)(x)= 2x^2 - 5 -3x - 3
Combine like terms
= 2x^2 -3x -8
Please answer this correctly
Answer:
3.00
Step-by-step explanation:
3.14 is rounded to 3.00
Answer:
141.3 m²
Step-by-step explanation:
V= πr²h
V=3.14*(6/2)²*5= 141.3 m²
Which operation should you perform last in the expression 32 + 2?
Answer:
Step-by-step explanation:
Adding the numbers because that is the only step. Making it the last operation.
There is a 0.9986 probability that a randomly selected 30 year old male lives through the year (based on data from the US department of Health and Human Services). A Fidelity life insurance company charges $161 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit. If a 30 year old male purchases the policy, what is his expected value?
Answer:
a) Surviving the year: $ -161. Not surviving: 99,839.
b) 0.9986 * -161 + (1-0.9986) * 100000 = -20.7746
c) As the expected value is negative from the male's perspective, it is positive from the insurance company's perspective. So as the number of people purchasing this insurance becomes large, the company's profit will converge to an average value of 20.7746 per male. So the company is indeed profitting.
A test was made of H0: μ1 = μ2 versus H1: μ1 < μ2. The sample means were and the sample standard deviations were and and the sample sizes were and Is H0 rejected at the 0.05 level? (Hint: First compute the value of the test statistic.)
Answer:
Step-by-step explanation:
Hello!
Hypotheses:
H₀: μ₁ = μ₂
H₁: μ₁ < μ₂
α: 0.05
Using the following sample information:
Sample 1
n₁= 15
X[bar]₁= 10
S₁= 4
Sample 2
n₂= 27
X[bar]₂= 8
S₂= 7
This is an example of a t-test for independent samples, assuming both unknown populations variances are equal the statistic is:
[tex]t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*16+26*49}{15+27-2} }= \sqrt{\frac{1498}{40} } = 6.119= 6.12[/tex]
[tex]t= \frac{(10-8)-0}{6.12*\sqrt{\frac{1}{15} +\frac{1}{27} } }= 1.01[/tex]
The p-value of this test is 0.1593
To decide using the p-value approach you have to use the following rule:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The calculated p-value is greater than the significance level, the decision is to not reject the null hypothesis.
Using a 5% significance level you can conclude that the hypothesis test is not significant and the population means of populations 1 and 2 are equal.
I hope this helps!
A park in the shape of quadrilateral PQRS is bordered by four sidewalks. Find the measure of each
exterior angle of the park.
15z=
7z=
7z=
11z=
Answer:
135°, 63°, 63°, 99°
Step-by-step explanation:
Find attached the diagram used in solving the question.
We would use formula for sum of interior angles to get each exterior angle.
From the diagram, we added additional variables to be able to solve for sum of interior angles.
Sum of angle on a straight line = 180°
a° +15z° = 180°
b° +7z° = 180°
c° +7z° = 180°
d° +11z° = 180°
Where a,b,c and d are interior angles
Sum of interior angles = 180(n-2)
n = number of sides
For quadrilateral, n= 4
a°+b°+c°+d° = 180(n-2)
180-15z +180-7z+180-7z+180-11z = 180(4-2)
720-40z = 180(2)
720 - 360 = 40z
z = 360/40
z = 9
Each exterior angle:
15z = 15×9 = 135°
7z = 7×9 = 63°
7z = 7×9 = 63°
11z = 11×9 = 99°
