Answers
Answer:
Triangle a: 44.7°
Triangle b: 30.5°
Triangle c: 67.4°
Triangle d: 56.6°
Step-by-step explanation:
Recall: SOHCAHTOA
a. Reference angle = [tex] \theta [/tex]
Opposite = 19
Hypotenuse = 27
Apply SOH:
[tex] sin(\theta) = \frac{Opp}{Hyp} [/tex]
[tex] sin(\theta) = \frac{19}{27} [/tex]
[tex] \theta = sin^{-1}(\frac{19}{27}) [/tex]
[tex] \theta = 44.7 degrees [/tex] (nearest tenth)
b. Reference angle = [tex] \theta [/tex]
Opposite = 33
Adjacent = 56
Apply TOA:
[tex] tan(\theta) = \frac{Opp}{Adj} [/tex]
[tex] tan(\theta) = \frac{33}{56} [/tex]
[tex] \theta = tan^{-1}(\frac{33}{56}) [/tex]
[tex] \theta = 30.5 degrees [/tex] (nearest tenth)
c. Reference angle = [tex] \theta [/tex]
Opposite = 12
Adjacent = 5
Apply TOA:
[tex] tan(\theta) = \frac{Opp}{Adj} [/tex]
[tex] tan(\theta) = \frac{12}{5} [/tex]
[tex] \theta = tan^{-1}(\frac{12}{5}) [/tex]
[tex] \theta = 67.4 degrees [/tex] (nearest tenth)
d. Reference angle = [tex] \theta [/tex]
Hypotenuse = 20
Adjacent = 11
Apply CAH:
[tex] cos(\theta) = \frac{Adj}{Hyp} [/tex]
[tex] cos(\theta) = \frac{11}{20} [/tex]
[tex] \theta = cos^{-1}(\frac{11}{20}) [/tex]
[tex] \theta = 56.6 degrees [/tex] (nearest tenth)
Related Questions
Burger Queen a popular fast food restaurant among college students has undertaken a study to determine the weights of the hamburgers served in its new location in San Marcos, TX. Half pounders should weigh at least 8 ounces. The weight is assumed to be normally distributed. A sample of 500 hamburgers reveals the average precooked weight to be 8.02 ounces, with a standard deviation of .4 ounce.
1. What is the probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces?
2. What is the probability that a hamburger selected at random with less than 7.52 ounces?
Answers
Answer:
1. 0.2422 = 24.22% probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces
2. 0.1056 = 10.56% probability that a hamburger selected at random with less than 7.52 ounces.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
A sample of 500 hamburgers reveals the average precooked weight to be 8.02 ounces, with a standard deviation of .4 ounce.
This means that [tex]\mu = 8.02, \sigma = 0.4[/tex]
1. What is the probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces?
This is the pvalue of Z when X = 8.02 subtracted by the pvalue of Z when X = 7.76. So
X = 8.02
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.02 - 8.02}{0.4}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
X = 7.76
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.76 - 8.02}{0.4}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a pvalue of 0.2578
0.5 - 0.2578 = 0.2422
0.2422 = 24.22% probability that a hamburger selected at random will weigh between 7.76 and 8.02 ounces.
2. What is the probability that a hamburger selected at random with less than 7.52 ounces?
This is the pvalue of Z when X = 7.52. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.52 - 8.02}{0.4}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a pvalue of 0.1056
0.1056 = 10.56% probability that a hamburger selected at random with less than 7.52 ounces.
Wendy can solve a brain teaser in 15 minutes. When she works with Arby, they can solve in 5 minutes. Which statement is true
Answers
Answer:
Wheres the statements?
Step-by-step explanation:
Farmer Brown is tilling her field. Farmer Brown tills 2/3 of an acre in 2/7 of an hour. What is Farmer Brown's unit rate of tilling?
Answers
Answer:
2 1/3 acres per hour
Step-by-step explanation:
If you divide both numbers by 2, you get 1/3 and 1/7. If 7 makes up an hour, then you multiply 1/3 by 7, which gets you 2.333.. which is equivalent to 2 1/3.
How many lemons are needed to fill 375 ml bottle of lemon juice if 2 large lemons fill 100ml
Answers
Answer:
Answer:
7 and half
Explanation:
cuz if the two lemin fill two then one will fill 50ml ,
then,7×50=350 the remaining is 25 ml which is half of 50 ml so this is half of one lemon.so the answer is 7 and half
Answer:
7 and a half
Step-by-step explanation:
2 lemons=100 ml
?=375 ml
Cross multiplication to get ? which will bring
(375×2)÷ 100 giving 7 ½
11. Which value makes the following inequality TRUE? 4 – 8x > 2 11
Answers
Answer:
If that number is 211, then any value below -26 will work
María vende pescado en el mercado modelo ella le ha prestado dinero a Juan 800 soles con el 10% al mes Así mismo le ha prestado dinero a Juana la cantidad de 12000 soles con el 10% al mes cuánto ganará María por los dos préstamos al mes
Answers
Answer:
Creo que $1,280
Step-by-step explanation:
12,000+800=12,800
12,800 x 10% =1,280
Which of the lists of letters all have rotational symmetry?
C,H, N, X
N.O.S. Z
H.J.N.S
F.H. X. Z
Answers
Answer:
N, O, S, Z, which will be B
Step-by-step explanation:
Michael has $1,000.95 in his checking account. He is going to spend $472.87 on a new television, and he will spend the rest on speakers that cost $48.00 each. Which of the following inequalities would determine the maximum number of speakers, x, Michael can buy without spending more money than he has in his account?
A.
$1,000.95 < $48.00x + $1,000.95
B.
$472.87 + $48.00 + x < $1,000.95
C.
$48.00x + $472.87 < $1,000.95
D.
$1,000.95 + $472.87 > $48.00 + x
Answers
Answer:
C bc 48 is the cost of sneakers, x is the number of sneakers, that plus the tv has to be less than 1000.95
Jenna has a maximum of $38 to spend at the movies. A ticket costs
$8.50 and she has x, dollars to spend on snacks. Which inequality
represents all of the possible values for x?
A. x ≥ 29.50
B. x ≤ 46.50
C. x ≥ 46.50
D. x ≤ 29.50
Answers
Why?
Because 37-8= 29.5
And you have a max of 29.5 to spend
You can spend 29.5 dollars or less (because that is the max)
Which one is not a characteristic of all parallelograms?
Answers
Answer:
Consecutive angles are supplementary is not character of parallelograms
Line I is parallel to line m. If the
measure of Z6 is 75°, what is the
measure of 24?
1/2
473
B
5/6 = 75
7/8
Enter
Answers
Answer:
75
Step-by-step explanation:
alternate interior angles are always equal, so that means 6 = 4 = 75.
Find the area of the semicircle. Round your answer to the nearest hundredth. YEAH IVE BEEN STUCK ON THIS help please I need the steps if possible:(
Answers
Answer:
your answer will be 127.17 sq in
Step-by-step explanation:
hope it helps you
have a wonderful day!!!
Answer:
=127.23
Step-by-step explanation:
we can start of by finding the area of a CIRCLE
18/2=9
9=radius
area of circle= pi*r squared
9 squared=81*pi=254.4690
Now we can half the area of the circle to find out the area of the semi circle as a semi circle is just half a circle therefore half the area of a circle
254.469/2=127.2345
127.2345=127.23
=127.23
Hope this helped
what is the answer to this math question 5 less than c is 47
Answers
47+5
Hddhhfhdhd
Answer:
Answer = 52
5+47= 52
done
In ΔEFG, the measure of ∠G=90°, the measure of ∠E=6°, and GE = 3.3 feet. Find the length of EF to the nearest tenth of a foot.
Answers
Answer:
EF = 3.3 ft
Step-by-step explanation:
cos 6 = 3.3/EF
0.9945 = 3.3/EF
EF = 3.32 ft
what is the GCF of 12a and 16ab
Answers
Answer:
4a
Step-by-step explanation:
Greatest Common Factor is the largest number that the two terms can be divided by
The largest number that these could be divided by is 4a
12a/4a=3
16ab/4a=4b
4a(3+4b)
The triangle below is a right triangle. What is the length of the missing side? Round your answer to the nearest whole number? A. 8 in.B. 9 in.C. 12 in.D. 80 in.
Answers
Answer:
B=9in
Step-by-step explanation:
To find the solution to this problem we will use the Pythagoras theorem.
[tex]c = {a}^{2} + {b}^{2} \\ = \sqrt{ {8}^{2} + {4}^{2} } \\ = 8.944... \\ = 9[/tex]
Answer:
your answer would be 9 in.
Step-by-step explanation:
I hope this makes your day a bit easier!!
Factor: 3.x2 + 7x + 2
Answers
Answer:
x= -1/3 and -2
I have made it in above picture
Please help I need help
Answers
Answer:
3
Step-by-step explanation:
just get everything but the h to the other side
divide by b1 + b2
1/2h = A/b1 + b2
then multiply by 2
h = 2A/b1 + b2
What is the vector sum of 7, 5 and 13, −5? 20, 0 20, 10 6, 0 6, 10
Answers
Answer:
{20, 0}.
Step-by-step explanation:
One morning, the temperature in Urbana, Illinois, was 15° Fahrenheit. By evening, the temperature had dropped 25° Fahrenheit. What was the temperature (in °F) that evening?
Answers
The temperature started at 15 degrees.
It dropped 25 degrees.
Subtract 25 from 15:
15 - 25 = -10
The temperature was -10 degrees.
HELP PLEASE THANK U
Answers
8 + 5 = 13 not 12
To make it similar, 8 needs to be 7. This is ONLY my guess, I’m not 100% confident in my answer
Naval intelligence reports that 5 enemy vessels in a fleet of 18 are carrying nuclear weapons. If 9 vessels are randomly targeted and destroyed, what is the probability that no more than 1 vessel transporting nuclear weapons was destroyed
Answers
Answer:
0.1471 = 14.71% probability that no more than 1 vessel transporting nuclear weapons was destroyed.
Step-by-step explanation:
Vessels are chosen without replacement, which means that we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Naval intelligence reports that 5 enemy vessels in a fleet of 18 are carrying nuclear weapons.
This means, respectively, that [tex]k = 5, N = 18[/tex].
9 vessels are randomly targeted and destroyed
This means that [tex]n = 9[/tex]
What is the probability that no more than 1 vessel transporting nuclear weapons was destroyed?
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,18,9,5) = \frac{C_{5,0}*C_{13,9}}{C_{18,9}} = 0.0147[/tex]
[tex]P(X = 1) = h(1,18,9,5) = \frac{C_{5,1}*C_{13,8}}{C_{18,9}} = 0.1324[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0147 + 0.1324 = 0.1471[/tex]
0.1471 = 14.71% probability that no more than 1 vessel transporting nuclear weapons was destroyed.
Which of the following could not be a value for x?
Answers
Answer: its B or D
Step-by-step explanation: please tell if im wrong
Lena is asked to write an explicit formula for the graphed geometric sequence.
On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).
What value, written as a decimal, should Lena use as the common ratio?
1.0
1.5
2.5
2.0
Answers
Answer:
C
Step-by-step explanation:
I took the quiz and got it right
The common ratio of the geometric sequence is r = 2.5
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the terms of the GP be represented as A
Now , A = 1 , 2.5 , 6.25
where the common ratio = second term / first term
On simplifying , we get
r = 2.5 / 1
r = 2.5
Hence , the common ratio is r = 2.5
To learn more about geometric progression click :
https://brainly.com/question/1522572
#SPJ7
I WILL GIVE BRAINLIEST :)
A car repair shop charges an hourly rate plus a pickup and delivery fee. The graph below represents the relationship between the total cost of the repair, including pickup and delivery fee, and the number of hours it takes the shop to complete the repairs.
Answers
Answer: I got 50x+$75 but I’m not too sure for the last step
Step-by-step explanation:
Answer:
y=50x+75
Step-by-step explanation:
y=125=225-125 Divide 3-1 (x-1)
y-125=50(x-1)
y=50x-50+125
y=50x+75
Given that the measure of ∠x is 90°, and the measure of ∠y is 64°, find the measure of ∠z.
Answers
Answer:
26°Step-by-step explanation:
Assuming that your figure is a triangle, we should keep in mind that all the interior angles of a triangle add up to 180°, always.
So, we have the values of angles x and y as 90° and 64°.
90 + 64 = 154° ⇒ Add them up.
Now, subtract 154 from 180 to get ∠z.
180 - 154 = 26°
In the isosceles trapezoid shown, GJ = 5, HI = 9, and GI = 8.6. Determine the length
of HJ.
Answers
Answer
8.6
Step-by-step explanation:
Answer:
8.6
Step-by-step explanation:I took the test
Work out the area of a rectangle with base, b = 22mm and perimeter, P = 50mm.
b
The diagram is not drawn to scale.
mm2
Answers
Answer: A=22^2
Step-by-step explanation: Hope this helps
What’s the answer and how to get it done without me
Answers
Answer:uhmmmmm
Step-by-step explanation:
*
Question 2
If a calculator is sold for $15.95, then the revenue in dollars, R, generated by this item
is given by the formula R=15.959, where a represents the number of calculators sold.
Use the formula to determine the revenue generated by this item if 40 calculators are
sold.
Answers
Answer:
Answer is in the photo so you have so look in this give wribsite