Using cosine rule, the value of angle Y in the triangle is 21.3 degrees
Cosine RuleThe cosine rule is a mathematical formula used to calculate the length of the sides of a triangle when the angles and one side are known. It states that the square of the length of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the angle between them.
Mathematically, this is expressed as;
y² = x² + w² - 2xwCos(y)
Data given;
w = 8.1 inx = 2.9 iny = 5.5 in∠Y = ?Substituting the values into the formula above;
y² = x² + w² - 2xwCos(y)
5.5² = 2.9² + 8.1² -2(2.9)(8.1)cosY
30.25 = 8.41 + 65.61 - 46.98cosY
30.25 = 74.02 -46.98cosY
46.98cosY = 74.02 - 30.25
46.98cosY = 43.77
cos Y = 43.77 / 46.98
cos Y = 0.9317
Y = cos⁻¹(0.9317)
Y = 21.3°
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a paper popcorn cone measures 4 inches in a diameter and is 9 inches high?
Explanation is in the file
tinyurl.com/wtjfavyw
Answer:
A
Step-by-step explanation:
Bc I said
Solve the equation.
n+75=105
Answer:
n = 30....................
Answer:
30
Step-by-step explanation:
n+75=105
We move all terms to the left:
n+75-(105)=0
We add all the numbers together, and all the variables
n-30=0
We move all terms containing n to the left, all other terms to the right
n=30
What is the area of the rectangle above?
A.
72 square units
B.
66 square units
C.
17 square units
D.
34 square units
I uploaded the answer to a file hosting. Here's link:
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can someone go to my profile and answer my recent questions ty
1) Silk Road 2) Increase of trading
Please help I urgently need it, I’ll give brainliest to whoever answers and 20 points!
Answer:
92.3
Step-by-step explanation:
Home to gas station: (0,0) to (6,2) = 6.3
Gas station to friends house: (6,2) to (4,-7) = 9.2
Freinds house to movie theatre: (4,-7) to (-7,-3) = 11.7
Movie theatre to ice cream: (-7,-3) to (-8,2) = 5.1
Ice cream to park: (-8,2) to (7,7) = 15.8
Park to friends house: (7,7) to (4,-7) = 14.3
Friends house to grocery store: (4,-7) to (-4,8) = 17
Grocery store to home: (-4,8) to (0,0) = 8.9
Add them together =
FOR THE SMART MATH PEOPLE
WILL GIVE BRAINLIEST
This figure shown is NOT a square because a square has all angles are 90º.
It is a rhombus and a parallelogram because they both have a parallel sides(At least 2). NOW GIVE ME BRAINLIEST!!!!
What is the image of the point (-2,7) after a rotation of 180° counterclockwise
about the origin?
180° rotation of any point about the origin gives the value with an alternate sign thus it will be (2,-7).
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.
Given a point let's say A(-2,7)
If we rotate any point on coordinate geometry by 180 degrees about the origin then the horizontal and vertical distinctions will remain the same but the sign will change as shown below.
A(-2,7) ← Second quadrent
A'(2,-7) → Fourth quadrant
Hence "180° rotation of any point about the origin gives the value with an alternate sign thus it will be (2,-7)".
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Which figure can be formed from the net?
What's the variable of x?
Step-by-step explanation:
in right angled triangle ;
hypotenuse² =( side 1)² +(side 2)²
(65)²=(25)² +(x)²
4225 = 625 + (x)²
4225 - 625 = x²
3580 = x²
59.83 = x
A drug made by a pharmaceutical company comes in tablet form. Each tablet is branded as containing 105 mg of the particular active chemical. However, variation in manufacturing results in the actual amount of the active chemical in each tablet following a normal distribution with mean 105 mg and standard deviation 1.513 mg.
A) Calculate the percentage of tablets that will contain less than 104 mg of the active chemical.
B) Suppose samples of 15 randomly selected tablets are taken and the amount of active chemical measured. Calculate the percentage of samples that will have a sample mean of less than 104 mg of the active chemical.
Answer:
a) 25.46% of tablets will contain less than 104 mg of the active chemical.
b) 0.52% of samples will have a sample mean of less than 104 mg of the active chemical.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Normal distribution with mean 105 mg and standard deviation 1.513 mg.
This means that [tex]\mu = 105, \sigma = 1.513[/tex]
A) Calculate the percentage of tablets that will contain less than 104 mg of the active chemical.
The proportion is the pvalue of Z when X = 104. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{104 - 105}{1.513}[/tex]
[tex]Z = -0.66[/tex]
[tex]Z = -0.66[/tex] has a pvalue of 0.2546
0.2545*100 = 25.46
25.46% of tablets will contain less than 104 mg of the active chemical.
B) Suppose samples of 15 randomly selected tablets are taken and the amount of active chemical measured. Calculate the percentage of samples that will have a sample mean of less than 104 mg of the active chemical.
Sample means from samples of 15. So, by the Central Limit Theorem:
[tex]n = 15, s = \frac{1.513}{\sqrt{15}} = 0.39[/tex]
The proportion is the pvalue of Z when X = 104. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{104 - 105}{0.39}[/tex]
[tex]Z = -2.56[/tex]
[tex]Z = -2.56[/tex] has a pvalue of 0.0052
0.0052*100 = 0.52
0.52% of samples will have a sample mean of less than 104 mg of the active chemical.
A random sample of students were surveyed as to how much non-school screen time
they had each week (for purposes of the survey, screen time was defined as: time
spent online, on social media, watching TV, or playing video games) and if their grade
average was above or below 80.
Screen Time
above below
8
8
less than 4 hours
18
16
4-8 hours
20
16
8-12 hours
11
17
more than 12 hours
What percent of the students who spend 4-8 hours a week on screens reported a
grade average above 802 Round your answer to the nearest tenth of a percent.
Answer:
the answer is 25 .
Step-by-step explanation:
$17.99
with an
11.25% tax
Answer:
your final price is 19.02
your ta rate is 5.75
Step-by-step explanation:
your
On each request the ith of n possible books is the one chosen with probability pi. To make it quicker to find the book the next time, the librarian moves the book to the left end of the shelf. Define the state at any time to be the sequence of books we see as we examine the shelf from left to right. Since all the books are distinct this list is a permutation of the set
{1, 2,... n}, i.e., each number is listed exactly once. Show that Ï(i1,... in)= pi1. pi^2/1-pi_1 . pi^3/1-pi_1- pi_2 ........ pi^n/1-pi_1- pi_2.....pi_n is a stationary distribution.
Answer:
attached below
Step-by-step explanation:
loops have permutations , steps to show that the given set of permutations is a stationary distribution is attached below
Two angles are supplementary. One angle measures (3x+8) and the other measures (6x+64) what is the value of X?
⚠️HELP DUE TODAY⚠️
The area of a rectangular garden is x^2- 5x - 24. Factor the trinomial to find the dimensions of the rectangular garden in terms of x
Answer: (why is it 5 points?) Thats ok.
5 times what X is - 24 meaning whatever X is also by sry i don't make a lot of sense but i'm smart and know the answer. I will change it later after i find out which shouldn't take too long.
Step-by-step explanation:
Thanks, stay safe, have a great life! Byes! Brainliest then i will give answer! ;) :) :P XD :3 (: hehe :)
Can y’all help me on question 19?!
Answer:
Its D
Step-by-step explanation:
Pleasseeeeeeeeee help[pppppppppp i will answer any of your questionsssss pleaseeeeeeeeeeee
Answer:
The dependent variable is c and the independent variable is s
Step-by-step explanation:
S does not rely on anything. C relies on the answer to the equation.
Find the area of the shaded region
Answer:
A
Step-by-step explanation:
8-6=2
6×2=12
12×2=24
Put your answer in cm^2
Harley invested $6,300 into an account that earns 3.5% simple interest. What is the total balance of the account after 5 years
Answer:
$7402.50 I think
Step-by-step explanation:
3.5(5)= 17.5 percent
175/1000* 6300= 17.5*63= 1102.5
6300+ 1102.5= 7402.5
if my answer helps please mark as brainliest.
Work out the difference between 77.5 and 2.27.
Answer:
75.23 is the answer for 77.5-2.27
Help me please I really need help whoever answers this question first gets a thanks and that’s worth five points
Answer:
5 in.
Step-by-step explanation:
Compare the original trapezoid and the enlarged trapezoid.
Trapezoid A B C D has side lengths 4 centimeters, 2 centimeters, 5 centimeters, 2 centimeters. Trapezoid W X Y Z has side lengths 10 centimeters, 5 centimeters, 12.5 centimeters, 5 centimeters.
What is the perimeter of trapezoid ABCD?
What is the perimeter of trapezoid WXYZ?
What is the scale factor for this enlargement?
Answer:
13, 32.5, 2.5
Step-by-step explanation:
Answer:
The answer is in the photo
Step-by-step explanation:
the given is a square pyramid. The side length of the base of the pyramid is 28 millimeters. The volume of the pyramid is 1296 cubic mm. What is the height of the pyramid
helpppppppppppppppppp
Answer:
19 units, left
Step-by-step explanation:
You can use a graphing tool or create a graph to show how these lines relate to one another. Then, count the units that have been translated and where the translation occurred.
An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 185 tons with a standard deviation of 35 tons. In a separate sample of 61 different fields using fertilizer B, the average crop yield is 175 tons with a standard deviation of 28 tons. When testing the hypothesis that there is no difference between the average yields using the different fertilizers, if the test statistic is 1.53 and the critical value is 2.57 then what is your conclusion concerning the null hypothesis?
Answer:
We do not reject the null
Step-by-step explanation:
Given that :
Sample size, n = 41
Test statistic ; Zstatistic ;= 1.53
Critical value ; Zcritical ; = 2.57
The null hypothesis H0 ;
H0: μ1 - μ2 = 0
Alternative hypothesis, H1 ;
H1: μ1 ≠ μ2
Decision region :
Reject Null ; if |Zstatistic ≥ Zcritical|
Zstatistic > Zcritical
Result :
1.53 < 2.57
Zstatistic < Zcritical
Hence, we do not reject the null ; there is no significant evidence that there is difference in the average yield of the two samples.
4x + 8y= -8
X= -2y + 1
Answer:
Step-by-step explanation:
In ASTU, S = 360 cm, t = 110 cm and u=450 cm. Find the measure of ZU to the
nearest 10th of a degree.
Answer:140.1
Step-by-step explanation:
Answer:
140.1
Step-by-step explanation:
Write the log equation as an exponential equation. You do not need to solve for x.
In (4x + 8) = 2 + 5
HELP
Elyssa bought a rectangular aquarium. The measurements, in feet (ft), are shown below.
How much water will it take to fill the aquarium
Answer:
[tex] 34 \frac{13}{20} \: {ft}^{3} [/tex]
Step-by-step explanation:
Water required to fill the aquarium
= Volume of the aquarium
[tex] = lbh \\ \\ = 4 \frac{2}{5} \times 3 \frac{1}{2} \times 2 \frac{1}{4} \\ \\ = \frac{22}{5} \times \frac{7}{2} \times \frac{9}{4} \\ \\ = \frac{11}{5} \times \frac{7}{2} \times \frac{9}{2} \\ \\ = \frac{693}{20} \\ \\ = 34 \frac{13}{20} \: {ft}^{3} [/tex]
solve using elimination x-2y=12 and 5x+3y=-44 *
(4,8)
(-4,8)
(4,-8)
(-4,-8)
Step-by-step explanation:
( x-2y=12)5
5x-10y=60
- 5x+3y=-44
____________
13y=-104
y=-104/13