By utilizing trigonometric identities,we got cos 2θ = -1519/1681.
Given that sin θ = 40/41 and θ is a positive acute angle, we can find cos θ using the Pythagorean identity sin²θ + cos²θ = 1. Rearranging the equation, we have cos²θ = 1 - sin²θ.
Substituting the given value, we get cos²θ = 1 - (40/41)² = 1 - 1600/1681 = 81/1681.
Now, we can find cos 2θ using the double-angle identity cos 2θ = cos²θ - sin²θ.
Substituting the known values, we have
cos 2θ = (81/1681) - (40/41)² = 81/1681 - 1600/1681 = -1519/1681.
Therefore, cos 2θ = -1519/1681.
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how do I solve this
Answer:
1. Given
2. Distributive Property
3. Combine like terms
4. APoE
5. SPoE
6. DPoE
I think that's the answer but I may be wrong since proofs are annoyingly difficult...
A manufacturer orders lots of steel rods from a supplier (each lot consists of thousands of rods). Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter. The quality manager accepts a lot if the mean length of the randomly selected sample of 64 rods from that lot is at least 4.005 meters, otherwise the lot is returned to the supplier. a) What percentage of the lots received by the manufacturer will be returned to the supplier
Answer:
84.13% of the lots received by the manufacturer will be returned to the supplier
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.
Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter.
This means that [tex]\mu = 4, \sigma = 0.04[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{0.04}{\sqrt{64}} = 0.005[/tex]
a) What percentage of the lots received by the manufacturer will be returned to the supplier
The proportion is the pvalue of Z when X = 4.005. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.005 - 4}{0.005}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.8413*100% = 84.13%
84.13% of the lots received by the manufacturer will be returned to the supplier
An engine operating on Dual cycle has a compression ratio of 12. The pressure and temperature at the start of adiabatic compression is 100 KPa. and 37 degree Centigrade. The peak pressure of the cycle is not no exceed 8000 KPa. and the heat supplied to the cycle is 2000 KJ per Kg. of air. Determine the cycle thermal efficiency
Find the measure of CD in parallelogram ABCD .
Answer:
Picture would be appreciated.
Find the measure of an angle that is positive and less than 360° in standard position for each reference angle. 68° in quadrant II: 75° in quadrant IV: 22° in quadrant III:
Answer:
Step-by-step explanation:
Reference angle for 68° in QII = 180°-68° = 112°
Reference angle for 75° in QIV = 360°-75° = 285°
Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 11 ounces. a. The process standard deviation is .20 ounces, and the process control is set at plus or minus standard deviations. Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)
The question supplied is incomplete :
The x parameters aren't given ; "Units with weights less than or greater than ounces will be classified as defects"
Assume the unit weights Given are ;
Units with weights less than 10.8 or greater than 11.2 ounces will be classified as defects
Just follow the procedure in the solution for any value of unit weight interval given.
Answer:
0.3173
Step-by-step explanation:
Mean weight, m = 11 ounces
Standard deviation, s = 0.2 ounces
Find the Zscore for each unit weight :
Z = (x - mean) / standard deviation
P(x < 10.8) :
Z = (10.8 - 11) / 0.2 = - 1
P(Z < - 1) = 0.15866
P(x > 11.2) :
Z = (11.2 - 11) / 0.2 = 1
P(Z > 1) = 0.84134
P(x < 11.2) - P(x < 10.8) = 1 - (P(Z < 1) - P(Z < - 1)) = 1 - 1 - (0.84134 - 0.15866) = 1 - 0.68268 = 0.31732
Hence, Probability of a defect is 0.3173
Please help:( I’m stuck on this problem
Answer:
x=33
Step-by-step explanation:
If you didn't know all of the angles in a triangle add up to equal 180
We are given to angles, 90 (the square indicates that its a right angle which is equal to 90) and 57
So to find the missing anlge we subtract the given angles from 180
180-90=90
90-57=33
therefore x=33
What is the volume of the prism?
2 cm
3cm
11 cm PLS HURRY
Answer:
66
Step-by-step explanation:
multiply everything together
the number y divided by 100 y. ?
Answer:
1/100
Step-by-step explanation:
Which values are solutions to × > 7? A. × = 11 and × = 1 B. × = 0 and × = 8 C. × = 8 and × = 11 D. × = -8 and × = 0
Answer:
C
Step-by-step explanation:
Q. You are employed at a grain processing
plant that sells cornmeal for $1.28 per pound.
If a sack of cornmeal weighs 4 pounds 12
ounces, how much does it cost?
A. $6.08
B. $4.95
C. $5.12
D. $6.40
Answer:
A (6.08)
Step-by-step explanation:
Hi! Here is how you would handle this problem :D
First, multiply 1.28 (money per pound) by 4 (whole pounds), you would get 5.12. Now be careful, because there is one more step! There are 16 ounces in a pound, so 12/16 would equal to 3/4 (75%). Multiply 1.28 by .75 to find out how much you would pay for those 12 ounces. Lastly, add 5.12 and .96 (that comes from 1.28 times .75), and you get 6.08! Hope this helped, and please leave me a brainly if you can!
Will mark brainliest!
What is the value of u?
Answer:
u=32
Step-by-step explanation:
Hey There!
Those are a pair of complementary angles we can tell because it has a square at the angle.
When angles are complementary they add up to 90
So given one angle we subtract that by 90 to find the missing angle
90-58=32
therefore u = 32
Selma went shopping and bought identical sweaters for each of 3 friends. If she spent $42, what was the cost of each sweater? Include your equation with your answer.
Answer:
14 dollars
Step-by-step explanation:
42 / 3 = x amount of dollars
14 = x
so every one sweater costs 14 dollars
Hope u help me pls I love u
Answer:c= a +b
Step-by-step explanation:
34(x+6)=(3x-2)
find x
Answer:
The answer to x is x= −206 /31
Step-by-step explanation:
Simplify both sides of the equation.
34(x+6)=3x−2
(34)(x)+(34)(6)=3x+−2(Distribute)
34x+204=3x+−2
34x+204=3x−2
Subtract 3x from both sides.
34x+204−3x=3x−2−3x
31x+204=−2
Subtract 204 from both sides.
31x+204−204=−2−204
31x=−206
Divide both sides by 31.
31x /31 = −206/ 31
x= −206 /31
Answer: x= −206 /31
PLEASE HELP I AM TIMED FOR 8 MORE MINUTES! I’ve been working on this for 1 hour!!
Answer:
21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
y=4x+1
replace x with 5
y=4x5+1
y=20+1
y=21
Omar’s tank is 3/10 full. After he buys 11 gallons of gas, it is 4/5 full. How many gallons can Omar’s tank hold?
Answer:
22 gallons.
Step-by-step explanation:
11 gallons took you from 3/10 to 4/5 (same as 8/10).
so the 11 gallons was 5/10- or 1/2 the tank.
if 11 gallons =half a tank, then a full tank is 22 gallons
Scan QR code and it takes to homework so u can answer question i will give brainliest to correct answer please answer correct
im just gonna take the points for falling for that.
A TV executive is interested in the popularity of a particular cable TV show. She has been told that a whopping 68% of American households would be interested in tuning in to a new network version of the show. If this is correct, what is the probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show
Answer:
0.0989 = 9.89% probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show
Step-by-step explanation:
For each household, there are only two possible outcomes. Either they will tune in to the show, or they wont. The probability of a household being tuned in to the show is independent of any other household. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
She has been told that a whopping 68% of American households would be interested in tuning in to a new network version of the show.
This means that [tex]p = 0.68[/tex]
If this is correct, what is the probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show
All 6 is [tex]P(X = 6)[/tex] when [tex]n = 6[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{6,6}.(0.68)^{6}.(0.32)^{0} = 0.0989[/tex]
0.0989 = 9.89% probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show
Which inequality is shown in this graph?
(0, 3)
5
(2, -3)
Answer:
It would be A
I think I forgot I didn't this like 2 weeks ago
At a diner, Hailey's lunch cost $6.75. Her sister's lunch cost $5.95. After lunch, they each had frozen yogurt that cost the same amount. Together the girls spent a total of $17.40. How much did each frozen yogurt cost?
Answer:
$2.35
Step-by-step explanation:
17.40-6.75-5.95=$4.70
4.70 divided by 2 = 2.35 each
For a sparkling apple juice recipe with two ingredients, Timmy uses 3 1/4 cups of apple juice and 4 2/3 cups of lemon-lime soda. How much juice is he making?
Answer:
anlamiyorum ne diyorsun
NEED HELP ON THIS ASAP
Answer:
34
Step-by-step explanation:
True or False? The chart below shows a linear relationship function.
X -1 0 4
Y 1 3 11
T. True, this is linear F. False, this is not linear
Answer:
False
Step-by-step explanation:
Each of 200 subjects were shown a proposed commercial and asked to identify the marketed product 5 minutes after the viewing. A 95% confidence interval was calculated, but the client indicated that the resultant margin of error is too large and must be one-fourth its current size. How large does the new sample need to be?
Answer:
Step-by-step explanation:
first off we need to know the original sample size and if it is in there then im just cant see it
Consider the expression 40+24 . Find the greatest common factor of the two numbers and use the distributive property to rewrite the expression
Hi there!
[tex]\large\boxed{8(5+3)}}[/tex]
The greatest common factor of 40 and 24 is 8.
8 goes into 40 5 times:
8 goes into 24 3 times.
We can rewrite this expression for distribution using the amount of times 8 goes into both numbers:
8(5 + 3)
Using this, we get:
8(5) + 8(3) = 40 + 24.
Pls, help solve this asap..
Answer:
the answer is 8
Step-by-step explanation:
3(8^2) + 1
8^2 = 64
64 x 3 = 192
192 +1 =193
-3 multiplied by 8.2
Answer:
-24.6
Step-by-step explanation:
-3*8.2= -24.6
For the most recent year available, the mean annual cost to attend a private university in the United States was $50,900. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500. Ninety-five percent of all students at private universities pay less than what amount
Answer:
95% of all students at private universities pay less than $58,302.5.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of $50,900, standard deviation of $4,500
This means that [tex]\mu = 50900, \sigma = 4500[/tex]
Ninety-five percent of all students at private universities pay less than what amount?
Pay less than the 95th percentile, and the amount is given by X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 50900}{4500}[/tex]
[tex]X - 50900 = 1.645*4500[/tex]
[tex]X = 58302.5[/tex]
95% of all students at private universities pay less than $58,302.5.
Problem 8
Tameeka's sunflower is currently 58 millimeters. She
notices that the sunflower grows 8 millimeters each day.
Write an expression to represent this situation.
Answer:
Step-by-step explanation:
if tameekas sunflower is 58 millmetters and grows 8 millmeters a day then in the 7 days she grew it, it has grown 58 millmeters.