Hi
we know that sin(A+B)=Sin(A)Cos(B)-Cos(A) Sin (B)
cos(2x)=1-2sin²(x)
sin(2x)=2sin(x)cos(x)
Exp:- Sin(3x)=Sin(x+2x)
Sin(x)cos(2x)+cos(x)sin(2x)
sin(x){1-2sin²(x)}+2cos²(x)sin(x)
sin(x)-2sin³(x)+2sin(x){1-sin²(x)}
sin(x)-2sin³(x)+2sin(x)-2sin³(x)
3sin(x)-4sin³(x)
Hope it helps....
The length of a rectangle is six times it’s width. If the area of the rectangle is 486 cm^2, find the perimeter.
Answer:
54 cm is the perimeter I think
A hotel manager calculates that 12% of the hotel rooms are booked. If the manager is right, what is the probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%?
Answer:
0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.
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 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.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A hotel manager calculates that 12% of the hotel rooms are booked.
This means that [tex]p = 0.12[/tex]
Sample of 556 rooms
This means that [tex]n = 556[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.12[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.12*0.88}{556}} = 0.0138[/tex]
What is the probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%?
This is the p-value of Z when X = 0.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.1 - 0.12}{0.0138}[/tex]
[tex]Z = -1.45[/tex]
[tex]Z = -1.45[/tex] has a p-value of 0.0735
0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.
See attached writing an equation for the graph
y=
Answer:
Step-by-step explanation:
-2*x +2
it is reveresed with a y interecept of 2
What is the surface area of the rectangular prism pictured below?
3 meters
9 meters
4 meters
Answer:
108 meters with the formula lxhxw
Math algebra 2 show you’re work plz
9514 1404 393
Answer:
(t, u, w) = (1, -2, -2)
Step-by-step explanation:
A graphing calculator makes short work of this, giving the solution as ...
(t, u, w) = (1, -2, -2)
__
There are many ways to solve this "by hand." Here's one of them.
Add the first and third equations. Their sum is ...
-3t +4w = -11 . . . . . [eq4]
Add this to twice the second equation. That sum is ...
(-3t +4w) +2(-4t -2w) = (-11) +2(0)
-11t = -11
t = 1
Substituting this into the second equation gives ...
-4(1) -2w = 0
w +2 = 0 . . . . divide by -2
w = -2 . . . . add -2
Substituting for t in the third equation lets us find u.
2(1) -2u = 6
-1 +u = -3 . . . . . divide by -2
u = -2 . . . . add 1
The solution is (t, u, w) = (1, -2, -2).
9.
Find the area of the shaded region.
6
6
The exact area is A =
square units.
Answer:
8. 36
Step-by-step explanation:
8.
The diameter of the square is x=[tex]\sqrt{6^{2} +6^{2} }\\[/tex] = [tex]\sqrt{72}[/tex] = 6 [tex]\sqrt{2}[/tex]
The diameter of the square is the diameter of the circle, therefore the radius of the circle is r = 6 [tex]\sqrt{2}[/tex]/2 = 3[tex]\sqrt{2}[/tex]
The area of the shaded region, which is a circle is A= π[tex]r^{2}[/tex] = π[tex](3\sqrt{2} )^{2}[/tex] = 36π
At a sale this week, a sofa is being sold for $117.60. This is a 72% discount from the original price. What is the original price?
Which angle is the vertical angle toBEC
Answer:
∠AED
Step-by-step explanation:
Vertical angles are the opposite angles of intersecting lines. ∠BEC and ∠AED are opposite and would therefore also be congruent angles.
Answer:
[tex]\angle BEC=\angle AED [vertical ~angle][/tex]
[tex]\angle AED~vertical~ angle ~to~ \angle BEC[/tex]
[tex]ANSWER:\angle AED[/tex]
-----------------------------
hope it helps...
have a great day!!
Nina and Amy began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Nina took a test in English and earned a 71.8, and Amy took a test in Social Studies and earned a 60.7. Use the fact that all the students' test grades in the English class had a mean of 71.7 and a standard deviation of 11.7, and all the students' test grades in Social Studies had a mean of 60.6 and a standard deviation of 10.5 to answer the following questions.
a) Calculate the z-score for Nina's test grade.
b) Calculate the z-score for Amy's test grade.
c) Which person did relatively better?
i. Nina
ii. Amy
iii. They did equally well.
Answer:
a) [tex]Z = 0.0085[/tex]
b) [tex]Z = 0.0095[/tex]
c) ii. Amy
Step-by-step explanation:
Z-score:
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.
Question a:
Nina took a test in English and earned a 71.8. In the English class had a mean of 71.7 and a standard deviation of 11.7.
This means that [tex]X = 71.8, \mu = 71.7, \sigma = 11.7[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{71.8 - 71.7}{11.7}[/tex]
[tex]Z = 0.0085[/tex]
Question b:
Amy took a test in Social Studies and earned a 60.7. Students' test grades in Social Studies had a mean of 60.6 and a standard deviation of 10.5.
This means that [tex]X = 60.7, \mu = 60.6, \sigma = 10.5[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60.7 - 60.6}{10.5}[/tex]
[tex]Z = 0.0095[/tex]
c) Which person did relatively better?
Amy had a higher z-score, so she did relatively better.
Cuál es el valor de x en la ecuación −7x+16=3x−4?
A.
2
Answer:
x=2
Step-by-step explanation:
16+4=3x+7x
20=10x
20/10=10x/10
2=x
A lift in a building starts with 7 passengers and stops at 10 floors.if each passenger is equally likely to get off at any floor and all passengers leave independently.what is the probability that atleast two passengers will get off at the same floor?
Answer:
Correct option is
C
10
5
10P
5
Total ways in which one passenger can stop =10
Total ways in which 5 passengers can stop =10∗10∗10∗10∗10
=10
5
We will select 5 floors from 10 floors and assign each individual to each floor to keep everyone isolated from each other
No. of ways in which no two persons stop at the same floor =10C
5
∗5!
=10P
5
⇒P(E)=10P
5
/10
5
PLSHELPASAPDFFFFFFFFFFFFFFFFFFFFFFFFFF
im struggling with the same one
Why does it help to rearrange
addends in Example B to show that
2.5n +9.9+(-3n) is equal to
2.5n + (-3n) + 9.9?
Answer:
You don't really need to do it, but it helps you keep things more organized and easier to follow. Imagine if you're doing some multi-variable equation,
2a + 5b + 4d + 3c + b + a + 2d
that looks like a mess, it'll be easier to look at if you put all the similar variables next to each others like this:
a + 2a + b + 5b + 3c + 2d + 4d
(a + 2a) + (b + 5b) + 3c + (2d + 4d)
now you can add them up much easier.
Find the median: 16.12.7.9.10.16
Answer:
hey hi mate
hope you like it
plz mark it as brainliest
Can someone just check my answers please? Please let me know which questions are wrong. Thank you for your time.
Find the value of z such that 0.05 of the area lies to the right of z. Round your answer to two decimal places.
Answer:
[tex]z = 1.6[/tex]
Step-by-step explanation:
Given
[tex]Pr = 0.05[/tex]
Required
The z value to the right
The z value to the right is represented as:
[tex]P(Z > z)[/tex]
So, the probability is represented as:
[tex]P(Z > z) = 0.05[/tex]
From z table, the z value that satisfies the above probability is:
[tex]z = 1.645[/tex]
[tex]z = 1.6[/tex] --- approximated
If a translation of T.3. - 8(x, y) is applied to square
ABCD, what is the y-coordinate of B'?
4
3
0-12
A
В
-8
-E
5
2
3
4
0
D
C
Answer:
Its C. -6
Step-by-step explanation:
The coordinates of point B after translation are (-2, -6).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation T(-3, -8) follows the rule:
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
(x, y)--->(x-3, y-8)
From the diagram you can see that point B has coordinates (1,2).
(1, 2)--->(1-3, 2-8)
(1, 2)--->(-2, -6)
According to the previous rule this point will transform in point B' with coordinates (-2,-6),
Hence, the coordinates of point B after translation are (-2, -6).
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ7
Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 grams. Assume that birth weight data are approximately bell-shaped. Part 1 of 3 (a) Estimate the number of newborns whose weight was less than 4171 grams. Approximately of the 732 newborns weighed less than 4171 grams. Part 2 of 3 (b) Estimate the number of newborns whose weight was greater than 1591 grams. Approximately of the 732 newborns weighed more than 1591 grams. Part 3 of 3 (c) Estimate the number of newborns whose weight was between 3311 and 5031 grams. Approximately of the 732 newborns weighed between 3311 and 5031 grams.
Answer:
a) 615
b) 715
c) 344
Step-by-step explanation:
According to the Question,
Given that, A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 gramsSince the distribution is approximately bell-shaped, we can use the normal distribution and calculate the Z scores for each scenario.Z = (x - mean)/standard deviation
Now,
For x = 4171, Z = (4171 - 3311)/860 = 1
P(Z < 1) using Z table for areas for the standard normal distribution, you will get 0.8413.Next, multiply that by the sample size of 732.
Therefore 732(0.8413) = 615.8316, so approximately 615 will weigh less than 4171For part b, use the same method except x is now 1591.
Z = (1581 - 3311)/860 = -2
P(Z > -2) , using the Z table is 1 - 0.0228 = 0.9772 . Now 732(0.9772) = 715.3104, so approximately 715 will weigh more than 1591.For part c, we now need to get two Z scores, one for 3311 and another for 5031.
Z1 = (3311 - 3311)/860 = 0
Z2 = (5031 - 3311)/860= 2
P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772
approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.
Find the circumference of a circle in terms of u with a radius of 10 ft.
100n ft
10 ft
5 ft
62.87 ft
20 ft
Answer:
[tex]2 \times \frac{22}{7} \times 10 = 62.87 [/tex]
Type your answer
(1 out of 4)
What is the value of the function when x = 3 in the
piecewise function
g(x) =
3x when x > 1
- 2x when x < 1
Answer:
9
Step-by-step explanation:
SCALCET8 3.9.015. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 35 ft from the pole
Answer:
[tex]X=6.67ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Height of pole [tex]H_p=15[/tex]
Height of man [tex]h_m=6ft[/tex]
Speed of Man [tex]\triangle a =4ft/s[/tex]
Distance from pole [tex]d=35ft[/tex]
Let
Distance from pole to man=a
Distance from man to shadow =b
Therefore
[tex]\frac{a+b}{15}=\frac{b}{6}[/tex]
[tex]6a+6b=15y[/tex]
[tex]2a=3b[/tex]
Generally the equation for change in velocity is mathematically given by
[tex]2(\triangle a)=3(\triangle b )[/tex]
[tex]2*4=3(\triangle b)[/tex]
[tex]\triangle a=\frac{8}{3}[/tex]
Since
The speed of the shadow is given as
[tex]X=\triangle b+\triangle a[/tex]
[tex]X=4+8/3[/tex]
[tex]X=6.67ft/s[/tex]
What is the following product?
(Xv7-3v8)(xv7-3v8)
Answer:
B
Step-by-step explanation:
I'm not really sure tho
Please help!!!!
I’m using Plato
1 by 4 ^ 256 is equal to 4 and 1 by 4 ^ 64 will be root 4 so here the answer will be 4 into 4 root 4
there option 4 will be correct
8. Solve the system using elimination.
3x - 4y = 9
- 3x + 2y = 9
Answer:
3x−4y=9 −3x+2y=9
Add these equations to eliminate x: −2y=18
Then solve−2y=18
for y: −2y=18 −2y −2 = 18 −2 (Divide both sides by -2)
y=−9
Now that we've found y let's plug it back in to solve for x.
Write down an original equation: 3x−4y=9
Substitute−9for y in 3x−4y=9: 3x−(4)(−9)=9
3x+36=9(Simplify both sides of the equation)
3x+36+−36=9+−36(Add -36 to both sides)
3x=−27 3x 3 = −27 3 (Divide both sides by 3) x=−9
Answer: x=−9 and y=−9
Hope This Helps!!!
help e please i’ll give brainliest
Answer:
363,000,000
..........
. a) In a group of 75 students, 20 liked football only, 30 liked cricket only and 18 did not like any of two games? (i) How many of them liked at least one game? (ii) Find the number of students who liked both the games. (iii) How many of them liked football? (iv) How many of them liked cricket? (v) Represent the result in a Venn diagram.
i)50
Steps
30+20=50
ii)7
Steps
75-(30+20)-18
=75-(50)-18
=7
iii)20
Steps
From the available data from the question
iv)30
Steps
From the available data from the questionl
v)From the attcged image file
So i have a puppy that im bottle feeding because the momma died. I have to feed him 4 ounces a day every 3 hours. I'm using a syringe that goes up to 3ML. There are 29MLs in an ounce so that means i would fill up my syringe 9 times for an ounce. There are 8 feeding sessions in 24hours and I'm trying to figure out how many MLs to feed every 3 hours. I know this is simple math but I haven't slept in 4 days since I've had the puppy and my brain hurts from the lack of sleep.. Pleae help!!
Answer:
116ML every 3 hours, 928ML a day
Step-by-step explanation:
You said it yourself if there is 29ML in one once and you need 4 ounces every 3 hours then 29 x 4 = 116.
All I need is number two
Suppose that the probability distribution for birth weights is normal with a mean of 120 ounces and a standard deviation of 20 ounces. The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is [ Select ] 68%. The probability that a randomly selected infant has a birth weight between 110 and 130 is [ Select ] 68%.
Answer:
The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is 68%.
The probability that a randomly selected infant has a birth weight between 110 and 130 is 38%.
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 120 ounces and a standard deviation of 20 ounces.
This means that [tex]\mu = 120, \sigma = 20[/tex]
The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is
p-value of Z when X = 140 subtracted by the p-value of Z when X = 100.
X = 140
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 120}{20}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84
X = 100
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 120}{20}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.16
0.84 - 0.16 = 0.68
The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is 68%.
The probability that a randomly selected infant has a birth weight between 110 and 130
This is the p-value of Z when X = 130 subtracted by the p-value of Z when X = 110.
X = 130
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130 - 120}{20}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.69
X = 110
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 120}{20}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.31
0.69 - 0.31 = 0.38 = 38%.
The probability that a randomly selected infant has a birth weight between 110 and 130 is 38%.
Four brands of lightbulbs are being considered for use in the final assembly area of the Ford F-150 truck plant in Dearborn, Michigan. The director of purchasing asked for samples of 200 from each manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are shown below. At the 0.10 significance level, is there a difference in the quality of the bulbs?
Manufacturer
A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
1) State the decision rule using 0.10 significance level. (Round your answer to 3 decimal places.)
Reject H0 if chi-square >
2) Compute the value of chi-square. (Round your answer to 3 decimal places.)
Chi-square value
Answer:
Decison region :
Reject H0 : if χ² > 6.251
12.229
Step-by-step explanation:
Given :
Manufacturer A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
Testing using the goodness of fit :
Chisquare = (observed - Expected)² / Expected
Expected Values:
19.25 19.25 19.25 19.25
180.75 180.75 180.75 180.75
Chi-Squared Values:
4.93831 0.262987 5.45779 0.392857
0.525934 0.0280083 0.581259 0.0418396
χ² = 4.93831 + 0.262987 + 5.45779 + 0.392857
+ 0.525934 + 0.0280083 + 0.581259 + 0.0418396 = 12.229
Degree of freedom, df = (4-1)(2-1) = 3*1= 3
The critical value,
χ² at 0.10, 3 = 6.251
Decison region :
Reject H0 : if χ² > 6.251
Reject H0 : 12.229 > 6.251
