prove the identity of sin(x+y)-sin(x-y)=2 cos(x) sin(y)

Step-by-step explanation:

-9 ≤ 7 − 8x

8x ≤ 16

x ≤ 2

Answer:

(a) The average baggage-related revenue per passenger is $15.70.

(b) The standard deviation of baggage-related revenue is $19.95.

(c) The expected revenue for 120 passengers is $1,884.

Step-by-step explanation:

Let the random variable X represent the baggage-related revenue per passenger.

It is provided that the baggage fees is $25 for the first bag and $35 for the second.

The probability model is:

    X :   0         25      60

P (X) : 0.54    0.34    0.12

(a)

Compute the average baggage-related revenue per passenger as follows:

[tex]E(X)=\sum {X\times P (X)}[/tex]

         [tex]=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70[/tex]

Thus, the average baggage-related revenue per passenger is $15.70.

(b)

Compute the standard deviation of baggage-related revenue as follows:

[tex]E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\[/tex]

[tex]SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}[/tex]

           [tex]=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95[/tex]

Thus, the standard deviation of baggage-related revenue is $19.95.

(c)

Compute the expected revenue for 120 passengers as follows:

[tex]E(R)=n\times E(X)[/tex]

        [tex]=120\times 15.7\\\\=1884[/tex]

Thus, the expected revenue for 120 passengers is $1,884.

Answer:

a is a value of 5 and b is is equal to 9

Step-by-step explanation:

all you have to do is get 16 and 4 by them self and take them out, and find the remaining numbers

Answer: a = 8, b = [tex]4\sqrt{5}[/tex]

Answer:

6(72)= 432 & 8(74.25)=594

594-432=162==> 162-80=82

Answer:

hope this helps, take care and stay safe

Step-by-step explanation:

you can do this by timing 6.5 by 2 which = 13. if you get stuck on questions like this, do the rewind effect, that is when you do the opposite of the question, which is what i did above, you can check this in 2 ways, on a calculator (if of course you are allow) or do the question again by using what you have work out, so 13 divide by 2 = 6.5.

The number 13 is divided by 2 to give the number 6.5.

Used the concept of divide which states that,

The division method is used to distribute a group of things into equal parts. The division is just the opposite of multiplications.

To find the number that is divided by 2 to give the number 6.5

Let us assume that the number = x

Hence, it can be written as,

x ÷ 2 = 6.5

x/2 = 6.5

Multiply both sides 2;

x = 2 × 6.5

x = 13

Therefore, the number of the given condition is 13.

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Answer:

1

Step-by-step explanation:

We need to points

(-1,0) and (0,1)

The slope is found by

m= (y2-y1)/(x2-x1)

m = (1-0)/(0- -1)

   = (1-0)/(0+1)

   = 1/1

The slope is 1

Answer:

1

Step-by-step explanation:

The slope is rise/run and can be found by counting how many units up and over you must go from one point on the line to another.

Therefore the answer is

1

Answer:

hope this is correct

Answer:

The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this quesstion:

[tex]\sigma = 1.5, n = 22[/tex]

So

[tex]M = 1.645*\frac{1.5}{\sqrt{22}} = 0.53[/tex]

The margin of error for a confidence interval for the population mean with a 90% confidence level is 0.53 hours.

Assuming [tex]A'[/tex] denotes the complement of the set [tex]A[/tex], i.e. all elements in the universal set that do not belong to [tex]A[/tex], then we can prove this in general.

To establish equality between two sets, you need to show that they are both subsets of one another.

Let [tex]x\in(A\cup B)'[/tex].

By definition of set complement, this means [tex]x\not\in A\cup B[/tex].

By definition of set union, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].

By definition of complement, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].

By definition of set intersection, [tex]x\in A'\cap B'[/tex].

Therefore [tex](A\cup B)'[/tex] is a subset of [tex]A'\cap B'[/tex], because membership of some arbitrary element in the first set directly implies membership in the second set.

Let [tex]x\in A'\cap B'[/tex]. The proof follows similarly as above.

By definition of intersection, [tex]x\in A'[/tex] and [tex]x\in B'[/tex].

By definition of complement, [tex]x\not\in A[/tex] and [tex]x\not\in B[/tex].

By definition of union, [tex]x\not\in(A\cup B)[/tex].

By definition of complement, [tex]x\in(A\cup B)'[/tex].

Therefore [tex]A'\cap B'[/tex] is a subset of [tex](A\cup B)'[/tex].

And hence both sets are equal, regardless of what the sets may be.

Answer:

- 1/3

Step-by-step explanation:

2y - 6x = 4

y - 3x = 2

y = 3x + 2

Slope of the given line = 3.

Slope of the perpendicular line is negative reciprocal = - 1/3.

Answer:

16/25

Step-by-step explanation:

4/10=40/100

24/100=24/100

40+24=64

64/100

16/25

Answer:

16/25

Step-by-step explanation:

The answer is 6 1/2 buckets.

What is did was turn the fractions into decimals to make it easier.  

So the ratio is 5.25 gallons per bucket. I divided 34 1/8 by 5 1/4 in decimal form (34.125/5.25) and got 6.5

So therefore, the answer is 6 1/2 buckets of water is needed ti fill up the tub.

Answer:

49.97% probability of getting one child of each sex

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution 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.

The probability that a couple’s first child is a boy is 0.512.

This means that [tex]p = 0.512[/tex]

The will have two children:

This means that [tex]n = 2[/tex]

(a) What is the probability of getting one child of each sex?

This is P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{2,1}.(0.512)^{1}.(0.488)^{1} = 0.4997[/tex]

49.97% probability of getting one child of each sex

Answer:

72

Step-by-step explanation:

s=9

t=8

therefore , st

9×8

= 72

Answer:

st

Putting the value of s and t in above equation

=> 9 × 8

=> 72

Answer:

The equilibrium point for the product (x,y) = (50,2300)

Step-by-step explanation:

The equilibrium point refers to the point in the demand and supply curves where we have the quantity demanded equals the quantity supplied at a particular price.

From the question, we can identify the following;

S(x) = 300 + 40x

D(x) = 4300 - 40x

Now, at the equilibrium point, S(x) = D(x)

This means that;

300 + 40x = 4300 -40x

80x = 4300-300

80x = 4000

x = 4000/80 = 50

Now, we input the value of x into any of the equation of the demand and supply to get the quantity.

Let’s use S(x) = 300 + 40x = 300 + 40(50) = 300 + 2000 = 2,300

The equilibrium point for the product (x,y) = (50,2300)

Answer:

a) test statistic, [tex]t_{s} = -4.20[/tex]

b) P-value = 0.0001

c) It can be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years

Step-by-step explanation:

There are 40 trading days, therefore, sample size, n = 40

Calculate the Sample mean:

[tex]\bar x = \frac{\sum x}{n} \\\bar x = \frac{4.153 +4.6228 + ...+...+5.4563}{40}\\\bar x = 5.5945[/tex]

Get the null and alternative hypothesis:

Null hypothesis, [tex]H_{0} : \mu = 7.52[/tex]

Alternative hypothesis, [tex]H_{a} : \mu \neq 7.52[/tex]

Calculate the sample standard deviation:

[tex]SD = \sqrt{\frac{\sum (x - \bar x)^{2} }{n - 1} } \\SD = \sqrt{\frac{(4.1531-5.5945)^{2} + (4.6228-5.5945)^{2}+...+ (5.4563-5.5945)^{2}}{39} } \\SD = \sqrt{\frac{327.6161}{39} } \\SD = 2.8983[/tex]

a) Calculate the test statistic:

[tex]t_{s} = \frac{\bar{x} - \mu}{SD/\sqrt{n} } \\t_{s} = \frac{5.5945 -7.52}{2.8983/\sqrt{40} }\\t_{s} = -4.20[/tex]

b) Calculate the P-value

Getting the P-value using the excel function:

P-value = (=T.DIST.2T(|ts|, df))

P-value = (=T.DIST.2T(4.20, 39))

P-value = 0.0001

c) If the level of significance, [tex]\alpha = 0.05[/tex]

The P-value (0.0001) < α(0.05), the null hypothesis is rejected.

It can therefore be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years

Answer:

2 units right

3 units up

Step-by-step explanation:

the graph y=(x+2)² is the parent function y=x^2 translated 2 units left

the graph y=x²+3 is the parent function y=x^2 translated 3 units up

so, the translation from y=(x+2)² to y=x²+3 is:

2 units right (to get to zero)

3 units up

(you can change the order if you want, it doesn't really matter here)

Answer:

Step-by-step explanation:

DO YOU MEAN :

[tex]4x + 5y = 7\\ 3x - 2y = -12\\Multiply-equation 1 -by -the-coefficient-of-x-in-equation-2\\multiply-equation-2 -by-the-co-efficient -of x -in-equation- 1\\\\3(4x + 5y = 7)\\4( 3x - 2y = -12)\\\\12x +15y=21\\12x -8y=-48[/tex]

Answer:

Since the spinners have been spun simultaneously, every side on each of the spinner carries equal probability of landing. In order for there to be only 10 possible outcomes, no more no less, the spinners cannot be identical. One of the spinner in two sided while the other spinner must then be a five sided spinner. Choosing this particular pair of spinners gives Nathan 10 possibilities of combinations.

Hope that answers the question, have a great day!

Answer:

The spinners he spins are the ones that together add up to ten numbers.

Step-by-step explanation:

Answer:

26 remainder 2

Step-by-step explanation:

5 - 3 =2

2 + 78 = 80

80 ÷ 3

3 can go into 8 twice remaining with 2

2 goes across to 0

3 can go into 20 6 times because 3×6= 18

so 3 into 20 is 6 remainder of 2

answer= 26 remainder of 2

Answer:

[tex]= 26 \frac{3}{2} \\ [/tex]

Step-by-step explanation:

[tex]5 - 3 + 78 \div 3 \\ 2 + 78 \div 3 \\ 80 \div 3 \\ = 26 \frac{3}{2} [/tex]

hope this helps you

Answer:

Maximum height: 33.7 meters

Time: 1.7 seconds

Step-by-step explanation:

Suppose we have a quadratic equation in the following format:

[tex]f(t) = at^{2} + bt + c[/tex]

In a is negative, the maximum point of the function happens at the time of

[tex]t_{v} = -\frac{b}{2a}[/tex]

And it's value is: [tex]f(t_{v})[/tex]

In this question:

[tex]f(t) = -4.9t^{2} + 17t + 19[/tex]

So [tex]a = -4.9, b = 17, c = 19[/tex]

The time of the maximum height is:

[tex]t_{v} = -\frac{b}{2a} = -\frac{17}{2*(-4.9)} = 1.7[/tex]

The maximum height is:

[tex]f(1.7) = -4.9*(1.7)^{2} + 17*1.7 + 19 = 33.7[/tex]

Answer:

A(w) = -w^2 + 100w

Step-by-step explanation:

just took the assignment

Finding the numeric value of the function, it is found that the area of the rectangle is of 2400 square feet.

---------------------------

The area of a rectangle of width w is given by:

[tex]A(w) = -w^2 + 100w[/tex]

In this question, we have a width of 40 ft, thus [tex]w = 40[/tex], and the area is of:

[tex]A(40) = -40^2 + 100(40) = -1600 + 4000 = 2400[/tex]

The area is of 2400 square feet.

A similar problem is given at https://brainly.com/question/24231879

Answer:

The Answer is D on Edge

Step-by-step explanation:

Answer:

D is the answer

Step-by-step explanation:

Answer:

[tex][0,Z_n][/tex]

Step-by-step explanation:

Z = the sales tax percentage for a randomly selected amazon purchase, where n = the total number of possible sales tax percentages for online purchases

Since Amazon is an online purchase, The set of possible values for the variable is a positive real number. It is a positive real number that must be within [tex]Z_n[/tex]. It cannot exceed the tax percentage for online purchases that can be found in Amazon. [tex]Z_n[/tex] is a set of online purchases that can be found on Amazon, therefore the set of possible values for the variable is [tex][0,Z_n][/tex]

Answer:

positive

Step-by-step explanation:

the higher the temp the higher the number of ice creams sold

The association would be positive between the variables.

Given that,
Recorded the daily high temperature and the daily amount of ice cream sold by an ice cream vendor at your favorite beach this summer, starting on Memorial Day weekend and ending on Labor Day weekend.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
As the temperature increases, people will love to eat the ice cream more, which increase the sales of the ice cream which implies that the association would be positive between the variable.

Thus, the association would be positive between the variables.

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Answer:

6.3 ft

Step-by-step explanation:

The perimeter of a parallelogram is given by

P = 2(l+w)

49.6 = 2 (18.5 +t)

Divide by 2

49.6/2 = 2/2 (18.5 +t)

24.8 = 18.5+t

Subtract 18.5

24.8-18.5 = t

6.3 = t

Answer:

Step-by-step explanation:

Obviously, factors can be written in any order. So, there are multiple answers to this question.

1. x^2 -2x -15 = (x -5)(x +3) . . . . (a, b, c, d) = (1, -5, 1, 3)

__

2. 2x^2 -6x -36 = 2(x^2 -3x -18) = 2(x -6)(x +3) . . . . (a, b, c, d) = (2, -12, 1, 3)

__

3. 4x^2 +10x +4 = 2(2x^2 +5x +2) = 2(2x +1)(x +2) . . . . (a, b, c, d) = (4, 2, 1, 2)

Answer:

The mean of sampling distribution of the proportion of the students who prefer later start times for school

                        μₓ = p = 0.63

Step-by-step explanation:

Explanation:-

Given sample size 'n' =200

given data Of the 200 students surveyed at the local high school, 126 say that they prefer earlier start times for school

sample proportion

                        [tex]p = \frac{x}{n} = \frac{126}{200} = 0.63[/tex]

The mean of sampling distribution of the proportion of the students who prefer later start times for school

                        μₓ = p = 0.63

Standard deviation of the proportion

                     [tex]S.D = \sqrt{\frac{p(1-p)}{n} } = \sqrt{\frac{0.63(1-0.63)}{200} } = 0.034[/tex]

Answer:

The critical value of t =3.012

Step-by-step explanation:

Solution

Recall that:

Bruce a store owner put together information on random sales of = 14 days

A significant level of =0.5%

The mean revenue per day = 65 dollars

Now,

We find he critical values using the partial t-table stated above

Thus,

The degree of freedom is given below:

n -1 = 14

14-1 =13

For a 0.005 level and right tailed test and with a 13 degree of freedom, the critical value of t =3.012.

Answer:

2 or 6

Step-by-step explanation:

The mode is always the number that repeats or is shown more than once. But there is no number that repeats. So your answer is No mode.