if there were only three types of music in the world pop,rock and rap and set A equals all the people in the world who prefer pop music,what is A`?

Answer:

113

Step-by-step explanation:

Let the number of adult tickets sold =a

Let the number of student tickets sold =s

A total of 259 tickets were sold, therefore:

a+s=259

Adult tickets were sold for $24 each and student tickets were sold for $16 each.

Total Revenue = $5,312

Therefore:

24a+16s=5,312

We solve the two derived equations simultaneously.

From the first equation

a=259-s

Substitute a=259-s into 24a+16s=5,312

24(259-s)+16s=5,312

6216-24s+16s=5,312

-8s=5,312-6216

-8s=-904

Divide both sides by -8

s=113

Therefore, 113 student tickets were sold.

Answer: option D on edge 2020

Step-by-step explanation:

if you reverse the formula for mean, then you just insert the numbers and you have your answer

Answer:

[tex]\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n[/tex]

Step-by-step explanation:

Rn(x) →0

f(x) = 10/x

a = -2

Taylor series for the function f at the number a is:

[tex]f(x) = \sum^\infty_{n=0} \frac{f^{(n)}(a)}{n!} (x - a)^n[/tex]

[tex]f(x) = f(a) + \frac{f'(a)}{1!}(x-a)+\frac{f"(a)}{2!} (x-a)^2 + ...[/tex] ............ equation (1)

Now we will find the function f and all derivatives of the function f at a = -2

f(x) = 10/x            f(-2) = 10/-2

f'(x) = -10/x²         f'(-2) = -10/(-2)²

f"(x) = -10.2/x³      f"(-2) = -10.2/(-2)³

f"'(x) = -10.2.3/x⁴     f'"(-2) = -10.2.3/(-2)⁴

f""(x) = -10.2.3.4/x⁵    f""(-2) = -10.2.3.4/(-2)⁵

∴ The Taylor series for the function f at a = -4 means that we substitute the value of each function into equation (1)

So, we get [tex]\sum^\infty_{n=0} - \frac{10(x+2)^n}{2^{n+1}}[/tex] Or [tex]\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n[/tex]

Taylor series  is a power series that gives the expansion of a function f (x) in the neighborhood of a point.

Taylor series is,   [tex]f(x)=f(a)+\frac{f'(a)}{1!}(x-a)+\frac{f''(a)}{2!}(x-a)^{2}+........[/tex]

[tex]f(x)=\sum_{n=0}^{\infty }-\frac{10(x+2)^{n}}{2^{n+1}}[/tex]

Here,  f(x) = 1/x  and a = -2

Now find derivative,

 f(x) = 10/x            f(-2) = 10/-2

f'(x) = -10/x²         f'(-2) = -10/(-2)²

f"(x) = 10.2/x³      f"(-2) = 10.2/(-2)³

f"'(x) = -10.2.3/x⁴     f'"(-2) = -10.2.3/(-2)⁴

Substituting above values in Taylor series expansion.

We get,   [tex]f(x)=\sum_{n=0}^{\infty }-\frac{10(x+2)^{n}}{2^{n+1}}[/tex]

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Answer:

12x/2 or 52/2

Step-by-step explanation:

Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.

Answer: See bolded below

Step-by-step explanation:

With the given f(x) and g(x) given, we can directly plug them in to solve. The inverse is to replace the y with x and x with y, then solve for y.

A. f(g(-4))=143

g(-4)=3(-4)+1

g(-4)=-12+1

g(-4)=-11

With g(-4), we plug that into f(x) to find f(g(-4)).

f(-11)=(-11)²-2(-11)

f(-11)=121+22

f(-11)=143

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

B. 9x²-1

(3x+1)²-2(3x+1)

(9x²+6x+1)-6x-2

9x²-1

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

C. g⁻¹(x)=(x-1)/3

x=3y+1

x-1=3y

(x-1)/3=y

Answer:

Step-by-step explanation:

y + 8 = 0(x - 0)

y + 8 = 0

y = -8

Answer:

657.96

Step-by-step explanation:

use formula A=P(1+r/n)^nt

A=500(1+.04/1)^1*7

A=500(1.04)^7

A=500(1.3159~)

A= 657.96~

Answer:

Option B

Step-by-step explanation:

The null hypothesis for a chi-square goodness of fit test states that the data are consistent with a specified distribution.

While the alternative hypothesis states that the data are not consistent with a specified distribution.

In this case study, the test is for a nose distribution. Thus the null hypothesis would be that the population has a normal distribution.

Answer:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

2¹³

13 x 13

Step-by-step explanation:

We simply find numbers that can multiply to 26 and write out the multiplication to get our answer.

Answer:

Step-by-step explanation:

Using the alternative hypothesis (µ < µ0),

To find the p-value with test statistic -1.25 and assuming a standard level of significance of 0.05, using a p value calculator, the p-value is 0.1057 which is great that 0.05. Thus, the results is not significant.

Using the p value calculation.

1. Check the left tailed z table as the test statistic is negative,

2. Then find the probabilitythat z is greater than your test statistic (look up your test statistic on the z-table- the value under 1.2 and 0.05 which is 0.8944

3. Then, find its corresponding probability, and subtract it from 1 to get your p-value- 1-0.8944 = 0.1056.

Answer: 12 mph

Step-by-step explanation:

20 minutes = 1/3 hour

Distance = speed x time

D = 27 x 1/3 = 09 miles

He had taken 45 minutes when he drove home

45 minutes = 3/4 hour

Speed = distance / time

Speed = 9 / 3/4

Speed = 12 mph

The average speed of Nick's journey back home is 12 mph.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

The first average speed at what Nick travels is 27 mph.

One day it took Nick 20 mins to drive to work.

Here, Distance = Speed × Time

= 27 × 20/60

= 27 × 1/3

= 9 miles

Nick had drove home using the same route, it had took Nick 45 minutes.

Here, speed = Distance/Time

= 9÷45/60

= 9×4/3

= 12 mph

Therefore, the average speed of Nick's journey back home is 12 mph.

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Answer:

49.8 nautical miles

Step-by-step explanation:

Recall that speed = distance/time

Time = 2hours

Speed = 12knots and 16 knots respectively

D = speed×time

D1 = 12×2 = 24

D2 = 16×2 = 32

Using the 'cosine rule' we have:

a^2 = b^2+c^2-2bc cos Θ

Where a =?

b =24

c = 32

Θ = 125°

a² = 24² + 32² - 2(24)(32)cos125°

a^2 = 576+1024 - 1536cos125°

a² = 1600 - 1536(-0.57357)

a² = 1600+881.0134

a² = 2481.0134

Then, a² = 2481.013406

a =√2481.013406

Hence, a = 49.8 nautical miles

In this exercise we must use the knowledge about triangles to calculate the distance that a ship will travel, in this way we find that:

49.8 nautical miles

First, remember the formula for distance, which is:

[tex]Speed = distance/time[/tex]

And knowing that the data reported in the exercise are:

So putting the values ​​informed in the distance formula, we have:

[tex]D = speed*time\\D_1 = 12*2 = 24\\D_2 = 16*2 = 32[/tex]

Using the 'cosine rule' we have:

[tex]a^2 = b^2+c^2-2bc cos \theta[/tex]

Find the a, will have:

[tex]b =24 \ \ \ c = 32 \ \ \ \theta = 125\\a^2 = 24^2 + 32^2 - 2(24)(32)cos125\\a^2 = 576+1024 - 1536cos125\\a^2 = 1600 - 1536(-0.57357)\\a^2 = 1600+881.0134\\a^2 = 2481.0134\\a=49.8[/tex]

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Answer:

Step-by-step explanation:

We would apply the future value which is expressed as

FV = C × [{(1 + r)^n - 1}/r]

Where

C represents the yearly payments of the young professional.

FV represents the amount of money

in your account at the end of 40 years.

r represents the annual rate.

n represents number of years or period.

From the information given,

r = 4% = 4/100 = 0.04

C = $76000

n = 40 years

Therefore,

FV = 76000 × [{(1 + 0.04)^40 - 1}/0.04]

FV = 76000 × [{4.8 - 1}/0.04]

FV = 76000 × 95

FV = P7220000

Answer:

30x - 18

Step-by-step explanation:

6(5x - 3)

Apply the distributive property.

6(5x) + 6(-3)

30x + - 18

Answer:

30x - 18 is your final answer

Answer:

P(Chase) > P(Ava)

700 > 587

Therefore, Ava's claim is wrong!

On day 14, Chase's bacteria population will be greater than Ava's bacteria population.

Step-by-step explanation:

Please refer to the attached image.

Ava's bacteria population is modeled by the following equation.

[tex]$ b(t) = 200(1+0.08)^t $[/tex]

Where t is time in days and b(t) is the population of the bacteria after t days.

The graph represents the population of Chase's bacteria.

Ava claims that on day 14, she will have more bacteria than Chase.

Let us compare the population of both bacteria.

Chase bacteria population when t = 14 days:

From the graph, the population is approximately 700 at t = 14 days

P(Chase) ≈ 700

Ava bacteria population when t = 14 days:

at t = 14 days

[tex]b(t) = 200(1+0.08)^t \\\\ b(14) = 200(1.08)^{14} \\\\ b(14) = 200 (2.93719)\\\\ b(14) = 587.44[/tex]

So, the population is approximately 587 at t = 14 days

P(Ava) ≈ 587

P(Chase) > P(Ava)

700 > 587

Therefore, Ava's claim is wrong!

On day 14, Chase's bacteria population will be greater than Ava's bacteria population.

Answer:

D

Step-by-step explanation:

Trust

Answer:

3

Step-by-step explanation:

To begin with notice that  

        [tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]

From that equation you get that

10 tan(x)  +  30tan(x) cot(x) = 30

therefore

tan(x) + 3 tan(x) cot(x) = 3

Answer:

The answer is option D.

Hope this helps you

Answer:

0.1/4-3/20=1/40-6/40=-1/8 200% of this is -1/4

Step-by-step explanation:

This shows that  200 percent of (0.020(5/4) + 3 ((1/5) - (1/4))) is -2.75

Given the expression as shown in the question:

[tex]200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{1}{5}- \frac{1}{4} )][/tex]

Expand the expression in the square bracket using the distribution law as shown:

[tex]=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{4-5}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{-1}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )-(\frac{3}{20} )]\\=200\% \ of \ [0.020(1.25 )-\frac{3}{20}]\\=\frac{200}{100} \times [0.025-0.15]\\=2 \times [-0.125]\\=-2.75[/tex]

Hence the correct answer to the expression is -2.75.

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Answer:

-2 < x < 35

Step-by-step explanation:

We have that the larger side has a larger opposite angle and the smaller sides and a smaller opposite angle.

The opposite angle of the 14 unit side is 37 °.

The opposite angle of the 13-unit side is (x + 2) °.

Since 13 <14, it would be:

x + 2 <37

we subtract 2 on both sides

x <35

The value of x must be less than 35.

Now, to form a triangle, the angle must be greater than 0.

x + 2> 0

we subtract 2 on both sides

x> -2

The value of x must be greater than - 2.

Therefore the answer would be:

-2 <x <35

Answer:

620 comic books

2480 / 4 is 620.

620 x 3 is 1860.

1860 + 620 is 2480.

Done!

Answer: [tex]2\sqrt{1+tant}+C[/tex]

Step-by-step explanation:

To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.

[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]

Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.

[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]

[tex]u=\sqrt{1+tant}[/tex]

[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]

Now that we have u and du, we can plug them back in.

[tex]\int\limits {2} \, du[/tex]

[tex]\int\limits{2} \, du=2u[/tex]

Since we know u, we can plug that in.

[tex]2\sqrt{1+tant}[/tex]

This may seem like the correct answer, but we forgot to add the constant.

[tex]2\sqrt{1+tant}+C[/tex]

Answer:

one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]

in decimal one side = 3.16

other side =  9.48

Step-by-step explanation:

In right angle

if two sides containing right angle is a and b and h is hypotenuse then

by Pythagoras theorem

a^2 + b^2 = h^2

__________________________________

let one side be x

given

One of the triangle’s legs is 3  times the length of the other leg

then other leg = 3x

given h = 10 cm

applying Pythagoras theorem

[tex]a^2 + b^2 = h^2\\x^2 + (3x)^2 = 10^2\\x^2 + 9x^2 = 100\\10x^2 = 100\\x^2 = 100/10 = 10\\x = \sqrt{10}[/tex]

Thus, one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]

[tex]\sqrt{10} = 3.16\\[/tex]

thus, in decimal one side = 3.16

other side = 3.16*3 = 9.48

Answer:

3.6

Step-by-step explanation:

We must first clarify how a number is rounded.

To round a number to unity we have to look at the first number after the comma.

If this number is less than 5 (1, 2, 3, 4) we should not do anything, but if that number is 5 or greater (5, 6, 7, 8, 9) we must add a unit to the number.

That is to say:

<5 do nothing

=> 5 round to the next number (+1)

So in the case of 3.55 it would be.

3.55 = 3.6

Answer:

A) 95% confidence interval for the population mean PEF for children in biomass households = (3.214, 3.386)

95% confidence interval for the population mean PEF for children in LPG households

= (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.

C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Step-by-step explanation:

A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.

Finding the critical value from the z-tables,

Significance level for 95% confidence interval

= (100% - 95%)/2 = 2.5% = 0.025

z (0.025) = 1.960 (from the z-tables)

For the children in the biomass households

Sample mean = 3.30

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.20

N = sample size = 755

σₓ = (1.20/√755) = 0.0436724715 = 0.04367

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 3.30 ± (1.960 × 0.04367)

CI = 3.30 ± 0.085598

95% CI = (3.214402, 3.385598)

95% Confidence interval = (3.214, 3.386)

For the children in the LPG households

Sample mean = 4.25

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.75

N = sample size = 750

σₓ = (1.75/√750) = 0.063900965 = 0.063901

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 4.25 ± (1.960 × 0.063901)

CI = 4.25 ± 0.125246

95% CI = (4.12475404, 4.37524596)

95% Confidence interval = (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.

The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.

Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂

The null hypothesis is

H₀: μ ≥ 0 or μ₁ ≥ μ₂

The alternative hypothesis is

Hₐ: μ < 0 or μ₁ < μ₂

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = 3.30

n₁ = 755

s₁ = 1.20

μ₂ = 4.25

n₂ = 750

s₂ = 1.75

σ = √[(1.20²/755) + (1.75²/750)] = 0.07740

z = (3.30 - 4.25) ÷ 0.07740 = -12.27

checking the tables for the p-value of this z-statistic

Significance level = 0.01

The hypothesis test uses a one-tailed condition because we're testing in only one direction.

p-value (for z = -12.27, at 0.01 significance level, with a one tailed condition) = < 0.000000001

The interpretation of p-values is that

When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.

Significance level = 0.01

p-value = 0.000000001

0.000000001 < 0.01

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.

C) For FEY for biomass households,

Sample mean = 2.3 L/s

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation = 0.5

N = sample size = 755

σₓ = (0.5/√755) = 0.0182

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 2.30 ± (1.960 × 0.0182)

CI = 2.30 ± 0.03567

95% CI = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Hope this Helps!!!

Answer:

Step-by-step explanation:

Given the function f(x,y) = [tex]\frac{4xy^{2} }{7x^{2} + y^{4} }[/tex], we are to show that lim (x, y)→(0, 0) f(x, y) exist. To show that, the following steps must be followed.

[tex]\lim_{(x,y) \to (0,0)} \frac{4xy^{2} }{7x^{2} + y^{4} }\\[/tex]

substituting the limit x = 0 and y = 0 into the function we have;

[tex]\frac{4(0)^{2} }{7(0)^{2} + (0)^{4} }\\= \frac{0}{0} (indeterminate)[/tex]

Since we got an indeterminate function, we will then substitute y = mx into the function as shown;

[tex]\lim_{(x,mx) \to (0,0)} \frac{4x(mx)^{2} }{7x^{2} + (mx)^{4} }\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2} x^{3} }{7x^{2} + m^{4}x^{4} }\\\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2} x^{3} }{x^{2}(7 + m^{4} x^{2}) }\\\lim_{(x,mx) \to (0,0)} \frac{4m^{2}x }{7 + m^{4} x^{2} }[/tex]

Substituting x = 0 , the limit of the function becomes;

[tex]\frac{4m^{2}(0) }{7 + m^{4} (0)^{2} }\\= \frac{0}{7}\\ = 0[/tex]

Since the limit of the function gives a finite value of 0 (the limit tends to 0). This shows that the limit exists.

Answer:

0

Step-by-step explanation:

Using the slope formula

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

  and the given points

m = ( 2-2)/ ( 3-4)

    = 0/ -1

    = 0

The slope is zero

Answer:

white

Step-by-step explanation:

plato

The solution is Option D.

The missing color from the tree diagram is given by the equation A = white

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the missing color from the tree diagram be represented as A

Now , the value of A is

Jenson has 3 clean T-shirts of white , red and orange

Jenson has 2 clean pairs of jeans of blue and gray

Now , substituting the values in the equation , we get

For every blue jeans = { white , red , orange }

For every gray jeans = { A , red , orange }

From the equation , we get

The value of A = white

Therefore, the value of A is white

Hence , the missing color is white

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Answer:

(x + 2) ^2 (x - 2) ^ 2 so A is the answer.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

for this you need to sub the value of -3 for x

Q(-3)=(-3)^2-(-3)-2

=9+3-2

=10

Answer:

Q= x - X/x - 2/x

Step-by-step explanation:

hope this helps !