Two different types of tickets are selling for the next big concert. Each hour, one hundred $65 tickets are sold for seats on the floor. Every two hours, one hundred and fifty $50 tickets are sold for seats in the stands. Determine the rate of sale for each type of ticket being sold.

Answer:

B) All real numbers except 0 and integer multiples of 8π∕5

Step-by-step explanation:

Cotangent function:

The cotangent function is given by:

[tex]y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}[/tex]

Domain:

All real values except those at which:

[tex]\sin{ax} = 0[/tex]

The sine is 0 for 0 and all integer multiples of [tex]\frac{1}{a}[/tex]

In this question:

[tex]a = \frac{5}{8}[/tex], so the values outside the domain are 0 and the integer multiples of [tex]\frac{8}{5}[/tex]. Then the correct answer is given by option b.

Given:

The set is:

[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]

To find:

The raster form of the given set.

Solution:

We know that, natural numbers are all positive integers.

Natural numbers: 1, 2, 3, 4,... .

The given set is:

[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]

Here, x is a natural number and it is less than -2, which is not possible.

Since all natural numbers are greater than or equal to 1, therefore the given set has no element.

[tex]\{x|x\text{ is a natural number less than }-2=\phi[/tex]

Therefore, the roaster form of the given set is [tex]\phi[/tex] or [tex]\{\ \}[/tex].

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Answer:

Step-by-step explanation:

Your have correctly identified the points of intersection, but you need to follow directions in your entry of those answers. "POLE" goes in the first answer slot. You may also be expected to rationalize the denominator, or provide the r value as a single term.

The points of intersection are ...

  POLE

  ((2+√2)/2, 3π/4)

  ((2-√2)/2, 7π/4)

Answer:

Please look at the picture

Step-by-step explanation:

Please look at the picture I have drawn it for you

9514 1404 393

Answer:

  split the number into equal pieces

Step-by-step explanation:

Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.

We have to assume that the number being split is positive and all of the parts are positive.

If we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.

Similarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...

  p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4

This will be maximized where its derivative is zero:

  p' = (1/4)(3x^2 -4nx +n^2) = 0

  (3x -n)(x -n) = 0 . . . . . . . . . . . . . factor

  x = n/3  or  n

We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.

A similar development can prove by induction that the parts must all be equal.

Answer:hi

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

10 x 6 = 60

Hope this helped! :)

Answer:

32

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x²=15-4x

divide by 3 on both sides

x²=5-[tex]\frac{4}{3}[/tex]x ​ ​

move everything to one side

x²+[tex]\frac{4}{3}[/tex]x ​-5 = 0

add the square of 1/2 the middle term of [tex]\frac{4}{3}[/tex]  but also subtract it too

x²+[tex]\frac{4}{3}[/tex]x +[tex]( \frac{2}{3} )^{2}[/tex]​-5-[tex]( \frac{2}{3} )^{2}[/tex]​ = 0

now use the property of a perfect square to rewrite

[tex](x+\frac{2}{3}) ^{2}[/tex] -5 -[tex]\frac{4}{9}[/tex] = 0

rewrite 5 as a fraction

[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{45}{9}[/tex]- [tex]\frac{4}{9}[/tex] = 0

add up the fractions

[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{49}{9}[/tex] = 0

move to the other side

[tex](x+\frac{2}{3}) ^{2}[/tex] = [tex]\frac{49}{9}[/tex]

take the square root of both sides :P

[tex]\sqrt{((x+\frac{2}{3}) ^{2} }[/tex]  = [tex]\sqrt{\frac{49}{9} }[/tex]

much easier looking now, just use algebra to solve for x

x + [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]

subtract  [tex]\frac{2}{3}[/tex]  from both sides

x + [tex]\frac{2}{3}[/tex] -  [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex] - [tex]\frac{2}{3}[/tex]

x = [tex]\frac{5}{3}[/tex]

:)  

​

Answer:

x = - 3, x = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Given

3x² =15 - 4x ( add 4x to both sides )

3x² + 4x = 15 ← factor out 3 from each term on the left side

3(x² + [tex]\frac{4}{3}[/tex] x) = 15

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + [tex]\frac{4}{3}[/tex] x

3(x² + 2([tex]\frac{2}{3}[/tex] )x + [tex]\frac{4}{9}[/tex] - [tex]\frac{4}{9}[/tex] ) = 15

3(x + [tex]\frac{2}{3}[/tex] )² - [tex]\frac{4}{3}[/tex] = 15 ( add [tex]\frac{4}{3}[/tex] to both sides )

3(x + [tex]\frac{2}{3}[/tex] )² = 15 + [tex]\frac{4}{3}[/tex] = [tex]\frac{49}{3}[/tex] ( divide both sides by 3 )

(x + [tex]\frac{2}{3}[/tex] )² = [tex]\frac{49}{9}[/tex] ( take the square root of both sides )

x + [tex]\frac{2}{3}[/tex] = ± [tex]\sqrt{\frac{49}{9} }[/tex] = ± [tex]\frac{7}{3}[/tex] ( subtract [tex]\frac{2}{3}[/tex] from both sides )

x = - [tex]\frac{2}{3}[/tex] ± [tex]\frac{7}{3}[/tex], then

x = - [tex]\frac{2}{3}[/tex] - [tex]\frac{7}{3}[/tex] = - 3

x = - [tex]\frac{2}{3}[/tex] + [tex]\frac{7}{3}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

0=70!!!!!!!!!!!!!!!!!!!!!!

Answer:

2 pounds

Step-by-step explanation:

so if we say we decrease 20% each year and we're only going one year. All you have to do is 2.5 - 20%

Answer:

See Below.

Step-by-step explanation:

We are given the equation:

[tex]\displaystyle y^2 = 1 + \sin x[/tex]

And we want to prove that:

[tex]\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1[/tex]

Find the first derivative by taking the derivative of both sides with respect to x:

[tex]\displaystyle 2y \frac{dy}{dx} = \cos x[/tex]

Divide both sides by 2y:

Find the second derivative using the quotient rule:

[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1[/tex]

Simplify:

[tex]\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1[/tex]

Combine fractions:

[tex]\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1[/tex]

Simplify:

[tex]\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1[/tex]

Cancel:

[tex]\displaystyle -\sin x + y^2 = 1[/tex]

Substitute:

[tex]-\sin x + \left( 1 + \sin x\right) =1[/tex]

Simplify. Hence:

[tex]1\stackrel{\checkmark}{=}1[/tex]

Q.E.D.

Answer: a = 25.67

Step-by-step explanation:

Answer:

The rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 feet is approximately 0.637 feet per second.

Step-by-step explanation:

The volume of the cone ([tex]V[/tex]), in cubic feet, is defined by the following equation:

[tex]V = \frac{\pi}{3}\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Radius, in feet.

[tex]h[/tex] - Height, in feet.

And there is the following ratio of the radius to the height is:

[tex]\frac{r}{h} = k[/tex] (2)

By applying (2) in (1):

[tex]h = \frac{r}{k}[/tex]

[tex]V = \frac{\pi}{3\cdot k}\cdot r^{3}[/tex] (3)

And the rate of change of the radius is found by differentiating on (3):

[tex]\dot V = \frac{\pi}{k}\cdot r^{2}\cdot \dot r[/tex] (4)

Where:

[tex]\dot V[/tex] - Rate of change of the volume, in cubic feet per second.

[tex]\dot r[/tex] - Rate of change of the surface of the water, in feet per second.

[tex]\dot r = \frac{k\cdot \dot V}{\pi\cdot r^{2}}[/tex]

If we know that [tex]k = \frac{1}{3}[/tex], [tex]\dot V = 24\,\frac{ft^{3}}{s}[/tex] and [tex]r = 2\,ft[/tex], then the rate of change of the radius of the surface of the water is:

[tex]\dot r = \frac{\left(\frac{1}{3} \right)\cdot \left(24\,\frac{ft^{3}}{s} \right)}{\pi\cdot (2\,ft)^{2}}[/tex]

[tex]\dot r = 0.637\,\frac{ft}{s}[/tex]

The rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 feet is approximately 0.637 feet per second.

Given:

The system of inequalities:

[tex]y\leq \dfrac{1}{2}x+2[/tex]

[tex]y<-2x-3[/tex]

To find:

Whether the points (–3,–2) and (3,2) are in the solution set of the given system of inequalities.

Solution:

A point is in the solution set of the given system of inequalities if it satisfies both inequalities.

Check for the point (-3,-2).

[tex]-2\leq \dfrac{1}{2}(-3)+2[/tex]

[tex]-2\leq -1.5+2[/tex]

[tex]-2\leq 0.5[/tex]

This statement is true.

[tex]-2<-2(-3)-3[/tex]

[tex]-2<6-3[/tex]

[tex]-2<3[/tex]

This statement is also true.

Since the point (-3,-2) satisfies both inequalities, therefore (-3,-2) is in the solution set of the given system of inequalities.

Now, check for the point (3,2).

[tex]2<-2(3)-3[/tex]

[tex]2<-6-3[/tex]

[tex]2<-9[/tex]

This statement is false because [tex]2>-9[/tex].

Since the point (3,2) does not satisfy the second inequality, therefore (3,2) is not in the solution set of the given system of inequalities.

Answer: The point (–3,–2) is in the solution set, and the point (3,2) is not in the solution set.

Please mark Brainliest Thank you :)

Answer:

see explanation

Step-by-step explanation:

Using the cosine addition formula

cos(A ± B ) = cosAcosB ∓ sinAsinB

Then considering the left side

cos²(45 + A) + cos²(45 - A)

= [ cos45cosA - sin45sinA ]² + [cos45cosA + sin45sinA]]²

= [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA - [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]² + [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA + [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]²

= [tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex] sin²A + [tex]\frac{1}{2}[/tex] cos²A + sinAcosA + [tex]\frac{1}{2}[/tex] sin²A

= cos²A + sin²A

= 1

= right side , then proven

Answer:

Step-by-step explanation:

cos 2x=cos²x-sin²x=cos²x-(1-cos²x)=cos²x-1+cos²x=2cos²x-1

2cos²x=1+cos2x

[tex]cos^2x=\frac{1}{2}(1+cos2x)[/tex]

cos²(45+A)+cos²(45-A)

[tex]=\frac{1}{2}(1+cos(90+2A))+\frac{1}{2}(1+cos(90-2A))\\=\frac{1}{2} (1-sin2A)+\frac{1}{2} (1+sin 2A)\\=\frac{1}{2} (1-sin2A+1+sin 2A)\\=\frac{1}{2} \times2\\=1[/tex]

cos (90-x)=sin x

cos (90+x)=-sin x

D

A

B

C

for more explanation please don't hesitate to just respond

Answer:

b

Step-by-step explanation:

2 * 3 to the -2 power. 3x-3=-9

2x-9=-18

Answer:

The last one. 4.

Step-by-step explanation:

The square root of a positive or negative number can't be negative. so it's positive 4.

Answer:

71, 69 and 63

71, 67 and 65

73, 67 and 63

75, 65 and 63

Answer:

[tex]A)\:x<12[/tex]

[tex]5(x+5)<85\\5x+25<85\\5x<85-25\\5x<60\\x<12[/tex]

OAmalOHopeO

Answer:

x < 12.................................

y'' - 6y' + 9y = 0

If y = C₁ exp(3x) + C₂ x exp(3x), then

y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))

y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))

Substituting these into the DE gives

(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))

… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))

… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))

= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))

… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))

… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)

= 0

so the provided solution does satisfy the DE.

Answer: 14/15 of a meter

Step-by-step explanation:

5 and 3 LCM is 15.

3/5 x 3 + 1/3 x 5= 9/15 + 5/ 15 = 14/15

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Answer:

Step-by-step explanation:

1. Input 3 for x and do the arithmetic.

  z(x) = x+1

  z(3) = 3+1 = 4 . . . . . the output is 4

__

2. The expression for n(x) has x in the denominator. The expression will be undefined when the denominator is zero, so x=0 cannot be used.

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Answer:

  (-13, 10)

Step-by-step explanation:

If M is the midpoint of segment DE, then ...

  D = 2M -E

  D = 2(-3, 4) -(7, -2) = (2(-3)-7, 2(4)+2) = (-13, 10)

The other end point is (-13, 10).

Answer:

The p-value of the test is 0.242 > 0.05, which means that this information does not indicate a difference between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

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]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Women:

51 out of 222, so:

[tex]p_1 = \frac{51}{222} = 0.2297[/tex]

[tex]s_1 = \sqrt{\frac{0.2297*0.7703}{222}} = 0.0282[/tex]

Men:

49 out of 174, so:

[tex]p_2 = \frac{49}{174} = 0.2816[/tex]

[tex]s_2 = \sqrt{\frac{0.2816*0.7184}{174}} = 0.0341[/tex]

Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts?

Either way, so a two tailed test to see if the difference of proportions is different of 0.

At the null hypothesis, we test if it is not different of 0, so:

[tex]H_0: p_1 - p_2 = 0[/tex]

At the alternative hypothesis, we test if it is different of 0, so:

[tex]H_1: p_1 - p_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_1 - p_2 = 0.2297 - 0.2816 = -0.0519[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0282^2+0.0341^2} = 0.0442[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.0519 - 0}{0.0442}[/tex]

[tex]z = -1.17[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the differences being of at least 0.0519, either way, which is P(|z| > 1.17), that is, 2 multiplied by the p-value of z = -1.17.

Looking at the z-table, z = -1.17 has a p-value of 0.121.

0.121*2 = 0.242

The p-value of the test is 0.242 > 0.05, which means that this information does not indicate a difference between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts.

Answer:

Creo que es 36

Step-by-step explanation

:D

Answer:

36

Step-by-step explanation:

Answer:

x-y=2

I don't get why they are asking you what is 2-5. That seems super basic compared to the other question it is with. Since 5-2=3, then 2-5 or -5+2=-3.

Step-by-step explanation:

We are going to use identity x^2-y^2=(x-y)(x+y)

x^2-y^2=10

(x-y)(x+y)=10

(x-y)(5)=10

Since (2)(5)=10, this implies x-y=2.

Solution :

Given data:

Mean, μ = $87,500

Standard deviation, σ =  $26,000

Sample number, n = 63

a). The value of [tex]$\mu_{x}$[/tex] :

   [tex]$\mu_x=\mu$[/tex]

       = 87,500

b). The value of [tex]$\sigma_x$[/tex] :

    [tex]$\sigma_x = \frac{\sigma}{\sqrt n}$[/tex]

   [tex]$\sigma_x = \frac{26000}{\sqrt {63}}$[/tex]

        = 3275.69

c). The shape of the sampling distribution is that of a normal distribution (bell curve).

d). The value z-score for the value =80,000.

   [tex]$z-\text{score} =\frac{\overline x - \mu}{\sigma - \sqrt{n}}$[/tex]

  [tex]$z-\text{score} =\frac{80000-87500}{26000 - \sqrt{63}}$[/tex]

                = -2.2896

                ≈ -2.29

e). P(x > 80000) = P(z > -2.2896)

                           = 0.9890

Answer:

[tex]{ \tt{ = ( log_{x}16)( log_{2}x) }}[/tex]

Change base x to base 2:

[tex]{ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}[/tex]