A movie theater has a seating capacity of 235. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1704, How many children, students, and adults attended?

Answer:

The correct answer is the first one.

Step-by-step explanation:

Let's analyse the effect of each modification in the function.

The value 6 multiplying the cot function means a vertical stretch.

The value of 3 multiplying the x inside the function is a horizontal compression, which causes the period to be 3 times lower the original period.

The original period of the cotangent function is pi, so the horizontal compression will make the period be pi/3.

The value of -pi/2 inside the cotangent function normally causes a horizontal shift of pi/2 to the right, but the x-values were compressed by a factor of 3 (horizontal stretch), so the horizontal shift will be 3 times lower: (pi/2) /3 = pi/6

And the value of 4 summing the whole equation is a vertical shift of 4 units up.

So the correct answer is the first one.

Answer:

option 1

Step-by-step explanation:

The correct graph will be the first one (A)

Answer: 168

Step-by-step explanation:

First, let's count the types of selection:

We can select:

Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)

Pack: standard, custom, or sport styling, (3 options)

type of transmission: Manual or automatic (2 options)

Color: (7 options)

The total number of combinations is equal to the product of the number of options in each selection:

C = 4*3*2*7 = 168

Answer: There will be no real solutions

Explanation: If the discriminant (the part under the radical in the numerator of the quadratic equation) is less than 0, there are no real solutions. If positive, there will be two real solutions. If 0, there will be one.

Answer:

increase of 30

Step-by-step explanation:

1255- 1075 = 180

This is an increase of 180

Divide by the number of numbers which is 6

180 /6 = 30

The mean will increase by 30

Answer:

+30

Step-by-step explanation:

1255- 1075 = 180

180 /6 = 30

Answer:

not rejecting the null hypothesis when it is false.

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.

For making the error, it should not reject the null hypothesis at the time when it should be false.

It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.

Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.

Learn more about error here: https://brainly.com/question/18831983

Answer:

Step-by-step explanation:

Given,

There are 8 seats in a row.

There are 8 seats in a row.4 seats are occupied.

Available seats = 8 - 4 = 4 seats

Fraction of seats available:

[tex] \frac{number \: of \: seats \: available}{total \: number \: of \: seats} [/tex]

[tex] = \frac{4}{8} [/tex]

Reduce the fraction with GCF 4

[tex] = \frac{1}{2} [/tex]

Hope this helps..

Best regards!!

Answer:

Your correct answer is that there are 4 seats available. The fraction version is 1/2

Step-by-step explanation:

Since there are 8 in a row and 4 are taken, subtract 8 by 4.

8 - 4 = 4 seats that are available.

Answer:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}[/tex]

[tex]P(First\ White) = \dfrac{3}{10}[/tex]

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

[tex]P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }[/tex]

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]

Answer:

y = -3.5x² + 2.7x -8.2

Step-by-step explanation:

the quadratic equation is set up as a² + bx + c, so just plug in the values

Answer:

[tex]-3.5x^2 + 2.7x -8.2[/tex]

Step-by-step explanation:

Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].

So, we can use your values of a, b, and c, and plug them into the equation.

A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].

B is 2.7, so the second term is [tex]2.7x[/tex]

And -8.2 is the C, so the third term is [tex]-8.2[/tex]

So we have [tex]-3.5x^2+2.7x-8.2[/tex]

Hope this helped!

Answer:

77

Step-by-step explanation:

At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.

Answer:

e

Step-by-step explanation:

e

Answer:

The spread of the data in Set B is greater than the spread of the data in Set A.

Step-by-step explanation:

Just took the test :3

Answer:

With calculator;√24.5 = 4.9497

With differentials;With calculator;√24.5 = 4.95

The value of the square root gotten using differentials is an approximate value of the one gotten with a calculator

Step-by-step explanation:

With calculator;√24.5 = 4.9497

Using differentials;

The nearest number to 24.5 whose square root can be taken is 25, so let us consider that x = 25 and δx = dx = - 0.5

Now, let's consider;

y = √x - - - (eq 1)

Differentiating with respect to x, we have;

dy/dx = 1/(2√x) - - - - (eq 2)

Taking the differential of eq 2,we have;

dy = (1/(2√x)) dx

Using the values of x = 25 and dx = 0.5,we have;

dy = (1/(2√25)) × 0.5

dy = 0.05

Now;

√24.5 = y - dy

√24.5 = √x - dy

√24.5 = √25 - 0.05

√24.5 = 5 - 0.05

√24.5 = 4.95

Answer:

a. 45/1024

b. 1/4

c. 15/128

d. 193/512

e. 9/256

Step-by-step explanation:

Here, each position can be either a 0 or a 1.

So, total number of strings possible = 2^10 = 1024

a) For strings that have exactly two 1's,

it means there must also be exactly eight 0's.

Thus, total number of such strings possible

10!/2!8!=45

Thus, probability is

45/1024

b) Here, we have fixed the 1st and the last positions, and eight positions are available.

Each of these 8 positions can take either a 0 or a 1.

Thus, total number of such strings possible

=2^8=256

Thus, probability is

256/1024 = 1/4

c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string.

Also, it means there must also be exactly three 0's

Thus, total number of such strings possible

10!/7!3!=120

Thus, probability

120/1024 = 15/128

d) Following are the possibilities :

There are six 0's, four 1's :

So, number of strings

10!/6!4!=210

There are seven 0's, three 1's :

So, number of strings

10!/7!3!=120

There are eight 0's, two 1's :

So, number of strings

10!/8!2!=45

There are nine 0's, one 1's :

So, number of strings

10!/9!1!=10

There are ten 0's, zero 1's :

So, number of strings

10!/10!0!=1

Thus, total number of string possible

= 210 + 120 + 45 + 10 + 1

= 386

Thus, probability is

386/1024 = 193/512

e) Here, we have fixed the starting position, so 9 positions remain.

In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.

Thus, total number of such strings possible

9!/2!7!=36

Thus, probability is

36/1024 = 9/256

Answer:

[tex]\boxed{x = 9}[/tex]

Step-by-step explanation:

m = -1/3

b = 7

And y = 4 (Given)

Putting all of the givens in [tex]y = mx+b[/tex] to solve for x

=> 4 = (-1/3) x + 7

Subtracting 7 to both sides

=> 4-7 = (-1/3) x

=> -3 = (-1/3) x

Multiplying both sides by -3

=> -3 * -3 = x

=> 9 = x

OR

=> x = 9

Answer:

x = 9

Step-by-step explanation:

m = -1/3

b = 7

Using slope-intercept form:

y = mx + b

m is slope, b is y-intercept.

y = -1/3x + 7

Solve for x:

Plug y as 4

4 = 1/3x + 7

Subtract 7 on both sides.

-3 = -1/3x

Multiply both sides by -3.

9 = x

Answer:

f(x) = (x + 6)² - 29

Step-by-step explanation:

Given

f(x) = x² + 12x + 7

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

x² + 2(6)x + 36 - 36 + 7

= (x + 6)² - 29, thus

f(x) = (x + 6)² - 29

answers are 6, and -29

Answer:

Hey there!

The cross section would be a rectangle. No matter where you cut the figure parallel to the base, the cross section would be a rectangle.

Let me know if this helps :)

Answer: Rectangle

Step-by-step explanation:

In a rectangular prism, every cross-section parallel to a side is a rectangle.

Hope it helps <3

Answer:

The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .

Step-by-step explanation:

We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

So, the area of an equilateral triangle =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

where, s = side of an equilateral triangle

A  =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

Cross multiplying the fractions we get;

[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]

[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]

Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;

[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]

Taking square root both sides we get;

[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

Answer:

[tex]y_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]  ,  [tex]y_2 = \left[\begin{array}{ccc}5\\1\\-6\\-1\end{array}\right][/tex]

Step-by-step explanation:

[tex]x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]    and [tex]x_2 = \left[\begin{array}{ccc}7\\-7\\-6\\1\end{array}\right][/tex]

Using Gram-Schmidt process to produce an orthogonal basis for W

[tex]y_1 = x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]

Now we know X₁ , X₂ and Y₁

Lets solve for Y₂

[tex]y_2 = x_2- \frac{x_2*y_1}{y_1*y_1}y_1[/tex]

see attached for the solution of Y₂

Answer:  A, B, and D

Step-by-step explanation:

Input the coordinates into the inequality to see which makes a true statement:

                             5x - 2y < 8

A) x = -1, y = 1       5(-1) - 2(1) < 8

                              -5  -  2   < 8

                                    -7     < 8       TRUE!

B) x = -3, y = 4       5(-3) - 2(4) < 8

                              -15  -  8   < 8

                                    -23    < 8     TRUE!

C) x = 4, y = 0       5(4) - 2(0) < 8

                              20  -  0   < 8

                                    20     < 8    False

D) x = -2, y = 3       5(-2) - 2(3) < 8

                              -10  -  6   < 8

                                    -16     < 8   TRUE!

Answer:

The infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} \frac{8/k}{\sqrt{k + 7}}[/tex] indeed converges.

Step-by-step explanation:

The limit comparison test for infinite series of positive terms compares the convergence of an infinite sequence (where all terms are greater than zero) to that of a similar-looking and better-known sequence (for example, a power series.)

For example, assume that it is known whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges or not. Compute the following limit to study whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] converges:

[tex]\displaystyle \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}[/tex].

Let [tex]a_k[/tex] denote each term of this infinite Rewrite the infinite sequence in this question:

[tex]\begin{aligned}a_k &= \frac{8/k}{\sqrt{k + 7}}\\ &= \frac{8}{k\cdot \sqrt{k + 7}} = \frac{8}{\sqrt{k^2\, (k + 7)}} = \frac{8}{\sqrt{k^3 + 7\, k^2}} \end{aligned}[/tex].

Compare that to the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] where [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}} = \frac{1}{k^{3/2}} = k^{-3/2}[/tex]. Note that this

Verify that all terms of [tex]a_k[/tex] are indeed greater than zero. Apply the limit comparison test:

[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}\\ &= \lim\limits_{k \to \infty} \frac{\displaystyle \frac{8}{\sqrt{k^3 + 7\, k^2}}}{\displaystyle \frac{1}{{\sqrt{k^3}}}}\\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{k^3}{k^3 + 7\, k^2}}\right) = 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\end{aligned}[/tex].

Note, that both the square root function and fractions are continuous over all real numbers. Therefore, it is possible to move the limit inside these two functions. That is:

[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\\ &= \cdots \\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\\ &= 8\left(\sqrt{\frac{1}{\displaystyle 1 + \lim\limits_{k \to \infty} (7/k)}}\right) \\ &= 8\left(\sqrt{\frac{1}{1 + 0}}\right) \\ &= 8 \end{aligned}[/tex].

Because the limit of this ratio is a finite positive number, it can be concluded that the convergence of [tex]\displaystyle a_k &= \frac{8/k}{\sqrt{k + 7}}[/tex] and [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}}[/tex] are the same. Because the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges, (by the limit comparison test) the infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] should also converge.

I hope this will help uh.....

Answer:

Step-by-step explanation:

Hello!

Regarding the reasons that traffic accidents occur:

28% are caused by distracted drivers using cell phones or texting

11% of the drivers' user their phones at any time

The probability of a driver having an accident is 5.26%

a)

DC = event that a randomly selected driver is using a cell phone.

P(DC)= 0.11

b)

TA = event that a randomly selected driver has a traffic accident.

P(TA)= 0.0526

c) and f)

If both events are related, i.e. dependent, then you would expect that the occurrence of one of these events will affect the probability of the other one. If they are not related, i.e. independent events, then their probabilities will not be affected by the occurrence of one or another:

If both events are independent P(TA|DC)= P(TA)

If they are dependent, then:

P(TA|DC)≠ P(TA)

P(TA|DC)= 0.28

P(TA)= 0.0526

As you can see the probability of the driver having an accident given that he was using the cell phone is different from the probability of the driver having an accident. This means that both events are related.

d) and e)

You have to calculate the probability that "the driver was distracted with the phone given that he had an accident", symbolically P(DC|TA)

P(DC|TA) = [tex]\frac{P(DCnTA)}{P(TA)}[/tex]

[tex]P(TA|DC)= \frac{P(TAnDC}{P(DC)}[/tex] ⇒ P(DC∩TA)= P(TA|DC)*P(DC)= 0.28 *  0.11= 0.0308

P(DC|TA) = [tex]\frac{0.0308}{0.0526}= 0.585= 0.59[/tex]

I hope this helps!

Answer:

  see below

Step-by-step explanation:

The rotated location of D' is (-2, 1). The "arrow" points to the left. The attached figure is the best I could do with your distorted image.

You have to rotate the figure 90 counterclockwise about the origin.

Answer:

[tex]\boxed{\sf \ \ 25 \ \ }[/tex]

Step-by-step explanation:

Hello,

we can see that

[tex]x^2-10x = x^2-2*5x[/tex]

is the beginning of

[tex]x^2-2*5x+5^2=(x-5)^2[/tex]

so we must add 5*5=25 to both sides of the equation to make the left side a perfect square trinomial

hope this helps

Answer:

25.

Step-by-step explanation:

To find the value that will make the left side a perfect-square trinomial, you need to find (b/2)^2. In this case, b = -10.

(-10 / 2)^2

= (-5)^2

= (-5) * (-5)

= 25

Once you add 25 to both sides, the left side becomes x^2 - 10x + 25, which is equal to (x - 5)^2.

Hope this helps!

Answer:

Option A is the correct option

Step-by-step explanation:

Since, we know that angle at center is double that of the circumference.

JL = 2 × 84°

calculate the product

= 168°

Hope this helps..

Best regards!!

Answer:

Option A is the correct answer.

Step-by-step explanation:

By the incribed angle theorem, we have

1/2of angle JKL.

so, JL = 84°×2

Therefore, the answer is 168°.

Hope it helps..

Answer:

6x + y = -18

Step-by-step explanation:

The given equation is,

y - 6 = -6(x + 4)

We have to rewrite this equation in the form of Ax + By = C

Where A, B and C are the integers.

By solving the given equation,

y - 6 = -6x - 24 [Distributive property]

y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]

y = -6x - 18

y + 6x = -6x + 6x - 18

6x + y = -18

Here A = 6, B = 1 and C = -18.

Therefore, 6x + y = -18 will be the equation.

Answer:

answer is

B) 36,72,80

Step-by-step explanation:

because is the right angle it is exactly 90°

Answer:

B

Step-by-step explanation:

Answer:

the 2nd one

Step-by-step explanation:

because the Minimum is 20

the Maximum is 31

the median is 23

20, 21, 22, 23, 25, 27,  31,

21, 22, 23, 25, 27

22, 23, 25,

23

Answer:

The first choice.

Step-by-step explanation:

When you are using y≥, then this means that the positive area needs to be shaded, but as you can see, the negative area is shaded, so the symbol '≤' would best fit this.

Now, that we see that, we can eliminate the 2nd and 4th option.

Now, looking at points (0, 2) and (2, 3), the slope is 1/2 <-- rise over run.

So, the first option will be correct!

Hope this helps:)

Answer:

You have selected the correct one!

Step-by-step explanation: