the following number of people attended last 10 screenings of a movie. mean median or mode

The value οf the variable y is 9 when k is -3 in the given question.

In mathematics and statistics, a variable is a quantity οr a characteristic that can take οn different values οr attributes. Variables can be classified as either quantitative οr categοrical, depending οn the type οf data they represent.

A quantitative variable is a variable that represents a numerical measurement οr quantity. Examples οf quantitative variables include height, weight, temperature, and incοme.

A categοrical variable is a variable that represents a grοup οr categοry. Examples οf categοrical variables include gender, race, and type οf car.

Given: y=k x

where, x= -3 and k= -3

we can find the value of y by multiplying k with x,

so, y=k x

now, putting values as follows:

we get, y = -3 × -3

               = 9

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Answer:

  a.

Step-by-step explanation:

Dilation does not change the direction (slope) of any lines. The slope of the image line is the same as the original when the line is subject to dilation. The y-intercept point (0, -2) will be multiplied by the dilation factor, so will become 4(0, -2) = (0, -8). The dilated line will have equation ...

  y = -1/4x -8 . . . . . matches choice A

Answer:

(x + 1)^2 + (y - 1)^2 = 74

Step-by-step explanation:

By looking at the graph, we can see the center of the circle is (-1, 1).

Next, we can find the radius. We are given the point (6, -4) is on the circle. The distance from the center to a point on a circle is the radius. We can plug the points (-1, 1) and (6, -4) into the distance formula to get the radius:

r = √([-1-6]^2 + [1-(-4)]^2)

r = √(49 + 25)

r = √74

The equation of a circle is denoted in the form:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center and r is the radius.

We can plug in the values we calculated:

(x + 1)^2 + (y - 1)^2 = 74

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:

-x + 18

Step-by-step explanation:

just add 16 and 2. this is the furthest it can be simplified

Answer:

(n ÷ 4) + 6 = 8

Step-by-step explanation:

Pretty sure I answered this before, but here you go.

Quotient means The answer when you divide' So we are working in the division.

n ÷ 4 is the division part

It says 'and' which can also mean addition. So we add 6. So far our equation is: (n ÷ 4) + 6 (Brackets are needed as we are dividing n by 4 and not dividing n by 4+6)

Lastly it says the answer must be 8 so we add that at the end. So the answer is:

(n ÷ 4) + 6 = 8

Answer:

It will take 1.43 hours for them to clean the car.

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this problem:

Together rate: 1/x

Tanya's rate: 1/2

Pat's rate: 1/5

Together rate = Tanya's rate + Pat's rate

\(\frac{1}{x} = \frac{1}{2} + \frac{1}{5}\)

\(\frac{1}{x} = \frac{5 + 2}{10}\)

\(\frac{1}{x} = \frac{7}{10}\)

\(7x = 10\)

\(x = \frac{10}{7}\)

\(x = 1.43\)

It will take 1.43 hours for them to clean the car.

Step 01:

Data

function C = 3/2 x - 5

m = 3/2 = 1.5

function D = ?

(-3 , -5) x1 = -3 y1 = -5

(0 , -1) x2 = 0 y2 = -1

m =?

Step 02

function D

slope formula

m = 4 / 3 = 1.33

m C > m D

3/2 > 4/3

The solution is:

The function C has the steeper slope.

A. Function C slope of, 3/2, has a steeper slope than Function D, 4/3

The cube root of -2i,

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

We can represent -2i in polar form as,

r(cosθ + i sinθ)

by computing its magnitude and angle.

The magnitude of -2i is 2

Since the absolute value of any imaginary number is equal to its magnitude.

To find the angle θ,

We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case,

The opposite side is -2 and the adjacent side is 0.

Therefore, we have tanθ = -2/0, which is undefined.

However,

We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.

So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).

Now, we need to find the value of θ/3. Since θ is undefined,

we will represent it as π/2 + 2πn,

where n is any integer.

So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.

Therefore, the cube root of -2i is equal to

⇒  ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]

Now put n = 0

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

This is the final form of the cube root of -2i in the required form.

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Answer:

41/25

Step-by-step explanation:

So (-1)¹⁰ equals 1 because any number multiplied by a positive exponent is positive. Next, you do (-22)⁰ which equals 1. Anything to the zeroth power equals one. Now you add 1 and 1 which equals 2. Then you do -(3/5)² which equals -9/25 (You do 3 * 3 which equals 9 and 5 * 5 which equals 25. You then add the negative sign outside the parenthesis to get -9/25). Then you multiply 2 by 25 so both numbers have a common denominator of 25. That equals 50/25 ( 50/25 is 2). You subtract 50/25 by 9/25. That equals 41/25.

Answer:

\(\frac{41}{25}\)

Step-by-step explanation:

\((-1)^{10} + ( -22)^{0} - (\frac{3}{5})\)

\(1 + (-22)^{0} - (\frac{3}{5})^{2}\)

\(1 +1 - (\frac{3}{5} )^{2}\)

\(1 + 1- \frac{9}{25}\)

add the numbers

\(2 -\frac{9}{25}\)

Calculate the difference

\(\frac{41}{25}\) ← Final answer! ~ Hope this helps~

The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

Given:

\($&\overline{A B} \cong \overline{D E} \\\) and

\($&\overline{A C} \cong \overline{D F}\)

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

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The triangles are not similar

Given data ,

Let the first triangle be ΔJKL

Let the second triangle be ΔMNP

Now , the corresponding sides are

JK / JL ≠ NM / MP

where the corresponding sides of similar triangles are not in the same ratio

And , the common angle to both the triangles is ∠J = ∠M

So , ∠J = ∠M and JK / JL ≠ NM / MP

Hence , the triangles are not similar

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Answer: 28.3 %

Step-by-step explanation:

60-43 = 17

17/60 = 0.283

Answer:

\(x = \frac{1}{3} \)

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒(\(\frac{1}{3x}\))

*rewrite to solve for x :

10⁰ = \(\frac{1}{3x}\)

1 = \(\frac{1}{3x}\)

1 · x = \(\frac{1}{3x}\) · x

1x = \(\frac{1}{3}\)

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = \(\frac{1}{3}\)

1. The correct exponential function for each graph is

a.  f(x) = 2ˣ is graph (III)     b. f(x) = 2⁻ˣ is graph (I)   c. f(x)= -2ˣ graph (II)  D. f(x) = -2⁻ˣ is graph (IV)

2. The evaluated exponential functions are;

a. f(1) = 1  b. f(-1) = 0.1  c. f(0) = 0.3

3. The exponential function for the graph  is f(x) = \(\frac{1}{2}^x\)

4. The model for the rate population is N(t) = 320 × \(2^{t}\) . After 8 years, the population will be 81,920.

5. The compounded interest after 2 years: 2628.17. After 3 years 2694.7. After 6 years 2904.57

6. The compounded interest after a) 3 years = 4221.81  b) 6 years = 5092.47  c) 9 years = 6142.69

7. At time t = 0, the mass is 13 kg. After 45 days, the mass is approximately 6.62 kg

1. For the exponential function,  

a. f(x) = 2ˣ has a coordinate (0,1).  f(1) = 2⁰ = 1 It matches (III)

b.  f(x) = 2⁻ˣ When x = -1, f(x) = 2,  x = 0, f(x) = 1, x = 1, f(x) = 0.5; x = 2, f(x) = 0.25. If you plot this coordinates, you will see the graph falls from left to right

c. f(x)= -2ˣ it should pass through  (0, -1),  x = -1, when f(x) = -0, x = 0, f(x) = -1, x = 1, f(x) = -2

d. f(x) = -2⁻ˣ will pass through the point (0, -1). When x = -1, f(x) = -2; x = 0, f(x) = -1; x = 1, f(x) = -0.5. The graph should rise from left to right.

2. If the exponential function is f(x) = 3ˣ⁻¹ then we evaluate

f(1) = 3¹⁻¹ = 3⁰ = 1

f(-1) = 3⁻¹⁻¹ = 3⁻² = 1/3² or 0.1

f(0) = 3⁰⁻¹ = 3⁻¹ = 1/3 or 0.3

3. For the graph whos exponential function should be in the form f(x) = aˣ, we can find the actual function by looking at the coordinated (-3, 8)

a⁻³ = 8

a = \(8^1/-3\)

a = 1/2

f(x) = (1/2)ˣ

4. The mouse population can be modeled as

N(t) = N₀ × (1 + \(r)^{t}\) ⇒ N(t) = 320 × \(2^{t}\)

After 8 years ⇒ N(8) = 320 × 2⁸

N(8) = 320 × 256

N(8) = 81920

5. We use the formula A = P(1 + \(r/n)^{nt}\)

$2500 invested at an annual interest rate of 2.5% compounded daily,

After 2 years (t = 2):                          After 3 years

A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ²⁾         A = A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ³⁾

A = 2628.17                                       A = 2694.7

After 6 years

A = 2500(1 + 0.025/365)⁽³⁶⁵ˣ⁶⁾

A = 2904.57

6. For a  continuous compounded interest, we use the formula;

A = P × \(e^{rt}\)

the principal is $3500, the interest rate is 6.25%, or 0.0625 as a decimal.

a) After 3 years:                 After 6 years:             After 9 years

A = 3500 × \(e^{0.0625 * 3}\)          A = 3500 × \(e^{0.0625 * 6}\)     A = 3500× \(e^{0.0625 * 9}\)

A = 4221.81                       A = 5092.47                A = 6142.69

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The closest option to the cone area is 923.2 m². 

A cone is a shape formed from a series of line segments or lines that connect a common point, called a vertex or vertex, to all points on the base of a circle that do not contain vertices. The distance from the apex of the cone to the base is called the height of the cone.

To solve this problem, we need to find the surface of the cone. Formula for the surface area of cone:

A = \(\pi\)r² + \(\pi\)rℓ

where r is the radius of the base, ℓ is the height of the depression, and π is a constant of approximately 3.14159.

First, we find the radius of the base. Since the bottom line of the cone is listed as 18 feet and we know the radius is 14 feet, we can use the Pythagorean theorem to find the height of the cone.

h² = ℓ² - r²

h² = 19.3² - 14²

h ≈ 11.48 feet

Now we can compute the surface.

A = \(\pi\)(14)² + \(\pi\)(14)(19.3)

A ≈ 923.2 square feet

So the closest option to the cone area is 923.2 m². 

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The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820  

a + s = 900

The number of adults ticket and student tickets is 380 and 520.

We have,

Adults ticket cost = $4

Student ticket cost = $2.5

Now,

Total amount earned = $2,820

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820   ______(1)

And,

The number of tickets sold = 900.

We can write as equation as:

a + s = 900 ______(2)

Now,

We have two equations.

4a + 2.5s = 2820

a + s = 900

Solving for s.

s = 900 - a

Substituting in (1)

4a + 2.5(900 - a) = 2820

Simplifying and solving for a.

4a + 2250 - 2.5a = 2820

1.5a = 570

a = 380

Now,

a + s = 900

380 + s = 900

s = 520

Therefore,

The number of adults ticket and student tickets is 380 and 520.

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Answer:

In costs $17.19

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

A polygon equals 360

360/15 = 24

20-8=12

6x7=42

i shall say this is correct

Answer:

43.2

Step-by-step explanation:

The right answers are:

Hope it helps.

please see the attached picture for full solution

Good luck on your assignment

Answer:

24

Step-by-step explanation:

8x3=24

12x2=24

Answer:

3600

Step-by-step explanation:

lcm stands for "lowest common multiple"

the lcm is 3600 when done with the prime factorization process

Answer:

3600

Step-by-step explanation:

Express each number as a product of its prime factors, that is

36 = 2² × 3²

75 = 3 × 5²

80 = \(2^{4}\) + 5

Now multiply each factor the greatest number of times it occurs in each of the 3 numbers.

2 → 4 times (that is \(2^{4}\) )

3 → twice (3² )

5 → twice (5² )

Thus

LCM = \(2^{4}\) × 3² × 5² = 16 × 9 × 25 = 3600

Answer:

lol the answer is the second one

Answer:

100 miles

Step-by-step explanation:

Let m be the number of miles.

\(100 + .30m = 50 + .80m\)

\(100 = 50 + .50m\)

\(.50m = 50\)

\(m = 100\)

Answer:

100

Step-by-step explanation:

You can put into a graph such as desmos and see where the lines intersect. the x value of the intersection is the answer you want.

Answer:

135.06 feet

Step-by-step explanation:

Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.

opposite side = x

adjacent side = 150 feet

angle = 42°

tan(42°) = x/150 feet

150 feet * tan(42°) = x

x = 135.06 feet