A store inventory showed the stock of a particular item as 52 after 18 were sold earlier that day. What was the inventory at the beginning of the day?

Answer:

  (x, y) = (0.5, -3)  or  (8, 12)

Step-by-step explanation:

You want x and y such that 8, 2x, 2y is an arithmetic sequence and 2x, 2y, 36 is a geometric sequence.

The difference of successive terms is a constant for an arithmetic sequence.

  2x -8 = 2y -2x

  2x -4 = y . . . . . . . . divide by 2, add x

The ratio of successive terms is a constant for a geometric sequence.

  2y/2x = 36/2y

  y² = 18x . . . . . . . . . simplify and cross multiply

We can substitute the expression for y from the arithmetic sequence into the expression for y² in the geometric sequence:

  (2x -4)² = 18x

  4x² -16x +16 = 18x . . . . . expand

  2x² -17x +8 = 0 . . . . . . . divide by 2, subtract 9x

  (2x -1)(x -8) = 0 . . . . . . . factor

The values of x that make the factors zero are x = 1/2 and x = 8. The corresponding values of y are 2{1/2, 8} -4 = {1, 16} -4 = {-3, 12}.

The values of x and y are (1/2 and -3) or (8 and 12).

__

Additional comment

The two sequences are ...

  8, 1, -6  and  1, -6, 36 — difference of -7, ratio of -6

or

  8, 16, 24  and  16, 24, 36 — difference of 8, ratio of 3/2

The area of the circular figure which is the top of a can drink with a diameter of 3 inches is about 7.065 square inches

A circular figure is one that has no edges or sharp corners, and which is essentially round (in the form of a disc or the path described by rotary motion) in shape.

A circular object occupies the largest area per diagonal compared to other regular shapes, as the circular inscribes other regular shapes within its circumference.

The shape in the figure is a circle

The diameter of the circle, D = 3 in.

The formula for finding the area of a circle, A, for which the diameter is presented as follows;

Area of the circle, A = π·D²/4

The approximation of the value of π to be used are 3.14 or 22/7

The area is obtained by plugging in the values of D and π in the formula for the area of a circle as follows;

The area of the figure is; A = 3.14 × 3²/4 = 7.065

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Answer:

B(-5, 3)

Step-by-step explanation:

(1 + x)/2 = -2

1 + x = -4

x = -5

(7 + y)/2 = 5

7 + y = 10

y = 3

B(-5, 3)

The width of rectangular prism shaped Brandon's flower bed is 9 meters.

As per the known information, the formula to calculate volume of rectangular prism is -

Volume of rectangular prism = length × width × height

Keep the values in formula to find the volume of rectangular prism

405 = 15 × 3 × width of rectangular prism

Performing multiplication on Right Hand Side of the equation

405 = 45 × width of rectangular prism

Rewriting the equation

Width of rectangular prism = 405/45

Performing division

Width of rectangular prism = 9 meters

Thus, the width is 9 meters.

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Answer:

see explanation

Step-by-step explanation:

the total cost is dependent on the number of rides she takes, then

the number of rides is the independent variable and the total cost is the dependent variable.

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(2)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (- 4, 2 ) into the partial equation

2 = - 2(- 4) + c = 8 + c ( subtract 8 from both sides )

- 6 = c

y = - 2x - 6 ← equation of line

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(3)

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 6 ) and (x₂, y₂ ) = (9, - 2 )

m = [tex]\frac{-2-6}{9-(-3)}[/tex] = [tex]\frac{-8}{9+3}[/tex] = [tex]\frac{-8}{12}[/tex] = - [tex]\frac{2}{3}[/tex] , then

y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (9, - 2 )

- 2 = - [tex]\frac{2}{3}[/tex] (9) + c = - 6 + c ( add 6 to both sides )

4 = c

y = - [tex]\frac{2}{3}[/tex] x + 4 ← in slope- intercept form

multiply through by 3 to clear the fraction

3y = - 2x + 12 ( add 2x to both sides )

2x + 3y = 12 ← equation in standard form

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(4)

linear function has the form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 200) and (x₂, y₂ ) = (2, 500) ← 2 ordered pairs from the table

m = [tex]\frac{500-200}{2-0}[/tex] = [tex]\frac{300}{2}[/tex] = 150

the ordered pair (0, 200 ) indicates that c = 200

y = 150x + 200 ← linear equation

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(5)

money left over f(x) is

f(x) = initial amount - expenses

    = 125 - (15 + 40 + 5x)

    = 125 - (55 + 5x)

    = 125 - 55 - 5x

    = 70 - 5x

that is

f(x) = - 5x + 70

The number line in the image below shows the solution to the inequality 3x - 8 > 7.

How to Create a Number Line that Shows the Solution of an Inequality?

Before we can create a number line that represents the solution of an inequality, we have to solve to find the solution first.

Given the inequality 3x - 8 > 7, solve for x:

3x - 8 + 8 > 7 + 8 (addition property of equality)

3x > 15

3x/3 > 15/3 (division property of equality)

x > 5

The solution is x > 5, therefore, the image attached below shows the number line of the solution.

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You can have 43 packs of the 645 markers (645 ÷ 15 = 43)

Step-by-step explanation:

First, you can make 42.33 packs of markers with 645 markers and 15 markers per pack. This is calculated by dividing the total number of markers (645) by the number of markers per pack (15), which gives you 42.33.

Here there is a 10% decrease in the number of streams each week after the song's release. From calculations the number of streams after sixth week is 8,503,056.

Let's look into the data given.

The initial number of streams, X₀ = 16,000,000

The percent decrease is 100- 90 = 10%

So the rate of decrease = 10/100 = 0.10

The period of time, n = 6

The equation to find the final number of streams, X =  X₀ (1-r)ⁿ

                                               = 16,000,000× (1-0.01)⁶

                                               = 8503056.

So the number of streams in the sixth week is 8,503,056

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Answer:

(B) 9,447,840

Step-by-step explanation:

Week         Streams

1                  16,000,000 x 90

2                 14,400,000 x 90

3                 12,960,000 x 90

4                 11,664,000 x 90

5                 10,497,600 x 90

6                 9,447,840 x 90

Therefore, the answer would be 9,447,840

The perimeter should be multiplied by 1/3

The side length of the square, which is 7.3 inches,

The square's surface area

Side x Side is Area = 7.3 x 7.3 = 53.29

The square's new area is multiplied by 1/9,

so area is equal to

1/9 x 53.29 and s is equal to 2.4333.

Using the length of the new square as the new perimeter, the square's new perimeter is equal to 9.733 times its side times.

Now that we have calculated the perimeter ratios, we can see that the square's side length is 7.3.

the perimeter is equal to 7.3 times 4 and equals 29.12; nevertheless,

the ratio of the perimeters of the first and second lengths is equal to

29.12/9.733 and is

therefore 3:1.

so, perimeter multiplied by 1/3

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Answer:

[tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]

Step-by-step explanation:

The following expression can be rewritten as:

[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a}[/tex]

In this case, we have to separate -1 out of a² since if a becomes even, the value of (-a)ª will become positive while (-a)ª becomes negative when a is odd.

We can apply the law of exponent when:

[tex]\displaystyle{\left(a \cdot b \cdot c \right)^m = a^m \cdot b^m \cdot c^m}[/tex]

Therefore:

[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^a\cdot a^{2a}\cdot b^a}\\\\\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^aa^{2a} b^a}[/tex]

This will make when a = even numbers, the expression is positive while negative when a is odd.

And no, the answer is not [tex]-a^{2a} b^a[/tex] since this will make the expression negative only but the problem can be positive when a = even number which is why we have to separate -1 out of -a² so that it meets the condition.

Hence, the answer is [tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]

The average velocity is 94.6km / hour

Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs. The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second (m/s or ms-1).

therefore average velocity = change in displacement / change in time

change in displacement = 485 - 154 = 331 km

change in time = 4:30-1:00 = 3 hours 30minutes = 3½ hrs

average velocity = 331/3.5

= 94.6km/hour

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Answer: a. $12, b. $12, c. $13, d. $12

Step-by-step explanation:

a. 1+1+1+1+1+1 = 6, 2+2+2=6, 6+6=12

b. 1+1+1+1=4, 2+2+2+2=8, 4+8=12

c. 1+1+1+1+1=5, 2+2+2+2=8, 5+8=13

d. 1+1+1+1+1+1+1+1=8, 2+2=4, 8+4=2

The amount of trace element collected by Owen is 59.3 g.

To calculate the amount of trace element collected by Owen, we first need to find the volume of the container. Given the radius of 6.7 cm and the height of 13.3 cm, the volume of the cylinder is given by:

V = π * r^2 * h = π * (6.7)^2 * 13.3 = 615.96 cm^3

Since there are 0.097 grams of the trace element per cubic centimeter of water, the amount of trace element in the container can be calculated as:

m = V * 0.097 g/cm^3 = 615.96 cm^3 * 0.097 g/cm^3 = 59.32 g

Rounding to the nearest tenth, the answer is 59.3 g.

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55 rooms should be set aside for full-paying skiers.

Now, According to the question:

Let C represents the contribution that is lost when a reservation is breached.

H represents the loss of opportunity that is associated with not having the availability of anything.

D rep the no- shows with regard to experience in the past

X represents the overbooked number.

All the values here represent the critical probability for yield management.

Let X rep the reserved seats for passengers with full fare

D rep the full fare tickets

F rep the price of full fare

D rep the price of discounted fare

Now, Solving the problem :

P(d< x) < (F -D)/ p × F

= (299 - 109)/0.8 × 299

=  71,012.5

The Z value for 0.71 probability is 0.5

U + Z* standard deviation = 50 + 0.5 *10

= 55 rooms

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Answer: Based on the formula I was taught, for your first problem it'd be the option that says 813.9 ft and for the second one it'd be your option with 2076.3 square inches.

Answer: D) 813.9 inches

Step-by-step explanation:

Formula for surface area of cylinder is:

A=2πrh+2πr2

r = 6

h = 15.6

A = 2π(6)(15.6) + 2π(6)^2

A = 187.2π + 2π(36)

A = 187.2π + 72π

A = 259.2π

If π is 3.14,

A = 259.2(3.14) = 813.9

Answer:

3

Step-by-step explanation:

The equation for slope is (y2-y1)/(x2-x1)

We have (0, -6) as our x1 and y1 and (2,0) as our y1 and y2. So now it's plug and play!

=(0-(-6))/(2-0)

=(0+6)/(2-0)

=(6)/(2)

Simplifying this we get 3/1 or in simple terms... 3

Liling will end up with four triangles if she starts with two tiny squares of material and cuts them on the diagonal. Knowing the areas of each of the four triangles will help us calculate the size of the larger square quilt block.

We are aware that the area of a square can be calculated by multiplying one side's length by itself (A = s2). Each of the small squares' ensuing triangles has a base and height that are equal to one-half of its side because the small squares were cut on the diagonal. Therefore, each triangle has a surface area of (1/2) x (1/2) x s2 = (1/4) x s2 = (s2)/4.

If the large quilt block is made up of four of these triangles, then the area of the quilt block is 4 x (s^2)/4 = s^2. Since the area of the large quilt block is 36 square inches, we can set up the equation:

s^2 = 36

To find the length of one side of the large quilt block (s), we can take the square root of both sides of the equation:

s = √36

s = 6 inches

So, the length of one side of the large quilt block is 6 inches, and the area of the block is 36 square inches.

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Step-by-step explanation:

6

7 47

42

-------

R 5

47 ÷ 7 = 6.71428571429

Answer:

= 16m² - 9

Step-by-step explanation:

(4m+3)(4m-3)

= 4m*4m + 4m*3 + 3*4m + 3*-3

= 16m² + 12m -12m - 9

= 16m² - 9

A table with two rows and columns of data represent a linear function.

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Is that a question? You don't seem to have anything linked or a question posted?

The length of MN for this problem is given as follows:

MN = 12.

The law of sines states that the sine of each angle is proportional to the side length opposite the angle.

The angle opposite to side MN is given as follows:

O.

Which is congruent to angle M, and the side opposite to angle M is:

NO = 12.

Hence the length of MN is also given as follows:

MN = 12.

(as it is opposite to a congruent angle to the opposite side with length of 12).

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Answer: C)39

Step-by-step explanation:

6x+507+317+3x=122

9x+824=122

9x=122-824

9x=-702

x=-78

6x+507

6(-78)+507

-468+507

=39

The volume of the container is 4,500 cm3.

Calculate the volume of the two cubes that make up the container.

For the cube on the left, the volume can be found by multiplying the length (15 cm) by the width (10 cm) by the height (10 cm).

15 cm × 10 cm × 10 cm = 1,500 cm3

For the cube on the right, the volume can be found by multiplying the length (20 cm) by the width (15 cm) by the height (10 cm).

20 cm × 15 cm × 10 cm = 3,000 cm3

Add the two volumes together to find the total volume of the container.

1,500 cm3 + 3,000 cm3 = 4,500 cm3

Therefore, the volume of the container is 4,500 cm3.

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Marcella started with 56 candles during her initial purchase

The given problem can be solved by arithmetic approach

Given,

After 8 weeks she has 160 candles

And also, she buys 13 more candles every week

To find her initial number of candles purchased,

Let her initial number of purchase of candles be 'x'

According to the question,

Initial number of candles + (8 weeks * 13 candles/week) = 160 candles

Substituting x, we get

x+(13*8)=160

or, x+104=160

or, x=160-104

or, x=56

Thus, we can say that initially Marcella had bought 56 candles.

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12 is the least common denominator between 3/4 and 7/12.

The least common denominator (LCD) of two or more fractions is the smallest number that can be divided by the denominators of each of the fractions without leaving a remainder.

The smallest number among all the common multiples of the denominators is the least common denominator when two or more fractions are provided.

Finding the least common multiple (LCM) of the denominators 4 and 12 will allow you to get the least common denominator of 3/4 and 7/12.

12 is the least frequent multiple of 4 and 12. Therefore, 12 is the least common denominator between 3/4 and 7/12.

Finding the denominators' multiples is another way to locate it. 43 = 12 is the least common multiple and the least common denominator, respectively.

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Panel (longitudinal) data is data that is collected over multiple time points.

It is composed of repeated measurements of the same items, such as age, ethnicity, gender, GPAs, and courses taken over a period of time. This type of data allows us to compare changes in the same variables over a period of time. For example, we can compare the GPA of an athlete student in Year 1 to their GPA in Year 4 and look for changes that may have occurred. We can also observe how the courses taken in Year 1 may have had an impact on the GPA in Year 4. Panel data is useful to analyze changes in a population over time and can be used to make predictions about future trends.

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Reporting on a mission, initiative, or the data obtained from it is known as debriefing. Debriefing can reduce problems associated with the use of deception by a researcher. So option a is correct.

Debriefing is the act of reporting on a mission, project, or the data gleaned from it. After an activity or event, a structured procedure examines the actions performed.

Technically speaking, it refers to a method of active intervention that is specialized and developed into more formal meanings like operational debriefing. It is divided into various categories, including, among others, psychological, military, and experiential debriefing.

The following crucial components are often included in effective debriefings:

1. Active participation that goes beyond merely taking criticism in a passive manner.

2. Developmental aim centred on growth and learning

3. A discussion of particular incidents

4. Information from several sources

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Answer:

10x+5y-30

Step-by-step explanation:

5(2x+y -6)

5x2=10

5x (-6)= -30

=10x+5y-30