A company sells widgets. The amount of profit, y, made by the company, is related to
the selling price of each widget, x, by the given equation. Using this equation, find out
what price the widgets should be sold for, to the nearest cent, for the company to
make the maximum profit.
y=
-3x² +239x-2268

There are 30240  different id cards can be made if there are five digits on a card and no digit can be used more than once.

a) If repetition is allowed, then there are 10 ways to choose each of 5 digits. Hence, by the multiplication rule, we obtain that the total number of possible different ID cards is:

10⋅10⋅10⋅10⋅10 = 10⁵= 100000.

b) If repeats are not allowed, there are 10 ways to choose the first number, 9 ways to choose the second number (because we chose 1 digit as the first number), and 9 ways to choose the third number. There are 8 ways, 7 ways, and 7 ways to choose the 4th number. 6 ways to select the digit to select and the 5th digit.

So according to the multiplication rule the answer is:

10 × 9× 8×7×6 = 30240.

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For given data , the equation of the regression line is:

y = 2.03 ln(x) - 0.205

Consider given data.

x  1 |  2   |   3   |  4    |   5        

y  1 | 21  | 121 | 621 | 3121

We need to find the equation of the regression line, if the given data linearized using logarithms.

Now we find the logarithms of y-values.

log(1) = 0

log(21) = 1.322

log(121) = 2.0828

log(621) = 2.7931

log(3121) = 3.4943

So, we get coordinates of the points: (1, 0), (2, 1.322), (3, 2.0828), (4, 2.7931), (5, 3.4943)

from the graph of given data, the equation of the regression line is:

y = 2.03 ln(x) - 0.205

where slope of the regression line is 2.03

and the y-intercept is c = -0.205

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According to the claim, cross product properties rather than determinants are used to define the vector i + j + k. By usig the supplied vectors a * (b *c) is < 27, -27, 18> and (a * b) * c is < 27, -27, 0>

A vector is a quantity or phenomenon with independent properties both to and direction. The scientific or geometrical depiction of a quantity is another meaning of the word. Among the components of vectors seen in nature are force, weight, electric interfering, and movement.

1). (j-k) * (k-i)

= (j*k) - (j*i) - (k*k) + (k*i)

= I - (-k) - (0) + (j) (j)

= i + j + k

(2). (a). (b*c)

[tex]\left|\begin{array}{ccc}j & j & k \\-3 & 3 & 0 \\0 & 0 & -3\end{array}\right|[/tex]  

= i(-9-0)-j(9-0)+k(0-0)

= -9i - 9j + 0k

= < -9, -9, 0>

Then, a*(b*c)

[tex]\left|\begin{array}{ccc}i & j & k \\1 & 3 & 3 \\-9 & -9 & 0\end{array}\right|[/tex]

i (0+27) - j (0+27) + k(-9 + 27)

= 27i -27j + 18k

= < 27, -27, 18>

(b). (a*b)

[tex]\left|\begin{array}{rrr}i & j & k \\1 & 3 & 3 \\-3 & 3 & 0\end{array}\right|[/tex]

= i(0-9) - j(0+9) + k (3+9)

= -9i - 9j + 12k

= < -9, -9, 12>

(a*b)*c

[tex]\left|\begin{array}{ccc}4 & j & k \\-9 & -9 & 12 \\0 & 0 & -3\end{array}\right|[/tex]

= i(27-0) - j(27-0) + k (0-0)

= 27i - 27j + 0k

= < 27, -27, 0>

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The complete question is-

True solution is a homogeneous mixture of two or more substances in which the particles of solute are dispersed uniformly throughout the solvent. An example of a true solution is a mixture of salt and water.

True solution is a type of homogeneous mixture in which the particles of solute ( the substance that is dissolved ) are dispersed uniformly throughout the solvent (the substance that is doing the dissolving). The particles of solute are too small to be seen with the eye and the mixture appears to be one single substance. An example of a true solution is a mixture of salt and water. The salt molecules are dispersed evenly throughout the water, producing a salty taste throughout the entire solution.

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By solving the given initial value the value of x(t) is [tex]\frac{F_0}{2 \omega^2}[/tex] (sinωt - ωt cosωt)

As per the data given in the question the given differential equation will be:

[tex]\frac{d^{2} x}{dt^{2} }[/tex] + [tex]\omega^2 x=f_0[/tex] sin ωt,

x(0) = 0, x'(0) = 0

Now we have to determine the value of x(t).

Consider the differential equation:

x'' + [tex]\omega^2 x=f_0[/tex] sin ωt, x(0) = 0, x'(0) = 0.

In order to translate a given derivative function with a real variable t into a complex function with a variable s, one uses the Laplace transformation.

Laplace transformation is important in the design of control systems. It is necessary to perform Laplace transforms on several functions in order to analyze the control system.

Apply Laplace transformation on both sides,

[tex]&\left(s^2 L\{x(t)\}\right.\left.-s y(0)-y^{\prime}(0)\right)+\omega^2 \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{s^2+\omega^2} \\[/tex]

[tex]&\left(s^2+\omega^2\right) \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{s^2+\omega^2} \\[/tex]

[tex]& \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{\left(s^2+\omega^2\right)^2} \\[/tex]

[tex]& x(t)=F_0 \omega \mathcal{L}^{-1}\left\{\frac{1}{\left(s^2+\omega^2\right)^2}\right\} \\[/tex]

[tex]& \Rightarrow x(t)=\frac{F_0 \omega}{2 \omega^3}[/tex] (sin ωt -ωt cos ωt)

[tex]& \Rightarrow x(t)\left.=\frac{F_0}{2 \omega^2}[/tex] (sin ωt -ωt cos ωt)

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Solve the given initial-value problem. [tex]\frac{d^{2} x}{dt^{2} }[/tex] + [tex]\omega^2 x=f_0[/tex] sin ωt, x(0) = 0, x'(0) = 0 and x(t)=?

Answer:

x=6

Step-by-step explanation:

[tex] \cos(60) = \frac{x}{12} \\ x = 12 \cos(60) = 6[/tex]

The ratio of 2 or more integers is known as fraction. The answer to the given expression is 3 13/16

Fractions are written as a ratio of two integers. Fractions are written in the form a/b

Given the expression below:

15/4 + 7/12 x 3/28

Required

Simplified form of the expression

On solving, we will have;

15/4 + (7/12 x 3/28)

15/4 + (1/4 x 1/4)

15/4 + 1/16

Find the LCM of the resulting sum

15/4 + 1/16= [4(15)+1]/16

15/4 + 1/16 = 61/16

15/4 + 1/16 = 3 13/16

Hence the answer to the given expression is 3 13/16

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Answer:

Step-by-step explanation:

It is unclear what is being asked in this question. The information provided does not make logical sense and it's hard to understand what is being asked. Could you please provide more information or rephrase the question?

The equation of the transaction of friend 1 is; y = 0.12x + 30

The equation of the transaction of friend 2 is; y = 0.15x + 15

The general form if the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Friend 1;

Cost of the new phone including monthly fee = $30

Cost per 100 minutes = $12

Thus, cost per minute = 12/100 = $0.12 per minute

The cost per minute is simply the slope here while $30 is the y-intercept and as such the equation is;

y = 0.12x + 30

Friend 2;

Cost of the new phone including monthly fee = $15

Cost per 100 minutes = $15

Thus, cost per minute = 15/100 = $0.15 per minute

The cost per minute is simply the slope here while $15 is the y-intercept and as such the equation is;

y = 0.15x + 15

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The expression that represents the length, in inches, of the third side of the triangle is 5 + 2 = 7 a 3 inches.

A triangle is a three-sided geometric shape that has three angles and three sides. The three sides all join together at the vertices to form a closed shape. Triangles are one of the most basic shapes and can be found in many objects and structures in nature, such as mountains, trees, and the human body. Triangles can also be seen in architecture, artwork, and mathematics.

This can be calculated by subtracting the sum of the two given side lengths (8 a 6 inches) from the given perimeter (9 a 12 inches). The difference of 1 a 6 inches is equal to the third side length of the triangle (7 a 3 inches).

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The required linear model is y = 3968.75x + 63,500 that represents the amount of fuel on the plane (as y), in gallons, as a function of the flight time(as x), in hours.

A linear function is defined as an equation in which the highest exponent of the variable is always one.

The graph is given in the question, as shown

Let y be represents the amount of fuel on the plane, in gallons,

And x represents the function of the flight time, in hours.

As per the given graph, we take two points (0, 63,500) and (16, 0)

y - 63,500 = [(0-63,500)/(16-0)](x-0)

y - 63,500 = (63,500/16)x

y - 63,500 = 3968.75x

y = 3968.75x + 63,500

Thus, the required linear model is y = 3968.75x + 63,500.

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Gina had an amount of 40.89 before her purchase

Gina made the following purchases

Notebook= 6.59

Backpack= 24.95

Pen= 3.98

She also paid 2.56 in sales tax and she had 2.81 left

Her initial amount before purchase is

6.59 + 24.95+3.98+2.56+ 2.81

= 40.89

Hence Gina had 40.89 before here purchase

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The total amount of time Martina spent doing these two assignments will be 13/20 Hr.

Total time taken by Martina to complete her chemistry assignment = (2/5) Hr.

Total time taken by the Martina to complete her maths assignment = (1/4) Hr.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

So, for determining the total amount of time martina spent doing these two assignment, we need to add the value of time taken by her in completing both the assignment.

So, the value of total amount of time taken by Martina for completing both the assignment will be = (2/5)+)1/4) Hr.

=(8+5)(20)=13/20 Hr.

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Answer:

No solution

Step-by-step explanation:

When the slopes are the same: 2, the lines will be parallel

Brand A's mean absolute deviation is 2.02, whereas brand B's is 1.905, showing that the two brands' mean absolute deviations ARE comparable.

A group of at least two numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for one given collection of numbers, including as the arithmetic mean approach, which utilizes the sum of the series' values, and the root - mean - square method, which takes the average of a group of products.

For every dot plot, determine the mean absolute deviation.

Deviation from the mean for Brand A:

The points are, 1,1,2,2,2,3,4,4,5,5,5,5,6,6,7,7,8,8,8,9

Mean = (1 + 1 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9)/20 = 98/20

Mean = 4.9

Mean Absolute Deviation = [(1 - 4.9) + (1 - 4.9) + (2 - 4.9) + (2 - 4.9) + (2 - 4.9) + (3 - 4.9) + (4 - 4.9) + (4 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (5 - 4.9) + (6 - 4.9) + (6 - 4.9) + (7 - 4.9) + (7 - 4.9) + (8 - 4.9) + (8 - 4.9) + (8 - 4.9) + (9 - 4.9)] / 20

= [(3.9) + (3.9) + (2.9) + (2.9) + (2.9) + (1.9) + (0.9) + (0.9) + (0.1) + (0.1) + (0.1) + (0.1) + (1.1) + (1.1) + (2.1) + (2.1) + (3.1) + (3.1) + (3.1) + (4.1)] / 20

= 40.4/20

Brand A's mean absolute deviation was 2.02, while Brand B's was:

The points are, 1,3,3,4,4,4,4,4,5,5,5,6,6,6,6,8,8,9,10,10

Mean = (1 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 8 + 8 + 9 + 10 + 10)/20

Mean = 111/20 = 5.55

Mean Absolute Deviation = [(1 - 5.55) + (3 - 5.55) + (3 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (4 - 5.55) + (5 - 5.55) + (5 - 5.55) + (5 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (6 - 5.55) + (8 - 5.55) + (8 - 5.55) + (9 - 5.55) + (10 - 5.55) + (10 - 5.55)] / 20

Deviation from the mean is 38.1/20.

Brand B's mean absolute deviation is 1.905.

As a result, the following judgment is made regarding the outcomes illustrated by the determine the exact location:

For brand A, the average absolute deviation is 2.02

For brand A, the average square deviation is 1.905.

For the two brands, the Average Absolute Deviation IS comparable.

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The complete question is-

Martin and Clara decide to keep track of the number of different colors in two brands of tennis shoes, brand A and brand B. Their results are represented by the dot plots. The mean absolute deviation for brand A is____ The mean absolute deviation for brand B is__ The mean absolute deviations for the two brands ___ similar.

Answer:

C) 8 : 1

Step-by-step explanation:

To find our ratio, we will multiply both sides by 20 to get rid of fractions, this gives us:

[tex]\frac{2}{5} * 20 : \frac{1}{20} * 20[/tex]

8 : 1

So, the ratio is C) 8 : 1.

The reason the answer is C), and not B) is because C) is the most simplified form.

Hope this helped!

Answer:

The answer is C) 1:8

Step-by-step explanation:

2/5 is equal to 8/20

so if you compare 8/20 to 1/20 the answer is c

The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 4∛(x¹⁰) + 5x³∛(8x)

Simplify the expression, then we have

⇒ 4∛(x¹⁰) + 5x³∛(8x)

⇒ 4∛[(x³)³ · x] + 5x³∛(2³ · x)

⇒ 4x³ ∛x + 10x³ ∛x

⇒ 14x³ ∛x

The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.

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The predicted sales for the week 6 is 746.

By applying a linear equation to the observed data, linear regression aims to demonstrate the link between two variables. According to the theory, one variable should be an independent variable and the other should be a dependent variable. For instance, the relationship between a person's weight and height is linear. As a result, this demonstrates a linear relationship between an individual's height and weight. The weight of the individual increases along with their height.

We can determine the intercept and slope values for the regression model in the instance of linear regression using an Excel method.

The equation is created from the aforementioned facts.

Forecast = A + B(x)

Where A is the intercept of the data, B is the slope, and x is the period.

Intercept = INTERCEPT ( RangeY, RangeX )

Slope = SLOPE (RangeY, Range X)

Now the data corresponds to an intercept value of 698 and a slope of 8.

Therefore, for period 6, x = 6

The equation = 698 + (8 * 6) = 746

The intermediate calculations are in the table below:

PERIOD   UNITS   FORECAST

______________________

1             700              706

2            724               714

3            720               722

4            728               730

5                                 738

6                                746

Therefore, the predicted sales for week 6 is 746.

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Answer:

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

Let the number of passed years be x.

Use the equation for half-life:

Substitute given values and solve for x:

Answer:

758.295 meters

Step-by-step explanation:

If for any reason my answer is wrong, feel free to correct me.

As per your question,

The airplanes accelerate uniformly at 2.7 meters per second^2

And they must reach a ground velocity of 64 m/s.

Therefore

S(Displacement) = u(initial velocity) x time + 1/2(acceleration x time^2)

Initial Velocity = 0 m/s(airplane is at rest)
Acceleration is 2.7m/s^2
Time = ?

Acceleration = Final Velocity - Initial Velocity / Time(t)

2.7 m/s^2 = 64 m/s - 0 m/s / t

2.7(t) = 64
t = 64/2.7

t = 23.703703...   rounded to 23.7

S = 0(23.7) + 1/2[2.7 x (23.7)^2]

S = 1/2(2.7 x 561.7)               561.69 is the original answer rounded to 561.7

S = 758.295 meters

Final Answer - An airport would require a runway of minimum length of 758.295 meters to accommodate aircraft of the respective specifications.

2.7 m/s^2 = 64 m/s 0 m/s/t

2.7(t) = 64

t = 64 ÷ 2,7

t = 23.703

or => 23,7

S = 0×(23.7) + 1/2[2,7 × (23,7)²]

S= 1/2(2.7 × 561.7)

S = 758.295 meters

the speed of the plane is 758.295 meters

The trainee's z-score is -1.5.

An illustration of a standardized score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Given:

Mean= 77

standard Deviation = 2

x= 74

Using z score formula

Z score = (x - μ)/ σ

Z score = (74 - 77)/ 2

Z score = -1.5

Now, the P-value from Z-Table:

P(x<74) = 0.066807

P(x>74) = 1 - P(x<74)

            = 0.93319

P(74<x<77) = 0.5 - P(x<74)

                  = 0.43319

Hence, the z- score is -1.5.

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Answer: The relationship between salary per week (s), number of weeks worked (w), and total income (t) is t = s * w.

Where t is the total income, s is the salary per week, and w is the number of weeks worked.

In Robert's case, s = $300, the equation would be t = $300 * w, where w is the number of weeks worked.

This equation shows that the total income (t) is directly proportional to the number of weeks worked (w) and the salary per week (s)

So, if Robert earns $300 every week, this equation would be t = $300 * w

Step-by-step explanation:

The cost will be $627,000 for about n = 59 units made.

We know that the polynomial function:

C(n) = 3n^3 - 4n^2 + 250b + 75,000

Gives the cost of producing n products.

We want to find the value of n, such that the cost is $627,000

So we need to solve the cubic equation:

3n^3 - 4n^2 + 250n + 75,000 = 627,000

Now we can subtract 627,000 in both sides to get:

3n^3 - 4n^2 + 250n - 619,500 = 0

And now we can graph that equation and find the intercepts:

There you can see that the intercept is at n = 59, so that is the answer.

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Paying from his UK account will be More profitable.

A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

Given, A Kenyan businessman US$100 to a company in the United States of America. The Kenyan can either pay through his account in Kenya or through his account in the United Kingdom.

if he pays in US Dollars:

1 US Dollar = 76.84 Kenya Shillings

100 US Dollars = 7,684 Kenya Shillings

If he pays in UK pounds:

1 Sterling Pound = 1.53 US dollars

And, 1 Sterling pound = 115.70 Kenya shillings

1 US Dollar = 1/1.53 US Pound

Thus,  1 US Dollar = 1/1.53 * 115.70 Kenya shillings

 1 US Dollar = 75.62  Kenya shillings

100 US Dollar = 7,562.09  Kenya shillings  

Therefore, Paying from his UK account will be More profitable.

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Answer: Hello sorry i read the question wrong at first. but the answer id relation 1, 2 and 3.

Step-by-step explanation: all inputs (x) have to have different outputs (y) :)

The negative z-score = -0.84 and the Positive Z-score = 0.84.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The shaded region in the question is symmetric about z = 0 and forms the middle part of the distribution.

Standard deviation is a measure of the spread or dispersion of a set of data. It tells us how much the individual observations in a dataset vary from the mean of the dataset.

The formula for the standard deviation of a dataset is:

σ = √( Σ (x_i - μ)^2 / n)

The middle shaded region is known as the central region, it represents the middle part of the distribution, and it covers the area between two Z-scores, one negative and one positive. The area of the central region is typically given as a percentage.

For example, if the shaded region represents 68% of the total area under the standard normal distribution curve, then the two Z-scores that form the boundaries of the shaded region are the Z-scores that correspond to the 16th and 84th percentiles of the standard normal distribution. These Z-scores are -0.84 and 0.84 respectively.

So, the negative z-score = -0.84 and the Positive Z-score = 0.84.

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The completed table specifying the values obtained from the proportional relationship between the time in minutes and the number of cages cleaned is presented as follows;

Minutes; [tex]{}[/tex]             15         30       60          90

Cages cleaned;  [tex]{}[/tex]2           4          8           12  

Please find attached the graph of the above table created with MS Excel.

A proportional relationship is one in which the values of the output variable is a constant multiple of the input variable.

The time it takes the owner of Paradise Pets to clean the 2 hamster cages = 15 minutes

The table of values obtained from a similar question is presented as follows;

Minutes; [tex]{}[/tex]               15     30            90

Cages cleaned; [tex]{}[/tex]   2                8            

The relationship between the number of cages cleaned and the time it takes, taken as a proportional relationship, indicates that we get;

Cages cleaned = k × Minutes

Where;

k = The constant of proportionality

k = Cages cleaned ÷ Minutes

The number of cages cleaned in 15 minutes = 2 cages, therefore;

k = 2 ÷ 15 = 2/15

The number of cages cleaned in 30 minutes is therefore;

Cages cleaned = (2/15) × 30 = 4

The cages cleaned in 30 minutes = 4 cages

The time it takes to clean 8 cages is found as follows;

Minutes = Cages cleaned ÷ k

Minutes to clean 8 cages = 8 ÷ (2/15) = 60

The time it takes to clean 8 cages = 60 minutes

The number of cages cleaned in 90 minutes = (2/15) × 90 = 12

The number of cages cleaned in 90 minutes = 12 cages

The completed table is therefore;

Minutes; [tex]{}[/tex]             15           30        60      90

Cages cleaned; [tex]{}[/tex]  2           4           8        12  

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Pie charts, bar charts, area charts, or bubble charts are the 3 types of graphs we use to compare data

The pie chart is used for relative comparison, which is strongly discouraged by a lot of data visualizers because it takes up too much space but the information value provided is very little unless more visual aids are provided which then is meaningless.

Bar charts are used for precise comparison, Comparing parts of a bigger set of data, highlighting different categories, or showing change over time.

Having a long categories label which offers more space, and If you want to illustrate both positive and negative values in the dataset.

If you want to compare volumes, use an area chart or a bubble chart.

The area chart shows part-to-whole relations and portrays the volume of your data and not just the relation to time.

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I would recommend asking many consumers a few brief questions in a survey. This method would help Bolt quickly and easily obtain a broad view of its consumers’ purchase original cost motivations, which could then be analyzed to develop more targeted strategies.

Surveys are a great way to quickly obtain a broad view of a target audience’s motivations for purchase. By asking many consumers a few brief questions, Bolt can gain insight into what motivates them to purchase their products, or why they may choose not to purchase them. This data can then be analyzed to develop more targeted strategies to increase sales. Surveys also provide an efficient way to sample a large number of people, allowing Bolt to get a representative statistical sample of its consumers’ motivations. This data can also be used to inform future marketing campaigns, allowing Bolt to better target their customers and maximize sales.

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