What is the discriminant of 9x2 + 2 = 10x? –356 –172 28 72

The face of a cube is in the shape of square :

The area of one face of cube is 6 in²

i.e. Area of square = 6 in²

Since the general expression for the area of square is Side x Side

The general expression for the total surface area of cube is : 6 side²

Substitute the value of side :

Total surface area of cube is 36 in²

For a 5.0 µC point charge moved within an electric field, the electric potential difference is mathematically given as

du=2*10^6

Generally, the equation for the change in potential energy is mathematically given as

dV=qdu

Therefore

10=5*10^{-6}*du

du=2*10^6

In conclusion, the electric potential difference

du=2*10^6

Read more about Electric

https://brainly.com/question/9383604

The number of observations in a complete data set with 10 elements and 5 variables is a. data.

In the context of data analysis, a complete data set refers to a collection of data that includes all the required observations or cases. In this scenario, the data set consists of 10 elements, which represent the individual observations or data points. Each element is associated with 5 variables, which are the characteristics or attributes being measured or observed.

Therefore, the number of observations in this data set is determined by the number of elements, which is 10. The term "observations" refers to the individual data points or cases in the data set. The other options, such as "variables" and "elements," do not accurately represent the count of observations in this context.

Hence, the correct answer is a. data, indicating that the number of observations in the complete data set is determined by the number of elements, which in this case is 10

To know more about data sets, visit:
brainly.com/question/29011762

#SPJ11

Answer:

47

Step-by-step explanation:

Answer:

x = 63

Step-by-step explanation:

180 = 47 + 70 + x

180 = 117 + x

180 - 117 = x

63 = x

A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

To know more about Demand Matrix here

https://brainly.com/question/13012912

#SPJ4

Answer:

Greatest number of pieces = 5

Pieces are 3 cm, 4 cm, 5 cm, 6 cm and 7 cm

Step-by-step explanation:

To find - You have 25 cm piece of ribbon. How many cuts do you need to make to obtain the greatest number of pieces, where each piece is a different length and the length of each piece is a whole number, in centimeters.

Proof -

If we cut the pieces in 1 part, then the ribbon cut into

1 + 24 , 2 + 23 , 3 + 22, 4 + 21, 5 + 20, 6 + 19, 7 + 18, 8 + 17, 9 + 16, 10 + 15, 11 + 14, 12 + 13

If we cut the pieces in 2 part, then the ribbon cut into

1 + 2 + 22, 1 + 3 + 21, and so on

The same process is going on

After that, we get

The greatest  number of pieces will be 5 and the cut we make on the ribbon is 3 + 4 + 5 + 6 + 7

∴ we get

Greatest number of pieces = 5

Pieces are 3 cm, 4 cm, 5 cm, 6 cm and 7 cm

Answer:

Hey bud the answer is: Reflect over the y-axis, reflect over the x‒axis, rotate 180°

Got the same question on the test. Sorry about the inconvienience of the other person.

Step-by-step explanation:

Reflect over the y-axis, reflect over the x-axis, and rotate 180° will be the same. Then the correct option is B.

It is the image of the point which is located in the opposite direction of a given point.

The trapezoidal ABCD is shown.

The trapezoidal ABCD rotated 180 degrees about the origin then it is reflected about the x-axis and y-axis. Then the image will remain the same.

More about the reflection link is given below.

https://brainly.com/question/15487308

#SPJ2

The limit as a definite integral on the given interval: \(\[ \lim_{{n \to \infty}} \sum_{{i=1}}^{n} \frac{1}{{1+dx}} \]\)

over the interval [1, 3] is 1.020.

To express the given limit as a definite integral, we can rewrite the summation as a Riemann sum and then take the limit as n approaches infinity.

The interval [1, 3] is divided into n subintervals of equal width

Δx = (3 - 1) / n = 2 / n.

The Riemann sum for the given expression is:

\(\[ \lim_{{n \to \infty}} \sum_{{i=1}}^{n} \frac{1}{{1+dx}} = \lim_{{n \to \infty}} \sum_{{i=1}}^{n} \frac{1}{{1+\frac{2}{n}}} \cdot \frac{2}{n} \]\)

Simplifying the expression inside the summation:

\(\[ = \lim_{{n \to \infty}} \sum_{{i=1}}^{n} \frac{2}{n+2} \cdot \frac{2}{n} \]\)

We can rewrite this sum as a definite integral:

\(\[ = \int_{{1}}^{{3}} \frac{2}{x+2} \, dx \]\)

So, the given limit can be expressed as the definite integral:

\(\[ \lim_{{n \to \infty}} \sum_{{i=1}}^{n} \frac{1}{{1+dx}} = \int_{{1}}^{{3}} \frac{2}{x+2} \, dx \]\)

Evaluating this definite integral will give us the exact value of the limit.

To evaluate the limit, we can calculate the definite integral:

\(\[ \int_{1}^{3} \frac{2}{x+2} \, dx \]\)

To do this, we can use the logarithm property of integration.

\(\[ \int \frac{2}{x+2} \, dx = 2 \ln|x+2| + C \]\)

Now, we can evaluate the definite integral:

\(\[ \int_{1}^{3} \frac{2}{x+2} \, dx = \left[2 \ln|x+2|\right]_{1}^{3} \]\)

Substituting the upper and lower limits into the expression:

\(\[ \left[2 \ln|3+2|\right] - \left[2 \ln|1+2|\right] \]\)

Simplifying:

\(\[ 2 \ln(5) - 2 \ln(3) \]\)

Finally, we can evaluate this expression:

\(\[ \approx 2 \cdot 1.609 - 2 \cdot 1.099 \approx 3.218 - 2.198 \approx 1.020 \]\)

Therefore, the value of the limit is approximately 1.020.

The complete question is:

"Express the limit as a definite integral on the given interval:

\(\[ \lim_{{n \to \infty}} \sum_{{i=1}}^{n} \frac{1}{{1+dx}} \]\)

over the interval [1, 3]."

Learn more about definite integral:

https://brainly.com/question/27746495

#SPJ11

All homerooms collected at least 60 cans, and some collected over 100, a typical number of cans collected is likely to be in the range of 75 to 98 cans, with a median value of 86 to 87 cans.

To determine a typical number of cans a homeroom collected, we can use the median number of cans collected, which is a measure of the central tendency that is not influenced by extreme values. The median number of cans collected was given as 86.5, so we can say that a typical number of cans collected by a homeroom is around 86 to 87 cans.

The interquartile range (IQR) is a measure of variability that represents the range of the middle 50% of the data. It was given as 23 cans, which means that the middle 50% of homerooms collected between 86.5 - 11.5 = 75 cans and 86.5 + 11.5 = 98 cans.

Given that every homeroom gathered at least 60 cans and some did so in excess of 100, the average amount of cans collected is probably between 75 and 98, with 86 to 87 cans serving as the median.

To learn more about typical number please click on below link.

https://brainly.com/question/4292168

#SPJ4

Answer:

Step-by-step explanation:

86.5

Step-by-step explanation:

Your monthly payments with taxes and insurance included would be $2,903.71. This is calculated by taking the loan amount of $450,000 and multiplying it by the simple interest rate of 6.00%. The result is $27,000, which is then divided by the length of the loan, 30 years. This gives you

the principal and interest portion of your monthly payment, which is $2,033.33. To that, you add your yearly taxes of $2,000 and insurance of $1,500, divided by 12 months, to get an additional $416.67 and $125, respectively. Adding these two numbers together gives you your total monthly payment of $2,903.71.

Answer:

X = 18

Step-by-step explanation:

x + 2x + 4x + 5x + 8x =360

20x = 360

20x/20= 360/20

x=18

The value of x in the pentagon angles is 3.6

Pentagon are polygons with five sides.

The exterior sides of the pentagon are given as follows:

Exterior angles formula for polygon is as follows:

where

n = number of sides

Therefore,

x + 2x + 4x + 5x + 8x = 360 / 5

x + 2x + 4x + 5x + 8x = 72

20x = 72

x = 72 / 20

x = 3.6

learn more on polygon here: https://brainly.com/question/22387429?referrer=searchResults

In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

Learn more about constraints here: brainly.com/question/29758137

#SPJ11

To find the vertical asymptotes of a rational function, we need to set the denominator equal to zero and solve for x.

To find the vertical asymptotes of a rational function, you need to determine the values of x that make the denominator of the function equal to zero.

Let's check the limit of our example function as x approaches each of the vertical asymptotes:

As x approaches 1 from the left side: f(x) approaches negative infinity

As x approaches 1 from the right side: f(x) approaches positive infinity

Therefore, x = 1 is a valid vertical asymptote.

As x approaches 3 from the left side: f(x) approaches positive infinity

As x approaches 3 from the right side: f(x) approaches negative infinity

Therefore, x = 3 is also a valid vertical asymptote.

The values of x that make the denominator zero are the vertical asymptotes of the function.

To know more about function here

https://brainly.com/question/28193995

#SPJ4

There are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

To find the number of unique 4-digit integers (excluding leading zeros) where the sum of the digits is 6, we can use a combinatorial approach.

Let's consider the four digits as four distinct positions: A, B, C, and D. The sum of the four digits is 6, so we need to distribute these six units among these four positions.

We can solve this problem using stars and bars. Imagine we have six stars (representing the six units) and three bars (representing the three dividers between the positions). The bars help us separate the units into four distinct positions.

For example, if we have the configuration "* | * * | * * | *," it represents the digits 1, 2, 2, and 1. The sum of these digits is 6.

The number of ways to arrange the six stars and three bars is given by the binomial coefficient (6 + 3 choose 3). Using the formula for combinations, we have:

(6 + 3) C 3 = (9 C 3) = 9! / (3! * (9 - 3)!) = 84.

So, there are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

Learn more about formula for combinations here:

https://brainly.com/question/13090387

#SPJ11

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = \(\int_a^b \delta\left|r^{\prime}(t)\right| d t\)

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

\(\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}\)

Further simplifying;

\(\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}\)

Now, use integration to find the mass of the wire;

       \(\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}\)

Therefore, the mass of the wire is estimated as 40π√2 units.

To know more about density function, here

https://brainly.com/question/27846146

#SPJ4

The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

The next step Juan will take is to multiply the second fraction by (x-2)/(x-2).

Given that Juan needs to rewrite this difference as one expression (3x/(x²-7x+10))-(2x/(3x-15)) and factor the denominator as (3x/(x-2)(x-5))-(2x/3(x-5)).

An algebraic expression in mathematics is an expression composed of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

The given expression is (3x/(x²-7x+10))-(2x/(3x-15))

Firstly, we will factored the denominator as

(3x/(x-2)(x-5))-(2x/3(x-5)).

Now, we will multiply and divide the second fraction by (x-2), we get

(3x/(x-2)(x-5))-((2x(x-2))/3(x-5)(x-2)).

Hence, the next step when subtracting these expressions (3x/(x-2)(x-5))-(2x/3(x-5)) is multiply the second fraction by (x-2)/(x-2).

Learn more about algebraic expression from here brainly.com/question/4344214

#SPJ4

skis per day is a total of 180 for three days

Poles per day is 36 which totals 180

Subtract the 18 dollars for the coupon

162 is the answer

Step-by-step explanation:

Answer:

The volume of shipping crate is 32 unit cubes.

Step-by-step explanation:

Given that:

Length of the crate = 4 units

Width of the crate = 2 units

Height of the crate = 4 units

Volume of shipping crate = Length * Width * Height

Volume of the crate = 4 * 2 * 4

Volume of crate = 32 unit cubes.

Hence,

The volume of shipping crate is 32 unit cubes.

Answer:

32 units

Step-by-step explanation:

Strictly speaking, to say that an apple is red means that B) it appears red.

When we say that an apple is red, strictly speaking, it means that it appears red.

The color we perceive is not an inherent property of the apple itself, but rather the result of how light interacts with the apple's surface and how our eyes perceive that interaction.

The color we see is a subjective experience influenced by various factors, such as lighting conditions, our perception of color, and any color deficiencies we may have.

While an apple may reflect and absorb certain wavelengths of light that we interpret as "red," it's important to recognize that color perception is subjective and can vary from person to person.

The statement "an apple is red" acknowledges that our perception of color is based on the appearance of the apple rather than making an absolute statement about its inherent color.

Learn more about perception of color

brainly.com/question/31831190

#SPJ11

The total amount of money that Johnny will have to pay is f(10) = 30.

What are expressions?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Given is that it costs Johnny $15 a month plus $1.50 per song to download music. This situation is represented by the expression →

1.5(x) + 15.

The expression is given by -

f(x) = 1.5(x) + 15

where [x] is the number of songs downloaded.

For [x] = 10 songs, the total amount of money that Johnny will have to

pay is -

f(10) = 1.5 x 10 + 15

f(10) = 15 + 15

f(10) = 30

Therefore, the total amount of money that Johnny will have to pay is f(10) = 30.

To solve more questions on amount visit the link below -

brainly.com/question/14591508

#SPJ4

The cost that Johnny has to pay to download 10 songs is 30$

as per given in the question,

johnny's  regular cost is 15$ a month

$1.50 is to be added for every song download

The cost to be find for 10 songs download

the equation which can be formed is

let x be the number of songs

1.5 times the number of songs + the cost of every month

therefore

1.5(x) + 15

the total number of songs to be downloaded is  10

so,

1.5(10) + 15

=> 15 +15

=> 30 $

Now the cost that has to pay by johnny after the downloading of 10 songs is 30 $

To learn more about cost :

https://brainly.com/question/17109853

#SPJ4

The required expression model is given as x + 8 / 6. Option B is correct.

Given that,
To determine the expression represents the calculation the sum of x and 8 is divided by 6

The equation model has defined as the model of the given situation in the form of an equation using variables and constants.

here,
According to the question,
The sum of x and 8 = x + 8
divided by 6
= x + 8 / 6

Thus, the required expression model is given as x + 8 / 6. Option B is correct.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ2

Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

Answer:

Step-by-step explanation:

9x-4>4x+7

-4x

5x-4>7

+4

5x>11/5

x>2.2

Answer:

9x-4x>7+8

5x > 15

X >3

So the answer is x >3

The vertex of the function defined as g(x) = f(x+2) is (8, 4).

From the question, we have the following parameters that can be used in our computation:

Vertex of f(x) = (6, 4)

For the function defined as g(x) = f(x+2), we have

Vertex = (x + 2, y)

Where

x = 6 and y = 2

Substitute the known values in the above equation, so, we have the following representation

Vertex = (6 + 2, 4)

Evaluate

Vertex = (8, 4)

Read more about quadratic function at

https://brainly.com/question/25841119

#SPJ1

Here is how you can use a while loop in Python to find the smallest integer n such that n^2 is greater than 12,000:
```python
n = 1
while n^2 <= 12000:
   n += 1
print(n)
```

In this code, we first initialize the variable `n` to 1. Then we use a while loop with the condition `n^2 <= 12000`, which means that we keep looping as long as n^2 is less than or equal to 12000. Inside the loop, we increment the value of `n` by 1 in each iteration using the `+=` operator. Once the loop condition is no longer satisfied (i.e., n^2 is greater than 12000), we exit the loop and print the value of `n`. This will give us the smallest integer n such that n^2 is greater than 12,000.

To learn more about while loop visit : https://brainly.com/question/26568485

#SPJ11

Answer:

135 degree

Step-by-step explanation:

Answer:

1 is C and 2 is B

Step-by-step explanation: