Solve each equation for x
2x+6x=1000

Answer:

x=7

Step-by-step explanation:

8(2x-10)+18=4x+22

distribute the 8

16x-80+18=4x+22

simplify

16x-62=4x+22

ads 62 to each side

16x=4x+84

subtract 4x from each side

12x=84

divide each side by 12

x=7

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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Answer:

The answer is 2

Step-by-step explanation:

| 2 | = 2 because whenever you have | 2 | or even | -2 | it always equals the postive number.

Ex:

| -3 | = 3

| 8 | = 8

hope this helps! :)

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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Answer:

Approximately 66.4 Meters

Step-by-step explanation:

So we have a rectangle with a width of 18.8 meters and a diagonal with 23.7 meters. To find the perimeter, we need to find the length first. Since a rectangle has four right angles, we can use the Pythagorean Theorem, where the diagonal is the hypotenuse.

\(a^2+b^2=c^2\)

Plug in 18.8 for either a or b. Plug in the diagonal 23.7 for c.

\((18.8)^2+b^2=23.7^2\\b^2=23.7^2-18.8^2\\b=\sqrt{23.7^2-18.8^2} \\b\approx14.4 \text{ meters}\)

Therefore, the length is 14.4 meters. Now, find the perimeter:

\(P=2l+2w\\P=2(14.4)+2(18.8)\\P=66.4\text{ meters}\)

Answer:

i think the answer is D

The correct option is (d) interval/ratio, nominal with 2 or more levels.

In ANOVA (Analysis of Variance), the independent variable is interval/ratio with 2 or more levels, and the dependent variable is nominal with 2 or more levels. Here, ANOVA is a statistical tool that is used to analyze the significant differences between two or more group means.

ANOVA is a statistical test that helps to compare the means of three or more samples by analyzing the variance among them. It is used when there are more than two groups to compare. It is an extension of the t-test, which is used for comparing the means of two groups.

The ANOVA test has three types:One-way ANOVA: Compares the means of one independent variable with a single factor.Two-way ANOVA: Compares the means of two independent variables with more than one factor.Multi-way ANOVA: Compares the means of three or more independent variables with more than one factor.

The ANOVA test is based on the F-test, which measures the ratio of the variation between the group means to the variation within the groups. If the calculated F-value is larger than the critical F-value, then the null hypothesis is rejected, which implies that there are significant differences between the group means.

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Using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The characteristics of normal distributions are as follows: Bell-like in its symmetry.

The distribution's mean and median, which are both at its center, are equal.

68 percent of the data, or approximately, falls within one standard deviation of the mean.

So, the formula is used to determine the Z score for a data point x in a normal distribution:

Z = z - mean/standard deviation

Now, use the formula to calculate the z value as follows:

Z = z - mean/standard deviation

Z = 25 - 16/6

Z = 9/6

Z = 3/2

Z = 1.5

Therefore, using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.

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Answer:

C) there are no solutions

Step-by-step explanation:

3x-6<3x+13

3x<3x+19

0<19

Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Answer:

its c 48.08 im pretty sure

Step-by-step explanation:

Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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Answer: 3/8

Step-by-step explanation:

There is no effect between flipping a coin and chosing a number.

This situation is known as a independent event.

P(AnB) = P(A)*P(B)

The situation A = Heads or tails of money = 1/2

The situation B = 6/8

It can be calculated as below:

Probability = Desired / All Event

Desired || Numbers between 3 and 10 are : 4,5,6,7,8,9 = 6 pieces

All Event || Numbers between 1 and 10 are : 2,3,4,5,6,7,8,9 =8 pieces

Consequently product the fractions.

1/2 * 6/8 = 6/16 = 3/8

Answer:

72

Step-by-step explanation:

Answer:

13.23 feet^2

Step-by-step explanation:

Answer:

This is required answer.

Step-by-step explanation:

Given that,

The relationship between the slope of the line and the side lengths of the triangles.

We know that,

The relation between slope and side lengths of the triangles

Slope :

Slope is the defined as a line.

Slope is equal to the vertical change divided by horizontal change.

Formula of slope,

\(slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Triangles :

Triangles are made by three sides.

The side of length of the triangle is the distance between the given coordinates.

Formula of length of side of triangle,

\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

Hence, This is required answer.

The one crate will indeed be enough to ship the 25,000 boxes with dimensions 10 cm x 10 cm x 20 cm.

The volume of a box is obtained by multiplying three measurements: length, width and height. The three measurements must be expressed in the same unit of measurement, whether in millimeters, centimeters or meters.

Knowing that the volume of the box is:

Length x Width x Height = 10 cm x 10 cm x 20 cm = 2000 cm³

So calculate the total volume :

Total volume = Volume of one box x Number of boxes = 2000 cm³ x 25,000 = 50,000,000 cm³

Calculate the volume of the shipping crate:

Length x Width x Height = 3 m x 3 m x 7 m = 63 m³

Converting the volume of the shipping in m to cm:

63 m³ x 1,000,000 cm³/m³ = 63,000,000 cm³

Therefore, one crate will indeed be enough to ship the 25,000 boxes with dimensions 10 cm x 10 cm x 20 cm.

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Answer:

70

Step-by-step explanation:

Answer:

The equivalent sum is \(100 + 83\).

Step-by-step explanation:

Hector must use the Distributive Property to make calculations quicker:

\(50 + 83 + 50\) (Given)

\(50 + 50 + 83\) (Conmutative Property)

\(50 \times (1+1) + 83\) (Distributive Property)

\(50 \times 2 + 83\) (Distributive Property)

\(2\times 50 + 83\) (Conmutative Property)

\(100 + 83\) (Multiplication)

\(183\) (Sum)

The equivalent sum is \(100 + 83\).

Answer: Your answer would be the distributive property

Step-by-step explanation: :) hope I helped

Checkpoint 4 will be higher than Checkpoint 3 by 108.

In our question, it is given that the Checkpoint 4 value is -99 and the Checkpoint 3 value is -207.

We will use Subtraction. What is Subtraction?

The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).

The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller. For instance, your friends consumed 7 of the 9 cupcakes you purchased for your birthday party. You are now down to two cupcakes. This can be expressed as a subtraction formula: 9 - 7 = 2, which means "nine less seven equals two." The result of subtracting 7 from 9 is 2, or (9 - 7) Here, we divided two numbers, 9, and 7, by one another to get the difference of 2.

Subtracting the value of Checkpoint 3 from Checkpoint 4, we get:

Checkpoint  - Checkpoint 3 = -207 -(-99)

= -207 + 99 = 108.

Therefore Checkpoint 4 will be higher than Checkpoint 3 by 108.

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The total thickness of all the components is 3/4 + 6/16 + t inches.

To find the smallest length of a bolt that will pass through all the given components, we need to determine the maximum thickness among them and then add it to the sum of their lengths.

The two pieces of tubing have thicknesses of 1/2 inch and 3/4 inch, respectively. Therefore, the maximum thickness among the tubing is 3/4 inch.

The two washers have thicknesses of 3/16 inch each. Since there are two washers, the total thickness of the washers is 2 * 3/16 = 6/16 inch.

The nut's thickness is not specified in the question, so let's call it t.

The total thickness of all the components is 3/4 + 6/16 + t inches.

To find the smallest length of the bolt, we need to add the total thickness to the sum of the lengths of the components. However, the lengths of the tubing, washers, and nut are not provided in the question.

If you provide the lengths of the tubing, washers, and nut, I can assist you further in determining the smallest length of the bolt.

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The total bill of the dinner to celebrate birthday including sales tax and tip to the nearest cent is $202.01

Cost of the meal = $168.34

Sales tax = 5% of $168.34

= 0.05 × 168.34

= $8.417

Tip = 15% of $168.34

= 0.15 × 168.34

= $25.251

Total bill = Cost of the meal + Sales tax + Tip

= $168.34 + $8.417 + $25.251

= $202.008

Hence, the total bill is $202.01 to the nearest cent.

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The store manager must work 40 hours that week, so he earns in that week is: ₹40x, using the concept of salary system.

Salary systems, also known as compensation plans or pay structures, are a set of procedures, rules, and procedures used by companies to compensate employees for their labor. Paychecks that are sent weekly, biweekly, or bimonthly are only one aspect of salary schemes.

In contrast, time-based systems pay employees based on the amount of hours they put in during the pay period. Employee attendance at work is more closely correlated with compensation than employee performance. Systems that reward or are based on output connect employee remuneration to accomplishments.

Let, assume the store manager earn ₹x per hour.

So, he work 40 hours that week, that means -

In a week he earn ₹x × 40

So, in a week he earns ₹40x

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Answer:

The answer is k = -12

Answer:

6+3

Step-by-step explanation:

Answer:

1040

Step-by-step explanation:

8 hours = 260

16 hours = 520

24 hours = 1040

The average rate at which Mr. Blade types is 30 words per minute.

Average or mean is a measure of central tendency where it defines the central number of a data set.

Average is calculated by dividing the total sum of the values of the dat set divided by the frequency or the number of data in the set.

Mr. Adi takes 9 minutes.

The average rate of Mr. Adi is 40 words per minute.

So in 9 minutes he writes 40 × 9 = 360 words in total.

Mr. Blade typed the same number of words.

he took 12 minutes to type it.

So average rate = total words typed ÷ time taken (in minutes)

Average rate= 360 ÷ 12 =30 words per minute.

Hence Mr. Blade writes at the average rate of 30 words per minute.

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Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).

If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.

from the question:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.

Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.

Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.

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Answer:

im thinking its B. Stretched vertically and shifted right

The vector parametric equation for the line through the point (-4,-4) that is perpendicular to the line ⟨1+4t,4-t⟩ is ⟨-4+t, -4+4t⟩.

To find a vector parametric equation for the line through the point (-4,-4) that is perpendicular to the line ⟨1+4t,4-t⟩, we need to first find the direction vector of the line we want to create. Since the line we want is perpendicular to ⟨1+4t,4-t⟩, its direction vector should be orthogonal to ⟨1, -1/4⟩ which is the direction vector of ⟨1+4t,4-t⟩.

So, we can find a direction vector for the line we want by taking the dot product of the direction vector of ⟨1+4t,4-t⟩ and any vector that is orthogonal to ⟨1, -1/4⟩. A convenient choice for an orthogonal vector is ⟨1, 4⟩ since their dot product is 1 * 1 + (-1/4) * 4 = 0.

Thus, a direction vector for the line we want is ⟨1, 4⟩. Now we can use the point (-4,-4) and the direction vector ⟨1, 4⟩ to find a vector parametric equation for the line we want:

x = -4 + t

y = -4 + 4t

So the vector parametric equation for the line through the point (-4,-4) that is perpendicular to the line ⟨1+4t,4-t⟩ is ⟨-4+t, -4+4t⟩.

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