A gas, oil and gasoline product company. I know knows that to produce a unit of gas requires 1/5 of the same 2/5 of oil and 1/5 of gasoline for producing a unit of oil requires 2/5 gas and 1/5 oil. To produce a unit of gasoline use a gas unit and an oil unit finally if you have a market demand of 100 units of each product, determine a gross production of each industry to meet your market.

solve it by the Gauss-Jordan method

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

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Given terms are :

let's solve for kinetic energy :

If three pencils, each measuring one foot in length, are laid end to end touching, the total distance covered by the row would be 3 feet.

Since each pencil is 1 foot long, when three pencils are laid end to end, they form a row that is 3 feet long. The key information here is that the pencils are touching, which means there are no gaps between them. Therefore, the row would extend for a total distance of 3 feet.

In this scenario, the correct answer is option a, 3 ft. The row would not extend beyond 3 feet because there are only three pencils, each measuring one foot in length. If there were more pencils or if they were not touching end to end, the total distance covered by the row would be different. However, based on the given information, the row formed by the three one-foot-long pencils would have a length of 3 feet.

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Answer:

six

Step-by-step explanation:

Six sigma is defined as the method or a set of techniques that provides the provides the organization tools and techniques to improve the capability and and be efficient of their business process. It is a concept of process improvement.

It refers to the achieving of a process variability very small so that the design specification represents six standard deviations which is above as well as below the process mean.

We want to solve the following equation

x² + 16x + 5 = 0

↓

x² + 16x = 5

We want to rewrite the equation so its left side is

(x + a)²

We know that

(x + a)² = x² + 2ax + a²

where a is a number, then, we want that the left side look something like

x² + 2ax + a²

Then we first want to find which must be the number a in this case.

Since 2 · 8 = 16, then the left side is

x² + 16x = x² + 2 · 8x

then, in this case a would be 8

a = 8

We want that the left side of our equation looks like:

x² + 2ax + a²

Since it has the first two terms

x² + 16x = 5

we have to add a² = 8² = 64

We add it both sides of the equation:

x² + 16x + 8² = 5 + 64

x² + 2 · 8x + 8² = 69

Now, we can write it as (x + a)²

x² + 2 · 8x + 8² = 69

↓ since (x + a)² = x² + 2ax + a²

(x + 8)² = 69

In order to solve the equation, we want to "leave x alone" on the left side:

(x + 8)² = 69

↓ squaring root both sides

(x + 8) = ±√69

x + 8 = ±√69

↓ taking 8 to the right side

x = - 8 ±√69

We have two solutions:

x₁ = - 8 -√69

x₂ = - 8 + √69

Since

Answer:

It's prime, the others are for English.

Step-by-step explanation:

Answer:

5 feet 4.4 inches tall

Step-by-step explanation:

The total number of sodium atoms in 92 grams of sodium can be calculated by using Avogadro's number and the molar mass of sodium.

To find the total number of sodium atoms, we need to first calculate the number of moles of sodium in 92 grams. The molar mass of sodium (Na) is approximately 22.99 grams/mol. By dividing the given mass (92 grams) by the molar mass, we can determine the number of moles of sodium.

92 grams of sodium / 22.99 grams/mol = 4 moles of sodium

Next, we can use Avogadro's number, which is approximately 6.022 x 10²³ atoms/mol, to convert the number of moles of sodium into the total number of sodium atoms.

4 moles of sodium x (6.022 x 10^²³ atoms/mol) = 2.409 x 10²⁴ sodium atoms .Therefore, there are approximately 2.409 x 10²⁴ sodium atoms in 92 grams of sodium.

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Answer:

B

Step-by-step explanation:

Answer:

y - 2  = -2x

Step-by-step explanation:

A point slope equation is of the form;

          y  = mx + c

c is the y intercept

y and x are coordinate values

m is the slope

        y - c = mx  is similar to the given problem,

         y -2  = ?

We need to find mx;

  m is the slope;

Given coordinates;

     (6,4) and (7,2)

x₁ = 6

y₁ = 4

x₂ = 7

y₂ = 2

Slope of a line  = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

Insert the parameters and solve;

   Slope of the line  = \(\frac{2 - 4}{7-6}\)   = -2

So,

                               y - 2  = -2x

2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.

What is volume ?

Let each side of  he square that's cut-off from each corner be represented by x.

This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.

Thus;

Volume of box is:

V = (15 − 2x)(15 − 2x)x

V = (15 − 2x)²x

V = (4x² - 60x + 225)x

V = 4x³ - 60x² + 225x

Let's differentiate with respect to x to get;

dV/dx = 12x² - 120x + 225

Maximum value of x is at dV/dx = 0

12x² - 120x + 225 = 0

Using quadratic formula, we arrive at;

x = 2.5 or 7.5

Now, let's find the second derivative of the volume;

d²V/dx² = 24x - 120

Putting x = 2.5 gives;

d²V/dx² = 24(2.5) - 120

d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative

At x = 7.5;

d²V/dx² = 24(7.5) - 120

d²V/dx² = 60

Thus, V is minimum at x = 7.5, since d²V/dx² is negative

Thus,we will use x = 2.5

Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)

V = 10 × 10 × 2.5

V = 250 Sq.inches

Dimensions are;

(15 − 2x) = 15 - 2(2.5) = 10 inches

(15 − 2x) = 15 - 2(2.5) = 10 inches

x = 2.5 inches

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Greetings from Brasil...

We need to use the Cosine Law in Any Triangle, so we can use Heron's formula.

AC² = AB² + BC² - 2.AB.BC.COS B

AC² = 11² + 9² - 2.11.9.COS 63

AC ≈ 10,63

Heron's Formula:

Area = √[P.(P - AB).(P - BC).(P - AC)]

where P = (AB + BC + AC)/2

P = (11 + 9 + 10,63)/2 ⇒ P ≈ 15,31

Area = √[15,31.(15,31 - 11).(15,31 - 9).(15,31 - 10,63)]

To set up this confidence interval, first identify the population parameter of interest, next select the appropriate estimator, then check the conditions for constructing the confidence interval that are: Randomization, Sample size and Distribution shape.

State:
Zachary wants to estimate the mean number of daily texts he sent over the past four years using a 90% confidence interval. He has an SRS of 50 days, with a daily average of 22.5 messages. The data is strongly skewed to the right with many outliers.

Plan:
1. Identify the population parameter of interest: The mean number of daily texts sent by Zachary over the past four years (µ).
2. Select the appropriate estimator: In this case, it's the sample mean = 22.5 messages.
3. Check the conditions for constructing the confidence interval:
  a. Randomization: Zachary used a simple random sample (SRS) of 50 days, which satisfies the randomization condition.
  b. Sample size: The sample size is n = 50, which is typically considered large enough for constructing a confidence interval.
  c. Distribution shape: Since the data is strongly skewed to the right with many outliers, the normality condition might not be satisfied. In this case, the Central Limit Theorem (CLT) may not apply, and the confidence interval might not be accurate.

Given the potential issue with the distribution shape, Zachary should consider either transforming the data to approximate normality or using a nonparametric method.

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Answer:

steps below

Step-by-step explanation:

5th level of Pascal triangle: 1,5,10,10,5,1

(1+2x)⁵ = 1*1⁵*(2x)⁰+5*1⁴*2x+10*1³*(2x)²+10*1²*(2x)³+5*1¹(2x)⁴+1*1⁰*(2x)⁵

           = 1 + 10x + 40x² + 80x³ + 80x⁴ + 32x⁵   .. (1)

(1-2x)⁵ =  1  - 10x + 40x² - 80x³  + 80x⁴ - 32x⁵  .. (2)

(1)+(2): (1+2x)⁵ + (1-2x)⁵ = 160x⁴ + 80x² +2

a + bx + cx ?? suppose it's ax⁴ + bx² + cx, if you have other set up.. adjust by yourself

a = 160,    b = 80,    c = 2

These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

Gregory most likely took an intelligence test, specifically the Wechsler Adult Intelligence Scale (WAIS). The WAIS is designed to measure an individual's cognitive abilities and is commonly used in psychological assessments. It consists of a full scale or total score, which is a combination of the verbal score and the performance score. The verbal score measures an individual's language and communication skills, while the performance score measures an individual's ability to solve problems and complete tasks. These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

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Therefore , the required function for this given problem is F(t) = 25 - 14t.

A function is a relationship between a set of allowable inputs and outputs, where each input is associated to exactly one output. Let A and B represent any two non-empty sets; only when every element in A has one end and only one image in B will the mapping from A to B be a function.

Here,

Given:

armando can scan about 14 items per minute

armando has 25 items in his cart

No of items scan in t minutes =14t

So

A)F(t) = 25 - 14t

Domain:[0,2]

Range:[0,25]

Therefore , the required function for this given problem is F(t) = 25 - 14t.

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Given:

Greg wants to estimate the percentage of people who lease a car. He surveys 340 individuals and finds out that 90 lease a car

Required:

What is the sample propoertion for the success?

Explanation:

Total individual =340

Individual who lease car=90

Now,

90 out of 340 people lease car.

Fraction of people leasing car

Percent of people leasing car

Answer:

26.471 is the answer.

Answer:

3

Step-by-step explanation:

The average rate of change of h(x) in the closed interval [ a, b ] is

\(\frac{h(b)-h(a)}{b-a}\)

Here [ a, b ] = [ 1, 2 ], then from the table

h(b) = h(2) = 0

h(a) = h(1) = - 3 , then

average rate of change = \(\frac{0-(-3)}{2-1}\) = \(\frac{3}{1}\) = 3

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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The area under the standard normal curve between z=â1.16 and z=â0.03 is 0.3663.

To find the area under the standard normal curve between z = -1.16 and z = -0.03, we will use the following steps:

1. Look up the z-values in the standard normal distribution table (or use a calculator or online tool that provides the corresponding probability values).
2. Subtract the probability value for z = -1.16 from the probability value for z = -0.03.
3. Round your answer to four decimal places.

Step 1: Look up the z-values in the standard normal distribution table.
- For z = -1.16, the corresponding probability value is 0.1230.
- For z = -0.03, the corresponding probability value is 0.4893.

Step 2: Subtract the probability values.
Area = P(-0.03) - P(-1.16) = 0.4893 - 0.1230

Step 3: Round the answer to four decimal places.
Area = 0.3663

So, the area under the standard normal curve between z = -1.16 and z = -0.03 is approximately 0.3663.

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Answer:

9

Step-by-step explanation:

you have to plug in the numbers and solve it, so it would go as follows:

-(-3^2)- 2(-5)(2) - /2/

-9 + 20 - 2 =

9

i hope this helps

Given:

∆y and dy.

∆x and dx.

Required:

To explain the difference between ∆y and dy, is there difference between ∆x and dx.

Explanation:

∆y and dy are same, dy/dx is the differentiation of y with respect to x or dx/dy is the differentiation of x with respect to y.

Whereas del y is the partial differential of x where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

In the same way ∆x and dx are same, dx/dy is the differentiation of x with respect to y or dy/dx is the differentiation of y with respect to x.

Whereas del x is the partial differential of y where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

Final Answer:

∆y and dy are same, dy/dx is the differentiation of y with respect to x or dx/dy is the differentiation of x with respect to y.

Whereas del y is the partial differential of x where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

In the same way ∆x and dx are same, dx/dy is the differentiation of x with respect to y or dy/dx is the differentiation of y with respect to x.

Whereas del x is the partial differential of y where we differentiate only one at a time keeping the other variables constant and we partially differentiate all to find who differential.

Two or more angles whose sum is 180° are called supplementary angles. The measure of the ∠y is 120°.

Two or more angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given the puck strikes the wall at an angle of 30°, it goes away at the same angle of 30°. Therefore, the measure of angle y can be found using the sum of the angle as a supplementary angle. Thus, we can write,

30° + ∠y + 30° = 180°

60° + ∠y = 180°

∠y = 180° - 60° = 120°

Hence, the measure of the ∠y is 120°.

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You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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Answer:

12.5 hours a week

Step-by-step explanation:

So far this week, you have worked 10 hours at your part-time job. This is 80% of the number of hours you work each week. How many hours do you work each week?

10 hours = 80%

80% = 0.8

10/0.8 = 12.5 hours a week

The problem involves calculating the probability that a patient who tests positive for HIV is not actually infected with HIV. Given that 8% of the patients tested are infected and that the test has a 92% true positive rate for infected patients and a 9% false positive rate for non-infected patients, we need to determine the probability of a false positive result.

Let's denote the events as follows:

A: Patient is infected with HIV

B: Patient tests positive for HIV

We are interested in finding P(A'|B), which represents the probability that a patient is not infected (A') given that they test positive (B).

According to Bayes' theorem, we can express this probability as:

P(A'|B) = (P(B|A') * P(A')) / P(B)

First, let's calculate P(B|A'), which represents the probability of testing positive given that the patient is not infected. Since the false positive rate is given as 9%, we have P(B|A') = 0.09.

Next, we need to calculate P(A'), which is the probability of not being infected. Since 8% of the patients are infected, the complement event (not being infected) has a probability of 1 - 0.08 = 0.92.

To calculate P(B), the probability of testing positive, we need to consider the total probability of testing positive, which includes both infected and non-infected patients. Therefore, we have:

P(B) = P(B|A) * P(A) + P(B|A') * P(A') = 0.92 * 0.08 + 0.09 * 0.92.

Finally, substituting these values into Bayes' theorem, we can calculate P(A'|B), the probability that a patient testing positive is not infected with HIV.

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Answer:

68°

Step-by-step explanation:

since the angle given is a complementary angle, we know that the sum of it must equal 180°

let the unknown angle below j be x so,

\(25+43+x=180\\x=180-25-43\\x=112\)

now since the angle on the left of j is equal to x we can say

\(x+j=180\\j=180-x\\j=180-112\\j=68\)

The correct option is b) Label.

In a chart, each data point, bar, slice, and so on has a unique label. This label is used to identify and differentiate the different elements within the chart. It provides a clear and concise description of what each element represents.

For example, in a bar chart that shows the sales of different products, each bar would have a label indicating the specific product it represents. This allows the viewer to easily understand which product corresponds to each bar.

The label is crucial in making the chart understandable and meaningful. Without it, the chart would be confusing and difficult to interpret. It helps to provide context and clarity to the data being presented.

While color, size, and position can also be used to distinguish between elements in a chart, they do not provide the same level of specificity as a label. Color, for instance, may be used to represent different categories, but it does not provide specific information about each individual element.

In summary, the unique label assigned to each data point, bar, slice, or other element in a chart is what helps identify and differentiate them. It provides a clear description of what each element represents, making the chart more understandable and meaningful.

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Answer: She ate 12 apples

Step-by-step explanation: 18 divided by 2 is 9 add 2 of 9 to the other 9 and you get 12 hope I helped

Answer:

she ate 10 apples

Step-by-step explanation:

I thought of it because there is only 18 apples all together

30

Given the expression for the instantaneous voltage expressed as:

Given the following parameter:

θ = 30⁰

Substitute the given parameter into the formula to have:

Therefore the instantaneous voltage when θ = 30⁰ is 30.