find the solution of this system of equation
-x-4y=-37 "-2x-5y=-53"

Answer:

  C = (11, 21)

Step-by-step explanation:

The relation AC = 3AB can be used to find the coordinates of C given those of A and B.

__

  C -A = 3(B -A)

  C = 3B -2A . . . . . add A to both sides

  C = 3(5, 9) -2(2, 3) = (15 -4, 27 -6) . . . . use the given points for A and B

  C = (11, 21)

Answer:

86°

Step-by-step explanation:

b = 29× 2 = 58

d= [180-(86+29)]×2 = 130

a=c=x

a+b+c+d = 360

2x+188= 360

2x= 172

x= 86

a = c = 86°

Answer:

If a sales person wants to earn $600 in 1 week they have to make $1000 dollar sale or a bunch of sales that can make $1000

Step-by-step explanation:

Because $600 - $450 gives you $150, and $150 is 15% of her sales to if we were to divide $150 by 0.15 ( 15% in decimal for ) we would get $1000 meaning 15% of 1000 is 150.

Hope this helps :)

The open interval of convergence is 1 then attached image.

We now approach series from a different perspective: as a function. Given a value of  x , we evaluate  f(x)  by finding the sum of a particular series that depends on  x  (assuming the series converges). We start this new approach to series with a definition.

A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum.

Let  {\(a_{n}\)}  be a sequence, let x be a variable, and let c be a real number.

∑(n=0 to ∞) \(a_{n} x^{n}\) = \(a_{0} +a_{1} x+a_{2} x^{2} +.....\)

∑(n=0 to ∞) \(a_{n} (x-c)^{n}\) = \(a_{0} +a_{1} (x-c)+a_{2} (x-c)^{2} +.....\)

One of the conventions we adopt is that  \(x^{0}\) = 1  regardless of the value of  x . Therefore

∑(n=0 to ∞) \(x^{n}\) = \(1+x+x^{2} +x^{3} +......\)

List of Integral Formulas

∫ 1 dx = x + C.

∫ a dx = ax+ C.

∫ \(x^{n}\) dx = ((\(x^{n+1}\))/(n+1))+C ; n≠1.

∫ sin x dx = – cos x + C.

∫ cos x dx = sin x + C.

Therefore,

The open interval of convergence is 1 then attached image.

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Answer:

It is c) 18 cm^3

Step-by-step explanation:

\(v = 3 \times 3 \times 2 \\ v = 18 \: {cm}^{3} \)

I hope that is useful for you :)

The function with y and x, representing cost and shipping charges will be y = 3.50x + 9.50.

The express that can be used to write the function is as follows-

Total amount = number of shirts × cost of shirts + shipping fee

Write the function based on the formula -

y = 3.50×x + 9.50

As stated x represents the number of shirts bought online. We know that shipping charges will be calculated once while cost of shirt will vary according to the number of shirts.

Hence the function will be -

y = 3.50x + 9.50

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Answer:

yes, going backwards, under sea level or to the left on a number line

Step-by-step explanation:

hopefully this helps. have a nice day

The possible values of the solutions to the equations are; (π/4, 7π/4)

We are given the equation;

sin(5x - π) = (√2)/2

Now, (√2)/2 is also expressed as 1/√2.

Thus;

sin(5x - π) = 1/√2

5x - π = sin⁻¹(1/√2)

5x - π = π/4

5x = π + π/4

5x = ⁵/₄π

Thus;

x = π/4

Now, since x < 2π, then it means it is in the fourth quadrant. Thus;

x = 7π/4

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Step-by-step explanation:

i think the answer is 63.5

Answer:

I agree it is 63.5 Fahrenheit

Step-by-step explanation:

The number of possible ways you can distribute the balls among the three boxes so that each box contains at least one ball = 21

Here we have 3 empty boxes.

Let us assume that a, b and c be these empty boxes.

and the total number of balls = 8

We need to distribute the balls among the three boxes so that each box contains at least one ball.

This means that a + b + c = 8

By allotting 1 ball to each box so that no box remains empty.

We get an equation a + b + c = 5

So, the possible number of ways to by allotting 1 ball to each box so that no box remains empty would be:

⁷C₂

Using combination formula:

⁷C₂

= 7! / 2!(7 - 2)!

= 21

Therefore,  the required number of ways = 21

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Probability that 79 or more seeds germinate is 0.138, or about 13.8%.

To approximate the probability that 79 or more seeds germinate, we can use a normal approximation to the binomial distribution. First, we need to find the mean and standard deviation of the number of seeds that germinate.

The mean is the expected value of a binomial distribution, which is equal to the product of the number of trials (90) and the probability of success (0.84):

mean = 90 x 0.84 = 75.6

The standard deviation of a binomial distribution is equal to the square root of the product of the number of trials, the probability of success, and the probability of failure (1 minus the probability of success):

standard deviation = sqrt(90 x 0.84 x 0.16) = 3.11

Next, we can use the normal distribution to approximate the probability that 79 or more seeds germinate. We need to standardize the value of 79 using the mean and standard deviation we just calculated:

z = (79 - 75.6) / 3.11 = 1.09

Using a standard normal distribution table (or calculator), we can find the probability that a standard normal variable is greater than 1.09:

P(Z > 1.09) = 0.138

This means that the approximate probability that 79 or more seeds germinate is 0.138, or about 13.8%.

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Answer:

3.25 miles

Step-by-step explanation:

Combine the total laps by doing 6 + 7 to get 13. Then, multiple 13 by 0.25 to get your sum of 3.25 miles.

Answer:

4 cars fit for 12 students. and

2 vans fit for 16 students.

Answer:

6 students in each van.

Step-by-step explanation:

Having van as x variable and car as y variable.

3x + y = 22

2x + 4y = 28

Step 1: Solve for y in 3x + y =22

y = 22 - 3x

Step 2: Substitute y = 22 - 3x into 2x + 4y =28

2x + 4(22-3x) = 28

2x + 88 - 12x = 28

=> -10x + 88 = 28

Step 3: Solve for x (which is one van) in -10x + 88 = 28,

-10x = 28 - 88

-10x = -60

=> x = 6  

Thus, we have 6 students that can fit in each van.  

Answer:

5 / 56 or 0.089

Step-by-step explanation:

We are given 5 / 14 x 4

5 / 56

This cannot be further simplified, so 5 / 56 will be the answer, if you need the answer in a decimal form it will be 0.089

Answer:

-8x-9y

Step-by-step explanation:

Hey There!

So basically this problem is asking you to simplify this expression using distributive property

The first step would be to distribute 7 into what is inside the parenthesis (2x and -3y)

2x*7=14x

-3y*7=-21y

so now we have 14x-21y + 4(3y-5x)

the next step would be to distribute 4 to what is inside the parenthesis (3y and -5x)

4*3y=12y

4*-5x=-20x

so now we have 12x-21y-20x+12y

the final step is to combine like terms

12x-20x=-8x

-21y+12y=-9y

so the simplified version of 7(2x - 3y) + 4(3y - 5x) is -8x-9y

Answer:

14x-21y+12y-20x. 14x-20x+12y-21y. -6x-9y

Answer:

the last answer is -1 :))))))

Answer:

Step-by-step explanation:

Given :-

AB = 5m

CB = 5m

CD = 8 m

AD = 4m

____________________________

\(\mathrm{Area \; of \; trapezoid = \cfrac{1}{2}\; (Sum\; of\; parallel\: sides)\times height}\)

\(\mathrm{Area = \cfrac{1}{2}\:(AB + CD)\times AD }\)

\(\mathrm{\cfrac{1}{2}\:(5m+8m)\times 4m }\)

\(\mathrm{\cfrac{1}{2} \times 13m\times 4m}\)

\(\mathrm{26m^2}\)

Therefore, the Area of the trapezoid is 26m².

_____________________

Hope this helps!

The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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Answer:

x = 2

Step-by-step explanation:

x = 2

\(2^{5} = 32\\\)

Answer:

3.6 D. decimal

Step-by-step explanation:

The amount of gasoline that was in the tank before refilling it was 11.5 gallons. Due to the above, it lacked 8.5 gallons to refill it again.

To calculate how many gallons were left to refill the tank, you need to know how much gasoline was in the tank.

According to the statement, the tank required \(8 \frac{5}{10}\) to fill up, then to know how much gasoline it had we must subtract this amount from the maximum capacity of gasoline that the tank requires as shown below:

\(8\frac{5}{10}\) = 8.5 gallons

20 - 8.5 gallons

= 11.5 gallons

Based on the above, the number of gallons in the tank was 11.5 gallons of gasoline.

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Answer:

r = 105

Step-by-step explanation:

Given quadratic equation:

x² − 9x − 6

Quadratic formula is given by:

(-b ± √b² - 4ac) ÷ 2a

For the equation: x² - 9x - 6

a = 1, b = -9 and c = -6

Substitute in the quadratic formula:

(-b ± √b² - 4ac) ÷ 2a

(-(-9) ± √(-9)² - 4(1*-6)) ÷ 2*1

= 9 ± √105 / 2

The solution of x² − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2

Therefore, the value of r is 105

The odds in favor of the event happening are 5 to 4.

We have,

To find the odds in favor of an event happening, we use the formula:

Odds in favor = Probability of the event happening / Probability of the event not happening

In this case,

The probability of the event happening is 5/9.

The probability of the event not happening is 1 - 5/9, which simplifies to 4/9. So the odds in favor of the event happening are:

Odds in favor

= 5/9 / 4/9

= 5/4

Therefore,

The odds in favor of the event happening are 5 to 4.

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Sure! Here's a code snippet in Octave to calculate \(c_j - z_j\) for all the variables in the Linear Programming Problem (LPP) table:

```octave

% Variables and coefficients

c = [coefficients]; % Replace [coefficients] with the actual coefficients for the variables

z = [coefficients]; % Replace [coefficients] with the actual coefficients for the objective function

% Calculate c_j - z_j

cj_minus_zj = c - z;

% Display the result

disp(cj_minus_zj);

```

In the code, you need to replace `[coefficients]` with the actual coefficients for the variables and the objective function. The variable `c` represents the coefficients of the variables, while `z` represents the coefficients of the objective function.

The calculation of \(c_j - z_j\) involves subtracting the coefficients of the objective function from the coefficients of the variables. This difference indicates the marginal improvement (or degradation) in the objective function value if the corresponding variable is increased by one unit while keeping other variables constant. By executing the code, you will get the values of \(c_j - z_j\) for all the variables, indicating their impact on the objective function. A positive value suggests that increasing the corresponding variable will increase the objective function value, while a negative value suggests a decrease in the objective function value.

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Answer:

a₁ = 16

Step-by-step explanation:

The sum to infinity of a geometric series is

S ∞ = \(\frac{a_{1} }{1-r}\)

where a₁ is the first term and r the common ratio , then

\(\frac{a_{1} }{1-0.2}\) = 20

\(\frac{a_{1} }{0.8}\) = 20 ( multiply both sides by 0.8 to clear the fraction )

a₁ = 0.8 × 20 = 16

assistant professors on the business faculty at state-supported institutions in Ohio make, on average, between $69,263 and $74,737 for nine months.

In Ohio's state-supported institutions, the

average incom for a sample of assistant professors in the business faculty for nine months is $72,000.

Since the sample size is unknown, it is difficult to draw any definitive conclusions based on this statistic

. However, we can use this mean to estimate the probable range of incomes for assistant professors at these institutions by calculating a confidence interval.For example, if we use a 95 percent confidence level, we can assume that the real average income for assistant professors in the business faculty at Ohio's state-supported institutions falls within a certain range of values

. Based on the sample mean of $72,000 and a standard deviation of $5,000, the 95 percent confidence interval is $69,263 to $74,737. This means that we are 95 percent confident that the real average income for assistant professors falls within this range.The interval reflects the range of values that the true average could fall within, given the uncertainty of the sample data.

Therefore, we can infer that assistant professors on the business faculty at state-supported institutions in Ohio make, on average, between $69,263 and $74,737 for nine months.

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The mean income for sample assistant professors on the business faculty at state-supported institutions in Ohio is $72,000 for 9 months.

Based on the information provided, the mean income for sample assistant professors on the business faculty at state-supported institutions in Ohio is $72,000 for 9 months.

To better understand this, let's break it down step by step:

1. The mean income refers to the average income earned by assistant professors on the business faculty in Ohio.
2. The sample represents a group of assistant professors who were surveyed or studied.
3. The business faculty refers to the department or area of expertise these assistant professors specialize in.
4. State-supported institutions in Ohio are public universities or colleges that receive funding from the state government.
5. The $72,000 represents the average income earned by assistant professors on the business faculty in Ohio over a period of 9 months. It does not include income earned during the summer months.
6. It's important to note that this figure may vary for different individuals based on factors such as experience, qualifications, and position within the faculty.

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The given English sentence is a tautology. The sentence "I either attend class or I do not" can be represented as a logical proposition using two elementary propositions: A for "I attend class" and B for "I do not attend class." The logical proposition becomes A ∨ B, where ∨ represents the logical operator "or."

To determine if this proposition is a tautology, we construct a truth table to evaluate all possible combinations of truth values for A and B. In this case, both A and B cannot be true simultaneously since attending and not attending class are mutually exclusive. Hence, the proposition A ∨ B is indeed a tautology, as it always evaluates to true regardless of the truth values assigned to A and B. Therefore, the given English sentence is a tautology. Let's analyze the possible truth values of A and B in a truth table:

| A |B  | A ∨ B |

|----|----|---------|

| T  |T  |   T     |

| T  |F  |   T     |

| F  |T  |   T     |

| F  | F |   F     |

As we can see, the proposition A ∨ B is true in all cases. This means that regardless of whether A is true or false, or whether B is true or false, the statement "I either attend class or I do not" is always true. It satisfies the definition of a tautology, which is a logical proposition that is true in every possible interpretation. Therefore, the given sentence is a tautology.

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