(-6-4) divided by (-5)

The system of equation to describe the situation below is x= 1.

What is equation?

an equation is a formula that is to expresses the equality of two expressions, by the  connecting them with in the equals sign.

The process of equting one thing with another is called the equation of science with objective.

Sol- Based on the given condition-

The formulate is- 36+2x=35+3x

Rearrange variables to the left side of the equation

2x-3x=35-36

Combine like terms

-x= 35-36

Calculate the sum or difference

-x=-1

Devide both side of the equation by the coefficient of variable we get

X=1

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Answer:

1,5,9

Step-by-step explanation:

Answer:

i think c

Step-by-step explanation:

The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.

The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;

(x²+3) (x³+4x) (x²+x-i-xi) = 0.

Hence, by further factorisation; we have;

x(x²+3) (x²+4) (x-i) (x+1) = 0.

The possible values of x are therefore;

x = 0;

x²+3 = 0; x = ±√3i

x² +4 = 0; x = ±2i

x -i = 0; x = i.

x +1 = 0; x = -1

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To show that w = u × v and v = w × u, we need to demonstrate that the cross product of vectors u and v yields the same result as the cross product of vectors w and u.

Given that u = v × w, let's calculate the cross product of w and u:

w × u = (u × v) × u

Since the cross product is not associative, we need to use the vector triple product identity:

w × u = u × (v × u) - (u · u) v

Since u is orthogonal to v, the dot product (u · v) is zero. Therefore, we can simplify the equation:

w × u = u × (v × u)

Next, let's calculate the cross product of v and u:

v × u = (u × v) × v

Using the vector triple product identity:

v × u = v × (u × v) + (v · v) u

Again, since u is orthogonal to v, the dot product (v · v) is zero:

v × u = v × (u × v)

Thus, we have shown that w = u × v and v = w × u, indicating that the cross products are equivalent in both directions.

In summary, when u, v, and w are orthogonal unit vectors, the cross product of u and v yields the same result as the cross product of w and u, as well as the cross product of v and w.

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Answer: a is the answer

Step-by-step explanation:

Answer:

The most likely result is that there will be no winners in the stadium.

Step-by-step explanation:

The odds of winning are 1 in 1 million, which means that there is a 99.9999% chance that any given person will not win. If there are 100,000 people in attendance at the game, then the expected number of winners is 0.1.

Answer:

x=2

Step-by-step explanation:

2

Answer:

x=2

Step-by-step explanation:

It's pretty simple all you have to do is get the xs together and then solve

Answer:

Step-by-step explanation:

y = 66x - 1200

The charity organisation has to sell a number of tickets to cover their production costs of $1,200. It is given that after selling 200 tickets they retain a net profit of $12,000. Net profit is deduced as: Total sales - total costs. Sales is calculated as total tickets x selling price per ticket.

If we let b represent the sales earned from selling tickets, then:

Net profit = total sales - total costs

12,000 = 200b - 1,200

We can then solve for b by taking the 1200 to the other side of the equal sign. When we do that the sign of that number changes. This is also the same as adding 1200 to both sides of the equal sign:

∴12000 + 1200 = 200b

13200 = 200b

To get the price of one single ticket, b, we need to divide both sides by 200.

∴ b = 66

This means that each ticket's selling price is $66.

So when when we take it back to the calculation of net profit then it becomes:

Net profit = total sales - total costs

y = 66x - 1200

To test:

y = 66x - 1200

= 66 (200 tickets) - 1200

= $12,000

To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.

We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.

Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30

Now let's find the population at any term n, using the recursive rule:

Step 1: Determine the base case, which is the initial population.
P₀ = 30

Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180

Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50

Using this recursive rule and the initial population, you can find the population at any given term n.

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To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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The derivative of the function h(x) is h'(x) = 3 x ln(x) - 3 x.

The function h(x) is defined as h(x) = ∫1^x 3 ln(t) dt. To find its derivative, we can use the Part 1 of the Fundamental Theorem of Calculus, which states that if f(x) is continuous on [a,b] and F(x) is an antiderivative of f(x), then the derivative of the integral ∫a^x f(t) dt is simply f(x).

In our case, we have f(t) = 3 ln(t), which is continuous on [1, e]. We can find an antiderivative of f(t) by integrating it with respect to t:

∫ 3 ln(t) dt = 3 t ln(t) - 3 t + C

where C is the constant of integration.

Using this antiderivative, we can apply the Fundamental Theorem of Calculus to find the derivative of h(x):

h'(x) = d/dx [∫1^x 3 ln(t) dt]

h'(x) = 3 x ln(x) - 3 x

Therefore, the derivative of the function h(x) is h'(x) = 3 x ln(x) - 3 x.

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Answer:

Option A

Step-by-step explanation:

Firstly, the negative (in -9) means that it is reflected over the x-axis. Then the 9 as a whole number means it is compressed vertically. X+3 means shifted three units to the left(It is the opposite for left and right in transformations.) Finally the -5 indicated it is shifted down by 5 units.

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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The vector w, we can express it as a linear combination of the given orthogonal vectors v₁, v₂, and v₃ is: w = (165, 2376, 3, 0, 0).

Here, we have,

To find the vector w, we can express it as a linear combination of the given orthogonal vectors v₁, v₂, and v₃.

Let's assume w = a₁v₁ + a₂v₂ + a₃v₃, where a₁, a₂, and a₃ are scalars.

Now, we can use the dot product properties to solve for a₁, a₂, and a₃. Since v₁, v₂, and v₃ are orthogonal, their dot products with each other are zero.

a₁(v₁ ⋅ v₁) + a₂(v₂ ⋅ v₁) + a₃(v₃ ⋅ v₁) = w ⋅ v₁

a₁(33) + a₂(0) + a₃(0) = 165

33a₁ = 165

a₁ = 5

a₁(v₁ ⋅ v₂) + a₂(v₂ ⋅ v₂) + a₃(v₃ ⋅ v₂) = w ⋅ v₂

a₁(0) + a₂(594) + a₃(0) = 2376

594a₂ = 2376

a₂ = 4

a₁(v₁ ⋅ v₃) + a₂(v₂ ⋅ v₃) + a₃(v₃ ⋅ v₃) = w ⋅ v₃

a₁(0) + a₂(0) + a₃(1) = -3

a₃ = -3

Therefore, we have:

w = 5v₁ + 4v₂ - 3v₃

Substituting the values of v₁, v₂, and v₃, we get:

w = 5v₁ + 4v₂ - 3v₃

w = 5(33, 0, 0, 0, 0) + 4(0, 594, 0, 0, 0) - 3(0, 0, 1, 0, 0)

w = (165, 0, 0, 0, 0) + (0, 2376, 0, 0, 0) - (0, 0, -3, 0, 0)

w = (165, 2376, 3, 0, 0)

Therefore, w = (165, 2376, 3, 0, 0).

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complete question:

(1 point) Suppose \( v_{1}, v_{2}, v_{3} \) is an orthogonal set of vectors in \( \mathbb{R}^{5} \). Let \( w \) be a vector in \( \operatorname{Span}\left(v_{1}, v_{2}, v_{3}\right) \) such that \( v

1

​

⋅v

1

​

=33,v

2

​

⋅v

2

​

=594,v

3

​

⋅v

3

​

=1 w⋅v

1

​

=165,w⋅v

2

​

=2376,w⋅v

3

​

=−3, then w=

The ratio by mass of copper to zinc in the alloy is 3:1.

To find the ratio by mass of copper to zinc in the alloy, we need to first calculate the total mass of the alloy. We can do this by adding the mass of copper and zinc:

Total mass of alloy = 13.5 g + 4.5 g = 18 g

Now we can find the ratio of copper to zinc by dividing the mass of copper by the mass of zinc:

Ratio of copper to zinc = 13.5 g / 4.5 g = 3:1

Therefore, the ratio by mass of copper to zinc in the alloy is 3:1.

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E(U) = 4, which is an integer.

What is Linearity of expectation?

Linearity of expectation is a fundamental property of expected value that states that the expected value of a sum or difference of random variables is equal to the sum or difference of their individual expected values.

To find E(U), where U = 2X - Y - 4, we can use the properties of expected value.

First, let's find the expected values of 2X, Y, and 4 separately using the linearity of expectation:

E(2X) = 2E(X) = 2 * 6 = 12

E(Y) = 4 (given)

E(4) = 4

Now, let's calculate the expected value of U:

E(U) = E(2X - Y - 4)

Since expected value is a linear operator, we can rearrange and simplify the expression:

E(U) = E(2X) - E(Y) - E(4)

= 12 - 4 - 4

= 4

Therefore, E(U) = 4, which is an integer.

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To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.

The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.

The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.

Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].

To find the displacement, we integrate the velocity function as follows:

Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.

To find the total distance traveled, we integrate the absolute value of the velocity function as follows:

Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.

By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.

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One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).

By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.

This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.

Option B holds true.

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When using a 95% confidence level, to achieve a 2% margin of error, If we are willing to increase the desired margin of error (to be larger than 2%), the sample size that we need will decrease.

The sample size required for a desired margin of error is inversely proportional to the square of the margin of error. This means that as the desired margin of error increases, the required sample size decreases.

In the given scenario, a 95% confidence level is used with a desired margin of error of 2%. This determines the initial sample size of 2,500.

If we are willing to accept a larger margin of error, let's say 3%, we can calculate the new sample size using the inverse square relationship. Since the desired margin of error is larger, the required sample size will be smaller.

To find the new sample size, we can set up the equation:

\((2,500)^2\) = (new sample size\()^2\) * (2%\()^2\) / (3%\()^2\)

Simplifying this equation, we find that the new sample size is approximately 1,111.

Therefore, if we are willing to increase the desired margin of error, the sample size that we need will decrease.

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Answer:

B

Step-by-step explanation:

negative slope so the line will go down and it has a less than sign so the shade will be below it

\(11+r =7\)

r=-4

Answer:

tan(Y) = 7/4

tan(Z) = 4/7

Step-by-step explanation:

Tangent ratios are the TOA of SOHCAHTOA.

tan( angle ) = opposite / adjacent

The graph represents a function because (a) Yes, because it passes the vertical line test.

The information that completes the question is added as an attachment

For a graph to represent a function, the graph must pass a vertical line test.

The vertical line test is such that a line drawn from the x-axis must intersect with the graph at only one point.

Based on the criteria above, the given graph would pass the vertical line test.

Hence, the graph represents a function because (a) Yes, because it passes the vertical line test.

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Answer:

The amount will be y = 970

Step-by-step explanation:

Equation 1:

y =  60 + 65x

Equation 2:

y = 200 + 55x

Solve for x and y

60 + 65x = 200 + 55x

10x = 140

x = 14

y = 200 + 55 (14)

y = 970

HOPE THIS HELPS :)

Answer:

1) 14 months

2) $970

Step-by-step explanation:

We know that the Community Gym charges a $60 membership fee and a $65 monthly fee.

So, we can write the following equation:

\(y=60+65m\)

Where y is the total cost, 60 is the one-time membership fee, and 65m is the cost for m months.

Workout Gym charges a $200 membership fee and a $55 monthly fee. So, we can write the following equation:

\(y=200+55m\)

Where y is the total cost, 200 is the one-time membership fee, and 55m is the cost for m months.

Question 1)

We want to know after how many months will the total amount of money paid to both gyms be the same. So, let's set the equations equal to each other:

\(60+65m=200+55m\)

To find the number of months, let's solve for m.

Subtract 55m from both sides:

\(60+10m=200\)

Subtract 60 from both sides:

\(10m=140\)

Divide both sides by 10:

\(m=14\)

So, after 14 months, the cost of going to Community Gym or Workout Gym will be the same.

Question 2)

To find the amount, simply substitute 14 back into either equation. Let's do it for both.

We have:

\(y=60+65m\)

Substitute 14 for m:

\(y=60+65(14)\)

Multiply and add:

\(y=60+910=\$970\)

We have:

\(y=200+55m\)

Substitute 14 for m:

\(y=200+55(14)\)

Multiply and add:

\(y=200+770=\$970\)

So, after 14 months, both gym will cost $970.

And we're done!

For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.

To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.

Given:

S = 26.32 (Initial value)

E = 55 (Expected value)

t = 3 (Years)

Standard deviation = 60% (of the expected value)

3-year interest rate = 2.4%

10-year interest rate = 3.1%

To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.

Minimum value calculation:

Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22

Therefore, the minimum value we would assign is 22.

To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.

Maximum value calculation:

Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88

Therefore, the maximum value we would assign is 88.

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the truth value of the proposition [A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)] when A and B are true and X and Y are false is also true.

we can break down the proposition into two parts:

1. A ⊃ ~(B · Y)
2. ~[B ⊃ (X · ~A)]

Since A and B are both true, we can simplify the first part to A ⊃ ~Y. Since Y is false, we know that ~Y is true. Therefore, the first part of the proposition is true.

For the second part, we can simplify it to ~(~B ∨ (X · ~A)). Since A and B are true, we can simplify this further to ~(~B ∨ X). Since X is false and B is true, we know that ~B ∨ X is true. Therefore, ~(~B ∨ X) is false.

Taking the equivalence of the two parts, we get true ≡ false, which is false. However, we are given that A and B are true and X and Y are false, so the main answer is that the truth value of the proposition is true.

the proposition [A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)] is true when A and B are true and X and Y are false.

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