1) The standard form of a linear equation is written as .
ax + by=c
a. Write the equation in slope-intercept form( y= mx + b)

b. Write the slope, y-intercept form of (a).
PLS HELP

The heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.

What is the equation of a circle in parametric form?

The equation of a circle in parametric form is given by x=acosθ,y=asinθ.

We can use the equation for a circle in standard form:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

In this case, the center of the propeller is (0, 13) and the radius is 3. So the equation of the circle is:

x² + (y - 13)² = 9

We can use this equation to find the x and y coordinates of the tip of each propeller.

For the blade at π/6 radians, we can use the parametric equations for a circle:

x = r cos(t) + h

y = r sin(t) + k

where t is the angle in radians.

Substituting r = 3, h = 0, k = 13, and t = π/6, we get:

x = 3 cos(π/6) + 0 = 3√3/2

y = 3 sin(π/6) + 13 = 13 + 3/2 = 15.5

So the height of the tip of the propeller blade at π/6 radians is 15.5 feet.

Using the same method for the blades at 5π/6 and 3π/2 radians, we get:

Blade at 5π/6 radians:

x = 3 cos(5π/6) + 0 = -3√3/2

y = 3 sin(5π/6) + 13 = 13 - 3/2 = 11.5

Height of tip: 11.5 feet

Blade at 3π/2 radians:

x = 3 cos(3π/2) + 0 = 0

y = 3 sin(3π/2) + 13 = 10

Height of tip: 10 feet

Therefore, the heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.

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Answer:

Since the prime factor '3' does not form a triplet , hence the given number is not a perfect cube.

No, it is not a perfect cube.

Step-by-step explanation:

3√3087 = 14.56

Answer:

yeah

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

13.85$

Step-by-step explanation:

105$-8$=97$

97$/7$=13.85$

Answer: About $13.86

Step-by-step explanation: To find how much the cost of the forks is, we need to subtract the value of the lunch box from the total cost, because we don't need to find the value of the lunch box. So:

105 - 8 = 97

So, now since he bought 7 forks, we need to divide 7 by 97. So:

97 / 7 = 13.857142857142858

So, we need to round to the nearest cent. So, the 7 is greater than 5, so we round up. So, we have $13.86 each. So, check, we do:

13.86(7) + 8

97.02 + 8

= 105.02

This is the closest he can buy for each fork is ABOUT $13.86. I hope this helps ;)

Answer:

Measure C, the Sacramento Community Stabilization and Fair Rent Charter Amendment is on the November ballot for the city of Sacramento after a lengthy court battle. The measure is written to supersede the Sacramento Tenant Protection Act, which was passed in 2019. Here are the results for Measure C as they come in:

Step-by-step explanation:

A rectangle with a diagonal of length x is twice as long as it is wide, the area of the rectangle is (B) 2x²/5..

Given that we have a rectangle with a diagonal of length x is twice as long as it is wide.

Let

L = length of rectangle,

W = width of rectangle and

D = length of diagonal = x

Given that the length of diagonal, x is twice as long as it is wide, we have that

L = 2W

Also, since it is rectangle, we have that

D² = L² + W²

D² = (2W)² + W²

D² = 4W² + W²

x² = 5W²

W² = x²/5

W = x/√5

W = x√5/5

since the length of the rectangle, L = 2W, we have that

L = 2W

= 2x√5/5

The area of the rectangle

The area of the rectangle is given by A = LW where

L = length of rectangle and

W = width of rectangle

So, A = LW

= 2x√5/5 × x√5/5

= 2x² × 5/25

= 2x²/5

So, the area of the rectangle is (B) 2x²/5

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The conditional statement "If a human being has 7 heads, then they have 11 arms" is false.

The statement is false because it is biologically impossible for a human to have 7 heads. The anatomy of a human being only allows for one head. Therefore, the statement is a contradiction and cannot be considered true.

Additionally, even if it were possible for a human to have 7 heads, it would not necessarily mean that they would have 11 arms. The statement makes an assumption that is not based on any scientific or logical evidence.

In conclusion, the statement "If a human being has 7 heads, then they have 11 arms" is false.

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The sketch to illustrate the question is given below

Since each of the bags are filled equally with 2 kilograms 450 grams of sand

Then we can sum two bags and compare the mass with 5 kilogram

We can see that the sum of two bags weighs 4 kilograms and 900 grams (4.90 kilograms) which is 100 grams less than 5 kilograms.

Thus we can conclude that the mass of 2 bags is LESS THAN 5 kilograms

area= b*h              

82.* 16.6

area= 1361.2     since i dont know the number after the decimal in 82. that was the only answer i could give

Answer:

Step-by-step explanation:

the simple interest formula= principal* interest rate*time

simple interest : 100000*%2*2 years

simple interest= 4000 dollars

compound quarterly : A=principal(1+r/4)^t

since it is quarterly and have 4 quarters in a year, and 8 in two years.

compound quarterly: 100000(1+0.03/4)^8=106159.88

it is better to invest with compound interest because it add 6159 dollars in two years to the investment of 100000 dollars.

the difference between the interest: 6159.88-4000=2159.88

Answer:

There are no graphs on the question

Step-by-step explanation:

To construct the first simplex tableau using the Big M method. The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

To construct the first simplex tableau using the Big M method, we first rewrite the problem in standard form as follows:

Maximize \(Z = 2x₁ + 5x₂ + 3x₃\)
subject to
\(x₁ - 2x₂ + x₃ + x₄ = 20\\2x₁ + 4x₂ + x₃ = 50\\x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0, x₄ ≥ 0.\)

To construct the initial simplex tableau, we introduce artificial variables x₅ and x₆ to the two equations.

The initial tableau is:

 Basis   |  x₁   |  x₂   |  x₃   |  x₄   |  x₅   |  x₆   |   RHS  
----------------------------------------------------------------------
    x₅    |   1    |   2    |   1    |   0    |   1    |   0    |   20    
    x₆    |   2    |   4    |   1    |   0    |   0    |   1    |   50    
----------------------------------------------------------------------
    -Z    |  -2    |  -5    |  -3    |   0    |   0    |   0    |   0    

The initial artificial basic solution is x₅ = 20 and x₆ = 50. The initial entering basic variable is x₁ and the leaving basic variable is x₅.

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Using the Big M method, the complete first simplex tableau for the given linear programming problem is constructed as follows:

┌─────────────┬──────┬───────┬───────┬─────┬─────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │ s₁  │ s₂  │ a₁  │      RHS    │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│      Z      │  2   │   5   │   3   │  0  │  0  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   x₁ - 2x₂  │  1   │  -2   │   1   │ -1  │  0  │  0  │     20      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│   2x₁ + 4x₂ │  2   │   4   │   1   │  0  │ -1  │  0  │     50      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₁      │  1   │   0   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₂      │  0   │   1   │   0   │  0  │  0  │ -M  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────┼─────────────┤

│     x₃      │  0   │   0   │   1   │  0  │  0  │ -M  │      0      │

└─────────────┴──────┴───────┴───────┴─────┴─────┴─────┴─────────────┘

The initial (artificial) basic solution is x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, a₁ = 0. The initial entering basic variable is x₁, which has the most positive coefficient in the objective row. The leaving basic variable is s₁, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the second row (20/1) is the smallest, so s₁ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first convert the given problem into standard form by introducing slack variables (s₁, s₂) for the inequalities and an artificial variable (a₁) for the equality constraint. We assign a large positive value (M) to the coefficients of the artificial variables in the objective row.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₁₂₃ are taken directly from the given problem. The slack variables and the artificial variable (a₁) have coefficients of 0 since they don't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables, slack variables, and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial (artificial) basic solution is obtained by setting the decision variables to 0, the slack variables and the artificial variable to the right-hand side values. In this case, x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 20, s₂ = 50, and a₁ = 0.

The initial entering basic variable is determined by selecting the most positive coefficient in the objective row, which is x₁ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. Since the ratio for the second row (20/1) is the smallest, s₁ leaves the basis.

The resulting tableau serves as the starting point for applying the simplex method to solve the linear programming problem iteratively.

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Answer:

A. step 1

Step-by-step explanation:

I think its A , because a negative plus a negative is a postive

Answer:

step 2 is the incorrect step

Answer:

= 4301693

Step-by-step explanation:

Given: 847x456+3599872+315589

Simplify the expression on the addition and multiplication sides:

386232 + 3915461

Then add:

= 4301693

Hello !

Answer:

\(\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Step-by-step explanation:

To find the volume of a cone with the radius of its base and its height, we will apply the following formula:

\( \sf V{cone} = \dfrac{\pi \times r^2 \times h}{3} \)

Where r is the radius of its base and h is its height.

Given:

Let's substitute our values into the formula:

\(\sf V{cone} = \dfrac{\pi (10)^2(23)}{3} = \dfrac{2300\pi}{3} \ \ \\\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Have a nice day ;)

Answer:

0.30

Step-by-step explanation:

P(x ≤ -3) = P(x=-3) + P(x=-5)

P(x ≤ -3) = 0.13 + 0.17

P(x ≤ -3) = 0.30

Answer:

0.30

Step-by-step explanation:

correct

The Radical Form (√x)  ,the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

The equation √x - 2 + 4 = x for x, we can follow these steps:

1. Begin by isolating the radical term (√x) on one side of the equation. Move the constant term (-2) and the linear term (+4) to the other side of the equation:

  √x = x - 4 + 2

2. Simplify the expression on the right side of the equation:

  √x = x - 2

3. Square both sides of the equation to eliminate the square root:

  (√x)^2 = (x - 2)^2

4. Simplify the equation further:

  x = (x - 2)^2

5. Expand the right side of the equation using the square of a binomial:

  x = (x - 2)(x - 2)

  x = x^2 - 2x - 2x + 4

  x = x^2 - 4x + 4

6. Move all terms to one side of the equation to set it equal to zero:

  x^2 - 4x + 4 - x = 0

  x^2 - 5x + 4 = 0

7. Factor the quadratic equation:

  (x - 1)(x - 4) = 0

8. Apply the zero product property and set each factor equal to zero:

  x - 1 = 0   or   x - 4 = 0

9. Solve for x in each equation:

  x = 1   or   x = 4

Therefore, the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

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The value of the test statistic is -1.75.

To test the claim that the percentage of uninsured patients is under the expected percentage of 32%, we can use a one-sample z-test. The null hypothesis is that the true percentage of uninsured patients is equal to 32%, while the alternative hypothesis is that the true percentage is less than 32%.

Using the sample data, we can calculate the sample proportion of uninsured patients as 40/160 = 0.25. We can then calculate the standard error of the sample proportion as sqrt[(0.32 x 0.68)/160] = 0.0385.

The test statistic can be calculated as (0.25 - 0.32)/0.0385 = -1.75.

To find the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator to find the probability of a z-score less than -1.75. The p-value is approximately 0.04.

Since the p-value is less than the typical significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the percentage of uninsured patients is under the expected percentage of 32%.

Therefore, the correct answer is -1.75, which is the calculated value of the test statistic.

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Answer:

5.83 ft

Step-by-step explanation:

Given that

Scale factor, n = 10

Wall in blueprint = 7 in

To find:

Length of actual wall = ?

Solution:

Whenever a blueprint is created for any house or building, it is made smaller by a scale factor.

Here this factor is 10 times.

That means, the blueprint size is 10 times smaller than that of its actual size.

Or we can say that actual wall of building is 10 times the wall of blueprint.

So, wall of building = 10 \(\times\) 7 = 70 inches

Now, we know that 12 inches = 1 ft

1 inch = \(\frac{1}{12}\ ft\)

70 inches = \(\frac{1}{12}\times 70\ ft = 5.83\ ft\)

so, the answer is Wall of building is 5.83 ft.

In conclusion, the correct answer is d) Straight.

The correct answer is d) Straight.

In geometry, an angle is formed by two rays that have a common endpoint. Angles can be classified based on the measure of their degree. A straight angle measures 180 degrees, which is the same as a straight line. It is formed by two opposite rays that point in opposite directions, and they create a straight line.

Therefore, an angle that measures 180 degrees is called a straight angle. In a straight angle, the two rays point in opposite directions and form a straight line. This angle is not acute, obtuse, or right because it doesn't form a triangle, and the degree measure is not less than 90 degrees or greater than 90 degrees.

In conclusion, the correct answer is d) Straight.

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Answer:

2) -3x+10

4) -4x+10+x

Step-by-step explanation:

Use the distributive property to get rid of the parentheses.

(2 × -2x) + (2 × 5) + x

-4x + 10 +x is correct, but the x's can be combined.

(-4x + x) + 10 = -3x + 10

\(\\ \sf\ast\Rrightarrow x^2-400\)

\(\\ \sf\ast\Rrightarrow (x)^2-(20)^2\)

\(\\ \sf\ast\Rrightarrow (x+20)(x-20)\)

Step-by-step explanation:

By the formula, [a²-b²=(a+b)(a-b)]

Hence, first option is correct

Answer: Its B. Side a is 2 inches long and side b is 1.5 inches long.

Step-by-step explanation:

The values represent the option (ii) If you were to play many cards, this is the average you should expect to pay per card.  

To calculate the average gold cost per card, we need to multiply each gold cost by its proportion and sum the results. This is equivalent to finding the weighted mean of the gold costs, with the proportions serving as the weights. Using the table values, we can calculate the average gold cost per card as follows:

Average gold cost per card = (1 x 0.13) + (2 x 0.21) + (3 x 0.48) + (4 x 0.18)

= 0.13 + 0.42 + 1.44 + 0.72

= 2.71

Therefore, on average, you should expect to pay 2.71 gold to play a card from your 74-card deck. This value represents the average amount of gold you will need to pay to play a card, not the most common amount or the amount you need to pay every time you play a card.

It is important to note that the actual gold cost for playing a card may vary from card to card, but the average gold cost per card should be close to the calculated value if you play a large number of cards.

Therefore, the correct option is (ii).

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Complete Question:

A certain game requires you to pay gold in order to play your cards. For a 74 card deck, the proportion of cards with various gold costs are given in the following table. Use 2 decimal places to answer the following questions when applicable.

Gold 1 2 3 4

Proportion 0.13 0.21 0.48 0.18

(a) What does this value represent?

(i) This is the most common amount of gold you will need to pay to play a card.

(ii) If you were to play many cards, this is the average you should expect to pay per card.

(iii) Every time you play a card, you will need to pay this much gold.

(iv) For every gold you spend, you should be able to play this many cards.

Hello !

\(a - (a - b) - b - (b - a)\\\\= a - a + b - b - b+a\\\\\boxed{= a - b}\)

Answer:

Step-by-step explanation:

a - ( a - b ) - b - ( b - a )

= a - a + b - b - b + a

= a - b

Answer:

5/6

Step-by-step explanation:

There is a 1 out of 2 chance that you will roll tails, so the probability is 1/2.

A number less than three is a 2 and 1, so the probability is 2/6.

Add 1/2 + 2/6. (Change 1/2 to 3/6 so you can add.)

3/6 + 2/6 = 5/6

I hope this is correct and helps you!

Answer:

Correct answer option A.

Step-by-step explanation:

We need to figure out the graph of

\(y= log_3(x + 2)\)

First of all, let us discuss graph of:

\(y=log_3x\)

\(y=log_31 = 0\) (\(\because\) log of 1 is always 0 irrespective of the base)

i.e. point (1, 0) lies on the graph.

i.e. \(x\rightarrow 1 \Rightarrow y\rightarrow -\infty\)

\(y =log_33 = 1\) i.e. point (3, 1)  lies on the graph

Graph of logarithmic function is always increasing.

Now, let us consider the graph of \(y= log_3(x + 2)\)

Please refer to attached graph as well.

Correct answer option A.

The correct option is A, just got it right (:

We can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

We have been given an expression  2x² + 12x + 8

We need to write given expression in the form a(a + b)² + c, where a, b and c are numbers.

2x² + 12x + 8

=  2x² + 12x + 18 - 18 + 8

= (√2x + 3√2)² - 10

= (√2)² (x + 3)² - 10

= 2(x + 3)² - 10

Comparing with a(a + b)² + c, where a, b and c are numbers.

a = 2, b = 3 and c = -10

Therefore, we can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

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