if the area of the vegetable garden is 170 square feet, which equation could be use to find the length of the tomato patch? select the correct answer.

John = 12 years old

Mike = 36 years old

=======================================================

Explanation:

j = John's current age

3j = Mike's current age, since he's three times as old as John.

Now fast forward the clock 12 years to get these future ages

j+12 = John's future age

3j+12 = Mike's future age

We're told that at this point in the future, Mike will be twice as old as John, so,

Mike's future age = 2*(John's future age)

3j+12 = 2*(j+12)

3j+12 = 2j+24

3j-2j = 24-12

j = 12

Therefore, John is currently 12 years old.

This makes Mike to be 3j = 3*12 = 36 years old currently.

Twelve years into the future John and Mike will be 12+12 = 24 and 36+12 = 48 respectively. Notice that 24*2 = 48 to help confirm the answers.

Answer: B: each electrician charges a different base fee

Step-by-step explanation:

Answer:

b.Each electrician charges a different base fee:

Explanation:

Each of the equations has two parts:

1- base fee that is independent of any variable (this would be the number that has no variable next to it)

2- an hourly rate depending on the number of hours x (this would be the number that has an x next to it)

For the first electrician:

y = 25x + 30

base fee = $30

hourly rate = $25

For the second electrician:

y = 30x + 25

base fee = $25

hourly rate = $30

For the third electrician:

y = 25x + 20

base fee = $20

hourly rate = $25

Now, let's check the choices:

a.Each electrician charges a different hourly rate:

This is incorrect as electricians 1 and 3 charge the same hourly rate ($25)

b.Each electrician charges a different base fee:

This is correct as all three base fees are different ($30, $20 and $25)

c.All three electricians charge the same hourly rate:

This is incorrect as electrician 2 has a different hourly rate

d. All three electricians charge the same base fee:

This is incorrect as the base fees for the three electricians are different ($30, $25 and $20)

The radius of the circle is half the diameter, so it is:

r = 12/2 = 6 feet

The area of the circle is given by the formula:

A = πr^2

Substituting r = 6 and π = 3.14, we get:

A = 3.14 * 6^2 = 113.04 square feet

Rounding to the nearest tenth, the area is:

A ≈ 113.0 square feet

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Answer:

D. 2x-3y=18

Step-by-step explanation:

1. multiply both sides by 3 to get rid of the fraction

( 3)(y)=(\(\frac{2}{3}\)x -6)(3)

2. That gives 3y=2x-18

3. subtract 2x on both sides

   3y=2x-18

 -2x = -2x

3. that gives -2x+3y=-18

4. then multiply by -1 to make 2x positive

 -1(-2x+3y=-18)

5. and that gives 2x-3y=18

Using the information given in the exercise, you can draw the following diagram:

Where β is the angle of depression (in degrees) from the edge of the diving board to the surface of the water where Sierra is located.

In order to find the measure of the angle of depression, you need to use the following Inverse trigonometric function:

In this case, you can identify that:

Therefore, substituting the values, you get the following result:

The answer is:

The correct answers are:

a. less a discount to yield 6.20%

d. plus a premium to yield 6.36%

Based on the provided information, the T bills maturing on August 2nd (8-2) are being offered at a bid yield of 6.36% and an ask yield of 6.20%.

To determine whether the T bills are being offered at a discount or a premium, we compare the bid yield and ask yield to the stated yields.

a. To yield 6.20% (ask yield), the T bills are being offered at a discount. Therefore, option a. "less a discount to yield 6.20%" is correct.

b. To yield 6.20%, the T bills are not being offered at a premium. Therefore, option b. "plus a premium to yield 6.20%" is incorrect.

c. To yield 6.36% (bid yield), the T bills are not being offered at a discount. Therefore, option c. "less a discount to yield 6.36%" is incorrect.

d. To yield 6.36%, the T bills are being offered at a premium. Therefore, option d. "plus a premium to yield 6.36%" is correct.

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Answer: 8.25$ + 2.25$m

hope this helped =)

Answer:

Its the last one

Step-by-step explanation:

-1/2 y(2y^3+8) is

-1 y^4 + 4 y

Answer:

\(x = 0\)

Step-by-step explanation:

Given

Represent the number with x.

So:

\(2 + x + x + x + x + x + x + x + x + x + x = 2\)

or

\(2 + 10x = 2\)

We want to solve for x

Subtract both sides by 2

\(2 - 2 + 10x = 2 - 2\)

\(10x = 0\)

Solve for x

\(x = \frac{0}{10}\)

\(x = 0\)

No other number aside 0, satisfy the property.

Answer:

False because for two fractions to be proportional they must be equivalent

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

The height of plant B growing at a rate of 3.33 centimeters per week should have a height of 19.98 cms.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

First we need two points (x, y) to obtain the slope.

Assuming height to be 'y' and weeks to be 'x'.

Therefore, (0, 0) and (3, 10) are the two points.

Slope(m) = (10 0)/(3 - 0).

Slope(m) = 10/3.

Slope(m) = 3.33

Now, To obtain the y-intercept.

10 = 3(3.33) + b

b = 0.01 Or neglegible.

Therefore y = 3.3x.

Now, In the 6th week, the height of plant B will be,

y = 3.33(6).

y = 19.98 or 20 cm.

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A The amount of money in a savings account with an annual interest rate of 1.5%

There are 30 ways to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.

To solve this problem, we need to use the formula for circular permutations, which is (n-1)! where n is the number of objects to be arranged in a circle. In this case, there are 6 people to be seated around a circular table, so the formula becomes (6-1)! = 5!.

However, we need to adjust this formula to account for the fact that two seatings are considered the same when everyone has the same two neighbors, regardless of whether they are right or left neighbors. To do this, we divide the result of the circular permutation by 2, since each seating has two possible orientations.

So the final answer is (5!)/2 = 60/2 = 30. There are 30 ways to seat six people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.

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Answer:2

Step-by-step explanation:

Answer:

-3 is the answer

Step-by-step explanation:

Answer: its A

Step-by-step explanation: Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(0,−1)

Focus: (0,−54)

Axis of Symmetry: x=0

Directrix: y=−3/4

x y

−2 −5

−1 −20

0 −1

1 −2

2 −5

Answer:

c = 6

Step-by-step explanation:

52 = 7 + 5(c = 3)

52 = 7 + 5c + 15

52 = 22 + 5c

-5c = 22 - 52

-5c = -30

c = \(\frac{-30}{-5}\)

c = 6

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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The total value of coins to create a silver mile following the specific rules stated is $38,114.18

63360 - 31650.48 = 31679.52 inches

A third of the distance is missing: 10559.84 inches

This means 10,559.84 inches/ 1.205 in = 8763.35 rounded to 8764

Total distance coverd 8,764 x 1.205 in = 10560.61

Total distance left: 31679.52 - 10560.61 = 21118,91 / 4 = 5279.72

This means 5279.72 / 0.750 =7039.62 rounded to 7040

7040 x 0.750 = 5280

Total distance left = 21118,91 -  5280 = 15,838.91 / 5 = 3167.782

This means 3167.82 / 0.705 = 4493.36 rounded to 4494

0.705 x 4494 = 3168.27

Total distance left = 15,838.91 - 3168.27 = 12670.64

This means 12670.64/ 0.835 = 15174.41 rounded to 15175

For this change the coins to dollars:

Susan B. Antony Silver dollars: 30462 = $30462

Half-dollars: 8764 = $4382

Quarters: 7040 = $1760

Dimes: 4494 = $561.75

Nickels: 15175 = $948.43

Total: $38114,18

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By substituting the values of A, S, D, and \(S^{(-1)}\) in the equation \(A = SDS^{(-1)}\), we can verify the diagonalization.

To find the matrix S, D, and \(S^{(-1)}\) such that \(A = SDS^{(-1)}\), we need to perform the diagonalization of matrix A.

Let's start by finding the eigenvalues of matrix A. The characteristic equation is given by:

|A - λI| = 0,

where A is the matrix, λ is the eigenvalue, and I is the identity matrix.

Using the given matrix A:

|12 - λ  -8|

|-6   2 -2|

| -2  -2  8| = 0.

Expanding the determinant and simplifying, we get:

(12 - λ)[(2 - λ)(8) - (-2)(-2)] - (-6)[(-6)(8) - (-2)(-2)] + (-2)[(-6)(-2) - (2)(-2)] = 0.

Simplifying further:

(12 - λ)[16 - 4λ + 4] + 36(8) + 4 = 0,

(12 - λ)(20 - 4λ) + 292 = 0,

240 - 48λ - 20λ + 4λ^2 + 292 = 0,

4λ^2 - 68λ + 532 = 0,

λ^2 - 17λ + 133 = 0.

Solving this quadratic equation, we find two distinct eigenvalues:

λ₁ = (17 + √(17^2 - 4(133))) / 2 = 8 + √7,

λ₂ = (17 - √(17^2 - 4(133))) / 2 = 8 - √7.

Next, we need to find the corresponding eigenvectors.

For λ₁ = 8 + √7:

Substituting back into (A - λI)X = 0, we get:

(12 - (8 + √7))x - 8y - 2z = 0,

-6x + (2 - (8 + √7))y - 2z = 0,

-2x - 2y + (8 - (8 + √7))z = 0.

Simplifying:

(4 - √7)x - 8y - 2z = 0,

-6x - √7y - 2z = 0,

-2x - 2y - √7z = 0.

Solving this system of equations, we find the eigenvector X₁ corresponding to λ₁.

Similarly, for λ₂ = 8 - √7, we find the eigenvector X₂.

Once we have the eigenvectors, we construct the matrix S by placing the eigenvectors as columns.

Finally, the diagonal matrix D is constructed by placing the corresponding eigenvalues along the diagonal.

Then, the inverse of matrix S, denoted as S^(-1), is calculated.

By substituting the values of A, S, D, and S^(-1) in the equation A = SDS^(-1), we can verify the diagonalization.

Therefore, the complete calculation involves finding the eigenvectors and performing matrix operations, which cannot be fully described in a text-based response. By using symbolic math software or a calculator to perform these calculations accurately.

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The probability that a poker hand consists of two jacks or two fives is approximately 0.009, or 0.9% when rounded to three decimal places.

To calculate the probability that a poker hand consists of two jacks or two fives, we need to determine the total number of possible two-card hands and the number of favorable outcomes (two jacks or two fives).

Step 1: Calculate the total number of possible two-card hands.
There are 52 cards in a standard deck. To form a two-card hand, we have 52 choices for the first card and 51 choices for the second card. Using the combination formula (nCr), the total number of possible hands is C(52, 2) = 52! / (2! * (52-2)!) = 1,326.

Step 2: Calculate the number of favorable outcomes.
There are 4 jacks and 4 fives in a deck, which gives us 8 possible cards to form our desired hands. For two jacks, there are C(4, 2) = 6 combinations. For two fives, there are also C(4, 2) = 6 combinations.

Step 3: Calculate the probability.
The total number of favorable outcomes is the sum of the combinations of two jacks and two fives, which is 6 + 6 = 12. Now, divide the number of favorable outcomes by the total number of possible hands:

Probability = (Number of favorable outcomes) / (Total number of possible hands) = 12 / 1,326 ≈ 0.00905

So, the probability that a poker hand consists of two jacks or two fives is approximately 0.009, or 0.9% when rounded to three decimal places.

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The equation of the parabola is y = -1/3 (\(x^2\)+4x).

What is parabola ?

  A bowl-shaped object forms a curve when the surface of the cone intersects a plane perpendicular to a straight line. Another curve is created when the moving point is moved such that the distance from the fixed point is equal to the distance from the fixed line. A parabola is a U-shaped curve representing the graph of a quadratic function. Graph of the equation y=x2,

Here the equation of the parabola is

=> y= a\(x^2\)+bx+c.

Now pt given points to find value of a, b, c .

=> y = a(x-p)(x-q)

=> y = a(x+2-2)(x+2+2)

=> y = a(x)(x+4)

Here the line passes through the point ,

(x,y) = (-1,1)

=> 1 = a(-1)(-1+4)

=> 1 = a (-3)

=> a = -1/3.

Now the equation is ,

y = a (x)(x+4)

=> y = -1/3 (\(x^2\)+4x)

Therefore the equation of the parabola is y = -1/3 (\(x^2\)+4x).

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let's call that point C, thus we get the splits of AC and CB

\(\textit{internal division of a line segment using ratios} \\\\\\ A(0,0)\qquad B(6,9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{2:1} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{1}\implies \cfrac{A}{B} = \cfrac{2}{1}\implies 1A=2B\implies 1(0,0)=2(6,9)\)

\((\stackrel{x}{0}~~,~~ \stackrel{y}{0})=(\stackrel{x}{12}~~,~~ \stackrel{y}{18}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{0 +12}}{2+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{0 +18}}{2+1} \right)} \\\\\\ C=\left( \cfrac{ 12 }{ 3 }~~,~~\cfrac{ 18}{ 3 } \right)\implies C=(4~~,~~6)\)

Answer:

0.83

Step-by-step explanation:

5 or more raise the score 4 or less let it rest

Elementary nostoligia :)

Answer:

Step-by-step explanation:

2

To develop the Branch and Bound (B&B) tree for the given problem, follow these steps:

1. Start with the initial B&B tree, where the root node represents the original problem.

2. Choose \($x_1$\) as the branching variable at node 0. Add two child nodes: one for

\($x_1 \leq \lfloor x_1 \rfloor$ \\(floor of $x_1$) and one for $x_1 \geq \lceil x_1 \rceil$ (ceiling of $x_1$).\)

3. At each node, perform the following steps:

  - Solve the relaxed linear programming (LP) problem for the node, ignoring the integer constraints.

  - If the LP solution is infeasible or the objective value is lower than the current best solution, prune the node and its subtree.

  - If the LP solution is integer, update the current best solution if the objective value is higher.

  - If the LP solution is non-integer, choose the fractional variable with the largest absolute difference from its rounded value as the branching variable.

4. Repeat steps 2 and 3 for each unpruned node until all nodes have been processed.

5. The node with the highest objective value among the integer feasible solutions is the optimal solution.

6. Optionally, backtrace through the tree to retrieve the optimal solution variables.

Note: The specific LP problem and its constraints are missing from the given question, so adapt the steps accordingly.

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The patient needs to take 4 tablets daily to receive the prescribed dose of 3 grams of the drug.

To determine how many tablets the patient needs to take daily, we need to divide the total amount of the drug prescribed by the dose of each tablet.

Since the patient is prescribed 3 grams of the drug daily, we first need to convert this to milligrams (mg), as the tablets are available in milligram form.

1 gram = 1000 milligrams, so 3 grams = 3,000 milligrams

The pharmacist has 750 mg tablets available, so we can calculate the number of tablets the patient needs to take daily by dividing the prescribed dose by the dose of each tablet:

Number of tablets = Prescribed dose ÷ Dose per tablet

Number of tablets = 3,000 mg ÷ 750 mg

Number of tablets = 4

Therefore, the patient needs to take 4 tablets daily to receive the prescribed dose of 3 grams of the drug.

Therefore, the patient will take 4 tablets daily.

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