Bus A and Bus B leave the the bus depot at 2 pm.

Bus A takes 15 minutes to complete its route once and bus B takes 25 minutes to complete its route once.

If both buses continue to repeat their route, at what time will they be back at the bus depot together?

Assume the buses have have no breaks in between routes.

Give your answer as a 12-hour clock time.

Answer:

The answer is 1001101

Step-by-step explanation:

77 base 10 to base 2 is 1001101

Answer:

Another order pair could be (30,10).

Every y value is "one-third of" every x value.

Answer: Domain: (-∞, 0) U (0, ∞)

Step-by-step explanation:

\(\frac{12}{x} *-8x^{3}\)

\(=-96x^2\)

Domain: (-∞, 0) U (0, ∞)

Answer:

87.357

Step-by-step explanation:

use TOA to solve for the missing angle

let x= angle

tan(x)=5200/240

x=87.357

Answer:

145 degrees

Step-by-step explanation:

Same side interior angles theorem.

Answer:

1/3

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

Of the given polynomials, only option C is a quartic trinomial, as it is degree 4 and consists of three monic terms, each having a coefficient of 1:-2x^4 + 7x^2 - 5

Step-by-step explanation:

A quartic trinomial is a degree 4 polynomial consisting of three distinct monic terms, each having the same coefficient. A monic term is a polynomial term whose highest exponent is 1 and whose coefficient is 1.

Option A is a quadratic trinomial (degree 2) and options B and D are not degree 4 trinomials.

Answer:

3n^2(n−7)^2

Hope this helps you a lot!!!! Also sorry I dont have work its hard to explain on a computer.

Answer:

\(\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}\)

Step-by-step explanation:

Given

\(\{(5, -9), (6, -6), (-3, 8), (9, -6)\}\)

\(\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}\)

\(\{(1, -1), (-5, 7), (4, -9), (-9, 7)\}\)

\(\{(8, -9), (-3, -6), (-4, 4), (1, -5)\}\)

Required

Which is not a function

An ordered pair is represented as:

\(\{(x_1,y_1),(x_2,y_2),(x_3,y_3),..........,(x_n,y_n)\}\)

However, for the ordered pair to be a function; all the x values must be unique (i.e. not repeated)

From options (a) to (d), option (b) has -6 repeated twice. Hence, it is not a function.

A. The height of the flagpole is 32 meters.

Let x be the height of the flagpole. According to the problem, we have two similar triangles: one formed by the flagpole and its shadow, and the other formed by the person and their shadow.

The height of the person is 2 meters and their shadow is 8 meters, so the ratio of their height to their shadow is 2/8 = 1/4. Similarly, the ratio of the height of the flagpole to its shadow is x/16.

Since the triangles are similar, these ratios must be equal: x/16 = 1/4. Solving for x, we get x = 16*4 = 64 meters. Therefore, the height of the flagpole is 64 meters.

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Answer:

you have to

Step-by-step explanation:

Answer:

2700 I think?

Step-by-step explanation:

Um 3/ 1/4 = 12 and 3 3/4 / 1/4 = 15 so 15 * 12 * 15 is 2700

The image is then dilated by a scale factor of half with a center of dilation of (1, 2); Preimage (8, 4), (4, -4), and (1, 2) → Image (1, 2), (2.5, -1), and (4.5, 3).

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

The coordinates of the vertices of the preimage will be;

(5, 10), (2, 4), (9, 2)

The coordinates of the vertices of the image will be;

(-9, -2), (-2, -4), (-5, -10)

This is equivalent to a reflection about the origin, and a rotation of 180° clockwise or anticlockwise about the origin.

Part B: Figure 2 to Figure 5

The coordinate points of figure 2 will be;

(-9, 2), (-5, 10), and (-2, 4)

The coordinate points of figure 5 will be;

(1, 2), (2.5, -1), and (4.5, 3)

The lengths of the sides of figure 2 will be;

√((10 - 2)² + ((-5) - (-9))²) = 4·√5

√((10 - 4)² + ((-5) - (-2))²) = 3·√5

√((2 - 4)² + ((-9) - (-2))²) = √53

The lengths of the sides of figure 5 will be;

√(((-1) - 2)² + (2.5 - 1)²) = (3·√5)/2

√((4.5 - 2.5)² + (3 - (-1))²) = 2·√5

√((4.5 - 1)² + (3 - 2)²) = (√53)/2

Thus, Figure 5 is Figure 2 dilated by a scale factor of 1/2(half )

Therefore, the given sides of Figure 2 and Figure 5 are rotated by 180°

1) The rotation of figure 2 by 180° about the origin to get;

(-9, 2), (-5, 10), and (-2, 4) →   (9, -2), (5, -10), and (2, -4)

2) The image is translated left by 1 blocks and up by 6 blocks as;  

(9, -2), (5, -10), and (2, -4)  →   (8, 4), (4, -4), and (1, 2)

3) The image is then dilated by a scale factor of half with a center of dilation of (1, 2);

Preimage (8, 4), (4, -4), and (1, 2) → Image (1, 2), (2.5, -1), and (4.5, 3).

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Answer:

To calculate the remaining grams of the isotope after 120 days, we need to determine the number of half-lives that have occurred within that time frame.

Given:

Half-life of the isotope = 70 days

Initial mass of the isotope = 600 grams

Time elapsed = 120 days

To find the number of half-lives, we divide the elapsed time by the half-life:

Number of half-lives = elapsed time / half-life

= 120 days / 70 days

≈ 1.714 (rounded to three decimal places)

Since we cannot have a fraction of a half-life, we consider the integer part, which is 1. This means that one full half-life has occurred within the 120-day period.

To calculate the remaining mass, we use the formula:

Remaining mass = Initial mass * (1/2)^(Number of half-lives)

Substituting the values:

Remaining mass = 600 grams * (1/2)^(1)

= 600 grams * 0.5

= 300 grams

Therefore, after 120 days, approximately 300 grams of the radioactive isotope remains.

Answer:

answers are below

Answer:

75

Step-by-step explanation:

Answer:

i think it's 5/4

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

.

Answer:

c) 3.4 in

Step-by-step explanation:

Answer:

10 cards

Step-by-step explanation:

So to do this problem, you can make an equation where x is the number of cards sold, which would be:

7x - 20 - 5x = 0

This is because she makes $7 for every card she sells (so 7x), she paid $20 for the booth (so -20), it costs her $5 to make every card (so -5x), and you want to see how many cards it will take for her to cover everything she spent (so it would equal 0).

Then, solving:

\(7x-20-5x=0\)

combine like terms

\(2x-20=0\)

add 20 to both sides

\(2x = 20\)

divide both sides by 2

\(x = 10\)

This means the answer is 10 cards

The variable X has a binomial distribution in the following distributions:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.

In a binomial distribution, we have a fixed number of independent trials (in this case, the number of patients), and each trial has only two possible outcomes (success or failure). The probability of success remains the same for each trial (in this case, the probability of the medicine working is 30%).

Option B does not represent a binomial distribution since it counts the number of patients for whom the medicine does not work, which is the complement of success. Option D is not a binomial distribution as it counts the number of doses each patient needs to take, which is not a success/failure outcome.

So, the correct answers are:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

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Answer:

hi,

Step-by-step explanation:

Let say P=(x,y) a point of the locus

\(Distance\ from\ P\ to\ (2,1)= \sqrt{(x-2)^2+(y-1)^2} \\Distance\ from\ P\ to\ (1,2)= \sqrt{(x-1)^2+(y-2)^2} \\\\\sqrt{(x-2)^2+(y-1)^2} =2*\sqrt{(x-1)^2+(y-2)^2} \\\\(x-2)^2+(y-1)^2=4*((x-1)^2+(y-2)^2)\\\\3x^2-4x+3y^2-14y+15=0\\\\\)

\(3x^2-4x+3y^2-14y+15=0\\3(x^2-2*\dfrac{2}{3} x)+3(y^2-2*\dfrac{7}{3}*y) +15=0\\3(x^2-2*\dfrac{2}{3}*x+\dfrac{4}{9})+3(y^2-2*\dfrac{7}{3}*y+\dfrac{49}{9} ) +15-\dfrac{4}{3}-\dfrac{49}{3}=0\\\\3(x-\dfrac{2}{3})^2+3(y-\dfrac{7}{3})^2-\dfrac{8}{3}=0\\\\\\\boxed{(x-\dfrac{2}{3})^2+(y-\dfrac{7}{3})^2=\dfrac{8}{9}}\\\\\)

Locus is the circle of center (2/3,7/3) and radius =2√2  /3.

Given:

The expression is:

\(8(39+11)\)

To find:

The simplified form of the given expression by using the Distributive Property.

Solution:

Distributive property of multiplication over addition:

\(a(b+c)=ab+ac\)

We have,

\(8(39+11)\)

Using Distributive property of multiplication over addition, we get

\(8(39+11)=(8\times 39)+(8\times 11)\)

\(8(39+11)=312+88\)

\(8(39+11)=400\)

Therefore, the correct option is D.

Answer:

A)  If the constant is grouped with x, the result will be a horizontal dilation.

Step-by-step explanation:

If a transformation happens inside the parent function, it is horizontal.

Applying the midsegment theorem, the value of x = 5

Recall:

Thus:

DE = 1/2(AC)

2x - 3 = 1/2(x + 9)

2(2x - 3) = x + 9

4x - 6 = x + 9

4x - x = 6 + 9

3x = 15

x = 5

Therefore, applying the midsegment theorem, the value of x = 5

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Answer:

Step-by-step explanation:

  [1]    3x - 4y = -24

  [2]    -x - 16y = -52

Graphic Representation of the Equations :

   -4y + 3x = -24        -16y - x = -52  

Solve by Substitution :

// Solve equation [2] for the variable  x

 [2]    x = -16y + 52

// Plug this in for variable  x  in equation [1]

  [1]    3•(-16y+52) - 4y = -24

  [1]     - 52y = -180

// Solve equation [1] for the variable  y

  [1]    52y = 180

  [1]    y = 45/13

// By now we know this much :

   x = -16y+52

   y = 45/13

// Use the  y  value to solve for  x

   x = -16(45/13)+52 = -44/13

Solution :

{x,y} = {-44/13,45/13}

The maximum profit per day is $600, and the soft-drink vendor must sell 1,500 cans to achieve this maximum profit.

The profit function for the soft-drink vendor is given by P(x) = -0.001x^2 + 3x - 1800. To find the maximum profit per day and the number of cans to sell for maximum profit, follow these steps:

1. Identify the quadratic function: In this case, it's P(x) = -0.001x^2 + 3x - 1800.

2. Find the vertex of the parabola, which represents the maximum profit point. The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a and b are the coefficients of the quadratic function (a = -0.001, b = 3).

3. Calculate the x-coordinate of the vertex: x = -3 / (2 * -0.001) = -3 / -0.002 = 1500.

4. Substitute the x-coordinate back into the profit function to find the maximum profit: P(1500) = -0.001(1500)^2 + 3(1500) - 1800 = $600.

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There are 15 different possibilities for the three whole numbers whose product is 120.

To find the different possibilities for the three whole numbers, we need to find all the ways we can multiply three whole numbers together to get 120, which is the product.

We can start by listing out the factors of 120:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

From this list, we can start trying out combinations of three numbers that multiply to 120. For example:

1 x 1 x 120 = 120
1 x 2 x 60 = 120
1 x 3 x 40 = 120
1 x 4 x 30 = 120
1 x 5 x 24 = 120
1 x 6 x 20 = 120
1 x 8 x 15 = 120
2 x 3 x 20 = 120
2 x 4 x 15 = 120
2 x 5 x 12 = 120
2 x 6 x 10 = 120
3 x 4 x 10 = 120
3 x 5 x 8 = 120
4 x 5 x 6 = 120

So there are 15 different possibilities for the three whole numbers that multiply to 120.
To find the different possibilities for the three whole numbers whose product is 120, we need to find the combinations of factors of 120.

Step 1: Find the prime factorization of 120.
\(120 = 2*2*2*3*5 (2^3 * 3 * 5)\)

Step 2: Identify the possible factors.
Using the prime factors, we can generate the different whole number factors for 120:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Step 3: Find the possible combinations of three whole numbers.
1. 1 × 1 × 120
2. 1 × 2 × 60
3. 1 × 3 × 40
4. 1 × 4 × 30
5. 1 × 5 × 24
6. 1 × 6 × 20
7. 1 × 8 × 15
8. 1 × 10 × 12
9. 2 × 2 × 30
10. 2 × 3 × 20
11. 2 × 4 × 15
12. 2 × 5 × 12
13. 2 × 6 × 10
14. 3 × 4 × 10
15. 3 × 5 × 8

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Set of factors can be rearranged in six different ways, there are actually 60 possible ways to arrange the factors into three numbers.

The possible combinations of three whole numbers that result in a product of 120.

One way to approach this is to list all the factors of 120 and then group them into sets of three.

Another method is to use prime factorization.

120 as a product of its prime factors: 2 x 2 x 2 x 3 x 5.

The possible combinations of three factors, we can use a combination formula.
The formula for the number of combinations of n items taken r at a time is:

\(nCr = n! / (r! \times (n-r)!)\)
In our case, n = 5 (the number of prime factors), and r = 3 (the number of factors we want to choose).

So, the number of possible combinations is:
\(5C3 = 5! / (3! \times 2!) = (5 \times 4 \times 3) / (3 \times 2) = 10\)
There are 10 different possibilities for the three whole numbers that multiply to 120.

These are:
\(\(2 \times 2  \times 30, 2  \times 3  \times 20, 2  \times 4 \times 15, 2  \times 5  \times 12, 2  \times 6  \times 10, 3  \times 4  \times 10, 3  \times 5  \times 8, 4  \times 5  \times 6, 3  \times 2  \times 20, and  5  \times 2  \times 12.\)\)
The order of the factors does not matter, so\(2 \times 3 \times 20\) is the same as\(3 \times 2 \times 20\).

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Answer:

\(\text{the volume of the prism =} \ 4\frac{1}{2} \ ft^3\)

Step-by-step explanation:

Formula _____________________

the volume of a prism = base × height

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

\(\text{base\ =} \ 2\times 1\frac{1}{2} =2\times \left( 1+\frac{1}{2} \right) =2\times \left( \frac{3}{2} \right) =3\)

\(\text{the volume of the prism =} \ 3\times \left( 1\frac{1}{2} \right) =3\times \left( \frac{3}{2} \right) =\frac{9}{2} =4\frac{1}{2}\)

Answer:

B

Step-by-step explanation:

The equation of the line is shown in the graph which passes through the points (2,3) and (0,-2) will be y-3=2.5(x-2). Option A is correct.

A straight line is a combination of endless points joined on both sides of the point.

It is given that, a line is drawn which passes through the points (2,3) and (0,-2).

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

The slope of the line is,

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{-2-3}{0-2} \\\\ m=\frac{5}{2}\)

The equation of the line will be,

y-y₁ =m(x-x₁)

y-3=5/2(x-2)

y-3=2.5(x-2)

Thus, the equation of the line shown in the graph which passes through the points (2,3) and (0,-2) will be y-3=2.5(x-2). Option A is correct.

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Answer:

I think D

Step-by-step explanation:

because all the information seems important