the bus comes at 8:05. It takes me 31 minutes to get to the bus stop. What time should I leave to catch the bus?

The volume of the cylinder is 98π cubic centimeters.

To find the volume of a cylinder, we use the formula:

Volume = π × [tex]r^2[/tex] × h

Given:

Radius (r) = 7 cm

Height (h) = 2 cm

Substituting the values into the formula, we have:

Volume = π × (7 [tex]cm)^2[/tex] × 2 cm

Calculating the values inside the parentheses:

Volume = π × 49 [tex]cm^2[/tex] × 2 cm

Multiplying the values:

Volume = 98π [tex]cm^3[/tex]

Therefore, the volume of the cylinder is 98π cubic centimeters.

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Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.

Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.

So the expression becomes:

-14 + 8

To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:

(-14) + (8) = -14 * 1 + (-14) * 8

This can be simplified as:

-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)

Finally, we can add the two negative numbers to get the result:

-14 + (-112) = -126

Therefore, the expression -14 - (-8) factors completely as -126.

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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y intercept will be 0,-6 .

Given,

Amplitude = 6

Time period = pi

Phase shift = pi/4

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side(perpendicular) to that of the hypotenuse in a right-angled triangle.

The sine function is used to find the unknown angle or sides of a right angled triangle.

Mathematically,

sinФ = p/h

Now ,

Let us assume the phase shift to be on right side.

So the graph will be at negative y axis.

Thus the points will be 0 , -6 .

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The balance after 4 years on $2000 at 4% is equal to $2320.

In Mathematics, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 2000 × 4/100 × 4

S.I = 2000 × 0.04 × 4

S.I = $320.

Next, we would calculate the future value as follows;

Future value, A = S.I + P

Future value, A = $320 + $2000

Future value, A = $2320.

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Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Answer:

900 kg

Step-by-step explanation:

Let's assume the cost price (C.P.) of sugar is Rs. x per kg.

The total quantity of sugar is 1500 kg.

Let the quantity of sugar sold at 8% profit be represented by y kg.

The quantity of sugar sold at 18% profit would then be (1500 - y) kg.

Using the rule of alligation, we can set up the following proportion:

(8% profit) y kg

-------------- = ------

(18% profit) (1500 - y) kg

Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).

The ratio of these differences is 2:3.

This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.

Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:

(2 kg) * (3/2) = 3 kg

Therefore, the quantity sold at 18% profit is 900 kg.

The square inches of cardboard paper used is 56.8 square inches

From the question, we have the following parameters that can be used in our computation:

The prism

The square inches of cardboard paper is the surface area of the pyramid

And this is calculated as

Area = bh + L(Sum of side lengths)

Using the above as a guide, we have the following:

Area = 2 * 3.2 + 6 * (2 + 3.2 + 3.2)

Evaluate

Area = 56.8

Hence, the square inches of construction paper used to make the container is 56.8 square inches

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The quotient of[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.

To simplify the expression[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10)),[/tex] we can use the rule for dividing fractions, which states that dividing by a fraction is the same as multiplying by its reciprocal.

Let's simplify the expression :

Simplify the numerator and denominator of the first fraction.

The numerator is 6x, and the denominator is (3x+15).

We can factor out a common factor of 3 from the denominator, which gives us 3(x+5).

So the first fraction simplifies to 6x / 3(x+5).

Simplify the numerator and denominator of the second fraction.

The numerator is (x^2+2x), and the denominator is [tex](x^2+7x+10).[/tex]

We can factor both the numerator and denominator:

Numerator: x(x+2)

Denominator: (x+5)(x+2)

Canceling out the common factor of (x+2), we are left with x / (x+5).

Multiply the two simplified fractions.

Multiplying the fractions, we get:

[tex](6x / 3(x+5)) \times (x / (x+5))[/tex]

Simplify the resulting expression.

Canceling out the common factor of (x+5) in the numerator and denominator, we are left with:

2x / 1

So the quotient simplifies to 2x.

Therefore, the quotient of [tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.

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The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]  

and the slope formula:

m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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When you know the volume of a prism and some dimensions, you can solve for an unknown dimension.

When armed with knowledge about the volume of a prism alongside certain known dimensions, the possibility emerges to determine an elusive dimension within the prism. By leveraging the given information, the missing dimension can be unearthed, unraveling the intricacies of the prism's complete set of measurements.

This calculation empowers us to gain a comprehensive understanding of the geometric structure, further enriching our grasp of its spatial characteristics. The interplay between the volume and the known dimensions acts as a gateway to unlocking the enigma of the unknown dimension.

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The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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If u =(1+i√3) and v=(1-i√3), product uv is: D. 4.

To find the product of u and v let us simply multiply them together:

u = 1 + i√3

v = 1 - i√3

uv = (1 + i√3)(1 - i√3)

Using the difference of squares formula (a² - b² = (a + b)(a - b)) we can simplify the expression:

uv = (1 + i√3)(1 - i√3)

uv= 1² - (i√3)²

uv= 1 - (-3)

uv= 1 + 3

uv= 4

Therefore the product uv is equal to 4.

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Both planes will reach the city at the same time again at 11 PM.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for this problem are given as follows:

As 5 and 3 are prime numbers, the least common factor is given as follows:

5 x 3 = 15.

15 hours after 8 AM is of 11 PM.

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Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.

In order to answer your question accurately, I would need the specific values for Manuel's profit and cost functions. The information you provided is incomplete, as you mentioned Manuel's initial profit hill is plotted in green on a graph, but the graph itself is not available for reference.

To determine how a change in fixed costs affects the profit-maximizing quantity, we typically analyze the cost and revenue functions. Without these functions or the corresponding data, it is not possible to provide an exact numerical answer.

However, I can explain the general concept. Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.

When fixed costs decrease, it reduces the overall cost of production for each level of output. This means that Manuel can achieve higher profits or reduce losses for any given level of sales. Consequently, the profit-maximizing quantity may change as a result.

If we assume that the decrease in the price of the permit is the only change in fixed costs and all other factors remain constant, the new profit hill can be expected to shift upward. This is because the reduction in fixed costs increases the potential for higher profits at each level of output.

Without more specific information about Manuel's profit and cost functions, it is not possible to determine the exact profit-maximizing levels before and after the decrease in the price of the permit.

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The equation of the parabola with focus (3, 4) and directrix y = 1 is [tex]x^2 - 6x - 12y + 57 = 0.[/tex]

To find the equation of a parabola with a given focus and directrix, we can use the standard form of the equation of a parabola:  

[tex]4p(y - k) = (x - h)^2[/tex]  

where (h, k) represents the coordinates of the vertex, and p is the distance between the vertex and the focus or directrix.

In this case, the focus is given as (3, 4), which means the vertex of the parabola will also be located at (3, 4).

The directrix is given as y = 1.

First, let's find the value of p, which is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p will be the distance between the vertex (3, 4) and the directrix y = 1.

Since the directrix is a horizontal line, the distance between the vertex and the directrix is the vertical distance, which is |4 - 1| = 3.

Now that we have the value of p, we can substitute it into the equation:

[tex]4p(y - k) = (x - h)^2[/tex]

Plugging in the values (h, k) = (3, 4) and p = 3, we get:

[tex]4(3)(y - 4) = (x - 3)^2[/tex]

Simplifying further:

[tex]12(y - 4) = (x - 3)^2[/tex]

Expanding the equation:

[tex]12y - 48 = x^2 - 6x + 9[/tex]

Bringing all terms to one side:

[tex]x^2 - 6x - 12y + 57 = 0[/tex]

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Step-by-step explanation:

Multiply the L side of the equation by  d/d   ( this is just multiplying by 'one' )

2/d  * d/d   =  2d / d^2

The length x in the similar triangles is given as follows:

x = 15 cm.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The proportional relationship for the side lengths in this triangle is given as follows:

x/25 = 9/15 = 18/30

Hence the value of x is obtained as follows:

x/25 = 9/15

15x = 25 x 9

x = 25 x 9/15

x = 15 cm.

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The first five terms of the following generalized Fibonacci sequence are -19, 14, -5, 9, 4

From the question, we have the following parameters that can be used in our computation:

The generalized Fibonacci sequence

In the sequence, we can see that the last two terms are added to get the new term

Also, we have

a(1) = -19

a(2) = 14

Using the above as a guide, we have the following:

a(3) = -19 + 14 = -5

a(4) = -5 + 14 = 9

a(5) = 9 - 5 = 4

Hence, the first five terms of the following generalized Fibonacci sequence are -19, 14, -5, 9, 4

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Answer:

When [tex]x=0[/tex], the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: [tex]f(x)=1\cdot 4^x[/tex]

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

189

Step-by-step explanation:

To multiply 31.5 percent by 600, you need to convert the percentage to a decimal by dividing it by 100 and then multiply it by 600.

31.5 percent = 31.5/100 = 0.315

Multiplying 0.315 by 600 gives us:

0.315 * 600 = 189

Therefore, 31.5 percent of 600 is equal to 189.

Answer:

Step-by-step explanation:

The  expression represents the total surface area of the prism is

2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

The term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the  sum of the areas of all the faces (including the bases) of the prism.

for the rectangular prism, the Total Surface Area can be calculated using the formula:

TSA = 2lw + 2lh + 2wh

where

l = 5

w = 4

h = 7

plugging in the values gives

TSA = 2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

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The area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is given as 3 cm and the width is given as 2 cm.

Area of the rectangle = Length * Width

Plugging in the given values:

Area = 3 cm * 2 cm

Multiplying 3 cm by 2 cm gives us:

Area = 6 cm²

Therefore, the area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

The area of a rectangle represents the amount of space enclosed within its boundaries. In this case, since the rectangle is two-dimensional, the area is measured in square units, which in this case is square centimeters (cm²).

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Answer:

Step-by-step explanation:

the answer is 69 the if we round of

4 will divide the 348 is 8 and 2 left, so you will write the two and move the 8 down, which is now 28, then divide the 28 by 4. It will be 7.

Answer:

Set your calculator to degree mode.

x^2 = 4^2 + 10^2 - 2(4)(10)(cos 29°)

x^2 = 46.0304

x = 6.78

The number that belongs in the green box is 6.78.