when juggling, a ball travels in a complete circle every 2 seconds. how many circle would the ball travel in two minutes?

The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:

-5y = -375

1. Given equations:

  - x + 3y = 350    (Equation 1)

  - 2x + 4y = 625   (Equation 2)

2. Multiply Equation 1 by 2:

  - 2(x + 3y) = 2(350)

  - 2x + 6y = 700    (Equation 3)

3. Subtract Equation 2 from Equation 3:

  - (2x + 6y) - (2x + 4y) = 700 - 625

  - 2x - 2x + 6y - 4y = 75

  - 2y = 75

4. Simplify Equation 4:

  -2y = 75

5. To isolate the variable y, divide both sides of Equation 5 by -2:

  y = 75 / -2

  y = -37.5

6. Therefore, the resulting equation is:

  -5y = -375

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Determine the value of x.

So there are 45 markers originally in each box.

Answer:

The quotient is 2x+1. The remainder is 2x-2

Step-by-step explanation:

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

The club must sell 18 jackets to break even

Step-by-step explanation:

Given:

C = 20x + 270

Where,

x = number of jackets

Equation for revenue R in terms of the number of jackets

Revenue = price × quantity

Price of the jacket = $35

Quantity of the jacket = x

Revenue = price × quantity

= 35 * x

R = 35x

Break even point is the point at which cost is equal to revenue, that is, no gain; no loss.

Cost = revenue

20x + 270 = 35x

270 = 35x - 20x

270 = 15x

x = 270 / 15

= 18

x = 18 jackets

The club must sell 18 jackets to break even

Answer:

torture

Step-by-step explanation:

I was just working on a prblem like this and I hate it

Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.

To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.

Total weekly cost = Fixed rate + Insurance cost + Gas cost

Total weekly cost = $49.00 + $14.00 + $12.00

Total weekly cost = $75.00

The cost for Thanh per month (four weeks) = Total weekly cost × 4

Cost for Thanh per month (four weeks) = $75.00 × 4

Cost for Thanh per month (four weeks) = $300.00

Therefore, Thanh's cost per month (four weeks) will be $300.00.

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Answer:

  (a)  $479.50

Step-by-step explanation:

You want to know how much the friend with the smaller bedroom will pay for rent if they split the $975 cost based on the square footage of each bedroom. The two bedrooms in the 1225 square foot property are 130 and 150 square feet.

Apparently, the cost of the non-bedroom area is to be split evenly. That common area is ...

  1225 ft² -(150 +130) ft² = 945 ft²

Then the proportion due from the occupant of the smaller bedroom is ...

  (945/2 +130)/1225 = 241/490 ≈ 0.49184

That fraction of the rent is ...

  0.49184 · $975 = $479.54

The nearest answer choice is $479.50.

__

Additional comment

If we were to assume the split is based only on bedroom size, then the rent paid for the 130 ft² space would be (13/28)($975) ≈ $452.68. This would be equivalent to splitting the rent for the common area in the same proportion as for the bedrooms.

We note that half the rent is $487.50, a number less than either of the last two answer choices. Those can be rejected for that reason. (The smaller bedroom is expected to pay less than half of the rent.)

Answer:

C) It is one-half the area of a rectangle of length 4 units and width 5 units.

The total area of the triangle is 10, which we get by multiplying the height (5) times the base (4), which will be 20, and then dividing by 2, which is 10!

Given this information, we can start eliminating answers.

A) It is twice the area of a rectangle of length 4 units and width 5 units. This is answer is wrong, as the area of a rectangle with a length of 4, and a width of 5, is 20. Meaning that in order for this to be true, the area of the rectangle must be 40, which it is not.

B) It is one-half the area of a rectangle of length 4 units and width 5 units.

This is answer is right, as the area of a rectangle with a length of 4, and a width of 5, is 20, and half of that would be 10, which is half of the area of the triangle!

C) It is twice the area of a square of side length 5 units.

This answer is also wrong because the area of a square with side lengths of 5 would be 25, which is not half of the area of the triangle. In order for this to be true, the area of the rectangle must be 50, which it is not.

D) It is one-half the area of a square of side length 5 units.

This answer is wrong because the area of a square with side lengths of 5, would be 25, which is not twice the the area of the triangle. In order for this to be true, the area of the rectangle must be 12.5, which it is not.

Answer:

\(p_{o} = 6\), \(r = 2\), \(p_{12} = 24576\).

Step-by-step explanation:

The value of \(p_{o}\) is the first value of the geometric series, that is, \(p_{o} = 6\).

If the series represents a geometric sequence, then \(r\) must be constant for every consecutive pair of elements, that is:

\(r_{1} = \frac{p_{1}}{p_{o}} = \frac{12}{6} = 2\)

\(r_{2} = \frac{p_{2}}{p_{1}} = \frac{24}{12} = 2\)

\(r_{3} = \frac{p_{3}}{p_{2}} = \frac{48}{24} = 2\)

Since \(r_{1} = r_{2} = r_{3} = 2\), \(r = 2\).

The geometric sequence can be represented by the following formula:

\(p_{n} = p_{o}\cdot r^{n}\), for \(n \in \mathbb{N}\)

The 12th element of the geometric sequence is: (\(p_{o} = 6\), \(r = 2\), \(n = 12\))

\(p_{12} = 6\cdot 2^{12}\)

\(p_{12} = 24576\)

The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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The five key points of the parent function are:

The function is given as:

y = -2 sin[2(x - 45)] + 1

The above function is a sine function, and the parent function of a sine function is

y = sin(x)

The properties of the above function are:

The transformed function is given as:

y = -2 sin[2(x - 45)] + 1

A sine function is represented as:

y = A sin[Bx + C] + D

Where:

Using the above representations, we have:

See attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1

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Answer:

third option

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Given

g(x) = \(3^{x}\) + 5 ← this represents a shift up of 5 units

Thus g(x) is the graph of f(x) translated up by 5 units

Answer:

\(\boxed{\sf{Option \: 3}}\)

Step-by-step explanation:

g(x) is translated up 5 units compared to f(x). In a vertical translation, when the graph is moved 5 units up, 5 is added to the function. When the graph is moved 5 units down, 5 is subtracted from the function. The graphs are shifted  in the direction of the y-axis.

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

The volume of the rectangular prism is 512 inches³

Step-by-step explanation:

Any cube has 6 square faces

Area of any square = L × L, where L is a length of each side

The volume of the cube = L × L × L

∵ The area of the top face of a cube = 16 inches²

→ Find which number multiply by itself = 16

∵ 16 = L × L

∵ 16 = 4 × 4

∴ L = 4 inches

Let us find the volume of 1 cube

∵ The volume of the cube = L × L × L

∵ L = 4 inches

∴ The volume of each cube = 4 × 4 × 4

∴ The volume of each cube = 64 inches³

∵ We will use 8 of this cube to make a rectangular prism

→ That means the volume of the rectangular prism is 8 times

   the volume of 1 cube

∴ The volume of the prism = 8 × volume of 1 cube

∵ The volume of each cube = 64 inches³

∴ The volume of the prism = 8 × 64

∴ The volume of the prism = 512 inches³

The volume of the rectangular prism is 512 inches³

Answer:

If a swimming pool contains 6.8 × 10³ gallons of water and is leaking at a rate of 12-1 gallons per second, then it will take (6.8 × 10³) / (12-1) = 6800 / 11 ≈ 618.18 seconds for all of the water to leak out of the pool. Since there are 3600 seconds in an hour, it will take approximately 618.18 / 3600 ≈ 0.17 hours or about 10 minutes for all of the water to leak out of the pool.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can start by using the leak rate to determine how much water is lost in one second:

12-1 gallons/second

Next, we can set up an equation to determine how many seconds it will take for all of the water to leak out of the pool:

6.8 × 10³ gallons / (12-1 gallons/second) = x seconds

Simplifying the expression on the left-hand side, we get:

6.8 × 10³ gallons / (12-1 gallons/second) = 6.8 × 10³ gallons / 11 gallons/second

= 618.18 seconds

Therefore, it will take 618.18 seconds for all of the water to leak out of the pool. To convert this to hours, we can divide by the number of seconds in an hour:

618.18 seconds / 3600 seconds/hour ≈ 0.172 hours

Therefore, it will take approximately 0.172 hours, or about 10.3 minutes, for all of the water to leak out of the pool.

Answer:

$56.10

Step-by-step explanation:

$0.34 removed for every dollar

.34 x 85 = $28.9 removed

85 - 28.9 = $56.10

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The two prime numbers that add up to 100005, based on the properties of prime numbers would be 2 and 100003.

To find the two prime numbers, the relevant relationship would be  the Goldbach's Conjecture. This posits that every even number greater than 2 can be expressed as the sum of two prime numbers.

So, to write an odd number as the sum of two prime numbers, one of the prime numbers has to be 2 because we know that 2 is the only even prime number.

The other number would therefore be:

= 100005 - 2

= 100003

100003 is a prime number so the two prime numbers are 2 and 100003.

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Answer:

x=4

Step-by-step explanation:

f(x) = 12 and f(x) = 3x

f(x) = 12 =  3x

12=3x

12/3=x

4=x

Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

Slope = 8/3

Given,

The table of linear function.

x :  -3  , 0 , 3,  6

y :  -5 , -3 , -1,  1

Slope = change in y over change in x

Slope = -3-(-5)/0 - (-3)

Slope = 8/3

Passing point = 0,-3

y-y1 = m (x - x1)

y-(-3) = 8/3(x - 0)

y + 3 = 8/3  x

y = 8/3  x -3

Hence, slope = 8/3 and linear function = y = 8/3  x -3

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Answer:

3x+2y=15 : y=-3/2x+15/2

y-4x=2 : y=4x+2

they are not parallel lines

Step-by-step explanation:

formula:

y=mx+b

The correct image include the following: B. Green: image A.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.

In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.

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Answer:

Step-by-step explanation:

You want the number of tickets of each kind sold if 169 tickets were sold for $1795, and lower box tickets were $12.50 while upper box tickets were $10.

Let x represent the number of lower box tickets sold. Then 169 -x is the number of upper box tickets sold. The total revenue is ...

  12.50(x) + 10.00(169 -x) = 1795.00

Simplifying, we get

  2.50x +1690 = 1795

  2.5x = 105 . . . . . . . . . . . subtract 1690

  x = 42 . . . . . . . . . . . . divide by 2.5; the number of lower box ticket sold

  169 -42 = 127 . . . . . . the number of upper box tickets sold

42 lower box and 127 upper box tickets were purchased.

Hence, the banquet's overall payroll came to $1,495 as the number of captains by their pay rate, and the number of hours worked.

We must first determine the rate of pay for each group of employees before multiplying that number by the total number of employees for the dinner. The pay rate for captains is as follows because they are paid 60% above the rest of the staff: Compensation for captains is $17 per hour plus 60% of that amount, or $17 plus $10.20, for a total hourly wage of $27.20. The pay rate for the remaining employees is: $17 per hour is the pay rate for waitresses, bartenders, and hosts. Now, we can determine the banquet's overall payroll using the formula below.

given

We must first determine the pay rate for each group of employees before multiplying that number by the total number of employees for the dinner.

The pay rate for captains is as follows because they are paid 60% more than the rest of the staff:

Compensation for captains is $17 per hour plus 60% of that amount, or $17 plus $10.20, for a total hourly wage of $27.20.

The pay rate for the remaining employees is:

$17 per hour is the pay rate for servers, bartenders, and hosts.

Now, we can determine the banquet's overall payroll using the formula below:

Total payroll is calculated by multiplying the number of servers by their pay rate, the number of bartenders by their pay rate, the number of hosts by their pay rate, the number of captains by their pay rate, and the number of hours worked.

Total payroll is (14 x $17) plus (5 x $17) plus (4 x $17) plus (2 x $27.20) x 5 = $238 plus $85 plus $68 plus $272 x 5

Total compensation: $1,495

Hence, the banquet's overall payroll came to $1,495 as the number of captains by their pay rate, and the number of hours worked.

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Answer:

First, you need to find the number 2/5 on the number line.

Now, you want to find (3/4) times (2/5)

Then the distance between 0 and the point you found earlier needs to be divided into four equal parts (because the denominator is 4)

sAnd because we have the factor (3/4), with a numerator equal to 3, we move from the origin 3 of these parts to the right, the point at where you arrived is the point (3/4)*(2/5)

Another way, which should give you the exact same point, is:

First locate the point (3/4) on the number line.

Now, you want to find (3/4) times (2/5)

The distance between zero and the denominator needs to be divided into 5 parts (because the denominator is 5)

Because the numerator is 2, you need to move, from the origin, two of these parts to the right.

The point where you end is the product (3/4)*(2/5)

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Given diagram drawn on the graph is parallelogram.

For find out 4th coordinate of parallelogram.

We must know the basics of graph.

Graph can defined as pictorial representation using data or point in the organized manner.

Graph having x-coordinate and y-coordinate.

For find out the location of point.

We must know how to locate coordinates.

For find X-point , parallel distance from y-axis.

For  find Y-point , parallel distance from x-axis.

Observe the given diagram.

Find out the parallel distances of x-axis and y-axis.

4th coordinate of parallelograms is c(2,-5).

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