8) Every Thursday, a restaurant gives a free drink to every 8th customer and a free dessert to every 12th customer. Which customer will be the first to get both a free drink and a free dessert? *​

Answer:

10X^2-39x+14

(5x-2)(2x-7

Answer:

$30.69

Step-by-step explanation:

The 8th term in the geometric sequence, where the first term is 4 and the common ratio is 2, is equal to 512.

In a geometric sequence, each term after the first is obtained by multiplying the preceding term by a constant called the common ratio. The formula for the nth term in a geometric sequence is given by:

a_n = a_1 * r^(n-1)

In this case, we are given that the first term (a_1) is equal to 4 and the common ratio (r) is 2. To find the 8th term (a_8) of the sequence, we can substitute these values into the formula:

a_8 = 4 * 2^(8-1)

Simplifying:

a_8 = 4 * 2^7

   = 4 * 128

   = 512

Therefore, the 8th term in the geometric sequence, where the first term is 4 and the common ratio is 2, is equal to 512.

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Distance from Detroit to columbus is 220 miles

It is given in the question,

The average speed Mrs. smith drove = 60 mph.

Returning, her average speed was 55 mph.

Time taken =  1/3 of an hour longer on the return trip

We have to Find total distance between Detroit and Columbus

So, Let the distance between Detroit and Columbus be "x" miles

Average speed = 60

So, time taken by her to cover distance of x miles with speed of 60 mph

Time = Distance / speed

=> t = x / 60

She Took x/60 hours to reach Columbus

While returning her speed was 55 mph.

So, time taken by her to cover the same distance but at a speed of 55 mph :

=> t = x / 55

Now we are given that she took 1/3 of hour more while returning .

So, \(\frac{x}{55} - \frac{x}{60} = \frac{1}{3}\)

⇒ x/660 = 1/3

=> x = 660/3

=> x = 220 miles

Hence ,  Detroit is 220 miles far from Columbus

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Answer:

4,725

Step-by-step explanation:

490x25=12,250

16,975-12,250=4,725

Hey there!

2a + 4 = 3

ADD 4 to BOTH SIDES

2a + 4 - 4 = 3 - 4

CANCEL out: 4 - 4 because that gives you 1

KEEP: 3 - 4 because it helps solve for the a-value

2a = 3 - 4

3 - 4 = -1

2a = -1

DIVIDE 2 to BOTH SIDES

2a/2 = -1/2

CANCEL out: 2/2 because it gives you 1

KEEP: -1/2 because it gives you the value of the a-value

a = -1/2

SIMPLIFY IT!

Therefore, your answer is: a = -1/2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The Rate of change is 34.6 miles per gallon .

The Rate Of Change can be calculated using the formula ,

Rate Of Change = Total miles travelled / Number of gallons of gas used.

It is given in the question that ,

William uses 7 gallons of gas

and

distance travelled = 242.2 miles

Substituting the values in Rate Of Change formula we get ,

Rate of Change = 242.2/7

=34.6

Therefore , If William uses 7 gallons of gas to drive 242.2 miles. The rate of change will be 34.6 miles per gallon.

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Answer:

5/2

Step-by-step explanation:

4(x + 7) = 38

x + 7 = 38/4

x = 38/4 - 7

x = 38/4 - 28/4

x = 10/4

x = 5/2

Reasoning:

1. Divide both sides by 4

2. Isolate variable by subtracting 7 on both sides

3. Convert 7 into an improper fraction to subtract constants

4. Simplify

42 adult tickets and 421 children tickets were purchased for the field trip, based on the given information that the total cost of the tickets was $995 and the children tickets cost $11 while the adult tickets cost $13, and the number of children tickets purchased was one more than ten times the number of adults tickets purchased.

Let's use variables to represent the unknown quantities in the problem:

Let x be the number of adult tickets purchased

Then the number of children tickets purchased is 10x + 1 (since it is one more than ten times the number of adults tickets purchased)

Using these variables, we can set up an equation based on the total cost of the tickets:

13x + 11(10x + 1) = 995

Simplifying and solving for x, we get:

23x + 11 = 995

23x = 984

x = 42.7826087 (rounded to 9 decimal places)

Since we can't purchase a fraction of a ticket, we'll round x down to the nearest whole number, which means 42 adult tickets were purchased. Then the number of children tickets purchased is:

10x + 1 = 10(42) + 1 = 421

So, 42 adult tickets and 421 children tickets were purchased.

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Answer:

60 words per minute...60/1...this is already in unit rate form

Answer:

x = -3

Topics are listed below.

Step-by-step explanation:

Topics of this question include:

Solve:

-Chetan K

Answer:

The value of x is 6.

Step-by-step explanation:

Concept :

Here, we will use the below following steps to find a solution using the transposition method:

\(\begin{gathered}\end{gathered}\)

Finding the value of x.

\(\begin{gathered}\quad\implies{\tt{9 - 4(5 - x)=3(x - 1) - 2 }}\\\\\quad\implies{\tt{9 - (4 \times 5 - 4\times x)=(3 \times x - 3 \times 1) - 2}}\\\\\quad\implies{\tt{9 - (20 - 4x)=(3x - 3) - 2}}\\\\\quad\implies{\tt{9 - 20- 4x=3x - 3- 2}} \\\\\quad\implies{\tt{- 11 - 4x=3x - 5}}\\\\\implies{\tt{- 4x + 3x = - 11 + 5}} \\ \\\implies{\tt{-x = - 6}}\\\\ \implies{\tt{ \cancel{-}\: x = \cancel{-} 6}}\\\\\quad\implies{\tt{x = 6}}\end{gathered}\)

Hence, The value of x is 6.

\(\rule{300}{2.5}\)

The probability mass function of W is P(W=-3) = 1/27, P(W=-1) = 6/27, P(W=1) = 12/27, and P(W=3) = 8/27.

Let us consider the possible outcomes of three tosses of the biased coin. There are a total of 8 possible outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT.

Since a head is twice as likely to occur as a tail, the probability of getting a head is 2/3 and the probability of getting a tail is 1/3.

Let W be a random variable giving the number of heads minus the number of tails in three tosses of the coin. Then, W can take on any value between -3 and 3.

To find the probability mass function (PMF) of W, we need to calculate the probability of each possible outcome. When all three coins come up heads (HHH), W = 3 - 0 = 3. The probability of this outcome is:

P(HHH) = (2/3)^3 = 8/27

When two coins come up heads and one comes up tails (HHT, HTH, THH), W = 2 - 1 = 1. The probability of each of these outcomes is:

P(HHT) = (2/3)^2 × (1/3) = 4/27

P(HTH) = (2/3)^2 × (1/3) = 4/27

P(THH) = (2/3)^2 × (1/3) = 4/27

So, P(W=1) = P(HHT) + P(HTH) + P(THH) = 12/27

When one coin comes up heads and two come up tails (HTT, THT, TTH), W = 1 - 2 = -1. The probability of each of these outcomes is:

P(HTT) = (2/3) × (1/3)^2 = 2/27

P(THT) = (2/3) × (1/3)^2 = 2/27

P(TTH) = (2/3) × (1/3)^2 = 2/27

So, P(W=-1) = P(HTT) + P(THT) + P(TTH) = 6/27

When all three coins come up tails (TTT), W = 0 - 3 = -3. The probability of this outcome is:

P(TTT) = (1/3)^3 = 1/27

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Answer:

25% of 3030 is 757.5, so basically she is saving 757.5 dollars

Answer:

y=5x+1

i'm pretty sure...

Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour

Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.

Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

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The inventory at January 31 using the weighted-average inventory method is $42,882, rounded to the nearest dollar.

To use the weighted-average inventory method, we need to calculate the weighted average unit cost of the inventory, and then use that to calculate the ending inventory.

To calculate the weighted average unit cost, we first need to calculate the total cost of the goods available for sale:

Total cost of goods available for sale = Beginning inventory + Purchases

= 89,424 + 62,160 + 84,451

= $236,035

Next, we need to calculate the total number of units available for sale:

Total units available for sale = Beginning inventory + Purchases

= 9,200 + 6,000 + 7,900

= 23,100

Now we can calculate the weighted average unit cost:

Weighted average unit cost = Total cost of goods available for sale / Total units available for sale

= 236,035 / 23,100

= $10.21

Finally, we can calculate the ending inventory using the weighted average unit cost:

Ending inventory = Units on hand at the end of the period × Weighted average unit cost

= 4,200 × 10.21

= $42,882

Therefore, the inventory at January 31 using the weighted-average inventory method is $42,882, rounded to the nearest dollar.

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Answer:

Starting with the expression n² - 2 - (n - 2)², we can simplify it by expanding the second term using the formula for the square of a binomial:

n² - 2 - (n - 2)² = n² - 2 - (n² - 4n + 4)

Next, we can combine like terms:

n² - 2 - (n² - 4n + 4) = n² - n² + 4n - 6

Simplifying further, we get:

n² - 2 - (n - 2)² = 4n - 6

To prove that this expression is always even, we can show that it can be written in the form 2k, where k is an integer.

So, let's rewrite the expression as:

4n - 6 = 2(2n - 3)

Since 2n - 3 is an integer (because n is an integer greater than 1), we have shown that 4n - 6 can be written in the form 2k, where k is an integer.

Therefore, we have proved algebraically that n² - 2 - (n - 2)² is always an even number.

Yes, it is possible that matrix a is not C This is because the sum of the dimensions of the eigenspaces is not equal to the size of the matrix. Specifically, the sum of the dimensions of the eigenspaces is 1 (for the one-dimensional eigenspace) + 2 (for the two-dimensional eigenspace) = 3, which is not equal to the size of the matrix, 4. Therefore, matrix a is not diagonalizable.  Since one of the eigenspaces is one-dimensional and another one is two-dimensional, the remaining eigenspace must also be one-dimensional.

Now, we know that a matrix is diagonalizable if and only if it has a basis consisting of eigenvectors. In other words, a matrix is diagonalizable if and only if the sum of the dimensions of its eigenspaces is equal to the dimension of the space.

In this case, the sum of the dimensions of the three eigenspaces is 1 + 2 + 1 = 4, which is the dimension of the space. Therefore, a is diagonalizable.

So, it is not possible for a matrix with three eigenvalues and eigenspaces of dimensions 1 and 2 to not be diagonalizable.

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To find the number of oranges in the box, we need to convert the mass of the box from kilograms to grams and then divide it by the mass of one orange in grams.

Given that the box of oranges has a mass of 4 kilograms, we need to convert this mass to grams. Since there are 1000 grams in one kilogram, the mass of the box is 4 x 1000 = 4000 grams.

Next, we divide the mass of the box (4000 grams) by the mass of one orange (80 grams) to find the number of oranges:

Number of oranges = Mass of the box / Mass of one orange

Number of oranges = 4000 grams / 80 grams

Number of oranges = 50

Therefore, there are 50 oranges in the box.

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Answer:

Step-by-step explanation:

If it is a Pythagorean Triple the hypotenuse and the legs of a right triangle will all be integer values where

c^2=a^2+b^2

In this case, this isn’t even a right triangle as

20^2+30^2=40^2

400+900=1600

1300!=1600

because 1300 does not equal 1600 this is not a Pythagorean Triple.

There are 3 tolls where Stephanie pays $ 4.05.

The distance between two points is the length of the path connecting them.

Here,

Distance covered by Stephanie = 12 1/4 miles

                                                     = 12.25 miles

Distance between two toll tax = 3 1/2 miles

                                                   = 3.5 miles

Number of Tolls = Total distance covered / Distance between two tolls

                            = 12.25 / 3.5

                            = 3.5

                            ≈ 3 tolls.

Cost of 1 toll = $ 1.35

Total amount paid on toll = 3 X 1.35

                                          = $ 4.05

Thus, there are 3 tolls where Stephanie pays $ 4.05.

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Answer:

500 boxes

Step-by-step explanation:

hey there,

< Since "p" stands for profits, change "p" to 0 (since the question says 0 profits).

Here is how your equation would look like:

\(0 = -n^2 + 300n + 100000\)

Pretend like "n" is "x" since that is the variable we are trying to find here.

Solve for "n". Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

"n" actually ends up equaling 500, -200.

Obviously, negative can't be the answer because you can't have a negative amount of boxes. So 500 boxes would be your answer. 200 CAN'T be your answer either because it is a negative!! >

Hope this helped! Feel free to ask anything else.

Therefore, the coefficient of variation of max{x1, x2, ..., x10} is 0.848.

To calculate the coefficient of variation of max{x1, x2, ... , x10}, we first need to find the mean and standard deviation of this random variable.

The probability that the maximum value is less than or equal to x is equal to the probability that each of the 10 variables is less than or equal to x. Since each variable is uniformly distributed on (0, 1), this probability is x^10.

Therefore, the cumulative distribution function (CDF) of the maximum variable is F(x) = x^10, for 0 < x < 1. Taking the derivative of the CDF, we get the probability density function (PDF) of the maximum variable:

f(x) = 10x^9

The mean of the maximum variable is given by:

E[max{x1, x2, ..., x10}] = ∫[0,1] x f(x) dx = ∫[0,1] 10x^10 dx = 1/11

To find the standard deviation, we need to calculate the second moment of the maximum variable:

E[(max{x1, x2, ..., x10})^2] = ∫[0,1] x^2 f(x) dx

Using integration by parts, we can evaluate this integral as:

E[(max{x1, x2, ..., x10})^2] = 10/132

Therefore, the variance of the maximum variable is:

Var[max{x1, x2, ..., x10}] = E[(max{x1, x2, ..., x10})^2] - (E[max{x1, x2, ..., x10}])^2 = 10/132 - (1/11)^2 = 879/14641

Finally, the coefficient of variation is the ratio of the standard deviation to the mean:

CV = sqrt(Var[max{x1, x2, ..., x10}]) / E[max{x1, x2, ..., x10}] = sqrt(879/14641) / (1/11) = 0.848

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In conclusion, to compute the chi-square value, we need to know the number of categories and use the appropriate formula or table to find the critical value. The degrees of freedom (df) will be equal to the number of categories minus one (df = k-1).

In the given question, we need to compute the chi-square value to determine the upper bound of the interval. The chi-square value depends on the degrees of freedom (df). To calculate it, we need to know the significance level (α) and the number of categories (k).

Since the question does not provide information about the number of categories, we cannot determine the exact degrees of freedom. However, we can assume that the number of categories is given, and proceed accordingly.

Assuming k is the number of categories, the degrees of freedom (df) will be (k-1).

For example, if there are 5 categories, the degrees of freedom will be (5-1) = 4.

The chi-square value is computed using a chi-square distribution table or a calculator. By using the significance level (α) and the degrees of freedom (df), we can determine the critical value.

In conclusion, to compute the chi-square value, we need to know the number of categories and use the appropriate formula or table to find the critical value. The degrees of freedom (df) will be equal to the number of categories minus one (df = k-1).

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Answer:

The df values for the A x B interaction are also 3,40

Step-by-step explanation:

The F-value for Factor A has df = 1, 40

The F-value for Factor B has df = 3, 40.

The df values for the A x B interaction are also 3,40

This is because the source of variation between columns has ( c- 1); rc(n-1) degrees of freedom and  the source of variation between  rows has (r-1); rc(n-1) degrees of freedom and the  source of variation of interaction

(between rows and columns)  has ( c-1) ( r-1); rc(n-1) degrees of freedom.

Therefore

Factor A:  ( c- 1); rc(n-1)    = 1,40

Factor B:    (r-1); rc(n-1)     = 3,40

Interaction : ( c-1) ( r-1); rc(n-1)   =  3*1,(40)= 3,40

where c refers to columns , r refers to rows and n refers to the total sample size.

Answer:

Step-by-step explanation:

7.

n=5 (given)

3n=15

3n-7=8

-10(3n-7)=-80

Check:

-10(3(5)-7)=-80

-10(15-7)=-80

-10(8)=-80

-80=-80

For 8 you can create your own descriptions of the next step (i.e Multiply both sides by 2) and just build a different equation from there.

Answer:

54 m squared

Step-by-step explanation:

If you look at it from a birds eye view, the post being in the middle, it's just a 9m*6m rectangle of feeding area.

To find the area that the sheep can feed on, we need to find the area of circle. The area that the sheep can feed on is  254.57 square meters.

We can approach this problem by drawing a diagram:

                 fence

    o------------|------------o

                  |

                  |

                  |

                  |

                  |

                  | 9m

                  |

                  |

                  |

                  |

                  |

                  |

                  |

                  o sheep

               post (6m)

The sheep is tethered to the post, and the rope has a length of 9 meters. The post is 6 meters away from the fence. The sheep can move around in a circle whose center is at the post, and whose radius is the length of the rope.

To find the area that the sheep can feed on, we need to find the area of this circle. The formula for the area of a circle is:

A = πr^2

where A is the area, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius.

In this case, the radius is 9 meters, so we have:

A = π(9)^2

 = π(81)

 ≈ 254.57 square meters

Therefore, the area that the sheep can feed on is approximately 254.47 square meters.

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To find the volume of the solid obtained by rotating the region under the curve over the interval [4, 7] about the x-axis, we can use the method of cylindrical shells.

The formula for the volume of a solid generated by rotating a curve f(x) about the x-axis, over an interval [a, b], is given by:

V = ∫[a, b] 2πx * f(x) * dx

In this case, the interval is [4, 7], so we need to evaluate the integral:

V = ∫[4, 7] 2πx * f(x) * dx

To find the function f(x), we need the equation of the curve. Unfortunately, you haven't provided the equation of the curve. If you can provide the equation of the curve, I will be able to help you further by calculating the integral and finding the volume.

Please provide the equation of the curve so that I can assist you in finding the volume of the solid.

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Answer:

$93.22

Step-by-step explanation:

bill = $79

tip = 18%

tip amount = tip % of bill

=18/100 * $79

=$1422/100

=$14.22

total cost = $79 + $14.22

=$93.22

Answer:

93.22

Step-by-step explanation:

Find the amount of the tip

79*18%

79 * .18

14.22

Add this to the amount of the bill

79+14.22

93.22