Sam and her friends went out to lunch. The bill for Sam's meal was $25.60 . How much did Sam pay if she left a 25% tip?

The values of u, v, u, v, and d(u, v) are given below:(a) u, v = 171(b) ||u|| = 13(c) ||v|| = 17(d) u/||u|| = (-12/13, 5/13), v/||v|| = (-8/17, 15/17)(e) d(u, v) = 2√29

Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v. The values of u, v, u, v, and d(u, v) are to be calculated.

Solution: Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v.

The dot product of u and v is given by u . v= (-12 * -8) + (5 * 15)u . v= 96 + 75u . v= 171

Now, we have to calculate the norm of u and v, which can be calculated as follows: ||u|| = √u1² + u2²||u|| = √(-12)² + 5²||u|| = √144 + 25||u|| = √169||u|| = 13

Similarly,||v|| = √v1² + v2²||v|| = √(-8)² + 15²||v|| = √64 + 225||v|| = √289||v|| = 17

Now, we have to calculate the unit vector of u and v. T

he unit vector of u and v is given by: u/||u|| = (-12/13, 5/13)v/||v|| = (-8/17, 15/17)Now, we have to calculate d(u, v). The formula to calculate d(u, v) is given by: d(u, v) = ||u - v||d(u, v) = √(u1 - v1)² + (u2 - v2)²d(u, v) = √(-12 - (-8))² + (5 - 15)²d(u, v) = √(-4)² + (-10)²d(u, v) = √16 + 100d(u, v) = √116d(u, v) = 2√29

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Answer:

There is exactly one solution: (3, 1)

Step-by-step explanation:

To graph these equations, you need to change them to slope intercept form:

x + y = 4 in slope intercept form is y = -x + 4 (subtract x frok both sides).

x - y = 2 in slope intercept form is y = x - 2 (subtract x from both sides then divide both sides by -1)*.

Now, all you have to do is graph both and find the point they cross at (the solution) which is (3, 1).

* = y can never be negative, which is why you divide by a -1 after subtracting x.

Hope this helps!

The type of data collected is Quantitative Data.

Quantitative data is a type of numerical data that is collected through methods such as measurements, surveys, or experiments. It involves numerical values that can be measured and analyzed using statistical techniques. This data can be further classified as discrete or continuous.

Discrete quantitative data consists of countable values that can be expressed in whole numbers, such as the number of people in a room, the number of cars in a parking lot, or the number of books in a library.

Continuous quantitative data consists of measurements that can take on any value within a range, such as weight, height, temperature, or time. Continuous data can be further divided into interval and ratio data, depending on the level of measurement and the presence or absence of a true zero point.

The data collected by the usher, which is the number of unoccupied seats in the movie theater, is a type of quantitative data. It involves numerical values that can be measured and analyzed mathematically.

#Complete Question - an usher records the number of occupied seats in a movie theater during each viewing of a film. identify the type of data collected.

(a) Quantitative data

(b) Qualitative data

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As the concentration of a light-absorbing species in a solution increases, the absorbance of the solution also increases. This relationship is known as the Beer-Lambert Law.

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Answer:

Step-by-step explanation:

∠8 = ∠6

∠8 = 7x - 36

∠8 +∠9 = 180   {Linear pair}

7x - 36 + 5x + 12 = 180

7x + 5x - 36 + 12 = 180

   12x  - 24 = 180

            12x = 180 + 24

           12x   = 204

               x = 204/12

x = 17

∠6 = 7x - 36  = 7*17 - 36 = 119 - 36 = 83

∠11 = ∠6    {Vertically opposite angles}

∠11 = 83

Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and  0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.

a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.

b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)

Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,

P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228

P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392

P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269

P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093

P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016

P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011

d) The mean and standard deviation of the distribution is given by:

mean = n*p = 5*0.256 = 1.28

standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995

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 y = 7x² is the set of ordered pairs that represent a function.

One clue that the relation is quadratic is found in the second difference:

The first differences are .

7 -0 = 7

28 -7 = 21

63 -28 = 35

112 -63 = 49

The second differences are .

21 -7 = 14

35 -21 = 14

49 -35 = 14

These are constant, indicating the function is 2nd-degree, or quadratic. The coefficient of the x² term is half the value of these second differences, so it will be 7.

When we compare y = 7x² with the given relation values, we find that no additional adjustment is needed in this rule.

for x=0, y = 7·0² = 0

for x=1, y = 7·1² = 7

for x=2, y = 7·2² = 28

for x=3, y = 7·3² = 63

for x=4, y = 7·4² = 112

A rule that represents the function is y = 7x².

In mathematics, the function  X to  Y assigns exactly one element of Y to each element of X. The set X is called the range of the function and the set Y is called the code interval of the function.

Types of operations can be classified into four types.

In mathematics, a basis function is an element of a certain basis of function space. Every function in a function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.

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The decimal form of the given number which is 5 3/4 is 5.75.

Given number = 5 3/4.

The given number is a fractional number, which is looking like a mixed fraction.

To write the mixed fraction into decimal form first, we have to write it into normal fraction, later we divide it to get the required decimal form.

To convert mixed fraction into normal fraction,

5 3/4 = ((4*5) + 3) / 4 = 23/4

So, the fraction is 23/4.

To convert the fraction into a decimal, we have to divide the numerator by the denominator as shown below,

23/4 = 5.75

From the above analysis, we can conclude that the decimal form of 5 3/4 is 5.75.

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Solution

For this case we can use the following equation:

m < A+ m < C= 180 º= m < B + m < D

Then since we know that m < A= 88º we can do this

m < C= 180º- 88º = 92º

then the correct answer is:

92º

Answer:

3x (3x-1)-10 (3x-1)

9x2-3x-30x+10 (the 2 in 9x2 is the square ok)

9x2-33x+10 Ans..

I hope this will help you

If this is incorrect forgive meplz

Answer: Solve for x

Any value of x makes the equation true.

All real numbers

Interval Notation:

(−∞,∞)

Step-by-step explanation:

(a) To calculate the probability of winning $1 million in both games by buying one scratch-off ticket from each game, we need to multiply the individual probabilities of winning in each game.

The probability of winning $1 million in the first game is 1 in 505,600, which can be expressed as 1/505,600.

Similarly, the probability of winning $1 million in the second game is also 1 in 505,600, or 1/505,600.

To find the probability of winning in both games, we multiply the probabilities:

P(win in both games) = (1/505,600) * (1/505,600)

Using scientific notation, this can be written as:

P(win in both games) = (1/505,600)^2

To evaluate this, we calculate:

P(win in both games) = 1/255,062,656,000

Therefore, the probability of winning $1 million in both games is approximately 1 in 255,062,656,000.

(b) The probability of winning $1 million twice in the second scratch-off game can be calculated by squaring the probability of winning in that game:

P(win twice in the second game) = (1/505,600)^2

Using scientific notation, this can be written as:

P(win twice in the second game) = (1/505,600)^2

Evaluating this, we find:

P(win twice in the second game) = 1/255,062,656,000

Therefore, the probability of winning $1 million twice in the second scratch-off game is approximately 1 in 255,062,656,000.

Note: The calculated probabilities are extremely low, indicating that winning $1 million in both games or winning $1 million twice in the second game is highly unlikely.

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Answer:

First Answer: 12.5 weeks

Third Answer: 16 minutes(I think it was a really long decimal so I rounded it up)

After answering the presented question, we can conclude that Yet, if you  interest  have money that you don't need right away, a CD can be an excellent option.

Divide the principal by the interest rate, period, and other factors to get simple interest. Marketing uses the formula return = principal + interest + hours. Interest may be calculated most readily with this method. Interest is most commonly calculated as a percentage of the principal balance. If he borrows $100 from a buddy and promises to repay it with 5% interest, he will only pay his share of the total interest. $100 (0.05) = $5. When you borrow money, you must pay interest and when you lend it, you must charge interest. Interest is usually computed as an annual percentage of the loan balance. This percentage is known as the loan's interest.

A Certificate of Deposit is the best account to earn a higher interest rate but with limited access to cash for a set period of time (CD). CDs normally provide greater interest rates than savings or money market accounts, but you must maintain your money in the account for a defined amount of time, known as the CD term.

You cannot withdraw your money without paying a penalty throughout the CD period, which might run from a few months to several years. This means you must be willing to lock up your money for the life of the CD period.

Yet, if you have money that you don't need right away, a CD can be an excellent option.

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Answer:

x = 15

Step-by-step explanation:

5 x 3

Answer and Step-by-step explanation:

\(\frac{x}{2}\) is the answer.

The initial part is having the person walk a certain amount (shown as x feet). Then, the amount of x (in terms of feet) is halved, or divided by 2.

#teamtrees #WAP (Water And Plant)

Answer:

x/2

Step-by-step explanation:

x halved is x divided by two, namely x/2.

Hope this helps!

xoxo,

cafeology

The position vector r (with components x1, x2, x3) and any vector v can be expressed as r = x1*i + x2*j + x3*k and v = a*i + b*j + c*k, respectively.

The dot product of two vectors is defined as the sum of the products of their corresponding components. Therefore, the dot product of r and v can be calculated as:

r · v = (x1*i + x2*j + x3*k) · (a*i + b*j + c*k)

     = (x1*a) + (x2*b) + (x3*c)

Here, we multiplied the corresponding components and summed them up. The dot product represents the scalar projection of one vector onto the other, which indicates the magnitude of one vector in the direction of the other.

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Answer:

2 yd. 33 in.

Step-by-step explanation:

- Convert yards to inches:

19 yd = 684 in

16 yd = 576 in

- Add to other inches:

684 + 28 = 712

576 + 31 = 607

- Subtract:

712 - 607 = 105

- Convert back to yards:

105 in = 2 yd 2.75 ft

2.75 ft = 33 in

Step-by-step explanation:

19 yd. 28 in

-16 yd. 31 in

=2 yd. 97 in

19yd28in-16yd31in

=8-1=7

2can not go in 3 borrow form 9

Answer:

The answer is fifteen because 24 divided by 8 is 3 and 5 x 3 is 15

Answer:

1/24

Step-by-step explanation:

We want to find the probability of picking a watermelon AND picking a green apple right after. These events are completely independent of each other as the watermelon is put back, and picking a watermelon/green apple does not affect the chances of getting the other the next/previous time. The formula for this is P(A) * P(B), with P(A) being the probability of event A happening and P(B) being the probability of event B happening. It does not matter which event is which.

Let's say picking a watermelon is event A and picking a green apple is event B.  There are 6 watermelons and 6+5+1 = 12 jolly ranchers, so there is a 6/12 = 1/2 chance of picking a watermelon. There is 1 green apple and still 12 jolly ranchers, so there is a 1/12 chance of picking a green apple jolly rancher.

Multiplying these two, we get (1/2) * (1/12) = 1/24

Answer:

  15.30

Step-by-step explanation:

You want f(2) if f(x) is an exponential function such that f(-3) = 9 and f(7) = 26.

Using the given points, we can write the function as ...

  \(f(x)=9\left(\dfrac{26}{9}\right)^{\dfrac{x-(-3)}{7-(-3)}}=9\left(\dfrac{26}{9}\right)^{\dfrac{x+3}{10}}\)

Then the value of f(2) is ...

  \(f(2)=9\left(\dfrac{26}{9}\right)^{\dfrac{2+3}{10}}=9\sqrt{\dfrac{26}{9}}=3\sqrt{26}\approx 15.29706\\\\\boxed{f(2)\approx15.30}\)

__

Additional comment

The form of the function is ...

  f(x) = a·b^((x-x₀)/i)

where a=value at the beginning of the interval, b is the ratio of ending to beginning values, and i=interval width: x₁ -x₀. This can be written as an exponential function of e, but this is the simplest way to use given values.

Here, the "interval" is -3 to +7, and the corresponding beginning and ending values are 9 and 26, respectively.

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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Answer:

True

Step-by-step explanation:

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces

it should be true. Let me know if I'm incorrect.

Answer:

I think C. 0.75

Step-by-step explanation:

The probability of seeing at least one robin in the next 5 birds is 0.75

The representations are given as:

Using the above representations, the numbers that represent an occurrence of seeing at least one robin in the next 5 birds are:

05716 16803 32177 92290 72794 14333 79019 05943 77510 74051 87238 86481 94036 12749 24005

The number of occurrence is:

Number = 15

The number of simulation is 20

So, the probability of seeing at least one robin is:

P = 15/20

Divide

P = 0.75

Hence, the probability of seeing at least one robin is 0.75

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a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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Answer:

43

Step-by-step explanation:

Answer:

x-1  when x>1

Step-by-step explanation:

|x-1| when x>1

If x is greater than 1  than x-1 will always be greater than 0

|x-1| can be rewritten as x-1

Answer:

12.2

Step-by-step explanation:

Answer:

12.2

Step-by-step explanation:

the tenth is shown       12.23

                                          I

                                          I

                                          I

after locating the tenth, we follow rounding principles. if the number to the right is 0-4, the place value you are looking at stays the same (which happens in our case). If the number to the right is 5+, we round the number to the left up so if it was 12.27, it would be 12.3

HOPE THIS HELPS *GIVE FWEE COOKIE*