While on vacation in Springfield, Tori went out for a dinner that cost $80. If sales tax in Springfield is 10% and Tori left a 20% tip on $80, what was the total cost of her meal?

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer: 247in

Step-by-step explanation:

Area of a circle is pi radius squared.

So that'll be 3.14 times 9 (because radius is halve if a diameter) squared.

First using Order of Operations squaring the 9, so that'll be 81.

Lastly you multiply π or 3.14.

So 81 x 3.14 is 247.  Which is rounded down to the nearest whole number.

Happy Solving.

The people do you have to sample size to be 95% certain you can identify a difference of 1% is 9604.

A minimum sample size is the number of participants required to provide findings that accurately reflect the community under investigation while yet maintaining the intended confidence interval (margin of error) and confidence level.

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

As we are given here a margin of error of 0.01. Also from standard normal tables, we have here:

P(-1.96 < Z < 1.96) = 0.95

Therefore 1.96 is the z critical value that is to be used here.

As we are not given a prior proportion value here, we take p = 0.5, to get a conservative value of the sample size.

The margin of error now is computed as:

MOE = x*P(1 - p)

n = 22 P(1-7 .)2 x 0.25 = 9604 MOE2

Therefore 9604 is the required minimum sample size here.

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Answer:

hshysywyyw6w6wywhwhwqhhwhwhh

Step-by-step explanation:

vejejjeejjejejejfjj237 68672_773837 8282×786766

bbdjdjejjefu8du uwj udej hbvv jjj un jududjdj8

The components of the vector v are \((5, 1, 0)\) and the unit vector u in the direction of v is \((5 / sqrt(26), 1 / sqrt(26), 0 / sqrt(26))\).

To find the components of the vector v with initial point p and terminal point q, we subtract the coordinates of p from the coordinates of q.

The components of the vector v are given by:

\(v = q - p\)
\(= (6, 2, 0) - (1, 1, 0)\)
\(= (6 - 1, 2 - 1, 0 - 0)\)
\(= (5, 1, 0)\)

Now, to find the unit vector u in the direction of v, we divide each component of v by the magnitude of v.

The magnitude of v, denoted as ||v||, can be calculated using the formula:
\(||v|| = sqrt(x^2 + y^2 + z^2)\)
where x, y, and z are the components of v.

In this case:
\(||v|| = sqrt(5^2 + 1^2 + 0^2)\)
\(= sqrt(25 + 1 + 0)\)
\(= sqrt(26)\)

Therefore, the unit vector u in the direction of v is given by:
\(u = v / ||v||\)
\(= (5, 1, 0) / sqrt(26)\)

Simplifying each component, we get:
\(u = (5 / sqrt(26), 1 / sqrt(26), 0 / sqrt(26))\)

Thus, the components of the vector v are (5, 1, 0) and the unit vector u in the direction of v is \((5 / sqrt(26), 1 / sqrt(26), 0 / sqrt(26)).\)

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The equivalent regular expression for the given DFA using Arden's theorem is (a+b)(a+bb+ba(a+b))*.

1. Start with the given DFA and its transition table:

  State | Input a | Input b

  ------|---------|---------

  1     | 3       | 2

  2     | 1       | 2

  3     | 2       | -

2. Apply Arden's theorem, which states that for a DFA with a single final state, the regular expression for that state can be obtained by substituting the regular expressions for the other states into the equation: R = S + RP, where R is the regular expression for the final state, S is the regular expression for the current state, and P is the regular expression for the next state.

3. Begin with state 1:

  - Substitute the regular expression for state 3 into the equation:

    1 = 3a + ε

  - Since state 3 has no outgoing transition for input b, it is represented as ε (empty string).

4. Move to state 2:

  - Substitute the regular expression for state 1 into the equation:

    2 = 1(a + b) + 2a + 3b

  - State 1 is represented as (a + b) from the previous step.

  - Note that 1 is substituted because it is the regular expression for the state itself.

5. Move to state 3:

  - Substitute the regular expression for state 2 into the equation:

    3 = 2b

  - State 2 is represented as b from the previous step.

6. Substitute the obtained regular expressions back into the previous equations until no new substitutions are made:

  - In this case, there are no new substitutions to be made.

7. The resulting regular expression for state 1 is (a + b)(a + bb + ba(a + b))*.

Therefore, the equivalent regular expression for the given DFA using Arden's theorem is (a + b)(a + bb + ba(a + b))*.

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Answer:

The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours

The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours

since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Step-by-step explanation:

The given parameters are;

The elapsed time by which Ms. Croft missed the boat = 5 hours

The speed of the cruise ship = 528 mi/day

The speed of the speedboat = 100 miles in 2.5 hours

The speed of the helicopter = 90 mph

The time it would take Ms. Croft to arrive at the harbor = 3.5 hours

Therefore, we have;

The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph

The location of the cruise after the first 5 hours = 5 × 22 = 110 miles

The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph

By traveling with a speed boat

The time at which Ms. Croft will intercept the cruise ship is given by the following relation;

40 mph × t = 22 mph × t + 110 miles

Which gives;

40 mph × t - 22 mph × t = 110 miles

18 mph = 110 miles

t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours

By taking the helicopter, we have;

Upon arrival at the harbor, after 3.5 hours, we find

90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles

90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles

68 mph × t = 77 miles + 110 miles = 187 miles

t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours

The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours

Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Answer:

Tax for Italian Salad=$0.20

Tax for Lasagna= $0.43

Tax for  Spaghetti =$0.21

Tax for Fettuccini Alfredo   =$0.36

Step-by-step explanation:

Hi, to answer this question we have to multiple the price of each item by the tax percentage in decimal form (divided by 100):

Italian Salad =$3.99  

Lasagna =$8.50  

Spaghetti =$4.29  

Fettuccini Alfredo =$7.17

Feel free to ask for more if needed or if you did not understand something.  

Answer: .20

              .33

              .21

              .36

Step-by-step explanation: 2020 edg

Explanation

using speed and distance relationship

Rate = distance / time

rafael runs 6 miles in 59 minutes

distance = 6 miles

time = 59 minutes

Rate = 6 / 59

Rate = 0.102 miles / minutes

to calculate how many miles he ran in minutes at the same rate

rate = 0.102 miles / minutes

Rate = distance / time

distance = rate x time

distance = 0.102 x 35

distance = 3.55 miles

approximately = 4 miles

Rafael ran 3.55 miles in 35 minutes

The answer is 3.55 miles

Work Shown:

\(5t +2r = 3t+10\\\\5t = 3t+10-2r\\\\5t-3t = 10-2r\\\\2t = 10-2r\\\\t = \frac{10-2r}{2}\\\\t = \frac{10}{2}-\frac{2r}{2}\\\\t = 5-r\\\\\)

f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6.

f(x) is concave up on the interval -6 ≤ x ≤ 0.

To determine where f(x) is concave up or concave down, we need to calculate the second derivative of f(x):

f(x) = x √(\(x^2\) + 36)

f'(x) = √\(x^2\) + 36) + \(x^2\) √(\(x^2\) + 36)

f''(x) = (x (\(x^2\) +72) )/((\(x^2\)+36)\(^(3\)/2))

To find where f(x) is concave up or concave down, we need to find where f''(x) > 0 (concave up) or f''(x) < 0 (concave down).

f''(x) = 0 when x = 0 or x = +/-6.

Thus, f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6, and concave up on the interval -6 ≤ x ≤ 0.

The inflection point for this function is at x = 0.

To find the minimum and maximum for this function, we need to look at the endpoints and critical points of the interval -5 ≤ x ≤ 6.

f(-5) = -5√61 and f(6) = 6√72, so the minimum occurs at x = -5 and the maximum occurs at x = 6.

Therefore:

f(x) is concave down on the interval -5 ≤ x ≤ -6 and 0 ≤ x ≤ 6.

f(x) is concave up on the interval -6 ≤ x ≤ 0.

The inflection point for this function is at x = 0.

The minimum for this function occurs at x = -5.

The maximum for this function occurs at x = 6.

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The slope of the line that goes through the origin and the point (6, -4) is -2/3.

To find the slope of a line that goes through two given points (x₁, y₁) and (x₂, y₂), you can use the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, one of the points is the origin, which has coordinates (0, 0), so x₁ = 0 and y₂ = 0. The other point is (6, -4), so x₂ = 6 and y₂ = -4. Substituting these values into the slope formula gives:

slope = (-4 - 0) / (6 - 0) = -4/6 = -2/3

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Answer: B,D,E on usatestprep

Step-by-step explanation:

Answer:

the answer is 50 are you trying to find the answer

Answer:

Step-by-step explanation:

4 + 6z - 15 = 6z - 11

2(3z -4) = 6z - 8

Here's the tricky part. You are only taking 8 away from 6z

The result is going to be larger than when you take away 11 from 6x

Try it

suppose z = 7

6*7 - 8 = 42 - 8 = 34

6*7 - 11 = 42 - 11 = 31

34>31

Answer:

c. r=14

Step-by-step explanation:

r+36=50

subtract 36 from both sides

r+36-36=50-36

r=14

The solution for x in the circle is x = 12

Since the measure of angle EFG is m∠EFG = 9x-7 and the measure of arc GE is 17x-2

We can determine the value of x using the inscribed angle theorem.

Thus, we have:

m∠EFG = 1/2 (arc GE)

9x-7  = 1/2 * (17x-2)

2(9x-7) = 17x - 2

18x - 14 = 17x - 2

18x - 17x = -2 + 14

x = 12

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The slope-intercept form of the line that passes through the point (1, 1) and has a slope of 1 is y = x.

To find the equation of the line in slope-intercept form, we need to determine its slope (m) and y-intercept (b).

Given that the line passes through the point (1, 1), we can use the point-slope form of a line:

y - y₁ = m(x - x₁)

Substituting the values x₁ = 1 and y₁ = 1, we have:

y - 1 = m(x - 1)

Since the slope (m) is given as 1, the equation becomes:

y - 1 = 1(x - 1)

Simplifying the equation, we have:

y - 1 = x - 1

Moving the constant terms to the right side of the equation, we get:

y = x

Therefore, the equation of the line in slope-intercept form is y = x. This equation represents a line that passes through the point (1, 1) and has a slope of 1.

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Answer:

circle

Step-by-step explanation:

The equation that can be used to create a table with the given information is `t = 6.5p + 2.5r`, where p is the number of persons, r is the number of rides and t is the total cost of admission and rides.

The equation that can be used to create a table with the given information is `t = 6.5p + 2.5r`, where p is the number of persons, r is the number of rides and t is the total cost of admission and rides.What is the given information?The given information is that admission to a local carnival costs $6.50 per person and $2.50 for each ride. Jenna wants to know how much it will cost her to ride a certain number of rides at the carnival.What is the equation that can be used to create a table?To create a table with the given information, we can use the equation `t = 6.5p + 2.5r`, where p is the number of persons, r is the number of rides and t is the total cost of admission and rides.Therefore, the equation that can be used to create a table with the given information is `t = 6.5p + 2.5r`, where p is the number of persons, r is the number of rides and t is the total cost of admission and rides.

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Answer:

98 is ur answer

xd hope it help u :)

Answer:

m

Step-by-step explanation:

When chosen 2 of the 16,701 mathematics degrees at random, the probability that at least 1 of the 2 degrees was earned by a woman is P(at least 1 women out of 2)= 70.4064%

P(women)=0.4560

We know the rule: P(not A) = 1−P(A)

We can then determine the probability of individuals who earned a degree but are not women:

P(not women) =1−P(women)=1−0.4560=0.5440

when we multiply we get,

P(A and B) = P(A)×P(B)

now we can then determine the probability of obtaining 2 individuals who earned a degree but are not women:

P(2 not women) = P(not women) × P(not women)

= 0.5440 × 0.5440 = 0.295936

now we can use the complement rule, and with this now we can then determine the probability of at least 1 degree earned by women:

P(at least 1 women out of 2) = 1−P(2 not women) = 1−0.295936

=0.704064

=70.4064%

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The replacement set, only \(x = 18\) makes the inequality \(x - 3 > 12\) true. The values \(x = 6\), \(x = 10\), and \(x = 14\) do not satisfy the inequality.

To determine which values in the replacement set make the inequality \(x - 3 > 12\) true, we can substitute each value from the replacement set into the inequality and evaluate whether the inequality holds.

Let's check each value:

1. For \(x = 6\):

  Substituting \(x = 6\) into the inequality, we have:

  \(6 - 3 > 12\)

  \(3 > 12\)

  The inequality is not true when \(x = 6\).

2. For \(x = 10\):

  Substituting \(x = 10\) into the inequality, we have:

  \(10 - 3 > 12\)

  \(7 > 12\)

  The inequality is not true when \(x = 10\).

3. For \(x = 14\):

  Substituting \(x = 14\) into the inequality, we have:

  \(14 - 3 > 12\)

  \(11 > 12\)

  The inequality is not true when \(x = 14\).

4. For \(x = 18\):

  Substituting \(x = 18\) into the inequality, we have:

  \(18 - 3 > 12\)

  \(15 > 12\)

  The inequality is true when \(x = 18\).

In summary, out of the values in the replacement set, only \(x = 18\) makes the inequality \(x - 3 > 12\) true. The values \(x = 6\), \(x = 10\), and \(x = 14\) do not satisfy the inequality.

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To solve this equation, you can multiply both sides by 28 to get rid of the fraction:

4 = x/28

4 * 28 = x/28 * 28

112 = x

So the value of x is 112.

Answer: x = 112

Step-by-step explanation:

4 = x/28

We times 28 on both sides

112= x

Now let test

4 = 112/28

4 = 4

So, x = 112 is the correct answer

Answer: The comparison that is true is −56 > −116.

Step-by-step explanation:

When comparing numbers, the greater number has a greater absolute value. The absolute value of a number is its distance from 0 on the number line, and is always a positive number. So, |-56| = 56 and |-116| = 116. Since 56 is greater than 116, it follows that -56 > -116.

Hi there, here's your answer:

-56 > -116

This is true as the smallest negative integer is -∞ and the greatest integer is -1.

-116 > 56

This is false as positive integers are always greater than negative integers.

-56 > 116

Just like the previous one, this is also false.

116 < 56

This is also false as 116 being a 3-digit number is obviously greater than 56, which is a 2-digit number.

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Answer:

Step-by-step explanation:

The candy bar cost, in dollars, is $1.05

Say the price of a piece of bubble gum is x.

This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.

We can then solve from there.

We have given that,

(x+1)+x=1.10

Simplify above expression

2x+1=1.10

2x=0.10 - Subtract From Both Sides

x=0.05 - Divide From Both Sides

So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.

What is the cost?

Cost is the value of money that a company had to spend to produce its goods or services.

Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.

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Answer:

Soda = 2.35

Pack of bubble gum = 1.15

Chocolate bar = 1.64

2.35 + 1.15 + 1.64 = 5.15

Answer: Dottie spent a total of $5.15.