A restaurant automatically charges a 20% gratuity if a party has 6 or more people. How much gratuity is added to a party of 6 on a $141 bill.

The rocket will hit the ground approximately 2.57 seconds after launch.

The equation given is:

y = -16x² + 177x + 98

where y represents the height of the rocket in feet, and x represents the time elapsed since launch in seconds. This is a quadratic equation in standard form, where the coefficient of x² is negative, indicating that the graph of the equation is a downward-opening parabola.

To find the time when the rocket hits the ground, we need to find the value of x when y = 0, since the rocket's height is zero when it hits the ground. We can substitute y = 0 into the equation and solve for x:

0 = -16x² + 177x + 98

We can then use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

where a = -16, b = 177, and c = 98.

Plugging in the values, we get:

x = (-177 ± √(177² - 4(-16)(98))) / 2(-16)

x = (-177 ± √(62721)) / (-32)

Simplifying further, we get:

x = (-177 ± 251) / (-32)

We can discard the negative value since time cannot be negative, and round the positive value to the nearest 100th of a second:

x ≈ 2.57 seconds

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The diagram below shows a square based pyramid. Point O is directly above the center of the base.

a) The length of AC = 26.87 cm

b) The perpendicular height = 66.961 cm

Considering ΔOAD,

cos 82° = [tex]\frac{19/2}{OC}[/tex]

OC = [tex]\frac{9.5}{cos \ 82}[/tex] = [tex]\frac{9.5}{0.1391}[/tex] = 68.296

Considering the base ABCD, the length of the diagonal AC,

It is given as [tex](AC)^2 = 19^2 + 19^2[/tex] = 361 + 361 = 722

AC = 26.87 cm

MC = [tex]\frac{1}{2}[/tex] (AC) = [tex]\frac{1}{2} (26.87)[/tex] = 13.435

Considering ΔOMC,

[tex](OM)^2 = (OC)^2 - (MC)^2 = (68.296)^2 + (13.435)^2[/tex]

= 4664.343 - 180.499 = 4483.844

OM = 66.961

Therefore, the length AC = 26.87 cm and the perpendicular height = OM = 66.961 cm.

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The value of the experimental probability of tossing heads is,

⇒ 1 / 3

We have to given that;

Coin Toss Results: T, H, T, H, T, H, T, T, T, T, H, T, H, T, T

Where, H stands for heads and T stands for Tails.

Hence, Total outcomes = 15

And, Head outcomes = 5

Thus, The value of the experimental probability of tossing heads is,

⇒ 5 / 15

⇒ 1 / 3

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Answer:

1. Maths has huge effect on daily basis.

2. I feel much more confident with math skills.

Step-by-step explanation:

1. Numerous ways in which maths influences our lives on a daily basis. When budgeting our expenses, measuring ingredients when cooking, calculating the amount of money we must pay for goods or services, and calculating the amount of time it will take to travel between two points, we all use maths. We also utilise maths to determine the best value for our money by comparing the costs of several options, computing savings or discounts, and so on. A lot of occupations, like engineering, science, finance, and technology, depend heavily on maths.

2. I am proficient and accurate at completing simple mathematical operations like addition, subtraction, multiplication, and division as well as calculating sales tax and interest. These abilities are crucial for daily living and, with practise, they emerge naturally. While many people have no trouble with these math concepts, others might. Recognising our mathematical strengths and shortcomings is crucial so that we may focus on enhancing our abilities and navigating daily life more comfortably and confidently.

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25 testers will require 40 days to complete 50 test cases.

Given that all the testers are equally productive i.e. they complete an equal number of tests in equal time.

According to the question, 50 testers can complete 25 test cases in 10 days

Number of tests completed in one day by 50 testers = 25 / 10

= 2.5

The number of tests completed in one day by a single tester = 2.5 / 50

= 0.05

The number of tests completed in one day by 25 testers = 0.05 X 25

= 1.25

The time taken to complete 50 tests by 25 testers = 50 / 1.25

= 40

Hence, 25 testers will require 40 days to complete 50 test cases.

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The complete question is =

50 testers can complete 25 test cases in 10 days. All testers are equally productive. A project has 25 testers and 50 test cases. How much time will they take to complete?

Answer: y=2+6

Step-by-step explanation:

The domain of the function from the given graph is [-4, 4]. Therefore, option A is the correct answer.

Domain = the set of all x-coordinates.

From the given graph, the zeros are (-4, 0) and (4, 0),

So, the domain of values are {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Interval notation -4≥x≤4

Therefore, option A is the correct answer.

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Effective:

Thirty children suffered broken bones last year because of outdated playground equipment.

Studies show that safe playground equipment helps promote children's development.  

Tax money spent on our children's safety is tax money well spent.

New playground equipment can be used to enhance our children's education.

Ineffective:

Other schools in the area have new playground equipment.

The nurse's office is conveniently located next to the playground.

Here, we have,

The education is a discipline that is concerned with methods of teaching and learning in schools or school-like environments as opposed to various non-formal and informal means of socialization (e.g., rural development projects and education through parent-child relationships).

Education can be thought of as the transmission of the values and accumulated knowledge of a society. In this sense, it is equivalent to what social scientists term socialization or enculturation.

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complete question:

In a speech about the importance of installing new and safer school playground equipment, which reasons most effectively express the speaker's viewpoint?

label as

Effective or Ineffective

Thirty children suffered broken bones last year because of outdated playground equipment.

Studies show that safe playground equipment helps promote children's development.

New playground equipment can be used to enhance our children's education.

Other schools in the area have new playground equipment.

Tax money spent on our children's safety is tax money well spent.

The nurse's office is conveniently located next to the playground.

Answer:

A) Vertical angles are congruent.

Answer:

3) tanθ = -√3

4) tanθ = undefined

Step-by-step explanation:

For your third problem, we are given:

[tex]\displaystyle{\cos \theta = -\dfrac{1}{2}}[/tex]

And [tex]\displaystyle{\theta}[/tex] lies in quadrant 2 which is [tex]\displaystyle{90^{\circ} < \theta < 180^{\circ}}[/tex]. Since tangent is the division of sine over cosine, and cosine is in negative while sine is positive according to unit circle in quadrant 2. Therefore, the value of tangent is negative.

We lack sinθ to find tanθ. Therefore, we have to find sinθ first. We can use the identity:

[tex]\displaystyle{\sin^2 \theta + \cos^2 \theta = 1}[/tex]

To solve for sinθ, subtract cos²θ both sides:

[tex]\displaystyle{\sin^2 \theta + \cos^2 \theta - \cos^2 \theta= 1-\cos^2 \theta}\\\\\displaystyle{\sin^2 \theta= 1-\cos^2 \theta}[/tex]

Substitute cosθ = -1/3. Therefore:

[tex]\displaystyle{\sin^2 \theta= 1-\left(-\dfrac{1}{2}\right)^2}\\\\\displaystyle{\sin^2 \theta= 1-\dfrac{1}{4}}\\\\\displaystyle{\sin^2 \theta=\dfrac{4}{4}-\dfrac{1}{4}}\\\\\displaystyle{\sin^2 \theta = \dfrac{3}{4}}[/tex]

Since the value of sinθ is positive in quadrant 2. Hence:

[tex]\displaystyle{\sin \theta = \sqrt{\dfrac{3}{4}}}\\\\\displaystyle{\sin \theta = \dfrac{\sqrt{3}}{2}}}[/tex]

Now find the value of tanθ by sinθ/cosθ. Therefore:

[tex]\displaystyle{\tan \theta = \dfrac{\dfrac{\sqrt{3}}{2}}{-\dfrac{1}{2}}}\\\\\displaystyle{\tan \theta = -\sqrt{3}}[/tex]

Therefore, tanθ = -√3.

Next, to your fourth problem. To find tanθ again but given that sinθ = -1 in range of 0 ≤ θ < 2π.

Again, we have to apply the identity like the third problem. In this case, we solve for cosθ so we have the formula of:

[tex]\displaystyle{\cos^2 \theta = 1-\sin^2 \theta}[/tex]

Substitute in sinθ:

[tex]\displaystyle{\cos^2 \theta = 1-(-1)^2}\\\\\displaystyle{\cos^2 \theta = 1-1}\\\\\displaystyle{\cos^2 \theta = 0}[/tex]

Therefore:

[tex]\displaystyle{\cos \theta = 0}[/tex]

Since tanθ is sinθ/cosθ. We have -1/0 which is undefined. Therefore there are no tanθ values.

The cosine of the angle is equal to √2/2.

The Pythagorean Identity states that in a right triangle with hypotenuse c and legs a and b, the following relationship holds:

a² + b² = c²

Where c is the longest side of the right triangle, called the hypotenuse, and a and b are the two shorter sides.

Using this identity, we can relate the sine and cosine of an angle as follows:

sin²θ + cos²θ = 1

where θ is the angle in question.

In this question, we are given that sinθ = (√2)/2 and that the angle θ terminates in Quadrant I.

Using the given value of sinθ, we can substitute it into the Pythagorean Identity as follows:

(sinθ)² + (cosθ)² = 1

(√2/2)² + (cosθ)² = 1

2/4 + (cosθ)² = 1

1/2 + (cosθ)² = 1

(cosθ)² = 1 - 1/2

(cosθ)² = 1/2

Taking the square root of both sides, we get:

cosθ = ± √(1/2)

Since we are in Quadrant I, we know that the cosine of the angle must be positive, so we can take the positive square root:

cosθ = √(1/2)

Simplifying the square root, we get:

cosθ = √2/2

Therefore, the cosine of the angle θ is √2/2, as required.

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Answer:

46°

Step-by-step explanation:

If you want to crack this problem, you have to remember one thing: triangles are awesome. They always add up to 180°. Let me show you how:

First, let's look at angle BOC. It's the third angle of triangle BOC, so we can find it by subtracting the other two angles from 180°:

Next, let's use a cool trick: angle AOD is an exterior angle of triangle AOB, which means it's equal to the sum of the two angles inside the triangle that are not touching it. Those are angles AOB and BOC. We can write this as an equation:

m∠AOD = m∠AOB + m∠BOC (2x + 12)° = (28)° + (190° - 10x) Now we can solve for x by doing some math magic:

Finally, we can plug in x into the expression for angle AOD and simplify:

m∠AOD = (2x + 12)° m∠AOD = (2 x 17.17 + 12)° m∠AOD = (34.34 + 12)° m∠AOD = 46.34°

And there you have it: angle AOD is 46.34°, which is pretty close to option 46°

footnotes for in-depth understanding:

I realized that angle AOB is part of a quadrilateral with the points A, O, B, and C. This shape has four angles that add up to 360°. Here's what I did:

I looked at the other three angles of the shape: angle AOC, angle BOC, and angle COA. I used the information they gave me to find their values. Angle AOC is double angle AOD, and angle COA is double angle DOC. So I wrote:

I also used the answer I got for angle BOC in the last question:

Then I used the fact that the four angles of the shape add up to 360° to make an equation and solve for angle AOB:

To find m∠AOB, I simplified and rearranged the equation:

So, the value of angle AOB is 154° - 6x. When x is equal to 17.17, as we found before, angle AOB is equal to 154° - (6 x 17.17), which is about 27°. That's how I found angle AOB.

The excluded points for the function are; x = -2 and x = 9

The excluded values of a function are the values of the independent variable (usually denoted as "x") that would make the function undefined.  In other words, the excluded values are the values that the independent variable cannot take on in order for the function to be well-defined.

We have that;

[tex]x^2 - 9x/x^2 - 7x - 18[/tex]

When we factor the denominator we have that;

[tex]( x + 2) (x - 9)[/tex]

Thus the points of discontinuity are x = -2 and x = 9

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The value of length x is given by, x = 98 mm.

So in the figure we can see that it is a scalene triangle.

And the lengths are given by,

VT = 57 mm

YK = 68 mm

TK = 129.2 mm

and the length of VK = x mm.

So, YV = (x - 68) mm

We have to find the value of this 'x' here.

Also we can conclude that TY is the angle bisector for the angle VTK in the triangle KTV.

So by angle bisector theorem we get,

YK/TK = YV/VT

68/129.2 = (x - 68)/57 [Putting the values given]

x - 68 = (68*57)/129.2

x - 68 = 30

x = 30 + 68

x = 98

Hence the value of x is, x = 98 mm.

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Answer: x = -2.

Step-by-step explanation:

-8x + 44 ≥ 60

Subtracting 44 from both sides, we get:

-8x ≥ 16

Dividing both sides by -8 (and reversing the inequality since we are dividing by a negative number), we get:

x ≤ -2

Next:

-4x + 50 < 58

Subtracting 50 from both sides, we get:

-4x < 8

Dividing both sides by -4 (and reversing the inequality), we get:

x > -2

Putting the two inequalities together, we get:

-2 < x ≤ -2

This means that the solution for x is x = -2.

Answer: 13086.45

Step-by-step explanation: 10000(1+0.03/4)^36

First, convert R as a percent to r as a decimalr = R/100r = 3/100r = 0.03 rate per year,Then solve the equation for AA = P(1 + r/n)ntA = 10,000.00(1 + 0.03/4)^(4)(9) A = 10,000.00(1 + 0.0075)^(36) A = $13,086.45 Summary:The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 3% per year compounded 4 times per year over 9 years is $13,086.45.

Answer:

x + 1.4x = 180

2.4x = 180

x = 75, so 1.4(75) = 105

They can improve their graph by doing the following ; Tips:

1. They should show which one represents 100% as a key

2. The height of the books compared to the percentages are not accurate

3. To simplify the graph, their should be a stack of books for each individual year

The polynomial equation passing through the point ( -2 , -18 ) is given by the function f(x) = x³ - 2x² - 7x + 8

Given data ,

A function with a graph that bounces off the x-axis at (-1,0), crosses it at (4,0), and goes through the point (-2,-18)

Now , the value of the function is

If a graph of a polynomial equation bounces off the x-axis at (-1,0), crosses it at (4,0), and goes through the point (-2,-18), it means that the function has a zero of multiplicity 2 at x=-1, a zero at x=4, and passes through the point (-2,-18)

To write a polynomial equation for this function, we can use the zero product property and write the factors that correspond to each of the zeros:

f ( x ) = (x + 1)² (x - 4)

On simplifying , we get

f ( x ) = x³ - 2x² - 7x + 8

Hence , the function is f ( x ) = x³ - 2x² - 7x + 8

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Using permutation, there 240 ways we can make an order.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.

The formula of permutation is given as;

P(n,r) = n!/(n-r)!

In the given question, we can choose one type of cone in 8 ways, 1 type of flavor in 5 ways and 1 type of topping in 6 ways, the total number of ways will be;

Number of ways = 8 * 5 * 6 = 240 ways

The total number of ways in which we can choose 8 type of cone, 5 flavors and 6 toppings in one order is 240 ways.

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Answer:

D

Step-by-step explanation:

The line in option D, y = 3x, does not intersect with any of the other lines.

To see this, we can first note that options A and B have slopes of -3 and 3, respectively, which means they are parallel lines. Therefore, they will never intersect.

Option C has a slope of 3 as well, but its y-intercept is -7, which is different from the y-intercept of line B, which is 7. This means that these two lines are not parallel and will intersect at some point.

On the other hand, line D has a slope of 3 and a y-intercept of 0 (since there is no constant term), which means it passes through the origin. Therefore, it will not intersect with any of the other lines unless one of the other lines also passes through the origin, which is not the case here.

Therefore, the line that does not intersect with any of the other lines is option D, y = 3x.

Answer:  B. y = 3x + 7 and y = -3x + 7 are parallel lines, so they do not intersect.

Step-by-step explanation:

Two lines in a plane may intersect at a point, be parallel, or be coincident (overlapping). To determine which of the given lines do not intersect, we need to find the slope of each line and check for parallelism.

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Therefore, we can write the equations of the given lines in slope-intercept form as follows:

A. y = -3x - 7 (slope m = -3)

B. y = 3x + 7 (slope m = 3)

C. y = 3x - 7 (slope m = 3)

D. y = 3x (slope m = 3)

From the slopes, we can see that lines B and C have the same slope of 3, so they are parallel. Therefore, they do not intersect at any point in the plane. Lines A and D have different slopes, so they are not parallel and will intersect at some point in the plane.

Answer:

P = 165/360 = 11/24 = about .46

= about 45.83%

The sample space for choosing 2 marbles from the bag with replacement

Purple Red Blue

Purple Purple, Purple Purple, Red Red, Blue

Purple Red, Purple Purple, Red Red, Blue

(option c)

To find the sample space, we need to list all possible outcomes. Since we are choosing two marbles, we can have three possible outcomes for the first marble: purple, red, or blue. Similarly, we can also have three possible outcomes for the second marble.

To construct the sample space, we need to list all possible pairs of the first and second marbles. Since we are choosing two marbles, the total number of pairs will be the product of the number of outcomes for each marble. In this case, we have three outcomes for each marble, so the total number of pairs will be:

3 x 3 = 9

Therefore, there are nine possible pairs of marbles that we can select from the bag with replacement. To represent the sample space in a table, we can list all possible pairs of marbles as follows:

Purple Red Blue

Purple Purple Purple

Purple Red Blue

Red Purple Red

Red Red Red

Blue Blue Blue

Blue Red Purple

Blue Red Blue

Purple Blue Red

Purple Blue Blue

Hence the correct option is (c).

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Gabriella would have in fraction 2/85 of the bricks left to use after tomorrow

Given that,

total number of bricks she bought = 85

The ratio of bricks she use yesterday = 53/85

The ratio of bricks she use today = 20/85

Following tomorrow, the fraction of the bricks still have,

1 -  (53/85 + 20/85)

= 1 - 83/85

= 2/85 of the bricks

Hence,

2/85 of bricks left.

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Answer:

1 over 16 or 1/16

Step-by-step explanation:

All thanks to the multiplication of probability rule, if you have the probability of 2 events and you want to know what the probability of them both happening is you simply multiply the two probabilities.

So the probability is 1/4 x 1/4=1/16

the probability is 1/16.

I hope my answer helps solve your problem, and teaches you some things.

Value of cosθ will be cosθ = (√2)/2 after using Pythagorean Identity.

The Pythagorean Identity states that sin²θ + cos²θ = 1. We can use this identity to find cosθ given that sinθ = (√2)/2 and θ terminates in Quadrant I.

Since sinθ = (√2)/2 and θ terminates in Quadrant I, we can draw a right triangle with angle θ in Quadrant I, opposite side equal to √2, adjacent side equal to 1, and hypotenuse equal to √3.

Using the Pythagorean Theorem, we can find the length of the hypotenuse as:

h² = a² + b²

√3² = 1² + (√2)²

3 = 1 + 2

3 = 3

So, the length of the hypotenuse is √3.

Now, we can use the Pythagorean Identity to find cosθ:

sin²θ + cos²θ = 1

Substituting sinθ = (√2)/2:

(√2/2)² + cos²θ = 1

Simplifying:

2/4 + cos²θ = 1

1/2 + cos²θ = 1

cos²θ = 1 - 1/2

cos²θ = 1/2

Since θ terminates in Quadrant I and sinθ is positive, we know that cosθ is also positive. Therefore, taking the positive square root of both sides, we get:

cosθ = √(1/2) = (√2)/2

So, cosθ = (√2)/2.

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The value of 2 digit number has order rotational of 2 is, 16

And, The value of 3 digit number has order rotational of 2 is, 931

Now, For a two-digit number with an order rotational of 2, it means that if you flip the digits, you get a different but still valid number.

Hence, There are a few such numbers, but one example is 16 which becomes 61 when you flip the digits.

And, For a three-digit number with an order rotational of 2, it means that if you rotate the digits, you get a different but still valid number.

And, There are also a few such numbers, but one example is 319 which becomes 931 when you rotate the digits.

Thus, The value of 2 digit number has order rotational of 2 is, 16

And, The value of 3 digit number has order rotational of 2 is, 931

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Answer:

60 degrees

Step-by-step explanation:

have a great day and thx for your inquiry :)

Answer:

6n+30

Step-by-step explanation:

Step 1:

Multiply 6 and n

Step 2:

Multiply 6 and 5

Step 3:

Put together!

have a great day and thx for your inquiry :)

Answer:

the answer is A

Step-by-step explanation:

distributive property states

a(b+c)=ab+ac

therefore

6(n+5)=6n+30