A car wash cost $12.50 at a local car-wash place. If you leave a 20% tip, how much are you actually leaving in tip? (What is the tip in dollars?)

The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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To calculate the number of four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit, we need to consider the following:

1. Selecting the suits: There are 4 suits in a deck (hearts, diamonds, clubs, and spades). We need to choose two suits out of these four.

2. Selecting the two cards of one suit: Once we have chosen the two suits, we need to select two cards from one of the chosen suits. There are 13 cards in each suit, so we can choose 2 cards from the 13 available.

3. Selecting the two cards of another suit: After selecting the first suit, we need to choose two cards from the remaining suit. Again, there are 13 cards to choose from.

To calculate the total number of four-card hands satisfying these conditions, we multiply the number of choices at each step. Therefore, the total number of such hands is:

4C2 * 13C2 * 13C2 = (4! / (2! * 2!)) * (13! / (2! * 11!)) * (13! / (2! * 11!))

= 6 * (13 * 12 / (2 * 1)) * (13 * 12 / (2 * 1))

= 6 * 78 * 78

= 36,432.

Therefore, there are 36,432 four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit.

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Given that the particle moves along the curve y=e^(2x) and the magnitude of its velocity is v=5ft/s.A particle moving along a curve is given by:y = e^(2x)Taking the derivative of this function with respect to time t will give the velocity function as follows;dy/dt = 2e^(2x) dx/dt ............................... (1)We know that the magnitude of velocity is constant v = 5ft/s.

Therefore, we can use the velocity function to solve for dx/dt and dy/dt as shown below;dx/dt = v/√(4e^(4x)) = v/(2e^(2x)) ................ (2)Substituting equation (2) into (1), we get;dy/dt = 2e^(2x) dx/dt = 2e^(2x) * v/(2e^(2x))=v = 5 ft/sHence, the y-component of velocity when the particle is at y = 8 ft is 5 ft/s.

Therefore, we can use the slope of the curve at point y = 8 ft to find the angle of the slope, then use trigonometry to solve for the x-component of velocity.

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Step-by-step explanation:

In the figure below, determine the perimeter of AEFG.

26

26

DG

2x + 15

39 units

55 units

66 units

o

82 units

The width of the path surrounding the garden is 1 meter.

To find the width of the path surrounding the garden, we need to factor the given area expression,\(4x^2 + 40x - 44,\) and identify the value of x.
Factor out the greatest common divisor (GCD) of the terms in the expression:
GCD of\(4x^2,\) 40x, and -44 is 4.

So, factor out 4:
\(4(x^2 + 10x - 11)\)
Factor the quadratic expression inside the parenthesis:
We need to find two numbers that multiply to -11 and add up to 10.

These numbers are 11 and -1.
So, we can factor the expression as:
4(x + 11)(x - 1)
Since we are looking for the width of the path (x), and it's not possible to have a negative width, we can disregard the negative value and use the positive value:
x - 1 = 0
x = 1.

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Answer:

n + 10

Step-by-step explanation:

im pretty sure thats right, im sorry if not but have a great day!

Answer:

I'm not tryna be a but do u know how to ask questions in the app

Step-by-step explanation:

pls

Rent, insurance, commissions, and other expenses could be added to the operating costs of a service-based business. Most of these expenses are regular daily expenses.

A continuing cost for maintaining a system, a business, or a product is known as an operating expense, operating expenditure, operational expenditure, operational expenditure, or OPEX.

The expense of creating or providing non-consumable pieces for the system or product is known as capital expenditure (capex).

For instance, the annual costs of paper, toner, power, and maintenance for a photocopier are opex, while the cost of the photocopier itself is capex.

Additional running costs for a service-based business could include rent, insurance, commissions, and other costs.

The majority of these costs are routine daily spending.

Costs that weren't directement necessary for those activities are referred to be non-operating expenses.

Therefore, rent, insurance, commissions, and other expenses could be added to the operating costs of a service-based business. Most of these expenses are regular daily expenses.

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Correct question:

A service business may have some additional operating expenses like rent, insurance, commissions, and so on. Most of these expenses are incurred on a ___ basis.

Therefore, the average value of the function \(f(x) = x^2 - 7\) on the interval [0,9] is 20.

To find the average value of the function \(f(x) = x^2 - 7\) on the interval [0,9], we need to evaluate the definite integral of the function over that interval and divide it by the length of the interval. The average value is given by:

=1/(b - a) * ∫[a,b] f(x) dx

In this case, a = 0 and b = 9, so we have:

Average value = 1/(9 - 0) * ∫[0,9] \((x^2 - 7) dx\)

Simplifying, we have:

Average value = 1/9 * ∫[0,9] \((x^2 - 7) dx\)

To find the integral, we evaluate each term separately:

∫[0,9] \(x^2\) dx = (1/3) * \(x^3\) | from 0 to 9

\(= (1/3) * (9^3 - 0^3)\)

= (1/3) * 729

= 243

∫[0,9] -7 dx = -7 * x | from 0 to 9

= -7 * (9 - 0)

= -7 * 9

= -63

Substituting these values back into the equation for the average value, we get:

Average value = 1/9 * (243 - 63)

= 1/9 * 180

= 20

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The largest angle in the triangle is approximately 108.46 degrees as the sides of the length are 745 feet.

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is often studied in mathematics and other fields.

To find the largest angle in the triangle, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of the angles opposite those sides. The formula is:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the length of the side opposite the angle C, and a and b are the lengths of the other two sides.

In this case, we want to find the largest angle, which is opposite the longest side, 745 feet. So we can let c = 745, a = 660, and b = 540, and solve for cos(C):

745^2 = 660^2 + 540^2 - 2(660)(540)cos(C)

Simplifying and solving for cos(C), we get:

cos(C) = (745^2 - 660^2 - 540^2) / (2(660)(540))

cos(C) = -0.3245

To find the angle C, we can take the inverse cosine of -0.3245 (which gives us the angle in radians), and convert it to degrees:

C = cos(-0.3245) ≈ 1.891 radians ≈ 108.46 degrees.

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Answer: \(y \leq -\frac{x}{2}-\frac{7}{2}\)

Step-by-step explanation:

\(-x-2y \geq 7\\\\x+2y \leq -7\\\\2y \leq -x-7\\\\y \leq -\frac{x}{2}-\frac{7}{2}\)

The function of the town's population is an exponential growth

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

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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Answer:

I believe is 3 4/6

Step-by-step explanation:

22/5  : 6/5

22/5 * 5/6

22/6

11/3

3 4/6

Answer:

11/3 or 3and2/3

Step-by-step explanation:

To change a mixed number into a fraction, you multiply the whole number by the denominator and add it to the numerator.

4 and 2/5 = 22/5

1 and 1/5 = 6/5

To divide fractions, flip one upside down and then multiply top by top, bottom by bottom

(22/5) / (6/5) = (22/5) x (5/6) = (22x5)/(5x6) = 110/20 = 11/3 or 3and2/3

The simplified form of the expression 2( ³√64 + √25 ) is 18.

Given the expression in the question;

2( ³√64 + √25 )

First, simplify each term.

2( ³√64 + √25 )

Rewrite 64 as 4³

2( ³√( 4³ ) + √25 )

Also, rewrite 25 as 5²

2( ³√( 4³ ) + √( 5² ) )

Now, pull the terms out of the radical, assuming positive real numbers.

Take the cube root of 4³

2( 4 + √( 5² ) )

Take the square root of 5²

2( 4 +  5  )

Add 4 and 5

2( 9 )

Multiply 2 and 9

18

Therefore, the simplified form is 18.

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The distance that exists from the point Z is given as 150,75 feet

The larger triangle is represented by the letters B, A, and C, and the smaller triangle is located here. These points are denoted as z and y, respectively, therefore we have supplied The value of b y is 201. A c equals 512 r, p equals 384 feet, and the z  must now be located. Triangles c, a, and b are simply comparable to triangles r, p, and q, which means that a c upon r p

To solve the problem we have

Δ RPG = ΔCAB

Δc / ΔB = by / zq

ZQ = BY * RP / Ac

= 201 * 384 / 512

= 150 . 75 FEET

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a police officer is determining where to park his vehicle in order to observe traffic at the red light. if AC=512 feet, RP= 384 feet, and point Y is 201 feet from point B, how far is point Z from point Q

After reduced speed when race resumes the number of laps left are 6 2/3 laps.

What is the definition of speed?

The following is the definition of speed:

The rate with which the position of an item changes .

The ratio of distance travelled to time taken in travelling is known as speed. Speed is a scalar number because it has only one direction and no magnitude.

Formula for Speed

The speed formula is as follows:

s=d/t

Where,

s= speed in metres per second, d = distance travelled in metres, and t = time in seconds.

Now,

Total laps left for the lead car= 7 1/2

After race is paused or reduced speed for race until 5/6 of a lap

so only 1/6 of a lap had normal racing

so total lap left is 15/2-1+1/6

=45-6+1/6

=40/6

=20/3

=6 2/3

Hence,

          when race resumes the number of laps left are 6 2/3 laps.

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(a) To find the probability that a player defeats all 3 opponents in a game, we need to multiply the individual probabilities of defeating each opponent. Since the probability of defeating each opponent is 75% or 0.75, we can calculate it as follows:

Probability of defeating all 3 opponents

\(\\= 0.75 * 0.75 * 0.75 \\= 0.4219\)

Therefore, the probability that a player defeats all 3 opponents in a game is \(0.4219\).

(b) To find the probability that a player defeats at least 2 opponents in a game, we need to consider three cases: defeating all 3 opponents, defeating exactly 2 opponents, and defeating exactly 1 opponent. The probability can be calculated as follows:

Probability of defeating at least 2 opponents = Probability of defeating all 3 opponents + Probability of defeating exactly 2 opponents + Probability of defeating exactly 1 opponent

Probability of defeating all 3 opponents

= \(0.4219\) (from part (a))

Probability of defeating exactly 2 opponents

\(= 3 * (0.75 * 0.75 * 0.25) \\= 0.4219\)

Probability of defeating exactly 1 opponent

\(= 3 * (0.75 * 0.25 * 0.25) \\= 0.1406\)

Probability of defeating at least 2 opponents

\(= 0.4219 + 0.4219 + 0.1406 \\= 0.9844\)

Therefore, the probability that a player defeats at least 2 opponents in a game is \(0.9844\).

(c) If the game is played 2 times, we need to find the probability that the player defeats all 3 opponents at least once in the two games. To calculate this probability, we can find the complementary probability that the player never defeats all 3 opponents in both games and subtract it from 1.

Probability of not defeating all 3 opponents in one game

\(= 1 - 0.4219 \\= 0.5781\)

Probability of not defeating all 3 opponents in both games

\(= 0.5781 * 0.5781 \\= 0.3341\)

Probability of defeating all 3 opponents at least once in two games

\(= 1 - 0.3341 \\= 0.6659\)

Therefore, the probability that the player defeats all 3 opponents at least once in two games is \(0.6659\).

By following the above calculations, we can determine the probabilities related to the player's performance in the game.

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Given:

The given endpoints are ( -2,10) and (-10, -12).

Required:

We need to find the midpoint of te given endpoints.

Explanation:

Consider the formua to find the midpoint.

Consider the points ( -2,10) and (-10, -12).

Final answer:

Answer:

4 oranges

Step-by-step explanation:

Step one:'

given data

A grocery store sells a bag of 5 oranges for $3.10

Required

The number of oranges bought for $2.48

Step two:

if  5 oranges cost $3.10

then x oranges will cost $2.48

cross multiply we have

3.1x= 5*2.48

divide both sides by 3.1

x=12.4 /3.1

x=4 oranges

In exercise 67, the region of integration is the triangle in the first quadrant that lies above the line y = (2/3)x + 3/2. The solid whose volume is given by the double integral is a pyramid with a triangular base. In exercise 68, the region of integration is the disk in the xy-plane centered at the origin with radius 6. The solid whose volume is given by the double integral is a hemisphere.

In exercise 67, the double integral is taken over the region R in the xy-plane defined by 0 ≤ x ≤ 3 and (2/3)x + 3/2 ≤ y ≤ 2. This region is a triangle in the first quadrant that lies above the line y = (2/3)x + 3/2.

To sketch the solid whose volume is given by the double integral, we consider the integrand f(x,y) = (1/2)(3x - 2y + 3). The double integral ∬R f(x,y) dy dx gives the volume of the solid bounded by the surface z = f(x,y) and the xy-plane over the region R.

We can see that the surface z = f(x,y) is a plane that intersects the xy-plane along the line y = (3/2)x + 3/2, and it intersects the y-axis at (0,3) and the x-axis at (1.5,0). Therefore, the solid whose volume is given by the double integral is a pyramid with a triangular base.

In exercise 68, the double integral is taken over the region R in the xy-plane defined by x^2 + y^2 ≤ 225. This region is a disk in the xy-plane centered at the origin with radius 6.

To sketch the solid whose volume is given by the double integral, we consider the integrand f(x,y) = √(225 - x^2 - y^2). The double integral ∬R f(x,y) dy dx gives the volume of the solid bounded by the surface z = f(x,y) and the xy-plane over the region R.

We can see that the surface z = f(x,y) is a hemisphere with radius 15 centered at the origin. Therefore, the solid whose volume is given by the double integral is a hemisphere.

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Answer:

the two factors are (x + 1 ) , (x - 5)

Step-by-step explanation:

The factors of the quadratic equation x² - 4x - 5 is (x + 1) (x - 5)

A quadratic equation is an algebraic expression whose power is raised to the second degree. The solution of a quadratic equation usually leads to a pair of two factors.

From the given question, we are going to look for two numbers:

Thus, the expansion of the quadratic equation will lead to the following factors:

= (x + 1) (x - 5)

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Scientists found an animal skull during an excavation and tested the amount of carbon -14 left in it. They found that 55 percent of the carbon-14 in the skull remained.

55% of the Carbon is left in the skull.

If A₀ was the original amount of Carbon, the amount of Carbon that is remaining will be 55% of A₀  which equals 0.55A₀

Using the given equation:

\(A = A_{o}e^{-0.000124t}\\\\ 0.55A_{o} = A_{o}e^{-0.000124t}\\ \\0.55 = e^{-0.000124t}\\\\In(0.55) = In(e^{-0.000124t})\\\\In(0.55) = -0.000124t*In(e)\\\\In(0.55) = -0.000124t\\\\\)

\(t = \frac{In(0.55)}{-0.000124} \\\\t = 4821\)

Rounding of to nearest year, we can conclude that the animal was buried 4821 years ago.

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Answer:3

Step-by-step explanation:

7x3=21 4x3=12 21÷12=9 3x3=9

Answer:

Step-by-step explanation:

7 × 3 = (3 × 3) + (4 × 3)

Answer:

-4 + -10

Step-by-step explanation:

Even with an addition sign, it still adds up to the same amount.

Hope this helps!

(Btw, if u get this right, pls do brainliest, I really need it! Thanks!)

The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

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Answer:

its true

Step-by-step explanation:

If a = b = c in an equilateral triangle and prove it \(r:R:r_1= 1:2:3\)

Step -1: Deducing the formulas.

 Here for any triangle R denotes circum radius.

and R = abc / 4Δ ​

(where a , b , c are 3 sides and △ is the area.)

r denotes in radius.

r = △ / S \((S = \frac{a+b+c}{2} )\)

\(r_1\) denotes radius opposites to A vertices.

\(r_ 1\) = △ / S -a

Step -2: Deducing value of R , r and \(r_1\)

Here let’s assume that the side length is a.

So, area △= \(\frac{\sqrt{3} }{4}a^2\)

\(S = \frac{a+b+c}{2} = \frac{3a}{2}\)

so, r= △/s = \(\frac{\frac{\sqrt{3} }{4}a^2 }{\frac{3a}{2} } =\frac{a}{2\sqrt{3} }\)

​ R= abc/ 4△ = \(\frac{a^3}{(4)\frac{\sqrt{3} }{4}a^2 }\)\(= \frac{a}{\sqrt{3} }\)

\(r_ 1\) = △ / S -a  \(= \frac{\frac{\sqrt{3} }{4}a^2 }{\frac{3a}{2}-a } =\frac{\sqrt{3a} }{2}\)

Step -3: Calculating the proportion of three.

So, \(r:R:r_1\) = \(\frac{a}{2\sqrt{3} } :\frac{a}{\sqrt{3} }:\frac{\sqrt{3}a }{2}\)

=> \(\frac{1}{2\sqrt{3} } :\frac{1}{\sqrt{3} }:\frac{\sqrt{3} }{2}\)

= 1 : 2 : 3

\(r:R:r_1= 1:2:3\)

Hence Proved.

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The event of Juan choosing at least one blue marker from the bag when randomly selecting 6 markers is certain.

In this scenario, Juan has a total of 7 markers in his bag, with 3 blue markers and 4 red markers. When he randomly chooses 6 markers from the bag, it is certain that he will select at least one blue marker. This is because there are more blue markers (3) than the number of markers he is selecting (6).

To understand why this event is certain, consider the worst-case scenario where Juan selects all 4 red markers first. Even in this case, there will still be 2 markers left in the bag, both of which are blue. Therefore, Juan is guaranteed to choose at least one blue marker when selecting 6 markers from the bag.

Since there are more blue markers available than the number of markers Juan is choosing, it is certain that he will select at least one blue marker. This makes the event of choosing at least one blue marker from the bag when randomly selecting 6 markers a certain event.

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