in triangle ABC AC =10 in. ,BC =2.5 in., and m angle C =63°. what is the area of triangle ABC?​

We can approach this problem by breaking down the two displacements of the ship into their respective x- and y-components and then adding them together to find the net displacement.

For the first displacement, the ship traveled 25° South of West for 250 miles. This can be broken down into an x-component and a y-component as follows:

x = 250 cos(25°) (to the west) y = -250 sin(25°) (to the south)

For the second displacement, the ship changed direction to 70° East of South and traveled 45 miles further. This can also be broken down into an x-component and a y-component:

x = 45 cos(70°) (to the east) y = -45 sin(70°) (to the south)

To find the net displacement, we can add the x-components and y-components separately:

total x = 250 cos(25°) + 45 cos(70°) total y = -250 sin(25°) - 45 sin(70°)

We can use these values to find the distance of the ship from its starting point by using the Pythagorean theorem:

distance = sqrt((total x)^2 + (total y)^2)

Substituting the values from above and evaluating:

distance = sqrt((250 cos(25°) + 45 cos(70°))^2 + (-250 sin(25°) - 45 sin(70°))^2)

distance ≈ 272.8 miles

To find the direction of the ship from its starting point, we can use the inverse tangent function to find the angle:

angle = atan(total y / total x)

Substituting the values from above and evaluating:

angle ≈ -65.1°

Since the angle is negative, we know that the direction is to the west of south. Therefore, the ship is approximately 272.8 miles away from its starting point in a direction that is 65.1° west of south.

The solution of the exponential equation 3^(3x-2) = 9^(4x-1) is x = 0.

We can solve this exponential equation for x by using logarithms. We can take the logarithm of both sides of the equation, using any base that we prefer. For instance, we can use the natural logarithm, ln:

ln(3^(3x - 2)) = ln(9^(4x - 1))

Now, we can use the properties of logarithms to simplify both sides of the equation. First, recall that ln(a^b) = b ln(a), for any positive value of a and any real value of b. Therefore, we have:

(3x - 2) ln(3) = (4x - 1) ln(9)

Next, we can use another property of logarithms, namely ln(a^b) = b ln(a) = ln(c) → a^b = c, to eliminate the natural logarithms from both sides of the equation. Specifically, we can rewrite ln(9) as ln(3^2), and then use the power rule for logarithms, ln(a^b) = b ln(a), to get:

(3x - 2) ln(3) = (4x - 1) ln(3^2) = 2 (4x - 1) ln(3)

Now, we can simplify the equation by multiplying out the coefficients of ln(3) on the left-hand side:

3x ln(3) - 2 ln(3) = 8x ln(3) - 2 ln(3)

Then, we can collect like terms:

3x ln(3) - 8x ln(3) = -2 ln(3) + 2 ln(3)

Finally, we can solve for x by factoring out ln(3) and dividing both sides by the resulting factor:

(3 ln(3) - 8 ln(3)) x = 0

-5 ln(3) x = 0

x = 0

Therefore, the solution of the exponential equation 3^(3x-2) = 9^(4x-1) is x = 0.

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By setting up the equation and solving for the unknown variable, we find that the number in question is -15. The answer provides a step-by-step method for solving an equation that represents a word problem.

Let's start by translating the given problem into an equation.

"The product of a number and -6" can be written as "-6x", where "x" is the unknown number. "Five times the sum of that number and 33" can be written as "5(x+33)".

Putting these together, we get:

-6x = 5(x+33)

Now we can solve for "x":

-6x = 5x + 165

-11x = 165

x = -15

Therefore, the number we're looking for is -15.

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Answer:

The answer to your problem is, g(3) = 18

Step-by-step explanation:

Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of                       - 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8

Listed in order 1 - 4

A. The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.

B. The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.

C. The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.

D. This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.

Thus the answer to your problem is, D. g(3) = 18

Sorry for the blurry picture!

Answer: Using the cofunction identity for tangent and cotangent:

cot(θ) = 1/tan(θ)

We can rewrite the given equation as:

cot(5θ - 32°) = 1/tan(θ + 26°)

Next, using the identity for the tangent of the sum of two angles:

tan(a + b) = (tan(a) + tan(b))/(1 - tan(a)tan(b))

We can rewrite the right side of the equation as:

1/tan(θ + 26°) = tan(90° - (θ + 26°)) = tan(64° - θ)

Substituting this back into the original equation:

cot(5θ - 32°) = tan(64° - θ)

Using the identity for the cotangent and tangent of the difference of two angles:

cot(a - b) = (cot(a)cot(b) - 1)/(cot(b) - cot(a))

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

We can rewrite the equation as:

(cot(5θ)cot(32°) - 1)/(cot(32°) - cot(5θ)) = (tan(64°)tan(θ) - tan(θ))/(1 + tan(64°)tan(θ))

Simplifying both sides:

(cot(5θ)cot(32°) - 1)/(cot(32°) - cot(5θ)) = (sin(64°)sin(θ))/(cos(64°)cos(θ) + sin(64°)sin(θ))

Cross-multiplying and simplifying:

cos(64°)cos(θ)cot(5θ) - sin(64°)sin(θ)cot(5θ) = -sin(64°)sin(θ)

cos(64°)cos(θ)cot(5θ) = sin(64°)sin(θ)(cot(5θ) + 1)

cos(64°)cos(θ)cot(5θ) = sin(64°)sin(θ)csc(5θ)

cos(64°)cos(θ) = sin(64°)sin(θ)sin(5θ)/cos(5θ)

cos(64°)cos(θ)cos(5θ) = sin(64°)sin(θ)sin(5θ)

Using the identity for the cosine of the sum of two angles:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

We can rewrite the equation as:

cos(64° + θ - 5θ) = 0

cos(64° - 4θ) = 0

64° - 4θ = 90° + k(180°) or 64° - 4θ = 270° + k(180°) where k is an integer

Solving for θ:

64° - 4θ = 90° + k(180°)

-4θ = 26° + k(180°)

θ = -(26°/4) - (k/4)(180°)

θ = -6.5° - 45°k

or

64° - 4θ = 270° + k(180°)

-4θ = 206° + k(180°)

θ = -(206°/4) - (k/4)(180°)

θ = -51.5° - 45°k

Therefore, there are two sets of solutions for θ, given by:

θ = -6.5

Step-by-step explanation:

The situation can be modeled by the following system of linear inequalities:

x ≥ 6 (The number of male volunteers should be at least 6)

x + y ≤ 15 (The total number of volunteers should be no more than 15)

y ≥ 0 (The number of female volunteers should be non-negative)

What is inequality model?

A formula exists for inequality. Less than, larger than, or not equal are used in place of the equal sign when there are inequalities. Rules for resolving disparities are unique. Here are a few examples of inequalities that are mentioned. When disparities are connected, the centre inequality can be jumped over.

The situation can be modeled by the following system of linear inequalities:

x ≥ 6 (The number of male volunteers should be at least 6)

x + y ≤ 15 (The total number of volunteers should be no more than 15)

y ≥ 0 (The number of female volunteers should be non-negative)

Explanation:

The first inequality states that the number of male volunteers, represented by x, should be greater than or equal to 6. This ensures that the science teacher has at least 6 male volunteers.

The second inequality states that the total number of volunteers, represented by x + y, should be no more than 15. This ensures that the science teacher does not exceed the maximum number of volunteers required for the competition.

The third inequality states that the number of female volunteers, represented by y, should be non-negative. This ensures that there are no negative values for the number of female volunteers.

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The dollar value, if Ahmed likes 4 times more the chocolate than the vanilla slice, then he finds C four times more valuable than V. Thus, Ahmed placed a chocolate slice is $1.75.

The foundational subject in mathematics, arithmetic covers operations with numbers. They include addition, subtraction, multiplication, and division. One of the major branches of mathematics, arithmetic serves as the cornerstone for students studying the subject of mathematics. Mathematical arithmetic is the study of the characteristics of the conventional operations on numbers.

Using C for the chocolate slice's value and V for the vanilla slice's value

4 slices × C + 4 slices × V = $14

If Ahmed  likes 4 times more the chocolate than the vanilla slice, then he finds C four times more valuable than V, thus

C = 4×V

4 slices ×4V + 4 slices ×V = $24

20 slices ×P = $14

P=$0.7/slice

V= 4×P = 4×$0.7/slice  = $2.8/slice

Thus for a slice that is half chocolate and half vanilla

value= 1/2 slice× C + 1/2 slice × V

= 1/2 slice ( $0.7 /slice + $2.8/slice)

=  $1.75

Hence,  Ahmed placed a chocolate slice is $1.75.

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Using the LIFO perpetual inventory method, the cost of the 18 units sold is $420.

The perpetual inventory strategy known as LIFO (Last In, First Out) is predicated on the idea that the most recent inventory purchases are sold first.

In order to account for the number of units sold, we use this method to count backward from the most recent inventory acquisition.

The business sold 18 units on November 8, which is more than its most recent purchase of 6 units on November 6. Therefore, starting with a total of 18 units, we first use the 10 units from the November 2 purchase and the 8 units from the November 6 buy.

10 units were bought on November 2 for a total of $220, or $22 each unit. The 8 pieces that were bought on November 6 cost $25 apiece, for a total of $200. Hence, $220 plus $200 equals $420 for the 18 units that were sold.

The cost of the 18 sold units, calculated using the LIFO perpetual inventory approach, is $420.

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The cosine of an angle in a right triangle is defined as the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse.

[tex]tanL = 15/8[/tex][tex]sinL = 15/17[/tex][tex]cosL = 8/17[/tex]

In a right triangle, the side opposite the right angle is called the hypotenuse (in this case, it's the side with length 17).

The other two sides are called the legs. We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:

hypotenuse^2 [tex]= leg1^2 + leg2^2[/tex]

For this triangle, we have:

[tex]17^2 = 8^2 + 15^2[/tex]

Simplifying this equation, we get:

[tex]289 = 64 + 225[/tex]

Therefore, the equation is true, and we have verified that this is a right triangle.

Now, we can use the trigonometric ratios to find the values of tanL, sinL, and cosL, where L is the angle opposite the leg with length 8.

The tangent of an angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Therefore, we have:

tanL = opposite/adjacent [tex]= 15/8[/tex]

The sine of an angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the hypotenuse. Therefore, we have:

sinL = opposite/hypotenuse [tex]= 15/17[/tex]

The cosine of an angle in a right triangle is defined as the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse. Therefore, we have:

cosL = adjacent/hypotenuse = 8/17

Therefore, , the values we found are:

[tex]tanL = 15/8[/tex]

[tex]sinL = 15/17[/tex]

[tex]cosL = 8/17[/tex]

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By using the trigonometric identities we get  ∅ = 0.5542.

The six trigonometric ratios serve as the foundation for all trigonometric equations. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The sides of the right triangle, such as the adjacent side, opposite side, and hypotenuse side, are used to describe each of these trigonometric ratios.

The given figure is a right-angled triangle.

We can use trigonometric identities,

Sin∅ =[tex]\frac{adjacent }{hypotenuse}[/tex]

Here we get the value adjacent = 10 and the hypotenuse = 19

Therefore we get the value,

sin∅ = [tex]\frac{10}{19}[/tex] = 0.5263

∅ = [tex]sin^{-1} (0.5263)[/tex]

∅ = 0.5542

Therefore the angle ∅ = 0.5542

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Answer:

distance = 180 km

Step-by-step explanation:

To find the total distance, we use this formula:

distance = speed * time

where speed is 48 km/hour and time is 3 [tex]\frac{3}{4}[/tex] hours.

inserting the value we get

distance = 48 km/hour × 3.75 hours

distance = 180 km

Answer:

X-intercept(s): (-3,0), (-8,0)

Y-intercept(s): (0,48)

Vertex: (-11/2,-25/2)

Step-by-step explanation:

X-intercepts: When you are finding the x-intercepts, there are two ways to find your x-intercepts like you can find in the Quadratic Formula or plug the equation into your calculator and see it on the graph/ table. If you like the quadratic formula, you need plug into the a, b, and c and it will look like x= -22±√(22^2)-4(2)(48))/2(2). It will be the same answer. on the another hand, if you like the calculator way, you get your calculator that need be TI-84 plus CE or TI-84 then go on y= then put your equation like 2x^2+22x+48 after that you click on graph. if you cant find the x-intercepts on the graph, you can do 2nd then above the graph buttom you can see it in the table. When you looking at the table, look for the 0s in the y table.

Y-intercept: When you are finding the y-intercepts, there are two ways to find your y-intercepts like you need plug in 0 for x or plug the equation into your calculator and see it on the graph/ table. If you like the quadratic formula, you need plug in 0 for x and it will look like y=2(0)^2 +22(0)+48. it would the get the same answer. if you like the calculator way, you get your calculator that need be TI-84 plus CE or TI-84 then go on y= then put your equation like 2x^2+22x+48 after that you click on graph. if you cant find the x-intercepts on the graph, you can do 2nd then above the graph buttom you can see it in the table. When you looking at the table, look for the 0s in the x table.

Vertex:

1. Get your equation in the form like this y=ax^2+bx+c

2. Calculate -b/2a. This is the x-coordinate of the vertex.

3. To find the y- coordinate of the vertex, simply plug the x to the quadratic equation and solve for y.

Comment if i am right or wrong

162,356 doctors were registered that year.

Explanation:

The questions says, "34.8% of all registered doctors are females"

(Consider, total number of registered doctors as [tex]x[/tex])

that's, [tex]34.8\%[/tex] of [tex]x[/tex] are female.

and [tex]34.8\%[/tex] of [tex]x[/tex] is 56,500.

Mathematically,

[tex]\dfrac{34.8}{100} \times x=56500[/tex]

[tex]x=56500\times\dfrac{100}{34.8}[/tex]

[tex]x=162356[/tex] doctors were registered that year.

La magnitud física que determina que un trabajador haga el trabajo en un tiempo menor que otro puede ser la RAPIDEZ.

La rapidez o también velocidad (si hablamos de vector) define porque un trabajador realiza un trabajo en 20 segundos y el otro en 12 segundos, significa que el primero es menos rápido que el segundo.  

De cierta manera pudieran estar otras magnitudes relacionadas como la potencia.

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The area of the trapezoid [tex]36^{2}[/tex] centimeters

To use the formula A = ¹h(b₁ + b₂) to find the area of a trapezoid, you need to know the height (h) and the lengths of the two parallel bases (b₁ and b₂).
For example,

The formula for finding the area of a trapezoid is A = ¹h(b₁ + b₂),

Where A represents the area of the trapezoid, h represents the height, and b₁ and b₂ represent the lengths of the two parallel bases.

By plugging in the given values for the height and bases and performing the necessary arithmetic operations, you can find the area of the trapezoid.

It's important to remember to use the correct units and follow the order of operations to obtain the correct result.

If the height of the trapezoid is 9 cm, the lengths of the two bases are 3 cm and 5 cm, you can plug these values into the formula to find the area :
A = ¹h(b₁ + b₂)

= ¹(9)(3 + 5)

= ¹(9)(8)

= 36 square centimeters
So, the area of this trapezoid is 36 square centimeters.
If you have different values for the height and bases, you can use the same formula to find the area.

Just make sure to use the correct units and follow the order of operations (parentheses first, then multiplication and division, then addition and subtraction).

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Option D is the correct answer, As a result, LM is 16.1 centimeters long.

The mid-segment of a triangle is aligned to the base and is half the length of the triangle.

MQ = therefore 1/2 LN.

LN = 16.1 centimeters because we know MQ = 8 cm.

MQ is parallel to side LM and half of its length because it is also the midpoint of the triangular LMN.

A line segment linking the midpoints of two of the triangle's sides is known as a mid-segment. It is half the length of the triangle's third edge and parallel to it. In other words, the mid-segment linking the midpoints of sides a and b has length c/2 and is parallel to side c if a triangle has sides of lengths a, b, and c.

Because of this, LM = 2MQ = 16.1 centimeters.

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Answer:

13%

Step-by-step explanation:

I have a test on  this  an i'm missing Cake batter. But I have sweet coconut and it says its 13%.

Answer:

The volume of the prism is 800(sqrt(3)) cubic inches.

Step-by-step explanation:

The volume of a triangular prism can be calculated by multiplying the area of the base (which is an equilateral triangle in this case) by the height of the prism.The area of an equilateral triangle can be calculated using the formula:A = (sqrt(3)/4) x s^2where A is the area and s is the length of one side of the triangle.In this case, the length of one side of the equilateral triangle is 20 inches, so we can substitute that into the formula:A = (sqrt(3)/4) x 20^2

A = (sqrt(3)/4) x 400

A = 100(sqrt(3)) square inchesNow that we have the area of the base, we can calculate the volume of the prism:V = A x h

V = 100(sqrt(3)) x 8

V = 800(sqrt(3)) cubic inches

To find the volume of a triangular prism, one must calculate the area of the base (in this case an equilateral triangle), and then multiply this by the height of the prism. Using the provided dimensions, the volume is calculated to be 800√3 cubic inches.

The question is asking us to find the volume of a triangular prism with an equilateral triangle as the base and a given height. The formula for the volume of a prism is Volume = Base Area * Height. Since the base is an equilateral triangle, its area can be calculated using the formula: Area = (sqrt(3) / 4) * side². By substituting the given side length of 20 inches, we find that the area of the base is sqrt(3) * 100 square inches. We then multiply this by the height of the prism, which is 8 inches, to find the total volume. So, the volume of the prism is 800√3 cubic inches.

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Answer: 4.5×10^0

Step-by-step explanation:

To calculate 9×10²/2×10², you can follow these steps:

Step 1: Simplify the expression by cancelling out the common terms:

9×10²/2×10² = (9/2)×(10²/10²)

Step 2: The 10² terms cancel each other out:

(9/2)×(10²/10²) = (9/2)×1 = 9/2

Step 3: Convert the simplified expression to scientific notation:

9/2 = 4.5, so the expression in scientific notation is 4.5×10^0 (since any number raised to the power of 0 is 1).

The result of the calculation is 4.5×10^0.

The pair of ratios that does not form a proportion is 103/24 and 5/40.

To check if two ratios form a proportion, we need to simplify them to their simplest form and compare them. If the two ratios are equal after simplification, then they form a proportion.

In this question, we are given five ratios: 103/24, 5/40, -30/15, 10/5, and 3/S.

To simplify the first ratio, we can divide both the numerator and denominator by their greatest common factor, which is 1. Therefore, the simplified form of 103/24 is 4.29 (rounded to two decimal places).

To simplify the second ratio, we can also divide both the numerator and denominator by their greatest common factor, which is 5. Therefore, the simplified form of 5/40 is 0.125.

When we compare these two simplified ratios, we can see that they are not equal. Therefore, the pair of ratios that does not form a proportion is 103/24 and 5/40.

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Which pair of ratios does NOT form a proportion?

103 24

5 40

-30 15

10 5

3 S

Answer:

B.

Step-by-step explanation:

I hope this is what you needed. =)

The claim that a line's reflection is actually two parallel lines is false. correct answer is option (A).

A line is reflected by another line, which is the original line's mirror image. Each point on the original line is reflected across a line of reflection, which is often perpendicular to the original line, to create the mirror image. The resulting line is consistent with the original line while being oriented in the other direction.

The statement that a line can be translated into another line with the same length and that it is parallel to the original line is true.

The statement that a line rotates into another line that is the same length and shape as the original line but is orientated at a different angle is also correct.

The rotation of a pair of parallel lines is also valid for a second pair of parallel lines that have the same distance between them but are orientated at a different angle from the initial pair.

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Answer:

a mode of negative number again gives the positive value

d. -(-61) =61 by multiplication sign rule

e. opposite of -61 =61

Answer: e

Step-by-step explanation:

the opposite is 61

The standard form of the expression is 2m² + m.

The standard form is referred to as the general way of representing any type of notation. The standard form formula represents the standard form of an equation which is the commonly accepted form of an equation. For example - The standard form of a polynomial is to write the terms with a higher degree first (descending order of degree) and its coefficients must be in integral form.

Combining like terms, we get:

(m² - m) + (2m + m²) = m² + m² - m + 2m

Simplifying further, we get:

2m² + m

Therefore, the sum of the given expressions is 2m² + m.

To write the answer in standard form, we arrange the terms in descending order of degree of the variable:

2m² + m = 2m² + 1m¹ + 0m⁰

So the standard form of the expression is 2m² + m.

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The average annual rate of change during the time period 2007-2012 is approximately 10,797 thousand subscribers per year.

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.

To find the average annual rate of change for this time period, we need to determine the total change in the number of cellular telephone subscribers from 2007 to 2012, and then divide by the number of years in the time period.

The total change in the number of subscribers from 2007 to 2012 is:

335,244 - 270,461 = 64,783

The number of years in the time period is:

2012 - 2007 + 1 = 6

So the average annual rate of change is:

64,783 / 6 = 10,797.17 (rounded to two decimal places)

If we round the average annual rate of change to the nearest unit, it would be 10,797 subscribers per year.

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The value of x cannot be determined and the answer is undefined.

To find the value of x in this scenario, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, triangle ABC is a right triangle with AB as the hypotenuse. So, we can use the Pythagorean theorem to solve for AC, which is equal to the square root of (AB^2 - BC^2).

Using the given values, we have:
AC = sqrt(16^2 - 8^2)
AC = sqrt(256 - 64)
AC = sqrt(192)
AC ≈ 13.86

Now, we can use triangle ACD to solve for x. This triangle is also a right triangle with CD as the hypotenuse. So, we can use the Pythagorean theorem again to solve for AD, which is equal to the square root of (CD^2 - AC^2).

Using the given values, we have:
AD = sqrt(9^2 - 13.86^2)
AD = sqrt(81 - 192.23)
AD = sqrt(-111.23)

We can't take the square root of a negative number, so there is no real solution for x in this scenario.

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the total tip left by Mary at the coffee shop is $0.11 + $0.99 = $1.10 (rounded to the nearest hundredth).

Why is it?

Let's break down the transactions and calculate the total tip left by Mary.

Mary orders a coffee at $2.15 and tips 5% at the counter:

Cost of coffee = $2.15

Tip = 0.05 x $2.15 = $0.11

Mary orders a latte at $4.50 and doesn't tip:

Cost of latte = $4.50

Mary orders another coffee at $2.15 and leaves a 15% tip for both the latte and coffee:

Cost of coffee = $2.15

Total cost of latte and coffee = $4.50 + $2.15 = $6.65

Tip = 0.15 x $6.65 = $0.99

Therefore, the total tip left by Mary at the coffee shop is $0.11 + $0.99 = $1.10 (rounded to the nearest hundredth).

A tip is an extra amount of money given as a gratuity or a gift to someone for their services, such as for a meal in a restaurant, a hairdresser, or a taxi driver. Tips are typically a percentage of the total cost of the service or goods provided.

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