12. Describe the graph of a quadratic function that has its vertex and a zero
at the same point.

The area of the triangle with side lengths of 25 cm, 7 cm, and 15 cm is approximately 209.27 cm².

To calculate the area of a triangle with side lengths of 25 cm, 7 cm, and 15 cm, we can use Heron's formula, which is a formula for finding the area of a triangle when only the side lengths are known:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides. The semi-perimeter is half the sum of the three sides:

s = (a + b + c) / 2

Substituting the given values, we get:

s = (25 + 7 + 15) / 2 = 23.5

Now we can use Heron's formula to calculate the area:

Area = √(23.5(23.5-25)(23.5-7)(23.5-15))

= √(23.5 * (-1.5) * 16.5 * 8.5)

= √(43,822.5)

≈ 209.27 cm²

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Julie is trekking to the Blue Ridge Mountains, therefore she is 10 1/12 miles from the beginning point M.

Distance in mathematics is a numerical representation of the actual area between two points. The shortest distance between those two points is how long the path is. The Pythagorean theorem, which asserts that in a right triangle, the sum of the squares of the lengths of the two legs (the sides perpendicular to one another) is equal to the square of the length of the hypotenuse, is used to determine the distance between two locations in a two-dimensional plane (the longest side, opposite the right angle).

given

We must determine Julie's total distance traveled before we can determine how far she is from the beginning location M. By combining the distances between each location, we may determine this:

3 3/8 miles from M to N

2 1/4 miles from N to P

P returning to M: 4 11/24 miles

We must identify a common denominator in order to aggregate these distances. Because it can be divided by 8, 4, and 3, we may pick 24 as the common denominator.

From M to N, the distance is 3 3/8 miles (or 27/8 kilometers). From N to P, it is 2 1/4 kilometers (or 9 kilometers).

We may now multiply the distances:

27/8 + 9/4 + 107/24 = (81 + 54 + 107) / 24

= 242/24

= 10 1/12

Julie is trekking to the Blue Ridge Mountains, therefore she is 10 1/12 miles from the beginning point M.

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Answer:

[tex]\huge\boxed{\sf 14 \ km}[/tex]

Step-by-step explanation:

7 hours = 98 km

Divide both sides by 7

7/7 hour = 98/7 km

[tex]\rule[225]{225}{2}[/tex]

According to the solving this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

The Nigerian visitor changed N70200 to rupees at a rate of 3 nairas to 35 rupees. Therefore,

70200 Nigerian naira = 70200 * 35 / 3 = 819500 Indian rupees

He spent 224,000 rupees, so the amount he invested at 41.5% per annum was:

819500 - 224000 = 595500 rupees

The simple interest he earned after 8 months at a rate of 41.5% per annum is:

595500 * (41.5/100) * (8/12) = 129702.5 rupees

So, the total amount he had after 8 months was:

595500 + 129702.5 = 725202.5 rupees

He then transferred this amount to his account in the Modern Bank of Nigeria at a rate of 21 rupees to 2 naira. Therefore,

725202.5 rupees = (725202.5 / 21) * 2 = 580162.5 Nigerian naira

this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.

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(a) The distribution of x is a binomial distribution with n=3 and p=0.41, where n is the number of trials (each of you playing level 4 one time) and p is the probability of success (defeating Bowser).

(b) The probability that only 1 of you defeats Bowser is given by the binomial probability formula:
P(x=1) = (3 choose 1)(0.41)^1(0.59)^2 = 0.411
(c) The variance of x is given by the formula:
Var(x) = np(1-p) = 3(0.41)(0.59) = 0.726
(d) The probability that you beat Bowser, regardless of whether your friends beat him or not, is simply the probability of success in one trial, which is 0.41.
(e) The distribution of y is a geometric distribution with p=0.41, where p is the probability of success (defeating Bowser).
(f) The probability that you play less than 3 times is given by the sum of the probabilities of playing 1 or 2 times:
P(y<3) = P(y=1) + P(y=2) = (0.41)^1(0.59)^0 + (0.41)^1(0.59)^1 = 0.651
(g) The expected number of times that you play is given by the formula:
E(y) = 1/p = 1/0.41 = 2.439

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The probability of choosing an odd prime number from 1 to 20 is 0.35

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The odd prime numbers between 1 and 20 are 3, 5, 7, 11, 13, 17, and 19. There are 7 odd prime numbers in this range.

The total number of possible choices is 20 (since there are 20 numbers in the range 1 to 20).

Therefore, the probability of choosing an odd prime number is:

number of odd prime numbers / total number of possible choices

= 7 / 20

= 0.35

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If a lorry travels 320km and uses 40 litres of petrol, the average rate of petrol usage for the lorry is 8 km per liter.

To find the average rate of petrol usage for the lorry, we need to divide the total distance traveled by the amount of petrol used. This will give us the number of kilometers traveled per liter of petrol.

In this case, the lorry traveled 320 km and used 40 liters of petrol, so we can calculate the average rate of petrol usage as follows:

Average rate of petrol usage = Total distance traveled / Amount of petrol used

= 320 km / 40 litres

= 8 km/litre

This means that for every liter of petrol used, the lorry can travel an average of 8 kilometers. This metric can be useful in comparing the fuel efficiency of different vehicles or in calculating the cost of a particular journey based on the price of petrol per liter.

In summary, calculating the average rate of petrol usage involves dividing the distance traveled by the amount of petrol used, resulting in a unit of km per liter.

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Answer: "An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.

Since 4.284 is not the square root of a negative number, it is not imaginary

Since 4.284 is a rational number from above, 4.284 is not an irrational number"

Step-by-step explanation: /\ I looked at a calculator for irrational numbers. Should be right, considering how it's well explained. Just search for "irrational number calculator". Dont rely on that. But it's there if

you need it! :)

No

It is a rational number since it is a fraction/decimal that isn't non-terminating, not is it pi or

The acceleration due to gravity on Earth is approximately 9.81 meters per second squared (m/s^2)

Acceleration due to gravity is the acceleration experienced by an object when it is dropped or falls freely in a gravitational field. On Earth, the value of acceleration due to gravity is approximately 9.81 meters per second squared. This means that if an object is dropped from a certain height, its velocity will increase by 9.81 m/s^2 for every second it falls.

The formula connecting mass and weight, W = m x g, shows that weight is directly proportional to the acceleration due to gravity. This means that as the value of acceleration due to gravity changes, the weight of an object will also change accordingly. The value of acceleration due to gravity is an important factor in various fields, including physics, engineering, and astronomy.

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The exponential function that relates the mass of the substance to the number of years since 2005 is: [tex]y = 600 \times e^(-0.048t)[/tex]  . [Where t is a number of years since 2005, and y is mass of the substance in milligrams at that time.]

An exponential function is a mathematical function of the form[tex]f(x) = a^x,[/tex] representing a rapid increase or decrease in value as x increases or decreases.

It represents a rapid growth or decay in value as the independent variable changes, and is used to model many natural phenomena such as population growth, compound interest, and radioactive decay.

The radioactive decay of the substance follows an exponential decay model. The formula for exponential decay is:

[tex]y = a * e^(-rt)[/tex]

Where:

y - amount of substance at time t.

a - initial amount of the substance.

r - decay rate per unit of time.

t - time elapsed since the start of the decay.

In this case, we know that the initial mass of the substance in 2005 was 600 milligrams. We also know that the substance decays by [tex]4.8[/tex]  % each year, which means that the decay rate per year is [tex]0.048[/tex]  (4.8% expressed as a decimal).

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Answer:

chocolate = $1.25

soft drink = $1.85

Step-by-step explanation:

Given price of chocolate is c and price of soft drink is s

Olivia: 5c + 2s = 9.95

Taylor: 6c + 6s = 18.60

6c + 6s = 18.60

divided by 6, we have

c + s = 3.1

=> s = 3.1 - c

Substitute s = 3.1 - c into

5c + 2s = 9.95

5c + 2(3.1 - c) = 9.95

5c + 6.2 - 2c = 9.95

3c = 9.95 - 6.2

3c = 3.75

c = 3.75/3 = 1.25

s = 3.1 - c = 3.1 - 1.25 = 1.85

1.  triangle = 180

7x7 = 49

180-49 = 131

2. 10x10 = 100 but since its a pyramid its degrees is 180

180-100=80

The discounted price of the camera is $270 and the price of the camera after the 40% increase is $378.

When the store offered a 40% discount on the original price of $450, the discounted price of the camera can be calculated as follows:

Discounted price = Original price - Discount

Discounted price = $450 - 40% x $450

Discounted price = $450 - $180

Discounted price = $270

Therefore, the discounted price of the camera is $270.

After the sale, the discounted price of the camera was increased by 40%. We can calculate the new price of the camera as follows:

New price = Discounted price + 40% x Discounted price

New price = $270 + 40% x $270

New price = $270 + $108

New price = $378

Therefore, the price of the camera after the 40% increase is $378.

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The point (a,2b) is on the line, and the equation of the line passing through (3a,0) and (0,3b) is y = (-a/b)x + 3b

We can use the two-point form of the equation of a straight line to find the equation passing through the points (3a,0) and (0,3b).

The two-point form of a straight line is given by,

y - y1 = m(x - x1)

where (x1, y1) and (x, y) are two points on the line, and m is the slope of the line.

Let's take the point (3a,0) as (x1, y1) and the point (0,3b) as (x, y). Then, we have:

y - 3b = [(0 - 3a)/(3b - 0)](x - 0)

Simplifying this, we get:

y - 3b = (-a/b)x

y = (-a/b)x + 3b

This is the equation of the line passing through (3a,0) and (0,3b).

Now, to show that this line passes through the point (a,2b), we substitute x = a and y = 2b into the equation of line:

2b = (-a/b)a + 3b

2b = -a + 3b

a = b

Therefore, the point (a,2b) is on the line

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Answer:

Step-by-step explanation:

The equation of the line with a slope of 1/6 passes through the point (-6, 5) is y=(1/6)x+6.

What is the equation of a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

Given that a line with a slope of 1/6 passes through the point (-6, 5). Therefore, we can write,

y = mx + c

Substitute the values,

5 = (1/6)(-6) + C

5 = -1 + C

5 + 1 = C

C = 6

Hence, the equation of the line with a slope of 1/6 passes through the point (-6, 5) is y=(1/6)x+6.

Answer:

y = (1/6)x + 7

Step-by-step explanation:

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We know that the line has a slope of 1/6 and passes through the point (-6, 6). To find the y-intercept, we can substitute the values of the point into the equation and solve for b:

y = mx + b

6 = (1/6)(-6) + b

6 = -1 + b

b = 7

Now that we know the slope and y-intercept, we can write the equation of the line in slope-intercept form:

y = (1/6)x + 7

Therefore, the equation of the line in slope-intercept form is y = (1/6)x + 7.

(Please could you kindly mark my answer as brainliest)

Answer:

a = 12.56637061

Step-by-step explanation:

a= 4 · π · r²

a= 4 · π · 1²

a= 4π

a= 12.56637061

a= 12.57

By speed formula, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.

What is speed?

Speed is defined as the distance travelled by an object in a given amount of time. Speed is a scalar quantity, meaning that it has magnitude but no direction.

Mathematically, speed is calculated as follows:

speed = distance / time

where "distance" is the distance travelled by the object, and "time" is the time it takes for the object to travel that distance.

Let's assume that Angela's shoveling rate is "a" and Franklin's shoveling rate is "f" (measured in driveways per hour). We can use the formula:

time = distance / rate

where "distance" is the length of the driveway (which we can assume to be 1 driveway) and "rate" is the shoveling rate (in driveways per hour).

According to the problem, Angela can shovel the driveway in 2 hours, so her shoveling rate is:

a = 1/2

When Franklin joins her, they can finish the driveway in 54 minutes, or 9/10 of an hour. Therefore, their combined shoveling rate is:

(a + f) = 1 / (9/10) = 10/9

We can now set up a system of equations to solve for "f".

First, we know that Angela and Franklin can finish the driveway in 9/10 of an hour:

1/2 + f = 1 / (9/10)

Multiplying both sides by 10/9, we get:

5/9 + (10/9)f = 1

Simplifying, we get:

(10/9)f = 4/9

f = (4/9) * (9/10)

f = 4/10

f = 2/5

Therefore, Franklin's shoveling rate is 2/5 of a driveway per hour. To find how long it would take him to shovel the driveway alone, we can use the formula:

time = distance/rate

time = 1 / (2/5)

time = 5/2

time = 2 1/2 hours

Therefore, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.

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The area of each part of the figure and then the whole figure, can be found to be :

The area of Triangle A would be :

= 1 / 2 x  Base x height

= 1 / 2 x ( 2 + 2 + 6 ) x 4

= 1 / 2 x 10 x 4

= 20 units ²

The area of Triangle D is :

= 1 / 2 x base x height

= 1 / 2 x 6 x 2

= 6 units ²

The area of the whole figure would then be:

= 20 + 2 + 4 + 6

= 32 units ²

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Answer:  b<-7/4

Step-by-step explanation:

Let's collect numbers with same variables to the same side:

-3-4>9b-5b

-7>4b

b<-7/4

Answer:

|a × [ob + (1 - o)a]| = √(7 - 8o(a · o) - 8(a · o)^2)

where k = 7 - 8o(a · o) - 8(a · o)^2.

Step-by-step explanation:

Given the position vectors of two points A and B as a and b respectively, where b is a unit vector, and the magnitude of a is twice that of b, we are asked to show that:

|a × [ob + (1-o)a]| = √k,

where k is a constant to be determined.

We can begin by expanding the vector inside the cross product:

ob + (1 - o)a = ob + a - oa

Since b is a unit vector, we can write:

ob = b - o

Substituting this into the previous equation, we get:

ob + (1 - o)a = b - o + a - oa = b + (1 - o)a - oa

Next, we can use the vector cross product formula:

|a × b| = |a||b|sinθ

where θ is the angle between a and b.

We are given that the angle between a and b is 60°, so we can substitute this value into the formula:

|a × b| = |a||b|sin60° = (2|b|)(1)(√3/2) = √3

Now we can calculate the cross product of a and the vector we just derived:

a × [ob + (1 - o)a] = a × (b + (1 - o)a - oa)

= a × (b + a - oa)

= a × b + a × a - a × oa

Since b is a unit vector, we know that a × b is a vector perpendicular to both a and b, and therefore perpendicular to the plane containing a and b. The vector a × a is 0 since the cross product of a vector with itself is 0. Finally, we can use the vector triple product to simplify a × oa:

a × oa = (a · a)o - (a · o)a = |a|^2 o - (a · o)a

Since |a| is twice |b|, we have:

|a|^2 = 4|b|^2 = 4

Substituting this back in, we get:

a × oa = 4o - (a · o)a

Putting it all together, we have:

a × [ob + (1 - o)a] = a × b + 4o - (a · o)a

Now we can take the magnitude squared of both sides:

|a × [ob + (1 - o)a]|^2 = (a × b + 4o - (a · o)a) · (a × b + 4o - (a · o)a)

Expanding the dot product, we get:

|a × [ob + (1 - o)a]|^2 = |a × b|^2 + 16o^2 + |a|^2(o · o) - 8o(a · o)b + 8(a · o)(a × b) - 2(a · o)^2|a|^2

Substituting the values we derived earlier, we get:

|a × [ob + (1 - o)a]|^2 = 3 + 16o^2 + 4(o · o) - 8o(a · o) + 0 - 2(a · o)^2(4)

= 7 - 8o(a · o) - 8(a · o)^2

Now we need to find the value of k such that the left-hand side equals k:

|a × [ob + (1 - o)a]|^2 = k

Using the vector triple product again, we can simplify the left-hand side as:

|a × [ob + (1 - o)a]|^2 = |a|^2|ob + (1 - o)a|^2 - ((a · [ob + (1 - o)a])^2)

Since we know that the magnitude of a is twice that of b, we have:

|a|^2 = 4|b|^2 = 4

Substituting this back in, we get:

|a × [ob + (1 - o)a]|^2 = 4|ob + (1 - o)a|^2 - ((a · [ob + (1 - o)a])^2)

Now we can substitute the expanded expression for ob + (1 - o)a:

|a × [ob + (1 - o)a]|^2 = 4|b + (1 - o)a|^2 - ((a · [b + (1 - o)a - oa])^2)

= 4|b|^2 + 8|b|(1 - o)(a · b) + 4(1 - o)^2|a|^2 - ((a · b + (1 - o)(a · b) - (a · o)(a · b))^2)

= 4 + 8(1 - o)(a · b) + 4(1 - o)^2(4) - ((a · b + (1 - o)(a · b) - (a · o)(a · b))^2)

= 28 - 8o(a · b) - 8(a · o)^2

Substituting this back into the previous equation, we get:

28 - 8o(a · b) - 8(a · o)^2 = k

Therefore, we have:

|a × [ob + (1 - o)a]| = √(28 - 8o(a · b) - 8(a · o)^2)  and

k = 28 - 8o(a · b) - 8(a · o)^2

Hope this helps! Sorry if it's wrong! If you need more help, ask me! :]

From the given information provided, the expected value of X = np, the variance of X = npq and the probability that X is odd is 0.4824 rounded to four decimal places.

(a) The probability of finding k defective items out of n can be calculated using the binomial distribution:

P(X=k) = C(n,k) ×[tex]p^k[/tex] × [tex]q^(n-k)[/tex], where C(n,k) is the binomial coefficient.

The possible values of K: 0, 1, 2, ..., n.

To show that the probability that X is even is 1/2[1+(1-2p)ⁿ], we use the binomial theorem to expand (p+q)ⁿ+(q-p)ⁿ as:

(p+q)ⁿ + (q-p)ⁿ = ∑[k=0,n]C(n,k) × [tex]p^k[/tex] × [tex]q^(n-k)[/tex] + ∑[k=0,n]C(n,k) × [tex](-1)^k[/tex] × [tex]p^k[/tex]× [tex]q^(n-k)[/tex]

The first sum corresponds to the probability of finding an even number of defective items, while the second sum corresponds to the probability of finding an odd number of defective items. Therefore,

P(X is even) = (1/2)[(p+q)ⁿ + (q-p)ⁿ]

= (1/2)[(p+q)ⁿ - (p-q)ⁿ] (since q-p = 1-2p)

= (1/2)[(1)ⁿ + (1-2p)ⁿ] (since p+q = 1)

Thus, the probability that X is even is 1/2[1+(1-2p)ⁿ].

(b) The expected value of X is:

E(X) = ∑[k=0,n]k × P(X=k)

= ∑[k=0,n]k × C(n,k) × [tex]p^k[/tex]× [tex]q^(n-k)[/tex]

Using the identity ∑[k=0,n]k × C(n,k) ×[tex]p^k[/tex] × [tex]q^(n-k)[/tex] = np, the expected value simplifies to:

E(X) = np

The variance of X is given by:

Var(X) = E(X²) - [E(X)]²

= ∑[k=0,n]k² × P(X=k) - (np)²

= ∑[k=0,n]k² × C(n,k) × [tex]p^k[/tex] × [tex]q^(n-k)[/tex]- n²p²

Using the identity ∑[k=0,n]k² × C(n,k) ×[tex]p^k[/tex] × [tex]q^(n-k)[/tex] = n(n-1)p² + npq, the variance simplifies to:

Var(X) = n(n-1)p² + npq - n²p²

= npq

(c) Using the formula for the expected value and variance of X, we can write:

0.0125 = E(X) = np

0.9875 = Var(X) = npq

Solving for p and q, we obtain:

p = 0.01 and q = 0.99

Therefore, the probability that X is odd can be calculated using the formula for the probability that X is even derived in part (a):

P(X is odd) = 1 - P(X is even)

= 1 - 1/2[1+(1-2p)ⁿ]

= 1 - 1/2[1+(1-2*0.01)ⁿ]

= 1/2[1-(0.98)ⁿ]

Substituting n = 1/0.98 ln(0.0125/0.01) = 24.68

P(X is odd) = 0.482

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The greatest number of tens that can live in the tens house is 9.

The greatest number of tens that can live in the tens house depends on how many digits there are in the number.

Let's start with a two-digit number, like 99. In this number, the leftmost digit represents the number of tens, so we want to find the largest digit that can be in that place.

Since we are limited to using only the digits 0-9, the largest digit that can be in the tens place is 9.

Now, let's consider a three-digit number, like 456. Again, we want to find the largest digit that can be in the hundreds place.

Since we are limited to using only the digits 0-9, the largest digit that can be in the hundreds place is also 9. So, we can have up to 9 groups of ten (or 90) in the hundreds place.

In the tens place, we can again have up to 9 groups of ten, and in the units place, we can have any digit from 0-9.

Therefore, the greatest number of tens that can live in the tens house in a three-digit number is 9.

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Answer:

The perimeter is the sum of all the sides of the rectangle. So, adding up all the given sides, we get:

Perimeter = 2u + u + 10 + u + 10 + 8u

Simplifying the expression by combining like terms, we get:

Perimeter = 12u + 20

Therefore, the simplified answer for the perimeter is 12u + 20.

Answer: Your welcome!

Step-by-step explanation:

y= 3x-2; This is a linear equation with a slope of 3 and a y-intercept of -2, which has the solution (3,4).

Thanks! #BO

Tristan has 14 nickels and 7 dimes worth of $1. 40.

This is because 1 nickel is worth 5 cents and 1 dime is worth 10 cents.

Let's use the following variables to represent the number of nickels and dimes Tristan has:

n = number of nickels

d = number of dimes

We know that Tristan has $1.40 worth of nickels and dimes. Each nickel is worth $0.05 and each dime is worth $0.10, so we can write an equation based on their values:

0.05n + 0.1d = 1.4

We also know that Tristan has twice as many nickels as dimes:

n = 2d

We can substitute n = 2d into the first equation and solve for d:

0.05(2d) + 0.1d = 1.4

0.1d + 0.1d = 1.4

0.2d = 1.4

d = 7

So Tristan has 7 dimes. Using n = 2d, we can find the number of nickels:

n = 2(7) = 14

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Answer: A ‍♀️

Step-by-step explanation:

Therefore, the density of the drink is approximately 1.04 grams per cm³.

Volume is a measure of the amount of space occupied by a three-dimensional object or substance. It is the amount of space inside an object or container and is usually measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

Given by the question.

To calculate the density of the drink, we need to first calculate the total mass of the drink, which is the sum of the masses of apple juice, fruit syrup, and sparkling water.

Mass of apple juice = volume of apple juice x density of apple juice = 35 cm³ x 1.04 g/cm³ = 36.4 g

Mass of fruit syrup = volume of fruit syrup x density of fruit syrup = 25 cm³ x 1.6 g/cm³ = 40 g

Mass of sparkling water = volume of sparkling water x density of sparkling water = 270 cm³ x 0.99 g/cm³ = 267.3 g

Total mass of the drink = mass of apple juice + mass of fruit syrup + mass of sparkling water

= 36.4 g + 40 g + 267.3 g

= 343.7 g

Now we can calculate the density of the drink by dividing the total mass by the volume of the drink:

Density of the drink = total mass of the drink / volume of the drink = 343.7 g / 330 cm³ = 1.04 g/cm³ (approx.)

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Answer: 37.5 million

Step-by-step explanation:

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