The following excerpt comes from the international bottled water association:

"in 2012, total u.s. bottled water consumption increased to 9.67 billion gallons, up from 9.1 billion gallons in 2011. in fact, 2012's consumption growth was the strongest it has been in five years. in addition, per-capita consumption is up 5.3 percent in 2012, with every person in america drinking an average of 30.8 gallons of bottled water last year. bottled water increased in absolute volume more than any other beverage category in the u.s. bottled water sales increased by 6.7 percent in 2012, and now total $11.8 billion."

(i) quantify the bottled water consumption increase from 2011 to 2012 in terms of relative change. (express your answer as a percent rounded correctly to the nearest tenth of a percent.)
%

(ii) if bottled water sales are up by 6.7% in 2012 to a total of $11.8 billion, what were the sales in 2011? (express your answer in billions of dollars rounded correctly to the nearest tenth.)
$
11.1
billion

(iii) estimate the per capita consumption from 2011 from data in the statement. (express your answer rounded correctly to the nearest tenth of a gallon.)
gallons

With the help of linear equation 3 3/5+x=7 1/5, Elana ran 3 3/5 miles.

What exactly is a linear equation?

A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0, for example, x-10=0. In this equation, x is a variable, A is a coefficient, and B is constant.

A linear equation in two variables has the conventional form Ax + By = C, for example, 2x-4y=10. The variables x and y are variables, the coefficients A and B are coefficients, and the constant C is a constant.

Now,

Given that Emily ran 3 3/5 miles.

and Emily and Elana together ran 7 1/5 miles

i.e. 3 3/5+x=7 1/5

where x= Miles Elana ran

then x=7 1/5 - 3 3/5

=3 3/5

hence,

      The  linear equation will be 3 3/5+x=7 1/5 and Elana ran 3 3/5 miles.

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Answer: 10

Step-by-step explanation:

77 divided by 11 is 7, and 110 divided by 11 is 10

Answer:

10

Step-by-step explanation:

The total cost of the fence, rounded to the nearest pound, is £656.

To calculate the total cost of the fence, we need to find the perimeter of the right-angled triangle-shaped field. The perimeter is the sum of the lengths of all three sides.

Given that the field has a right angle and one angle measures 52°, we can use trigonometry to determine the lengths of the sides.

Let's denote the lengths of the sides as follows:

The side opposite the 52° angle as a

The side adjacent to the 52° angle as b

The hypotenuse (the longest side) as c

Using trigonometric ratios, we have:

tan(52°) = a / b

Rearranging the equation, we get:

a = b * tan(52°)

We also know the length of side b is 151 m.

Plugging in the values, we find:

a = 151 * tan(52°) ≈ 118.63 m

Now, we can calculate the hypotenuse c using the Pythagorean theorem:

c = √(a^2 + b^2) = √(118.63^2 + 151^2) ≈ 193.17 m

The perimeter of the triangle is the sum of the three sides:

Perimeter = a + b + c ≈ 118.63 + 151 + 193.17 ≈ 462.8 m

Finally, to calculate the total cost of the fence, we multiply the perimeter by the cost per meter:

Total cost = Perimeter * Cost per meter = 462.8 * £1.42 ≈ £656.34

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Answer:its B

Step-by-step explanation:

We Prοved that tanθ + cοtθ = secθcscθ using trigοnοmetry identified.

Trigοnοmetry is a branch οf mathematics that deals with the study οf angles, triangles, and their relatiοnships with each οther. It invοlves the study οf the prοperties and functiοns οf triangles, as well as the relatiοnships between angles and sides οf triangles.

Tο sοlve the equatiοn Tanθ + cοtθ = secθcscθ, we can start by expressing each term in terms οf sine and cοsine functiοns:

⇒ \($\mathrm{tan}\,\theta+\mathrm{cot}\,\theta\)

\($\Rightarrow\frac{\mathrm{sin}\ \theta}{\mathrm{cos}\,\theta}+\frac{\mathrm{cos}\,\theta}{\mathrm{sin}\,\theta}$\)

\($\Rightarrow{\frac{\sin^{2}\ \theta+\cos^{2}\!\theta}{\sin\theta.\cos\theta}}$\)

\($={\frac{1}{\sin\theta.\cos\theta}}$\)

= secθ·cscθ

Hence, Proved that tanθ + cotθ = secθcscθ

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Complete question:

Prove that tanθ + cotθ = secθcscθ.

Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by Economic needs.

By economic need Elaine is trying to get a company that would pay her more. Hence the need to go for the Unionized company.

This is given that the Unionized company is said to earn more than the other company. Hence her motivation is due to her economic needs.

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When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression

Answer:

(2,0)

Step-by-step explanation:

Simply plug in the coordinates. y= 3x - 6, so in this case 0= 3(2) - 6 or 0=0, making the point on the line. If the equation is not true like when using (0,3) and getting 3= -6, then the point is not on the line.

(a) The predictor variable is Fall in feet and the response variable is Duration in seconds.

(b) The slope is in seconds per foot.

(c) The slope may be negative, as greater drop heights generally result in longer travel times.

(a) The predictor variable in this regression is Drop, which represents the drop height of the roller coaster, in feet, in feet. The response variable is Duration, which represents the duration of the trip, in seconds, in seconds.

(b) The units of slope in this regression are seconds per foot. This means that for each unit of increase in descent height in feet, the travel time will increase or decrease the value of the slope, measured in seconds per foot.

(c) The slope can be negative, as greater drop heights generally result in longer ride times, and the Tower of Terror roller coaster, which was exceptionally short despite its large drop height, has were removed from the analysis.

Therefore, the remaining 90 roller coasters in the dataset likely exhibit a negative relationship between drop height and time, meaning that as drop height increases, ride time decreases .

The Low R-value squared 29.4% means that the relationship between roller coaster drop and ride time in the data set is highly variable, but the negative slope indicates a general downward trend.

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First let's calculate the number of students who will buy lunch 5 times next week and it is given by:-

So 175 students will buy lunch 5 times.

Similarly let's find number of students who will buy lunch 4 times

75 students will buy 4 times

Similarly on calculation we get 50 students will buy 3 times, 50 students will buy 2 times , 90 students will buy 1 time.

So total number of lunches that will be sold will be

So total 1,515 lunches will be sold .Hence the correct option is (A).

Answer:  125000000000

Step-by-step explanation:

Step-by-step explanation:

5,000 × 5,000 × 5,000

= 125,000,000,000

a) x-intercepts: Set f(x) equal to zero and solve for x.

b) y-intercepts: Evaluate f(0).

c) vertical asymptotes: Set the denominator equal to zero and solve for x.

d) horizontal asymptotes: Determine the degrees of the numerator and denominator polynomials.

e) holes in the graph: Simplify the rational function and identify any common factors in the numerator and denominator.

f) intervals where f(x) is positive or negative: Analyze the signs of the numerator and denominator in different intervals.

g) If the horizontal asymptote is y=0, it indicates that the function approaches the x-axis as x tends to infinity or negative infinity.

a) To find the x-intercepts of the function f(x), we need to set f(x) equal to zero and solve for x. This can be done by equating the numerator, cx + d, to zero and finding the corresponding values of x.

b) To determine the y-intercept, we evaluate f(0) by substituting x = 0 into the function. This gives us the value of f(x) when x = 0, which represents the point where the graph intersects the y-axis.

c) Vertical asymptotes occur when the denominator of the function is equal to zero. By setting the denominator, ax + b, equal to zero and solving for x, we can identify the vertical asymptotes of the function.

d) Horizontal asymptotes are determined by the degrees of the numerator and denominator polynomials. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients. And if the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

e) To identify holes in the graph, we simplify the rational function by canceling out any common factors between the numerator and denominator. If there are common factors that cancel out, it indicates the presence of holes in the graph at those particular x-values.

f) To determine the intervals where f(x) is positive or negative, we analyze the signs of the numerator and denominator in different intervals. If the numerator is positive and the denominator is positive in a given interval, f(x) is positive in that interval. If the numerator is negative and the denominator is positive, f(x) is negative, and vice versa.

g) If the horizontal asymptote is y = 0, it means that as x approaches positive infinity or negative infinity, the function approaches the x-axis. This indicates that the function's values become arbitrarily close to zero as x becomes extremely large or small.

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Engineering

Answer:

177147

Step-by-step explanation:

Well in "simpler" terms \(3^{11}\) is really just

3×3×3×3×3×3×3×3×3×3×3

Multiply everything and you get 177147

Hope you have a good day and luck in finding good memes!

Answer:

21/24

Step-by-step explanation:

The 24 for the 24ths must be in the denominator.

What do you multiply 8 by to get 24? Answer: 3.

That means you must multiply both the 7 in the numerator and the 8 in the denominator to change the fraction to 24ths.

7/8 × 3/3 = 21/24

Answer:

Step-by-step explanation:

i think 1

Answer:

There are 36 girls

Step-by-step explanation:

So you find find out how much boys are there for one number in the ratio

48 divided by 4 = 12

So there are 12 people in one radio number

Multiply that by how much girls there are in the ratio

12 * 3 = 36

There are 36 girls

Answer:

36 girls

Step-by-step explanation:

3 ÷ 4= 0.75

0.75 × 48=36 girls

Hope that helps :)

Sorry if wrong

Answer:

Step-by-step explanation:

$603.5

Answer:39.65

Step-by-step explanation:

turn 6.5% to 0.065

610 x 0.065=39.65

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Answer:The answer is It has no slope because x2 - x1 in the formula m=y2-y1-x2-x1 is zero, and the denominator of a fraction cannot be zero

Step-by-step explanation:

I did the quiz

bottom was cut off a bit its 4=b

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

The distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.

The two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations.

In problem 9, we can use trigonometry to find the distance, d, of the fire from the road. Let x be the distance from Star Point Ranger Station to the fire, and let y be the distance from Twin Pines Ranger Station to the fire. Then, we have:

tan(34°) = d/x

tan(14°) = d/y

Multiplying both sides of each equation by the respective denominator and simplifying, we get:

d = x tan(34°)

d = y tan(14°)

Since the two expressions for d are both equal, we can set them equal to each other and solve for x and y:

x tan(34°) = y tan(14°)

x = (y tan(14°))/tan(34°)

Substituting the value we found for y in problem 7, which was y = 6.15 miles, we get:

x = (6.15 miles) * tan(14°) / tan(34°) ≈ 2.94 miles

Therefore, the distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.

Now, let's check our answers using both expressions for d:

d = x tan(34°) ≈ 2.94 miles * tan(34°) ≈ 2.94 miles * 0.704 = 2.07 miles

d = y tan(14°) ≈ 6.15 miles * tan(14°) ≈ 6.15 miles * 0.249 = 1.53 miles

As we can see, the two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations. If we use the exact values, we would get slightly different values for d, but they would still be very close.

In real life, it is important to be as accurate as possible when dealing with emergencies such as fires. However, in this case, the difference between the two values of d is relatively small, so it may not have a significant impact on the response to the fire. Nevertheless, it is important to use the most accurate values possible to ensure the safety of those involved.

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Answer: Vertical stretch by a factor of 3.

The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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Answer:

i like ur pp

Step-by-step explanation:

The value of w given that k is 15 is 30

From the given diagram, the sum of the two vectors moving in the same direction is equal to the vector moving in the opposite direction.

Equating this to -w%

-2k% = -w%

-2k = -w

w = 2k

If  k = `5

w = 2(15)

w = 30

Hence the value of w given that k is 15 is 30

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The initial velocity (vi) of the ball, when shot into the catcher, is approximately 367.5 m/s.

To solve Eq. 7.5 and Eq. 7.6 for v1​ in terms of m, M, g, and h, we will substitute the given values of m, M, and h into the equations.

Eq. 7.5: mv1​ = (m+M)V2​

Eq. 7.6: (m+M)V22​ = (m+M)gh

Given:

m = 50.0 g (mass of the ball)

M = 200.0 g (mass of the catcher)

h = 15.0 cm (rise in the center of mass)

First, let's solve Eq. 7.6 for V2​ by dividing both sides by (m+M):

V22​ = gh

Next, substitute the expression for V2​ into Eq. 7.5:

mv1​ = (m+M)(gh)

Now, solve for v1​ by dividing both sides by m:

v1​ = (m+M)(gh) / m

Substituting the given values:

v1​ = (50.0 g + 200.0 g)(9.8 m/s²)(0.15 m) / (50.0 g)

Calculating the expression:

v1​ = (250.0 g)(9.8 m/s²)(0.15 m) / (50.0 g)

v1​ = 367.5 m/s

Therefore, the initial velocity (vi) of the ball, when shot into the catcher, is approximately 367.5 m/s.

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Answer:

You can calculate Interest on your loans and investments by using the following formula for calculating simple interest: Simple Interest= P x R x T ÷ 100, where P = Principal, R = Rate of Interest and T = Time Period of the Loan/Deposit in years.

Formula: Simple Interest=P×r×t where: P=Principal amount; r=Annual interest rate; t=...

Principal Amount: Principal Amount remains constant on Simple Interest

Meaning: Simple Interest is calculated on the Principal Amount for the entire tenure

Calculation: It is easy to calculate Simple Interest

Answer:

To calculate simple interest, you can use a specific formula:

I (interest) = p (principal) x r (rate) x t (time)

Important: Rate is always a decimal, and time must be a compatible unit that matches with the rate (months, years, etc.).

If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch

The area of a triangle is 96 sq. inches

Let base be b

Its altitude is 2 inches greater than five times its base.

a=5b+2

ab/2=A

(5b+2)b/2=96

(5b+2)b=192

5b²+2b=192

5b²2+2b-192=0

On solving the quadrartic equation,

we get

b=6

a=32

Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs

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