PACKAGING A packaging plant quality assurance agent compares the surface area and volume of packages to ensure the packages will be transported
economically. The most popular package size is a cylinder with a height of 18 inches. Let r be the radius of the base, then write and simplify an expression that
represents the ratio of the surface area to the volume of the cylinder.
The ratio of the surface area to the volume of the cylinder is

The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25

Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.

The amount of medicine in the 10 grams of 15% solution is

0.15 × 10 = 1.5 grams

The amount of medicine in the 25 grams of 10% solution is

0.10 × 25 = 2.5 grams

So the total amount of medicine in the original mixture is,

1.5 + 2.5 = 4 grams

Now let x be the amount of pure medicine added.

The total amount of medicine in the final mixture is,

4 + x

The total amount of solution in the final mixture is,

10 + 25 + x

So the concentration of the final mixture is,

(4 + x) / (10 + 25 + x)

We know that this concentration is 25%, so we can write:

(4 + x) / (10 + 25 + x) = 0.25

This is the equation that represents the situation.

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The given question is incomplete, the complete question is:

A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation

Answer:

(5x+40)+x+2(2x+20)=360

5x+40+x+4x+40=360

10x+80=360

10x=360-80

10x=280

x=28°

substitute x=28° into (5x+40)

=140+40= 180

therefore line Ac is the diameter of a he circle because a diameter divides a circle into 2 equal part and the angle on the line is 180° showing that the circle is on a straight line

The smaller number is 5.5 and the larger number is 15.5.

Let's start by assigning variables to the two unknown numbers. Let x be the smaller number and y be the larger number.

From the problem statement, we know that:

x + y = 25 (the sum of the two numbers is 25)

y = 3x - 3 (the larger number is 3 less than three times the smaller)

We can use the second equation to solve for y in terms of x, by adding 3 to both sides:

y + 3 = 3x

Then, we can substitute this expression for y into the first equation:

x + (y + 3) = 25

Substituting y + 3 with 3x, we get:

x + 3x = 22

Combining like terms, we get:

4x = 22

Finally, we solve for x by dividing both sides by 4:

x = 5.5

Now that we know x, we can use the equation y = 3x - 3 to find y:

y = 3(5.5) - 3 = 15.5

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The  probability that at least 3 customers out of the first 6 will buy bread is 88.3% that is option B.

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the potential outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

The formula used is :

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

65% of customers who come into this store buy bread, hence p = 0.65.

A sample of 6 customers is taken, hence n = 6.

The probability that at least 3 customers out of the first 6 will buy bread is given by:

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

In which

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

P(X = 3) = C₆,₃(0.65)³ x (0.35)³ = 0.2355

P(X = 4) = C₆,₄(0.65)⁴ x (0.35)² = 0.328

P(X = 5) = C₆,₅(0.65)⁵ x (0.35)¹ = 0.2437

P(X = 6) = C₆,₆(0.65)⁶ x (0.35)⁰ = 0.0754

Then,

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

= 0.2355 + 0.328 + 0.2437 + 0.0754 = 0.8826

The probability that at least 3 customers out of the first 6 will buy bread is 0.8826 ≈ 88.3%.

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Complete  question;

A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?

23.5%

88.3%

11.7%

76.5%

The statement "dispersion models are selected based on the phase of the material being modeled in a release scenario" is true as Different dispersion models are needed for different phases (gas, liquid, solid) due to differences in behavior and transport mechanisms.

Dispersion models are used to predict the spread of pollutants, and they depend on the physical and chemical properties of the material being released.

Generally, different models are used for each phase of the material, such as the Gaussian plume model for gases, the plume rise model for heated gases, and the particle dispersion model for particles.

Each of these models is based on different characteristics and equations which allow for the most accurate prediction of the dispersion of pollutants.

For example, the Gaussian plume model considers the wind velocity, turbulence, and buoyancy of the released material, whereas the plume rise model considers the momentum, thermal expansion, and buoyancy of the released material.

Therefore, dispersion models are selected based on the phase of the material being modeled in a release scenario.

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The new cost of the order is 62.7% of the original price where still 4.5% sales tax had to pay.

A discount is a reduction in the price of an item or service, usually expressed as a percentage of the original price.

Let's assume the original cost of the order was $x.

        0.6x + 0.027x = 0.627x

Therefore, the new cost of the order is 62.7% of the original price.

For example, if the original cost of the order was $20, then the discounted price is $12 (60% of $20), and the sales tax is $0.324 (4.5% of $12). The final cost of the order would be $12.324.

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The average speed of the total journey is 75 kilometres per hour.

Anil completes the 72 kilometres journey between Bristol and Cardiff for 48 minutes. He then drive 69 kilometres from Cardiff to Swansea at an average speed of 60 kilometres per hour.

Therefore, let's find Anil average speed for the total of his journey as follows:
speed of his first journey = distance / time

speed of his first journey = 72 / 48

speed of his first journey = 1.5 km/minutes = 90 km/hrs

Therefore,

average speed of the total journey = 90 + 60 / 2

average speed of the total journey = 150 / 2

average speed of the total journey = 75 kilometres per hour

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Answer: D

Step-by-step explanation:

Its the fairest way to pick a random person

Answer: If adding predictor variables to a regression model never reduces r2, you can include all the available predictor variables in the model, as long as they have a significant correlation with the dependent variable. However, having too many variables in a model may lead to overfitting, resulting in poor model generalization. In addition, some predictor variables may not be useful, while others may be collinear. As a result, it is usually recommended to use a stepwise regression method, which selects the best subset of predictor variables that improve the model's performance, without including irrelevant or collinear variables.r2 adj: R2 adj is the adjusted R2 value of a regression model. R2 adj is a statistical measure of how well the regression model fits the observed data. It is similar to the R2 value, but takes into account the number of predictor variables in the model, in addition to the sample size. The adjusted R2 value increases when a new predictor variable improves the model's fit, but decreases when the new predictor variable does not improve the model's fit or is collinear with other predictor variables.

The adjusted R2 value ranges from 0 to 1, with higher values indicating better model fit.

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Thus, 4.0 moles of NH3 would be produced when 6.0 moles of H2 react with sufficient N2.

Suppose 6.0 mol of H2 reacts with sufficient N2 to produce ammonia, NH3. We can determine the number of moles of NH3 produced using stoichiometry.The balanced chemical equation for the reaction is:[tex]3H2(g) + N2(g) → 2NH3(g)[/tex]

From the equation, we can see that 3 moles of H2 react with 1 mole of N2 to produce 2 moles of NH3.

Therefore, using the mole ratio from the balanced equation, we can calculate the number of moles of NH3 that would be produced when 6.0 mol of H2 reacts with [tex]N2:6.0 mol H2 × (2 mol NH3/3 mol H2) = 4.0 mol NH3[/tex]

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Answer: 20/3 mph or 6.667 mph.

Step-by-step explanation:

Since the athlete runs 1/3 of a mile per 1/20 of an hour, to find how much they run in an hour, you multiply both values by 20 to get: the athlete runs 20/3 miles per 20/20 of an hour, or 20/3 miles per hour.

The probability of getting one marble of each color will be 0.044.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A random event's recurrence is the subject of this area of mathematics. The range of the number is 0 to 1. The degree to which something is likely to happen is essentially what probability means. You will discover the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

In this question,

Total number of balls=4+5+6=15

probability of red ball= 4/15

probability of white ball = 5/14  (Since the number of balls are decreasing

probability of blue ball= 6/13

probability of getting one marble of each color= 4/15×5/14×6/13    

                                                                              = 0.044

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Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.

Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.

Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.

This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.

To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.

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Answer:

Step-by-step explanation:

You can read the answers right off the graph.

a)  When t=5: Find 5 on the x-axis (time (h)), go straight up vertically until you hit the line, then go straight to the left horizontally until you hit the y-axis (distance (km));  at that point d ≈ 14 km

b)  When d=20:  Find 20 on the y-axis (distance (km)), go straight to the right horizontally until you hit the line, then go straight down vertically until you hit the x-axis (time (h));  at that point t ≈ 7 hr

Answer:

Step-by-step explanation:

Your equation is 0.75L +  0.5L + x = 2L
x = Orange juice

0.75L + 0.5L = 1.25L
2L - 1.25L = 0.75L

[tex]\frac{0.75L}{2L}[/tex] is your fraction
[tex]\frac{75}{200}[/tex]  simplified is [tex]\frac{3}{8}[/tex]
I hope this helped,

The constant of proportionality is the cost per unit. In this case, it can be calculated by dividing the cost of 1 motorcycle by the number of motorcycles.

Unit is an individual item or segment of a larger whole. It is used to measure or quantify different elements or entities, including physical objects, abstract concepts, and even people. In mathematics, a unit is a number or quantity that is equal to one. In the physical sciences, a unit is a standard amount of a certain quantity, such as a kilogram or an hour. In economics, a unit is a measure of a certain commodity or factor of production, such as labor or capital.

Constant of Proportionality = Cost per Motorcycle = 4,590 / 1 = 4,590

Using this constant of proportionality, we can complete the table as follows:

Number of Motorcycles

Cost

Manufactured

0

1

3

8

15

$

$0.00

$4,590.00

$13,770.00

$36,720.00

$68,850.00

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The constant of proportionality is 4,080.00. Using this constant, we can calculate the cost for each number of motorcycles.

A constant is a quantity or value that remains unchanged over time. It is a fixed value that does not vary and is unaffected by external influences. Constants are used in mathematics, physics, chemistry, and other sciences to represent a fixed value.

Number of Motorcycles
Cost
Manufactured
0
1
3
8
15
$
$0.00
$4,590.00
$12,240.00
$22,950.00
25
$37,275.00
The constant of proportionality is the rate of increase in cost as the number of motorcycles manufactured increases. This can be calculated by dividing the cost of each number of motorcycles by the number of motorcycles.
For example, when 1 motorcycle is manufactured, the cost is $4,590.00, so the constant of proportionality is $4,590.00 / 1 = $4,590.00.
When 3 motorcycles are manufactured, the cost is $12,240.00, so the constant of proportionality is $12,240.00 / 3 = $4,080.00.
Therefore, the constant of proportionality is 4,080.00. Using this constant, we can calculate the cost for each number of motorcycles.

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The expected profit of Ayo is  $ 79.95.

The probability of an event happening can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Here in this problem, we use probability to calculate the total profit. Calculate the probability of winning 150 people so that we can calculate the total winning amount of 150 persons.

Now calculate the total amount gained by Ayo by costing each turn. Now subtract both values and will get the expected profit.

Here we have

Ayo runs fairground games

In each turn, a player rolls a fair dice numbered from 1 - 6 and a spin numbered 1 - 5

Every player can win £ 8 or £ 3

In total there are 150 to play

Here probability of winning £ 8 i.e rolling 2 and rolling 5  

= [ 1/6 × 1/5 ] = 1/30  

Probability of winning £ 3 i.e getting at least one 3 in roll or spin

Here we have taken 3 cases that are getting 3 in a roll but not in spin, getting 3 in a spin but not in roll, and getting 3 in both roll spin

= [ 1/6 × 4/5 ] + [5/6 × 1/5 ] + [ 1/6 × 1/5 ]  

= 4/30 + 5/30 + 1/30 = 10/30 = 1/3

Hence, the expected amount in 1 a single game

= 8 × 1/30 + 3 1/3 = 8/30 + 1 = 0.267 + 1 = 1.267

There are 150 player  

Total amount won by 150 = 150 (1.267) = $ 190.05  

Here It cost a player 1.80 for every turn  

Ayo will get for 150 players = 1.80 × 150 = $ 270

If 150 players won $ 190.05,

then the profit won by Ayo = 270 - 190.05 = 79.95

Therefore,

The expected profit of Ayo is  $ 79.95.

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Hi!

The power of 7 to make 2,401 is 4.

Written out ↓ ↓ ↓

7 x 7 = 49 (Thats the first 2 sevens)
49 x 7 = 343 (Three)
343 x 7 =  2,401 (Four)

= 7^4

Hope this helps!
~~PicklePoppers~~

This equation represents the linear relationship between the dependent variable (y) and the independent variable (x) with a slope of 2 and a y-intercept of -3.

However, I can provide a general example using common terms in algebra:
Terms: Dependent variable (y), independent variable (x), slope (m), and y-intercept (b).
To represent a linear relationship between two variables, we can use the equation of a straight line, which is often written as:
[tex]y = mx + b[/tex]
Here's what each term in the equation represents:
1. y: This is the dependent variable, meaning its value depends on the value of the independent variable (x). In a graph, it is usually represented on the vertical axis.
2. x: This is the independent variable, which can take any value within a given range. It is usually represented on the horizontal axis in a graph.
3. m: This is the slope of the line, representing the rate at which the dependent variable (y) changes with respect to the independent variable (x). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.
4. b: This is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
simply plug in the values for the slope (m) and y-intercept (b). For example, if the slope is 2 and the y-intercept is -3, the equation would be:
[tex]y = 2x - 3[/tex]

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Answer:

1.8 kilometers

hope this helped

Answer:

1 8/10 kilometers

Step-by-step explanation:

u keep on adding 3 on to 3/10th 6 times then u get a improper fraction and turn that into a fraction and u get ur answer

hope it helps

The surface area is

[tex]2(5\times4)+2(5\times2)+2(4\times2)=[/tex]

[tex]40+20+16=[/tex]

76 square yards

Answer:

The surface area of the prism.

5 yd, 4 yd, 2 yd

Step-by-step explanation:

You're welcome.

Since there are students who play both sports, the events of playing basketball and playing soccer are not mutually exclusive.

A Venn diagram is a visual representation of sets or groups and their relationships to one another.

It consists of two or more circles or other shapes that overlap, with each shape representing a different set, and the overlap representing the elements that belong to both sets.

Looking at the diagram, we see that there is a region where the two circles overlap, which means there are elements (points) that are in both circles. Therefore, the events shown in the Venn diagram are not mutually exclusive.

In this particular case, the circles represent the events of students who play basketball and students who play soccer, respectively. The overlap represents students who play both basketball and soccer.

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The complete question is given below-

The solution to the conversion of units are:

iii) 1 km 200 m - 500 m = 700 m

iv) 876 m + 1 km 500 m = 2km 376 m

v) 2 km 50 m - 950 m = 1 km 100 m

iii) We want to solve:

1 km 200 m - 500 m

From conversion factors, we know that:

1 km = 1000 m

Thus:

1 km 200 m = 1000m + 200 m = 1200 m

Thus:

1 km 200 m - 500 m = 1200 m - 500 m

= 700 m

iv) We want to solve:

876 m + 1 km 500 m

From conversion factors, we know that:

1 km = 1000 m

Thus:

876m = 0.876 km

1 km 500 m = 1.5 km

Thus:

876 m + 1 km 500 m = 0.876 km + 1.5 km

= 2.376 km or 2km 376 m

v) We want to solve:

2 km 50 m - 950 m

From conversion factors, we know that:

1 km = 1000 m

Thus:

2 km 50 m = 2.05 km

950m = 0.95 km

Thus:

2 km 50 m - 950 m = 2.05 km - 0.95 km

= 1.1 km or 1 km 100 m

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According to Pythagorean Theorem, The length of the horizontal portion of the support, x, is 3.87 feet.

The length of the horizontal portion of the support, x, can be determined by using the Pythagorean Theorem. The Pythagorean Theorem states that a2 + b2 = c2, where a and b are the sides of a right triangle and c is the hypotenuse.

In this case, a = 7 feet, b = x, and c = 8 feet. We can use the Pythagorean Theorem to solve for x: 72 + x2 = 82, or 49 + x2 = 64. This can be solved for x to get x2 = 15 and x = √15 ≈ 3.87 feet.

Therefore, the length of the horizontal portion of the support, x, is 3.87 feet.

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When the width of a rectangle is increasing at a rate, and the length increases at a rate, the rate at which the area increases can be determined by multiplying the rates of the width and the length.

When the width and length of a rectangle increase at certain rates, the area of the rectangle also changes at a specific rate. The rate of change of the area is determined by multiplying the rates of change of the width and length.

This is because the area of a rectangle is calculated by multiplying its width and length, and therefore any change in either dimension affects the overall area. The product of the rates of change of the width and length gives the overall rate of change of the area.

Therefore, the rate at which the area is increasing when the width of a rectangle is increasing at a rate, while the length increases at a rate can be calculated using the above formula.

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There are 12 red socks and 18 black socks in a sock drawer. If you randomly choose two socks at once, the probability you get a matching pair is 50%.

The probability of getting a matching pair of socks can be calculated as follows:

First, we can calculate the total number of ways to choose 2 socks out of 30:

C(30, 2) = 30! / (2! * (30-2)!) = 435

Now, we need to calculate the number of ways to choose 2 socks such that they are both black or both red:

Number of ways to choose 2 black socks: C(18, 2) = 153

Number of ways to choose 2 red socks: C(12, 2) = 66

Therefore, the total number of ways to choose a matching pair of socks is 153 + 66 = 219.

Finally, we can calculate the probability of getting a matching pair of socks by dividing the number of ways to choose a matching pair by the total number of ways to choose 2 socks:

P(matching pair) = 219 / 435 ≈ 0.5034

Therefore, the probability of getting a matching pair of socks is approximately 0.5034 or 50.34%.

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The height of a 100-lb flamingo can be estimated by assuming that it would be proportional to the height of the 20-lb pink flamingo. Based on this assumption, the 100-lb flamingo would be 6 ft tall.

The leg length of a 100-lb flamingo can be estimated by assuming that it would also be proportional to the leg length of the 20-lb pink flamingo. Using this assumption, the 100-lb flamingo would have legs 4 ft in length.

These assumptions are reasonable given that the difference in size of the two flamingos is only a factor of 5. This means that the size difference between the two is not large enough to drastically change the proportions of their bodies. Thus, it is a fair assumption that the proportions of their height and leg length would remain roughly the same.

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The probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45 is [tex]P(X) = 100Cx (0.4)^x (1-0.4)^(100-x).[/tex]

The formula is [tex]P(X) = nCx (p)^x (1-p)^(n-x)[/tex], where n is the number of trials, x is the number of successes, and p is the probability of success for one trial. In this case, n represents the number of teenagers sampled, x represents the number of teenagers who own a smartphone, and p represents the probability that any one teenager owns a smartphone.

First, let us calculate p. The probability of success (owning a smartphone) is the proportion of the sampled teenagers who own a smartphone, which is between 0.35 and 0.45. Since the probability of success lies between 0.35 and 0.45, we can take the average of these numbers, which is 0.4. This number (0.4) is p.

Next, let us calculate x. The number of successes (teenagers who own a smartphone) is the proportion of the sampled teenagers who own a smartphone, which is between 0.35 and 0.45. Since the number of successes lies between 0.35 and 0.45, we can take the average of these numbers, which is 0.4. This number (0.4) is x.

Finally, we can calculate n. We know that the number of teenagers sampled is 100, so n = 100.

[tex]P(X) = 100Cx (0.4)^x (1-0.4)^(100-x).[/tex]

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Accοrding tο the Pythagοrean theοrem, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is 53 ft.

The Pythagοrean theοrem is a fundamental result in Euclidean geοmetry that describes the relatiοnship between the three sides οf a right-angled triangle.

In equatiοn fοrm, this can be written as:

c² = a² + b²

where c is the length οf the hypοtenuse, and a and b are the lengths οf the οther twο sides (alsο knοwn as the legs) οf the right-angled triangle.

In this case, the tοwer, the grοund, and the guy wire fοrm a right triangle. We knοw the height οf the tοwer is 45 ft, and the hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured tο the grοund is 28 ft. Let's call the length οf the guy wire c. Then, we have:

a = 28 ft (hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured)

b = 45 ft (height οf the tοwer)

c = length οf the guy wire (hypοtenuse)

Using the Pythagοrean theοrem, we can sοlve fοr c:

[tex]a^2 + b^2 = c^2[/tex]

[tex]28^2 + 45^2 = c^2[/tex]

[tex]784 + 2025 = c^2[/tex]

[tex]2809 = c^2[/tex]

[tex]c = \sqrt{(2809)[/tex]

c ≈ 53 ft

Therefοre, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is apprοximately 53 ft.

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The number of days that it would take to lose 10 pounds, given the calories in the morning latte is 97 days.

Determine the total number of calories you need to burn to lose 8 pounds:

Calories to burn = Pounds to lose × Calories per pound

Calories to burn = 8 × 3,500 = 28,000

Calculate the number of calories you save per day by giving up your morning latte:

Daily calorie savings = Calories in latte

Daily calorie savings = 290

Determine how many days it would take to burn the total number of calories needed to lose 8 pounds:

Days to lose weight = Calories to burn / Daily calorie savings

Days to lose weight = 28,000 / 290 = 97 days

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Full question is:

Assuming the rest of your diet remains constant, how many days will it take you to lose 8 pounds? You must burn an extra 3500 Calories to lose 1 pound of body weight. (your daily latte contains 290 Calories. You want to lose weight by giving up your morning latte and drinking water instead.)