A zorb is a large inflated ball within a ball. The formula for the radius r of a sphere with surface area A is given by r=\sqrt((A)/(4\pi )) . Calculate the radius of a zorb whose outside surface area is 49.29 sq m.

Note that the  input value for which the statement f(x) = g(x) is true are

3.5 and 10/3

In this question , we have a graph given, and we have to find the x coordinate of the intersection point .

From the graph , the input value is approximately 3.3 .

In the graph, f(x) = 3

And for g(x), we need the slope and y intercept .

Slope is the ratio of rise and run .

Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .

So the equation of g(x) = (3/2)x - 2

Since we need to factor f(x) = g(x)

Substituting the values of the two functions, we will get

3 =  (3/2)x - 2

Adding 2 to both sides

5 =  (3/2)x

Cross multiply and you have

10 = 3x

x = 10/3

So  the  input value for which the statement f(x) = g(x) is true are

3.5 and 10/3

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Answer:

The tan of angle A is equal to a/b, where a and b are the lengths of the opposite and adjacent sides of the angle respectively. In this case, we have a = 15, b = 8, which gives us a tan of 15/8 or approximately 1.875.

The zeros in a function are where it passes through the x-axis and  to find the zeros, set the equation equal to zero, then solve for x.

The zeros of a function are the values of the input variable (usually denoted as x) that make the output of the function equal to zero.

In other words, if you graph the function, the zeros are the points where the graph crosses the x-axis.

To find the zeros of a function, you need to set the function equal to zero and solve for the input variable.

This means you're looking for the x-values that make the function equal to zero.

Once you've found the zeros, you can use them to graph the function and analyze its behavior.

Hence, the zeros in a function are where it passes through the x-axis and  to find the zeros, set the equation equal to zero, then solve for x.

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An office building of 21,000 f t squared would require 140 air vents according to the recommendation of 2 air vents for every 300 f t squared of floor space.

Based on the recommendation of 2 air vents for every 300 f t squared of floor space, we can calculate the number of air vents required for an office building of 21,000 f t squared by dividing the total floor space by 300 and multiplying the result by 2.

21,000 / 300 = 70
70 x 2 = 140

Therefore, an office building of 21,000 f t squared would require 140 air vents according to the recommendation of 2 air vents for every 300 f t squared of floor space.

It is important to note that this is just a recommendation and the actual number of air vents required may vary depending on factors such as ceiling height, insulation, and other building characteristics. It is always best to consult with an HVAC specialist to determine the appropriate number and placement of air vents for optimal air circulation and comfort in a building.

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Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

Let's use a system of equations to solve this problem. Let x be the number of lollipops sold and y be the number of fruit snacks sold. From the problem, we know that:
- The price of each lollipop is $1.50, so the total amount of money earned from selling x lollipops is 1.5x.
- The price of each fruit snack is $1.25, so the total amount of money earned from selling y fruit snacks is 1.25y.
- Yesterday, Nakeisha made $18.25 from selling a total of 13 lollipops and fruit snacks, so we can write the equation:
1.5x + 1.25y = 18.25
We also know that Nakeisha sold a total of 13 lollipops and fruit snacks, so we can write the equation:
x + y = 13
Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:
- Rearrange the second equation to solve for one variable in terms of the other:
x + y = 13
y = 13 - x
- Substitute y = 13 - x into the first equation:
1.5x + 1.25y = 18.25
1.5x + 1.25(13 - x) = 18.25
- Simplify and solve for x:
1.5x + 16.25 - 1.25x = 18.25
0.25x = 2
x = 8
- Substitute x = 8 back into y = 13 - x to find y:
y = 13 - x
y = 13 - 8
y = 5
Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

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The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

The view factor (F) from Surface A to Surface B can be calculated using the formula:

F = A / (A + B)

where A and B are the areas of Surface A and Surface B, respectively.

The area of a triangle can be calculated using Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.

For Surface A:

a = 2 cm

b = 3 cm

c = 4 cm

s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm

Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))

= √(4.5 * 2.5 * 1.5 * 0.5)

=√(5.625) ≈ 2.37 cm²

For Surface B:

a = 2 cm

b = 4 cm

c = 3 cm

s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm

Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))

= √(4.5 * 2.5 * 0.5 * 1.5)

=√(5.625) ≈ 2.37 cm²

Now we can calculate the view factor (F):

F = Area_A / (Area_A + Area_B)

= 2.37 / (2.37 + 2.37)

≈ 0.5

Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

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Answer:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 2.

Answer:

The surface area of the right triangular prism is 168 cm².

Step-by-step explanation:

The formula for the surface area of a right triangular prism is SA=bh+pl, where p=b+h+c

P=b+h+c

P=4+3+5

=12

SA=bh+pl

SA=(4)(3)+(12)(13)

SA= 12+156

SA=168 cm²

For more information on how to find the surface are of right triangular prisms, check out "Triangular Prism - Volume, Surface Area, Base and Lateral Area Formula, Basic Geometry" by the Organic Chemistry Tutor.

Hope this helps!

The numbers that are elements of both the subset of odd numbers and the subset of multiples of 3 are 3 and 9.

The odd numbers in the set are {1, 3, 5, 7, 9} and the multiples of 3 in the set are {3, 6, 9}.

The elements that are in both subsets are the ones that appear in both sets, which are only 3 and 9.

Therefore, the numbers 3 and 9 are the elements that are in both the subset of odd numbers and the subset of multiples of 3.

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To calculate the probability that at least one of the six lightbulbs selected from the shipment is defective, we need to first calculate the probability that all of them work and then subtract that from 1. Therefore, the probability that at least one of the six lightbulbs is defective is 0.2649 or 26.49%.

The probability that a single lightbulb is defective is 0.05 and the probability that it works is 0.95. Therefore, the probability that all six lightbulbs work is:
0.95 x 0.95 x 0.95 x 0.95 x 0.95 x 0.95 = 0.7351
To calculate the probability that at least one of the six lightbulbs is defective, we need to subtract this from 1:
1 - 0.7351 = 0.2649
Therefore, the probability that at least one of the six lightbulbs is defective is 0.2649 or 26.49%. In other words, there is a little over a one in four chance that at least one of the six lightbulbs selected is defective.

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Answer:

---------------------

Use the slope equation:

Substitute given values for the slope and coordinates and and solve for h:

The value of h is - 6.

Gaurav bought 500 mangoes for Rs. 1000, which means that he bought each mango for Rs. 2.

He packed the mangoes into small boxes with 25 in each, so he made a total of 500/25 = 20 boxes.

He sells each box for Rs. 60, so he makes a total of 20 x Rs. 60 = Rs. 1200 from selling all the boxes.

To find the profit, we need to subtract the cost of the mangoes from the total revenue.

The cost of 500 mangoes was Rs. 1000, so the profit is:

Profit = Rs. 1200 - Rs. 1000 = Rs. 200

Therefore, Gaurav made a profit of Rs. 200 by selling the mangoes.

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Answer:

9

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

58 = 7x -5

Add + 5 to both sides

58+5 = 7x - 5 + 5

63 = 7x + 0

63 = 7x

Divide both sides by 7 to isolate the variable x.

63/7 = 7x/7

9 = x

So x = 9.

Check your answer:

7(9) - 5 = 63-5 = 58 so it works!

The correct option for the demand requirement constraint in a production scheduling LP is option (c): beginning inventory + production - ending inventory = demand.

In a production scheduling LP, the demand requirement constraint represents the balance between the available inventory and the demand for the product. The constraint ensures that the production and inventory levels are sufficient to meet the specified demand.

Option (c) represents this relationship accurately by stating that the beginning inventory, production, and ending inventory, when subtracted from each other, should equal the demand. This equation reflects the concept of maintaining a balance between the production output and inventory changes to meet the demand

Option (a) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Option (b) is also incorrect because it uses the equality (=) symbol, which implies an exact balance between the inventory and demand, disregarding the changes in inventory.

Option (d) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Therefore, option (c) is the correct representation of the demand requirement constraint in a production scheduling LP.

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The exponential function has a horizontal asymptote at y = –3 will be; f (x) = –3^x – 3.

We get a horizontal asymptote for a function;

Note that the x-axis (y=0) is the horizontal asymptote.

Since the question asked for a function with asymptotic behaviors of y = -3,

we can shift the function 3 units above by changing Q to +3.

The exponential function has a horizontal asymptote at y = –3 will be;

f (x) = –3^x – 3.

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The percentage of Mr. Reyes total compensation that was withheld for federal taxes is given as follows:

14.2%.

From the table, we have that the parameters for this problem are given as follows:

Hence the proportion of Mr. Reyes total compensation that was withheld for federal taxes is given as follows:

8802.26/61987.5 = 0.142.

Then the percentage is given as follows:

0.142 x 100% = 14.2%.

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As the project progresses, the actual finish times (AFs) of completed activities play a crucial role in determining various aspects of the project schedule.

The AFs are used to calculate the earliest start and earliest finish times for the remaining activities in the network diagram. These calculations are based on the dependencies between activities and the actual durations of completed activities.

By considering the AFs, the project team can determine the earliest possible start and finish times for the remaining activities, taking into account the sequence of activities and any imposed constraints. This information helps in managing the project schedule and identifying any potential delays or critical paths.

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∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

20 water fountains can be made when the cost is 770.

Verbal statement: The cost equals 30 times the fountains for cats plus 170

Step-by-step explanation:

Lets review the defined variables.

f = fountains for cats

C = cost

We are given the value of the cost, but not the amount of fountains for cats. This means we will have to solve for f in the equation.

Substitute 770 for C

[tex]770=30f+170[/tex]

Subtract 170 on both sides

[tex]600=30f[/tex]

Divide by 30

[tex]20=f[/tex]

20 water fountains can be made when the cost is 770.

To prove this, plug our numbers into the expression.

[tex]30(20)+170[/tex]

[tex]600+170[/tex]

[tex]770[/tex]

So our answer is correct.

This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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When point O is between points M and N on line segment MN. O is the midpoint of line segment MN if

O ON + OM = MN

In geometry the midpoint is the point that divides a line segment into two equal parts

It is the point that is equal distance from both endpoints of the segment.

In this case the endpoints are M and N, the midpoint is point O, which is the point that is halfway between M and N, so that ON = OM. and adding the points returns the original line MN

Therefore, we have that ON + OM = MN

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Customers at the old store bought milkshakes about 20.46% of the time.

Customers at the new store bought milkshakes about 26.29% of the time.

Of all the milkshakes sold at Ezra's Ice Cream Shops, 59.29% were sold at the old store.

To calculate the percentages, we need to find the conditional probabilities based on the given information.

Let's calculate the percentages step by step:

Customers at the old store bought milkshakes about:

Milkshakes sold at the old store = 13,400

Total sales at the old store

= 52,100 (Ice Cream) + 13,400 (Milkshakes) = 65,500

Percentage

= (Milkshakes sold at the old store / Total sales at the old store) x 100

Percentage = (13,400 / 65,500) x 100 ≈ 20.46%

Customers at the new store bought milkshakes about:

Milkshakes sold at the new store = 9,200

Total sales at the new store = 25,800 (Ice Cream) + 9,200 (Milkshakes) = 35,000

Percentage = (Milkshakes sold at the new store / Total sales at the new store) x 100

Percentage = (9,200 / 35,000) * 100 ≈ 26.29%

Of all the milkshakes sold at Ezra's Ice Cream Shops, the percentage sold at the old store:

Total milkshakes sold at both stores = Milkshakes sold at the old store + Milkshakes sold at the new store = 13,400 + 9,200 = 22,600

Percentage = (Milkshakes sold at the old store / Total milkshakes sold) x 100

Percentage = (13,400 / 22,600) x 100 ≈ 59.29%

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Answer:

To find the perimeter of a scale drawing, we need to use the same scale factor that was used to create the drawing. In this case, the scale factor is 7 inches: 28 feet, or 1 inch: 4 feet. This means that every inch in the drawing represents 4 feet in the actual floor.

To find the perimeter of the floor in the scale drawing, we need to add up the lengths of all the sides. Since the floor is rectangular, it has two pairs of equal sides. The length of the floor is 28 feet, so the length of the scale drawing is 28 / 4 = 7 inches. The width of the floor is 24 feet, so the width of the scale drawing is 24 / 4 = 6 inches.

The perimeter of the scale drawing is then:

7 + 6 + 7 + 6 = 26 inches

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Line 4 of Raya's solution is the B. Distributive property of equality.

Line 4 of Raya's solution to 2.5(6.25x + 0.5) = 11 is shown as follows:

2.5(6.25x + 0.5) = 11

15.625x + 1.25 = 11

The correct reason for line 4 of Raya's solution is the Distributive property of equality. This property states that for any real numbers a, b, and c, a(b + c) = ab + ac. In line 4 of Raya's solution, the Distributive property is applied to distribute 2.5 to the terms inside the parentheses (6.25x and 0.5).

To see why the Distributive property is used, let's consider the expression 2.5(6.25x + 0.5). To simplify this expression, we can use the Distributive property as follows:

2.5(6.25x + 0.5) = 2.5(6.25x) + 2.5(0.5)

Now, we can use the Multiplication property of equality to simplify the expression further:

15.625x + 1.25 = 11

This means that 15.625x + 1.25 is equal to 11, and we can continue solving for x.

In summary, the Distributive property of equality is used to simplify expressions by distributing a factor to the terms inside parentheses. In Raya's solution to 2.5(6.25x + 0.5) = 11, the Distributive property is applied to simplify the expression before solving for x. Therefore, Option B is correct.

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The angular velocity of the connecting rod is w = 1.939 rad/s

Given data ,

To determine the angular velocity of the connecting rod CD at the instant angle θ = 30 degrees, we need to consider the relationship between the angular velocities of different components in a mechanism. In this case, we can use the concept of relative velocity

The angular velocity of the connecting rod CD can be found using the following equation

ω_CD = ω_AB + ω_BC

angular velocity of CD = angular velocity of AB x (AB/CD) x sin(u) x (1/cos(u))

angular velocity of CD = 4 rad/s x (10/20) x sin(30) x (1/0.825)

Therefore , the angular velocity is CD = 1.939 rad/s

Hence , the angular velocity is w = 1.939 rad/s

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The probability of drawing one paisley tie is 0.43

Three paisley ties and four solid ties are in a dresser. Therefore, the probability if drawing out one paisley tie without looking can be calculated as follows:

The total number of ties is the sum of the paisley ties and solid ties, which is 3 + 4 = 7.

Therefore, the probability of drawing out 1 paisley tie without looking is as follows:

probability of drawing out 1 paisley tie without looking = 3 / 7

probability of drawing out 1 paisley tie without looking = 0.42857142857

Hence , the probability of drawing out one paisley tie without looking is 0.43

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The graph that correctly represents the data in the table for this problem is given as follows:

Top right graph.

On the definition of a function, the y-intercept is given by the value of y for which the input assumes a value of zero.

Hence, on the graph of a function, the y-intercept is the value of y for which the graph touches or crosses the y-axis.

From the table, we have that when x = 0, y = 4, hence the graph should cross the y-axis at y = 4, hence the top right graph is the correct option in the context of this problem.

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There is only one triangle with sides measuring 3, 4, and 5.

When no side is specified, an infinite number of triangles are created.

If side lengths are not given, the three angles will result in an infinite number of triangles that are unique.

In this case the three sides of the triangle are specified and condition like this leads to formation of one unique triangle which a right triangle

This is a well known right triangle, the sides given is also known as a Pythagorean triple.

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The pairs of simultaneous equations have their x and y values to be (a) x+y=5 and xy=x+3: (1, 4) and (2, 3) & (b) 2x+y=5 and x² + y² =10: (x, y) = (1, 3) and (3, -1)

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

The pairs of simultaneous equations can be solved using a graphical method

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

(a) x+y=5 and xy=x+3

x and y values:

(x, y) = (1, 4) and (2, 3)

(b) 2x+y=5 and x² + y² =10

x and y values:

(x, y) = (1, 3) and (3, -1)

See attachment for graphs

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Answer:

6 cups

Step-by-step explanation:

When two things are directly proportional (e.g. y and x), we can model the relationship with the direct variation equation, which is

y = kx, where

Step 1:  To find k, we can allow y to represent Jackie's total revenue from selling lemonade ($9) and x to represent the quantity of cups of lemonade sold ($3):

9 = 3k

k = 3

Step 2:  Now that we've found the constant of proportionality, we can plug in 18 for y and 3 for k, allowing us to solve for x:

18 = 3x

6 = x

Thus, in order for Jackie to earn $18, she must sell 6 cups in all.