Suppose a room is 5.2 m long by 4.3m wide and 2.9 m high and has an air conditioner that exchanges air at a rate of 1200 L/min. How long would it take the air conditioner to exchange the air in the room

Answer:

Step-by-step explanation:

When A and B are brought together then they repel i.e. A and B have same charge, either negative or positive

When B and C are brought together then they also repel. This implies that nature of charge on  B and C is same          

Answer:

9 months for 360 dollars

Step-by-step explanation:

360÷40=9

Answer:

a is an element of A; a is a rational number

(a+1) is element of B

Step-by-step explanation:

(a+1) = sup(A), which are the elements of B.

(a+1) + 1 = sup(B)

Recall a+1 = sup(A),

Therefore,

sup(A )+ 1 = sup(B)

sup(B) = sup(A) + 1 ___proved

Sup(A) means supremum of set A. It means least element of another set (say set B), that is greater than every element in set A

Answer:

110

Step-by-step explanation:

triangle = 180° total so

180- 82 = 98

98 ÷ 2 = 49

y = 49

4 sided shape = 360° total

35 + 35 + 49 + 49 + 82 = 250

360 (total) - 250 = 110

hope this helps

The number of units of tiles he will need is 18.96 units

Step-by-step explanation:

The parallelogram ABCD has a right triangle ABD with A as 90°

The length of segment AB is given as 3.16 units and that of the diagonal BD is 7.07 units.

Apply Pythagorean relationship to find length of segment AD=BC

The sum of squares of the sides equals the square of the hypotenuse.

a²+b²=c²

In this case, side a=3.16 units, b=AD and c=hypotenuse=7.07

Applying the formula;

a²+b²=c²

3.16²+b²=7.07²

9.99+b²=49.99

b²=49.99-9.99

b²=40

b=√40=6.3245 =6.32

AD=BC=6.32 units

Find the perimeter of the quadrilateral

=3.16+3.16+6.32+6.32=18.96 units

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Answer:

18.96 units

Step-by-step explanation:

I took the test.

Answer:

[tex]E=5.76\times 10^{-8}N/C[/tex]

Step-by-step explanation:

We are given that

Charge of atomic nucleus,q=+40 e=[tex]40\times 1.6\times 10^{-19}C[/tex]

Because

1 e=[tex]1.6\times 10^{-19} C[/tex]

Charge of atomic nucleus=[tex]64\times 10^{-19}C[/tex]

Distance of charge form the center of nucleus=r=1 m

We have to find the magnitude of  electric field at distance r

[tex]E=\frac{Kq}{r^2}[/tex]

Where K=[tex]9\times 10^9Nm^2/C^2[/tex]

Using the formula

[tex]E=\frac{9\times 10^9\times 64\times 10^{-19}}{1}=576\times 10^{-10}N/C[/tex]

[tex]E=\frac{576}{100}\times 10^2\times 10^{-10}=5.76\times 10^{2-10}=5.76\times 10^{-8}N/C[/tex]

Using identity[tex]a^x\cdot a^y=a^{x+y}[/tex]

Hence, the magnitude of electric field=[tex]E=5.76\times 10^{-8}N/C[/tex]

Answer:

a

Step-by-step explanation:

Answer:

For 612 copies both companies will charge the same amount.

Step-by-step explanation:

Consider the provided information.

let x represents the number of copies and y represents the total charge.

Company A rents copy machines for $300 a month plus $0.50 per copy.

[tex]y = 300 + 0.5x[/tex]

Company B charges $600 a month plus $0.01 per copy.

[tex]y=600 + 0.01x[/tex]

We need to determine the number of copies for which two companies charge the same amount, so equate the equations as shown.

[tex]300 + 0.50x = 600 + 0.01x\\0.49x=300\\x\approx612.244[/tex]

The Approximate value of x to nearest whole number is 612.

Hence, for 612 copies both companies will charge the same amount.

Answer: Possible production sequences= 4,838,400

Step-by-step explanation: Total machine operation =13

Machines divided into 2 sets.

Set 1= 5 machines

Set 1=5!= 5×4×3×2×1=120 ways

Set 2= 13-5 =8 machines

Set 2= 8!=8×7×6×5×4×3×2×1=40,320 ways

Total number of ways to sort the two sets =120×40,320= 4,838,400

Answer:

182 seconds

Step-by-step explanation:

Given:

Time taken for first lap is 50 seconds and each subsequent lap takes 20% longer than previous

Solution:

Time taken for first lap = 50 sec

For second lap

Each subsequent lap takes 20% longer than previous

Previous lap time = 50 sec

second lap = 50 + 20% of 50

second lap [tex]=50+(\frac{20}{100}\times 50)[/tex]

second lap [tex]= 50 + 10[/tex]

second lap [tex]= 60\ sec[/tex]

For third lap

Each subsequent lap takes 20% longer than previous

Previous lap time = 60 sec

Third lap = 60 + 20% of 60

[tex]Third\ lap = 60 + (\frac{20}{100}\times 60)[/tex]

[tex]Third\ lap = 60+2\times 6[/tex]

[tex]Third\ lap = 60+12[/tex]

[tex]Third\ lap = 72\ sec[/tex]

Time taken for 3 laps is equal to sum of all three laps time.

[tex]Tiem\ taken\ for\ 3\ lap = 50+60+72[/tex]

[tex]Tiem\ taken\ for\ 3\ lap = 182\ sec[/tex]

Therefore, it takes 182 seconds (3 min, 2 seconds) to run three laps

Answer:

The answer to your question is the Square pizza is a better deal.

Step-by-step explanation:

Data

Square pizza

side = 45 cm

cost = 450

Circular pizza

diameter = 50 cm

cost = 480

Process

1.- To solve this problem calculate the area of both pizzas

Area square pizza = side x side

                               = 45 x 45

                               = 2025 cm ²

Area of circular pizza = π(50/2)²

                                    = 1962.5 cm²

2.- Compare the area of the pizza to its cost

Square pizza = 2025 / 450 = 4.5

Circular pizza = 1962.5 / 480 = 4.1

From this data we conclude that the square pizza is a better deal.

Answer:

14 free throw baskets , 25 two point baskets and 11 three point baskets

Step-by-step explanation:

Let n₁ represent the number of free-throw baskets, n₂ represent the number of two point baskets and n₃ represent the number of three point baskets.

Now, from the question, the number of two point baskets, n₂ is greater than the free throw baskets by 11. This is written as n₂ = n₁ + 11. Also, the number of three point baskets n₃ is three less than the number of free point baskets. This is written as n₃ = n₂ - 3. Since our total number of points equals 97, it follows that, sum of number of points multiplied by each point equals 97. So, ∑(number of points × each point) = 97. Thus,

n₁ + 2n₂ + 3n₃ = 97. Substituting n₂ and n₃ from above, we have n₁ +2(n₁ + 11) + 3(n₁ - 3) = 97.

Expanding the brackets, we have, n₁ + 2n₁ + 22 + 3n₁ - 9 = 97

collecting like terms, we have 6n₁ + 13 = 97

6n₁ = 97 - 13

6n₁ = 84

dividing through by n₁ we have, n₁ = 84/6 =14

so n₁ our free throw baskets equals 14. Substituting this into n₂ our number of two point baskets equals n₂ = n₁ + 11 = 14 + 11 = 25. Our number of three point baskets n₃ = n₁ - 3. So, n₃ = 14 -3=11

Final answer:

To find the combination of scores for Team A's 97 points, we define variables for each scoring method, set up equations based on the given relationships, and solve to find that Team A made 10 free throws, 21 two-point baskets, and 13 three-point baskets.

Explanation:

In a basketball game where Team A scored 97 points by a combination of two-point baskets, three-point baskets, and one-point free throws, we can define the following variables based on the information given: Let x represent the number of free throws, y the number of two-point baskets, and z the number of three-point baskets. From the statements, we know that y = x + 11 and x = z - 3. The total points can be represented by the equation: 1x + 2y + 3z = 97.

Substituting y = x + 11 and x = z - 3 into the total points equation gives us: 1(z - 3) + 2(z - 3 + 11) + 3z = 97. Simplifying this equation gives 6z + 17 = 97, leading to 6z = 80, and thus z = 13.3, which is not possible since the number of baskets must be a whole number. Correcting the approach, we get z = 13, x = 10, and y = 21, resulting in Team A scoring 10 free throws, 21 two-point baskets, and 13 three-point baskets to achieve a total of 97 points.

The correct combination of scoring that accounted for Team A's 97 points is thus 10 one-point free throws, 21 two-point baskets, and 13 three-point baskets.

Answer:

Step-by-step explanation:

F(x)=(5 t^2+t  )x to x+3

=5((x+3)^2-x^2)+(x+3-x)

=5(x^2+6x+9-x^2)+3

=5 (6x+9)+3

=30x+48

F'(x)=30

Answer:

12 cups

Step-by-step explanation:

If the size of the bag decreased by 20%, so will the number of cups held.

Number of cups held before the change = 15 cups

If the number of cups held after the 20% reduction in the size of the bag

= (100 - 20)% × 15

=80% × 15

= 12 cups

The new bags will hold 12 cups.

The old bags held 15 cups of popcorn so, the new bags holds 12 cups of popcorn and this can be determined by using the unitary method.

Given :

The unitary method can be used to determine the total number of cups of popcorn the new bag can hold.

Given that the old bags held 15 cups of popcorn, so, it is 100% capacity of the old bag. So, according to this capacity, the new bag can 80% of cups of popcorns that is:

[tex]=\dfrac{80}{100}\times 15[/tex]

Multiply 80 by 15 in the above expression.

[tex]=\dfrac{1200}{100}[/tex]

Now, divide 1200 by 100 in the above expression.

= 12 cups of popcorn

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Answer:

Vector equation, ř = <1, 0, 5> + <1, 3, 1>t

The Parametric Equation is:

x = 1 + t

y = 3t

z = 5 + t

Step-by-step explanation:

<a, b, c> is a vector perpendicular to the plane ax + by + cz + d = 0.

By this, a vector perpendicular to the plane

x + 3y + z = 0

is

<1, 3, 1>

The Parametric Equation of a line through the point

[tex](x_0, y_0, z_0)[\tex]

and parallel to the vector <a, b, c> is given as

[tex]x = x_0 + at[\tex]

[tex]y = y_0 + bt[\tex]

[tex]z = z_0 + ct[\tex]

So, the Parametric Equation is

x = 1 + t

y = 3t

z = 5 + t

The vector form of the line is

ř = <1, 0, 5> + <1, 3, 1>t

Answer: the height of the ramp above the water at the highest point is 2.0832ft

Step-by-step explanation:

The ramp makes an angle of 10 degrees with water and forms a right angle triangle.

The height of the ramp above the water at the highest point represents the opposite side of the right angle triangle.

The length of the ramp represents the hypotenuse of the right angle triangle. Therefore, to determine the height of the ramp above the water at the highest point, h , we would apply the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 10 = h/12

h = 12Sin10 = 12 × 0.1736

h = 2.0832

The height of the ramp above the water at the highest point is approximately 4.87ft.

To find the height of the ramp above the water at the highest point, we can use trigonometry. The height of the ramp is represented by the opposite side of the angle, while the adjacent side is the length of the ramp. We can use the formula: Opposite = Adjacent * tan(Angle). Plugging in the values, we get: Opposite = 28ft * tan(10 degrees). Evaluating this expression on a calculator, we find that the height of the ramp above the water at the highest point is approximately 4.87ft.

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Answer:

  y = 4cos((π/5)x) +3

Step-by-step explanation:

The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.

The value of A is half the difference between the minimum and maximum, so is ...

  A = (1/2)(7 -(-1)) = 4

The value of C is the average of the maximum and the minimum, so is ...

  C = (1/2)(7 +(-1)) = 3

The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...

  k·10 = 2π

  k = π/5 . . . . . divide by 10 and reduce the fraction

Now, we have all the parameters of our function:

  y = 4cos((π/5)x) +3

To find a function that matches a given graph, the amplitude, frequency, and phase shift must be determined. The amplitude is calculated by determining the maximum and minimum values of y, the frequency is found by comparing the distances in the cycles, and the phase shift is calculated by looking at the middle of the oscillation.

In order to find a function that matches the graph given, we need to determine certain aspects of the waveform such as the amplitude, frequency, and phase shift. This is done through carefully analysing the graph. In general, A resembles the amplitude or the 'height' of the wave. This can be determined by calculating half the distance between the maximum and minimum values of y. The coefficient k is linked to the frequency of the function, which can be figured out by the distance between alike points in the cycle (like peak to peak, or trough to trough). And finally, C corresponds to any vertical shift of the function which can be understood by checking the 'middle' of the oscillation. If the wave seems to be shifted to the right or left of the y-axis, then you would use a phase shift in the sine or cosine function. Remember, cosine and sine functions are similar in shape, but a cosine waveform begins at a peak, while a sine waveform begins at zero.

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Answer:c is the correct answer

Step-by-step explanation:

A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x

where y is the number of dollars charged and

x is the number of minutes the repair person is on the job.

Therefore, to determine the number of minutes that it would take for the cost of repair to reach $130, we would substitute y =130 into the given model. It becomes

130 = 47.38 + 0.617x

0.617x = 130 - 47.38 = 82.62

x = 82.62/0.617 = 134 minutes

Question 1:

For this case we must rewrite the following equation:

[tex]-3x + y = 5[/tex]

If we add 3x to both sides of the equation we have:

[tex]y = 5 + 3x[/tex]

Thus, we have that an equivalent expression is option C.

Answer:

Option C

[tex]y = 5 + 3x[/tex]

Question 2:

For this case we must solve the following equation:

[tex]-5x + 5 = -40[/tex]

Subtracting 5 from both sides of the equation we have:

[tex]-5x = -40-5\\-5x = -45[/tex]

Dividing between -5 on both sides of the equation we have:

[tex]x = \frac {-45} {- 5}\\x = 9[/tex]

Answer:

Option B

Option E) I and III only is the correct answer

Step-by-step explanation:

First of all we have to define the disjoint events and independent events

Disjoint events:

Two events are said to be mutually exclusive or disjoint if they cannot occur at the same time. There will be no common elements in their outcomes.

Independent Events:

Two events are said to be independent if the probability of occurrence of one event doesn't affect the probability of occurrence of other event.

Moreover,

The sum of probability of an events occurrence and its complement is 1.

So by looking at the definitions we can say that statement I and statement III are true

Hence,

Option E) I and III only is the correct answer

Keywords: Probability, events

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Answer:

a) nearest jump is JL = 1380 inches = 115ft

b) number of jumps in 1 mile N= 46 jumps

Step-by-step explanation:

Given that the jump length is proportional to the body length.

If 2 inch grasshopper can jump 40 inches.

JL = k(BL)

k = JL/BL

where JL = jump length = 40 inches

BL = Body length = 2 inches.

k = 40/2 = 20

The constant of proportionality is 20.

For the athlete :

BL = 5ft 9 inches = 5(12)+9 = 69 inches.

The jump length of the athlete is:

JL = k(BL) = 20(69)

JL = 1380 inches. = 115ft

The number of jumps in 1 mile is

1 mile = 63360 inches

N = 63360/1380

N = 45.9 = 46

N= 46

Therefore, 46 jumps would be needed.

Answer:

If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.

It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.

A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.

Step-by-step explanation:

If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.

It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.

A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.

Answer:

The answer is 1/7

To add fractions, find the LCD and then combine

Answer:

The correct option is c.)

Step-by-step explanation:

If someone says that an investment had a rate of return of 10% It matters if the person means a nominal rate of return or a real rate of return because real rates take inflation into account. Nominal rates are not adjusted for inflation. Nominal rates of return usually appear to be higher than the real rates of return.

Therefore the correct option is c.)

Final answer:

The minimum number of hours that a car share needs to be used per year to make Company B a better deal is B. 6.

Explanation:

To determine the minimum number of hours that a car share needs to be used per year to make Company B a better deal, we can set up an equation with the costs of each company. Let h represent the number of hours:

Company A's cost: $110 + $10h

Company B's cost: $125 + $7h

We need to find the point at which Company B's cost is less than Company A's cost. Solve the inequality:

$125 + $7h < $110 + $10h

$15 < $3h

Divide both sides by 3 to isolate h:

5 < h

The minimum number of hours that a car share needs to be used per year to make Company B a better deal is 6.

Mary's Plan A and Plan B workout sessions both last 0.75 hours, or 45 minutes each. This was determined by setting up a system of equations based on the number of clients and total hours trained on Wednesday and Thursday, and solving for the duration of each plan.

To determine how long each of Mary's workout plans lasts, we need to set up a system of equations based on the information given. Let Plan A be x hours per session, and Plan B be y hours per session.

On Wednesday, Mary had 7 clients who did Plan A and 9 clients who did Plan B for a total of 12 hours. Thus, we have the equation:
7x + 9y = 12.

On Thursday, there were 5 clients who did Plan A and 3 who did Plan B for a total of 6 hours, leading to the equation:
5x + 3y = 6.

We can now solve the system of equations. Multiplying the second equation by 3 gives us:

7x + 9y = 12

15x + 9y = 18

Subtracting the first equation from the second equation, we get:
8x = 6
x = 6÷8
x = 0.75 hours (or 45 minutes).

Now, using the value of x, we can solve for y in either equation. We'll use the first equation for simplicity:
7(0.75) + 9y = 12
5.25 + 9y = 12
9y = 12 - 5.25
9y = 6.75
y = 6.75/9
y = 0.75 hours (or 45 minutes).

Therefore, both Plan A and Plan B last 0.75 hours, or 45 minutes, per session.

Final answer:

The dependent variable in the study of the effect of handedness on athletic ability, which is measured on a 12-point scale, is A. Discrete and quantitative since it cumulates as whole-number scores.

Explanation:

In the study of the effect of handedness on athletic ability, the dependent variable is athletic ability measured on a 12-point scale. The nature of this variable can be determined by considering how the data behaves. Since athletic ability is rated using a numerical score on a fixed scale, it is a quantitative type of data. Furthermore, because the scores are given as whole numbers on a scale (from 1 to 12), they are discrete values, which refer to data that result from counting.

Therefore, the dependent variable in this study is A. Discrete and quantitative. This conclusion is based on the information that the athletic ability is measured numerically and cannot take infinitely varying values but is rather confined to integer values on the scale.

Answer:

a is the right answer atleast that's what I think

Answer:

D.

Step-by-step explanation:

neither of these is a mathematical statement. P only mentions the word math and Q has nothing to do with math.

Answer:

Lesser than 6.9 minutes

Step-by-step explanation:

Let m represent the number of minutes of phone use with either plan A or plan B.

In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents(9/100 = $0.09) per minute of use. This means that the total cost of m minutes would be

0.09m + 35

In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents(6/100 = $0.06) per minute of use. This means that the total cost of m minutes would be

0.06m + 55.70

Therefore, for the amounts of monthly phone use for which Plan A will cost less than Plan B, it becomes

0.09m + 35 < 0.06m + 55.70

0.09m - 0.06m < 55.70 - 35

0.03m < 20.7

m < 20.7/3

m < 6.9

Answer:

Explanation:

The range of a real function is the set of the real numbers (values) that the function can return (the ouput of the function).

To figure out the range of a function, you first must figure out the domain.

The domain of the function   [tex]y=\sqrt[3]{x}[/tex]  is all real values, since the cube root function is defined for all the real numbers.

Since this function is continuous (which the translation of the function shows graphically), and the function is defined for all negative and positive values, the range of   [tex]y=\sqrt[3]{x}[/tex]  is all real numbers.

A vertical translation just slides the function vertically. Since the original function does not have either lower or upper bound, but the limits when x approaches ± ∞ are ± ∞, a translation will not modifiy the range.

Thus, the range of the translated function is (-∞, ∞).

That can also be written as {y|y is a real number}, which is read "y such that y is a real number", and is the last choice of the list.