2. An apartment is 8m in length, 5m in width and 3M in height. How many people can be invited to a party if each person requires 5m³ of air space?​

The answers to all parts shown below.

Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root. Radicand - A number or expression inside the radical symbol.

Given:

We have to find the Square/Cube Factors

1. 5/6√3

Now, rationalizing

5/6√3 x √3/ √3

= 5√3 / 18

2. √3/ (7- 3√5)

Now, rationalizing

= √3/ (7- 3√5) x (7+ 3√5) / (7+ 3√5)

= √3(7+ 3√5) / 4

3. 8/ (4 + 5√2)

Now, rationalizing

= 8/ (4 + 5√2) x  (4 - 5√2)/  (4 - 5√2)

= -8 (4 - 5√2)/ 34

4. 7 ∛(48 [tex]m^{18} n^{13}[/tex])

= 14 [tex]m^6[/tex][tex]n^4[/tex]∛6n

5.[tex]2\sqrt{\left(-300x^{18}\right)}[/tex]

=[tex]20\sqrt{3}\sqrt{-x^{18}}[/tex]

6. (4+ 7√10)²

= 4² + (7√10)²+ 2 (4)( 7√10)

= 16 + 490 + 56√10

= 506 + 56√10

7. (6- 7√3) x (6+ 7√3)

= 6² - (7√3)²

= 36 - 147

= -111

8. 11√50[tex]x^{12}y^5[/tex]

= 55[tex]x^6[/tex]y²√2y

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Answer: You would be going 30 miles per hour if you traveled 8 miles in 16 minutes

Step-by-step explanation:

Answer:

x=3/2

Step-by-step explanation:

(x+1)(x+2)(4) = (24x-1)
4(x^2+3x+2) = 24x-1
4x^2+12x+8 = 24x-1

4x^2-12x^2+9 = 0

(2x-3)^2 = 0

2x-3 = 0

x = 3/2

The possible values of variable {x] are -

{x} = 1.146   or   {x} = 1.854.

Given is that the dimensions of a rectangular prism are (x + 1) feet by (x + 2) feet by 4 feet.

We can write the volume of the rectangular prism as -

Volume = length x width x height

4(x + 1)(x + 2) = (24x - 1)

(x + 1)(x + 2) = 6x - 1/8

6x - (x + 1)(x + 2) = 1/8

Solving the equation graphically, we get -

x = 1.146   or   x = 1.854

Therefore, the possible values of variable {x] are -

{x} = 1.146   or   {x} = 1.854.

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ANSWER :

hope it helped

ExPLANATION:

Answer:

f(n) = 23-5n

Step-by-step explanation:

The initial number everywhere is always 23, so that's the start number. Than for every "n" it subtracts 5.

In a density curve, the proportion of data is represented by the area under the curve.

Therefore the answer is "area under the curve".

The area under the curve represents the probability or proportion of data within a certain interval. The curve itself represents the distribution of the data and the shape of the curve provides information about the type of distribution (e.g. normal, skew, etc.).

The intervals on both the horizontal and vertical axis are used to measure the density of the data, but they do not represent the proportion of data themselves. The length of the curve has no significance in representing the proportion of data.

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Answer:

23.558

Step-by-step explanation:

u know how the thing goes

The correct derivative expressions of the given ones are -

[tex]$1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0[/tex]

[tex]$2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =[/tex][tex]$\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8[/tex]

[tex]$3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20[/tex]

It is given that -

[tex]$\int\limits^3_8 {f(x)} \, dx = 6\\[/tex]

and

[tex]$\int\limits^3_8 {g(x)} \, dx[/tex]

The correct statements of the given are -

[tex]$1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0[/tex]

[tex]$2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =[/tex][tex]$\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8[/tex]

[tex]$3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20[/tex]

Therefore, the correct derivative expressions of the given ones are -

[tex]$1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0[/tex]

[tex]$2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =[/tex][tex]$\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8[/tex]

[tex]$3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20[/tex]

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Answer:

  C.  ∫(f·g)dx = -12 is incorrect

Step-by-step explanation:

You want to know which of the integral expressions is incorrect given ...

[tex]\displaystyle \int_3^8{f(x)}\,dx=6\ \ \text{ and }\int_3^8{g(x)}\,dx=-2[/tex]

Expression A has the same value for upper and lower limits of the integral. The area being integrated has zero width, so its value will be zero, as shown in expression A.

Expression E has the limits reversed from those in expression B, so the value of that integral will be the opposite of the value shown for B. Both of these integral expressions (B, E) are correct.

The integral of a sum is the sum of the integrals. This is shown in expressions B, D, and E, all of which are correct.

In general, the integral of a product will have no relation to the product of integrals. Hence expression C is NOT necessarily correct.

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Let x be the number of toppings and y be the cost of the sundae. We know that a sundae costs $2 without any toppings, and each topping costs $0.50. Therefore, the equation that describes the relationship between x and y is:

y = 2 + 0.5x

This equation can be represented on a graph, with x on the horizontal axis and y on the vertical axis. As x increases, y increases by $0.50 for each additional topping. The graph will be a line with a slope of 0.5 and y-intercept of 2, meaning that the line passes through the point (0,2) and rises by $0.50 for each unit increase in x.

The perimeter of the parallelogram is 24 units

The formula for calculating the perimeter of a parallelogram is given as;

P = 2( a+ b)

Given that the parameters are;

From the diagram shown, we have the values as the distance between points, we have ;

a = 4 - 1

a = 3

b = 4

Substitute the values

Perimeter , P = 2(3×4)

expand the bracket

Perimeter, P = 24 units

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Answer: (-∞, -5)

Step-by-step explanation:

When plotted on a line graph there will be an open circle on negative five and your line would be going infinitely off to the left.

Answer:

To avoid cutting out a fraction of an inch, we need to choose a value of x that is a factor of both 36 inches and 48 inches, since those are the lengths of the sides of the rectangular sheet of cardboard we are using.

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The largest factor that both 36 and 48 have in common is 12. However, we can't choose x to be 12 inches because that would mean the length and width of the rectangular box would also be 12 inches, which is too small for our purposes.

Therefore, we should choose x to be the next largest factor that both 36 and 48 have in common, which is 6 inches. This means we will cut six 6-inch by 8-inch rectangles from the cardboard sheet.

The dimensions of the rectangular box will be:

Length = 2x + 2h = 2(6 in) + 2(8 in) = 12 in + 16 in = 28 in

Width = 2x + 2w = 2(6 in) + 2(12 in) = 12 in + 24 in = 36 in

Height = h = 8 in

Therefore, the dimensions of the rectangular box are 28 inches by 36 inches by 8 inches

The value of p is 5/8

A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.

Examples of complex fraction include ½/¾, ⅚/½

⅚/p = ⅔/½

= 5/6 ÷ p = ⅔ ÷ 1/2

= 5/6 × 1/p = 2/3 × 2/1

= 5/6p = 4/3

15 = 24p

divide both sides by 24

p = 15/24

p = 5/8

therefore the value of p is 5/8

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Answer:

2: 0.6

3: 0.1

Step-by-step explanation:

When you horizontally stretch the parent function f(x)=x² by a factor of 4, the new function becomes f(x)= (1/4) x².

The function can be stretched or shrunk in different directions to produce new functions that are similar in shape but differ in size and orientation.

When you horizontally stretch the function f(x)=x² by a factor of 4, the function becomes

=> f(x)= (1/4) x².

To understand this, let's look at the equation of the parent function in detail.

The equation of the parent function f(x)=x² can be written as

=> y=x².

The x values represent the horizontal distances from the origin, and the y values represent the vertical distances from the origin.

When you stretch the function horizontally by a factor of 4, it means that the x values will be multiplied by 4. In other words, the distance from the origin in the x direction will be four times larger. The new equation of the stretched function will be

=> y= (1/4) (4x)².

We can simplify this equation to y= (1/4) x².

In mathematical terms, the horizontal stretching of a function is equivalent to multiplying the independent variable (x) by a constant factor. In this case, the constant factor is 1/4. The constant factor of 1/4 in the equation

=> y= (1/4) x²

represents the horizontal stretch by a factor of 4. The effect of this horizontal stretch is that the parabolic shape of the function will be wider and flatter compared to the parent function. The shape of the parabolic graph of the stretched function will be similar to the parent function, but the x values will be multiplied by 4.

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The area of the given figure above can be calculated through the addition of the area of a rectangule and the area of a trapezium would be = 110km²

The area of the rectangle= length× width

where length = 17km

width = 4km

area = 17×4= 68km²'&&&&&&

The area of trapezium; = ½(a+b)h

where a= 12 km

B= 17-12 = 5 km

h = 3+4 = 7 km

area = ½(5+7)×7

= ½× 12×7

= 6×7 = 42km²

Therefore the area of the figure = 68+42 = 110km²

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Answer:

8.417

Step-by-step explanation:

The amount of 101 inches is equal to 8.4167 feet.

To convert inches to feet, we divide the number of inches by 12, since there are 12 inches in 1 foot.

As 1 foot= 12 inches

Therefore, to convert 101 inches to feet, we divide 101 by 12:

= 101 inches / 12 inches/foot

= 8.4167 feet

So, 101 inches is equal to 8.4167 feet.

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Answer:

Step-by-step explanation:

(5/3)[tex]d^{3}[/tex]*(-1/3)[tex]x^{3}[/tex]=(-5/9)[tex]d^{3} x^{3}[/tex]

Answer:

Let -5x+y=-3 be the first equation, and 3x-8y=24 be the second. Let's manipulate the first equation by adding 5x to both side; resulting in y=-3+5x, or 5x-3. Now let's plug in 5x-3 for wherever y has been in the second formula. 3x-8(5x-3)=24. This is now pretty straightforward to solve for x. We distribute the 8 into (5x-3) and get 3x-40x-24=24. -48=27x. x=-48/27, x=-16/9.

Now let's plug in the x for either one of the equations to get y. 3(-16/9)+8y=24. -16/3+8y=24. 8y=24+16/3. 24y=72+16. 24y=88. y=88/24, y=11/3.

Step-by-step explanation:

a) The value of P(A∩B) = 0.

b) The value of P(A|B) = 0.

c) P(A|B) is not equal to P(A). A and B are independent events.

d) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.

e) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.

a) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.

b) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.

c) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.

However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).

d) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.

If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.

e) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.

Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.

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Complete question is:

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.

a) What is P(A∩B)?

b) What is P(A | B)?

c) Is P(A | B) equal to P(A)?

Are events A and B dependent or independent?

d) A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

e) What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

The marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.

To find the marginal benefit in this range, we need to calculate the additional benefit of selling one more bouquet within this range.

First, let's find the benefit per bouquet in the range between selling 400 and 600 bouquets:

Total benefit in the range = $7,200 - $4,800 = $2,400

Number of bouquets in the range = 600 - 400 = 200

Benefit per bouquet in the range = Total benefit / Number of bouquets = $2,400 / 200 = $12

So for each bouquet sold within the range between 400 and 600, the benefit is $12.

Therefore, the marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.

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The value of the angles x is 121 degrees

It is important to note that the sum of interior angles of a polygon takes the expression

(n -2) 180

Then, we have;

(6-2) 180

720

Then, add all the angles and equate to 720. we get;

105 + 88 + 142 + 140 + 124 + x = 720

Add the values

599 + x = 720

Collect the like terms

x = 720 - 599

x = 121 degrees

Hence, the value is 121 degrees

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Answer:

22yrs

Step-by-step explanation:

So, the money will grow to $600 in about$$ 22 years.

Answer:

Step-by-step explanation:

2y>-5

y>-2.5

Based on the definition of similar triangles, the length of PR is 16 units.

In similar triangles, corresponding sides are in proportion. This means that if two triangles are similar, their corresponding sides will have the same ratio.

Therefore, we will have the proportion:

8/6 = (x + 7 + x - 1) / (x + 7)

4/3 = (2x + 6) / (x + 7)

Cross multiply:

3(2x + 6) = 4(x + 7)

6x + 18 = 4x + 28

6x - 4x = -18 + 28

2x = 10

x = 5

PR = x + 7 + x - 1

PR = 2x + 6 = 2(5) + 6

PR = 16 units

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Answer:

- 1/2< x ≤ 3

Step-by-step explanation:

The filled circle (at point 3) indicates that 3 is included in the inequality and the clear circle at -1/2 indicates that -1/2 is not included

The total area of the US is equal to 3,537,438 square miles.

An equation is an expression shows the relationship between two or more numbers and variables.

A equation is a statement with two equal sides and an equal sign in between. An equation is, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that the total land area of the United States is about 3,483,511 square miles more than the total land area of Tennessee, is about 53,927 square miles.  

We need to write and solve an equation to find the total land area of the United States.

Now, according to the given information,  

Total land area of the United States is 3,483,511 square miles more than the total land area of Tennessee, is 53,927 square miles  

Total land area = 3,483,511 + 53,927

= 3,537,438

Hence, the total area of the US =  3,537,438 square miles.

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The measurement of AB is given as follows:

AB = 16.23.

The three trigonometric ratios are defined as follows:

For the angle of 52º, we have that:

Hence the measurement of AB is obtained as follows:

cos(52º) = 10/AB

AB = 10/cos(52º)

AB = 10/0.616

AB = 16.23.

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For a cardboard:

The area of the cardboard is:

Length = 1 m 5 cm = 105 cm

Breadth = 80 cm

Area = Length x Breadth = 105 cm x 80 cm = 8400 cm²

The area of the cardboard in square meters is:

1 m = 100 cm

Length = 1 m 5 cm = 105 cm = 1.05 m

Breadth = 80 cm = 0.8 m

Area = Length x Breadth = 1.05 m x 0.8 m = 0.84 m²

The area covered by the ribbons is the area of the cardboard that is not painted. From the previous calculations, we know that the area of the cardboard is 8400 cm² and the area that was painted is 4700 cm². Therefore, the area covered by the ribbons is:

Area covered by ribbons = Total area of the cardboard - Area that was painted

Area covered by ribbons = 8400 cm² - 4700 cm²

Area covered by ribbons = 3700 cm²

The area of the cardboard is (105 cm) x (80 cm) = 8400 cm².

The area covered by the ribbons is 3700 cm².

So, the area of the cardboard that was painted is 8400 cm² - 3700 cm² = 4700 cm².

The area of the cardboard is 8400 cm² or 0.84 m². The area covered by the ribbons is 3700 cm². So, the area that needs to be painted is the difference between the area of the cardboard and the area covered by the ribbons, which is:

8400 cm² - 3700 cm² = 4700 cm²

To convert to square meters, we divide by 10000:

4700 cm² ÷ 10000 = 0.47 m²

Therefore, the cost of painting the remaining area is:

0.47 m² × ₹25/m² = ₹11.75

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The number of quarters minted in 2018 is 2 and the mass of a quarter is 0.006 kg

The number of quarters minted in 2018 is 2 x 10°, which in standard form is simply 2. The mass of a quarter is 6 x 10^-3 kg, which in standard form is 0.006 kg. So, the number of quarters minted in 2018 is 2 and the mass of a quarter is 0.006 kg

A unit of mass is a unit used to measure mass. Mass is a physical property of an object that is used to explain various observed object behaviors.

In everyday life, mass is always synonymous with weight. But in reality, mass and weight are different. The weight is caused by the interaction between the mass and the Earth's gravitational field.

For example, an object with a weight on earth, when it is sent into outer space or to another planet, the object has no weight because there is no gravity. However, the object still has the same mass.

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