The vertical height of a right circular conical tent is 4m and the volume of space inside it is 968/7 cubic metre. Find the canvas required to make the tent.

Final answer:

The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.

Explanation:

The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.

Steps to find the nonpermissible value:

Identify the denominator of the expression, which is (Y-3).

Set the denominator equal to zero: Y - 3 = 0.

Solve for y: Y = 3.

Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.

In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.

For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.

Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.

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Final answer:

Ben incorrectly assumed that ¼ of two pizzas combined would still be ¼; however, the correct sum is ¼ + ¼ which equals ½ of a pizza. To add fractions, only the numerators are added when denominators match. Mastery of fractions is critical in both academics and day-to-day life.

Explanation:

Ben's error lies in the misunderstanding of fractions and how they add up. If Ben has two pizzas and each has ¼ left, combining the two portions does not result in having ½ of a pizza, but instead, he would have ¼ + ¼ which equals ½. This is because when adding fractions, you only add the numerators (the top numbers) if the denominators (the bottom numbers) are the same. Therefore, ¼ of one pizza plus ¼ of another pizza would equal ½ of a pizza. It's important to understand that fractions represent parts of a whole and that these parts must be added correctly to find the total amount.

Being comfortable with fractions is important not only for academic success but also for everyday life, such as understanding discounts, following recipes, or splitting bills. Utilizing real-life examples like these can help strengthen one's intuitive sense of fractions and make mathematical concepts more relatable.

Answer:

Step-by-step explanation:

Pepe is putting a fence in his backyard to enclose the garden in the form of a triangle.

In the garden already has sides enclosed with 8 feet and 5 feet.

We know a triangle is possible when sum of length of two sides > third side

so third side < 8 + 5

or third side should be less than 13.

The probability that at least one of the three children gets the disease from their mother is 97.3%.

To find the probability that at least one child gets the disease from their mother when a female carrier of the gene has three children, we can follow these steps:

1. Define the probabilities:

  - Probability that a child gets the disease from their mother (given): [tex]\( P(D) = 0.70 \)[/tex].

  - Probability that a child does not get the disease from their mother: [tex]\( P(D^c) = 1 - P(D) = 0.30 \)[/tex].

2. Identify the total number of children:

  - Number of children: [tex]\( n = 3 \)[/tex].

3. Calculate the probability that none of the children get the disease:

  - For all three children to not get the disease, the probability is [tex]\( (P(D^c))^n = (0.30)^3 \)[/tex].

4. Find the probability that at least one child gets the disease:

  - The probability that at least one child gets the disease is the complement of the probability that none of the children get the disease.

  - Thus, [tex]\( P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) \)[/tex].

Let's do the calculations step by step.

Step-by-Step Calculations:

1. Calculate the probability that none of the children get the disease:

  [tex]\[ P(\text{none of the children get the disease}) = (P(D^c))^3 = (0.30)^3 \][/tex]

2. Perform the exponentiation:

  [tex]\[ (0.30)^3 = 0.30 \times 0.30 \times 0.30 = 0.027 \][/tex]

3. Calculate the probability that at least one child gets the disease:

  [tex]\[ P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) = 1 - 0.027 = 0.973 \][/tex]

Conclusion:

The probability that at least one child gets the disease from their mother is [tex]\( 0.973 \)[/tex], or 97.3%.

Consider the coordinate plane:

1. The origin is the point where Sharon and Jacob started - (0,0).

2. North - positive y-direction, south - negetive y-direction.

3. East - positive x-direction, west - negative x-direction.

Then,

The distance between two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be calculated using formula

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.[/tex]

Therefore, the distance between  Jacob and Sharon is

[tex]D=\sqrt{(12-(-4))^2+(-5-3)^2}=\sqrt{16^2+8^2}=\sqrt{256+64}=\sqrt{320}=8\sqrt{5}\approx 11.18\ m.[/tex]

Answer: 1. C)  5/18, 25/90

2.  A) 6/10

Step-by-step explanation: 1) We need to find the ratios those makes a proportion:

Let us check given options one by one.

3/15, 12/55  

Converting them into simplest fractions.

3÷3/15÷3 = 1/5

12/55 can't be reduce more.

1/5 ≠ 12/55

So, 3/15, 12/55  don't form a proportion.

8/24, 12/35

Converting them into simplest fractions.

8÷8/24÷8 = 1/3

12/35 can't be reduce more.

8/24 ≠ 12/35

So, 8/24, 12/35 don't form a proportion.

So, 5/18, 25/90 form a proportion.

4/11, 16/25

Converting them into simplest fractions.

4/11 and 16/25 both can't be reduce more.

4/11≠16/25

So, 4/11, 16/25 don't form a proportion.

___________________________________________________

Let us reduce 9/15 into simplest fraction.

Now, let us convert each and every option in simplest fractions.

16÷1/21÷1 = 16/21

36÷2/50÷2 = 18/25

45÷5/70÷5 = 9/14

We can see 6/10 gives lowest fraction 3/5 as 9/15 gives.

Therefore, 6/10 form a proportion with 9/15.

Answer:

The land should be recorded in the purchaser's books at : $153,000.

Step-by-step explanation:

Since the parcel of land is purchased by the company for $153,000, hence the land should be recorded in the purchaser's books at : $153,000.

The simplified expression is √10 - √14 + √15 - √21.

To simplify the expression (√2 + √3)(√5 - √7), we can use the distributive property of multiplication.

Expanding the expression, we get:

(√2 + √3)(√5 - √7) = √2 x √5 + √2 x (-√7) + √3 x √5 + √3 x (-√7)

Now, simplifying each term with FOIL method we have:

√2 * √5 = √(2 x 5) = √10

√2 * (-√7) = -√(2 x 7) = -√14

√3 * √5 = √(3 x 5) = √15

√3 * (-√7) = -√(3 x 7) = -√21

Combining the simplified terms, we get:

√10 - √14 + √15 - √21

Therefore, the simplified expression is √10 - √14 + √15 - √21.

In this process, we applied the distributive property to expand the expression and then simplified each term by multiplying the square roots together. Finally, we combined the like terms to obtain the simplified expression.

For more such answers on the FOIL method

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Answer:

√10 + √15 - √14 - √21

Step-by-step explanation:

(√2 + √3)(√5 - √7)

= √2(√5 - √7) + √3(√5 - √7)

= √10 - √14 + √15 - √21

= √10 + √15 - √14 - √21

Answer:

[tex]40\ m^{3}[/tex]

Step-by-step explanation:

we know that

If two figures are similar then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> scale factor

x-----> the volume of the dilated cone

y-----> the volume of the original cone

[tex]z^{3}=\frac{x}{y}[/tex]

In this problem we have

[tex]z=1/5[/tex]

[tex]y=5,000\ m^{3}[/tex]

substitute and solve for x

[tex](1/5)^{3}=\frac{x}{5,000}[/tex]

[tex](1/125)=\frac{x}{5,000}[/tex]

[tex]x=5,000/125=40\ m^{3}[/tex]

ok so original perimeter = 12 +12 + 17 +17 = 58 mm

if dimensions are multiplied by 12:

12*12 = 144 and 17*12 = 204

 new perimeter = 144 +144 +204 +204 = 696 mm

696 / 58 = 12

so the perimeter increased by a factor of 12, answer is A

Answer:

The perimeter is increased by a factor of 12.

Option (a) is correct .

Step-by-step explanation:

Formula

Perimeter of a rectangle = 2 (Length + Breadth)

As given

A rectangle has a length of 12 millimeters and a width of 17 millimeters.

Perimeter of a rectangle = 2 × (12 + 17)

                                         = 2 × 29

                                         = 58 millimeters ²

As given

when the dimensions are multiplied by 12 .

New Length = 12 × 12

                    = 144 millimeter

New Breadth = 17 × 12

                      = 204 millimeter

Thus

New Perimeter of a rectangle = 2 × (144 + 204)

                                         =  2 × 348

                                         = 696 millimeter²

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = \frac{696}{58}[/tex]

[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = 12[/tex]

Therefore the perimeter is increased by a factor of 12.

Option (a) is correct .

Is there a viable solution when time is 30 minutes? Answer: No, the tub will be empty by then. 

A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute.

Let w be the quarts of water left in the tub.

Let t be the time in minutes.

So, the equation to model this situation is :

Modelling equation: [tex]w=50-2.5t[/tex]

This equation is viable only up to when t is 20 minutes. That will give w = 0. More than 20 minutes is not possible.

The correct answer is:

A=4

B=5

hopes this helps you and future people!

Answer:

a = 4 and b = 5

Step-by-step explanation:

The simplest form of square root of eighty can be written as:

[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]

Now as it is a square root function, we will pair up the four 2's in two pairs.

And will take out [tex]2\times2[/tex] outside the square root.

Making the answer = [tex]2\times2\sqrt{5}[/tex]

or [tex]4\sqrt{5}[/tex]

So, a = 4

and b = 5

Final Answer:

The point (0,0) does not satisfy the inequality [tex]y ≥ x^2[/tex] + x - 4, as 0 is not greater than or equal to -4. Additionally, it does not satisfy [tex]y > x^2 + 2x + 1[/tex], as 0 is not greater than 1. Therefore, (0,0) does not meet the conditions of the system of inequalities.

Step-by-step explanation:

The point (0,0) is not a solution to the given system of inequalities. First, considering the inequality [tex]y ≥ x^2 + x - 4[/tex], when substituting x=0 and y=0 into the equation, we find that 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the conditions of the first inequality. Moving on to the second inequality, [tex]y > x^2 + 2x + 1[/tex], substituting x=0 and y=0 results in 0 not being greater than 1.

Consequently, (0,0) fails to meet the requirements of the second inequality as well. In summary, the point (0,0) does not simultaneously satisfy both inequalities, rendering it unsuitable as a solution to the system.

Analyzing solutions to systems of inequalities involves evaluating each inequality independently to ensure the chosen point satisfies all conditions. In this instance, the failure of (0,0) to satisfy either inequality demonstrates that it does not conform to the system's criteria. When dealing with systems of inequalities, it is essential to carefully assess each component to accurately determine the solution set.

No, (0,0) is not a solution to the given system.

The system consists of two inequalities: y ≥ x^2 + x - 4 and y > x^2 + 2x + 1. To check whether (0,0) is a solution, substitute x = 0 and y = 0 into both inequalities. For the first inequality, x^2 + x - 4 becomes -4, and 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the first inequality. Moving on to the second inequality, x^2 + 2x + 1 becomes 1, and 0 is not greater than 1. Hence, (0,0) fails to satisfy the second inequality as well. As a result, (0,0) is not a solution to the system of inequalities.

In summary, by substituting the coordinates of (0,0) into both inequalities, we find that the point does not meet the conditions set by either inequality. Therefore, (0,0) is not a solution to the system. This conclusion is based on the specific values obtained through substitution, demonstrating that the coordinates do not satisfy the given inequalities.