A hotel swimming pool measures 20 m by 8m.The hotel manager wants to put a 2 m wide deck around the pool. Caluculate the area of the deck.

Answer: .75 + .25x ≤ 7

Step-by-step explanation: The x equals the amount that you can buy for each item.

The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the sides of a right triangle.

The Pythagoras Theorem states that : in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of squares of lengths of other two sides.

Mathematically, the Pythagoras Theorem is written as:

⇒ c² = a² + b² ;

where c is = length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.

The Converse of Pythagoras Theorem states that : If in a triangle, the square of the length of the longest side is equal to the sum of squares of lengths of other two sides, then triangle is a right triangle.

Both the Pythagorean Theorem and its converse apply only to right triangles, which are triangles that have a right angle .

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The total number of cows is given by the equation c = 182 cows and the total number of legs of cows is n = 728 legs

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total number of cows and goats = 452

So , c + g = 452   be equation (1)

And , ( 5/7 )c = ( 13/27 )g

On simplifying the equation , we get

c = ( 13 x 7 ) / ( 5 x 27 ) g

c = ( 91/135 )g   be equation (2)

Substituting the value of c in equation (1) , we get

( 91 / 135 ) g + g = 452

On further simplification , we get

( 91 + 135 ) / 135 g = 452

( 226 / 135 ) g = 452

Divide by 226 on both sides of the equation , we get

( 1/135 )g = 2

Multiply by 135 on both sides of the equation , we get

g = 270 goats

Now , the number of cows = 452 - 270 = 182 cows

The number of legs = 182 x 4 = 728 legs

Hence , the number of cows is 182 cows

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The student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.

To find the minimum score the student needs on the fourth test, we can use the formula for the average of four numbers:

Average = (sum of the numbers) / 4

We know that the student needs an average of at least 80 to earn a grade of B, and we also have the scores for the first three tests: 77, 77.25, and 81.25. So, we can set up the equation:

80 = (77 + 77.25 + 81.25 + x) / 4

where x is the score the student needs on the fourth test. Solving for x:

80 = (235.5 + x) / 4

320 = 235.5 + x

x = 320 - 235.5

x = 84.5

So, the student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.

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Using the concept of proportions, the first rate does not form a proportion while the second rate form a proportion and the the cost of 9 pizza is $152.55

Proportion is a mathematical concept that refers to the relationship between two values or sets of values. It expresses the relative sizes of two or more quantities and can be represented as a fraction, decimal, or percentage.

6.

16 players for 24 teams

20 players for 32 teams

Let's find the ratio of player to team if they're consistent.

16 / 24 = 2/3 ≠ 20 / 32 = 5/8

The rates do not form a proportion.

7.

10 inches in 6 hours

80 inches in 2 days

10 / 6 = 5/3  = 80 / 48 = 5/3

The rates form a proportion.

8.

4 pizza = 67.80

9 pizza = x

Cross multiply both sides

4x = 67.80 * 9

4x = 610.2

x = 610.2 / 4

x = 152.55

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To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element. All elements in the set have a multiplicative inverse except for 0.

To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element (usually 1).

For example, in the set {1, 2, 3, 4, 5} under multiplication modulo 6, we have:

The multiplicative inverse of 1 is 1 (1 x 1 = 1 mod 6).

The multiplicative inverse of 2 is 4 (2 x 4 = 8 = 1 mod 6).

The multiplicative inverse of 3 is 5 (3 x 5 = 15 = 3 x 1 = 1 mod 6).

The multiplicative inverse of 4 is 2 (4 x 2 = 8 = 2 x 4 = 1 mod 6).

The multiplicative inverse of 5 is 3 (5 x 3 = 15 = 3 x 5 = 1 mod 6).

Note that every element in the set has a multiplicative inverse except for 0. This is because any number multiplied by 0 is 0, not 1.

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Answer:

654

Step-by-step explanation:

An increase of 9% would mean 1.09 times 600 which equals 654

Answer:

-7.5 OR -7 1/2

Step-by-step explanation:

20.5 - 28 = -7.5

OR

20 1/2 - 28 = -7 1/2

Answer:

Since ∠1 and ∠2 are vertical angles, they have equal measure. And since ∠3 and ∠4 are right vertical angles, they have measure 90° each.

Since ∠3 is adjacent to both ∠1 and ∠2, we can say that:

∠1 + ∠3 = 180°

∠2 + ∠3 = 180°

Adding these two equations together:

∠1 + ∠2 + 2∠3 = 360°

Substituting the values we have:

∠1 + ∠2 + 2(90°) = 360°

∠1 + ∠2 + 180° = 360°

Solving for ∠1 + ∠2:

∠1 + ∠2 = 180° - 180° = 0°

Finally, the sum of the measure of ∠4 and the measure of ∠1 minus the measure of ∠2 is:

∠4 + (∠1 - ∠2) = 90° + (∠1 - 0°) = 90° + ∠1

So the answer is 90° + ∠1.

The height of the cylinder is 18 cm and its volume is 450π cubic centimeters, given that the radius of its base is 5 cm and its total surface area is 165πcm².

A right circular cylinder is a three-dimensional geometric shape with a circular base and a curved surface that extends upward in a cylindrical fashion.

Let's begin by identifying the formula for the total surface area of a cylinder. It is given by:

Total surface area = 2πr(h + r)

Where r is the radius of the base, h is the height, and π is a mathematical constant (approximately 3.14). We are given that the total surface area of the cylinder is 165πcm², and the radius of its base is 5 cm. Substituting these values in the formula, we get:

165π = 2π(5 + h)5 + 2π(5)²

Simplifying this equation, we get:

165π = 10πh + 150π

Dividing both sides by 10π, we get:

h + 15 = 33

Therefore, the height of the cylinder is 18 cm (33 - 15).

Now, let's find the volume of the cylinder. The volume of a cylinder is given by:

Volume = πr²h

Substituting the values of r and h, we get:

Volume = π(5)²(18)

Simplifying this equation, we get:

Volume = 450π

Therefore, the volume of the cylinder is 450π cubic centimeters.

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Complete Question:

The total surface area of a right circular cylinder is 165πcm². If the radius of its base is 5 cm; find its height and volume.

Answer:

121

Step-by-step explanation:

1242-150=1092/9 = 121 (remainder 3)

Answer: 121

Step-by-step explanation: 1241 - 150 / 9

Answer:

Step-by-step explanation:

He is now 14 years old because if you minus 21 and 7, it will be 14

Answer:

If your friend says that he will be 21 years old in seven years, then he is currently 21 - 7 = 14 years old.

Step-by-step explanation:

The statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

To determine which statement about 4 √2x + 4 √x + 3 = 0 is true, we need to solve the equation.

However, it is not possible to solve the equation exactly because it contains square roots. We can simplify the equation by multiplying both sides by the conjugates of the square roots, which eliminates the square roots.

Multiplying both sides by (2x + x + 3) / (2x + x + 3), we get:

(4 √2x + 4 √x + 3) * (2x + x + 3) / (2x + x + 3) = 0 * (2x + x + 3) / (2x + x + 3)

Expanding the left-hand side, we get:

12x + 6 = 0

Solving for x, we get:

x = -1/2

So, the statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

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(a) Potential on the opposite sides of the positive and negative plates is 8475 V and -8475 V, respectively. (b). 772 m/s is the speed at which the positive plate will be struck.

A more technical or sophisticated phrase, velocity, is occasionally used interchangeably with speed to refer to extremely high rates of linear or circular speed, such as the velocity of a bullet.

a). Positivplate should be on the right and negativeplate should be on the left.

Potential equals zero at the center of the plates.

Electric field between it plates: 30e⁻⁶/8.85e⁻¹² (338 V/m) = sigma/e0

Potential is equal to 3389830x, where x is the distance in meters from the center of the plates.

Where x is the distance in meters from the center of the plates, the potential to the left of either the middle point equals -3389830x.

Potential outside of the positive plate is equal to 3389830*0.005/2, or 8475 V.

The potential is -8475 V on the contrary side of the negative plate.

Potential between it plates is equal to -8474 + 3389830x, where x is the distance in meters from the negative plates.

b). Electron energy at the positive plate is equal to [8475 - -8475]. eV = 2*8475*1.6e⁻¹⁹ = 2.712*10⁻¹⁵ J

Speed = sqrt(2E/m) = sqrt(2*2.712e-15/9.1e⁻³¹) = 772 meters per second.

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The sine of Z is 0.834.

Assume that "α" is the angle in a right triangle XYZ. The sine formula is then given as Sin = Opposite side/ Hypotenuse.

Using the Pythagorean theorem, we can find the length of side Y:

Y² = X² + Z²

Y² = 7² + ( √(21) )²

Y² = 49 + 21

Y² = 70

Y = √(70)

Now we can use the definition of sine:

sin(Z) = opposite/hypotenuse

sin(Z) = X / Y

sin(Z) = 7 / √(70)

sin(Z) = (7 / 10) √(70)

So the sine of Z is (7 / 10) √(70), or approximately 0.834.

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Answer:

Step-by-step explanation:

c

a

An article appearing in a certain journal included the following acrylamide content for five brands of biscuits. 344 , 294, 333, 276, 248. The mean acrylamide level (in nanograms/gram) is 299.

In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values. It is commonly referred to as the average.

To calculate the mean, all the data values are added together, and then this sum is divided by the number of data points in the dataset. The formula for calculating the mean is:

mean = (sum of values) / (number of values)

To calculate the mean acrylamide level, we need to add up all the acrylamide levels for the five brands of biscuits and divide the sum by the total number of brands.

Sum of acrylamide levels = 344 + 294 + 333 + 276 + 248 = 1495

Total number of brands = 5

Mean acrylamide level = (Sum of acrylamide levels) / (Total number of brands) = 1495 / 5 = 299

Therefore, the mean acrylamide level is 299 nanograms/gram.

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Answer: Width = 45 feet; Length = 15 feet;

Step-by-step explanation: Start by substituting 3w for the length because it says that in the problem. We know that 2(L+W) equals the perimeter. Since we substituted 3w for length we get 8w for the perimeter. Divide 120 by 8 to find that the width is 15 feet and plug it into 3w to get the length of 45 feet.

Answer:

45 feet and 15 feet are the length and width

Step-by-step explanation:

P = 120 feet

a (length) = 3 * b (width)

P = 2 * (a + b)

P = 2 * (3b + b)

P = 2 * 4b

P = 8 * b

                           => 8b = 120 feet

P = 120 feet

b = 120 / 8

b = 15 feet

a = 3 * b

a = 3 * 15

a = 45 feet

Using the distributive property, we can write (z-5)(z+3) is equal to  [tex]z^2[/tex] - 2z - 15.

Let us expand the expression (z-5)(z+3).

We will distribute the terms in the first set of parentheses (z-5) to the terms in the second set of parentheses (z+3) as follows -

(z-5)(z+3) = z(z+3) - 5(z+3)

Now, we will simplify the expression by distributing z to both terms inside the first set of parentheses, and then distributing -5 to both terms inside the second set of parentheses as follows -

z(z+3) - 5(z+3) = [tex]z^2[/tex] + 3z - 5z - 15

Combining the like terms, we get,

(z-5) (z+3) = [tex]z^2[/tex] - 2z - 15

Therefore, (z-5)(z+3) is equal to  [tex]z^2[/tex] - 2z - 15.

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The distance is a function of time and the slope of the distance time graph will give the speed

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the first quantity be represented as Distance D

Let the second quantity be represented as Time T

Now , the function is given as

The distance D is a function of time and the slope of the line between the x and y axis of the distance time graph will give us the speed

Substituting the values in the equation , we get

Let the y axis represent the distance D

And , let the x axis represent the time T

So , Slope m = y / x

On simplifying the equation , we get

Slope m = Distance / Time = Speed

Hence , the distance is a function of time

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Answer: 15%

Step-by-step explanation:

54 divided by 360 = 0.15%

The height of the triangular prism will be 100mm.

The three-dimensional object has a base of triangular shape and has some height is called a triangular prism.

Given that the height and the base of the triangular shape of the triangular prism are 8 mm and 6.9 mm respectively. The volume of the prism is V = 2760 cubic mm.

The height of the triangular prism will be calculated as:-

Volume = 1/2 x b x h x H

2760 = 1/2 x 8 x 6.9 x H

H = 100 mm

Therefore, the height of the prism is 100mm.

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the unit rate is 6/5 inches per hour, or approximately 1.2 inches per hour.

The unit rate in inches per hour can be found by dividing the amount of rain falling per unit of time by the corresponding unit of time. In this case, we have 4/5 inches falling every 2/3 hours, so we can find the unit rate by dividing 4/5 by 2/3:

(4/5) / (2/3) = (4/5) X (3/2) = 6/5 inches per hour

So the unit rate is 6/5 inches per hour, or approximately 1.2 inches per hour.

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Answer: No, because not all of the corresponding sides are proportional

Step-by-step explanation:

If you set up ratios for corresponding sides, you will see they all evaluate to different numerical results. This means that the sides are not in a fixed ratio, which leads us to conclude the the shapes are not scalar multiples of each other. Two of those angles are congruent though!

Option (a) The quantity supplied rises by 165. To determine the change in the total supply of meals in your survey when the price increases from $8 per meal to $9 per meal, we need to compare the quantity of meals supplied at the $8 and $9 prices across all food trucks.

From the table, we can see that the quantity of meals supplied at the $8 price per meal is as follows:

Mario's Taco Stand: 140

Curbside Chargrilled Burgers: 210

Chuckin' Clouds BBQ: 175

Burrito Dan's: 240

La Jefa Cubanos: 150

What a Jrk Jamaican Food: 220

The total quantity supplied at $8 per meal is 1,135 meals.

At the $9 price per meal, the quantity of meals supplied is as follows:

Mario's Taco Stand: 160

Curbside Chargrilled Burgers: 240

Chuckin' Clouds BBQ: 200

Burrito Dan's: 260

La Jefa Cubanos: 190

What a Jrk Jamaican Food: 250

The total quantity supplied at $9 per meal is 1,300 meals.

The change in the total supply of meals is the difference between the total quantity supplied at $9 per meal and the total quantity supplied at $8 per meal, which is:

1,300 - 1,135 = 165

Therefore, the answer is (a) The quantity supplied rises by 165.

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Complete question is in the image

The equation represents how many grams of the compound will remain after 4 hours m(4) = 0.285m₀

Radiation and decay are important concepts in nuclear physics. The rate at which radioactive compounds decay is measured in terms of half-life and the decay constant.

To solve this problem, we can use the exponential decay equation, which describes the rate of decay of a radioactive substance.

In this scenario, we are interested in finding the remaining mass of the radioactive compound, which can be obtained by multiplying the number of remaining atoms by the atomic mass of the substance. The equation for the remaining mass is:

m(t) = N(t) x m

where:

m(t) represents the mass of the radioactive substance remaining at time t.

N(t) is the number of radioactive atoms remaining at time t.

m is the atomic mass of the substance.

To determine the values of N0 and λ for our radioactive compound, we can use the decay rate given in the problem. If the compound decays at a rate of 27% per hour, it means that the remaining fraction of the substance after each hour is 0.73 (i.e., 100% - 27% = 73%). Therefore, the decay constant can be calculated as follows:

ln(0.73) = -λ

λ = 0.312

Next, we can use the initial mass of the compound (320 grams) and the exponential decay equation to find the remaining number of atoms at 4 hours:

[tex]N(4) = N_0 \times e^{-0.312 x 4}[/tex]

N(4) = N₀ x 0.285

Since we don't know N₀, we can express it in terms of the initial mass and the atomic mass:

N₀ = m₀ / m

where:

m₀ is the initial mass of the radioactive compound.

m is the atomic mass of the substance.

Substituting this into the previous equation, we get:

N(4) = (m₀ / m) x 0.285

Finally, we can use the equation for the remaining mass to find the answer:

m(4) = N(4) x m

m(4) = (m₀ / m) x 0.285 x m

m(4) = 0.285m₀

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The number of gifts ason can wrap  with the ribbon he has is 12.

A quantity that is multiplied or divided between one set of units and another is termed as a conversion factor. If a conversion is required, it must be carried out with the right conversion factor to generate a value that is identical.

To change a value or expression from one form to another.

Now in the given question,

ason wraps a gift using one third of a foot of ribbon.

he has total ribbon of 4 feet.

so, we have the equation,

[tex]\frac{1}{3} x=4\\\\x=12[/tex].

hence, 12 gifts can be wrapped with the ribbon ason has.

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They are skating in the same direction, how long will it take Sam to catch up to tom

will take Sam 2.72 seconds to catch up to Tom.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

To find out how long it will take Sam to catch up to Tom, we can use the following formula:

time = distance / (rate of Sam- the rate of Tom)

In this case, the distance is 120 ft (the distance between Tom and Sam when they start speed skating) and rate of Sam is 50 ft/sec, and the rate of Tom is 44 ft/sec.

Plugging these values into the formula, we get:

time = 120 / (50 - 44) = 120 / 6 = 20

So it will take Sam 20 seconds to catch up to Tom.

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In part (a), we used the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample mean. The CLT states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.

The conditions for the CLT are:

The sample is randomly drawn from the population.

The sample size is large (usually, n >= 30 is considered large enough).

The samples are independent.

In this case, we assume that the sample was randomly drawn from the population of diameters, and the sample size of 25 is large enough to satisfy the second condition. The samples are assumed to be independent, as we are sampling without replacement from a large population.

Therefore, we can apply the CLT and use the normal distribution to approximate the sampling distribution of the sample mean.

For a sample of size 2, the sample mean will still have a sampling distribution, but the CLT may not be applicable. If the population distribution is highly skewed or has heavy tails, a sample size of 2 may not be sufficient to smooth out the sampling distribution, and it may not be normal.

In this case, a normal approximation may not be appropriate, and other methods, such as bootstrapping or permutation tests, may be more appropriate for inference.

In summary, the normal approximation based on the CLT is valid for large sample sizes, regardless of the population distribution. For small sample sizes, other methods may be more appropriate, and the normal approximation may not be valid if the population distribution is highly skewed or has heavy tails.

Question: The basal diameter of a sea anemone is an indicator of its age. The density curve shown here represents the distribution of diameters in a certain large population of anemones; the population mean diameter is 4.2cm, and the standard deviation is 1.4cm.

Let Y dash represent the mean diameter of 25 anemones randomly chosen from the population.

(a) Find the approximate value of Pr{4 ≤ Ydash ≤ 5}.

(b) Why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? Would the same approach be equally valid for a sample of size 2 rather than 25?Why or why not?

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Answer: 5/12

Step-by-step explanation:

- For the ease of the problem, turn them into improper fractions, so it would be:

13/3 divided by 14/5 divided by 26/7

- Next, let's turn the equation from division to multiplication. This can be done by flipping the fractions of everything being divided, so:

13/3 times 5/14 times 7/26

- We can cross out some parts of the fraction, like 13 and 26, 14 and 7, which simplifies our equation to:

1/3 times 5/2 times 1/2 = 5/12

Answer:

[tex]\dfrac{5}{12}[/tex]

Step-by-step explanation:

Given equation:

[tex]4 \frac{1}{3} \div 2 \frac{4}{5} \div 3 \frac{5}{7}[/tex]

Convert the mixed numbers into improper fractions:

[tex]\dfrac{4 \times 3+1}{3} \div \dfrac{2 \times 5+4}{5} \div \dfrac{3 \times 7+5}{7}[/tex]

[tex]\dfrac{13}{3} \div \dfrac{14}{5} \div \dfrac{26}{7}[/tex]

[tex]\textsf{Apply the fraction rule:} \quad \dfrac{a}{c}\div\dfrac{b}{d}=\dfrac{a}{c}\times \dfrac{d}{b}[/tex]

[tex]\dfrac{13}{3} \times \dfrac{5}{14} \times \dfrac{7}{26}[/tex]

Multiply the fractions:

[tex]\dfrac{13\times5\times7}{3 \times14 \times 26}[/tex]

[tex]\dfrac{455}{1092}[/tex]

The greatest common factor of 455 and 1092 is 91.

Therefore, divide the numerator and denominator by the GCF:

[tex]\dfrac{455 \div 91}{1092\div 91}=\dfrac{5}{12}[/tex]