The ability to determine the age of some individuals can be difficult if there are not quality government records of birth.
Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and
an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally
distributed with a mean of 19.1 years and a standard deviation of 16.1 months. Complete parts (a) through (d).

If there were 756 students in the school and each student receives 10 pamphlets on the tooth brushing drills, the total number of pamphlets given out, using multiplication operation, is 7,560.

Multiplication operation is one of the four basic mathematical operations.

Multiplication operation involves the number being multiplied (the multiplicand), the multiplier or the number multiplying the multiplicand, and the product, which is the result.

The number of pamphlets given to each student on tooth brushing drills = 10

The total number of students at the school.

The total number of pamphlets given out to the students = 7,560 (756 x 10)

Thus, based on multiplication operation, the total pamphlets were 7,560.

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The segment cg has a length of 5 before dilation and 10 after dilation, making it the correct result of the dilation.

In mathematics, a dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the space.Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

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Knowing that the drum is a cylinder, we will get that:

Here we can see that the drum is a cylinder, remember that the circular areas of a cylinder of radius R and height H are:

A = 2*3.14*R^2

And the curved surface is:

S = 2*3.14*R*H

Here we can see that:

R = 21cm

H = 9.5cm

a) The area of leather needed is:

A = 2*3.14*(21cm)^2 = 2,769.48 cm^2

b) The area of wood needed is:

S = 2*3.14*21cm*9.5cm = 1,378.42 cm^2

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The factorized expression au maximum is:

(3x+6)(84x³ - 189x² + 20x + 69)

To factorize the given expression au maximum, (3x+6)(4x−9)+(3x+6)(7x−3)(3x+6)(4x−9)+(3x+6)(7x−3), follow these steps:

Look for common factors in the terms. Notice that (3x+6) is a common factor in all terms.

Factor out the common factor, (3x+6), from each term:

(3x+6)[(4x−9) + (7x−3)(3x+6)(4x−9) + (7x−3

Now simplify the expression inside the brackets:

(3x+6)[(4x−9) + (21x² - 39x - 18x + 27)(4x−9) + (7x−3)]

Distribute the terms inside the brackets:

(3x+6)[(4x−9) + (84x³ - 153x² - 36x² + 63x - 108x + 81) + (7x−3)]

Combine like terms:

(3x+6)[(4x - 9) + (84x³ - 189x² + 9x + 81) + (7x - 3)]

Add the terms inside the brackets:

(3x+6)[84x³ - 189x² + 20x + 69]

So, the factorised expression au maximum is:

(3x+6)(84x³ - 189x² + 20x + 69)

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Father : 50 years old

Son : 10 years old

Answer:

To find out which cake is the most expensive per serving, we need to calculate the cost per serving for each cake.

The first cake serves 2 people and costs $4.50. So the cost per serving is:

$4.50 ÷ 2 = $2.25 per serving

The second cake serves 8 people and costs $10.00. So the cost per serving is:

$10.00 ÷ 8 = $1.25 per serving

The third cake serves 10 people and costs $20.00. So the cost per serving is:

$20.00 ÷ 10 = $2.00 per serving

Therefore, the first cake is the most expensive per serving, at $2.25 per serving.

The null hypothesis was rejected as the mean of the sweetness losses was greater than the critical value. Thus, the cola did lose sweetness.

1. State the null hypothesis: The null hypothesis is that the cola did not lose sweetness.

2. Determine the level of significance: The level of significance is 5%.

3. Calculate the test statistic and The test statistic is calculated by subtracting the mean of the sweetness losses from zero.

4. Make a decision: If the test statistic is greater than the a critical value, then the null hypothesis should be rejected and the cola did lose sweetness. which is greater than the a critical value of 0.05. Therefore, the null hypothesis should be rejected and the cola did indeed lose sweetness.

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Answer:

8

Step-by-step explanation:

Use PEDMAS

P - Parenthesis

E - Exponents

D -Division

M - Multiplication

A & S - Addition and subtraction.      [tex]\bf 7 + (2 +6)^2 \div 4 * (\dfrac{1}{2})^2 = 7 + 8^2 \div 4 * \dfrac{1}{16}\\\\\\\text{\bf First perform the operation inside the parenthesis and then the exponents}[/tex]

                                [tex]= 7 + 64 \div 4 * \dfrac{1}{16}[/tex]

Here, exponents 8² = 64 is done

                                [tex]\bf = 7 + 16 * \dfrac{1}{16} \ {(\bf Division \ is \ done)}[/tex]

                                 = 7 + 1

                                 = 8

Answer:

wait I big speak. it's important for learn how.

Answer:

green is x ≥ -3

blue is y < -2x - 4

Step-by-step explanation:

The weight of the first basket full of apples is 8.66 kilograms more as compare to weight of the second basket.

Number of full of apples basket with Tommy = 2

Weight of first basket full of apples = 18.63 kilograms

Weight of second basket full of apples = 9.97 kilograms

Weight of first basket is greater than the weight of the second basket.

More weight in first basket

= Subtract the weight of the second basket from the weight of the first basket

⇒ More weight in first basket  = Weight of first basket - Weight of second basket

⇒ More weight in first basket = ( 18.63 - 9.97 ) kilograms

⇒ More weight in first basket = 8.66 kilograms

Therefore, the first basket weighed 8.66 kilograms more than the second basket.

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Based on the description, this study is most prone to differential misclassification of exposure status. The correct answer is A.

The description of the study suggests that the nurses who collected the data were poorly trained in the use of the male pattern baldness scale. This means that they may have misclassified some men as having male pattern baldness when they did not actually have it, and vice versa.

This misclassification of exposure status (i.e., male pattern baldness) is more likely to be differential because the nurses were unaware of the purpose of the study and did not know whether the men were cases or controls. This means that their misclassification of exposure status is likely to be influenced by the outcome (i.e., MI).

For example, if the nurses believed that male pattern baldness was a risk factor for MI, they may have been more likely to classify cases as having male pattern baldness and controls as not having it, even if this was not accurate. This would result in differential misclassification of exposure status, which can bias the study results. The correct answer is A.

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answer:Average velocity is displacement divided by the time over which the displacement occurs. v avg = displacement time = Δ d Δ t = d f − d 0 t f − t 0. Velocity, like speed, has SI units of meters per second (m/s), but because it is a vector, you must also include a direction.

Step-by-step explanation:

To find the total area of the pool and the walkway, we can add the areas of the pool and the walkway together.

Let's assume that the pool has dimensions of length L and width W, and that the walkway has a uniform width of 2 feet all around the pool. This means that the dimensions of the pool plus the walkway will be (L + 4) feet by (W + 4) feet, since we add 2 feet on each side.

The area of the pool alone is given by L x W. The area of the pool plus the walkway is then given by (L + 4) x (W + 4). To simplify, we can use FOIL (First, Outer, Inner, Last) method to expand the expression:

(L + 4) x (W + 4) = LW + 4L + 4W + 16

Therefore, the polynomial expression that represents the total area of the pool and the walkway is:

A(L,W) = LW + 4L + 4W + 16

where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.

1.Start by assuming that the pool has dimensions of length L and width W, in feet.

2.Since Mrs. Smith wants to add a 2-foot walkway around the edge of the pool, we need to add 2 feet to both the length and width of the pool to get the dimensions of the pool plus the walkway. This means that the dimensions of the pool plus the walkway are (L + 2) feet by (W + 2) feet.

3.To find the area of the pool alone, we can simply multiply the length by the width: A_pool = L x W.

4.To find the area of the pool plus the walkway, we need to multiply the length and width of the larger rectangle that includes both the pool and the walkway. This rectangle has dimensions of (L + 2) feet by (W + 2) feet. Therefore, the area of the pool plus the walkway is:

A_total = (L + 2) x (W + 2)

5.We can simplify this expression by using the distributive property of multiplication. We first multiply L by W to get LW. Then, we multiply L by 2 and W by 2 to get 2L and 2W, respectively. Finally, we add 2 x 2 = 4 to account for the extra area added by the walkway. Therefore, the total area of the pool plus the walkway can be written as:

A_total = LW + 2L + 2W + 4

6.Finally, we can rewrite this expression as a polynomial in standard form, by rearranging the terms in descending order of degree:

A_total = LW + 2L + 2W + 4

    = LW + 2L + 2W + 0x² + 4

    = 0x² + LW + 2L + 2W + 4

So the polynomial expression that represents the total area of the pool and the walkway is:

A(L,W) = LW + 2L + 2W + 4

where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.

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The probability that they will all be non fiction is 0.0667. The solution has been obtained by using hyper-geometric distribution.

What is hyper-geometric distribution?

When sampling from a small population without replacement, the hyper-geometric distribution is a discrete probability distribution that determines the likelihood that an event occurs k times in n trials.

The formula is

P (X = x) = h (x, N, n, k) = [tex]\frac{C_{k,x} * C_{N-k, n-x} }{C_{N,n} }[/tex]

We are given

x = 4

N = 10 + 12 = 22

n = 4

k = 12

Substituting this in the formula, we get

⇒P (X = 4) = h (4, 22, 4, 12) = [tex]\frac{C_{12,4} * C_{22-12, 4-4} }{C_{22,4} }[/tex]

⇒P (X = 4) = h (4, 22, 4, 12) = [tex]\frac{C_{12,4} * C_{10, 0} }{C_{22,4} }[/tex]

⇒P (X = 4) = h (4, 22, 4, 12) = 0.0667

Hence, the probability that they will all be non fiction is 0.0667.

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Answer:

4

Step-by-step explanation:

Let x be the number of shirts that Rachel can buy, and y be the number of pants she can buy. Then the cost equation would be:

Cost = 25x + 20y

Since Rachel has a total budget of $200, we can write:

25x + 20y ≤ 200

To find the maximum number of shirts that Rachel can buy if she buys 5 pants, we can substitute y = 5 into the inequality and solve for x:

25x + 20(5) ≤ 200

25x ≤ 100

x ≤ 4

Therefore, Rachel can buy a maximum of 4 shirts if she buys 5 pants.

Answer:

5³×z²*³×x³*³

Answer=125z⁶x⁹

The fractions between 0 and 1, we have represented on a number line, include 1/4, 2/4, and 3/4. All of these have equal intervals of 0.25.

To plot 1/4, 2/4 and 3/4 on the number line, we need to divide the interval between 0 and 1 into four equal parts. Each part will represent 1/4.

We can label the fractions at 0 and 1 as shown below:

0   1/4   2/4   3/4   1

Now we can plot the given fractions on the number line as shown below:

0   1/4   2/4   3/4   1

         o     o     o

        1/4   2/4   3/4

We can divide the fractions to get the difference of intervals. This can be done as follows:

2/4-1/4 = 0.25, also:

3/4-2/4 = 0.25.

Any portion of a whole number that is stated as one number multiplied by another is referred to as a fraction. One-half of something, for instance, is represented by the fraction 1/2. Another approach to represent a portion of a full number is with a decimal.1/2 is same as 0.25 as a decimal.

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If Zoe the goat is tied to a corner of a rectangular barn measuring 15m by 25m in the middle of a field, Zoe can graze within an area of 2660.5 sqm.

The area of the field that Zoe can graze depends on the length of the rope, which is not given in the problem. However, we can use the Pythagorean theorem to find the length of the diagonal of the barn, which represents the maximum length of the rope.

The diagonal of a rectangle with sides of length 15 meters and 25 meters can be found using the Pythagorean theorem:

diagonal² = 15² + 25²

diagonal² = 225 + 625

diagonal² = 850

diagonal =[tex]\sqrt{850}[/tex] ≈ 29.15 meters

This means that the maximum length of the rope is about 29.15 meters. The area that Zoe can graze is a circle with radius equal to the length of the rope. We can use the formula for the area of a circle to find this area:

Area = π(radius)²

Area = π(29.15)²

Area ≈ 2660.5 square meters

Therefore, the correct answer is approximately 2660.5 square meters

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6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.

To calculate the original length given that 6% of it is 570m, we can use the following formula: Original length = (570 ÷ 0.06) Original length = 9500mTo solve this problem, firstly the percentage of 6% needs to be converted into a decimal by dividing 6 by 100. This will give us 0.06. Then, the original length is found by dividing the given value of 6% (570m) by the decimal equivalent (0.06). Therefore, the original length is 9500m. To summarise, 6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.

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The activity involved multiplying two polynomials using the distributive property to find the product, which has a degree equal to the sum of the degrees of the terms being multiplied together.

The activity involved multiplying two polynomials. This involves using the distributive property to multiply each term of one of the polynomials with each term of the other polynomial.

For example, when multiplying [tex]2x2+10x-36[/tex] with 3 we use the distributive property to get [tex]6x2+30x-108[/tex].

To find the product of two polynomials, each term of one polynomial must be multiplied with each term of the other polynomial. The terms of the product of two polynomials will have the same degree as the sum of the degrees of the terms being multiplied together.

For example, when multiplying [tex]2x2-32[/tex] with 4 we use the distributive property to get [tex]8x2-128[/tex]. Here the degree of the product is 2, which is the sum of the degrees of the terms being multiplied together [tex](2+0=2)[/tex].

To multiply two polynomials, we use the distributive property to multiply each term of one polynomial with each term of the other polynomial. The degree of the product will be the sum of the degrees of the terms being multiplied together.

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Complete question:

What is the product of [tex]2x^2+10x-36[/tex] and [tex]3x-4[/tex]?

The factors of 16 are 1, 2, 4, 8, and 16, so we have:

P = {1, 2, 4, 8, 16}

Divisors are another name for factors. As a result, they can equally split into the number of which they are a factor. In other words, they do not even leave a remnant when you divide with them. For instance, 36 has a factor of 4 in it.

We can write the sets P, Q, and R using set-builder notation as follows:

P = {1, 2, 4, 8, 16} (the factors of 16)

Q = {0, 4, 8, 12, 16} (the multiples of 4 less than 17)

R = {12, 13, 14, 15, 16} (the whole numbers from 12 to 16)

The multiples of 4 less than 17 are 4, 8, 12, and 16. However, Q is defined as the complement of this set, so we have:

Q = {-3, -2, -1, 0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}

The whole numbers from 12 to 16 are 12, 13, 14, 15, and 16, so we have:

R = {12, 13, 14, 15, 16}

Due to the fact that it is a combination of 4 and less than 17, we have included 0 in set Q.

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The combined area of all the circles is 907.46 sq. cm.

The area of a given circle is the amount of space that the circle would cover in a 2 dimensional plane. The area of a circle can be determined by;

area of a circle = π r^2

In the given question, the diameters of the circles form a segment that is 68 cm. Thus;

diameter of one circle = 68/ 4

                       = 17 cm

So that,

radius of each circle = diameter/ 2

                                  = 17/ 2

                                  = 8.5 cm

area of each circle = 3.14 *(8.5)^2

                               = 226.865

The area of the circles combined = 4*226.865

                                   = 907.46

The combined area of all the circles is 907.46 sq. cm.

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The location of A using graphs, is at (4, -1).

An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.

Here in the question,

Coordinates of A= (8,2)

Now it is dilated by a scale factor of 1/2. So,

New coordinates, A' = (8/2,2/2)

= (4,1)

Now the triangle is reflected over the x-axis.

A' now becomes A" which is (4, -1).

Therefore, the new coordinate of A is (4, -1).

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The complete question is:

Triangle ABC is shown on the coordinate plane. Triangle on coordinate plane with vertices A at 8 comma 2, B at 10 comma 6, and C at 4 comma 4. Triangle ABC is dilated by a scale factor of one half about the origin and then reflected over the x-axis. What is the location of A″ after the sequence of transformations? (8, −2) (4, 1) (4, −1) (−4, 1)

The probability of picking a 2 and then picking a number less than 4will be 0.56%

By simply dividing the favοrable number οf pοssibilities by the entire number οf pοssible οutcοmes, the prοbability οf an οccurrence can be determined using the prοbability fοrmula. Because the favοrable number οf οutcοmes can never exceed the entire number οf οutcοmes, the chance οf an event οccurring might range frοm 0 tο 1.

The number οf favοurable οutcοmes tο all pοssible οutcοmes οf an event is the ratiο, which is knοwn as prοbability. The number οf gοοd οutcοmes can be represented by the symbοl x fοr an experiment with 'n' number οf οutcοmes. The fοllοwing equatiοn can be used tο determine an event's prοbability.

Yοu pick a card at randοm. Withοut putting the first card back, yοu pick a secοnd card at randοm.

1/13 chance οf picking a 5.

4/51 chance οf picking a 3 οn secοnd draw.

4/(13*51) οf dοing these sequentially = 0.56%

Hence the prοbability will be 0.56%

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Answer:

x= 3

Step-by-step explanation:

Since triangle is equilateral...

2y = 25x - 15

And....

Here,

2y + 2y + 2y = 180

6y = 180

y = 180/6

= 30

Again,

2y = 25x -15

2*30 + 15 = 25 x

x = 75/25

= 3

Answer:

B

Step-by-step explanation:

the answer is B please see on the attached.

The answer fοr this is Substitutiοn Prοperty

What is Substitutiοn Prοperty?  

The substitutiοn prοperty is a cοncept in algebra that is used tο substitute the value οf a given variable οr a quantity intο an expressiοn tο find the value οf the unknοwn. In simple wοrds, we can say that the substitutiοn prοperty is used tο replace the value οf a quantity in an equatiοn οr an expressiοn tο sοlve a mathematical prοblem. We will discuss the meaning οf the substitutiοn prοperty οf equality, the substitutiοn prοperty in geοmetry, and the direct substitutiοn prοperty in limits in the fοllοwing sectiοns.

Substitutiοn Prοperty is cοnsidered as οne οf the mοst intuitive οf the mathematical prοperties that yοu'll prοbably encοunter. Yοu may have been using substitutiοn withοut even knοwing it. This prοperty says that if x=y, then in any true equatiοn invοlving y, yοu can replace y with x, and yet yοu'll still have a true equatiοn.

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Take a loοk at the attached example shοwn below.

Thus, out of 40 problems, 6 problems will have two parts problems which is 15% of the 40.

The phrase "percent" refers to a number out of 100 or per 100. The term is derived from the Roman expression per centum, which means "by the hundred." Hence, a single percent would be one of those hundred units, and one percent, for every one hundred of anything.

Given data:

Out of 100 problems -  15% have two parts.

Out of 100 problems -  85% will not have two parts.

Thus, out of 40 problems, also 15% will contain two parts.

Then,

Number of two-part problem = 15% of 40

Number of two-part problem = 15 * 40 / 100

Number of two-part problem =  600 / 100

Number of two-part problem = 6

Thus, out of 40 problems, 6 problems will have two parts which is 15% of the 40.

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Answer:

$6.49

Step-by-step explanation:

The original admission price was $5.50, and it increased by 18%. Let's find 18% of 5.50 and then add it to $5.50, meaning $5.50 would increase by 18% (of itself.)

So 18% of 5.50 = 0.99 ( thats 0.18 x 5.50)

Add the 99 cents (0.99) to $5.50

and then you get $6.49

here is the equation I used:

(5.50 x 0.18) + 5.50

hope this helped :)