13. Measuring bone density Individuals with low bone
density have a high risk of broken bones (fractures).
Physicians who are concerned about low bone density
(osteoporosis) in patients can refer them for special-
ized testing. Currently, the most common method for
testing bone density is dual-energy X-ray absorptiom-
etry (DEXA). A patient who undergoes a DEXA test
usually gets bone density results in grams per square
centimeter (g/cm²) and in standardized units.
7.
Judy, who is 25 years old, has her bone density
measured using DEXA. Her results indicate a bone
density in the hip of 948 g/cm² and a standardized
score of z = -1.45. In the reference population of
25-year-olet women like Judy, the mean bone density
in the hip is 956 g/cm².6
(b) Use the information provided to calculate the standard
deviation of bone density in the reference population.

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is given by the binomial probability formula:

P(X = k) = (n choose k) \(* p^k * (1-p)^(n-k)\)

where X is the random variable representing the number of heads, n is the total number of coin flips, k is the number of heads obtained, and p is the probability of getting a head on any individual flip.

Since we are assuming that the coin is fair, p = 0.5. Let's say you flipped the coin n times and obtained k heads. Then the probability of obtaining exactly k heads with a fair coin is:

P(X = k) = (n choose k \(* 0.5^k * ()1-0.5)^(n-k)\)

We don't know what n or k are, so we can't compute the exact probability. However, we can use the fact that the coin is fair to get an estimate. If we assume that the number of heads obtained is roughly half of the total number of flips, then k = n/2. Plugging this into the formula, we get:

\(P(X = n/2) = (n choose n/2) * 0.5^(n/2) * (1-0.5)^(n/2)\)

Simplifying this expression, we get:

\(P(X = n/2) = (n choose n/2) * 0.5^n\)

Now, we want to find the probability of obtaining exactly as many heads as we just obtained. Let's say we flipped the coin 10 times and obtained 5 heads. Then we want to find P(X = 5), which is:

P(X = 5) = (10 choose 5) \(* 0.5^5 * (1-0.5)^(10-5)\) = 0.2461

Therefore, the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

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\(b \: .) \: \: - 67.2\)

hope it helps

The inverse for f(x) = 12 - x is f^-1(x) = -x + 12

Define Inverse Function

An inverse function or an anti function is defined as a function, which can reverse into another function.

The given equation is ,

f(x) = 12 - x

We can also write like this,

y = 12 - x

Now, for the inverse just swap x and y like this

x = 12 - y

x - 12 = - y

y = -x + 12

Now, we know

y = f^-1(x) = -x + 12

Hence, f^-1(x) = -x + 12

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The required result is (3x + 40)/(x + 4)(x + 4).

To perform the indicated operation of subtraction on the two rational expressions and reduce the answer to the lowest term we need to follow the given steps :

Given expressions are : (8)/(x + 4) - (5x - 8)/(x^(2) + 8x + 16) The LCM of (x + 4) and (x^2 + 8x + 16) is (x + 4) (x + 4). The given expressions can be written as follows: (8(x + 4))/(x + 4)(x + 4) - ((5x - 8))/(x + 4)(x + 4)

We can simplify the above expression by multiplying each term by the denominator of the other term, we get(8(x + 4))/(x + 4)(x + 4) - ((5x - 8))/(x + 4)(x + 4)

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

= (8x + 32 - 5x + 8)/(x + 4)(x + 4)  

= (3x + 40)/(x + 4)(x + 4)

Hence, the required result is (3x + 40)/(x + 4)(x + 4).

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Relational databases are heavily based on the mathematical concept of: Set Theory. The correct option is (A).

Relational databases are based on the principles of set theory, which deals with sets of elements and their relationships with each other. In a relational database, data is organized into tables, with each table representing a set of related data.

The tables are then related to each other through the use of keys, which allow for the establishment of relationships between different sets of data. The principles of set theory also govern the use of operations such as union, intersection, and difference, which can be used to manipulate the data in the tables.

Therefore, the mathematical concept of set theory is a fundamental part of the design and use of relational databases.

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Answer:

3 ways

Step-by-step explanation:

From the question:

Number of acres of the land = 100 acres

1 cow = 10 acres of land

1 sheep = 3 acres of land

To fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is calculated as:

1) 1 cow and 30 sheep

1 cow × 10 acres + 30 sheep × 3 acres

10 + 90 = 100 acres

2) 4 cows and 20 sheep

4 cow × 10 acres + 20 sheep × 3 acres

40 + 60 = 100 acres

3) 7 cows and 10 sheep

7 cow × 10 acres + 10 sheep × 3 acres

70 + 30 = 100 acres

Therefore, to fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is 3 ways

As x approaches positive infinity (∞), the function f(x) approaches a negative infinity (-∞).

To determine this value, we need to simplify the given function and analyze its behaviour. Given the function\(f(x) = -2(2-4x)^2 + 3\) we can simplify it as follows:\(f(x) = -2(4x^2 - 16x + 16) + 3\)

f(x) =\(-8x^2 + 32x - 32 + 3\)

f(x) =\(-8x^2 + 32x - 29\)

Now, as x approaches positive infinity (∞), we can observe the behaviour of the leading term\((-8x^2)\) of the function. Since the coefficient of \(x^2\)is negative (-8), the function will tend to negative infinity as x approaches positive infinity (∞). Therefore, as x approaches positive infinity (∞), f(x) approaches negative infinity (-∞). In mathematical notation, we can express the end behavior of the function as: As x → ∞, f(x) → -∞

Hence, as x approaches positive infinity (∞), we will observe that the function f(x) approaches negative infinity (-∞).

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From given data:

The number of blocks that could fit in one box is:

Now the number os blocks could fit in three box is:

The height of the prism is 7.1m

A prism is a solid shape that is bound on all its sides by plane faces.

Surface area is the amount of space covering the outside of a three-dimensional shape.

The surface area of a prism is expressed as;

SA = 2B +ph

where B is the base area , p is the perimeter of the base and h is the height of the prism

The base of the triangle is calculated as;

√ 10² -8.7²

√100- 75.69

= √24.31

= 4.93m

If half base = 4.93

then the base = 4.93 × 2 = 9.86m

area of the base = 1/2 × 9.86 × 8.7

= 42.9 m²

perimeter of the base = 10+10 + 9.86

= 29.86 m²

Surface area = 297

Therefore ;

297 = 2 × 42.9 + 29.86h

29.86h = 297 - 85.8

29.86h = 211.2

h = 211.2/29.86

h = 7.1 m

Therefore the height of the prism is 7.1 m

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The inequality that represents the possible values for the number of tables sold, tt, and the number of chairs sold, cc is $200cc + $650tt > $12,000.

Here are inequality signs and what they mean:

total cost of chairs sold + total cost of tables sold > $12,000

$200cc + $650tt > $12,000

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Answer:

10

Step-by-step explanation:

from 99 to 91 give us reminder

so reminders in 91 will be 1

92 will be 2

93 will 3

and so on to the 99 will be 9

but in 100 will not be there any reminder so, 10 cannot be the reminder

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

The Area of triangle with the given height 10 cm and base 6 cm is calculated to be  30 square centimeters.

To calculate the area of a triangle with height 10 cm and base 6 cm, we can use the formula:

Area = (1/2) x Base x Height

Substituting the given values, we get:

Area = (1/2) x 6 cm x 10 cm

Area = 30 square cm

Therefore, the area of the triangle is 30 square centimeters.

We can see that the area of the triangle is calculated by multiplying the base and height and then dividing the result by 2. In this case, the height of the triangle is 10 cm and the base is 6 cm, so the area is 30 square cm. This formula can be used to calculate the area of any triangle, regardless of its size or shape.

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The complete question is :

Calculate the Area of triangle with the height 10 cm and base 6 cm .

the heart shape is primarily characterized by its curved, symmetrical form, with any straight lines or modifications being secondary to the essential shape of the symbol.

A heart shape is a symmetrical and stylized representation of the human heart, typically depicted as a symbol of love, affection, or romance.

The heart shape consists of two curved, semi-circular shapes joined together at the bottom to form a point, or a cleft. The top of the heart is rounded and the bottom is pointed, creating the characteristic shape that we associate with the symbol of a heart.

While the overall shape of a heart is curved, there may be some straight lines in certain depictions or variations of the symbol. For example, in some stylized or simplified versions of the heart shape, the curves may be straightened or simplified into straight lines. However, even in these simplified versions, the basic curved structure of the heart shape remains recognizable.

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The slope of the equation is m that is derivative of the given function if you take the graph of ln (K) and 1/T. I t makes intercept at ln[A] and the slope is given by m= -Ea/R that means option D is correct.

For many physical and chemical reactions, the relationship between reaction rate and temperature is described by the Arrhenius equation.

Based on hydrolysis S2 peak data measured at multiple heating rates and burial histories occurring over geological time scales, Arrhenius-equation first-order reactions are useful for modelling the timing and temperatures of petroleum generation from organic-rich shakes and oestrogens at laboratory scales.

The slope of the equation is m that is derivative of the given function if you take the graph of ln (K) and 1/T. I t makes intercept at ln[A] and the slope is given by m= -Ea/R that means option D is correct.

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The derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

To find the derivative of F(x) = xª sec¯¹ (x²). we will use the chain rule of differentiation.

Then we can rewrite the given function as:

F(x) = xª sec¯¹ (x²)

Using the chain rule, the derivative of y with respect to x as;

dy/dx

= d/dx [cos⁻¹(x)]

= -1/√(1 - x²) * d/dx [x]

= -1/√(1 - x²)

Sincey = sec⁻¹(1/x)

sec(y) = 1/x

cos(y) = x

-sin(y) dy/dx = 1

dy/dx = -1/sin(y)

Using the Pythagorean identity sin²(y) + cos²(y) = 1,

sin(y) = √(1 - cos²(y)) = √(1 - x²)

Substituting

dy/dx = -1/√(1 - x²)

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The derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

To determine the derivative of F(x) = xª sec¯¹ (x²). we will use the chain rule of differentiation.

Given function as:

F(x) = xª sec¯¹ (x²)

The derivative of y with respect to x as;

sec(y) = 1/x

cos(y) = x

-sin(y) dy/dx = 1

dy/dx = -1/sin(y)

Using the Pythagorean identity sin²(y) + cos²(y) = 1,

sin(y) = √(1 - cos²(y)) = √(1 - x²)

Substituting

dy/dx = -1/√(1 - x²)

Therefore, the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²)

and

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Given function is `f(x) = 2x^3 + 15x^2 - 84x + 13`.Now, to find the values of `x` where horizontal tangent occurs, we need to differentiate the given function and equate it to zero.

If we get  two values of `x` for which the derivative is zero, then the graph of the given function has two horizontal tangents.

The derivative of the given function `f(x)` can be found using the power rule, as follows: `f'(x) = 6x^2 + 30x - 84`.Now, equating `f'(x) = 0`, we get: `6x^2 + 30x - 84 = 0`.Simplifying the above quadratic equation by dividing both sides by 6, we get: `x^2 + 5x - 14 = 0`.We can factorize the above quadratic equation as: `(x + 7)(x - 2) = 0`.Therefore, the roots of the above equation are: `x = -7` and `x = 2`.

Hence, the negative value of `x` where a horizontal tangent occurs is `-7`.And, the positive value of `x` where a horizontal tangent occurs is `2`.Answer: The negative value of `x` where a horizontal tangent occurs is `-7` and the positive value of `x` where a horizontal tangent occurs is `2`.

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Answer:

The value of y in the equation is 10

Step-by-step explanation:

3y = 22 + 8

3y = 30

y = 30/3

Therefore; Y = 10

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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Answer:

correct

Step-by-step explanation:

Answer:

d = 122°

Step-by-step explanation:

d and 58° are a linear pair and sum to 180° , that is

d + 58° = 180° ( subtract 58° from both sides )

d = 122°

Abrielle earns $1.25 more per hour than Zane.

Answer:

(a) 8

(b) 4

(c)5

Step-by-step explanation:

We are given multiple parts and we  need to provide the correct answer among the given options, also we need to prove that rest of the answers are wrong.

(a). X + 12 = 20 ( 12,8,20,0)

X= 20 -12

X= 8, so only 8 is the correct answer and rest are wrong.

Proof: lets take other given options into consideration

X= 12

X+12 =12+ 24 which is wrong because X+12 is already given as 20.

similarly,

X=20

X+12 = 20+12 = 36, which is wrong because X+12 is already given as 20.

X= 0

X+12 = 0+12 = 12, which is wrong because X+12 is already given as 20.  

(b). P - 4 = 0 (4,-4,8,0)

P-4 = 0

P= 4, So only 4 will give the correct answer and not the other options.

P= -4 = -4 -4 = -8, which is wrong because P-4 is is already given as 0.

similarly,

P = 8  = 8-4 = 4, which is wrong because P-4 is is already given as 0.

P = 0, 0-4 = -4 , which is wrong because P-4 is is already given as 0.  

(c). 2y - 3 = 7 (0,3,5,7)

       2y = 7 + 3

       2y = 10

          y = 5, only 5 will satisfy this given equation and rest will be wrong,

y = 0

2y-3 = 7

2(0) -  3 = 7

-3 = 7 which is not correct as LHS and RHS must be same.

similarly,

y = 3

2y-3=7

2(3) - 3 =7

6-3 = 7

3=7 which is again wrong.

y = 7

2(7) -3 =7

14-3 = 7

11=7, which is wrong.

Therefore the given options for the correct answers is verified and the wrong answers are given as the proof.

Answer:

1/64 is 0.015625 in decimals

Answer:

-12

Step-by-step explanation:

−|−4n|

Let n =3

−|−4*3|

−|−12|

Taking the absolute value, or the non negative value

-  (12)

-12

Answer:

-1 2/3, -1/5, -0.1, 1 5/6, 1.9

Step-by-step explanatio

Answer:

its b i think

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

They can't add 5 into it because they are not like terms if it was 5h instead then yes you could but it is just 5.

There are 472 more buttons bought by Vance than beads.

For the stated question table is made.

So,

Total number of beads bought by Vance = Number of beads(2 packages of large beads) + Number of beads(1 package of medium beads).

= (2 × 96) + (1 × 64)

= 2 × (90 + 6) + 64

= (2 × 90) + (2 × 6) + 64

= 180 + 12 + 64

= 256 beads

Now,

Total number of buttons bought by Vance = Total number of buttons (2 packages of large buttons) + Number of buttons (2 packages of medium buttons)

= (2 × 56) + (2 × 38)

= 2 × (50 + 6) + 2 × (30 + 8)

= (2 × 50) + (2 × 6) + (2 × 30) + (2 × 8)

= 100 + 12 + 600 + 16

= 728 buttons

Thus,

Difference for the number of buttons and beads

= 728 – 256

= 472 beads

So,

Therefore, there are 472 more buttons bought by Vance than beads.

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