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 total number of blocks is 659.

Given that there is 9 in one's place of the total number of blocks. It is also given that the number in the hundreds place is 1 more than the number in the tens place.

If we assume x as the number on hundreds place and y as the number on tens place, then according to the question:

x=y+1                                                                                                          ......(1)

Also, the sum of hundreds and tens place numbers is 11.

x+y=11                                                                                                       ......(2)

substitute the value of x from equation (1) in equation (2)

y+1+y=11

=>2y=10

=>y=5

Now substitute the value of y in equation (1);

x=5+1

x=6

Therefore, number on the hundreds place is 6 and on the tens place is 5 and the total number is 659.

Learn more about Numbers at:

brainly.com/question/580070

#SPJ4

If a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function is "false" statement.

A matrix function can be defined in a variety of ways (or matrix-valued function). One manner is in which the function takes the shape of a matrix, rather than numbers, the matrix contains functions. A(t), for example, is a 2 x 2 matrix function.

Some key features regarding the matrix function are-

To know more about  complex plane, here

https://brainly.com/question/26125074

#SPJ4

The complete question is-

If a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function. (True/False)

Answer: D because Angle D = Angle L

The volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

for given question,

We need to find the volume of the solid whose base is the region bounded between the curve y = x³ and the y-axis from y = 0 to y = 1 and whose cross section taken perpendicular to the y-axis are squares.

Now we rewrite given curve y = x³ in terms of x.

[tex]x=\sqrt[3]{y}[/tex]

Since the length of the side of each cross sectional square is [tex]2\sqrt[3]{y}[/tex], the cross sectional area A(y) can be given by

A(y) = [tex](2\sqrt[3]{y})^2[/tex]

A(y) = [tex]4y^{\frac{2}{3} }[/tex]

The region is bounded from y = 0 to y = 1

so, the volume V can be found by,

[tex]V=\int\limits^1_04y^{\frac{2}{3} }~dy\\\\V=4\int\limits^1_0 y^{\frac{2}{3} }~dy\\\\V=4\times \frac{3}{5} \\\\V=\frac{12}{5}\\\\V=2.4[/tex]

Therefore, the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.

Learn more about the volume here:

https://brainly.com/question/12649605

#SPJ4

Answer:

(3/2,1/2)

Step-by-step explanation:

y=2x^2-6x+5

a=2

b=-16

substitute the coefficients into the expression

x= - -6/2x2

x=3/2

y=2x^2-6x+5, x=3/2

calculate the function value for x=3/2

y=1/2

(3/2,1/2)

Answer: 0.0000413

Step-by-step explanation:

The -5 exponent is the amount of zeros that go behind 413.

Answer:

3.73

Step-by-step explanation:

The hundredths place is two places to the right of the decimal so the number doesn't need to change.

Answer: y=-1.5x-1

Step-by-step explanation:

A(-8,-2)   B(4,6)    C(x,y) - the midpoint of the line

1. Calculate the coordinates of the midpoint of the segment using the formula:

[tex]\displaystyle\\C(x,y)=(\frac{x_A+x_B}{2} ,\frac{y_A+y_B}{2})\\\\ C(x,y)=(\frac{-8+4}{2},\frac{-2+6}{2})\\\\ C(x,y)=(\frac{-4}{2} ,\frac{4}{2})\\ C(x,y)=(-2,2)\\Thus,\ C(-2,2)[/tex]

2. Find the slope of the line AB using the formula:

[tex]\displaystyle\\The\ slope=\frac{y_B-y_A}{x_B-x_A} \\\\The\ slope=\frac{6-(-2)}{4-(-8)} \\\\The\ slope=\frac{6+2}{4+8} \\\\The\ slope=\frac{8}{12} \\\\The\ slope=\frac{2}{3}[/tex]

3. Find the slope of the line perpendicular to the line AB:

[tex]\displaystyle\\The \ \perp slope=-\frac{1}{the\ slope} \\\\The \ \perp slope=-\frac{1}{\frac{2}{3} } \\\\The \ \perp slope=-\frac{3}{2}[/tex]

4. Find an equation for the perpendicular bisector of the line segment:

[tex]\displaystyle\\The \perp\ slope=\frac{y-y_C}{x-x_C} \\\\-\frac{3}{2}=\frac{y-2}{x-(-2)} \\-\frac{3}{2} =\frac{y-2}{x+2} \\[/tex]

Multiply both parts of the equation by (x+2):

[tex]\displaystyle\\y-2=(-\frac{3}{2} )(x+2)\\\\y-2=-\frac{3}{2}x+(-\frac{3}{2})(2)} \\\\y-2=-\frac{3}{2}x-3 \\\\y-2+2=-\frac{3}{2}x-3+2\\\\ y=-\frac{3}{2}x-1\\\\ y=-1.5x-1[/tex]

Answer:

y=-5x-7

Step-by-step explanation:

For lines to be parallel with one another, that means they have to have the same slope. The slope of this equation is -5

From there we have to find the b (or the y-intercept) of the new equation. To do this we plug in the slope and the x and y from the given point (-2,3) into the equation y=mx+b and solve for b:

3=-5(-2)+b

3=10+b

-7=b

Finally, we make a new equation with the b (-7) and slope (-5):

y=-5x-7

DON'T READ IF YOU DON'T WANT TO/ALREADY KNOW HOW TO DO THIS FOR A LINE PERPENDICULAR TO THE GIVEN LINE:

To find a line perpendicular to (y=-5x+1), you do everything the same as before but instead of using -5 as the slope for your new equation (including the one you use for solving for the new b) you use it's negative reciprocal. That basically means you switch the numbers numerator and denominator and switch the sign. Remember, every whole number has a denominator of 1, so it'll look like this:

-5/1 turns into 1/5

Then you use 1/5 as the slope for the new equation by plugging in the x and y of the given point and solving for b like we did before. Finally you take the 1/5 as the slope and the b you solved for and put those into a equation like you did before and bam.

If you're confused after reading that then forget everything I said.

hope this helps :D

The solutions for the expressions are given as follows:

6. y = 12.

7. w = -20.

8. x = 30.

The expression is given by:

4/3y = 16.

Applying cross multiplication:

4y = 48

y = 48/4

y = 12.

The expression is given by:

w/(-2.5) = 8

Applying cross multiplication:

w = -2.5 x 8

w = -20.

The expression is given by:

(1/5)x - 2 = 4.

Isolating x:

(1/5)x = 6.

Applying cross multiplication:

x = 6 x 5

x = 30.

More can be learned about expressions at https://brainly.com/question/26676095

#SPJ1

Answer: the width of the rectangle is 14 units

Let's denote the length of the rectangle to be x and the width to be y.

The first sentence tells us that the length, x , is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. x = 2y - 4.

In the question given that the perimeter of the rectangle is 76 units

Perimeter of a rectangle is 2( length + breadth )

According to the question :

76 = 2(x + y)

76 = 2(2y – 4 + y)

76 = 2(3y – 4 )

76 = 6y – 8

84 = 6y

y = 14 units

putting the value of in x = 2y – 4

x = 2(14) – 4

x = 24 units

learn more about perimeter of the rectangle here:

https://brainly.com/question/24571594

#SPJ9

The cube root of 27 is 3√t=3, which indicates that 3√t.

Cube root, or the cube root of a number, is simply the square root of that number. It can be used in various mathematical contexts to simplify complicated calculations. For example, when dealing with complex fractions and rational numbers (numbers that have a decimal point), the cube root can be used to solve problems more quickly and accurately.

We are aware that 5×5×5×5 Equals 125. Therefore, 125 is known as the cube of 5. Finding a number's cube root, on the other hand, entails doing the cube operation in reverse and is symbolised by the symbol.

A number x's cube roots are the integers y that answer the equation.

3√t is the cube root of 27,so 3√t=3 .

3√3

3×3×3=27

Hence the correct answer Is option (b) 3√t is the cube root of 27,so 3√t=3 .

To learn more about cube roots here:

https://brainly.com/question/12726345

#SPJ9

The probability that a randomly selected point of the diagram lies within the circular region as requested in the task content is; π/4.

It follows from the task content that the probability that a randomly selected point of the diagram lies within the circular region is to determined.

This probability in discuss is equal to the ratio of the area of the circle to the area of the rectangle.

Consequently, the area of the circle is equal to;

πr².

However, since the side length of the square, which is the diameter of the circle is; 2r; it follows that it's area is;

2r × 2r = 4r².

Therefore, the probability is; πr²/4r².

When expressed in its simplest exact form, we have;

π/4.

Therefore, The probability that a randomly selected point of the diagram lies within the circular region as requested in the task content is; π/4.

Read more on probability;

https://brainly.com/question/13604758

#SPJ1

Answer:

Step-by-step explanation:

To find the scale factor, take the value of one side length from the scaled copy and divide it by the value of the corresponding side length of the original.

39/13 = 3

Therefore, the scale factor is 3.

The total possible ways of arranging 30 students in two groups of sizes 4 and 6 respectively are 6309453150, which is obtained by using the prerequisite knowledge of combinations.

What is the combination?

A combination is a mathematical procedure that deduces the number of feasible selections in a collection of articles in which the order of the selection does not matter. In combinations, you can choose any items in any order. Its formula is given by C(n,r) = n! / (n - r)! r!)

Calculation of the total possible ways of arranging two focus groups of students with sizes 4 and 6 respectively

Given a group of 30 students

Two focus groups are to be arranged in sizes 4 and 6 respectively

Total number of possible ways to arrange the two focus groups = C(30,4) × C(26,6)

Using the formula for combination, we get,

T.F.O = [30! / (26! 4!)] × [26! / (20! 6!)]

T.F.O = 27405 × 230230

         = 6309453150

Hence, the required possible ways to arrange two groups are given by 6309453150.

To know more about the Combination, visit here:

https://brainly.com/question/11732255

#SPJ4

Answer: 296 with a remainder of 1 (I'm guessing this by mental math, btw, why not just use a calculator, the calc is your best chance for a right answer anyway)

Edit: Used calc, was close lol, 296.5 is the exact answer

Step-by-step explanation:

P.S: Question, is that supposed to be divided or square rooted?

Anyway, I'll explain it since I can't leave it hanging:

2*2 = 4 so 5-4 = 1 and bring 9 down, after that 2*9 = 18, so it becomes 1, and then bring down 3 for 13, and 6*2 = 12, so 13-12 = 1, and that is 296 with a remainder of 1.

The sum of any number and zero is the original number: Identity property

When two numbers are added, the sum is the same regardless of the order of addends: Commutative property

When three or more numbers are added, the sum is the same regardless of how the addends are grouped: Associative property

A + B = B + A if A and B are any two whole numbers.

In other words, the sum of two whole numbers is true regardless of how the addends—or real numbers—are arranged.

Any order will work for adding the numbers. Even if the numbers are rearranged, the sum of the two numbers remains the same.

When an is a whole number, A + 0 equals 0 + A.

In other words, the number itself is equal to the sum of any whole number and zero. In other words, zero is the only whole number that when added to, does not alter the value (identity) of the original number.

The additive identity or identity element for the addition of whole numbers is the integer 0 (zero).

When zero is added to a number, the result is unchanged.

If any three whole numbers are A, B, and C, then (A + B) + C = A + (B + C)

In other words, whole number addition is associative.

Any group or placement of the numbers has no effect on the sum when three or more are added.

To know more about commutative, associative, and identity properties, visit:

https://brainly.com/question/28387735

#SPJ9

"The ratio of the number of male staff to the number of female staff is 2:3."

This means if [tex]x[/tex] is the number of male staff, and [tex]y[/tex] is the number of female staff, then these numbers occur in a fixed ratio such that

[tex]\dfrac xy = \dfrac23[/tex]

The sentence does not say anything about the actual number of staff members. There's no reason to believe that there are 50 people working.

What it does say is that 2/5 = 40% of the team is made of males and 3/5 = 60% is made of females.

(a) Of the males, 20% = 1/5 of them are under the age of 20. This means that 20% of 40% of the entire staff is made up of males under 20, or

2/5 × 1/5 = 2/25 = 8%

Of the females, 40% = 2/5 are under the age of 20. So 40% of 60% are females under 20, which comes out to

3/5 × 2/5 = 6/25 = 24%

Adding these up, we get a total of 8% + 24% = 32%.

(b) Yes, any change to the team would adjust this percentage.

Consider a smaller example of a team of 4, 1 each of male/female and under/over 20. 1/4 = 25% of this team is female and under 20. If we add one more under-20 female, the new ratio is 2/5 = 40%. If we add one more member to any other group, the new ratio is 1/5 = 20%.

Answer:

6 miles

Step-by-step explanation:

1 1/2 miles x 4 days= 6 miles over 4 days

The measure of the missing angles are d= 77° , e= 31° ,and f = 72°.

As given in the question,

Angle e is vertically opposite to the given angle 31°

⇒Measure of angle e = 31°

Angle d is vertically opposite to the given angle 77°

⇒Measure of angle d = 77°

Angle e , Angle f and angle d are linear pairs

⇒∠e +∠f +∠d =180°

⇒31° +∠f + 77°=180°

⇒ ∠f =180° -108°

⇒ ∠f =72°

Therefore, the measure of the missing angles are d = 77° , e = 31° and

f = 72°.

Learn more about angles here

brainly.com/question/28451077

#SPJ1

Answer:

y≤-1

Step-by-step explanation:

Subtract 9 from both sides

4-9 = -5

Divide the remainding by 5

-5 / 5 = -1

The minimum will be $ 0. If the theft occurs , company will have to pay the claim. Hence Option B will be correct.

What is probability and example?

The variety of strategies for success. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

$ 0 and $ 200

This is because both the insured will pay $ 100 premium each , hence total revenue of company can be $ 200 maximum.

The minimum will be $ 0. If the theft occurs , company will have to pay the claim. Hence Option B will be correct.

Learn more about probability

brainly.com/question/11234923

#SPJ4

Answer:

27-7=4d+6d

20=10d

d=20/10

therefore; d=2

The angles ∠YWZ and ∠XWY are 36° and 144° respectively.

To learn more about angles, visit :

https://brainly.com/question/13954458

#SPJ9

The geometry term represented by the statement "If two points are given, then exactly one line can be drawn through those two points." is "geometric postulate".

Postulates are assertions that are believed to be correct in the absence of evidence.

In this sense, the main feature of the postulate is its widespread acceptance by the scientific community, that is, by the vast majority of scientists who are committed to its investigation.

To know more about the geometric postulate, here

https://brainly.com/question/10440639

#SPJ9

We can be 99% certain the baseball game will end by 5.22pm.

A cut-off Number is a number mentioned in the applicable Final Terms as such, or if no number is provided, the Specific Number is presumed to be five.

In binary classification, the threshold or cut-off represents the chance that the prediction is correct. It represents the cost of false positives or false negatives.

Let the cutoff be A.

so,

P(X ≤ A) = 0.99

[tex]P\left(\frac{X-\mu}{\sigma} \leq \frac{a-2.5}{0.37}\right)=0.99[/tex]

[tex]P\left(Z \leq \frac{a-2.5}{0.37}\right)=0.99[/tex]

[tex]\Phi\left(\frac{a-2.5}{0.37}\right)=\Phi(2.33)\\[/tex]

(a - 2.5)/.37 = 2.33

a = 3.3621

a = 3hours and (0.3621 * 60) = 22 minutes

We can be 99% certain the baseball game will end by 5.22pm.

To know more cut-off probability visit:

https://brainly.com/question/13800349

#SPJ4

I understand that the question you are looking for is:

The probability that the baseball game will cut into the program is 0.0885.

Can you provide a cut-off time by which you can be 99% sure that the baseball game would end?

Cutting a cake into 8 pieces is a chemical change.

Now,

When the cake is cut, the pieces cannot be joined again and form a cake.

Hence, Cutting a cake into 8 pieces is a chemical change.

To learn more about physical and chemical changes, refer to the link: https://brainly.com/question/17384175

#SPJ4

All statements are true, but if you try to reverse them they won't necessarily be true.

let us start

Square ⇒ Has 4 sides

But if something has 4 sides it doesn't mean it's a square (example: rectangle)

Angle is 80° ⇒ acute angle

But acute angle is any angle below 90°, not just 80° so the reverse isn't true.

x – 17 = 4 ⇒ x = 21

And if we reverse

x = 21 ⇒ x – 17 = 4

we see that it's true for either direction.

x = 7 ⇒ |x| = 7

But |x| = 7 doesn't mean that x has to be 7, x can also be -7, so the reverse isn't true.

learn more about of converse here

https://brainly.com/question/1468445

#

SPJ9