Using the normal distribution, the standard deviation of bone density in the reference population is of 5.52 g/cm².
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the parameters are given as follows:
[tex]X = 948, z = -1.45, \mu = 956[/tex]
Hence we solve for [tex]\sigma[/tex] to find the z-score as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.45 = \frac{948 - 956}{\sigma}[/tex]
[tex]-1.45\sigma = -8[/tex]
[tex]\sigma = \frac{8}{1.45}[/tex]
[tex]\sigma = 5.52[/tex]
The standard deviation of bone density in the reference population is of 5.52 g/cm².
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The length of a rectangle is four less than twice its width. If the perimeter of the rectangle is 76 units, what is its width?
a
13
b
14
c
20
d
26
e
28
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
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determine the equation of the line that is parallel to the given line (y=-5x+1), through the given point (-2,3)
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
Can+you+provide+a+cut-off+time+by+which+you+can+be+99%+sure+that+the+baseball+game+would+end?
We can be 99% certain the baseball game will end by 5.22pm.
What does the term "cut-off" signify in mathematics?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.
What exactly is the cut-off probability?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.
According to the given information: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.
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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?
Which conditional has the same truth value as it’s converse
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.
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Is cutting a cake into 8 pieces a chemical or a physical change? explain your answer.
Cutting a cake into 8 pieces is a chemical change.
What is a physical and chemical change?In a physical change, the substance's shape or appearance changes, but the type of matter it contains stays the same. In contrast, when matter undergoes a chemical change, at least one new substance with novel features is created.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.
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Solve equation.
27-6 d=7+4 d
Answer:
27-7=4d+6d
20=10d
d=20/10
therefore; d=2
Statement: If two points are given, then exactly one line can be drawn through those two points. Which geometry term does the statement represent?
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".
What are termed as the geometric postulate?Postulates are assertions that are believed to be correct in the absence of evidence.
Postulates serve two functions: they explain undefined terms and they serve as a foundation for proving those certain statements. The Postulates of Euclid: A line segment is defined by two points.A line segment can be enlarged along a line indefinitely.A postulate is a fundamental concept in geography that denotes a hypothesis that is believed to be correct in the given factor.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.
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Write 4.13 ×10 with exponent -5 in standard form.
Answer: 0.0000413
Step-by-step explanation:
The -5 exponent is the amount of zeros that go behind 413.
What is the measure of angle F?
Answer: D because Angle D = Angle L
A map of Québec has a scale of 1:1 500 000. On map, the distance between Trois-Rivières and Québec City is 2⅝ in. What is the distance between these cities to the nearest mile?
The number of blocks has 9 in the ones place the number in the hundreds place is one more than the numbers in the tens place those two numbers equal 11 how many blocks are there?
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.
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Find the measure of the missing angles.
d =
e
e=
fd
77°
O
31°
ƒ=
0
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°.
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Make sense and persevere point y is in the interior of
The angles ∠YWZ and ∠XWY are 36° and 144° respectively.
WX and WZ are two opposite rays, so they form a straight line.So, the angle ∠XWZ is equal to 180°.Y is an interior point of ∠XWZ.We are given that the angle ∠XWY is 4 times the angle ∠YWZ.Let the angle ∠YWZ be "x".Then, the angle ∠XWY is equal to 4x.The sum of the angles, i.e., the angle ∠XWZ is 5x.5x is equal to 180°.x is equal to 180°/5.x is equal to 36°.Thus, the angle ∠YWZ is 36°.The angle ∠XWY is 4*36°.Thus, the angle ∠XWY is 144°.To learn more about angles, visit :
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You are running a camp of 30 students, including johnand jane.3
What is the total possible ways you can arrange2 focus groupsof students one group being size 4 , and the othersize 6.?
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.
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The diagram below consists of a square with unknown side lengths and an inscribed circle. What is the probability that a randomly selected point of the diagram lies within the circular region? State your answer in exact form and explain how you found it.
The probability that a randomly selected point of the diagram lies within the circular region as requested in the task content is; π/4.
What is the probability that the a randomly selected point on the diagram lies within the circular region?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.
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Find 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
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.
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val runs 1 1/2 miles each day. She has run for 4 days. How far has she run altogether
Answer:
6 miles
Step-by-step explanation:
1 1/2 miles x 4 days= 6 miles over 4 days
both nadia and samantha are applying to insure their car against theft. nadia lives in a secure neighborhood, where the probability of theft is 10%. samantha lives in a lesser secure neighborhood where the probability of theft is 25%. both nadia and samantha own cars worth $10,000, and are willing to pay $100 over expected loss for insurance. if the insurance company can correctly anticipate the adverse selection,
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.
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Identify the property of addition described as commutative, associative, or identity.
The sum of any number and zero is the original number.
When two numbers are added, the sum is the same regardless of the order of addends.When three or more numbers are added, the sum is the same regardless of how the addends
are grouped.
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
What is the Commutative Property of Addition?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.
What is the Additive Identity of Addition?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.
What is the Associative Property of Addition?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.
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HELPPP!! Please!! algebra stuff
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 .
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Sketch the graph using partial factoring.
y = 2x^2 - 6x + 5
(You don't need to draw it if you answer. Just show how to find the vertex and zeros.)
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)
The right triangle on the right is a scaled copy of the right triangle on the left. Identify
the scale factor. Express your answer as a whole number or fraction in simplest form.
13
13
13/3
13/3
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.
solve the inequality 5y+9≤4
Answer:
y≤-1
Step-by-step explanation:
Subtract 9 from both sides
4-9 = -5
Divide the remainding by 5
-5 / 5 = -1
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
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.
What is matrix function?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-
The function is designated only for t values that specify all 4 of the elements in the this example matrix.A matrix function can also be defined as a function which calculates a (generally square) matrix A; in other words, it is a process of mapping one matrix to another. Some researchers defined matrix functions just on complex plane ℂ. Higham (2008), for example, emphasizes the definition as involving a scalar function f and a matrix A ∈ ℂ∧(n x n).To know more about complex plane, here
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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)
PLEASE SHOW WORK
STEP-BY-STEP
The solutions for the expressions are given as follows:
6. y = 12.
7. w = -20.
8. x = 30.
What is the solution to expression 6?The expression is given by:
4/3y = 16.
Applying cross multiplication:
4y = 48
y = 48/4
y = 12.
What is the solution to expression 7?The expression is given by:
w/(-2.5) = 8
Applying cross multiplication:
w = -2.5 x 8
w = -20.
What is the solution to expression 6?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.
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did I do Question A right and I need help for (B)
the Math question is on the Image.
"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%.
Please this awnser asap pls no equation just the awsner pls
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.
Cuál es un número primo divisor de 30?
A. 5
B. 10
C. 6
D. 15
Find an equation for the perpendicular
bisector of the line segment whose
endpoints are (-8, -2) and (4, 6).
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]
Convert 6000 meters into miles. Round your answer to the nearest hundredth
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.