Reliability refers to the consistency of measures, whereas validity refers to the truthfulness of a measurement.
What do we mean by measure?The size, capacity, or amount of something determined by measurement. Use equal amounts of ingredients. Something used for measurement (such as a ruler or cup). A unit used to measure. A foot is a measure of length.
What is statistics in mathematics?Statistics is a science concerned with developing and studying methods for measure, collecting, analyzing, interpreting, and presenting empirical data.
Significance of statistics:Statistics is the branch of mathematics for collecting, analyzing and interpreting data. Statistics can be used to predict the future, determine the likelihood of certain events occurring, and answer research questions.
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Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0 . A random sample of 59 people is taken. Step 2 of 2 : What is the probability that the mean IQ score of people in the sample is less than 99 ? Round your answer to 4 decimal places, if necessary.
The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.
what is probability ?The probability that an event will happen or a claim will be correct is measured by statistical mechanics, a branch of mathematics. The possibility of an occurrence is a positive integer and 1, where about 0 represents how likely the event is to occur and value of 1 indicates certainty. A probability is a numerical illustration of the possibility that a specific activity will take place. Probabilities can also be expressed using percentages extending from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a comprehensive set of equally likely choices that lead to a specific occurrence.
given
This is Z's pvalue for X = 98. So
Z = 98 -100 / 15
Z = -0.133
Z = -0.133 pvalue of 0.4470
The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.
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Factor 1 - 2.25x8.
(1 - 1.5x 4) 2
(1.5 + x 4)(1.5 - x 4)
(1 + 1.5x 4)(1 - 1.5x 4)
The factor of 1 - 2.25x⁸ is (1 + 1.5x⁴) (1 - 1.5x⁴).
The correct option is C.
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
Given:
An expression,
1 - 2.25x⁸.
Simplifying to the factored form.
1² - (1.5x⁴)²
= (1 + 1.5x⁴) (1 - 1.5x⁴)
Therefore, (1 + 1.5x⁴) (1 - 1.5x⁴) is the factored form.
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The figure below is a parallelogram. Based on what we know about consecutive angles of a parallelogram, write and equation and solve for x.
The value of x in the given paralellogram is 12.
What is parallelogram?
"It is a quadrilateral with parallel opposite sides."
"The opposite angles of parallelogram are equal. "
For given question,
Two of the angles in a parallelogram measure 8x° and 7x°
The measure of an angle opposite to 8x° is also 8x°
In a similar manner, an angle opposite to 7x° is measured as 7x°.
So, we have the four angles of parallelogram as 8x°, 7x°, 8x°, 7x°
We are know that the total angle of a quadrilateral is 360°.
⇒ 8x° + 7x° + 8x° + 7x° = 360°
⇒ (5 + 7 + 5 + 7) x = 360
⇒ 30x = 360
⇒ x = 12
Therefore, the value of x is 15.
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resoudre [tex]30*\sqrt{5}² + 13*\sqrt{5}-6[/tex]
The simplified expression for this problem is given as follows:
[tex]43\sqrt{5} - 6[/tex]
How to simplify the expression?The expression for this problem is defined as follows:
[tex]30\sqrt{5} + 13\sqrt{5} - 6[/tex]
To simplify the expression, we combine the like terms, which are the terms that have the same rational, thus:
[tex]30\sqrt{5} + 13\sqrt{5} = 43\sqrt{5}[/tex]
Combining along with the subtraction by 6, the complete simplified expression is given as follows:
[tex]43\sqrt{5} - 6[/tex]
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prove that a square matrix and its transpose have the same characteristic polynomial, and therefore the same set of eigenvalues. g
The eigenvalues of a matrix are roots of its characteristic polynomial using this we prove that a square matrix and its transpose have the same characteristic polynomial.
What is a matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.
Recall that the eigenvalues of a matrix are roots of its characteristic polynomial.
Hence if the matrices A and A Transpose have the same characteristic polynomial, then they have the same eigenvalues.
So we show that the characteristic polynomial pA(t)=det(A−tI) of A is the same as the characteristic polynomial p[tex]A^T[/tex] (t)=det(A ^T−tI)of the transpose [tex]A^T[/tex].
We have,
p[tex]A^T[/tex](t)=det([tex]A^T[/tex] −tI) =det([tex]A^T[/tex] −tI T )
=det((A−tI) [tex]A^T[/tex] )
=det(A−tI)
=pA(t)
Since I ^T =I
Since det([tex]B^T[/tex] )=det(B)for any square matrix B
Therefore, we obtain p[tex]A^T[/tex] (t)=pA(t), we conclude that the eigenvalues of A and [tex]A^T[/tex] are the same.
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Write 2^-x × 3^-x × 6^2x × 3^2x × 2^2x as a power of 6
Answer:
[tex]6 {}^{3x} [/tex]
Step-by-step explanation:
Given expression to us is ,
2^{-x} . 3^{-x} . 6^{2x} . 3^{2x} . 2^{2x}
We can rewrite it as ,
[2^{-x} . 2^{2x} ] [ 3^{-x} . 3^{2x}] . 6^{2x}
we know a^m . a^n = a^{m+n} , so ;
2^{-x +2x} . 3^{-x+2x} . 6^2x
simplify,
2^x . 3^x . 6^{2x}
we know a^m . b^m = (ab)^m , so ;
(2*3)^x . 6^{2x}
6^x . 6^2x
6^{x+2x}
6^{3x}
And we are done!
Answer:
[tex]6^{3x}[/tex]
Step-by-step explanation:
Given exponential expression:
[tex]2^{-x} \cdot 3^{-x} \cdot 6^{2x} \cdot 3^{2x} \cdot 2^{2x}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]
[tex](2\cdot 3)^{-x} \cdot 6^{2x} \cdot (3 \cdot 2)^{2x}[/tex]
Multiply the numbers:
[tex]6^{-x} \cdot 6^{2x} \cdot 6^{2x}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]6^{(-x+2x+2x)}[/tex]
Therefore:
[tex]6^{3x}[/tex]
Write an equation in slope-intercept form of the line that satisfies the given conditions.
Through (6, 3); parallel to 7x-y=3
The equation of the line is
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. If a line is parallel to another line, it means they have the same slope. To find the slope of the line 7x - y = 3, we can rearrange it into slope-intercept form: y = 7x - 3. So, the slope of the line 7x - y = 3 is 7.
Since the line we want to find is parallel to 7x - y = 3 and has a slope of 7, the equation of the line can be written as y = 7x + b, where b is the y-intercept. To find b, we use the point (6, 3) as a solution:
y = 7x + b
3 = 7 * 6 + b
3 = 42 + b
b = -39
So, the equation of the line that passes through (6, 3) and is parallel to 7x - y = 3 is y = 7x - 39.
Find the area of the right triangle.
Be sure to include the correct unit in your answer.
24 cm
25 cm
Answer:
300 cm^2
Step-by-step explanation:
An area of a triangle is b*h/2.
Therefore, plug in the base and height into the equation.
24cm * 25cm / 2 = area
600cm^2 / 2 = area
300cm^2 = area
if Δabc≅Δpqr, then ac≅
ac is congruent to pr because those sides correspond
What is the value of the expression above?
A 98
B 150
C 51
D 198
Answer:
C (51)
Explanation
Please help I will give brainliest
l=7m
Step-by-step explanation:
here us the answer of the solution
What is the area of a rectangle with length of 7 and width of 4x? Simplify
]Answer:
The area of a rectangle is calculated by multiplying its length by its width. If the length of the rectangle is 7 and its width is 4x, the area can be found by performing 7 * 4x. The answer would be 28x square units, where x represents the unit of measurement.
When planning a more strenuous hike, Erin figures that she will need at least 0.8 liters of water for each hour on the trail. She also plans to always have at least 1.50 liters of water as a general reserve. If x represents the duration of the hike (in hours) and y represents the amount of water needed (in liters) for a hike, the following inequality describes this relation: y greater or equal than 0.8 x plus 1.5
Answer:
the inequality y ≥ 0.8x + 1.5 accurately describes the relation between the duration of the hike (x) and the amount of water needed (y). This inequality means that for any duration of the hike (x), the amount of water needed (y) must be greater than or equal to 0.8x + 1.5.
Answer:
Step-by-step explanation:
3 liters of water for 4 hours of hiking.
Joanna is currently watching 6.4 hours of T.V per day. She made a goal to reduce the amount to 1.6 hours per day . what is the amount now?
Answer: 4.8
Step-by-step explanation:
6.4 - 1.6 = 4.8
The ratio of hydrogen atoms to nitrogen atoms in a container is 2:3 what is the value of 2:3
The value of 2:3 can be written as a fraction: 2/3.
What is the ratio?
In mathematics, a ratio is a comparison of two quantities, often expressed as a fraction or using the colon (:) symbol. Ratios are used to indicate the relative size or amount of two or more things.
For example, the ratio of the length of a rectangle to its width can be expressed as a fraction, where the numerator represents the length and the denominator represents the width.
The ratio of hydrogen atoms to nitrogen atoms is 2:3.
This means that for every 2 hydrogen atoms, there are 3 nitrogen atoms in the container. The value of the ratio 2:3 is a way of expressing the relative quantity of hydrogen atoms to nitrogen atoms in a simplified form. It can also be written as a fraction: 2/3.
Hence, the value of 2:3 can be written as a fraction: 2/3.
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If ST = p + 31, RU = 6p + 14, and VW = 4p + 53, what is the value of p?
Answer:
If we subtract 14 from both sides of the equation for RU, we get 6p = RU - 14, or 6p = RU - 14. We can then substitute this expression for 6p into the equation for ST to get:
ST = p + 31
ST = (RU - 14) + 31
Expanding RU, we get:
ST = RU - 14 + 31
ST = RU + 17
Since RU = 6p + 14, we can substitute this expression into the above equation to solve for p:
ST = 6p + 14 + 17
ST = 6p + 31
Finally, we can subtract 31 from both sides of the equation to find p:
ST - 31 = 6p + 31 - 31
ST - 31 = 6p
ST - 31 = 6p
p = (ST - 31) / 6
So, to find the value of p, we need to know the value of ST.
Solve and explain the method you chose to use (distributive property, FOIL, multiplying special cases): (c+3)^2
After resolving [tex](c+3)^{2}[/tex] , c = -3, and the approach is an example of the distributive property of equations.
What is equations?Its simplest form has been thought to be the figure is probably smallest equivalent fraction. How or when to determine the basic form. Look for shared factors throughout the denominator and numerator. A fractional number can sometimes be checked to discover if it is a power of 2. A statement having two equal sides and an equal sign in the middle is referred to as a mathematical equation. Every variable's degree courses are listed in descending order as in general form of any equation. The formula for a linear equation is x + b = 0. The general form of a three separate linear equation is an x + b y + c = 0. (or something similar). Either conditioned equations or identities are categories for mathematics. An identity holds true for whatever value of the variables.
Given,
[tex](c+3)^{2}[/tex]
= by using formulas of [tex](a+b)^{2}[/tex]
by distributive property
[tex]c^{2}[/tex] + [tex]3^{2}[/tex] + 6c
= [tex]c^{2}[/tex] + 9 + 6c
= [tex]c^{2}[/tex] + 6c + 9 = 0
[tex]c^{2}[/tex] + 3c + 3c + 9 = 0
= c ( c + 3 ) + 3 ( c + 3)
= (c + 3 )(c+ 3)
c = - 3
After resolving [tex](c+3)^{2}[/tex], c = -3, and the approach is an example of the distributive property of equations.
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9x-7y=-5
-3x+7y=11
how do we solve this?
The system of equations is solved by graphing as shown in the image, where the solution is (1, 2).
How to Solve a System of Equations by Graphing?A system of equations can be solved by graphing each line that represents each equation, then find the point where they both intercept.
Thus, the coordinates of the point where the two linear equations intercept will be the solution of the system of equations.
Given the system, 9x - 7y = -5 is the red line while -3x + 7y = 11 represents the blue line. Both intercept at (1, 2), which is the solution of the equations.
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a group of students and adults are going to the museum and have spent a total of $115 on tickets. Adult tickets cost $5 each and student tickets cost $3 each. There are 25 more students than adults in the group. How many students are in the group and how many adults are in the group?
A group of students and adults are going to the museum and have spent a total of $115 on tickets. Adult tickets cost $5 each and student tickets cost $3 each. There are 25 more students than adults in the group therefore the number of students are in the group are 35 and the number of adults in the group are 5.
What is Cost?This is referred to as the value of money that has been used up to produce something or deliver a service.
Since we were told that Adult tickets cost $5 each and student tickets cost $3 then $5 × 5 = $25 and $3 × 30 = $90. Therefore the total is $115.
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Maryann runs on a 3/4-mile track at the neighborhood trail. She runs 8 1/2 laps on Saturday.How many more laps does Maryann need to run on Sunday in order to run 10 1/2 total miles over two-day weekend?
A. 9.25 laps
B. 5 1/2 laps
C. 2 laps
D. 1.50 laps
Maryann needs to run 2 more laps to run on Sunday .
What does one lap mean?Lap can be referred as One complete trip around a race track οr from one end of a swimming pool to the other: Fοr example, Each lap of the track is 400 meters.
Given:
Maryann runs : 3/4-mile track
She runs on Saturday: 8 1/2 laps = 17/2
Total miles to cover = 10 1/2 = 21/2
more laps does Maryann need to run on Sunday
= Total miles to cover - She runs on Saturday
= 21/2 - 17/2
= 4/2
= 2
Hence , Maryann needs to run 2 more laps to run on Sunday .
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Graphing and substitution, please help!
1) How many more acres are there at Navajo Monument than at George Washington Carver Monument?
Number of acres more there at Navajo Monument than at George Washington Carver Monument is 120.
How to find the area of some object?Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.
Given;
The area of navajo monument= 360acres
The area of George Washington Carver Monument = 240 acres
Now
More area navajo monument has =area of navajo monument - area of George Washington Carver Monument
=360-240
=120
Therefore, the extra area navajo monument has is 120 acres.
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Taye pays $0.06 sales tax on each dollar he spends. If he buys a new bike for $237.00, how much sales tax will Taye pay?
Answer: $14.22
Step-by-step explanation: 237*0.06
The May 1, 2009, issue of a certain publication reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1,000s of $).
592 817 577 608 353 1,281 412 535 550 679
(a) Calculate and interpret the sample mean and median.
The sample mean is x = thousand dollars and the sample median is x tilde= thousand dollars.
This means that the average sale price for a home in this sample was $ and that half the sales were for less than the _____mean median price, while half were more than the _____ mean median price.
(b )Suppose the 6th observation had been 985 rather than 1,281. How would the mean and median change?
(c) Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations. (Round your answer to the nearest hundred dollars.)
(d) Calculate a 15% trimmed mean. (Round your answer to the nearest hundred dollars.)
This means that the average sale price for a home in this sample was "$773" and that half the sales were for less than the median price of "$577", while half were more than the median price of "$577".
(a) To calculate the sample mean, we add up all the values and divide by the number of values:
x = (592 + 817 + 577 + 608 + 353 + 1,281 + 412 + 535 + 550 + 679)/10 = 7,727/10 = $773
The sample median is the middle value when all the values are ordered from smallest to largest:
353, 412, 535, 550, 577, 608, 592, 679, 817, 1,281
The median is 577.
This means that the average sale price for a home in this sample was $773 and that half the sales were for less than the median price of $577, while half were more than the median price of $577.
(b) If the 6th observation had been 985 rather than 1,281, the new mean would be calculated as:
x = (592 + 817 + 577 + 608 + 353 + 985 + 412 + 535 + 550 + 679)/10 = 7,610/10 = $761
The new median would still be $577.
(c) To calculate a 20% trimmed mean, we first need to find the two smallest and two largest observations, then remove them and take the average of the remaining values:
Two smallest: 353, 412
Two largest: 1,281, 817
Remaining values: 535, 550, 577, 608, 592, 679
The trimmed mean is (535 + 550 + 577 + 608 + 592 + 679)/6 = $592
(d) To calculate a 15% trimmed mean, we first need to find the three smallest and three largest observations, then remove them and take the average of the remaining values:
Three smallest: 353, 412, 535
Three largest: 817, 1,281, 679
Remaining values: 550, 577, 608, 592
The trimmed mean is (550 + 577 + 608 + 592)/4 = $576.
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covert to slope intercept form:
5x-3y=15
Answer:y=5/3 x-5
Step-by-step explanation: first find the y-intercept, when the x value is 0 that is the y intercept, then the equation becomes -3x=15, there you get
x=-5, then do the same to the other to get the x value so you get the points (0,-5), and (3,0) there you find the slope and plug in
4x - y = 3
3x + y = 4
Answer: (x, y) = (5/4, 2).
The given system of equations is:
4x - y = 3
3x + y = 4
We can solve for x and y using either substitution or elimination method.
By substitution, we can solve for y in one of the equations and substitute that value into the other equation to solve for x.
Starting with 4x - y = 3, we can add y to both sides to isolate x:
4x = 3 + y
Then, we can substitute this expression for y into the second equation:
3x + (3 + y) = 4
Expanding the right side, we get:
3x + 3 + y = 4
3x + 3 = 4 - y
3x = 1 - y
x = (1 - y)/3
Now, we can substitute the expression for x into the first equation:
4((1 - y)/3) - y = 3
4(1 - y)/3 = 3 + y
4 - 4y/3 = 3 + y
1 - 4y/3 = y + 3
-3y/3 = -2
y = 2
Finally, we can substitute the value of y into one of the original equations to find x:
4x - 2 = 3
4x = 5
x = 5/4
So, the solution to the system of equations is (x, y) = (5/4, 2).
At a local elementary school, 35 percent of all students have brown eyes, 45 percent have brown hair, and 60 percent have brown hair or brown eyes. A student will be selected at random from the school. Let E represent the event that the selected person has brown eyes, and let H represent the event that the selected person has brown hair.Are E and H mutually exclusive events?A- Yes, because P(E∩H)=0P(E∩H)=0.
B- Yes, because P(E∩H)=0.2P(E∩H)=0.2.
C- Yes, because P(E∩H)=0.6P(E∩H)=0.6.
D- No, because P(E∩H)=0.2P(E∩H)=0.2.
E- No, because P(E∩H)=0.6
The required events E and H are not mutually exclusive, because they can both occur at the same time.So D - No, because P(E∩H) = 0.20 is correct.
What are mutually exclusive events?The events E and H are not mutually exclusive, because they can both occur at the same time. In other words, a student can have both brown eyes and brown hair.
According to question:The probability that a student has both brown eyes and brown hair, P(E∩H), can be found using the formula:
P(E∩H) = P(E) + P(H) - P(E or H)
where P(E) is the probability of having brown eyes, P(H) is the probability of having brown hair, and P(E or H) is the probability of having either brown eyes or brown hair.
Given that:
P(E) = 0.35
P(H) = 0.45
P(E or H) = 0.60
So,
P(E∩H) = 0.35 + 0.45 - 0.60 = 0.20
So, the answer is D - No, because P(E∩H) = 0.20.
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the SULT club has 4,000 members all age 25 with independent future lifetimes. The mortality for each member follows the Standard Ultimate LIfe Table. Calculate the largest N, using the normal approximation, such that the probability that there are at least N survivors at age 95 is at least 90%.
The largest N such that the probability that there are at least N survivors at age 95 is at least 90% is approximately 136.43.
The normal approximation can be used to estimate the number of survivors at a given age when the mortality follows the Standard Ultimate Life Table. The normal approximation assumes that the number of survivors follows a normal distribution.
Let X be the number of survivors at age 95. Then, the mean (μ) and standard deviation (σ) of X can be calculated using the following formula:
μ = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾
σ = √(4,000 * (1 - e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾) * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾)
Next, we can find the value of N such that P(X >= N) >= 0.9 using the standard normal distribution.
z = (N - μ) / σ
P(X >= N) = 1 - P(X < N) = 1 - Φ(z)
where Φ(z) is the cumulative distribution function of the standard normal distribution.
We want to find the largest N such that P(X >= N) >= 0.9, so we need to find the smallest z such that Φ(z) <= 0.1. The value of z can be found using a standard normal table or a calculator with normal distribution functions.
With a calculator, we get that z = 1.28. So, N = μ + z * σ.
Plugging in the values we calculated earlier, we get:
N = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾ + 1.28 * √(4,000 * (1 - e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾) * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾)
N = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾⁾ + 1.28 * √(4,000 * (1 - e^⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾) * e^⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾⁾
N = 4,000 * 0.0337 + 1.28 * √(4,000 * (1 - 0.0337) * 0.0337)
N = 132.8 + 1.28 * √(4,000 * 0.966 * 0.0337)
N = 132.8 + 1.28 * √(13.97376)
N = 132.8 + 3.63323
N ≈ 136.43
So, the largest N such that the probability that there are at least N survivors at age 95 is at least 90% is approximately 136.43.
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A Triangular Prism with equilateral triangle faces has Volume of 84cm³ and a Length of 12cm. Find the base area of this prism.
Got this on my test, don't know how to do it lol.
Answer:
7cm²
Step-by-step explanation:
volume of a triangular prism=1/2×b×h×l
1/2×b×h=cross sectional area
84cm³=C.A×12
C.A=84/12
base area=7cm²
4. How many distinct 6-digit numbers can be made using the digits 1, 1, 1, 2, 2, 3?
a. 108
b. 60
c. 220
d. 216
e.729
Answer:
B. 60
Step-by-step explanation:
Since the digits 1, 1, 1, 2, 2, 3 are repeated, we use the concept of permutations with repetition. In this case, we can choose the first digit to be any one of the three, the second digit to be any one of the three, and so on. Therefore, the total number of distinct 6-digit numbers that can be made is 3 × 3 × 3 × 3 × 3 × 3 = 729.
However, we need to exclude the numbers that start with a 0 (i.e., numbers like 011112 or 001122). Therefore, the final answer is 729 - 3 = 726, which is the number of 6-digit numbers that do not start with a 0. The number of 6-digit numbers that start with a 0 is 3 (111120, 111202, 112102), so the total number of distinct 6-digit numbers is 726 - 3 = 60.