He made the mistake on line 1.
2x^2 - 8x + 5....move the 5 to the other side
2x^2 - 8x = -5....now divide by 2
x^2 - 4x = -5/2
x^2 - 4x + 4 = -5/2 + 4
(x - 2)^2 = -5/2 + 8/2
(x - 2)^2 = 3/2
x - 2 = (+-)sqrt 3/2
x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2
He made mistake on line 1.
Complete question -Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27
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Angela is making snack bags for a hiking trip with her friends she has 28 granola bars and 45 package packs of string cheese. If the snacks are to be identical without any food left over how many snack bags can she make.
I need to figure out if its GCF or LCM
If the snacks are to be identical without any food left over only one snack bags can be made by Angela
The number of granola bars = 28
The number of pieces of dried fruit = 45
If the snack bags should be identical without any food left over, then we need to find out the greatest number of snack bags, we should find out the Greatest common factor(GCF) or highest common factor(HCF) between 28 granola bars and 45 packages of string cheese
Since , factors of 28 = 1, 2, 4,7,14,28
Factors of 45 = 1, 3,5,9,15,45
Common factors of 28 and 45 = 1
Greatest Common factors of 28 and 45 = 1
Hence, the greatest common factor of 28 and 45 is 1 as only 1 is the common factor in the factors of 28 and the factors of 45.
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paulina and montrose are developing a personality survey and they want to obtain an estimate of its reliability. paulina administers the survey to a group of employees one day and then she administers the exact same survey to the same employees the following week. montrose took a different approach and developed two different, yet equivalent forms of the survey and administered both forms to a sample of employees. paulina is most likely assessing reliability, while montrose is most likely assessing reliability
Paulina is most likely assessing "Test-retest reliability", while Montrose is most likely assessing "Parallel forms reliability."
What is termed as reliability?The consistency with which a method attempts to measure something is indicated by its reliability. The same method applied to the same sample in the same conditions should yield the same results. If not, the measurement method may be unreliable.
Some key points related to the reliability are-
Test-retest reliability assesses the consistency of the findings when the same test is performed on the same sample at different points in time. When measuring something which you expect to remain constant in your sample, you use it.The correlation among two equivalent versions of the a test is measured by parallel forms reliability. When you have two distinct evaluation tools or sets of questionnaire prepared to measure the same thing, you use it. It is often necessary to develop different versions of tests in educational assessment.To know more about the Test-retest reliability, here
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Evaluate each expression the equation is b(9-c) those are on top and on bottom we have a^2. B=6 a=4 and c=8
Hey there!
b(9 - c) / a^2
= 6(9 - 8) / 4^2
= 6(1) / 4^2
= 6/4 * 4
= 6/16
= 6 ÷ 2 / 16 ÷ 2
= 3/8
Therefore, your answer should be:
3/8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The graph of the absolute value parent function, f(x) = Ixl, is stretched
horizontally by a factor of 6 to create the graph of g(x). What function is g(x)?
O A. g(x) = |x|
B. g(x) = 16x1
C. g(x) = x + 6|
O D. g(x) = 61x1
Transformations are used to move a function from one position to another. The function of g(x) is g(x) = | x/6|.
Given that:
f(x) = |x|
The rule of a horizontal stretch by factor k is:
(x, y) → (x/k,y)
This means that:
g(x) = f(x/k)
In this case, k = 6
So, we have:
g(x) = f(x/6)
Calculate f(x/6)
f(x/5) = |x/6|
Hence, the function of g(x) is
g(x) = |x/6|.
A function is defined as a relation between a set of inputs, each with an output. Simply put, a function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. Functions are commonly denoted by f(x). x is the input.
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B
Name the obtuse angle
A
D
159 160 170
E
Answer: It is m<BAE or measure of angle BAE
Step-by-step explanation:
1. Based by the m<CAE, 135 - 45 equals to 90, so that is not an obtuse angle, m<BAD is the same thing, so those 2 aren't it
2. m<CAD is 65, which is way too low for an obtuse angle, and m<DAE is way too small as well since it's angle is 25, making m<BAE a correct answer
HELOPPP
What number is 0.1 more than 30.7?
Responses
30.71
30.71
30.8
30.8
31.7
31.7
31.8
Answer:
Step-by-step explanation:
its 30.8. this is because .7 + .1 = .8 . Now just add that to the 30 and you get 30.8
Answer:
30.8
Step-by-step explanation:
All you have to do is take the 0.1 and add it to the 30.7 so you would add it to the .7 which gives you 8 and now just put the 30 back with your decimal
Find parametric equations for the line passing through the points p(2, 4, 2) and q(5, 5, 3).
The parametric equations for the line passing through the points p(2, 4, 2) and q(5, 5, 3) are x=2+5t, y=4+5t and z=2+3t.
What is parametric equation?
The same values may be expressed by a variety of alternative parameterizations because parametric representations are typically non-unique (see the "Examples in two dimensions" section below).
In addition to curves and surfaces, higher dimensional algebraic varieties can also be described by parametric equations; in this case, the number of parameters is equal to the dimension of the manifold or variety, and the number of equations is equal to the dimension of the space in which the manifold or variety is taken into account (for curves the dimension is one and one parameter is used, for surfaces dimension two and two parameters, etc.).
In kinematics, where the motion of an object is represented by equations using time as the parameter, parametric equations are frequently utilized.
Calculations:
Parametric equation of line PQ is
x=2+5t,y=4+5t and z=2+3t
parametric equation of line AB is
x=x1+tx2, y=y1+ty2 and z=z1+tz2
Here as we have P(2,4,2) and Q(5,5,3)as two points,
parametric equation of line
PQ is x=2+5t, y=4+5t and z=2+3t
i.e.
x=2+5t, y=4+5t and z=2+3t
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Please help asap!!!!
Answer:
A
Step-by-step explanation:
how do I solve
-3(1+6r)=14-r
Answer: -1
Step-by-step explanation:
Multiply -3 to (1+6r)
-3 - 18r = 14 - r
Then, group like terms and change the signs
-18r + r = 14 + 3
Add
-17r = 17
Divide 17 by 17 to solve for r
r = 17/-17
r = -1
Need help right now with this math problem
Answer:
85
Step-by-step explanation:
To find the mean, you have to add all the scores up and divide it by how many scores there are. In this case, there are seven scores, so we first add them up.
70+75+80+85+90+95+100=595
Now, we divide 595 by 7.
595/7=85
Hope this helps!
Have a wonderful day! :D
Answer: It is 5.3 based by rounding by it's tenth
Step-by-step explanation:
1. Add it all, in this case (3*2) + (7*2) + (8*2) + 1 which equals to 6 + 14 + 16 + 1
2. This then becomes 20 +17, which is 37, which we then divide by 7 becomes 5.285, or 5.3
Suni needs to repay her school loan in 4 years.How much must she semiannually deposit into an account that pays 0.9% interest, compounded semi annually, to have $100,000 to repay the loan?
Suni needs to deposit $12,304.45 semiannually to have $100,000 to repay the loan at 0.9% interest.
What are periodic payments?Periodic payments are equal payments made periodically to settle a mortgage loan.
The periodic payment for a loan can be computed using an online finance calculator.
Data and Calculations:N (# of periods) = 8 times (4 years x 2)
I/Y (Interest per year) = 0.9%
PV (Present Value) = $0
FV (Future Value) = $100,000
Results:
PMT = $12,304.45
Sum of all periodic payments = $98,435.60 ($12,304.45 x 8)
Total Interest $-1,564.40
Thus, the periodic deposit that Suni needs to make semiannually to have $100,000 to repay the loan at 0.9% interest is $12,304.45.
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Ted works as a nurse anesthetist. He is
paid a semimontly salary of $3,950. What
is his annual salary?
Answer:
94800
Step-by-step explanation:
Answer:
94,800
Step-by-step explanation:
Well semimonthly means 2 times a month
If you multiply 3,850 by 2 you get 7,900
Then simply multiply 7,900 by 12 (12 months in a year) and you get 94,800
The sum of the squared deviation scores is ss = 20 for a population of n = 5 scores. what is the variance for this population?
When the sum of the squared deviation scores is SS=20 for a population n=5 scores, then the variance for this population is 4
Given,
The sum of the squared deviation scores SS= 20
Population of n= 5
Then the variance = SS/n
Substitute the values in the equation
The variance = [tex]\frac{20}{5}[/tex]
=4
Hence, when the sum of the squared deviation scores is SS=20 for a population n=5 scores, then the variance for this population is 4
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0.3. human iq scores are approximately normally distributed with a mean of 100 and a standard deviation of 15. the minimum iq score for the top 10% of the population.
The minimum IQ score for the top 10% of the population is 0.0179.
Standard deviation:
Standard deviation means the root of the variance in the given grouped or ungrouped data.
The standardized value is the value decreased by the mean, divided by the standard deviation:
z = (x- μ) / σ
where
x: the observation (a specific value that you are calculating the z-score for).
Mu(μ): the mean.
Sigma(σ): the standard deviation.
Given,
The human IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15.
Here we need to find the minimum IQ score for the top 10% of the population.
We know that,
x = 131.5
μ = 200
σ = 15
So, when we apply the values on the formula,
Then we get,
=> z = 131.5 - 100 /15
=> z = 2 .10
Determine the corresponding probability using table A-2:
=> P(Z>2.10) = 1 − P(Z<2.10)
=> 1 − 0.9821
=> 0.0179
Therefore, the minimum IQ score for the top 10% of the population is 0.0179.
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Which expression has a value of less than 2 when x=5? select all that apply.
A. x to the power of zero divided by 4
B. x to the power of one divided by 7 to the power of zero
C. (50 divided by x to the power of 2) to the power of zero
D. 2( 10 divided by x) to the power of zero
F. x to the power of zero divided by x to the power of 2
The expressions that have numeric value of less than 2 when x = 5 are:
A. x to the power of zero divided by 4.
C. (50 divided by x to the power of 2) to the power of zero
E. x to the power of zero divided by x to the power of 2
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For item a, the expression is:
x^0/4 = 1/4 < 2.
For item b, the expression is:
x/(7^0) = x.
When x = 5, the expression has a numeric value of 5 > 2.
For item c, the expression is:
(50/x^2)^0 = 1 < 2.
For item d, the expression is:
2(10/x)^0 = 2 x 1 = 2 = 2.
For item e, the expression is:
x^0/x^2 = 1/x^2.
When x = 5, the expression has a numeric value of 1/25 < 2.
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the midpoint of uv is m(10, 6). one endpoint is v(10, 7). find the coordinates of the other endpoint u.
The answer is u = (10, 5)
Step-by-step explanation:
Imagine u = (x, y)
10 = x/2 + 10/2
10 = x/2 + 5
20 = x + 10
x = 20 - 10
x = 10
u = (10, y)
6 = y/2 + 7/2
6 = y/2 + 3.5
12 = y + 7
y = 5
u = (x, 5)
Thus, u = (10, 5)
simplify
the square root of 5 times 3 to the square root of 5
a= 5 and 5/6
b= 5 and 1/6
c= 5 and 2/3
d=5 and 7/6
Answer:
Step-by-step explanation:
C
is 80.279 and 18/25 a rational.or irrational
Answer:
both are rational numbers
Step-by-step explanation:
Answer:
both are irrational numbers.
Step-by-step explanation:
Rewrite: [tex]15\frac{1}{6}[/tex]% as a decimal. Round to the nearest thousandths.
Rewriting 15 1/6 as a decimal, rounded to the nearest thousandths, is: 1,516.667.
How to Rewrite a Number as a Decimal?To rewrite the percentage, 15 1/6% as a decimal do the following as shown below:
Convert 15 1/6 from mixed number to an improper fraction:
91/6
Multiply 91/6 by 100:
91/6 × 100
= 9,100/6
Divide
9,100/6 = 1,516.667
Thus, rewriting 15 1/6 as a decimal, rounded to the nearest thousandths, is: 1,516.667.
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The assembly time for a product is uniformly distributed between 2 to 10 minutes. what is the value of probability density function in the interval between 2 and 10?
The value of probability density function in the interval between 2 and 10 is 0.125.
What is probability density function?A probability density function (PDF), also referred to as the density of a continuous random variable (CRV), is a mathematical function whose value at any particular sample (or point) in the sample space (the range of possible values that the RCV can take), can be interpreted as providing a relative likelihood that the RCRV's value would be close to that sample. Since there are an infinite number of possible values to begin with, the probability per unit length for a continuous random variable to take on any particular value is 0, but the value of the PDF at two different samples can be used to infer, in any given draw of the random variable, even though the absolute likelihood is zero.
Given the assembly time for a product is uniformly distributed between 2 to 10 minutes.
The Probability density function in the internal between 2&10
pdf=1/10-2 = 1/8pdf = 0.125
The probability density function in the interval between 2 and 10 is 0.125.
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A person needs $
4500 to visit foreign countries. If $ 1 = NRs. 120.92 and the bank charge 2% as onmmission, bow many Nepali rupees does the person require to exchange $4500? Find it.
Nepali rupees that the person requires to exchange $4500 will be equal to NRs. 555,022.8.
We know that:
$ 1 = NRs. 120.92
We are also given that a person needs $ 4500 to visit foreign countries.
Also, for the conversion, bank charges commission as 2 %
Now, $ 4500 in NRs. will be calculated by multiplying 120.92 with $ 4500.
$ 4500 = NRs. 120.92 × 4500
$ 4500 = NRs. 544,140
Now the commission charged by the bank will be:
2 % of 544,140
Commission = 2 / 100 × 544,140
Commission = NRs. 10,882.8
So, the amount the person will require to get $ 4500 will be = NRs. 544,140 + 10,882.8
= NRs. 555,022.8
Therefore, Nepali rupees that the person requires to exchange $4500 will be equal to NRs. 555,022.8.
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meaning of prime numbers
Answer:
the number which has no factors is known as prime number
Answer: numbers that have only 1 and itself as factors.
Step-by-step explanation:
a car starts from a point at 2:00 p.m. and travels north at 40 mph. another car starts from the same point at 3:00 p.m. and travels west at 50 mph. after the second car has traveled 1 h, at what rate is the distance between the two cars changing?
The distance between the cars changes by 60.42mph.
What is distance?Distance is a measurement of how far apart two objects or locations are. Distance in physics or common language can refer to a physical length or an assumption based on other factors. |AB| is a symbol that can be used to represent the distance between two points. "Distance from A to B" and "Distance from B to A" are frequently used interchangeably. A distance function or metric is a technique to describe what it means for elements of some space to be "close to" or "far away" from each other in mathematics. It is a generalization of the idea of physical distance. Through dimensions like time, space, and isolation, an object may be psychologically distanced from itself.
Calculations:
[tex]d=\sqrt{80^{2}+50^{2} } \\[/tex]
d=94.34
1st car -- 40mph/hr
2nd car-- 50 mph/hr
The positions of cars at 4pm
Distance travelled by 1st car = 80m
Distance travelled by 2nd car = 50m
[tex]d^{2}=a^{2} +b^{2}[/tex]
2d.dd/dt=2a(da/dt) +2b(db/dt) =d(dd/dt) =a(da/dt)+b(db/dt)=94.34(dd/dt)=50*50+80*40
dd/dt=(2500+3200)(94.34) =60.419
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estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the u.s., per year. suppose that there are about 3 × 108 people in the united states, approximately half of the them have cars, each car drives an average of 12,000 mi per year, and consumes a gallon of gasoline for each 20 mi .
The number of gasolines is 1,800,000 miles driven.
What are gasolines?Gas is known as an aliphatic hydrocarbon. All in all, gas comprised of particles made out of nothing, yet hydrogen and carbon organized in chains. Fuel particles have from seven to 11 carbons in each chain. Gas or petroleum is a straightforward, oil determined combustible fluid that is utilized principally as a fuel in most flash touched off gas powered motors. Fuel is as of now thought to be frozen in the event that it transforms into a thick slop or wax. To absolutely keep away from frozen gas inside the vehicle, center around forestalling the fuel line from freezing during winter. Fuel fumes are heavier than air, so they choose the ground and travel like a fluid. Along these lines, they frequently track down their direction into channels, storm cellars, and sewer lines.
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1 let (sn) and (tn) be sequences and suppose there exists n0 such that sn ≤ tn for all n>n0. show lim inf sn ≤ lim inf tn and lim sup sn ≤ lim sup tn. hint: use definition 10.6 and exercise 9.9(c).
The statement lim infn sₙ > lim infn tₙ and lim sup sₙ ≤ lim sup tₙ is proved such that sₙ ≤ tₙ for all n≥n₀.
What do you mean by inf and sup?The biggest element in P, if one exists, that is less than or equal to each element of S is known as the infimum of a subset S of a partially ordered set P. As a result, the phrase largest lower bound is also frequently employed. A set's infimum is its highest upper bound, while its supremum is its lowest upper bound. The supremum is the smallest upper bound of a set, whereas the maximum is the largest member of a set. The largest number in one column that is less than or equal to the target value in the other column is found using the greatest lower bound (glb) operator. The smallest number that is larger than or equal to the target number is discovered using the least upper bound (lub) operator.
Let us suppose that sₙ ≤ tₙ if n≥N, but that
lim infn sₙ > lim infn tₙ.
Let [tex]E_{s}[/tex] denote the set of all subsequential limits of {sₙ}, and let [tex]E_{t}[/tex] denote the set of all subsequential limits of {tₙ}. Then
inf [tex]E_{s}[/tex] >inf [tex]E_{t}[/tex].
This implies that there exists some x∈[tex]E_{t}[/tex] such that inf [tex]E_{s}[/tex] >x>inf [tex]E_{t}[/tex]., since otherwise inf [tex]E_{t}[/tex]. would not be the greatest lower bound of [tex]E_{t}[/tex]. Hence some subsequence of {tₙ}, say {tₙ}, converges to x< inf [tex]E_{s}[/tex].
lim sup sₙ ≤ lim sup tₙ.
Let [tex]E_{s}[/tex] denote the set of all subsequential limits of {sₙ}, and let [tex]E_{t}[/tex] denote the set of all subsequential limits of {tₙ}. Then
sup [tex]E_{s}[/tex] ≤ sup [tex]E_{t}[/tex].
This implies that there exists some x∈[tex]E_{t}[/tex] such that sup [tex]E_{s}[/tex] ≤ x ≤ sup [tex]E_{t}[/tex]., since otherwise sup [tex]E_{t}[/tex]. would be the greatest lower bound of [tex]E_{t}[/tex]. Hence some subsequence of {tₙ}, say {tₙ}, converges to x< sup [tex]E_{s}[/tex].
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Solve for X. I need help please
Tai wants to frame a 3 x 5 picture surrounded by 2 inches of mat. How large will her frame need to be?
if c is a matrix with five rows and three columns, then what is the minimum possible number of rows of zeros in any row echelon form
the minimum possible number of rows of zeros in any row echelon form is 2
What is echelon form of a matrix?
If a matrix in linear algebra has the structure that comes from a Gaussian elimination, it is said to be in echelon form. The bottom row has solely zeros, as do all other rows. A nonzero row's pivot, also known as the leading coefficient, is always located strictly to the right of the leading coefficient of the row above it.
The row echelon form of 5 × 3 matrix is given by -
[tex]\left[\begin{array}{ccc}1&a&b\\0&1&d\\0&0&1\\0&0&0\\0&0&0\end{array}\right][/tex]
As we can see, the number of rows containing zeros are 2.
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two polynomials with integer coefficients are relatively prime in q[x] if and only if the ideal they generate in z[x] contains a (nonzero) integer
Certain polynomials with integer coefficients fall into the category of substantially prime polynomials in q[x] if and only if the ideal they create in z[x] contains a (nonzero) integer.
What are polynomials?A polynomial is an expression in mathematics that consists of indeterminates (also known as variables and coefficients) that exclusively uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. x2 4x + 7 is an illustration of a polynomial of one uncertain x.
In both mathematics and science, polynomials are widely used. For instance, they are used to define polynomial functions, which can be found in a variety of contexts, from basic chemistry and physics to economics and social science, and they are used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to encode a wide range of problems, from simple word problems to complex scientific problems.
Calculations:
Let d=degP.
Then the Q-vector space V=Q[X]/(P) is d-dimensional.
The residue classes modulo (P) of X2,X3,X5,… are linearly dependent over Q, so there exist a2,a3,a5,…∈Z not all zero such that a2X2+a3X3+a5X5+⋯∈(P).
This shows that there is Q∈Z[X], Q≠0 such that PQ=a2X2+a3X3+a5X5+⋯.
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An airliner makes a 3,000 mile flight in 7 hours. What is the airliners average rate of speed in miles per hour ?
To find the average rate of speed per miles an hour, do the following equation: miles ÷ hour = miles per hour.
So, we divide 3,000 ÷ 7 = 428.5714285714 but we can make round it to 429.
The airliners average rate of speed in miles per hour is 429 miles per hour.