The statement is false, as it is possible for three vectors to not span Rn but still lie on the same plane, such as the three vectors (1,1,1), (2,2,2), and (3,3,3), which all lie on a plane that passes through the origin.
(a) In order for three vectors un, U2, U3 to span Rn, all possible values of n must be 3 or greater. This is because three vectors can only span a 3-dimensional space or higher. Therefore, any n greater than or equal to 3 will work.
(b) Since {u, uy, u3} is a spanning set for Rn, then {u, u, + u2, u, -u3} is also a spanning set for Rn. This is because adding or subtracting any of the vectors in the original set will still form a set of three vectors that span Rn.
(c) This statement is always true. If three vectors ui, uy, u3 are linearly independent, then any linear combination of those three vectors (such as u,, u, + u2, u, -u3) will also be linearly independent.
(d) This statement is also always true. If three vectors ui, uy, u3 are linearly independent, then any linear combination of those three vectors (such as u,, u, + u2, u, -u3) will also be linearly independent.
(e) This statement is false. It is possible for three vectors ui, uy, u3 to not span Rn but still lie on the same plane. For example, the three vectors (1,1,1), (2,2,2), and (3,3,3) do not span R3, but they all lie on the same plane that passes through the origin (x+y+z=0).
The statement is false, as it is possible for three vectors to not span Rn but still lie on the same plane, such as the three vectors (1,1,1), (2,2,2), and (3,3,3), which all lie on a plane that passes through the origin.
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68 times the difference between a number and 45 is equal to the number plus −98
Answer:
The number can be expressed in multiple forms
Fraction form [tex]x=\frac{2962}{67}[/tex] or decimal form [tex]x=44.21[/tex]
Step-by-step explanation:
Lets break the problem down
"times" is multiplication *
The difference between 2 numbers is subtraction [tex](x-y)[/tex]
A number plus a number is addition [tex]x+y[/tex]
[tex]68(x-45)=x+-98[/tex]
Lets solve for [tex]x[/tex].
Lets start on the left side.
Distribute 68 to the terms inside the parenthesis.
[tex]68x-3060=x+-98[/tex]
A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign.
[tex]68x-3060=x-98[/tex]
Subtract [tex]x[/tex] from both sides of the equation.
[tex]68x-3060-x=-98[/tex]
Subtract [tex]x[/tex] from [tex]68x[/tex].
[tex]67x-3060=-98[/tex]
Add 3060 to both sides of the equation.
[tex]67x=2962[/tex]
Divide both sides of the equation by 67.
[tex]x=\frac{2962}{67}[/tex] or as a decimal [tex]x=44.21[/tex]
suppose that a sphere passes through the point and has center . (a) find the distance between the points and
The distance between two points in three-dimensional space is a measure of the separation between the two points. In this case, the two points are the center of a sphere and a point that the sphere passes through.
To find the distance, we can use the distance formula in three dimensions, which is an extension of the distance formula in two dimensions. The distance formula is:
d = √((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)
where (x1, y1, z1) is the center of the sphere and (x2, y2, z2) is the point that the sphere passes through. The square root of the sum of the squares of the differences between the corresponding coordinates gives the distance between the two points.
In this problem, the center of the sphere is not given, so it is not possible to calculate the distance between the sphere and the point. The center of the sphere is a crucial piece of information needed to solve this problem.
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The buckingham fountain holds 725 gallons of water. due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour. let y represent the amount of water in gallons after x hours of leaking
An equation represent the given scenario is 725=y-12.5x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the Buckingham fountain holds 725 gallons of water.
Due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour.
Let y represent the amount of water in gallons after x hours of leaking.
Now, equation is 725=y-12.5x
Therefore, an equation is 725=y-12.5x.
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the domain of f. f(1)=10, f(2)=-7, f(3)=4
Answer: The domain of the function f refers to the set of all input values (x) for which the function is defined. Based on the information provided, it is not possible to determine the full domain of the function f. The only information provided are the outputs (f(1)=10, f(2)=-7, f(3)=4) for specific input values (1, 2, 3).
Step-by-step explanation:
andre and priya are tracking the number of steps they walk. andre records that he can walk 6000 steps in 50 minutes. priya writes the equation y
Andre walks more steps than Priya
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
To solve this problem, we have to state the equation using the information of the problem:
Calculating Andre's steps we have:
y(Andre) = 6000 steps/50 minutes
y(Andre) = 120 steps/ minute
If the total of hours is 5 hours we convert hours to minutes and we have:
5 hours * (60 minutes/ 1 hours) = 300 minutes
Andre's steps in 300 minutes are:
y(Andre) = 120 steps/ minute * 300 minutes
y(Andre) = 36000 steps
Now we calculate the steps of Pria with the equation given:
y=118x
y(Pria) = 118*300
y(Pria) = 35400 steps
36000 steps > 35400 steps
y(Andre) > y(Pria)
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Correctly written question:
Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps?
the following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes). quarter-mile times: 0.92 0.96 1.04 0.93 1.00 mile times: 4.52 4.35 4.60 4.71 4.51 after viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. use the standard deviation and the coefficient of variation to summarize the variability in the data. quarter-milers standard deviation (to decimals) coefficient of variation (to decimal) % milers standard deviation (to decimals) coefficient of variation (to decimal) % does the use of the coefficient of variation indicate that the coach's statement should be qualified? (i) yes; the coefficient shows that as a percentage of the mean, the quarter-milers' times show less variability. (ii) no; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability. choose the correct answer. - select your answer -
No; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability.
How did we arrive at this assertion?To summarize the variability in the data, we can calculate the standard deviation and the coefficient of variation for both the quarter-mile and mile runners.
Standard deviation:
Quarter-mile times:
mean = (0.92 + 0.96 + 1.04 + 0.93 + 1.00) / 5 = 0.97
differences from mean = [0.92 - 0.97, 0.96 - 0.97, 1.04 - 0.97, 0.93 - 0.97, 1.00 - 0.97] = [-0.05, -0.01, 0.07, -0.04, 0.03]
squared differences = [0.0025, 0.0001, 0.0049, 0.0016, 0.0009]
sum of squared differences = 0.01
standard deviation = √(sum of squared differences / (number of data points - 1)) = sqrt(0.01 / 4) = 0.049
Mile times:
mean = (4.52 + 4.35 + 4.60 + 4.71 + 4.51) / 5 = 4.56
differences from mean = [4.52 - 4.56, 4.35 - 4.56, 4.60 - 4.56, 4.71 - 4.56, 4.51 - 4.56] = [-0.04, -0.21, 0.04, 0.15, -0.05]
squared differences = [0.0016, 0.0441, 0.0016, 0.0225, 0.0025]
sum of squared differences = 0.0727
standard deviation = √(sum of squared differences / (number of data points - 1)) = sqrt(0.0727 / 4) = 0.139
Coefficient of variation:
Quarter-mile times: coefficient of variation = standard deviation / mean = 0.049 / 0.97 = 0.051 (to 2 decimal places)
Mile times: coefficient of variation = standard deviation / mean = 0.139 / 4.56 = 0.0305 (to 4 decimal places)
The use of the coefficient of variation indicates that the coach's statement should be qualified. The coefficient shows that as a percentage of the mean, the mile runners' times have less variability (3.05%) compared to the quarter-mile runners' times (5.1%). So, the answer is (ii) no; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability.
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Can any one help with the circled ones
The value of variables x and y are, x = 67 and y = 40.
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
Figure is shown in image.
Now, By definition of vertically opposite angle,
⇒ (y + 23)° = 63°
Solve for y;
⇒ y + 23 = 63
Subtract 23 both side,
⇒ y + 23 - 23 = 63 - 23
⇒ y = 40
And, By definition of supplementary angles, we get;
⇒ (2x - 17)° + 63° = 180°
Solve for x;
⇒ 2x - 17 + 63 = 180
⇒ 2x + 46 = 180
⇒ 2x + 46 - 46 = 180 - 46
⇒ 2x = 134
⇒ x = 134/2
⇒ x = 67
Thus, The value of variables x and y are, x = 67 and y = 40.
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circles $\omega$ and $\gamma$, both centered at $o$, have radii $20$ and $17$, respectively. equilateral triangle $abc$, whose interior lies in the interior of $\omega$ but in the exterior of $\gamma$, has vertex $a$ on $\omega$, and the line containing side $\overline{bc}$ is tangent to $\gamma$. segments $\overline{ao}$ and $\overline{bc}$ intersect at $p$, and $\dfrac{bp}{cp}
The ratio of bp to cp in equilateral triangle abc, with a on circle omega(Ω), bc tangent to circle omega(Ω), and p being the intersection of ao and bc, is [tex]\frac{2}{\sqrt{3} }[/tex].
Let's label the center of the larger circle omega(Ω) as O, and the center of the smaller circle gamma(Γ)as G. Draw a perpendicular from O to the line containing side overline{BC}, and label the intersection point as X. By tangency, GX is a radius of gamma(Γ), so GX = 17.
Also, $\overline{OX} = 20. By the Pythagorean Theorem, OP = [tex]\sqrt{OX^{2} -PX^{2} }[/tex] = [tex]\sqrt{20^{2}-17^{2} }[/tex] = [tex]\sqrt{289}[/tex]. Let BP = x. Then CP = [tex]\frac{BC}{2} -x[/tex] = [tex]\frac{BC}{2} -x[/tex] = [tex]\frac{BC-2x}{2}[/tex]. Therefore, [tex]\frac{BP}{CP}[/tex] = [tex]\frac{x}{\frac{BC-2x}{2} }[/tex]= [tex]\frac{2x}{BC-2x}[/tex] = [tex]\frac{2x}{BC}[/tex].
To find BC, we use the fact that ΔABC$ is equilateral. Therefore, AO = BO = CO = 20. Let's apply the Law of Cosines to triangle ABO:
[tex]AB^{2} =AO^{2} +BO^{2} -2.AO.BO.cosA[/tex]
[tex]AB^{2} =20^{2} +20^{2} -2.20.20.cos(60)[/tex]
[tex]AB^{2} =800[/tex]
[tex]AB=\sqrt{800} =20\sqrt{2}[/tex].
Therefore, [tex]BC=AB=20\sqrt{2}[/tex], and [tex]\frac{BP}{CP} =\frac{2x}{BC}=\frac{2x}{20\sqrt{2} }[/tex].
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use the quadratic formula to solve the quadratic equation:
x²-2x+2=0
The solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The quadratic formula to find solution of an equation is
x=-b±√b²-4ac/2a
The given equation is x²-2x+2=0
a=1, b=-2, c=2
x=2±√4-4(1)(2)/2(1)
x=2±√-4/2
x=2±2i/2
x=1+i, 1-i
Hence, the solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0
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woman bought 1.8 kg of chicken and 1.6 kg of meat. The chicken cost N5.40 and the meat cost #6.40. If she had bought 2.4 kg of chicken and 2 kg of meat, how much would she have had to pay?
The amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2
What is the unit price?The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service
Given that, a woman bought 1.8 kg of chicken and 1.6 kg of meat. The chicken cost $5.40 and the meat cost $6.40,
We need to find, if she had bought 2.4 kg of chicken and 2 kg of meat, how much would she have had to pay,
To find the same, we will first find the unit price of each,
Unit price = total price / total quantity
Since, 1.8 kg of chicken costs $5.40,
Therefore, 1 kg will cost = 5.40 / 1.8 = $3
Similarly,
If 1.6 kg of meat costs $6.40,
Therefore, 1 kg will cost = 6.40 / 1.6 = $4
Now, to find the cost of 2.4 kg of chicken and 2 kg of meat, we will multiply the unit prices to the required quantities,
Therefore,
2.4 kg of chicken will cost = 2.4 x 3 = $7.2
2 kg of meat will cost = 2 x 4 = $8
In total, she had to pay = 8+7.2 = $15.2
Hence, the amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2
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Dough has 5 hours to make an on time delivery 273 mile# away. Dough drives at a constant speed of 55 miles per hour. Will Doug make the delivery by the deadline. Explain
Answer:
Yes, He'll make it
Step-by-step explanation:
If Doug travels at 55 MPH for 5 hours, he will have driven 275 miles. Since the deadline and his current speed allow him to drive farther than his set location at 273 miles, then Doug should be able to make it within the time given.
A bag contains 12 colored marbles. Dan drew a single marble from the bag 25 times, replacing the marble each time. He recorded drawing a red marble 9 times, a yellow marble 6 times, a blue marble 4 times, and a green marble 6 times. Based on these results, what is a reasonable conclusion about the makeup of the marbles in the bag?
A logical inference on the composition of the marbles in the bag is that there are approximately 3 green, 2 blue, 4 red, and 3 yellow marbles.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, A bag containing 12 colored marbles. Dan drew a single marble from the bag 25 times, replacing the marble each time.
He recorded drawing a red marble 9 times.
Thus, the number of red marvels = 12 * 9 /25
the number of red marvels = 4.32 or 4
He recorded drawing a yellow marble 6 times,
Thus, the number of yellow marbles = 12 *6/25
the number of yellow marbles = 2.88 or 3 approx
He recorded drawing a blue marble 4 times,
Thus, the number of blue marbles = 12 *4/25
the number of blue marbles = 1.92 or 2 approx
He recorded drawing and a green marble 6 times.
Thus, the number of green marbles = 12 *6/25
the number of green marbles = 2.88 or 3 approx,
Therefore, A reasonable conclusion about the makeup of the marbles in the bag is that there are approx 3 green marbles, 2 blue marbles, 4 red marbles, and 3 yellow marbles.
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what is the value of x?
x^2-10x+25
Answer:
(x-5)^2
Step-by-step explanation:
(50 POINTS AND BRAINLYEST)
Please answer them all :)
A dilation that makes a shape larger is a(n)....
Question 4 options:
expansion
contraction
reflection
rotation
Question 5 (1 point)
Saved
A dilation that makes a shape smaller is a(n)....
Question 5 options:
expansion
contraction
reflection
rotation
Question 6 (1 point)
The resulting shape after a transformation is completed is called the...
Question 6 options:
final shape
pre-image
image
result
Question 7 (1 point)
The number that is used to determine if a dilated shape has been expanded or contracted is the...
Question 7 options:
scale factor
center of dilation
origin
really important number
Solve the Initial Value please
The solution of the initial value problem is y = -3x/(3㏑x - 1)
What an initial value problem?An initial value problem is a differential equation in which the initial value of the function is given.
How to solve the initial value problem?Now we have the initial value problem
y' = (xy + y²)/x² , y(1) = 3.
We notice that it is a homogeneous differential equation.
What is a homogeneous differential equation?A homogeneous differential equation is a differential equation in which the powers of x and y are the same.
So, we proceed to solve the equation as folows.
Let y = vx.
So,
y/x = v and
dy/dx = xdv/dx + v
We now substitute these into the differential equation, we have that
y' = (xy + y²)/x²
dy/dx = (xy/x² + y²/x²
xdv/dx + v = y/x + (y/x)²
xdv/dx + v = v + v²
xdv/dx = v²
So using the method of separation of variables, we have
dv/v² = dx/x
Thus Integrating both sides, we have
∫dv/v² = ∫dx/x
-v⁻¹ = ㏑x + C
-1/v = ㏑x + C
We now substitute v = y/x into the equation, we have
- 1/y/x = ㏑x + C
-x/y = ㏑x + C
So, making y subject of the formula, we have
y = -x/(㏑x + C)
Since y(1) = 3, we have
3 = -1/(㏑1 + C)
3 = -1/(0 + C)
3 = -1/C
C = -1/3
So, y = -x/(㏑x + (-1/3))
y = -x/(㏑x - 1/3)
y = -x/(3㏑x - 1)/3
y = -3x/(3㏑x - 1)
So, the solution is y = -3x/(3㏑x - 1)
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Use Table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. Give your answers to four decimal places.
a) z < -0.67=
b) z > -0.67=
c) z < 1.46=
d) -0.67 < z < 1.46=
a) The proportion of observations, P(z < -0.67) = 0.2514.
b) The proportion of observations, P(z > -0.67) = 0.7486.
c) The proportion of observations, P(z < 1.46) = 0.9279.
d) The proportion of observations, P(-0.67< z < 1.46) = 0.6765.
A z-table, or standard normal table, helps to reveals what percentage of values fall below a certain z-score in a normal distribution. We have a standard normal table present above .
a) P( z < -0.67 )
Split -0.67 such as (-0.6 + 0.07 ) and look -0.6 in first column and 0.07 in first row then look cross value. So, P( z < -0.67 )
= 0.2514
b) P( z > - 0.67 ) = 1 - P( z < -0.67 )
From part (a ) , P( z < -0.67 ) = 0.2514
So, P( z > - 0.67 ) = 1 - 0.2514 = 0.7486
=> P( z > - 0.67 ) = 0.7486
c ) P( z < 1.46 ) = 1 - P( z < -1.46 )
Using Table, P( z < -1.46 ) is,
=> P( z < -1.46 ) = 0.0721
So, P( z < 1.46 ) = 1 - 0.0721 = 0.9279
=> P( z < 1.46 ) = 0.9279
d) P(-0.67 < z < 1.46 ) = P( z < 1.46) - P( z < -0.67 ) from part( a) , P( z < -0.67 ) = 0.2514
and from par (c) , P( z < 1.46 ) = 0.9279
So, P(-0.67 < z < 1.46 ) = 0.9279 - 0.2514
= 0.6765
=> P(-0.67 < z < 1.46 ) = 0.6765
Hence, all the required proportion are determined.
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Complete question:
Use The above table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. Give your answers to four decimal places.
a) z < -0.67=
b) z > -0.67=
c) z < 1.46=
d) -0.67 < z < 1.46=
A ∩ B = ∅, P(A) = 0.4, P(A ∪ B) = 0.9. Find P(B)
Find P(B).
If intersection of A & B null set and P(A) = 0.4, P(A ∪ B) = 0.9 then P(B) = 0.5
What are sets ?In mathematics, a set is a collection of distinct objects, called elements, which can be anything from numbers, to letters, to functions, or even other sets. The objects in a set are unordered, meaning their position or arrangement doesn't matter. Sets are often denoted using curly braces {} and the elements within the set are separated by commas.
For example, the set of positive even numbers less than 10 can be written as {2, 4, 6, 8}.
Given that,
A ∩ B = ∅,
P(A) = 0.4,
P(A ∪ B) = 0.9,
P(B) = ?
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.9 = 0.4 + P(B) - 0
P(B) = 0.9 - 0.4
= 0.5
Hence, the probability of event B is 0.5
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how do i do a problem with y-x in it
Answer:
It depends on the question as x and y are variables. so they can be any number
Step-by-step explanation:
write the expression in algebraic form. [hint: sketch a right triangle, as demonstrated in example 3.] tan(arcsec(x/3))
The expression tan(arcsec(x/3)) can be written [tex]1/3 \sqrt{x^2-9}[/tex] in algebraic form.
The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.
The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to [tex]1/3 \sqrt{x^2-9}[/tex].
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Catherine rolls a standard 6-sided die five times, and the product of her rolls is 600. How many different sequences of rolls could there have been? (The order of the rolls matters.)
There could be 150 sequences of rolls
How to find the different sequences of rolLLet's find the sets of 5 integers less than or equal to 6 that could multiply to 300 (where order doesn't matter for right now):
1, 2, 5, 5, 6
1, 3, 4, 5, 5
2, 2, 3, 5, 5
Now let's find the number of unique ways we could reorder these sets
There are
5!/2!=60 ways to order {1, 2, 5, 5, 6}
There are
5!/2! =60 ways to order {1, 3, 4, 5, 5}
There are
5!/2!2! =30 ways to order {2, 2, 3, 5, 5}
There could have, therefore, been 60 + 60 + 30 = 150 different sequences of rolls
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Write equivalent fractions for the numbers 1 and 2 10.3
The fractions and the equivalent equations is solved
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
a)
Let the value of fraction A = 3
Now , the value of 3/1 = 3
The value of 6/2 = 3
The value of 12/4 = 3
Therefore , the equivalent fractions are 3/1 , 6/2 and 12/4
b)
Let the value of fraction A = 4
Now , the value of 4/1 = 4
The value of 8/2 = 4
The value of 16/4 = 4
Therefore , the equivalent fractions are 4/1 , 8/2 and 16/4
c)
Let the value of fraction A = 1
The value of 3/3 = 1
The value of 12/12 = 1
Therefore , the equivalent fractions are 3/3 and 12/12
d)
Let the value of fraction A = 4
The value of 40/10 = 4
The value of 8/2 = 4
Therefore , the equivalent fractions are 40/10 and 8/2
e)
Let the value of fraction A = 3
The value of 12/4 = 3
The value of 18/6 = 3
Therefore , the equivalent fractions are 12/4 and 18/6
Hence , the fractions are solved
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It takes Stan two hours to clean the kitchen.
Judy can clean the same kitchen in 1.5
hours. Find how long it would take them if
they worked together.
Answer:
Step-by-step explanation:
it would take 30minutes
What is the greatest common factor of 50,12,and 8
Answer:
2
Step-by-step explanation:
well I so yeah and this plus that
The greatest common factor of 50,12,and 8 is,
⇒ 2
We have to given that,
All the numbers are,
⇒ 50, 12 and 8
Now, We know that,
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Here, Numbers are,
50 = 2 x 5 x 5
12 = 2 x 2 x 3
8 = 2 x 2 x 2
Hence, The greatest common factor of 50,12,and 8 is,
⇒ 2
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determine the magnitude of the resultant of the two forces applied at a. round your answer to one decimal place.
Answer:
I'm sorry, but without additional information such as the magnitude, direction, and orientation of the two forces, it is impossible to determine the magnitude of the resultant.
On your instructors quizzes you expect a score of 100% when you study in a 60% when you don’t suppose the probability that you study is .8 given these facts compute the expected average of all your quizzes 
The expected average of all your quizzes is 92%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Expected score when you study = 100%
Expected score when you don't study = 60%
Probability that you study = 0.8
Probability that you don't study = 1 - 0.8 = 0.2
Expected Value or mean of the random variable X is,
E(X) = Σ(x P(x))
Expected average = (100 × 0.8) + (60 × 0.2)
= 92
Hence the expected value of all your quizzes is 92%.
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How do 1/4 and 3/5 compare
Answer:
Is 3/5 greater than 1/4? Is 3/5 bigger than 1/4? Is 3/5 larger than 1/4? These are all the same questions with one answer.
To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:
3/5 = 0.6
1/4 = 0.25
Then, we compare the two decimal numbers to get the answer.
0.6 is greater than 0.25.
Therefore, 3/5 is greater than 1/4 and the answer to the question "Is 3/5 greater than 1/4?" is yes.
Which means that this equation is also true: 3/5 > 1/4
Step-by-step explanation:
Note: When comparing fractions such as 3/5 and 1/4, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.
A gallon of paint can cover 250 square feet. Find how many gallon containers of paint
should be bought to paint 3 coats on each wall of a rectangular room with dimensions
16 feet by 8 feet and walls that are 10-feet tall.
Number of gallon containers of paint required are 2.
How to find the surface 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;
A gallon of paint can cover 250 square feet
The paint should be bought to paint 3 coats on each wall of a rectangular room with dimensions 16 feet by 8 feet and walls that are 10-feet tall.
Now,
The surface area for 3 coats on the wall;
=2(16*10)+2(8*10)
=320+160
=480
1gallon covers 250sq ft
For 480sq ft
=480/250
=1.92
Therefore, to paint he room of given area approximately 2 cans will be required.
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find the numerical value of each expression. (round your answers to five decimal places.) (a) cosh(7)
The numerical value of cosh(7) is 25.78543.
The hyperbolic cosine function, cosh(x), is the inverse of the hyperbolic sine function, sinh(x). It is defined as the sum of the series cosh(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + …, where x is any real number and n! is the factorial of n.
To find the numerical value of cosh(7), we need to evaluate the series at x = 7. To do this, we start by calculating the first two terms of the series, 1 and 7²/2!. The first term is 1, and the second term is 7²/2! = 49/2 = 24.5. Then we add them together to get the result cosh(7) = 25.5.
To get a more accurate result, we can add more terms to the series. For instance, by adding the third term, 7⁴/4!, we get cosh(7) = 25.5 + 585/24 = 25.70833. We can continue this process to get an even more accurate result.
After adding the sixth term, 7⁶/6!, we get cosh(7) = 25.70833 + 90090/720 = 25.78542.
Finally, we round the result to five decimal places to get cosh(7) = 25.78542 ≈ 25.78543.
The numerical value of cosh(7) is 25.78543.
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examine the two figures above. which illustrates a society that produces more capital goods than consumer goods?
The figure on the left illustrates a society that produces more capital goods than consumer goods, as indicated by a Total Value of Goods difference of $200.
The figure on the left illustrates a society that produces more capital goods than consumer goods. This is because the total value of the capital goods is greater than the total value of the consumer goods. This can be calculated using the formula Total Value of Goods (TVG) = Price of Goods x Quantity of Goods. By using this formula we can calculate that the TVG of the capital goods is $400 (20 x 20) and the TVG of the consumer goods is $200 (10 x 20). The difference between the two is $200, indicating that the society is producing more capital goods than consumer goods.
The figure on the left illustrates a society that produces more capital goods than consumer goods, as indicated by a Total Value of Goods difference of $200.
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Use this table to answer the question. Read the question carefully!
Infections in Hospital Infections after Release No Infections Total
Hospital 1 350 110 450 910
Hospital 2 175 210 350 735
Hospital 3 210 35 75 320
Hospital 4 437 587 4300 5324
Hospital 5 89 21 356 466
Hospital 6 67 175 298 540
Total 1328 1138 5829 8295
What was the percent of Infections in Hospital for Hospital 6?
The percent of infections for Hospital 6 is given as follows:
44.81%.
How to obtain the percentage?The percentage is obtained applying the proportions in the context of this problem.
A proportion is applied because a percentage is calculated with the division of the number of desired outcomes by the number of total outcomes, a result which is then multiplied by 100%.
Out of 540 patients in Hospital 6, 67 were infected in hospital and 175 after release, hence the percentage is obtained as follows:
P = (67 + 175)/540 = 44.81%.
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