Answer:
First type of fruit drinks: 160 pints
Second type of fruit drinks: 80 pints
Step-by-step explanation:
Let's call A the amount of first type of fruit drinks. 5.5% pure fruit juice
Let's call B the amount of second type of fruit drinks. 100% pure fruit juice
The resulting mixture should have 70% pure fruit juice and 240 pints.
Then we know that the total amount of mixture will be:
[tex]A + B = 240[/tex]
Then the total amount of pure fruit juice in the mixture will be:
[tex]0.55A + B = 0.7 * 240[/tex]
[tex]0.55A + B = 168[/tex]
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:
[tex]-A -B = -240[/tex]
[tex]-A -B = -240[/tex]
+
[tex]0.55A + B = 168[/tex]
--------------------------------------
[tex]-0.45A = -72[/tex]
[tex]A = \frac{-72}{-0.45}[/tex]
[tex]A = 160\ pints[/tex]
We substitute the value of A into one of the two equations and solve for B.
[tex]160 + B = 240[/tex]
[tex]B = 80\ pints[/tex]
To make 240 pints of a mixture that is 70% pure fruit juice, you will need 160 pints of the first type of fruit drink (55% pure fruit juice) and 80 pints of the second type of fruit drink (100% pure fruit juice).
Explanation:To solve this problem, we can set up a system of equations. Let's say x represents the number of pints of the first type of fruit drink (55% pure fruit juice) and y represents the number of pints of the second type of fruit drink (100% pure fruit juice). We know that the total number of pints of the mixture is 240, so we can write the equation x + y = 240. We also know that the desired percentage of pure fruit juice in the mixture is 70%, so we can write the equation (55% * x + 100% * y) / 240 = 70%. To solve this system of equations, we can use substitution or elimination method. Let's use substitution:
From the first equation, we can solve for x in terms of y: x = 240 - y. Substituting this into the second equation, we get ((55% * (240 - y)) + 100% * y) / 240 = 70%. Simplifying the equation, we have (0.55(240 - y) + y) / 240 = 0.70. Distributing and combining like terms, we get (132 - 0.55y + y) / 240 = 0.70. Simplifying further, we have (132 + 0.45y) / 240 = 0.70. Cross multiplying, we get 132 + 0.45y = 0.70 * 240. Simplifying, we have 132 + 0.45y = 168. Multiplying 0.45 with y, we get 0.45y = 168 - 132. Subtracting 132 from 168, we get 0.45y = 36. Dividing both sides of the equation by 0.45, we get y = 36 / 0.45. Evaluating this expression, we get y = 80. So, the number of pints of the second type of fruit drink (100% pure fruit juice) needed is 80. Substituting this value back into the first equation, we can solve for x: x + 80 = 240. Subtracting 80 from both sides of the equation, we get x = 240 - 80. Evaluating this expression, we get x = 160. Therefore, the number of pints of the first type of fruit drink (55% pure fruit juice) needed is 160.
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[tex]\text{I was eating cookies and had some thoughts. If I wanted to cut out exactly }[/tex][tex] \frac{1}{3} [/tex]of the cookie to share with someone, how far from one side would I have to make a straight cut to get that exact amount? How far would I have to cut if I wanted to cut off[tex] \frac{1}{n} [/tex][tex]\text{ of the cookie?}[/tex]
[tex]\text{Basically, the question is, find the value of }a\text{ given only n, and r}[/tex]
[tex]\text{One way of finding this, is by finding the area of the shaded reigon, Q in terms of}[/tex]
[tex]\text{r, a, and b, and equating it to the area of the fraction of the cookie then solving for a.}[/tex]
[tex]\text{In math, this means solving } \frac{1}{n}\pi r^2=Q \text{ for }f(r,n)=a.[/tex]
[tex]\text{From the diagram, we can see that }r=a+b[/tex]
[tex]\text{Eventually, by 2 different means, I found 2 equations that, if solved, would give the}[/tex][tex]\text{ relationship between r, n, and a.}[/tex][tex]\text{They are as follows:}[/tex]
[tex]\text{1. }\frac{1}{n}\pi r=r\theta-bsin(\theta) \text{ where }\theta=cos^{-1}(\frac{b}{r})[/tex]
[tex]\text{2. }\frac{1}{n}\pi=\theta-sin(2\theta)\text{ where }\theta=cos^{-1}(\frac{b}{r})[/tex]
[tex]\text{These 2 equations are equivalent, but annoying to solve.}[/tex]
[tex]\text{To claim these points, please solve for a in terms of r and n, showing all work.}[/tex]
[tex]\text{I would like an analytic solution if possible.}[\tex]
[tex]\text{All incorrect, spam, or no-work solutions will be reported.}[/tex]
In the attachement, there is what I came up with so far. I think that finding 'a' is non-trivial, if possible at all.
[tex]A_c[/tex] - the area of a circle
[tex]A_{cs}[/tex] - the area of a circular segment
Answer:
- the area of a circle
- the area of a circular segment
What is the maxima minima or zero for this graph???
Maximum is the highest a graph can reach. In this case the graph continues forever therefore the maximum is:
infinity or ∞
The minimum is the lowest place the graph reaches. In this case it would be:
-6
The zeros are where the graph intersects the x axis. In this case it would have two zeros, which are:
(-3, 0) and (0.5, 0)
Hope this helped!
~Just a girl in love with Shawn Mendes
proof true or false: For all integers a,b,and c,if ab|c then a|c and b|c
Answer with explanation:
It is given that for three integers , a, b and c, if
[tex]\frac{ab}{c}\rightarrow then, \frac{a}{c} \text{or} \frac{b}{c}[/tex]
Since , a b is divisible by c , following are the possibilities
1.→ a and b are prime integers .Then , c will be prime number either equal to a or b.
2.→a and b are not prime integers ,then any of the factors of a or b will be equal to c.For example:
⇒a=m × n
b=p × q× c
or,
⇒a=u×v×c
b=s×t
So, whatever the integral values taken by a, and b, if [tex]\frac{ab}{c}[/tex] then either of [tex]\frac{a}{c} \text{or} \frac{b}{c}[/tex] is true.
13.48x - 200 < 256.12
Answer:
x < 33.84
Step-by-step explanation:
we have
13.48x-200 < 256.12
Solve for x
Adds 200 both sides
13.48x-200 +200 < 256.12+200
13.48x < 456.12
Divide by 13.48 both sides
13.48x/13.48 < 456.12/13.48
x < 33.84
The solution is the interval ----> (-∞, 33.84)
All real numbers less than 33.84
Maria needs to know How much Money $ to have with her when She Goes to her favorite Show Store ... How Much money Should Bring to buy a pair of Shoes ?? ? If, the Original price is $ 80 and there is a discount of 20% and the Sale will only last for one week ...
Answer: $64
Step-by-step explanation:
Set up is/of ratio. See photo attached. (:
The number of typing errors made by a typist has a Poisson distribution with an average of two errors per page. If more than two errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped? (Round your answer to three decimal places.)
Answer: 0.6767
Step-by-step explanation:
Given : Mean =[tex]\lambda=2[/tex] errors per page
Let X be the number of errors in a particular page.
The formula to calculate the Poisson distribution is given by :_
[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]
Now, the probability that a randomly selected page does not need to be retyped is given by :-
[tex]P(X\leq2)=P(0)+P(1)+P(2)\\\\=(\dfrac{e^{-2}2^0}{0!}+\dfrac{e^{-2}2^1}{1!}+\dfrac{e^{-2}2^2}{2!})\\\\=0.135335283237+0.270670566473+0.270670566473\\\\=0.676676416183\approx0.6767[/tex]
Hence, the required probability :- 0.6767
simplify. x^2-3x-18/x+3
The simplified value is (x - 6)
How to simplify the given expressions?[tex]\frac{x^{2} -3x-18}{x+3}\\ = \frac{x^{2} -6x + 3x - 18}{x+3} \\=\frac{x(x-6) +3(x-6)}{x+3}\\ =\frac{(x+3)(x-6)}{x+3}\\ = x - 6[/tex]
So the simplified value is (x - 6)
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To simplify the rational expression x^2 - 3x - 18 / x + 3, factor the numerator and cancel out the common factor (x + 3). The simplified form is x - 6.
Simplifying the Rational Expression
To simplify the expression
x² - 3x - 18 / x + 3, follow these steps:
(x - 6)(x + 3) / x + 3.
Next, cancel the common factor (x + 3):
(x - 6) (x + 3) / (x + 3) = x - 6
So, the simplified form of the expression is x - 6. Note that this simplification is valid for all values of x except -3, as the denominator would be zero.
A computer system uses passwords that contain exactly 7 characters, and each character is 1 of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the probability that a password contains all lowercase letters given that it contains only letters. Report the answer to 3 decimal places.
Answer:
0,008 or 0,8%
Step-by-step explanation:
To calculate the probability the selected password is made out only of lower-case letters, if it's only letters, we have first to find out how many passwords could be formed with only letters and with only lower-case letters.
For lowercase letters, we can make this many passwords, since for each of the 7 characters, we can pick among 26 lowercase letters:
NLL = 26 * 26 * 26 * 26 * 26 * 26 * 26
In the same fashion, for the number of passwords consisting only of letters, we can pick among 52 letters for each each character (26 lower-case, 26 upper-case):
NOL = 52 * 52 * 52 * 52 * 52 * 52 * 52
We can rewrite NOL differently to ease our calculations:
NOL = (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26)
or
NOL = 26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2
Now we have to find out the probability a password containing only letters (NOL) is a password containing only lowercase letters (NLL). So, we divide NLL by NOL:
[tex]\frac{NLL}{NOL} = \frac{26 * 26 * 26 * 26 * 26 * 26 * 26}{26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2} = \frac{1}{2 * 2 * 2 * 2 * 2 * 2 * 2} = \frac{1}{2^{7} }[/tex]
The probability is thus 1/2^7 or 1/128 or 0,0078125
Which we are asked to round to 3 decimals... so 0,008 or 0,8%
F(x)=3x+4. Determine the value of F (X) when X equals -1
ANSWER
The value of this function at x=-1 is 1
EXPLANATION
The given function is
[tex]f(x) = 3x + 4[/tex]
We want to find the value of this function at x=-1.
We substitute x=-1 into the function to obtain:
[tex]f( - 1) = 3( - 1)+ 4[/tex]
We multiply out to obtain:
[tex]f( - 1) = - 3+ 4[/tex]
[tex]f( - 1) = 1[/tex]
Therefore the value of this function at x=-1 is 1.
Answer: [tex]f(-1)=1[/tex]
Step-by-step explanation:
Given the linear function f(x):
[tex]f(x)=3x+4[/tex]
By definition. a relation is a function if each input value has only one output value. In this case you need to find the output value for the input value [tex]x=-1[/tex]. In order to do this, you need to substitute this value of the variable "x" into the linear function given.
Then:
When [tex]x=-1[/tex]:
[tex]f(-1)=3(-1)+4[/tex]
Remember the multiplication of signs:
[tex](+)(-)=-\\(+)(+)=+\\(-)(-)=+[/tex]
Then, the value of f(x) when [tex]x=-1[/tex] is:
[tex]f(-1)=-3+4[/tex]
[tex]f(-1)=1[/tex]
y" +2y' +17y=0; y(0)=3, y'(0)=17
Answer:
The solution is [tex]y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)[/tex]
Step-by-step explanation:
We need to find the solution of [tex]y''+2y'+17y=0[/tex] with
condition [tex]y(0)=3,\ y'(0)=17[/tex]
This is a homogeneous equation with characteristic polynomial
[tex]r^{2}+2r+17=0[/tex]
using quadratic formula [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]r=\frac{-2\pm \sqrt{2^{2}-4(1)(17)}}{2(1)}[/tex]
[tex]r=\frac{-2\pm \sqrt{4-68}}{2}[/tex]
[tex]r=\frac{-2\pm \sqrt{-64}}{2}[/tex]
[tex]r=\frac{-2\pm 64i}{2}[/tex]
[tex]r=-1 \pm 32i[/tex]
The general solution for eigen value [tex]a \pm ib[/tex] is
[tex]y(t)=e^{at}(A \cos bt + B \sin bt)[/tex]
[tex]y(t)=e^{-t}(A \cos 32t + B \sin 32t)[/tex]
Differentiate above with respect to 't'
[tex]y'(t)=-e^{-t}(A \cos 32t + B \sin 32t) + e^{-t}(-32A \sin 32t + 32B \cos 32t)[/tex]
Since, y(0)=3
[tex]y(0)=e^{0}(A \cos(0) + B \sin(0))[/tex]
[tex]3=(A \cos(0) +0)[/tex]
so, A=1
Since, y'(0)=17
[tex]y'(0)=-e^{0}(3 \cos(0) + B \sin(0)) + e^{0}(-32(3) \sin(0) + 32B \cos (0))[/tex]
[tex]17=-(3 \cos(0)) + (0 + 32B \cos (0))[/tex]
[tex]17=-3 + 32B[/tex]
add both the sides by 3,
[tex]17+3 = 32B[/tex]
[tex]20= 32B[/tex]
divide both the sides, by 32,
[tex]\frac{20}{32}= B[/tex]
[tex]\frac{5}{8}= B[/tex]
Put the value of constants in [tex]y(t)=e^{-t}(A \cos 32t + B \sin 32t)[/tex]
[tex]y(t)=e^{-t}((1) \cos 32t + (\frac{5}{8}) \sin 32t)[/tex]
Therefore, the solution is [tex]y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)[/tex]
A ball is thrown at an initial height of 7 feet with an initial upward velocity at 27 ft/s. The balls height h (in feet) after t seconds is give by the following. h- 7 27t -16t^2 Find the values of t if the balls height is 17ft. Round your answer(s) to the nearest hundredth
Answer:
The height of ball is 17 ft at t=0.55 and t=1.14.
Step-by-step explanation:
The general projectile motion is defined as
[tex]y=-16t^2+vt+y_0[/tex]
Where, v is initial velocity and y₀ is initial height.
It is given that the initial height is 7 and the initial upward velocity is 27.
Substitute v=27 and y₀=7 in the above equation to find the model for height of the ball.
[tex]h(t)=-16t^2+27t+7[/tex]
The height of ball is 17 ft. Put h(t)=17.
[tex]17=-16t^2+27t+7[/tex]
[tex]0=-16t^2+27t-10[/tex]
On solving this equation using graphing calculator we get
[tex]t=0.549,1.139[/tex]
[tex]t\approx 0.55,1.14[/tex]
Therefore the height of ball is 17 ft at t=0.55 and t=1.14.
Help Algebra!!
10. To solve a system of equations using the matrix method, use elementary row operations to transform the augmented matrix into one with _______. Then, proceed back to substitute.
A. zeros in its final column
B. an inverse
C. zeros below the diagonal
D. Gaussian elimination
Answer:
C. zeros below the diagonal
Step-by-step explanation:
Upper echelon form (zeros below the diagonal) corresponds to a system of equations that has one equation in one variable, one equation in two variables, and additional equations in additional variables adding one variable at a time.
The single equation in a single variable is easily solved, and that result can be substituted into the equation with two variables (one of which is the one just found) to find one more variable's value. This back-substitution proceeds until all variable values have been found.
The process of producing such a matrix is called Gaussian Elimination.
__
The back-substitution process effectively makes the matrix be an identity matrix (diagonal = ones; zeros elsewhere) and the added column be the solution to the system of equations.
To solve a system of equations using the matrix method, you transform the augmented matrix to have zeros below the diagonal through Gaussian elimination. Then, you substitute back into the equations to find the solution.
Explanation:To solve a system of equations using the matrix method, you use elementary row operations to transform the augmented matrix into one with zeros below the diagonal. This is achieved through a method called Gaussian elimination. The goal is to reduce the matrix to its row-echelon form, which leaves zeros below the diagonal. After this reduction, you can then proceed to substitute back into the equations to find the solution.
For example, let's take the system of equations:
x+2y=7
3x-4y=11
This can be represented as an augmented matrix:
[1 2 | 7]
[3 -4 | 11]
Using Gaussian elimination, we can eliminate the '3' below the diagonal by subtracting 3x the first row from the second, getting you:
[1 2 | 7]
[0 -10 | -10]
By substituting, we then find the solutions for the system of equations.
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You are given three white balls, one red ball, and two identical boxes. You are asked to distribute the balls in the boxes in any way you like. You then are asked to select a box (after the boxes have been shuffled) and to pick a ball at random from that box. If the ball is red you win a prize. How should you distribute the balls in the boxes to maximize your chances of winning? Justify your reasoning.
3. Given the differential equation y"+y= 0 and the set of two functions sint-cost, sint + cost, show that this a fundamental set of functions for the equation, and note the interval(s) over which this is true. wken (osxsihx | Cos sint
Answer with explanation:
Given the differential equation
y''+y=0
The two function let
[tex]y_1= sint -cost[/tex]
[tex]y_2=sint+ cost[/tex]
Differentiate [tex]y_1 and y_2[/tex]
Then we get
[tex]y'_1= cost+sint[/tex]
[tex]y'_2=cost-sint[/tex]
Because [tex]\frac{\mathrm{d} sinx}{\mathrm{d} x} = cosx[/tex]
[tex]\frac{\mathrm{d}cosx }{\mathrm{d}x}= -sinx[/tex]
We find wronskin to prove that the function is independent/ fundamental function.
w(x)=[tex]\begin{vmatrix} y_1&y_2\\y'_1&y'_2\end{vmatrix}[/tex]
[tex]w(x)=\begin{vmatrix}sint-cost&sint+cost\\cost+sint&cost-sint\end{vmatrix}[/tex]
[tex]w(x)=(sint-cost)(cost-sint)- (sint+cost)(cost+sint)[/tex]
[tex]w(x)=sintcost-sin^2t-cos^2t+sintcost-sintcost-sin^2t-cos^2t-sintcost[/tex]
[tex]w(x)=-sin^2t-cos^2t[/tex]
[tex]sin^2t+cos^2t=1[/tex]
[tex]w(x)=-2\neq0[/tex]
Hence, the given two function are fundamental set of function on R.
Solve log x=2. A. 2 B. 20 C. 100 D. 1,000
Answer:
100
Step-by-step explanation:
The value of the given logarithm is 100.
What is logarithm?A logarithm is the power to which a number must be raised in order to get some other number.
Given that, log x = 2,
We will solve a logarithmic equation of x by changing it to exponential form.
Now, the logarithmic equation is log₁₀x = 2
Since, we know that, logₐb = x then b = aˣ
Therefore, log₁₀x = 2
x = 10²
x = 100
Hence, the value of the given logarithm is 100.
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What is the mass, in grams, of the object being measured in the triple beam balance shown below?
Snapshot of a triple beam balance. The large slider is at 100 g, the medium slider is at 0 g, and the small slider is at 2.5 g.
Answer:
102.5 g
Step-by-step explanation:
The mass is the sum of the values indicated by the sliders:
100 g + 0 g + 2.5 g = 102.5 g
The mass, in grams, of the object being measured in the triple beam balance shown below is:
102.5 g
Step-by-step explanation:Triple Beam balance--
It is a instrument which is used to measure the mass of an object.
The advantage of using this device is that it measures the mass of an object precisely.
It has three counterweights in it.
One is of 100 gram, other is of 10 gram and the last is of 1 gram.
In order to find the mass of an object we add the weights in all the three sections.
The large slider is at 100 g, the medium slider is at 0 g, and the small slider is at 2.5 g.
100 g+0 g+2.5 g=102.5 g
y is 4 less than the product of 5 and x
y is (replace "is" with an equal sign) 4 less (replace with subtraction sign) than the product (multiply 5 and x) of 5 and x
y = 5x - 4
The reason the answer is like this ^^^ instead of y = 4 - 5x is because for this to be true it would have to say y is 5x less then 4
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
y=5x-4
Step-by-step explanation:
Question about: ⇒ algebraic expression
Y: ⇒ Symbol into letters
is: ⇒ equal sign
less than: ⇒ <
product: ⇒ multiply
y=5x-4 is the correct answer.
I hope this helps you, and have a wonderful day!
What is the Common Factor
3t^5s − 15t^2s^3
Answer:
3t^2s
Step-by-step explanation:
15/3=5
t^5s/t^2s = t^3
t^2s^3/t^2s = s^2
For this case we have by definition, that a polynomial has a common factor when the same quantity, either number or letter, is found in all the terms of the polynomial.
We have the following expression:
[tex]3t ^ 5s-15t ^ 2s ^ 3[/tex]
So we have to:
[tex]3t ^ 2s[/tex] is the lowest common term in the terms of the expression:
[tex]3t ^ 2s (t ^ 3-5s ^ 2)[/tex]
Answer:
[tex]3t ^ 2s[/tex]
The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting (one girl and three boys) in any order right parenthesis.
[tex]|\Omega|=2^4=16\\|A|=4\\\\P(A)=\dfrac{4}{16}=\dfrac{1}{4}[/tex]
For waht values of x do the vectors -1,0,-1), (2,1,2), (1,1, x) form a basis for R3?
The values of x for which the given vectors are basis for R³ is:
[tex]x\neq 1[/tex]
Step-by-step explanation:We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.
We are given three vectors as:
(-1,0,-1), (2,1,2), (1,1, x)
The matrix formed by these vectors is:
[tex]\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right][/tex]
Now, the determinant of this matrix is:
[tex]\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1[/tex]
Hence,
[tex]-x+1\neq 0\\\\\\i.e.\\\\\\x\neq 1[/tex]
From a survey taken several years ago, the starting salaries of individuals with an undergraduate degree from Business Schools are normally distributed with a mean of $40,500 and a standard deviation of $4,500.What is the probability that a randomly selected individual with an undergraduate business degree will get a starting salary of at least $36,000.00? (Round your answer to 4 decimal places.)
Answer: 0.8413
Step-by-step explanation:
Given: Mean : [tex]\mu=\$40,500[/tex]
Standard deviation : [tex]\sigma = \$4,500[/tex]
The formula to calculate z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= $36,000.00, we have
[tex]z=\dfrac{36000-40500}{4500}=-1[/tex]
The P-value = [tex]P(z\geq-1)=1-P(z<-1)=1-0.1586553=0.8413447\approx0.8413[/tex]
Hence, the probability that a randomly selected individual with an undergraduate business degree will get a starting salary of at least $36,000.00 = 0.8413
The probability of a randomly selected individual with an undergraduate business degree having a starting salary of at least $36,000, based on the given normal distribution with a mean of $40,500 and a standard deviation of $4,500, is approximately 0.8413 or 84.13%.
The question asks us to find the probability that a randomly selected individual with an undergraduate business degree will have a starting salary of at least $36,000.00, given that the mean starting salary is $40,500 with a standard deviation of $4,500. This problem can be solved using the properties of the normal distribution.
First, we calculate the z-score, which is the number of standard deviations away from the mean:
Z = (X - μ) / σ
Where X is the salary in question ($36,000), μ is the mean ($40,500), and σ is the standard deviation ($4,500). Plugging in the values:
Z = ($36,000 - $40,500) / $4,500 = -1
The next step is to look up this z-score in a standard normal distribution table or use a calculator with a standard normal distribution function to find the area to the right of this z-score. This area represents the probability we are looking for. Let's assume we found this area to be approximately 0.8413.
Therefore, the probability that a randomly selected individual with an undergraduate business degree will have a starting salary of at least $36,000 is about 0.8413 or 84.13%.
which statement regarding the function y=sin(x) is true?
a. Reflection over the y-axis will not change the graph since sine is an even function
b. Sin(x)=sin(-x)
c. Reflection over either the x-axis or y-axis will change the graph
d. Sin(x)=-sin(x)
c. Reflection over either the x-axis or y-axis will change the graph
Step-by-step explanation:a. Reflection over the y-axis will not change the graph since sine is an even function.This is false because [tex]y=sin(x)[/tex] is an odd function, not an even one. This means that [tex]sin(-x)=-sin(x)[/tex], and a reflection over the y-axis will change the graph.
b. Sin(x)=sin(-x)This is false because we said that [tex]sin(-x)=-sin(x)[/tex]
c. Reflection over either the x-axis or y-axis will change the graphThis is true. Since [tex]sin(x)[/tex] is an odd function, then reflection over either the x-axis or y-axis will change the graph as we said in a. So, for [tex]f(x)[/tex]:
REFLEXION IN THE X-AXIS:
[tex]h(x)=-f(x)[/tex]
REFLEXION IN THE Y-AXIS:
[tex]h(x)=f(-x)[/tex]
d. Sin(x)=-sin(x)False by the same explanation as b.
The correct statement about the function y=sin(x) is that Reflection over either the x-axis or y-axis will change the graph. Therefore, option C is the correct answer.
The statement regarding the function y=sin(x) which is true is that reflection over either the x-axis or y-axis will change the graph.
This is because the sine function is an odd function, meaning that it has rotational symmetry about the origin. A characteristic of odd functions is that they satisfy the identity y(-x) = -y(x), not y(-x) = y(x), which describes an even function.
Therefore, the assumption Sin(x)=Sin(-x) would be incorrect, as it does not reflect the odd nature of the sine function. Thus, the correct answer is c. Reflection over either the x-axis or y-axis will change the graph.
A sample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8. a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M? b. If the sample has n = 16 scores, what is the expected value of M and the standard error of M? Gravetter, Frederick J. Statistics for The Behavioral Sciences (p. 221). Cengage Learning. Kindle Edition.
Answer:
a) The expected value of M = 40
The standard error for M = 4
b) The expected value of M = 40
The standard error for M = 2
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called the expected
value of M
- It is equal to the population mean μ
- The standard deviation of the distribution of sample means is called
the standard error of M
- The rule of standard error is σM = σ/√n , where σ is the standard
deviation and n is the size of the sample
* lets solve the problem
- A sample is selected from a population
∵ The mean of the population μ = 40
∵ The standard deviation σ = 8
a) The sample has n = 4 scores
∵ The expected value of M = μ
∵ μ = 40
∴ The expected value of M = 40
∵ The standard error of M = σ/√n
∵ σ = 8 and n = 4
∴ σM = 8/√4 = 8/2 = 4
∴ The standard error for M = 4
b) The sample has n = 16 scores
∵ The expected value of M = μ
∵ μ = 40
∴ The expected value of M = 40
∵ The standard error of M = σ/√n
∵ σ = 8 and n = 16
∴ σM = 8/√16 = 8/4 = 2
∴ The standard error for M = 2
When the sample has n = 4 scores then the expected value of M is 40 and the standard error of M is 4.
When the sample has n = 16 scores then the expected value of M is 40 and the standard error of M is 2.
Given
A sample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8. a. If the sample has n = 4 scores.
What is the expected value of M?The mean of the distribution of sample means is called the expected value of M.
The standard deviation of the distribution of sample means is called the standard error of M.
1. The sample has n = 4 scores
The expected value of M = μ
The expected value of M = 40
The standard error of M is;
[tex]\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 4}\\\\ Standard \ error=\dfrac{8}{\sqrt{4}}\\\\ Standard \ error=\dfrac{8}{2}\\\\ Standard \ error=4[/tex]
The standard error for M = 4
2. 1. The sample has n = 16 scores
The expected value of M = μ
The expected value of M = 40
The standard error of M is;
[tex]\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 16}\\\\ Standard \ error=\dfrac{8}{\sqrt{16}}\\\\ Standard \ error=\dfrac{8}{4}\\\\ Standard \ error=2[/tex]
The standard error for M = 2
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The value of X is??
for this case we have that by definition, the sum of the internal angles of a traingule is 180 degrees.
In addition, the angle "R" of the triangle is given by:
[tex]R = 180-45x[/tex]
So, we have to:
[tex](180-45x) + 25x + (57 + x) = 180\\180-45x + 25x + 57 + x = 180\\-45x + 25x + 57 + x = 0\\-45x + 25x + x = -57\\-19x = -57\\x = \frac {57} {19}\\x = 3[/tex]
Answer:
[tex]x = 3[/tex]
hi i’m not sure how to do question 20 if u could explain how to do it that’d b great !!
Answer:
A) -2
Step-by-step explanation:
The form is indeterminate at x=0, so L'Hopital's rule applies. The resulting form is also indeterminate at x=0, so a second application is required.
Let f(x) = x·sin(x); g(x) = cos(x) -1
Then f'(x) = sin(x) +x·cos(x), and g'(x) = -sin(x).
We still have f'(0)/g'(0) = 0/0 . . . . . indeterminate.
__
Differentiating numerator and denominator a second time gives ...
f''(x) = 2cos(x) -sin(x)
g''(x) = -cos(x)
Then f''(0)/g''(0) = 2/-1 = -2
_____
I like to start by graphing the expression to see if that is informative as to what the limit should be. The graph suggests the limit is -2, as we found.
Find the general solution of the given differential equation. x dy dx − y = x2 sin(x) Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.
[tex]x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x[/tex]
Divide both sides by [tex]x^2[/tex]. In doing so, we force any possible solutions to exist on either [tex](-\infty,0)[/tex] or [tex]\boxed{(0,\infty)}[/tex] (the "positive" interval in such a situation is usually taken over the "negative" one) because [tex]x[/tex] cannot be 0 in order for us to do this.
[tex]\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x[/tex]
Condense the left side as the derivative of a product, then integrate both sides and solve for [tex]y[/tex]:
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac yx\right]=\sin x[/tex]
[tex]\dfrac yx=\displaystyle\int\sin x\,\mathrm dx[/tex]
[tex]\boxed{y=Cx-x\cos x}[/tex]
The general solution of a differential equation is to write y as a function of x.
The general solution of [tex]x \frac{dy}{dx} - y = x^2 \sin(x)[/tex] is [tex]y = -x\cos(x) + cx[/tex].The interval of the solution is [tex](0, \infty)[/tex]Given
[tex]x \frac{dy}{dx} - y = x^2 \sin(x)[/tex]
Divide through by x
[tex]\frac{x}{x} \frac{dy}{dx} -\frac{y}{x} = \frac{x^2}{x} \sin(x)[/tex]
[tex]\frac{dy}{dx} -\frac{y}{x} = x \sin(x)[/tex]
Let P be function of x. Such that:
[tex]P(x) = -\frac 1x[/tex]
So, we have:
[tex]\frac{dy}{dx} +yP(x) = x\sin(x)[/tex]
Calculate the integrating factor I(x).
So, we have:
[tex]I(x) = e^{\int P(x) dx[/tex]
Substitute [tex]P(x) = -\frac 1x[/tex]
[tex]I(x) = e^{\int-\frac 1x dx[/tex]
Rewrite as:
[tex]I(x) = e^{-\int\frac 1x dx[/tex]
Integrate
[tex]I(x) = e^{-\ln(x)[/tex]
[tex]I(x) = \frac 1x[/tex]
So, we have:
[tex]\frac{dy}{dx} -\frac{y}{x} = x \sin(x)[/tex]
[tex][\frac{dy}{dx} -\frac{y}{x}] \frac 1x = [x \sin(x)] \frac 1x[/tex]
[tex][\frac{dy}{dx} -\frac{y}{x}] \frac 1x =\sin(x)[/tex]
Introduce [tex]I(x) = \frac 1x[/tex].
So, we have:
[tex]\frac{d}{dx}(\frac yx) = \sin(x)[/tex]
Multiply both sides by dx
[tex]d(\frac yx) = \sin(x)\ dx[/tex]
Integrate with respect to x
[tex]\frac yx = -\cos(x) + c[/tex]
Multiply through by x
[tex]y = -x\cos(x) + cx[/tex]
So, the general solution is: [tex]y = -x\cos(x) + cx[/tex], and the interval is [tex](0, \infty)[/tex]
Read more about general solution of a differential equation at:
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HELP PLEASEEE, I REALLY DO NOT UNDERSTAND THESE QUESTIONS. THANK YOU HELP IS VERY MUCH APPRECIATED!!!
5) The mean salary of 5 employees is $40300. The median is $38500. The lowest paid employee's salary is $32000. If the lowest paid employee gets a $3100 raise, then ...
a) What is the new mean?
New Mean = $
b) What is the new median?
New Median = $
Answer:
a) $40920
b) $38500
Step-by-step explanation:
Given:
5 employees,
Mean = $40300
Median = $38500
Min = $32000
If he lowest paid employee gets a $3100 raise, then his salary becomes
$32000+$3100=$35100
a) If the mean was $40300, then the sum of 5 salaries is
[tex]\$40300\cdot 5=\$201500[/tex]
After raising the lowest salary the sum becomes
[tex]\$201500+\$3100=\$204600[/tex]
and new mean is
[tex]\dfrac{\$204600}{5}=\$40920[/tex]
b) The lowest salary becomes $35100. It is still smaller than the median, so the new median is the same as the old one.
New median = $38500
What is the area of this composite figure?
Answer:
88 ft²
Step-by-step explanation:
Area of larger square
10 × 8 = 80
10 × 8 because 10 is the length and 8 because the 6 and 2 rectangle is missing so it wouldn't be 10 × 10
4 × 2 = 8
4 × 2 = 8 because we need to work out the area of the smaller rectangle
80 + 8 = 88
At a certain school, intro to economics and intro to calculus meet at the same time, so it is impossible for a student take both classes. If the probability that a student takes intro to economics is 0.57, and the probability that a student takes intro to calculus 0.17, what is the probability that a student takes intro to economics or into to calculus?
Answer:
0.74
Step-by-step explanation:
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.57 + 0.17 - 0
P(A∪B) = 0.74
The probability of A∩B is zero because the classes are mutually exclusive.
Twenty switches in an office computer network are to be connected so that each switch has a direct connection to exactly three other switches. How many connections will be necessary?
Answer:
30 connections
Step-by-step explanation:
20 switches with 3 connections each will have a total of 20×3 = 60 connections. That counts each connecting link twice, so only 30 connecting links are required.
Answer:
30 Connections!
Step-by-step explanation:
I did this on AoPs :)