Answer: [tex]H_0:\mu\geq431\\\\H_a:\mu<431[/tex]
Step-by-step explanation:
Given : A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 431 gram setting. t is believed that the machine is underfilling the bags.
Claim : [tex]\mu<431[/tex]
We know that the null hypothesis always have equals sign , then the required set of hypothesis for the situation :-
[tex]H_0:\mu\geq431\\\\H_a:\mu<431[/tex]
A grocery bag can be classified as either paper or plastic. Suppose that 97% of grocery bags are classified as plastic. (a) Two grocery bags are chosen at random. What is the probability that both grocery bags are plastic? (b) Five grocery bags are chosen at random. What is the probability that all five grocery bags are plastic? (c) What is the probability that at least one of five randomly selected grocery bags is paper? Would it be unusual that at least one of five randomly selected grocery bags is paper?
Answer with explanation:
Given : The probability of grocery bags are classified as plastic = 0.97
(a) f two bags are chosen at random.
Then , the probability that both grocery bags are plastic is given by :-
[tex]^2C_2(0.97)^2(1-0.97)^0=0.9409[/tex]
(b) If five grocery bags are chosen at random.
Then , the probability that all five grocery bags are plastic is given by :-
[tex]^5C_5(0.97)^5(1-0.97)^0\approx0.8587[/tex]
(c) The probability of getting paper = 1-0.97=0.03
The probability that at least one of five randomly selected grocery bags is paper :-
[tex]P(x\geq1)=1-P(0)\\\\1-^5C_0(0.03)^0(0.97)^5\\\\=1-(0.03)^0(0.97)^5=0.1412659\approx0.14>0.05[/tex]
Thus , it would not be unusual that at least one of five randomly selected grocery bags is paper.
Probability is used to determine the chances of an event
The probability that both grocery bags are plastic is 0.9409The probability that all five grocery bags are plastic is 0.8587The probability that at least one grocery bags is paper is 0.1413It would not be unusual that at least one of five randomly selected grocery bags is paper.[tex]p = 97\%[/tex] -- chances that a bag is plastic
(a) Both plastics selected are plastic
This is calculated as:
[tex]P(2) = p^2[/tex]
So, we have:
[tex]P(2) = (97\%)^2[/tex]
[tex]P(2) = 0.9409[/tex]
Hence, the probability that both grocery bags are plastic is 0.9409
(b) All five are plastic
This is calculated as:
[tex]P(5) = p^5[/tex]
So, we have:
[tex]P(5) = (97\%)^5[/tex]
[tex]P(5) = 0.8587[/tex]
Hence, the probability that all five grocery bags are plastic is 0.8587
(c) At least one of the five is paper
The probability that none of the five is paper is the same as the probability that all five is plastic.
So:
[tex]P(None) = 0.8587[/tex]
Using complement rule,
[tex]P(At\ least\ 1) = 1 - P(None)[/tex]
So, we have
[tex]P(At\ least\ 1) = 1 - 0.8587[/tex]
[tex]P(At\ least\ 1) = 0.1413[/tex]
Hence, the probability that at least one grocery bags is paper is 0.1413
The above probability is greater than 0.05
Hence, it would not be unusual that at least one of five randomly selected grocery bags is paper.
Read more about probabilities at:
https://brainly.com/question/11234923
Vernon’s work for finding the value of x is shown below.

Step 1: 16x + 8 = 76
Step 2: 16x = 68
Step 3: x = 4.25
Did Vernon solve for the correct value of x? If not, explain where he made his error.
Yes, he solved for the correct answer.
No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other.
No, he should have added 8 to both sides rather than subtracting 8 from both sides.
No, he should have multiplied both sides by 16 rather than dividing both sides by 16.
Answer:
No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other.
Step-by-step explanation:
He was using the measurements of m∠AED & m∠CED, which are supplementary angles, not vertical angles (therefore making them, when combined, equal to 180°).
If they were vertical angles (at the case of m∠AED & m∠BEC, or the other pair), then yes, they will be congruent. But in this case, they are not, so you don't solve it like they are vertical angles.
~
Answer:
B is the answer.
Step-by-step explanation:
Yes, he solved for the correct answer.
No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather than setting ∠AED and ∠DEC equal to each other.
No, he should have added 8 to both sides rather than subtracting 8 from both sides.
No, he should have multiplied both sides by 16 rather than dividing both sides by 16.
Pierre sold 340 tickets for a concert. Balcony tickets cost $5 while tickets for the lower floor cost $10. If Pierre sold $2,700 worth of tickets, how many lower floor tickets did he sell?
Answer:
He sold 200 lower floor tickets.
Step-by-step explanation:
Consider the provided information.
Pierre sold 340 tickets for a concert.
Let Balcony tickets represents by x and lower floor ticket represents by y.
As we know he sold 340 tickets in total, i.e.
x + y = 340 ......(1)
Balcony tickets cost $5 while tickets for the lower floor cost $10.
If he sold x balcony tickets, so the money he got after selling x balcony tickets is 5x. Similarly, If he sold y lower floor tickets, so the money he got after selling y lower floor tickets is 10y.
Pierre sold $2,700 worth of tickets, i.e.
5x + 10y = 2700 ......(2)
Now use elimination method to solve the system of equations:
Multiply the equation (1) with 5 and subtract them as shown below:
5x + 5y = 1700
5x + 10y = 2700
_____________
-5y = -1000
y = 200
Thus, he sold 200 lower floor tickets.
Madison is picking out some movies to rent, and she has narrowed down her selections to 7 foreign films, 3 horror films, 6 action movies, and 4 dramas. How many different combinations of 9 movies can she rent if she wants all 4 dramas?
Final answer:
Madison can choose from 4368 different combinations of 9 movies, including all 4 dramas and 5 out of the 16 non-drama movies.
Explanation:
Madison is picking out movies to rent and wants all 4 dramas out of her 9 selections. With 7 foreign films, 3 horror films, 6 action movies, and 4 dramas, the total number of non-drama movies is 16 (7+3+6). Since she must select all 4 dramas, she needs to choose the remaining 5 movies from the 16 non-drama movies available.
To find how many different combinations of 9 movies she can rent, we use the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of items to choose from, r is the number of items to choose, and ! denotes factorial, representing the product of all positive integers up to that number.
The question asks us to calculate C(16, 5) because Madison is choosing 5 movies out of the 16 non-drama movies. This calculation yields:
C(16, 5) = 16! / [5!(16-5)!] = 4368
Therefore, there are 4368 different combinations of 9 movies Madison can rent if she wants all 4 dramas.
Find the area of the region trapped between LaTeX: y=1-2x^2 y = 1 − 2 x 2 and LaTeX: y=\left|x\right| y = | x | , shown above. The answer is LaTeX: \frac{A}{12} A 12 . Below, enter only the whole number LaTeX: A A .
The area is given by the integral,
[tex]\displaystyle\int_{-1/2}^{1/2}(1-2x^2-|x|)\,\mathrm dx[/tex]
The integrand is even, so we can simplify the integral somewhat as
[tex]\displaystyle2\int_0^{1/2}(1-2x^2-|x|)\,\mathrm dx[/tex]
When [tex]x\ge0[/tex], we have [tex]|x|=x[/tex], so this is also the same as
[tex]\displaystyle2\int_0^{1/2}(1-2x^2-x)\,\mathrm dx[/tex]
which has a value of
[tex]2\left(x-\dfrac23x^3-\dfrac12x^2\right)\bigg|_0^{1/2}=2\left(\dfrac12-\dfrac1{12}-\dfrac18\right)=\boxed{\dfrac7{12}}[/tex]
so that A = 7.
If a 42-piece set of stainless steel flatware costs $113.40 at a certain store, what is the cost (in dollars) per piece?
Answer:$2.7 dollars per piece
Step-by-step explanation: Divide 113.40 by 42
$2.7 per piece is the answer.
$113.40 / 42 piece set of stainless steel = $2.7
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
What are problem-solving and examples?Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Learn more about Problem-solving here: brainly.com/question/13818690
#SPJ2
In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where f(x, y, z) is evaluated at the center (xi, yj, zk) of the box Bijk. Use the Midpoint Rule to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.)triple integrals of cos(xyz) dV,where B = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2}
To approximate the volume with 8 boxes, we have to split up the interval of integration for each variable into 2 subintervals, [0, 1] and [1, 2]. Each box will have midpoint [tex]m_{i,j,k}[/tex] that is one of all the possible 3-tuples with coordinates either 1/2 or 3/2. That is, we're sampling [tex]f(x,y,z)=\cos(xyz)[/tex] at the 8 points,
(1/2, 1/2, 1/2)
(1/2, 1/2, 3/2)
(1/2, 3/2, 1/2)
(3/2, 1/2, 1/2)
(1/2, 3/2, 3/2)
(3/2, 1/2, 3/2)
(3/2, 3/2, 1/2)
(3/2, 3/2, 3/2)
which are captured by the sequence
[tex]m_{i,j,k}=\left(\dfrac{2i-1}2,\dfrac{2j-1}2,\dfrac{2k-1}2\right)[/tex]
with each of [tex]i,j,k[/tex] being either 1 or 2.
Then the integral of [tex]f(x,y,z)[/tex] over [tex]B[/tex] is approximated by the Riemann sum,
[tex]\displaystyle\iiint_B\cos(xyz)\,\mathrm dV\approx\sum_{i=1}^2\sum_{j=1}^2\sum_{k=1}^2\cos m_{i,j,k}\left(\frac{2-0}2\right)^2[/tex]
[tex]=\displaystyle\sum_{i=1}^2\sum_{j=1}^2\sum_{k=1}^2\cos\frac{(2i-1)(2j-1)(2k-1)}8[/tex]
[tex]=\cos\dfrac18+3\cos\dfrac38+3\cos\dfrac98+\cos\dfrac{27}8\approx\boxed{4.104}[/tex]
(compare to the actual value of about 4.159)
The Midpoint Rule for triple integrals approximates the integral of a function by taking the function's value at the midpoint of sub-boxes into which the domain is divided. In this problem, B is divided into eight 1x1x1 sub-boxes, and cos(xyz) is evaluated at each sub-box's center.
Explanation:The Midpoint Rule for triple integrals is a method for approximating the value of a triple integral over a box B by dividing the box into smaller sub-boxes and evaluating the function at the midpoint of each sub-box.
For the given integral of cos(xyz) over the box B defined by the ranges 0 ≤ x ≤ 2, 0 ≤ y ≤ 2, and 0 ≤ z ≤ 2, we are asked to divide B into eight sub-boxes of equal size.
This involves calculating the midpoints for each sub-box (xi, yj, zk) and then evaluating the function at these points.
The size of each sub-box would be 1 x 1 x 1 since the original box dimensions are 2 x 2 x 2.
The midpoints for the sub-boxes will be at (0.5, 0.5, 0.5), (0.5, 0.5, 1.5), (0.5, 1.5, 0.5), (0.5, 1.5, 1.5), (1.5, 0.5, 0.5), (1.5, 0.5, 1.5), (1.5, 1.5, 0.5), and (1.5, 1.5, 1.5).
The volume of each sub-box is 1, so the Riemann sum becomes the sum of cos(xyz) evaluated at these midpoints times the volume of each sub-box.
After calculating the Riemann sum, it provides an approximate value for the triple integral.
The actual calculation would require substituting each midpoint into the function cos(xyz) to get the respective value for each sub-box, then summing these values and finally multiplying by the volume of a single sub-box to get an approximation for the entire integral.
PROBLEM 1 Verify that the differential equation (2x y)dx +(x - 6y)dy = 0 is exact and then solve the associated differential equation
Answer with explanation:
⇒(2 x y )d x+(x-6 y) d y=0
P= 2 x y
Q=x-6 y
[tex]P_{y}=2 x\\\\Q_{x}=1[/tex]
So this Differential Equation is exact.
To solve this, we will first evaluate,[tex]\varphi (x,y)[/tex].
[tex]\varphi_{x}=P\\\\\varphi_{y}=Q\\\\\varphi=\int P d x\\\\= \int 2 x y dx\\\\\varphi=x^2 y\\\\\varphi(x,y)=x^2y+k(y)------(1)[/tex]
Differentiating with respect to , y
[tex]\varphi'(x,y)=x^2+k'(y)=Q=x-6 y\\\\\rightarrow x-6 y-x^2=k'(y)\\\\ k(y)=\int (x-6 y -x^2) dy\\\\k(y)=x y-3 y^2-x^2 y+f\\\\\varphi(x,y)=x^2y+x y-3 y^2-x^2 y+f\\\\\varphi(x,y)=x y-3 y^2+f[/tex]
Substituting the value of , k(y) in equation 1.
This is required Solution of exact differential equation.
if abc=1 prove that 1/(1+a+b^-1) + 1/(1+b+c^-1) +1/(1+c+a^-1) =1
Answer with explanation:
It is given that, abc=1
[tex]\rightarrow \frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}\\\\\rightarrow \frac{b}{b+ab+1}+\frac{c}{c+bc+1}+\frac{a}{a+ac+1}\\\\abc=1\\\\\rightarrow \frac{b}{b+ab+abc}+\frac{c}{c+bc+abc}+\frac{a}{a+ac+abc}\\\\\rightarrow \frac{1}{1+a+ac}+\frac{1}{1+b+ab}+\frac{1}{1+c+bc}\\\\\rightarrow \frac{1}{abc+a+ac}+\frac{1}{1+b+ab}+\frac{1}{1+c+bc}\\\\\rightarrow \frac{1+a}{a(bc+1+c)}+\frac{c}{c+bc+1}\\\\\rightarrow\frac{1+a+ac}{a(bc+1+c)}\\\\\rightarrow\frac{1+a+ac}{abc+a+ac)}\\\\\rightarrow\frac{1+a+ac}{1+a+ac)}\\\\=1[/tex]
Hence proved.
Answer:
ABC=1
Step-by-step explanation:
A client has an order for 1000 mL 0.45 Saline to be infused over 8 hours. How many mL/hr should the IV pump be programmed for?
Answer:
125 mL/h
Step-by-step explanation:
Intravenous pumps are used when there is a need of constant pumping of fluids into the body. Injecting every hour with the required volume causes damage.
Volume of 0.45 saline = 1000 mL
Time to be infused = 8 hours
The Intravenous pump should be programmed in the following way
[tex]\frac{Volume}{time}=\frac{1000}{8}\\\Rightarrow flow\ rate=125\ mL/hr[/tex]
Hence, the IV pump should be programmed for 125 mL/hr.
How much should you invest now at 7 1/4% simple annual interest in order to earn $190 interest in 4 months?
Answer:
so principal amount is $7862.07
Step-by-step explanation:
Given data
rate = 7*1/4 % = 29/4 %
interest = $190
time = 4 months = 4/12 year
to find out
principal
solution
we know the simple interest formula i.e.
interest = ( principal × rate × time ) /100 ..................1
now put all value rate time and interest in equation 1 we get interest here
interest = ( principal × rate × time ) /100
190 = ( principal × 29/4 × 4/12 ) /100
principal = 190 × 12 ×100 / 29
principal = 7862.068966
so principal amount is $7862.07
help please, really confused
Answer:
1a. y = 5x +3
1b. y = -1/7x + 2
1c. y = 2x +3
2a. y = -1/2x +3; slope = -1/2, y-intercept = +3
2b. y = 3/2x +6; slope = 3/2, y-intercept = +6
Step-by-step explanation:
Apparently the "y-intercept form" referred to is the one more commonly called "slope-intercept form." That form is ...
y = mx + b . . . . . . . . m is the slope; b is the y-intercept
You arrive at this form by solving each equation for y. You do that the same way you solve any equation for any variable: undo what is done to the variable of interest.
In these general form equations, the y-variable term has a value multiplying y and some other terms added to that. First of all, you subtract the added terms (from both sides of the equation). This transforms ...
ax +by +c = 0
into
by = -ax -c
Next, you divide by the constant that is multiplying y. Of course all terms on both sides of the equation are divided by that, so you now have ...
y = (-a/b)x -c/b
The slope is -a/b, and the y-intercept is -c/b.
___
1a. 5x -y +3 = 0
-y = -5x -3 . . . . . subtract non-y terms
y = 5x +3 . . . . . . divide by -1
__
1b. x +7y -14 = 0
7y = -x +14 . . . . . subtract non-y terms
y = -1/7x +2 . . . . .divide by 2
__
1c. 6x -3y +9 = 0
-3y = -6x -9 . . . . subtract terms not containing y
y = 2x +3 . . . . . . divide by -3
__
2a. x +2y -6 = 0
2y = -x +6 . . . . . subtract non-y terms
y = -1/2x +3 . . . . divide by 2 -- this is graphed as the red line below
__
2b. 3x -2y +12 = 0
-2y = -3x -12 . . . . subtract non-y terms
y = 3/2x +6 . . . . . divide by -2 -- this is graphed as the blue line below
_____
Comment on the 2nd problem
Of course, the y-intercept (constant term in slope-intercept form) is the point on the y-axis where the line crosses. The slope tells you the ratio of "rise" to "run". That is, a slope of -1/2 means the line drops one unit for each 2 units it goes to the right. A slope of 3/2 means the line increases (rises) by 3 units for each 2 units it goes to the right.
Determine whether f(x) = –5x^2 – 10x + 6 has a maximum or a minimum value.
Find that value and explain how you know
First,
We are dealing with parabola since the equation has a form of,
[tex]y=ax^2+bx+c[/tex]
Here the vertex of an up - down facing parabola has a form of,
[tex]x_v=-\dfrac{b}{2a}[/tex]
The parameters we have are,
[tex]a=-5,b=-10, c=6[/tex]
Plug them in vertex formula,
[tex]x_v=-\dfrac{-10}{2(-5)}=-1[/tex]
Plug in the [tex]x_v[/tex] into the equation,
[tex]y_v=-5(-1)^2-10(-1)+6=11[/tex]
We now got a point parabola vertex with coordinates,
[tex](x_v, y_v)\Longrightarrow(-1,11)[/tex]
From here we emerge two rules:
If [tex]a<0[/tex] then vertex is max valueIf [tex]a>0[/tex] then vertex is min valueSo our vertex is minimum value since,
[tex]a=-5\Longleftrightarrow a<0[/tex]
Hope this helps.
r3t40
Compute the total and annual return on the following investment Five years after paying $2900 for shares in a startup company, you sell the shares for $1900 (at a loss). The total return is (Do not round until the final answer Then round to the nearest tenth as needed) The annual return is (Do not round until the final answer. Then round to the nearest tenth as needed)
Answer:
total return is -34.4828 % and The annual return is - 8.1094 %
Step-by-step explanation:
given data
principal amount of share = $2900
selling amount pay = $1900
time period (t) = 5 years
to find out
total return and The annual return
solution
we know interest formula
amount = principal [tex](1 + r/100)^{t}[/tex]
put all these value amount principal, time n we get rate
1900 = 2900 [tex](1 + r/100)^{5}[/tex]
[tex](1 + r/100)^{5}[/tex] = 1900/2900
1 + r/100 = 0.9189
r = −8.1094
The annual return is - 8.1094 %
and total return is ((selling amount pay - principal amount ) / principal amount ) × 100
put these value and we get total return
total return = ((1900 - 2900) / 2900 ) × 100
total return = -0.344828 × 100
total return = -34.4828 %
discrete math:
find the rule for determining when a number is divisible by 11.
Answer:
Step-by-step explanation:
Divisibility rule when a number is divisible by 11:
Take the alternating sum of digits in a number read from left to right .If that is divisible by 11 then the the given number is divisible by 11.
It is a divisibility rule of 11.
Let 1342 is a number .The number is divisible by 11 or not
Alternating sum of digits =1-3+4-2=0
The alternating sum of digits is divisible by 11 .
Therefore, the number 1342 is divisible by 11.
Let a number 2728
Alternating sum of digits = 2-7+2-8=-11.
The alternating sum of digits is divisible by 11 .
Therefore, the number 2728 is divisible by 11.
The rule for determining divisibility by 11 involves alternately adding and subtracting a number's digits; if the result is 0 or divisible by 11, the original number is too. Examples illustrate the application of the divisibility test.
Rule for Divisibility by 11
The rule for determining when a number is divisible by 11 is quite straightforward. To apply the rule, you alternate between adding and subtracting the digits of the number in question from left to right. If the resulting sum (which may be negative) is 0 or divisible by 11 itself, then the original number is divisible by 11. For example, consider the number 2728. Apply the rule like this: 2 - 7 + 2 - 8 = -11. Since -11 is divisible by 11, 2728 is also divisible by 11.
Examples
Another example: Take the number 5831. Using the rule: 5 - 8 + 3 - 1 = -1, which is not divisible by 11, hence 5831 is not divisible by 11.
This divisibility test is a fantastic example of how certain mathematical rules are used to quickly determine properties of numbers without needing to perform long divisions.
The graph is a transformation of one of the basic functions. Find the equation that defines the function.
Answer:
f(x) = -logx + 4.
Step-by-step explanation:
y = -log x approaches the point (0, 1) but this approaches (0, 5)
Looks like the graph of - log x + 4.
Answer:
[tex]y = 5-\sqrt{x}[/tex]
Step-by-step explanation:
Note that the graph shown is a transformation of the parent function
[tex]y = \sqrt{x}[/tex]
The main function cuts the x-axis at x = 0 and has no negative values of y. In addition, the main function is always growing.
Note that the function shown is decreasing and intercepts the y-axis at y = 5.
Therefore, the graph of the main function has been reflected on the x-axis and displaced 5 units upwards.
If we do y = f(x) then to reflect the main function on the x-axis and move it upwards 5 units we make the following transformation
[tex]y = -f(x) + 5[/tex].
Then the graphed function is:
[tex]y = 5-\sqrt{x}[/tex]
Use De Morgan's laws to write an equivalent statement for the sentence. The bus does not have an engine or the people do not have money.
Which statement is equivalent to the given sentence?
A. It is false that the bus has an engine and the people have money.
B. The bus has an engine and the people have money.
C. It is false tht the bus has an engine or the people have money.
D. The bus has an engine and the people do not have money.
Please show work legibly as I do not see well.
Answer:
A. It is false that the bus has an engine and the people have money.
Step-by-step explanation:
Given statement is -
The bus does not have an engine or the people do not have money.
The De Morgan's laws states that the complement of the union of two given sets is the intersection of their complements.
Also, the complement of the intersection of these two sets is the union of their complements.
negative (p ∨ q)⇔ p ∧ negative q
So, here option A is correct. It is false that the bus has an engine and the people have money.
Final answer:
Using De Morgan's laws, the equivalent statement for 'The bus does not have an engine or the people do not have money' is 'It is not the case that the bus has an engine and the people have money,' which corresponds to answer choice A.
Explanation:
The question asks to use De Morgan's laws to write an equivalent statement for the sentence: "The bus does not have an engine or the people do not have money." Let's denote 'the bus has an engine' by A and 'the people have money' by B. The original statement can be written in logical form as ¬A ∨ ¬B, which using De Morgan's laws, translates to ¬(A ∧ B). This means that the equivalent statement is: "It is not the case that the bus has an engine and the people have money." Therefore, the correct answer is A.
Solve the inequality and graph the solution on a number line.
–3(5y – 4) ≥ 17
please show work!
Answer:
Step-by-step explanation:
In order to solve the inequality, follow the simple steps:
–3(5y – 4) ≥ 17 .
Dividing both sides with -3:
5y - 4 ≤ -17/3 (the sign of the inequality becomes opposite whenever a negative number is either multiplied or divided on both the sides of the inequality).
Adding 4 on both sides:
5y ≤ -5/3
Dividing 5 on both sides:
y ≤ -1/3.
This shows that all the values of y less than and equal to -1/3 satisfy the inequality.
The number line has been attached. Since it involves ≤ sign, therefore, a filled circle will be used to plot the inequality. Less than means that all the values on the left hand side of the number line will be included. This is denoted with an arrow (see the diagram)!!!
Dopamine is available as 400 mg in 250 mL of D5W. A 2 year old weighing 12 kg is receiving 10 mcg/kg/min. How many hours will the infusion last?
Answer:
55.5556 hours.
Step-by-step explanation:
Let's solve the problem.
The amount of dopamine rate applied to a person is based on the formula: 10mcg/kg/min. Such relation can be express as follows:
(10mcg/kg/min)=
(10mcg/kg)*(1/min)
Now by multiplying by the weight (12 kg) of the 2 years old person, we have:
(10mcg/kg)*(1/min)*(12kg)=
(10mcg*12kg/kg)*(1/min)=
(120mcg)*(1/min)=
120mcg/min, which is the rate of dopamine infusion, which can be express as:
(120mcg/min)*(60min/1hour)=
(120mcg*60min)/(1hour*1min)=
7200mcg/hour=
1hour/7200mcg, which means that for each hour, 7200mcg dopamine are infused.
Because the D5W product has 400 mg of dopamine, then we need to convert 400 mg to X mcg of dopamine in order to use the previous obtained rate. This means:
Because 1mcg=0.001mg then:
(400mg)*(1mcg/0.001mg)=
(400mg*1mcg)/(0.001mg)=
400000mcg, which is the amount of dopamine in D5W.
Now, using the amount of dopamine in D5W and the applied rate we have:
(rate)*(total amount of dopamine)=hours of infusion
(1hour/7200mcg)*(400000mcg)=hours of infusion
(1hour*400000mcg)/(7200mcg)=hours of infusion
(55.5556 hours) =hours of infusion
In conclusion, the infusion will last 55.5556 hours.
Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach? 1.3 ft 2.6 ft 26.0 ft 27.6 ft
Answer:
Option D.
Step-by-step explanation:
Arianna kicks a soccer ball into the air with an initial velocity = 42 feet per second
If the starting height of the ball is 0 feet then we have to find the approximate maximum height the soccer ball attached.
Since we know vertical motion is represented by
v² = u² - 2gh
Where v = final velocity of the object
u = initial velocity of the object
g = gravitational force
h = h = maximum height achieved by the object
Here v = 0, u = 42 feet per second and g = 32 feet per second²
Now we plug in these values in the formula
0 = (42)² - 2(32)(h)
1764 = 64h
[tex]h=\frac{1764}{64}[/tex]
h = 27.56 feet
≈ 27.60 feet
Therefore, maximum height achieved by the soccer ball is 27.6 feet.
Option D is the answer.
Answer:
Option D is 2.76 ft
Step-by-step explanation:
Its correct
Suppose that a movie theater snack bar turns over its inventory of candy 3.3 times per month. (Round your answer to 2 decimal places.) If the snack bar has an average of 340 boxes of candy in inventory, what is its average daily sales rate for candy
Answer:
The average daily sales rate for candy is 37.4.
Step-by-step explanation:
We know that,
[tex]\text{Inventory turnover }= \frac{\text{Total sale}}{\text{Average inventories}}[/tex]
[tex]\implies \text{Total sale}=\text{Inventory turnover }\times \text{Average inventories}[/tex]
Given,
Inventory turnover of candies = 3.3,
Average inventories = 340
So, sale of candies = 3.3 × 340 = 1122
Now,
[tex]\text{Average daily sales rate}=\frac{\text{total sale}}{\text{Number of days}}[/tex]
Since, 1 month = 30 days ( approx ),
Hence, the average daily sales rate for candy = [tex]\frac{1122}{30}[/tex]=37.4
Thorium 234 is a radioactive substance that decays at a rate proportional to the amount present. 1 gram of this material is reduced to 0.8 grams in one week
(a) Find an expression that expresses the amount of Thorium 234 present at any time
(b) Find half life of Thorium 234
(c) Find amount of Thorium 234 present after 10 weeks
Answer: a) [tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
b) 3.15 weeks.
c) 0.11 grams
Step-by-step explanation:
a) radioactive decay follows first order kinetics and thus Expression for rate law for first order kinetics is given by:
[tex]k=\frac{2.303}{t}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = ?
t = time taken for decomposition = 1 week
a = initial amount of the reactant = 1 g
a - x = amount left after decay process = 0.8 g
Now put all the given values in above equation, we get
[tex]k=\frac{2.303}{1}\log\frac{1}{0.8}[/tex]
[tex]k=0.22weeks^{-1}[/tex]
2) To calculate the half life, we use the formula :
[tex]t_{\frac{1}{2}=\frac{0.693}{k}[/tex]
[tex]t_{\frac{1}{2}=\frac{0.693}{0.22}=3.15weeks[/tex]
Thus half life of Thorium 234 is 3.15 weeks.
3) amount of Thorium 234 present after 10 weeks:
[tex]10=\frac{2.303}{0.22}\log\frac{1}{a-x}[/tex]
[tex](a-x)=0.11g[/tex]
Thus amount of Thorium 234 present after 10 weeks is 0.11 grams
Studies have documented that 75% of college business students cheat on final exams. A business professor monitored a random sample of 40 students via web cameras as they took their final exam.The probability that exactly 30 of the students monitored cheat on the final exam is:(Round your answer to 4 decimal places)
Answer:
The probability is 0.1444.
Step-by-step explanation:
Let X be the event that college business students cheated on final exams,
Since, the probability that student cheats on exam, p = 75 % = 0.75,
So, the probability that student does not cheat on exam, q = 1 - p = 0.25,
The binomial distribution formula,
[tex]P(x)=^nC_r p^r q^{n-r}[/tex]
Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
The probability that exactly 30 of the students monitored cheat on the final exam out of 40 students is,
[tex]P(X=30)=^{40}C_{30} 0.75^{30} 0.25^{40-30}[/tex]
[tex]=847660528\times 0.75^{30} \times 0.25^{10}[/tex]
[tex]=0.144364346356[/tex]
[tex]\approx 0.1444[/tex]
The correct probability that exactly 30 of the 40 students monitored cheat on the final exam is 0.0256.
To solve this problem, we can use the binomial probability formula, which is given by:
[tex]\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \][/tex]
Given:
- ( n = 40 ) (the number of students monitored),
- ( k = 30 ) (the number of students who cheat),
- ( p = 0.75 ) (the probability of a student cheating on the final exam).
We can plug these values into the binomial probability formula:
[tex]\[ P(X = 30) = \binom{40}{30} \cdot (0.75)^{30} \cdot (1-0.75)^{40-30} \][/tex]
First, calculate the binomial coefficient:
[tex]\[ \binom{40}{30} = \frac{40!}{30!(40-30)!} \][/tex]
Next, calculate the powers of p and (1-p) :
[tex]\[ (0.75)^{30} \] \[ (0.25)^{10} \][/tex]
Now, multiply these values together:
[tex]\[ P(X = 30) = \binom{40}{30} \cdot (0.75)^{30} \cdot (0.25)^{10} \][/tex]
Using a calculator or a software tool, we can compute the exact value of the probability:
[tex]\[ P(X = 30) \approx 0.0256 \][/tex]
Therefore, the probability that exactly 30 of the 40 students monitored cheat on the final exam is approximately 0.0256 when rounded to four decimal places.
Find the general solution to y'" - y" + 2y = 0
Answer: The required general solution is
[tex]y(x)=Ae^{-x}+e^x(B\cos x+C\sin x).[/tex]
Step-by-step explanation: We are given to find the general solution of the following differential equation :
[tex]y^{\prime\prime\prime}-y^{\prime\prime}+2y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let y = y(x) and [tex]y=e^{mx}[/tex] be an auxiliary solution of equation (i).
Then, we have
[tex]y^\prime=me^{mx},~~~y^{\prime\prime}=m^2e^{mx},~~~y^{\prime\prime\prime}=m^3e^{mx}.[/tex]
Substituting these values in equation (i), we have
[tex]m^3e^{mx}-m^2e^{mx}+2e^{mx}=0\\\\\Rightarrow (m^3-m^2+2)e^{mx}=0\\\\\Rightarrow m^3-m^2+2=0~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mx}\neq0]\\\\\Rightarrow m^2(m+1)-2m(m+1)+2(m+1)=0\\\\\Rightarrow (m+1)(m^2-2m+2)=0\\\\\Rightarrow m+1=0~~~~~\Rightarrow m=-1[/tex]
and
[tex]m^2-2m+2=0\\\\\Rightarrow (m^2-2m+1)+1=0\\\\\Rightarrow (m-1)^2=-1\\\\\Rightarrow m-1=\pm\sqrt{-1}\\\\\Rightarrow m=1\pm i~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{where }i^2=-1][/tex]
So, we get
[tex]m_1=-1,~~m_2=1+i,~~m_3=1-i.[/tex]
Therefore, the general solution of the given equation is given by
[tex]y(x)=Ae^{m_1x}+e^{1\times x}(B\cos 1x+C\sin 1x)}\\\\\Rightarrow y(x)=Ae^{-x}+e^x(B\cos x+C\sin x).[/tex]
Thus, the required general solution is
[tex]y(x)=Ae^{-x}+e^x(B\cos x+C\sin x).[/tex]
Graduation is 3 years away and you want to have $850 available for a trip. If your bank is offering a 3-year CD (certificate of deposit) paying 2% simple interest, how much do you need to put in this CD to have the money for your trip?
Answer:
We need to put $801.88 amount in the bank.
Step-by-step explanation:
given that
t=3 yr
Need amount $850 after 3 yr so P= $850
Interest rate=2%
We know that for simple interest
[tex]P=A\left(1+\dfrac{rt}{100}\right)[/tex]
Where r is the Interest rate,t is the time,A is the present amount and P is principle amount after t time.
Here given that P= $850
So now putting the values
[tex]850=A\left(1+\dfrac{2\times 3}{100}\right)[/tex]
So A=$801.88
We need to put $801.88 amount in the bank.
Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 3 hours. Working alone, it takes the slower worker 8 hours longer to do the job than the faster worker. How long does it take each to do the job alone?
Answer:
Faster worker takes 4 hours and slower worker takes 12 hours.
Step-by-step explanation:
Let x be the time ( in hours ) taken by faster worker,
So, according to the question,
Time taken by slower worker = (x+8) hours,
Thus, the one day work of faster worker = [tex]\frac{1}{x}[/tex]
Also, the one day work of slower worker = [tex]\frac{1}{x+8}[/tex]
So, the total one day work when they work together = [tex]\frac{1}{x}+\frac{1}{x+8}[/tex]
Given,
They take 3 hours in working together,
So, their combined one day work = [tex]\frac{1}{3}[/tex]
[tex]\implies \frac{1}{x}+\frac{1}{x+8}=\frac{1}{3}[/tex]
[tex]\frac{x+8+x}{x^2+8x}=\frac{1}{3}[/tex] ( Adding fractions )
[tex]3(2x+8)=x^2+8x[/tex] ( Cross multiplication )
[tex]6x+24=x^2+8x[/tex] ( Distributive property )
[tex]x^2+2x-24=0[/tex] ( Subtraction property of equality )
By quadratic formula,
[tex]x=\frac{-2\pm \sqrt{100}}{2}[/tex]
[tex]x=\frac{-2\pm 10}{2}[/tex]
[tex]\implies x=4\text{ or }x=-6[/tex]
Since, hours can not negative,
Hence, time taken by faster worker = x hours = 4 hours,
And, the time taken by slower worker = x + 8 = 12 hours.
To solve this work rate problem, we set up an equation with combined work rates and find that the faster worker takes 3 hours alone, while the slower worker takes 11 hours alone.
Explanation:The question states that two secretaries can stuff envelopes together in 3 hours. The slower worker takes 8 hours more than the faster worker to complete the job alone. To find how long it takes each secretary to complete the job alone, we can set up an equation using the reciprocal of their work rates.
Let x be the time it takes for the faster worker to stuff the envelopes alone. Then, the slower worker will take x + 8 hours. The work rate of the faster worker is 1/x and the slower worker's rate is 1/(x + 8). Working together, their combined work rate is 1/3 per hour (since they complete the task in 3 hours).
The combined work rate equation will be:
1/x + 1/(x + 8) = 1/3
To solve this equation:
Multiply every term by the common denominator, which is 3x(x + 8).This gives us 3(x + 8) + 3x = x(x + 8).Simplify and solve the resulting quadratic equation.This results in x² + 8x - 3x - 24 = 0, which simplifies to x² + 5x - 24 = 0.Factor the quadratic equation to find the values of x.The factors of 24 that add up to 5 are 8 and -3, so (x + 8)(x - 3) = 0.Therefore, x = 3 or x = -8. Since time cannot be negative, we disregard x = -8.The faster worker takes 3 hours and the slower worker takes 3 + 8 = 11 hours.As a result, the faster worker takes 3 hours to complete the job alone, and the slower worker takes 11 hours to complete the job alone.
Among 8846 cases of heart pacemaker malfunctions, 375 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 8846 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
Step-by-step explanation:
Probability, P = [tex]\frac{no. of favourable outcomes}{Total no. of possible outcomes}[/tex]
Out of 8846 heart pacemaker malfunctions cases, caused by firmware cases are 375
then, no. of cases not caused by firmware are:
8846 - 375 = 8471
Probability for three different pacemakers respectively is given by:
P(1) = [tex]\frac{8471}{8846}[/tex]
we select the next malfunctioned pacemaker from the remaining i.e., out of 8471, excluding the chosen malfunctioned pacemaker
P(2|1) = [tex]\frac{8470}{8845}[/tex]
Therefore, the events are not independent of each other
Now, if the selection is without replacement, then
P(3|1 & 2) = [tex]\frac{8469}{8844}[/tex]
Now, by general multiplication rule(as the events are not independent):
P(none of the 3 are caused by malfunction) =
[tex]\frac{8471}{8846}\times\frac{8470}{8845}\times\frac{8469}{8844}[/tex]
= 0.9019
P(none of the 3 are caused by malfunction) = 90.19%
The probability is high, therefore the whole batch will be accepted.
Probability of an event represents the chances of that event to occur.
The probability of the entire batch to get selected is 0.879Yes, this procedure is likely to result in the entire batch being accepted.What is the multiplication rule of probability for independent events?Suppose there are n mutually independent events.
The probability of their simultaneously occurrence is given as
[tex]P(A_1 \cap A_2 \cap ... \cap A_n) = P(A_1) \times P(A_2) \times ... \times P(A_n)[/tex]
(This is true only if all those events are mutually independent).
The probability of getting a failure(malfunction) in a randomly selected pacemaker for the given case is
[tex]\dfrac{375}{8846} \approx 0.042[/tex]
The probability of a pacemaker working fine = 1- its failure probability = 1 - 0.042 = 0.958
Since each of the 3 selected pacemakers are independent for their failure or success of each other, thus, if we have:
[tex]A_1[/tex] = Event of properly working of first pacemaker
[tex]A_2[/tex] = Event of properly working of second pacemaker
[tex]A_3[/tex] = Event of properly working of third pacemaker
Then, as all three are independent for their working from each other, thus,
[tex]P(A_1 \cap A_2 \cap A_3) = P(A_1) \times P(A_2)\times P(A_3) = (0.958)^3 \approx 0.879\\\\\begin{aligned}{P(\text{batch getting selected}) &= P(\text{All three pacemaker working})\\& = P(A_1 \cap A_2 \cap A_3) \\&\approx 0.879\\\end{aligned}[/tex]
Thus, as this probability is high, thus, this procedure is likely to result in the entire batch being accepted.
Thus,
The probability of the entire batch to get selected is 0.879Yes, this procedure is likely to result in the entire batch being accepted.Learn more about multiplication rule of probability here:
https://brainly.com/question/14399918
Evaluate ∫ C → F ⋅ → d r where → F ( x , y , z ) = ⟨ 1.75 y z cos ( x y z ) , 1.75 x z cos ( x y z ) , 1.75 x y cos ( x y z ) ⟩ and C is the line segment joining the point ( 5 , π 2 , 1 5 ) to the point ( 6 , 1 6 , π 6 ) . g
[tex]\vec F(x,y,z)=\dfrac74\cos(xyz)\langle yz,xz,xy\rangle[/tex]
Computing the line integral directly is cumbersome, if not impossible by elementary means. Let's instead try to determine if [tex]\vec F[/tex] is conservative. We look for a scalar function [tex]f(x,y,z)[/tex] such that [tex]\nabla f=\vec F[/tex]. We should have
[tex]\dfrac{\partial f}{\partial x}=yz\cos(xyz)[/tex]
(ignoring the 7/4 for a moment). Integrating both sides wrt [tex]x[/tex] gives
[tex]\displaystyle\int\cos(xyz)yz\,\mathrm dx=\sin(xyz)+g(y,z)[/tex]
Then differentiating wrt [tex]y[/tex] gives
[tex]\dfrac{\partial(\sin(xyz))}{\partial y}=xz\cos(xyz)=xz\cos(xyz)+\dfrac{\partial g}{\partial y}[/tex]
[tex]\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)[/tex]
Differentiating wrt [tex]z[/tex] gives
[tex]\dfrac{\partial(\sin(xyz))}{\partial z}=xy\cos(xyz)=xy\cos(xyz)+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]
So we have (and here we re-introduce the 7/4)
[tex]f(x,y,z)=\dfrac74\sin(xyz)+C[/tex]
and by the fundamental theorem of calculus,
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\vec r=f(\vec b)-f(\vec a)[/tex]
where [tex]\vec a[/tex] and [tex]\vec b[/tex] are vectors representing the start- and endpoints of [tex]C[/tex]. So
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\frac74\sin\frac\pi6-\frac74\sin\frac\pi2=\boxed{\frac78}[/tex]
The problem asks to evaluate a line integral of a given function over a line segment. The process involves parameterization of the line segment, substitution into the vector function, and finally integration. However, due to complexity of the function, an exact solution might be difficult to achieve.
Explanation:The problem asks us to evaluate a line integral, specifically ∫ C → F ⋅ → d r, where the function → F ( x , y , z ) = ⟨ 1.75 y z cos ( x y z ) , 1.75 x z cos ( x y z ) , 1.75 x y cos ( x y z ) ⟩, and C is the line segment joining two points.
To solve this problem, we need to take the vector field through each of the points of the line segment C. We then cross multiply these results, and calculate the magnitude to get the final answer. However, due to the complex nature of the function → F, an exact analytical solution might be difficult to attain and numerical methods might be required.
Please take note that this is a simplified explanation and actual calculations would be much more complex involving steps like parameterization of the line segment, substituting it into the vector function, and then taking integral.
Learn more about Line Integral here:https://brainly.com/question/34566674
#SPJ3
20. Use Barrow's a, e method to determine the slope of the tangent line to the curve x^3 + y^3=C^3
Answer: Slope would be,
[tex]-\frac{x^2}{y^2}[/tex]
Step-by-step explanation:
Here, the given curve,
[tex]x^3 + y^3=C^3[/tex]
[tex]\implies x^3 + y^3 - C^3=0[/tex]
In Barrow's method,
Steps are as follows,
Step 1 : put, x = x - e, y = y - a
[tex](x-e)^3 + (y-a)^3 - C^3=0[/tex]
[tex]x^3-3x^2e+3xe^2-e^3+y^3-3y^2a+3ya^2-a^3+C^3=0[/tex]
Step 2 : Reject terms which do not contain a or e,
[tex]-3x^2e+3xe^2-e^3-3y^2a+3ya^2-a^3=0[/tex]
Step 3 : Reject all terms in which a or e have exponent greater than 1,
[tex]-3x^2e-3y^2a=0[/tex]
Step 4 : Find the ratio of a : e,
[tex]-3y^2a=3x^2e[/tex]
[tex]\implies \frac{a}{e}=-\frac{x^2}{y^2}[/tex]
Hence, the slope of the given curve is [tex]-\frac{x^2}{y^2}[/tex]
Which of the following is equivalent to the formula =C2+C3+C4+C7?
=SUM(C2:C7)
=SUM(C2,C4:C7)
=SUM(C2, C3, C4:C7)
=SUM(C2:C4, C7)
Answer:
=SUM(C2:C4, C7)
Step-by-step explanation:
In excel 'C' represent the cell ( intersection of row and column ),
Also, '=sum( )' represents the function of addition in the excel,
Also, when we operate all consecutive cells from [tex]Cn[/tex] to [tex]Cm[/tex]
Then under the function formula we write [tex]Cn:Cm[/tex]
And, when we operate a cell [tex]Cn[/tex] with non consecutive cell [tex]Cl[/tex]
Then under the function formula we write [tex]Cn, Cl[/tex]
Hence, C2+C3+C4+C7 can be written as,
=SUM(C2:C4, C7)