The DF value we get after is 143 and the integration value we get is 1.76
What is a value ?
Value in ethics and social sciences refers to the degree of significance of something or an activity, with the goal of deciding the best courses of action to take or the best ways to live, or to define the significance of certain activities.
The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. Consider this: If we take 45 into consideration. The tens column is where the fourth digit is located in this instance.
The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important."
(a)
DF for Factor A = 6 - 1 = 5
DF for Factor B = 4 - 1 = 3
DF for Interaction of Factor A and B = 5*3 = 15
Number of replications per cell = 6
Total no of observations = 6*(N_Factor A)*(N_Factor B) = 6 * 6 * 4 = 144
DF Residuals = 144 - 5 - 3 - 15 - 1 = 120
Total DF = N - 1 = 143
(b) Critical F values
Factor A = F(5,120) = 2.30
Factor B = F(3,120) = 2.69
Interaction = F(15,120) = 1.76
(c) As F statistics for Factor A, Factor B as well as Interaction is >> Fc, Hence we can Reject the Null Hypothesis and warrant the rejection of the claim for equality of means
Hence there is a significant difference in Factor A and there is a significant difference in Factor B.
(d) As the F statistics for Interaction = 4.2 >> Fc (1.76), Hence we can conclude that there is a significant Interaction impact of Factor A and Factor B.
Hence there is a significant difference for Interaction term.
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2. A gas in a flexible container with volume 8L has a temperature of 400 K. If the temperature of the gas changes to 200 K, what is the expected new volume of the gas?
A. 2 L
B. 4 L
C. 16 k
D. 32 L
The volume of the gas becomes 4L. Option B is correct.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
From the ideal gas equation, we know that,
Volume is directly proportional to the temperature,
So,
V₁ / V₂ = T₁ / T₂
Where,
V₁ and T₁ are the initial pressure and temperature,
V₂ and T₂ are the final pressure and temperature.
Substitute the values,
8 / V₂ = 400 / 200
V₂ = 4
Thus, the volume of the gas becomes 4L. Option B is correct.
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When a company sales x units of a product, its profits P can be determined
using the profit function
P(x) =
-2x² + 40x + 280
a) How many units must be sold to maximize profit?
b) What is the maximum profit?
(a) There are 10 units must be sold to maximize profit.
(b) The maximum profit is 480.
what is profit?
A profit is an income that is given to the owner in an efficient market production process in accounting. The owner's primary interest in the income-formation process of market production is profit, which is a measure of profitability. Different profit metrics are frequently employed.
Given:
A company sales x units of a product, its profits P can be determined
using the profit function P(x) = -2x² + 40x + 280 ..(1)
We have to find the maximum profit.
Differentiate equation (1) w.r.t x
P'(x) = -4x +40 ..(2)
-4x + 40 = 0
4x = 40
x = 10
Again differentiate equation (2) w.r.t x
P''(x) = -4 which is negative.
Hence, there are 10 units must be sold to maximize profit.
Now, to find the maximum profit.
Plug x = 10 in equation (1)
P(10) = -2(10)^2 + 40(10) + 280
= -200 + 400 + 280
P(10) = 480
Hence, the maximum profit is 480.
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The table shows the heart rates of different animals...
Animal
Cat
Cow
Hamster
Horse
Cat:
Heart Rate (beats/min)
Cow:
150
65
Find the unit rates for each animal in mass per heart rate
Horse:
450
Input: xx-x/x g/ xxx beat per min (i.e. 300-1/4 g/ 1 beat per min)
44
Hamster: (Put answer as a decimal to the nearest hundredth [2 places behind the decimal])
Mass (9)
2000
800,000
60
1,200,000
POSSIBLE POINTS: 1
B
The unit rates for each animal in mass per heart rate (beats/minute) are as follows:
Animal Unit RateCat 13.33g/1 beat per min
Cow 12,307.69g/1 beat per min
Hamster 1.36g/1 beat per min
Horse 2,666.67g/1 beat per min
What is the unit rate?The unit rate is the ratio of two different variables expressed in a common denominator.
The unit rate is the quotient of the division operation between, for instance, the mass of an animal and its heart rate.
In this instance, the mass of the animal is the numerator with the heart rate used as the denominator.
Animal Heart Rate Mass (g) Unit Rate
(beats/min) (mass per heart rate)
Cat 150 2,000 13.33g/1 beat per min (2,000/150)
Cow 65 800,000 12,307.69g/1 beat per min (800,000/65)
Hamster 44 60 1.36g/1 beat per min (60/44)
Horse 450 1,200,000 2,666.67g/1 beat per min (1,200,000/450)
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PLEASE HELP
Simplify the expression 4x³ × 2x³
3
A) 8x^6
B) 8x⁹
C)2x^6
D) 2x⁹
Answer:it isA
Step-by-step explanation:
Answer:
8x^6
Step-by-step explanation:
Add the exponents and multiply the numbers
6 3 points F L(2x-48) 32 W Using the diagram above find the value of x and use it to find the measures of all the missing angles. X = type your answer..... m/FOW= m/FLW= m/OLW= = type your answer... type your answer... type your answer.....
The value of x is 80
The measure of angle FOW, m ∠FOW, is 80°
The measure of angle FLW, m ∠FLW, is 112°
The measure of angle OLW, m ∠OLW, is = 68°
Calculating the measure of anglesFrom the question, we are to determine the measure of the missing angles
From the given diagram, we can write that
(2x - 48)° = x° + 32°
Solve for x
(2x - 48)° = x° + 32°
2x° - 48° = x° + 32°
Subtract x° from both sides of the equation
2x° - x° - 48° = x° - x° + 32°
x° - 48° = 32°
Add 48° to both sides of the equation
x° - 48° + 48° = 32° + 48°
x° = 32° + 48°
x° = 80°
Therefore,
x = 80
Calculating the m ∠FOW
m ∠FOW = x°
m ∠FOW = 80°
Calculating the m ∠FLW
m ∠FLW = (2x - 48)°
m ∠FLW = (2(80) - 48)°
m ∠FLW = (160 - 48)°
m ∠FLW = 112°
Calculating the m ∠OLW
m ∠OLW + m ∠FOW + m ∠OWL = 180° (Sum of angles in a triangle)
m ∠OLW + 80° + 32° = 180°
m ∠OLW + 112° = 180°
m ∠OLW = 180° - 112°
m ∠OLW = 68°
Hence, the measure of m ∠OLW is 68°
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During surgery, patient's circulatory system requires at least 50 milligrams of an anesthetic: The amount of anesthetic present hours after 70 milligrams of anesthetic administered given by the following T(t) 70(0.727)t (a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system 30 minutes after the anesthetic is administered? (b) How long_ to the nearest minute can the operation last if the patient does not recelve additional anesthetic?
63 mg of anesthetic is present in the patient’s circulatory system.
The operation can last for 20 minutes.
During surgery, a patient’s circulatory system requires at least 50 mg of an anesthetic. The amount of anesthetic present t hours after 70 mg of anesthetic is administered is given by the following,
T(t) = 70 × (0.727) ^t
Time = 1/3 hours
T (1/3) = 70 × (0.727) ^1/3
= 70 × ∛ 0.727
= 70 × 0.899176
= 62.94232
To the nearest mg: 63mg
Now,
63 = 70 × (0.727) ^t
63/70 = (0.727) ^t
0.9 = (0.727) ^t
Log0.9 = log (0.727) ^t
Log0.9 = t × log (0.727)
T = log0.9 / log0.727
T = 0.330461
T = 0.330461 hours
= 20 minutes
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Determine which integer in the solution set will make the equation true
Answer:
2
Step-by-step explanation:
First, we must add 14 to both sides to put the variable and coefficient alone.
4s - 14 = -6
+14 +14
4s = 8
s = 2
107 km Big Goldtown. 805km Little Goldtown. 107km Old Goldtown The distance between Little Goldtown and Old Goldtown is A) 805km+107km. B) 805km-107km. C) 107km+107km+805km
The distance between Little Gold town and Old Gold town is 805km-107km.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common usage can refer to a physical length or an estimation based on other factors.
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.
Given: 107 km Big Gold town. 805km Little Gold town. 107km Old Gold town.
We have to find the distance between little gold town and old gold town.
Here, 805km Little Gold town. 107km Old Gold.
Hence, the distance between Little Gold town and Old Gold town is 805km-107km.
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Find the volume of the composite solid (STEP BY STEP PLEASE) 15 POINTS
Answer: 226.19
Step-by-step explanation:
Using the formula for a cyclinder{ V=πr2h} and inputing the values given in the diagram, (the radius and height given) you get 28.27.
Then adding the cone's volume (V=πr2h/3) and inputing that values in the diagram (the radius and height) you get 197.92.
Adding those values you got from the cyclinder and cone together, you get the volume of the composite solid.
Find the standard deviation for each data set. Use the standard deviations to compare the pair of data sets. fastest recorded speeds of various large wild cats (miles per hour): 70 45 25 45 35 35 40 40 25 fasted recorded speeds of various birds in flight (miles per hour): 216 103 96 56 63 35 50 32 55 25 25 20
The standard deviation of the large wild cats is ō=
The standard deviation of the birds in flight is ō=
The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate _____ from the mean than the fastest recorded speeds of birds in flight.
A. Less
b. more
(a) The standard deviation of the large wild cats is 25.5 (b) The standard deviation of the birds in flight is 33 (c) The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight . Option A
How to determine the standard deviation?We should understand that standard deviation looks at the amount of deviation from the means of the set of data.
(a) (70+45+25+45+35+35+40+40+25)÷9 = 40
mean is = 40
(x-m) =30+5+-15+5+-5+-5+0+0+-15)
(x-m)²=(900+25+225+25+25+25+0+0+225)=1450/9
Standard deviation = √650
Standard deviation = 25.5
(b) x= (216+103+96+56+63+35+50+32+55+25+25+20)=776
Mean(m)=776/12=65
(x-m)=151+38+31+-9+-2+-30+-15+-33+-10+-40+-40+-45
Now the square of the deviations from the mean is
(x-m)²=(7396+1444+961+81+4+900+225+1089+100+1600+1600+2025)÷12
=1452
Standard deviation = √1452=33
(c) Therefore, from the calculations, the standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight
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(c) Solve by Completing the Square (Round answers to the nearest tenth)
x²+10 x+2=2 x+5
After solving the equation by Completing the square , the answer is x = 0.4 , x = -8.4 .
In the question ,
it is given that ,
the equation is x² + 10x + 2 = 2x + 5,
rewriting the equation ,
we get ,
x² + 8x - 3 = 0
adding 3 to both sides ,
we get ,
x² + 8x = 3 ,
For the method of completing the square ,
we take half of the second term's coefficient, and square it, then add it to both sides.
that is 8/2 = 4 .
the equation becomes ;
x² + 2*x*4 + 4² = 3 + 4²
(x + 4)² = 3 + 16
(x + 4)² = 19
taking root on both the sides ,
we get ,
x + 4 = ±√19
So , x = -4 + √19 or x = -4 - √19
Simplifying further ,
we get ,
x = 0.35889 or x = -8.35889
rounding to the nearest tenth we get
x = 0.4 or x = -8.4 .
Therefore , the solution of the given equation is x = 0.4 , x = -8.4 .
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3) Lourdes got a plant as a birthday gift. Her plant grows an average of 1 2/5 inches every month. How long will it take for the plant to grow a full 10 2/3
Answer:
7 13/21 months
Step-by-step explanation:
10 2/3 ÷ 1 2/5 =
= 32/3 ÷ 7/5
= 32/3 × 5/7
= 160/21
= 7 13/21
Answer: 7 13/21 months
Let X1,X2,...,Xn be a random sample of size n from a geometric distribution for which p is the probability of success.
(a) Use the method of moments to find a point estimate for p.
(b) Explain intuitively why your estimate makes good sense.
a) X1+X2 have distribution Bi(n1+n2, p)
b) P(X1 + X2 = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
Since both variables are independent but they have the same probability parameter, you can interpret that like if the experiment that models each try in both variables is the same. When you sum both random variables toguether, what you obtain as a result is the total amount of success in n1+n2 tries of the same experiment, thus X1+X2 have distribution Bi(n1+n2, p).
b)
Note that, if X2 = k, then X1+X2 = 1 is equivalent to X1 = 1-k. Since X1 and X2 are independent, then P(X1+X2 = 1| X2 = K) = P(X1=1-k|X2=k) = P(X1 = 1-k).
If k = 0, then this probability is equal to P(X1 = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X1 = 0) = (1-p)ⁿ¹
Thus,
P(X1+X2 = 1) = P(X1+X2 = 1| X2 = 1) * P(X2=1) + P(X1+X2 = 1| X2 = 0) * P(X2 = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
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592 x 43 in standard algorithm
Answer:
25456
Step-by-step explanation:
592 over 43
592
x 43
multiply 3 by 2, 9 and 5. 3 by 2 is 6. 3 by 9 is 27. 3 by 5 is 15.
add a zero at the second row then,
multiply 4 by 2, 9, 5. 4 by 2 is 8. 4 by 9 is 36. 4 by 5 is 20.
if you aligned them properly, when you add them you should get 25456
I'll try to include a picture of my work, hopefully you can see it**
6x+6y=90 9x+2y=79 What pair of numbers solves the system?
Answer:
(7, 8)
Step-by-step explanation:
equation 1: [tex]6x+6y=90[/tex]
equation 2: [tex]9x+2y=79[/tex]
This system of equations can be solved for using the elimination method.
First, multiply both sides of the first equation by 3/2 to match the number of x's in both equations so that when we subtract the first equation from the second, the x's cancel and we can solve for y.
[tex]\left(\dfrac{3}{2}\right)\left(6x+6y\right)=(90)\left(\dfrac{3}{2}\right)[/tex]
[tex]9x + 9y = 135[/tex]
Next, subtract this from the second equation.
[tex]9x+2y=79[/tex] ← eq. 2
[tex]\underline{- (9x+9y=135)}[/tex] ← modified eq. 1
[tex]0 - \, 7y \, = -56[/tex]
Then, solve for y by dividing by 7.
[tex]7y = 56\\\overline{\, 7 \ } \ \ \ \ \overline{\ 7 \: }[/tex]
[tex]y=8[/tex]
So, the y-coordinate of the solution pair is 8.
Now that we've solved for the y, all we have to do to get x is plug the solved y-value back into one of the equations. I'll use the first equation.
[tex]6x+6y=90[/tex]
[tex]6x + 6(8) = 90[/tex]
↓ multiplying out 6 and 8
[tex]6x + 48 = 90[/tex]
↓ subtracting 48 from both sides
[tex]6x = 90 - 48[/tex]
[tex]6x = 42\\\overline{\: 6 \: } \ \ \ \ \, \overline{\: 6 \: }[/tex]
[tex]x = 7[/tex]
So, the x-coordinate of the solution pair is 7.
Finally, put the x- and y-coordinates together into an ordered pair in the form [tex](x, y)[/tex].
(7, 8)
Answer:
(7, 8) is the required pair of numbers---------------------------
Given system6x + 6y = 90, 9x + 2y = 79.Solve it by substitutionFirst, simplify the first equation by dividing all terms by 6:
x + y = 15Then solve it for y:
y = 15 - xNow, substitute this into the second equation:
9x + 2(15 - x) = 799x + 30 - 2x = 797x = 79 - 307x = 49x = 7Finally, find the value of y:
y = 15 - 7y = 8The pair of numbers is (7, 8).
start by thinking of the number 22 as divided into 22 individual items and the variables x1, x2, and x3 as three categories into which these items are placed. since each xi is a positive correct: your answer is correct. integer, start by placing one item in each category and distribute the remaining items among the categories. the number of solutions to the equation that satisfy the given condition is the number of ways to place all the items into the categories. thus, the answer is 20 incorrect: your answer is incorrect. .
The number of solution to the equation is 210 when consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃.
Given that,
Consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃ . acting as the three categories into which these items are sorted. Since each x is a true affirmative, your response is accurate. Put one item in each category to begin with, then divide the remaining items across the categories. The number of classification schemes for all the objects is the number of solutions to the equation satisfying the given criteria. In light of this, your response of 20 is erroneous.
We know that,
Number 22 is divided into 22 individual items ,
The three categories in which these items are placed are x₁, x₂ and x₃ .
x₁+x₂+x₃=22----->equation(1)
(x₁-1)+(x₂-1)+(x₃-1)=22-3=19
Let
a=x₁-1,
b=x₂-1 and
c=x₃-1.
So,
a+b+c= 19 ----->equation(2)
So , the number of ways of arranging 21 characters in which 19 are same(A) and 2 are same (J)
= 21!/(2! × 19!)
= 21×10 = 210
Therefore, the number of solution to the equation is 210 when consider the number 22 as being composed of 22 distinct items, with the variables x₁, x₂ and x₃.
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Can someone explain what division algorithm is? I’m not sure I understand this?
Answer:
The division algorithm is an algorithm that specifies how to perform the division of one number (called the dividend) by another number (called the divisor) to obtain the quotient and the remainder.
For example, if we want to divide 15 by 4, we can use the division algorithm to find the quotient and remainder. In this case, we have:
15 = 4 * 3 + 3
So, the quotient is 3 and the remainder is 3.
If it's not clear for you yet, you can wait for another answer, maybe better explained.
Easier example (the classic one with apples):
Imagine you have a bunch of apples, and you want to divide them equally among a group of friends. The division algorithm can help you figure out how many apples each friend gets, and how many apples are left over.
Here's an example, let's say you have 15 apples, and you want to divide them among 4 friends. Using the division algorithm, we can figure out that each friend gets 3 apples, and there will be 3 apples left over.
To use the division algorithm, you start by dividing the number of apples (15) by the number of friends (4). This gives us the number of apples each friend gets, which is called the "quotient." In this case, the quotient is 3.
Then, we take the remainder, which is the number of apples that are left over after we divide them evenly among the friends. In this case, the remainder is 3.
So, each friend gets 3 apples, and there are 3 apples left over.
Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. For two events M and N, P(M)=0.6, P(N|M)=0.9, and P(N|M′)=0.2. Find P(M′|N.)
For two events M and N, P(M)=0.6, P(N|M)=0.9, and P(N|M′)=0.2. Then P(M′|N.) is 0.7
This can be easily solved if we know the formula:
P(A or B) = P(A) + P(B) - P(A and B)
So, for this problem, we can modify the formula to be:
P(M or N) = P(M) + P(N) - P(M and N)
Using given information, we can solve:
P(M or N) = P(M) + P(N) - P(M and N)
P(M or N) = 0.6 + 0.2 - 0.1
P(M or N) = 0.7
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Show that the set of numbers in the interval [0,1] having decimal expansions using only odd digits is closed. Describe this set by a Cantor set type construction.
T be the set of all points x in [0,1] by a Cantor set type construction is x=∑∞n=1 qn/4n
for some sequence of qns with each qn∈{1,3}.
What is Cantor set type construction?
The Cantor set is a collection of points situated on a single line segment that possesses a variety of odd characteristics.
By deleting the center third of a line segment and then repeating the process with the remaining shorter segments, the Cantor ternary set, the most popular construction, is created. The ternary construction was only briefly described by Cantor as an illustration of a more basic concept—that of a perfect set that isn't dense anywhere.
According to the given question:
The proportion (i.e., measure) of the unit interval that is left can be determined by subtracting the entire length as the Cantor set is defined as the set of points that are not excluded.
T be the set of all points x in [0,1] by a Cantor set type construction is x=∑∞n=1 qn/4n
for some sequence of qns with each qn∈{1,3}.
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For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount. Type either a numerical value or the word no. Do not round the answer. Units are in parentheses, so do not convert your answer 2.6 (trillions of dollars) (millions of metric tons) 4.0 (trillions of dollars) (millions of metric tons) 7.1 (trillions of dollars) (millions of metric tons
For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount is 1300.715.
What is carbon dioxide ?
Our atmosphere contains carbon dioxide, an odorless and colorless gas. According to its chemical composition, CO2, it is made up of one carbon atom joined to two oxygen atoms. It is a waste product created both by burning fossil fuels and by human bodies.
Given regression eq.
[tex]$$\hat{y}=166.92+115.725$$[/tex]
* Given [tex]$x=2.6$[/tex]
[tex]$$\begin{aligned}& \hat{y}=166.9(2.6)+115.725 \\& \hat{y}=549.665\end{aligned}$$[/tex]
* Given [tex]$x=4.0$[/tex]
[tex]$$\begin{aligned}& \hat{y}=166.9(4.0)+115.725 \\& \hat{y}=783.325\end{aligned}$$[/tex]
* Given [tex]$x=7.1$[/tex]
[tex]$$\hat{y}=166.9(7.1)+115.725$$[/tex]
[tex]\hat{y}=1300.715[/tex]
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pdf state the number of complex zeros the possible number of real and imaginary zeros and the possible rational zeros for each function
First possibility: 2 positive roots 0 negative roots 4 imaginary roots
Second possibility: 0 positive 0 negative 6 imaginary
Let f(x) = 4x6-4x3+8
f(x) has 2 sign changes. So, by Descartes's Rule of Signs, f(x) has either 2 positive roots or none.
f(-x) = 4(-x)6-4(-x)3+8 = 4x6+4x3+8
f(-x) has no significant changes. So, by Descartes's Rule of Signs, f(x) has no negative roots.
f(x) has degree 6. So, by counting multiplicities, there are a total of 6 roots.
First possibility: 2 positive roots 0 negative roots 4 imaginary roots
Second possibility: 0 positive 0 negative 6 imaginary
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a nail is measured with a ruler and its length is reported as 5.46 cm. select all the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
If the nail is measured with a ruler and its length is 5.46 cm , then the correct statements are :
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ;
(b) The uncertainty is in the final digit of the measurement .
The Uncertainty of a number helps to estimates in comparison of experimental numbers .
it is given that , the reported length of the ruler is = 5.46 cm ;
we know that ,
the uncertainty In any number , is present in last digit only ,
the place value of the last digit in 5.46 is 0.01 .
So , uncertainty can be expressed by reporting measurement as 5.46 ± 0.1 cm
Therefore , the correct statements about the certainty and uncertainty are (a) and (b) .
The given question is incomplete , the complete question is
A nail is measured with a ruler and its length is reports as 5.46 cm.
Select ALL the statements that are correct about the certainty and uncertainty represented in this recorded measurement.
(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ,
(b) The uncertainty is in the final digit of the measurement ,
(c) All three digits shown in the measurement are known with certainty ,
(d) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.01 cm .
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1. Assume there are 5 red balls, 6 blue balls, and 4 green balls. If the balls are removed from the box one at a time, in how many different orders can the balls be removed assuming two balls of the same type are indistinguishable.
2. Give a recursive definition of the set of all even positive integers not divisible by 3.
Please write clearly so I can study from it! Try not to skip steps as much as you can.
Thank you!
There are 1307674368000 possible methods to remove each ball from the box one at a time.
what is probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. examination of events subject to probability.
given,
the quantity of balls inside a box ,
four red balls
6 balls in blue
four green balls
The variety of ways the balls can be taken out of the box one at a time must be determined.
Here,
Combination is possible because order is imperceptible;
mixture formula; nCr is equal to n!/r1(n-r)!
Here, There are 15 balls in the box overall (5 + 4 + 6 balls).
Then.
¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000
that is
There are 1307674368000 ways in which we can take the balls out of the box one at a time.
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Which expression is equivalent to 3√x^5y^?
The equivalent expression for the given expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression ∛x⁵y.
expression is equivalent to ∛x⁵y is
[tex](x^5y)^{\frac{1}{3} }[/tex]
= [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]
The equivalent expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.
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What is 7/2 with a denominator of 10
Answer: 35/10
Step-by-step explanation:
if you have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.
7 by 5 35
2 by 5 10
The value of 7/2 with a denominator of 10 is 35/10
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
(we used the identity [tex](b-c)(b+c) = b^2 - c^2 )[/tex]
We actually rationalize just for the use of that later denominator or numerator
We have 7/2 and need a denominator of 10 all you need to do is multiply 7/2 by 5/5.
7 × 5 = 35
2 × 5 = 10
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write and find the general solution of the differential equation that models the verbal statement. evaluate the solution at the specified value of the independent variable. the rate of change of p is proportional to p. when t
When t = 3869, the rate of change of p is proportional to p.
What is differential equation?A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.
Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three. Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.
The primary focus of studying differential equations is on the solutions—the collection of functions that satisfy each equation—as well as the characteristics of those solutions.
Only the most basic differential equations can be solved using explicit formulas, but many features of a particular differential equation's solutions can be deduced without doing an exact calculation.
When a closed-form expression is used, it is common for.
According to our question-
The revised equation is then
P=5000exp(-0.0513t)
Find P at t=5 now.
P=5000 exp(-0.0513×5)
P=5000 ×exp(-0.25647) (-0.25647)
P=5000 × 0.77378
P=3868.89.
P = 3869. Roughly
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Suppose you observed the following sample:
6.2, 7.4, 9.6, 11.5, 13.5
Compute the 2nd sample moment. (please type in the exact number, do not round your answer)
449.86
To compute the moment of the second sample, we need to compute the sum of the squares of the sample values.
This formula is:
Sum = ∑(x_i^2)
After inserting the example values:
Sum = 6.2^2 + 7.4^2 + 9.6^2 + 11.5^2 + 13.5^2
Simplifying this formula to:
Total = 38.44 + 54.76 + 92.16 + 132.25 + 181.25
Adding these terms gives us the following final result:
Total = 449.86
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The mortgage amount of a new home 170,000. The bank required a 8.6% down payment.
What was the original price before the down payment was made?
Answer: 15,507.44.
Step-by-step explanation: To find the original price of the home before the down payment was made, you need to use the following formula:
Original price = Mortgage amount / (1 - Down payment percentage)
Plugging in the values given in the question, you get:
Original price = $170,000 / (1 - 8.6%)
The original price of the home before the down payment was made is $<<170000/(1-.086)=185507.44>>185,507.44.
This means that the down payment amount was $185,507.44 - $170,000 = 185507.44-170000=15,507.44.
Find the area of the shape.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
Area = [tex]\pi x^{2}[/tex] For a full circle. This is 1/4 of a circle
A= [tex]\frac{\pi 2^{2} }{4}[/tex] = [tex]\frac{\pi 4}{4}[/tex] = [tex]\pi[/tex]
Answer : The area of the shape is, 111.02 units 2
The designers of a water park have sketched a preliminary drawing of a new slide. The length of the ladder is I - 40 feet, and its angle of elevation is 60 (segure). 60 (a) Find the height of the slide. (Round your answer to two decimal places) - (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance ander travels (c) Safety restrictions require the angle of depression of the slide to be no less than 25 and no more than 30°. Find an interval for how far ander travels hortzontally (round me values to one decimal place. Enter your answer using interval notation
The interval for horizontal distance is
(59.9 ,74.2) ( ranging from 59.9 feet to 74.2 feet)
As per given in the question,
The length of the ladder (l) is 40feet
The angle of elevation in the triangle is [tex]60^0[/tex]
a) In a Δ ABC
One angle is given as 60 and the one side length (length of ladder) is given as 40 feet
The height of the slide is
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]sin60^0[/tex] = [tex]\frac{h}{40}[/tex] where the value of ( [tex]sin60^0={\frac{\sqrt{3} }{2} }[/tex])
=> [tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{h}{40}[/tex]
=> h = 20[tex]\sqrt{3}[/tex]
Approximately the height of the slide is 34.64 feet
b) In Δ DEF,
[tex]\theta = tan^{-1} \frac{h}{d}[/tex] ----( 1)
=> [tex]Tan^{-1} (\frac{34.6}{d} )[/tex]
c) the angle of depression is [tex]\theta=25^0[/tex] and [tex]\theta=30^0[/tex]
first for the value [tex]\theta=30^0[/tex]
substitute the value of [tex]\theta[/tex] in equation (1)
[tex]tan30^0=(\frac{34.63)}{d})[/tex] where the value of ( [tex]Tan 30^0=\frac{1}{\sqrt{3} }[/tex])
=> [tex]\frac{1}{\sqrt{3} } =\frac{34.63}{d}[/tex]
=> d = 59.99
now
substitute the value [tex]\theta=25^0[/tex] in equation (1)
[tex]tan25^0=(\frac{34.6}{d} )[/tex]
=> d = 74.28
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