Step-by-step explanation:
Consider the provided information.
Division by zero is not defined in our number system.
You can understand this if you think about how division and multiplication are related.
For example:
4 divided by 2 is 2 because 2 times 2 is 4
Now 4 divided by 0 is x would mean that 0 times x = 4
But there is no value for x so that 0 times x =4. Because 0 times a number is 0.
Or
4/0 means Into how many groups of zero could you separate four blocks?
It doesn't matter how many zero groups you have, as they'd never add up to four.
0+0+0+0=0.
You can add zero billions time still add up to zero.
That the reason behind "division by zero is not allowed in our number system."
Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z).
c(t) = (t^2, 2t − 6, 3sqrt(t)), t > 0; F(x,y,z) = ( y+6, 2, 9/2z)
c'(t) = ?
F(c(t)) = ?
Answer:
The given curve c(t) is a is a flow line of given velocity vector field F(x, y, z).
Step-by-step explanation:
We are given the following information in the question:
[tex]c(t) = (t^2, 2t-6, 3\sqrt{t}), t > 0\\\\ F(x, y, z) =(y+6, 2, \frac{9}{2z} )[/tex]
Now, we evaluate the following:
[tex]c'(t) = \frac{d(c(t))}{dt} = (2t, 2, \frac{3}{2\sqrt{t}} )[/tex]
Now, we have to evaluate:
[tex]F(c(t)) = (2t-6+6, 2, \frac{9}{6\sqrt{t}} ) = (2t, 2, \frac{3}{2\sqrt{t}} )[/tex]
When F(c(t)) = c'(t), then c(t) is a flow line of given velocity vector field F(x, y, z).
Since, [tex]F(c(t)) = c'(t)[/tex], we can say that c(t) is a flow line of given velocity vector field F(x, y, z).
The derivative of c(t) is calculated by differentiating each component with respect to t, resulting in c'(t)=(2t, 2, 3/2*t^(-1/2)). The velocity field F(c(t)) is found by substituting the equation of c(t) into F(x, y, z), resulting in F(c(t))=(2t+6, 2, 3/2*t^(-1/2)). As the results are equivalent, it's confirmed that c(t) is a flow line of the velocity vector field F(x, y, z).
Explanation:In order to show that the curve c(t) is a flow line of the velocity vector field F(x, y, z), we first need to find c'(t), the derivative of c(t), and F(c(t)), the velocity field evaluated at the points along the curve c(t).
First, let's find c'(t). c(t) is given by (t^2, 2t − 6, 3sqrt(t)), so its derivative c'(t) is given by differentiating each component with respect to t: c'(t)=(2t, 2, 3/2*t^(-1/2)).
Next, let's find F(c(t)). F(x,y,z) is given by (y+6, 2, 9/2*z) so F(c(t)) is evaluated by substituting the equation of c(t) into F(x, y, z). Thus F(c(t))=(2t+6,2,3/2*t^(-1/2)).
Since F(c(t)) and c'(t) are equivalent, c(t) is indeed a flow line of the velocity vector field F(x, y, z).
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4. Television viewing reached a new high when the Nielsen Company reported a mean daily viewing time of 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household. a. What is the probability that a household views television more than 3 hours a day? b. What is the probability that a household spends 5 – 10 hours watching television more a day? c. How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households?
Answer:
(a) 0.9838 (b) 0.6553 (c) 13.05198
Step-by-step explanation:
We have that the daily viewing time is a random variable normally distributed with mean and standard deviation
[tex]\mu[/tex] = 8.35 hours and
[tex]\sigma[/tex] = 2.5 hours
respectively. If we call the random variable X, the density function of this random variable is given by
f(x) = [tex]\frac{1}{\sqrt{2\pi}2.5}\exp[-\frac{(x-8.35)^{2}}{2(2.5)^{2}}][/tex], and we can calculate the next probabilities using a computer or a table from a book.
(a) P(X>3)=[tex]\int\limits^{\infty}_3 {f(x)} \, dx[/tex]=0.9838
in the R statistical programming language we use the instruction pnorm(3, mean = 8.35, sd = 2.5, lower.tail = FALSE)
(b) P([tex]5\leq X\leq 10[/tex]) = [tex]\int\limits^{10}_5 {f(x)} \, dx[/tex] = 0.6553
in the R statistical programming language we use the instruction
pnorm(10, mean = 8.35, sd = 2.5) - pnorm(5, mean = 8.35, sd = 2.5)
(c) You should find a value [tex]x_{0}[/tex] such that
[tex]P(X\geq x_{0}) = 0.03[/tex], this value is [tex]x_{0}[/tex]=13.05198
The instruction qnorm(0.03, mean = 8.35, sd = 2.5, lower.tail = FALSE) give us 13.05198 in the R statistical programming language.
Answer:
a. P=0.98
b. P=0.66
c. The top 3% of all TV viewing households watch 12.95 hours or more.
Step-by-step explanation:
We have a normal distribution with these parameters:
[tex]\mu=8.35\\\\\sigma=2.50[/tex]
a. What is the probability that a household views television more than 3 hours a day?
To calculate this, first we calculate the z-value for X=3 and then calculate the probability according to the standard normal distribution.
[tex]z=(X-\mu)/\sigma=(3-8.25)/2.50=-2.1\\\\P(X>3)=P(z>-2.1)=0.98214[/tex]
b. What is the probability that a household spends 5 – 10 hours watching television more a day?
[tex]z_1=(X_1-\mu)/\sigma=(5-8.25)/2.50=-1.3\\\\z_2=(X_2-\mu)/\sigma=(10-8.25)/2.50=0.7\\\\P(5<X<10)=P(-1.3<z<0.7)\\\\P(-1.3<z<0.7)=P(z>-1.3)-P(z>0.7)=0.9032-0.2412=0.662[/tex]
c. How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households?
To calculate this we have to know the z-value for [tex]P(z>z_1)=0.03[/tex].
This z-value, according to the standard normal distribution is z=1.88.
Then, we can calculate the number of hours X as:
[tex]X=\mu+z*\sigma=8.25+1.88*2.5=8.25+4.7=12.95[/tex]
The top 3% of all TV viewing households watch 12.95 hours or more.
Show that if A and B are similar nxn matrices, then det(A)=det(B).
Step-by-step explanation:
To prove it we just use the definition of similar matrices and properties of determinants:
If [tex] A,B[/tex] are similar matrices, then there is an invertible matrix [tex]C[/tex], such that [tex] A=C^{-1}BC}[/tex] (that's the definition of matrices being similar). And so we compute the determinant of such matrix to get:
[tex]det(A)=det(C^{-1}BC)=det(C^{-1})det(B)det(C)[/tex]
[tex]=\frac{1}{det(C)}det(B)det(C)=det(B)[/tex]
(Determinant of a product of matrices is the product of their determinants, and the determinant of [tex]C^{-1}[/tex] is just [tex]\frac{1}{det(C)}[/tex])
20 units Humulin R insulin in 100 mL of normal saline (NS) to infuse for 20 hours. (Round to the nearest tenth if applicable) a. How many units per hour will be infused? ________ b. How many milliliters per hour will be infused? ________
Answer:
a) 1 unit per hour will be infused.
b) 5mL per hour will be infused.
Step-by-step explanation:
Each question can be solved as a rule of three with direct measures, that means we have a cross multiplication.
a. How many units per hour will be infused?
20 units are going to be infused in 20 hours. How many units are going to be infused each hour?
1 hour - x units
20 hours - 20 units
[tex]20x = 20[/tex]
[tex]x = \frac{20}{20}[/tex]
[tex]x = 1[/tex]
1 unit per hour will be infused.
b. How many milliliters per hour will be infused?
100mL are going to be infused in 20 hours. How many mL are going to be infused each hour?
1 hour - x mL
20 hours - 100 mL
[tex]20x = 100[/tex]
[tex]x = \frac{100}{20}[/tex]
[tex]x = 5[/tex]
5mL per hour will be infused.
In high school, some students have been confused to believe that 22/7 is already the actual value of π or an acceptable approximation. Show that 355/113 is a better approximation in terms of absolute and relative errors.
Answer:
The absolute and relative error of 355/113 compared with π is less than when π is compared with 22/7, that's why 355/113 is a better approximation for the actual value of π.
Step-by-step explanation:
The absolute error is the difference between a value measured and the real value.
abs = π - approximation of π
The relative error indicates how large the absolute error is when compared with the actual value of π.
Now, let's calculate the absolute an relative error for each approximation of π, for simplicity the calculations will be rounded to 4 decimal digits.
rel = abs / π
For 22/7abs = π - 22/7
abs = -0.0013
rel = (π - 22/7) / π
rel = -0.0402 %
For 355/113abs = π - 355/113
abs = -2.6676 x10-7
rel = (π - 355/113) / π
rel = -8.4914 x10-6 %
You can see that both the value of the absolute and relative error for the 355/113 approximation are smaller numbers, in conclusion, 355/113 is a better approximation for π.
The owner of a bike shop that produces custom built bike frames has determined that the demand equation for bike frames is given by the equation
D(q) = –6.10q^2 –5q + 1000
where D(q) is the price in dollars and q is the number of bike frames demanded per week. The supply equation for bike frames is
S(q) = 3.20q^2 + 10q – 80
where q is the quantity the supplier will make available per week in the market when the price is p dollars. Find the equilibrium point (q, p) rounded to the nearest hundredth.
Answer:
equilibrium point (10,340)
Step-by-step explanation:
To find the equilibrium point, equal the demand and the supply:
[tex]D(q)=S(q)\\\\-6.10q^2-5q+1000=3.2q^2+10q-80[/tex]
Reorganize the terms in one side and reduce similar terms:
[tex]3.2q^2+6.1q^2+5q+10q-80-1000=0\\\\9.3q^2+15q-1080=0[/tex]
that's a cuadratic equation, solve with the general formula when:
a=9.3, b=15, c=-1080
[tex]q_{1}=\frac{-b+\sqrt{b^{2}-4ac} }{2a}\\\\q_{2}=\frac{-b-\sqrt{b^{2}-4ac} }{2a}\\\\q_{1}=\frac{-15+\sqrt{(-15)^{2}-4(9.3)(-1080)} }{2(9.3)}\\\\q_{1}=\frac{-15+201}{18.6}\\\\q_{1}=\frac{186}{18.6}\\\\q_1=10[/tex]
q can't be negative because it is the quantity of bike frames, so:
[tex]q_{2}=\frac{-b-\sqrt{b^{2}-4ac} }{2a}\\\\q_{2}=\frac{-15-\sqrt{(-15)^{2}-4(9.3)(-1080)} }{2(9.3)}\\\\q_{2}=\frac{-15-201}{18.6}\\\\q_{2}=\frac{-216}{18.6}\\\\[/tex]
This value of q can't be considered.
Then substitute the value of q in D(q) to find the price p:
[tex]D(10) = -6.10(10)^2-5(10) + 1000\\\\D(10)=340=p[/tex]
The equilibrium point (q,p) is (10,340).
To find the equilibrium point in supply and demand equations, calculate where the two equations intersect to determine the equilibrium quantity and price.
Equilibrium Point Calculation:
Set D(q) = S(q) to find the equilibrium point.Replace D(q) and S(q) with their respective equations.Solve for q to find the equilibrium quantity and then substitute q back into either D(q) or S(q) to find the equilibrium price.Exercise 4.X3 Make a reasonable conjecture about the nth term in the sequence. 5 9 15 23 33
Answer:
Conjecture: next term is 45
Step-by-step explanation:
One very common sequence is one where the difference between one term and the previous one follows a recognizable pattern. Let's inspect the difference from one term to the previous one in the sequence:
Difference from 9 to 5: 9 - 5 = 4
Difference from 15 to 9: 15 - 9 = 6
Difference from 23 to 15: 23 -15 = 8
Difference from 33 to 23: 33-23= 10
At this point the pattern is clear, the differences are just even numbers increasing 2 by 2. We would expect next difference to be 12, and so the next term on the sequence should be 33 + 12 = 45.
A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim?
Answer:
The business should reject the supplier's claim as mean length is not equal to claimed value of 26.70 inches.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 26.70 inches
Sample mean, [tex]\bar{x}[/tex] = 26.77 inches
Sample size, n = 48
Alpha, α = 0.05
Population standard deviation, σ = 0.20 inches
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 26.70\text{ inches}\\H_A: \mu \neq 26.70\text{ inches}[/tex]
We use Two-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{26.77 - 26.70}{\frac{0.20}{\sqrt{48}} } = 2.425[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = 1.96[/tex]
Since,
[tex]z_{stat} > z_{critical}[/tex]
We reject the null hypothesis and accept the alternate hypothesis. Thus, the business should reject the supplier's claim as mean length is not equal to claimed value of 26.70 inches.
Bea T. Howen, a sophomore college student, lost her scholarship after receiving a D in her "Music Appreciation" course. She decided to buy a snow plow to supplement her income during the winter months. It cost her $5550.00. Fuel and standard maintenance will cost her an additional $8.25 for each hour of use..
(a) Find the cost function C(x) associated with operating the snow plow for x hours.
If she charges $36.00 per hour write the revenue function R(x) for the amount of revenue gained from x hours of use.
(b) Find the profit function P(x) for the amount of profit gained from x hours of use.
How many hours will she need to work to break even?
Answer:
(a) C(x) = 5550 +8.25x
(b) R(x) = 36x
(c) P(x) = 27.75x -5550; 200 hours to break even
Step-by-step explanation:
(a) Howen's costs include fixed costs and a cost per hour. Then her total cost will be the sum of the fixed cost (5550) and the product of hours (x) and the cost per hour (8.25):
C(x) = 5550 +8.25x
__
(b) Howen plans to charge a given amount (36) per hour, so her revenue will be the product of that amount and the number of hours she works:
R(x) = 36x
__
(c) Her profit function is the difference between revenue and cost:
P(x) = R(x) -C(x)
P(x) = 36x -(5550 +8.25x)
P(x) = 27.75x -5550
Howen's break-even point is the number of hours required to make profit be zero:
0 = 27.75x -5550
0 = x - 200 . . . . . . . . . divide by 27.75
200 = x . . . . . . . . . . . . add 200
She needs to work 200 hours to break even.
Bea's cost function for operating her snow plow is C(x) = 5550.00 + 8.25x. Her revenue function for the amount she earns is R(x) = 36.00x. The profit function, which is the revenue minus the cost, simplifies to P(x) = 27.75x - 5550. To break even, she needs to work approximately 200 hours.
Explanation:The cost function C(x) for operating the snow plow for x hours includes the initial cost of the snow plow plus the hourly operating cost. This can be written as C(x) = 5550.00 + 8.25x.
The revenue function R(x), representing the amount of revenue gained from x hours of use, can be given as R(x) = 36.00x as she charges $36 for each hour.
The profit function P(x), representing the amount of profit, is the revenue function minus the cost function.so, P(x) = R(x) - C(x) which simplifies to P(x) = 36x - (5550 + 8.25x). Simplify that to get P(x) = 27.75x - 5550.
To find when she breaks even, we set the profit function equal to zero and solve for x:
0 = 27.75x - 5550
Adding 5550 to both sides gives: 27.75x = 5550
Dividing both sides by 27.75 gives: x ≈ 200. Therefore, she needs to work approximately 200 hours to break even.
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Solve the linear system by Gaussian-Jordan elimination. a) x1 + x2 + 2x3 = 8 b) x – y + 2z - w = -1 – x1 – 2x2 + 3x3 = 1 2x + y - 22 – 2w = -2 3x1 – 7x2 + 4x3 = 10 -x + 2y – 4z +w=1 3x – 3w = -3
Answer:
Solution for the linear system:
a) [tex]X_1=3, X_2=1, X_3=2[/tex]
b) [tex]x= w-1\\y=2z[/tex]
z and w are free, meaning that can have any value, for this reason, this system has infinite solutions.
Step-by-step explanation:
Gaussian-Jordan elimination consists of taking an augmented matrix, and transform it into its Row echelon form by means of row operation. For notation, R_i will be the transform column, and r_i the actual one.
Linear System a)
First, you have to convert the system into matrix notation, in this case, column 1 corresponds to variable x_1, column 2 to x_2, column 3 to x_3 and column 4 to the system constants:
[tex]\left[\begin{array}{cccc}1&1&2&8\\-1&-2&3&1\\3&-7&4&10\end{array}\right][/tex]
Transform to 0 every number in the rows under the first row.Operations:
[tex]R_2=r_1+r_2\\R_3=-3r_1+r_3[/tex]
[tex]\left[\begin{array}{cccc}1&1&2&8\\0&-1&5&9\\0&-10&-2&-14\end{array}\right][/tex]
Transform the -1 of the second row into 1Operations:
[tex]R_2=-r_2[/tex]
[tex]\left[\begin{array}{cccc}1&1&2&8\\0&1&-5&-9\\0&-10&-2&-14\end{array}\right][/tex]
Transform to 0 the numbers under the 1 in the second rowOperations:
[tex]R_3=10r_2+r_3[/tex]
[tex]\left[\begin{array}{cccc}1&1&2&8\\0&1&-5&-9\\0&0&-52&-104\end{array}\right][/tex]
Transform the -52 in the row 3 into 1Operations:
[tex]R_3=-\frac{1}{52}r_3[/tex]
[tex]\left[\begin{array}{cccc}1&1&2&8\\0&1&-5&-9\\0&0&1&2\end{array}\right][/tex]
Now write the matrix like linear equations[tex]x_1+x_2+2x_3=8\\x_2-5x_3=-9\\x_3=2[/tex]
Now that you know the valuo of x_3, you can solve the system starting from the bottom up, then find x_2 and finally x_1[tex]x_3=2\\x_2=-9+5*2=1\\x_1=8-1-4=3[/tex]
Linear System b)
For this system, the process is the same as the above.
Convert the system into matrix form
[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\2&1&-2&-2&-2\\-1&2&-4&1&1\\3&0&0&-3&-3\end{array}\right][/tex]
Operations:
[tex]R_2=-2r_1+r_2\\R_3=r_1+r_3\\R_4=-3r_1+r_4[/tex]
[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\0&3&-6&0&0\\0&1&-2&0&0\\0&3&-6&0&0\end{array}\right][/tex]
Operations:
[tex]R_2=\frac{1}{3}r_2[/tex]
[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\0&1&-2&0&0\\0&1&-2&0&0\\0&3&-6&0&0\end{array}\right][/tex]
Operations:
[tex]R_3=-r_2+r_3\\R_4=-3r_2+r_4[/tex]
[tex]\left[\begin{array}{ccccc}1&-1&2&-1&-1\\0&1&-2&0&0\\0&0&0&0&0\\0&0&0&0&0\end{array}\right][/tex]
Now you can write the system as equations:
[tex]x-y+2z-w=-1\\y-2z=0[/tex]
For w and z there is no unique answer, so the system result is expressed in terms of those variables. This system has infinite solutions.
Solution:
[tex]x= w-1\\y=2z[/tex]
z and w are free values.
Define arcwise(=path) connectedness of a set in a metric space. State a relation between arcwise connectedness and connectedness of a set.
Answer:
See definitions and relation below
Step-by-step explanation:
Given points x and y of a certain set S in a metric space, a path from x to y is a continuous map f:[a,b]-->S of some closed interval [a,b] in the real line into S, such that
f(a)=x and f(b)=y
In this case, we can also say that the points x and y are joined by a path or arc.
A set S in metric space is said to be path connected or arcwise connected if every pair of points x, y of S can be joined by a path.
The relation between arcwise connectedness and connectedness of a set is that every arcwise connected set is also connected, but the converse does not hold; not every connected space is also path connected.
As an example, consider the unit square [0,1]X[0,1] with the dictionary order topology.
It can be proved that this space is connected but not path connected.
Arcwise connectedness is defined as the presence of a continuous path between any two points in a set in a metric space. There is a relation between arcwise connectedness and connectedness, where any path connected set is also connected, but the converse is not necessarily true.
Explanation:A set in a metric space is said to be arcwise connected or path connected if there exists a continuous curve or path that connects any two points in the set.
The relation between arcwise connectedness and connectedness of a set is that any arcwise connected set is also connected, but the converse is not necessarily true. In other words, every path connected set is connected, but not every connected set is path connected.
For example, consider a set consisting of two separate points in a metric space. This set is connected because we cannot find two disjoint open sets that cover the set, but it is not arcwise connected because there is no continuous path connecting the two points.
In Mary's first math test she scored 87%. The mean and standard deviation for the class were 71% and 18% respectively. In her second math test, Mary scored 66%. The mean and standard deviation for the class were 53% and 14% respectively. In which test did Mary do better relative to the rest of the class? Explain your reasoning. (Hint: find the z-scores corresponding to her two test scores.)
Answer:
Step-by-step explanation:
Since your population are the students in math class, you can use the z-score formula [tex]z=(x-\mu)/\sigma[/tex] in order to comparing the two math test scores. Where [tex]\mu [/tex] is the mean for the class, [tex]\sigma [/tex] is the standars deviation and x is Mary score.
For the first test [tex]\mu=.71 , \sigma=.18,x=.87[/tex] , so ,[tex]z_{1} = (.87-.71)/(.18)=.88[/tex].
For the second test [tex]\mu=.53 , \sigma=.14,x=.66[/tex] , so ,[tex]z_{1} = (.66-.53)/(.14)=.93[/tex]
Mary do better in the second test, relative to the rest of the class (because [tex].88 \leq .93[/tex], it means the second score is nearer to the mean score of the class than the first one )
Part D 1 light-minute in miles Express your answer using three significant figures. ? mi 1 light minute Request Answer Submit
Answer:
1 light-minute ≈ 1.12×10⁷ miles, three significant figures.
Step-by-step explanation:
Light-second is equal to the distance traveled per second by light in space, which is equal to 299,792,458 metres. Other units used are light-day, light-hour and light-minute.
Significant figures are the figures or digits of a number that carry meaning and contribute to the precision of the given number.
1 light-minute = 1.118×10⁷ miles, has four significant figures.
To express this number in three significant figures, the given number is rounded.
1 light-minute = 1.118×10⁷ miles ≈ 1.12×10⁷ miles, has three significant figures, as the non-zero digits are significant.
A city is holding a referendum on increasing property taxes to pay for a new high school. In a survey of 458 likely voters, 254 said that they would vote "yes" on the referendum. Create a 95% confidence interval for the proportion of likely voters who will vote "yes" on the referendum. Use Excel to create the confidence interval, rounding to four decimal places.
Answer:
The confidence interval is -5.3444 to 6.453 .
Step-by-step explanation:
We are given that In a survey of 458 likely voters, 254 said that they would vote "yes" on the referendum.
So, n = 458
x = 254
We will use sample proportion over here
[tex]\widehat{p}=\frac{x}{n}[/tex]
[tex]\widehat{p}=\frac{254}{458}[/tex]
[tex]\widehat{p}=0.5545[/tex]
Confidence level = 95% = 0.95
Level of significance = 1-0.95 = 0.05
z value at 0.05 significance level = 1.96
Formula of confidence interval : [tex]\widehat{p}-x\times \sqrt{\frac{\widehat{p} \times (1-\widehat{p})}{n}[/tex] to [tex]\widehat{p}+x\times \sqrt{\frac{\widehat{p} \times (1-\widehat{p})}{n}[/tex]
Confidence interval : [tex]0.5545-254\times \sqrt{\frac{0.5545\times (1-0.5545)}{458}}[/tex] to [tex]0.5545+254\times \sqrt{\frac{0.5545\times (1-0.5545)}{458}}[/tex]
Confidence interval : [tex]-5.3444[/tex] to [tex]6.453[/tex]
Hence The confidence interval is -5.3444 to 6.453 .
Answer:
Step-by-step explanation:
We have given,
x=254
n=458
Estimate for sample proportion
Level of significance is =1-0.95=0.05
Z critical value(using Z table)=1.96
Confidence interval formula is
=(0.5091,0.6001)
Lower limit for confidence interval=0.5091
Upper limit for confidence interval=0.6001
A water tank has a diameter of 15 ft and is 22 ft high. a. What is the volume of the tank in ft?? b. In m?? c. In cm?
Answer:
a) [tex]V = 3887.72 ft^{3}[/tex]
b)[tex]V = 104.97 m^{3}[/tex]
c)[tex]V = 104,968,468.538 cm^{3}[/tex]
Step-by-step explanation:
A tank has the format of a cylinder.
The volume of the cylinder is given by:
[tex]V = \pi r^{2}h[/tex]
In which r is the radius and h is the heigth.
The problem states that the diameter is measured to be 15.00 ft. The radius is half the diameter. So, for this tank
[tex]r = \frac{15}{2} = 7.50[/tex] ft
The height of the tank is 22 ft, so [tex]h = 22[/tex].
a) Volume of the tank in [tex]ft^{3}[/tex]:
[tex]V = \pi r^{2}h[/tex]
[tex]V = pi*(7.5)^2*22[/tex]
[tex]V = 3887.72 ft^{3}[/tex]
b) Volume of the tank in [tex]m^{3}[/tex]:
We must convert both the radius and the height to m.
Each feet has 0.30 m, so:
Radius:
1 feet - 0.30m
7.5 feet - r m
[tex]r = 7.5*0.30[/tex]
[tex]r = 2.25m[/tex]
Height
1 feet - 0.30m
22f - h m
[tex]h = 22*0.30[/tex]
[tex]r = 6.60m[/tex]
The volume is:
[tex]V = \pi r^{2}h[/tex]
[tex]V = pi*(2.25)^2*6.60[/tex]
[tex]V = 104.97 m^{3}[/tex]
c) Volume of the tank in [tex]cm^{3}[/tex]:
Each m has 100 cm.
So [tex]r = 2.25m = 225cm[/tex]
[tex]h = 6.60m = 660cm[/tex]
The volume is:
[tex]V = \pi r^{2}h[/tex]
[tex]V = pi*(225)^2*660[/tex]
[tex]V = 104,968,468.538 cm^{3}[/tex]
Chef needs to prepare 32 Servings of cooked beans, each portion 3 oz. How 29. any 12 oz. cans should Chef order, if the Yield factor per can is 0.8 a. 8 cans b. 10 cans c. 6.4 cans d. 120 cans e. NONE of the above answers are corredt
Answer:
10 cans
Step-by-step explanation:
Number of servings to be prepared = 32
Weight of each pound = 3 oz
Yield factor per can = 0.8
Now,
Total weight of the cans = 32 × 3 = 96 oz
Actual weight required with yield factor 0.8 = [tex]\frac{96\ oz}{0.8}[/tex] = 120 oz
Therefore,
The number of 12 oz cans required = [tex]\frac{120}{12}[/tex] = 10 cans
The Chef should order 10 cans.
Explanation:To determine how many 12 oz. cans the Chef should order, we need to calculate the total amount of cooked beans required.
Since each serving is 3 oz. and there are 32 servings, the total amount needed is
3 oz. * 32 = 96 oz..
The yield factor per can is 0.8, so each can provides 0.8 * 12 oz. = 9.6 oz.
Therefore, the Chef should order 96 oz. / 9.6 oz. per can = 10 cans.
Learn more about Calculating the number of cans needed here:https://brainly.com/question/31942594
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The discount points are 3% which represents $2,700. The buyer down payment is 20%. What is the purchase price of the property? (Please show all steps)
Answer: The purchase price of the property is $112,500.
Step-by-step explanation:
Let the original value of property be 'x'.
Discount rate = 3%
Amount of discount = $2700
According to question, it becomes,
[tex]\dfrac{3}{100}\times x=2700\\\\x=\dfrac{2700\times 100}{3}\\\\x=\$90000[/tex]
Rate of down payment = 20%
So, Remaining rate of payment = 100-20 = 80%
So, Purchase price of the property would be
[tex]\dfrac{80}{100}\times x= 90000\\\\0.8\times x=90000\\\\x=\dfrac{90000}{0.8}\\\\x=\$112,500[/tex]
Hence, the purchase price of the property is $112,500.
Jane is 20 lbs heavier than Alive. If Jane's weight is 120% that of Alice, find the weight of Alice
Answer:
Alice's weight is 100 lbs.
Step-by-step explanation:
Let's denote Jane's weight by J, and Alice's weight by A.
The exercise says that Jane is 20 lbs heavier than Alice. So that if you add 20 lbs to Alice's weight, you get Jane's weight. In equation form:
[tex]20+A=J[/tex]
It also mentions that Jane's weight is 120% that of Alice. So that if you multiply Alice's weight by 1.2, you get Jane's weight. In equation form:
[tex]1.2 \cdot A=J[/tex]
Plugging this second equation onto the first equation, we get:
[tex]20+A=1.2A[/tex]
And now solving for A:
[tex]20=1.2A-A[/tex]
[tex]20=0.2A[/tex]
[tex]\frac{20}{0.2}=A[/tex]
[tex]100=A[/tex]
Therefore Alice's weight is 100 lbs.
When you don't seem to get any better, you eventually end up in the hospital. The doctor orders 120 mg of medicine to be given twice a day. The nurse comes in with 6 tablets and tells you that there are 30 mg in each tablet. Is this the correct dosage? If not, how many tablets should you get?
Answer:
It isn't the correct dosage, you should get 8 tablets.
Step-by-step explanation:
First, if the doctors orders 120 mg twice a day, it means that you need 240 mg of medicine. That is calculated as:
120 mg * 2 = 240 mg
Then if each tablet has 30 mg, the number of tablets that you should get is calculated as:
[tex]\frac{240mg}{30mg} = 8[/tex]
So, 240 mg of medicine are equivalents to 8 tablets.
8 tablets are different of 6 tablets, so the dosage given by the nurse is incorrect and you should get 8 tablets every day.
(Discrete Mathematics) If m and n are nonzero integers, show that (2m+3n)/5mn is a rational number.
Answer:
[tex]\frac{(2m+3n)}{5mn}=\frac{2}{5n}+\frac{3}{5m}[/tex] is a rational number for any m and n; nonzero integers.
Step-by-step explanation:
We have been given that 'm' and 'n' are nonzero integers. We are asked to show that [tex]\frac{(2m+3n)}{5mn}[/tex] is a rational number.
We can rewrite our given number as:
[tex]\frac{2m}{5mn}+\frac{3n}{5mn}[/tex]
Cancelling out common terms:
[tex]\frac{2}{5n}+\frac{3}{5m}[/tex]
Since 'm' and 'n' are nonzero integers, so each part will be a rational number.
We know that sum of two rational numbers is always rational, therefore, our given number is a rational number.
Solve the initial value problem: y'(x)=(4y(x)+25)^(1/2) ,y(1)=6. you can't really tell, but the '1/2' is the exponent
Answer:
[tex]y(x)=x^2+5x[/tex]
Step-by-step explanation:
Given: [tex]y'=\sqrt{4y+25}[/tex]
Initial value: y(1)=6
Let [tex]y'=\dfrac{dy}{dx}[/tex]
[tex]\dfrac{dy}{dx}=\sqrt{4y+25}[/tex]
Variable separable
[tex]\dfrac{dy}{\sqrt{4y+25}}=dx[/tex]
Integrate both sides
[tex]\int \dfrac{dy}{\sqrt{4y+25}}=\int dx[/tex]
[tex]\sqrt{4y+25}=2x+C[/tex]
Initial condition, y(1)=6
[tex]\sqrt{4\cdot 6+25}=2\cdot 1+C[/tex]
[tex]C=5[/tex]
Put C into equation
Solution:
[tex]\sqrt{4y+25}=2x+5[/tex]
or
[tex]4y+25=(2x+5)^2[/tex]
[tex]y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}[/tex]
[tex]y(x)=x^2+5x[/tex]
Hence, The solution is [tex]y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}[/tex] or [tex]y(x)=x^2+5x[/tex]
Draw Conclusions The decimal 0.3 represents What type of number best describes 0.9, which is 3.0.3? Explain
Answer:
The product represent the number [tex]3\times 0.3=0.9[/tex]
Step-by-step explanation:
To find : The decimal 0.3 represents What type of number best describes 0.9, which is 3.0.3?
Solution :
0.3 represents [tex]0.3=\frac{3}{10}[/tex]
0.9 represents [tex]0.9=\frac{9}{10}[/tex]
If we multiply 0.3 by 3 we get 0.9
As, [tex]3\times 0.3=3\times \frac{3}{10}[/tex]
[tex]3\times 0.3=\frac{9}{10}[/tex]
[tex]3\times 0.3=0.9[/tex]
Therefore, The product represent the number [tex]3\times 0.3=0.9[/tex]
Convert 26inches into meters
Answer:
0.6604 m
Step-by-step explanation:
The convertion from inches to meters is 1 inch= 0.024 meters, so:
26 inches = 26 inch* 0.024 meters/inch = 0.6604 meters
Good luck!
Find #(A u B u C) if #A = #B = #C = 17, #(A n B) = 5, #(B n C) = 6, #(An C) = 7, and #(A n B n C-2. You may find it helpful to draw a Venn diagram.
Answer:
35
Step-by-step explanation:
Given that A,B, C are three non empty sets.
[tex]n(A) =n(B) =n(C) =17\\n(A \bigcap C) = 7\\n(A \bigcap B) = 5\\n(B \bigcap C) = 6\\n(A \bigcap B \bigcap C) = 7[/tex]
Use the addition theory for finding no of elements in union of two or more sets
We have addition theorem as
[tex]n(AUBUC) = n(A)+n(B)+n(C)-n(A \bigcap B)-n(B \bigcap C)-n(A \bigcap C)+n(A \bigcap B \bigcap C)[/tex]
Now substitute for each entry from the given information
[tex]n(AUBUC) = 17+17+17-5-6-7+2\\= 53-18\\=35[/tex]
An investment project involves an immediate outlay of $8 million. The net cash flows received at the end of years 1, 2, and 3 will be $3 million, $4 million, and $2 million. A 10% discount rate is applicable so that the present value factors for years 1, 2, and 3 are 0.9091, 0.8264, and 0.7513. The NPV of the investment will be: (a) (b) (c) (d) $1 million $9 million $0.46 million $7.54 million
Answer:
(c) 0.46 million
Step-by-step explanation:
As provided immediate cash outlay = $8 million.
This will represent cash outflow at period 0, as it is made immediately, no time period has lapsed.
Cash inflows as provided and the respective present value factor are:
Year Cash Inflow Factor Discounted Value
1 $3 million 0.9091 $2,727,300
2 $4 million 0.8264 $3,305,600
3 $2 million 0.7513 $1,502,600
Total present value of cash inflow = $7,535,500
Therefore, net present value = $7,535,500 - $8,000,000 = - $464,500
That is - 0.46 million
Correct option is
(c) 0.46 million
(Order is anti-symmetric) If a > b and b > a, then a = b. (e) a
Answer:
a=b
Step-by-step explanation:
An antisymmetric relation () satisfies the following property:
If (a, b) is in R and (b, a) is in R, then a = b.
This means that if a|b and b|a then a = b
If a|b then, b can be written as b = an for an integer n
If b|a then a can be written as a= bm for an integer m
Now we have b = (a)n = (bm)n
b = bmn
1 =mn
But since m and n are integers, the only two integers that satisfy this property would be m = n = 1
Therefore, b = an = a (1) = a ⇒b = a
If you are asked to provide a set of two or more numeric answers, separate them with commas. For example, to provide the year that Sputnik (the first satellite to be sent into orbit around the Earth) was launched and the year humans first walked on the Moon, you would enter 1957,1969 in the answer box. A rectangle has a length of 5.50 m and a width of 12.0 m . What are the perimeter and area of this rectangle?
Answer: Perimeter = 66 cm and area =[tex]66\ m^2[/tex]
Step-by-step explanation:
The perimeter of rectangle is given by :-
[tex]P=2(l+w)[/tex], where l is length and w is width of the rectangle.
Given : A rectangle has a length of 5.50 m and a width of 12.0 m .
Then, the perimeter of rectangle :
[tex]P=2(12+5.50)\\\\\Rightarrow\ P=2(17.50)=35\ m[/tex]
Also, area of rectangle is given by :-
[tex]A=l\times w=5.50\times12=66 \ m^2[/tex]
Area of rectangle = [tex]66\ m^2[/tex]
Suppose you go shopping for a new futon bed for your room. The model you really like happens to be on sale for $400. It's original price is $700. What percent of the original price will you save if you purchase it?
Answer:
If you purchase it, you are going to save 0.43 = 43% of the original price
Step-by-step explanation:
This problem can be solved by a rule of three.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
In this problem, we have the following measures:
-The prices
-The percentage that the price represents.
As the value of one measure increases, so do the value of the other. It means that we have a direct rule of three.
The problem states that the model you really like happens to be on sale for $400. It's original price is $700.
You saved $700-$400 = $300.
What percent of the original price will you save if you purchase it?
How much is $300 of $700.
$700 - 1
$300 - x
700x = 300
[tex]x = \frac{300}{700}[/tex]
[tex]x = 0.43[/tex]
If you purchase it, you are going to save 0.43 = 43% of the original price
Please help I can’t find the primes.
Answer:
the primes are all the even numbers in the equation
Step-by-step explanation:
Write the negation, contrapositive, converse, and inverse for the following statement. (Assume that all variables represent fixed quantities or entities, as appropriate.) If n is divisible by 6, then n is divisible by 2 and n is divisible by 3.
Final answer:
The negation, contrapositive, converse, and inverse of a statement relating the divisibility of a number by 6, 2, and 3 are constructed by logically altering the original condition and consequent. These reflect different ways to express the relationship between the divisibility properties.
Explanation:
The original statement is: "If n is divisible by 6, then n is divisible by 2 and n is divisible by 3." Let's define the following propositions:
P: n is divisible by 6.
Q: n is divisible by 2.
R: n is divisible by 3.
The original statement can be written in logical form as P → (Q ∧ R).
Negation
The negation of the original statement is: "It is not the case that if n is divisible by 6, then n is divisible by 2 and n is divisible by 3." In logical form: ¬(P → (Q ∧ R)).
Contrapositive
The contrapositive of the original statement is: "If n is not divisible by 2 or n is not divisible by 3, then n is not divisible by 6." In logical form: (¬Q ∨ ¬R) → ¬P.
Converse
The converse of the original statement is: "If n is divisible by 2 and n is divisible by 3, then n is divisible by 6." In logical form: (Q ∧ R) → P.
Inverse
The inverse of the original statement is: "If n is not divisible by 6, then n is not divisible by 2 or n is not divisible by 3." In logical form: ¬P → (¬Q ∨ ¬R).