Answer:
[tex]10.08-1.64\frac{0.1}{\sqrt{6}}=10.013[/tex]
[tex]10.08+1.64\frac{0.1}{\sqrt{6}}=10.147[/tex]
So on this case the 90% confidence interval would be given by (10.013;10.147)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma =0.1[/tex] represent the population standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
The mean calculated for this case is [tex]\bar X=10.08[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that [tex]z_{\alpha/2}=1.64[/tex]
Now we have everything in order to replace into formula (1):
[tex]10.08-1.64\frac{0.1}{\sqrt{6}}=10.013[/tex]
[tex]10.08+1.64\frac{0.1}{\sqrt{6}}=10.147[/tex]
So on this case the 90% confidence interval would be given by (10.013;10.147)
What is 1/6 divide by 1/3
0.555555556 so that's it hope this helped
Answer:
0.5
Step-by-step explanation:
Because I said so
What are the functions of money?
Answer:
The functions of money are:
Function # 1. A Medium of Exchange: ...
Function # 2. A Measure of Value: ...
Function # 3. A Store of Value (Purchasing Power): ...
Function # 4. The Basis of Credit: ...
Function # 5. A Unit of Account: ...
Function # 6. A Standard of Postponed Payment:
Explanation:
My parents are bankers.
How do I express the following as a fractional part of a year?
3 month
55 days
1 month
7 months
120 days
Answer:
See below.
Step-by-step explanation:
A year has 12 months and 365 days.
3 months: 3/12 year = 1/4 year
55 days: 55/365 year = 11/73 year
1 month: 1/12 year
7 months = 7/12 year
120 days = 120/365 year = 24/73 year
Answer:
3 months = 3/12 | 55 days = 55/365 | 1 month = 1/12 | 7 months = 7/12 | 120 days = 120/365
Step-by-step explanation:
All you have to do is write the numbers with the total underneath. With months, it is out of 12 because there are 12 months in a year. With days, it is out of 365 days because there are 365 days in total in a year.
If needed, simplify the answer to its simplest form
Lena is a college basketball player who has made 75%, percent of the free-throws she has attempted in her career. she decided to practice a new technique for shooting her free-throws. lena was curious if this new technique produced significantly better or worse results. she tried the new technique and made 70%, percent of 50 attempts. here's lena's alternative hypothesis: ha : the proportion of attempts made using this new technique is. what is an appropriate way for lena to finish her alternative hypothesis a.equal to 75% b.not equal to 75% c.not equal to 70% d.equal to 70%
Answer:
b
Step-by-step explanation:
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of the sphere x2 + y2 + z2 = 9. (Hint: Note that S is not a closed surface. First compute integrals over S1 and S2, where S1 is the disk x2 + y2 ≤ 9, oriented downward, and S2 = S1 ∪ S.)
Close off the hemisphere [tex]S[/tex] by attaching to it the disk [tex]D[/tex] of radius 3 centered at the origin in the plane [tex]z=0[/tex]. By the divergence theorem, we have
[tex]\displaystyle\iint_{S\cup D}\vec F(x,y,z)\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F(x,y,z)\,\mathrm dV[/tex]
where [tex]R[/tex] is the interior of the joined surfaces [tex]S\cup D[/tex].
Compute the divergence of [tex]\vec F[/tex]:
[tex]\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2[/tex]
Compute the integral of the divergence over [tex]R[/tex]. Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:
[tex]\begin{cases}x(\rho,\theta,\varphi)=\rho\cos\theta\sin\varphi\\y(\rho,\theta,\varphi)=\rho\sin\theta\sin\varphi\\z(\rho,\theta,\varphi)=\rho\cos\varphi\end{cases}\implies\begin{cases}x^2+y^2+z^2=\rho^2\\\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi\end{cases}[/tex]
So the volume integral is
[tex]\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5[/tex]
From this we need to subtract the contribution of
[tex]\displaystyle\iint_D\vec F(x,y,z)\cdot\mathrm d\vec S[/tex]
that is, the integral of [tex]\vec F[/tex] over the disk, oriented downward. Since [tex]z=0[/tex] in [tex]D[/tex], we have
[tex]\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k[/tex]
Parameterize [tex]D[/tex] by
[tex]\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath[/tex]
where [tex]0\le u\le 3[/tex] and [tex]0\le v\le2\pi[/tex]. Take the normal vector to be
[tex]\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=-u\,\vec k[/tex]
Then taking the dot product of [tex]\vec F[/tex] with the normal vector gives
[tex]\vec F(x(u,v),y(u,v),0)\cdot(-u\,\vec k)=-y(u,v)^2u=-u^3\sin^2v[/tex]
So the contribution of integrating [tex]\vec F[/tex] over [tex]D[/tex] is
[tex]\displaystyle\int_0^{2\pi}\int_0^3-u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac{81\pi}4[/tex]
and the value of the integral we want is
(integral of divergence of F) - (integral over D) = integral over S
==> 486π/5 - (-81π/4) = 2349π/20
The process involves applying the Divergence Theorem over a closed surface formed by adding a bottom disk to the sphere and converting the given surface integral into a volume integral which is easier to calculate. F(x, y, z) must be used accurately in all calculations.
Explanation:To solve this problem, we need to apply the Divergence Theorem to evaluate the surface integral of the given vector field F(x, y, z) over the top half of the sphere. Before we do that, we must first compute the integrals over S1 and S2, where S1 is the disk x² + y² ≤ 9, oriented downward, and S2 = S1 ∪ S.
On applying the Divergence Theorem over a closed surface S₁ + S₂ obtained by adding a bottom disk to the sphere, we can convert the given surface integral into a volume integral over the region inside the closed surface.
Once we obtain this volume integral, this should simplify our calculations, as volume integrals are typically easier to evaluate than surface integrals. This strategy utilises the power of the Divergence Theorem, which connects the flow of a vector field across a surface to the behavior of the field inside the volume enclosed by the surface.
Remember to use the correct vector field formulas for F when calculating the integrals over S1 and S2. Ensure each step is carefully followed so errors are not made.
Learn more about Divergence Theorem here:https://brainly.com/question/33180298
#SPJ3
Rover’s dog bowl is pictured below. Approximately how much water does it hold? Use 3.14 for π and round your answer to the nearest cubic inch.
Answer:
57 in³
Step-by-step explanation:
Area of cylinder= [tex]\pi {r}^{2} h[/tex]
Let's find the radius.
Radius= Diameter ÷2
Radius= 6 ÷2
Radius= 3 in.
Area of Rover's dog bowl
= 3.14(3)²(2)
= 56.52
= 57 in³ (nearest cubic inch)
Answer:
57 in3
Step-by-step explanation:
A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than 5 ? Select three
options
choosing 1 blue marble
choosing 1 red marble
ll choosing 1 red marble, not replacing it, and then choosing a blue marble
choosing 1 white marble, replacing it, and choosing another white marble
choosing 1 white marble
Save and Exit
Submit
Mark this and retum
Answer:
choosing 1 red marble ; choosing 1 white marble, replacing it, and choosing another white marble ; and choosing 1 white marble
Step-by-step explanation:
There are 2+3+5 = 10 marbles. The probability of choosing 1 blue marble is 2/10 = 1/5; this is not greater than 1/5.
The probability of choosing 1 red marble is 3/10; this is greater than 2/10, which is the same as 1/5.
The probability of choosing 1 red marble is 3/10; not replacing it and choosing a blue marble would then be a probability of 2/9. Together this is a probability of 3/10(2/9) = 6/90 = 3/45; this is smaller than 9/45, which is the same as 1/5.
The probability of choosing 1 white marble is 5/10 = 1/2; replacing it and choosing another white marble would be 1/2. Together this is a probability of 1/2(1/2) = 1/4; this is greater than 4/20, which is the same as 1/5.
The probability of choosing 1 white marble is 5/10 = 1/2. This is greater than 2/10, which is the same as 1/5.
Answer:
b,d,e are the awnsers
Step-by-step explanation:
What is another name used for permanent cement?
Answer:
Zinc Phosphate cement
Answer:
luting agent
Step-by-step explanation:
For which of the following procedures would you include a temporary
luting agent is basicslly the same thing
Select the correct answer.
What is the solution for p in the equation?
1/3p + 1/2p = 7/6p +5 + 4
A.
p = -6
B.
p = -1
C.
p = 1
D.
p = 6
To solve for p in the equation 1/3p + 1/2p = 7/6p + 5 + 4, you need to combine like terms and isolate p. The solution is p = 27.
Explanation:To solve for p in the equation 1/3p + 1/2p = 7/6p + 5 + 4, you need to combine like terms and isolate p on one side of the equation.
Multiply the fractions by their respective denominators to eliminate the fractions. This gives us 2/6p + 3/6p = 7/6p + 9.
Combine like terms. On the left side, 2/6p + 3/6p = 5/6p. On the right side, 7/6p + 9 remains unchanged.
Subtract 5/6p from both sides to isolate p. This gives us 7/6p - 5/6p = 9.
Combine like terms on the left side. 7/6p - 5/6p = 2/6p.
Simplify the equation further. 2/6p = 9 can be reduced to 1/3p = 9.
Multiply both sides of the equation by the reciprocal of 1/3, which is 3/1. This gives us p = 9 * (3/1) = 27.
Therefore, the solution for p in the equation is p = 27.
The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a Normal distribution with mean that varies slightly from year to year and standard deviation 6.0. You plan to take an SRS of size n of the students who took the ACT exam this year and compute the mean score of the students in your sample. You will use this to estimate the mean score of all students this year. In order for the standard deviation of to be no more than 0.1, how large should n be
Answer:
The sample size must be atleast 3600
Step-by-step explanation:
We are given the following in the question:
The scores of individual students on the American College Testing (ACT) Program is a bell shaped distribution that is a normal distribution.
Population standard deviation = 6.0
We want that the sample standard deviation should not be more than 0.1.
Thus, the standard error should not be more than 0.1.
Standard error =
[tex]=\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting values, we get,
[tex]\dfrac{\sigma}{\sqrt{n}}\leq 0.1\\\\ \dfrac{6}{\sqrt{n}} \leq 0.1\\\\ \sqrt{n}\geq 60\\n\geq 3600[/tex]
Thus, the sample size must be atleast 3600
The University of Montana ski team has nine entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the nine team entrants achieve first, second, and third places
Answer:
504 ways
Step-by-step explanation:
The first position can go in 9 ways
The second position can go to the team in 8 ways
The third position can go to the team in 7 ways
Therefore, the first,second and third position can go to the team in:
9 X 8 X 7=504 ways
or Simply, we can use Permutation.
[tex]^9P_3=504[/tex] ways
What can we conclude for the following linear homogeneous equation? t2y''+3ty'+y=0, t>0. y1=t is a solution. By the method of reduction of order, we can ALWAYS find another independent solution y2 satisfying W(y1,y2)≠ 0 y1=t−1 is a solution. By the method of reduction of order, we can ALWAYS find another independent solution y2 satisfying W(y1,y2)≠ 0 None of these y1=t is a solution. By the method of reduction of order, we can SOMETIMES find another independent solution y2 satisfying W(y1,y2)≠ 0 y1=t−1 is a solution. By the method of reduction of order, we can SOMETIMES find another independent solution y2 satisfying W(y1,y2)≠ 0
Answer:
Required conclusion is that if [tex]y_1, y_2[/tex] satisfies given differential equation and wronskean is zero then they are considered as solution of that differential equation.
Step-by-step explanation:
Given differential equation,
[tex]t^2y''+3ty'+y=0[/tex] [tex] t>0\hfill (1)[/tex]
(i) To verify [tex]y_1(t)=t[/tex] is a solution or not we have to show,
[tex]t^2y_{1}^{''}+3ty_{1}^{'}+y_1=0[/tex]
But,
[tex]t^2y_{1}^{''}+3ty_{1}^{'}+y_1=(t^2\times 0)=(3t\times 1)+t=4t\neq 0[/tex]
hence [tex]y_1[/tex] is not a solution of (1).
Now if [tex]y_2=t-1[/tex] is another solution where [tex]y_2(t)=t-1[/tex] then,
[tex]t^2y_{2}^{''}+3ty_{2}^{'}+y_2=0[/tex]
But,
[tex]t^2y_{2}^{''}+3ty_{2}^{'}+y_2=(t^2\times 0)+(3t\times 1)+t-1=4t-1\neq 0[/tex]
so [tex]y_2[/tex] is not a solution of (1).
(ii) Rather the wronskean,
[tex]W(y_1,y_2)=y_{1}y_{2}^{'}-y_{2}y_{1}^{'}=(t\times 1)-((t-1)\times 1)=t-t+1=1\neq 0[/tex]
Hence it is conclude that if [tex]y_1, y_2[/tex] satisfies (i) along with condition (ii) that is wronskean zero, only then [tex]y_1, y_2[/tex] will consider as solution of (1).
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have an average compressive strength of more than 1300KN=m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture has standard deviation ? = 60. Let ? denote the true average compressive strength.
Answer:
Check the explanation
Step-by-step explanation:
Hypotheses are:
[tex]H_o[/tex] : μ 1300, [tex]H_a[/tex] : μ > 1300
The distribution of test statistics will be normal with mean
mean 1300
and standard deviation
[tex]sd=\frac{\sigma}{\sqrt{n}}=\frac{68}{\sqrt{11}}[/tex]=20.50277
Now z-score for T-1331.26 and μ 1300 is
-1300-1.52 1331.26 1300 68/V11
[tex]z=\frac{1331.26-1300}{68/\sqrt{11}}= 1.52[/tex]
So the probability distribution of the test statistic when H0 is true is
a = P(z > 1.5247) = 0.0643
What type of triangle, if any can be formed with angle measures of 32 degrees, 126 degrees, and 32 degrees?
Answer 1 only an obtuse triangle
Answer 2 either an acute isosceles triangle or an obtuse isosceles triangle
Answer 3 only an acute isosceles triangle
Answer 4 no triangle
No triangle can be formed.(answer 4)
What is triangle?In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees
We have,
Angles of triangle= 32 degrees, 126 degrees , 32 degrees
We know,
All triangles must have angles that measure up to 180 degrees.
[tex]32^{o} +126^{o} + 32^{o}[/tex]
=[tex]190^{o}[/tex] > [tex]180^{0}[/tex]
Hence ,That means that is no triangle can be formed.
To learn more about triangle from here
https://brainly.in/question/3318722
#SPJ2
The sum of the given angles exceeds 180 degrees, which violates the basic rule of triangles, so no triangle can be formed with these measures.
Explanation:To determine what type of triangle can be formed with angle measures of 32 degrees, 126 degrees, and 32 degrees, we need to consider two rules: First, the sum of the angles in any triangle must be 180 degrees. Second, the classification of whether a triangle is acute, obtuse, or right is based on the measures of its angels.
Adding the given angles together (32 degrees + 126 degrees + 32 degrees), we get 190 degrees. Since this sum is greater than 180 degrees, it violates the first rule of triangles. Therefore, no triangle can be formed with these given angle measures.
A waste management service attempts to design routes so that each of their trucks pick-up on average
four tons of garbage or less. A garbage collector believes, however, that he averages picking up more
than four tons of garbage per day and decides to perform a hypothesis test.
Identify a Type II error in the context of this hypothesis test.
a) Concluding that the garbage collector picks up on average more than 4 tons of garbage per day when,
in fact, he doesn’t.
b) Not concluding that the garbage collector picks up on average more than 4 tons of garbage per day
when, in fact, he does.
c) Concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact, he
picks up more.
d) Not concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact,
he does.
I'm confused with the wording but my guess is between B and C
Answer:
The correct option is (c).
Step-by-step explanation:
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.
β = Probability of accepting H₀ when H₀ is false.
In this case we need to test the hypothesis whether the garbage collector's belief is true or not.
The hypothesis can be defined as:
H₀: The garbage collector averages picking up four tons of garbage per day, i.e. μ = 4.
Hₐ: The garbage collector averages picking up more than four tons of garbage per day, i.e. μ > 4.
Consider that the garbage collector made a type II error while drawing the conclusions of the test.
This implies that the garbage collector failed to reject the null hypothesis incorrectly.
That is, he concluded that the he picks up on average four tons of garbage per day, when in fact he picks up more than four tons of garbage every day.
Thus, the correct option is (c).
Answer:4 tons
Step-by-step explanation:
just because ik;;;:)
Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the first card is an ace, or the second a deuce, or the third a three, or, . . . , or the thirteenth a king, or the fourteenth an ace, and so on, we say that a match occurs. Note that we do not require that (13n + 1)th card be any particular ace for a match to occur but only that it be an ace. Compute the expected number of matches that occur.
Answer:
The expected number of matches that occur is 4.
Refer below for the explanation.
Step-by-step explanation:
Refer to the picture for complete steps.
Tommy Wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. In fact, his time between pitches are normally distributed with a mean of seconds and a standard deviation of seconds. What percentage of his times between pitches are longer than seconds
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Tommy Wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. In fact, his time between pitches are normally distributed with a mean of 29 seconds and a standard deviation of 2.1 seconds. What percentage of his times between pitches are longer than 31 seconds ?
Given Information:
Mean pitching time = μ = 29 seconds
Standard deviation of pitching time = σ = 2.1 seconds
Required Information:
P(X > 31) = ?
Answer:
[tex]P(X > 31) = 17.11 \%[/tex]
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We want to find out the probability that what percentage of his times between pitches are longer than 31 seconds.
[tex]P(X > 31) = 1 - P(X < 31)\\P(X > 31) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\P(X > 31) = 1 - P(Z < \frac{31 - 29}{2.1} )\\P(X > 31) = 1 - P(Z < \frac{2}{2.1} )\\P(X > 31) = 1 - P(Z < 0.95)\\[/tex]
The z-score corresponding to 0.95 is 0.8289
[tex]P(X > 31) = 1 - 0.8289\\P(X > 31) = 0.1711\\P(X > 31) = 17.11 \%[/tex]
Therefore, 17.11% of his times between pitches are longer than 31 seconds.
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.9 1.4, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.95 then go for 0.05 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Solve for 3x minus one equals 27
Answer:
the answer is 9.3
Step-by-step explanation:
Answer:
9.
Step-by-step explanation:
You would subtract the one to isolate the variable so 3x = 27 then divide by 3 so the answer is 9.
Expression is equivalent 1/3+(3/4+2/3)?
The expression 1/3 + (3/4 + 2/3) is equivalent to 7/4.
Explanation:The expression is equivalent to 1/3 + (3/4 + 2/3). To solve this expression, we need to simplify the inner parentheses first. Adding 3/4 and 2/3, we get a common denominator of 12:
3/4 + 2/3 = 9/12 + 8/12 = 17/12Now, we can substitute the simplified fraction back into the original expression:
1/3 + (3/4 + 2/3) = 1/3 + 17/12To add the fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12:1/3 + 17/12 = 4/12 + 17/12 = 21/12Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:21/12 = (3 * 7) / (3 * 4) = 7/4Therefore, the expression 1/3 + (3/4 + 2/3) is equivalent to 7/4.
Short=7 Long=
30 60 90 triangle
Final answer:
To find the "long" side opposite the 60° angle in a 30-60-90 triangle with a "short" side length of 7, we multiply 7 by √3 to get 7√3.
Explanation:
The student appears to be asking about the relationships between the sides of a 30-60-90 triangle, which is a special type of right triangle. In such a triangle, the sides are in the ratio 1:√3:2. So, if the "short" side opposite the 30° angle is given as 7, then the "long" side opposite the 60° angle can be found by multiplying the short side by √3. To find the hypotenuse (opposite the 90° angle), we would multiply the short side by 2.
Step-by-step to find the long side:
Identify the given "short" side, which is opposite the 30° angle, as 7.Use the special triangle ratio for a 30-60-90 triangle to find the "long" side by calculating 7 × √3.Therefore, the length of the "long" side opposite the 60° angle is 7√3.
Of the 4,700 students at Medium Suburban College (MSC), 50 play collegiate soccer, 60 play collegiate lacrosse, and 96 play collegiate football. Only 4 students play both collegiate soccer and lacrosse, 5 play collegiate soccer and football, and 17 play collegiate lacrosse and football. No students play all three sports. ____ % of the college soccer players also play one of the other two sports at the collegiate level.
Answer:
18%
Step-by-step explanation:
Of the 50 soccer players, 4 play soccer and lacrosse, and 5 play soccer and football. That is, 9 of the 50 players also play one of the other sports.
9/50 × 100% = 18%
18% of soccer players also play another sport.
On a very hot summer day, 5 percent of the production employees at Highlander Steel are dehydrated. The production employees are randomly selected for a special in-depth study on dehydration. What is the probability of randomly selecting 8 production employees on a hot summer day and finding that none of them are dehydrated
Answer:
P(X=0) = 0.0332
Step-by-step explanation:
5% of the employees are dehydrated. I.e. p = 5/100
p = 0.05
The percentage of employees that are not dehydrated = 100-5 = 95%
q = 1 - p = 1 - 0.05
q = 0.95
A total of 8 employees were randomly selected. n = 8
This is a binomial distribution question
P(X =r) = nCr (p^r)q^(n-r)
n = 8, r = 0
n -r = 8-0 = 8
P(X = 0) = 8C0 (0.05^0)(0.95^8)
8C0 = 1
P(X=0) = 1 * 1* 0.6634
P(X=0) = 0.6634
Answer:
The probability of picking 8 employee and none of them is dehydrated is 0.66
Step-by-step explanation:
P(employee is dehydrated) = 5%=5/100=1/20= 0.05
P(employee not dehydrated) = 1 - 0.05= 0.95
The probability of picking 8 employee and they are not dehydrated is:
= (0.95)^8
= 0.6634204312890625
= 0.66
n a study of the accuracy of fast food drive-through orders, Restaurant A had 314 accurate orders and 61 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.147less thanpless than0.206. What do you conclude?
Answer:
a. 0.1576<p<0.2310
b. The two restaurants likely have similar order rates which are inaccurate.
Step-by-step explanation:
a. We first calculate the proportion, [tex]\hat p[/tex]:
[tex]\hat p=\frac{61}{314}\\\\=0.1943[/tex]
-We use the z-value alongside the proportion to calculate the margin of error:
[tex]MOE=z\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=1.645\times \sqrt{\frac{0.1943(1-0.1943)}{314}}\\\\=0.0367[/tex]
The confidence interval at 90% is then calculated as:
[tex]CI=\hat p\pm MOE\\\\=0.1943\pm 0.0367\\\\=[0.1576,0.2310][/tex]
Hence, the confidence interval at 90% is [0.1576,0.2310]
b. From a above, the calculated confidence interval is 0.1576<p<0.2310
-We compare the calculated CI to the stated CI of 0.147<p<0.206
-The two confidence intervals overlap each other and have the same value for 0.1576<p<0.206
-Hence, we conclude that the two restaurants likely have similar order rates which are inaccurate.
A buyer owes a supplier $820. The terms were 3/10, n/60. Within 10 days, the buyer sent in a payment of $140. How much is the new balance? (Round your answers to the nearest hundredth)
Answer:
The new balance is $675.8
Step-by-step explanation:
Solution
Given that
The total amount of loan = $820.
The terms were = 3/10, n/60
Within 10 days, the buyer sent in a payment of =$140
What is the new balance =?
Now,
3/10 = if the amount is paid in 10 days, a discount of is included
n/60 = This means that all amount should be paid within 60 days
Thus,
$140 for 3/10 as this is paid within 10 days
140 *3% = 140 * 3/100
we get
=$4.2 of discount
Then,
The balance amount becomes $ 820 - 140 -4.2
=$675.8
Ms.Foster built a hexagon by combining two trapezoids that were exactly the same size and shape. What fraction of the area of the whole shape is each trapezoid?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
1. Let's draw the trapezoids, then combine them. The first trapezoid has larger Base measuring 4.67 cm, parallel and minor base =2, an area of 4.98
2. Since the other one is a copy, same area, same base. The junction of both trapezoids generates a hexagon. We have another trapezoid with an area of 4.98. The hexagon has a total area of 9.96
3. So each trapezoid has exactly 1/2 of the area of the hexagon.
At crescent high school, 108 students plan on going to an in-state college and 63 students plan on going out of state college what is the ratio of students planning on going to an in state college to students planning on going to an out state college
Answer:
12/7
Step-by-step explanation:
To set up a ratio of "thing 1" to "thing 2", build a fraction with "thing 1" on top (numerator) and "thing 2" on the bottom (denominator).
The ratio of in-state students to out-of-state students is [tex]\frac{108}{63}[/tex] and this can be simplified ("reduced") by dividing both numbers by 9 to get the fraction 12/7.
Final answer:
Explanation on finding the ratio of students planning in-state college to out-of-state college.
Explanation:
The ratio of students planning on going to an in-state college to students planning on going to an out-of-state college:
To find the ratio, you need to divide the number of students planning in-state college by the number planning out-of-state college.
Number of students planning in-state college: 108
Number of students planning out-of-state college: 63
Ratio: 108:63 which simplifies to 36:21 or 12:7
A charge q1 = 5 μC, is at the origin. A second charge q2 = -3 μC is on the x-axis 0.8 m from the origin. The electric field at a point on the y-axis 0.5 m from the origin is:
Answer:
[tex]\vec{E}=\vec{E_1}+\vec{E_2}=[25856\hat{i}+163443.2\hat{j}]N/C[/tex]
Step-by-step explanation:
The electric field is given by:
[tex]E=k\frac{q_1q_2}{r^2}[/tex]
k: Coulomb's constant = 8.98*10^9 Nm^2/C^2
at the point P(0,0.5m) you have both x ad y component of the electric field. For the particle q1 you have:
[tex]\vec{E_1}=Ex\hat{i}+Ey\hat{j}\\\\\vec{E_1}=0\hat{i}+(8.89*10^9Nm^2/C^2)\frac{(5*10^{-6}C)}{(0.5m)^2}\hat{j}=179600N/C\hat{j}[/tex]
for the particle q2, it is necessary to compute the angle between the E vector and the axis, by using the distance y and x. Furthermore it is necessary to know the distance from q2 to the point P.
[tex]\vec{E_2}=Excos\theta \hat{i}-Eysin\theta \hat{j}\\\\\theta=tan^{-1}(\frac{0.5}{0.8})=32\°\\\\r=\sqrt{0.5^2+0.8^2}=0.94m\\\\\vec{E_2}=(8.89*10^9Nm^2/C^2)\frac{(-3*10^{-6C})}{(0.94m)^2}[cos(32)\hat{i}-sin(32)\hat{j}]\\\\=[25856.06\hat{i}-16156.71\hat{j}]N/C[/tex]
Finally, by adding E1 and E2 you obtain:
[tex]\vec{E}=\vec{E_1}+\vec{E_2}=[25856\hat{i}+163443.2\hat{j}]N/C[/tex]
solve for x: logx(16)=2
Answer:
4, -4
Step-by-step explanation:
Take the (+2)th root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
x = 4 , − 4
Solve for x.
2(4x− 9) = 5(x − 4)
Answer:
2(4x− 9) = 5(x − 4)
=>8x- 18= 5x-20
=>8x-5x= -20+18
=>3x = -2
=>x= -2/3
If you double a number and then add 32, you get two ninths
of the original number. What is the original number?
Answer:
The number is -18
Step-by-step explanation:
Let x be the original number
2x +32 = 2/9x
Multiply each side by 9 to get rid of the fractions
9(2x +32) =9* 2/9x
18x +288 = 2x
Subtract 18x from each side
18x-18x+288 = 2x-18x
288 = -16x
Divide each side by -16
288/-16 = -16x/-16
-18 =x
Answer:
–18
Step-by-step explanation:
let the number is [tex]x[/tex], from the problem we know that
[tex]2x+32=\frac{2}{9}x
\\9x+144=x
\\x=-\frac{144}{8}=-18[/tex]