A population has mean 555 and standard deviation 40. Find the mean and standard deviation of sample means for samples of size 50. Find the probability that the mean of a sample of size 50 will be more than 570. 2. A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 miles. Five such tires are manufactured and tested. On the assumption that the actual population mean is 38,500 miles and the actual population standard deviation is 2,500 miles, find the probability that the sample mean will be less than 35,000 miles. Assume that the distribution of lifetimes of such tires is normal. A normally distributed population has mean 1,200 and standard deviation 120. Find the probability that a single randomly selected element X of the population is between 1,100 and 1,300. Find the mean and standard deviation of X for samples of size 25. Find the probability that the mean of a sample of size 25 drawn from this population is between 1,100 and 1,300. 4. Suppose the mean weight of school children's book bags is 17.5 pounds, with standard deviation 2.2 pounds. Find the probability that the mean weight of a sample of 30 book bags will exceed 18 pounds. 5. The mean and standard deviation of the tax value of all vehicles registered in NCR are u-550,000 and o=80,000. Suppose random samples of size 100 are drawn from the population of vehicles. What are the mean ux and standard deviation ox of the sample mean X? 6. The IQs of 600 applicants of a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 12. If the college requires an IQ of at least 95, how many of these students will be rejected on this basis regardless of their other qualifications? 7. The transmission on a model of a specific car has a warranty for 40,000 miles. It is known that the life of such a transmission has a normal distribution with a mean of 72,000 miles and a standard deviation of 12,000 miles. • What percentage of the transmissions will fail before the end of the warranty period? What percentage of the transmission will be good for more than 100,000 miles?
Answers
1) The probability that the mean of a sample of size 50 will be more than 570 is approximately 0.0047, or 0.47%.
2) P(z < -3.1304) is a negligible smaller area in the z-score.
3) P(1100 < x< 1300) ≈ P(|z|<4.166) almost equal to 1.
4) The probability that the mean weight of a sample of 30 book bags will exceed 18 pounds is 0.1075.
5) The mean ux and standard deviation ox of the sample mean X are: 550000 and 80000.
6) 29 students of these students will be rejected on this basis regardless of their other qualifications.
7) 0.38% percentage of the transmissions will fail before the end of the warranty period.
0.99% percentage of the transmission will be good for more than 100,000 miles.
Here, we have,
To find the mean and standard deviation of sample means for samples of size 50, we can use the properties of the sampling distribution.
The mean of the sample means (μₘ) is equal to the population mean (μ), which is 555 in this case. Therefore, the mean of the sample means is also 555.
The standard deviation of the sample means (σₘ) can be calculated using the formula:
σₘ = σ / √(n)
where σ is the population standard deviation and n is the sample size. In this case, σ = 40 and n = 50. Plugging in these values, we get:
σₘ = 40 / √(50) ≈ 5.657
So, the standard deviation of the sample means is approximately 5.657.
Now, to find the probability that the mean of a sample of size 50 will be more than 570, we can use the properties of the sampling distribution and the standard deviation of the sample means.
First, we need to calculate the z-score for the given value of 570:
z = (x - μₘ) / σₘ
where x is the value we want to find the probability for. Plugging in the values, we get:
z = (570 - 555) / 5.657 ≈ 2.65
Using a standard normal distribution table or calculator, we can find the probability associated with this z-score:
P(Z > 2.65) ≈ 1 - P(Z < 2.65)
Looking up the value for 2.65 in the standard normal distribution table, we find that P(Z < 2.65) ≈ 0.9953.
Therefore,
P(Z > 2.65) ≈ 1 - 0.9953 ≈ 0.0047
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Related Questions
So I have this question I don't understand, It says Combine terms
5x+3y+8x+x+10y-15
Please let me know if you have a respond
Have a great day
Answers
Answer:
14x+13y-15
Step-by-step explanation:
This is pretty simple. When it asks to combine terms, simply add up all of the same terms. So, all the numbers with x, all with y, and all with no value. For example, for x, we simply add up 5x+8x+x, with x equaling 1.
Hope this helps!
Answer:
14x+13y−15
Step-by-step explanation:
\(5x+3y+8x+x+10y-15 \\ 5x + 8x + x + 10y + 3y - 15 \\ 13x + x + 13y - 15 \\ 14x+13y−15 \)
Given the following: A=(
0
2
1
−3
),B=(
−2
2
1
3
),C=(
−2
1
−1
1
). Find the value of 3BC−2AB. (5 marks) B. Using the matrix method or otherwise, solve the following system of simultaneous equations.
x+2y−z=6
3x+5y−z=2
−2x−y−2z=4
Answers
This gives us X =\(A^(-1)\)* B, where X represents the values of x, y, and z that satisfy the given equations. By performing the necessary matrix operations, we can find the solution to the system of simultaneous equations.
To find the value of 3BC - 2AB, we need to calculate the matrix products of B, C, and A, and then apply the given scalar coefficients. For the system of simultaneous equations, we can solve it using the matrix method, which involves creating coefficient and constant matrices and performing matrix operations to find the values of x, y, and z.
To find 3BC - 2AB, we first calculate the matrix products of B and C, and then multiply the result by 3. Similarly, we calculate the matrix product of A and B and multiply it by -2. Finally, we subtract the two resulting matrices. By performing these operations, we obtain the desired value of 3BC - 2AB.
For the system of simultaneous equations, we can represent the equations in matrix form as AX = B, where A is the coefficient matrix, X is the matrix of variables (x, y, and z), and B is the constant matrix. We can then use the inverse of A to solve for X by multiplying both sides of the equation by\(A^(-1).\)
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Solve the following system of equations. 4x = 15y 17 + y = -13
Answers
aldosterone stimulates the reabsorption of sodium while enhancing potassium secretion.
a. true b. false
Answers
I believe that may be false
Answer:
Step-by-step explanation:
True.
Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.
This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.
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one week ty made (3x + 4) dollars. The following week he made (x + 8) dollars. How much more did he make the first week?
Answers
Answer:
(2x – 4) dollars
Step-by-step explanation:
Find the directional derivative of the function at the given point in the direction of the vector v.
f(x, y) = 7 e^(x) sin y, (0, π/3), v = <-5,12>
Duf(0, π/3) = ??
Answers
The directional derivative of the function at the given point in the direction of the vector v are as follows :
\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)
Where:
- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)
- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)
- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)
Now, let's substitute the values into the formula:
Given function: \(\(f(x, y) = 7e^x \sin y\)\)
Point: \(\((0, \frac{\pi}{3})\)\)
Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)
Gradient of \(\(f\)\) at the point \(\((0, \frac{\pi}{3})\):\)
\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)
To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:
\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)
\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)
Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:
\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)
\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)
Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):
\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)
Using the dot product formula:
\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)
Simplifying:
\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)
So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)
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Susan's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has more than 45 liters. What are the possible numbers of minutes Susan could add water? Use t for the number of minutes. Write your answer as an inequality
Answers
Given that Susan's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has more than 45 liters.
Let's represent the number of minutes she adds water by t. The total amount of water in the tank after t minutes is given by 15 + 5t liters. For the total amount of water to be greater than 45 liters: 15 + 5t > 45 Subtract 15 from both sides. 5t > 30 Divide by 5 on both sides. t > 6
Therefore, Susan could add water for more than 6 minutes. Thus, the possible numbers of minutes Susan could add water is given by the inequality t > 6. Given that Susan's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has more than 45 liters.
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Locate the absolute extrema of the function f(x)=x^3−12x on the closed interval [0,3].
Select one:
a. no absolute max; absolute min:(0,0)
b. absolute max:(2,−16); absolute min:(0,0)
c. absolute max:(0,0); absolute min:(2,−16)
d. no absolute max or min
e. absolute max:(0,0); no absolute min
Answers
The absolute extrema of the function f(x) = x^3 - 12x on the closed interval [0, 3] are: Absolute maximum: (2, -16) and absolute minimum: (0, 0).
Explanation:
To locate the absolute extrema of the function f(x) = x^3 - 12x on the closed interval [0, 3], we need to evaluate the function at the critical points and endpoints within the given interval.
1. Critical points:
To find the critical points, we set the derivative of f(x) equal to zero and solve for x:
f'(x) = 3x^2 - 12 = 0
x^2 - 4 = 0
(x - 2)(x + 2) = 0
x = 2, x = -2
2. Endpoints:
Evaluate the function f(x) at the endpoints of the interval:
f(0) = 0^3 - 12(0) = 0
f(3) = 3^3 - 12(3) = -9
Now, we compare the function values at the critical points and endpoints to determine the absolute extrema:
f(0) = 0 is the absolute minimum on the interval [0, 3].
f(2) = 2^3 - 12(2) = -16 is the absolute maximum on the interval [0, 3].
Therefore, the correct answer is option (b): Absolute max: (2, -16); Absolute min: (0, 0).
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name the relationship of these angles
Answers
2) adjacent
3) adjacent
4) complementary
5) vertical
6) adjacent
7) linear pair
8) vertical
Which of the following tools is used to capture data packets over time(continuously or overnight)?PuTTYTraffic AnalyzerWiresharkNetWitness Investigator
Answers
Wireshark is the tool used to capture data packets over time, either continuously or overnight.
Wireshark is a powerful network protocol analyzer that allows you to capture and examine data packets flowing through a network. It provides a comprehensive set of features for capturing, analyzing, and interpreting network traffic.
With Wireshark, you can capture packets from various network interfaces and save them to a capture file for later analysis. It supports capturing packets in real-time, allowing you to monitor network activity as it happens.
Wireshark offers detailed packet-level inspection, allowing you to examine packet headers, payloads, protocols, and other relevant information.
Furthermore, Wireshark supports numerous protocols and provides protocol-specific decoders to interpret and analyze different network protocols. It also offers advanced features like packet coloring, statistical analysis, packet comparison, and the ability to export captured data for further analysis or sharing with others.
Overall, Wireshark is widely used by network administrators, security professionals, and developers to diagnose network issues, troubleshoot problems, analyze network performance, and investigate security incidents by capturing and analyzing data packets over time.
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What is the median number of books read?
Answer options with 5 options
A.5
B.8
C.9
D.10
E.11
Answers
Answer:
The answer is B:8
Step-by-step explanation:
because when you line up the numbers in order
5 6 7 8 11 11 15
The middle number is 8
NEED THIS ASAP 50 POINTS UWU
Which property of equality should you apply to keep the equation 22 . a = 242 in balance when solving?
The division property of equality
The subtraction property of equality
The reflexive property
The substitution property of equality
Answers
A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.
What is the subtraction property of equality?In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.
Based on the information provided above, we can logically deduce the following equation:
22 . a = 242
22 × a = 242
By applying the division property of equality, we have the following:
a = 242/22
a = 11.
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Urgently need help step by step explanation needed
Answers
Answer:
p=8
Step-by-step explanation:
-5log(p+1)+2=-8
-5log(p+1)=-10
log(p+1)=2
p+1=9, p=8
Direction: Name at least 2 examples of each of the following terms below from figure 2.
1.angle
2.line segment
3.ray
Answers
Answer:
1.acute angle
right angle
2.pencil
the edge of a table
3.a Ray from light
a Ray from sun
Answer:
Angle = LABC and LACD
Line segment = AB and DC
Ray = AB and CD
the expression 9.78(4.3x + 5.15) simplifies to
Answers
Answer: 42.097x+50.4185
Step-by-step explanation:
You are given an isosceles trapezoid ABCD with median XY. Complete the following.
AX = 3, CD =?
Answers
Answer:
hi, because XY is a median:
\(3 \times 2 = 6 \\ cd = 6\)
please give brainly, please
student researchers wanted to see whether a short delay between seeing a list of words and when people were asked to recall them would hinder memorization. the subjects were shown a list of words to memorize for 1 minute and were then given 1 minute to recall as many words as they could. each subject did this once with no delay between memorizing and recall and another time with a 30-second wait between memorizing and recall. they were randomly assigned the order of the two conditions. the number of words memorized under each condition can be found in the statcrunch data set memorizingwords. questions: use the appropriate simulation applet to calculate an approximate p-value. is there strong evidence that a short delay hinders the memorization process? explain.
Answers
The appropriate simulation applet to calculate an approximate p-value is 0.0077.
The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.
Delay or no delay, answer: the number of words remembered
The mean distance between words remembered with and without delay over time is null, or zero.
Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.
Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.
The mean distance in words remembered is 1.85.
1)0.0077 as the p-value
2)Strong data suggests that a brief delay impairs memorization.
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HELP ME I WILL GIVE BRAINLIEST
Answers
Answer: 42.0
Step-by-step explanation:
Re-write the equation 3 x minus y = 4 in slope-intercept form. a. y = 3 x minus 4 c. y = negative 3 x minus 4 b. y = 3 x 4 d. y = negative 3 x 4
Answers
The slope-intercept form of the equation of straight linr 3x - y = 4 is the option a) y = 3x - 4
The given equation is 3x - y = 4
The general slope-intercept form of a straight line is
y = mx + c
Here,
m is the slope of the straight line
and
c is the point at which x = 0 and the straight line intersects Y-axis, i.e the y-intercept
We are given
3x - y = 4
to make it to the form of the general equation we will bring 3x to RHS to get
-y = -3x + 4
removing the minus sign from y gives us the slope-intercept form
a) y = 3x - 4
Correct Question
Re-write the equation 3x - y = 4 in slope-intercept form.
a. y = 3x - 4
b. y = 3x + 4
c. y = -3x - 4
d. y = -3x + 4
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Lesson question: How does adding the two equations in a system allow you to solve it?
ANSWER FAST PLEASE
Answers
Answer:
Step-by-step explanation:
y-terms cancel out and are eliminated as a result of adding the two equations.
manny’s pizza shows declining sales over the last few months. their net profit in hundreds of dollars follows the arithmetic sequence 4, 1, −2, −5, …, −56. what is their total profit over this time period?
Answers
Answer:
The total profit over this period is -546
Step-by-step explanation:
Given
Sequence: 4, 1, −2, −5, …, −56
Required
Determine the total profit
To do this, we simply calculate the sum of terms (Sn)
\(S_n = \frac{n}{2}(a + T_n)\)
But first, we need to determine the value of n using
\(T_n = a + (n - 1)d\)
Where:
\(T_n = -56\)
\(a = 4\)
\(d = 1 -4= -3\)
Substitute these values in the above formula, we have:
\(-56 = 4 + (n - 1) * -3\)
\(-56 = 4 -3n +3\)
Collect Like Terms
\(3n = 56 + 4 + 3\)
\(3n = 63\)
\(n = 63/3\)
\(n = 21\)
Recall that:
\(S_n = \frac{n}{2}(a + T_n)\)
This gives:
\(S_n = \frac{21}{2}(4 - 56)\)
\(S_n = \frac{21}{2}(-52)\)
\(S_n = 21 * -26\)
\(S_n = -546\)
The total profit over this period is -546
I need help for grades!!!
Answers
Yes, the relation shown is a function because every element in the domain has only one distinct image in the co-domain.
Give an example of an asymmetric relation on the set of all people.
Answers
An example of an asymmetric relation on the set of all people is the "is taller than" relation.
In the "is taller than" relation, if person A is taller than person B, it implies that person B is not taller than person A. The relation is one-way and does not hold in the opposite direction. For example, if John is taller than Sarah, it does not mean that Sarah is taller than John. This relationship is asymmetric because it does not have a symmetric counterpart where both individuals are taller than each other. It is important to note that the "is taller than" relation is subjective and may vary based on individual comparisons and measurements.
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fastt
13. Calculate the compound interest of an annuity due of BD400 paid each 4 months for 6.2 years if the nominal rate is 3% thirdly? (3 Points)
Answers
Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.
Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)
whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as
:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1
(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,
the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:
A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17
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Each side of a checkerboard measures
40 cm. What is the length of its
diagonal?
Answers
The length of diagonal of the checkerboard is \(40\sqrt{2} cm\).
The Pythagoras theorem can be applied to a right angle triangle. It states that the square of hypotenuse is equal to sum of square length of base and height of the triangle. Mathematically: Hypotenuse² = Perpendicular² + Base². The diagonal of a square divides the square in two right triangles.
The each side of a checkerboard measures 40 cm, that means checkerboard is a square. So, applying the Pythagoras theorem in the triangle formed by diagonal and two sides of square,
\(D^2=S^2+S^2\\D^2=40^2+40^2\\D=40\sqrt{2} cm\)
Where D is the length of diagonal and S is the length of side of checkerboard.
Therefore, the length of the diagonal of checkerboard is \(40\sqrt{2} cm\).
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Right Answer Gets Brainliest
A number b minus 6.9 is less than or equal to 12. Write this word sentence as an inequality.
Answers
Answer:
b-6.9 ≤ 12
Step-by-step explanation:
Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.
answer below:
–9 = 7x2 –
⇒ 56 x
–9 +
⇒ 112 = 7(x2 – 8x +
⇒ 16 )
56, 112, 16 in that order
Answers
Answer:
it's actually 28+/-√721/7
Step-by-step explanation:
help me please quickly
Answers
Answer:
Step-by-step explanation:
1. 9
2. 32
3. 813
4. 264
5. 169
what is a negative number that is greater than -10?
Answers
Answer:
-5
Step-by-step explanation:
explanation: simple
1. Line L contains points (4, -1) and (4,9). Point P has coordinates (1,6)
Answers
The distance between the point and the line is 3 units.
Find the equation for line L
Begin by finding the slope of the line through the given points, (4,-1) and (4,9) ; its intercept:
m = (y₂ - y₁) / (x₂ - x₁)
= (9 - (-1) ) / 4 - 4
= 10 / 0
= Undefined
Because the slope is undefined, then line L is a vertical line which has an x-intercept of (4,0):
x=4
Because, line L is vertical, then the line w perpendicular to it is a horizontal line that passes through (1,6)(1,6) so its equation is y=6. Hence, L and w intersect at (4,6) which we will denote as Q.
The perpendicular distance is the distance from point P(1,6) to point Q(4,6) which is simply the absolute value of the difference of the x-coordinates:
d = | 1 - 4 |
= |-3|
= 3
Hence, The distance between the point and the line is 3 units.
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