The mean salary at a local industrial plant is $28,600$28,600 with a standard deviation of $4400$4400. The median salary is $25,300$25,300 and the 61st percentile is $29,000$29,000.
Step 2 of 5:
Based on the given information, determine if the following statement is true or false.
Joe's salary of $35,060$35,060 is 1.401.40 standard deviations above the mean.
Answers
The statement Joe's salary of $35,060$35,060 is 1.401.40 standard deviations above the mean is false.
To determine if the statement is true or false, we need to calculate the number of standard deviations Joe's salary of $35,060 is above the mean.
Given:
Mean salary = $28,600
Standard deviation = $4,400
Joe's salary = $35,060
To calculate the number of standard deviations above the mean, we can use the formula:
Number of standard deviations = (X - μ) / σ
Where:
X is the value we want to compare (Joe's salary)
μ is the mean
σ is the standard deviation
Plugging in the values, we have:
Number of standard deviations = (35,060 - 28,600) / 4,400
= 6,460 / 4,400
≈ 1.4727
Therefore, Joe's salary of $35,060 is approximately 1.4727 standard deviations above the mean, not 1.40.
The statement is false.
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Related Questions
A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is ___. a. 0.450 b. 0.9505 c. 0.0495 d. 0
Answers
The probability that the sample mean will be greater than 57.95 is 0.0495.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.
To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.
Normal probability distributionProblems of normally distributed samples can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z=\dfrac{X-\mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit TheoremThe Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).
In this problem, we have that:
\(\mu=53,\sigma=21,\text{n}=49,\text{s}=\frac{21}{\sqrt{49} }=3\)The probability that the sample mean will be greater than 57.95
This is 1 subtracted by the p-value of Z when X = 57.95. So
\(Z=\dfrac{X-\mu}{\sigma}\)
By the Central Limit Theorem
\(Z=\dfrac{X-\mu}{\text{s}}\)
\(Z=\dfrac{57.95-53}{3}\)
\(Z=1.65\)
\(Z=1.65\) has a p-value of 0.9505.
Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495
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WILL GIBE BRAINLEST
Which figures are polygons?
Select each correct answer.
Figure A
Figure B
Figure C
Figure D
Answers
Notice how A, B, and D have more than 3 straight edges. This qualifies the shape to be a polygon. The minimum sides a shape can have to be qualified as a polygon is 3 sides.
Answer choice C cannot be a polygon because it doesn’t meet the polygon minimum. Also answer choice C has a curved line which is not allowed within polygons.
Question 2 of 6 View Policies Current Attempt in Progress Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____
Answers
Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.
Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____
Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.
Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)
Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14
Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.
Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w
Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w
Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.
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There are 14 dogs at the dog park on a busy Saturday. 2 of them are springer spaniels.
What is the probability that a randomly selected dog is a springer spaniel?
Write your answer as a fraction or whole number.
Answers
Answer:1/7
Step-by-step explanation: You take the amount that are springer spaniels and you put them with the whole of the dogs in the park 14 so you would have 2/14. You can reduce this fraction to 1/7 by dividing both the top and bottom of the fraction by 2.
They are selling shoes for 97 dollars.
You take 50 dollars from your mom.
And 50 dollars to your dad.
You buy them and they give you back 3 dollars.
You return 1 to your mom.
And you return 1 to your dad.
And you keep a dollar.
I mean, you already owe 49 to your mom.
And 49 to your dad.
And 49 plus 49 is 98 plus the one you stayed 99
And the other dollar?
Answers
Головоломка, яку ви представили, є звичайною загадкою, а відповідь полягає в тому, що математика помилкова.
Ключова проблема полягає в тому, щоб додати 49 доларів, які ви повинні кожному з батьків, щоб отримати 98 доларів, а потім додати 1 долар, який ви залишили, щоб отримати 99 доларів. Це означає, що долар відсутній, а це не так. Математика просто не працює, тому що немає сенсу додавати суми боргів різним людям, ніби вони є частиною однієї суми.
Щоб чіткіше розбити транзакції:
Ви починаєте з $0.
Ви берете 50 доларів у своєї мами, тож у вас є 50 доларів, а у неї – 50 доларів.
Ви берете у свого тата 50 доларів, тож у вас є 100 доларів, а в нього – 50 доларів.
Ви витрачаєте 98 доларів на предмети, залишаючи вам 2 долари, а вашим батькам – по 50 доларів.
Ви повертаєте 1 долар кожному з батьків, отже у вас є 0 доларів, а у кожного з батьків -49 доларів.
Ви залишаєте решту $1.
Отже, немає жодного пропущеного долара чи розбіжності в математиці. Загальна сума залучених грошей становить 100 доларів на початку та 100 доларів наприкінці, причому 98 доларів витрачено на предмети, а 2 долари залишаються у вашому розпорядженні.
If h(x) = f(x) - g(x) = 2x, at what x-value will f(x) = g(x) + 20?
a) x = 20
b) x = 10
c) x = 5
d) x = 2
Answers
Answer:
B
Step-by-step explanation:
This is a neat question
f(x) - g(x) = 2x Add g(x) to both sides
f(x) = g(x) + 2x
Now you need the right hand side to have 20 added to g(x).
2x must = 20
2x = 20 Divide by 2
x = 20/2
x = 10
So the answer must be x = 10
if a clock shows it is 3 o'clock, how could you describe the smaller angle made by the two hands of the clock? Solve this problem any way you choose.
Answers
Answer: 5 1/4
Step-by-step explanation:
Answer:
90°
Step-by-step explanation:
The minutes hand is vertical pointing straight up.
The hours hand is horizontal pointing right.
The smaller angle between the hands is 90°.
Which statements are correct?
Answers
Answer:
there are no statement, but if this is a multiple-choice answer, I would have to guess it is B
Step-by-step explanation:
Hope this helps!
Calculate each value for ⊙P. Use 3.14 for π and round to the nearest tenth.
please help!! will mark brainliest!!
Answers
Answer:
226.19 inches
Step-by-step explanation:
If a train travels 420 miles in 24 hours, what is its unit rate of travel?
16 mph
19.5 mph
17.5 mph
15.2 mph
Answers
17.5mph
420÷24= 175
Hope this helped you- have a good day bro cya)
Answer:
17.5mph
Step-by-step explanation:
a hole of radius 12r is bored through the middle of a cylinder of radius 7r > 12r at right angles to the axis of the cylinder. set up, but do not evaluate, an integral for the volume v cut out.
Answers
The integral for the volume V of the cut out is 2016πr^3.
The volume V of the cut out can be found using the integral:
V = ∫[A(x)]dx
Where A(x) is the area of the cross section of the cut out at a given x-value and the integral is taken over the length of the cut out.
In this case, the cross section of the cut out is a circle with radius 12r, so A(x) = π(12r)^2 = 144πr^2.
The length of the cut out is the diameter of the cylinder, or 2(7r) = 14r.
Therefore, the integral for the volume V of the cut out is:
V = ∫[144πr^2]dx from x = 0 to x = 14r
V = 144πr^2∫dx from x = 0 to x = 14r
V = 144πr^2(14r - 0)
V = 2016πr^3
So the integral for the volume V of the cut out is 2016πr^3.
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A particular satellite is 10 ft wide. A
model of it was built with a scale of 1 in :
2 ft. How wide is the model?
Answers
3 ft
Step-by-step explanation:
bought 11 pounds of rice for $5. How many dollars did she pay per pound of rice? dollars per pound round your answers to the nearest hundredth.
Answers
Answer:
$2.20
Step-by-step explanation:
11/5=2.2
Answer:
0.45
Step-by-step explanation:
$5 for 11 lb
$5/(11 lb) = $0.45/lb
Many students take online courses because they are more convenient for their schedules. What are some of the tradeoffs for taking an online course in a subject such as math? What tools are you using to overcome these challenges?
Answers
Taking an online course in subjects like math offers several advantages, such as flexibility and convenience. However, there are also tradeoffs and challenges associated with online math courses.
One tradeoff is the lack of immediate face-to-face interaction with instructors and peers. In a traditional classroom setting, students can ask questions and receive immediate feedback. In an online course, communication may be asynchronous, leading to potential delays in getting clarifications or resolving doubts.
Another challenge is the need for self-discipline and motivation. Without the structure of regular in-person classes, students must manage their time effectively, stay motivated, and be proactive in their learning. Online courses require self-direction and independent study skills.
To overcome these challenges, various tools and strategies can be helpful. Online math courses often provide discussion forums, email communication, or virtual office hours with instructors for student-teacher interaction. Additionally, online platforms may offer multimedia resources, video tutorials, and interactive simulations to enhance understanding and engagement.
Students can also form virtual study groups or join online math communities to connect with peers and collaborate on problem-solving. Personal organization tools, such as calendars and task management apps, can assist in staying on track with assignments and deadlines.
Ultimately, success in an online math course requires self-motivation, effective time management, active participation, and utilizing available resources and support systems.
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convert 8 and 2/8 feet into one length
Answers
Recall that one foot is 30.48 cm, also
\(8\frac{2}{8}=8.25.\)Therefore, 8.25 feet is 251.46 cm.
Answer: 251.46 cm.
use the integral test to determine whether the series is convergent or divergent. [infinity] 7 n4 n = 1 evaluate the following integral. [infinity] 1 7 x4 dx since the integral ---select--- finite, the series is convergent or divergent. n=1 te the following integral. Since the integral is ''t finite, the series is I convergent, v' .
Answers
The statement "Since the integral is finite, the series is convergent" is incorrect.
To use the integral test to determine whether the series [infinity] 7 n4 n = 1 is convergent or divergent, we need to evaluate the following integral: [infinity] 1 7 x4 dx.
Integrating 7 x4 with respect to x gives us (7/5) x5. Evaluating this from 1 to infinity gives us [(7/5) (infinity)5] - [(7/5) 1^5] = infinity, which means the integral is divergent.
Since the integral is divergent, the series [infinity] 7 n4 n = 1 is also divergent.
The statement "Since the integral is finite, the series is convergent" is incorrect.
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Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Answers
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
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4.17. for a standard normal random variable z, compute (a) p(z ≥ 0.99) (b) p(z ≤ −0.99) (c) p(z < 0.99) (d) p(|z| > 0.99) (e) p(z < 10.0) (f) p(z > 10.0) (g) with probability 0.9, variable z is less than what?
Answers
Answer: 1.28
Step-by-step explanation:
1. P(Z > 0.99) = 1 -Ф (0.99) = 1-0.8389 = 0.1611
2.P(Z <-0.99) = Ф(-0.99) = 0.161 (known that from [a] by symmetry)
3.P(Z <0.99) = Ф(0.99) = 0.8389
4. P(Z >0.99) = P(Z <-0.99) + P(Z > 0.99) = 2(0.1611) = 0.3222
The value z = 10.0 is out because it is too large. On comparing with the largest value, z = 3.99,
we get
5. P(Z < 10.0) > P(Z <3.99) = 1.0
6.P(Z > 10.0)<P(Z > 3.99) =10.0
7. On solving the equation
Ф(Z) = 0.9
for Z.
In Table A4, find the value of z corresponding to the probability 0.9. The nearest value is Ф(1.28) = 0.8997. Therefore, z ≈ 1.28
Can any kind soul help me please
Answers
Answer:
(i) we will be finding the acceleration here, in the first 20 seconds the velocity was 10
a = velocity/time
a = 10/20
a = 0.5 ms -2
(ii) difference in distance of the bus and bicycle will be given by formula of velocity
velocity of bicycle
10 * 80 = distance
800 metres
velocity of bus
for first 20 seconds( distance= velocity* time)
200 metres
from 20 seconds to 60 seconds, it will be for 40 seconds
then distance will be,
400 metres
final 20 seconds
200 metres
adding the distances of bus it will be 800 metres.
the difference in distance will be 0 metres.
this is wat i think
the volume of a cube whose edge is 6cm long is
Answers
Answer:
216 cm^3
Step-by-step explanation:
Volume of a cube=s^3
6 cm^3=216 cm^3
determine the type of distribution for the following situation: draw marbles from a bag containing 5 red marbles, 6 blue marbles and 4 green marbles with replacement and count the number of blue marbles.
Answers
The probability distribution for this situation is a binomial distribution.
Probability Distribution of a Random Variable:Giving the values of the random variable along with the corresponding probabilities is called the probability of the random variable probability distribution of a random variable. It is a mathematical function that provide the probabilities of various outcomes in an event.
We have to determine the type of distribution for this situation, we need to consider two essential properties: the type of random variable and the conditions under which it occurs.
We have :
Draw marbles from a bag containing 5 red marbles,
6 blue marbles and
4 green marbles with replacement and count the number of blue marbles.
Therefore, this situation satisfies the conditions of a binomial distribution.
In our case, X represents the number of blue marbles drawn, k can take on values from 0 to the number of marbles drawn, n is the number of marbles drawn, p is the probability of drawing a blue marble, which is 0.4, and (n choose k) is the number of ways to choose k blue marbles from n marbles, which is given by:
(n choose k) = n! / (k! * (n-k)!)
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1/4(8x-4)=
need help please answer
Answers
Answer:
2x-1 is the answer (or if you're trying to multiply it, the answer is -8.)
Step-by-step explanation:
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answers
Answer:
816 square feet
Step-by-step explanation:
13(16+20+12) + 16(12) = 816
in an octagon, the interior angles are in the ratio 1:2:3:4:5:6:7:8. what is the measure of the smallest angle?
Answers
The measure of the smallest angle is 30° in an octagon when the interior angles are in the ratio 1:2:3:4:5:6:7:8.
The sum of the interior angles of an octagon is (8 - 2) x 180° = 1080°.
Let x be the minimum angle measure and write down the other angle equations concerning x using the ratios given.
2x, 3x, 4x, 5x, 6x, 7x, 8x.
by adding all the angles we get,
x + 2x + 3x + 4x + 5x + 6x + 7x + 8x = 36x.
Since the sum of the interior angles of an octagon is 1080°,
Simplifying the equation:
36x = 1080
x = 30
The minimum angular dimension is x = 30°.
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The probability of spinning a number that can be divided by 3 is 3/10
Predict in 40 spins how many times you would spin a number divisible by 3
Answers
Answer:
12
Step-by-step explanation:
The probability of spinning a number that can be divided by 3 is 3/10
Predict in 40 spins how many times you would spin a number divisible by 3
In 40 spins 13 times you would spin a number divisible by 3.
GivenThe probability of spinning a number that can be divided by 3 is 3/10.
We have to determine
Predict in 40 spins how many times you would spin a number divisible by 3?
In the number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
The numbers are divisible by 3 are 3, 6, 9.
Then,
The probability of spinning a number that can be divided by 3 is 3/10.
Therefore,
In the number 40 spins,
There are 13 numbers which are divisible by 3.
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39.
Hence, In 40 spins 13 times you would spin a number divisible by 3.
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What is the perimeter of JKLM?
Answers
Start with the 60, 60, 60 degree triangle, one of the sides are 12 so all the other sides are 12. So we have 12+12+12+9=45
what is 3 1/2 x 2 2/3
Answers
Answer:
ill answer it when im done with my homwork i see u need help buddy
Step-by-step explanation:
Answer:
Step-by-step explanation:
3 1/2 * 2 2/3 = 28/3= 9 1/3
hope this helped<3!!..
Solve using linear combination.
2e - 3+ - 9
e + 35= 18
Which ordered pair of the form (e. f) is the solution to the system of equations?
Answers
e = -17. 2 x -17 - 3 + 9
-34 - 3 + 9
== -28
hope this helps
Answer:
(3,5)
Step-by-step explanation
3=e and 5=f (but I guess u accidentally put a plus sign)
so 2e= 6 and 3f=15, and 6-15=-9 so this checks out
Next e=3 and 3f=15 (that 5 in the second problem should be an f) and 3+15-18 again is checks out so 3,5 must be correct yada yada yada goodnight.
-I'm usually more professional explaining problems but i broke it down for ya, when I get over this drowsiness I'll be back to my usually math pro self
Last week, Tracy walked her dog 2 2/5 miles. Maria walkedher dog 3 times as far. How many total miles did both girlswalk their dogs?
Answers
Answer:
48/5 miles
Explanation:
First, we need to convert the mixed number 2 2/5 into a fraction as follows:
\(\begin{gathered} A\frac{b}{c}=\frac{(A\times c)+b}{c} \\ 2\frac{2}{5}=\frac{(2\times5)+2}{5}=\frac{10+2}{5}=\frac{12}{5} \end{gathered}\)Therefore, Tracy walked her dog 12/5 miles.
Then, Maria walked her dog 3 times as far, so Maria walked her dog:
\(3\times\frac{12}{5}=\frac{3\times12}{5}=\frac{36}{5}\)So, Maria walked her dog 36/5 miles.
Now, both girls walk their dogs a total of:
\(\frac{12}{5}+\frac{36}{5}=\frac{12+36}{5}=\frac{48}{5}\)So, the answer is 48/5 miles.
the radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.6 in/s. at what rate is the volume of the cone changing when the radius is 144 in. and the height is 138 in.?
Answers
Answer:
Let's use the formula for the volume of a right circular cone to solve this problem:
V = (1/3)πr^2h
We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.
Using the chain rule of differentiation, we can express the rate of change of the volume as follows:
dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)
To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:
dV/dr = (2/3)πrh
dV/dh = (1/3)πr^2
Substituting the given values and their rates of change, we have:
dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)
dV/dt = 55,742.4 - 1,994,598.4
dV/dt = -1,938,856 in^3/s
Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.
Step-by-step explanation: