Answer:
Take an example in a triangle:
The orthocenter is the intersection point of 3 altitudes.
The centroid is the intersection point of 3 medians.
The circumcenter is the intersection point of 3 bisectors.
Centroid, orthocenter, and circumcenter are collinear.
Hope this helps!
:)
Find the value of x a)10 b)6 c)5
Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of hours per household. Use a normal probability distribution with a standard deviation of hours to answer the following questions about daily television viewing per household.
a. what is the probability that a household views television between 6 and 8 hours a day (to 4 decimals)?
b. How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)?
c. What is the probability that a household views television more than 5 hours a day (to 4 decimals)?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Television viewing reached a new high when the global information and measurement 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 between 6 and 8 hours a day (to 4 decimals)?
(b.) How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)?
(c.) What is the probability that a household views television more than 5 hours a day (to 4 decimals)?
Solution:
Let x be the random variable representing the television viewing times per household. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 8.35
σ = 2.5
a) the probability that a household views television between 6 and 8 hours a day is expressed as
P(6 ≤ x ≤ 8)
For x = 6,
z = (6 - 8.35)/2.5 = - 0.94
Looking at the normal distribution table, the probability corresponding to the z score is 0.1736
For x = 8
z = (8 - 8.35)/2.5 = - 0.14
Looking at the normal distribution table, the probability corresponding to the z score is 0.4443
Therefore,
P(6 ≤ x ≤ 8) = 0.4443 - 0.1736 = 0.2707
b) the top 5% means greater than 95%. It means that the sample mean is greater than the population mean and the z score is positive. The corresponding z score from the normal distribution table is 1.645. Therefore,
(x - 8.35)/2.5 = 1.645
Cross multiplying, it becomes
x - 8.35 = 2.5 × 1.645 = 4.11
x = 4.11 + 8.35 = 12.46
c) the probability that a household views television more than 5 hours a day is expressed as
P(x > 5) = 1 - P(x ≤ 5)
For x = 5
z = (5 - 8.35)/2.5 = - 1.34
Looking at the normal distribution table, the probability corresponding to the z score is 0.0901
Therefore,
P(x > 5) = 1 - 0.0901 = 0.9099
Solve for x.
6(x - 1) = 9(x + 2)
x = -8
X = -3
X = 3
x = 8
Answer:
[tex]x=-8[/tex]
Step-by-step explanation:
[tex]6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}[/tex]
[tex]6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{24}{-3}\\Simplify\\\frac{-3x}{-3}=\frac{24}{-3}\\\mathrm{Simplify\:}\frac{-3x}{-3}:\quad x\\\frac{-3x}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3x}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\\=x\\\mathrm{Simplify\:}\frac{24}{-3}:\quad -8\\\frac{24}{-3}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{3}=8\\=-8\\[/tex]
Answer:
x=-8
Step-by-step explanation:
6(x-1)= 9(x+2)
6x-6= 9x+18
6x-9x= 18+6
-3x= 24
-3x÷-3= 24÷-3
x=-8
Please answer this correctly
Answer:
[tex]10\dfrac{5}{8}[/tex]
Step-by-step explanation:
The perimeter of a shape is the sum of the lengths of the sides.
[tex]2\dfrac{1}{8}+3\dfrac{3}{16}+2\dfrac{1}{8}+3\dfrac{3}{16}=10\dfrac{5}{8}[/tex] yards
Hope this helps!
Answer:
10 5/8
Step-by-step explanation:
The perimeter is the sum of all sides
2 1/8 + 3 3/16 + 2 1/8 + 3 3/16
Add the whole numbers
2 + 3 + 2 + 3 = 10
Add the fractions
1/8+ 1/8 + 3 3/16 + 3 3/16
2/8 + 6/16
1/4 + 3/8
2/8+3/8 = 5/8
Put them back together
10 5/8
What is six thousandths as a number?
Answer:
6000
Step-by-step explanation:
6 six
60 sixty
600 six hundred
6000 six thousand
//have a great day//
Please answer this correctly without making mistakes
Area = 0.785
Area=0.79
I hope it helps
A truncated cube is a convex polyhedron with 36 edges and 24 vertices. A truncated tetrahedron is a convex polyhedron
with 18 edges and 12 vertices.
How do the number of faces of a truncated cube and a truncated tetrahedron compare?
The truncated cube has 6 more faces than the truncated tetrahedron.
The truncated cube has 8 more faces than the truncated tetrahedron.
The truncated cube has 12 more faces than the truncated tetrahedron.
The truncated cube has 18 more faces than the truncated tetrahedron.
Answer:
The truncated cube has 6 more faces than the truncated tetrahedron.
Step-by-step explanation:
==>Given:
truncated cube=>
edges (E) = 36
vertices (V) = 24
faces (F) = ? (unknown)
According to Euler's polyhedron formula, Vertices (V) - Edges (E) + Faces (F) = 2, let's find how many faces the truncated cube has
=> 24 - 36 + F = 2
- 12 + F = 2
F = 2 + 12
F = 14
truncated tetrahedron=>
edges (E) = 18
vertices (V) = 12
faces (F) = ? (unknown)
Using V - E + F = 2, find F
=>12 - 18 + F = 2
- 6 + F = 2
F = 2 + 6
F = 8
Comparing the faces of the truncated cube (14) and the truncated tetrahedron (8), the truncated cube has 6 more faces than the truncated tetrahedron (14 - 8 = 6)
Answer:
Answer A:The truncated cube has 6 more faces than the truncated tetrahedron.
Step-by-step explanation:
PLZ I NEED URGENT HELP
What is the mean time to get from home to school in the morning for these six students? 2. What is the mean time to get from school to home in the afternoon for these six students? 3. For which distribution does the mean give a more accurate indicator of a typical time? Explain.
Answer:
Step-by-step explanation:
morning mean: 14 mins
afternoon: 14 mins
both morning and afternoon have the same mean time
A pizza chain monitors the total weight of pepperoni that goes on its deluxe pepperoni pizzas to make sure customers are satisfied and product isn't being wasted. Suppose that for pizzas in this population, these weights are strongly skewed to the left with a mean of 250 g and a standard deviation of 8 g. Management takes a random sample of 64 of these pizzas and calculates the mean weight of the pepperoni on the pizzas. Assume that the pizzas in the sample are independent.
What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas LaTeX: \bar x is within 1 g of the true mean?
Answer:
68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 250, \sigma = 8, n = 64, s = \frac{8}{\sqrt{64}} = 1[/tex]
What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean?
This is the pvalue of Z when X = 64 + 1 = 65 subtracted by the pvalue of Z when X = 64 - 1 = 63. So
X = 65
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 64}{1}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
X = 63
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{63 - 64}{1}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.
Can someone help me With This
Answer:
D
Step-by-step explanation:
Find out if they match in all of them
Hope this helps
Find the value of x in the parallelogram below.
Answer:
x=106 degrees
Step-by-step explanation:
The two opposite angles in a parallelogram are always the same and we know 360 degrees in a parallelogram.
x+x+74+74=360.
2x+148=360
2x=212
x=106 degrees
in a dog show there will be a gold and silver medal awarded. there are 3 finalists. in how many different ways can the 2 medals be awarded?
Answer: There can be 2 gold 1 silver, 2 silver one gold, 3 silver, or 3 gold.
I'm not really sure if this is correct but I hope this helps:)
If a pizza is cut into 6 slices, what is the angle measure for each slice?
Joanna went school supply shopping. She spent $33.33 on notebooks and pencils. Notebooks cost
$1.85 each and pencils cost $1.39 each. She bought a total of 21 notebooks and pencils. How many of
each did she buy?
Answer:
Joanna bought 21 items that come out to a total of $33.33. She bought 9 notebooks and 12 pencils.
Step-by-step explanation:
Notebooks (N) = $1.85 Pencils (P) = $1.39
9N+12P= $33.33
9*1.85=16.65
12*1.39=16.68
16.65+16.68=33.33
Elmo likes music. He wondered if listening to music while studying will improve scores on an exam. Fifty students who were to take the midterm in a week agreed to be part of a study. Half were randomly assigned to listen to classical music while studying for the exam. The other half were told not to listen to any music while studying for the exam. A hypothesis test is to be performed to determine if the average score of those listening to music while studying for the exam was higher than for those who did not listen to any music while studying for the exam. Let X be the midterm scores of those who listened to classical music while studying, and Y be the midterm scores of those who did not listen to any music while studying. Which of the following is the correct alternative hypothesis?
A. The average midterm score for those who listen to classical music while studying is higher than the average midterm score for those who don't listen to music while studying.
B. The midterm scores of those who listen to classical music while studying are the same as midterm scores of those who don't listen to music while studying.
C. There is a difference in the mean midterm scores between those who listen to classical music while studying and those who don't listen to music while studying
D. There is no difference in the mean midterm scores between those who listen to classical music while studying and those who don't listen to music while studying
Answer: A. The average midterm score for those who listen to classical music while studying is higher than the average midterm score for those who don't listen to music while studying.
Step-by-step explanation:
An Alternative Hypothesis is one that disproves the Null Hypothesis in that it believes that indeed there is a change in the dependent variable due to a change in the independent variable.
The Alternative Hypothesis essentially aims to prove the assertion of the Researcher that there is an effect as a result of the introduction of a variable.
Null Hypothesis on the other hand believes that no significant difference exists between a change in a dependant Variable as a result of a change in an independent one.
The correct answer above therefore is that indeed music while studying inspires people to do better in exams than those who do not listen to music while studying. This is the alternative hypothesis because it believes that there was a change in the exam results due to reading while studying.
An electronic system has each of two different types of components in joint operation. Let X and Y denote the lengths of life, in hundreds of hours, for components of type I and type II, respectively. The performance of a component is independent for each other. Let E(X) = 4, E(Y) = 2, E(X2) = 24, E(Y2) = 8.
The cost of replacing the two components depends upon their length of life at failure and it is given by C = 50 + 2X + 4Y.
(i) Compute the average cost of replacing the two components. Your final answer must be a number.
(ii) Compute the standard deviation of cost of replacing the two components. Your final answer must be a number.
Answer:
a
The average cost is [tex]E(C) = 66[/tex]
b
The standard deviation of cost is [tex]\sigma = 9.798[/tex]
Step-by-step explanation:
From the question we are told that
[tex]E(X) = 4[/tex]
[tex]E(Y) = 2[/tex]
[tex]E(X^2) = 24[/tex]
[tex]E(Y^2) = 8[/tex]
The cost of replacing the two component is C = 50 + 2 X + 4 Y
The variance of X is mathematically represented as
V(X) = [tex]E(X^2) - [E(X)]^2[/tex]
Substituting values
[tex]V[X] = 24 - 4^2[/tex]
[tex]V[X] =8[/tex]
The variance of Y is mathematically represented as
V(Y) = [tex]E(Y^2) - [E(Y)]^2[/tex]
Substituting values
[tex]V[Y] = 8 - 2^2[/tex]
[tex]V[X] =4[/tex]
The average of replacing the two component is
[tex]E(C) = 2 * E(X) + 4* E(Y)[/tex]
substituting value
[tex]E(C) = 50 + 2 * (4) + 4* (2)[/tex]
[tex]E(C) = 66[/tex]
The variance of replacing the two component is
[tex]V(C) = V(50 + 2X +4Y)[/tex] Note: The variance of constant is zero
and X and Y are independent
=> [tex]V(C) = 2^2 * V(X) + 4^2 * V(Y)[/tex]
substituting values
=> [tex]V(C) = 4 * 8 + 16 * 4[/tex]
=> [tex]V(C) = 32 + 64[/tex]
=> [tex]V(C) = 96[/tex]
The standard deviation is
[tex]\sigma = \sqrt{V(C)}[/tex]
substituting values
[tex]\sigma = \sqrt{96}[/tex]
[tex]\sigma = 9.798[/tex]
Help is appreciated ❤
Simplify the radical expression -2 √250
Answer:
-10 sqrt(10)
Step-by-step explanation:
-2 sqrt(250)
We know that sqrt(ab) = sqrt(a) sqrt(b)
-2 sqrt(25*10)
-2 sqrt(25)*sqrt(10)
-2 *5*sqrt(10)
-10 sqrt(10)
What is the circumference of the circle shown below (round your answer to nearest tenths)
Answer:
A. 38.3
Step-by-step explanation:
[tex]circumference \\ \: \: \: \: \: = 2 \times radius \times \pi \\ or =diameter \times \pi \\ thus \: the \: answer \: is \\ 12.2 \times 3.14 = 38.3 \\ ( \: a \: ) [/tex]
Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of time, the first person standing at point A hears the burst. Six seconds later, the second person standing at point B hears the burst. If the person at point B is due west of the person at point A and if the display is known to occur due north of the person at point A, where did the fireworks display occur? Note that sound travels at 1100 feet per second.
Answer: approximately 5148 feet directly north of point A
This is equivalent to 0.975 miles
==============================================================
Explanation:
Check out figure 1 (attached image below) to see how the drawing is set up.
Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.
Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.
The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.
Note that triangle ABC is a right triangle. The 90 degree angle is at point A.
We can use the pythagorean theorem to solve for x
See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.
This means the sound wave takes about 4.68 seconds to go from point C to point A.
With this x value, we can compute the expression 1100x to get
1100*x = 1100*4.68 = 5,148 feet
To convert this to miles, divide by 5280
(5148)/(5280) = 0.975
Therefore,
5148 feet = 0.975 miles
3 lines intersect. A horizontal line with points G, N, K intersects a vertical line with points J, N, M at point N and forms a right angle. The third line contains points H, N, L and intersects the other lines at N. It is diagonal and cuts through angles J N G and M N K. Which statements are true regarding the diagram? AngleGNH and AngleHNJ are complementary. AngleJNK and AngleKNL are supplementary. AngleKNL and AngleLNM are complementary. mAngleHNK + mAngleKNL = 180° mAngleMNG + mAngleGNH = 90°
Answer:
A, C, D
Step-by-step explanation:
Answer: A , C , D
Step-by-step explanation: edge2022
I have a question about this.
Ying Zyiyu covered the first 300 miles of a trip going at 60 mph and the last hundred going at 40 mph. What was his average speed for the entire trip?
Answer:
53.33mph
Step-by-step explanation:
Let's calculated the total time spent on the journey first;
For the first 300miles the time spent is ;
From Distance = speed× time
time = Distance/ speed
= 300/60 = 5 hours
Similarly for the last 100mile the time taken is ;
100/40 = 2.5 hours
Total time spent = 5 +2.5 = 7.5 hours
Total distance covered 400miles
Therefore average speed = 400/7.5 =53.33mph
Answer:
53.33 mph
Step-by-step explanation:
I just wanted to say that the other guy's answer is correct, I checked :)
Which calculation could not be used to find the percentage change
between 16 and 20?
look at the image attached and explain why
Answer:
Option (B).
Step-by-step explanation:
Percentage change between two numbers a and b can be calculated by the formula,
% change = [tex]\frac{|b-a|}{a}\times 100[/tex]
Where, (b - a) = Change in values
a = Initial value
If a = 16 and b = 20
Percentage change between 16 and 20 will be,
= [tex](\frac{20-16}{16})\times 100[/tex]
= [tex]\frac{4}{16}\times 100[/tex]
= 25%
If a = 20 and b = 16,
Percentage change = [tex]\frac{|16-20|}{20}\times 100[/tex]
= 20%
Therefore, %change between 16 and 24 may be 16% or 20%.
Option (A),
[tex]\frac{20-16}{16}\times 100[/tex] = 25%
Option (B),
[tex]\frac{20}{16}-1\times 100[/tex] = 1.25 - 1 × 100
= 1.25 - 100
= -98.75%
Option (C),
[tex]100\times \frac{1}{4}[/tex] = 25%
Option (D),
[tex]\frac{(20-16)}{20}\times 100[/tex] = 20%
Therefore, we can not use the calculation used in Option (B).
Which expression is equivalent to -80?
-415
-415
4.V5;
45
Answer:
It would be 4.v5
What is the value of x?
Answer:
Oioj[
Step-by-step explanation:
Step-by-step explanation:
Write the equation to solve it in order to know the exact value of X.
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
252
Step-by-step explanation:
The total cost (in dollars) for a company to manufacture and sell x items per week is C = 40 x + 640 , whereas the revenue brought in by selling all x items is R = 66 x − 0.2 x 2 . How many items must be sold to obtain a weekly profit of $ 200 ?
Answer:
The company must sell 60 or 70 items to obtain a weekly profit of 200.
Step-by-step explanation:
The profit is the difference between the revenue and the cost of a given task, therefore:
[tex]\text{profit} = R - C\\\text{profit} = 66*x - 0.2*x^2 - (40*x + 640)\\\text{profit} = 66*x - 0.2*x^2 - 40*x - 640\\\text{profit} = - 0.2*x^2 + 26*x - 640[/tex]
To have a profit of 200, we need to sell:
[tex]-0.2*x^2 + 26*x - 640 = 200\\-0.2*x^2 + 26*x -840 = 0\text{ } *\frac{-1}{0.2}\\x^2 -130 + -4200 = 0\\x_{1,2} = \frac{-(-130) \pm \sqrt{(-130)^2 - 4*1*(-4200)}}{2*1}\\x_{1,2} = \frac{130 \pm \sqrt{16900 + 16800}}{2}\\x_{1,2} = \frac{130 \pm \sqrt{100}}{2}\\x_{1,2} = \frac{130 \pm 10}{2}\\x_{1} = \frac{130 + 10}{2} = \frac{140}{2} = 70\\ x_{2} = \frac{130 - 10}{2} = \frac{120}{2} = 60[/tex]
The company must sell 60 or 70 items to obtain a weekly profit of 200.
Can anyone help me with this question?
Answer:
x= 60°, y = 80°, z = 40°
Step-by-step explanation:
Look at the line substending 40° and Z°; you would see that both lines are parallel and so their angles are they the same.
Hence z= 40° { corresponding angles of parallel lines}
Similarly;
Look at the line substending 60° and x°; you would see that both lines are parallel and so their angles are they the same.
60° = x° { corresponding angles of parallel lines}
Now looking at the angle between x and y; let's call the angle between them r
And you would observe closely that r = z° = 40°{ vertically opposite angles are equal}
Note that x + r + y = 180°{ angle on a straight line}
y = 180° - ( x + r)
y = 180 - (60+40)
y = 180° - 100°
= 80°
Multiply
4.2
x0.6
Type
Type an integer or a decir
Answer:
2.52
Step-by-step explanation:
4.2 × 0.6
Multiply the terms.
= 2.52
Answer:
2.52
hope it helps
Step-by-step explanation:
4.2 x 0.6
To solve this first, you simply multiply 42*06
(Exclude the decimal point)
42 x 6
= 252
Now since there are two numbers after the point (one is 4.2 and one is 0.6)
Move 252 two decimal places to left
= 2.52
Which numbers are the extremes of the proportion shown below
Answer:
3 and 8 are the extremes of the given proportion (first listed answer option)
Step-by-step explanation:
In a proportion of the type:
[tex]\frac{A}{B} =\frac{C}{D}[/tex]
the values "A" and "D" are called "extremes of the proportion, while "B" and "C" are called the "means" of the proportion.
This comes from writing it as: A : B = C : D
where we observe that A and D are the more "extreme" values being further away from the equal sign than the quantities B and C which are more towards the middle (center of the proportion).
So in your case, the numbers 3 and 8 are the extremes
Answer:
3 and 8
Step-by-step explanation:
