Angle C is inscribed in circle O.
AB is a diameter of circle O.
What is the measure of angle B?
Answer:
The measure of m∠B = 19°.
Step-by-step explanation:
Given
Angle C is inscribed in circle O.m∠A = 71°As we know that an angle inscribed in a semicircle is always a right angle.
So from the given diagram,
m∠C = 90°As we know that the sum of the three interior angles is equal to 180.
so
m∠A + m∠B + m∠C = 180°
71° + m∠B + 90° = 180°
m∠B = 180° - 71° - 90°
m∠B = 19°
Therefore, the measure of m∠B = 19°.
Answer:
Step-by-step explanation: 19
Mr. Jones gave some statistics for the Unit 1 Math test:
Mean = 70
Median = 75
Based on this information, which statement is NOT true?
A) The data is skewed to the left.
B) More people passed than failed.
C) Exactly half the class failed the exam (<70).
D) A person that scored a 74 scored lower than half the class.
Answer:
The Correct answer is C
Step-by-step explanation:
because i just took it.
Answer:
c
Step-by-step explanation:
The length Of a rectangular air filter is 1 inches less than twice the width. Find the length and width of the filter if the area is 378 square inches
Answer:52
Step-by-step explanation:
A carpenter is constructing a straircase in a house. The distance from the first floor to the basement is 10.3 feet. The staircase will be 17.9 feet long. What angle do the stair make with the basement floor?
Answer:
35.1°
Step-by-step explanation:
sin θ = 10.3 / 17.9
θ = sin⁻¹(10.3 / 17.9)
θ = 35.1°
Answer:
157.075 and yes
Step-by-step explanation: turst me
The graphs below have the same shape. Complete the equation of the red graph. Enter exponents using the caret (^); for example, enter x2 as x^2. Do not include "F(x) =" in your answer.
Answer:
f(x) = 1-x^2
Step-by-step explanation:
The graph of f(x) is just shifted down 3 units
A shift down is a subtraction
f(x) = g(x) -3
= 4- x^2 -3
=1-x^2
Answer:
1 - x^2
Step-by-step explanation:
F(x) is 3 units down. So,
G(x) - 2 = 4 - x² - 3
F(x) = 1 - x²
the sum 27 and a number g
Answer:
27 + g is how you write if u want a solution tell me what G is = to
Step-by-step explanation:
1. (Sec. 6.1) In a random sample of 80 components of a certain type, 12 are found to be defective. (a) Give a point estimate for the proportion of all such components that are not defective. (b) A system is to be constructed by randomly selecting two of these components and connecting them in a series. The series will function only if neither component is defective. Give an estimate for the proportion of all such systems that will function properly.
Answer:
(a) 0.85
(b) 0.7225
Step-by-step explanation:
(a) The point estimate for the proportion of all such components that are not defective is given by the number of non-defective units in the sample divided by the sample size:
[tex]p=\frac{80-12}{80}\\p=0.85[/tex]
The proportion is 0.85.
(b) Assuming that the sample is large enough to accurately provide a point estimate for the whole population, this can be treated as a binomial model with probability of success (non-defective part) p = 0.85. Since both components must be non-defective for the system to work, the probability of two successes in two trials is:
[tex]P(x=2) = 0.85^2\\P(x=2) = 0.7225[/tex]
An estimate of 0.7225 for the proportion of all such systems that will function properly.
2. If 1 cm3 of iron has a mass of 7.52 g, what is the mass of an iron bar of rectangular cross section with
the dimensions shown?
120.0 cm
3.2 cm
í
1.7 cm
Answer:
248cm
Step-by-step explanation:
8. A machine making
mango pieces puts 8
pieces in each snack
packet. The machine
makes 88 pieces in 1
minute. How many
packets are filled
every minute?
9. A carpenter mal
tables. Some ha
legs and some
legs. He plans t
tqbles with 3 le
tables with 4
many legs will
<?
Answer:
8. 11 packets
Step-by-step explanation:
8. If the machine makes 88 pieces in 1 minute and puts 8 pieces in each snack packet 88÷8=11 so, 11 packets are filled each minute.
I cannot read 9. as it is cut off, so i can't answer it :)
Final answer:
In an economy with 100 workers who can produce either four cakes or three shirts, they can make 400 cakes or 300 shirts, respectively, when all are dedicated to one task.
Explanation:
Calculating Production Output
If an economy has 100 identical workers with each one capable of producing either four cakes or three shirts, we can calculate the total production of each good. When all workers are cooking, the number of cakes that can be produced in this economy is 400 cakes (100 workers × 4 cakes per worker).
Conversely, if all workers are sewing shirts, then the total number of shirts produced is 300 shirts (100 workers ×3 shirts per worker).
A plane can fly 1200 miles in the same time as it takes a car to go 320 miles. If the car travels 110 mph slower than the
plane, find the speed of the plane.
____mph
Given:
A plane can fly 1200 miles in the same time as it takes a car to go 320 miles. The car travels 110 mph slower than the plane.
We need to determine the speed of the plane.
Speed of the plane:
Let the speed of the plane be x.
Equating the time taken by the plane and the time taken by the car using the formula,
[tex]Time=\frac{Distance}{Speed}[/tex]
Thus, we have;
[tex]\frac{1200}{x}=\frac{320}{x-110}[/tex]
Cross multiplying, we get;
[tex]1200(x-110)=320x[/tex]
Simplifying, we get;
[tex]1200x-132000=320x[/tex]
[tex]880x=132000[/tex]
[tex]x=150[/tex]
Thus, the value of the speed of the plane is 150 mph
Final answer:
The speed of the plane is found by setting up an equation based on the relationship between distance, speed, and time for both the plane and the car. After setting up the equations and equating the times, we find that the plane's speed is 150 mph.
Explanation:
To find the speed of the plane, we can set up an equation based on the relationship between distance, speed, and time. Let's denote the plane's speed as x mph. Then the car's speed would be x - 110 mph. Since they travel for the same amount of time, we can write two equations:
Time for plane = 1200 miles / x mph
Time for car = 320 miles / (x - 110) mph
These two times are equal, so we set the equations equal to each other:
1200 / x = 320 / (x - 110)
To solve for x, cross-multiply and solve the resulting quadratic equation:
1200(x - 110) = 320x
1200x - 132,000 = 320x
1200x - 320x = 132,000
880x = 132,000
x = 132,000 / 880
x = 150 mph
Therefore, the speed of the plane is 150 mph.
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Recall that a percent is a ratio of a number to 100. For example 39% means 39 out of 100.
1.Last year, there were 20 students on the track team. Eight of them competed in the long
jump. What percent of the team members competed in the long jump?
Answer:
1.6% should be right.
Step-by-step explanation:
What value of n makes the equation 2/3 times in equals 4/9 true
Answer:
the answer is 3/2
Step-by-step explanation:
because when you divide it you have to do keep change flip so you change 4/9 to 9/4 and divide it by 2/3 to get 3/2 so you put it in the equation to see if it is correct
The equation is a linear function, and the value of n that makes the 2/3 times n equals 4/9 true is 2/3
How to determine the value of n?The equation in the question implies that:
2/3 of n equals 4/9
This equation can be expressed as:
2/3 * n = 4/9
Multiply both sides by 3
3 * 2/3 * n = 3 * 4/9
Evaluate the product
2 * n = 4/3
Divide both sides by 2
n = 2/3
Hence, the value of n that makes the 2/3 times n equals 4/9 true is 2/3
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Aiden learned 12new words. Wyatt learned 6 new words How many times as many new words as Wyatt did Aiden learn
Answer:
2
Step-by-step explanation:
6×2=12
That is how I got the answer.
Answer:
2
Step-by-step explanation:
(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) I equation editorEquation Editor 1. For all n>2, nn3−2<2n2, and the series 2∑1n2 converges, so by the Comparison Test, the series ∑nn3−2 converges. equation editorEquation Editor 2. For all n>2, 1n2−1<1n2, and the series ∑1n2 converges, so by the Comparison Test, the series ∑1n2−1 converges. I equation editorEquation Editor 3. For all n>2, n+1−−−−−√n>1n, and the series ∑1n diverges, so by the Comparison Test, the series ∑n+1−−−−−√n diverges. I equation editorEquation Editor 4. For all n>2, ln(n)n2>1n2, and the series ∑1n2 converges, so by the Comparison Test, the series ∑ln(n)n2 converges. I equation editorEquation Editor 5. For all n>1, 1nln(n)<2n, and the series 2∑1n diverges, so by the Comparison Test, the series ∑1nln(n) diverges. I equation editorEquation Editor 6. For all n>1, n7−n3<1n2, and the series ∑1n2 converges, so by the Comparison Test, the series ∑n7−n3 converges.
Answer:
I.
CORRECT.
II.
CORRECT.
III.
CORRECT.
IV.
CORRECT.
V.
INCORRECT.
VI.
CORRECT
Step-by-step explanation:
To understand let us restate the comparison test in simple terms.
Comparison test :
Given [tex]\text{Series}_A[/tex] and [tex]\text{Series}_B[/tex] such that [tex]\text{Series}_A < \text{Series}_B[/tex] , then
1. If [tex]\text{Series}_B[/tex] converges then [tex]\text{Series}_A[/tex] converges as well.
2. If [tex]\text{Series}_A[/tex] diverges then [tex]\text{Series}_B[/tex] diverges as well.
Now to give you a more intuitive idea of what is going on, think about it like this. When the series on top converges it is like an "upper bound" for what you have on the bottom, therefore what you have on the bottom has to converge as well.
Similarly if what you have on the bottom explotes, then what you have on top will explote as well.
That's how I like to think about that intuitively.
Now, using those results let us examine the statements.
I.
[tex]\frac{1}{n} < \frac{ln(n)}{n}[/tex]
Since the infinite sum of 1/n diverges in fact the infinite sum of ln(n)/n does not converge.
Therefore, CORRECT.
II.
[tex]\frac{\arctan(n)}{n^3} < \frac{\pi}{2}\frac{1}{n^3}[/tex]
Since the infinite sum of [tex]\frac{\pi}{2}\frac{1}{n^3}[/tex] is in fact convergent then [tex]\frac{\arctan(n)}{n^3}[/tex] converges as well using the comparison theorem. Therefore
CORRECT.
III.
[tex]\frac{n}{2-n^3} < \frac{1}{n^2}[/tex]
Once again [tex]1/n^2[/tex] does converge so what you have on the bottom converges as well. Therefore
CORRECT.
IV.
[tex]\frac{\ln(n)}{n^2} < \frac{1}{n^{1.5}}[/tex]
Once again [tex]\frac{1}{n^{1.5}}[/tex] converges therefore since it is on top what is on the bottom converges as well. Therefore.
CORRECT.
V.
[tex]\frac{\ln(n)}{n} < \frac{2}{n}[/tex]
Now the fact that [tex]\frac{2}{n}[/tex] diverges does not necessarily imply that what you have on the bottom diverges. Therefore
INCORRECT.
VI.
That is correct as well since what you have on top converges therefore what you have on the bottom converges as well.
What is the whole number for 6/1?
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Because 1/1 = 1 whole and you add 5 more 1/1 and you get 6/1 so their is 6 wholes
Solve the equation, 4 - (x + 1) = 6.
Answer:
X=-3
Step-by-step explanation
First of all, remove the parenthesis by distributing the value of the negative sign so it would be 4-x-1=6 , next find the like terms which is 4-1 is 3. so 3-x=6.
transpose the 3 to the other side so it would be -x=6-3
-x=3 divide both sides by -1. X=-3
Suppose a recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10.4 ft. A
biologist observing a huge field of mature plants of this particular species of sunflower thinks that the mean height is shorter
than reported. He measures the heights of 45 randomly selected sunflowers and finds the mean height to be 10.1 ft.
The hypotheses of interest are :
(A) H0 : µ = 10.1 vs Ha : µ < 10.1
(B) H0 : µ > 10.4 vs Ha : µ = 10.4
(C) H0 : ¯x = 10.1 vs Ha : ¯x > 10.1
(D) H0 : ¯x = 10.1 vs Ha : ¯x < 10.1
(E) H0 : µ = 10.4 vs Ha : µ < 10.4
Answer: (E) H0 : µ = 10.4 vs Ha : µ < 10.4
Step-by-step explanation:
The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.
From the given situation,
The recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10.4 ft. This is the null hypothesis.
The biologist sunflower thinks that the mean height is shorter than reported. This is the alternative hypothesis.
Therefore, the correct null and alternative hypotheses are
(E) H0 : µ = 10.4 vs Ha : µ < 10.4
An 8-foot by 5-foot section of wall is to be covered by square tiles that measure 4 inches on each side. If the tiles are not cut, how many of them will needed to cover the wall ?
Answer:
30 tiles
Step-by-step explanation:
SO we need to find the area of the wall so we do
8 feet * 5 feet = 40 feet squared
then we find that area in inches
40*12=480
Now we find the area of the tiles
4*4=16
So now we divide to find how many tiles are needed
480/16=30
Our answer is 30
The number P, in hundreds of bacteria in a sample, can be modeled by the Equation P= T^4+ 5T^3 + 5T^2 + 6t where t is measured in weeks. explain how to determine the number of weeks which the population would be greater than 10,000
Answer:
The values of T which satisfies the inequality are: [tex](8.8, \infty)[/tex]
Step-by-step explanation:
In the equation [tex]P= T^4+ 5T^3 + 5T^2 + 6T[/tex]
Represent P by 10,000Write an inequality where the expression is greater than 10000: [tex]T^4+ 5T^3 + 5T^2 + 6T>10000[/tex]Get 0 on one side of the inequality.[tex]T^4+ 5T^3 + 5T^2 + 6T-10000>0[/tex]
Graph the polynomial function. We have real x-intercepts of 8.84 and -11.38.Determine intervals where the graph is above the x-axis. Since negative values of x in this situation are irrelevant, the values of T which satisfies the inequality are: [tex](8.8, \infty)[/tex]We now test a value from the set of solution to see if it is valid.Let T=9[tex]T^4+ 5T^3 + 5T^2 + 6T>10000\\9^4+ 5(9)^3 + 5(9)^2 + 6(9)>10000\\10665>10000[/tex]
Since 10665 is grater than 10000, the result is reasonable.
in an after school program, 70% of 400 students play soccer. how many students play soccer?
Answer:
its 280
Step-by-step explanation:
What is the Inverse operation needed to solve for p?
765 = p - 254
Answer:
Adding 254 to both sides.
This is an inverse operation.
On the right side of the equation, there is a -254, which you need to get rid of in order to isolate p. (You have to isolate p to find the value)
So, since it is -254, you would do +254 on BOTH sides of the equation. Hope this helps!!
The inverse operation needed to solve for p in the equation 765 = p - 254 is addition.
Explanation:To solve for p in the equation 765 = p - 254, we need to isolate p on one side of the equation. To do this, we can use the inverse operation of subtraction, which is addition. By adding 254 to both sides of the equation, we get:
765 + 254 = p - 254 + 254
Simplifying the equation gives us:
1019 = p
Therefore, the inverse operation needed to solve for p is addition.
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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.04. If 469 are sampled, what is the probability that the sample proportion will be less than 0.03
Using the normal distribution and the central limit theorem, it is found that there is a 0.1335 = 13.35% probability that the sample proportion will be less than 0.03.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
The true proportion is of p = 0.04.469 people are sampled, hence n = 469.The mean and the standard error are given by:
[tex]\mu = p = 0.04[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.04(0.96)}{469}} = 0.009[/tex]
The probability that the sample proportion will be less than 0.03 is the p-value of Z when X = 0.03, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.03 - 0.04}{0.009}[/tex]
[tex]Z = -1.11[/tex]
[tex]Z = -1.11[/tex] has a p-value of 0.1335.
0.1335 = 13.35% probability that the sample proportion will be less than 0.03.
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In 1992, the U.S. Senate was composed of 57 Democrats and 43 Republicans. Of the Democrats, 38 had served in the military, whereas 28 of the Republicans had served. If a senator selected at random is found to have served in the military, what is the probability that the senator is Republican
Answer: 0.66
Step-by-step explanation:
The United States senate had 57 Democrats and 43 Republicans which makes the total numerous of senators 100.
38 Democrats had served in the military while 28 Republicans has served in the military which makes the total number of senators that had served in the military 66.
Probability of a Republican senator that had served in the military will be:
What is the answer to -t+9-4t=59?
Answer:
-10
Step-by-step explanation:
combine like terms -5x+9=59 subtract 9 from both side and get -5x=50 so x=-10
Answer:
-10
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−t+9−4t=59
−t+9+−4t=59
(−t+−4t)+(9)=59(Combine Like Terms)
−5t+9=59
−5t+9=59
Step 2: Subtract 9 from both sides.
−5t+9−9=59−9
−5t=50
Step 3: Divide both sides by -5.
−5t −5 = 50−5
t=−10
What is the area of the prism below pls help ASAP
Answer:
volume is 3 1/2 units³
Step-by-step explanation:
The question asks for area, but the answers have dimensions of volume.
__
The volume is the product of the length, height, and width dimensions:
V = LWH = (2)(1)(1 3/4) = 2 6/4 = 3 1/2 . . . . units³
The volume is 3 1/2 cubic units.
When drawn in standard position, an angle B has a terminal ray that lies in the second quadrant and sin(B)=5/13. Find the value of cos(B), (show your answer as a fraction). Please show all your work
Please a help here.
Thank you
Answer:
[tex]\cos{B} = -\frac{12}{13}[/tex]
Step-by-step explanation:
For any angle B, we have the following trigonometric identity:
[tex]\sin^{2}{B} + \cos^{2}{B} = 1[/tex]
In this problem, we have that:
[tex]\sin{B} = \frac{5}{13}[/tex]
So, applying the trigonometric identity:
[tex]\sin^{2}{B} + \cos^{2}{B} = 1[/tex]
[tex](\frac{5}{13})^{2}) + \cos^{2}{B} = 1[/tex]
[tex]\cos^{2}{B} = 1 - (\frac{5}{13})^{2})[/tex]
[tex]\cos^{2}{B} = 1 - \frac{25}{169}[/tex]
[tex]\cos^{2}{B} = \frac{169}{169} - \frac{25}{169}[/tex]
[tex]\cos^{2}{B} = \frac{144}{169}[/tex]
[tex]\cos{B} = \pm \sqrt{\frac{144}{169}}[/tex]
[tex]\cos{B} = \pm \frac{12}{13}[/tex]
In the second quadrant, the cosine is negative. So
[tex]\cos{B} = -\frac{12}{13}[/tex]
Final answer:
The cosine in the second quadrant is negative, giving cos(B) = -12/13.
Explanation:
To find the value of cos(B) when an angle B is in standard position with its terminal ray in the second quadrant and given that sin(B) = 5/13, we can use the Pythagorean identity:
sin²(B) + cos²(B) = 1.
First, we square the sine value to get sin²(B):
sin²(B) = (5/13)² = 25/169.
Now we use the Pythagorean identity to find cos²(B):
cos²(B) = 1 - sin²(B) = 1 - 25/169 = 144/169.
Since angle B is in the second quadrant, the cosine value must be negative.
Therefore, cos(B) = -√(cos²(B)) = -√(144/169).
The square root of 144/169 is 12/13, and thus:
cos(B) = -12/13.
What is one way you can calculate 0.25 times 0.044 as a decimal?
Answer:
0.011
Step-by-step explanation:
let's see so first
first you line the numbers on the right (DO NOT ALINE DECIMAL POINTS)
second, starting from on the right multiply each digit in the top number by each digit in the bottom number just as whole numbers .
after add the products
The capacity of n elevator is 12 people or 1968 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 1968/12=164 pounds. Suppose the people have weights that are normally distributed with a mean of 171 lb and a standard deviation of 34 lb.
a. find the probability that if a person is randomly selected, his weight will be greater than 164 pounds.
The probability is approximately ___
b. Find the probability that 12 randomly selected people will have a neam that is greater than 164 pounds.
Answer:
a) 58.32% probability that his weight will be greater than 164 pounds.
b) 76.11% probability that 12 randomly selected people will have a neam that is greater than 164 pounds.
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 problem, we have that:
[tex]\mu = 171, \sigma = 34[/tex]
a. find the probability that if a person is randomly selected, his weight will be greater than 164 pounds.
This is 1 subtracted by the pvalue of Z when X = 164. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{164 - 171}{34}[/tex]
[tex]Z = -0.21[/tex]
[tex]Z = -0.21[/tex] has a pvalue of 0.4168
1 - 0.4168 = 0.5832
58.32% probability that his weight will be greater than 164 pounds.
b. Find the probability that 12 randomly selected people will have a neam that is greater than 164 pounds.
Now [tex]n = 12, s = \frac{34}{\sqrt{12}} = 9.81[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{164 - 171}{9.81}[/tex]
[tex]Z = -0.71[/tex]
[tex]Z = -0.71[/tex] has a pvalue of 0.2389
1 - 0.2389 = 0.7611
76.11% probability that 12 randomly selected people will have a neam that is greater than 164 pounds.
Suppose a batch of steel rods produced at a steel plant have a mean length of 170170 millimeters, and a standard deviation of 1010 millimeters. If 299299 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by greater than 0.70.7 millimeters? Round your answer to four decimal places.
Answer:
Required probability is 0.2262
Step-by-step explanation:
given data
mean length = 170 millimeters
standard deviation = 10 millimeters
sample n = 299
population mean by greater than = 0.7 millimeters
solution
we consider here batch of steel rod produced = x
probability that mean length sample that differ than the population mean greater than 0.7 required probability is
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 1 - P ( [tex]\bar {x} -\mu[/tex] ≤ 0.7 ) .................1
so we take here value
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 1 - [ P ( -0.7 ≤ [tex]\bar {x} -\mu[/tex] ≤ 0.7 ) ]
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 1 - [ P ( [tex]\frac{-0.7}{\frac{10}{\sqrt{299}}}[/tex] ≤ [tex]\frac{\bar {x} -\mu}{\frac{\sigma }{\sqrt{n}}}[/tex] ≤ [tex]\frac{0.7}{\frac{10}{\sqrt{299}}}[/tex] )
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 1 [ P ( - 1.21 ≤ Z ≤ 1.21 ) ]
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 1 ( P ( Z ≤ 1.21 ) - P ( Z ≤ - 1.21 ) )
we use here excel function that
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 1 - { (=NORMSDiST (1.21) - (=NORMSDiST (-1.21) }
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 1 - ( 0.8869 - 0.1131 )
P ( [tex]\bar {x} -\mu[/tex] > 0.7 ) = 0.2262
so required probability is 0.2262
To find the probability that the sample mean length of steel rods differs from the population mean by more than 0.7 millimeters, we calculate the standard error, convert 0.7 mm to a z-score, and then find the two-tailed probability using the standard normal distribution.
Explanation:To calculate the probability that the mean length of a sample of steel rods will differ from the population mean by more than 0.7 millimeters, we must use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed as the sample size gets larger (which holds true in this case since we have 299 rods).
We can apply this theorem to find the standard error of the mean (SEM), which is the standard deviation of the sample mean distribution, calculated as σ/√n (population standard deviation/square root of sample size).
With σ = 10 millimeters and n = 299, the SEM is 10/√299 = 0.5787 millimeters. To find the probability that the sample mean differs from the population mean by more than 0.7 millimeters, we convert 0.7 millimeters to a z-score by dividing by the SEM: z = 0.7/0.5787 = 1.2096.
Using the standard normal distribution, we find the probability for the corresponding z-score and then calculate the two-tailed probability, as we are looking for the probability that the sample mean is either above or below the population mean by 0.7 millimeters. However, to provide the exact figure, we would need a z-table or software to get the precise probability.
Finally, we find that the distribution of the sample mean will have higher probabilities closer to the population mean, as described in the provided information.
Volume round to the nearest tenth
Answer:
504 in.
Step-by-step explanation:
6 · 12 · 7 = 504
Answer:
504in^3
Step-by-step explanation:
voluke of rectangular prism formula: LWH
where l=length(7)
w=width(12)
h=height(6)
so
7*12*6=504
504in^3