Answer:
a) CI = ( 148,69 ; 243,31 )
b) n = 189
Step-by-step explanation:
a) If the Confidence Interval is 95 %
α = 5 % or α = 0,05 and α/2 = 0,025
citical value for α/2 = 0,025 is z(c) = 1,96
the MOE ( margin of error is )
1,96* s/√n
1,96* 163,7/ √46
MOE = 47,31
Then CI = 196 ± 47,31
CI = ( 148,69 ; 243,31 )
CI look very wide ( it sems that if sample size was too low )
b) Now if s (sample standard deviation) is 175, and we would like to have only 50 ppm width with Confidence level 95 %, we need to make
MOE = 25 = z(c) * s/√n
25*√n = z(c)* 175
√n = 1,96*175/25
√n = 13,72
n = 188,23
as n is an integer number we make n = 189
Explain the relationship between variance and standard deviation. Can either of these measures be negative? Explain. Choose the correct answer below. A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative. B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative. C. The variance is the negative square root of the standard deviation. The variance can be negative but the standard deviation can never be negative. D. The standard deviation is the negative square root of the variance. The standard deviation can be negative but the variance can never be negative.
Answer:
A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.
Step-by-step explanation:
As we know that
The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation
In mathematically
[tex]\sigma = \sqrt{variance}[/tex]
And,
[tex]variance = \sigma^2[/tex]
Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive
Hence, the correct option is a.
Answer:
B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting or . (b) Compute the probability of randomly selecting or or . (c) Compute the probability of randomly selecting or .
Answer: See answer in the attached file
Step-by-step explanation:
Graph a line that contains the point (-7,-4)and has a slope of - 2/3
Hi there! :)
Answer:
Given the information, we can write an equation in slope-intercept form
(y = mx + b) to graph the line:
Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the
x-coordinate given for 'x':
-4 = -2/3(-7) + b
-4 = 14/3 + b
Solve for b:
-12/3 = 14/3 + b
-12/3 - 14/3 = b
-26/3 = b
Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)
Some points on the line include:
(-7, -4)
(-4, -6)
(0, -26/3)
(2, -10)
(5, -12)
a student showed the steps below while solving the equation 14=log5(2x-3) by graphing. which step did the student make the 1sr error
Answer:
[tex]x= \frac{5^{14}+3}{2}[/tex]
Step-by-step explanation:
The correct steps to solve the equation are:
[tex]14=log_5(2x-5)[/tex]
[tex]5^{14}=5^{log_5(2x-3)}[/tex]
Because [tex]a^{log_am}=m[/tex]
So, solving we get:
[tex]5^{14}=2x-3[/tex]
Sum 3 on every side:
[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]
Dividing by 2 into both sides:
[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]
So, the answer is [tex]x= \frac{5^{14}+3}{2}[/tex]
Answer: Step 2
Step-by-step explanation:
This is correct according to Edge 2021
Find the number of four-digit numbers which are not divisible by 4?
Answer: without trying each calculation individually, 6750 4-digit numbers are not divisible by 4
Step-by-step explanation: From 1000 to 9999 there are 9000 4-digit numbers 9999 - 999 = 9000.
Eliminate all the odd numbers 9000/2 = 4500
Eliminate the even numbers divisible by 2 but not by 4. 4500/2 = 2250
9000 - 2250 = 6750.
Lisa is 34 years old. Two years ago, she was twice as old as her brother. How old is her brother now?
Answer:
18
Step-by-step explanation:
Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.
Math question, need help
In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.
Answer:
[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]
First answer is correct.
Step-by-step explanation:
we know that,
[tex] {x}^{a} = {x}^{b} [/tex]
[tex]a = b[/tex]
So, according to that,
[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]
Therefore,
[tex]2x - 1 = 5x - 14[/tex]
College Calculus - hyperbolic functions (see attachment)
Answer:
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Step-by-step explanation:
Using the fundamental theorem of calculus
Taking the derivative of the integral gives back the function
Since the lower limit is a constant when we take the derivative it is zero
d/dx [tex]\int\limits^x_4 {g(t)} \, dt = g(x)[/tex]
g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))
Replacing t with x
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.18.
1. Which of the following is a type I error?
a. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
b. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
c. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
d. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
2. Which is the following is a type II error?
a. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
b. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
c. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
d. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
Answer:
Type I error: Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
Type II error: Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
Step-by-step explanation:
We are given the following hypothesis below;
Let p = proportion of people who write with their left hand
Null Hypothesis, [tex]H_0[/tex] : p = 0.18 {means that the proportion of people who write with their left hand is equal to 0.18}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.18 {means that the proportion of people who write with their left hand is different from 0.18}
Type I error states that we would reject the null hypothesis given the fact that the null hypothesis was actually true. Or in other words, the probability of rejecting a true hypothesis.
So, according to our question, Type I error is to Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
Type II error states that we would accept the null hypothesis given the fact that the null hypothesis was actually false. Or in other words, the probability of accepting a false hypothesis.
So, according to our question, Type II error is Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
Given a rectangle with an area of 20 square units, if the width is x units and the length is x + 1 units, what is the difference between the length and the width?
Answer: 1unit.
Step-by-step explanation:
Area of the rectangle
A = length × width
Since the area = 20 and the width is x and the length is x + 1.
We now substitute for the values in the above formula and solve for x
20 = x × x + 1
20 = x( x + 1 ), we now open
20 = x² + x , then re arrange.
x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means
Here, I am going to solve using factorization by grouping
x² + x - 20 = 0
x² + 5x - 4x - 20 = 0
x( x + 5 ) - 4( x + 5 ) = 0
( x + 5 )( x - 4 ). = 0
Therefore, the solution for x will be
x = -5 or 4, but x can not be -5 ( negative), so x = 4.
Now the difference between width and the length can easily be calculated from the above,
Width = 4 (x) , and length = 5 (4 + 1),
Now difference will be
5 - 4 = 1unit.
What is m Please help me
Answer:
Angle BCA = 70
Angle CAB = 20
Step-by-step explanation:
Not sure what angle you meant, so I'll give you all of them <3
Angle BCA = 70 degrees, because If two angles form a line, they add up to 180. (110+x=180, x = 70)
Angle CAB = 20 degrees, because there are 180 degrees in a triangle, so 90+70+x=180, x = 20
Hope it helps <3
Answer:
BCA = 70
CAB = 20
ABC=90
Step-by-step explanation:
ABC is 120 because the square indicates that
BCA = 70 because angles on a straight line add up to 180.
110+x=180
x=180-110
=70
Angle CAB = 20 degrees, because angles in a triangle add up to 180
90+70+x=180
x = 180-(90+70)
=180-160
=20
Please mark as brainliest
limit xtens to 0 x^2logx^2 what is the ans of interminate forms?
Rewrite the limit as
[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]
Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get
[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]
Identify the reference angle ∅ for each given angle, 0.
Answer:
When Ø = 300°, Ø = 60 degrees.
When Ø = 225°, Ø = 45 degrees.
When Ø = 480°, Ø = 60 degrees.
When Ø = -210°, Ø = 30 degrees.
Step-by-step explanation:
Reference angles are in Quadrant I (0° to 90°).
1. Find 300° (Quadrant IV) on the unit circle. Since it's in Quadrant IV, you use 360 - 300 = 60° to get your answer.
2. Find 225° (Quadrant III) on the unit circle. Since it's in Quadrant III, you use 225 - 180 = 45° to get your answer.
3. The angle 480° is not on the unit circle. To find its corresponding angle between 0° and 360°, use 480 - 360 = 120°. Then, find 120° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 120 = 60° to get your answer.
4. The angle -210° is not on the unit circle. To find its corresponding angle between 0° and 360°, use -210 + 360 = 150°. Then, find 150° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 150 = 30° to get your answer.
mark wants to invest $10,000 for his daughter’s wedding. Some will go into a short term CD that pays 12% and the rest in a money market savings account that pays 5% interest. How much should he invest at Each rate if he wants to earn $1095.00 in interest in one year.
What is x? The angle x
Answer:
x=60
Step-by-step explanation:
This is an equilateral triangle which means all the sides are equal.
If all the sides are equal then all the angles are equal
180/3 = 60
x=60
Answer:
x= 60°
Step-by-step explanation:
We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°
The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additional $150 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 17 tons of sugar.
Answer:
C = $6050
Equation:
To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:
[tex]3500+150(S)=C[/tex]
3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.
Solving the equation
To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.
[tex]3500+150(17)=C[/tex]
150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.
Our answer is: C = $6050
Find the domain for the rational function f of x equals quantity x end quantity divided by quantity x minus 5 end quantity.
Answer:
All real numbers except for 5.
Step-by-step explanation:
[tex]f(x)=\frac{x}{x-5}[/tex]
The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.
Thus, we need to find the zero(s) of the denominator to determine the domain.
[tex]x-5=0[/tex]
[tex]x=5[/tex]
Therefore, the domain of the rational function is all real numbers except for 5.
In set builder notation, this is:
[tex]\{x|x\in \mathbb{R}, x\neq 5\}[/tex]
Stella bought a dinette set on sale for $725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount?
Answer:
40%
Step-by-step explanation:
1299-725= 574
574/1299 x 100 = 44.19%
The rate of discount on the dinette set = 44.2%.
What is a discount?Often, goods are sold at a price that is lower than their marked price. The price at which the good is sold is called the selling price and the difference between the marked price and the selling price is the discount.
Discount = Marked Price - Selling Price.
Rate of Discount = Discount/Marked Price * 100%.
How to solve the given question?In the question, we are given that Stella bought a dinette set on sale for $725. The original price was $1,299.
We are asked to calculate the rate of discount on the dinette set.
The marked price of the dinette set = $1299.
The selling price of the dinette set = $725.
∴ The discount on the dinette set = the marked price of the dinette set - the selling price of the dinette set = $1299 - $725 = $574
∴ The rate of discount on the dinette set = the discount on the dinette set/the marked price of the dinette set *100%
or, The rate of discount on the dinette set = 574/1299 * 100%
or, The rate of discount on the dinette set = 0.4418 * 100%
or, The rate of discount on the dinette set = 44.18% ≈ 44.2% (to the nearest tenth of a percent)
∴ The rate of discount on the dinette set = 44.2%.
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Find the value of a A.130 B.86 C.58 D.65
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
If the average American sleeps 8 hours a night, with a standard deviation of 1 hour, and I plan on gathering a sample of 12 college students to compare to this population, find the following:
mu =
sigma =
mu_x bar =
sigma_x bar =
Answer:
8 hours
1 hour
8 hours
0.288675
Step-by-step explanation:
We complete the answer as follows;
mu = mean = 8 hours
sigma = standard deviation= 1 hour
Mu_x bar = mu = 8 hours
sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675
CAN ANYONE HELP ME PLEASE? Two numbers total of 52 and have a difference of 30. Find the two numbers. The larger number is ? and the smaller number is ?
Answer:
41 and 11.
Step-by-step explanation:
Let's say the 2 numbers are x and y.
Since they add up to 52, x + y = 52.
Seeing as the difference is 30, x - y = 30 assuming x is the larger number.
We have left:
x + y = 52
x - y = 30
By solving these simultaneous equations (adding the 2 equations together for instance), we are left with 2x = 82
Therefore x = 41.
Since x + y = 52
41 + y = 52
Therefore y = 11
Therefore we have: the larger number is 41 and the smaller number is 11.
PLEASE HELP----- T.A. =
Answer:
vol = 96
Step-by-step explanation:
Area of a triangle = 1/2 * b * h
b = 4
h = 6
A = 0.5 * 4 * 6
A = 12
length = 8
vol = Area * length
vol = 12 * 8
vol = 96
Answer:
(104 + 16 sqrt 13)
Step-by-step explanation:
i did this on my school, it was correct
To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called:____________
Answer:
Convenience sampling.
Step-by-step explanation:
To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called convenience sampling.
Convenience sampling can be defined as a sampling method which involves the researcher selecting or collecting data that is easily available or choosing the individuals who are easiest to reach in a population. It is a type of non-probability method of sampling where the first or easiest available data source is being used by the researcher without other requirements.
In this scenario, to gather information on customer satisfaction, the researcher went to the store most likely situated in a shopping mall to collect data from six (6) customers in each stores.
Some of the advantages of convenience sampling are low cost, data are collected quickly, lesser rules etc.
Help ASAP!!!
A recursive sequence is a sequence where each term is found by adding a common difference
True or false
Answer:
True
Step-by-step explanation:
Select the correct answer. Consider matrices A, B, and C:
Answer:
i think it is c. i may be incorrect, i am sorry!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I did the math
Which of the following is the correct name for below?
A.
Midsegment
B.
Perpendicular Bisector
C.
Angle Bisector
D.
Midpoint
Answer: B. Perpindicular Bisector.
Step-by-step explanation:
BD is a perpindicular bisector because it splits CE into 2 equal segments via a right angle.
Answer:
midsegement
Step-by-step explanation:
Find the value of x.
Answer:
[tex]\huge\boxed{x=\sqrt{21}}[/tex]
Step-by-step explanation:
ΔABD and ΔBCD are similar (AAA).
Therefore the corresponding sides are in proportion:
[tex]\dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]
Substitute
[tex]BD=x;\ CD=3;\ AD=7[/tex]
[tex]\dfrac{x}{3}=\dfrac{7}{x}[/tex] cross multiply
[tex](x)(x)=(3)(7)\\\\x^2=21\to x=\sqrt{21}[/tex]
In the search to determine if car 1 is slower to accelerate than car 2, the mean time it takes to accelerate to 30 miles per hour is recorded (Note: a car is slower to accelerate if it takes more time to accelerate). Twenty trials of the acceleration time for each car are recorded, and both populations have normal distributions with known standard deviations. What are the hypotheses used in this test
Answer:
Step-by-step explanation:
The happiest used in a test in statistics are the null and the alternative hypothesis. The null hypothesis is usually the default statement while the alternative hypothesis is thevopposite of the null hypothesis.
In this case study, the null hypothesis is u1 = u2: the average mean time it takes to accelerate to 30 miles per hour for car 1 is the same as that for car 2.
The alternative hypothesis is u1 > u2: the mean time it takes to accelerate to 30 miles per hour is greater than that for car 2 thus car 1 is slower to accelerate as it takes more time.
Find the measure of angle angle AGE in the figure below. Enter only the number.
Help please!
Answer:
AGE = 129 degrees
Step-by-step explanation:
Two angles whose sum is 180° are called supplementary angles. The measure of ∠AGE in the given figure is 129°.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
In the given figure, line segment CE is a straight line. Therefore, the sum of the angles formed on the same side of the line will be a linear pair.
Thus, the measure of the angles can be rewritten as,
∠AGC + ∠AGE = 180°
51° + ∠AGE = 180°
∠AGE = 180° - 51°
∠AGE = 129°
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Find the probability of each event. A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Eight horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet?
Answer: [tex]\dfrac{1}{56}[/tex]
Step-by-step explanation:
Total horses = 6
Number of ways to choose top 3 finishers in order = 3! = 6
Number ways to select 3 horses out of 8 in order = [tex]^8P_3[/tex] [By permutations]
[tex]=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336[/tex]
Now, the probability that the gambler will win his bet =
[tex]\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}[/tex]
[tex]=\dfrac{6}{336}\\\\=\dfrac{1}{56}[/tex]
Hence, the required probability = [tex]\dfrac{1}{56}[/tex]