Answer:
Step-by-step explanation:
Population proportion, p = 5000/20000 = 0.25
We would set up the hypothesis test.
For the null hypothesis,
p = 0.25
For the alternative hypothesis,
p > 0.25
Considering the population proportion, probability of success, p = 0.25
q = probability of failure = 1 - p
q = 1 - 0.25 = 0.75
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 96
n = number of samples = 300
P = 96/300 = 0.32
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.32 - 0.25)/√(0.25 × 0.75)/300 = 2.8
The calculated test statistic is 2.8 for the right tail and - 2.8 for the left tail
Since α = 0.025, the critical value is determined from the normal distribution table. The z score for the lower and upper tail of the curve is - 1.96 and 1.96
In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Since - 2.8 < - 1.96 and 2.8 > 1.96, we would reject the null hypothesis.
Therefore, the correct option is
a. Since the critical test value is 1.96, we are going to reject the null hypothesis. The rental chain store should open a store in this area.
Which best explains whether 9 is a solution to the inequality x greater-than 9? It is not a solution because 9 is not greater than 9. It is not a solution because 9 is not less than 9. It is a solution because 9 is greater than 9. It is a solution because 9 is less than 9.
Answer:
"It is not a solution because 9 is not greater than 9."
Step-by-step explanation:
[tex]x>9\\[/tex]
If x is 9, then the inequality would be untrue because x must be GREATER than 9 not equal or greater.
Answer:
It is not a solution because 9 is not greater than 9.
Step-by-step explanation:
i took the test and got it right hope it helps :)
The equation f(x) is given as x2_4=0. Considering the initial approximation at
x0=6 then the value of x1 is given as
Select one:
O A. 10/3
O B. 7/3
O C. 13/3
O D. 4/3
Answer:
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
Step-by-step explanation:
This exercise represents a case where the Newton-Raphson method is used, whose formula is used for differentiable function of the form [tex]f(x) = 0[/tex]. The expression is now described:
[tex]x_{n+1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})}}[/tex]
Where:
[tex]x_{n}[/tex] - Current approximation.
[tex]x_{n+1}[/tex] - New approximation.
[tex]f(x_{n})[/tex] - Function evaluated in current approximation.
[tex]f'(x_{n})[/tex] - First derivative of the function evaluated in current approximation.
If [tex]f(x) = x^{2} - 4[/tex], then [tex]f'(x) = 2\cdot x[/tex]. Now, given that [tex]x_{0} = 6[/tex], the function and first derivative evaluated in [tex]x_{o}[/tex] are:
[tex]f(x_{o}) = 6^{2} - 4[/tex]
[tex]f(x_{o}) = 32[/tex]
[tex]f'(x_{o})= 2 \cdot 6[/tex]
[tex]f'(x_{o}) = 12[/tex]
[tex]x_{1} = x_{o} - \frac{f(x_{o})}{f'(x_{o})}[/tex]
[tex]x_{1} = 6 - \frac{32}{12}[/tex]
[tex]x_{1} = 6 - \frac{8}{3}[/tex]
[tex]x_{1} = \frac{18-8}{3}[/tex]
[tex]x_{1} = \frac{10}{3}[/tex]
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
If 11+11 = 4 and 22+22 = 16 and 33+33 = 36 how do you get the answer
Answer:
Its basically a riddle
11 + 11 = 2 x 2 = 4
22 + 22 = 4 x 4 = 16
33 + 33 = 6 x 6 = 36
If a coin is tossed 4 times, and then a standard six-sided die is rolled 3 times, and finally a group of two cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer: 4,582,656
Step-by-step explanation:
A coin is tossed 4 times,
2^4 outcomes: 16
and then a standard six-sided die is rolled 3 times, 6^3
216 outcomes:
and finally, a group of two cards is drawn from a standard deck of 52 cards without replacements
It says a “group”, so, I guess the order doesn’t matter… So it is “52 choose 2”
52*51/ (2*1) = 26*51
how many different outcomes are possible?
16*216*26*51 = 4,582,656
What is the common difference between successive terms in the sequence?
0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...
–0.1
–0.01
0.01
0.1
Answer:
0.1
Step-by-step explanation:
0.36-0.26=0.1
hope u understand
Answer:
A
Step-by-step explanation:
plsssssssssssssssssssssssssssssss help
Answer:
X=166°Solution,
<ABE+<ABC=180
<ABE=180-97
<ABE=83°
<ABC=<ACB=83°
<ABC+<ACB+<CAB=180
<CAB=180-83-83
<CAB=14
<DAC+<CAB=180
<DAC+14=180
<DAC=180-14
<DAC(X)=166°
Hope this helps...
Good luck on your assignment...
What is the measure of AC?
Enter your answer in the box.
Answer:
21
Step-by-step explanation:
Since angle ABC is an inscribed angle, its measure is half that of arc AC. Therefore:
[tex]2(3x-1.5)=3x+9 \\\\6x-3=3x+9 \\\\3x-3=9 \\\\3x=12 \\\\x=4 \\\\AC=3(4)+9=12+9=21[/tex]
Hope this helps!
Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is, 21°.
What is the Inscribed Angle theorem?We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.
Given that,
The inscribed angle is, (3x - 1.5)
And the Intercepted arc AC is, (3x + 9)
So, We get;
(3x - 1.5) = 1/2 (3x + 9)
2 (3x - 1.5) = (3x + 9)
6x - 3 = 3x + 9
3x = 9 + 3
3x = 12
x = 4
Thus, The Intercepted arc AC is,
(3x + 9) = 3×4 + 9
= 21°
Learn more about the Inscribed Angle theorem visit:
brainly.com/question/5436956
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Carlos is almost old enough to go to school! Based on where he lives, there are 666 elementary schools, 333 middle schools, and 222 high schools that he has the option of attending.
Answer:
There are 36 education paths available to Carlos based on the schools around where he lives.
Step-by-step explanation:
Complete Question
Carlos is almost old enough to go to school. Based on where he lives, there are 6 elementary schools, 3 middle schools, and 2 high schools that he has the option of attending. How many different education paths are available to Carlos? Assume he will attend only one of each type of school.
Solution
We can use mathematics or manually writing out the possible combinations of elementary, middle and high school that Carlos can attend.
Using Mathematics
There are 6 elementary schools, meaning Carlos can make his choice in 6 ways.
There are 3 middle schools, meaning Carlos can make his choice in 3 ways.
Together with the elementary school choice, Carlos can make these two choices in 6 × 3 ways.
There are 2 high schools, Carlos can make his choice in 2 ways.
Combined with the elementary and middle school choices, Carlos can make his choices in 6×3×2 ways = 36 ways.
Manually
If we name the 6 elementary schools letters A, B, C, D, E and F.
Name the 3 middle schools letters a, b and c.
Name the 2 high schools numbers 1 and 2.
The different combinations of the 3 choices include
Aa1, Aa2, Ab1, Ab2, Ac1, Ac2
Ba1, Ba2, Bb1, Bb2, Bc1, Bc2
Ca1, Ca2, Cb1, Cb2, Cc1, Cc2
Da1, Da2, Db1, Db2, Dc1, Dc2
Ea1, Ea2, Eb1, Eb2, Ec1, Ec2
Fa1, Fa2, Fb1, Fb2, Fc1, Fc2
Evident now that there are 36 ways in which the 3 stages of schools can be combined. There are 36 education paths available to Carlos based on the schools around where he lives assuming that he will attend only one of each type of school.
Hope this Helps!!!
Answer:
36 education paths
Step-by-step explanation:
Hope this helps!
The purchasing manager for a chain of grocery stores is interested in customer's preference for non-alcoholic beverages. She wondered if there was a relationship between the customer's beverage preference and the customer's income class. She randomly sampled 500 customers and asked their non-alcoholic beverage preference (soft drinks, energy drinks, fruit juices, vitamin water, or other) and what their income class is (lower class, lower middle class, middle class, upper middle class, upper class). Assuming all conditions are satisfied, which of the following tests should the manager use to test her hypothesis?
A. The chi-square test of homogeneity.
B. The goodness-of-fit chi-square test.
C. The chi-square test of independence.
D. The two-sample z-test for proportions.
Answer:
Option C
Step-by-step explanation:
The chi-square test of independence is used to determined whether there is a relationship between two categorical variable which in this study is to establish if there is a relationship between a customer's beverage preference and his/her income class (these are categorical variables).
The null hypothesis would be that no relationship exists between the variables while the alternative would be that there is a relationship between the two variables.
Find the equation for the line containing the points (-2,-5) and (6,3)
Answer:
y = x - 3
Step-by-step explanation:
Do rise/run to find the slope
8/8 = 1
y = x + b
Plug in a point to find the y-intercept
-5 = -2 + b
-3 = b
The equation will be y = x - 3
a triangle has a base length of 15.4 cm. the area of the triangle is 65.45 cm.
Answer:
8.5 cm
Step-by-step explanation: The formula for the area of a triangle is base times height divided by 2. To find the original number before dividing by 2 you have to multiply 65.45 times 2, which is 130.9. The length is 15.4 and the original number before dividing by 2 is 130.9 to find the height divide 130.9 by 15.4 which is 8.5. If you plug in the value height is 8.5 cm , length is 15.4 and multiply it and divide it by 2 you will get 65.45.
multiply and remove all perfect square roots. Assume y is positive. √12
Answer:
2√3
Step-by-step explanation:
Step 1: Find perfect square roots
√4 x √3
Step 2: Convert
2 x √3
Step 3: Answer
2√3
Let f(x)= x^3 −6x^2+11x−5 and g(x)=4x^3−8x^2−x+12. Find (f−g)(x). Then evaluate the difference when x=−3 x=−3 .
Answer: (f-g)(x)= -138
Step-by-step explanation:
A professional employee in a large corporation receives an average of μ = 39.8 e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 38 employees showed that they were receiving an average of x = 33.1 e-mails per day. The computer server through which the e-mails are routed showed that σ = 16.2. Has the new policy had any effect? Use a 10% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee.
Answer:
Step-by-step explanation:
Null hypothesis: u = 39.8
Alternative: u =/ 39.8
Using a one sample z test: the formula is
z = x-u / (sd/√n)
Where x = 33.1 u = 39.8, sd= 16.2 and n = 38
Thus we have:
z = 33.1-39.8 / (16.2/√38)
z = -6.7 / (16.2/6.1644)
z = -6.7/ 2.6280
z= -2.5495
To be able to arrive at a conclusion, we have to find the p value, the p value at a 0.1 significance level for a two tailed test is 0.0108. This is way less than 0.1 thus we will reject the null and conclude that there has been a change (either way) in the average number of e-mails received per day per employee. Yes, the new policy had an effect.
Please answer this correctly without making mistakes I want genius,expert or ace people to answer this correctly
Answer:
It would decrease by 9.
Step-by-step explanation:
52 is the original mean or the initial mean.
43 is the final mean.
52-43 = 9
So 9 is the difference.
Hope this helped!
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 18% each week. The following function represents the weekly weed growth: f(x) = 86(1.18)x. Rewrite the function to show how quickly the weeds grow each day.
Answer:
[tex]f(x) = 86(1.0257)^{x}[/tex]
Step-by-step explanation:
The growth of the function after t days can be modeled by the following function:
[tex]f(x) = f(0)(1 + \frac{r}{7})^{x}[/tex]
In which f(0) is the initial value and r is the weekly rate. Since a week has 7 days, to find the equation for the daily growth, we divide by 7.
In this question:
We have that [tex]f(0) = 86, r = 0.18[/tex]
So
[tex]f(x) = f(0)(1 + \frac{r}{7})^{x}[/tex]
[tex]f(x) = 86(1 + \frac{0.18}{7})^{x}[/tex]
[tex]f(x) = 86(1.0257)^{x}[/tex]
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.12 gallons. A previous study found that for an average family the variance is 5.29 gallons and the mean is 17 gallons per day. If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water
Answer:
[tex]n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762[/tex]
So the answer for this case would be n=762 rounded up to the nearest integer
Step-by-step explanation:
Information given
[tex]\bar X = 17[/tex] represent the mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma= \sqrt{5.29}= 2.3[/tex] represent the standard deviation
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.12 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The confidence level is 85%, the significance level would be [tex] \alpha=1-0.85 = 0.15[/tex] and [tex]\alpha/2 =0.075[/tex] the critical value for this case would be [tex]z_{\alpha/2}=1.440[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762[/tex]
So the answer for this case would be n=762 rounded up to the nearest integer
Need help ASAP Thankyou!!!
Answer:
216
Step-by-step explanation:
To find the volume of the pyramid we have to do length * width * height / 3
The length is 9yd
The width is 8yd
The height is 9yd
So 9 * 9 * 8 = 648
648 / 3 = 216
3 squared times 3 squared simplified
Answer:
3^4
Step-by-step explanation:
3^2*3^2
3*3*3*3
3^4
Solve: x + 7 < 3 plsss help me
Answer:
The answer is -4.
Step-by-step explanation:
You should get this answer if you do 3 - 7.
The function f(x) is given by the set of ordered pairs.
{(8,3), (0, 4), (1, 5), (2, -1), (-6, 10)}
Which is true regarding the function?
f(-3) = 8
f(3) = 5
f(8) = 0
f(-6) = 10
Answer: f(-6) = 10.
Step-by-step explanation: This above equation is the only one that contains both coordinates of one of the ordered pairs in the correct order, so it is the answer.
Farhan has three pieces of rope with lengths of 140cm, 168cm and 210cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length and that there is no leftover rope. (i) What is the greatest possible length of each of the smaller pieces of rope? How many smaller pieces of rope can he get altogether?
give correct answer
Answer:
The greatest possible length is 14 cm.
The total number of smaller pieces is 37.
Step-by-step explanation:
The greatest common factor of these three numbers is 14.
Total number of smaller pieces = 10+12+15 = 37
Best Regards!
Suppose you want to have $0.5 million saved by the time you reach the age of 30 years and suppose that you are 20 years old now. If you can earn 5% on your funds, how much would you have to invest today to reach your goal?
Answer:
$306,956,6268
Step-by-step explanation:
Future value, FV = Present value PV [1 + rate]^t
PV = FV/[1 + rate]^t
PV = 500,000/[1.05]^10
PV = $306,956,6268
Can someone please help me with this problem?
Answer: -13
Step-by-step explanation:
c-2y
= -5-2(4)
= -5 - 8
= -13
Answer:
-13
Step-by-step explanation:
[tex]c=-5\\y=4\\c-2y=\\-5-(4*2)=\\-5-8=\\-13[/tex]
The expression is equal to -13 when [tex]c=-5[/tex] and [tex]y=4[/tex].
How long dose it take to travel 84 miles at an average speed of 30 mph? Give your answer in hours and minutes
Answer:
2 hours and 48 minutes
Step-by-step explanation:
Time = Distance/Speed
= 84/30
= 2.8 hours
To convert 2.8 hours into hours and minutes, 2.8*60 = 168 minutes. Therefore the time taken to travel 84miles is 2 hours and 48 minutes
Answer:
In hours:
Time = 2.8 hours
In minutes:
Time = 168 minutes
Step-by-step explanation:
Given:
Distance = 84 miles
Speed = 30 mph
Required:
Time = ?
Formula:
Speed = Distance/Time
Solution:
Time = Distance/Speed
Time = 84/30
In hours:
Time = 2.8 hours
In minutes:
Time = 168 minutes
I need help pleaseee!
Step-by-step explanation:
we can use o as the center of the circle
OB=13
EB=12
OE=?
OE^2 +EB^2=OB^2
OE^2+12^2=13^2
OE^2=169-144
OE=
√25
OE=5
OC=OE+EC
EC =13-5
EC=8
The maximum height of a vehicle that can safely pass under a bridge is 12 feet 5 inches. A truck measures 162 inches in height. Which best explains whether or not the truck can pass safely under the bridge?
162 inches is 13.5 feet or 13 feet 6 inches, so it would not fit underneath the bridge
Answer:
The truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.
Ken runs 12 miles in a marathon. Every 3.5 miles, he stopes to take a drink. How many times does he stop during the marathon ?
Answer:
Brainleist!
Step-by-step explanation:
12/3.5
3.42857142857
round down so its 3!
15. Simplify sin(90° - O) cos 0 - sin(180° +0) sin e.
Answer: cos²(θ) + sin(θ)sin(e)
Step-by-step explanation:
sin (90° - θ)cos(Ф) - sin(180° + θ) sin(e)
Note the following identities:
sin (90° - θ) = cos(x)
sin (180° + θ) = -sin(x)
Substitute those identities into the expression:
cos(x)cos(x) - -sin(x)sin(e)
= cos²(x) + sin(x)sin(e)
g An irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent for textbooks was $121.60. If the standard deviation of the population was $6.36, find the 90% confidence interval of the true mean.
Answer:
A 90% confidence interval of the true mean is [$119.86, $123.34].
Step-by-step explanation:
We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.
Also, the standard deviation of the population was $6.36.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean amount of money spent on textbooks = $121.60
[tex]\sigma[/tex] = population standard deviation = $6.36
n = sample of students = 36
[tex]\mu[/tex] = population mean
Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.645) = 0.90
P( [tex]-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]121.60-1.645 \times {\frac{6.36}{\sqrt{36} } }[/tex] , [tex]121.60+1.645 \times {\frac{6.36}{\sqrt{36} } }[/tex] ]
= [$119.86, $123.34]
Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].