Answer:
the g's contributing term for the overall uncertainty of P is [tex]dP_g = [\frac{dg}{g}][/tex]
Step-by-step explanation:
From the question we are told that
The pressure is [tex]P = P_o + \rho gh[/tex]
The first step in determining the uncertainty of P in by obtaining the terms in the equation contributing to it uncertainty and to do that we take the Ln of both sides of the equation
[tex]ln P = lnP_o + ln(\rho gh )[/tex]
=> [tex]ln P = lnP_o + ln \rho + ln g + ln h[/tex]
Then the next step is to differentiate both sides of the equation
[tex]\frac{d(ln P)}{dP} = \frac{d(ln P_o)}{dP_o} + \frac{d(ln \rho)}{d\rho} +\frac{d(ln g)}{dg} + \frac{d(ln h)}{dh}[/tex]
=> [tex]\frac{dP}{P} = \frac{dP_o}{P_o} + \frac{d \rho}{\rho} +\frac{d g}{g} + \frac{d h}{h}[/tex]
We asked to obtain the contribution of the term g to the uncertainty of P
This can deduced from the above equation as
[tex]dP_g = [\frac{dg}{g}] P[/tex]
Suppose a horse is galloping at 19 mph toward a clown, and the clown is racing toward the horse on an ATV which can sustain a speed of 15mph. They are 50 miles apart from one another and start at the exact same moment in time. How much time will it take for the horse and clown to collide?
Answer:
It will take 1.47 hours for the horse and clown to collide
Step-by-step explanation:
They are driving toward each other, in opposite directions.
So to find their speed of approximation, we add their speeds.
19 mph + 15 mph = 34 mph.
This means that each hour, they are 34 miles closer.
How long it takes for them to find each other if they are 50 miles apart?
1 hour - 34 miles
x hours - 50 miles
[tex]34x = 50[/tex]
[tex]x = \frac{50}{34}[/tex]
[tex]x = 1.47[/tex]
It will take 1.47 hours for the horse and clown to collide
5-3+78 divided by 3=
Answer:
26 remainder 2
Step-by-step explanation:
5 - 3 =2
2 + 78 = 80
80 ÷ 3
3 can go into 8 twice remaining with 2
2 goes across to 0
3 can go into 20 6 times because 3×6= 18
so 3 into 20 is 6 remainder of 2
answer= 26 remainder of 2
Answer:
[tex]= 26 \frac{3}{2} \\ [/tex]
Step-by-step explanation:
[tex]5 - 3 + 78 \div 3 \\ 2 + 78 \div 3 \\ 80 \div 3 \\ = 26 \frac{3}{2} [/tex]
hope this helps you
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and d are integers 1. x^2-2x-15=(ax+b)(cx+d) 2. 2x^-6x-36x=2x(ax+b)(cx+d) 3. 4x^2+10x+4=(ax+b)(cx+d) . Fill in the table with the missing values of a, b, c, and d.
Answer:
(1, -5, 1, 3)(2, -12, 1, 3)(4, 2, 1, 2)Step-by-step explanation:
Obviously, factors can be written in any order. So, there are multiple answers to this question.
1. x^2 -2x -15 = (x -5)(x +3) . . . . (a, b, c, d) = (1, -5, 1, 3)
__
2. 2x^2 -6x -36 = 2(x^2 -3x -18) = 2(x -6)(x +3) . . . . (a, b, c, d) = (2, -12, 1, 3)
__
3. 4x^2 +10x +4 = 2(2x^2 +5x +2) = 2(2x +1)(x +2) . . . . (a, b, c, d) = (4, 2, 1, 2)
What is the slope of this line?
Answer:
1
Step-by-step explanation:
We need to points
(-1,0) and (0,1)
The slope is found by
m= (y2-y1)/(x2-x1)
m = (1-0)/(0- -1)
= (1-0)/(0+1)
= 1/1
The slope is 1
Answer:
1
Step-by-step explanation:
The slope is rise/run and can be found by counting how many units up and over you must go from one point on the line to another.
Therefore the answer is
1
of is directly proportional toy and x = 45 when
= 3, find
an equation connecting and
m) the value of x when y s6
me the value of when12
of is directly proportional to Pando = 28 when
P4
Answer:
if x=ky, where k is constant.
value of x
45/3=k3/3
15=k, constant is 15
value of x when y =6
x=ky
x=15(6)
x=80
The supply and demand for a product are related to price by the following equations, where y is the price, in dollars, and x is the number of units, in thousands. Find the equilibrium point for this product. yequalsS(x)equals300plus40x yequalsD(x)equals4300minus40x
Answer:
The equilibrium point for the product (x,y) = (50,2300)
Step-by-step explanation:
The equilibrium point refers to the point in the demand and supply curves where we have the quantity demanded equals the quantity supplied at a particular price.
From the question, we can identify the following;
S(x) = 300 + 40x
D(x) = 4300 - 40x
Now, at the equilibrium point, S(x) = D(x)
This means that;
300 + 40x = 4300 -40x
80x = 4300-300
80x = 4000
x = 4000/80 = 50
Now, we input the value of x into any of the equation of the demand and supply to get the quantity.
Let’s use S(x) = 300 + 40x = 300 + 40(50) = 300 + 2000 = 2,300
The equilibrium point for the product (x,y) = (50,2300)
Please answer this correctly
Answer:
6.3 ft
Step-by-step explanation:
The perimeter of a parallelogram is given by
P = 2(l+w)
49.6 = 2 (18.5 +t)
Divide by 2
49.6/2 = 2/2 (18.5 +t)
24.8 = 18.5+t
Subtract 18.5
24.8-18.5 = t
6.3 = t
The volume of a stock is the number of shares traded for a given day. Several years ago, a certain company's stock had a mean daily volume of 7.52 million shares, according to a reputable financial news outlet. A random sample of 40 trading days in a recent year was obtained and the volume of shares traded on those days was recorded, with the accompanying results.
Required:
a. Find the test statistic:
b. Find the P-value
c. The level of significance is .05. what can be concluded from the hypothesis?
Volume (millions of shares)
4.1531 2.8893
4.6228 6.0203
5.6386 6.2774
4.5822 3.968
5.6903 4.0065
4.4313 11.2343
7.3941 2.6991
9.0557 3.2285
7 9800 4.2762
10.1556 3.2913
3.4189 5.8544
4.5624 2.6153
7.3287 8.1435
9.1723 5.3304
3.6798 4.1807
4.2868 5.3668
5.5448 1.7945
3.7656 5.0502
4.0201 3.1832
3 .798 5.4563
Answer:
a) test statistic, [tex]t_{s} = -4.20[/tex]
b) P-value = 0.0001
c) It can be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years
Step-by-step explanation:
There are 40 trading days, therefore, sample size, n = 40
Calculate the Sample mean:
[tex]\bar x = \frac{\sum x}{n} \\\bar x = \frac{4.153 +4.6228 + ...+...+5.4563}{40}\\\bar x = 5.5945[/tex]
Get the null and alternative hypothesis:
Null hypothesis, [tex]H_{0} : \mu = 7.52[/tex]
Alternative hypothesis, [tex]H_{a} : \mu \neq 7.52[/tex]
Calculate the sample standard deviation:
[tex]SD = \sqrt{\frac{\sum (x - \bar x)^{2} }{n - 1} } \\SD = \sqrt{\frac{(4.1531-5.5945)^{2} + (4.6228-5.5945)^{2}+...+ (5.4563-5.5945)^{2}}{39} } \\SD = \sqrt{\frac{327.6161}{39} } \\SD = 2.8983[/tex]
a) Calculate the test statistic:
[tex]t_{s} = \frac{\bar{x} - \mu}{SD/\sqrt{n} } \\t_{s} = \frac{5.5945 -7.52}{2.8983/\sqrt{40} }\\t_{s} = -4.20[/tex]
b) Calculate the P-value
Getting the P-value using the excel function:
P-value = (=T.DIST.2T(|ts|, df))
P-value = (=T.DIST.2T(4.20, 39))
P-value = 0.0001
c) If the level of significance, [tex]\alpha = 0.05[/tex]
The P-value (0.0001) < α(0.05), the null hypothesis is rejected.
It can therefore be concluded from the hypothesis that the company's stock has a mean value that is not 7.52 million shares i.e. the mean stock has changed in recent years
Boris is riding a ferris wheel at a carnival. After a time t, his height H above the ground is given by the following formula. H=a cos(bt)+c Find Boris's height above the ground when a=-15m,b=2.241 rad/s,t=3s, and c=23m
Answer:
Boris height above the ground is 9.428m
Step-by-step explanation:
Boris height above the ground is given by the formula;
H = a cos(bt) + c
Now, we are told that,
a = -15m
b = 2.241 rad/s
t = 3s
c = 23m
Plugging in the relevant values, we have;
H = -15 cos (2.241 * 3) + 23
H = -15 cos(6.723 rad) + 23
cos(6.723rad) = 0.9048
Thus,
H = (-15 × 0.9048) + 23
H = 9.428 m
So boris height above the ground is 9.428m
Which of the following is a polynomial function in factored form with zeros at –6, –2, and 3?
f(x) = (x – 6)(x – 2)(x + 3)
f(x) = (x + 6)(x + 2)(x – 3)
f(x) = x3 + 5x2 – 12x – 36
f(x) = x3 – 5x2 – 12x + 36
Answer:
(b)
Step-by-step explanation:
You can clearly see that putting each factor equal to 0 , we get -6 , -2 , 3
Jack has a summer job caddying at a golf course. Jack earns $120
a week. By rounding his weekly income to the nearest hundred
dollars, find a reasonable estimate for his total income during the
12 week summer.
A) $700
B) $800
C) $1200
D) $1700
An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have only one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.a) The average baggage-related revenue per passenger is: $(please round to the nearest cent)b) The standard deviation of baggage-related revenue is: $(please round to the nearest cent)c) About how much revenue should the airline expect for a flight of 120 passengers?(please round to the nearest dollar)
Answer:
(a) The average baggage-related revenue per passenger is $15.70.
(b) The standard deviation of baggage-related revenue is $19.95.
(c) The expected revenue for 120 passengers is $1,884.
Step-by-step explanation:
Let the random variable X represent the baggage-related revenue per passenger.
It is provided that the baggage fees is $25 for the first bag and $35 for the second.
The probability model is:
X : 0 25 60
P (X) : 0.54 0.34 0.12
(a)
Compute the average baggage-related revenue per passenger as follows:
[tex]E(X)=\sum {X\times P (X)}[/tex]
[tex]=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70[/tex]
Thus, the average baggage-related revenue per passenger is $15.70.
(b)
Compute the standard deviation of baggage-related revenue as follows:
[tex]E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\[/tex]
[tex]SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}[/tex]
[tex]=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95[/tex]
Thus, the standard deviation of baggage-related revenue is $19.95.
(c)
Compute the expected revenue for 120 passengers as follows:
[tex]E(R)=n\times E(X)[/tex]
[tex]=120\times 15.7\\\\=1884[/tex]
Thus, the expected revenue for 120 passengers is $1,884.
In an isosceles triangle, the equal sides are 2/3 if the length of the base. Determine the measure if the base angles.
Please help me with good explanation, I have a trig exam soon!
Answer:
41.41°
Step-by-step explanation:
In ∆ABC below, the legs are 4 and the base is 6.
So, the legs are ⅔ the length of the base.
In ∆CBD,
cosB = BD/BC = 3/4 = 0.75
B = arccos 0.75 = 41.41°
The base angles are each 41.41°
The measure should be 41.41°
Calculation of the measure:Since In ∆ABC , the legs should be 4 and the base should be 6.
Now
the legs are two-third the length of the base.
Also,
In ∆CBD,
cosB [tex]= BD\div BC = 3\div 4 = 0.75[/tex]
So,
B = arccos 0.75 = 41.41°
Therefore, we can concluded that The base angles are each 41.41°
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if you have a population of 40million people and 2million of them are from out of town. what percentage of them are out of towners??
Answer:
5%
Step-by-step explanation:
There are 2000000 people out of town and 4000000 people in total.
Solution for 2000000 is what percent of 40000000:
2000000:40000000*100 =
(2000000*100):40000000 =
200000000:40000000 = 5
Now we have: 2000000 is what percent of 40000000 = 5
Question: 2000000 is what percent of 40000000?
Percentage solution with steps:
Step 1: We make the assumption that 40000000 is 100% since it is our output value.
Step 2: We next represent the value we seek with x
Step 3: From step 1, it follows that 100%= 40000000.
Step 4: In the same vein, x%=2000000.
Step 5: This gives us a pair of simple equations:
100%=40000000(1).
x%=2000000(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
100%/x%=40000000/2000000
Step 7: Taking the inverse (or reciprocal) of both sides.
⇒ x=5%
Therefore, 2000000 is 5% of 40000000.
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4x + 5y = 7 3x – 2y = –12 Multiply each equation by a number that produces opposite coefficents for x or y
Answer:
Step-by-step explanation:
DO YOU MEAN :
[tex]4x + 5y = 7\\ 3x - 2y = -12\\Multiply-equation 1 -by -the-coefficient-of-x-in-equation-2\\multiply-equation-2 -by-the-co-efficient -of x -in-equation- 1\\\\3(4x + 5y = 7)\\4( 3x - 2y = -12)\\\\12x +15y=21\\12x -8y=-48[/tex]
A poll of a random sample of1400 adults reported that respondents slept an average of 6.5 hours on weekdays and 7.2 hours on weekends, and that 20% of respondents got eight or more hours of sleep on weekdays, whereas 43% got eight or more hours of sleep on weekends. To compare the means or the percentages using inferential methods, should you treat the samples on weekdays and weekends as independent samples or as dependentsamples?
A. Independent Samples
B. Dependent Samples
Answer:
b) Dependent sample
Step-by-step explanation:
Given:
Sample size, n = 1400
The average sleep of the respondents in weekdays = 6.5 hours
The average sleep of the respondents in weekends = 7.2 hours
% with eight or more hours of sleep on weekdays = 20%
% with eight or more hours of sleep on weekends = 43%
Required: To Check if the samples on weekdays and weekends are independent or dependent.
When samples are independent, it means one sample does not influence the other and vice versa, while samples are said to be dependent if the outcome of one test influences the outcome of the other. The tests might be from a similar population or from various populations.
In this case, the sample gathered are from similar population because same sample is used for both weekdays and weekends. Therefore, we can say the sample is a paired sample.
The samples on weekdays and weekends are dependent since same people are used, also since sleep on weekdays and sleep on weekends may influence each other.
The formula for the perimeter of a rectangle is p = 2 l + 2 w. Which is the equivalent equation solved for w? StartFraction P minus 2 l Over 2 EndFraction = w StartFraction P + 2 l Over 2 EndFraction = w P + l = w P minus l = w
Answer:
Correct option: first one
"StartFraction P minus 2 l Over 2 EndFraction = w"
Step-by-step explanation:
First we start from the perimeter equation:
P = 2*l + 2*w
Then, we need to solve for w, so we need to isolate it.
The first step is subtracting 2*l from both sides of the equation:
P - 2*l = 2*w
Then, we divide both sides by 2:
w = (P - 2l) / 2
So the correct option is the first one:
"StartFraction P minus 2 l Over 2 EndFraction = w"
Answer:
Its the first one
Step-by-step explanation:
i got it right on edge
(1 + 1 -2 +3) lllllllllllllllllllllllllllllllllllllll
Answer:
3
Step-by-step explanation:
1+1= 2 + -2=0 + 3 = 3
Answer:
[tex]3[/tex]
Step-by-step explanation:
[tex](1 + 1 -2 +3)[/tex]
[tex]1+1-2+3[/tex]
[tex]2+1[/tex]
[tex]=3[/tex]
A construction company distributes its products by trucks loaded at its loading station. A backacter in conjunction with trucks are used for this purpose. If it was found out that on an average of 12 trucks per hour arrived and the average loading time was 3 minutes for each truck. A truck must queue until it is loaded. The backacter’s daily all-in rate is GH¢ 1000 and that of the truck is GH¢ 400.
a) Compute the operating characteristics: L, Lq, W, Wq, and P.
b) The company is considering replacing the backacter with a bigger one which will have an average service rate of 1.5 minutes to serve trucks waiting to have their schedules improved. As a manager, would you recommend the new backacter if the daily all-in rate is GH¢ 1300.
c) The site management is considering whether to deploy an extra backwater to assist the existing one. The daily all-in-rate and efficiency of the new backwater is assumed to be the same as that of the existing backwater. Should the additional backwater be deployed?
Answer:
a idk
Step-by-step explanation:
A researcher is interested in determining the average number of years new teachers remain in the classroom. If past information shows a standard deviation of 5 years, what size sample should be taken so that at 95% confidence the margin of error will be 6 months or less?
1. Sam deposits$700 in an investment saving account. The annual
interest rate is 4.5%/annually compounded monthly. Determine
the amount after 7 years.
Answer:
The total amount in 7 years is: $958.62
Step-by-step explanation:
Recall the formula for compound interest:
[tex]A=P\,(1+\frac{r}{n} )^{n\,t}[/tex]
where:
A is the Accrued value (total in the account including accumulated interest), and in our case the unknown.
P is the Principal (amount initially deposited), and in our case $700.
r is the annual percent rate (but in decimal form) in our case 0.045
n is the number of compoundings done per year, and in our case 12 since it is compounded monthly
t is the time in years of the deposit.
Then the formula becomes:
[tex]A=P\,(1+\frac{r}{n} )^{n\,t}\\A=700\,(1+\frac{0.045}{12} )^{12\,*\,7}\\A=958.61657[/tex]
which can be rounded to the cents: $958.62
if the base of a right angled triangle is 4cm and its area is 20^2, find its height
Answer:
80cm
Step-by-step explanation:
i worked it out like this
2x4=8
then that means
20x4=80
Answer:
80 is the answer
Suppose that you record the daily high temperature and the daily amount of ice cream sold by an ice cream vendor at your favorite beach this summer, starting on Memorial Day weekend and ending on Labor Day weekend. Would you expect to find a positive or negative association between these variables? Explain briefly.
Answer:
positive
Step-by-step explanation:
the higher the temp the higher the number of ice creams sold
The association would be positive between the variables.
Given that,
Recorded the daily high temperature and the daily amount of ice cream sold by an ice cream vendor at your favorite beach this summer, starting on Memorial Day weekend and ending on Labor Day weekend.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
As the temperature increases, people will love to eat the ice cream more, which increase the sales of the ice cream which implies that the association would be positive between the variable.
Thus, the association would be positive between the variables.
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Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: (a) What is the probability of getting one child of each sex?
Answer:
49.97% probability of getting one child of each sex
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The sex of a children is independent of other children, so we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that a couple’s first child is a boy is 0.512.
This means that [tex]p = 0.512[/tex]
The will have two children:
This means that [tex]n = 2[/tex]
(a) What is the probability of getting one child of each sex?
This is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{2,1}.(0.512)^{1}.(0.488)^{1} = 0.4997[/tex]
49.97% probability of getting one child of each sex
lee and maya are collecting leaves for an art project. lee collects 24-100 of the total leaves needed. maya collects 4-10 of the total leaves needed. What fraction of the total number leaves did they collect altogether
Answer:
16/25
Step-by-step explanation:
4/10=40/100
24/100=24/100
40+24=64
64/100
16/25
Answer:
16/25
Step-by-step explanation:
I need help please.
Answer:
∠W = 81°
Step-by-step explanation:
Triangle OGD is isosceles, so angle OGD has the same measure as angle ODG, 17°.
Triangle OGF is isosceles, so angle OGF has the same measure as angle OFG, 49°.
Angle DGF is the difference between angle OGF and angle OGD:
∠DGF = 49° -17° = 32°
External angle W is equal to the sum of remote internal angles DGF and OFG:
∠W = 32° +49°
∠W = 81°
Hand sanitizer containing 70% ethanol (HL+) is recommended to prevent the transmission of the rhinovirus (RV) that causes the common cold. A study with 212 subjects was conducted. Subjects were assigned at random to either the HL+ group, which used hand sanitizer after hand washing, or a control group, which did not use hand sanitizer after hand washing. The number of subjects with and without RV infection in the two groups over the ten week study are below. RV Infection Yes No HL+ Group 49 67 Control Group 49 47 (a) (2 points) Is this an experiment or observational study? Why? (b) (2 points) What is the response variable? Is it qualitative or quantitative? (c) (5 points) Does the data suggest that the RV infection rate of subjects using hand sanitizer is significantly (a = 0.05) lower? Perform the appropriate procedure and include all the steps. (d) (2 points) Construct and interpret a 95% confidence interval to estimate the difference between the two proportions.
Answer:
a) Experiment
b) Proportion of subjects infected. Quantitative
c) Null hypothesis failed to be rejected. P-value=0.101.
There is not enough evidence to support the claim that the RV infection rate of subjects using hand sanitizer is significantly lower.
d) The 95% confidence interval for the difference between proportions is (-0.223, 0.047).
As we can see, the value 0 (meaning no difference between the proportions) is included in the interval. This can be interpreted the sam wat that the hypothesis test: at 95% confidence, we can not assurre that there is significant difference between the proportions.
Step-by-step explanation:
a) This is an experiment, as the groups are designed by the researcher. The individuals are then asigned randomly to one of both groups.
b) The response variable is the proportion of subjects infected. This variable is quantitative, as is a sum of positive cases divided by the total amount of subjects in the group.
c) This is a hypothesis test for the difference between proportions.
The claim is that the RV infection rate of subjects using hand sanitizer is significantly lower.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
The significance level is 0.05.
The sample 1 (HL+ group), of size n1=116 has a proportion of p1=0.4224.
[tex]p_1=X_1/n_1=49/116=0.4224[/tex]
The sample 2 (Control group), of size n2=96 has a proportion of p2=0.5104.
[tex]p_2=X_2/n_2=49/96=0.5104[/tex]
The difference between proportions is (p1-p2)=-0.088.
[tex]p_d=p_1-p_2=0.4224-0.5104=-0.088[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{49+49}{116+96}=\dfrac{98}{212}=0.4623[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4623*0.5377}{116}+\dfrac{0.4623*0.5377}{96}}\\\\\\s_{p1-p2}=\sqrt{0.0021+0.0026}=\sqrt{0.0047}=0.0688[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.088-0}{0.0688}=\dfrac{-0.088}{0.0688}=-1.28[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=P(z<-1.28)=0.101[/tex]
As the P-value (0.101) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the RV infection rate of subjects using hand sanitizer is significantly lower.
d) We want to calculate the bounds of a 95% confidence interval.
For a 95% CI, the critical value for z is z=1.96.
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4623*0.5377}{116}+\dfrac{0.4623*0.5377}{96}}\\\\\\s_{p1-p2}=\sqrt{0.0021+0.0026}=\sqrt{0.0047}=0.0688[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.0688=0.1348[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.088-0.1348=-0.223\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.088+0.1348=0.047[/tex]
The 95% confidence interval for the difference between proportions is (-0.223, 0.047).
As we can see, the value 0 (meaning no difference between the proportions) is included in the interval. This can be interpreted the sam wat that the hypothesis test: at 95% confidence, we can not assurre that there is significant difference between the proportions.
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Solution,
Diameter=16.8 cm
Radius=16.8/2=8.4 cm
Area of circle=pi r^2
= 3.142*(8.4)^2
=3.142*70.56
=221.69952 cm^2
hope it helps
Good luck on your assignment
Macy spent 2 hours working on homework. She spent 1/4
of that time working on math.
How much time did Macy spend on her math homework?
Answer:
1/2 h or 30 min
Step-by-step explanation:
2 h * 1/4 = 2/4 = 1/2 h or 30 min
Solve the following equation, if possible, and determine the number of solutions.
6y+4−3y−7=3(y−1)
write one answer for the number of solutions, and write at least one answer that explains your answer for the number of solutions.
6y+4−3y−7=3(y−1)
Opening the bracket we notice that it will yield same thing for both sides of the equation.
There is only one way to solve the equation because it's clear that y = 0
So it's by opening the bracket.
So the value for y is equal to zero
