Answer:
756
Step-by-step explanation:
This is a combination problem. Combination has to do with selection.
If we are to select r objects out of a oiil of n objects, this can be done in nCr number of ways as shown;
nCr = n!/(n-r)!r!
From the question, there are 4 meats and 9 vegetables to choose from. If the customer is to select 2 different meats and 4 different vegetables from the available ones, this can be done as shown
4C2 (selection of 2 different meats from 4meats) and 9C4(selection of 4 different vegetables from 9 total vegetables)
The total number of ways this can be done is 4C2 × 9C4
= 4!/(4-2)!2! × 9!/(9-4)!4!
= 4!/2!2! × 9!/5!4!
= 4×3×2!/2!×2 × 9×8×7×6×5!/5!×4×3×2
= 6 × 9×7×2
= 756ways
This means 756 different supreme choice pizzas can be made.
the sum of the measures of the angles of any triangle is 180 degrees. in triangle ABC, angles A and B have the same measure, of bile the measure of angle C is 72 degrees larger than each of A and B. what are the measures of the three angles?
Answer:
A=36
B=36
C=108
Step-by-step explanation:
A =B
2A+C=180
C is greater than A
2A+(A+72) =180
SIMPLIFY
3A +72=180
-72 ON BOTH SIDES
3A=108
DIVIDE BY 3
A=36
SO
B=36
36 TIMES 2 IS 72
180-72=108
SO
C=108
hope this helps
Answer:
Angle C= 108
Angles A and B=36
Step-by-step explanation:
180-72=108
108-72= 36
Check
36+36=72
72+108=180
Which expression converts 100 inches per minute to feet per minute?
O
100 inches
1 minute
60 minutes
1 hour
O
100 inches
1 minute
X
1 hour
60 minutes
100 inches
1 minute
X
1 foot
12 inches
O
100 inches
1 minute
12 inches
1 foot
Another question lol take your time
Answer:
100 inches Over 1 minute times × 1 foot Over 12 inches
Step by Step explanation
Remember that
1ft=12in
The expression converts 100 inches per minute to feet per minute is
100 inch / min x 1 ft/ 12 inch.
What is unit conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. Time can be expressed in minutes rather than hours, and distance can be expressed in miles, kilometres, feet, or any other measurement unit.
We know
1 feet = 12 inch
We have to convert 100 inches per minute to feet per minute.
So, 100 inches
= 100 inch / min x 1 ft/ 12 inch
= 8.33 ft per minute
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A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 80 businesses at random. Of these, 46 return the questionnaire mailed by the committee.
a) What is the population for this sample survey?
The population in this situation is _______ (none, some, most, or all) of the __________(local business or college students) .
b) What is the sample?
The sample is the ______(enter exact number) of ___________ (local business or college students) selected.
c) What is the rate (percent) of nonresponse?
Answer:
a) The population population in this situation is all the local business
b) The sample is the 80 of local business selected.
c) The rate of nonresponse is 42.5%.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
The population for this survey is all New York State residents, while the sample are the 1000 New York State residents.
From telephone book listings, the committee chooses 80 businesses at random.
Survey: 80 businesses.
Population: All businesses in the college town.
Then
a) What is the population for this sample survey?
The population population in this situation is all the local business
b) What is the sample?
The sample is the 80 of local business selected.
c) What is the rate (percent) of nonresponse?
80 - 46 = 34 non-responses, out of 80
34/80 = 0.425
0.425*100 = 42.5%
The rate of nonresponse is 42.5%.
Please help me answer the question, answer problem 1 and 2
please see the attached picture for full solution
Hope it helps...
Good luck on your assignment,
select the point that is a solution to the system of inequalities
This point is below both the red diagonal line and the blue parabola. We know that the set of solution points is below both due to the "less than" parts of each inequality sign.
In contrast, a point like (2,2) is above the parabola which is why it is not a solution. It does not make the inequality [tex]y \le x^2-3x[/tex] true. So this is why we can rule choice A out.
Choice C is not a solution because (4,1) does not make [tex]y \le -x+3[/tex] true. This point is not below the red diagonal line. We can cross choice C off the list.
Choice D is similar to choice A, which is why we can rule it out as well.
Identify a reason why we should be skeptical of any claim or statistical evidence involving the following: A study shows that during the early 20th century, a strong correlation existed between the number of people who owned radios and the number of people put into insane asylums. Therefore, people who owned a radio were more likely to be declared insane and put into an insane asylum.a. correlation does not imply causality b. misleading graph c. self-interest survey d. voluntary response survey
Answer:
Option A
Step-by-step explanation:
Correlation does not imply causality. Correlation shows whether and how strongly pairs of variables are related.
Causality shows a situation between two events where one event is affected by the other
We would be skeptical of this survey because it is very difficult to assume that people who owned a radio were more likely to be declared insane and put into an insane asylum as listening to the radio cannot cause insanity unless proven.
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
Complete question:
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
a. How much cheese does Mai use per Pizza
b. At this rate how much cheese will she need to make 15 Pizza's
Answer:
a. ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. amount of cheese to make 15 pizzas= 2.5 × 15 = 37.5 ounces of cheese
Step-by-step explanation:
Mai is making a personal pizzas .For 4 pizza she uses 10 ounces of cheese. This means Mai uses 10 ounces of cheese in weight to make just 4 pizzas.
a. How much cheese does Mai use per Pizza
Not she uses 10 ounces of cheese to make 4 pizzas. Therefore,
If 4 pizzas requires 10 ounces of cheese
1 pizza will require ? ounces of cheese
cross multiply
ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. At this rate how much cheese will she need to make 15 Pizza's
Since she requires 2.5 ounces of cheese to make 1 pizza
? ounces of cheese will be required to make 15 pizzas
cross multiply
amount of cheese to make 15 pizzas = 2.5 × 15 = 37.5 ounces of cheese
Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and work-piece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The article "Variables Affecting Mist Generation from Metal Removal Fluids" (Lubrication Engr., 2002: 10-17) gave the accompanying data on x = fluid flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than some value:
x: 89 177 189 354 362 442 965
y: .40 .60 .48 .66 .61 .69 .99
a. Make a scatterplot of the data. By R.
b. What is the point estimate of the beta coefficient? (By R.) Interpret it.
c. What is s_e? (By R) Interpret it.
d. Estimate the true average change in mist associated with a 1 cm/sec increase in velocity, and do so in a way that conveys information about precision and reliability.
e. Suppose the fluid velocity is 250 cm/sec. Find the mean of the corresponding y in a way that conveys information about precision and reliability. Use 95% confidence level. Interpret the resulting interval. By hand, as in part d.
f. Suppose the fluid velocity for a specific fluid is 250 cm/sec. Predict the y for that specific fluid in a way that conveys information about precision and reliability. Use 95% prediction level. Interpret the resulting interval. By hand, as in part d.
Answer:
Step-by-step explanation:
a) image attached
b) Lets do the analysis in R , the complete R snippet is as follows
x<- c(89,177,189,354,362,442,965)
y<- c(.4,.6,.48,.66,.61,.69,.99)
# scatterplot
plot(x,y, col="red",pch=16)
# model
fit <- lm(y~x)
summary(fit)
#equation is
#y = 0.4041 + 0.0006211*X
# beta coeffiecients are
fit$coefficients
coef(summary(fit))[, "Std. Error"]
# confidence interval of slope
confint(fit, 'x', level=0.95)
The results are
> summary(fit)
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5 6 7
-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***
x 6.211e-04 7.579e-05 8.195 0.00044 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.05405 on 5 degrees of freedom
Multiple R-squared: 0.9307, Adjusted R-squared: 0.9168 # model is able to capture 93% of the variation of the data
F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403 , p value is less than 0.05 , hence model as a whole is significant
> fit$coefficients
(Intercept) x
0.4041237853 0.0006210758
> coef(summary(fit))[, "Std. Error"]
(Intercept) x
3.458905e-02 7.579156e-05
> confint(fit, 'x', level=0.95)
2.5 % 97.5 %
x 0.0004262474 0.0008159042
c)
> x=c(89,177,189,354,362,442,965)
> y=c(0.40,0.60,0.48,0.66,0.61,0.69,0.99)
>
> ### linear model
> model=lm(y~x)
> summary(model)
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5 6 7
-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***
x 6.211e-04 7.579e-05 8.195 0.00044 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.05405 on 5 degrees of freedom
Multiple R-squared: 0.9307, Adjusted R-squared: 0.9168
F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403
s_e is the Residual standard error from the model and its estimated value is 0.05405. s_e is the standard deviation of the model.
d) 95% confidence interval
> confint(model, confidence=0.95)
2.5 % 97.5 %
(Intercept) 0.3152097913 0.4930377793
x 0.0004262474 0.0008159042
Comment: The estimated confidence interval of slope of x does not include zero. Hence, x has the significant effect on y at 0.05 level of significance.
e)
> predict(model, newdata=data.frame(x=250), interval="confidence", level=0.95)
fit lwr upr
1 0.5593927 0.5020485 0.616737
f)
> predict.lm(model, newdata=data.frame(x=250), interval="prediction", level=0.95)
fit lwr upr
1 0.5593927 0.4090954 0.7096901
When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation for each option. Graph each line and use the graph to answer the question. You will need to upload a picture or screenshot of your graphs.
Answer:
it´s b
Step-by-step explanation:
what is -10 3/10,000 as a decimal number
Answer: 0.0003
Step-by-step explanation: Solution for fraction 3/10000 to decimal conversion
In the given, we want to convert 3 / 10000 to decimal form, we can compute this by dividing numerator 3 by denominator 10000
3/10000 = 0.0003
Hope this helps ❤A survey was sent out to re-evalute the proportion of people who play games on pc computers, as the last study on the topic had been gathered four years prior. This survey was done specifically to test the possibility that fewer people are playing games on pc computers. The previous study found that 81% of people were playing games on pc computers. The current study, with 861 participants, found that 53% of people who responded play on a pc computer.
Calculate the p-value and determine if we should accept or reject H0 under alpha = 0.05.
Answer:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
Step-by-step explanation:
Info given
n=861 represent the random sample
[tex]\hat p=0.53[/tex] estimated proportion of people who responded play on a pc computer
[tex]p_o=0.81[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion decreases from 81%, the system of hypothesis are.:
Null hypothesis:[tex]p\geq 0.81[/tex]
Alternative hypothesis:[tex]p < 0.81[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
I Need help ASAP!!!
Answer:
x = 15, AOB = 15, BOC = 165
Step-by-step explanation:
Assume that this is a straight line
2x - 15 + 11x = 180
Combine like terms
13x - 15 = 180
Add 15 on both sides
13x = 195
Divide 13 on both sides
x = 15
Substitute x for 15 in both equations
2(15) - 15 = 15
11(15) = 165
(For checking purposes, 165 + 15 = 180)
Use a significance level of α= 0.05 and use the given information for the following:
Required:
a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
"we dont gaf abt no bii, we dont giveeaf abt no bii and if i was you i wouldnt kiss her on the lips"
Akmal, Bakri and Cadin share their mother medical expenses which cost RM4200. Cadin pays RM2100 while akmal pays three quarters of Bakri amount. Find the ratio of the expenses shared by Akmal to Bakri to Cadin
Answer:
The ratio of the expenses shared by Akmal to Bakri to Cadin is 7 : 4 : 3
Step-by-step explanation:
The 3 of them shares their mother medical expenses which cost RM4200 . There mother medical expenses is RM4200 in total. Cadin pays RM2100 which is half of their mother medical expenses. Then Akmal pays three quarters of Bakri amount.
Let
The amount Bakri pays = a
Akmal pays = 3/4 of a
Akmal pays = 3/4a
Therefore,
a + 3a/4 = 2100
4a + 3a/ 4 = 2100
7a/4 = 2100
cross multiply
7a = 8400
divide both sides by 7
a = 8400/7
a = 1200
Therefore,
Bakri pays =RM 1200
Akmal pays = 3/4 × 1200 =RM 900
The ratio of the expenses shared by AKmal to Bakri to Cadin is expressed as 2100 : 1200 : 900. Divide through by 300
7 : 4 : 3
Which equation can be used to solve for b?
B
5 cm
С
10 cm
b
30
A
O tan(30)=5/b
O tan(30)=b/5
O tan(30)=10/b
O tan(30)=b/10
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent:
[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: oppo. = 5 \\ let \: adj. = b \\ let \: θ = 30[/tex]
[tex] \tan(30) = \frac{5}{b} [/tex]
The correct answer is option (A) tan(30)=5/b
Tangent functionThe tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.How to solve this problem?The steps are as follow:
The right angle triangle is given whose sides are as follow:AB = 10 cm
BC = 5 cm
AC = b cm
To find the tan(30) we will use following formula:tan(x) = opposite side / adjacent side
tan(30) = BC / AC
tan(30) = 5 / b
So, the correct answer is option (A) tan(30)=5/b
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A farmer planted corn in two different fields. He planted 500 seeds of regular corn in Field A and 500 seeds of experimental corn in Field B. At
harvest time, more ears of corn had grown in Field A than in Field B. The farmer concluded that more corn grew in Field A because of the type
of corn planted.
Choose two other possible variables that could have caused more corn to grow in Field A.
Answer:
1. More pollination process in the regular corn planted in field A than that of field B.
2. Low pest and insect attack on corn planted in field A compared to that of B.
Step-by-step explanation:
1. Pollination is the process in which a plant becomes fertilized, so as to produced seeds. The process requires some agent which could be; air, human, wind etc.
Therefore more pollination of the corn planted in field A than those in B would lead to more yield (ears of corn harvested) than that of B.
2. Pests and insects are agents which could reduce the yield of the corn after harvest. Comparing the two fields A and B, if the corn planted in field A were not affected by pests or insects, while those planted in B were affected, then more ears of corn would be harvested in field A.
Answer:
a,c, And gg gamer
Step-by-step explanation:
What’s the correct answer for this?
Answer:
B and F
Step-by-step explanation:
When we'll slice a triangular prism, a square and triangle would be formed
a football team had 50 players at the start of the season, but then some players left the team. After that, the team had 42 players
Answer:
50 = p + 42
Step-by-step explanation:
The unknown part of this equation is the variable p, the number of people that left. So you want to add p to 42 and that will give you the total number of football players, which is 50. In order to get p, you need to get it by itself and make it equal something. Subtract 42 from both sides and you are stuck with 50-42 = p
p = 8
Answer:
50-p=42
Step-by-step explanation:
Laura placed a bucket of water in her garden. Over the course of a week, she watched the water evaporate and recorded the volume of water left in the bucket each day.
Laura found the linear model that best fit the data was V=5.00−0.25n, where n is the number of days since she first placed the bucket and V is the volume of water, in liters, remaining in the bucket.
How many liters of water evaporated from the bucket every day?
How may liters where inside the bucket when Laura first placed it in the garden?
Answer:
1. 0.5 L; 2. 5.00 L
Step-by-step explanation:
V = 5.00 - 0.5n
If you include units, the equation becomes
V(in litres) = 5.00 L - (0.5 L/day) × (n days)
1. Rate of evaporation
When you include the units, it becomes easier to see that the water is evaporating at a rate of 0.5 L/day.
That is, 0.5 L of water evaporates each day.
The negative sign shows that the volume of water is decreasing.
2. Volume at the beginning
At the beginning of the experiment, n = 0. Then
V = 5.00 -0.5×0 = 5.00 - 0 = 5.00 L
The bucket originally contained 5.00 L of water.
Avantraveling 20 miles per hour can stop in 60 feet. If a van is traveling 32 miles per hour what is it’s stopping distance
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Measure of arcURN = 270°
In radians:
270° = 270π/180
270° = 3π/2
Now
Area of sector = 1/2r²∅
= 1/2(10)²(3π/2)
= 50(3π/2)
= 75π
5. There are 400 students in the senior class at Oak Creek High School. All 2 points
of these students took the SAT. The distribution of their SAT scores is
approximately normal. The number of students who scored within 2
standard deviations of the mean is approximately *
-3
-2
0
1
2.
3
Answer:
The number of students who scored within 2 standard deviations of the mean is 380.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
The number of students who scored within 2 standard deviations of the mean is approximately
By the Empirical Rule, 95% of the students scored within 2 standard deviations of the mean
Out of 400
0.95*400 = 380
The number of students who scored within 2 standard deviations of the mean is 380.
Answer: 380
Step-by-step explanation: 95% of 400 is 380
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. -6 ≤ y ≤ 9
Step-by-step explanation:
→Looking at the graphed function, you can see that the line starts at when y = -6. Then the function slowly increases, until it finally stops when y = 9.
→This means that the range (y-values) of the function can be from -6 through 9.
The correct answer should be "A. -6 ≤ y ≤ 9."
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
No Solutions
2x+5+2x+3x= _ x +_
One Solution
2x+5+2x+3x=_ x + _
Infinitely Many Solutions
2x+5+2x+3x= _x +_
Answer:
7x+16x+17x+5Step-by-step explanation:
No Solutions
There will be no solutions when the left side is inconsistent with the right side:
2x +5 +2x +3x = 7x +1
7x +5 = 7x +1 . . . . . . no value of x will make this true
__
One Solution
There will be one solution when the left side and right side are not inconsistent and not the same.
2x +5 +2x +3x = 6x +1
7x +5 = 6x +1
x = -4 . . . . . . . . add -6x-5 to both sides
__
Infinitely Many Solutions
There will be an infinite number of solutions when the equation is true for any value of x. This will be the case when the left side and right side are identical.
2x +5 +2x +3x = 7x +5
7x +5 = 7x +5 . . . . . true for all values of x
_____
Comment on these solutions
You have not provided the contents of any of the drop-down menus, so we cannot say for certain what the answers should be--except in the case of "infinitely many solutions." For "no solutions", the coefficient of x must be 7 and the constant must not be 5. For "one solution" the coefficient of x cannot be 7, and the constant can be anything.
Answer:
No Solutions: 7x+1
One Solution: 6x+1
Infinitely Many Solutions: 7x+5
Written as a simplified polynomial in standard form, what is the result when
(x + 1)2 is subtracted from 7x2 - 4x + 6?
Answer:
The resultant polynomial is: [tex]6x^2-6x+5[/tex]
Step-by-step explanation:
We need to subtract [tex](x+1)^{2}[/tex] from [tex]7x^2-4x+6[/tex]
so, we start by performing the multiplication involved in the perfect square of the binomial [tex](x+1)[/tex], and obtain its expression in separate terms that can be combined:
[tex](x+1)^{2}=(x+1)\,(x+1)=x^2+x+x+1=x^2+2x+1[/tex]
Now we can subtract this trinomial from [tex]7x^2-4x+6[/tex], and combining like terms to get the resultant polynomial expression:
[tex]7x^2-4x+6-(x^2+2x+1)=7x^2-4x+6-x^2-2x-1=7x^2-x^2-4x-2x+6-1=6x^2-6x+5[/tex]
Then the resultant polynomial is: [tex]6x^2-6x+5[/tex]
If f(3x − 1) = 6x − 1, find f(x) and f(0)
f(3x - 1) = 6x - 1
Rewrite 6x - 1 as a function of 3x - 1:
6x - 1 = 6x - 2 + 1 = 2(3x - 1) + 1
That is,
f(3x - 1) = 2(3x - 1) + 1
which means
f(x) = 2x + 1
and so
f(0) = 2*0 + 1 = 1
In 1990, there were 4,500 deaths due to lung diseases in miners aged 20 to 64 years. The expected number of deaths in this occupational group, based on age-specific deaths rates from lung diseases in all males aged 20 to 64 years, was 1,800 during 1990. What is the standardized mortality ratio (SMR) for lung disease in miners
Answer:
2.5
Step-by-step explanation:
We have that the standardized mortality ratio (SMR) is the relationship between the number of deaths observed in a year, that is, those that occurred and the number of expected deaths, that is, those that were predicted.
SMR = observed / expected
therefore if we replace we have:
SMR = 4500/1800
SMR = 2.5
Which means that the standardized mortality ratio (SMR) is 2.5
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 53 units of a small appliance with a standard deviation of 12 units. During the same point in time last year, a random sample of 49 stores had mean sales of 41 units with standard deviation 6 units.
It is of interest to construct a 95 percent confidence interval for the difference in population means ?1??2, where ?1 is the mean of this year's sales and ?2 is the mean of last year's sales.
Enter values below rounded to three decimal places.
(a) The estimate is: _________ .
(b) The standard error is: ____________________ .
Answer:
The 95% confidence interval for the difference of means is (7.67, 16.33).
The estimate is Md = 12.
The standard error is sM_d = 2.176.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.
The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.
The difference between sample means is Md=12.
[tex]M_d=M_1-M_2=53-41=12[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{36}+\dfrac{6^2}{49}}\\\\\\s_{M_d}=\sqrt{4+0.735}=\sqrt{4.735}=2.176[/tex]
The degrees of freedom are:
[tex]df=n_1+n_2-1=36+49-2=83[/tex]
The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.
The margin of error (MOE) can be calculated as:
[tex]MOE=t \cdot s_{M_d}=1.989 \cdot 2.176=4.328[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 12-4.328=7.67\\\\UL=M_d+t \cdot s_{M_d} = 12+4.328=16.33[/tex]
The 95% confidence interval for the difference of means is (7.67, 16.33).
Classify the triangle by its sides, and then by its angles.
7 m
7 m
9.9 m
Classified by its sides, the triangle is a(n)
▼
isosceles
scalene
equilateral
triangle.
Classified by its angles, the triangle is a(n)
▼
acute
right
obtuse
triangle.
Answer:
isosceles
Step-by-step explanation:
— 3х + 7 < 19 ?
Help plz
Answer:
x > -4
Step-by-step explanation:
— 3х + 7 < 19
Subtract 7 from each side
— 3х + 7-7 < 19-7
-3x < 12
Divide each side by -3, remembering to flip the inequality
-3x/-3 > 12/-3
x > -4
Just like any of your two-step equations, in this inequality,
start by isolating the x term which in this case is -3x by
subtracting 7 from both sides.
This gives us -3x < 12.
Solving from here, we divide both sides by -3.
However, when solving inequalities, you need to watch out.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.
So we end up with x > -4.
