Answer:
0.89
Step-by-step explanation:
First, let’s find out what one tomato costs. To do this, we need to find the unit rate.
To find the unit rate, divide the cost by the number of tomatoes.
cost/number of tomatoes
It costs $3.55 for 24 tomatoes.
cost=3.55
number of tomatoes=24
Substitute these values in.
3.55/24
0.147916666666667
Each tomato costs $0.147916666666667
Now, we have to find out what 6 tomatoes cost.
Multiply the number of tomatoes by the cost of one tomato
number of tomatoes * cost of one
number of tomatoes=6
cost of one= 0.147916666666667
Substitute these values in.
6* 0.147916666666667
0.8875
Round to the nearest cent or hundredth.
The 7 in the thousandth place tells us to round the 8 in the hundredth place up to a 9.
0.89
6 tomatoes will cost about 0.89.
f(x) = (x - 5)(5x + 2)
lesser x =
greater x =
Answer:
hope
this
is
correct
what is the arc measure of minor arc DE in degrees?
help lol
Answer:
DE= 39°
Step-by-step explanation:
(4w+ 4 )+(4w+8)= 180
Solve for w
8w + 12 = 180
8w = 180-12
8w = 168
W= 21°
(4w+ 4)+(2w+11)+DE = 180
But w= 21°
((4*21 )+4)+((2*21)+11)+DE = 180
88 + 53 + DE = 180
DE = 180-88-53
DE= 39°
The points J(-1,-9) and K(5,1) are endpoints of a diameter of circle S. Which equation represents circle S? A. (x − 2)2 + (y + 4)2 = 34 B. (x − 2)2 + (y + 4)2 = 136 C. (x + 2)2 + (y − 4)2 = 34 D. (x + 2)2 + (y − 4)2 = 136
Answer:
the equation of the circle is
[tex](x-2)^2+(y+4)^2 = 34[/tex]
Step-by-step explanation:
Recall that the equation of a circle is given by [tex](x-h)^2+(y-k)^2 = r^2[/tex] where r is the radius, and (h,k) is the center. Recall that given two points that are the endpoints of a diameter, the center of the circle is their correspondent midpoint. Also, recall that given points (a,b), (c,d) their midpoint is obtained by [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
In this case we are given the endpoints (-1,-9), (5,1). So the center of the circle is the midpoint obtained by [tex](\frac{-1+5}{2},\frac{-9+1}{2}) = (2, -4)[/tex]. Recall that the radius of a circle is the distance from the radius to any of the points of the circle. So, the radius is the distance between the center and the point (-1,-9). We will calculate r^2, by using the distance formula. REcall that the distance between points (a,b), (c,d) is given by
[tex]\sqrt[]{(a-c)^2+(b-d)^2}[/tex]. So, its square is
[tex](a-c)^2+(b-d)^2[/tex].
In our case,
[tex]r^2 = (2-(-1))^2+(-4-(-9))^2 = 3^2+5^2 = 34[/tex]
So, the equation of the circle is
[tex](x-2)^2+(y+4)^2 = 34[/tex]
There are about 208,000,000,000 different 8-letter passwords that can be formed using a 26-letter
alphabet.
Express this number using scientific notation.
0 2.08 x 1011
O 208 10
O 20.8 x 1010
0 0.208 x 1012
Answer:
2.08 x 10^11
Step-by-step explanation:
To put a number into scientific notation you move the decimal to the spot right after the first digit. To figure out what the power is you count how many digits you moved it past in order to get to the spot you want it (right after the first digit; in this case the 2)
So in this case you would move the decimal from the end of the number backwards past 9 zeros, the 8, and another zero, which is a total of 11 digits.
From there you take the number with the new decimal place and multiply by 10 to the power of the number you counted earlier, which for this example is 11
So the final answer is 2.08 x 10^11
Manuel is 6 years older than melissa. In 6 years the sum of their ages will be 52. How old is manuel now?
_______years old
Answer:
58
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
lolololololololol
The yellow boxes on the bottom are the answers. Please help TYSM
Answer:
[tex]1.\ 8p = 64, p =8[/tex]
[tex]2. -\dfrac{w}{4} = 8, w = -32[/tex]
[tex]3. -5c = -20, c =4[/tex]
[tex]4.\ 9m=45, m = 5[/tex]
[tex]5. \dfrac{b}{25} = -3, b =-75[/tex]
[tex]6. \dfrac{d}{-2} = 20, d=-40[/tex]
Step-by-step explanation:
Now let us see the detailed solution of each part:
Part 1:
[tex]8p -15 = 49\\\Rightarrow 8p =49+15\\\Rightarrow 8p = 64\\\Rightarrow p =8[/tex]
Part 2:
[tex]\dfrac{-w}{4}+18=26\\\Rightarrow \dfrac{-w}{4} = 26-18\\\Rightarrow \dfrac{-w}{4} = 8\\\Rightarrow -w = 8 \times 4\\\Rightarrow w =-32[/tex]
Part 3:
[tex]-5c-15=-35\\\Rightarrow -5c = -35 +15\\\Rightarrow -5c = -20\\\Rightarrow c = 4[/tex]
Part 4:
[tex]9m +10=55\\\Rightarrow 9m =55-10\\\Rightarrow 9m =45\\\Rightarrow m =5[/tex]
Part 5:
[tex]\dfrac{b}{25}-83=-86\\\Rightarrow \dfrac{b}{25} = -86 +83\\\Rightarrow \dfrac{b}{25} = -3\\\Rightarrow b = -75[/tex]
Part 6:
[tex]\dfrac{d}{-2}+85=105\\\Rightarrow \dfrac{d}{-2} = 105-85\\\Rightarrow \dfrac{d}{-2} = 20\\\Rightarrow d=20 \times -2\\\Rightarrow d =-40[/tex]
Please refer to attached image for the answers.
G
The measure of ZJHG is
degrees.
Answer: 70°
Step-by-step explanation:
You can tell by the protractor that you should read from the right side because that is where the protractor starts at 0°. Lookin at the angle, the line JH is to 70°. Therefore, the measure of ∠JHG is at 70°.
Simplify
sin^2x+tan^2x+cos^2x
Answer:
sec²x
Step-by-step explanation:
sin²x + tan²x + cos²x
sin²x + cos²x + tan²x
1 + tan²x ( sin²x + cos²x = 1 )
sec²x ( 1 + tan²x = sec²x )
Answer:
Step-by-step explanation:
SIN^2x + tan^2 x + cos^2x
= x( sin^2 + tan^2+cos^2)
=x(1+tan^2) since sin^2+cos^2 =1
=xsec^2 ( since sec^2 = 1+tan^2)
=sec^2x
hope it helps
True or False? The segments shown below could form a triangle?
Answer:
True
Step-by-step explanation:
First start at B point than go to C point than go to A point
Nobody knows this one :(
Find x
A) 9
B)-9
C)6
D)-6
Answer:
-9
Step-by-step explanation:
164-43=121
121-139=-18
-18/2=-9
Answer:
-9
Step-by-step explanation:
164= x-43
164-43=x
x=121
164-43=121
121-139=18
-18/2= -9
Which statement is true about the circumference of a circle?
15
O The circumference is the measurement around the circle.
O The circumference is the measurement of the radius.
O The circumference is the measurement of the diameter
The circumference is double the radius
Answer:
the first one the measurement around the circle
Write a quadratic function f whose only zero is −10.
function is: f(x)=(x+10)^2
The quadratic function f whose only zero is −10 should be [tex]f(x)=(x+10)^2[/tex].
What is a quadratic function?A quadratic function should be the one of the form f(x) [tex]= ax^2 + bx + c[/tex], where a, b, and c are numbered with a not equal to zero. The graph of a quadratic function is a curve known a parabola.
So here we assume that the The quadratic function f whose only zero is −10 should be [tex]f(x)=(x+10)^2[/tex].
Learn more about function here: https://brainly.com/question/13223520
One study revealed that a child under the age of 10 watches television 4.5 hours per day. A group of families from a certain comunity would like to beleive that their children watch television less than the national average. A random sample of 14 children from the community yielded a mean of 4.1 hours per day with standard deviation of 1.2. Test the appropriate hypothesis at the level of significance 0.01. Assume the viewing time is normally distributed and interpret your results.
Answer:
[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]
The degrees of freedom are given by:
[tex] df=n-1= 14-1=13[/tex]
And the p value would be:
[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.
Step-by-step explanation:
Information given
[tex]\bar X=4.1[/tex] represent the sample mean
[tex]s=1.2[/tex] represent the sample deviation
[tex]n=14[/tex] sample size
[tex]\mu_o =4.5[/tex] represent the value to test
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is less than 4.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 4.5[/tex]
Alternative hypothesis:[tex]\mu < 4.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]
The degrees of freedom are given by:
[tex] df=n-1= 14-1=13[/tex]
And the p value would be:
[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.
A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette deck)ie one of each. A purchaser is offered a choice ofmanufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
CD Player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette Deck: Onkyo, Sony, Teac, Technics
A switch board display in the store allows a customer to hooktogether any selection of components (consisting of one of eachtype). Use the product rules to answer the following questions.
a. In how many ways can one component of each type beselected?
b. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
c. In how many ways can components be selected if noneis to be sony?
d. In how many ways can a selection be made if at leastone sony component is to be included?
e. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component? Exactly onesony component?
Answer:
Step-by-step explanation:
(a)
The number of receivers is 5.
The number of CD players is 4.
The number of speakers is 3.
The number of cassettes is 4.
Select one receiver out of 5 receivers in [tex]5C_1[/tex] ways.
Select one CD player out of 4 CD players in [tex]4C_1[/tex] ways.
Select one speaker out of 3 speakers in [tex]3C_1[/tex] ways.
Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.
Find the number of ways can one component of each type be selected.
By the multiplication rule, the number of possible ways can one component of each type be selected is,
The number of ways can one component of each type be selected is
[tex]=5C_1*4C_1*3C_1*4C_1\\\\=5*4*3*4\\\\=240[/tex]
Part a
Therefore, the number of possible ways can one component of each type be selected is 240.
(b)
The number of Sony receivers is 1.
The number of Sony CD players is 1.
The number of speakers is 3.
The number of cassettes is 4.
Select one Sony receiver out of 1 Sony receivers in ways.
Select one Sony CD player out of 1 Sony CD players in ways.
Select one speaker out of 3 speakers in ways.
Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.
Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.
By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,
Number of ways can one components of each type be selected
[tex]=1C_1*1C_1*3C_1*4C_1\\\\=1*1*3*4\\\\=12[/tex]
Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.
(c)
The number of receivers without Sony is 4.
The number of CD players without Sony is 3.
The number of speakers without Sony is 3.
The number of cassettes without Sony is 3.
Select one receiver out of 4 receivers in 4C_1 ways.
Select one CD player out of 3 CD players in 3C_1 ways.
Select one speaker out of 3 speakers in 3C_1 ways.
Select one cassette out of 3 cassettes in 3C_1 ways.
Find the number of ways can components be selected if none is to be Sony.
By the multiplication rule, the number of ways can components be selected if none is to be Sony is,
[tex]=4C_1*3C_1*3C_1*3C_1\\\\=108[/tex]
[excluding sony from each of the component]
Therefore, the number of ways can components be selected if none is to be Sony is 108.
(d)
The number of ways can a selection be made if at least one Sony component is to be included is,
= Total possible selections -Total possible selections without Sony
= 240-108
= 132
Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.
(e)
If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,
[tex]= \text {Total possible selections with at least one Sony} /\text {Total possible selections}[/tex]
= 132 / 240
= 0.55
The probability that the system selected contains exactly one Sony component is,
[tex]= \text {Total possible selections with exactly one Sony} /\text {Total possible selections}[/tex][tex]\frac{1C_1*3C_1*3C_1*3C_1+4C_11C_13C_13C_1+4C_13C_13C_13C_1}{240} \\\\=\frac{99}{240} \\\\=0.4125[/tex]
Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.
If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.
Plz help fast Jack, John, Lily, and Sara want to take a picture together. In how many ways can they are arranged?
Answer:
The best estimate would be around 10-16
Step-by-step explanation:
The think is that they can be in many orders and since there is four of them it would be more orders.
Hope this helps
Bassima evaluated the expression below. 2 (12 minus 14) squared minus (negative 5) + 12 = 2 (negative 2) squared minus (negative 5) + 12 = 2 (negative 4) minus (negative 5) + 12 = negative 8 + 5 + 12 = 9. What was Bassima’s error? Bassima did not multiply 2 and 12 first. Bassima evaluated Minus (negative 5) as 5. Bassima added and subtracted before multiplying. Bassima evaluated (Negative 2)
Answer:
I can confirm d
Step-by-step explanation:
Hen evaluated (Negative 2) squared as
What is an Expression?An expression is a number, a variable, or a combination of numbers and variables and operation symbols
How to solve it?Hen evaluated the expression below. 2 (12 minus 14) squared minus (negative 5)+12=2 (negative 2) squared minus (negative 5) + 12 =2(negative 4) minus (negative 5) +12= negative 8+ 5+12=9. What was hen's error? He did not multiply 2 and 12 first. Hen evaluated Minus (negative 5) as 5. He was added and subtracted before multiplying. Hen evaluated (Negative 2) squared as
Learn more about the expression:
https://brainly.com/question/1280754
#SPJ2
Zara travelled in a train moving at an average speed of 120km/h and covered a distance of 40km towards East. i. Calculate the time taken by the train to cover this distance.
Answer:
20 minutes
Step-by-step explanation:
Distance= 40 km
Speed= 120 km/h
Time= distance/speed= 40/120= 1/3 hour= 20 min
Answer:
Time = 0.33 hrs
Step-by-step explanation:
Given:
Speed = 120 km/hr
Distance = 40 km
Required :
Time = ?
Formula:
Speed = Distance/Time
Solution:
Time = Distance / Speed
Time = 40/120
Time = 0.33 hrs
The area of the triangle below is 2/5 square foot. What is the length, in feet, of the base of the triangle? Area = bh/2
Answer:
2/3 feet.
Step-by-step explanation:
We have to calculate the length of the base of the triangle, in this case they give us the area of the triangle but still it is necessary to know the height of the triangle to calculate the length of the base, otherwise it would be impossible.
I have found an image where the graph is, which I will attach where you can see that the height is 6/5 ft. The area of the triangle is:
A = b * h / 2
solved for b which is the length of the base of the triangle would be:
b = 2 * A / h
replacing:
b = 2 * (2/5) / (6/5)
b = 20/30
b = 2/3
Which means that the length of the base of that triangle is 2/3 feet.
AnswerSo C:
Step-by-step explanation:
What is the mean of the following set of data?
{6,9,3, 8, 9,3,4}
Answer:
6
Step-by-step explanation:
Add all the numbers together and divide by the amount of numbers
6+9+3+8+9+3+4= 42
42/7 = 6
Answer:
6
Step-by-step explanation:
To find the mean or the average of the data set, you add all the numbers together and then divide the sum by the number of numbers in the data set.
6+9+3+8+9+3+4 =42
Then divided by the # of terms.
42/7= 6
The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next.Under 25 years old At least 25 years old Chocolate 40 15 Vanilla 20 40 Swirl 15 20What is the probability a randomly selected customer prefers Vanilla yogurt or is at least 25 years old?
Answer:
63.33% probability a randomly selected customer prefers Vanilla yogurt or is at least 25 years old
Step-by-step explanation:
A probability the number of desired outcomes divided by the number of total outcomes.
We are given the following chart:
Under 25 | At least 25
Chocolate: 40 | 15
Vanila: 20 | 40
Swirl: 15 | 20
What is the probability a randomly selected customer prefers Vanilla yogurt or is at least 25 years old?
There are 150 customers, which is the number of total outcomes.
Of those, 75 are at least 25 and 20 are under 25 and prefer Vanilla yogurt. So the number of desired outcomes is 75 + 20 = 95
95/150 = 0.6333
63.33% probability a randomly selected customer prefers Vanilla yogurt or is at least 25 years old
A newly proposed endoscopy method used to screen for colon cancer is tested among a random sample of the population. Given that 16 individuals from a test population of 100,000 individuals has colon cancer and 14 individuals test positive for colon cancer, the researchers should determine the sensitivity of the newly proposed screening method is .875.
a. True
b. False
Answer: True
Step-by-step explanation:
Sensitivity in such a scenario is used to measure the accuracy of the screening method. In other words, how effective is the screening method at detecting Colon Cancer.
The sensitivity of the method can be calculated by dividing the amount of people that it showed as positive by the number of people that were actually tested.
The number of people who showed positive were 14 and the amount of people tested were 16.
Sensitivity therefore is,
= 14/16
= 0.875
They should indeed determine the sensitivity of the newly proposed screening method to be .875.
hello
Which of the below is more closer to 1
a)1+ 1/2
b)1- 1/8
c)1+ 1/5
d)1- 1/3
e)1+ 1/10
Answer:
1/10
Step-by-step explanation:
1 + 1/2 = 1 1/2
1 - 1/8 = 7/8
1 + 1/5 = 1 1/5
1 - 1/3 = 2/3
1 + 1/10 = 1 1/10
One and one tenth is closest to one because one tenth is the smallest amount that would need to be added or taken away to get exactly one. Hope I helped!
Answer:
E
Step-by-step explanation:
the sum of a number and 9 is -7. What does that mean or what's the equation
Answer: x+9= -7
Step-by-step explanation:
What this statement means is that the sum or combining/adding of 9 and another number gives you -7 as the answer. We can write an equation to figure out what the other number is.
Let's use x as the unknown/other number.
x+9= -7
That is what your set up equation would look like. To solve for x, you simply subtract 9 on both sides.
x=-16
Is 1.06 greater than 0.6
Answer:
it is
Step-by-step explanation:
Given f(x) = 6x + 2, find f(x-3)
Answer:
6x -16
Step-by-step explanation:
f(x) = 6x + 2
f(x-3) =
Replace x with x-3
f(x) = 6(x-3) + 2
Distribute
= 6x - 18 +2
= 6x -16
The right answer is 6x-16
please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
A survey said that 3 out of 5 students enrolled in higher education took at least one online course last fall. Explain your calculations and reasoning for the following: a) If you were to pick at random 1 student enrolled in higher education, what is the probability that student took at least one online course? b) If you were to pick at random 1 student enrolled in higher education, what is the probability that student did not take an online course? c) Now, consider the scenario that you are going to select random select 4 students enrolled in higher education. Find the probability that All 4 students selected took online courses
Answer:
a) 60% probability that student took at least one online course
b) 40% probability that student did not take an online course
c) 12.96% probability that all 4 students selected took online courses.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they took at least one online course last fall, or they did not. The probability of a student taking an online course is independent of other students. 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.
3 out of 5 students enrolled in higher education took at least one online course last fall.
This means that [tex]p = \frac{3}{5} = 0.6[/tex]
a) If you were to pick at random 1 student enrolled in higher education, what is the probability that student took at least one online course?
This is P(X = 1) when n = 1. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{1,1}.(0.6)^{1}.(0.4)^{0} = 0.6[/tex]
60% probability that student took at least one online course.
b) If you were to pick at random 1 student enrolled in higher education, what is the probability that student did not take an online course?
This is P(X = 0) when n = 1.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{1,1}.(0.6)^{0}.(0.4)^{1} = 0.4[/tex]
40% probability that student did not take an online course
c) Now, consider the scenario that you are going to select random select 4 students enrolled in higher education. Find the probability that all 4 students selected took online courses
This is P(X = 4) when n = 4.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]
12.96% probability that all 4 students selected took online courses.
1 Point
In mathematics, when we talk about a(n) we are talking about some of
the people, places, or things under consideration.
Answer:
Population
Step-by-step explanation:
In mathematics, when we talk about the people, places, or things under consideration, we are referring to the population. The Population is the entire sum of objects in a study. When a researcher wants to study factors that concern a particular set of people, places, or things, the group under study is the population. For example, the researcher might want to do a study on the amount of food consumed by Brazilian students in the year 2019. The Brazilian students represent the population, because they are the group of people being studied.
The population under study might sometimes be difficult to study as a whole. For example, the study of the entire Brazilian students might be cumbersome. In such cases, a sample can be drawn from the population and studied, or the population narrowed down a little more, so that it can be easily studied.
correct answer gets brainliest Please explain as well 3x+5y=21 4x-2y = -24
Answer:
x=-3 y=6
Step-by-step explanation:
it was a easyone ,don't forget to mark me as a brainlinest .☺️
The expected duration of the project (average) is 30 days and variance is 16. 1. What is the probability that the project will be completed on day 32 or earlier? 2. Suppose the official deadline for the project is 34 days. What is the probability that the project will be delayed?
Answer:
1. 69.15% probability that the project will be completed on day 32 or earlier
2. 15.87% probability that the project will be delayed
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 30, \sigma = \sqrt{16} = 4[/tex]
1. What is the probability that the project will be completed on day 32 or earlier?
This is the pvalue of Z when X = 32. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32 - 30}{4}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a pvalue of 0.6915
69.15% probability that the project will be completed on day 32 or earlier
2. Suppose the official deadline for the project is 34 days. What is the probability that the project will be delayed?
This is 1 subtracted by the pvalue of Z when X = 34. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{34 - 30}{4}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
1 - 0.8413 = 0.1587
15.87% probability that the project will be delayed
The owners of Prim's Pizza are concerned that many of their customers are starting to purchase pizza from The Pizza Palace because of its new pizza, which has fewer calories than Prim's. A random sample of 100 medium pizzas from Prim's found a mean of 240 calories and a standard deviation of 8.6 calories. A random sample of 100 medium pizzas from The Pizza Palace found a mean of 210 calories and a standard deviation of 5.7 calories. Which of the following formulas gives a 95% confidence interval for the difference in mean calories between a Prim's Pizza medium pizza and a medium pizza from The Pizza Palace?
Answer:
[tex] (240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953[/tex]
[tex] (240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047[/tex]
And the confidence interval for the difference is between:
[tex] 27.953 \leq \mu_1 -\mu_2 \leq 32.047[/tex]
Step-by-step explanation:
We have the following info given:
[tex] \bar X_1 = 240[/tex] sample mean for medium Pizzas from Prim's
[tex] \bar X_2 = 210[/tex] sample mean for medium Pizzas from Pizza Place
[tex] s_1 =8.6[/tex] sample deviation for Prim's
[tex] s_2 =5.7[/tex] sample deviation for Pizza Palca
[tex] n_1 =n_2 = 100[/tex] sample size selected for each case
The confidence interval for the difference of means is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
And for the 95% confidence we need a significance level of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the degrees of freedom are given by:
[tex] df= n_1 +n_2 -2= 100+100-2 =98[/tex]
And the critical value would be
[tex] t_{\alpha/2}= 1.984[/tex]
And replacing we got:
[tex] (240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953[/tex]
[tex] (240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047[/tex]
And the confidence interval for the difference is between:
[tex] 27.953 \leq \mu_1 -\mu_2 \leq 32.047[/tex]
Answer:
E
Step-by-step explanation:
30 plus or minus 1.98 sqrt 8.6^2/100 + 5.7^2/100
