Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
This is a left tailed test.
Step-by-step explanation:
A hypothesis test is to be performed to determine whether last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.79.
Then, the claim that will be expressed in the alternative hypothesis is that the monthly bill is lower than $47.79.
The null hypothesis will state that the monthly bill does not differ significantly from $47.79.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
As we only want to test if its lower, we are interested only in the left tail of the distribution. We want to know if the test statistic is below the critical value to conclude if we have evidence for our claim. This is then a left tailed test.
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]
Jar A contains four liters of a solution that is 45% acid. Jar B contains five liters of a solution that is 48% acid. Jar C contains one liter of a solution that is k % acid. From jar C, 2/3 liters of the solution is added to jar A, and the remainder of the solution in jar C is added to jar B. At the end both jar A and jar B contain solutions that are 50% acid. Find k.
Answer:
k= 80%
Step-by-step explanation:
Jar A contains 4*0.45 L acid, and 4 L of a solution of acid.
Jar B contains 5*0.48 L acid., and 5 L of a solution of acid.
Jar C contains 1*k/100 = k/100 acid, and 1 L of a solution.
50% = 0.5
For jar A.
(2/3)*k/100 L acid is added to jar A.
Now jar A contains 4*0.45 L + (2/3)*k/100 L acid, and it has (4+2/3)L of a solution.
L solute/L solution = 0.5
[4*0.45 L + (2/3)*k/100 L]/(4+2/3)L = 0.5
[1.8 + (2k/300)]/[(12+2)/3] = 0.5
[1.8 + (2k/300)]/[14/3] = 0.5
[1.8 + (2k/300)]= 0.5*(14/3)
(2k/300) = 0.5*(14/3) - 1.8
2k = (0.5*(14/3) - 1.8)*300
k = (0.5*(14/3) - 1.8)*300/2 =80
k= 80%
We also can find k using jar B.
(1/3)k/100 L acid is added to jar B.
Now jar B contains 5*0.48 L+ (1/3)k/100 L acid, and it has (5+1/3) L of a solution.
L solute/L solution = 0.5
[5*0.48 L+ (1/3)k/100 L ]/(5+1/3)L= 0.5
[5*0.48 + (1/3)k/100 ]/(5+1/3)= 0.5
This equation also gives k=80%
Check.
We can check at least for jar A.
Jar A has 4L solution and 4*0.45=1.8 L acid.
2/3 L of the solution from jar C was added, and now we have 4 2/3 L of solution.
(2/3)* 80%= (2/3)*0.8 acid was added from jar C.
Now we have [1.8 +(2/3)*0.8] L acid in jar A.
L solute/L solution = [1.8 +(2/3)*0.8] L /(4 2/3) L = 0.5 or 50% as it is given that jar A has 50% at the end.
Sue invests £9000 in an account for one year.
At the end of the year, interest is added to the account.
Sue pays tax on this interest at a rate of 20%.
She pays £30.24 tax.
Work out the percentage interest rate for the account.
Answer:
The interest rate = 1.68%
Step-by-step explanation:
Sue invests £9000 in an account for one year.
She pays £30.24 at a rate of 20%
So 20% of the interest =£ 30.24
Let the interest be x
X0.2= 30.24
X=£ 151.2
The total interest was£ 151.2
The rate R at which generated this interest
R = (100*151.2)/(1*9000)
R= 15120/9000
R= 1.68%
The interest rate = 1.68%
Area of composite shapes
Find the area of the shape shown below.
Answer:
32 units
Step-by-step explanation:
The large triangle on top has an area of 20, cause 4*10 = 40
40/2 = 20.
the square on the bottom has an area of 4, well, cause 2*2 = 4.
The smaller triangle on the left has an area of 2, cause 2*2=4
4/2=2
The triangle on the right, has an area of 6, because 6*2=12
12/2=6
20+4+2+6 = 32
Answer:
32 Units =)
Step-by-step explanation:
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°
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
PLEASE ANSWER ASAP (exponential and logarithms)
Answer:
1.4650 (the first option in the list of possible answers)
Step-by-step explanation:
Start by isolating the exponential expression on one side of the equal sign, thus subtracting 2 from both sides:
[tex]2+3^x=7\\3^x=7-2\\3^x=5[/tex]
Now, in order to solve for "x", we need to lower the exponent, and for that purpose we use logarithm base "3":
[tex]3^x=5\\x=log_3(5)[/tex]
In order to find this logarithm, we use the change of base formula:
[tex]log_3(5)=\frac{log(5)}{log(3)} =1.46497...[/tex]
which rounded to four decimals gives: 1.4650
What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the mean time to complete a tax form?
Answer:69
Step-by-step explanation:
Because i am smart.
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
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
A triangle undergoes a sequence of transformations. First the triangle is dilated by a scale factor of 1/3 about the orgin. The the triangle is reflected over the x axis. Finally, the triangle is translated left 3 units and up 2 units. How does the image triangle compare to the preimage triangle
Answer:
Since there was a dilation, the two triangles will be similar. The scale factor is less than one and is a reduction, therefore, the image will be smaller than the pre-image.
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.
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
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°.
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
4
4
Step-by-step explanation:
x litres of 15% solution + y litres of 19% solution= 8 gallons of 17% solution
disinfectant content of the final solution= 8*0.17= 1.36 gallons
0.15x+0.19y=1.36
x+y= 8 ⇒ x=8-y
0.15*(8-y)+0,19y= 1.361.2-0.15y+0.19y=1.360.04y=0.16y= 0.16/0.04y=4 gallonsx= 8-4= 4 gallonsWhat is the volume of the cylinder below?
O A. 70K units
O B. 2257, units
O C. 1757 units
O D. 357 units
Answer:
V = V = 175 pi units^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V =pi ( 5)^2 ( 7)
V = 175 pi units^3
Item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm
Answer:
Step-by-step explanation:
item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm
You did not state the diameter or radius of the window
so, i will use 90cm as the diameter of the window
First, I'd calculate the half circumference of the window.
The formula for circumference is [tex]c = 2\pi r[/tex],
Half of it would just be [tex]c/2 = r\pi[/tex]
Since our diameter is 90 cm, our radius is 45 cm.
Circumference =
[tex]=45\pi \\= 141.37 cm[/tex]
circumference is also the same with perimeter
so, the answer is 141.37cmto nearest tenth = 141.4cmAnswer:
141.4cm
Step-by-step explanation:
=>
please give barinlist
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 .☺️
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
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
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.
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.
divide a number line from 0 to 1 into 8 equal lengths. What should he label the first tick mark to the right of 0?
Answer:
1/8
Step-by-step explanation:
since it is divided to 8 equal parts then the first tick is 1/8
Is 1.06 greater than 0.6
Answer:
it is
Step-by-step explanation:
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
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:
Which of the following source documents is used to summarize all of the costs incurred for a specific job?
Answer:
job cost sheet.
Step-by-step explanation:
When planning or working on a specific project/job all the actual costs that are incurred for that job are written down in the job cost sheet. This report is an entire compilation that should be created by the accounting department and then distributed to all the members of the management department who then analyze it and determine whether the job was correctly bided. This sheet gets updated as the job is undergoing and fully completed when the job is closed.