Answer:
[tex]\dfrac{14}{29}[/tex]
Step-by-step explanation:
Let P(A) be the probability that goggle of type A is manufactured
P(B) be the probability that goggle of type B is manufactured
P(E) be the probability that a goggle is returned within 10 days of its purchase.
According to the question,
P(A) = 30%
P(B) = 70%
P(E/A) is the probability that a goggle is returned within 10 days of its purchase given that it was of type A.
P(E/B) is the probability that a goggle is returned within 10 days of its purchase given that it was of type B.
[tex]P(A \cap E)[/tex] will be the probability that a goggle is of type A and is returned within 10 days of its purchase.
[tex]P(B \cap E)[/tex] will be the probability that a goggle is of type B and is returned within 10 days of its purchase.
[tex]P(E \cap A) = P(A) \times P(E/A)[/tex]
[tex]P(E \cap A) = \dfrac{30}{100} \times \dfrac{5}{100}\\\Rightarrow P(E \cap A) = 1.5 \%[/tex]
[tex]P(E \cap B) = P(B) \times P(E/B)[/tex]
[tex]P(E \cap B) = \dfrac{70}{100} \times \dfrac{2}{100}\\\Rightarrow P(E \cap B) = 1.4 \%[/tex]
[tex]P(E) = 1.5 \% + 1.4 \% \\P(E) = 2.9\%[/tex]
If a goggle is returned within 10 days of its purchase, probability that it was of type B:
[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]
[tex]\Rightarrow \dfrac{1.4 \%}{2.9\%}\\\Rightarrow \dfrac{14}{29}[/tex]
So, the required probability is [tex]\dfrac{14}{29}.[/tex]
a cinema seats 280 people. if 98 people are in the cinema what percentage of seats are filled?
Answer:
35%
Step-by-step explanation:
The total number of cinema seats can seat 280 people. Since 98 people take up 98 seats of the cinema, they are taking up 98 cinema seats out of the 280 cinema seats originally available.
As a fraction this would be written as [tex]\frac{98}{280}[/tex] .
What you want to do is then divide 98 by 280 or 98/280, to get 0.35.
To get the percentage of seats filled, you must multiply the decimal you get by 100.
So it should look like this and your result should be 35%.
[tex]\frac{98}{280} = 0.35 *100=35[/tex]%
Which category is not one of the major responsibilities of state government?
A. Economic development
B. Corrections
C. Electrical power
D. Law enforcement
Answer: C electricity
Step-by-step explanation:
It is
In a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten," according to The NDP Group, the market-research company that conducted the poll. A researcher wonders if a smaller proportion of students at her university would respond in the same fashion. Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten. A statistician carries out a significance test of the null hypothesis that the proportion wanting to reduce gluten at the university is the same as for all adults versus the alternative hypothesis that a smaller proportion p of students would say they want to reduce or be free of gluten. What is the value of the standardized test statistic for this significance test? A) – 0.100 B) – 1.250 C) 0.200 D) – 1.091
Answer:
The value of the standardized test statistic for this significance test is -1.25.
Step-by-step explanation:
We are given that in a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten".
The researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten.
Let p = population proportion of students wanting to reduce gluten at the university.
So, Null Hypothesis, [tex]H_0[/tex] : p = 30% {means that the proportion wanting to reduce gluten at the university is the same as for all adults}
Alternate Hypothesis, [tex]H_A[/tex] : p < 30% {means that a smaller proportion of students would say they want to reduce or be free of gluten}
The test statistics that would be used here One-sample z test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of students who would say they want to reduce or be free of gluten = [tex]\frac{5}{25}[/tex] = 0.20
n = sample of students taken = 25
So, the test statistics = [tex]\frac{0.20-0.30}{\sqrt\frac{0.20(1-0.20)}{25} {} }[/tex]
= -1.25
The value of standardized z test statistic is -1.25.
Using the z-distribution, it is found that the value of the standardized test statistic for this significance test is:
D) –1.091
At the null hypothesis, we test if the proportion is of 0.3, that is:
[tex]H_0: p = 0.3[/tex]
At the alternative hypothesis, we test if the proportion is of less than 0.3, that is:
[tex]H_1: p < 0.3[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.3, n = 25, \overline{p} = \frac{5}{25} = 0.2[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.2 - 0.3}{\sqrt{\frac{0.3(0.7)}{25}}}[/tex]
[tex]z = -1.091[/tex]
A similar problem is given at https://brainly.com/question/24166849
Graph the equation y=x²-8x+7 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answer:
vertex is: (4,-9)
y intercept= (0,7)
roots= (1,0) and (7,0)
Step-by-step explanation:
so we can use factoring to solve this quadratic equation real quick:
x^2-7x-1x+7
x(x-7)
-1(x-7)
(x-1)(x-7)=0
x-1=0
x=1
x-7=0
x=7
(1,0) and (7,0) are the roots
axis of symmetry: 8/2=4
substitute axsis of symmetry in equation to get vertex:
4^2-8(4)+7
16-32+7
-16+7=-9
vertex is: (4,-9)
y intercept= (0,7)
roots= (1,0) and (7,0)
Hope this helps
Avicenna, a major insurance company, offers five-year life insurance policies to -65 year-olds. If the holder of one of these policies dies before the age of 70 , the company must pay out $24,200 to the beneficiary of the policy. Executives at Avicenna are considering offering these policies for $573 each. Suppose that for each holder of a policy there is a 2% chance that they will die before the age of and 70 a 98% chance they will live to the age of 70.
Answer:
The question is about the least amount to charge each policyholder as premium
The least premium is $484
Step-by-step explanation:
The least amount of premium to charge for this policy is the sum of the expected values of outcome of both instances of policyholder dying before the age of 70 and living after the age of 70 years
expected value of dying before 70 years=payout*probability=$24,200*2%=$484
Expected of living after 70=payout*probability=$0*98%=$0
sum of expected values=$484+$0=$484
Note that payout is nil if policyholder lives beyond 70 years
The premium of $573 means that a profit of $89 is recorded
Choose the correct answer.
1. What is the value of the 5
in 5,307?
A5,000
B 500
C 50
D 5
please help !!!!!
Answer:
A. 5,000 is the value.
Step-by-step explanation:
The 5 is in the thousands place.
Answer:
A
Step-by-step explanation:
It is in the thousands place
PLEASE HELP!! DUE!!!!
Write the slope-intercept form of an equation for the line that passes through the given point and is parallel to the graph of the given equation. (−5, 6) and 12x+9y=3
Answer:
The equation is,
[tex]y = - \frac{4}{3}x - \frac{2}{3} [/tex]
Step-by-step explanation:
When a line is parallel to the other line, they will have the same gradient :
[tex]12x + 9y = 3[/tex]
[tex]9y = - 12x + 3[/tex]
[tex]y = - \frac{12}{9} x + \frac{3}{9} [/tex]
[tex]y = - \frac{4}{3} x + \frac{1}{3} [/tex]
We have already found the gradient. Next, we have to substitute the gradient and coordinates into the slope-form equation, y = mx + b :
[tex]y = mx + b[/tex]
Let m = -4/3,
Let x = -5,
Let y = 6,
[tex]6 = - \frac{ 4}{3} ( - 5) + b[/tex]
[tex]6 = \frac{20}{3} + b[/tex]
[tex]b = 6 - \frac{20}{3} [/tex]
[tex]b = - \frac{2}{3} [/tex]
.A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. A typical Saturday morning shopper who does not participate in this program spends $120 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $130 on average during a recent Saturday, with standard deviation $40. Is this statistical proof that the shoppers participating in the loyalty program spent more on average than typical shoppers?a.State the null and the alternative hypotheses.b.Find the p-value of the test.
Answer:
a) Null hypothesis:[tex]\mu \leq 120[/tex]
Alternative hypothesis:[tex]\mu > 120[/tex]
b) [tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
The degrees of freedom are given by:
[tex] df = n-1 = 80-1=79[/tex]
The p value for this case taking in count the alternative hypothesis would be:
[tex]p_v =P(t_{79}>2.236)=0.0141[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=130[/tex] represent the sample mean for the amount spent each shopper
[tex]s=40[/tex] represent the sample standard deviation
[tex]n=80[/tex] sample size
[tex]\mu_o =120[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value f
Part a
We want to verify if the shoppers participating in the loyalty program spent more on average than typical shoppers, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 120[/tex]
Alternative hypothesis:[tex]\mu > 120[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
The degrees of freedom are given by:
[tex] df = n-1 = 80-1=79[/tex]
The p value for this case taking in count the alternative hypothesis would be:
[tex]p_v =P(t_{79}>2.236)=0.0141[/tex]
A bag contains 1 yellow, 2 blue, 4 green, and 3 red marbles. A marble is drawn and replaced. Then a
second marble is drawn.
Part A
What is P (blue, then blue)?
Part B
What is P (green, then red)?
Answer:
Step-by-step explanation:
total = 1 + 2 + 4 + 3 = 10
blue then blue = 2/10 * 2/10 = 1/5 * 1/5 = 1/25
green then red = 4/10 * 3/10 = 12/100 = 3/25
There were 3,342 students enrolled at a university of those students 587 graduated in may over the sumer 32 students left the university and 645 new students enrolled in the fall how many students were enrolled in the fall
Answer:
645
Step-by-step explanation:
it says 645 were inrolled in the fall
Math question please help
Answer:
y = -7x +8
Step-by-step explanation:
The slope-intercept form of the equation of a line is ...
y = mx +b
where m represents the slope, and b represents the y-intercept. The y-intercept is the value of y when x=0. Here, you have m=-7 and b=8. Your equation is ...
y = -7x +8
Write an equation of the line passing through the point A(2, 0) that is parallel to the line y = 3x−5
Answer:
y = 3x-6
Step-by-step explanation:
y = 3x−5
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
m =3
Parallel lines have the same slope
We have the slope m=3 and a point (2,0)
y = mx+b
y = 3x+b
Substituting the point into the equation to solve for b
0 = 3(2)+b
0 = 6+b
b = -6
y = 3x-6
Answer:
y = 3x - 6
Step-by-step explanation:
Parallel lines have the same slope,
So m = 3
y - 0 = 3(x - 2)
y = 3x - 6
S. Solve the following system of equations algebraically.
3x-y = 0
5x + 2y = 22
Part II: Combine the two equations to eliminate one of the variables. Show the result of this
combination below. (2 points)
Answer:
11x = 22(x, y) = (2, 6)Step-by-step explanation:
Twice the first equation can be added to the second to eliminate the variable y.
2(3x -y) +(5x +2y) = 2(0) +(22)
11x = 22 . . . . . . . the result of the combination
__
Solving this gives ...
x = 2
Substituting into the first equation gives ...
3(2) -y = 0
y = 6
The solution is (x, y) = (2, 6).
7.6 cm
3.7 cm
Find the area of the parallelogram.
Answer:
7cm²
Step-by-step explanation:
write the ratio 6.5 : 3.25 in the form n : 1
Answer:2:1
Step-by-step explanation:
6.5:3.25
6.5/3.25=2/1
6.5:3.25=2:1
therefore n=2
The amounts of money Gillian earned each week from babysitting are $5, 10, $20, $10, $15, $5, $42, $5. How is the mean of the data set affected when the outlier is removed?
Answer:
The mean will increase, after the outlier is removed.
Can someone plz help....!.!.!.!.!!.!.!.!.
Answer:
~ x = 12 centimeters of the route on map ~
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. We can see that we have to determine the cm of the route on the map, so let us convert the 1.8 kilometers ⇒ centimeters:
1.8 km = 180,000 cm
2. Given the information, let us create a proportionality as such:
1 = 15,000 ⇒ x - centimeters of the route on the map
x 180,000
3. Now let us cross multiply, and solve through simple algebra for x:
15,000 * x = 180,000,
x = 12 centimeters of the route on map
Idk what it is asking.
Answer:
Jumbo burger with fried is 75%
chicken with salad is 65%
Step-by-step explanation:
you first split the burger and sides. You add up the sides to find the salad. Then add up the sides and burgers
Answer:
What is the probability that he order a Jumbo Burger with Regular Fries or a Chicken Sandwich with a Salad? Make an area or tree diagram to help with the problem.
Answer to question: 20% for Jumbo Burger with Regular Fries and 10.5% for Chicken Sandwich with a Salad.
Step-by-step explanation:
You are going to find the probability that he order a Jumbo Burger with Regular Fries or a Chicken Sandwhich with a Salad by using a area model or a tree diagram. Although you ddin't ask me to solve it, I'm gonna help you with it anyways.
Sandwhiches:
50% - Jumbo Burger (JB)
30% - Chicken Sandwich (CS)
20% - Regular Burger (RB)
Sides:
40% - Curly Fries (CF)
35% - Salad (S)
25% - Regular Fries (RF)
Acronyms
Jumbo Burger (JB) + Curly Fries (CF) = JBCF
Jumbo Burger (JB) + Salad (S) = JBS
Jumbo Burger (JB) + Regular Fries (RF) = JBRF
Chicken Sandwich (CS) + Curly Fries (CF) = CSCF
Chicken Sandwich (CS) + Salad (S) = CSS
Chicken Sandwich (CS) + Regular Fries (RF) = CSRF
Regular Burger (RB) + Curly Fries (CF) = RBCF
Regular Burger (RB) + Salad (S) = RBS
Regular Burger (RB) + Regular Fries (RF) = RBRF
Probability of combinations:
JBCF = 0.5 x 0.4 = 0.20
JBS = 0.5 x 0.35 = 17.5
JBRF = 0.5 x 0.25 = 12.5
CSCF = 0.3 x 0.4 = 12
CSS = 0.3 x 0.35 = 10.5
CSRF = 0.3 x 0.25 = 7.5
RBCF = 0.2 x 0.4 = 8
RBS = 0.2 x 0.35 = 7
RBRF = 0.2 x 0.25 = 5
Your tree diagram should look something like this:
CF(40%)- outcome - JBCF (20%)
/
(50%)JB --- S(35%)- outcome - JBS (17.5%)
\
RF(25%)- outcome - JBRF (12.5%)
CF(40%)- outcome - CSCF (12%)
/
(30%)CS --- S(35%)- outcome - CSS (10.5%)
\
RF(25%)- outcome - CSRF (7.5%)
CF(40%)- outcome - RBCF (8%)
/
(20%)RB --- S(35%)- outcome - RBS (7%)
\
RF(25%)- outcome - RBRF (5%)
Hope this helps because this took forever :D
just need the first question
Answer:
[2,3)
Step-by-step explanation:
[0,1), [0,1),[0,1),[0,1)
[1,2), [1,2),[1,2),[1,2),[1,2),[1,2),[1,2),[1,2)
[2,3),[2,3),[2,3),[2,3),[2,3),[2,3),[2,3),[2,3),[2,3),[2,3),[2,3)
[3,4),[3,4),[3,4),[3,4),[3,4),[3,4),[3,4)
A tv programme begins at 7:45 and ends 50 minutes later what time does it finish
Answer:
8:35
Step-by-step explanation:
if u see every hour has 60 mins in it, so if u see 7:45 can be said as 7 hours and 49 mins
what u have to do is first add the mins, so add 45 and 50
45+50=95
every hour has 60 mins, so convert the mins to secs
95 mins=1hr35mins
and the 1hr35mins to 7:00
1hr35mins+7hr=8hr35mins or 8:35
A tv program begins at 7:45 and ends 50 minutes later the TV program ends at 8:35.
What is time?In math, time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.
We know that every hour has 60 minutes in it.
In 7:45 it has 7 hours and 45 minutes
The TV program duration is 50 minutes
So, 45+50=95
Now, 95 minutes has 1 hour 35 minutes
Add 1 hour 35 minutes to 7:00
That is, 7 hours + 1 hour 35 minutes
= 8 hours 35 minutes
Therefore, the TV program ends at 8:35.
Learn more about time here:
https://brainly.com/question/15356513.
#SPJ3
Sheila earns $8 per hour at her afterschool job. After working one week, she received a paycheck for $104. Write and solve an equation to find the number of hours Sheila worked. Fill in the blank with the solution only.
Answer:
13
Step-by-step explanation:
It should just be 104 divided by 8 which equals=13
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
answer would be A because it u factor it out you will get your initial equation
Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 20% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female.
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is_____.
P = Desired outcomes divided by the total outcomesm me
Answer:
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Prefers swimming on weekends.
Event B: Being female.
25% prefer swimming on weekends
This means that [tex]P(A) = 0.25[/tex]
It is found that 20% of the members in that city prefer swimming on weekends and are female
This means that [tex]P(A \cap B) = 0.2[/tex]
So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2}{0.25} = 0.8[/tex]
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.
What is the volume of a cylinder with a radius of 7.5 cm and a height of 20 cm
is 1 1/12 more than 1 1/3 ?
A driveway is 25 meters long how long the driveway in centimeters
Answer:
2500
Explanation : a meter is 100 centimeters long so you would multiply 25 by 100 to get 2500
Answer: 2,500 centimeters
Step-by-step-Explanation: To convert 25 meters into centimeters, we use the conversion factor for meters and centimeters
which is 100 centimeters = 1 meter.
Next, notice that we're converting from a larger unit, meters, to a smaller unit, centimeters and when we go from a larger unit to a smaller unit, we multiply by the conversion factor.
So we multiply 25 by the conversion factor, 100 which gives us 2,500.
So 25 meters = 2,500 centimeters.
Tyson wants to buy some juice pouches. He has four options to choose from.
Which option has the lowest cost per pouch?
O A 8 pouches for $2.04
O B 10 pouches for $2.69
O C 12 pouches for $2.80
O D 16 pouches for $3.80
Explanation:
x = number of pouches
y = cost for having x number of pouches
To find the unit cost, divide y over x
For choices A through D we have the following unit costs
y/x = 2.04/8 = 0.255y/x = 2.69/10 = 0.269y/x = 2.80/12 = 0.233 (approximately)y/x = 3.80/16 = 0.2375We see that 0.233 is the lowest unit cost, so therefore, Choice C is the lowest cost per pouch.
Raven is considering taking out a 30-year loan with monthly payments of
$145 at an APR of 1.3%, compounded monthly, and this equates to a loan of
$43,205.56. Assuming that the APR and the length of the loan remain fixed,
which of these is a correct statement?
Answer:
If Raven's monthly payment were $125, the amount of the loan that she is considering taking out would be less than $43,205.56.
Step-by-step explanation:
If you think about it this way it may be more simple. If the APR stays constant then a greater payment will result in a greater loan. The opposite is also true meaning a lesser payment will result in a lesser loan. If the amount Raven pays is greater than $145 then the loan will be greater than $43,205.56. If the amount she pays is less than $145 then the loan will be less than $43,205.56. Of the options, only one of these situations will be present. In my case, the correct option was a payment of $125 will result in a lesser loan than $43,205.56.
Answer:
If Raven's monthly payment were $125, the amount of the loan that she is considering taking out would be less than $43,205.56.
Step-by-step explanation:
Use the figure to find the measures of the numbered angles.
Answer:
Hope this helps pls mark brainliest
f(x)=-9x^2-2x and g(x)=-3x^2+6x-9, find (f-g)(x) and (f-g)(-4)
Answer:
(f - g)(x)= - 6 {x}^{2} - 8x + 9
(f - g)(-4!)= - 55
Step-by-step explanation:
[tex]f(x) = - 9 {x}^{2} - 2x, \: \: g(x) = - 3 {x}^{2} + 6x - 9 \\ (f - g)(x) = f(x) - g(x) \\ = - 9 {x}^{2} - 2x - (- 3 {x}^{2} + 6x - 9) \\ = - 9 {x}^{2} - 2x + 3 {x}^{2} - 6x + 9 \\ \purple{ \boxed{ \bold{(f - g)(x)= - 6 {x}^{2} - 8x + 9}}} \\ (f - g)( - 4)= - 6 {( -4 )}^{2} - 8( - 4) + 9 \\ = - 6 \times 16 + 32 + 9 \\ = - 96 + 41 \\ \red{ \boxed{ \bold{(f - g)( - 4)= - 55}}}[/tex]
