Answer:
0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6.
This means that [tex]\mu = 30, \sigma = 6[/tex]
5 consecutive weekdays.
This means that [tex]n = 5, s = \frac{6}{\sqrt{5}} = 2.6832[/tex]
What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?
This is 1 subtracted by the pvalue of Z when X = 35.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 30}{2.6832}[/tex]
[tex]Z = 1.86[/tex]
[tex]Z = 1.86[/tex] has a pvalue of 0.9686
1 - 0.9686 = 0.0314
0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount
Verify the identity.
Please show your work.
Step-by-step explanation:
To prove :
( 1 - sin x ) ( 1 + sin x ) = sec² x
LHS : -
( 1 - sin x ) ( 1 + sin x )
Formula / Identity : -
( a - b ) ( a + b ) = a² - b²
Here,
a = 1
b = sin x
( 1 - sin x ) ( 1 + sin x )
= 1 - sin² x
Identify : -
sin² θ + cos² θ = 1
cos² θ = 1 - sin² θ
Similarly,
1 - sin² x
= cos² x
= RHS
Hence verified.
The deer population at the local reserve grows exponentially. The current population is 125 deer and the relative growth rate is 16% per year. Find the number of years required for the deer population to be 400.
Answer:
About 7.84 years before the deer population is 400
Step-by-step explanation:
So first we write our equation
125(1.16)^x = 400
Then we divide all sides by 125
1.16^x=3.2
x log 1.16 = log 3.2
06445798922x=0.50514997832
x= 7.83688700862
7.83688700862 years to go!
Liz has 4 times as many points as Joey in a video game. Together they have fewer than 150 points. Which inequality can be used to determine the least number of points that Joey can have?
A. 4x+4<150
B. 4x+4≤ 100
C. 4x+x<150
D.4x+x≥150
I will select u as brilliant :)
Answer:
C. 4x + x < 150
Step-by-step explanation:
x = Joey's points
4x = Liz's Points
together they have fewer than 150 points means the inequality is < 150
So the answer is: 4x + x < 150
Answer:
This may help you I think so
Somebody please help me. This is geometry. The goal is to find the missing side with A similarity statement. But the more I try on this, it becomes more confusing. Please help. Thx.
Answer:
50Step-by-step explanation:
Given:
qrst ~ nkpmThe ratio of corresponding sides (consider the order of letters in the name of figures):
rs/ kp = qt / nmrs / 35 = 60 / 42rs = 35*60/42rs = 50Answer:
Solution given:
qrst~nkpm
since the side of similar quadrilateral are proportional so
qt/mn=rs/kp
60/42=?/35
?=60/42×35=50
missing side =50 is your answer
1. I need some help
2. Answer question step by step
3. Dont Troll or you will be reported
Answer:
The shapes are triangles with same base and height
The area of a triangle is the half of the product of the base and height
A = 1/2bh is same for both shapes, so they have same area
Amy and Sara's ages are consecutive even integers. The product of their ages is 528. If Sara is
younger, how old is Amy?
Write an equation that can be used to find their ages.
Answer:
24
Step-by-step explanation:
Sara = x age
Amy = x+2 when Sara x = 22 Amy is x + 2 = 24
Product of ages = 528 so............
x(x+2) = 528
x² + 2x - 528 = 0 solve for x I did it graphically first to get x = -24, 22
(x+24) (x-22) = 0
(x+24) = 0 (x-22) = 0
x = -24 x = 22 since you really can't have a negative age
5647+34566= please hurry and answer don't put the answer in a link
Answer:
40213........................
Answer:
5647+34566=40213 is your answer
Which of the following is equal to / 9.4
A lumberyard charges $ 1 per cut to trim boards. Bob buys a 12-ft board and wants it out into twelve 1-ft pieces. How much will he be charged for the cutting? The correct answer is $11.
Answer:11
Step-by-step explanation:
There are 11 cuts to make 12 pieces on 1ft each
Giving Brainlest !!!!! If your bank offered you 3% interest on $5,000 in your savings account , how much money would you have in your account at the end of the year after interest ?
Answer: $5,150
Step-by-step explanation:
5000x0.03=150+5000=5,150
Martin can travel 174 miles in 3 hours. At this rate, how far can he travel in 7 hours?
325 miles
398 miles
400 miles
406 miles
Answer: 406 miles
Step-by-step explanation: First you have to figure out how many miles he traveles per hour and to do that you divide 174 by 3 to get 58. Then multiply that by 7 because that is the amount of hours he should be traveling to get 406
Answer:
406 miles
Step-by-step explanation:
First find how far Martin can travel in 1 hour, then multiply by 7(hours):
174 ÷ 3 = 58
58 × 7 = 406
The researchers chilled the beverages to 6°C. Participants drank the beverages at the same time each day for three days. During the 3 days of the experiment, the researchers feed each participant the same diet. On the third day participants spent 24 hours in a calorimeter chamber to measure their energy metabolism. The medical journal Obesity published the results in 2007. What is the purpose of double-blinding?
a. To control unintentional researcher bias in the execution of the experiment
b. To control for the participants' prior beliefs about energy drinks
c. To control both unintentional research bias and participant prior beliefs
Answer:
C. To control both unintentional research bias and participant prior beliefs
Step-by-step explanation:
Double blinding is a type of study where neither the participants nor the researchers know the treatment or intervention that the participants receive until the whole study/research is completed. This is very important because it means that the results gotten from the study have a very slim chance of being biased.
Thus,the correct answer is option C as it includes both the researcher and the participants
Beth wants to buy Christmas lights to decorate her new home. At various stores, Beth found lights priced from $6.99 a strand to $25.99 a strand. Beth bought almost $200 worth of the cheapest lights so that she could have as many lights on her house as possible. For Beth, Christmas lights are a(n) _____.
Answer:
Christmas lights are price based shopping products
Step-by-step explanation:
From the question we understand that, Beth bought as many cheapest lights as possible. This means that she places value over quantity than quality.
The above is an illustration of price based shopping products where customers (in this case, Beth) see all products (in this case, Christmas lights) as similar products, irrespective of their different qualities (after all, they all light Christmas trees).
Because of this, the customer will opt for least expensive items, leaving the more expensive items.
at a high school, there are 3,510 students. the ratio of seniors to juniors to sophomores to freshmen is 4:6:5:3. How many students are in each class
Answer:
seniors: 780
juniors: 1170
sophomores: 975
freshmen: 585
Step-by-step explanation:
4 + 6 + 5 + 3 = 18
3510/18 = 195
195(4) = 780
195(6) = 1170
195(5) = 975
195(3) = 585
A company manufacturing a roadside lighting system wants to estimate the average illuminance (brightness) at sunset. The illuminance at sunset for the past 10 days was as follows: 406, 385, 389, 383, 352, 379, 388, 343, 368, 387 lux. Construct a 95% confidence intervals for the average illuminance at sunset. Assume that the illuminance at sunset is approximately normally distributed.
Answer:
(364.595 ; 391.405)
Step-by-step explanation:
Given the sample data:
406, 385, 389, 383, 352, 379, 388, 343, 368, 387
Using calculator :
Sample mean, xbar = 378
Standard deviation, s = 18.74
Confidence interval :
Xbar ± Margin of error
Margin of Error = Tcritical * s/√n
TCritical at df = 24 ; 0.05 = 2.262
Margin of Error = 2.262 * 18.74/√10 = 13.405
Lower boundary = (378 - 13.405) = 364.595
Upper boundary = (378 + 13.405) = 391.405
(364.595 ; 391.405)
Directions: Evaluate the following combinations and determine the value of the
unknown. Write the complete solutions in your answer sheet.
1. nCs = 126
2. 10Cr= 252
3. C(n, 5) + 8 = 9
4. C(n+1, 7) = 01
5. C(6r, 6-1) = 12 + C(4,2)
what is the answer with solution po
Answer:
1. C(9,4) : n=9, s=4
2. C(10,5) : r=5
3. C(5,5) : n=5
4. C(7,7) : n=6
5. C(18,17) : r=3
Step-by-step explanation:
In a swimming competition, Peter swam 600m and Gabriel swam 2km .What is the ratio of Peter’s distance to Gabriel’s? Give your answer in its simplest form.
b. Express the ratio 20cm to 15m in the form 1: n
c. Express the ratio 60 cm to 20 m in the form 1 : n
Answer:
Yes, because Gabriel is the swimming. He was in 2nd or maybe 10th.
Answer:
Step-by-step explanation:
HELP MEEEE PLEASEEEEEE
Answer:
The area of the circle is 27
Step-by-step explanation:
Using the formula given to us, we know that the area of the circle = pi times the radius squared. This gives us an indication of what we need to do. We must first understand that the radius of the circle is 3. Multiply the radius by the 2nd power (multiply 3 by 3), and we get 9. They then ask us to substitute 3 for pi, meaning instead of pi times 9, it's 3 times nine, and 3*9=27. And there is your answer.
PLEASE HELP ASAP ???
Answer:
-1
Step-by-step explanation:
4 more than 5 times a number
Answer:
5x + 4
Step-by-step explanation:
4 more = +4
5 times a number = 5x
Violet is making pizzas for a pizza party. Each pizza requires 5/16 pound of cheese. How many pounds of cheese does she need to make 11 pizzas? Express your answer in simplest form.
1,000 meters is the same as 1
It is equal to 1 kilometer
Please mark brainliest
Please help!!! ABCD is a square with diagonals intersecting at E. What is the length of BE
Answer:
[tex]BE = 4\sqrt2[/tex]
Step-by-step explanation:
Given
The attached square
Required
Find BE
First, we calculate BD (the diagonal) using Pythagoras theorem.
[tex]BD^2 = BA^2 + AD^2[/tex]
Since the shape is a square, then
[tex]BA = AD = 8[/tex]
So:
[tex]BD^2 = 8^2 + 8^2[/tex]
[tex]BD^2 = 2(8^2)[/tex]
Take square roots
[tex]BD = \sqrt{2(8^2)[/tex]
[tex]BD = \sqrt{2} * 8[/tex]
[tex]BD = 8\sqrt{2}[/tex]
BE is half BD.
So:
[tex]BE = \frac{1}{2} * BD[/tex]
[tex]BE = \frac{1}{2} * 8\sqrt2[/tex]
[tex]BE = 4\sqrt2[/tex]
Dave's Candy Store is having a 15% off sale on gourmet candy. Jamal paid $37.40 for a gourmet candy basket that was on sale. What was the original price of the candy basket?
The original price of the gourmet candy is $44, as per linear equation.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."
Given, the percent of discount at Dave's candy store is 15% = 0.15.
Sale price of a gourmet candy is $37.40.
Let, the original price of the gourmet candy is x.
Therefore, [x - (x × 0.15)] = 37.40
⇒ (x - 0.15x) = 37.40
⇒ 0.85x = 37.40
⇒ x = (37.40/0.85)
⇒ x = 44
Therefore, the original price of the gourmet candy is $44.
Learn more about a linear equation here: brainly.com/question/2984088
#SPJ2
If cos theta =12/13.find 1+cot theta
Answer:
17/5
Step-by-step explanation:
If cosθ = 12/13, find (1+cotθ)
As shown in the diagram attached,
Cotθ = 1/tanθ = adjacent/opposite
From the diagram attached,
cotθ = 12/a................... Equation 1
But we can find the value of a by using pythagoras theorem
13² = 12²+a²
169 = 144+a²
a² = 169-144
a² = 25
a = √25
a = 5.
Substitute the value of a into equation 1
Therefore,
cotθ = 12/5
(1+cotθ) =(12/5)+1 = (5+12)/5
(1+cotθ) = 17/5
6:45 + 85
No links pls
so first you wanna break down the 85 minutes so 1 hour is 60 minues now its 7:45 but we still have 25 minutes left sow now we add the minutes it will be 8:05
8:05 is the answer
Answer:
Step-by-step explanation:
A gym offers classes for students to attend. If both the range and median number of students attending each class was 13 students, which of the following box-and-whisker plots could represent the number of students attending the classes?
Answer:
3
one
will represent
the student
Question 18 (5 points)
If two lines are perpendicular to the same line, then they are
to each other.
A) congruent
B) perpendicular
C) parallel
D) complementary
Plss help mark brain list a lot of point
Answer:
arc TQ= 69° (44 + 25)
arc QR = 155° (180 - 25)
arc TS = 111° (360 - 44 - 25 - 155 - 25)
arc SQR = 335° (360 - 25)
arc RQT = 224° (155 + 25 + 44)
Pleaseeeee help!!! I’ll give you best answer!!!!
Solve the equation with the quadratic formula *
10) 3x² =-10x – 5
1-5+2V10 -5 - 2V10
A)
3
3
-5+ V10 -5 - V10
B)
3
3
25
C) -4
4
15+ V10 5 - V10
D)
33
Answer:
B) x = (-5 + √10)/3 and (-5 - √10)/3 is the answer.
Step-by-step explanation:
3x² + 10x + 5 = 0
a = 3
b = 10
c = 5
Finding the Discriminant (D),
D = b² - 4ac
D = 10² - 4 × 3 × 5
D = 100 - 60
D = 40
√D = 2√10
Using quadratic formula,
x = (-b ± √D)/2a
x = (-b + √D)/2a
x = (-10 + 2√10)/2 × 3
Taking out the common factor 2,
x = (-5 + √10)/3
Similarly,
x = (-b - √D)/2a
x = (-10 - 2√10)/2 × 3
x = (-5 - √10)/3
Answer:
[tex]\huge \red {\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}[/tex]
Step-by-step explanation:
[tex]3 {x}^{2} = - 10x - 5 \\ 3 {x}^{2} + 10x + 5 = 0 \\ equating \: it \: with \\ a {x}^{2} + bx + c = 0 \\ a = 3 \: \: b = 10 \: \: c = 5 \\ now \: by \: quadratic \: formula \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ plug \: a = 3 \: \: b = 10 \: \: c = 5 \: in \: the \\ above \: formula \\ x = \frac{ - 10 \pm \sqrt{ {(10)}^{2} - 4(3)(5) }}{2 \times 3} \\ x = \frac{ - 10 \pm \sqrt{ {100} - 60}}{6} \\ x = \frac{ - 10 \pm \sqrt{40}}{6} \\ x = \frac{ - 10 \pm2 \sqrt{10}}{6} \\ x = \frac{ 2(- 5 \pm \sqrt{10})}{6} \\ x = \frac{ - 5 \pm \sqrt{10}}{3} \\ x = \purple{ \bold{\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}}[/tex]