Answer:
Hence,
a) The probability that the sample average would be less than 90 pounds is 0.0210.
b) The probability that the sample average would be between 98 and 105 pounds is 0.5045.
c) The probability that the sample average would be less than 112 pounds is 0.9935.
d) The probability that the sample average would be between 93 and 96 pounds is 0.1341.
Step-by-step explanation:
a) [tex]P(X < 90) = P(Z < (90 - 99.9) / (30\sqrt(38)))[/tex]
= P(Z < -2.03) = 0.0210
b )[tex]P(98 < x <105) = P((98 -99.9) / (30 \sqrt(38)) < Z < (105 -99.9) / (30 \sqrt(38)))[/tex]
= P(-0.39 < Z < 1.05) = 0.5045
c ) [tex]P(X < 112) = P(Z < (112 - 99.9) / (30\sqrt(38)))[/tex]
= P(Z < 2.49) = 0.9935
d )[tex]P(93 < x < 96) = P((93 -99.9) / (30 \sqrt(38)) < Z < (96 -99.9) / (30 \sqrt(38)))[/tex]
= P( -1.42 < Z < -0.8 )
= 0.2119 - 0.0778 = 0.1341
A local church holds an annual raffle to raise money for a new roof. They sell only 500 tickets at $50 each. This year's prizes include: $3,000 in cash, four $100 Amazon gift cards, and two $75 Visa gift cards. You buy one ticket. What is your mathematical expectation for this game
Answer:
The expectation for an event with outcomes:
{x₁, x₂, ..., xₙ}
Each one with probability:
{p₁, p₂, ..., pₙ}
Is:
Ev = x₁*p₁ + ... + xₙ*pₙ
There are 500 tickets sold.
1 of these, wins $3,000 (this is the event x₁)
4 of these, wins $100 (this is the event x₂)
2 of these, wins $75 (this is the event x₃)
The others do not have a prize.
So the probability of winning the $3000 is equal to the quotient between the number of tickets with that prize (1) and the total number of tickets (500)
p₁ = 1/500
Similarly, the probability of winning $100 will be:
p₂ = 4/500
And for the $75 prize:
p₃ = 2/500
Then the probability of not winning is:
p₄ = 493/500
Then the expected value for a single ticket is:
Ev = $0*493/500 + $75*2/500 + $100*4/500 + $3000*1/500
Ev = $7.1
If you take in account that you pay $50 for the ticket, the actual expectation should be:
E = $7.10 - $50 = -$42.90
A test is worth 30 points. Multiple-choice questions are worth 2 point and short-answer questions are worth 3 points. If the test has 13 questions, how many multiple-choice questions are there?
A son is 8 years old. his father is 5 times as old. How old will the father be when he is twice as old as his son?
2067 Supp Q.No. 2a Find the sum of all the natural numbers between 1 and 100 which are divisible by 5. Ans: 1050
5
Answer:
1050
Step-by-step explanation:
Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.
There is a easier method.
E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference
Back to the problem, we can use the sum of arithmetic series formula,
[tex]y = x( \frac{z {}^{1} + {z}^{n} }{2} )[/tex]
Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms
The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.
[tex]y = 20( \frac{5 + 100}{2} )[/tex]
[tex]y = 20( \frac{105}{2} )[/tex]
[tex]y = 1050[/tex]
Simplify expression 1 1/2
Answer:
3/2 or 1.5
Step-by-step explanation:
Hey there!
[tex]\huge\boxed{\mathsf{1\dfrac{1}{2}}}}\\\huge\boxed{\mathsf{\rightarrow \dfrac{1\times1+2}{2}}}\\\\\\\huge\boxed{{1\times1+2}}\\\huge\boxed{= 1+2}\\\huge\boxed{=3}\\\\\\\huge\boxed{\rightarrow \mathsf{\dfrac{3}{2}}}\\\\\\\huge\boxed{\textsf{Answer: }\bf \dfrac{3}{2}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
One time Maria took 27 minutes to walk 1.8km to school. She left home at 07:48 . Write down the time Maria arrived at school
Answer:
8:15
Step-by-step explanation:
Find the value of x to the nearest tenth of a degree.
20.4
21.8
42.9
68.2
Answer:
Answer is 20.4 .........
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
D. 72 heads in 100 flips
Step-by-step explanation:
A probability calculator will tell you the probabilities of the given outcome with a fair coin are ...
A: 0.0625
B: 0.04395
C: 0.15498
D: 3.9×10^-6
__
It is "improbable" that a fair coin will give 72 heads in 100 flips. So, it is reasonable to assume the coin is not fair if that is the result.
find the intercept and graph the following linear equations: 2x+y=1
plz include x and y intercepts
Answer:
2(1)+y =1 for × intercept
2x+(1)=1 for y intercept
WILL MARK BRAINLIEST PLEASE SHOW WORK :)
Answer:
(1). A = 18 cm² ; (2). TR = 18 units
Step-by-step explanation:
E
Homework: Practice
Exam 3
Question 7
Find the standard deviation for the group of data items.
14, 15, 16, 16, 17, 18
The standard deviation is
(Simplify your answer. Round to two decimal places as needed.)
9
Answer:
Step-by-step explanation:
Solve for x.
2(3x - 7) = 16
Simplify your answer as much as possible.
X =
Answer:
x = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
2(3x - 7) = 16
Step 2: Solve for x
[Division Property of Equality] Divide 2 on both sides: 3x - 7 = 8[Addition Property of Equality] Add 7 on both sides: 3x = 15[Division Property of Equality] Divide 3 on both sides: x = 5Answer:
X=5
Step-by-step explanation:
divide by 2 on both sides first then you have
3x-7 = 8
take 7 to the other side so that you have an X factor on one side, thus
3x =15
then divide by 3 to remain with X
X = 5
If one big rectangle represents one whole what fraction of area is shaded gold in the two rectangle
Answer:
15/8
Step-by-step explanation:
one big rectangle is 1 or 8/8 and the other is 7 out of 8, therefore we have 8/8+7/8 = 15/8.
Can someone help me ASAP!!!?
Answer:
√x-x-2x³+√x+x
= 2√x-2x³
= -2x³+2√x
which is option A
Adam runs 13 miles in 143 minutes. How many minutes does it take him to run one mile? Adam runs at a rate of minutes per mile.
Answer:
Adam runs at a rate of 11 minutes per mile.
Step-by-step explanation:
Take 143 minutes and divide by 13 miles and you will get the answer of 11 minutes.
PLEASE MARK ME BRAINEIST.
Answer:
it would take him 11 minuets to run a mile
Step-by-step
143 divided by 13 is 11 which means each mile takes 11
you can also check the answer by multiplying 13 times 11 which is 143
The Demand function for a product is given by:
D(q) = - 0.0003q^2 - 0.04q + 23.56
where q is the number of units sold and D(q) is the corresponding price per unit, in dollars. What is the average rate of change of Demand between 40 and 175 units sold?
Answer:
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Step-by-step explanation:
Average rate of change:
The average rate of a function f(x) in an interval [a,b] is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]D(q) = -0.0003q^2 - 0.04q + 23.56[/tex]
What is the average rate of change of Demand between 40 and 175 units sold?
[tex]a = 40, b = 175[/tex]. So
[tex]D(40) = -0.0003*40^2 - 0.04*40 + 23.56 = 21.48[/tex]
[tex]D(175) = -0.0003*175^2 - 0.04*175 + 23.56 = 7.3725[/tex]
So
[tex]A = \frac{f(b) - f(a)}{b - a} = \frac{7.3725 - 21.48}{175 - 40} = -0.1045[/tex]
The average rate of change of Demand between 40 and 175 units sold is of -0.1045.
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.74. (a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to
Answer:
The answer is "(4.518, 5.182)"
Step-by-step explanation:
[tex]\sigma = 0.74[/tex]
The aveage porosity for a sample of [tex]n = 19[/tex] specimens is
[tex]\bar{x}=4.85[/tex]
Thus, the[tex]95\%[/tex] confidence interval for the true mean is
[tex]=\bar{x}\pm Z_{\frac{0.05}{2}} \frac{\sigma}{\sqrt{n}}\\\\=4.85\pm 1.96 \frac{0.74}{\sqrt{19}}\\\\=4.85\pm 0.332\\\\=(4.518, 5.182)[/tex]
Therefore, one can state that the true average porosity will lie between 4.518 and 5.182 with the 95\% confidence.
A California distributor of sporting equipment expects to sell 10,000 cases of tennis balls during the coming year at a steady rate. Yearly carrying costs (to be computed on the average number of cases in stock during the year) are $10 per case, and the cost of placing an order with the manufacturer is $45. Determine the economic order quantity, that is, the order quantity that minimizes the inventory cost.
The economic order quantity is 300 cases of tennis balls.
The economic order quantity (EOQ) is the minimum quantity that the distributor can order per order to minimize inventory costs.
Data and Calculations:
Sales of tennis balls for the coming year = 10,000 units
Carrying (holding) costs per case = $10
Cost of placing orders with the manufacturer = $45 per order
Economic Order Quantity (EOQ) = square root of (2 * Annual Demand/Sales * Ordering cost)/Carrying cost per case
= square root of (2 * 10,000 * $45)/$10
= square root of 90,000
= 300 cases of tennis balls
This implies that the distributor will place about 33 orders (10,000/300) in the coming year. With each order, the quantity placed is 300 units.
Thus, the economic order quantity that will minimize the California distributor's inventory costs for the year is 300 cases of tennis balls.
Learn more about economic order quantity here: https://brainly.com/question/9068415
whats the value of 5 in the product of 6,541 x 100
Answer:
50,000
Step-by-step explanation:
The product would be 654,100. Replace the other numbers to find the value of 5. The value of 5 is 050,000 or 50,000.
I hope this helps!
Help me please! thanks
9514 1404 393
Answer:
5. (a) Polygon Angle-Sum Theorem
6. (c) 360°
Step-by-step explanation:
5. The sum of the angles is shown as 540°. The theorem that tells you the sum of angles in an n-gon is the "polygon angle sum theorem."
__
6. The sum of exterior angles around any (convex) polygon is 360°. (This is where the angle-sum theorem comes from.)
we make a sequence of figures with tiles. The first four figures have 1,4,7 and 10 tiles, respectively. How many tiles will the 15th figure have?
Answer:
43
Step-by-step explanation:
1 , 4 , 7 , 10
→ Find the difference between each term
4 - 1 = 3, 7 - 4 = 3 and 10 - 7 = 3
→ Put this into the nth term format
3n + x
→ Write the 3 times tables above the sequence and find what you need to take away from the times tables to get to the sequence
3 , 6 , 9 , 12
1 , 4 , 7 , 10
→ Minus 2
3n - 2
→ Substitute 15 as n
3 × 15 - 2 = 43
(3x - 2)^5 =(3x - 2)^2
Answer:
x=3/2,1
Step-by-step explanation:Given
(3x-2)ˆ5-(3x-2)ˆ2=0
(3x-2)ˆ3(3x-2)ˆ2-(3x-2)ˆ2=0
(3x-2)ˆ2{(3x-2)ˆ3-1}=0
(3x-2)ˆ2=0 Or (3x-2)ˆ3-1=0
3x-2=0 Or(3x-2)ˆ3=1
x=3/2 Or 3x-2=1, x=1
what is the value of tan 0 in the unit circle below? (square root3/2,1/2)
Answer:
√3/3
Step-by-step explanation:
To obtain Tan θ ;
From trigonometry, tan θ = sin θ / cosθ
Given the paired value : (√3/2, 1/2)
The (cosine, sine ) pair ;
Tan θ = sin (1/2) / cos (√3/2)
Tan θ = (1/2 ÷ √3 / 2) = 1 / 2 * 2 / √3 = 2 / 2√3 = 1 / √3
Tan θ = 1 / √3
Rationlaizing the denominator :
1/√3 * √3/ √3 = √3/√9 = √3/3
find two ordered pairs for x-4y=2
Answer:
x-4y=2 can be written as y=(x-2)/4
(2,0) when x=2, y=0 and (6,1) when x=6, y=1
Question 24 of 58
Four classmates collect data by conducting a poll. They
ask students chosen at random how many books they
have to read for English class.
• Kevin interviews 25 students.
• Mary interviews 92 students.
• Sydney interviews 24 students.
• Caleb interviews 31 students.
Whose results are probably the most trustworthy?
O A. Mary's
OB. Sydney's
C. Kevin's
D. Caleb's
SUBMIT
Write the standard form of the equation of the circle with radius 3 and center (−4,−10)
Answer:
(x + 4)² + (y + 10)² = 9
Step-by-step explanation:
The standard equation of a circle is written as seen below
(x - h)² + (y - k)² = r²
Where (h,k) is at the center and r is the radius
We want to find the standard equation of a circle that has a radius of 3 and a center at (-4,-10)
Remember r = radius so r = 3
and (h,k) is at center so h = -4 and k = -10
Now to find the standard equation of the circle we simply plug in the values of the variables (h,k and r) into the standard equation of a circle formula.
Equation of a circle: (x - h)² + (y - k)² = r²
r = 3, h = -4 and k = -10
Plug in values
(x - (-4))² + (y - (-10))² = 3²
Simplify
(x + 4)² + (y + 10)² = 9
And we are done!
A football team is currently number 19 in overall offence. They have gotten 1,940 yards, while the number one
offence has received 2,728 yards. They've both played four games. How many more yards per game is the top
team receiving?
Answer:
20
that's grbrhrhbrhshsheheehebbebdbshwjwwmkwkw
Answer:
197 yards per game
Step-by-step explanation:
divide both values by 4 and subtract the value of the losing team from the value of the winning team to get your answer.
The manager of a movie theater is standing outside the theater complex one evening. He will be asking the moviegoers questions.
Which questions can the manager ask that will result in discrete quantitative data? Check all that apply.
What movie did you just see?
What genre of movie is your favorite?
How much did you spend at the movies today?
Did you order anything from the concession stand?
Answer:
It's How much did you spend at the movies today?
Step-by-step explanation:
The question can the manager asks "How much did you spend at the movies today?". Then the correct option is C.
What is discrete quantitative data?A discrete quantitative parameter has a clear mathematical explanation but could only take certain integer values (instead of every value in intervals).
The manager of a movie theater is standing outside the theater complex one evening.
He will be asking the moviegoers questions.
Then the questions can the manager ask that will result in discrete quantitative data will be
How much did you spend at the movies today?
The question can the manager asks "How much did you spend at the movies today?"
Then the correct option is C.
More about the discrete quantitative data link is given below.
https://brainly.com/question/12831013
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A patient consumes 2,000 calories of which 1200 calories were from carbohydrates. What percent of calories were from carbohydrates? Round the answer to the nearest integer.
Answer:
60%
Step-by-step explanation:
1200/2000=.6 or 60%
60%of calories were from carbohydrates.
What is percentage?a relative value that represents one tenth of any amount. One percent (symbolized as 1%) is equal to 100 parts; hence, 100 percent denotes the complete amount, and 200 percent designates double the amount specified. percentage. Percentile in mathematics is a related topic.
Given
1200/2000=.6 or 60%
Hence, 60%of calories were from carbohydrates.
To learn more about percentage refer to:
https://brainly.com/question/843074
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What is the inverse of the function g (x) = 5 (x - 2)
Answer:
g − 1 ( x ) = x/ 5 + 2
Step-by-step explanation:
See the pic for solutions :)
