Using the normal distribution and the central limit theorem, it is found that his risk is of 0.0456.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 20 ounces and standard deviation of 2 ounces, hence [tex]\mu = 20, \sigma = 2[/tex].Sample of 4 packages, hence [tex]n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]The risk is the probability of being more than 2 ounces from the mean, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Applying the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2}{1}[/tex]
[tex]Z = 2[/tex]
The risk is P(|Z| > 2), which is 2 multiplied by the p-value of Z = -2.
Looking at the z-table, Z = -2 has a p-value of 0.0228.0.0228 x 2 = 0.0456
The risk is of 0.0456.
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The sum of two numbers is x . If one of the numbers is 12, what is the other?
Answer:
x - 12
Step-by-step explanation:
Given
12 + ? = x ( subtract 12 from both sides )
? = x - 12
The other number is x - 12
the diameter of an iron ball used in putting the hot is 12cm the density of the iron is 7.89/cm3 calculate the mass of the ball in kg
Answer:
Step-by-step explanation:
radius r of iron ball r=12/2=6 cm
volume of iron ball=4/3 πr³
=4/3π×6³
=288 π cm³
≈288×3.14
=904.32 cm³
density=7.89gm /cm³(unit not mentioned)
mass of iron ball=904.32×7.89=7135.0848 gm.=7.135 kg
288π×7.89≈7138.703 ≈7.139 kg (if density is 7.89 gm/cm³)
I need help with finding the slope.
Answer:
The slope is -2
Step-by-step explanation:
24+18a=
help i can not get the answer
Devon's father is installing new wood flooring. He bought boards that are 10 ft long, 3/4 in. thick, and 11/24 in. wide. Determine the number of boards Devon's father will need for a 10 ft by 16 1/2 ft room. Plz plz help and the way to solve it plz!!!
Answer:
36 boards
Step-by-step explanation:
The boards are as long as the room, so I only had to worry about the width. If the boards were 1/2 ft wide, I would need 2 boards for every foot of width. For 16 ft, I would need 32 boards.
Instead of dividing, I wrote the equivalent multiplication by multiplying by the reciprocal of 11/24 (the reciprocal of 11/24 is 24/11)
I simplified by dividing both 2 and 24 by 2, and both 11 and 33 by 11.
Therefore he needs 36 boards
help lol
The FOIL method helps you remember how to multiply each term in one ____________ by each term in the other ____________.
The FOIL method helps you remember how to multiply each term in one binomial by each term in the other binomial.
What is FOIL method?FOIL is the standard method of multiplying two binomials.
The word FOIL is an acronym for the four terms of the product:
First (“first” terms of each binomial are multiplied together)Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second)Inner (“inside” terms are multiplied—second term of the first binomial and first term of the second)Last (“last” terms of each binomial are multiplied)We try to explain this using an example.
[tex]= (2x+1)(3x+ 5)\\\\=(2x * 3x) + (2x * 5) + (1* 3x) + (1 *5)\\\\= 6x^{2} + 10x + 3x + 5\\\\= 6x^{2} + 13x + 5[/tex]
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Item 3 Solve. 7 2/5=2/3x−4 1/2 Enter your answer as a mixed number in simplest form in the box.
The simplified form of the expression 7 ²/₅ = (2/3) x - 4 ¹/₂ for the value of x is 357/20 or 17.85.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
7 ²/₅ = (2/3) x - 4 ¹/₂
Simplify the expression,
37/5 = (2/3)x - 9/2
37/5 + 9/2 = (2/3)x
(74 + 45) / 10 = (2/3)x
119 / 10 = (2/3)x
357/20 = x
x = 357 / 20
x = 17.85
The simplest form for the value of x, of the given expression, is 357 / 20.
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how many times does 15 go into 142 please no links thank you 71 points
Answer 15 and 16 and get 50 points
No link
Answer:
(1) x=5 (2) I think the answer to 16 is 3/5 but not 100% sure
Step-by-step explanation:
(1) 29=5x+4
Step 1: Flip the equation.
5x+4=29
Step 2: Subtract 4 from both sides.
5x+4−4=29−4
5x=25
Step 3: Divide both sides by 5.
5x /5 = 25 /5
x=5
5. Write the following numbers in order from least to greatest. 1.23; 1.2; 2.31; 3.2
Petra jogs 3 miles in 30 minutes. At this rate, how long would it take her to jog 13 miles?
Answer:
390 minutes I do believe.
Step-by-step explanation:
Find the distance between the points (
–
9.5,4.1) and (2.7,4.1).
Answer:
Step-by-step explanation:
Distance formula: [tex]d=\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}[/tex]
[tex]d=\sqrt{(4.1-4.1)^{2}+(2.7-9.5)^{2}}=\sqrt{(-6.8)^{2}} = 6.8[/tex]
Note that distance is always positive
Twelve football teams are playing in a league. Each team played each of the other teams exactly once. How many matches were played in the league? *
1 point
a. 72
b. 66
c. 11
d. 132
Each team will play with 11 other teams. Hence each team plays 11 games. Hence a total of 11*12 =132 games but since each game involves two teams divide 132/2 = 66 so B
Seven less than one-third a number is greater than six more than one-fourth the
number.
Answer:
The number is 60
Step-by-step explanation:
Find the distance between the points (13, 20) and (18, 8).
13
7
11
Answer: 13
Step-by-step explanation:
See attached graph.
A third point (18,20) may be added to the two given points to form a right triangle with sides 5 and 12. The distance, x, between the original two points is given by x^2 = 5^2 + 12^2
x^2 = 25 + 144
X^2 = 169
x = 13
Solve 6(x - 3) + 7 = -5.
The answer will be:- x = 1
Laura is training to run a race. She keeps track of the number of miles she runs. She has been training for 5 weeks, and she has run a total
of 40 miles. At what rate has she been running, in miles per week?
Answer:
8 miles per week!
Step-by-step explanation:
40 miles / 5 weeks = 8!
so it would be 8 miles per week.
i hope this helps!!
Solve for x then y.
y+10=-1/6(x-6)
Answer:
y= -x/6-9
x= -6y-54
Step-by-step explanation:
I need help on two questions here’s the first one!
Antawn wrote a decimal. The value of the 8 in Antawn’s decimal is equal to 8 x 1/10. Which of the following numbers could be Antawn’s decimal?
A. 86.05
B. 68.05
C. 60.85
D. 60.58
Here’s the second question!
Brooklyn rode her bike a total of 75.8 miles in 3 days. She rode 25.2 miles on Friday and 16.9 miles on Saturday. How many miles does she ride her bike on Sunday?
A. 33.7
B. 34.7
C. 42.1
D. 117.9
Answer:
these are what I ythink the answers are
1) C
2)A
For 1. the answer is B
If £2000 is placed into a bank account that pays 3% compound interest per year,
how much will be in the account after 2 years?
The average age of kishan and dolma is 15 years and that of dolma and shaswat is 14 years .If kishan is 17 years old ,find the age of dolma and shaswat.
Help me to find answer
Answer:
dolma is 13 and shaswat is 15
Step-by-step explanation:
lets say kishan is k, dolma is d, and shaswat is 14. (k+d)/2 is 15 so k+d=30. (d+s)/2=14 so d+s=28. since k=17, d=13 and s=15
3. At the bank, Sheila made 6 deposits, each in the same amount. Her sister Sherri made 5 deposits, each in the same amount. Each of Sherri's deposits was $10 more than each deposit Sheila made. Both sisters deposited the same amount in the end. How much did each sister deposit each time?
(a) Write an equation. Let x represent the amount of one of Sheila’s deposits.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.
Step-by-step explanation:
x = one deposit of Sheila
x + 10 = one deposit of Sherri
so,
6x = 5(x + 10) = 5x + 50
x = 50
x + 10 = 60
so, as check, the original equation must be true for these values :
6×50 = 5×(50 + 10) = 5×60
300 = 300
correct.
Sheila deposited 6 times $50 every time. so, in total, she deposited $300.
Sherri deposited 5 times $50+$10 = $60 every time. so, in total, she too deposited $300.
Old McDonald's 3 hens lay the same number of eggs one week. This gives Old McDonald's wife enough eggs for two recipes. One recipe requires 10 eggs and the other recipe requires 2 eggs. How many eggs did each hen lay?
Last month, a carpenter made 2 tables. This month, he made 50% fewer tables. How many tables did the carpenter make this month?
Answer:
1
Step-by-step explanation:
2 divided by 2
Answer:
1 table
Step-by-step explanation:
2 x 0.5 = 1
Hope this helps!
9. What are all the values for y?Plug in the x value into the equation to find 1 point
y. Equation is y=-2x + 1*
Answer: C
Step-by-step explanation: see picture
what could be the value of x in the equation x/2+ 15 =64
Answer:
x = 98
Step-by-step explanation:
[tex]\frac{x}{2}[/tex] + 15 = 64 ( subtract 15 from both sides )
[tex]\frac{x}{2}[/tex] = 49 ( multiply both sides by 2 to clear the fraction )
x = 98
mr johnson borrowed $750 for 1 year. he has to pay 6% simple interest. how much interest will he pay?
Answer:
795$
Step-by-step explanation:
750 x 0.06 = 45
750 + 45 = 795
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
[tex]x = \frac{3}{ \sqrt{2} } [/tex]
Step-by-step explanation:
[tex] {x}^{2} + {x}^{2} = {3}^{2} \\ 2 {x}^{2} = 9 \\ {x}^{2} = \frac{9}{2} \\ x = \frac{3}{ \sqrt{2} } \\ x = 2.121[/tex]
PLS HELP ASAP ILL GIVE BRAINLKEST
Answer:
Its the bottom one x>5
Step-by-step explanation:
Write equation for the graph
Answer:
y = -4x + 4
Step-by-step explanation:
slope formula: y = mx + b
b is always y intercept which is when the line crosses through the y axis while the x coordinate is at 0. that would make it 4. now we find another point which would be (-1,8)
use change in y/change in x
we already have 2 points
(0,4)
(-1,8)
change in x: -1
change in y: 4
4/-1
slope: -4