Answer:
14
Step-by-step explanation:
(4*5)+(2*3)
20-6
14.
A certain brand of candies have a mean weight of 0.8616g and a standard deviation of 0.0518 based on the sample of a package containing 447 candies. The package label stated that the net weight is 381.8g If every package has 447 candies the mean weight of the candies must exceed 381.8/447=0.8542 for the net contents to weight at least 381.8g.
a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.
The probability is ________.
(round to four decimal places as needed)
b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.
the probability that a sample of 447 candies will have a mean of 0.8542g or greater is __________.
(round to four decimal places as needed)
c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Answer:
a) The probability is 0.5557 = 55.57%.
b) The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
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.
Mean weight of 0.8616g and a standard deviation of 0.0518
This means that [tex]\mu = 0.8616, \sigma = 0.0518[/tex]
a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.
This is 1 subtracted by the pvalue of Z when X = 0.8542. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0518}[/tex]
[tex]Z = -0.14[/tex]
[tex]Z = -0.14[/tex] has a pvalue of 0.4443
1 - 0.4443 = 0.5557
The probability is 0.5557 = 55.57%.
b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.
Sample of 447 means that [tex]n = 447, s = \frac{0.0518}{\sqrt{447}} = 0.00245[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0245}[/tex]
[tex]Z = -3.02[/tex]
[tex]Z = -3.02[/tex] has a pvalue of 0.0013
1 - 0.0013 = 0.9987
The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
What is the area of ACDE to the nearest whole number?
Area of ACDE =
Answer:
Step-by-step explanation:
Area of rectangle ABCD = 84.
BC=x
We can use pythagorean to find x. 12^-6^2=c^2
C=6root3
6root3*6/2 = area of triangle ABC
ABC=18root3
Area of ACDE=84-18root3 which equals about 53
The trapezoid below is formed from two triangles and a rectangle. What is the area of the trapezoid?
9 cm
3 cm
6 cm
3 cm
A 81 cm 2
B 108 cm 2
C 67.5 cm 2
D 54 cm 2
Answer:
A. 81 cm^2
Step-by-step explanation:
9*6 = 54
9*3 = 27
54+27 = 81
You are standing on the ground (height of 0) and kick a ball across the park with an initial velocity of 64 feet per second. Using the vertical motion model, calculate each of the following: Don't forget units
a. What is the highest height the ball reaches?
b. When will the ball be at the highest height?
c. How long is the ball in the air?
I need this question to be answered it's 30 points and please no links just leave the answer
The volume of a pool should be measured using which of the following units?
cubic yards
cubic feet
square feet
gallons
Answer:
Square feet
Step-by-step explanation:
Hope this helped
The radius of a chord and a tangent line are_ at the point of tangency
Answer:
fine
cause of it's fine point of tangency
The angle between the lines xy=0 is
(a) 00
(b) 60°
(c) 90°
(d) 120°
Answer:
(c) 90°
Step-by-step explanation:
Given
[tex]xy = 0[/tex]
Required
The angle between the line
First, solve for x and y
[tex]xy = 0[/tex]
[tex]x = 0[/tex] or [tex]y=0[/tex]
This means that: y axis and x axis
The angle between the two axes is 90 degrees
Hence: (c) is correct
Determine if each set of coordinates form a horizontal or vertical line.
a. (-3, 6) & (-3, 2)
b. (8, 4) & (-3, 4)
c. (11, -5) & (-9, -5)
d. (9, -3) & (9, -12)
Answer:
a. vertical
b. horizontal
c. horizontal
d. vertical
Step-by-step explanation:
if the x coordinate changes it's horizontal and if the y coordinate changes it's vertical
7 over 6 divided by 4
Answer:
0.29
Step-by-step explanation:
I used a calculator
What is the fewest number of quarters, nickels, and pennies that can be fairly exchanged for 2 quarters, 6 nickels, and 9 pennies?
Answer:
Your answer is 3 quarters, 2 nickels, and 4 pennies
Step-by-step explanation:
2 quarters plus 6 nickels plus 9 pennies is equal to 89 cents. So if we subtract 75(3 quarters) we get 14 which is less than 25 therefore we must only use nickels and pennies from now on. If we take 14 and subtract 10(2 nickels) we get 4 which less than 5 leaving us only to use pennies, which one a piece so it must be 4 pennies. Hope this helps!
A probability calculator is required on this problem; answer to six decimal places. Suppose we will flip a fair coin 100 times. Using a calculator, find the probability of getting between 42 and 58 heads (inclusive) in two ways: By a Normal approximation: 0.910869 Exactly: 0.920609 How far off is the Normal approximation
Answer:
0.910870.911374 0.000504Step-by-step explanation:
Number of toss ( n ) = 100
probability of a head in 1 toss ( p ) = 0.5
Hence : np = 100 * 0.5 = 50 > 5, also n( 1-p) = 50 > 5
mean value ( μ ) = np = 50
std = √ n(p)(1-p) = √100(0.5)(0.5) = 5
Using Normal approximation
P( 42 ≤ x ≤ 58 ) = P ( 42-0.5 ≤ x ≤ 58 + 0.5 )
= P( (41.5 - 50) / 5 < Z < (58.5 - 50) / 5 )
= P ( -1.7 < Z < 1.7 )
= 0.91087
Using Calculator to get the exact value
P( 42 ≤ x ≤ 58 ) = 0.911374
How far off is the Normal distribution (Absolute value of error )= | 0.911374 - 0.91087 | = 0.000504
the initial deposit into an account?
a. compound interest
b. simple interest
c. interest rate
d. principal
Answer:
B
Step-by-step explanation:
Simple interest is based on the principal amount of a loan or deposit.
Find the area (in square centimeters) of a regular pentagon
Answer:
Given
apothegm [a]=3.2cm
since Pentagon has 5 equal side
perimeter [P]=5×4.6=23cm
now
Area of regular pentagon
A=1/2 aP=1/2×3.2×23=36.8cm²
What is the length of the unknown leg in the right triangle?
Answer:
There is no triangle.
Step-by-step explanation:
Answer:
Your final answer is √32 miles.
Step-by-step explanation:
Josie baked a cake and ate .6 of it. Express this decimal as a percent and as a fraction.
Step-by-step explanation:
Hi,
To write this answer as a percent, simply divide it by 10.
6/10 is the same thing as 60%.
As a fraction, it's 6/10.
As a percent it's 60%
I hope this helps :)
what are 2 challenges that Will Smith faced
Answer:
Will Smiths wife cheated on him!
Step-by-step explanation:
Can someone help me pls
I think the answer is B) Find m (arc DC)
Kym used the integer tiles to find the sum of (–3)+6.The line showed that the answer is negative 3.Which of the following does Kym need to do to get the correct answer
Answer:I need points
Step-by-step explanation:
adsfnsafasfj;ljfdksfas;lfkjdf;lksdfjsdlksfajf
Answer:
remove the zero pairs
so B
Step-by-step explanation:
2b + 8 =? I don't know this one either
What’s the answer please help me no links at all if you do I will report
Answer: 78
Step-by-step explanation:
Sully is having a party and wants to fill his swimming pool. If he only uses his hose, it takes 3 hours more than if he only uses his neighbor's hose. If he uses both hoses together, the pool fills in 5 hours. How long does it take for each hose to fill the pool (in hr)?
Answer:
It takes the neighor's hose 3 hours to fill the pool and it takes Sully's hose 6 hours to fill the pool if each filled alone.
Step-by-step explanation:
This is a work problem, and the way these are done is to figure the amount that each can do based on how much can get done in a single hour.
First thing, in order to have only one variable, we have to put one hose in terms of the other hose.
We know that it takes the neighbor's hose a certain amount of time (there's our unknown) to fill the pool and that it takes Sully's hose that same time plus 3 hours.
neighbor's hose can get the job done in x time
Sully's hose can get the job done in x + 3 time
Now we will figure out how much each can do in a single hour.
If the neighbor's hose takes x hours to fill the pool, then it can get
of the pool filled in 1 hour.
If Sully's hose takes x + 3 hours to fill the pool, then it can get
of the pool filled in 1 hour.
The sum of these takes 2 hours total and 1/2 of the pool gets filled in 1 hour.
Our equation then is:
This equation states in words:
"the amount of the pool that the neighbor's hose can fill in an hour plus the amount of the pool that Sully's hose can fill in an hour will fill half the pool".
Solving for x will give us that time.
Begin to solve this by finding the LCM of those denominators and getting rid of the fractions by reducing. The LCM will be 2x(x + 3). Multiplying each term by that LCD looks like this:
In the first term the x's cancel out, in the second term the (x + 3) cancels out, and in the last term the 2's cancel out leaving us with:
and simplifying gives us:
This is a quadratic that will have to be factored to solve for those values of x. Combine like terms and get everything on one side to get:
Factor this however you find easiest to get the values:
x = 3 hours and x = -2 hours
We all know that the 2 things in math that will never EVER be negative are times and distances/measures, so we can disregard the -2 and say that
x = 3 hours.
To answer our question, then;
It takes the neighbor's hose 3 hours to fill the pool; it takes Sully's hose 3+3 hours = 6 hours to fill the pool.
Each side of a square potholder is 21 centimeters long.
What is the area of the potholder?
The answer is a 441 cm area
What is 140% of 60
Pls help I need help pls pls pls pls pls pls
Answer:
84
Step-by-step explanation:
To calculate how much 140% of 60 does we need to multiply 60 with 140 then divide it by 100
60 x 140 ÷ 100 = 84
Order the angles in each triangle from smallest to largest
Answer:
<E, <F, <G
Step-by-step explanation:
Brainliest for correct answer
Answer:
I got 678.58401 but i think it is C. 648n cubic units
Step-by-step explanation:
An element with mass 800 grams decays by 8.2% per day. How much of the element is remaining after 15 days,
to the nearest 10th of a gram?
Given:
The initial mass of an element is 800 grams.
Decay rate = 8.2% per day
Number of days = 15
To find:
The remaining element after 15 days.
Solution:
The exponential decay model is
[tex]y=a(1-r)^t[/tex]
Where, a is the initial value r is the rate of interest and t is time period.
Putting [tex]a=800,r=0.082,t=15[/tex] in the above formula, we get
[tex]y=800(1-0.082)^{15}[/tex]
[tex]y=800(0.918)^{15}[/tex]
[tex]y=221.68188[/tex]
[tex]y\approx 221.7[/tex]
Therefore, the mass of the remaining element is 221.7 grams.
Triangles ABC and XYZ are shown below. A student knows that AX and 2cm 22. The student claims that AABC is similar to AXYZ
Determine whether each statement below can be used as part of a justification for the claim that ABC is similar to AXYZ Select Yes or No for each statement.
Yes No
AC
A dilation of AABC by scale factor k =
through center results in A4'B'C where A'C = XZ
Triangle A'B'C, which results from a dilation of ABC such that A'c = XZ, is congruent to AXY2 by Angie-Side-Angle (ASA) O
There exists a sequence of rigid transformations and dilations that carries A4BC to AXYZ, so it follows that AABC is similar to AXYZ OO
sorry i couldn't answer tho
The mean breaking strength of a ceramic insulator must be at least 10 psi. The process by which this insulator is manufactured must show equivalence to this standard. If the process can manufacture insulators with a mean breaking strength of at least 9.5 psi, it will be considered equivalent to the standard. A random sample of 50 insulators is available, and the sample mean and standard deviation of breaking strength are 9.32 psi and 0.21 psi, respectively. a. State the appropriate hypotheses that must be tested to demonstrate equivalence.
Answer:
H0: u ≥ 9.5
Ha: u < 9.5
Step-by-step explanation:
The null hypothesis and the alternate hypothesis are reverse of each other.
The claim is either set as the null or alternate hypothesis
The null hypothesis is : H0: u ≥ 9.5 the mean breaking strength of a ceramic insulator is at least 9.5 which is considered equivalent to the standard.
The alternate hypothesis is: Ha: u < 9.5 the mean breaking strength of a ceramic insulator is less than 9.5 which is not considered equivalent to the standard.
Consider the equation below.
Determine which equation has the same solutions as the given equation.
Answer:
A) (x - 5)² = 36
Step-by-step explanation:
x² - 10x - 11 = 0
A) CORRECT
(x - 5)² = 36
x² - 10x + 25 = 36
x² - 10x + 25 - 36 = 0
x² - 10x - 11 = 0
What is the answer to this?
9514 1404 393
Answer:
$125 per car
Step-by-step explanation:
The problem statement tells you Jazmin's pay goes up by $125 for each car she sells. That rate of change is $125 per car.