A soft drink machine outputs a mean of 28 ounces per cup. The machine's output is normally distributed with a standard deviation of 2 ounces. What is the probability of filling a cup between 30 and 31 ounces? Round your answer to four decimal places.
Answers
Answer:
Normally distributed => get ready the normal probability table, or equivalent.
mu = mean = 28 oz
sigma = standard deviation = 2 oz
Need to find P(30 to 31), the probability of filling between 30 and 31 oz.
Solution:
With normal probabilities,
P(30 to 31) = P(X<31) - P(X<30), i.e. the difference of the right tails for X=30 and X=31.
Calculate the Z scores
Z(X) = (X-mu)/sigma
Z(31) = (31-28)/2 = 1.5
P(X<31) = P(Z<1.5) = 0.9331928
Z(30) = (30-28)/2 = 1.0
P(X<30) = P(Z<1.0) = 0.8413447
Therefore,
probability of filling between 30 and 31 oz
= P(X<31) - P(X<30)
= 0.9331928 - 0.8413447
= 0.09184805
= 0.0918 (to 4 decimal places)
Step-by-step explanation:
Related Questions
On a cruise ship there are two options for an Internet connection. The first option is a fee of $5 plus an additional $0.25 per minute. The second option cost $50 for an unlimited number of minutes. For how many minutes, m, is the first option cheaper than the second option? BRAINLIEST!!!
Answers
Answer:
m=180
Step-by-step explanation:
5+0.25m=50
-5. -5
0.25m=45
divide both terms by 0.25
m=180
with the first option you can get 180minuts or 3hours for the equivalent of the $50 option.
hope this helps :)
Verónica Ana y Luis pintan una barda y les pagan 300 cuánto dinero debería recibir cada quien
Answers
Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.
Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).
Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.
Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.
how can you use pythagora's theorem to solve problems involving right-angled triangles
Answers
Using Pythagorean theorem, the length of the ladder is 10ft
What is Pythagorean Theorem?In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:
x² = y² + z²
In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.
To calculate the length of the ladder, we can write the formula as;
x² = 8² + 6²
x² = 64 + 36
x² = 100
x = √100
x = 10
The length of the ladder is 10 feet
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Michael is buying 4.5 pounds of apples, and Shane is
buying 3.12 pounds of apples. If apples cost $1.31 per
pound, how much will they spend all together?
Answers
Answer:
9.9822 pounds or 9.98 poundsStep-by-step explanation:
(4.5+3.12)x1.31= 9.98222.(3x²-5)-5=9
Ayuda/help
Answers
Answer:
2
Step-by-step explanation:
2(3x²-5)-5=9
6x²-10-5=9
6x²-15=9
6x²=9+15
6x²=24
x²=24/6
x²=4
x=2
(IMAGE IS ATTACHED. PLEASE HELP! GIVING 100 POINTS)
What is the value of x?
Enter your answer in the box.
Answers
Answer:
x = 50
Step-by-step explanation:
→ Make the equations equal to each other
2 ( x + 10 ) = 3x - 30
→ Expand brackets
2x + 20 = 3x - 30
→ Minus 3x from both sides
-x + 20 = -30
→ Minus 20 from both sides
-x = -50
Opposite angles are equal
\(\\ \sf\longmapsto 2(x+10)=3x-30\)
\(\\ \sf\longmapsto 2x+20=3x-30\)
\(\\ \sf\longmapsto 3x-2x=30+20\)
\(\\ \sf\longmapsto x=50\)
the time it takes a runner to complete a race is inversely related to the speed of the runner if a runner can complete a race in 40 minutes while running at 8 mph how long will it take the runner to complete the race running at 9 mph t
Answers
S = v*t = 8 * 40/60 = 16/3 m
=> t = s/v = 16/(3*9) = 35.555555 minutes
The table shows several points for function h(x).
Which point is on the graph of the inverse function h
*(x)?
X
0
3
6
9
12
15
h(x)
1
6
12
2
8
9
0 (0, 1)
O (6,3)
O (9, -15)
O (12,-8)
Answers
c
Step-by-step explanation:
8877284857944764477$68+)(
Answer:
B
Step-by-step explanation:
e2021 on god
The following selected information was extracted from the records of B Solomon.
1. B Solomon, the owner of Solomon Traders, bought a new Machine for R250 000 on 1 July 2013.
2. On 1 October 2014, he purchased a second Machine for R350 000 cash.
3. On 30 June 2015, the Machine bought during 2013 was sold for R120 000 cash.
4. It is the business’ policy to depreciate Machines at 20% per annum on cost.
REQUIRED:
Prepare the following ledger accounts reflecting all applicable entries, in the books of Solomon Traders, properly balanced/closed off, for the years ended 31 March 2016:
1.1. Accumulated depreciation.
1.2. A Machines realisation.
NB: Show all calculations as marks will be awarded for calculations.
Answers
1.1. Accumulated depreciation:
The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.
1.2. Machine realization:
The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.
1.1. Accumulated Depreciation:
To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.
Machine bought on 1 July 2013:
Cost: R250,000
Depreciation rate: 20% per annum on cost
Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000
Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000
Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000
Accumulated depreciation for the machine bought on 1 July 2013:
As of 31 March 2014: R50,000
As of 31 March 2015: R100,000
As of 31 March 2016: R150,000
1.2. Machine Realisation:
To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.
Machine's original cost: R250,000
Accumulated depreciation as of 30 June 2015: R100,000
Net book value as of 30 June 2015:
R250,000 - R100,000 = R150,000.
On 30 June 2015, the machine was sold for R120,000.
Realisation amount: R120,000
To record the sale:
Debit Cash: R120,000
Debit Accumulated Depreciation: R100,000
Credit Machine: R250,000
Credit Machine Realisation: R120,000
Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).
These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.
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The four models each show two parallel lines cut by a transversal and some angle measures formed by the
intersection of the lines.
What are the values of angle measures a and b in model 4?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.
19° 71° 90° 109° 180° 119°
The value of a is _____, and the value of b is _____.
Answers
The value of a is 71°, and the value of b is 109°.
What is a parallel line?A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.
When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;
Corresponding angles, Alternate Interior Angles, Alternate Interior Angles, Alternate Exterior Angles and Consecutive Interior Angles.From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.
That is 180 - 71 = 109°
Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.
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9. Find the volume of a cone with a radius of 10 mm and a height of 6 mm.
O 628 mm³
O 600 mm³
O 1,884 mm 3
O 1,254 mm
Answers
Answer:
Step-by-step explanation:
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume of the cone, r is the radius of the base, and h is the height of the cone.
Substituting the given values, we have:
V = (1/3)π(10 mm)^2(6 mm)
V = (1/3)π(100 mm^2)(6 mm)
V = (1/3)π(600 mm^3)
V = 200π mm^3
Using a calculator to approximate π to 3.14, we get:
V ≈ 628.32 mm^3
Therefore, the answer is O 628 mm³.
how many 1/6 centimeters of yarn are there in 3/4 centimeters of yarn?
Answers
Answer:
Its 639 if that dosent help contact me ill help guadianeany time.
Step-by-step explanation:
The temperature in a hotel is 21 °C.
The temperature in the hotel is 26,7°C warmer than at the top of the mountain.
The temperature at the top of the mountain is 3.2°C colder than at the bottom of the mountain.
Work out the temperature at the bottom of the mountain.
Answers
The temperature at the bottom of the mountain is 50.9 °C.
Let's work through the given information step by step to find the temperature at the bottom of the mountain.
The temperature in the hotel is 21 °C.
The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.
Let's denote the temperature at the top of the mountain as T_top.
So, the temperature in the hotel can be expressed as T_top + 26.7 °C.
The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.
Let's denote the temperature at the bottom of the mountain as T_bottom.
So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.
Now, let's combine the information we have:
T_top + 26.7 °C = T_bottom - 3.2 °C
To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:
T_bottom = T_top + 26.7 °C + 3.2 °C
T_bottom = T_top + 29.9 °C
Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:
T_bottom = 21 °C + 29.9 °C
T_bottom = 50.9 °C
Therefore, the temperature at the bottom of the mountain is 50.9 °C.
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 24
and AD = 8, what is the length of AC?
Answers
Answer:
The answer is 72 cm.
Step-by-step explanation:
See attachments above^^
When working for a District Attorney, an investigator analyzed the leading digits of the amounts from 784 checks issued by seven suspect insurance companies. The frequencies were found to be 0, 12, 0, 73, 482, 186, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's Law, the check amounts appear to result from fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's Law. What is the value of the test statistic? Does it appear that the checks are the result of fraud?
Answers
Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.
Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.
To test for goodness-of-fit with Benford's Law, we can use the chi-squared goodness-of-fit test. The null hypothesis is that the observed frequencies follow Benford's Law, while the alternative hypothesis is that they do not.
We can start by calculating the expected frequencies for each leading digit based on Benford's Law. According to Benford's Law, the expected proportion of leading digits is
P(d) = log10(1 + 1/d), where d is the leading digit (1, 2, ..., 9).
Then, we can calculate the expected frequencies by multiplying the proportion by the sample size
Expected frequency for digit d = P(d) * sample size.
Using this formula, we can calculate the expected frequencies for each digit
Expected frequencies: 3.542, 2.019, 1.518, 1.221, 1.028, 0.886, 0.778, 0.697, and 0.643.
We can use these expected frequencies and the observed frequencies to calculate the chi-squared statistic
chi-squared = Σ (observed frequency - expected frequency)² / expected frequency
We can then compare this value to the chi-squared distribution with 8 degrees of freedom (since there are 9 digits and one constraint, which is that the frequencies must add up to the sample size). Using a significance level of 0.05 and a chi-squared distribution table or calculator, the critical value is 15.51.
Plugging in the observed and expected frequencies, we get
chi-squared = (0 - 3.542)²/3.542 + (12 - 2.019)²/2.019 + (0 - 1.518)²/1.518 + (73 - 1.221)²/1.221 + (482 - 1.028)²/1.028 + (186 - 0.886)²/0.886 + (8 - 0.778)²/0.778 + (23 - 0.697)²/0.697 + (0 - 0.643)²/0.643
chi-squared = 756.153
Since the calculated chi-squared statistic (756.153) is greater than the critical value (15.51), we reject the null hypothesis and conclude that the observed frequencies are not consistent with Benford's Law. This suggests that the check amounts are the result of fraud.
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Identify the common difference in the following arithmetic sequence.
-17, -13,-9,-5...
Answers
Answer:
+4
Step-by-step explanation:
How do we get from -17 to -13
-17+4 = -13
How do we get from -13 to -9
-13+4 = -9
The common difference is +4
Solve for n. 2 (4 + n) = 28
Answers
Answer:
n = 10
Step-by-step explanation:
=> 2(4 + n) = 28
=> 2(4) + 2(n) = 28
=> 8 + 2n = 28
=> 2n = 28 - 8
=> 2n = 20
=> n = 20/2
=> n = 10
Answer:
n = 10
Step-by-step explanation:
2(4 + n) = 28
Distribute:
(8 + 2n) = 28
Eliminate Parenthesis:
8 + 2n = 28
Cancel Out:
2n = 20
Divide:
n = 10
In Exploration 4.1.1 problem 3 pre calc
Answers
The reference triangle is a right triangle and therefore, the properties of
the reference triangle are similar to right triangle properties.
The correct options are as follows;
The reference triangle always have a leg perpendicular to the x-axis, the hypotenuse is positive, and θ is the angle adjacent to the x-axis and hypotenuse.ReasonsThe reference triangle is formed by the construction of a perpendicular
to the x-axis from the terminal side of an angle, oriented in the standard
position.
Therefore;
The reference triangle is a right triangle that always has a leg perpendicular to the x-axis.The hypotenuse is taken as positive, given that the magnitude of the hypotenuse is the square root of the sum of the squares of the legs.In the first quadrant, the reference angle, θ, is the same as the standard position angle and it is given by the angle formed between the x-axis and the hypotenuse side.The correct options are therefore;
In Trigonometry it is important that the right triangle (reference triangles)
have a consistent orientation. The reference triangles always have a leg
perpendicular to the x-axis, the hypotenuse positive and the θ is
adjacent to the x-axis and hypotenuse.
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A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.
Which equation can we use the total number of penguins living in the building?
Answers
The equation that represent the number of penguins is (6 × 4) + (3 × 6) + (3 × 6) = p.
How to find the equation to represent a situation?A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.
Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:
Hence,
(6 × 4) + (3 × 6) + (3 × 6) = p
where
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Prove that for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
Answers
Answer:
Below
Step-by-step explanation:
Suppose that m and n are both even numbers.
So we can express them as the product of 2 and another number.
● n = 2×a
● m = 2×b
● m-n = 2b-2a
● m-n = 2(b-a)
m-n is an even number since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that both n and m are odd numbers.
● n = 2a+1
● m = 2b+1
● m-n = 2b+1-(2a+1)
● m-n = 2b+1-2a-1
● m-n = 2b-2a
● m-n = 2(b-a)
So m-n is even since it is divisible by 2.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Suppose that m is odd and n is even ir vice versa
● n = 2a or n= 2a+1
● m = 2b+1 or m = 2b
● m-n = 2b+1-2a or m-n = 2b-2a-1
● m-n = 2(b-a) +1 or m-n = 2(b-a)-1
In both cases m-n isn't even.
■■■■■■■■■■■■■■■■■■■■■■■■■■
So m-n is even if and only if m and n are odd or m and are even
Answer:
Case 1
both m and n are even
Therefore m/2 and n/2 are integers
Then,
m-n
=2(m/2 - n/2)
Since m/2 and n/2 are integers
Then m/2 - n/2 will be an integer
Therefore,
m-n = 2(Z)
Where Z is an integer
Since 2 is a factor of m-n
Therefore m -n is even
Case 2
Both m and n are odd
m-n
= 2(½m - ½n)
When an odd number is divided by 2 it gives an integer and a remainder of 1
Therefore
½m = Y + ½
And
½n = Z + ½
Where Y and Z are integers
Then
m-n = 2(Y+½-Z-½)
= 2(Y-Z)
Y-Z will also be an integer
m-n= 2A
Therefore m-n is even
Case 3
One is odd and the other even
m-n = 2(m/2 - n/2)
Assume m is even and n is odd
From the discussions above
m-n = 2(Y - Z - ½)
m-n = 2(A - ½)
Hence m-n is not even because when is divided by two it doesn't give an integer.
Therefore for all integers m and n, m - n is even if, and only if, both m and n are even or both m and n are odd.
I need help I need an equivalent expression to this please
Answers
Multiply each term in the parentheses by -3 then Multiply the numbers
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
Answer:
a: Angle EBD
b: Can't really phrase this well, a semicircle that is to the left or right of diameter BD
c: Arc EDC
d: 80 degrees
e: 180
Step-by-step explanation:
An inscribed angle is an angle with all 3 points on the circumference of a circle.
A semicircle is half a circle
A major arc is an arc greater than 180 degrees
The inner angle is 80 degrees
Arc BCD is half a circle so its 360/2=180 degrees
Are they like terms? 3y & 3x
Answers
Answer:
no
Step-by-step explanation:
Answer:
No because they dont have the same variables
Step-by-step explanation:
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3 ft long with a diameter of 1.8 ft. Suppose oil is drained at a rate of 1.7 ft³ per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Answers
Answer:
4 minutes
Step-by-step explanation:
You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)
VolumeThe volume of a cylinder can be found using the formula ...
V = (π/4)d²h . . . . . . . diameter d, height h
Then the volume of the oil tank is ...
V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³
TimeThe time it takes to empty the tank is found by dividing the volume by the rate:
(7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min
It will take about 4 minutes to empty the tank.
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A square pyramid has a base length of 6 inches and a height of 8 inches.
What is the volume of this pyramid?
Enter your answer in the box.
Answers
The volume of the pyramid will be equal to 96 in^3.
We are given that square pyramid has a base length of 6 inches and a height of 8 inches.
Suppose that the height of the pyramid is of h units, then:
\(v = \dfrac{l \times w \times h}{3} \: \rm unit^3\) is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, thus its area is:
\(b = l \times w\: \rm unit^2\)
Therefore, the volume of the pyramid;
V = 1/3 a^2 h
V = 1/3(6^2)(8)
V = 1/3(36)(8)
V = 96 in^3
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B=(3,5,6,9) and C=(2,4,6,8) Find (A). A/B (B). B/C C. A/C (D). C/A
Answers
Answer:
The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.
Need help on finding g .
Answers
The numeric values for this problem are given as follows:
g(-1) = -2.g(2) = 0.g(3) = 0.5.How to obtain the numeric values of the function?The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.
For x between -2 and 2, the function is defined as follows:
g(x) = -(x - 1)² + 2.
Hence the numeric value at x = -1 is given as follows:
g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.
For x at x = 2 and greater, the function is given as follows:
g(x) = 0.5x - 1.
Hence the numeric values at x = 2 and x = 3 are given as follows:
g(2) = 0.5(2) - 1 = 0.g(3) = 0.5(3) - 1 = 0.5.A similar problem, also featuring numeric values of a function, is given at brainly.com/question/28367050
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Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
A. 1: √3
B. √2:√√3
C. 1: √2
D. √ √√3
DE √ √√2
F. 25: 6
Answers
It should be noted that the ratio between the lengths of the two legs is B. 1: ✓3.
It should be noted that the ratio between the lengths of the two legs will be equal to the tangent.
In this case, tan (30°) = ✓3/3
Tan (60°) = ✓3
Therefore, the ratio between the lengths of the two legs of a 30-60-90 triangle will be 1 : ✓3.
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We have a bag that contains 100 balls, 50 of them red and 50 blue. Select 5 balls at random. What is the probability that 3 are blue and 2 are red?
Answers
Answer:
Likely, I think I havent been in this for a long time so i may be a little rusty. But anyways, I hope this helped!
Step-by-step explanation:
32% is the probability that 3 are blue and 2 are red.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
We have a bag that contains 100 balls, 50 of them red and 50 blue.
We, Select 5 balls at random.
the probability that 3 are blue and 2 are red = 50C3*50C2/50C5
solving we get,
19600*1225/75287520
=24010000/75287520
=0.32
=32%
Hence, 32% is the probability that 3 are blue and 2 are red.
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James filled a number of bags with apples when he went apple picking. He recorded the weight of each bag. This line plot shows his results.
How much more does one of the heaviest bags weigh than one of the lightest bags?
Enter your answer as a mixed number in simplest form
Answers
The number of more does one of the heaviest bags weigh than one of the lightest bags filled by James with apples is 5/4.
What is dot plot or line plot?The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.
The number of more does one of the heaviest bags weigh than one of the lightest bags filled by James with apples is
James filled a number of bags with apples when he went apple picking. He recorded the weight of each bag. This line plot shows his results.
Note that the value of 1/4 is 0.25 which is less than the value of 1/2 which is 0.5.The value of 3/4 is 0.75.In the line plot, in the 6th section, we get the highest value as 5 1/2. Similarly, the lowest value in the line plot is 4 1/4.
The difference between these values is,
\(d=5\dfrac{1}{2}-4\dfrac{1}{4}\\d=\dfrac{5\times2+1}{2}-\dfrac{4\times4+1}{4}\\d=\dfrac{10+1}{2}-\dfrac{16+1}{4}\\d=\dfrac{11}{2}-\dfrac{17}{4}\\d=\dfrac{11\times2-17}{4}\\d=\dfrac{5}{4}\)
Thus, the number of more does one of the heaviest bags weigh than one of the lightest bags filled by James with apples is 5/4.
Learn more about the dot plot here;
https://brainly.com/question/15853311
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