(d) A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 100ml of coffee. The machine actually dispenses a mean amount of 105ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispenses into each cup is normally distributed, find the standard deviation of the amount of coffee dispensed per cup in ml.
Answers
Answer:
The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Step-by-step explanation:
Let the random variable X denote the amount of coffee dispensed by the machine.
It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.
It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.
And 10% of the cups contain less than the amount stated on the sign.
To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,
\(z=\frac{X-\mu}{\sigma}\)
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of z for the above probability is, z = -1.28.
*Use a z-table
Compute the value of standard deviation as follows:
\(z=\frac{X-\mu}{\sigma}\)
\(-1.28=\frac{100-105}{\sigma}\)
\(\sigma=\frac{-5}{-1.28}\)
\(=3.90625\\\\\approx 3.91\)
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Related Questions
Find the balance in the account: $2,000 principal, earning 7% compounding semi-annually, after 25 years
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.07}{2}\right)^{2\cdot 25}\implies A=2000(1.035)^{50} \implies A \approx 11169.85\)
Ravi says,” if 10 years are added to my age, then my age becomes 25.”if Ravi’s present age is x years,
then find the linear equation satisfying the given condition.
Answers
Answer:
The linear equation satisfying the given condition is,
\(x=t+15\)
where x is Ravi's age and t is the number of years
(after 10 years (t=10) his age becomes 25)
Step-by-step explanation:
Let x be Ravi's age
Now, his current age is unknown, but if you add 10 to it, then it becomes 25, so
x + 10 =25
so, his current age is x = 25 =10
x = 15
Now, we find the linear equation satisfying the given condition,
Let t be the number of years that have passed since the present time
so, if 0 years have passed, his age will be 15 years
after 1 year, his age will be 16 years
after 10 years, his age will be 25 years and so on
so
\(x = t + 15\)
this satisfies the given condition, since if we add ten years i.e t = 10,
then we get 25
The equation is:
⇨ x + 10 = 25Work/explanation:
Here's the linear equation for Ravi's age.
Ravi's age is x.
If you add 10 to x you get x + 10.
That gives 25.
So the linear equation is x + 10 = 25.
Please answer will give branliest eeeeeee
Answers
Answer:
D. 8M
Step-by-step explanation:
multiplication doesn't require a sign it can be represented by a constant together with a variable like 8M is the same as 8•M
all the other options represent addition and subtraction, not multiplication
hope this helps chu <3
Find the values of x and y when the smaller triangle has an area of 54 cm2.The value of x is cm and the value of y is cm.(Type exact answers, using radicals as needed. Rationalize all denominators.)
Answers
The two triangles are similar triangles. As such, the following is true:
\((\frac{\text{side length of smaller triangle}}{\text{side length of bigger triangle}})^2=\frac{Area\text{ of smaller triangle}}{\text{Area of bigger triangle}}\)Thus, we first have to compute the area of the bigger triangle, as follows:
\(\text{Area =}\frac{1}{2}\times base\times height\)Since, for the bigger triangle, base = 81cm, and height = 36cm, we have:
\(\begin{gathered} \text{Area =}\frac{1}{2}\times base\times height \\ \Rightarrow\text{Area =}\frac{1}{2}\times81\times36 \\ \Rightarrow\text{Area =}\frac{2916}{2}=1458 \\ \Rightarrow Area=1458cm^2 \end{gathered}\)Now, we find x and y, as follows:
\(\begin{gathered} (\frac{x}{36})^2=\frac{54}{1458} \\ \Rightarrow(\frac{x}{36})^2=\frac{1}{27} \\ \Rightarrow\frac{x}{36}=\sqrt[]{\frac{1}{27}}=\frac{1}{\sqrt[]{27}} \\ \Rightarrow\frac{x}{36}=\frac{1}{\sqrt[]{9\times3}}=\frac{1}{\sqrt[]{9}\times\sqrt[]{3}}=\frac{1}{3\times\sqrt[]{3}} \\ \Rightarrow x=36\times\frac{1}{3\times\sqrt[]{3}}=\frac{36}{3\sqrt[]{3}}=\frac{12}{\sqrt[]{3}} \\ \Rightarrow x=\frac{12}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{12\sqrt[]{3}}{\sqrt[]{9}}=\frac{12\sqrt[]{3}}{3}=4\sqrt[]{3} \\ \Rightarrow x=4\sqrt[]{3}\text{ cm} \end{gathered}\)Now, y can be obtained similarly:
\(\begin{gathered} (\frac{y}{81})^2=\frac{54}{1458} \\ \Rightarrow(\frac{y}{81})^2=\frac{1}{27} \\ \Rightarrow\frac{y}{81}=\sqrt[]{\frac{1}{27}}=\frac{1}{\sqrt[]{27}} \\ \Rightarrow\frac{y}{81}=\frac{1}{\sqrt[]{9\times3}}=\frac{1}{\sqrt[]{9}\times\sqrt[]{3}}=\frac{1}{3\times\sqrt[]{3}} \\ \Rightarrow y=81\times\frac{1}{3\times\sqrt[]{3}}=\frac{81}{3\sqrt[]{3}}=\frac{27}{\sqrt[]{3}} \\ \Rightarrow y=\frac{27}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{27\sqrt[]{3}}{\sqrt[]{9}}=\frac{27\sqrt[]{3}}{3}=9\sqrt[]{3} \\ \Rightarrow y=9\sqrt[]{3}\text{ cm} \end{gathered}\)The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly selects 45 customers and records the amount of time from the moment they stand in the back of a line until the moment the cashier scans their first item. He calculates the mean and standard deviation of this sample to be
Answers
Complete question:
The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly selects 45 customers and records the amount of time from the moment they stand in the back of a line until the moment the cashier scans their first item. He calculates the mean and standard deviation of this sample to be barx = 4.2 minutes and s = 2.0 minutes. If appropriate, find a 90% confidence interval for the true mean time (in minutes) that customers at this supermarket wait in a check-out line
Answer:
(3.699, 4.701)
Step-by-step explanation:
Given:
Sample size, n = 45
Sample mean, x' = 4.2
Standard deviation \( \sigma \) = 2.0
Required:
Find a 90% CI for true mean time
First find standard error using the formula:
\( S.E = \frac{\sigma}{\sqrt{n}} \)
\(= \frac{2}{\sqrt{45}}\)
\( = \frac{2}{6.7082} \)
\( SE = 0.298 \)
Standard error = 0.298
Degrees of freedom, df = n - 1 = 45 - 1 = 44
To find t at 90% CI,df = 44:
Level of Significance α= 100% - 90% = 10% = 0.10
\(t_\alpha_/_2_, _d_f = t_0_._0_5_, _d_f_=_4_4 = 1.6802\)
Find margin of error using the formula:
M.E = S.E * t
M.E = 0.298 * 1.6802
M.E = 0.500938 ≈ 0.5009
Margin of error = 0.5009
Thus, 90% CI = sample mean ± Margin of error
Lower limit = 4.2 - 0.5009 = 3.699
Upper limit = 4.2 + 0.5009 = 4.7009 ≈ 4.701
Confidence Interval = (3.699, 4.701)
3. Find the slope
(it says its too short thats why im writing this)
Answers
Answer:
\(\displaystyle m=\frac{2}{3}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (0, 3)
Point (-3, 1)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [SF]: \(\displaystyle m=\frac{1-3}{-3-0}\)[Fraction] Subtract: \(\displaystyle m=\frac{-2}{-3}\)[Fraction] Simplify: \(\displaystyle m=\frac{2}{3}\)a hiking trail is 3 4/5 miles long. terence 5/8 of the trail how many miles does terence walk
Answers
Answer:
\(2.375\,\,miles\)
Step-by-step explanation:
Given: Length of a hiking trail is \(3\frac{4}{5}\,\,miles\)
Terence travels \(\frac{5}{8}\) of the length of a hiking trail
To find: Distance travelled by Terence
Solution:
Whole numbers refer to natural numbers together with 0.
A fraction represents a part of a whole.
A whole number and a fraction combined into mixed fraction.
Distance travelled by Terence = \(\frac{5}{8}(3\frac{4}{5})=\frac{5}{8}(\frac{19}{5})=\frac{19}{5}=2.375\,\,miles\)
Olivia picked 256 strawberries. She divided the strawberries evenly into 6
baskets. How many strawberries are in each basket? How many are left over
Answers
Answer:
42 strawberries in each backet with 4 left over
Step-by-step explanation:
256 divided by 6=42.6666667
42x6=252
256-252
Answer:
42 with 4 left over
Step-by-step explanation:
256/6
4 2
6. 256
4
24
16
12
4
description of set D={3,6,9,12,15}
Answers
Answer:
The set D has 5 elements - 3, 6, 9, 12, and 15, all of which are multiples of 3.
A sample of 2,000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers 0 1,910 1 46 2 18 3 12 4 9 5 or more 5 Total 2,000 Click here for the Excel Data File What is the probability that a particular driver had exactly two speeding violations
Answers
Answer:
The probability that a particular driver had exactly two speeding violations is 0.009.
Step-by-step explanation:
We are given that a sample of 2,000 licensed drivers revealed the following number of speeding violations;
Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2000
Now, the data means that 1,910 drivers had 0 speeding violations and so on.
Now, we have to find the probability that a particular driver had exactly two speeding violations, that means;
Number of drivers having exactly two speeding violations = 18
Total numbers of drivers = 2000
So, the required probability = \(\frac{\text{No. of drivers having two speeding violations}}{\text{Total no. of drivers}}\)
= \(\frac{18}{2000}\) = 0.009
Help me find the answer to this please. And also explain how to slove these problems.
Answers
Answer:
B and C
Step-by-step explanation:
Minimum and Maximum points occur when the gradient of the function is equal to 0. Graphically this looks like a bend such that the function dips from decreasing to increasing (the gradient goes form being negative to positive) and vice versa.
A minimum point occurs where all the nearby values are higher than that of the point in question.
A maximum point occurs where all the nearby points are lower than the point in question.
By looking at the graph, there is a maximum point around (4.5, 1.5) which is consistent with B but not A (since A talks about a minimum point)
By looking at the graph, there is a minimum point around (0.5, 1.5) which is consistent with C.
I've highlighted areas of interest below so hopefully that's helpful :>
Its factorial math pleaseHelp.
Answers
\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)
Please help...........
Answers
Answer:
A Linear
B Quadratic
C Quadratic
D Linear
Step-by-step explanation:
Calculus please help
Answers
f(x) is discontinuous.
Since LHS ≠ RHS ≠ f(x).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
here, we have,
We have,
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Now,
A x = 1
LHS of f(x) = lim f((h - 1)) = (h - 1 - 1) = 0 -2 = -2
RHS of f(x) = lim f(h + 1) = (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1
f(1) = x + 1 = 1 + 1 = 2
We see that,
LHS ≠ RHS ≠ f(x)
So,
f(x) is not continuous, it is discontinuous.
Thus,
f(x) is discontinuous.
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The complete question.
Show that the following functions are continuous or discontinuous at x = 1.
f(x) = x + 1, for x ≤ 2
f(x) = 2x - 1, for 1 < x < 2
f(x) = x - 1, for x < 1
Prove the identity
secx-1/ tan x= tanx/ secx+1
To verify the identity, start with the left side and transform it to obtain the right side. Choose the correct step and transform the expression according to the step chosen.
secx-1/ tan x= sec-1 / tanx
Answers
Answer:
Proved
Step-by-step explanation:
The options are not given. So, I will solve from scratch
Given
\(\frac{secx-1}{tan x}= \frac{tanx}{secx+1}\)
Required
Prove
Multiply the right-hand side by \(\frac{secx + 1}{secx + 1}\)
\(\frac{secx-1}{tan x} * \frac{secx + 1}{secx + 1}= \frac{tanx}{secx+1}\)
Apply difference of two squares on the numerator
\(\frac{sec^2 x - 1}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}\)
In trigonometry:
\(tan^2x = sec^2x - 1\)
So, we have:
\(\frac{tan^2 x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}\)
\(\frac{tan x * tan x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}\)
tan x cancels out
\(\frac{tan x}{secx + 1} =\frac{tanx}{secx+1}\)
Proved
6 bags of coins each contain 10 nickels and the same number of pennies. Altogether, the bags contain 180 coins. Write and solve an equation to find the number of pennies in each bag.
Answers
Each bag contains 20 pennies and we have 6 such bags.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information let the number of pennies in each bag is 'x'
and we have 6 such bags.
Therefore, The equation can be formed as,
6(10 + x) = 180.
60 + 6x = 180.
6x = 180 - 60.
6x = 120.
x = 120/6.
x = 20.
So, The number of pennies in each bag is 20.
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Use the distance formula to find the distance between the points (−1,6) and (−1,7).
Answers
The required distance between the points (−1,6) and (−1,7). is 1 unit.
Given that,
using the distance formula to evaluate the distance between the points (−1,6) and (−1,7).
Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the values in the above equation,
D = √[[-1 + 1]² + [7 - 6]²]
D = √[0 + 1]
D = 1
Thus, the required distance between the points (−1,6) and (−1,7). is 1 unit.
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A health club charges a one-time sign-up fee and a monthly membership fee. The
equation y = 28x + 50 represents what the health club charges. Find the rate of
change.
Answers
Answer:
The rate of change is 28.
Step-by-step explanation:
The equation is in slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept.
Consider the functions below. f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6. Which of the following statements is true?
A.
As x approaches infinity, the value of g(x) eventually exceeds the values of both f(x) and h(x).
B.
Over the interval [3, 5], the average rate of change of g and h is more than the average rate of change of f.
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
D.
As x approaches infinity, the values of g(x) and h(x) eventually exceed the value of f(x).
Answers
The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.
What is increasing function?
⇒ The function is said to be increasing if the y value increases as the x value increase over a given range
What is average rate of change?
⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another
As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)
And it is true for the interval [0,2]
The faster the growth rate higher the average rate of change
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Answer:
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
Solve the quadratic equation by using either a numeric or a graphic approach. x squared minus 16 x minus 64 = 0 a. x = -11.1 or x = -12.4 c. x = 16.3 or x = -2.9 b. x = 19.3 or x = -3.3 d. x = 1.3 or x = -3.4
Answers
Answer:
B.
Step-by-step explanation:
\(x^2 - 16x - 64 = 0\)
\((x-8)^2 = 128\)
\(x = 8 + \sqrt{128}\)
or
\(x=8-\sqrt{128}\)
so x = 19.3
or x = 3.3
Lupita bought the square picture frames.
HIJK ~ LMNO. The ratio between the lengths of their sides is 2:1. If the length of side IJ = 10 inches, what is the length of side MN?
Answers
IJ : MN = 2 : 1
10 : MN = 2 : 1
MN = 5 inches
Answer:
5
Step-by-step explanation:
3.19=
3.4
+
2.1
c
3.4+2.1c
Answers
Answer:
Step-by-step explanation:
3.19=3.4+2.1c3.4+2.1c c= -1/44 = -0.02272...
graph the line passing through (−4,−1) whose slope is m=-4/5
Answers
Answer:
\(y=-\frac{4}{5}x-\frac{21}{5}\)
Step-by-step explanation:
The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):
\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)
To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting m = -4/5, x = -4, and y = -1, we can solve for b:
-1 = (-4/5)(-4) + b
-1 = 3.2 + b
b = -4.2
Therefore, the equation of the line is:
y = (-4/5)x - 4.2
To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:
y = (-4/5)x - 4.2
y = (-4/5)(0) - 4.2
y = -4.2
So the y-intercept is (0,-4.2).
Using this point and the given point (-4,-1), we can draw a straight line passing through both points.
Here is a rough sketch of the graph:
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| *
| /
| /
| /
-----*--------
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The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.
Please help me out with this one
Answers
Answer:
B. t= 10n +15
Step-by-step explanation:
(ASAP!!!) According to a government website, 42% of US citizens are Democrats, 34% are Republicans, and 24% are Independents. A local municipality would like to know if the distribution of political party affiliation among its citizens differs from the nationwide percentages. A random sample of 500 citizens of the municipality is selected. In the sample, 200 were Democrats, 187 were Republicans, and 113 were Independents. What is the value of the chi-square test statistic and P-value?
Find the chi-square table here.
A. χ2 = 2.48, P-value is between 0.10 and 0.15
B. χ2 = 2.48, P-value is greater than 0.25
C. χ2 = 2.58, P-value is between 0.10 and 0.15
D. χ2 = 2.58, P-value is greater than 0.25
Answers
The correct answer is: χ2 = 2.48, P-value is between 0.10 and 0.15.
First, let's calculate the expected frequencies for each political party affiliation in the sample:
Expected frequency for Democrats: 0.42 x 500 = 210
Expected frequency for Republicans: 0.34 x 500 = 170
Expected frequency for Independents: 0.24 x 500 = 120
Next, we can set up the chi-square test:
χ² = Σ((O - E)² / E)
Where:
O = observed frequency
E = expected frequency
Let's calculate the chi-square test statistic:
χ² = ((200-210)² / 210) + ((187-170)² / 170) + ((113-120)² / 120)
Calculating the above expression gives us:
χ² = (10² / 210) + (17² / 170) + (7² / 120)
χ^2 = 100/210 + 289/170 + 49/120
χ^2 ≈ 0.476 + 1.700 + 0.408
χ^2 ≈ 2.584
The calculated chi-square test statistic is 2.584.
Since we have 3 political party affiliations, the degrees of freedom would be 3 - 1 = 2.
Looking at the chi-square distribution table with 2 degrees of freedom, we find that the P-value for a chi-square test statistic of 2.584 is between 0.10 and 0.15.
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Factor the expression 42a+14b using the gcf
Please figure this out quickly
Answers
If you are trying to factor it is 14(3a+b).
But if you are looking for the greatest common factor it is 14.
The GCF of 42a + 14b is 14 which is 14(3a + b).
What is GCF?GCF stands for the greatest common factor of two or more two given terms. A number is GCF of two or more than two terms is the highest term that divides the given terms completely.
Given, 42a + 14b and we have to factor this with a GCF.
In terms of variables a and b, there is no common factor.
In terms of 14 and 42 GCF is 14 as 14 is the highest no. that divides these two nos. completely.
So, 42a + 14b.
= 14(3a + b).
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y + 2 = -3(x - 4). What is the slope?
Answers
Answer:
m=-3
Step-by-step explanation:
The number of gallons of gasoline used varies directly with the number of miles
driven. If 45 gallons of gasoline have been used after driving 625 miles, how
many gallons would be used after driving 900 miles? *
Answers
64.8 miles or just 65 miles
Help please
The answer choices are
A) x=3/x
B)x=9/x
C)0=3/x+x
D)0=9/x+x
Answers
Answer:
A
Step-by-step explanation:
What are the polar coordinates of the point P shown below?
Select the correct answer below:
(5,5π4)
(4,−5π4)
(5,7π4)
(4,5π4)
(4,7π4)
(5,−5π4)
Answers
Answer:(4,5π/4)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 4, so r=4. The angle of the point is 5π4, so θ=5π4. Thus, the polar coordinates are (4,5π4).