Assume that the weights of quarters are approximately normally distributed with a mean of 5.67 g and a standard deviation of 0.07 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected
Answers
Answer: 1.94%
Step-by-step explanation:
Given: The weights of quarters are approximately normally distributed with \(\mu=5.67\ g\) and \(\sigma=0.07\ g\).
Machine will only accept coins weighing between 5.48 g and 5.82 g.
Let X be the weight of quarters.
The probability that legal quarters will be rejected = P(X<5.48)+P(X>5.82)
\(=P(\dfrac{X-\mu}{\sigma}<\dfrac{5.48-5.67}{0.07})+P(\dfrac{X-\mu}{\sigma}>\dfrac{5.82-5.67}{0.07})\\\\=P(Z<-2.714)+P(Z>2.142)\ \ \ \[Z=\dfrac{X-\mu}{\sigma}]\\\\=(1-P(Z<2.714))+(1-P(Z<2.142))\ \ \ \ [P(Z<-z)=1-P(Z<z)=P(Z>z)]\\\\=(1- 0.9967)+(1-0.9839)\ \ \ \ [\text{By p-value table}]\\\\= 0.0033+0.0161=0.0194=1.94\%\)
Hence, the percentage of legal quarters will be rejected = 1.94%
Related Questions
A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 10.4 seconds.
Answers
Answer:
1.61.6 248248
Step-by-step explanation:
which describes the correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass
Answers
Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.
To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:
Step 1: Draw the angle ABC with a straightedge.
Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.
Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.
Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.
Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.
In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.
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What is the approximate value of θ if tan θ = 7/9
Answers
Answer:
37.9°-----------------------
Taking the inverse tangent (arctan) of the given ratio 7/9.
Use a calculator or trigonometric table to find:
θ ≈ arctan(7/9)The approximate value of θ is 37.9°.
Mr. Arnold's class children make hand prints in the round clay mold for their parents the mall has a diameter of 12 cm what is the molds radius
Answers
Answer:
6
Step-by-step explanation:
the radius is half of the diameter
hope this helped :)
I NEED HELP PLEASE, THANKS! :)
The senior class is having a fundraiser to help pay for the senior trip. Selling a box of chocolates yields a profit of $2.45, while selling a box of cookies yields a profit of $2.70. The demand for cookies is at least twice that of chocolates, but the amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolates produced. Assuming that the senior class can sell every box that they order, how many boxes of each should they order to maximize profit if they cannot order more than 1950 boxes combined? (Show work)
Answers
Answer:
1600 boxes of cookies; 350 boxes of chocolates
Step-by-step explanation:
Let x and y represent the numbers of boxes of cookies and chocolates to order, respectively. The constraints seem to be ...
x ≥ 2yx ≤ 550 +3yx + y ≤ 1950The objective function we want to maximize is ...
p = 2.70x +2.45y
_____
Looking at the problem, we see that cookies yield the most profit, so we'd like to maximize the boxes of cookies sold within the allowed limits.
There are two limits on x:
x ≤ 550 +3y
x ≤ 1950 -y
x will be as large as it can be if it bumps up against these limits simultaneously:
550 +3y = 1950 -y
4y = 1400 . . . . . . . . . add y-550
y = 350
x = 1950 -350 = 1600
Profit will be maximized for an order of 1600 boxes of cookies and 350 boxes of chocolates.
_____
The "feasible region" of the solution is where the three constraint inequalities overlap. It is a quadrilateral with vertices at (0, 0), (550, 0), (1300, 650), and (1600, 350). We can reject the ones with x or y being 0. Per our analysis above, the solution of interest is (x, y) = (1600, 350), since it maximizes x.
The usual protocol for solving a linear programming model like this is to evaluate the objective function at each of the vertices. With a little thought about the problem, we have saved some evaluation effort.
For a binomial experiment, is it possible for the probability of success to change from one trial to the next? I figure that the answer would be no, that as long as the trials are independent (a feature of a binomial experiment, right?), then it would not be possible for the probability of success to change, Am i understanding it correctly?
Answers
Answer:
Yup you get it! (Probability doesn't change, it is constant for all trials)
Step-by-step explanation:
In binomial experiments, you have two conditions, a success and failure is how they often put it. In this experiment, the probability of success has to be the same for each trial to constitute it as a binomial experiment.
Basically there's 4 rule you need to satisfy for an experiment to be considered binomial:
1) Has to have fixed number of trials. Eg, n=1,2,3.....x x= finite number (we cannot have infinte trials)
2) Each trial is independent of one another. (One trial doesn't influence another trials probability/outcome)
3) Only two outcomes (very important) because as name suggests bi- (bi usually means two)
4) Probability of each outcome/condition is constant from one trial to another
the wheel of a bike has a diameter of 27 inches. find the circumference of the wheel.
Answers
The circumference of the wheel of the bike given the diameter is 84.78 inches
What is the circumference of the wheel?As evident from the task content; it is required that the circumference of the bike's wheel be determined.
Given that the Diameter of the wheel = 27 inches
Recall; Radius = diameter / 2
= 27/2
= 13.5 inches
π = 3.14
Since the formula for the Circumference of the wheel which is circular = 2πr
= 2 × 3.14 × 13.5
= 84.78 inches
In conclusion, the circumference of the wheel according to the given description is 84.78 inches.
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simplify 5^3x5^-4 im in desperate need of some help with this
Answers
The value of the exponents 5^3 * 5^-4 is 0.2
We have been the expression as
5^3 * 5^-4
Here we can see that in the second term in the above expression which is 5^-4, the power is negative which is -4.
We know that the numbers which have powers if reciprocated, the sign on the powers get changed. That is if the power is positive and reciprocated it will change to negative. And if it is negative it will convert into positive. So, 5^-4 can be written as 1/5^4.
Numerically, 5^-4 = 1/5^4
Now we can solve the expression as follows,
= 5^3 * 5^-4
= 5^3 * 1/5^4
=1/5^1
= 1/5
=0.2
Hence the value of the exponent is 0.2.
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HELP!!!!!!!!!!!!!!!!!!
Answers
Answer:
D 0.89275
Step-by-step explanation:
Ngân hàng trung ương bán trái phiếu chính phủ
Answers
Answer:
Trong hoạt động mở, Fed mua và bán chứng khoán chính phủ trên thị trường mở. Nếu FED muốn tăng cung tiền, nó sẽ mua trái phiếu chính phủ. ... Ngược lại, nếu FED muốn giảm cung tiền, nó sẽ bán trái phiếu từ tài khoản của mình, do đó thu về tiền mặt và loại bỏ tiền ra khỏi hệ thống kinh tế.
Step-by-step explanation:
em yêu
Find the value of X. Round your answer to the nearest tenth please
Answers
The value of x from the figure is 17.82 units
SOH CAH TOA identity1) From the first figure.
Opposite side = x
Adjacent = 12
Using the SOH CAH TOA identity
tan53 = opp/adj
tan53 = x/12
x = 12tan53
x = 15.92 units
2) Using the SOH CAH TOA identity
cos27 = adj/hyp
cos27 = x/20
x = 20cos27
x = 17.82units
Hence the value of x from the figure is 17.82 units
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f(x)=x^2+12x+35, solve f(x)>0
Answers
Step-by-step explanation:
Solve the eq f(x) =0x^2+5x+7x+35=0
x*x+5x+7x+5*7=0
x(x+5)+7(x+5)=0
(x+7)*(x+5)=0
x=-7 or x=-5
Now solve f(x) >0So the function is positive (>0) when
x<-7 and when x>-5
Kate kicked 25 goal shots at soccer practice and scored on 13 of them. What percent of shots did she make
Answers
Answer:
52%
Step-by-step explanation:
If 25% is the 100% only multiply 13 by 4 and thats it
I need help worth 25 points please help
Answers
the answer is on the pictures
sorry if their wrong
x=1/2 (or 1)
y=3/4
Guys I need help, if a couch costs 200 dollars and is marked up 300 percent, what is the cost?
Answers
Answer:
200 X 300% =$600.00
Step-by-step explanation:
If line BG and CF are parallel,then the supplement of BIE = the supplement of GMD. Is this statement correct? Explain your answers
Answers
The supplement of BIE equals the supplement of GMD is a false assertion if lines BG and CF are parallel.
Describe the supplement angle.Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the total of angle 130° and angle 50° is 180°, hence they are supplementary angles.
Lines BG and CF are parallel, as shown in the figure.
If BIE = X, then its supplement of BIE will be 180 - X;
similarly, if GMD = Y, then its supplement of GMD will be 180 - Y.
Since BG and CF are parallel, the supplements of BIE and GMD are interior angles on the same side ( as shown in figure)
and for parallel line the interior angle on the same side is 180
so 180 - X and 180 -Y there sum should be 180
They cannot be equal
line BG and CF are parallel, then the supplement of BIE = the supplement of GMD are not equal.
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I’m confused, any help?
Answers
Answer:
D
Step-by-step explanation:
Trust me its D because to equal f(x)--->Inf., you need to have x equal a negative
Write an equation of a parabola in vertex form. Vertex (0,-3) and passes through (-8,5)
Answers
The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3.
The vertex form of the equation of a parabola is:
y = a(x-h)² + k
where the vertex = (h, k)
The given vertex, (h, k) = (0, -3)
The line passes through the (-8, 5)
x = -8, y = 5
Substitute x = -8, y = 5, h = 0, y = -3 into the equation to solve for a
y = a(x - h)² + k
5 = a(-8-0)² + (-3)
5 = a(-8)² - 3
-8a = 5+3
-8a = 8
a = 8/-8
a = -1
Substitute a = -1, h = 0, k = -3 into y = a(x - h)² + k
y = -1(x - 0)² - 3
The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3
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Study these equations:
f(x) = 2x – 4
g(x) = 3x + 1
What is h(x) = f(x)g(x)?
h(x) = 6x2 – 10x – 4
h(x) = 6x2 – 12x – 4
h(x) = 6x2 + 2x – 4
h(x) = 6x2 + 14x + 4
Answers
Answer:
6x2-10x-4
Step-by-step explanation:
hx=(2x-4)(3x+1)
hx=2x(3x+1)-4(3x+1)
hx=6x2+2x-12x-4
hx=6x2-10x-4
Write 40/64 in simplest
Answers
Side XY of triangle XYZ is extended to point W, creating a linear pair with ∠WYZ and ∠XYZ.
Triangle X Y Z. Point W extends from side X Y. Angle Z is 36 degrees, angle Y is x degrees, and exterior angle W Y Z is 100 degrees.
What is the value of x?
Answers
Answer:
\(x= 80^o\)
Step-by-step explanation:
Given
\(\angle Z = 36^o\)
\(\angle WYZ = 100^o\)
Required
Find x
\(\angle WYZ\) and x are on a straight line.
So:
\(\angle WYZ + x= 180^o\)
Make x the subject
\(x= 180^o -\angle WYZ\)
Substitute known value
\(x= 180^o -100^o\)
\(x= 80^o\)
Answer:
80 is correct
Step-by-step explanation:
ou are working with the penguins dataset. you want to use the summarize() and mean() functions to find the mean value for the variable body mass g. you write the following code: penguins %>% drop na() %>% group by(species) %>% add the code chunk that lets you find the mean value for the variable body mass g.
Answers
The mean body mass of the Adelie species is 3706.164 g.
Original chunk of code:
penguins %>%
drop_na() %>%
group_by(species) %>%
The code chunk summarize(mean(body_mass_g)) lets you find the mean value for the variable body_mass_g. The correct code is
penguins %>% drop_na() %>% summarize (mean(body_mass_g)).
The summarize () function displays summary statistics. We can use the summarize() function in combination with other functions - such as mean(), max(), min() - to calculate specific statistics. In this case, you use mean() to calculate the mean value for body mass.
Hence, The mean body mass for the Adelie species is 3706.164 g.
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The US consumes an average of 5.25 million metric tons of bananas per year. There are 317 million people in the US and there are 1000 kg in 1 metric ton. It costs $2.10 per kilogram for these bananas. How much money will the US spend on bananas this year?
Answers
Consumption of Bananas in a year = 5.25 million metric tons [5,250,000]
We know 1000 kg = 1 metric ton, So, the consumption of bananas, in kgs will be:
\(5,250,000\times1000=5,250,000,000\operatorname{kg}\)The cost of 1 kg of bananas is $2.10
So, the total cost would be:
\(5,250,000,000\operatorname{kg}\times\$2.10\/kg=\$11,025,000,000\)Thus, the amount of money the US will spend on bananas this year:
$11, 025, 000, 00018 is divisible by both 2 and 3 it is also divisible by 2 into 36 similarly a number is divisible by both 4 and 6 can we say that the number must also be divided by 4 and 2 6 24 if not give an example to justify your answer
Answers
Answer:
no; 12
Step-by-step explanation:
A number divisible by 4 and 6 will be divisible by their least common multiple, 12. If it is an odd multiple of 12, it will not be divisible by 24.
Examples:
12÷4 = 3; 12÷6 = 2; 12 is not divisible by 24
24÷4 = 6; 24÷6 = 4; 24 is divisible by 24
36÷4 = 9; 36÷6 = 6; 36 is not divisible by 24
Easy math equations giving brainlest
Answers
Answer:
Problem 7 = 7, Problem 6 = 1
Step-by-step explanation:
Problem 7:
(x+3)/5 = 2
x+3 = 10
x = 7
Problem 6:
c = 12
-1/3*12 = -4
-4+5 = 1
You will need a pencil and paper.
Nick is deciding what to wear. He has two baseball hats and wants to wear either a sweatshirt or a sweater. How many different combinations are possible?
4 combinations
5 combinations
6 combinations
7 combinations
Answers
The number of different combinations that are possible for Nick, given his baseball hats are A. 4 combinations.
How to find the number of combinations?Nick has two options for hats, and two options for sweatshirts/sweaters. To find the number of combinations, we can multiply the number of options for each item.
There are two baseball hats and two clothes - sweatshirt and sweater.
The number of combinations is:
= 2 (hats) x 2 (sweatshirts/sweaters)
= 4 combinations
In conclusion, as regards the number of combinations that Nick can make, there are four.
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which expression is equivalent to 3(9p+2r)
Answers
Answer:
27p+6r
Step-by-step explanation:
3(9p+2r)
1 Solve the product 3(9p+3 2r)
3⋅9p+3x2r
Multiply 3 times 9
27p+3x2r
Final Answer
27p+6r
Which fractions are equal to 0.6
1 over 6,60 over 100,1 over 60,6 over 10
Answers
a line passes through the point (8.5) ABD has a slope of -8.2
Answers
The equation of the line is expressed in slope-intercept form as:
y = -8.2x - 60.6
How to Find the Equation of a Line?The equation of a line that passes through point (8, 5) and has a slope of -8.2 can be written in slope-intercept form as y = mx + b, where we have:
m as the slope
b as the y-intercept.
Find the y-intercept by substituting x = 8, y = 5, and m = -8.2 into y = mx + b:
5 = -8.2(8) + b
5 = 65.6 + b
5 - 65.6 = b
b = -60.6
Substitute m = -8.2 and b = -60.6 into y = mx + b:
y = -8.2x - 60.6
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Three friends divide two bags of apples equally between them. Enter the division represented by this situation as a fraction.
Answers
Answer:
3/5
Step-by-step explanation:
Answer: I would say 3 divided by 2 or it would be 3/2.
Step-by-step explanation: Hit me up if i got it right:)