Clyde Cement wants to analyze a shipment of bags of cement. He knows the weight of the bags is normally distributed so he can use the standard normal distribution. He measures the weight of 600 randomly selected bags in the shipment. Next, he calculates the mean and standard deviation of their weights. The mean is 50 lbs and the standard deviation is 1.5 lbs. What percentage of the bags of cement will weigh less than 50 lbs.? 50 60 75 80
Answers
Answer:
50%
Step-by-step explanation:
First, draw a normal distribution plot to use for the analysis of the data. Starting at the mean in the centre. Add one standard deviation for each interval to the right, and subtract one standard deviation for each interval to the right. See attached image. According to the empirical rule, 68% of data lies within one standard deviation of the mean, 95 % of the data is within two st. dev. and 99.7% of the data is within 3 st. dev. of the mean.
From the graph it can be deducted that half of the data will lie below 50, which makes it 50%.
An easier way of determining the answer is to use the definition of a mean. A mean is the number that,when all the data is placed in ascending order, lies right in the middle of all the data.
In a normal distribution, 50% of the values lie below the mean. Therefore, 50% of the bags will weigh less than 50 lbs.
The question involves understanding the properties of a normal distribution where the mean weight of the bags is 50 lbs, and the standard deviation is 1.5 lbs. To determine the percentage of bags weighing less than 50 lbs, we look at the standard normal distribution. Since 50 lbs is the mean, exactly 50% of the bags will weigh less than this amount. This is because, in a normal distribution, the mean divides the distribution so that half the values are below the mean and half are above it.
Related Questions
If ∆JKL ≅ ∆PQR, which one of these is not a pair of corresponding parts? ∠J and ∠P and ∠L and ∠R and
Answers
Answer:
J and P
Step-by-step explanation:
The quotient of 12 times an unknown number and 13 is 6. What is the value of the unknown number?
Answers
12x = 78
x = 6.5
A circle has a radius of 10 centimeters. If 7/8 of the circle is cut away, what is the area of the remaining portion? Use 3.14 for π.
A) 44.86 cm2
B) 3.93 cm2
C) 39.25 cm2
D) 358.86 cm2
Thank you :)
Answers
A=pi*R^2
And we will have:
A=3,14*100 => A=314
Now we need to know how much 7/8 of 314 is:
(87,5%) 7/8*314 = 274,75
The only thing left to do is the diference between the 2 values 314 (100%) and 274,75 (87,5%), wich will be:
314-274,75=39,25
C .
what is an equation of the line in slope intercept form m=3 and the y-intercept is (0 4)
Answers
y = 3x + 4
hope this helps, God bless!
Fred the clown can create 17 animal balloons every 15 minutes.how many animal balloons he could create in 30 minutes and in 60 minutes.
Answers
Answer:
34 balloons in 30 minutes.
68 balloons in 60 minutes.
Step-by-step explanation:
We have been given that Fred the clown can create 17 animal balloons every 15 minutes. We are asked to find the number of balloons created by Fred in 30 minutes and 60 minutes.
To find number of balloons created by Fred in 30 minutes, we will multiply 17 by 2 as 30 is 2 times 15.
[tex]\text{Balloons created in 30 minutes}=2\times 17[/tex]
[tex]\text{Balloons created in 30 minutes}=34[/tex]
Therefore, Fred can create 34 balloons in 30 minutes.
To find number of balloons created by Fred in 60 minutes, we will multiply 17 by 4 as 60 is 4 times 15. This means Fred will create 4 times more balloons in 60 minutes than 15 minutes.
[tex]\text{Balloons created in 60 minutes}=4\times 17[/tex]
[tex]\text{Balloons created in 60 minutes}=68[/tex]
Therefore, Fred can create 68 balloons in 60 minutes.
A water tank is in the shape of a cone.Its diameter is 50 meter and slant edge is also 50 meter.How much water it can store In it ? it releases water to a gated apartment building at the rate of 400 liters per second. In how many minutes tank will be empty?
Answers
Assessing the situation:
Let's get a feel for the shape of the problem here: what step should we be aiming to get to by the end? We want to find out how long it will take, in minutes, for the tank to drain completely, given a drainage rate of 400 L/s. Let's name a few key variables we'll need to keep track of here:
[tex]V[/tex] - the storage volume of our tank (in liters)
[tex]t[/tex] - the amount of time it will take for the tank to drain (in minutes)
We're about ready to set up an expression using those variables, but first, we should address a subtlety: the question provides us with the drainage rate in liters per second. We want the answer expressed in liters per minute, so we'll have to make that conversion beforehand. Since one second is 1/60 of a minute, a drainage rate of 400 L/s becomes 400 · 60 = 24,000 L/min.
From here, we can set up our expression. We want to find out when the tank is completely drained - when the water volume is equal to 0. If we assume that it starts full with a water volume of [tex]V[/tex] L, and we know that 24,000 L is drained - or subtracted - from that volume every minute, we can model our problem with the equation
[tex]V-24000t=0[/tex]
To isolate [tex]t[/tex], we can take the following steps:
[tex]V-24000t=0\\ V=24000t\\ \frac{V}{24000}=t [/tex]
So, all we need to do now to find [tex]t[/tex] is find [tex]V[/tex]. As it turns out, this is a pretty tall order. Let's begin:
Solving for [tex]V[/tex]:
About units: all of our measurements for the cone-shaped tank have been provided for us in meters, which means that our calculations will produce a value for the volume in cubic meters. This is a problem, since our drainage rate is given to us in liters per second. To account for this, we should find the conversion rate between cubic meters and liters so we can use it to convert at the end.
It turns out that 1 cubic meter is equal to 1000 liters, which means that we'll need to multiply our result by 1000 to switch them to the correct units.
Down to business: We begin with the formula for the area of a cone,
[tex]V= \frac{1}{3}\pi r^2h [/tex]
which is to say, 1/3 multiplied by the area of the circular base and the height of the cone. We don't know [tex]h[/tex] yet, but we are given the diameter of the base: 50 m. To find the radius [tex]r[/tex], we divide that diameter in half to obtain r = 50/2 = 25 m. All that's left now is to find the height.
To find that, we'll use another piece of information we've been given: a slant edge of 50 m. Together with the height and the radius of the cone, we have a right triangle, with the slant edge as the hypotenuse and the height and radius as legs. Since we've been given the slant edge (50 m) and the radius (25 m), we can use the Pythagorean Theorem to solve for the height [tex]h[/tex]:
[tex]h^2+25^2=50^2\\ h^2+625=2500\\ h^2=1875\\ h=\sqrt{1875}=\sqrt{625\cdot3}=25\sqrt{3}[/tex]
With [tex]h=25\sqrt{3}[/tex] and [tex]r=25[/tex], we're ready to solve for [tex]V[/tex]:
[tex]V= \frac{1}{3} \pi(25)^2\cdot25\sqrt{3}\\ V= \frac{1}{3} \pi\cdot625\cdot25\sqrt{3}\\ V= \frac{1}{3} \pi\cdot15625\sqrt{3}\\\\ V= \frac{15625\sqrt{3}\pi}{3} [/tex]
This gives us our volume in cubic meters. To convert it to liters, we multiply this monstrosity by 1000 to obtain:
[tex]\frac{15625\sqrt{3}\pi}{3}\cdot1000= \frac{15625000\sqrt{3}\pi}{3}[/tex]
We're almost there.
Bringing it home:
Remember that formula for [tex]t[/tex] we derived at the beginning? Let's revisit that. The number of minutes [tex]t[/tex] that it will take for this tank to drain completely is:
[tex]t= \frac{V}{24000} [/tex]
We have our [tex]V[/tex] now, so let's do this:
[tex]t= \frac{\frac{15625000\sqrt{3}\pi}{3}}{24000} \\ t= \frac{15625000\sqrt{3}\pi}{3}\cdot \frac{1}{24000} \\ t=\frac{15625000\sqrt{3}\pi}{3\cdot24000}\\ t=\frac{15625\sqrt{3}\pi}{3\cdot24}\\ t=\frac{15625\sqrt{3}\pi}{72}\\ t\approx1180.86[/tex]
So, it will take approximately 1180.86 minutes to completely drain the tank, which can hold approximately [tex]V= \frac{15625000\sqrt{3}\pi}{3}\approx 28340615.06[/tex] L of fluid.
Write an expression of the verbal phrase: the quotient of twelve and the product of three times x
Answers
The expression of the verbal phrase 'the quotient of twelve and the product of three times x' is 12 / (3x).
Explanation:The verbal phrase 'the quotient of twelve and the product of three times x' can be expressed as:
12 / (3x)
In this expression, '12' represents the dividend or numerator, '3' represents the factor or multiplier, and 'x' represents the variable or unknown. The quotient symbol '/' represents division, and the multiplication symbol 'x' represents the product of three times x.
What are expressions like 4(3+2) and 4(3)+4(2) called
Answers
what is 0.0018 in scientific notation
Answers
=
1.8 x 10^-3
Scientific notation makes it easier to work with very small numbers, like 0.0018.
To express the number 0.0018 in scientific notation, we need to rewrite it as a product of a number between 1 and 10, and a power of 10. Here are the steps:
Identify the Initial Decimal Point Position: The number 0.0018 initially has the decimal point immediately after the zero whole part, before any significant figures.
Move the Decimal Point to the Right: Move the decimal point to the right until there is exactly one non-zero digit to the left of the decimal point. For 0.0018, moving the decimal point three places to the right converts it to 1.8.
Count the Moves: In this case, we moved the decimal three places to the right. Each move to the right represents a negative exponent in scientific notation.
Write in Scientific Notation: The scientific notation form of 0.0018 is written as:
[tex]1.8 \times 10^{-3}[/tex]
The [tex]10^{-3}[/tex] indicates that the decimal point was moved three places to the right.
The picture below shows a pole and its shadow: What is the height of the pole? A.196 B.244 C.388 D.364
Answers
Answer: 364
Step-by-step explanation: a^2+b^2=c^2
27^2+b^2=365^2
729+b=133,225
-
729 cancel that out then
133,225
-
729
————
132,496 squared~ 364
Identify the transformations that map rectangle A to triangle A
Answers
Answer:
It is D. I just did it. D) reflect over y-axis, translate 4 units right, then translate 10 units down
Step-by-step explanation:
A 5 in by 7in photograph is surrounded by a frame of uniform width the area of the frame equals the area of the photograph find the width of the frame
Answers
Let x be the
width of the frame.
Area of the picture is 5*7 = 35 sq in
Area of the frame given as the same, frame = 35 sq in also
Therefore the total area (picture & frame) will be 70 sq in
A simple equation would be made and it will look like this: (7+2x) * (5+2x) =
70
Using the FOIL
method
35 + 14x + 10x + 4x^2 = 70
4x^2 + 24x + 35 - 70 = 0; subtract 70 from both sides:
4x^2 + 24x - 35 = 0
unluckily this will not factor easily, so we should use the quadratic equation:
where: a = 4; b = 24; c = -35
x = -b sqrt b^2 – 4*a*c divided by 2 * a
x
= -24 ±
sqrt 24^2 -4*4*(-35) divided by 2*4
x = -24 ±sqrt 576 -
-(560) divided by 8
x = -24 ± sqrt 576 + 560 divided by 8
x = -24 ± sqrt1136
divided by 8
x = -24 + 33.7046 divided by 8
x = 9.7046 divided by 8
x =1.213 inches is the answer
And object is traveling at a steady speed of 8 2/3 mph how long will it take to object to travel 5 1/5 miles
Answers
which is just 36 minutes.
You have 12 cups of granola and 8 1/2 cups of peanuts to make trail mix. What is the greatest number of full batches of trail mix you can make? Explain how you found your answer. ( The Trail Mix Recipe : 2 2/3 cups granola, 1 1/3 cups of peanuts )
Answers
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is:
A)5
B)3
C) 2.5
D) 0.2
The slope represents:
A)The total cost of the taxi ride
B)The total number of miles driven
C)The cost per mile traveled
D) the initial cost of the ride
Answers
the slope is 2.5
i know this because:
(0,2) (6,18)
18-2 = 16/6 = 2.5
6 - 0 =16/6 = 2.5
Given the quadratic function 3x^(2) =8x-5 what are the values of x?
Answers
3x^2 - 8x + 5 = 0 move all terms to one side
3x^2 - 3x - 5x + 5 = 0 split them into two terms
3x(x - 1) - 5(x - 1) = 0 factor out common terms in the first two terms, then the last two terms.
(x - 1)(3x - 5) = 0
x = 1, 5/3
hope this helped, God bless!
Answer:
The values of x are [tex]\frac{5}{3}[/tex] and 1.
Step-by-step explanation:
Given quadratic function[tex]3x^2=8x-5[/tex]
We have to solve for x.
Consider the given quadratic function [tex]3x^2=8x-5[/tex]
This can be written as [tex]3x^2-8x+5=0[/tex]
We can solve the above quadratic equation using middle term split method,
-8x can be written as -3x - 5x
Thus, the equation becomes,
[tex]3x^2-8x+5=0[/tex]
[tex]\Rightarrow 3x^2-3x-5x+5=0[/tex]
Taking 3x common from first two term and -5 common from last two terms, we get,
[tex]\Rightarrow 3x(x-1)-5(x-1)=0[/tex]
[tex]\Rightarrow (3x-5)(x-1)=0[/tex]
Now using zero product property [tex]a.b=0 \Rightarrow a=0\ or\ b=0[/tex] , we have,
[tex]\Rightarrow (3x-5)=0[/tex] or [tex]\Rightarrow (x-1)=0[/tex]
[tex]\Rightarrow x=\frac{5}{3}[/tex] or [tex]\Rightarrow x=1[/tex]
Thus, The values of x are [tex]\frac{5}{3}[/tex] and 1.
in the diagram below eg=100, ef=4x-20, and fg=2x+30
Answers
The lengths of segments x=15, EF=40, FG=60.
To solve for x, we can use the fact that the total length of segment EG is equal to the sum of the lengths of segments EF and FG.
EG = EF + FG
Substituting the given values, we get:
100 = 4x - 20 + 2x + 30
Combining like terms, we get:
100 = 6x + 10
Subtracting 10 from both sides, we get:
90 = 6x
Dividing both sides by 6, we get:
15 = x
Therefore, the value of x is 15.
We can now solve for the lengths of segments EF and FG.
EF = 4x - 20
Substituting the value of x, we get:
EF = 4(15) - 20
EF = 60 - 20
EF = 40
FG = 2x + 30
Substituting the value of x, we get:
FG = 2(15) + 30
FG = 30 + 30
FG = 60
Therefore, the lengths of segments EF and FG are 40 and 60, respectively.
Answer:
x = 15
EF = 40
FG = 60
Jose drives a truck for a soft drink company. His truck is filled with
15-ounce cans and 70-ounce bottles. Let c be the number of 15-ounce cans the truck is carrying, and let b be the number of 70-ounce bottles.Suppose the truck can carry at most 6000 pounds (96,000 ounces).
Using the values and variables given, write an inequality describing this.
PLEASE HELP! I'm struggling so much
Answers
wt = 14 x + (820-x) 70
Answer : 15c+70b<96,000
Step-by-step explanation:
Which is greater 300 kelvins or 34 degrees Celsius ? Show your work
Answers
To answer this item, we are to convert one of the unit to the other. The approach to answering is to convert the 34 degrees Celsius to kelvin by the equation,
T = C + 273.15
Substituting the known value,
T = (34) + 273.15 = 307.15 K
Since 307.15K is greater than 300K then, the greater value is 34 degrees C.
ANSWER: 34 degrees C
Solve for x: −2x − 4 > 8 (1 point)
x < −6
x > −6
x < −2
x > −2
Answers
-2x > 12
x < -6
answer
x < −6
Option A : x < -6 is the correct choice.
We have a inequality -
−2x − 4 > 8
We have solve and find the solutions to this inequality.
What is an Inequality in mathematics ?An inequality compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
−2x − 4 > 8
Add 4 on both sides -
-2x - 4 + 4 > 8 + 4
-2x > 12
Multiply both sides by -1, we get -
2x < - 12
Divide by 2 on both sides -
x < -6
Hence, x < -6 represents the solution of the inequality.
To solve more questions on Solving inequalities, visit the link below -
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What does it mean for event b to be independent of event​ a?
Answers
What is the slope of the line passing through the points (2,7) and (-1,3)?
Answers
Slope of line passing through 2 points, The slope of line passing through points (2,7) and (-1,3) is 4/3.
What is formula for slope of line passing through 2 points?Slope=(y2-y1)/(x2-x1)
The line is passing through two points (2,7) and (-1,3).
The formula for slope is (y2-y1)/(x2-x1).
x1=2,x2=-1,y1=7,y2=3
Slope=3-7/-1-2
=-4/-3
=4/3
Therefore slope of line is 4/3 if line passing through the points (2,7) and (-1,3).
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An item costs $410 before tax, and the sales tax is $20.50 . find the sales tax rate. write your answer as a percentage.
Answers
The percentage of sales tax is 5%.
Given that, an item costs $410 before tax, and the sales tax is $20.50.
What is the sales tax?Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.
Let x% be the sales tax.
Now, x% of 410 = 20.50
0.01x ×410 = 20.50
⇒ 4.1x=20.50
⇒ x=20.50/4.1
⇒ x=5
Therefore, the percentage of sales tax is 5%.
To learn more about the sales tax visit:
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Factor 9x^6 – 16y^6 completely. First factor each term. 9x^6 = (__)2 16y^6 = (__)2
Then use a2 – b2 = (a – b)(a + b).
Show your work.
9x^6 – 16y^6 =
Answers
9 is 3^2 and 16 is 4^2
x^6 is (x^3)^2
so for the answer. factor each term
9x^6 = (3x^3)^2
16y^6 = (4y^3)^2
see that "a" is 3x^3 and "b" is 4y^3 ? put it all together
= (3x^3 - 4y^3)(3x^3 + 4y^3)
Answer:
see the equation they want you to use. factor to make it like that.
9 is 3^2 and 16 is 4^2
x^6 is (x^3)^2
so for the answer. factor each term
9x^6 = (3x^3)^2
16y^6 = (4y^3)^2
see that "a" is 3x^3 and "b" is 4y^3 ? put it all together
= (3x^3 - 4y^3)(3x^3 + 4y^3)
Step-by-step explanation:
Name four angles between 0 and 360 degrees with a reference angle of 20 degrees Show work
Answers
i.e. 20°, 160°, 200° and 340°
Answer with explanation:
Reference Angle =20°
Angle Lies in First Quadrant.
⇒≡Reference Angle of 20°, which should lie between 0° and 360° can be evaluated by using the formula=360°n+20°, for n=0,1,2,3,4,....
So,First Reference angle of 20°=20°
Second reference angle of 20°=360°× 1+20°=380°
Third Reference angle of 20°=360°× 2+20°
=720°+20°
=740°
Fourth Reference angle of 20°=360°×3+20°
=1080°+20°
=1100°
A car travel at an average speed of 48 miles per hour. how many miles does it travel in 4 hours and 15 minutes
Answers
or
48 miles in 60 minutes
4 Hours and 15 minutes are 255 minutes
48/60=.08 miles per minute
255 * .08 = 204 miles
The pair of figures is similar. Find x. Round to the nearest tenth if necessary.
Answers
23(17) = 40x
391/40 = x
9.775 = x
The pair of triangle shown in the diagram are similar. Similar triangle have proportional corresponding sides. So you can write a proportion connecting all given known and unknown sides:
[tex]\dfrac{23}{40}=\dfrac{x}{17}.[/tex]
From here you have that
[tex]40\cdot x=23\cdot 17,\\ \\x=\dfrac{23\cdot 17}{40}=\dfrac{391}{40}=9.775\approx 9.8\ cm.[/tex]
Answer: 9.8 cm.
The sides of the cubes are numbered 1 through 6. If they are both tossed, what is the probability that they will both be a 2?
Answers
it will be 1/36 because the probability of rolling a 2 on one dice is 1/6 so the chance of rolling a 2 on the second dice as well would be 1/36
When Cullen cleaned behind his dresser, he found 73 cents, all in nickels and pennies. There were 25 coins. How many were nickels?
Answers
The number of coins is 25, so we get this equation.
n + p = 25
The value of the coins is 0.05 per nickel, and 0.01 per penny.
0.05n + 0.01p = 0.73
Now you have a system of equations.
n + p = 25
0.05n + 0.01p = 0.73
Solve the first equation for n:
n = 25 - p
Now substitute into the second equation.
0.05(25 - p) + 0.01p = 0.73
1.25 - 0.05p + 0.01p = 0.73
-0.04p = -0.52
p = 13
There were 13 pennies.
Now we substitute 13 for p in n + p = 25 to find out the number of nickels.
n + 13 = 25
n = 12
There are 13 pennies and 12 nickels.
Check: 13 pennies and 12 nickels does total 25 coins.
13 * 0.01 + 12 * 0.05 = 0.13 + 0.60 = 0.73
The value is $0.73.
Our answer is correct.
Best answer ????...........
Answers
-6 - -2 = -4
-5 - - 1 = -4
so y would = x -4
-6 = -2-4
-5 = -1-4
Answer is C