Complete Question
The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.
Required:
a) Find the probability that the drink is less than 11.9 fluid ounces
b) Find the probability that the drink is between 11.6 and 11.9 fluid ounces
c) Find the probability that the drink is more than 12.6 fluid ounces. Can this be considered an unusual event? Explain your reasoning.
Answer:
a
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
b
[tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
c
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Yes It is an unusual event
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 12.1[/tex]
The standard deviation is [tex]\sigma =0.3[/tex]
Generally the probability that the drink is less than 11.9 fluid ounces is mathematically represented as
P(X < 11.9 ) = P(\frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} )
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex] P(X < 11.9 ) = P(Z< -0.667 ) [/tex ]
From the z table the area under the normal curve to the left corresponding to -0.667 is
P(Z< -0.667 ) = 0.25239
So
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
Generally the probability that the drink is between 11.6 and 11.9 fluid ounces is mathematically represented as
[tex] P( 11.6 < X < 11.9 ) = P( \frac{11.6 -12.1}{0.3} < \frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} ) [/tex]
[tex]P( 11.6 < X < 11.9 ) = P( -1.667 < Z < -0.667 ) [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = P( Z < -0.667) - P ( Z < -1.667 ) [/tex]
From the z table the area under the normal curve to the left corresponding to -1.667 is
P(Z< -1.667 ) = 0.047757
So
[tex]P( 11.6 < X < 11.9 ) = 0.25239 - 0.047757 [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
Generally the probability that the drink is more than 12.6 fluid ounces is mathematically represented as
P(X > 12.6 ) = P(\frac{X -\mu}{\sigma } > \frac{12.6 - 12.1}{0.3} )
[tex] P(X >12.6 ) = P(Z> 1.667 ) [/tex ]
From the z table the area under the normal curve to the right corresponding to 1.667 is
P(Z> 1.667 ) = 0.047757
So
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Given that this probability is less than 0.05 , it mean it is an unusual event
Please could you show the working out as well:)
Answer:
( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{15}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{2 + 5}{15}[/tex] = [tex]\frac{7}{15}[/tex]
[tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{18-7}{21}[/tex] = [tex]\frac{11}{21}[/tex]
[tex]\frac{7}{15}[/tex] , [tex]\frac{1}{2}[/tex] , [tex]\frac{11}{21}[/tex]
LCD (2, 15, 21) = 210
[tex]\frac{98}{210}[/tex] , [tex]\frac{105}{210}[/tex] , [tex]\frac{110}{210}[/tex]
105 - 98 = 7
110 - 105 = 5 ⇒ [tex]\frac{11}{21}[/tex] is closer to [tex]\frac{1}{2}[/tex] ⇒ ( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation
h = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
t 0.87 s
t 4 s
t = 8.5 s
t = 16 s
Answer:
B on edge 2022
Explanation:
Picture:
The time it takes the rock to reach the canyon floor is 8.5 seconds.
Option C is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Using the quadratic formula.
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 0, and c = 255.
Now,
Plugging in the values.
t = (-0 ± √(0² - 4(-16)(255))) / 2(-16)
t = (± √(16320)) / (-32)
t = (± 128) / (-32)
So,
The solutions for t.
t = 4 seconds (taking the negative solution)
t = 8.5 seconds (taking the positive solution)
We can eliminate t = 0.87 seconds and t = 16 seconds as they are not solutions to the equation.
Therefore,
The time it takes the rock to reach the canyon floor is 8.5 seconds.
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What is the following product?
RootIndex 4 StartRoot 7 EndRoot times RootIndex 4 StartRoot 7 EndRoot times RootIndex 4 StartRoot 7 EndRoot times RootIndex 4 StartRoot 7 EndRoot
4 (RootIndex 4 StartRoot 4 EndRoot)
4 StartRoot 7 EndRoot
74
7
Answer:
the answer A .4 (RootIndex 4 StartRoot 4 EndRoot)
Step-by-step explanation:
The product of the radical is [tex]50176\sqrt{7}[/tex]
Multiplication of RadicalData:
[tex]4\sqrt{7} *4 \sqrt{7} * 4\sqrt{7} * 4\sqrt{7} * 4\sqrt{7}[/tex]To multiply the given radical, we can start by solving
[tex]4\sqrt{7} *4 \sqrt{7} * 4\sqrt{7} * 4\sqrt{7} * 4\sqrt{7}[/tex]
We should know that multiplying two identical radicals will give just one of the entity.
[tex]\sqrt{x} * \sqrt{x} = x\\x\sqrt{y} * x\sqrt{y}= (x*x)\sqrt{y}=x^2\sqrt{y}[/tex]
Using this system, we can solve the giving problem.
Let's multiply this through and get the final answer.
[tex]4\sqrt{7} *4 \sqrt{7} * 4\sqrt{7} * 4\sqrt{7} * 4\sqrt{7} = 50176\sqrt{7}[/tex]
The product of the radical is [tex]50176\sqrt{7}[/tex]
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a piece of metal has a mass of 2210g the volume of the metal is 260cm3 what is the density of the piece of metal
Answer:
The density is 8.5 g/cm³
Step-by-step explanation:
The density formula is density = mass/volume
When we plug our numbers into the formula, we get:
Density = 2210 / 260
We can then solve and get our answer 8.5 g/cm³
It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³.
How are density, volume and mass of a substance related?Suppose that a finite amount of substance is there having its properties as:
The mass of substance = m kg
The density of substance = d kg/m³
The volume of that substance = v m³
Then, they are related as:
[tex]d = \dfrac{m}{v}[/tex]
It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 .
density = mass/volume
When we substitute our numbers into the formula, we get:
Density = 2210 / 260
Density = 8.5 g/cm³
It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³
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If the mean of 20 prices is $10.39, and 5 of the items with a mean of $10.99 are sampled, what is the mean of the other 15 prices?
Answer:
$10.19
Step-by-step explanation:
We are told:
If the mean of 20 prices is $10.39
We have to find the total price
= Mean × number of prices
= 20 × $10.39
= $207.8
5 of the items with a mean of $10.99 are sampled
We would also find the total price
Mean × Number of samples
$10.99 × 5
= $54.95
what is the mean of the other 15 prices?
We find the total prices of the 15 prices
= Total 20 prices - Total of 5 prices
= $207.8 - $54.95
= $152.85
The mean of the other 15 prices
= $152.85/15
= $10.19
I put D since I believe HL applies here but am not sure. Could anybody please help?
====================================================
Explanation:
Check out the diagram below.
On the left side shows ASA can be used to prove the triangles congruent. Note the color coding to see how the angles match up. Also note that the segment TR is between angles STR and SRT. The order is important because ASA is different from AAS.
Angle STR = Angle VTU because they are vertical angles
Angle SRT = Angle VUT since they are alternate interior angles. Note how SR is parallel to UV. If the lines weren't parallel, then the alternate interior angles would not be congruent.
We can use AAS because if we know two angles of a triangle, we can find the third angle. Despite the fact that something like RST looks like a right angle, we don't have enough info to say it is or not. The square angle marker is missing. So it could be 90 degrees, or it might be something like 89 degrees instead. We don't have enough info. So we cannot use HL.
AAA or AA is not a congruence theorem. It's a similarity theorem. So we cross this off the list.
Solve for indicated variable
Answer:dusy
Step-by-step explanation:
Answer:
h = SA/(2πr) - r
Step-by-step explanation:
From what I understood of the the statement, we have to solve the equation for the variable h. So, we just have to isolate that variable in one side. See:
[tex]SA = 2\pi r^2 + 2\pi rh\\\\2\pi rh = SA - 2\pi r^2\\\\h = \dfrac{ SA - 2\pi r^2}{2\pi r}\\\\\boxed{h = \dfrac{SA}{2\pi r} - r}[/tex]
Brian has 17 fewer marbles
than Kyle. Brian has
21 marbles. How many
marbles does Kyle have?
Answer:
the answer to your question is 38.
There are 38 marbles does Kyle have.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Brian has 17 fewer marbles than Kyle.
And, Brian has 21 marbles.
Now,
Let number of marbles Kyle have = x
Then, Number of marbles Brian have = x - 17
But, Brian has 21 marbles.
So, We get;
x - 17 = 21
x = 21 + 17
x = 38
Thus, There are 38 marbles does Kyle have.
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(1,2) and parallel to 3x+4y=12
Answer:
y=-3/4x+10/4
Step-by-step explanation:
1) Change given equation to slope intercept form:
3x+4y=12
4y=12-3x
y=3-(3/4)x
y=-(3/4)x+3
2) Parallel lines have the same slope, so the first part of the equation is:
y=-(3/4)x+b
3) To find b, we plug in y=2 and x=1 given the prompt:
2=-(3/4)(1)+b
2=-3/4+b
2 3/4=b
10/4=b
4) Therefore, the correct equation is:
y=-3/4x+10/4
The graph shows the number of centimeters a particular plant grows over time. Given the points (0,0) and (6,9), how many centimeters does the plant grow per week?
Answer: 4/5 or 0.8
Step-by-step explanation: To find how much it grows over time, we have to find the slope. to do that, we need to have two points with exact points on the graph, so (0,0) and (4,5). the equation for slope is rise/run. it rises 4, and runs 5. so 4/5.
If two sides of a triangle are 7 and 14, the third side may be?
Answer:
it would be 2
Step-by-step explanation:
Answer:
smaller than the sum of the other two sides
In this case less than 21
Step-by-step explanation:
Triangle Inequality Theorem
What is the area of a square with sides of length 9?
O A. 54 square units
B. 81 square units
O C. 18 square units
O D. 36 square units
SUE
12. pesos de 100 es: %
Answer:
la respuesta es 80 pesos espero que te ayude
the ratio 60 miles per hour is an example of a because it has two measurements having different units of measure
Answer:
180
Step-by-step explanation:
Answer: ejejejwjfmfmdnc
Step-by-step explanation:
HELP! write y+4 =-2/3(x-9) in standard form
please help me write the expressions I'm terrible at word problems!!
Answer:
Expression: 2.89+(1.28x3) Answer: 6.73
Step-by-step explanation:
Number 1
5(2y-3)-4y=8-2y-15
Justify each step with a property of algebra. Drag the property to the correct row.
Please help thanks :)
Answer:
A) Symmetric Property Of Equality
Step-by-step explanation:
[tex]The\ symmetric\ property\ of\ equality\ just\ says\ that\ , if\ the\ LHS=RHS; then; RHS=LHS[/tex]
[tex]Here,\\-5=x\\x=-5[/tex]
In the orchestra, there
are eight violinists in the
front row. How many
different ways can
they be seated?
Explanation:
We have 8 choices for the first slot, 7 for the second, and so on. We count our way down until we have 1 choice left for the eighth slot.
We'll get 8*7*6*5*4*3*2*1 = 40,320 different permutations.
You could use the nPr formula
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
with n = 8 and r = 8 to get the same result. The exclamation marks indicate factorials.
The 8 violinists can be seated in 40,320 ways.
What is permutation?A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Given In the orchestra, there are eight violinists in the front row,
the sitting arrangement of violinists is done with the help of permutation,
ⁿPₓ = n!/(n - x)!
here n = 8 and x = 8
(n - x)! = (8 - 8)!
(n - x)! = = 0! = 1
⁸P₈ = 8!/1
⁸P₈ = 8 x 7 x 6 x 5 x 4 x 3 x 2 x1
⁸P₈ = 40,320
Hence they can be seated in 40,320 ways.
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There were 3 squirrels and 18 acorns on Josh's back porch. What was the ratio of acorns to squirrels? Enter your answer in reduced form.
Answer: 1:6
Step-by-step explanation:
Reduce each side of the ratio
Answer:
For every 1 squirrel there are 6 acorns
Step-by-step explanation:
u just divide 18 by 3
In parallelogram WXYZ, what are the coordinates of the point of intersection of WY and ZX?
Point of Intersection = ____ ____
Answer:
Point of intersection of WY and ZX is (3.5, 3.5).
Step-by-step explanation:
Since, diagonals of a parallelogram bisect each other,
Point of intersection of the diagonals will be midpoint of each diagonal.
By this property, midpoint (x, y) of the segment joining W(-2, 6) and Y(9, 1) will be,
[tex]x=\frac{x_1+x_2}{2}[/tex]
x = [tex]\frac{-2+9}{2}[/tex] = 3.5
Similarly, y-coordinate of the midpoint will be,
y = [tex]\frac{y_1+y_2}{2}[/tex]
y = [tex]\frac{6+1}{2}[/tex] = 3.5
Therefore, point of intersection of the diagonals of the given parallelogram will be (3.5, 3.5).
On Saturday, Nikki and Tyler walked to the local farmer’s market. Nikki bought 8 apples for $6. Tyler bought 3 fewer apples than Nikki. How much did Tyler spend on apples?
Answer: 3.75
Step-by-step explanation:
8 apples = $6
4 apples = $3
2 apples = $1.5
1 apple = 0.75
3 +.75= 3.75
Answer:
3.75
Step-by-step explanation:
8/6 is 75 cents 8-3 is 5 75 cents x 5 3.75
Twice the sum of a number and five is equal to six
Answer:
-2
Step-by-step explanation:
Let the no. be x
So, By question,
2(x+5)=6
x+5=3
x=-2
Answer:
2(n+5)=6
Step-by-step explanation:
twice=2*
the sum of a number and five= (n+5)
equals six-=6
------------------------------------------
DISTRIBUTE= 2n+10=6 (Distributive Property)
subtract 10 on both sides= 2n=-4 (subtraction Property of Equality)
divide by two on both sides= n=-2 (Division Property)
Explain to me in words how you would find the slope of this line and then tell me the answer and how u got it
......
Explanation:
The slope of the line is found by the method: rise/run
You calculate how much the slope rises(goes up) and divide it by run(goes horizontal).
One more thing to note is that: the slope is negative BECAUSE ITS DECREASING.
Your answer: -3/2
Help plsssssssssssssssssssssss thanks so much
Answer:
4 3/8
Step-by-step explanation:
1 1/4 * 3 1/2
9[tex]\frac{2}{4}[/tex] or 9[tex]\frac{2}{4}[/tex]
Step-by-step explanation:
So when it says he biked 3[tex]\frac{1}{2}[/tex] ur suppose to add it 3 times then u add the both ones on the top and u get 2 then the answer u get is either 9[tex]\frac{2}{4}[/tex] or 9[tex]\frac{2}{2}[/tex]
which pair of lines are perpendicular lines?
Answer:
D.) y = -1/4x - 6 and y = 4x + 11
Step-by-step explanation:
If two lines are perpendicular, that means that their slopes are opposite reciprocals, or that the product is equal to -1. -1/4 times 4 is -1, so they are perpendicular.
can u pls help me with this question
Answer:
The correct answer is D, 6/8.
Step-by-step explanation:
For ratios or fractions an equivalent fraction has the same value but just more pieces. Think of it like a pizza. But to make sure they are equivalent you have to multiply or divide them by a fraction equal to 1. In other words the numerator and the denominator have to be the same number. So, when we multiply 3/4 by 2/2 you get 6/8 because 3 x 2 = 6 (numerators) and 4 x 2 = 8 (denominators).
If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. Stay safe and please mark brainliest! :)
Compare. Select <, >, or=.
3.568 ? 3.577
Answer:
3.568 < 3.577
Step-by-step explanation:
3.568 < 3.577
So 3.577 is greater than 3.568
Jack has a saving account of value $65,550 at the start. The saving account has an interest rate of 3% that is compounded every six months. How long will it take Jack to have $100,000 in his account?
Given:
Principal value = $65,550
Rate of interest = 3% compounded every six month
To find:
The taken to have $100,000 in Jack's account.
Solution:
The formula for amount is
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is time in number of years.
Interest compounded every six month. It means, interest compounded 2 times in an year.
Substitute A=100000, r=0.03 and n=2 in the above formula.
[tex]100000=65550(1+\dfrac{0.03}{2})^{2t}[/tex]
[tex]\dfrac{100000}{65550}=(1+0.015)^{2t}[/tex]
[tex]1.525553=(1.015)^{2t}[/tex]
Taking log on both sides.
[tex]\log (1.525553)=\log (1.015)^{2t}[/tex]
[tex]\log (1.525553)=2t\log (1.015)[/tex]
[tex]\dfrac{\log (1.525553)}{2\log (1.015)}=t[/tex]
[tex]t=14.1838928[/tex]
[tex]t\approx 14.18[/tex]
Therefore, after 14.18 year the amount will reach at $100,000 or we can say that in 15th year the amount will reach at $100,000.
How far is the robot claw from the winter lane
Answer:
4 blocks.
Step-by-step explanation: