The empirical rule states that in a normal distribution, 68% of the observations lie within 1 standard deviation from the mean, 95% of the observations lie within 2 standard deviations from the mean, and , 99.7% of the observations lie within 3 standard deviations from the mean.
a) - Mean = U = 330 grams
standard deviation= [tex]\sigma=40 \: grams[/tex]
As per the empirical rule, 68% of the observations lie within 1 standard deviation from the mean.
Let [tex]X_1[/tex] and [tex]X_2[/tex] be the 2 random value, between which 68% of the observations lie.
Mathematically,
[tex]X1=U-\sigma[/tex]
[tex]X1[/tex] = 330 - 40
[tex]X1[/tex] = 290
Similarly,
[tex]X1=U-\sigma[/tex]
[tex]X1[/tex] = 330 + 40
[tex]X1[/tex] = 370
Thus, about 68 % of organs will be between 290 and 370 grams in weight.
b) - In this, we need to find the percentage of organs weighing between 250 grams and 410 grams.
We can rewrite 250 as follows:
250= 330− 80 ⇒ 30−2(40) ⇒ 330−2(σ)
The above value (250) lies within 2 standard deviations from the mean.
Similarly,
We can rewrite 410 as follows:
410 = 330+80 ⇒ 330+2(40) ⇒ 330+2(σ)
The above value (410) lies within 2 standard deviations from the mean.\
As per the empirical rule, 95% of the observations lie within 2 standard deviations from the mean.
Thus, 95% of organs weighs between 250 grams and 410 grams.
c)-As we have calculated in part(b) that 95% of the organs lie within 250 and 410 grams.
So, area outside these values = Total area under curve - 95%
= 100 - 95 ⇒ 5%
So, 5% of the area lies outside the 250 and 410 grams range.
From the property of normal curve, we know that the area under the curve is divided into 2 equal parts.So, we divide the area- 5% into 2 equal parts which gives 2.5%.
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A freight elevator can hold a maximum weight of 2,500 pounds. A 180-pound person has a load of boxes to deliver. Some of the boxes weigh 25 pounds each, and some weigh 60 pounds each. Complete parts (a)-(c). Question content area bottom Part 1 a. Write and graph an inequality that represents the number of boxes the elevator can hold in one trip if the person is not in the elevator. Let x represent the number of 25-pound boxes, and let y represent the number of 60-pound boxes. Write an inequality that represents the number of boxes the elevator can hold in one trip if the person is not in the elevator.
The inequality is 25x + 60y + 180 ≤ 2500. x and y are variables.
What is inequality?
In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, whether it is less than or greater than.
Given that a 180-pound person has a load of boxes to deliver. There are types of boxes. The weight of the first type of box is 25 pound and the second type of box is 60 pounds.
Let x represent the number of 25-pound boxes, and let y represent the number of 60-pound boxes.
The weight of x number of boxes is 25x
The weight of y number of boxes is 60y
The person carrying the box means he is also in the elevator.
The total weight of the boxes and the person is 25x + 60y + 180.
The elevator can hold a maximum weight of 2,500 pounds.
The wight of the boxes and the person must be less than or equal to 2500 pounds.
The inequality is
25x + 60y + 180 ≤ 2500
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show solutions if any 20. -7x + 7y = 1
2x - 2y = -18
The equations are two parallel lines, then the system of equations has no solutions.
How to solve the system of equations?Here we have a system of equations:
-7x + 7y = 1
2x - 2y = -18
Now, if we multiply the second equation by (7/2) we will get:
(7/2)*(2x - 2y) = -18*7/2
7x - 7y = -63
If we multiply this by -1 we will get:
-1*(7x - 7y) = -1*-63
-7x + 7y = 63
Then the system of equations becomes:
-7x + 7y = 1
-7x + 7y = 63
Notice that the left side is equal in both equations but the right side is different, then the system has no solutions.
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The table shows conversions of common units of capacity.
Units of Capacity
Customary System Units
Metric System Units
1 gallon
3.79 liters
1 quart
0.95 liters
1 pint
0.473 liters
1 cup
0.237 liters
How many deciliters are equivalent to 9 cups? Use the conversion table to find the answer. Round to the nearest tenth.
21.3 dL
42.7 dL
213.3 dL
426.6 dL
According to the unit conversion table, there are 21.3 dL in 9 cups.
What is unit conversion?The unit conversion is the term used when we convert a unit of a quantity into another unit but the quantity remains the same.
Given that,
A table showing conversions for common units of capacity
Units of capacity
Customary System Units Metric System Units
1 gallon 3.79 liters
1 quart 0.95 liters
1 pint 0.473 liters
1 cup 0.237 liters
We are asked to find there are how many deciliters which is equivalent to 9 cups,
Since,
1 cup = 0.237 liters
1 liter = 10 dL
Therefore,
1 cup = 0.237 x 10 = 2.4 dL
9 cups = 2.4 x 9
= 21.3
Hence, according to the unit conversion table, there are 21.3 dL in 9 cups.
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What is the area of the base of this right triangular prism?
Check the picture below.
I need two linear equations representing the situation. The information is in the picture
Answer:
[tex]x - y = 14[/tex]
[tex]x + y = 58[/tex]
Step-by-step explanation:
x = Number of tickets
y = Number of tickets your friend sells
Together, you and your friend sell 58 tickets: [tex]x + y = 58[/tex]
You sell 14 more tickets than your friend: [tex]x = y + 14[/tex]
= [tex]x -y = 14[/tex]
∴System of linear equations:
[tex]x - y = 14[/tex]….(equation i)
[tex]x + y = 58[/tex]….(equation ii)
True or False. assume the variables x, y, and z have each been assigned an integer value. write a fragment of code that assigns the least of these three variables to another variable named min.
True. The variables x, y, and z have each been assigned an integer value.
Here is a fragment of code that assigns the least of three integer variables to another variable named min:
min = x # initialize min to the value of x
if y < min: # check if y is less than min
[tex]min = y[/tex] # [tex]update min to the value of y if y is less than min[/tex]
if z < min: # check if z is less than min
[tex]min = z[/tex] # [tex]update min to the value of z if z is less than min[/tex]
In this code, the variable 'min' is first initialized to the value of 'x'. Then, the code checks if 'y' is less than 'min', and if so, updates the value of 'min' to 'y'. Finally, the code checks if 'z' is less than 'min', and if so, updates the value of 'min' to 'z'. At the end of this code fragment, the variable 'min' will contain the least of the three variables 'x', 'y', and 'z'.
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A quantity with an initial value of 200 grows continuously at a rate of
4% per second. What is the value of the quantity after 1.55 minutes, to the nearest hundredth?
Answer:
8252.88
Step-by-step explanation:
This question is a little tricky. you have to use the time a little differently.
Continuously Compounding formula:
P(t)=P(0)e^(rt)
P(0) = initial or starting value
e = constant, on calculator but around 2.718
r = rate
t = The time. usually expressed annually. For example continuously compounding for 6 months, the time would be 0.5. This question is different because we have to treat seconds as "years"
Final Form:
200((e)^(0.04 * 93))
Answer: 8252.88
A bag contains 12 marbles. Three are green, 7 are orange, and 2 are white. A marble is randomly selected. What is the probability that it is not orange?
The probability that the bag is not orange is given as follows:
p = 5/12.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
In this problem, the parameters are given as follows:
A total amount of 12 marbles.A desired amount of 12 - 7 = 5 non-orange marbles.Hence the probability that the bag is not orange is given as follows:
p = 5/12.
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How many feet apart is 535 and -8
Answer:
543 fee
Step-by-step explanation:
The difference between 535 and -8 is the distance between them, but it is not specified in what unit this distance should be measured. If you meant to find the difference in feet, then:
535 - (-8) = 535 + 8 = 543
So the distance between 535 and -8 in feet is 543 feet.
Which job/profession makes the most money?
1. Doctor
2. Microbiologist
3. Chemist
4. Vet
5. Paramedic
6. Writer/Poet
7. Fashion Designer
8. Engineer(of any kind)
The professions such as doctors, engineers (particularly in fields such as petroleum, software, or aerospace), and certain types of business executives tend to have some of the highest earning potentials.
Which job/profession makes the most money?The income of a job or profession can vary widely based on a variety of factors, such as location, experience, education, and demand.
According to the Bureau of Labor Statistics (BLS) in the United States, the highest-paying occupations as of 2021 are typically in the medical, dental, and managerial fields, with physicians and surgeons ranking as the highest-earning profession. However, it's important to note that there are many other factors that can impact earnings, such as the specific field of medicine, the size and type of organization or company, and geographic location.
Ultimately, the earning potential of a job or profession can depend on a wide range of factors, and it's important to research and consider all of them when deciding on a career path.
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Which statement describes the relationships between x and y in these two equations?
y = 13x
y = x + 13
In y = 13x, the value of y is 13 more than the value of x, and in y = x + 13, the value of y is 13 times the value of x.
In y = 13x, the value of y is 13 times the value of x, and in y = x + 13, the value of y is 13 more than the value of x.
In y = 13x and y = x + 13, the value of y is 13 times more than the value of x.
In y = 13x and y = x + 13, the value of y is 13 more than the value of x.
Which situation can be represented by y=12x?
Frank is y years old. This is half the age of his older sister, Margret, who is x years old.
Yvonne has y dollars. This is one half more dollars than her friend Marie who has x dollars.
A recipe calls for x eggs. This is half the number of required bananas which is represented by y.
The town of Maryville has x people. This is half as much as the town of Sunnyside which as y people.
The statement that describes the relationship is: option B.
The situation that can be represented by the equation y = 12x is: B. "Yvonne has y dollars. This is one half more dollars than her friend Marie who has x dollars."
How to Describe the Relationship between x and y in a n Equation?In the equation y = 13x, y is equal to 13 times x. This means that y increases by a factor of 13 for every increase in x.
In the equation y = x + 13, y is equal to x plus 13. This means that y is always 13 more than x.
Therefore, the answer is:
B. "In y = 13x, the value of y is 13 times the value of x, and in y = x + 13, the value of y is 13 more than the value of x."
The equation y = 12x means that y is equal to 12 times x. In the given situation, Yvonne has y dollars and Marie has x dollars. Yvonne has 12 times more dollars than Marie, and one half more than Marie. Therefore, the situation can be represented by y = 12x.
The correct answer is:
B. "Yvonne has y dollars. This is one half more dollars than her friend Marie who has x dollars."
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Money and finances are considered "taboo" as topics of conversation. However, you have a friend who bragged about
having paid in over $5,500 to Social Security last year. Estimate how much money they earned!
The amount earned is $88,709.68
What is a social security tax?It is a payroll tax that is paid on wages earned by employees.
We have,
We will assume the current Social Security tax rate for employees as 6.2%.
Now,
The amount earned.
= 5,500 / 6.2%
= 5500 / 0.062
= $88,709.68
Thus,
The amount earned is $88,709.68
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EM bisects DEF and m/DEF = 83.6°. Find m/DEM and m/MEF.
m/DEM
The measure of angles ∠DEM and ∠MEF will be the same which is 41.8 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
EM bisects DEF and ∠DEF = 83.6°. Then the measure of the angle ∠DEM and ∠MEF will be the same. Then we have
∠DEM + ∠MEF = ∠DEF
∠DEM + ∠DEM = 83.6°
2∠DEM = 83.6°
∠DEM = 41.8°
The measure of angles ∠DEM and ∠MEF will be the same which is 41.8 degrees.
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Would this be correct?
12. The ratio of flour to eggs in a pancake recipe is constant. The pancake recipe uses 5 cups of flour
for each egg.
Cups of Flour
30
Number of Eggs
2
5
Complete the table with the missing numbers using the flour to egg ratio from the pancake recipe
The required table
Cups of Flour Number of Eggs
10 2
25 5
30 6
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, The ratio of flour to eggs in a pancake recipe is constant.
The pancake recipe uses 5 cups of flour for each egg.
Since,
With one egg we need a total number of cups of flour = 5
Thus,
For 2 eggs, we need a total number of cups of flour = 5*2
For 2 eggs, we need a total number of cups of flour = 10
For 5 eggs, we need a total number of cups of flour = 5*5
For 5 eggs, we need a total number of cups of flour = 25
Thus, the required table
Cups of Flour Number of Eggs
10 2
25 5
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Find the value of x. Round to the
nearest tenth.
12
X=[?]
Mrs. Trahan samples her class by selecting every third person on her class list. Which type of sampling method is this?
Simple
Systematic
Stratified
Cluster
The type of sampling method used by Mrs. Trahan is clustering method. The correct option is 4.
A population is divided into many clusters that are representative of homogenous traits and have an equal probability of being included in the sample using the sampling technique known as cluster sampling.
Using this sampling approach, researchers examine a sample that includes a variety of sample criteria, including demographics, lifestyle, background, or any other population characteristic that may be the subject of the research being done. This approach is typically used when a statistical population is made up of comparable but internally heterogeneous groupings. Cluster sampling divides the population into smaller, more productive groups, allowing the researchers to obtain data without picking the full population.
Types of Cluster Samplings:
Single-stage Cluster Sampling Two-stage Cluster SamplingMultiple-stage Cluster SamplingHence this is all about clustering method in sampling technique.
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What is the rate of change in this graph?
The rate of change in the given graph is 21/4.
The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:
Rate of change = Δy / Δx
To calculate the rate of change of the given graph, we need to identify 2 points first. We take:
(0, 0)
(4, 21)
Rate of change = Δy / Δx
Rate of change = y₂ - y₁
x₂ - x₁
Rate of change = 21 - 0
4 - 0
Rate of change = 21/4
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A translation composed with a rotation maps quadrilateral ABCD to quadrilateral EFGH. If m∠BCD = 27.9°, what is m∠FGH?
The measurement of angle FGH is 27.9° after transformation.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, a translation composed with a rotation maps quadrilateral ABCD to quadrilateral EFGH. and m ∠ BCD = 27.9°, we are asked to find measurement of angle FGH,
We know that, any transformation or set of transformation will make similar figures, and similar figures have congruent corresponding angles,
Therefore,
m ∠ BCD = m ∠ FGH
m ∠ BCD = m ∠ FGH = 27.9°
Hence, the measurement of angle FGH is 27.9° after transformation.
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an angle of a pentagon is 120 the other on angle are equal to one another find the side of the other angle
Answer:
105°
Step-by-step explanation:
You want the measure of the remaining angles of a pentagon if one of the angles is 120° and the remaining angles are congruent to each other.
PentagonThe sum of the interior angles of a pentagon is 180* × (5 -2) = 540°. If one of the angles is 120°, the sum of the other four is ...
540° -120° = 420°
Then each of those four congruent angles has a measure of ...
420°/4 = 105°
The size of the other angles is 105°.
The Community Swimming Pool charges a flat rate of $50 for a birthday party plus $2.50 for each person. Deborah can’t spend more than $100. How many friends can she invite?
Answer:
she can only invite 20 people max
Step-by-step explanation:
2.50x20= 50 + fee =100
Assume the distance from San Francisco to Big Sur California is 240 kilometers. Han Fei leaves Big Sur on her bicycle heading for San Francisco at 20 kilometers per hour; at the same time Mohammed leaves San Francisco in his car heading to Big Sur on the same route averaging 40 miles per hour. How far from San Francisco will Han Fei be when Mohammed meets her in his car?
Answer: When Mohammed meets Han Fei, she will be 74.6 kilometers away from San Francisco.
Step-by-step explanation:
First, we need to convert Mohammed's speed from miles per hour to kilometers per hour, as Han Fei's speed is given in kilometers per hour.
40 miles per hour = 64.37 kilometers per hour (approximately)
Now, let's determine how long it will take Mohammed to reach the point where he meets Han Fei:
time = distance ÷ speed
time = 240 km ÷ 64.37 km/h
time ≈ 3.73 hours
So, after 3.73 hours, Mohammed will meet Han Fei.
In that time, Han Fei will have traveled:
distance = speed × time
distance = 20 km/h × 3.73 h
distance ≈ 74.6 km
Graph and find he area of the figure with vertices (-2, -2), (0, 0), (3, -2)
Answer:
see image,
Area = 5 units^2
Step-by-step explanation:
Graph three points to make a triangle.
Use
Area = 1/2•b•h
to find the area.
Fortunately, the base is horizontal and the height is vertical, so we can just count the squares to find those lengths. (If they aren't horizontal and vertical, then you need distance formulas)
see image.
Question 48 what is the area if the mat is 184 in
The length and width of the rectangular board is 27 inches and 23 inches respectively
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the mat be = 184 inches²
Area of Rectangle = Length x Width
Substituting the values in the equation , we get
Let the area of the larger rectangle be = ( 2x - 3 ) ( x + 8 )
Let the area of the smaller rectangle be = ( 2x - 7 ) ( x + 4 )
Now , the area of mat = area of the larger rectangle - area of the smaller rectangle
So , 184 = ( 2x - 3 ) ( x + 8 ) - ( 2x - 7 ) ( x + 4 )
On simplifying the equation , we get
2x² - 3x + 16x - 24 - [ 2x² + x - 28 ] = 184
On further simplification , we get
12x + 4 = 184
Subtracting 4 on both sides of the equation , we get
12x = 180
Divide by 12 on both sides of the equation , we get
x = 15
So , the length of the board = ( 2x - 3 ) = 27 inches
And , width of the board = ( x + 8 ) = 23 inches
Hence , the dimensions of the rectangular board is 27 x 23 inches²
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the apothem is the perpendicular distance from the _____ of a regular polygon to any one of its sides.
The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.
A closed, two-dimensional, flat or planar structure with straight sides is referred to as a polygon. Its sides do not bend in any way. A polygon's sides are also referred to as its edges. A polygon's vertices (or corners) are the places where two sides converge. Polygons and polyhedrons are two names for geometric shapes having three or more sides. The names of a few polygons are listed below. In order to link and develop projects and blockchains that are compatible with Ethereum, Polygon (MATIC), a cryptocurrency and technological platform, was introduced. A fully closed polygon is a flat, two-dimensional form with straight sides. They must have straight sides. Any number of sides can be found in polygons.
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Find KJ and CB. Show your work.
The length of KJ is 9 unit.
The length of CB is 10 unit.
What is Mid segment Theorem?The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.
Given:
12. Using Mid segment theorem
Mid segment= 1/2 of Triangle base
Mid segment= 1/2 x 18
Mid segment (KJ) = 9
13. Using Mid segment theorem
Mid segment= 1/2 of Triangle base
x+ 19 = 1/2(x+ 29)
2x + 38 = x+ 29
x = -9
So, length of CB = x + 19 = 10 unit
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Match the new coordinates that define the figure after dilation with a center at the origin by the given scale factor.
List of new coordinates: (0, 6) , (0, 4/3) , (1, 0) , (1, 4/3) , (6, 0) , (4/3, 0) , (9/2, 0) , (9/2, 6)
Scale factor 1/3:
(List all coordinates under scale factor 1/3)
Scale Factor 3/2:
(List all coordinates under scale factor 3/2)
Point NOT USED:
(List all coordinates under Point NOT USED if they couldn't be used)
[PLEASE ANSWER CORRECTLY!]
The given coordinates are all used (0, 6), (0, 4/3), (1, 0), (1, 4/3), (6, 0), (4/3, 0), (9/2, 0), (9/2, 6)
What is coordinate?Coordinating refers to the process of organizing or synchronizing different elements or parts to work together in a harmonious and efficient manner towards a common goal or objective. In other words, coordinating involves bringing together various people, resources, activities, or tasks in a way that maximizes their effectiveness and minimizes any conflicts or inefficiencies.
given to the question.
Scale factor 1/3:
The new coordinates after dilation with a center at the origin by a scale factor of 1/3 are obtained by multiplying the original coordinates by 1/3. Hence, we have:
(0, 6) --> (0, 2)
(0, 4/3) --> (0, 4/9)
(1, 0) --> (1/3, 0)
(1, 4/3) --> (1/3, 4/9)
(6, 0) --> (2, 0)
(4/3, 0) --> (4/9, 0)
(9/2, 0) --> (3/2, 0)
(9/2, 6) --> (3/2, 2)
Scale Factor 3/2:
The new coordinates after dilation with a center at the origin by a scale factor of 3/2 are obtained by multiplying the original coordinates by 3/2. Hence, we have:
(0, 6) --> (0, 9)
(0, 4/3) --> (0, 2)
(1, 0) --> (3/2, 0)
(1, 4/3) --> (3/2, 2)
(6, 0) --> (9, 0)
(4/3, 0) --> (2, 0)
(9/2, 0) --> (27/4, 0)
(9/2, 6) --> (27/4, 9)
Point NOT USED:
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1/4 x = 3/2
FIND
X
PLEASE
The height of an object at any time can be found with the polynomial - 16t ^ 2 + 550 where t is the time in seconds. How high is the object after 3.5 seconds?
Answer:
354 m
Step-by-step explanation:
to find the height substitute t = 3.5 into the height polynomial
height = - 16(3.5)² + 550 = - 16(12.25) + 550 = - 196 + 550 = 354
How many liters each of 30% and 10% acid should be mixed to obtain 20 liters of 20% acid?
The quantity of liters of both 30% and 10% acid that will make up the 20liters would be= 15 liters and 5 liters respectively.
How to calculate the liters of both given acids?The quantity of liters of 30% acids ;
= 30+10 = 40
= 30/40×20/1
= 600/40
= 15 liters of 30 % acid will make up 20 liters of 20% acid.
The quantity of liters of 10% acids:
= 10/40× 20/1
= 200/40
= 5 liters of 10% acid will make up 20 liters of 20% acid.
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