When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.
A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.
Given,
Mean of the weights = 102.4 kg
Standard deviation = 13.9 kg
To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, [tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]
Where, [tex]\sigma[/tex]=standard deviation
n= number of reindeer
substitute the values in the formula,
[tex]\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667[/tex]
Now,
[tex]P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)[/tex]
from z-score table,
=0.1492
Thus, the probability the their mean weight is less than 100 kg is 0.1492.
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Your question is incomplete, here is the complete question.
The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg
if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?
PLEASE HELP URGENT WITH 4 AND 6
The solution is
a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01
b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125
The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
a)
Let the principal be P = amount after first period = $ 402
Now , the rate of interest r = 6 %
The compound interest is calculated by compounding monthly
Now , the interest for the second period = ( PRT / 100 x 12 )
Substituting the values in the equation , we get
The interest for the second period = ( 402 x 6 x 1 ) / 1200
The interest for the second period = $ 2.01
The amount after the second period = amount after first period + interest for the second period
The amount after the second period = 402 + 2.01
The amount after the second period = $ 404.01
b)
Let the principal be P = $ 18260
The rate of interest r = 2.5 %
The compound interest is calculated by compounding quarterly
Now , the interest for the first period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the first period = ( 18260 x 2.5 ) / 400
The interest for the first period = 45650 / 400
The interest for the first period = $ 114.125
The amount for the first period = 18260 + 114.125
The amount for the first period = $ 18,374.125
Now , the principal for the second period = interest + amount of first period
The principal for the second period = $ 18,374.125
The rate of interest = 2.5 %
The interest for the second period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the second period = ( 18374.125 x 2.5 ) / 400
The interest for the second period = 45935.3125 / 400
The interest for the second period = $ 114.83828125
The amount for the second period = 18,374.125+ 114.84
The amount for the second period = $ 18,488.96
Hence , the amount and interest is calculated
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the perimeter of a square is 48 centimeters, what is the area in square centimeters
Answer:
144cm²
Step-by-step explanation:
If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.
48/4 = 12cm
Then, to find the area, you need to multiply 12 by 12.
12 cm x 12 cm = 144cm²
Hope this helps :)
luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
Luka will require 24 cups of water to make lemonades as calculated from the data given.
The quantity of sugar which he use is twice the amount of lemon which he us ,
= 2 x 3 = 6
and ,
as we know the amount of water is 4 times as much as lemon juice
Therefore, amount of water
= 4 * 6
= 24
A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.
A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.
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Please help! Division of Polynomials, Find the quotient and remainder.
First:
Quotient: [tex]2x^{2} -11x+58[/tex]
Remainder: [tex]-294[/tex]
Second:
Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]
Remainder: [tex]422[/tex]
Third:
Quotient: [tex]2x-3[/tex]
Remainder: [tex]12[/tex]
please help, this is my finals & i don’t know it
Answer:
i think that answer is correct
Step-by-step explanation:
The following figure was drawn using a straightedge and a compass. Where was the point of the compass located in order to make the arcs?
1. points X and Y
2. point D
3. point C
4. points A and B
The point of the compass located in order to make the arcs is points X and Y.
Define arc.An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.
Given
The following figure was drawn using a straightedge and a compass.
The point of the compass located in order to make the arcs:
1. points X and Y
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solve for x.
enter your answer as a mixed number in simplest form in the box.
x =
Answer:
x + x - x = x
explanation:
give us the actual formula lol
If you vertically compress the absolute value parent function, F(x) = |x|, by multiplying by 3/4, what is the equation of the new function?
A. G(x) = | 3/4 x |
B. G(x) = |x| - 3/4
C. G(x) = 3/4 |x|
D. G(x) = | x + 3/4 |
Answer:G(x) = 3/4 |x|, nevertheless that is the same that G(x) = |3/4x|.
Step-by-step explanation:
Note that given that 3/4 is less than 1 the original function is compressed.
- Take care <3
Which statement can you conclude is true from
the given information?
Given: AB is the perpendicular bisector of IK.
( please help me , answers my questions )
As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.
What is perpendicular bisector?
A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.
What is the perpendicular of two points?
A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.
Option J can not be true as A can not be the midpoint of IK as A is not on IK. Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.
Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.
Option G) i.e m∠IAJ also does not true necessarily true. The reason is simple i.e AJ is arbitrary.
So, Option f) i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ is true.
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Word Problems: (please write out the equations and solve it)
1. David is going out for a pizza. The Pizza costs $10.50 plus $1.50 for each extra
topping ,x. Write an equation to represent the total cost of the pizza, t.
Dependent variable:
Independent variable:
Equation:
Use your equation to determine the total cost of the pizza with 3 extra
toppings.
The total cost of the pizza is
Dependent variable: t (total cost of the pizza)
Independent variable: x (number of extra toppings)
Equation: t = 10.50 + 1.50x
To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:
t = 10.50 + 1.50(3)
t = 10.50 + 4.50
t = 15.00
So the total cost of the pizza with 3 extra toppings is $15.00.
What is Dependent Variables?
The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.
What is Independent Variables?
Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.
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Write the answer in the blank.
What number is 280 more than 220?
Answer: 500
Step-by-step explanation:
280 + 220 is 500
Answer:
The number is 500.
Step-by-step explanation:
Let's assume that,
→ Missing number = x
Forming the equation,
→ x = 220 + 280
Now the value of x will be,
→ x = 220 + 280
→ [ x = 500 ]
Hence, the number is 500.
Helppppp meeeee guyssss
In a group of 500 people determine how many are suspects in the following scenario.
A wallet was stolen from an office in a building with 500 employees. The suspect was wearing black pants, a white button-down shirt, and a multicolored tie. In one of the offices in the building, the following data was collected.
30 people total in the office
22 wearing a white button down shirts
16 wearing black pants
7 wearing a multicolored tie
Using the data, how many suspects are there?
Using the given data, the number of suspects is; 7
How to find the intersection of mathematical sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.
However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
Now, we are told that;
Total number of people in the office = 30 people
Number of people wearing a white button down shirts = 22
Number of people wearing black pants = 16
Number of people wearing a multicolored tie = 7
Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;
The number of suspects = A ∩ B ∩ C = 7 people
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Hello can someone help me out with these two questions!?!?! This will help me a lot thank you! :D
The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
The inequalities are,
2( x +6 ) > -6( x +1) +2
2x + 12 > -6x - 6 + 2
2x + 6x > -12 - 6 +2
8x > -16
x > -2
-3x - 1 ≥ 20
-3x ≥ 21
x ≥ -7
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Nick has two pet rabbits.His Flemish giant rabbit weighs 5 times as much as his Holland lop rabbit,If nich's Flemish rabbit weighs 12 more pounds than his Holland lop rabbit,how much does his Flemish giant rabbit weight?
Answer:The Flemish giant rabbit weighs 32 pounds.
Step-by-step explanation:
let g be a polynomial function of x where g(x) = 2x^3 + 5x^2 - 28x - 15 Given (x - 3) is a factor of g, what is the reminder of g(x) + (x - 3)?
The remainder of polynomial g(x) divides (x - 3) that is g(x) / (x - 3) is 0.
What is polynomial?
A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.
Given: g(x) = 2x^3 + 5x^2 - 28x - 15
(x - 3) is a factor of g(x).
We have to find the remainder of g(x) / (x - 3).
Consider,
2x^2 + 11x + 5
[tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]
- 2x^3 -6x^2
____________________________
11x^2 - 28x
- 11x^2 - 33x
____________________________
5x - 15
- 5x - 15
_______________________________
0
Hence, the remainder of polynomial g(x) divides (x - 3) that is
g(x) / (x - 3) is 0.
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STEP BY STEP please help me asap please !!!???
Answer:
(A) 19 times, 16 people.
Step-by-step explanation:
There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.
The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.
Since the Caterpillar cannot run a fraction of a time, it must run 19 times.
There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.
Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.
Tell me if this helped :)
fast as you can. point slope form. algebra 1)
Answer: Y=mx+b
Step-by-step explanation:
Hi sorry for the mistake this is the photo I was meant to post and I need help with number 6(iii)
Answer:
-2
Step-by-step explanation:
Given,
g(x) = f(4)
or, 2 - 4x = 3*4 - 2
or, 2 - 4x = 10
or, 2 - 10 = 4x
or, -8 = 4x
or, x = -2
Solve the equation -3.5(x-14)+9x=5.5x + 49. Which statement is true ?
Answer:
Step-by-step explanation:
Answer:
-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.
Step-by-step explanation:
Madelyn and Kaia are competing to see who can sell the most tickets for the Winter Dance. On Monday, Madelyn sold 22 and then sold 30 per day after that.
Kaia sold 53 on Monday and then sold 20 per day after that.
Write an equation to represent the number of tickets that Madelyn sold.
Write an equation to represent the number of tickets that Kaia sold.
Write a system of equations. What is the appropriate method for solving the system?
Solve the system of equations. Explain the meaning of your solution.
The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;
Tickets sold by Madelyn is; y = 22 + 30·x
Tickets sold by Kaia is; y = 53 + 20·x
A system of equation obtained from the details in the question can be presented as follows
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.
The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.
What is an equation?An equation consists of two expressions that are joined by the 'equals to' (=) sign.
The number of tickets for the Winter Dance Madelyn sold = 22
Number of tickets per day Madelyn sold after that = 30 per day
Number of tickets Kaia sold on Monday = 53
Number of tickets per day Kaia sold after that = 20 per day
Let x represent the number of days since Monday, and let y represent the number of tickets sold
Therefore;
The number of tickets Madelyn sold, y = 22 + 30·x
The number of tickets Kaia sold, y = 53 + 20·x
The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x
30·x - 20·x = 53 - 22 = 31
10·x = 31
x = 31 ÷ 10 = 3.1
The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days
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Ryanne is 14. Her brother's age is three more than half her age. How old is her brother?
OA 7
OB. 8.5
OC. 10
OD. 31
Question
Answer:
10 years old
Step-by-step explanation:
what does a z-score tell us about an individual observation in a data set? it is the number of standard deviations an observation is away from the mean. the midpoint of the sorted sample data set the sum of all data values divided by the number of data items. the average. the most frequently occurring data value in the set. none of the above
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.
A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.
The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.
Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.
Therefore,
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
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