The probability of obtaining a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
What are the four types of probability?Probability is the branch of mathematics concerned with the occurrence of a random event, and there are four types of probability: classical, empirical, subjective, and axiomatic.
The readings at freezing on a set of thermometers are normally distributed, with a mean () of 0°C and a standard deviation () of 1.00°C. We want to know how likely it is that we will get a reading between -0.08°C and 1.68°C.
To solve this problem, we must use the z-score formula to standardise the values:
z = (x - μ) / σ
where x is the value for which we want to calculate the probability, is the mean, and is the standard deviation.
The lower bound is -0.08°C:
z1 = (-0.08 - 0) / 1.00 = -0.08
1.68°C is the upper bound:
z2 = (1.68 - 0) / 1.00 = 1.68
We can now use a standard normal distribution table or calculator to calculate the probabilities for each z-score.
The probability of obtaining a z-score of -0.08 or less is 0.4681, and the probability of obtaining a z-score of 1.68 or less is 0.9535, according to the table. We subtract the probability associated with the lower bound from the probability associated with the upper bound to find the probability of obtaining a reading between -0.08°C and 1.68°C:
P(-0.08°C x 1.68°C) = P(z1 z z2) = P(z 1.68) minus P(z -0.08) = 0.9535 - 0.4681 = 0.4854
As a result, the chance of getting a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
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have to 4. Thandi works for an organisation that packs food parcels for the poor. A company has donated 19 boxes of assorted tins, each containing 55 cans. Calculate how many cans each family will receive if there are 95 families to feed
If there are 95 families to feed then each family will receive 11 cans of assorted tins.
What is assorted tins?Assorted tins typically refer to cans or containers of food items that come in different varieties or flavors.
According to question:To calculate the number of cans each family will receive, we need to first determine the total number of cans in the 19 boxes.
19 boxes × 55 cans per box = 1045 cans
Now we can divide the total number of cans by the number of families to determine the number of cans each family will receive:
1045 cans ÷ 95 families = 11 cans per family (rounded to the nearest whole number)
Therefore, each family will receive 11 cans of assorted tins.
For example, a box of assorted tins may contain cans of different types of vegetables, fruits, soups, or other food items. The specific assortment may vary depending on the context and the supplier. In the context of the given question, the 19 boxes of assorted tins likely contain cans of different types of food that will be packed into food parcels for the poor.
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A system of equations is shown. 2x-y= 15 y=9 What is the value of x in the solution to this system?
Answer:
x=12
Step-by-step explanation:
2x-y=15
y=9
2x-9=15
2x=24
x=12
What is this question asking? What does it mean by floor plan? A step-by-step explanation would be very much appreciated.
Answer:
this is when you want to draw a sketch of a building
For numbers 3, 4, and 5, find the value of the indicated length(s) in ⨀C. A and B are points of tangency. Simplify all radicals.
I just need help with these three problems!
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
what is circle ?A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.
given
AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.
We can apply the Pythagorean theorem to segment AB as follows:
[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]
AB² = 50
AB = √50 = 5√2
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
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Let f(x)=3-x and g(x)=1/x.
f/g(x)
ANSWER THIS QUESTION FAST WILL GIVE BRAINLIEST
In each triangle, M, N, and P are the midpoints of the sides. Name a segment parallel to the one given.
Answer: MN || VT
Step-by-step explanation:
We can see that MN is vertical, and the only angle that is vertical, is VT. And we can see that they don't obstruct their lines (meaning that they don't intersect), and keep going for infinity. So, VT would be the only parallel line to the one given.
Hope this helps
determine if the transformation is one to one and/or onto. justify your answers. give an explanation for each of these properties.
To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.
In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.
On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.
To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.
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The given question is incomplete, the complete question is:
How to determine the transformation is one to one and/or onto?
What is the answer? Need help!!!
it takes 6 painters 4 1/2 to paint these classroom. calculate how long 3 painters will take to complete the same job
The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI
it is false. 0 is not a natural number. it is a whole number
Graph the system below and write its solution
Y=1/4x-3
-x+4y=-4
The graph of the system of equations is shown below:
The solution of the system is given by the point of intersection of the two lines which is (20/7, -7/2).
Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 4.
a(t) = eti − 6k
v(0) = 2i + 9j + k, r(0) = 0
The velocity vector and position vector and position vector at t=4 is r(4) = (e₄+2)i+36j - 44k.
a(t) = eti - 6k
Since we know that v(t) = ∫ a(t) dt
= ∫ (eti - 6k) dt
= ∫6ti-6tk+c
where c is the arbitrary vector valued constant
since it is given that
v(0) = 2i + 9j + k
therefore from above
v(0) = e * 0i - 6(0) * k + c
2i + 9j + k =i+c
C= i +9j+k
therefore,
v(t) = eti - 6tk + i + 9j + k
= (et + 1) * i + 9j + (- 6t + 1) * k
Since we know that velocity vector can be found by integration of acceleration vector.
Since, v(t) = (et + 1) * i + 9j + (- 6t + 1) * k
and we know that
R(t) = ∫ v(t)dt
= ∫ of [(a + 1)i + 9j+(-6t + 1)k]dt =(a+t)i+9tj+(-3ta+t)k+C
where C is an arbitrary vector constant.
Now,
Since it given that r(0)=0 therefore
r(0) =(e0+1)+9(0)j)+(-3(0)2+0)x+C
0=2i+ C
C= -2i
therefore
r(t)= (et+t)i+9tj+(-3t+t)k-2i
r(t)=(a+t-2)1+9tj+(-3t+t)k
Since we know that position vector can be found by integration of velocity vector
r(4) = (e4+4-2)i+9(4)j + (-3(4)+4)k
r(4) = (e4+2)1+36j-44k
Now we have found the velocity vector and position vector and position vector at t=4 which are as follows:
v(t) =(et+1)i+9j+(-6t+1)k
r(t) =(et+t-2)i+9tj+(-3t2+t)k
r(4) = (e₄+2)i+36j - 44k
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Esmanol A spinner with 12 equally sized slices has 4 yellow slices, 3 red slices, and S blue slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a slice that is not yellow?
The probability of spinning a slice that is not yellow is equal to the total number of non-yellow slices divided by the total number of slices.
Total number of non-yellow slices = 9 (3 red + 5 blue)
Total number of slices = 12
Therefore, the probability of spinning a slice that is not yellow is 9/12 or 75%.
This year, the ratio of Alan's age to Bernice's age is 1:2. Four years ago, the total age of Alan and Bernice was 55 years. How old is Alan this year?
Answer:
21 years old
Step-by-step explanation:
Set Alan's age as x, Bernice's age as y
2x=y
x-4+y-4=55
x+y=63
3y=63
x=21
y=42
find the following answers
Answer:
hope it helps
Step-by-step explanation:
based on the given condition formulate
when a child turns 18 years old the money in the account will be a birthday gift. The grandfather's choosing in between two options. option one and account that grows by 10.5% each year or option two and account that grows by $20 each year. which option will result in a better 18th birthday gift explain your reasoning.
10.5% is better because 20 dollers is good but it not gonna increase like 10.5%
June uses 192 jellybeans for every dozen (12) plastic eggs she fills. How many plastic eggs can she fill with 1,152 jellybeans?
Answer: June uses 192 jellybeans for every dozen (12) plastic eggs she fills, which means she uses 192/12 = <<192/12=16>>16 jellybeans per plastic egg.
To find how many plastic eggs can be filled with 1,152 jellybeans, we can divide 1,152 by the number of jellybeans per egg:
Number of eggs = 1,152 ÷ 16 = <<1152/16=72>>72
Therefore, June can fill 72 plastic eggs with 1,152 jellybeans.
Step-by-step explanation:
Question 25 (2 points)
Suppose the Math Department has 17 full-time faculty members. If 3 are selected to
attend a conference in Las Vegas, in how many different ways can you selected the 3
individuals?
3
17
680
4080
Answer:
680 ways
Step-by-step explanation:
C(17, 3) gives 17! / (14! 3!), or (17*16*15)/6 = 680 ways to select the 3 individuals.
Hope this helped!
which direction does the gradient v point in the direction of maximum increase or maximum decrease in v
The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.
The gradient of a scalar-valued function is a vector that points in the direction of the maximum increase of the function.
In other words, if we consider a point in the domain of the function and take the gradient at that point, the direction of the gradient vector indicates the order in which the function increases the most from that point. Conversely, the negative gradient points in the direction of the maximum decrease of the function.
Specifically, let f be a scalar-valued function of n variables [tex](f: R^n - > R),[/tex]and let x be a point in the domain of f. The gradient of f at x is defined as the vector:
[tex]grad f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)[/tex]
where ∂f/∂xi denotes the partial derivative of f with respect to xi evaluated at x, the direction of the gradient vector grad f(x) at x is the direction in which f increases the most from x, and the magnitude of the gradient vector is the rate of change of f at x in that direction.
The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.
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a man allowed 10 discount on the fixed price of an piece of a land and offered 5 commision to the broker if he received 256500 what was the fixed price of land
The fixed price of the land is 296257.50.
What is discount?
Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.
Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.
Here the discount on the fixed price = 10%
Commission for the broker = 5%
If total amount = 100%+10% = 110%
Then received amount = [tex]\frac{110}{100}\times256500[/tex]
=> Received amount = 282150
Now 5% commission then,
=> [tex]\frac{105}{100}\times 282150[/tex] = 296257.50.
Hence the fixed amount of the land before discount is 296257.50.
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Between 11pm and midnight on Thursday night Mystery pizza gets an average of 5.9 telephone orders per hour
URGENT
Answer:157
Step-by-step explanation:
it just is =]
if cot0=3/4 and the terminal point determined by 0 is in quadrant 3, then
If cotθ = 3/4 then cosθ = -3/5 is the right option according to the rules of trigonometry.
What is Trigonometry?Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is primarily concerned with the study of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their applications in various fields such as engineering, physics, and navigation.
What are angles of triangle?A triangle is a three-sided polygon, and its angles are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
First, we know that cot(0) = adjacent / opposite = 3/4.
In quadrant 3, the adjacent side is negative and the opposite side is positive, so we can draw a right triangle in quadrant 3 with adjacent side -3 and opposite side 4.
The hypotenuse can be found using the Pythagorean theorem.
h² = adjacent²+ opposite²
h² = (-3)^2 + 4^2
h²= 9 + 16
h² = 25
h = 5
So we have a right triangle in quadrant 3 with adjacent side -3, opposite side 4, and hypotenuse 5.
Using the definitions of the trigonometric functions, we can find the values of the other functions:
sin(0) = opposite / hypotenuse = 4/5
cos(0) = adjacent / hypotenuse = -3/5
tan(0) = opposite / adjacent = -4/3
csc(0) = hypotenuse / opposite = 5/4
sec(0) = hypotenuse / adjacent = -5/3
cot(0) = adjacent / opposite = 3/4 (given)
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The number of the words formed with letters of the word 'PROBLEM' with neither start with O nor end with E.
The number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E is 3600.
The word PROBLEM has 7 letters, which can be arranged in 7! (factorial) ways, i.e. [tex]7*6*5*4*3*2*1 = 5040.[/tex]
Now to calculate the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E, we can first calculate the number of words which start with O or end with E.
For words starting with O, there are 6 letters left and these can be arranged in 6! ways, i.e.[tex]6*5*4*3*2*1 = 720.[/tex]
For words ending with E, there are again 6 letters left and these can be arranged in 6! ways, i.e. [tex]6*5*4*3*2*1 = 720[/tex].
Now the total number of words which start with O or end with E will be the sum of two, i.e. 720 + 720 = 1440.
Therefore, the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E will be the total number of words minus the total number of words which start with O or end with E, i.e. 5040 - 1440 = 3600.
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Find the value of f(4) for the function F(a) = 4 (a+3)-8
What is the solution for those?
And if you can please add the explanations
The required simplified forms are 3x - 1, 6x , 2x² - 10x , a + 2b , 15x - 8 , x² + 2x + 6 , x² - y² , 6x² - 22x.
What is Equation?the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.
According to question:Simplified forms of the equation are
[tex]$c: 3(x-2)+5=3x-6+5=3x-1$[/tex]
[tex]$f: 2x(3-x)+x^2=6x-x^2+x^2=6x$[/tex]
[tex]$i: 7x^2-5x(x+2)=7x^2-5x^2-10x=2x^2-10x$[/tex]
[tex]$c: 2a-(a-2b)=2a-a+2b=a+2b$[/tex]
f: [tex]$3x-4(2-3x)=3x-8+12x=15x-8$[/tex]
[tex]$x(x+4)-2(x-3)=x^2+4x-2x+6=x^2+2x+6$[/tex]
[tex]$x(x+y)-y(x+y)=(x-y)(x+y)=x^2-y^2$[/tex]
[tex]$o: 4x(x-3)-2x(5-x)=4x^2-12x-10x+2x^2=6x^2-22x$[/tex]
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In Exercise 5.1, we determined that the joint distribution of Y1, the number of contracts awarded to firm A, and Y2, the number of contracts awarded to firm B, is given by the entries in the following table.
The marginal probability function of Y1 was derived in Exercise 5.19 to be binomial with n = 2 and p = 1/3. Find
a E ( Y 1 ).
b V ( Y 1 ).
c E ( Y 1 − Y2).
Reference
Contracts for two construction jobs are randomly assigned to one or more of three firms, A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1, or 2 contracts. a Find the joint probability function for Y1 and Y2.
b Find F(1, 0).
The marginal probability function E(Y1) = 2/3, variance of a binomial distribution is V(Y1) = 4/9, and E(Y1-Y2) = 0, using the joint probability function for Y1 and Y2 and the fact that they have binomial distributions with n=2 and p=1/3.
The marginal probability function of Y1 is binomial with n=2 and p=1/3, as given in Exercise 5.19. Therefore, we have:
E(Y1) = np = 2(1/3) = 2/3.
The variance of a binomial distribution with parameters n and p is given by np(1-p), so we have:
V(Y1) = np(1-p) = 2(1/3)(2/3) = 4/9.
We can use the linearity of expectation to find E(Y1-Y2):
E(Y1 - Y2) = E(Y1) - E(Y2)
We know that E(Y1) = 2/3 from part (a), but we need to find E(Y2). Using the same reasoning as in part (a), we find that the marginal probability function of Y2 is also binomial with n=2 and p=1/3. Therefore, we have:
E(Y2) = np = 2(1/3) = 2/3.
Substituting these values into the expression for E(Y1-Y2), we get:
E(Y1 - Y2) = 2/3 - 2/3 = 0.
Therefore, E(Y1-Y2) is equal to 0.
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Lisa records the amount of time she plans to spend for each reading session during a one month period on the line plot
5. If Lisa redistributes the total time
equally over all her reading sessions,
how long will each session be?
Answer:
Step-by-step explanation:
25 POINTS, PLS EXPLAIN! Which sum or difference is modeled by the algebra tiles? Select the correct answer. (-2x + 3) + (3x − 4) (-2x + 3) − (3x − 4) (2x − 3) + (-3x + 4) (2x − 3) − (-3x + 4)
Answer: Consider the expression (2x − 3) − (-3x + 4).
First, distribute the negative sign and rewrite the expression:
2x − 3 + 3x – 4.
Then, model the polynomial.
There are no zero pairs, so the difference is 5x − 7.
Step-by-step explanation:
PLATO
Label all of the angle measures on the transversal.
Remember you can find all of the angles since you know one of them is 45 degrees.
The transversal angle of 45 is angle6.
What are angles?Two lines intersect at a location, creating an angle.
An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.
Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.
In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.
An angle has two primary components: the arms and the vertex. T
he two rays' shared vertex serves as their common terminal.
Hence, The transversal angle of 45 is angle6.
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mathematicians divide the world of numbers into at least seven subsets. list seven subsets and define each
Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.
Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".
Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".
Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".
Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".
Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.
Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".
Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".
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