We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Based on the sample bag of Dream Pop candy, we can calculate the probability of getting each flavor.
If all bags have equally likely flavors, then each flavor should have the same probability of being selected.
However, we can see from the sample that this is not the case.
To communicate this to the boss, we can calculate the probability of getting two different flavors and compare them.
For example:
The probability of getting a grape flavor is 16/40 or 0.4
The probability of getting a lemon flavor is 6/40 or 0.15
These probabilities are not equal, indicating that the flavors are not equally likely.
We can also compare the probabilities of getting two other flavors, such as:
The probability of getting a strawberry flavor is 12/40 or 0.3
The probability of getting a blueberry flavor is 6/40 or 0.15
Again, these probabilities are not equal, further indicating that the flavors are not equally likely.
Therefore,
We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.
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Mark is going to an awards dinner and wants to dress appropriately. He is running behind schedule and asks his little brother to randomly select an outfit for him.
Mark has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of his possible outfits are listed below.
Let
A
AA be the event that Mark's little brother selects an outfit with a white shirt and grey slacks and
B
BB be the event that he selects an outfit with a black shirt.
What is
P
(
A
or
B
)
P(A or B)P, left parenthesis, A, start text, space, o, r, space, end text, B, right parenthesis, the probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt?
Mary is 21 years old. She buys 50/100/25 liability insurance, and collision and
comprehensive insurance, each with $500 deductibles. What is her total annual
premium? Round to the nearest dollar. Do not state the units. Be sure to show work.
Liability Insurance
Type Amount Premium
25/50 $240
50/100 $385
100/300 $450
Property damage 25 $210
50 $150
100 $140
Collision and comprehensive premiums
$250 $172 $112
$500 $102 $87
$750 $85 $52
Rating factor
Age
17-20 male Female
3.1 1.64
21-24. 2.53. 1.22
25-29 1.73 1.0
According to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
What is multiplication ?In mathematics, multiplication is an arithmetic operation that combines two or more numbers to produce a product. It is represented by the symbol "×" or "*", or by placing the numbers next to each other with no symbol between them.
According to the given information:Mary is 21 years old, so according to the rating factor table, her rating factor is 1.22 for a female.
For liability insurance, Mary has chosen the 50/100/25 coverage, which means $50,000 for bodily injury per person, $100,000 for bodily injury per accident, and $25,000 for property damage per accident. The premium for this coverage is $385.
For collision and comprehensive insurance, Mary has chosen a $500 deductible, so her premiums are $102 for collision and $87 for comprehensive.
To find the total annual premium, we add up the premiums for liability insurance and collision/comprehensive insurance:
Total premium = Liability premium + Collision premium + Comprehensive premium
Total premium = $385 + $102 + $87
Total premium = $574
Therefore, according to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
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sams rectangular swimming pool has a volume of 600 cubic feet, the neighbors pools the same length and height but the width is three times larger. what is the volume of the neighbors pool?
Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:
lwh = 600
For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:
l(3w)h = 3lwh = 3(600) = 1800 cubic feet
Therefore, the volume of the neighbor's pool is 1800 cubic feet.
Step-by-step explanation:
ellas normal rate of pay is $10.40 an hour.
How much is she paid for working 5 hours overtime one Saturday at time-and-a-half?
Answer:
52
Step-by-step explanation:
10.40 TIMES 3
Find an equation for a sinusoidal function that has period 47, amplitude 1, and contains the point
(-л, 2).
Write your answer in the form f(x) = Asin (Bx + C) + D, where A, B, C, and D are real numbers.
f(x) =
The sine function with the desired features is given as follows:
F(x) = sin(3.5π(x + π/2)) + 1.
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are listed as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function has an amplitude of 1, hence the parameter A is given as follows:
A = 1.
The period is of 4/7, hence the coefficient B is given as follows:
2π/B = 4/7
4B = 14π
B = 3.5π.
The function contains the point (-π, 2), hence the phase shift and the vertical shift are given as follows:
c = π/2, as the function has it's maximum value at x = π, while the standard function has at x = π/2.d = 1, as the function oscillates between 0 and 2.Hence the function is:
F(x) = sin(3.5π(x + π/2)) + 1.
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Two cellphone companies are offering different rate plans. Rogers is offering $19.99 per month, which includes a
maximum of 200 weekday minutes plus $0.35 for every minute above the maximum. TELUS is offering $39.99 for a
maximum 300 weekday minutes, but it charges $0.10 for every minute above the maximum. Above how many minutes
would TELUS be the better choice?
I give brainliest for the answer
The intersection of two parallel lines; x = 10 metres.
Describe another angle using an example.Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.
The alternate interior angles are equal because of the parallel lines characteristic.
Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.
Setting these two angles equal to each other, we can get:
x+20 = 2x+10
Simplifying this equation, we get:
x = 10.
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Pls help me right now
I’m not sure what the limit would be if it’s discontinued but defined
The graph's function limit at x=4 is 6.
Define limitIn mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.
The formal definition of the limit of a function f(x) as x approaches a value a is as follows:
For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.
Limit f(x) at x tend to 4⁺ =6.
Limit f(x) at x tend to 4⁻ =6
Hence, the graph's function limit at x=4 is 6.
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given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
√9+25 = 28
π-4 = -0.8571
³√-27 = -3
2 / 3 = 0.6667
18÷2 = 9
√-27 = 5.196
What is surdsIn mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).
We have √9+25 = 28
find the square root of 9 = 3
3 + 25 = 28
π-4 = 3.14 - 4
= -0.8571
³√-27 = ³√3³
= 3
2÷3 = 0.6667
18÷2 = 9
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question:
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
find the value of the terms
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D: Please !!!!
The width of the top of the bookcase should be approximately 12.2 inches to give Bria's soap carving collection an area of 300 square inches.
How do you compute the area of a square inch?Simply multiply the length and width measurements to get the area of your square or rectangular area in square inches.
Assume the bookcase's top is rectangular, with length "L" and width "b". Because the area of a rectangle is the product of its length and width, we get:
L * b = 300
To find "b," we can rearrange the equation as follows:
b = 300 / L
We don't have enough information to directly solve for "L," but we can make an educated guess based on the figure provided. Based on the illustration, the bookcase appears to be roughly twice as long as it is wide. So let us suppose:
L ≈ 2b
When we plug this into the equation above, we get:
b = 300 / (2b) (2b)
To simplify, we have:
b^2 = 150
When we take the square root of both sides, we get:
b ≈ 12.2
We have, rounded to the nearest tenth of an inch:
b ≈ 12.2 inches
As a result, the width of the top of the bookcase should be approximately 12.2 inches in order to give Bria's soap carving collection a 300-square-inch area.
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PLS HELP FAST 50 POINTS + BRAINLIEST
Answer:
Anna had 23 sweets in her bag at the start of the day.
Step-by-step explanation:
Let's use working backwards to find out how many sweets were in the bag at the start of the day.
At the end of lesson 4, Anna had 1 sweet left in her bag. So, before she gave a sweet to her teacher in lesson 4, she had 2 sweets left in her bag.
In lesson 3, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 3, she had 2 x 2 + 1 = 5 sweets in her bag.
In lesson 2, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 2, she had 5 x 2 + 1 = 11 sweets in her bag.
In lesson 1, she gave out half of the sweets in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 1, she had 11 x 2 + 1 = 23 sweets in her bag.
Therefore, Anna had 23 sweets in her bag at the start of the day.
TRUE/FALSE. Every random sample of the same size from a given population will produce exactly the same confidence interval for μ.
FALSE. Every random sample of the same size from a given population will not produce exactly the same confidence interval for μ.
The confidence interval is a statistical measure used to estimate the range of values within which a population parameter is likely to fall. The confidence interval is calculated based on the sample mean and standard deviation, as well as the level of confidence desired.
Suppose we take a random sample of size n from a population, and calculate the confidence interval for the population mean using this sample. The sample mean and the sample standard deviation will be used to estimate the true population mean and the population standard deviation, respectively. However, as the sample is random, each sample—despite being drawn from the same population—will have different values for the sample mean and standard deviation. Thus, different samples will produce different confidence intervals for the population mean.
Moreover, the size of the sample also affects the width of the confidence interval; larger samples tend to produce more precise estimates of the population mean, while smaller samples yield larger confidence intervals. Therefore, random samples of different sizes from a given population will also produce different confidence intervals.
In summary, the confidence interval is a statistical measure that provides a range of likely values for the population parameter, such as the population mean. While it can be calculated using any random sample from a population, different samples of the same size or different sizes will generally produce different confidence intervals.
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Find the missing length indicated
The answer of the given question based on finding the missing length of a triangle the answer is , None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.
What is Triangle?In geometry, triangle is two-dimensional polygon with three straight sides and three angles. It is one of basic shapes in geometry and can be defined as closed figure with three line segments as its sides, where each side is connected to two endpoints called vertices. The sum of interior angles of triangle are 180° degrees.
Triangles are classified based on length of their sides and measure of their angles. A triangle can be equilateral, isosceles, or scalene based on whether all sides are equal, two sides are equal, or all sides are different, respectively.
To find the missing length indicated, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this triangle, we can see that the two legs have lengths of 9 and 16, and the hypotenuse has length X. So we can write:
9²+ 16² = X²
Simplifying the left-hand side:
81 + 256 = X²
337 = X²
Taking the square root of both sides (and remembering that X must be positive, since it is a length):
X = sqrt(337)
X ≈ 18.3575
So the missing length indicated is approximately 18.3575. None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.
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look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?
Therefore, the only statement that is true is: "The new area is 6 times the original area."
What is area?Area is a measure of the size or extent of a two-dimensional surface or region, such as the surface of a square, rectangle, circle, triangle, or any other shape. It is expressed in square units, such as square meters, square feet, or square centimeters.
Here,
If the side lengths of a square are tripled, the new side length will be 2 mm x 3 = 6 mm.
The original area of the square is:
Area = side length x side length = 2 mm x 2 mm = 4 mm²
The new area of the square with tripled side lengths will be:
New area = new side length x new side length = 6 mm x 6 mm = 36 mm²
Therefore, the new area of the square will be 36 mm².
To determine which of the following statements about its area will be true, we need to see which statements are true for the new area of 36 mm²:
A. The new area is 6 times the original area. This statement is true because 36 mm² is 6 times larger than 4 mm².
B. The new area is 3 times the original area. This statement is false because 36 mm² is 9 times larger than 4 mm², not 3 times larger.
C. The new area is equal to the original area. This statement is false because the new area of 36 mm² is much larger than the original area of 4 mm².
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Complete question:
look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?
The ratio of the new area to the old area will be 2:1
The ratio of the new area to the old area will be 6:1.
The ratio of the new area to the old area will be 1:2.
The ratio of the new area to the old area will be 4:1.
Find the exact value of the expression: tan270 degrees
Answer:
What is the Value of Tan 270 Degrees? The value of tan 270 degrees is undefined. Tan 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .) ⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .
please marke a a brainalist pls
Which graph matches the function given:
The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.
What is a piecewise function?A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.
The intervals of the piecewise function are;
f(x) = √(x + 5) if x < -2
f(x) = |x + 1| -2 ≤ x ≤ 2
f(x) = (x - 2)² if x > 2
The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²
The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2
The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.
The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.
The correct option for the graph of the piecewise function is therefore the third option.
Please find the attached the graph of the piecewise function created with MS Excel
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the larger leg of a right triangle is 7cm more than the smaller leg the hypotenuse is 17cm find each leg
Answer:
So the lengths of the legs are approximately 8.6 cm and 15.6 cm.
Step-by-step explanation:
Let's call the smaller leg "x" and the larger leg "x + 7". According to the Pythagorean theorem, we know that:
x^2 + (x + 7)^2 = 17^2
Expanding the square on the left side and simplifying, we get:
2x^2 + 14x - 210 = 0
Dividing both sides by 2, we get:
x^2 + 7x - 105 = 0
Now we can solve for x using the quadratic formula:
x = (-7 ± sqrt(7^2 - 4(1)(-105))) / 2(1)
x = (-7 ± sqrt(649)) / 2
x ≈ -15.6 or x ≈ 8.6
Since we're dealing with lengths of sides in a triangle, we can't have a negative value for x. So we discard the negative solution and conclude that the smaller leg is approximately 8.6 cm.
To find the larger leg, we add 7 to x:
x + 7 ≈ 15.6 cm
Estimate the product. Then find each product 3/4 8 1/2
PLEASE HELP
The product of the number 3/4 and 8 1/2 is 51/8.
What is mixed fraction and improper fraction?A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.
The given numbers are 3/4 and 8 1/2.
Convert the mixed number to an improper fraction:
8 1/2 = (8 x 2 + 1) / 2 = 17/2
Then, we can multiply the fractions:
3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8
Hence, the product of 3/4 and 8 1/2 is 51/8.
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help ASAP PLSSSS
The table of values represents a linear function.
Enter the rate of change of this function.
The rate of change (or slope) of this linear function is -1/2.
Describe Linear Function?A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.
The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.
Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.
The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
Let's use the points (0, -3) and (2, -4) to calculate the slope:
slope = (-4 - (-3)) / (2 - 0)
slope = -1 / 2
Therefore, the rate of change (or slope) of this linear function is -1/2.
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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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Please help!!!!!!!!!!!!!!
Step-by-step explanation:
try this option (see the attachment), answers are marked with red colour.
The bar graph in the following graphic represents fictional net exports in billions of dollars for five countries.
Net exports are obtained by subtracting total imports from total exports; a negative net export means the
country imported more goods than it exported.
Net Exports (Billions of dollars)
United States
Denmark
China
Germany
Spain
-150 -100
-50
Net Exports (Billions of dollars)
What is the sum of net exports for Germany and China ?
a.
-80 billion dollars
b. 180 billion dollars
0 50 100 150
C. 90 billion dollars
d. 150 billion dollars
[tex]80[/tex] billion dollars' worth of net exports were made by China and Germany. The first claim is accurate.
What do the terms "export" and "import" mean?Export is the process of supplying goods and services to some other nation. Contrarily, importing is the act of acquiring goods from outside and transferring them into one's own nation.
What does GDP export mean?The domestic product (GDP) is a measure of all the products and services generated in the United States; thus, changes in exports change significantly in the demand for goods and services made in the United States abroad.
The total of China's and Germany's net exports would be:
[tex]50[/tex] billion + [tex]30[/tex] billion [tex]= 80[/tex] billion
As a result, Germany & China's consolidated net exports amounted to [tex]80[/tex] billion u.s. dollars, reflecting answer option (a).
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The result of adding 15 to x and dividing the answer by 4 is the same as taking x from 80. a Express this statement as an algebraic equation. b Hence find the value of x.
Answer:
(15+x)÷4 = 80-x
by criss cross we'll get:
15+x = 4(80-x)
15+x = 320-4x
x+4x=320-15
5x = 305
x = 61
please help with with this math
The slope of this linear function is equal to: B. -2/9.
The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.
The value of each expression is: C. a) 2, b) 1/2, c) 2/9.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - 10)/(6 - (-3))
Slope (m) = (8 - 10)/(6 + 3)
Slope (m) =
Slope (m) = -2/9.
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the given parameters, we have:
Volume of cylinder, V = 3.14 × 5² × 10
Volume of cylinder, V = 785 m³
(√2)² = 2
(1/√2)² = 1/2
(√2/3)² = 2/9
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Between which two consecutive integers does [tex]\sqrt138[/tex]lie?
The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.
To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.
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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.
138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.
Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.
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To approximate binomial probability plx > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. O plx > 7.5) O plx >= 9) O plx > 9) O plx > 8.5)
The appropriate 0.5 adjusted formula for normal approximation is option (d) p(x > 8.5)
The appropriate 0.5 adjusted formula for normal approximation to approximate binomial probabilities when n is large is
P(Z > (x + 0.5 - np) / sqrt(np(1-p)))
where Z is the standard normal variable, x is the number of successes, n is the number of trials, and p is the probability of success in each trial.
To approximate binomial probability p(x > 8) when n is large, we need to use the continuity correction and find the appropriate 0.5 adjusted formula for normal approximation. Here, x = 8, n is large, and p is unknown. We first need to find the value of p.
Assuming a binomial distribution, the mean is np and the variance is np(1-p). Since n is large, we can use the following approximation
np = mean = 8, and
np(1-p) = variance = npq
8q = npq
q = 0.875
p = 1 - q = 0.125
Now, using the continuity correction, we adjust the inequality to p(x > 8) = p(x > 8.5 - 0.5)
P(Z > (8.5 - 0.5 - 8∙0.125) / sqrt(8∙0.125∙0.875))
= P(Z > 0.5 / 0.666)
= P(Z > 0.75)
Therefore, the correct option is (d) p(x > 8.5)
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The given question is incomplete, the complete question is:
To approximate binomial probability p(x > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. a) p(x > 7.5) b) p(x >= 9) c) p(x > 9) d) p(x > 8.5)
let a and b be positive integers, where a and b do not equal 0. for what limit expression does l'hospital's rule apply? (1 point)
For a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.
L'Hospital's rule applies to limit expressions of the form 0/0 or infinity/infinity. Specifically, if we have a limit expression of form f(x)/g(x), where f(x) and g(x) both approach 0 or infinity as x approaches a certain value, then L'Hospital's rule may be applied to find the limit of the expression.
It is important to note that L'Hospital's rule can only be applied if the limit of the derivative of f(x) divided by the derivative of g(x) exists and is finite, or if the limit of the derivative of f(x) divided by the derivative of g(x) approaches infinity or negative infinity.
Therefore, for a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.
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given f(x) and g(x) find the value of (gof)(5)
Answer:
Assuming that (gof)(5) means (g(f(5))):
(gof)(5) = g(f(5)) = g(3x + 7) = 5x + 2
Therefore, (gof)(5) = 5(3x + 7) + 2 = 15x + 17.
Use implicit differentiation to find an equation of the tangent line to the curve sin(x+y)=8x−8y at the point (π,π)
The equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).
To discover the equation of the tangent line to the curve sin( x y) = 8x- 8y on the point( π, π), we want to apply implicit differentiation to discover the pitch of the tangent line at that point.
We begin through differencing both sides of the equation with reference to xcos( x y)( 1 dy/ dx) = eight- 8dy/ dx
After, we can simplify the expression by isolating the terms beholding dy/ dx on one aspect
cos( x y) cos( x y) dy/ dx = 8- 8dy/ dx
8 cos( x y)) dy/ dx = 8- cos( x y)
dy/ dx = ( 8- cos( x y))( 8 cos( x y))
Now we're suitable to discover the pitch of the tangent line at the factor( π, π) by plugging in x = π and y = π into the expression we simply derived
dy/ dx = ( 8- cos( 2π))( 8 cos( 2π))
dy/ dx = ( 8- 1)/( 8 1)
dy/ dx = 7/ nine
Thus, the pitch of the tangent line to the curve sin( x y) = 8x- 8y at the factor( π, π) is7/9.
To find the equation of the tangent line, we can use the point- slope form of the equation
y- y1 = m( x- x1)
In which m is the pitch we simply set up, and( x1, y1) is the point( π, π). Plugging in the values, we get
y- π = ( 7/ nine)( x- π)
Simplifying, we get
y = ( 7/ nine) x-( 2π/ nine)
Thus, the equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).
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