The vertex form equivalent to the given expression; 2x² + 8x as required to be determined in the task content is; 2 (x + 2)² + 8.
What is the vertex form equivalent of the expression?The vertex form equivalent of the given expression can be determined as follows;
2x² + 8x
2 (x² + 4x)
2 ( (x + 2)² + 4)
= 2 (x + 2)² + 8.
Ultimately, the vertex form equivalent of the given expression as required is; 2 (x + 2)² + 8.
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While Mike was visiting his sister in Arlington, he bought an aquarium that was marked down 60% from an original price of $100. If the sales tax in Arlington is 5%, what was the total cost of the aquarium?While Mike was visiting his sister in Arlington, he bought an aquarium that was marked down 60% from an original price of $100. If the sales tax in Arlington is 5%, what was the total cost of the aquarium?
The total cost of the aquarium that Arlington bought after markdown and including sales tax is $42.
What is meant by the markdown of the price?
The markdown is the price that separates an item's current, lowered price from its original, full price. Typically, a percentage is used to express it. Retailers can offer their products at a discount thanks to markdown.
Discounts are distinct from markdowns. Markdowns give everyone the chance to buy products for a lower price. However, some customers may only be eligible for discounts, such as students.
Markdown = (difference of prices / actual selling price) x 100
Given,
Original Cost of aquarium = $100
Marked down price = 100 - 0.60 * 100= 100 - 60 = $40
Sales tax = 5%
Sales tax is the percentage of the price at which the aquarium was bought i.e the markdown price.
Sales tax = 5% of $40 = 0.05 * 40 = $2
Total cost = marked down price + sales tax = $40 + $2 = $42
Therefore the total cost of the aquarium that Arlington bought after the markdown and including sales tax is $42.
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Pleaseh help me! Find the missing side length using trig!
Answe[tex]3\sqrt{2)[/tex]
Step-by-step explanation:
Adding and subtracting rational expressions, What is the difference? 2x+5/x^2-3x - 3x+5/x^3-9x - x+1/x^2-9?
After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9 .
We first simplify each expression inside the parentheses :
that means :
⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;
⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³) ;
⇒ (x + 1/x² - 9) = (-9 + x + 1/x²) ;
Now we substitute these expressions into original equation/expression :
we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)
Simplifying further ,
we get ;
⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x² ;
On Combining the like terms, we get ;
⇒ 4x - 4/x² - 5/x³ + 9
Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.
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The given question is incomplete , the complete question is
Adding and subtracting rational expressions, Simplify the rational expression (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9) .
If () = √, () = + 5 and h() = 2 − 1 , find the following.
a) ( ∘ )(4)
b) (∘)(4)
c) (h∘∘)(−5)
d) ( ∘ )()
e) (∘)
f) (h∘)
a) (f ∘ g)(4) = 2
b) (g ∘ f)(4) = √2 + 5
c) (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5)
d) (g ∘ f)(x) = √(x + 5) + 5.
e) (f ∘ g)(x) = √(√x + 5) + 5
f) (h ∘ f)(x) = 2 - 1/ (√x + 5)
What is Function?
A function is an expression or relationship that involves one or more variables. It has several inputs and outputs.
a) (f ∘ g)(4) means plugging in the value of 4 into g(x) and then plugging the result into f(x). So we have:
g(4) = √4 + 5 = √9 = 3
f(g(4)) = f(3) = √3 + 5 = 2
Therefore, (f ∘ g)(4) = 2.
b) b) (g ∘ f)(4) means plugging in the value of 4 into f(x) and then plugging the result into g(x). So we have:
f(4) = √4 = 2
g(f(4)) = g(2) = √2 + 5
Therefore, (g ∘ f)(4) = √2 + 5.
c) (h ∘ g ∘ g)(-5) means plugging in the value of -5 into g(x) twice, and then plugging the result into h(x). So we have:
g(-5) = √(-5) + 5 = √(20) = 2√5
g(g(-5)) = g(2√5) = √(2√5) + 5
h(g(g(-5))) = h(√(2√5) + 5) = 2 - 1/ (√(2√5) + 5)
Therefore, (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5).
d) (g ∘ f)(x) means plugging in the function f(x) into g(x), which gives:
g(f(x)) = √(x + 5) + 5
Therefore, (g ∘ f)(x) = √(x + 5) + 5.
e) (f ∘ g)(x) means plugging in the function g(x) into f(x), which gives:
f(g(x)) = √(√x + 5) + 5
Therefore, (f ∘ g)(x) = √(√x + 5) + 5.
f) (h ∘ f)(x) means plugging in the function f(x) into h(x), which gives:
h(f(x)) = 2 - 1/ (√x + 5)
Therefore, (h ∘ f)(x) = 2 - 1/ (√x + 5).
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Please find the missing side length using trig!
The missing side is [tex]5\sqrt{3}[/tex].
What are basic Trigonometric functions?
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.
In a Right-angled triangle, the tangent of an angle is equal to the opposite side/adjacent side.
from the given figure,
tan 60° = x/5
[tex]\sqrt{3}=\frac{x}{5}\\ x=5\sqrt{3}[/tex]
Therefore, The missing side is [tex]5\sqrt{3}[/tex].
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The table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify the correlation of coefficient. Round your answer to three decimal places
The value of correlation cofficient between the number of people who complete successfully complete each jump, y and height of jump, x is equals to the - 0.091.
We have a table which consists height ( in feet ), x and completions, y present above figure. We have to calculate the correlation coefficient for variables x and y. Correlation coefficients are used to measure how strong the relationship is between two variables. The commonly used cofficient in linear regression is Pearson's correlation (also called Pearson's R) coefficient . Formulas return a value between -1 and 1, where,
A strong positive relationship, r = 1Strong negative relationship, r= -1A result of zero indicates no relationship at all.Formula used to determine the cofficient is r = (n∑ xy - (∑x)(∑y))/√[ n∑x² - (∑x)²][n∑y² - (∑y)²]
Here, n = 6, ∑xy = 375.8 , ∑ x =22.4, ∑y
= 102, ∑ x² = 96.5, ∑y² = 1978
so, r = 6×(375.8) - 102(22.4))/√[(6×96 - (22.4)²)(6×1978 - 102²)]
= -30/329.68
= - 0.091
Hence, required value of r is - 0.091.
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Complete question:
The above table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify the correlation of coefficient. Round your answer to three decimal places.
pls help me pls plsplsssssssssssss
Answer:
8 to 2
Step-by-step explanation:
because u have 8 cocca and 2 sugar
Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. Write equivalent ratios to determine the amount of green and white paint she will need to purchase.
Based on the information, Wendy will need to purchase 48 quarts of paint
How to calculate the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house.
The amount of paint needed will be:
= 4/1 × 12
= 48 quarts
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Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. a. Write equivalent ratios to determine the amount of green and white paint she will need to purchase. b. If there are 4 quarts in 1 gallon, how many quarts of paint does she need to purchase
If 7 book cost rs 300 than 5 same books find the cost of a book
When the cost of 7 books is equal to Rs 300 more than the 5 same books then the cost of a single book is equal to Rs 150.
Let us consider Rs 'x' be the cost of a single book .
Equation to represents the given expression 7 books is equal to Rs 300 more than the 5 same books is :
⇒ 7x = 300 + 5x
Subtract 5x from both the side of the equation we get,
⇒ 7x -5x = 300 + 5x - 5x
⇒ 2x = 300
Divide both the side by 2 we get,
⇒ 2x / 2 = 300 / 2
⇒ x = Rs. 150
Therefore, the cost of a single book as per the given condition of 7 books is equal to Rs 300 more than the 5 same books is given by Rs 150.
The above question is incomplete, the complete question is:
If 7 books cost Rs. 300 more than 5 books, find the cost of a book.
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How many ways can a family of mother, father, and 3 children stand in a row if the mother and father stand at the ends of the row?
Answer:
12 ways
Step-by-step explanation:
the mother and father can either stand at the front/back or back/front respectively (2 ways)
that leaves 3 children in the middle -- there are 3 choices for the first child to go, 2 for the second, and 1 for the third = 3! = 6
6 ways for the children * 2 ways for the parents = 12 ways
Find the formulas for the nth term of each sequences
1. 3, 5, 9, 17, ...
2. 2/5, 3/6, 4/7, 5/8, ...
Answer:
1. 2^n + 1.
2. (n +1)/(n + 4)
Step-by-step explanation:
1. 3 5 9 17....
3 = 2^1 + 1
5 = 2^2 + 1
9 = 2^3 + 1
17 = 2^4 + 1
Therefore the nth term is
2^n+ 1 .
2. Looking at the fractions we see that:
Numerators are 2, 3, 4 ,5..
and denominators are 5, 6, 7, 8
So the nth term is
(n + 1) / (n + 4)
Please Answer ASAP!
Please Give A Clear Answer Too!!
Answer:
x + y = -9
Step-by-step explanation:
let x = -8, y = -1
the equation that passes through the point (-8,-1) is x + y = -9
a farmer measures the height of every tree in a large orchard in centimeters. the farmer wishes to present the data by grouping the results into groups of 25 cm. which graphical display would be most appropriate to display the results?
A histogram would be the most appropriate graphical display to present data by grouping the results into groups of 25 cm.
A histogram is a graphical representation of data that shows the distribution of a set of continuous data by dividing the data into bins (or intervals) and showing the frequency of observations within each bin. The histogram provides a visual representation of the distribution of data, showing the shape, central tendency, and spread of the data.
In this case, the farmer has measured the height of every tree in a large orchard in centimeters and wants to present the data in groups of 25 cm. To create a histogram for this data, the first step would be to divide the data into bins, or intervals, of 25 cm.
Once the bins are created, the next step is to count the number of observations (tree heights) that fall within each bin. This information can be represented as a bar graph, where the height of each bar represents the frequency of observations within the corresponding bin.
By presenting the data in this way, the farmer can easily see the distribution of tree heights in the orchard. The shape of the histogram can indicate whether the data is symmetrical, skewed, multimodal, or uniform.
The central tendency of the data can be determined by looking at the peak of the histogram, which represents the most frequent range of tree heights. The spread of the data can be determined by looking at the width of the histogram and the range of tree heights represented.
In conclusion, a histogram is the most appropriate graphical display to present the results of the tree heights in groups of 25 cm because it provides a visual representation of the distribution of the data and allows the farmer to see the shape, central tendency, and spread of the tree heights in the orchard.
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PLEASE HELPPP me ASAP and show your work. If I get 2 questions I will mark one person BRAINLIEST. So PLEAASEEEEEEEEEEE Help on #4, #7, and #8 DUE TONIGHT
QUESTION 4: m∠A = 53 degrees
QUESTION 7: Area of triangle PQR is 23.6 unit²
QUESTION 8: Using cosine law, JK = 3.1 units
How to find the angle and area of triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
QUESTION 4
tan A = 9.6/7.2
A = arctan(9.6/7.2)
A = 53 degrees
QUESTION 7
Area of ΔPQR = 1/2 * 6 * 8 * sin 80
Area of ΔPQR = 23.6 unit²
QUESTION 8
JK = √(6² + 8² - 2*6*8*cos 20°) (cosine law)
JK = 3.1 units
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PLEASE PLEASE PLEASE PLEASE PLEASE ANSWER THIS ASAP!!!!!!!!!!!!!THIS IS MATH I AM GIVING 50 POINTS!!!!!!!!!
Yu Yan makes a wall hanging from a piece of fabric. For the first part, she cuts off 1/3 of the length of the original piece of fabric. For the next two parts, she cuts off 10 inches and 5 inches from the length of the remaining fabric. In total, she cuts 35 1/2 inches from the length of the original piece of fabric. How long was the original piece of fabric? Write and solve an equation. Check your solution.
The length of the original piece of fabric, given the proportion cut by Yu Yan and the amount cut in total, is 75 .75 inches
How to find the original length of fabric ?Assume that the original length of fabric was denoted as x, this means that the first cutting by Yu Yan took out :
= 1 / 3 x
The equation would then be :
x - 1 / 3 x - 10 - 5 = 35 + 1 / 2
x - 1 / 3 x - 10 - 5 = 35 . 5
The length of the original fabric is:
2 / 3x = 35. 5 + 10 + 5
x = 50. 5 ÷ 2 / 3
x = 50. 5 x 3 / 2
x = 75 .75 inches
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(d) 1, 4, 16, ____, 256, 1024, ...
The missing number in the sequence is 64
How to determine the missing numberFrom the question, we have the following parameters that can be used in our computation:
1, 4, 16, ____, 256, 1024, ...
Using the above as a guide, we have the following:
To obtain the next term, we can multiply the previous term by 4:
So, we have
Next term = 16 * 4
Next term = 64
Therefore, the next term in the sequence is 64.
The completed sequence is: 1, 4, 16, 64, 256, 1024, ...
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which expression gives the distance between the two points (2,3) and (4,-3)
The expression that will give the distance between points is option D i.e. √(2 - 4)² + (3 + 3)². The solution has been obtained by using distance formula.
What is the distance formula?
The distance between two locations on a coordinate plane can be calculated using the distance formula. The distance equation is written as d = √(x₂ - x₁)² + (y₂ - y₁)².
We are given two points as (2,3) and (4,-3).
So, x₁ = 2, y₁ = 3, x₂ = 4, y₂ = -3
Now, substituting these values in the distance formula, we get
d = √(2 - 4)² + (3 + 3)²
Hence, the expression that will give the distance between points is option D.
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Full question has been attached below
What is the range of the function?
23
4
2
4
9
16
Answer:
Step-by-step explanation:
The Vikings, who discovered Iceland, used Ravens to help find land.
True
False
Answer: TRUE Flóki reportedly released three ravens, and then sailed in the general direction that they flew, eventually discovering Iceland.
Step-by-step explanation:
The binomial (x+5) is a factor of x² + 8x + 15. What is the
other factor?
O (x+3)
O (x + 7)
(x+12)
O (x+13)
4X
Factor 2
Product
Factor 1
Reset
The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
Given that binomial (x+5) is a factor of x² + 8x + 15.
We need to find the other factor.
Let us solve x² + 8x + 15=0
x² + 5x +3x+ 15=0
x(x+5)+3(x+5)=0
(x+3)(x+5)
So the other binomial factor is x+3.
Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.
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The United States Postal Service has an online guide to make life easy for people using their
postal service. This is an extract.
First Class Mail
First class mail must be used for handwritten or personal correspondence.
First Class Mail Rates - single piece rates
$0.44
First ounce (oz.) Letter size mail
Each additional oz. or fraction
First ounce Flat size mail **
Each additional oz. or fraction
First ounce Parcel ***
Each additional oz. or fraction
Standard Postcard ****
$0.17 per oz. up to 3.5 oz.
$0.88
$0.17 per oz. up to 13 oz.
$1.22
$0.17 per oz. up to 13 oz.
$0.28
* Letters: (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W,
max. weight 3.5 oz). Letter size mai over 3.5 ounces, see Flat size prices.
**Flats: (min. dimension: 11.5 L, 6.125" H, 0.25"W; max. dimension: 15 L, 12 H, 0.75 W).
*** Parcels: Anything larger.
**** Postcards: (min. dimension: 5L, 3.5" H, 0.007"W; max. dimension: 61, 4.25 H, 0.016 W).
I want to send two items through the post using first class mail.
One fts into an envelope 20 L, 10°H and 4"W and weighs 10oz.
The other fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz.
How much are the items going to cost me to send?
The amount of money that the items will cost you to send through United States Postal Service would be = $13.3
How to calculate the total amount of money for the Postal Services?The dimensions of the first envelope = 20 L, 10°H and 4"W
The weight of the first envelope = 10 ounce.
The first envelope is a parcel because the dimensions are larger than 11.5 L, 6.125" H, 0.25"W.
The price per ounce = $1.22
10 ounce = 1.22×10 = $12.2
The dimensions of the second envelope = 8 L, 5" H and 0.20 W.
The weight of the second envelope = 2.5 ounce.
The second letter is of normal letter size because of the dimensions (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W, max. weight 3.5 oz)
The price per ounce = $0.44
2.5 ounce = 2.5× 0.44 = $1.1
The total price = 12.2+1.1 = $13.3
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HELP DUE TONIGHT!!!
Answer:
1. $1900
2. $9
Step-by-step explanation:
Part a:
‘If she doesn’t sell any copies of History is Fun’ means x = 0:
[tex]y = 1900 + 9(0)[/tex]
∴ y = Melissa’s total pay = $1900
Part b:
Rearranging the equation:
[tex]y = 9x + 1900[/tex]
∴m = slope of equation = positive 9
c = y-intercept = 1900
The shape of the graph would be increasing or ascending. And since the Number of copies (x) can never be negative, this means that the amount of pay CANNOT be less than $1900. The amount of $1900 is her minimum pay
The value of m for this equation indicates the change in Melissa’s total pay for every copy she sells.
∴Change in Melissa’s total pay = 9 dollars
Given AB
and DC, complete the flowchart proof below. Note that the last statement reason have both been filled in for you.
The completed flowchart proof is that ΔΑΒΕ = ΔCDE
What is Geometry?Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and dimensions of objects in space. It is concerned with the properties of points, lines, curves, surfaces, and solids, as well as the relationships between them.
How to prove this:
<ABD = <BDC
(alternate angles)
<BAC = <ACD
(alternate angles)
Hence, BE = ED (given)
So, ΔΑΒΕ = ΔCDE
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Use the word bank to complete the statements below.
A reflection over the x-axis.
A vertical stretch by 11 units.
A translation left by 5 units.
A translation up 4 units.
What is reflection over graph?The reflection of a function across the x- or y-axis is another transformation that may be used. In contrast to a horizontal reflection, which reflects a graph horizontally across the y-axis, a vertical reflection reflects a graph vertically across the x-axis.
An illustration of a transformation is a reflection, which flips a shape (referred to as the pre image) over a line (referred to as the line of reflection) to produce a new shape (called the image). Imagine what would happen if you flipped the form over the line in order to graph a reflection.
Here, f(x) = 1/x²
Now, reflect the graph over the x-axis to obtain the graph of:
f(x) = -1/x²
Now, stretch the graph vertically by 11 units to get the graph of:
f(x) = -11/x²
Again, translate the graph left by 5 units to obtain the graph of:
f(x) = - 11 / (x + 5)²
Now, translate the graph up by 4 units to obtain the graph of:
f(x) = 4 - {11 / (x + 5)²}
Hence,
A reflection over the x-axis. A vertical stretch by 11 units. A translation left by 5 units. A translation up 4 units.
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X is a normally distributed random variable with mean 25 and standard deviation 9.
What is the probability that X is less than 16?
The required probability that X is less than 16 is approximately 0.15866 or 15.86%.
What is the Z -a score?A Z-score is stated as the fractional model of data point to the mean using standard deviations.
Here,
We can use the standard normal distribution to find the probability that a normally distributed random variable, X, is less than a certain value. To use the standard normal distribution, we need to standardize X by subtracting the mean and dividing by the standard deviation:
Z = (X - μ) / σ
In this case, X has a mean of 25 and a standard deviation of 9,
Z = (16 - 25) / 9
z = -1
To find the probability that X is less than 16, we need to find the corresponding value of Z using the standard normal distribution table or a calculator.
P(Z < -1) ≈ 0.15866
Therefore, the probability that X is less than 16 is approximately 0.15866 or 15.86%.
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In a restaurant there are
8 starter dishes
15 main dishes
9 dessert dishes
Jane is going to choose one of the following combinations for her meal.
a starter dish and a main dish
or a main dish and a dessert dish
or a starter dish, a main dish and a dessert dish
How many different ways are there for her to choose the meal?
Answer:
there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.
Step-by-step explanation:
First, we need to find the number of different combinations of a starter dish and a main dish. This is simply the number of combinations of 2 items from 8 starters and 15 main dishes, which can be calculated using the formula for combinations:
C(8 + 15, 2) = C(23, 2) = (23 * 22) / (2 * 1) = 276
Similarly, the number of different combinations of a main dish and a dessert dish is:
C(15 + 9, 2) = C(24, 2) = (24 * 23) / (2 * 1) = 276
Finally, the number of different combinations of a starter dish, a main dish, and a dessert dish is:
C(8 + 15 + 9, 3) = C(32, 3) = (32 * 31 * 30) / (3 * 2 * 1) = 5680
In total, there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.
Calculate the angle marked y in
the diagram below.
by=||
57°
y
Step-by-step explanation:
2y+57=180
2y=180-57
2y=123
y=123/2=61.5°
y=61.5
Answer:
61.5
Step-by-step explanation:
As the lines are parallel you can use the alternate angle rule.
So within the triangle you have 57 + x + x ( y is equal to the other angle because the lines are the same length and angle highlighted by the double lines )
And so...
180 - 57 = 123
123/2 = 61.5
the circumference of head sizes of newborns is approximately normal with mean 13.5 inches and standard deviation of 0.75 inches. what percent of babies have a head circumference greater than 14 inches?
A 24.8% of babies have a head circumference greater than 14 inches.
What is Circumference?The circumference of a circle is the length of the curved boundary or the perimeter of the circular shape. It is a measurement of the distance around the circle and is equal to the arc length of the circle if it were opened up and straightened out into a line segment. The circumference of a circle is related to its diameter by the formula: C = π * d
To calculate the percentage of babies with a head circumference greater than 14 inches, we need to find the area under the normal distribution curve to the right of 14 inches.
First, we need to convert 14 inches to the standard units (z-score). We can do that using the following formula:
z = (14 - 13.5) / 0.75 = 0.67
Next, we can use a standard normal distribution table to find the area to the right of z = 0.67. The value from the table is approximately 0.752.
Therefore, approximately 75.2% of babies have a head circumference less than or equal to 14 inches, and 24.8% of babies have a head circumference greater than 14 inches.
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1.an alternative to ols is least absolute deviation (lad) regression, in which the regression line is selected to minimize the sum of the absolute vertical differences (rather than squared differences) between the line and the data. explain how this might reduce sensitivity to outliers.
The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
Regression analysis is a powerful statistical tool used to estimate the relationship between two or more variables. The ordinary least squares (OLS) method is the most commonly used regression method. However, the OLS method is sensitive to outliers in the data.
LAD regression is a robust alternative to OLS regression because it minimizes the sum of the absolute vertical differences between the regression line and the data points. This method is also known as L1 regression.
Let's consider an example of a simple linear regression model with n observations, where Y is the dependent variable and X is the independent variable.
The OLS method estimates the parameters of the regression line by minimizing the sum of the squared vertical differences between the observed data points and the predicted values of the regression line.
In mathematical terms, the OLS method can be represented as follows:
minimize the sum of squared vertical differences,
min(β₀, β₁) ∑ (yₐ - β₀ - β₁ xₐ)²
However, if the data contains outliers, the OLS method may produce biased estimates of the parameters of the regression line, leading to incorrect predictions. On the other hand, LAD regression minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line.
In conclusion, the LAD regression is an alternative to OLS that reduces the sensitivity to outliers. The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
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