the coordinates of point P are ((Ax + Bx) / 2, (Ay + By) / 2).
How to find?
If we want to find the coordinates of point P on the directed line segment from A to B such that P is the length of the line segment from A to B, we can use the following formula:
P = (1 - t)A + tB
where A and B are the coordinates of the two endpoints of the line segment, t is a scalar between 0 and 1, and P is the coordinates of the point we are trying to find.
When t = 1, we get the coordinates of point B, and when t = 0, we get the coordinates of point A. When t is between 0 and 1, we get a point on the line segment from A to B.
To find the point P that is the length of the line segment from A to B, we set t = 1/2, which gives us:
P = (1 - 1/2)A + (1/2)B
= (1/2)A + (1/2)B
So the coordinates of point P are the average of the coordinates of A and B:
Px = (Ax + Bx) / 2
Py = (Ay + By) / 2
where (Ax, Ay) and (Bx, By) are the coordinates of points A and B, respectively.
Therefore, the coordinates of point P are ((Ax + Bx) / 2, (Ay + By) / 2).
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Complete Question:
What are the Cartesian coordinates of point P on the directed line segment from point A to point B such that point P is located at a distance equal to the length of the line segment from point A to point B?
Two trains A and B left the same station at the same time. The speed of
train A is 105 kmph, while train B's is 87 kmph. If they travel in the same
direction, how far apart will they be in three hours?
Answer:
Step-by-step explanation:
Since they are traveling in the same direction, the distance between them increases at a rate of the difference of their speeds.
The relative speed of train A with respect to train B is:
105 kmph - 87 kmph = 18 kmph
In three hours, the distance between them will be:
Distance = Speed x Time
Distance = 18 kmph x 3 hours
Distance = 54 km
Therefore, the two trains will be 54 kilometers apart after three hours.
i have a reed. i know not its length. i broke from it one cubit and it fit 60times along the length of my field. i restored to the reed what i had broken off and it fit 30 times alone the wifth of my Field. the area of my field is 375 square nindas. what was the original length of the reed? 1nandas:12cubits
The original length of the reed is 3.83 nindas which can be calculated by using the information given in the question.
What is area?Area is a two-dimensional measurement of a surface or space. It is a measure of how much space is occupied by a two-dimensional object or surface. The area of a shape is determined by multiplying the length and width of the shape together.
Firstly, we need to calculate the width of the field. As the reed fits 30 times along the width, this implies that the width of the field is 30 times the length of the reed. Therefore, the width of the field is 30 x length of the reed.
Now, we need to calculate the area of the field. As the area of the field is given as 375 nindas², this implies that the area of the field is equal to 375 nindas².
We can substitute the width of the field (30 x length of the reed) into the equation for the area of the field, to yield: 375 nindas² = (30 x length of the reed) x length of the reed.
Solving for length of the reed, we get: length of the reed = (375/30)1/2 = 3.83 nindas.
Therefore, the original length of the reed is 3.83 nindas.
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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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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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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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Lines m and n are parallel lines cut by a transversal, line q. Which of the following is not supplementary to angle 7?
The vertex is frequently identified by the letter that appears in the middle, like the letter V. Angles are often measured in degrees, and degrees are used to characterize angles. Thus, option C is correct.
What is the different angle?Angle 7 is perpendicular to angle 3, and angle 3 is supplementary to angle 8, therefore they both fall along a straight line. Hence, angle 8 is complementary to angle 7.
Since they form a straight line and are opposite angles, angles 5 and 7 are supplementary. Hence, angle 5 is complementary to angle 7.
The only angle in the figure that is not a support for angle 7 is angle 6. If angles 6 and 7 do not overlap but share a vertex and side, then they are considered neighbouring.
Because they do not go to a straight line, angles 6 and 7 are not extra in this case. The answer is therefore Angle 6.
Therefore, They are not always complementary, even if two nearby angles come together to create a straight line.
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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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find the radius of a circle whose area is 28½cm²
Answer: 3 cm
Step-by-step explanation:
The formula for the area of a circle is A = πr², where A is the area and r is the radius. We are given that the area of the circle is 28½ cm².
So, 28½ = πr²
We need to solve for r. Dividing both sides by π, we get:
r² = 28½/π
r² = 9
Taking the square root of both sides, we get:
r = 3√1 = 3 cm
Therefore, the radius of the circle is 3 cm.
PLEASE HELLP IM AWARDING 100 POINTS FOR THIS What is the scale factor, or constant of proportionality from Figure 1 to Figure 2?
Enter your answer as a decimal in the box.
Answer:
4:9
Step-by-step explanation:
Answer:
Scale factor = 2.25
Step-by-step explanation:
To find the scale factor between two similar shapes, we need to compare the corresponding sides of the shapes.
The scale factor is the ratio of the length of any side of one shape to the length of the corresponding side on the other shape.
From inspection of the given diagram, the ratio of the corresponding sides of the two similar figures is:
⇒ Figure 1 : Figure 2 = 8 : 18
Therefore, to find the scale factor from Figure 1 to Figure 2, divide the side length of Figure 2 by the corresponding side length of Figure 1:
[tex]\implies \sf Scale\;factor=\dfrac{18}{8}=2.25[/tex]
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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.
Part y Wa g on, Inc., provides musical entertainment at weddings, dances, and various other functions. The company performs adjusting entries monthly but prepares closing entries annually on December 31. The company recently hired Jack Armstrong as its new accountant. Jack’s first assignment was to p re p are an income statement, a statement of retained earnings, and a balance sheet usin g an adjusted trial balance given to him by his predecessor, dated December 31, the current year.
From the ad j usted trial balance, Jack p re p ared the followin g set of financial statements.
Preparation of a Corrected set of Financial Statements :
Income Statements :
PARTY WAGON .INC
INCOME STATEMENT
FOR THE YEAR ENDED DECEMBER 31
CURRENT YEAR
Party Revenue Earned
156,000
Total Revenue
156,000
Expenses :
Insurance Expenses
2,160
Office Rent Expense
14,400
Supplies Expense
1,440
Salary Expense
90,000
Repair and Maintainence expense
2,400
Travel Expense
7,200
Miscellaneous Expense
4,320
Interest Expense
5,280
Depreciation - Van
9,600
Depreciation -Music and Equipment
8,400
Total Expenses
145,200
Income Before Income Tax
10,800
Less : Income Tax Expense
2,400
Net Income
8,400
How to explain the financial statementJack included balance sheet accounts in the income statement, therefore the corrected income statement consisting of revenue and expenses accounts is provided above.
Statement of Retained Earnings :
Retained Earnings (As per adjusted trial balance) 18,000
Add : Net Income 8,400
Less : Dividends (1,200)
Retained Earnings Dec 31, Current Year 25,200
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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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How many fractions between and inclusive can be written with a
denominator of 15?
The number of fractions between 0 and 1 (inclusive) with a denominator of 15 can be found using the formula (n-1)/n, where n is the denominator.
So, to answer your question, we can use the formula and plug in 15 for the value of n:
(15-1)/15 = 14/15
Therefore, there are 14 fractions between 0 and 1 (inclusive) with a denominator of 15.
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
Answer: 24
Step-by-step explanation:
To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.
Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.
The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.
Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19
Radius of the circle = 4.19/60 = 0.07
Angle of sector = 360 - 60 = 300 degrees
Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041
The area of the triangle can be found using the formula:
Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24
Therefore, the total area of the composite figure is:
0.0041 + 24 = 24.0041
Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.
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
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Bacteria in a petri dish double the area they cover every day. If the dish is covered
after 16 days, on what day was only one quarter of it covered?
Which equation calculates the total amount of milk needed to make 7 milkshakes if each milkshake requires 3 4 cup of milk? A. 7 × 3 4 = 21 28 cups B. 7 + 3 4 = 7 3 4 cups C. 7 × 1 4 = 7 4 , or 1 3 4 cups D. 7 × 3 4 = 21 4 , or 5 1 4 cups
Answer:
D
Step-by-step explanation:
7/1 times 3/4 equals 21/4 cups of milk
f(s) = 3s + 2
p(s) = s^3+ 4s
Find (f • p)(-5)
The value of (f • p)(-5) is 1885 when functions are given as f(s) = 3s + 2 and p(s) = s³+ 4s.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is often represented by an equation or formula, and can be visualized as a graph. Functions are widely used in various areas of mathematics, science, engineering, and other fields to model real-world phenomena and solve problems.
Here,
f(s) = 3s + 2
p(s) = s³+ 4s
To find (f • p)(-5), we need to first find f(-5) and p(-5), and then multiply them together. To find f(-5), we substitute -5 into the function f(s) and simplify:
f(-5) = 3(-5) + 2
= -13
To find p(-5), we substitute -5 into the function p(s) and simplify:
p(-5) = (-5)³ + 4(-5)
= -125 - 20
= -145
Now we can multiply f(-5) and p(-5) together to find (f • p)(-5):
(f • p)(-5) = f(-5) * p(-5)
= (-13) * (-145)
= 1885
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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.
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?
In the isosceles trapezoid, what is the length of LA?
A) 15
B) 17
C) 16
Answer:
A) 15 idek
Step-by-step explanation:
Calculate
the LCM of 5 and 20
do the following statements describe red pulp or white pulp? drag and drop the labels into the corresponding boxes.
After labeling with the corresponding boxes , The statements which describes Red pulp and white pulp are as follow:
1. Red pulp 2. Red Pulp 3. White Pulp 4. Red pulp
5. White Pulp 6. White Pulp 7. Red Pulp.
Red Pulp:
The red pulp of the spleen is made up of connective tissue (also known as Bill Roth's cord) and numerous sinusoids of the spleen which appear red due to excess blood. Its main function is to filter antigens, microorganisms and defective or worn out red blood cells from the blood.
The spleen consists of red and white pulp, separated by the marginal zone; 76-79% of a normal spleen is made up of red pulp. Unlike white pulp, which contains mostly lymphocytes (such as T cells), red pulp is made up of several types of blood cells, including platelets, granulocytes, red blood cells, and plasma.
White Pulp:
White pulp is the histological name for the areas of the spleen (so called because they appear whiter in rough sections than the surrounding red pulp), which make up approximately 25% of the spleen. The white pulp is entirely composed of lymphoid tissue.
Specifically, the white pulp contains several regions with distinct functions:
The periarteriolar lymphatic sheaths (PALS) are usually associated with the arteriolar supply to the spleen; they contain T lymphocytes.
Lymphoid follicles with dividing B lymphocytes located between the PALS and the marginal zone bordering the red pulp. This region produces IgM and IgG2.
These molecules play a role in the opsonization of extracellular organisms, in particular encapsulated bacteria.
The marginal zone exists between the white pulp and the red pulp. It is located away from the central arterioles, close to the red pulp. It contains antigen-presenting cells (APCs), such as dendritic cells and macrophages. Some white pulp macrophages are of a special type called metallolipid macrophages.
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Team A scored twice as many points as Team B. If the total number of points scored by both teams was 12, find the number of points scored by each team.
Answer:
Step-by-step explanation:
Let x be the number of points scored by Team B.
Then, Team A scored twice as many points, or 2x.
The total number of points scored by both teams is 12, so we can set up the equation:
x + 2x = 12
Combining like terms, we get:
3x = 12
Dividing both sides by 3, we get:
x = 4
So Team B scored 4 points, and Team A scored twice as many, or 8 points.
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
5. What is the difference between (-3)² and 3²
Answer:
the difference is the first one, (-3)^2, is negative while the other is positive
Step-by-step explanation:
15. In the figure, ABCD is a trapezoid. Given
that length of BE equals to the length
CE, find the area of triangle ADE.
Triangle ADE has a surface area of 75 cm².
What is the triangular area formula?Triangle area determination. Use the equation area = 1/2 * base * height to determine a triangle's surface area. Decide which side will serve as the triangle's base, then calculate the triangle's height from that base.
Using similarity to determine y's value
AD/BD = AE/BE
y/(a-x) = y/x
yx = y(a-x)
x = a/2
This fact can be used to determine the height of the trapezoid:
h = √(BC² - [(AB-DC)/2]²)
= √(10² - [2²]²)
= 8
Now that we know how long MD is, we can:
As a result of the triangles ADE and BDE's resemblance, we can now determine the value of y:
y/BD = AE/BE
y/(a-x) = y/x
yx = y(a-x)
x = a/2
Substituting x = a/2 and BD = AB - DC = 10 - 6 = 4, we get:
y/4 = AE/(a/2)
y = 2AE/a
Substituting y = 2AE/a in the above equation, we get:
(2AE/a)/4 = AE/(a/2)
AE = (a/2)²/2
We may now apply the triangle's area formula, ADE:
Area of ADE = (1/4) x y x (a+b)
= (1/4) x 2AE/a x (a+b)
= (1/8) x (a²/2) x (a+b)
= (1/16) x a² x (a+b)
Substituting a = 10 and b = 6, we get:
Area of ADE = (1/16) x 10² x (10+6)
= 75 cm².
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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.
The standard deviation of the scores on a skill evaluation test is 497
points with a mean of 1754
points.
If 302 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 44
points? Round your answer to four decimal places.
Answer:
497/√302 = 49.7
z-score = (44-0)/49.7 = 0.88
Probability = 0.8133
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)
