100 Points! Expand (2d+3)^6. Please show as much work as possible. Thank you! Photo attached.
Answers
The expansion will be 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729
How to expand the valueWe can expand (2d+3)^6 using the binomial theorem, which states that:
(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn-1 * a^1 * b^(n-1) + nCn * a^0 * b^n
where nCk is the binomial coefficient, given by:
nCk = n! / (k! * (n-k)!)
Expanding (2d+3)^6 using this formula, we get:
(2d+3)^6 = 6C0 * (2d)^6 * 3^0 + 6C1 * (2d)^5 * 3^1 + 6C2 * (2d)^4 * 3^2 + 6C3 * (2d)^3 * 3^3 + 6C4 * (2d)^2 * 3^4 + 6C5 * (2d)^1 * 3^5 + 6C6 * (2d)^0 * 3^6
Simplifying each term using the binomial coefficient formula, we get:
(2d+3)^6 = 1 * 64d^6 * 1 + 6 * 32d^5 * 3 + 15 * 16d^4 * 9 + 20 * 8d^3 * 27 + 15 * 4d^2 * 81 + 6 * 2d * 243 + 1 * 1 * 729
Simplifying each term further, we get:
(2d+3)^6 = 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729
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Related Questions
Jason bought 91.5 pounds of fruit for a class party. The class ate 0.2 pounds of the fruit. How much fruit is left?
Answers
91.3 pounds of fruit are left
Jason bought = 91.5 pounds
class ate = 0.2 pounds
You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.
91.5 - 0.2 = 91.3 pounds
.
An exponential function is written as F(x) = a b, where the coefficient a is
the base bis positive but not equal to 1, and the exponent x is any
number.
A. an exponent
B. a constant
C. a variable
D. an integer
Answers
In the exponential function F(x) = ab^x, the variable x is an exponent.
Identifying the meaning of xIn the exponential function F(x) = ab^x, the variable x is an exponent.
The function F(x) represents a value that grows or decays exponentially with respect to x.
The base b is a positive constant that determines the rate of growth or decay, and the coefficient a determines the initial value of the function.
The variable x can be any number
However, it is always the exponent that determines the value of the function F(x) for a given input x.
Therefore, the correct answer is A. an exponent.
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The circle graph represents the hair color of middle-school students. There were 800 middle-school students surveyed. Use the circle graph.
Hair Color
Red
5%
Blonde
30%
Black
25%
Brown
40%
How many students have red hair?
Answers
40 students have red hair.
We have,
Red color= 5%
Black = 25%
Brown = 40%
Blonde= 30%
Total middle school students = 800
So, the number of red haired student
= 5% of 800
= 5/100 x 800
= 5 x 8
= 40 students
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Find the absolute value of –0.909.
Answers
Answer:
0.909
Step-by-step explanation:
Absolute value is basically the positive value of a number in this case. The symbol of absolute value is ||, and so, the answer is:
|-0.909| = 0.909
Hence, the answer is 0.909, just make the answer positive if they ask for the absolute value of a number.
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Anthony measures the height of a plant at the beginning and the end of summer. Beginning of summer in June the pant was 12 3/8 inches but at the ending of summer in September the plant was 14 inches.
PT1.A. How many inches did the plant grow?
PT2.B. Anothony planted the seed in March. How much did the plant grow per month prior to him measuring in June?
Answer both questions
Answers
The height of the plant, the time Anthony plants the seed and the number of months, analyzed using an assumption of a constant growth rate indicates;
PT1.A; 1 5/8 inches
PT2.B; 4 1/8 inches per month
What is a growth rate?A growth rate is the rate at which the a quantity being measured increases per unit time.
The height of the plant at the beginning of the summer in June = 12 3/8 inches
Height of the plant at the end of the summer in September = 14 inches
PT1.A. The amount by which the plant grows is therefore;
14 - 12 3/8 = 14 - 99/8 = (112 - 99)/8 = 13/8
13/8 = 1 5/8
The length in inches by which the plant had grown from June to September = 1 5/8 inches
PT2.B. The amount by which the plant had grown per month, can be found by assuming a linear relationship in the growth rate of the plant
The number of months between March and June = 6 - 3 = 3 months
The growth rate of the plant per month is therefore;
Growth rate = (12 3/8)/3 = (99/8)/3 = 33/8
33/8 = 4 1/8
The growth rate of the plant = 4 1/8 inches per month
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You are offered the following terms on a loan of $2250: 9.25 % interest per year paid back over 36 months. If monthly payments are $79.84, how much interest will you have paid once this loan is paid in full?
a) $624.24
b) $655.24
c) $2874.24
d) $1242.50
e) None of the above
Answers
Answer: $624.24.
Step-by-step explanation:
To find the total amount of interest paid on the loan, we first need to find the total amount of money repaid over the course of 36 months.
The total amount repaid is the monthly payment multiplied by the number of months:
Total amount repaid = Monthly payment x Number of months
Total amount repaid = $79.84 x 36 = $2,874.24
To find the total amount of interest paid, we need to subtract the original amount borrowed from the total amount repaid:
Total interest paid = Total amount repaid - Original amount borrowed
Total interest paid = $2,874.24 - $2,250 = $624.24
Therefore, the total amount of interest paid on the loan is $624.24.
What is the sum of the exterior angles of a 100000-gon
Answers
Answer: 17999640
Step-by-step explanation:
The number of sides (100000) - 2. This gives you 99998 sides. Then you multiply it by 180. This equals 17999640
Answer: The sum of the exterior angles of a polygon is always 360 degrees. This is because when you travel around the exterior of a polygon, you make one complete revolution of 360 degrees.
To find the measure of each exterior angle of a regular n-gon (a polygon with n sides and angles of equal measure), you divide the total sum of the exterior angles (360 degrees) by the number of sides or angles in the polygon.
So for a regular 100000-gon, each exterior angle measures 360/100000 = 0.0036 degrees.
To find the sum of all the exterior angles in a 100000-gon, we multiply the measure of one exterior angle by the number of exterior angles (which is also equal to the number of sides/vertices in the polygon).
The number of exterior angles in a 100000-gon is also 100000, so:
Sum of exterior angles = 0.0036 degrees/angle × 100000 angles = 360 degrees
Therefore, the sum of the exterior angles of a 100000-gon is 360 degrees.
Step-by-step explanation:
Joel received a 5,000 gift from his grandmother when he turned 18 and graduated from high school Joel deposited that money into a savings account that offered 7 percent simple interest how much will Joel have 20 years later
Answers
Joel will have 12000 after 20 years. The solution has been obtained by using simple interest.
What is simple interest?
Simple interest is the cost of borrowing that is computed using the original principal amount alone and a constant interest rate.
We are given that Joel received a 5,000 gift from his grandmother when he turned 18 and he deposited that money into a savings account that offered 7 percent simple interest.
So, the total interest earned
⇒ Interest = (7% of 5000) * 20
⇒ Interest = 350 * 20
⇒ Interest = 7000
So, the total amount after 20 years will be,
⇒ Amount = Interest + Principal
⇒ Amount = 7000 + 5000
⇒ Amount = 12000
Hence, Joel will have 12000 after 20 years.
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6. Which transformation(s) must be applied to object A to place it in the position of object B?
rotation, reflection, and translation
reflection and translation
rotation and reflection
rotation and translation
Answers
The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).
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Answer:
b. reflection and translation
Step-by-step explanation:
Colleen is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Hartford was $250. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answers
Answer: Increase in percentage by 42% and with baggage 43.2%.
Step-by-step explanation:
we know that the price is increased from $250 to $ 335
the percentage change by increasing the price is
$355 - $ 250 = $105
percentage change will be change/original = 105/250*100 = 42%
additional charges $ 50, $105+ $50 = 155
percentage change = 155/355*100 = 43.2%
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What is the least whole number that rounds to 570 when rounded to the nearest ten?
What is the greatest whole number that rounds to 570 when rounded to the nearest ten?
Use the number pad to enter your answers in the boxes.
Least number:
Greatest number:
Answers
Answer:
Least: 565
Greatest: 574
Step-by-step explanation:
564 would round down to 560 and 575 would round to 580
Helping in the name of Jeus.
The least whole number that rounds to 570 when rounded to the nearest ten is 570. The greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
Explanation:To find the least whole number that rounds to 570 when rounded to the nearest ten, we need to look at the digit in the tens place. In this case, the tens digit is 7. Since the number can only round up or down, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 570 than to 580, we can round down to 570. Therefore, the least whole number that rounds to 570 when rounded to the nearest ten is 570 itself.
On the other hand, to find the greatest whole number that rounds to 570 when rounded to the nearest ten, we again need to look at the digit in the tens place. Since the tens digit is 7, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 580 than to 570, we can round up to 580. Therefore, the greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
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Approximately of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
Answers
The fraction of Earth that is not made up of ocean = 1/4.
Explain about the fraction:The numbers we are familiar with are whole numbers, such as 1, 2, and so on.
Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.
In essence, a fraction explains how a portion of a group interacts with the entire group.
Given that-
fraction of Earth made up of water = 3/4The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water
The fraction of Earth that is not made up of ocean = 1 - 3/4
The fraction of Earth that is not made up of ocean = (4 - 3)/4
The fraction of Earth that is not made up of ocean = 1/4
Thus, the fraction of Earth that is not made up of ocean = 1/4.
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Complete question:
Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answers
Answer: 104%
Step-by-step explanation: 26% times 4 years
[tex](a\sqrt{b} + c\sqrt{d}) - b\sqrt{a} ) .(d\sqrt{c} - \sqrt{ab} +abc)[/tex]
PLEASE STEP BY STEP EXPLANATION, I PREFER PHOTOS
Answers
The simplified expression is adbc - bc - abd√c - b√ad√c + acd√b + cd√ab.
Define distributive propertyIn mathematics, the distributive property is a property of operations that involves multiplying a factor by a sum or difference of terms. The distributive property states that the product of a factor and a sum or difference of terms is equal to the sum or difference of the products of the factor with each term individually. In other words, for any numbers a, b, and c, the distributive property can be expressed as:
a(b + c) = ab + ac
Given expression
(a√b+c√d)-b√a)×(d√c-√ab+abc)
Simplifying the expression
(a√b+c√d-b√a)×(d√c-√ab+abc)
by simplifying the given expression using the distributive property of multiplication:
(a√b+c√d-b√a)×(d√c-√ab+abc)
= adbc + acd√b - abd√c - b√ad√c + cd√ab - bc
= adbc - bc - abd√c - b√ad√c + acd√b + cd√ab
Therefore, the simplified expression is adbc - bc - abd√c - b√ad√c + acd√b + cd√ab.
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4)
Northbrook Middle School surveyed 325 students to learn more about their after-schoo
activities. They found that 90 students are in a club and play a sport. 140 total students
play a sport and 200 total students are in a club. Construct a two-way relative freques
table summarizing the data.
Plays a Sport
In a Club
Not In a Club
Total
Doesn't Play a
Sport
Total
Answers
Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).
What is frequency?Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.
90 students are in a club and play a sport.
140 total students play a sport.
Therefore, 140 - 90 = 50 students play a sport but are not in a club.
The total number of students who play a sport is 140 + 50 = 190.
200 total students are in a club.
Therefore, 200 - 90 = 110 students are in a club but do not play a sport.
The total number of students who do not play a sport is 325 - 190 = 135.
The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.
This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.
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2. Ramiro has accepted three credit card invitations and now has three cards with limits of $7,000, $5,000, and $9,500. He currently has these cards charged up to 75 percent of his limit. How much does he owe?
Answers
Ramiro has three credit cards with limits of $7,000, $5,000, and $9,500, respectively. Assuming he charged each of them up to 75 percent of its limit, the amount he owes on each card is:
Card 1: 75% of $7,000 = $5,250
Card 2: 75% of $5,000 = $3,750
Card 3: 75% of $9,500 = $7,125
To calculate the total amount Ramiro owes, we add up the amounts he owes on each card: $5,250 + $3,750 + $7,125 = $16,125
Therefore, Ramiro currently owes a total of $16,125 on his three credit cards.
A pipe is made of 1cm thick, has a radius of 11cm. Find the volume of the metal used in making 2.4cm of pipe
Answers
Shinto worshippers believed in ____ which were divine spirits that lived in nature.
A.Abrile
B.Ronin
C.Shogun
D.Kami
Answers
Answer:
Shinto worshippers believed in Kami, which were divine spirits that lived in nature. The Kami were believed to be present in all things, including rocks, trees, animals, and humans, and were worshipped and honored through various rituals and ceremonies. Shinto is the traditional religion of Japan, and while it does not have a single founder or doctrine, the belief in Kami is a central tenet of the faith. Today, many Japanese people practice Shinto alongside other religions such as Buddhism or Christianity.
formula for finding revolution
Answers
The formula for finding revolution is
Revolutions = Distance traveled / Circumference of the object.
What are Revolutions:In physics and mechanics, revolutions refer to the number of times an object completes a full circular motion around an axis or a point.
A revolution is a complete turn around a fixed point or axis, and it is often measured in terms of rotations per minute (RPM) or cycles per second.
For example, a car tire completes one revolution when it turns once completely around its axis. Similarly, a planet completes one revolution when it completes one full orbit around its star.
The formula for finding revolution:
The formula for finding the number of revolutions of a rotating object is:
Revolutions = Distance traveled / Circumference of the object
Where distance traveled is the linear distance that the object has covered, and circumference is the distance around the circular cross-section of the object.
Therefore,
The formula for finding revolution is
Revolutions = Distance traveled / Circumference of the object.
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what is the greatest common factor that can be used to reduce [tex]\frac{36}{90}[/tex]
Answers
greatest common factor, which is 18.
What is greatest common factor?
The largest factor that all of the numbers share is known as the greatest common factor (GCF) of a set of numbers.
One way to do this is to list the factors of both 36 and 90 and find their common factors. The factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 90 are:
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The common factors of 36 and 90 are:
1, 2, 3, 6, 9, 18
Therefore, the greatest common factor of 36 and 90 is 18.
To reduce the fraction 36/90, we can divide both the numerator and denominator by 18:
36 ÷ 18 = 2
90 ÷ 18 = 5
So, 36/90 can be reduced to 2/5 by dividing both the numerator and denominator by their greatest common factor, which is 18.
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given that log x = 3, log y=7
PLEASE HELP SOLVE 20 PTsS
Answers
log(4x²y) = log(4) + log(x²) + log(y)
= 0.6 + 2*log(x) + log(y) (since log(x²) = 2*log(x))
= 0.6 + 2*3 + 7 (since log(x) = 3 and log(y) = 7)
= 13.6
Therefore, log(4x²y) ≈ 13.6.
= 0.6 + 2*log (x) + log (y) (since log (x2) =
2*log (x))
= 0.6 + 2*3 + 7 (since log (x) = 3 and log (y) =
=13.6
Therefore, log (4x3y) = 13.6.
A bakery owner wants to keep his bakery open a few more hours every evening. He wants to
conduct a survey to determine whether extending the bakery's hours would be what customers
want. Which survey method would likely produce the most representative sample?
A. Ask 20 of the bakery's employees as they arrive for work.
B. Ask the first 20 customers who enter the bakery tomorrow.
C. Ask 20 of the bakery's regular suppliers as they make deliveries.
D. Ask 20 customers as they visit the bakery over the course of a day.
Answers
"Ask 20 customers as they visit the bakery over the course of a day." would likely produce the most representative sample.
What is sample?In statistics, a sample refers to a group of individuals or objects that are selected from a larger population and used to represent that population for the purpose of statistical analysis and inference. A sample is often used because it is impractical or impossible to examine every member of the population, so a smaller group is chosen that is expected to be representative of the larger population. The goal of sampling is to obtain accurate and reliable information about the population by studying the characteristics of the sample.
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The mean starting salary for nurses is 67,694 dollars nationally. The standard deviation is approximately
10,333 dollars. Assume that the starting salary is normally distributed.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
a) State the random variable.
rv X a randomly selected nurse
b) Find the probability that a randomly selected nurse has a starting salary of 78371.8 dollars or more.
c) Find the probability that a randomly selected nurse has a starting salary of 91407.1 dollars or less.
d) Find the probability that a randomly selected nurse has a starting salary between 78371.8 and 91407.1
dollars.
e) Find the probability that randomly selected nurse has a starting salary that is at most 41861.5 dollars.
f) is a starting salary of 41861.5 dollars unusually low for a randomly selected nurse?
Why or why not?
Select an answer
g) What starting salary do 65% of all nurses have more than?
Round your answer to two decimal places in the first box.
Put the correct units in the second box.
Answers
Therefore, 65% of all nurses have a starting salary of more than $71,725.31.
Random variable: X, the starting salary of a randomly selected nurse.
b) P(X ≥ 78371.8) = 1 - P(X < 78371.8)
Using the Z-score formula:
z = (X - μ) / σ = (78371.8 - 67694) / 10333 ≈ 1.03
Looking up the probability in the standard normal table or using a calculator, we get:
P (Z ≥ 1.03) ≈ 0.1492
Therefore, P (X ≥ 78371.8) ≈ 0.1492.
c) P (X ≤ 91407.1)
Using the Z-score formula:
z = (X - μ) / σ = (91407.1 - 67694) / 10333 ≈ 2.30
Looking up the probability in the standard normal table or using a calculator, we get:
P(Z ≤ 2.30) ≈ 0.9893
Therefore, P (X ≤ 91407.1) ≈ 0.9893.
d) P (78371.8 < X < 91407.1) = P(X < 91407.1) - P(X < 78371.8)
Using the Z-score formula:
z1 = (78371.8 - 67694) / 10333 ≈ 1.03
z2 = (91407.1 - 67694) / 10333 ≈ 2.30
Looking up the probabilities in the standard normal table or using a calculator, we get:
P(Z < 1.03) ≈ 0.8498
P(Z < 2.30) ≈ 0.9893
Therefore, P (78371.8 < X < 91407.1) ≈ 0.9893 - 0.8498 ≈ 0.1395.
e) P (X ≤ 41861.5)
Using the Z-score formula:
z = (41861.5 - 67694) / 10333 ≈ -2.50
Looking up the probability in the standard normal table or using a calculator, we get:
P (Z ≤ -2.50) ≈ 0.0062
Therefore, P (X ≤ 41861.5) ≈ 0.0062.
f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse, because it is more than 3 standard deviations below the mean. A salary this low would be in the bottom 0.62% of all nurse salaries.
g) To find the starting salary that 65% of all nurses have more than, we need to find the z-score that corresponds to the 65th percentile, and then use the Z-score formula to solve for X.
Using a standard normal table or calculator, we find that the z-score corresponding to the 65th percentile is approximately 0.3853.
Using the Z-score formula:
z = (X - μ) / σ
Substituting μ = 67694, σ = 10333, and z = 0.3853, we get:
0.3853 = (X - 67694) / 10333
Solving for X, we get:
X = 10333(0.3853) + 67694 ≈ 71725.31
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if h(x) =x+2/x-2, then dy/dx= ?
Answers
dy/dx = [(x - 2)(1) - (x + 2)(1)]/(x - 2)^2
Simplifying the numerator:
dy/dx = (-4)/(x - 2)^2
So the derivative of h(x) with respect to x is -4/(x - 2)^2.
Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.
Using this rule, we can find the derivative of h(x) as follows:
h(x) = (x + 2) / (x - 2)
h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator
h'(x) = (-2 - 2x) / (x - 2)^2
Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.
Step-by-step explanation:
What is the average of these numbers?
45 46 50 52 51 59 55 51 42 44
51 55 60 62 52 54 47 74 52 52
59 52 65 45 58 59 59 52 54 65
Answers
Explanation: Add all the numbers together and divide by the number of numbers.
if g(x) = 3x+7x-1, then f'(x)=?
Answers
Answer: f'(x) = 10
Step-by-step explanation: To find f'(x), we need to take the derivative of g(x) with respect to x.
The derivative of 3x is 3, and the derivative of 7x is 7. Since the derivative of a constant is 0, the derivative of -1 is 0. Therefore, we can simplify g(x) to:
g(x) = 3x + 7x - 1 = 10x - 1
The derivative of 10x is 10, and the derivative of a constant is 0. Therefore, f'(x) = 10.
Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Denver was $225. Now the cost
is $365. What is the percent increase? What would be the percent increase if the airline charges an additional $50
baggage fee with the new ticket price?
Answers
The percent increase in the cost of an airline ticket is 62.22% (approx)
The percent increase in the cost of the airline ticket with the additional $50 baggage fee is 84.44% (approx)
Calculating the percentage:To find the percentage of increase find the difference between the old and new cost of tickets. Now multiply the ratio of the resultant difference and the intial cost of the ticket by 100.
Here we have
Two weeks ago, the cost to fly from Hartford to Denver was $225.
Now the cost is $365.
The percent increase in the cost of the airline ticket from $225 to $365 can be calculated as follows:
Here the difference between the old and new ticket prices is given by
=> $365 - $225 = $140
The percentage of change = 140/225 (100) = 62.22%
The airline charges an additional $50 baggage fee
The new ticket price = $365 + $50 = $415.
Hence, the difference between the old and new ticket prices is
=> $415 - $225 = $190
The percentage of change = [190/225] × 100 = 84.44%
Therefore,
The percent increase in the cost of an airline ticket is 62.22% (approx)
The percent increase in the cost of the airline ticket with the additional $50 baggage fee is 84.44% (approx)
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Question 1 (10 marks)
Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100
meters races is reviewed, and the finishing times (in seconds) were as below:
13.4
15.6
13.1
14.5
14.2
13.3
15.3
It is reasonable to assume his finishing times are normally distributed.
(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.
(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at
95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as
the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))
Question 2 (20 marks)
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
Answers
Question A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)
Question B) Option II) narrower is the correct Option.
How to solveLet X be the time required to finish 100 meters race competition with Tom ( in seconds.)
A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)
x = 14.2
s^2= 0.9867
s= 0.9933
t \aplha/2, n-1 = 3.7074
Margin of error= 1.3919
lower bound= 12.8081
upper bound= 15.5919
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What’s the length of side AB?
Answers
tan = 1/√3= perpendicular/ base
1/√3 = AB / AC
AB / 6 = 1/√3
AB = 6/√3
What is the domain of the function graphed at right?
Answers
Answer:
d. x > 2 or x < -2
Step-by-step explanation:
Domain describes the range of x-values in a function.
Domain
The domain of a graph is all of the x-values covered by the function. The domain does not reflect the y-values of a function. This means that answers A and B are automatically wrong.
By looking at the graph, we can tell that there is a gap where some x-values are not covered. This gap is known as a discontinuity. The discontinuity begins at -2 and ends at 2. All of the x-values in the discontinuity are not a part of the domain, and any parts of the graph that are continuous, are included in the domain. The graph is continuous at all points greater than 2 and less than -2, so all of those values are included in the domain. Now, we just need to find out if the endpoints are included in the domain.
Included Values
We know that the domain includes all x-values greater than 2 and less than -2, but we need to know if the domain includes 2 and -2. On a graph, included values will be shown as a closed circle and non-included values will be shown as an open circle. By looking at the graph, we can tell that 2 is not included but -2 is. This means that the domain is x > 2 or x < -2 because the domain does not include x = 2.
