Answer: Voluntary Response
Step-by-step explanation:
The question was, "Mrs. Finn had a terrible experience at a hotel last weekend. The water was cold, the bathroom wasn't cleaned, and it smelled really bad. She decided to write a horrible review on travel.com about the experience."
And we're asked to evaluate whether this is
A) Statistic
B) Random Sampling
C) Voluntary Response
A statistic is "any quantity computed from values in a sample which is considered for a statistical purpose."
Random sampling is "a method of data collection and analysis designed to select a representative sample of respondents out of a larger population."
Finally, we have voluntary response which is "a deliberately chosen reaction to a stimulus that may require a complex coordination of excitatory and inhibitory impulses with feedback from visual, motor, and other systems."
Out of all of the following definitions, voluntary response is what fits this scenario best. Voluntary response usually includes the response of people with very strong opinions, and recalling how Mrs. Finn reacted to her hotel, I'd say it fits.
Given: PP(xx) = x^3−2x^2 + 9x−18
a) How many roots does P(x) have?
b) What are the possible rational roots?
c) Find all the roots.
a) Number of roots in the given polynomial is three.
b) Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}
c) The roots of the given polynomial are {2, 3i, -3i}.
Given polynomial is `P(x) = x³ - 2x² + 9x - 18`.a) Number of roots in the given polynomial is three. b) Possible rational roots of the given polynomial are expressed in the form of `p/q`, where p is a factor of the constant term `-18` and q is a factor of the leading coefficient `1`.Constant term of the given polynomial is `-18`. The factors of `-18` are 1, 2, 3, 6, 9, and 18. Leading coefficient of the given polynomial is `1`. The factors of `1` are ±1.∴ Possible rational roots of the given polynomial are {±1, ±2, ±3, ±6, ±9, ±18}.c) Let us check whether the possible rational roots satisfy the given polynomial. To check the roots, we can use synthetic division, which is an efficient method to check the roots of a polynomial. When `x = -1` is substituted in the given polynomial, we get P(-1) = (-1)³ - 2(-1)² + 9(-1) - 18= -1 + 2 - 9 - 18= -26, which is not equal to `0`.When `x = 1` is substituted in the given polynomial, we get P (1) = 1³ - 2(1)² + 9(1) - 18= 1 - 2 + 9 - 18=-10, which is not equal to `0`.
When `x = -2` is substituted in the given polynomial, we get P(-2) = (-2)³ - 2(-2)² + 9(-2) - 18= -8 + 8 - 18 - 18= -36, which is not equal to `0`.When `x = 2` is substituted in the given polynomial, we get P(2) = 2³ - 2(2)² + 9(2) - 18= 8 - 8 + 18 - 18= 0, which is equal to `0`.∴ `x = 2` is a root of the given polynomial. By using synthetic division method, we can find the remaining two roots. x - 2 | 1 - 2 9 - 18| | 2 0 18| | 1 0 9 0|Therefore, the factors of the given polynomial are `(x - 2)(x² + 9)`.The quadratic factor, `x² + 9`, does not have any real roots, as the discriminant is negative.∴ The roots of the given polynomial are {2, 3i, -3i}.
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Un mueblero compró lo siguiente dos camas a 7565 pesos cada una un juego de sala a 26500 un ropero a 17869 pesos y llevaba 65500 cuánto dinero le sobra
The amount that is left over is: 65,500 - 59,499 = 6,001 pesos. A furniture dealer or business owner is referred to as a "mueblero" in Spanish.
The cost of the furniture was 2 x 7565 = 15,130 pesos in camas.
1 x 26,500 is equal to 26,500 pesos in a game of pool.
One times 17,869 equals 17,869 pesos in a rope.
Total expenditures were 15,130, 26,500, 17,869, and 59,499 pesos.
The amount that is left over is: 65,500 - 59,499 = 6,001 pesos.
A furniture dealer or business owner is referred to as a "mueblero" in Spanish. The question asks how much money the mueblero has left over after making the purchases since he had a specific amount of money to spend and acquired a number of items of furniture for his store.
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Rob's favorite shampoo is available in two sizes: regular and economy. Each size and its price are shown in the table. Size regular economy Quantity (oz) 20 40 Price ($) $8.00 $10.00 6. A coupon offers $1.00 off the regular size. Which size is the better buy then?. pls someone answer its due in 48 minutes
Answer: To determine which size is the better buy, we need to calculate the cost per ounce for each size, taking into account the coupon for the regular size.
For the regular size, the cost per ounce is:
$8.00 / 20 oz = $0.40 per oz
With the $1.00 coupon, the cost for the regular size becomes:
$8.00 - $1.00 = $7.00
So the cost per ounce for the regular size with the coupon is:
$7.00 / 20 oz = $0.35 per oz
For the economy size, the cost per ounce is:
$10.00 / 40 oz = $0.25 per oz
Therefore, the economy size is the better buy as it costs only $0.25 per oz compared to $0.35 per oz for the regular size with the coupon.
Step-by-step explanation:
This is 5/6 problems finish them all each is 10 points 60 total.
The value of angle X in the given right triangle HXV is 59.5 ⁰.
What is the value of x in the right triangle?The value of angle X in the given right triangle HXV is calculated by applying SOH CAH TOA identity as shown below.
SOH ⇒ sin θ = opposite side / hypothenuse side
CAH ⇒ cos θ = adjacent side / hypothenuse side
TOA ⇒ tan θ = opposite side / adjacent side
For the given triangle HXV, the value of angle X is calculated as follows;
cos X = 33 / 65
cos X = 0.5077
X = arc cos ( 0.5077 )
X = 59.5 ⁰
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Two times the sum of 5 and some number is 30. What is the number?
Answer:
10
Step-by-step explanation:
5+10=15
15×2=30
so the answer to your question is 10
Answer:
x = 10.
Step-by-step explanation:
Given: Two times the sum of 5 and some number is 30. What is the number?
First, write the equation:
2(5 + x) = 30
Simplify the brackets with distribution property:
10 + 2x = 30
Then collect like terms:
2x = 30 - 10
Finally, calculate:
2x = 20 (Divide both sides by 2)
x = 10
Compute the expected age of a super shopper. (Round your answer to two decimal places. )
(A) The expected age μ of a super shopper 41.81
and, (B) the standard deviation σ for ages of super shoppers is 12.67
Given the data:
Age range, years 18-28 29-39 40-50 51-61 62 and over
Midpoint (x) 23 34 45 56 67
Percent of super shoppers 9% 46% 22% 11% 12%
Midpoint, x : 23 34 45 56 67
Frequency, f : 0.09_ 0.46 _ 0.22 __0.11 __ 0.12
The mean (m)= Σfx / Σf
= [(23 × 0.09) + (34 × 0.46) + (45 × 0.22) + (56 × 0.11) + (67 × 0.12)] ÷
(0.09 + 0.46 + 0.22 + 0.11 + 0.12)
= 41.81 / 1
Therefore, Mean = 41.81
Standard Deviation:
The standard deviation (or σ) is a measure of the distribution of data from the mean. A low standard deviation means the data is clustered around the mean, and a high standard deviation means the data is more scattered.
Standard deviation = Sqrt[(Σ(X² * f) / Σf) - m²)]
= ((23²× 0.09) + (34²× 0.46) + (45²× 0.22) + (56²× 0.11) + (67²× 0.12)) / 1
1908.51 - 41.81^2
= √(160.4339)
= 12.666250
= 12.67
Complete Question:
Age range, years 18-28 29-39 40-50 51-61 62 and
over Midpoint x 23 34 45 56 67
Percent of super shoppers 9% 46% 22% 11% 12%
For the 62-and-over group, use the midpoint 67 years.
(a) Compute the expected age μ of a super shopper. (Round your answer to two decimal places.)
μ = yr
(b) Compute the standard deviation σ for ages of super shoppers. (Round your answer to two decimal places.)
σ = yr
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What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
m = - 1
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-2,0) (0, -2)
We see the y decrease by 2, and the x increase by 2, so the slope is
m = -2/2 = -1
So, the slope is -1
Answer:
m = - 1
Step-by-step explanation:
Find three consecutive even integers if 3 times the first iteger is 2 times the the third
The solution is that the three consecutive even integers are 8, 10, and 12.
Let's assume the first even integer to be x. Since we are looking for three consecutive even integers, the second even integer will be x + 2, and the third even integer will be x + 4.
According to the problem statement, 3 times the first even integer is equal to 2 times the third even integer, which can be written mathematically as:
3x = 2(x + 4)
Solving for x, we get:
3x = 2x + 8
x = 8
Therefore, the first even integer is 8, and the second and third even integers are 10 and 12, respectively.
We can verify that 3 times the first even integer is indeed equal to 2 times the third even integer:
3(8) = 24
2(12) = 24
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Johanna measured the height and petal length of all the flowers in her garden. She plotted her results and found that the relationship between the variables suggests a weak positive linear association with 1 outlier.
The graph that might be made by Johanna is graph (3).
Johanna has two variables: height and petal length. She plotted these variables on a graph to determine the relationship between them.
However, Johanna also found that there is one outlier in her data.
Each point on the graph represents the height and petal length of a single flower in Johanna's garden. The x-axis represents the height of the flower, and the y-axis represents the petal length.
Since there is a weak positive linear association between the two variables, the points on the scatter plot will be generally moving upwards from left to right.
In conclusion, Johanna's graph is most likely a scatter plot that shows the weak positive linear association between the height and petal length of the flowers in her garden, with one outlier that stands out from the rest of the data.
Hence the correct graph is (3).
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Complete Question:
Johanna measured the height and petal length of all the flowers in her garden. She plotted her results and found that the relationship between the variables suggests a weak positive linear association with 1 outlier.
Which of the following might be the graph Johanna made?
Here is a quadrilateral ABCD. All the measurements are in centimetres. The perimeter of ABCD is 52 centimetres. Work out the length of DC.
The sοlutiοn οf the given prοblem οf quadrilateral cοmes οut tο be DC = 12 .
A quadrilateral is what?In mathematics, a rectangle is a fοur-sided οbject with fοur cοrners. Either "quad" οr "array οf inventive ideas" are Latin terms that were used tο cοin the phrase (meaning "side"). Fοur cοrners, fοur areas, and fοur cοrners are the three cοmpοnents οf a rectangle. Cοnvex and cοncave are the twο primary varieties οf cοnvex and cοncave fοrms. Cοnvex quadrilaterals alsο include the subdivisiοns οf trapezοids, geοmetric shapes, angles, rhοmbuses, and squares.
Here,
Assuming that ABCD is a trapezοid with parallel sides AB and CD, we can use the knοwledge that the perimeter οf a trapezοid is equal tο the sum οf its οppοsite sides tο cοnstruct the fοllοwing equatiοn:
=> AB = 52 + CD = BC + AD
Assuming AB = 13 and BC = 15, the equatiοn can be simplified as fοllοws:
=> 13 + CD + 15 + AD = 52
=> CD + AD = 24
=> DC = 12
Hοwever, we are unable tο determine the length οf DC οr AD withοut additiοnal details regarding the angles οr side lengths οf the trapezοid. As a result, there is nο clear sοlutiοn.
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Complete question:
For the following discrete probability distribution, xi: 3,5,6,7,10 p1: 0,1 0,3 0,3 0,2 0,1What is the mean? What is the standard deviation (to 3 significant digits)?
a) The mean of the given probability distribution is 5.9.
b) The standard deviation of the given probability distribution is 4.64 (to 3 significant digits).
The mean and standard deviation of the discrete probability distribution with xi = 3, 5, 6, 7, 10 and p1 = 0.1, 0.3, 0.3, 0.2, 0.1 are as follows: Calculation of Mean The mean of the discrete probability distribution is calculated by multiplying each xi value by the probability pi, and then adding all the products together.μ = ∑ (xi . pi) = (3 × 0.1) + (5 × 0.3) + (6 × 0.3) + (7 × 0.2) + (10 × 0.1) = 5.9 Therefore, the mean of the given probability distribution is 5.9.Calculation of Standard Deviation The standard deviation of the discrete probability distribution is calculated using the formula below:σ = √[∑(xi - μ)² . pi]The calculations involved in finding the standard deviation are as follows:(3 - 5.9)² × 0.1 = 3.61(5 - 5.9)² × 0.3 = 0.49(6 - 5.9)² × 0.3 = 0.09(7 - 5.9)² × 0.2 = 0.49(10 - 5.9)² × 0.1 = 16.81σ² = 21.49Therefore, the variance is 21.49σ = √21.49 ≈ 4.639 ≈ 4.64 (to 3 significant digits)Hence, the standard deviation of the given probability distribution is 4.64 (to 3 significant digits).
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the patient has formula feedings through a feeding tube. she is given 250 ml every 4 hours (0400, 0800, 1200, 1600, 2000, 2400) around the clock. the nurse gives 100 ml of water after each feeding. what is the patient's intake in the 2300 to 0700
The patient has formula feedings through a feeding tube. She is given 250 ml every 4 hours (0400, 0800, 1200, 1600, 2000, 2400) around the clock. The nurse gives 100 ml of water after each feeding.
The intake of the patient from 2300 to 0700 would be 750 ml.
The formula for calculating the patient's intake from 2300 to 0700
The formula to calculate the patient's intake from 2300 to 0700 is the following:
7 hours after 2300 ⇒ 7+24 - 23 = 8 hours before 0800
Thus, the patient's intake from 2300 to 0800 would be:
From 2300 to 2400 = 250 ml
From 2400 to 0400 = 250 ml
From 0400 to 0800 = 250 ml
From 0800 to 0700 = 100 ml (as it is less than 4 hours)
Total Intake = 250 ml + 250 ml + 250 ml + 100 ml = 850 ml
Intake from 2300 to 0700 = Total intake - Intake from 0800 to 0700
Intake from 0800 to 0700 = 100 ml
Total Intake = 850 ml - 100 ml = 750 ml
Therefore, The patient is receiving formula feedings through a feeding tube, administered every 4 hours (at 0400, 0800, 1200, 1600, 2000, and 2400). Following each feeding, the nurse administers 100 ml of water. It can be calculated that the patient's total intake during the period from 2300 to 0700 would be 750 ml.
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Sol has to paint 365. 7 square feet of wall space. He wants to paint 0. 4 of the area light green. How many square feet does he want to paint light green?
Sol wants to paint 146.28 square feet of the wall light green.
The problem states that Sol has to paint 365.7 square feet of wall space, but he wants to paint only a fraction of the total area light green. The fraction he wants to paint light green is given as 0.4.
To find out how many square feet of the wall he wants to paint light green, we need to multiply the total area of the wall by the fraction of the area he wants to paint light green.
So, we can calculate the area of the wall that Sol wants to paint light green as:
Area of wall to be painted light green = 0.4 x 365.7
= 146.28 square feet
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Merisa spent 3/4 of her money on a dictionary. She spent 1/2 of the remainder on a calculator. The dictionary cost $30 more than the calculator. How much did the dictionary cost?
The dictionary cost $36 if Merisa spent 3÷4 of her money on a dictionary. She spent 1÷2 of the remainder on a calculator.
What is Algebraic expression ?
In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.
Let M be the total amount of money Merisa had before she made any purchases.
Merisa spent 3÷4 of her money on a dictionary, which means she spent 1÷4 of her money on the calculator and other expenses.
So, the amount of money she had left after buying the dictionary is:
M - 3÷4 M = 1÷4 M
She then spent 1÷2 of the remainder on a calculator, so:
(1÷2) (1÷4 M) = 1÷8 M
Let's call the cost of the calculator C.
We know that the dictionary cost $30 more than the calculator, so:
D = C + $30
We can now set up an equation to solve for C:
C + $30 = 3÷4 M
C = 3÷4 M - $30
And we also know that:
C = 1÷8 M
We can substitute the second equation into the first equation and solve for M:
1÷8 M + $30 = 3÷4 M
3÷4 M - 1÷8 M = $30
5÷8 M = $30
M = $48
So, Merisa had $48 before she made any purchases.
We can now use this to find the cost of the dictionary:
D = C + $30
D = (1÷8 M) + $30
D = ($6) + $30
D = $36
Therefore, the dictionary cost $36.
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A group of people were asked if they had run a red light in the last year. 313 responded "yes", and 286 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
[tex]0.523[/tex]
Step-by-step explanation:
Total number of respondents = 313 + 286 = 599
Number who responded yes = number running a red light
[tex]\text P(\text {ran a red light)}}\\\\=\dfrac{\text{Number who ran a red light}}{\text{Total number of respondents}}\\\\= \dfrac{313}{599}\\\\= 0.52253[/tex]
Rounded to 3 decimal places the probability is [tex]0.523[/tex]
A drink recipe book has a table that shows the proportional relationship between cups of water and cups of lemon juice for different amounts of lemonade. In the table, enter the number of cups of water needed for 1 cup of lemon juice
The ratio of water to lemon juice is 7:1. Thus, 7 cups of water are needed for 1 cup of lemon juice.
The table shows the proportional relationship between the amount of water and lemon juice needed to make lemonade in different quantities. The ratio of cups of water to cups of lemon juice remains constant for each quantity of lemonade. For example, to make 2 cups of lemonade, 1.5 cups of water are needed for every 1 cup of lemon juice. This means that if you want to make 4 cups of lemonade, you would need to double the amount of water and lemon juice required for 2 cups. This proportional relationship can be helpful in scaling the recipe up or down to make different quantities of lemonade.
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Complete question:
A drink recipe book has a table that shows the proportional relationship between cups of water and cups of lemon juice for different amounts of lemonade. If you need 6 cups of lemonade, the table shows you need 1 cup of lemon juice. Enter the number of cups of water needed for 1 cup of lemon juice.
Cups of Lemon Juice Cups of Water
1 4
2 8
3 12
4 16
There are 32 stamps.on each roll. Mark has 288 stamps. How many rolls does he have?
Answer:
9
Step-by-step explanation:
No. of rolls Mark have =
[tex] \frac{288}{32} = 9[/tex]
pls mrk me brainliest
(09.02 MC)
Which equation could be used to solve for the measure of angle P?(1 point)
Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x degrees. Angle P is labeled y degrees. Angle Q is labeled z degrees. Angle R is labeled w degrees.
In order to solve for the measure of angle P, the equation x + y + z + w = 360° can be used.
What is an angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians and are used to describe the direction of two intersecting lines in a plane. Angles are also used to measure the central angle of a circle and the angle between two curves.
This equation is known as the Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle or a quadrilateral equals 360°. The measure of each angle of the quadrilateral can be used in the equation to solve for the measure of angle P, which is labeled as y. This equation can be written as x + y + z + w = 360° and then solved for the measure of angle P by subtracting x + z + w from both sides of the equation. This would result in y = 360° - (x + z + w). By substituting the measure of each angle into the equation, the measure of angle P can be found.
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a tank 12m long, 8m wide and 5m deep is to be made. it is open at the top, determine the iron sheet required for the fabrication. also find volume in litres
Answer:
Surface area of the sheet: 296 square meters
Area of tank: 480 cubic meters
Step-by-step explanation:
Don't forget your units!
"determine the iron sheet required for the fabrication" is asking for the surface area of the rectangular prism.
This is found by adding the five sides of the prism. The top side is excluded because it is open.
Front and back: 2(12m * 5m) = 120m^2
Left and right: 2(8m * 5m) = 80m^2
Floor: (12m * 8m) = 96m^2
120m^2 + 80m^2 + 96m^2 = 296m^2
The volume is found using standard methods. The open top does not have an impact here.
12m * 8m * 5m = 480m^3
help pls 1/3(3m+6)-2(2m+6)
1/3(3m+6)-2(3m+6)
Answer:
-5m - 10
Step-by-step explanation:
1/3(3m+6)-2(3m+6)
= 1m + 2 - 6m - 12
= -5m - 10
So, the answer is -5m - 10
Answer:
-5(m+2)
Step-by-step explanation:
1/3(3m+6)-2(3m+6)
combine like terms
-5/3(3m+6)
Distribute
-5m - 10
common factor
-5(m+2)
A table costs five times as much as a chair. A trader bought six more chairs than tables and spent $18 594. If a chair costs $1033,how many chairs and tables did he buy
The trader bought 3 512 tables and 6(3 512) = 21 072 chairs.A table costs five times as much as a chair.
The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,5t = 18 594 - 1033 5t = 17 561 t = 17 561/5 t = 3512.2Let c be the number of chairs and t be the number of tables.As the table costs 5 times as much as the chair, the total cost of the tables is 5t. The total cost of the chairs is c. The total cost of the tables and chairs is 5t + c = $18 594.Therefore, 5t + c = 18 594.The cost of a chair is given as $1033. So, c = 1033Substituting c = 1033 in 5t + 1033 = 18 594,
5t = 18 594 - 1033 5
t = 17 561
t = 17 561/5
t = 3512.2Therefore, the trader bought 3 512 tables and 6(3 512) = 21 072 chairs.
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How is 0.136¯¯¯¯ written as a fraction in simplest form?
Enter your answer in the box.
ANSWER QUICK FOR 50 POINTS
Answer:
17/125
Step-by-step explanation:
0.136×1000÷1×1000=136/1000
136/1000=17/125
Find the area under the standard normal curve that lies between z = −2. 30 and z = 1. 8
The area under the standard normal curve between z=-2.30 and z=1.8 by using the cumulative distribution function is 0.957.
Finding the area under the standard normal curve between two points requires the use of the cumulative distribution function. This function is given by the formula:
F(z) = 1/2 (1 + erf(z/√2))
Where erf is the error function.
We will use this formula to find the area under the standard normal curve between z=-2.30 and z=1.8.
The area under the standard normal curve between z=-2.30 and z=1.8 can be found using the following equation:
Area = F(z2) - F(z1)
Where z1 is the lower bound of the area and z2 is the upper bound of the area.
For our example, z1 = -2.30 and z2 = 1.8.
We can plug these values into the equation to find the area under the standard normal curve between z=-2.30 and z=1.8:
Area = F(1.8) - F(-2.30)
We can then use the cumulative distribution function to find the values for F(1.8) and F(-2.30):
F(1.8) = 1/2 (1 + erf(1.8/√2)) = 0.966
F(-2.30) = 1/2 (1 + erf(-2.30/√2)) = 0.009
Substituting these values into the equation:
Area = 0.966 - 0.009
Area = 0.957
Therefore, the area under the standard normal curve between z=-2.30 and z=1.8 is 0.957.
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PLEASE HELP ME ON THIS QUICK(Image)
The statement that is correct about the two angles that are said to be linear pair would be = <ABC and <CBD are adjacent angles. That is option A
What is a linear pair of angles?A linear pair exists between angles that are on a straight line that are formed when two lines intersect eachother leading to the formation of the adjacent angles.
The linear angles are there said to be adjacent angles and the sum of these two angles are always = 180°.
Therefore from the given statements, the correct option about the two angles which are linear paired angles is that they are also adjacent to each other.
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four minus three times a number is less than twenty-five
Answer:
the answer could be: 1,2,3,4,5,6,7. If you are not sure about the answer than substitute the number that you pick and solve as if it was a normal equation.
Step-by-step explanation:
4-(3*x)<25
example:
4-(3*1)<25
4-3<25
1<25
What is 4.5-4x evaluated
Answer:
Step-by-step explanation:
Help pls
(2.75 x 10-2) (2.5 × 108) X
Multiplying two numbers written in scientific notation can be done by multiplying their coefficients and adding their exponents, such as [tex](2.75 x 10^-2)[/tex] x [tex]10^(-2+8)[/tex] = [tex]6.875 x 10^6[/tex].
What does an expression mean?
Instead of using estimates produced at random, it is better to use rolling integer variables that can be increasing, decreasing, or blocking. They could only help one another by sharing tools, information, or solutions to issues.
In the given question,
(2.75 x [tex]10^-2[/tex]) (2.5 × [tex]10^8[/tex]) X
To multiply two numbers written in scientific notation, you can simply multiply their coefficients and add their exponents. So:
(2.75 x [tex]10^-2[/tex]) (2.5 × [tex]10^8[/tex]) = (2.75 x 2.5) x [tex]10^(-2+8)[/tex] = 6.875 x [tex]10^6[/tex]
The result is 6.875 x 10⁶, which is the sum of (2.5 x 10⁸) and (2.75 x 10⁻²).
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Suppose a point has polar coordinates (4, - (3pi)/4) with the angle measured in radians. Find two additional polar representations of the point. Write each coordinate in simplest form with the angle in [- 2pi, 2pi]
If a point has polar coordinates (4, - (3pi)/4) with the angle measured in radians, two additional polar representations of the points are (4, 5pi/4) and (4, -11pi/4)
To find two additional polar representations of the point (4, - (3pi)/4), we need to add and subtract integer multiples of 2pi from the angle measure while keeping the same radius.
First, let's add 2pi to the angle measure:
(4, - (3pi)/4 + 2pi) = (4, 5pi/4)
This gives us a new polar representation of the same point with a positive angle measure within the interval [-2pi, 2pi].
Next, let's subtract 2pi from the angle measure:
(4, - (3pi)/4 - 2pi) = (4, -11pi/4)
This gives us another polar representation of the same point with a negative angle measure within the interval [-2pi, 2pi].
Therefore, the three polar representations of the point (4, - (3pi)/4) are:
(4, - (3pi)/4)
(4, 5pi/4)
(4, -11pi/4)
Each of these polar representations describes the same point in the polar coordinate system, but with a different angle measure.
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a fair die is rolled 14 times. let be the number of faces that appear exactly three times. which of the following expressions appear in the calculation of var(x)
The variance of a fair die that has been rolled 14 times and the number of faces that appear exactly three times is 2.33.
The variance of X can be calculated using the following formula:
Var(X) = Σ(P(X=x)*(x-μ)²)/N
Where Σ represents the summation of all possible outcomes, P(X=x) is the probability of an event occurring, x is the possible outcome, μ is the mean of all possible outcomes, and N is the number of trials.
In this case, the number of possible outcomes of a fair die is 6, and since the die has been rolled 14 times, N = 14. To calculate the mean, we use the formula μ = ΣP(X=x)*x, and in this case, the mean would be 3 since each face appears exactly 3 times.
Therefore, Var(X) = Σ(P(X=x)*(x-3)²)/14. We can then calculate the variance of X by substituting in the probabilities for each face: P(X=1) = 1/14, P(X=2) = 1/14, P(X=3) = 1/14, P(X=4) = 1/14, P(X=5) = 1/14, and P(X=6) = 1/14.
This yields a variance of 2.33, as calculated below:
Var(X) = (1/14 * (1-3)² + 1/14 * (2-3)² + 1/14 * (3-3)² + 1/14 * (4-3)² + 1/14 * (5-3)² + 1/14 * (6-3)²)/14
= 2.33.
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A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.05. On visiting a holiday resort for seniors, he sells 12 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 12 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. a) What is the expected number of policies that will pay out before the insured parties have reached age 61? b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?
The probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.
The answer is as follows: The expected number of policies that will pay out before the insured parties have reached age 61 isE(x) = np = 12 × 0.05 = 0.6Therefore, the expected number of policies that will pay out before the insured parties have reached age 61 is 0.6.b) The variance of the number of policies that will pay out before the insured parties have reached age 61 isVar(x) = np(1-p) = 12 × 0.05(1-0.05) = 0.570Therefore, the variance of the number of policies that will pay out before the insured parties have reached age 61 is 0.570.c) To find out the probability that at least two policies will pay out before the insured parties have reached age 61, we can use the complement rule that is:P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)P(X = 0) = (0.95)^12 = 0.2835 (probability that none of the 12 policies will pay out before the insured parties have reached age 61)P(X = 1) = 12C1(0.05)(0.95)^11 = 0.3765 (probability that only one of the 12 policies will pay out before the insured parties have reached age 61)Therefore,P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) = 1 - 0.2835 - 0.3765 = 0.3400Therefore, the probability that at least two policies will pay out before the insured parties have reached age 61 is 0.3400.
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