The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is (9.7, 14.7).
Here, we have,
1. Identify the given information:
- Confidence level (c) = 0.95
- Sample mean (x) = 12.2
- Sample standard deviation (s) = 3.0
- Sample size (n) = 8
2. Determine the degrees of freedom (df) for the t-distribution:
- df = n - 1 = 8 - 1 = 7
3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:
- You can use a t-table or an online calculator for this.
- The t-value for a 0.95 confidence level and 7 df is approximately 2.365.
4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):
- ME = t-value * (s / sqrt(n))
- ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5
5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):
- Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7
- Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7
So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).
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$5850 is invested at 6.5% compounded continuously. How long will it take for the balance to reach $11700? Round your answer to two decimal places.
Answer:10.66 years. Punch again to double check
Step-by-step explanation:
A=Pe^(rt)
11700=5850e^(.065t)
isolate the variable expression
2=e^(.065t) divide by 5850
ln2=lne^(.065t) take the natural log of both sides
ln2=.065t. Bring down the power, lne equals
t is about 10.66 years. Divide ln2 by .065
what is the value of RP
The calculated value of the length RP is 107 units
Calculating the value of the length RPFrom the question, we have the following parameters that can be used in our computation:
The circles and the tangent lines
Start by calculating the segment PQ using the following Pythagoras theorem
PQ² = (50 + 11)² + 11²
Evaluate
PQ² = 3842
So, we have
PQ = 62
The value of the length RP is then calculated as
RP = PQ + TU
So, we hav
RP = 62 + 45
Evaluate
RP = 107
Hence, the value of the length RP is 107 units
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consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?
Sum
Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10
Mean = 36.7 / 10
Mean = 3.67
To find the median, we need to put the values in order:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4
The middle number is the median, which is 3.35 in this case (3.2+3.5)/2.
To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.
To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:
2.5, 2.6, 2.8, 3.1, 3.2
The median of this lower half is 2.8, so Q1 = 2.8.
To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:
3.7, 3.8, 4.1, 9.4
The median of this upper half is 3.95, so Q3 = 3.95.
To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
IQR = 3.95 - 2.8
IQR = 1.15
1.5 times the IQR is 1.5 * 1.15 = 1.725.
The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.
Answer:
Step-by-step explanation:
Mean is the average of the data vales : 38.7 (sum of all values) divided by 10 (the number of values). Mean = 38.7/10 = 3.87
Median is the "middle" number" = put the date in order and find the middle value:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4, since there is no middle data value, find the average of the 2 in the middle.
3.2 + 3.5/2 = 6.7 ÷ 2 = 3.35 - median
All values appear once so there is no mode.
First quartile is the middle of the lower set of data = 2.8
Third quartile is the middle of the upper set = 3.8
The outlier is 9.4.
How to calculate the outlier:
First you need the IQR which is the diffence of Q3 - Q1,
so the IQR is 3.8- 2.8 = 1
Outliers are the quartile + or - (1.5)(IQR)
Q1 -(1.5)(1) = 2.8 - 1.5 = 1.3
Q3 - (1.5)(1)= 3.8 + 1.5 =4.5
So anything below 1.3 or above 4.5 is an outlier.
There is one 9.4
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for pi.
O 1.254 square meters
O 312 square meters
O2, 822 square meters
O 314 square meters
Answer:
(a) 1.254 square metersStep-by-step explanation:
We are given a figure, consisting of a right triangle with a circle cut out of it.
To Calculate : area of the shaded region below,
First Let's find the Area of the right triangle:
Area(triangle) = 1/2 × Base × Height
= 1/2 × 56 × 56
= 1/2 × 3136
= 3136/2
= 1568 m².
Now, We are diameter of the circle = 20 m
Radius of the circle = 20/2 = 10 m
Area of circle = πr²Acc. to question we have to use 3.14 as an
approximation for pi.
Area (circle) = 3.14 × 10 × 10
Area (circle) = 3.14 × 100
Area (circle) = 314 m²
Area of shaded region = Area of triangle - Area of circle =
= 1568 m² - 314 m²
= 1.254 square meters
Therefore, The approximate area of the shaded region is 1.254 square meters.
Option (a) is the required answer
Use the even and odd properties of the following functions to answer the questions:
a) If secθ=-3.1,then sec(-θ)=?
b)If sinθ=0.62,then sin(-θ)=?
Answer:
[tex]sec(-\theta)=-3.1[/tex]
[tex]sin(-\theta)=-0.62[/tex]
Step-by-step explanation:
Part a.
[tex]sec(\theta)[/tex] is related to [tex]cos(\theta)[/tex] through a reciprocal relationship [tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex].
Since [tex]cos(\theta)[/tex] is an even function (reflecting left-right across the y-axis doesn't change the graph), then [tex]sec(\theta)[/tex] is also an even function.
For any input in the domain, even functions produce the same output if the opposite of the input is used. In other words, if "f" is an even function, for all x in the domain of f, [tex]f(x)=f(-x)[/tex].
Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.
[tex]sec(-\theta)=-3.1[/tex]
Part b.
The [tex]sin(\theta)[/tex] function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.
However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph. Visually, this is an "odd" function.
For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output. In other words, if "g" is an odd function, for all x in the domain of g, [tex]-g(x)=g(-x)[/tex].
Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.
[tex]sin(-\theta)=-0.62[/tex]
Suppose that the function h is defined as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the five definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = -3 between x = -2.5 and x = -1.5.y = -2 between x = -1.5 and x = -0.5.y = -1 between x = -0.5 and x = 0.5.y = 0 between x = 0.5 and x = 1.5.y = 1 between x = 1.5 and x = 2.5.More can be learned about piece-wise functions at brainly.com/question/19358926
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help please PLEASE !!!!!
Answer:
Positive Association
Complementary Angles
Negative Association
Clusters in Data
Supplementary Angle
Non-linear Association
Step-by-step explanation:
Match the boxes on the left to the answers:
Positive Association
Complementary Angles
Negative Association
Clusters in Data
Supplementary Angle
Non-linear Association
If the median of a data set is 13 and the mean is 13, which of the following is most likely?
Select the correct answer below:
a. The data are skewed to the left.
b. The data are skewed to the right.
c. The data are symmetrical.
Answer:
C
Step-by-step explanation:
if the mean and median are the same, the graph will be symmetrical
Select all that apply. By making the financially irresponsible decision of maxing out your credit card limit, you might...
A) not have money for an emergency situation.
B) get a very low interest rate when you want to buy a house.
C) not be able to buy the things you need.
D) have enough saved up for retirement.
By making the financially irresponsible decision of maxing out your credit card limit, you might not have money for an emergency situation.
As, There is no foolproof technique to determine how much you can spend in excess of your credit limit, but you can go over it.
When determining the risk of accepting an over-the-limit transaction, card issuers may take into account a number of criteria, including your prior payment history.
Now, maxing out credit card leads to negative results.
So, either not have money for an emergency situation or not be able to buy the things you need.
But we can still spend after maxing out the limit.
Thus, not have money for an emergency situation is correct option.
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Based on the scenario, determine if it would be better to use the mean or median to describe the data set.
1 Workers at a plant are trying to show that they work too many hours. There are five part-time workers along with ten full time workersWhat summary statistic would best defend their position?
2Mrs. Smith is trying to show that her class did really well on the last test. She has four students that should have been in honors mathbut instead stayed in regular math. What summary statistic should she use to defend her position?
3. A CEO is trying to determine the average salary of his workersHe has some workers that work part- time and some very highly paid workersIf he wants a true idea of the average salarywhat summary statistic should he use?
4. Henry is trying to determine his average test grade in a class. All of his grades have been within five points of each other. He needs the average in order to calculate his overall gradeWhat summary statistic should he use?
____median
____median
____mean
____mean
1. It would be better to use the median to describe the data set.
2. It would be better to use the median to describe the data set.
3. It would be better to use the mean to describe the data set as the average salary of the workers is to be calculated.
4. It would be better to use the mean to describe the data set as the average test grade of the class is to be calculated.
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Factor the polynomial completely. If the polynomial is prime, so state.
x2 - x - 35
The given polynomial is a prime polynomial.
The given polynomial is
x² - x + 35
Since we know that discriminant of quadratic polynomial
p(x)= ax² + bx + c is b² - 4ac
Therefore, discriminant of the given polynomial be,
⇒ (-1)² - 4x1x35
⇒ - 139
Since discriminant is negative number so it has no real roots.
And an irreducible or primal polynomial is a polynomial with integer coefficients that cannot be factored into polynomials of lower degree and also with integer coefficients.
Hence it is not factored completely.
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The table below shows the amount of time 80 people spent watching television during a week.
Time (hours)
Frequency
0 < h ≤ 10
5
10 < h ≤ 20
15
20 < h ≤ 30
50
30 < h ≤ 40
10
Calculate an estimate for the mean time spent watching television.
Give your answer to 1 d.p.
An estimate for the mean time spent watching television is approximately 24.375 hours.
How to calculate the meanMidpoint of 0 < h ≤ 10 = (0 + 10) / 2 = 5
Midpoint of 10 < h ≤ 20 = (10 + 20) / 2 = 15
Midpoint of 20 < h ≤ 30 = (20 + 30) / 2 = 25
Midpoint of 30 < h ≤ 40 = (30 + 40) / 2 = 35
Sum of observations = (5 × 5) + (15 × 15) + (25 × 50) + (35 × 10) = 125 + 225 + 1250 + 350 = 1950
Total number of observations = 5 + 15 + 50 + 10 = 80
Mean = Sum of observations / Total number of observations = 1950 / 80 = 24.375
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Please solve quickly will give brainlest if correct!!!!!
The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Writing the sum using the sigma notationFrom the question, we have the following parameters that can be used in our computation:
[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]
From the above expression, we can see that the different expression in each term is
9/n
So, we introduce a variable
Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
When represented using the sigma notation, we have
[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
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3. A room is 17 feet by 16 feet. Carpet for the room costs
$101 per square yard.
How much will it cost to carpet the room?
Question 1
Answer: First, let's convert the room's dimensions from feet to yards, since the carpet cost is given per square yard:
17 feet = 5.67 yards (rounded to two decimal places)
16 feet = 5.33 yards (rounded to two decimal places)
Next, we can calculate the area of the room in square yards by multiplying these values:
Area = 5.67 yards × 5.33 yards = 30.23 square yards (rounded to two decimal places)
Finally, we can multiply the area by the cost per square yard to get the total cost:
Total cost = 30.23 square yards × $101/square yard = $3,056.23 (rounded to two decimal places)
Therefore, it will cost $3,056.23 to carpet the room.
Question 2 (1 point)
Thomas's football team lost 3 yards in their first drive while Derrek's
football team gained 5 yards in their first drive. The first drives for each
team can be compared on a number line, where 0 represents the line
of scrimmage for each play.
Select the correct numbers for Derrek and Thomas' football teams.
Oa Derrek's Team has-5
Ob Thomas' Team has +3
OcThomas' Team has -3
Od Derrek's Team has +5
The correct numbers for Derrek and Thomas' football teams are :
c. Thomas' Team has -3d. Derrek's Team has +5How to find the numbers ?According to the information given, Thomas's football team lost 3 yards in their first drive, which means they moved backward 3 yards from the line of scrimmage. This can be represented as -3 on the number line.
On the other hand, Derrek's football team gained 5 yards in their first drive, which means they moved forward 5 yards from the line of scrimmage. This can be represented as +5 on the number line.
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25 POINTS
Which is the BEST definition of dilation?
A: a transformation that either reduces or enlarges an object in the coordinate plane
B: a transformation that spins an object in the coordinate plane
C: a transformation that either slides or shifts an object in the coordinate plane
D: a transformation that flips an object in the coordinate plane
Answer: A
Step-by-step explanation:
A dilation is not a rigid transformation, which means it has to scale the object into a different measure. So, enlarging or reducing the size of an object is a dilation.
What's the answer to this problem
The function shows that the chairs and sofas the manufacturer should produce to earn that profit is C. (6, 12) P= 1,260
How to explain the functionThe profit function is P = 50x + 80y.
In order to find the optimal production quantities that will maximize the profit function, we need to determine which vertex yields the highest profit.
From the given vertices, we can see that the profit at (0,0) is 0. The profit at (0,15) is 1,200, and the profit at (6,12) is 1,260.
Therefore, the manufacturer should produce 6 chairs and 12 sofas to earn a profit of 1,260.
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find the area of the shaded region
The area of the shaded region is 51.75 in².
From the figure
Radius of semicircle = √25² - 20²
=√625- 400 = 15 inch
Now, Area of Trapezium = 1/02 ( a +b ) h
= 1/2 (17 + 37) x 15
= 1/2 (54) x 15
= 27 x 15
= 405 in²
Then, Area of Shaded region
= Area of Trapezium - Area of semicircle
= (405 - πr²)
= 405 - 353.25
= 51.75 in²
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find x
find x
find x
USE THE FACTOR THEOREM
YES OR NO
Answer:
yes
Step-by-step explanation:
the factor theorem says if (x + a) is a factor of a polynomial f(x) then f(- a) = 0
given (x+ 5) then if f(- 5) = 0 , (x + 5) is a factor
4[tex](-5)^{4}[/tex] + 16(- 5)³ - 6(- 5)² + 73(- 5) + 15
= 4(625)+ 16(- 125) - 6(25) - 365 + 15
= 2500 - 2000 - 150 - 350
= 500 - 500
= 0
then (x + 5) is a factor of the given polynomial
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 108 cm, find its length and width.
Answer:
Let the width of the rectangle be w. Then the length of the rectangle is 5w.
The perimeter of a rectangle is the sum of all four sides. So, the perimeter of the rectangle is 2w+2(5w)=108 cm.
Simplifying the right side of the equation, we get 12w=108 cm.
Dividing both sides of the equation by 12, we get w=9 cm.
Since the width is 9 cm, the length of the rectangle is 5w=5(9)=45 cm.
Therefore, the length of the rectangle is 45 cm and the width is 9 cm.
Kyle has three times as much money in his savings account as Hayden Hayden has twice as much money in his savings account as Jeremy combine Kyle Hayden and Jeremy have a total of 612 how much money does Kyle have in his account
Kyle has $306 in his account so, right answer is Option D.
Let Kyle's money = x
Hayden's money = y
Jeremy's money = z
Given that Kyle has three times as much money in his savings account as Hayden.
x = 3y .....Eqn 1
Hayden has twice as much money in his savings account as Jeremy.
z = 2y ..... Eqn 2
Now Combined Kyle, Hayden, and Jeremy have a total of $612.
x+y+z=612 .....Eqn 3
Putting value of x and z from Eqn 1 and 2 in Eqn 3
6y = 612
y = 106
Putting in Eqn 1;
x = 306
Thus, Kyle has $306 in his account.
The right answer is Option D.
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Suppose that you are taking a course where the total class grade is the weighted average of your homework, worksheets, quizzes and tests.
The homework is worth 15% of the course grade, worksheets are worth 20% of the course grade, the quizzes are worth 25% of the course grade, and tests are worth 40% of the course grade. To get a B in the course, you must have an overall average of at least 80%.
Your current grades in each category are:
Homework =
73
%, Worksheets =
79
%, and Quizzes =
84
%.
What is the minimum test average you need to get a B in the course?.
Your answer is:
% (Round to at least 1 decimal place)
The minimum grade you need to get a B in the course is given as follows:
x = 80.625.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The grades and their percentages are given as follows:
73 worth 15%.79 worth 20%.84 worth 25%.x worth 40%.You want a grade of 80, hence the minimum test average is obtained as follows:
0.15 x 73 + 0.2 x 79 + 0.25 x 84 + 0.4x = 80
47.75 + 0.4x = 80
x = (80 - 47.75)/0.4
x = 80.625.
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In QA, if m/DBG= 32° and mGFE = 149°, find mDG.
A. mDG = 62°
B. mDG=85°
C. mDG = 107°
D. mDG = 117°
E
Mark this and return
The tangent secant exterior angle measure theorem indicates that the measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°, the correct option is the option B.
B. m[tex]\widehat{DG}[/tex] = 85°
What is the tangent secant exterior angle measure theorem?The tangent secant exterior angles theorem states that if two secant or tangent or a secant and tangent intersect on the exterior to a circle, the measure of the angle formed is half the difference of the arcs they intercept.
The possible options in the question indicates that the possible drawing in the consists of a tangent and a secant, with the angle m∠DBG, being external to the circle.
The tangent secant exterior angle measure theorem indicates that we get;
m∠DBG = (1/2) × (m[tex]\widehat{GFE}[/tex] - m[tex]\widehat{DG}[/tex])
The question indicates; m[tex]\widehat{GFE}[/tex] = 149°
m∠DBG = 32°
Therefore;
32 = (1/2) × (149° - m[tex]\widehat{DG}[/tex])
149° - m[tex]\widehat{DG}[/tex] = 2 × 32° = 64°
m[tex]\widehat{DG}[/tex] = 149° - 64° = 85°
The measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°
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Collect a set of data (from the internet) about any school-appropriate topic. Examples: rainfall data, and testing scores. Or make up your own set of data. The data set must contain at least 20 values. Fill out the questions below regarding your data.
1. List your data below in numerical order.
2. Explain your data. What does each data point represent?
3. What is the mean of your data?
4. What is the minimum and maximum within your data?
Here is the data collected as a result of the experiment.
1) Numerical order is: 0.20, 0.20, 0.46, 0.46, 2.10, 2.10, 5.50, 11.80, 12.20, 12.20, 13.22, 14.65, 16.07, 17.49, 18.91, 20.33, 20.50, 20.50, 21.75, 23.18
2) The data represents rainfall in millimeters over a 20-day period.
3) Mean = 11.69 mm.
4) The minimum rainfall is 0.20 mm ;
the maximum is 23.18 mm.
1) The data is listed as follows.
0.20 12.20 2.10 0.46 20.50 5.50 11.80 13.22 14.65 16.07 17.49 18.91 20.33 21.75 23.18 0.20 12.20 2.10 0.46 20.502) The data represents the amount of rainfall in millimeters over a 20 day period.
3) The mean rainfall over the 20 day period is 11.69 mm.
= (0.20 + 0.20 + 0.46 + 0.46 + 2.10 + 2.10 + 5.50 + 11.80 + 12.20 + 12.20 + 13.22 + 14.65 + 16.07 + 17.49 + 18.91 + 20.33 + 20.50 + 20.50 + 21.75 + 23.18) /20
Mean (x) = 11.69 mm.
3) The minimum rainfall is 0.20 mm and the maximum is 23.18 mm.
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3 1/2 be classified as integer
Answer:
False.
Step-by-step explanation:
A integer in math is defined as a whole number. Therefore, the presence of fractions (which, in this case, is 1/2) and decimals, would mean that the term is in fact, not a integer.
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The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
The correct option regarding which bus has the least spread among the travel times is given as follows:
Bus 14, with an IQR of 6.
How to solveTo obtain measures of spread, we can use the dot plot to visualize the frequency of each observation in the data-set, and then calculate the interquartile range (IQR).
For a group of 15 students, we can find the quartiles as follows:
The first quartile (Q1) is the median of the first half of the data-set, which consists of the first seven students.
Looking at the dot plot, the fourth dot represents the median of the first half. For Bus 14, Q1 = 12. For Bus 18, Q1 = 9.
The third quartile (Q3) is the median of the second half of the data-set, which consists of the last seven students. Looking at the dot plot, the eleventh dot represents the median of the second half. For Bus 14, Q3 = 18.
For Bus 18, Q3 = 16.
We can then calculate the IQR as the difference between Q3 and Q1:
For Bus 14, IQR = Q3 - Q1 = 18 - 12 = 6.
For Bus 18, IQR = Q3 - Q1 = 16 - 9 = 7.
Based on the IQR values, we can conclude that Bus 14 is more consistent than Bus 18, as it has a lower IQR.
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17. The Amethyst Woodstar species of
hummingbird beats its wings about
80 times per second. If there are
60 seconds in a minute, about how
many times does the Amethyst
Woodstar beat its wings in
9 minutes?
A 12,600
B 37,800
C50,400
D 43,200
Answer: D
Step-by-step explanation: 60x9=540 and 540x80=43,200
Given this unit circle what is the value of x
Answer:
[tex]x=-\dfrac{\sqrt{51}}{10}[/tex]
Step-by-step explanation:
You want the value of x in the third quadrant of a unit circle where y = -7/10.
Pythagorean theoremThe radius of a unit circle is 1, so the Pythagorean theorem tells you the magnitude of the value of x is ...
1² = x² +(7/10)²
x = -√(1 -49/100) = -√(51/100) . . . . . . x < 0 in the third quadrant
x = (-√51)/10
A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 5 and the second roll is a total of at least 4.
The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4 is 0.764 or 76.4%.
What is the probability?The probability is the chance that an expected event occurs out of many possible events.
For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.
The event that the first roll is a total of at least 5 = A
In the event that the second roll is a total of at least 4 = B
The number of faces on each die, n = 6
The probability of event A = ³⁰/₆ = ⁵/₆
The probability of event B = ³³/₃₆ = ¹¹/₁₂
Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ × ¹¹/₁₂
= ⁵⁵/₇₂ = 0.764
Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.
Learn more about dice probabilities at https://brainly.com/question/23955312.
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