Answer:
To find the distance between a point and a line in a plane, we can use the formula:
distance = |Ax + By + C| / √(A^2 + B^2)
where A, B, and C are the coefficients of the general form of the line equation (Ax + By + C = 0), and (x,y) are the coordinates of the point.
First, we need to rewrite the given line equation in the standard form (y = mx + b):
2x - 3y = -2
-3y = -2x - 2
y = (2/3)x + 2/3
Now we can identify the slope (m) and y-intercept (b) of the line:
m = 2/3
b = 2/3
Next, we can find the equation of the perpendicular line that passes through the point (1,2), since the distance between the point and the line will be the length of the segment connecting the point to the intersection of these two lines. The slope of a line perpendicular to a line with slope m is -1/m, so the equation of the perpendicular line passing through (1,2) is:
y - 2 = (-3/2)(x - 1)
y = (-3/2)x + (7/2)
Now we need to find the intersection of the two lines by solving the system of equations:
y = (2/3)x + 2/3
y = (-3/2)x + (7/2)
(-3/2)x + (7/2) = (2/3)x + 2/3
(-13/6)x = -5/6
x = 5/13
y = (2/3)(5/13) + 2/3
y = 11/13
So the intersection point of the two lines is (5/13, 11/13). Now we can use the distance formula to find the distance between this point and the given point (1,2):
distance = √[(5/13 - 1)^2 + (11/13 - 2)^2]
distance = √[(36/169) + (25/169)]
distance = √(61/169)
distance = √61/13
The closest answer choice is (A) √13, but the simplified expression is actually √61/13. Therefore, none of the answer choices provided are completely accurate.
Step-by-step explanation:
What questions please help me thanks
1. The monthly payment for Loan A is roughly $516.40.
2. The total interest for Loan A is roughly $1590.4
How do we calculate the monthly payment and total interest?We've been given the formula: PMT = (P(r/n)) / [1 - (1 + r/n)^-nt] to calculate the monthly payment loan.
If we should insert the figures given to the formula, it should be
PMT = (17000(0.059/12)) / [1 - (1 + 0.059/12)^(-12*3)]
PMT = 516.40
To calculate total interest for loan A, we use the formula (PMT x n x t) - P.
If we insert the figure provided, it should be;
(598.87 x 12 x 3) - 17000
= $1590.4
The above answer is in response to the question below as seen in the picture;
Suppose that you decide to borrow $17,000 for a new car. Installment loan A: 3 years at 5.9%. Use PMT = (p(r/n))/ [1 - (1 + r/n)^-nt]
Find the monthly payment and the total interest for loan A. The monthly payment for Loan A is $..............
Find more exercises on monthly payment for Loan;
https://brainly.com/question/22803498
#SPJ1
How do I find the squareroot?
Answer:
Step-by-step explanation:
Factoring a square root means that you are finding the closest numbers that multiply together. The easiest square roots are ones that factor directly into squares, such as √100, but more complicated ones involve several square roots, such as √225. Here are the steps to finding the square root using factoring:
1. Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. For √100, the factors would be √(10 x 10). The factors of √225 would be √(25 x 9).
2. Separate the factors into their own square roots. Because both factors of √100 are 10, the square root of 100 is 10. For √225, you would separate the factors under their own square root signs, so the formula would be √25 x √9.
3. Solve for the individual squares. Next, you would find the squares of each of the individual factors. √25 = 5 and √9 = 3. The remaining formula will look like 5 x 3.
4. Finish solving the equation. Now that you know what the simplified squares are, you will find that 5 x 3 = 15. So, √225 = 15.
Hope that helps!
The claim is that for a smartphone carrier's data speeds at airports, the mean is 18.00 Mbps. The sample size is n= 14 and the test statistic is t= -2.645 .
whats the P-value?
According to given information the P-value is approximately 0.016.
What is P-value?In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed results, under the assumption that the null hypothesis is true.
According to given information:To find the P-value for this hypothesis test, we need to use a t-distribution with degrees of freedom equal to n-1 = 14-1 = 13. Since the test statistic is t = -2.645, we need to find the area under the t-distribution curve to the left of t.
Using a t-table or calculator, we can find that the area to the left of t = -2.645 with 13 degrees of freedom is approximately 0.008. This is the probability of observing a t-value less extreme than -2.645, assuming the null hypothesis is true.
Since this is a two-tailed test (we are testing whether the true mean is less than or greater than 18.00 Mbps), we need to double the one-tailed P-value to get the two-tailed P-value. Therefore, the P-value is approximately 0.016 (i.e., 2 x 0.008).
So, the P-value is approximately 0.016.
To know more about P-value visit:
https://brainly.com/question/13786078
#SPJ1
Indirect measurement, pls help, I am stuck on this question.
The building is 246 feet tall.
What are similar triangles?Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.
To determine the height of the building, we have;
height of pole = 7 ft
total length of the building's shadow = 167 ft
the length of the shadow of the pole = 4.75 ft
Let the height of the building be represented by h. On comparison, we have;
4.75/ 167 = 7/h
4.75h = 167 x 7
= 1169
h = 1169/ 4.75
= 246.11
The building is 246 ft. tall.
Learn more about similar triangles at https://brainly.com/question/21140865
#SPJ1
NO LINKS!! URGENT HELP PLEASE!!!
Movies generally lose 23% of its audience for each week it is in the theatre. A movie STARTED with an audience of 196 people per viewing.
a. Equation: ________________
b. Make a chart and fill in the table for the first ten weeks.
c. Graph the function. Label each axis with a title and scale
Answers:
a) The equation is y = 196(0.77)^x
b) The chart is shown below
c) The graph is shown below
================================================
Explanation:
Part (a)
One template of an exponential equation is y = ab^x
a = starting valueb = connected to the growth rate or decay rateIn this case
a = 196b = 1-0.23 = 0.77If 23% of the audience leaves, then 77% remains. This is another way to see where b = 0.77 comes from. Exponential decay will have 0 < b < 1.
Therefore, the equation is y = 196(0.77)^x
Other equations are possible.
-------------------
Part (b)
I'll be using LibreOffice spreadsheet to make the table. Any spreadsheet software will do.
Type x into cell A1
Type 0 and 1 into cells A2 and A3 in that order.
Select cells A2 and A3. Pull down the small marker at the bottom right corner. Pull this marker down to cell A12 to get values 2 through 10 (which will be in cells A4 to A12).
Now move to cell B1. Type in y = 196(0.77)^x in this cell.
In cell B2, type in "=ROUND(196*(0.77)^A2)" without quotes. As you can probably guess, the ROUND function will round to the nearest whole number. The calculation 196*(0.77)^A2 computes the result of y = 196*0.77^x when plugging x = 0 which is in cell A2.
Do not forget about the equal sign up front.
After cell B2 is filled in, hit enter. Then pull down the smaller marker at the bottom right corner to cell B12. A bunch of whole numbers should fill in cells B3 to B12
This is what you should get for your table
[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{y} = 196(0.77)^{\text{x}}\\\cline{1-2}0 & 196\\\cline{1-2}1 & 151\\\cline{1-2}2 & 116\\\cline{1-2}3 & 89\\\cline{1-2}4 & 69\\\cline{1-2}5 & 53\\\cline{1-2}6 & 41\\\cline{1-2}7 & 31\\\cline{1-2}8 & 24\\\cline{1-2}9 & 19\\\cline{1-2}10 & 14\\\cline{1-2}\end{array}[/tex]
x = week number
y = viewer count (approximate)
Example calculation:
Plug in x = 5 to get y = 196*0.77^5 = 53.05297 approximately which rounds to y = 53. Therefore, we estimate there would be about 53 people in the audience for week 5.
-------------------
Part (c)
You could use a spreadsheet to make the graph, but I find GeoGebra is more friendly for graphing. But we'll be using the data we just made in the spreadsheet.
Select cells A2 through B12. This is the 11 row by 2 column block of x,y data pairs. Do not select the headers at the top.
Copy that data and paste it into GeoGebra's spreadsheet mode.
Then select that same block of data in GeoGebra. Right-click to go to "create" then to "list of points". It will do as it describes. Eleven points will show up in the graph window. Resize and adjust the window if needed.
I'm using the following window parameters
xMin = -5xMax = 20yMin = -20yMax = 220The graph is shown in the screenshot below.
Answer:
[tex]\textsf{a.} \quad \textsf{Equation:} \;\;\;y=196(0.77)^x[/tex]
b. See below.
c. See attachment.
Step-by-step explanation:
We can model the given situation using an exponential decay equation since the weekly change in audience is a constant percentage change.
Exponential decay formula[tex]\boxed{y=a(1-r)^x}[/tex]
where:
a is the initial value.r is the percentage decrease (in decimal form).x is the time period.Given the movie started with an audience of 196 people viewing, a = 196.
Given the movie loses 23% of its audience each week, r = 0.23.
As the movie loses a constant percentage of its audience each week, let x be the number of weeks.
Substitute the values of a and r into the formula and simplify:
[tex]y=196(1-0.23)^x[/tex]
[tex]y=196(0.77)^x[/tex]
Therefore, the equation that models the given scenario is:
[tex]\boxed{y=196(1-0.23)^x}[/tex]
Create a table for the first ten weeks by substituting the values of x from zero through 10 into the equation. Round each number to the nearest whole number.
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}$Weeks$\;x&$Audience$\;y\\\cline{1-2}\vphantom{\dfrac12}0&196\\\cline{1-2}\vphantom{\dfrac12}1&151\\\cline{1-2}\vphantom{\dfrac12}2&116\\\cline{1-2}\vphantom{\dfrac12}3&89\\\cline{1-2}\vphantom{\dfrac12}4&69\\\cline{1-2}\vphantom{\dfrac12}5&53\\\cline{1-2}\vphantom{\dfrac12}6&41\\\cline{1-2}\vphantom{\dfrac12}7&31\\\cline{1-2}\vphantom{\dfrac12}8&24\\\cline{1-2}\vphantom{\dfrac12}9&19\\\cline{1-2}\vphantom{\dfrac12}10&14\\\cline{1-2}\end{array}[/tex]
The graph of the function is an exponential decay curve, which starts at (0, 196) and approaches zero as x approaches infinity.
The x-axis represents the number of weeks and the y-axis represents the audience size.
Use a scale of x : y = 1 : 10.
Plot the points from the table and draw a smooth curve through them that approaches zero as x approaches infinity.
How is the product of a complex number and a real number represented on the complex plane?
Consider the product of 2−4i and 3.
Drag a value or phrase into each box to correctly complete the statements
Answer:
2 root 5
6 root 5
are the same
Step-by-step explanation:
Answer:
[tex]2\sqrt{5} \\6\sqrt{5}[/tex]
are the same
Step-by-step explanation:
3x+2=8 what is the value of x
Answer:
x = 2
Step-by-step explanation:
3x + 2 = 8
Subtracting both sides by 2 we get,
=> 3x + 2 - 2= 8 - 2
=> 3x = 6
=> x = 6/3
=> x = 2
Please answer this question quickly
FOR 35 POINTS
I WILL GIVE BRAINLIEST
Answer: 0
Step-by-step explanation:
[tex]log_{3} log_{5} log_{2} 32[/tex]
Let's evaluate
[tex]log_{2}32[/tex] this is the same as
[tex]2^{x}=32[/tex] 2*2*2*2*2=32
or
you can think of it as 2 to the what power is 32
so x=5
now substitute that in for [tex]log_{2}32[/tex]
[tex]log_{3} log_{5} 5[/tex]
Now evaluate [tex]log_{5}5[/tex]
5 to the what power is 5
=1
substitute into [tex]log_{3} log_{5} 5[/tex]
[tex]log_{3} 1[/tex]
3 to the what power is 1
=0
Anything to the 0 power is 1 (it's a rule)
MARKING AS BRAINLIST PLS HELP
Answer:
The angle of C is 118.6
Step-by-step explanation:
Determine the function is positive, negative, increasing, or decreasing. Then describe the end behavior of the function.
The function is positive and increasing.
Given is an exponential function y = √4x,
So, since all the value of the function will be above x-axis therefore, the function is positive.
Now,
Differentiating the function,
y' = d(√4x)/dx
y' = 1/2 × [tex]4x^{-1/2[/tex]
y' = 1/2√4x
y' = 1/4√x
Since, y' > 0, therefore, the function is increasing.
Now,
For functions with exponential growth, we have the following end behavior.
The end behavior on the left (as x → -∞), it has a horizontal asymptote at y = 0,
The end behavior on the right (as x → ∞), y→ ∞.
Learn more about exponential function click;
https://brainly.com/question/14355665
#SPJ1
How do you write 9.6522 as a percentage
Linda agreed to lend money to Alex at a rate of 9 percent per year,
contingent he would pay her 300.00 in interest over a four year period. What was the minimum mount Alex could borrow
Answer:
$731.71
Step-by-step explanation:
300 over 4 years = 75$ per yr
9% per year so 4 years interest = (1+9%)^4 = 1.41
so effective int rate for 4 years is 41%.
41% * x = 300
x = $731.71
The accompanying data represent the percentages of teenagers in various countries that have used certain drugs. Complete parts (a) through (c)
below.
Country
Drug 1, x
Other Drugs, y
A
23
3
B с
17 41
2 21
D52
E
38
15
(=
(Round to two decimal places as needed.)
F
18
9
G
23
15
HS2
5
1
8
NO
2
CI
J
54
32
K
:
H
35
25
a. Determine the correlation coefficient between the percentage of teenagers who have used Drug 1 and the percentage who have used other drugs.
Answer:
-1.82
Step-by-step explanation:
It won't let me write the explanation for some reason. I'll put it in the comments below
320.041 - 47.96 multiple it for me
Answer:
320.041 - 47.96 = 272.081
Step-by-step explanation:
I need more information on what you want me to do.
Do you want me to:
Multiply 320.041 by 47.96?
Subtract 47.96 from 320.041?
Multiply the difference between 320.041 and 47.96 by 47.96?
Multiplying 320.041 by 47.96 gives 152,399.6896.
Subtracting 47.96 from 320.041 gives 272.08.
Multiplying the difference between 320.041 and 47.96 by 47.96 gives 13049.0048.
find the circumference of a circle circumscribed about a right triangle with legs 5 centimeters and 3 centimeters
Answer:
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).
Step-by-step explanation:
To find the circumference of a circle circumscribed about a right triangle with legs 5 cm and 3 cm, we can use the Pythagorean theorem to find the length of the hypotenuse, which is also the diameter of the circle.
Using the Pythagorean theorem, we have:
c^2 = 5^2 + 3^2
c^2 = 25 + 9
c^2 = 34
c = sqrt(34)
So the diameter of the circle is sqrt(34) cm, and the radius is half of the diameter, or sqrt(34)/2 cm.
The circumference of a circle is given by the formula:
C = 2 * pi * r
where pi is approximately 3.14 and r is the radius of the circle.
Substituting the value of the radius, we get:
C = 2 * 3.14 * sqrt(34)/2
C = 3.14 * sqrt(34)
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).
what is the best measure of sensors to use in the set of data below 12, 8, 15, 45, 7, 13 mean, median, mean or median, mode?
Answer:
The best measure of central tendency to use in a set of data depends on the characteristics of the data and the specific objective of the analysis. Let's examine the given data set: 12, 8, 15, 45, 7, 13.
Mean: The mean, also known as the average, is calculated by summing up all the values in the data set and dividing by the total number of values. The mean is sensitive to extreme values and can be influenced by outliers. In this case, the mean is calculated as (12 + 8 + 15 + 45 + 7 + 13) / 6 = 100 / 6 ≈ 16.67.
Median: The median is the middle value in a data set when the values are arranged in ascending or descending order. The median is not affected by extreme values and is a good measure to use when there are outliers or when the data is not symmetrically distributed. In this case, when the data set is arranged in ascending order, the median is 13, as it is the middle value.
Mode: The mode is the value that appears most frequently in a data set. It is a useful measure when we want to identify the most common value in the data set. In this case, the mode is not applicable as there are no repeated values in the data set.
Based on the characteristics of the given data set, the median is a good measure to use as it is not affected by extreme values and provides a central value that represents the middle of the data set. The mean may be influenced by the outlier value of 45, and the mode is not applicable in this case. So, the best measure of central tendency to use in this data set would be the median.
part B write a numerical expression of angle C
The index of refraction of the second material is 1.27.
We are given that;
Angle= 59°
Randomized Variables 1 = 1.47θ1 = 59°θ2 = 69°
Now,
To find n2, we can rearrange Snell’s law as:
n2 = n1 sin θ1 / sin θ2
Plugging in the given values, we get:
n2 = 1.47 sin 59° / sin 69°
n2 = 1.47 (0.857) / (0.934)
n2 = 1.27 (rounded to two decimal places)
Therefore, by the expression the answer will be 1.27
To know more about an expression follow;
brainly.com/question/19876186
#SPJ1
2. Why was the Constitutional Convention held?
lengte
A. Each state's government was too weak.
B. Americans wanted to win independence from England.
C. The national government was too weak.
D. The states wanted to form the first American government.
Anyone pls
what is the inverse of f(x)=(4x-9)^1/2
The inverse of f(x) = [tex](4x-9)^{1/2[/tex] when the variables of x and y are switched is [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
What is an Inverse of a Function?Inverse of a function is a function which can be reversed into another function. It is also a function that undoes the action of the another function.
How to determine this
When f(x) = (4x-9)^1/2
To determine the inverse, [tex]f(x)^{-1}[/tex]= y
y = (4x-9)^1/2
y = [tex]\sqrt{4x-9}[/tex]
By squaring both sides
y^2 = 4x - 9
By swapping the variables
x^2 = 4y - 9
Subtracting 9 from both sides
x^2 +9 = 4y
divide through by 4
[tex]\frac{x^{2}+9 }{4}[/tex] = 4y/4
y = [tex]\frac{x^{2}+9 }{4}[/tex]
Therefore [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
Read more about Inverse of a Function
https://brainly.com/question/19425567
#SPJ1
The Hartford offered an annuity that pays 5.5% compounded monthly.
What equal monthly deposit should be made into this annuity in order
to have $100000 in 10 years?
If an annuity pays 5.5% compounded monthly, then the "equal-monthly-deposit" to have $100000 in 10 years is $627.
In order to calculate the "monthly-deposit" needed to accumulate $100,000 in 10 years at 5.5% compounded monthly, we use the formula for the future value of an annuity:
Which is : FV = P × [(1 + r)ⁿ - 1]/r,
where:
FV is "future-value" = $100000,
P = monthly deposit
r = monthly interest rate (5.5%/12 = 0.00458)
n = number of months (10 years × 12 months per year = 120 months)
Substituting the values,
We get,
⇒ 100000 = P × [(1 + 0.00458)¹²⁰ - 1]/0.00458,
⇒ P = 100000 × 0.00458 / [(1 + 0.00458)¹²⁰ - 1],
⇒ P ≈ $627,
Therefore, an equal monthly deposit is approximately $627.
Learn more about Annuity here
https://brainly.com/question/28015034
#SPJ1
There are only red counters, blue counters and green counters in a bag.
number of red counters: number of blue counters: number of green
counters = 1:3:7
A counter is going to be taken at random from the bag.
Complete the table below to show each of the probabilities that the counter will be red or blue or green.
(2 marks)
Answer:
Color Probability
Red 1/11
Blue 3/11
Green 7/11
Step-by-step explanation:
The total number of counters in the bag is 1+3+7=11. The probability of selecting a red counter is 1/11, because there is only one red counter in the bag. The probability of selecting a blue counter is 3/11, because there are three blue counters in the bag. Similarly, the probability of selecting a green counter is 7/11, because there are seven green counters in the bag.
Find the length of CD. The length of BE is 28in
The length of the segment CD given the length of BE is 42 inches
Finding the length of CD given the length of BEFrom the question, we have the following parameters that can be used in our computation:
The length of CD = ?The length of BE is 28inUsing the proportional ratio from the triangle, we have
CD = 1.5 * BE
substitute the known values in the above equation, so, we have the following representation
CD = 1.5 * 28
Evaluate
CD = 42
HEnce, the lengtth is 42 inches
Read more about similar triangles at
https://brainly.com/question/14285697
#SPJ1
Please help asap!!!!!
Answer:
[tex]f(-1) = -2\\[/tex]
[tex]f(0)=0[/tex]
[tex]f(1)=2[/tex]
Step-by-step explanation:
f(x)=2x
1) f(-1) = 2(-1) = -2
2) f(0) = 2(0) = 0
3) f(1) = 2(1) = 2
60. What is the slope of a line that passes through the point (-1, 1) and is parallel to a line that passes through
(3, 6) and (1,-2)?
The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
What is slope?The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.
In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].
Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.
To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.
The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:
[tex]$y - 1 = 4(x - (-1))$[/tex]
[tex]$y - 1 = 4x + 4$[/tex]
[tex]$y = 4x + 5$[/tex]
Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
For more questions related to coordinate
https://brainly.com/question/29660530
#SPJ1
The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
What is slope?The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.
In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].
Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.
To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.
The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:
[tex]$y - 1 = 4(x - (-1))$[/tex]
[tex]$y - 1 = 4x + 4$[/tex]
[tex]$y = 4x + 5$[/tex]
Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
For more questions related to coordinate
https://brainly.com/question/29660530
#SPJ1
Help!!
You flip a coin and roll a dice. The resultant outcome table where H means heads, T means Tails, and the number represents what number was rolled on the dice. The outcome list is as follows: Coin Toss H H H H H H TTTTTT Die Roll 1 2 3 4 5 6 1 2 3 1 2 3 4 5 6 What is the probability that the coin reads heads or tails and the dices number is less than or equal to 6?
The probability that the coin reads heads or tails and the dices number is less than or equal to 6 is 1/3 or approximately 0.333.
How to calculate the probability that the coin reads heads or tails and the dices number is less than or equal to 6?There are 12 possible outcomes in the table where the coin reads heads or tails and the dice roll is less than or equal to 6. These are:
Coin Toss: H, Die Roll: 1
Coin Toss: H, Die Roll: 2
Coin Toss: H, Die Roll: 3
Coin Toss: H, Die Roll: 4
Coin Toss: H, Die Roll: 5
Coin Toss: H, Die Roll: 6
Coin Toss: T, Die Roll: 1
Coin Toss: T, Die Roll: 2
Coin Toss: T, Die Roll: 3
Coin Toss: T, Die Roll: 4
Coin Toss: T, Die Roll: 5
Coin Toss: T, Die Roll: 6
Out of these 12 outcomes, 6 have the coin reading heads and 6 have the coin reading tails. So, the probability that the coin reads heads or tails and the dice number is less than or equal to 6 is:
P(heads or tails and dice number <= 6) = P(heads and dice number <= 6) + P(tails and dice number <= 6)
= 6/36 + 6/36
= 12/36
= 1/3
Therefore, the probability is 1/3 or approximately 0.333.
Learn more about probabilities at https://brainly.com/question/24756209
#SPJ1
7. El área de un terreno de forma rectangular es 4332 m?. Si de ancho mide la tercera parte de su medida de largo, ¿Cuáles son las dimensiones del rectángulo?
find dy/dx of y= ln(1-x^2/1+x^2)
The derivative of y with respect to x is:
[tex]dy/dx = -4x / (1 - x^4)[/tex]
How to find derivative ?The chain rule and the quotient rule must be utilized in order to determine the derivative of y with respect to x.:
First, we can rewrite y as follows:
[tex]y = ln[(1 - x^2)/(1 + x^2)][/tex]
Let's define two functions:
[tex]u = 1 - x^2[/tex]
[tex]v = 1 + x^2[/tex]
Then, y can be rewritten in terms of u and v as:
y = ln(u/v)
Now, we can use the chain rule to find the derivative of y with respect to u and v, respectively:
[tex]dy/du = 1/u\\dy/dv = -1/v[/tex]
Using the quotient rule, we can find the derivative of y with respect to x:
[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)[/tex]
[tex]du/dx = -2x\\dv/dx = 2x[/tex]
Substituting in the values we get:
[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)\\= (1/u) * (-2x) + (-1/v) * (2x)\\= -2x/(1 - x^2) - 2x/(1 + x^2)\\= -4x / (1 - x^4)[/tex]
Therefore, the derivative of y with respect to x is:
[tex]dy/dx = -4x / (1 - x^4)[/tex]
know more about differentiation visit :
https://brainly.com/question/24898810
#SPJ1
2.1. Consider the following pattern. 2.1.1 complete the table. (match-sticks were used to make each shape) (6marks) Shape No. of match-sticks Rule 1 4 2 7 3 10 4 13 6 241 10 40 43 21 82
(-23u^4 z^2 +32u^7 z^7 -12u^2 z) ÷ -4u^4 z^2
you need 18 lb of peeled and cored apples to make applesauce.apples have a yield percentage of 78%, how many pounds of whole apples are needed
You would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.
Explanation:
To find out how many pounds of whole apples are needed to make 18 lbs of peeled and cored apples with a yield percentage of 78%, we can use the following formula:
Pounds of whole apples needed = (Pounds of peeled and cored apples needed) / Yield percentage
Plugging in the values we have:
Pounds of whole apples needed = 18 lb / 0.78Pounds of whole apples needed = 23.077 lb (rounded to three decimal places)
Therefore, you would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.