Answer:
We can use Bayes' theorem to calculate P(R), which states that the probability of an event A given event B is equal to the probability of B given A multiplied by the probability of A, divided by the probability of B:
P(R|T) = P(T|R) * P(R) / P(T)
We can rearrange this equation to solve for P(R):
P(R) = P(R|T) * P(T) / P(T|R)
We are given that P(RI-T) = 0.25, which can be written as:
P(R∩T) = P(R|T) * P(T) = 0.25
We are also given that P(-R|T) = 0.2, which can be written as:
P(-R∩T) = P(-R|T) * P(T) = 0.2 * 0.1 = 0.02
We can use the law of total probability to find P(T|R):
P(T|R) = P(RI-T) / P(R) = 0.25 / P(R)
We can substitute these values into the equation for P(R) to get:
P(R) = P(R|T) * P(T) / P(T|R)
= 0.25 / [P(T|R) * P(T) + P(-R|T) * P(T)]
= 0.25 / [0.25 + 0.02]
= 0.1060
Therefore, the answer is option C: 0.1060.
50 Points! Multiple choice algebra question. Write the expression x^4+5x^2-8 in quadratic form, if possible. Photo attached. Thank you!
Answer:
A!!!!!!!!!!!!!!!!!!!!!!!!!
100 Points! Algebra question. Please show as much work as possible. Photo attached. Thank you!
The value of the constant term k in the exponential model of the bacteria population is k ≈ 0.0972
What is an exponential function?An exponential function is one in which the input variable is part of the exponent of the expression for the function.
The function for the population of the bacteria indicates;
[tex]P(t) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\cdot t)}}[/tex]
The population of the bacteria after t = 1 hour is P(1) = 10,532
Therefore;
[tex]P(1) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\times 1)}} = 10,532[/tex]
[tex]1 + 1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532}[/tex]
[tex]1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532} - 1[/tex]
[tex]e^{(-k\times 1)} = \frac{\frac{22,000}{10,532} - 1}{1.2}[/tex]
Taking the natural logarithm of both sides, we get;
[tex]\ln (e^{(-k\times 1)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = -k = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex] ≈ -0.0972 (rounded to 4 decimal places)
-k ≈ -0.0972
k ≈ 0.0972Learn more on exponential functions here: https://brainly.com/question/15662160
#SPJ1
Which of the following vectors represents u + v?
The vector u+v can be represented as < √85, -41.19° >, which is obtained by adding vector u marked on the y-axis from 0 to 6 and vector v marked on the x-axis from 0 to -7 on a coordinate plane.
To add vectors on the coordinate plane. The vector u is marked on the y-axis from 0 to 6, and the vector v is marked on the x-axis from 0 to -7.
To add them, we start at the tail of u and move horizontally to the left by 7 units (since v has a negative x-component) and then vertically up by 6 units (since u has a positive y-component) to reach the head of the resulting vector. This gives us the vector u+v.
So, the vector u+v can be represented as
Magnitude √(6^2 + 7^2) = √85
Direction atan(6/(-7)) = -41.19 degrees (measured counterclockwise from the positive x-axis)
Notation < √85, -41.19° >
To know more about vector:
https://brainly.com/question/29740341
#SPJ1
Please reply me as soon as possible with step by step answer for this
The length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
What is the length of the curve?To use the arc length formula, we need to find the derivative of the curve y = 5 - 4x:
y' = -4
Then, we can use the arc length formula:
L = ∫[a,b] √(1 + (y')^2) dx
where a and b are the limits of integration. In this case, a = -2 and b = 2.
L = ∫[-2,2] √(1 + (-4)^2) dx
= ∫[-2,2] √(17) dx
= √(17) * [x]_(-2)^(2)
= 4√(17)
So the length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
To check this answer, we can note that the curve is a line segment with endpoints (-2, 13) and (0.75, 1), and we can calculate its length using the distance formula:
L = √((0.75 - (-2))^2 + (1 - 13)^2)
L = √(18.25 + 144)
L = √(162.25)
L = 4√(17)
This matches our previous answer, so we can be confident that the length of the curve is 4√(17).
Learn more about the length of a curve at: https://brainly.com/question/29364263
#SPJ1
Factor by grouping. Then supply the term that is missing below. 4mn+3m+8n+6=(m+2)(?+3)
Answer:
4mn + 3m + 8n + 6 = (m + 2)(4n + 3)
The missing term is 4n.
What is the answer?
A) Yes
B) No
Answer:
Step-by-step explanation:
No
Help please
Expand the logarithm as much as possible
logy^10
Using some logarithm properties we will get the expanded expression:
log(y^10) = 10*ln(y)/ln(10)
How to expand the logarithm?So there are two logarithm properties that we can use here, these are:
logₙ(x) = ln(x)/ln(n)
and:
logₙ(x^a) = a*logⁿ(x)
Now let's go to our expression, it is:
log(y^10)
Using the second property we can remove the exponent, then we will get:
log(y^10) = 10*log(y)
Now we can use the first rule, remember that log(x) has a base of 10, then we can write:
10*log(y) = 10*ln(y)/ln(10)
That is the expession expanded.
Learn more about logarithms at:
https://brainly.com/question/13473114
#SPJ1
HELP FASTTTTT PLAZSSSS
Adam works as an account manager for a local insurance company. He makes $3500 per month, after taxes. He sticks to a strict monthly budget to make sure that he is able to pay for all of his expenses each month. Look at the list below of the items Adam must budget for each month. He gives a specific percentage of his income to each item. Use his monthly income and the percentage of each item to determine how much Adam will need to budget for each expense. 30% for rent/mortgage $ 15% for Insurances $ 12% for food $ 8% for utilities $ 10% for savings $ 5% for fun $ 7% for clothing $ 3% for personal items $ 10% charitable giving $ How much money will Adam have left over after budgeting for each item on the list? $
Answer:
see below
Step-by-step explanation:
Given a $3500 net income per month and a list of budget percentages, you want to know the budget amounts for each item, and the amount left over.
AmountsEach budget amount is the product of the net income and the associated budget percentage. Those products are ...
rent: $1050insurance: $525food: $420utilities: $280savings: $350fun: $175clothing: $245personal: $105charity: $350Left overThe sum of these amounts is $3500, so there will be $0 left over.
__
Additional comment
The list is stored in the variable 'b' by the first line in the calculator. Then these values are multiplied by the net income to get the budget amounts.
Please answer correctly and explain reasoning for brainliest (If correct) and thanks!
What are the coordinates of A’?
Check the picture below.
a triangle has vertices P(-4,8), I (0,2) and N (4,-2). What are. the coordinates of the centroid of the triangle
The coordinates for the centroid of the triangle is (0, 2.67)
How do we calculate the centroid of the triangle?The centroid of a triangle is the place where the three medians of the triangle meet or intersect.
To find the centroid of the triangle, we use the formula
(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3
We add all the x coordinates together and divide by 3, we also do the same for the y coordinates.
It becomes x = (-4 + 0 + 4)/3
y = (8 + 2 + (-2))/3
Therefore, the centroid is (0, 2.67)
Find more exercise on centroid;
https://brainly.com/question/10708357
#SPJ1
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
A. Using the formula for area of rectangle, the length of the rectangular space is: 2x - 3
B. The expression to prove this is: (2x - 3) * 4x = 8x² - 12x
What is the Area of a Rectangle?To find the area of a rectangle, multiply the width and the length together. This means: Area = length * width.
Part A: We are given that area of the rectangular space is expressed as 8x² - 12x, if the width is 4x, then:
Length of the rectangular space = (8x² - 12x) / 4x = 4x(2x - 3)/4x
Length = 2x - 3
Part B: To prove this, we have:
length * width = 8x² - 12x
Substitute:
(2x - 3) * 4x = 8x² - 12x
Learn more about area of rectangle on:
https://brainly.com/question/29604954
#SPJ1
Use the general form of the equation for an ellipse with center (0,0) with a vertex at (5,0) and a co-vertex at (2,0)
Need answers to this by 20 min please!
Dividing cubic polynomials by linear divisor
The solution to each of the given polynomials are:
1) x² + 3x - 4
2) x² - 4x + 4
3) x² - 7x + 8
4) x² - 13 - (15/(x + 3)
How to carry out polynomial division?1) We want to divide the polynomial. Thus:
x² + 3x - 4
x + 2| x³ + 5x² + 2x - 8
- x³ + 2x²
3x² + 2x
- 3x² + 6x
- 4x - 8
- -4x - 8
0
2) We want to divide the polynomial. Thus:
x² - 4x + 4
x - 2| x³ - 6x² + 12x - 8
- x³ - 2x²
- 4x² + 12x
- -4x² + 8x
4x - 8
- 4x - 8
0
3) We want to divide the polynomial. Thus:
x² - 7x + 8
x + 3| x³ - 4x² - 13x + 24
- x³ + 3x²
- 7x² - 13x
- -7x² - 21x
8x + 24
- 8x + 24
0
4) We want to divide the polynomial. Thus:
x² - 13
x + 3| x³ + 3x² - 13x - 15
- x³ + 3x²
- 0x² - 13x
- -7x² - 13x
0 - 15
Read more about Polynomial Division at: https://brainly.com/question/25289437
#SPJ1
8.G.1.2 A mathematical puzzle uses four triangles with the dimensions show below. Which of the following triangles are congruent? A. P and Q B. Q and R C. R and S D. S and P
The triangles which are congruent are P and Q. So, the correct answer is A).
Triangles are congruent if they have the same shape and size. This means that all corresponding angles and sides are equal. In this case, we can use the side lengths to determine which triangles are congruent.
Triangle P and Q have the same side lengths, so they are congruent (A). Triangle Q and R do not have the same side lengths, so they are not congruent (not B). Triangle R and S do not have the same side lengths, so they are not congruent (not C).
Triangle S and P do not have the same side lengths, so they are not congruent (not D). Therefore, the answer is A. Triangles P and Q are congruent.
To know more about congruent:
https://brainly.com/question/12413243
#SPJ1
--The given question is incomplete, the complete question is given
" 8.G.1.2 A mathematical puzzle uses four triangles with the dimensions show below. Which of the following triangles are congruent? A. P and Q B. Q and R C. R and S D. S and P "--
Share your own multi-step combination problem
My own multi-step combination problem is given below:
Amanda was planning a dinner party for 10 people, and she want to choose a menu of 3 fruit , 2 meat pie, and 2 desserts. Amanda have a total of 5 fruit , 4 meat pie, and 3 desserts to choose from. How many different dinner menus can Amanda create?How do you solve the multi-step combination?To solve this problem, Amanda need to use the formula for combinations and it is:
nCr = n! / (r! x (n-r)!)
where:
n = total number of items to select from
r is the number of items to select.
First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:
5C3
= 5! / (3! x (5-3)!)
= 10
Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be
4C2
= 4! / (2! x (4-2)!)
= 6
Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:
3C2
= 3! / (2! x (3-2)!)
= 3
To have the total number of dinner menus, we have to multiply these three numbers together:
= 10 x 6 x 3
= 180
Therefore, one can say that Amanda have 180 different dinner menus that she can be create.
Learn more about multi-step combination from
https://brainly.com/question/2191693
#SPJ1
Vanessa purchased a used car on a payment plan. Four months after purchasing the car, the balance was $1,200. Seven months after purchasing the car, the balance was $975.
Write an equation that models the balance y after t months.
y =
t +
The equation that models the balance y after t months is y = -75t + 1,500
To write an equation that models the balance y after t months, we need to use the given information to determine the rate at which the balance is decreasing. We can use the formula for a straight line, y = mx + b, where m is the slope and b is the y-intercept.
We can start by finding the change in the balance over the three-month period from four to seven months after the purchase:
Change in balance = $1,200 - $975 = $225
The rate of change can be calculated by dividing the change in the balance by the number of months:
Rate of change = $225 / 3 months = $75 per month
We can use this rate of change as the slope of the equation:
y = -75t + b
To find the y-intercept b, we can use the fact that the balance was $1,200 four months after the purchase:
1,200 = -75(4) + b
b = 1,500
Therefore, the equation that models the balance y after t months is:
y = -75t + 1,500
To learn more about equation click on,
https://brainly.com/question/30170275
#SPJ1
Laquita has $3,500 a month in cash inflows and $3,240 a month in forecasted cash
outflows. How much can she contribute annually to her liquidity fund?
Answer: $3120
Step-by-step explanation:
3500-3240
=260
260*12=3120
solve for x image attached please help x, 3 ,7 set up the proportion x/3=?
The proportion relation obtained from the similar triangles indicates that the x/3 = 10/x
What are similar triangles?Similar triangles are triangles that have the same shape but their sizes may vary.
The proportion equation from the image based on the ratio of the corresponding sides of the similar right triangles can be found as follows;
The side x is the hypotenuse side of the smallest right triangle
The ratio x/3, is equivalent to the ratio of the hypotenuse side to the shortest side of the right triangle
The corresponding ratio in the medium triangle is ((x² - 3²) + 7²)/(x² - 3²)
((x² - 3²) + 7²)/(x² - 3²) = (x² + 40)/(x² - 3²)
The corresponding ratio in the large similar right triangle is (7 + 4)/x = 10/x
Therefore, the corresponding ratio is; x/3 = 10/x
The proportion is; x/3 = 10/x
Learn more on similar triangles here: https://brainly.com/question/30850803
#SPJ1
What are the solutions to the system of equations?
y=x^2−5x−6
y=2x−6
(−1, 0) and (−6, 0)
(7, 8) and (0, −6)
(−6, 0) and (0, −1)
(−1, 0) and (0, −6)
Please answer- I will report you if you do not answer and only want the points.
The solutions of the system of equations are (0, -6) and (7, 8)
How to find the solution of the system of equations?
Here we have the system of equations:
y=x^2−5x−6
y=2x−6
To solve this, we need to solve the equation:
x^2 - 5x - 6 = 2x - 6
x^2 - 7x = 0
x*(x - 7) = 0
We can see that the two solutions are:
x = 0
x = 7
Evaluating the line in these values we get:
y = 2*0 - 6 = -6
y = 2*7 - 6 = 8
Then the solutions are (0, -6) and (7, 8)
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
I Need help with this question
Answer:
The answer is A.
Step-by-step explanation:
For this graph, you are using the linear equation formula: y = mx + b
m is the slope (rise/run)b is the y-intercept (where the line crosses zero at the y-intercept)if the area of the triangle is 8 15/16ths and the base is 5 1/2, what is the height
Answer:
h=.34
Step-by-step explanation:
1/2(bh)=A
1/2(5.5*h)=8.9375
5.5h=1.875
h=.34
Use the Law of Cosines. Find length x.
(Round the final answer to one decimal place as needed. Round all intermediate values to two decimal places as needed.)
18.2
Step-by-step explanation:
AB² =AC² + CB² -2(AC)(CB)CosA
X²=(17)² + (10)² - 2 (17)(10) Cos80
x² = 289 + 100- 340 cos 80
x= √289+100-340cos80
x= 18.2
the line is parellel to graph of 2x-3y=7 and contains the point (-3,-3)
The equation of the line parallel to the graph of 2x - 3y = 7 and containing the point (-3,-3) is y = (2/3)x - 1.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph: 2x - 3y = 7.
First, we need to rearrange the given equation into slope-intercept form (y = mx + b) by solving for y:
2x - 3y = 7
-3y = -2x + 7
y = (2/3)x - 7/3
The slope of the given line is 2/3.
Hence, any line parallel to it will also have a slope of 2/3.
Using the point-slope form, we determine the equation of the line that passes through (-3,-3) and has a slope of 2/3:
y - y1 = m(x - x1)
y - (-3) = (2/3)(x - (-3))
y + 3 = (2/3)x + 2
y = (2/3)x - 1
Therefore, the equation of the line is y = (2/3)x - 1.
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
What are some common order of operation mistakes that students make when evaluating expressions? Make a list and share two examples in the Discussion Board; then explore the lists your peers have posted and respond to one that you find particularly insightful.
Some of the common order of operation mistakes that students make when evaluating expressions are the use of basic mathematical operations.
What is a mistake?You should know that an error or fault results from defective judgment, deficient knowledge, or carelessness.
A combination of numbers, letters, and relational operators containing at least one operation is deemed a mathematical expression. Additionally, it must also include variables and/or numbers, excluding an equal sign.
Some prevalent errors include using both a positive and a negative sign, using two negative signs, and misusing brackets.
By being unable to comprehend the problems accurately, learners often commit significant errors while assessing formulations, which underscores the importance of employing fundamental mathematical operations.
Learn more about the use of mathematical operations on https://brainly.com/question/29751180
#SPJ1
I’m not sure how to do the graph and it’s not letting me advance :(
Y=85.468x+ 985.029
R=0.988
To plot the above linear regression on a graph, follow the procedures outlined below.
What are your options?You may use the following steps to plot the supplied data on a graph:
1) Create an x- and y-axis coordinate plane.
2) Label the x-axis with the numbers 1 through 13 (to represent the 13 data points).
3) Label the y-axis with a suitable scale that encompasses the data's greatest and lowest values (e.g., 0 to 2200 with 200 increments).
4) For each point, try to find the associated x -value on the x-axis and the corresponding y-value on the y- axis, and then place a point at the intersection of the two values.
For example, if the first point is (1, 1000), you would identify the x-axis point labeled "1" and the y-axis point labeled "1000" and add a point at it intersection.
5) based on the pattern in the data, connect the points of the coordinares using a line or a curve. Because the data appears to increase gradually with some fluctuations in this case, a line connecting the points would be appropriate.
After plotting the data on the graph, you may study the pattern and draw inferences about the data's trend over time. Please see the attached sample graph.
Learn more about linear regression:
https://brainly.com/question/29665935
#SPJ1
The area of the rectangle shown is 352 square inches. What are the dimensions of the rectangle? Write the dimensions from least to greatest.
Length= 4x Width= x+3 Area=352
Answer:
11 in and 32 in-------------------------
Given a rectangle with dimensions of:
l = 4x in, w = x + 3 in,And area of A = 352 in²Use area equation and find the value of x:
A = lw352 = 4x(x + 3)88 = x(x + 3)88 = x² + 3xx² + 3x - 88 = 0x² + 11x - 8x - 88 = 0x(x + 11) - 8(x + 11) = 0(x - 8)(x + 11) = 0x = 8 or x = - 11The second root is ignored as being negative.
The dimensions of the rectangle are:
l = 4*8 = 32 inw = 8 + 3 = 11 inAfter 2 hours, 36% of a certain element remains. If a sample has an initial amount of 100 grams, how many hours will it take until only 1 gram remains? Provide an answer supported by valid mathematical reasoning and/or calculations.
It will take approximately 12.85 hours until only 1 gram of the element remains.
If after 2 hours, 36% of the initial amount remains, then the remaining amount is 0.36 times 100 grams, which is 36 grams. Let's define the amount of the element remaining after time t in hours as R(t). Since the element is decaying exponentially, we can model it with the equation R(t) = 100[tex](0.36)^t[/tex].
We want to find how many hours it will take until only 1 gram remains. We can set R(t) equal to 1 gram and solve for t:
1 = 100[tex](0.36)^t[/tex]
Taking the logarithm of both sides, we get:
ln(1) = ln(100[tex](0.36)^t[/tex])
0 = ln(100) + t*ln(0.36)
t = -ln(100)/ln(0.36)
Using a calculator, we find that t ≈ 12.85 hours.
To learn more about decay click on,
https://brainly.com/question/28334849
#SPJ1
find the taylor polynomial t3(x) for the function f centered at the number a. f(x) = cos(x), a = pi/2
The Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
We get the derivatives :
pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....
f(x) = cos(x)
f'(x) = -sin(x)
f''(x) = -cos(x)
f'''(x) = sin(x)
We the evaluate these derivatives at x = pi/2:
f(pi/2) = cos(pi/2) = 0
f'(pi/2) = -sin(pi/2) = -1
f''(pi/2) = -cos(pi/2) = 0
f'''(pi/2) = sin(pi/2) = 1
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
the Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.
Learn more about Taylor polynomial at:
brainly.com/question/2533683
#SPJ1
What is the equation through the points: (6, 5), (8, -2)
ASAP please
The equation of the line passing through the points (6, 5) and (8, -2) is[tex]y = -\frac{7}{2} x + 26[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values:
m = (-2 - 5) / (8 - 6)
m = -7/2
Using the point-slope form, plug in one of the given points and slope m = -7/2 to find the equation of the line.
Let's use the point (6, 5):
y - y₁ = m(x - x₁)
[tex]y - 5 = -\frac{7}{2}( x - 6 )\\\\y - 5 = -\frac{7}{2} x + 21\\\\y = -\frac{7}{2} x + 21 + 5\\\\y = -\frac{7}{2} x + 26[/tex]
Therefore, the equarion of the line is [tex]y = -\frac{7}{2} x + 26[/tex].
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
