Out of 60 bikes in the repair department, 25 need two repairs and the range of bikes that need both tire and handlebar repairs without needing to fix the seat is 25 out of 60 bikes.
Let's use F, H, and S to represent the events that a bike has a flat tire, bent handlebars, and ripped seat, respectively. Then, we are given:
P(F) = 0.25
P(H) = 0.05
P(S) = 0.10
P(F ∩ H ∩ S) = 1/12
We want to find the number of bikes in the repair department and the number of bikes that need two repairs.
Let N be the total number of bikes in the repair department. Then, the number of repairs needed for each category is:
Flat tires: 0.25N
Bent handlebars: 0.05N
Ripped seats: 0.10N
The number of bikes that need all three repairs is:
P(F ∩ H ∩ S)N = (1/12)N
The number of repairs needed for these bikes is:
3P(F ∩ H ∩ S)N = (1/4)N
The number of repairs needed for bikes that need only two repairs is:
2[P(F ∩ H) + P(F ∩ S) + P(H ∩ S)]N = (5/12)N
The number of repairs needed for bikes that need only one repair is:
[P(F) + P(H) + P(S)]N = 0.4N
The total number of repairs needed is given as 101, so we have:
(1/4)N + (5/12)N + 0.4N = 101
Simplifying this equation gives:
N = 60
Therefore, there are 60 bikes in the repair department.
The number of bikes that need two repairs is:
(5/12)N = 25
Next, we need to find the range of bikes that need both the tires and handlebars repaired without needing to fix the seat. Let's use T and H to represent the events that a bike needs tire and handlebar repairs, respectively. We want to find P(T ∩ H ∩ not S).
We know that P(T ∩ H ∩ S) = P(F ∩ H ∩ S) = 1/12. Also, P(S) = 0.10, so P(not S) = 0.90. Therefore:
P(T ∩ H ∩ not S) = P(T ∩ H) - P(T ∩ H ∩ S)
= 2[P(F ∩ H) + P(F ∩ H ∩ S) + P(H ∩ S)] - P(F ∩ H ∩ S)
= 2(5/12) - 1/12
= 5/12
So, less than half of all the bikes have a ripped seat, and the range of bikes that need both the tires and handlebars repaired without needing to fix the seat is 5/12 of all the bikes, or 25 out of 60 bikes.
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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)
Graph the parabola.
y=x^2-2x+4
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
A graph of the parabola with five points on the parabola is shown below.
What is the vertex form of a quadratic equation?In Mathematics and Geometry, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.For the given quadratic function, we have;
y = x² - 2x + 4
When x = 0, we have:
y(0) = 0² - 2(0) + 4
y(0) = 4
When x = 2, we have:
y(2) = 2² - 2(2) + 4
y(2) = 4
When x = -2, we have:
y(-2) = -2² - 2(-2) + 4
y(-2) = 12
When x = 4, we have:
y(4) = 4² - 2(4) + 4
y(4) = 12
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Please answer correctly and explain reasoning for brainliest (If correct) and thanks!
What are the coordinates of A’?
Check the picture below.
If cosθ=-1/3 and θ is in quadrant III, find the exact values of sinθ,tanθ,secθ,cscθ,and cotθ. You can use the identities or x, y, r.
The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
Given: cosθ = -1/3 and θ is in quadrant III.
This means that sinθ = ± √(1 - (cosθ)2).
We know that cosθ is negative, so sinθ will be negative.
Therefore, sinθ = -√(1 - (-1/3)2 )
sinθ = - √(1 - 1/9)
sinθ = -√8/9
tanθ = sinθ/cosθ
tanθ = (-√8/9)/-1/3
tanθ = √8/3
secθ = 1/cosθ
secθ = 1/-1/3
secθ = -3
cscθ = 1/sinθ
cscθ = 1/-√8/9
cscθ = -√9/8
cotθ = cosθ/sinθ
cotθ = -1/3/-√8/9
cotθ = √9/8
Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
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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].
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For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose the best description of its solution. If the system has exactly one solution, give its solution. (see attached)
The systems of linear equations can be classified as "consistent dependent," "consistent independent," or "inconsistent" as follows:
A. System A = Inconsistent (No solution)
B. System B = Consistent dependent (Indefinitely many solutions)
C. System C = Consistent independent (A unique solution)
How to identify the systems of linear equationsTo identify the systems of linear equations, you first need to note the meaning of the different systems of equations. First, the Consistent dependent has two equations that represent the same line, so they intersect at infinitely many points and any point on the line represents a solution to the system.
Next, the Consistent independent has the two equations represented by two distinct non-parallel lines, so they intersect at exactly one point, which is the unique solution to the system.
Finally, the Inconsistent has two equations that are represented by two distinct parallel lines, so they do not intersect, and there is no solution to the system.
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HELP FASTTTTT PLAZSSSS
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!.
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Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints.
The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100
What is an inequality?The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.
The specified equations obtained from the constraints in slope intercept form are;
y = -0.5·x + 7; The region below the graph is shaded
y = -0.75·x + 9; The region below the graph is shaded
x = 0; The region to the right of the line x = 0 is shaded
y = 0; The region above the line y = 0 is shaded
The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9
Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3
The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)
The value of the function g for each of the feasible region are therefore;
g(0, 0) = 8 × 0 + 12 × 0 = 0
g(0, 7) = 8 × 0 + 12 × 7 = 84
g(8, 3) = 8 × 8 + 12 × 3 = 100
g(12, 0) = 8 × 12 + 12 × 0 = 96
The maximum possible value of g therefore is 100, which is the value at the point (8, 3)Please find attached the graph of the inequalities showing the feasible region created with MS Excel
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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.
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what principal will have majority value of $10,000 at 8.25% p.a in three months?
__________________________________
Simple Interest: A = P × i ÷ 100 × n = 10,000 × 8.25 ÷ 100 × 3= 247.5= 10,000 + 247.5= $10,247.5 Compound Interest: A = P (1 + i ÷ 100) n = 10,000 (1 + 8.25 ÷ 100) ³= $12,684.80The Compound Interest Principal Will Have Majority Value In 3 Months__________________________________
I would be thankful if you help
To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:
[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]
Understanding MatrixThe solution provided above uses a method of matrix called Echelon.
Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.
By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.
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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
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The simplest form of log5+log6-log2
The simplest form of log5+log6-log2 is: log15.
What is the simplest form?Let us simplify log5 + log6 - log2 by making use logarithmic rules:
log a + log b = log (ab)
log a - log b = log (a/b)
So,
log5 + log6 - log2
= log (5 x 6) - log2
= log30 - log2
Now let make use of the logarithmic rule:
log a - log b = log (a/b) = log a - log b
log30 - log2
= log (30/2)
= log15
Therefore the simplest form is log15.
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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
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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
After 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.
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help with this word problem
The height of the school building is approximately 4.38 meters (rounded to the nearest hundredth).
How to calculate the heightJX / BX = JM / BT
Substituting the known values, we get:
(d1 + d2) / h = d1 / (h - 1.75)
(d1 + d2) * (h - 1.75) = d1 * h
d1 * h + d2 * h - 1.75 * d1 - 1.75 * d2 = d1 * h
d2 * h - 1.75 * d1 - 1.75 * d2 = 0
h = (1.75 * d1 + 1.75 * d2) / d2
h = (1.75 * 8.75) / 3.5
h = 4.375
The height of the school building is approximately 4.38 meters
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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 inWhat 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.
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Please see the attached
Please help solve graphs
The graphs are:
1) not one-to-one
2) one-to-one
3) not one-to-one
Are the graphs one-to-one?A graph represents an one-to-one function only if.
We can't draw a vertical line that touches the graph twice or more.
We can't draw an horizontal line that touches the graph twice or more.
For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.
Similarly forthe third graph, the line y = 0 touches two points-
So these two are not one-to-one.,
For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.
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Use the FOIL method to find the product. Express the product in descending powers of the variable.
(7+6x)(1-5x)
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.
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What is the answer?
A) Yes
B) No
Answer:
Step-by-step explanation:
No
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
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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.
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
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.
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)