The probability that they two people are chosen and travel by different transport is 47/144
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability is given as sample space / total outcome
Probability to travel by car p(C)= 5/12
Probability to travel by bus P(B)= 4/12=1/3
Probability to travel by train P(T)= 3/12= 1/4
for two people chosen at random
P(C ×B)= 5/12×1/3= 5/36
P(B×T)= 1/3×1/4= 1/12
P(C×T)= 1/4×5/12= 5/48
Therefore the probability that the two chosen travel by different car is
P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48
= 141/432
divide through by 3
= 47/144
Hence the get the required answer.
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Write a quadratic equation that goes through
the points (1,-3), (2,-5), and (-1,-11).
Answer:
1-3+2-5+-1-11
Step-by-step explanation:
I hope this helps :’)
which expression is equivalent to (2x3 +3x+7) / (x2 + x +10)
The simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.
Let us solve the given algebraic expression by the long division method:
We are given the expression:
(2x^3 + 3x + 7) / (x^2 + x + 10)
We need to perform the division of the given algebraic expression:
x^2 + x + 10 ) 2x^3 + 3x + 7 ( 2x - 2
2x^3 + 2x^2 + 20x
- - -
-2x^2 - 17x + 7
-2x^2 - 2x - 20
+ + +
-15x + 27
So,
quotient = 2x - 2
remainder = -15x + 27
Thus, the simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.
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In 1994, the moose population in a park was
measured to be 3280. By 1997, the
population was measured again to be 4120.
If the population continues to change
linearly:
Find a formula for the moose population, P,
in terms of t, the years since 1990.
P(t)
=
What does your model predict the moose
population to be in 2006?
To answer this question we will use The Linear Programming concept
The formula for the moose population is
The moose population in 2006 would be
We use the year 1990 as the base year for creating the equation of the moose population. We could assume that:
The moose population of the year: P(x)
The moose population in year 1990: a
The year difference to 1990: x
The linear change of the moose population: b
Hence, we could make some assumption about the relationship between each elements mentioned above, where the moose population of the year would be depends on the linear change of the population added into the original moose population in year 1990. We could write this relationship into the equation (i):
P(x) = a + bx ... (i)
Using data provided from the question, we could make some other equations and find the value of b:
P(x) = a + bx
P(4) = a + 4b = 3280 ---> year 1994 ... (ii)
P(7) = a + 7b = 4120 ---> year 1997 ... (iii)
We could do some eliminations between equations (ii) and (iii)
3280 = a + 4b
4120 = a + 7b -
840 = 3b
b = 280 ... (iv)
After finding the value of b, we could subtitute its value into equation (ii) to find the value of a:
3280 = a + 4b
3280 = a + 4(280)
3280 = a + 1120
a = 2160 ... (v)
After finding the value of a and b, we could rewrite the equation (i) by inserting the and b values.
P(x) = a + bx
P(x) = 2160 + 280x ... (vi)
Next, we will predict the moose population to be in 2006.
First, we should determine the value of x, the difference between the year 2006 to the base year 1990.
x = 2006 - 1990
x = 16 ... (vii)
We would subtitute the equation (vii) into equation (vi) to predict the moose population to be in 2006:
P(16) = 2160 + 280(16)
P(16) = 6640...(viii)
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Samantha invested $1000 in an account that pays 5% interest
compounded annually. Assuming no deposits or withdrawals are
made, find how much money Samantha would have in the account 18
years after her initial investment. Round to the nearest tenth (if
necessary).
The amount of money Samantha would have in the account 18 years after her initial investment is $2406.61
The principal amount = $1000
The interest rate = 5%
Time period = 18 years
The interest is compounded annually
The compound interest
A = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Where A is the final amount
P is the principal amount
r is the interest rate
t is the time period
n is the number of times the interest applied
A = [tex]1000(1+0.05)^{18}[/tex]
A = 1000 × 2.40661
Multiply the terms
A = $2406.61
Hence, the amount of money Samantha would have in the account 18 years after her initial investment is $2406.61
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A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If .x machines are made, then the unit cost is given by the function C (x)=0.5x²-320x+68,684. What is the minimum unit cost?
Do not round your answer.
According to the concept of quadratic equation, the minimum cost for the x ray machine is $17, 484
Quadratic equation:
Basically, the polynomial equation with highest degree of two is called a quadratic equation.
The general equation is given by ax² + bx + c = 0, where a ≠ 0.
Given,
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of machines made. If .x machines are made, then the unit cost is given by the function C (x)=0.5x²-320x+68,684.
Here we need to find the minimum unit cost.
Here we know that the standard form of a quadratic is given by:
=> ax² + bx + c
From this function, we have to calculate the value of x as,
=> x = -b/ 2a
While we compare the standard form with the given function,
=> C (x)=0.5x²-320x+68,684.
Then we get the value of
=> a = 0.5
=> b = -320
=> c = 68,684
So, the value of x is calculated as,
=> x = -(-320) / 2(0.5)
=> x = 320 / 1
=> x = 1
Now, we have to plug this value into original function would give us the minimum (unit cost):
=> C(320) = 0.5(320)²- 320 (320) + 68,684.
=> C(320) = 0.5(102400) - 102400 + 68, 684
=> C(320) = 51200 - 102400 + 68684
=> C(320) = 17, 484
Therefore, the minimum unit cost is $17, 484
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Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 30 liters
of 60% acid solution?
Gabe needs ___ of the 40% solution.
He needs 10 litres of solution of 40% and 20 litres of 70% solution to make 30 litres of 60% acid solution.
According to the question,
We have the following information:
Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution.
Now, let's take x litres of 40% solution and y litres of 70% solution.
So, we have the following expressions:
x+y = 30
x = 30-y ....(1)
40x/100 + 70y/100 = 30*60/100
Dividing 100 on the numerator by 100 on denominator:
40x+70y = 1800
Dividing both sides by 10:
4x+7y = 180
Putting the value of x from equation 1:
4(30-y)+7y = 180
120-4y+7y = 180
120+3y = 180
Subtracting 120 from both the sides:
3y = 180-120
3y = 60
y = 60/3
y = 20
Now, putting this value of y in equation 1:
x = 30-y
x = 30-20
x = 10
Hence, he needs 10 litres of 40% solution and 20 litres of 70% solution to make 30 litres of 60% acid solution.
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One batch of pink paint uses 2 cups of red paint and 7 cups of white paint. Mai made a large
Amount of pink paint using 14 cups of red paint.
1. How many batches of pink paint did she make?
2. How many cups of white paint did she use?
Answer:
Mai made 7 batches of pink paint.
Mai used 49 cups of white paint.
Step-by-step explanation:
Part 1. Every 2 cups of red paint are 1 batch of pink paint. This means to find the number of batches of pink paint Mai made, we need to divide 14/2. 14/2 = 7. This means she made 7 batches of pink paint.
Part 2. For every 2 cups of red paint, there are 7 cups of white paint.
For every 1 cup of red paint, there are 3.5 cups of white paint.
This means that we need to multiply 14 x 3.5.
14 x 3.5 = 49.
This means she used 49 cups of white paint.
Ted is a freshman attending a 4-year college. He has been approved for an $8,000 subsidized federal loan at 4.29% for 10 years. How much will the U.S. Department of
Education subsidize in interest costs during his 4.5-year non-payment period?
Answer:
$1544.40
Step-by-step explanation:
You want to know the amount of interest cost subsidized by the Department of Education during the 4.5-year non-payment period on an $8000 subsidized federal loan at 4.29%.
InterestThe interest accrued on the loan amount is found by the simple interest formula:
I = Prt
The principal is $8000, the rate is 4.29%, and the time period is the non-payment period, 4.5 years. The interest is ...
I = $8000·0.0429·4.5 = $1544.40
The DoE will subsidize $1544.40 in interest during the non-payment period.
__
Additional comment
For the purpose of this problem, the 10-year period of the loan is irrelevant, as we're only concerned with the 4.5 year period before repayment starts. Because the loan is subsidized, that interest is never "capitalized" and is not due to be repaid by the borrower.
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Determine whether the following probability is empirical or classical.
Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.
A. Empirical
B. Classical
In this backgammon game, the probability used is Classical one.
Probability:
Probability refer the possible way of happening the particular event.
Given,
Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.
Here we need to identify whether the given probability is empirical or classical.
In order to find the type of probability, first we have to know the definition of each of them.
So, classical probability means the the statistical concept that measures the likelihood (probability) of something happening where as the empirical probability means the probability that is based on historical data.
Therefore, based on the definition, the given situation is purely based on the classical probability.
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Mar. 1) Egert invested $159,000 cash along with $22,300 in office equipment in the company.
The transactions of Egert's Company are entered in the general journal as follows:
General JournalDate Account Titles Debit Credit
Mar. 1 Cash $159,00
Office Equipment $22,300
Common stock $181,300
Mar. 2 Prepaid Rent $1,200
Cash $1,200
Mar. 3 Office equipment $3,300
Office supplies $1,580
Accounts Payable $4,880
Mar. 6 Cash $4,300
Service Revenue $4,300
Mar. 9 Accounts Receivable $7,800
Service Revenue $7,800
Mar. 12 Accounts Payable $4,800
Cash $4,800
Mar. 19 Prepaid Insurance $5,300
Cash $5,300
Mar. 22 Cash $4,700
Accounts Receivable $4,700
Mar. 25 Accounts Receivable $4,200
Service Revenue $4,200
Mar. 29 Dividends $5,400
Cash $5,400
Mar. 30 Office supplies $900
Accounts Payable $900
Mar. 31 Utility expenses $800
Cash $800
What is the general journal?The general journal is the first accounting record of a business transaction.
The general journal identifies the accounts involved in each transaction, specifying which will be debited or credited in the general ledger.
Transaction Analysis:Mar. 1 Cash $159,00 Office Equipment $22,300 Common stock $181,300
Mar. 2 Prepaid Rent $1,200 Cash $1,200
Mar. 3 Office equipment $3,300 Office supplies $1,580 Accounts Payable $4,880
Mar. 6 Cash $4,300 Service Revenue $4,300
Mar. 9 Accounts Receivable $7,800 Service Revenue $7,800
Mar. 12 Accounts Payable $4,800 Cash $4,800
Mar. 19 Prepaid Insurance $5,300 Cash $5,300
Mar. 22 Cash $4,700 Accounts Receivable $4,700
Mar. 25 Accounts Receivable $4,200 Service Revenue $4,200
Mar. 29 Dividends $5,400 Cash $5,400
Mar. 30 Office supplies $900 Accounts Payable $900
Mar. 31 Utility expenses $800 Cash $800
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Question Completion:1 Egert invested $159,00 cash along with $22,300 in office equipment in the company in exchange for common stock. 2 The company prepaid $1,200 cash for six months' rent for an office. The company's policy is to record prepaid expenses in balance sheet accounts. 3 The company made credit purchases of office equipment for $3,300 and office supplies for $1,580. Payment is due within 10 days. 6 The company completed services for a client and immediately received $4,300 cash. 9 The company completed a 7,800 project for a client, who must pay within 30 days. Mar. 12 The company paid $4,800 cash to settle the account payable created on March 3. Mar. 19 The company paid $5,300 cash for the premium on a 12-month insurance policy. The company's policy is to record prepaid expenses in balance sheet accounts. Mar. 22 The company received $4,700 cash as partial payment for the work completed on March 9. Mar. 25 The company completed work for another client for $4,200 on credit. Mar. 29 The company paid $5,400 cash in dividends. Mar. 30 The company purchased $900 of additional office supplies on credit. Mar. 31 The company paid $800 cash for this month's utility bill.
Enter the transactions in the general journal.
What is the sum
5/7 + 1/2 + 3/4
Answer: The sum is 55/28.
Alternate Answer: 1 27/28
Step-by-step explanation:
In this equation, the common denominator between the three fractions would be twenty eight.
5/7 converts to 20/28
1/2 converts to 14/28
3/4 converts to 21/28
After adding all the new fractions together, you get 55/28.
A baker makes 164 cupcakes. To complete an order, he needs 36 more cupcakes. He packs the cupcakes in boxes t
each hold 9 cupcakes. How many boxes will the baker need to pack the whole order?
A) 14 boxes
B) 15 boxes
22 boxes
23 boxes
what is logarithm 4096^x=8
Answer:
Step-by-step explanation:
(4096)ˣ = 8
log ₂ (4096)ˣ = log ₂ 8
x·log ₂ (4096) = log ₂ 8
x = log ₂ 8 / log ₂ (4096)
x = log ₂ 2³ / log ₂ 2¹²
x = 3 / 12
x = 1 / 4
Which graph represents the given equation? A. A parabola declines through (negative 1, 4), (negative 1, 3), (0, 2) and (1 point 5, negative 4 point 5) and rises through (2, negative 4), (3, 0) and (4, 6) on the x y coordinate plane. B. A parabola declines through (negative 4, 5), (negative 3 point 5, 2), (negative 3, 0) and (negative 1 point 5, negative 4 point 5) and rises through (0, negative 2), (1, 3) and (1, 4) on the x y coordinate plane. C. A parabola declines through (negative 2 point 3, 5), (negative 2, 2) and (negative 0 point 5, negative 3 point 1) and rises through (0, negative 2), (1, 4) and (1, 5) on the x y coordinate plane. D. A parabola declines through (negative 1, 5), (negative 0 point 5, 2), (0, negative 2) and (0 point 5, negative 3 point 1) and increases through (2, 2), (2 point 5, 5) on the x y coordinate plane.
The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.
How to obtain the graph of a quadratic function?To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:
The x-intercepts, which are the roots of the function.The y-intercept, which is the value of y when the function crosses the y-axis.The vertex, which is the turning point of the function.The function for this problem is defined as follows:
y = 1.5x² + 4x - 2.
Hence the numeric values of the coefficients are listed as follows:
a = 1.5, b = 4, c = -2.
Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:
x = -3.09 -> hence the function passes through point (-3.09, 0).x = 0.43 -> hence the function passes through point (0.43, 0).The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).
The x-coordinate of the vertex is given as follows:
x = -b/2a = -4/3 = -1.33.
Hence the y-coordinate of the vertex is of:
y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.
Missing InformationThe problem asks for the graph of the following function:
y = 1.5x² + 4x - 2.
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Suppose the probability that it will rain is 3 over 10.
What is the probability that it will not rain?
What are the odds in favor of rain occurring?
Answer: the probability that it will not rain is 70% (you might need to do 7/10)
the odds in favor of the rain occuring is 30% (again, you might need to do 3/10)
Step-by-step explanation:
since the probability that it will rain is 3/10, there is only 7/10 left, so it is more likely to not rain than to rain.
Since it will rain 3/10 times, it is 30% for the second problem
Give me brainliest please!
A regular polygon has 20 sides. If one of its angles measures (5h − 12)°, what is the value of h?
The value of h in the given polygon is 34.8°
What is a regular polygon?A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides or edges of a polygon are made of straight line segments connected end to end to form a closed shape. The point where two line segments meet is called vertex or corners, and subsequently, an angle is formed. If a polygon contains congruent sides, then that is called a regular polygon.
The sum of the interior angles of a regular polygon = (n - 2) x 180
where n = number of sides of the polygon
here n = 20
Sum of the interior angle = (20 - 2) x 180
Sum of the interior angle = 3240°
which also means that 20(5h - 12) = 3240
100h -240 = 3240
100h = 3240+240
100h = 3480
h = 3480/100
h = 34.8°
In conclusion, the value of h = 34.8°
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the distance between two cities is 4 kilometeres. how many meters apart are the two cities
Answer: 4000
Step-by-step explanation: x by 1000
Simplify -1 2/3 minus 9 2/5
Answer:
one ninths
Step-by-step explanation:
1/3-2/9 - fraction calculator. The result is 1/9 ≅ 0.1111111 = one ninth.
Travis had a box of 68 french fries. He gave 13 french fries to each of f friends. Which expression shows how many french fries he had left after giving some to his friends? A. 68 - f × 13 B. (68 + f) × 13 C. 68 + f × 13 D. (68 - f) × 13
The expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f, so option A is correct.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
The total no of french fries = 68,
The no of friends = f,
The no of french fries given to each friend = 13
The equation according to the question is given as,
The french fries left = The total no of french fries - The no of french fries given to each friend × The no of friends
Substitute the values,
The french fries left = 68 - 13 × f
Therefore, the expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f.
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Yearly budget 1200 you spend 350 what percentage is spent
Answer:
29.16% is spent
you have to divide 350 by 1200 then multiply by 100 then the answer will come
Write the polynomial in standard form, name it using the degree and number of terms, identify the constant and the leading coefficient:(3x-8)^2(2x+5)
Answer:
It is a binomial, so it is (ax+b)^2. In this case, a=3, b=-8, and there are 2 terms. The constant is 64 and the leading coefficient is 9.
What's 237 to the square root?
Answer:
heyyy
Step-by-step explanation:
Simplify.
-6√7.4√5
-2√35
24√√35
-24 √√35
The simplified form of the expression is -24√35
Expression
Basically, an expression is the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given,
Here we have the expression -6√7.4√5
Now, we have to simplify the expression.
While we looking into the given expression, we have identified that the expression is in the form of multiplication,
So, the first step in solving the expression is to group the similar element,
So, the grouped form of the expression is,
=> (-6 x 4).(√7 x √5)
Now, we have to perform the multiplication on it, then we get,
=> -24√35
Therefore, the simplified form of the expression is -24√35
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programing problem :
Scenario: The county tax office calculates the annual taxes on property using the following formula:
Property tax = property value × 0.0065
Every day, a clerk in the tax office gets a list of properties and must calculate the tax for each property on the
list. You have been asked to design a program that the clerk can use to perform these calculations.
In your interview with the tax clerk, you learn that each property is assigned a lot number, and all lot numbers
are 1 or greater. You decide to write a loop (while) that uses the number 0 as a sentinel value. During each
loop iteration, the program will ask the clerk to enter either a property’s lot number, or 0 to end.
The program to illustrate the information will be:
This function gets the value of the property from the user,
# calculates the tax, then displays the value of the tax
def show_tax():
# getting the value of the property from the user
property_value = float(input("Enter the property value: "))
# calculating the tax
property_tax = property_value * 0.0065
# displaying the value of the tax
print("Property tax: $ {0:.2f}".format(property_tax))
How to illustrate the information?This program will receive the lot number from the user, while the lot number does not equal 0, then it gets the value of the property from the user, calculates the tax, then displays the value of the tax
The main() function will receive the lot number from the user,
# while the lot number does not equal 0,
# call the show_tax() function then ask for the next lot number.
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what is the derivative of tan(cos(t)) with respect to t at t=pi/2
The derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
What is differentiation?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is tan(cos(t)). The derivation will be done as below,
[tex]\dfrac{d}{dx}tan(cos(t))=sec^2(cos(t)\dfrac{d}{dx}(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(t)sec^2(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(\dfrac{\pi}{2} )sec^2(cos\dfrac{\pi}{2})\\\\\dfrac{d}{dx}tan(cos(t))=sec^2(0)\\\dfrac{d}{dx}tan(cos(t))=1[/tex]
Therefore, the derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
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What equation that line passes through the point P(1/3,4) and has no slope.
The equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.
According to the question,
We have the following information:
Point through which line is passing = (1/3,4)
Slope of the line = 0
We know that the following formula is used to find the equation of the line passing through a point:
y-y' = m(x-x')
We have x' = 1/3 and y' = 4.
y-4 = 0(x-1/3)
y-4 = 0
Adding 4 on both sides of the equation:
y = 4
Hence, the equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.
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I need help
y= 350x + 1.25
Answer: 351.25
Step-by-step explanation:
unless there is more to the question that I am not seeing that is the answer.
Question 3(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O4, 8, 11
O6, 8, 13
O√3, √5, 8
O√3, √13, 4
PLEASE HELP WILL GIVE BRAINLIST
Answer:
ok i got you its two;)
Step-by-step explanation:
Equipment was acquired at the beginning of the year at a cost of $36,000. The equipment was depreciated using the double-declining-balance method based on an estimated useful life of ten years and an estimated residual value of $700.
Question Content Area
a. What was the depreciation for the first year?
fill in the blank
b. Assuming the equipment was sold at the end of year 2 for $8,860, determine the gain or loss on the sale of the equipment.
fill in the blank
The depreciation for the first year is $28,800.
If the equipment is sold for $8,860 at the end of year 2, the loss on the sale is $-14,180.
What is the depreciation in year 1 and the loss on the sale?
Depreciation is the method used in expensing the cost of an asset. The double declining method is an exponential method that is used to expense the cost of an asset.
Depreciation expense using the double declining method = Depreciation factor x cost of the asset
Depreciation factor for the double declining method = 2 x (1/useful life)
Depreciation expense in year 1 = (2 / 10) x $36,000 = $7,200
Book value at the beginning of year 2 = cost of the asset - depreciation in year 1
$36,000 - $7,200 = $28,800
Depreciation in year 2 = (2/10) x $28,800 = $5,760
Book value at the end of year 2 = book value at the end of year 1 - depreciation in year 2
$28,800 - $5,760 = $23,040
Loss = sales price - cost price
Loss = $8,860 - $23,040 = $-14,180
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Factor -4 out of -8+20 expression
Answer: -3
Step-by-step explanation: