Answer: 6.708
Step-by-step explanation:
a(-1,6)
b(5,3)
ab =( (-1-5)^2+(6-3)^2)^(1/2)
ab=(36+9)^(1/2)
ab=6.708
One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded?.
The number of different ways the prizes can be awarded is 161700
How to determine the number of different ways can the prizes be awarded?From the question, we have the following parameters that can be used in our computation:
Total number of people, n = 100Total numbers of winners, r = 3 i.e. the first, the second, the thirdThe number of different ways the prizes can be awarded is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 100 and r = 3
Substitute the known values in the above equation
Total = ¹⁰⁰C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 100!/97!3!
Evaluate
Total = 161700
Hence, the number of ways is 161700
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a hot-air balloon has a 1414-foot diameter that is being deflated at a rate of 0.250.25 feet per minute. how many minutes, xx, will it take before the balloon has shrunk to a diameter of 88 feet?
The amount of time it would take for the balloon's diameter to decrease to 8 feet is 56 minutes.
What is an example of diameter?
If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.
In how long would the diameter have decreased to 8 feet?
A circle's diameter is determined by drawing a line across its center, touching both ends of its circumference.
Minutes are calculated as diameter/decline.
56 minutes from 14/0.25
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suppose that you have 600 feet of rope and want to use it to make a rectangle. what dimensions should you make your rectangle if you want to enclose the maximum possible area?
The dimensions of the rectangle should be 150 feet by 400 feet in order to enclose the maximum possible area.
To explain this step by step:
Step 1: We know that the perimeter of a rectangle is equal to 2*length + 2*width.
Step 2: Since we have 600 feet of rope, we can plug this number into the equation: 2*length + 2*width = 600
Step 3: To solve for the length and width, we can divide both sides by 2: length + width = 300
Step 4: We can then separate the equation into two equations: length = 300 - width and width = 300 - length
Step 5: Since we want to find the maximum possible area, we should set width equal to the larger number, 300, and set length equal to the smaller number, 300 - width.
Step 6: Plugging this into the equation, we get: width = 300 and length = 300 - width = 300 - 300 = 0.
Step 7: Therefore, the maximum possible area that can be enclosed with 600 feet of rope is 150 feet by 400 feet dimensions.
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Math Question Attached
Answer:
D
Step-by-step explanation:
A simpler way to see it, of course, is that the mentioned line segments lie on the same line, so they must have the same slope.
The coupon rate of a bond determines the percentage of interest earned on the bond each year. Samantha purchased a five-year municipal bond for $600. After the bond matured five years later, she had received a total of $720 in principal plus interest payments. What is the coupon rate of Samantha's bond?
4%
5%
10%
12%
20%
The required coupon rate of Samantha's bond is 4%.
Explain coupon rate of bond.The coupon rate is the annual income an investor can expect to receive while holding a particular bond. It is fixed when the bond is issued and is calculated by dividing the sum of the annual coupon payments by the par value. At the time it is purchased, a bond's yield to maturity and its coupon rate are the same.c
According to question:We have,
principal amount = $600
Amount after five year = $720
Interest of five year = $(720 - 600) = $120
Then,
Interest of one year = $120/5 = $24
Now,
Coupon rate = ($24/600)×100 = 4%
Thus, required coupon rate is 4%.
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In a study of helicopter usage and patient survival, among the 56,074 patients transported by helicopter, 235 of themleft the treatment center against medical advice, and the other 55,839 did not leave against medical advice. If 40 of
the subjects transported by helicopter are randomly selected without replacement, what is the probability that none
of them left the treatment center against medical advice?
The probability is
(Round to three decimal places as needed.)
The probability, which is calculated using the hypergeometric distribution, is 0.845, or 84.5%.
Given,
The answer to this question involves using the hypergeometric distribution because the patients are randomly selected from the sample without replenishment.
Hypergeometric distribution:
The probability of x successes is given by:
P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]
The parameters are:
x is the number of successes.
N is the size of the population = 56074
n is the size of the sample = 40
k is the total number of desired outcomes = 235
The number of unique combinations of x objects from a set of n elements is provided by the following formula:
Cₙ,ₓ = n! / x! (n - x)!
The probability that none left against medical advice is P(X = 0), so:
P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]
P(X = 0) = h(0, 56074, 40, 235) = (C₂₃₅, ₀ × C₅₆₀₇₄₋₄₀, ₄₀₋₀) / C₅₆₀₇₄, ₄₀
= (C₂₃₅, ₀ × C₅₅₈₃₉, ₄₀) / C₅₆₀₇₄, ₄₀
= 0.845
The probability is 0.845 = 84.5%.
Therefore,
The probability that none of them left the treatment center against medical advice is 0.845 = 84.5%
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Rewrite 16a4b + 8ab3 using a common factor.
2a4b(8 + 4ab3)
4ab(4a3 + 8ab3)
8ab(2a4b + 8ab3)
8ab(2a3 + b2)
The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.
What is GCF?GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.
The given expression is,
16a⁴b + 8ab³
Simplify the expression, by factor method,
8 x 2 x a x a x a x a x b + 8 x a x b x b x b
The common term is 8ab,
8ab(2a³ + b²)
The required expression is 8ab(2a³ + b²).
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What type of pair of angles are∠2 and angle∠11 ?
The type of pair of angles that are∠2 and angle∠11 is an alternate interior angles.
What is an alternate interior angle?When a transversal intersects two coplanar lines, alternate interior angles are formed. They are on the inside of the parallel lines, but on the outside of the transversal.
Angles with the same size that occur on opposite sides of the transversal line are known as alternate angles. The following alternate angles are equal: By drawing a Z shape, we can frequently identify interior alternate angles: Alternate angles are classified into two types: alternate interior angles and alternate exterior angles.
To understand alternate interior angles, imagine a set of parallel lines and then a line intersecting them. The intersecting line is known as a transversal, and all of the angles formed by the parallel lines are known as interior angles.
Both angles are interior angles that lie alternately to each other on the transversal line r. Therefore, they are alternate interior angle.
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Select the correct answer. What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]? x f(x) -6 2.5 -2 2.5 0 2 2 0 3 5 A. 5 B. 2.5 C. 1 D. 0.5\
The average rate of change of f(x), represented by the table of values, over the interval [-2, 3] is: D. 0.5.
What is an average rate of change?An average rate of change is sometimes referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [-2, 3]:
a = -2; f(a) = 2.5
b = 3; f(b) = 5
Substituting the given parameters into the formula, we have the following;
Average rate of change = (5 - 2.5)/(3 - (-2))
Average rate of change = 2.5/5
Average rate of change = 0.5.
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what is the solution to f(x)=g(x) ? select each correct answer.
The solution to f(x) = g(x) is
x = 0
x = 1
What do you mean by a solution?
We can substitute a value, or values, for a variable (such as x), making the equation true and thus finding a solution. All values of x in the domain, such that f(x) = g, are the solutions if two functions, f, and g, both map to the same co-domain.
as in: x + 2 = 7.
5 + 2 = 7 is what we get when we substitute 5 for x.
Given that 5 + 2 = 7, x = 5 is a solution.
Solution Explained:
A set of values in the table that tell us what the values of each function f(x) and g(x) are for a given value for the variable "x" is already giving us a hint.
We can infer from the table that f(x) decreases when x>0 and moves in the opposite way when x0.
G(x) follows a distinct path; it grows as x increases and shrinks as x lowers.
As a result, there is not much room for equality between the two functions.
You can thus utilize the points shown in the table to begin your test.
f(0)= 0,25 ^ 0=1 since a number raised to 0 is always 0.
g(0)=-0.75 * 0 + 1 = 1
f(1)=0.25^1=0.25 since a number raised to 1 is always equals to itself
g(1)=-0.75*1+1=0.25
So f(x)=g(x), when x=1 and when x=0
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A barn is 100 feet long and 40 feet wide (see figure). A cross section of the roof is the inverted catenary given below. Find the number of square feet of roofing on the barn. (Round your answer to the nearest whole number.)
The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
What is integration?
It is defined as the mathematical approach to calculating the smaller parts or components.
It is given that:
A barn is 100 feet long and 40 feet wide.
Find the first derivative of the given function:
After solving the above integration:
= 20(e - 1/e)
The roofing = 100(20(e - 1/e))
= 4701 square feet
Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
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The wholesale price for a desk is $144 .A certain furniture store marks up the price by 20%.Find the price of the desk in the furniture store. Round the nearest cent,as necessary
The printed price of the desk on the furniture store is $173. It can be solved by the concept of cost price and selling price.
What is cost price and selling price?
Cost price is the price of the object at which it is purchaged and selling price is the price of the object at which it is sold. If cost price is more than the selling price then the seller will earn a loss. If the cost price is less than then the selling price then the seller will earn a profit.
The cost price of the furniture = $144
Now, 20% of cost price is,
[tex]=\$ 144\times\frac{20}{100}\\=\$28.8[/tex]
Now, price of furniture on the store = Cost price + 20% of cost price
= $144 + $28.8
= $172.8$
Round off the price = $173
Hence, the printed price of the desk on the furniture store is $173.
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3x + 2 ≥ 4x + 8 solve and graph the solution to the inequality
answer : x≤-6
steps:
3x+2≥4x+8
-x≥6
x≤-6
Answer:
x≤−6
View graph below
Step-by-step explanation:
x≤−6
Solution Steps
3x+2≥4x+8
Subtract 4x from both sides.
3x+2−4x≥8
Combine 3x and −4x to get −x.
−x+2≥8
Subtract 2 from both sides.
−x≥8−2
Subtract 2 from 8 to get 6.
−x≥6
Divide both sides by −1. Since −1 is negative, the inequality direction is changed.
x≤−6
X could be from -6 to -infinity.
Which of the following is NOT true of the sample variance when the samples are independent and normally distributed?
it decreases as the number of sample values increases it is an unbiased point estimate of the population variance
it has a normal sampling distribution it remains constant as the number of sample values increases
it has a skewed sampling distribution
Option C, which states that the sample variance is constant as the number of sample values rises when the samples are independent and regularly distributed
Each sampling distribution's variability declines as the sample size go up, becoming more and more leptokurtic. The sample distribution's range is less than the original population's range.
The margin of error & sample size has an inverse relationship, meaning that as sample size rises, sampling error falls. It is because the findings would be more accurate the more evidence you had.
The distribution's dispersion is gauged by the standard error. The dispersion decreases as the sample size increases and the distribution's mean moves closer to the population mean.
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assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of 9.6. if 144 people are randomly selected, find the probability that their mean blood pressure will be less than 125.
The probability that the mean blood pressure will be less than 125 is 0.9938
The mean of the pressure readings = 123
The standard deviation = 9.6
Total population = 144
The value is less than 125
The equation of the z-score is
z-score = (Observed value - Mean ) / (Standard deviation /[tex]\sqrt{N}[/tex])
Substitute the values in the equation
z-score = (125 - 123) / (9.6/[tex]\sqrt{144}[/tex])
= 2 / (9.6/12)
= 2 / 0.8
= 2.5
Using the statistical table
The probability of that their mean blood pressure less than 125
P(z < 2.5) = 0.9938
Therefore, the probability is 0.9938
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Use the theorem in Sec. 77, involving a single residue, to evaluate the integral of f (z) around the positively oriented circle |z| 3 when intergral c f(z) dz, f(z) = (z^3(1-3z))/(1+z) (1+2z^4)
The integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi times the sum of the residues of the poles of f (z) inside the circle.
The poles of f (z) inside the circle are z = 0 and z = −1/2.
The residue at z = 0 is f (0) = 0.
The residue at z = −1/2 is f (−1/2) = −7/16.
Therefore, the integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi (−7/16) = −7πi/8.
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When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 55 days by 15 workers. How many days would it take to build a similar house with 33 workers?
Answer: 25 days
Step-by-step explanation:
We know that it takes 55 days with 15 workers, so we need to find how many days it takes with 1 worker by taking 55 timed 15 = 825 days for 1 worker.
Then we take 825 divided by 33 and get 25 days for 33 workers.
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Solve the system by graphing and identify and state the number of solutions y=-x+1. Y=1/3x-3
By graphing the system of equations, we will see that the solution is x = 3 and y = -2
How to solve the system of equations graphically?
Here we have te following system of equations:
y = -x + 1
y = (1/3)*x - 3
To solve the system we can graph bot equation in the same coordinate axis and try to identify the intersection points between the graphs.
Below you can see the graph
We can see that the interception point is (3, - 2), then the solution to the system of equations is x = 3 and y = -2.
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list three ways a rectangle and a square are different
Answer:
one way is that they both have four sides.
another way is that they both have straight lines.
and the other way is that they both have 4 corners.
Step-by-step explanation:
Answer:
According to the web: "A square has four equal sides. In a rectangle, the opposite sides are equal. The diagonals of a square bisect each other at 90°. The diagonals of a rectangle bisect each other at different angles."
Step-by-step explanation:
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
A team of A4 paper contain 500 heet. The ize of each paper i 297mm long and 210mm wide. The volume of the team i 37422cm cube. Find the thickne of each heet of paper,leaving your anwer in cm
Using the conversion factor, we can say that each sheet of paper is 0.0012mm thick.
What is the conversion factor?A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.
The amount is often expressed as a fraction or ratio with a multiplication factor.
So, 500 sheets of A4 paper make up a conventional ream. Each paper measures 297mm in length by 210mm broad, and one ream contains 3742.2cm of paper.
to change cm to mm
3742.2cm = 37422 mm
Sheet 1's surface
(297mm) X 210mm) = 62370mm²
1st volume sheet:
37422mm : 500 = 74.844mm
One sheet's thickness is:
74.844mm : 62370mm = 0.0012mm
Therefore, each sheet of paper is 0.0012mm thick.
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Correct question:
A ream of A4 paper contains 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm find the thickness of each sheet of paper answer in millimeters
The variables a and b are proportional. When a=12 we
know b=3. What is the value of a when b=5?
O 17
9
20
O 14
Answer:
b = 20
Step-by-step explanation:
the variables a and b are proportional , so the equation relating them is
a = kb ← k is the constant of proportion
to find k use the condition a = 12 , b = 3
12 = 3k ( divide both sides by 3 )
4 = k
a = 4b ← equation of proportion
when b = 5 , then
a = 4 × 5 = 20
A hot chocolate recipe calls for 2/3 cup of milk.Slade wants to make 1/2 of the recipe.How much milk should Slade use?
Answer: Slade should use 1/3 cup of milk
Step-by-step explanation:
2/3 divided by 1/2 = 1/3
In other words, if you have 2 of something and you give someone half, you would give them 1.
On a map of a park three inches represents twenty feet, how many inches would represent 12 feet?
Answer:
1.8 inches
Step-by-step explanation:
Terry has a goal of making $300 in commission for the week if her commission is based on 18% of sales how much does she need to sell to make her goal
The amount of sales Terry must make is $1667
How to determine the amount in sales?
From the question, we have the following parameters that can be used in our computation:
Commission = 18% of sales
Commission = $300
These parameters mean that
Commission = 18% of sales
Substitute the known values in the above equation, so, we have the following representation
18% of sales = 300
Divide both sides by 18%
Sales = 1667
Hence, the amount is $1667
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Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2x
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A tax of 5% is applied to the bill.
Zoe decides to leave a tip of 15% on the entire bill (including the tax).
let the bill cost $x.
So, the price after tax and tip
= x+ 5% of x+ 15% of x
= x + 0.05x + 0.15x
= x + 0.20x
= 1.2x
Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x
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Solve for x.
y=69
5x+15=y+2x-5
The solution of x in the equation is 79/3
How to determine the solution of x?From the question, we have the following parameters that can be used in our computation:
y = 69
5x + 15 = y + 2x - 5
Substitute y = 69 in the equation 5x + 15 = y + 2x - 5
So, we have
5x + 15 = 69 + 2x - 5
Collect the like terms
This gives
5x - 2x =69 - 5 + 15
Evaluate the like terms
This gives
3x = 79
Divide both sides by 3
x = 79/3
Hence, the solution is 79/3
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For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: f (x) = negative 9 x squared + 7 x Table A a b c up or down y-intercept -9 -7 0 down (0,0) Table B a b c up or down y-intercept 2 7 0 down (0,0) Table C a b c up or down y-intercept 9 7 0 down (0,0) Table D a b c up or down y-intercept -9 7 0 down (0,0) a. Table A c. Table C b. Table B d. Table D
Examining the function -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0
How to find the y interceptsWhere a parabolic curve opens up or down in this case depends on the sign on the coefficient of the x².
The coefficient of x² is a and in this function is -9
A negative coefficient leads to opening downwards while a positive coefficient will result to opening upwards
The y intercept
-9x² + 7x = 0
x(-9x + 7) = 0
x = 0
-9x + 7 = 0
-9x = -7
x = 7/9
the y intercept is 0 ad 7/9
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The dinner bill came to $72.48 and Julio tipped the waiter 15%. What is the total price of dinner?
Answer: $83.35
Step-by-step explanation:
Find 15% of 72.48 = 10.87
10.87 + 72.48 = 83.35
You go to a store that is offering a 20% discount for students! You
decide to buy a book for $15.40. You also have a coupon for $5 off after
the discounted price. What is the cost of the book after the discount and
coupon?
The cost of the book after the discount and coupon is $7.32
How to determine the cost of the book?From the question, we have the following parameters that can be used in our computation:
Amount = $15.40
Coupon = $5 offer
Discount = 20% off
This means that
Total amount = Amount * (1 - Discount) - Coupon
So, we have
Total amount = 15.40 * (1 - 20%) - 5
Evaluate
Total amount = 7.32
Hence, the total amount = 7.32
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What is the slope of a line parallel to a line whose equation is 10x+12y=-120
The slope of a line parallel to the line having equation 10x+12y=-120 is -5/6.
What is the slope of a line parallel to another line?
Parallel lines are coplanar and they never intersect.
Slope is a measure of the angle of a line from the horizontal.
Since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.
According to the given question:
Given equation of line is 10x+12y=-120
Converting this to slope-intercept form we get
y = -5/6 x + 10
Clearly slope of this line is -5/6
Any line parallel to this line will have the same slope
Therefore the slope of a line parallel to the given line is -5/6
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