The distance between (-3 , -3) and (2 , 9) is 13cm The midpoint of the line segment joining (-3 , -3 )and (2 , 9) is
(-1/2 , 3)
Explanation:Given two points, (-3 , -3) and (2 , 9).
to find the distance between two points,
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
by substituting the values,
d = [tex]\sqrt{(2 - (-3))^{2} + (9-(-3))^{2} }[/tex]
d = [tex]\sqrt{5^{2} + 12^{2} }[/tex]
d = [tex]\sqrt{25 + 144}[/tex]
= [tex]\sqrt{169}[/tex]
= 13 cm
distance between (-3,-3) and (2,9) = 13 cm
to find the midpoint,
midpoint = (x₁ + x₂)/2, (y₁ + y₂)/2
= ((-3 + 2)/2 , (-3 + 9)/2 )
= ((-1 /2) , (6/2))
= (-1/2 , 3)
so the midpoint between (-3 , -3) and (2 , 9) is (-1/2 , 3).
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what is 0.5 percent of 3.2
Answer:
0.016
Step-by-step explanation:
Remember that "of" means to multiply and percent (%) means out of 100. So we would multiply 3.2 by 0.5 and get 1.6 then you move the decimal 2 times to the right and get 0.016. Have a Great Day! ;)
Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.For her parents' anniversary party, Laura is considering using one of two venues. A hotel in Dayton will cost $693 for a reservation, plus $51 per person. A restaurant in the same city will cost $60 per person, in addition to $684 for the reservation. In order to make the best decision. Laura figures out how many attendees it would take to have the venues cost thesame amount. How many attendees would that be? What would the total cost be?
Answer:
• The number of attendees = 1
,• Total Cost = $744
Explanation:
Let the number of attendees = n
A hotel in Dayton will cost $693 for a reservation, plus $51 per person.
[tex]\text{ Hotel's Cost, H\lparen n\rparen}=693+51n\cdots(1)[/tex]A restaurant will cost $60 per person, in addition to $684 for the reservation.
[tex]\text{ Restaurant's Cost, R\lparen n\rparen}=684+60n\cdots(2)[/tex]We want to find the number of attendees(n) at which the venues cost the same amount.
Equate the cost equations (1) and (2) above:
[tex]693+51n=684+60n[/tex]Solve the equation for n:
[tex]\begin{gathered} \text{Subtract 51n from both sides of the equation.} \\ 693+51n-51n=684+60n-51n \\ 693=684+9n \\ \text{Subtract 684 from both s}\imaginaryI\text{des of the equat}\imaginaryI\text{on} \\ 693-684=684-684+9n \\ 9=9n \\ \text{ Divide both sides by 9} \\ \frac{9}{9}=\frac{9n}{9} \\ n=1 \end{gathered}[/tex]The number of attendees it would take for the cost to be the same amount is 1.
We determine the total cost using any of the equations:
[tex]\begin{gathered} \begin{equation*} 693+51n\cdots(1) \end{equation*} \\ Total\text{ Cost}=693+51(1)=\$744 \end{gathered}[/tex]The total cost will be $744.
Hans paid $37.51 Employment Insurance (El) on his monthly income of $2168.21.
What was the El rate?
The EI rate is 17.3%
How to calculate the EI rate ?The first step is to write out the parameters given in the question
Hans employment insurance is $37.51
Hans monthly income is $2168.21
The EI rate can calculated as follows
37.51/2168.21 × 100
= 0.0173 × 100
= 17.3%
Hence the EI rate is 17.3 %
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Hey can anyone pls answer these problems!!! find the area and perimeter pls show work
The areas of each figure are listed below:
Case 2 - Triangle: 20 in²
Case 3 - Composite figure: 72 ft²
Case 4 - Parallelogram: 45
Case 5 - Rhombus: 39 m²
Case 6 - Composite figure: 94 cm²
Case 9 - Composite figure: 101 m²
How to calculate the areas of triangles, quadrilaterals and composite figures
In this problems we must calculate the areas of triangles, quadrilaterals and composite figures formed by triangles and quadrilaterals. Now we proceed to present the areas for each case:
Case 2
The area of the triangle is the sum of the areas of the two right triangles:
A = (1 / 2) · (3 in) · (4 in) + (1 / 2) · (7 in) · (4 in)
A = 6 in² + 14 in²
A = 20 in²
Case 3
The area of the composite figure is the sum of the areas of the rectangle and two right triangles:
A = (1 / 2) · (6 ft) · (6 ft) + (8 ft) · (6 ft) + (1 / 2) · (2 ft) · (6 ft)
A = 18 ft² + 48 ft² + 6 ft²
A = 72 ft²
Case 4
The area of the parallelogram is the product of the length of its base and the length of its height:
A = b · h
A = 9 · 5
A = 45
Case 5
The area of the irregular rhombus is equal to the sum of the areas of the four triangles:
A = 2 · (1 / 2) · (4 m) · (3 m) + 2 · (1 / 2) · (3 m) · (9 m)
A = 12 m² + 27 m²
A = 39 m²
Case 6
The area of the composite figure is the sum of the areas of the three rectangles:
A = (10 cm) · (5 cm) + (8 cm) · (4 cm) + (4 cm) · (3 cm)
A = 50 cm² + 32 cm² + 12 cm²
A = 94 cm²
Case 9
The area of the composite figure is the sum of the areas of a right triangle and two rectangles:
A = (1 / 2) · (3 m) · (10 m) + (3 m) · (10 m) + (8 m) · (7 m)
A = 15 m² + 30 m² + 56 m²
A = 101 m²
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EspooThe orde graph shows how a family spends its annual Income. If $71,050 is used for Auto, Food, and clothing combined, what is the total annual income?HousingSavingFood1996Insurance$IDх$?entertainment14%Clothing17会Ayte
we know that
Auto ----> 13%
Food ----> 19%
Clothing ----> 17%
13%+19%+17%=49%
$71,050 ------> represents 49%
Applying proportion, find out how much represents 100%
71,050/49=x/100
solve for x
x=(71,050/49)*100
x=145,000
therefore
The answer is $145,000help meeeeeeeeeeeeeeeeeeeeeee
thank you
The function notation f(-5) has a value of -6
How to solve the function?From the question, we have the function definition to be f(-5)
Also, we have the graphs to be f(x) and g(x)
The equation of the first graph is illustrated by the blue curve f(x), while the second is illustrated by the red curve
Because the function is f(x), we make use the blue curve
On the blue curve, we have
f(-5) = -6
The interpretation of the above equation is that
When x = -5, the blue curve has a value of -6
This means that the function f(-5) has a value of -6
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PLS HELP FAST!! Question due in 5 minutes!!!
Answer:
hypotenuse 3 leg 1 =1 leg2=
The graph shows the earnings of two employees working at the same company both earn money at constant rates please help me figure out which table the unit rate that matches each graph thank you so much
On the first graph, when x moves 1 unit, that is, from x = 2 to x = 3, the change in y is
[tex]\begin{gathered} \Delta y=y_2-y_1 \\ =87-58 \\ =29 \end{gathered}[/tex]Unit rate of the first graph is $29 per hour.
On the second graph, when x moves 1 unit, that is, from x = 0 to x = 1, the change in y is
[tex]\begin{gathered} \Delta y=y_2-y_1 \\ =22-0 \\ =22 \end{gathered}[/tex]Unit rate of the second graph is $22 per hour.
I attached a picture with a practice problem from my prep guide, it has 5 questions that are included with the problem. You will find that below. I am having trouble doing this, and need help,Please note that this is complex and lengthy. 1. What is the balance of Albert’s $2000 after 10 years?2. What is the balance of Marie’s $2000 after 10 years??3. What is the balance of Han’s $2000 after 10 years??4. What is the balance of Max’s $2000 after 10 years?? Lastly, 5. Who is $10,000 richer at the end of this competition?
This is a question on present and
We are required to find out how much the future sums of the $2000 handed to them will amount to. This will test our knowledge on simple and compound interest.
Our approach is to take each one's case and analyse the appreciation or depreciation of the sums assigned using the appropriate formulae.
The compound interest formula goes thus:
[tex]F=P(1+\frac{i}{m})nm[/tex]Where:
F = future sum
P = Present sum / Principal
i = interest rate
n = no. of years
m = number of compounding periods in a year.
The simple interest rate formula goes thus:
[tex]F=Pi\text{n}[/tex]Albert:
Firstly, he had $1000 compounded monthly by 1.2%
[tex]\begin{gathered} F=1000(1+\frac{0.012}{12})^{10\times12} \\ F=\text{ \$1,127.43} \end{gathered}[/tex]He lost 2% of $500 over the course of the 10 years.
[tex]F=500(100\text{ \% - }2\text{ \%) = 500(0.98)= \$490}[/tex]Firstly, he had $500 compounded monthly by 0.8%
[tex]F=500(1+\frac{0.008}{1})^{10}=541.47[/tex]Total sum he gained over the course of the 10 years:
[tex]1127.43+490+541.47\text{ = \$2,158.90}[/tex]Marie:
Firstly, she had $1500 compounded quarterly by 1.4%
[tex]\begin{gathered} F=1500(1+\frac{0.014}{4})^{10\times4} \\ F=\text{ \$1,724}.99 \end{gathered}[/tex]She lost $500 by 4% over the course of the 10 years.
[tex]F=500(100\text{ \% + 4 \%) = 500(1.04)= \$}520[/tex]Total sum gained by Marie over the course of the 10 years:
[tex]\text{ \$1724.99 + \$520 = \$2,244.99}[/tex]Hans
He had $2000 compounded annually by 0.9%
[tex]\begin{gathered} F=2000(1+\frac{0.009}{1})^{10} \\ F=\text{ \$}2187.47 \end{gathered}[/tex]Total sum gained by Hans over the course of the 10 years:
[tex]\text{ \$2187.47}[/tex]Max:
$1000 decreased in value exponentially at a rate of 0.5% annually.
[tex]1000(1-\frac{0.005}{1})^{10}=\text{ \$951.11}[/tex]He had $1000 compounded biannually by 1.8%
[tex]\begin{gathered} F=1000(1+\frac{0.018}{2})^{10\times2} \\ F=\text{ \$}1196.25 \end{gathered}[/tex]Total sum gained by Max over the course of the 10 years:
[tex]\text{ \$9}51.11+\text{ \$1196.25=\$2,147.36}[/tex]
How do we solve the circumference of a semi-circle?
Answer:
[tex]C\text{ = }\pi r[/tex]Explanation:
Formula for calculating the circumference of a circle is expressed as;
[tex]C\text{ = 2}\pi r[/tex]r is the radius
Since a semi-circle is half of a circle, then the circumference will be half of cirumference of a circle as shown;
[tex]\begin{gathered} C\text{ = }\frac{2\pi r}{2} \\ C\text{ = }\pi r \end{gathered}[/tex]This gives the circumference of s semicircle where r is the radius of the semi circle
Can someone help me with this geometry question? I am pretty sure it’s 67
Solution
Step 1:
The angle at the center is twice the angle at the circumference.
Step 2:
[tex]\begin{gathered} m\angle PMN\text{ = 134} \\ m\angle PON\text{ = ?} \\ m\angle PMN\text{ = 2m}\angle PON \\ 134\text{ = 2m}\angle PON \\ m\angle PON\text{ = }\frac{134}{2} \\ m\angle PON\text{ = 67} \end{gathered}[/tex]Answer
m
The rabbit population in Logan County, which is currently at 6,516 rabbits, is increasing by 15% each year. How many rabbits will there be in 7 years?If necessary, round your answer to the nearest whole number.
Given data;
The current rabbit population in the Logan country = 6516.
the increse in the population each year = 15 %.
to find the population of rabbit after 7 years.
so, 15 % of 6516 is,
use the formula,
[tex]\begin{gathered} A=p_0(1+\frac{1}{n})^{nt}_{} \\ \end{gathered}[/tex][tex]\begin{gathered} p(t)=6516(1+\frac{0.15}{1})^t \\ p(t)=6516(1.15)^t \\ p(7)=6516(1.15)^7 \\ p\mleft(t\mright)=6516\mleft(2.66\mright) \\ =17332.68 \end{gathered}[/tex]there will be 17333 rabbits will there be in 7 years
Thus, the answer is 17333.
A twelve-foot ladder is leaning against a wall. If the ladder reaches 8 ft. high on the wall, what is the angle the ladder forms with the ground to the nearest degrees?
Solution
Recall: SOHCAHTOA
[tex]\begin{gathered} sin\theta=\frac{8}{12} \\ \\ \theta=sin^{-1}0.6667 \\ \theta=41.81^0 \\ \end{gathered}[/tex]The final answer
[tex]\theta=42^0[/tex]Determine a series of transformations that would map Figure F onto Figure G. 12 11 10 9 8 Figure G7 6 4 3 1 2 3 4 5 6 7 8 9 10 11 12 -12-11-10-9-8-7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -6 N . Figure F -8
To find the series of transformations that would map Figure F onto Figure G
We will choose one side to figure out the transformations
So, Look at the vertical side of the figure F which has the end points (1 , -3) and (1 , -5)
The image of this side will be the horizontal side of figure G with the end points ( -3 , 1 ) and (-5,1)
so, we need to rotate it
So, the series of transformation will be :
Reflection
To find the rule of reflection
Note ( 1 , -3 ) → (-3 , 1)
this mean ( x , y ) → (y,x)
Which mean reflection over y = x
The same can obtained by translation 2 units up then rtation 90 clockwise
Help me out please please help me please put
Answer: X=2 X=-7
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
At an important meet, rosalba won the 200 meters in 26.39 seconds. Rosalba ran at an average rate of?
We have to find the average rate of meters per second (also known as average speed).
We can calculate it as the quotient between the distance and the time:
[tex]v=\frac{d}{t}=\frac{200\text{ m}}{26.39\text{ s}}\approx7.58\text{ m\textbackslash s}[/tex]Answer: the average rate is approximately 7.58 m/s.
A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words.
The random variable X is the ounces of water in the bottle.
What is a random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a sample space of potential outcomes to a measured space, frequently the real numbers.
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable is a numerical representation of the result of an experiment in statistics. Discrete random variables are those that can only take on a finite number or an infinite series of values.
According to the provided information, it is known that a bottle of water contains 12.05 fluid ounces; hence it is clear that the random variable X will be the ounces of water.
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Nikhil sells digital cameras. He bought a DSLR camera for 24,000. He sold the camera for
€25,500.
What is Nikhil's profit per 100?
Answer:
He makes €100,000
Step-by-step explanation:
First, subtract 25,000- 24,000= 1000
Then, multiply 1000*100
€100,000 is how much he makes
If a car travels for 0 hours, it will travel
0 mile(s). This means it will pass through the point
0. Use the slope to move 3 units to the right of the origin and
enter your response here unit(s) up to find the point
enter your response here that can be used to graph the relationship.
just need to solve bottom part i already did the top
The correct statement will be;
⇒ If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0, 0). Use the slope to move 3 units to the right of the origin and 3 units up to find the point (3, 3) that can be used to graph the relationship.
What is Equation of line?
The equation of line with slope m and passes through the point
(x₁, y₁) defined as;
⇒ y - y₁ = m (x - x₁).
Given that;
The relation between the distance and time is shown in graph.
Now,
When we move 3 units to the right then, the graph is meet at point 3 up to, for the distance and time.
This point is meet at point (3, 3).
Thus, The correct statement will be;
⇒ If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0, 0). Use the slope to move 3 units to the right of the origin and 3 units up to find the point (3, 3) that can be used to graph the relationship.
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For her phone service, Ashley pays a monthly fee of $19, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is$72.15.What are the possible numbers of minutes she has used her phone in a month?Use m for the number of minutes, and solve your inequality for m.
Given:
Ashley pays a monthly fee of $19, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is $72.15.
Required:
Find the possible numbers of minutes she has used her phone in a month.
Use m for the number of minutes, and solve your inequality for m.
Explanation:
The initial amount paid by Ashley = $19
The additional amount per minute = $0.05
Let the number of minutes used in the phone = m
The least amount that is charged in a month = $72.15
Now by using the given information
[tex]19+0.05m\ge72.15[/tex]Solve for m as:
[tex]\begin{gathered} 0.05m\ge72.15-19 \\ 0.05m\ge53.15 \\ m\ge\frac{53.15}{0.05} \\ m\ge1063 \end{gathered}[/tex]Thus at least 1063 minutes were used on Ashley's phone in a month.
Final Answer:
The least possible minutes are 1063.
write the following equation in a function form.3x+4y=0
You have the following equation:
[tex]3x+4y=0[/tex]To write the previous equation in a function form consists in solving for y, just as follow:
3x + 4y = 0 subtract 3x both sides
4y = -3x divide by 4 both sides
y = -3/4 x
Hence, the function for of the given equation is:
y = -3/4 x
which is the best estimate of the amount of interest you will save if if you take the 5% of loan instead of the 6% loan?
For the 5% loan, you will pay a total of:
[tex]219\cdot25=5475[/tex]For the 6% loan, you will pay a total of:
[tex]221\cdot25=5525[/tex]if if you take the 5% of loan instead of the 6% loan you will save:
[tex]5525-5475=50[/tex]Answer:
$50
Please help me graph and answer this question
The graph of the inequality is attached below
Graph of InequalityTo solve this problem, we need to solve the inequality and then plot the graph on a number line.
What is Inequality?
inequality, In mathematics, is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions
Applying absolute rule;
[tex]-4\leq x-2\leq 4\\x - 3\geq -4 and x - 2 \leq 4\\x - 2 \leq 4; \\x \leq 6\\x \geq -2[/tex]
Combining the overlapping intervals;
[tex]-2\leq x\leq 6[/tex]
Kindly find the attached image as the graph on a number line below.
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The rectangle below has an area of x^2-15x+56x
2
−15x+56x, squared, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters.
What expression represents the width of the rectangle?
The rectangle below has an area of x²-15x+56. (x-7) and are the binomials (x-8). Given that the length is (x-7) and the width is, respectively (x-8).
Given that,
The rectangle below has an area of x²-15x+56.
We have to find the width of the rectangle.
A quadrilateral (4-sided polygon) with two sets of parallel and equal sides called length and width is what is meant by the term "rectangle." The sum of these two is equal to the area of a rectangle. A quadratic equation represents the area. When a quadratic equation is factored, the result is a product of two binomials, such as (x-q)(x-r) = 0, where q and r are the equation's roots or zeros. Making use of the quadratic formula, you may determine this:
x=[tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Here, a is 1 b is -15 and c is 56.
x=[tex]\frac{-15\pm\sqrt{15^{2}-4(1)(56) } }{2(1)}[/tex]
x=[tex]\frac{-15\pm\sqrt{225-224 } }{2}[/tex]
x=[tex]\frac{-15\pm\sqrt{1} }{2}[/tex]
[tex]x=\frac{-15\pm1 }{2}[/tex]
Take the plus 1st
x=-15+1/2
x=-14/2
x=-7
Now take minus
x=-15-1/2
x=-16/2
x=-8
Therefore, (x-7) and are the binomials (x-8). Given that the length is (x-7) and the width is, respectively (x-8).
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Given the figure below, find the values of x and z.
95°
z°
(6x-23)
Answer: z=95 and x=18
Step-by-step explanation: the lines are both straight and the whole 6x blahb blah blah is not needed since the line is 180 degrees and 180-95=85 so 6x-23=85 which x=18 and it also has to be 95 so z=95
i need to know minor arc, chord, tangent line, central angle, secant line, major arc, radius, and inscribed angle
Based on your picture, we can say the following:
- Minor arc: The curve between points B and E
- Chord: AB
- Tangent line: The line which goes through points DE
- Central angle: ECB
- Secant line: The line which goes through points AE
- Major arc: The curve between points B and B going through A
- Radius: CE and CB
- Inscribed angle: EAB
two sets of 5 different numbers that have the same standard deviation but different mean
The sets of 5 different numbers with same standard deviation but different mean are {2,4,6,8,10} and {20,22,24,26,28}.
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values.
Values having a low standard deviation are more likely to be within a narrow range of the mean (also known as the anticipated value) of the collection than values with a high standard deviation.The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is equal to the square root of that variable's variance. It is more algebraically straightforward than the average absolute deviation, but being less reliable in practice. The standard deviation is a useful statistic because, unlike the variance, it is expressed in the same unit as the data.Let us consider two data sets :{2,4,6,8,10} and {20,22,24,26,28}
Now for the first set:{2,4,6,8,10}
Mean = (2+4+6+8+10)÷5 = 30÷5 = 6
Standard deviation = 3.16
Now for the second set:{20,22,24,26,28}
Mean = (22+24+26+28+20)÷5 = 120÷5 = 24
Standard deviation = 3.16
Therefore these two data sets have same standard deviation but different mean.
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if i walked to my parents house for Thanksgiving and lived 25.6 miles away, and it took me 4 hrs to get there is it true tht my constant speed would be 4.6 mph?
Distance walked over time
25.6 miles away, are going to walk
lets find if
25.6/ 4 = 4.6?
Then 25.6 = 24 + 1.6 =
so. 25.6/4= 24/4 + 1.6/4 = 6 + 0.4 = 6.4
So its NOT TRUE that constant speed is 4.6 mph
If we graph the terms of a factored form of a quadratic equation individually, what type of graphs do you get?
The factored form of function does not affect the trajectory of the graph.
Given that,
If we graph the terms of a factored form of a quadratic equation individually, what type of graphs do you get is to be discussed?
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
here,
The graph of a quadratic equation is a parabolic structure, when structuring the graph of the factor of the quadratic function it outcome same as the graph of the quadratic function itself.
Thus, the factored form of function does not affect the trajectory of the graph.
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4. What is the discount and special sale price of a pair of shoes regularly priced $120 when the store has a 33% off sale /(round to the nearest dollar)? 5.a retailer purchase a $3 toy in as a markup rate of 150%. determine the markup and the regular retail price of the toy. 6. Jody received a 30% Commission on the profit when he sells over 20 cars in a month . if he sold 23 cars in October, resulting in $15000 profit for the dealership , how much did Joe earn in commission ?7.how much would be in an account when you turn 18 if, on the day you were born, 1000 were disposed into the account which returned 6% simple interest, and no longer disposes or withdrawals were made ?
Let's begin by identifying key information given to us:
Shoe Price = $120
Discount rate = 33% = 0.33
The Discount price of the shoe is calculated below:
[tex]\begin{gathered} DiscountPrice=ShoePrice-(ShoePrice\cdot DiscountRate) \\ DiscountPrice=120-\lbrack120\cdot(0.33)\rbrack=120-39.6 \\ DiscountPrice=80.40 \end{gathered}[/tex]Therefore, the discount price is $80.40
