the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
Why it is and how to form a graph?
To find the month with the lowest amount of precipitation, we need to find the minimum value of the quadratic equation y = –0.04088x²2 + 0.4485x + 1.862.
Using calculus, we can find the minimum point of the quadratic function by taking its derivative and setting it equal to zero:
y' = -0.08176x + 0.4485
0 = -0.08176x + 0.4485
x = 5.484
This means that the minimum value of the function occurs at x = 5.484. Since x represents the month number (with January being 1), we can conclude that the month with the lowest amount of precipitation is February (the second month in the table).
To verify this, we can plug in x = 2 into the quadratic equation:
y = –0.04088(2)²2 + 0.4485(2) + 1.862
y = 2.31752
Therefore, the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
To graph the function, we can plot the points given in the table and connect them with a smooth curve. Here is a completed table with the missing values:
Month (x) Precipitation
January 1 2.27 inches
February 2 2.32 inches
March 3 2.57 inches
April 4 2.94 inches
May 5 3.43 inches
June 6 3.94 inches
July 7 2.72 inches
August 8 2.86 inches
September 9 2.59 inches
October 10 2.03 inches
November 11 1.46 inches
December 12 1.03 inches
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Answer:
D: December
The given model for precipitation in Phoenix, Arizona is y = –0.04088x2 + 0.4485x + 1.862, where x is the month number (1 for January, 2 for February, and so on) and y is the precipitation in inches. We can use this model to fill in the missing values in the table:
| Month (x) | Precipitation |
|-----------|---------------|
| January | 2.27 inches |
| February | 2.27 inches |
| March | 2.24 inches |
| April | 2.18 inches |
| May | 2.09 inches |
| June | 1.98 inches |
| July | 1.84 inches |
| August | 1.68 inches |
| September | 2.59 inches |
| October | 1.50 inches |
| November | 1.30 inches |
| December | 1.08 inches |
According to the table, Phoenix received the lowest amount of precipitation in **December** with **1.08 inches** of precipitation, so the correct answer is **D. December**.
Find the circumference of a circle with diameter, d = 1.26m.
Give your answer rounded to 2 DP
Answer: b
Step-by-step explanation: just took it on edge.
Write a quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0)
A quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0) is equals to the f(x) = (1/3)( x² + 10x + 16).
A quadratic function is a polynomial function with one or more variables, the highest degree of the variable is two. It is also called the polynomial of degree 2. The form of quadratic function is
f(x) = ax² + bx + c ----(1)
is determined by three points and must be a≠ 0. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs (-8,0), (-5,-3), and (-2,0) and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point ( -8,0), x = -8, y = f(x) = 0 in equation (1),
=> 0 = a(-8)² + b(-8) + c
=> 64a - 8b + c = 0 --(2)
Similarly, for second point ( -5,-3) , f(x) = -3, x = -5
=> - 3 = a(-5)² + (-5)b + c
=> 25a - 5b + c = -3 --(3)
Continue for third point (-2,0)
=> 0 = a(-2)² + b(-2) + c
=> 4a -2b + c = 0 --(4)
So, we have three equations and three values to determine.
Subtract equation (4) from (2)
=> 64 a - 8b + c - 4a + 2b -c = 0
=> 60a - 6b = 0
=> 10a - b = 0 --(5)
subtract equation (4) from (3)
=> 21a - 3b = -3 --(6)
from equation (4) and (5),
=> 3( 10a - b) - 21a + 3b = -(- 3)
=> 30a - 3b - 21a + 3b = 3
=> 9a = 3
=> a = 1/3
from (5) , b = 10a = 10/3
from (4), c = 2b - 4a = 20/3 - 4/3 = 16/3
So, f(x)= (1/3)( x² + 10x + 16)
Hence, required values are 1/3, 10/3, and 16/3.
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The graph below shows petrol prices at two petrol stations, Station X and Station
Y.
Ellie went to one of the petrol stations and bought 20 litres of petrol for £24.
a) Did Ellie go to Station X or Station Y?
b) How much would 15 litres of petrol cost at the same station?
Give your answer in pounds (£).
Cost (£)
Cost against amount of petrol
40
30
20
10-
5
10 15 20 25
Amount of petrol (litres)
Key
Station X
Station Y
At Station Y, 15 litres of gasoline would cost £18.
What is cost in?Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.
Ellie must have visited Station Y because she paid $24 for 20 litres of gasoline, proving that she did.
b) We can observe from the graph that 20 litres of gasoline at Station Y costs £24. With the help of this data, we can calculate how much a litre of gasoline costs:
Cost of 1 litre of petrol = Cost of 20 litres of petrol / 20
Cost of 1 litre of petrol = £24 / 20
Cost of 1 litre of petrol = £1.20
Therefore, 15 litres of petrol at Station Y would cost:
Cost of 15 litres of petrol = Cost of 1 litre of petrol x 15
Cost of 15 litres of petrol = £1.20 x 15
Cost of 15 litres of petrol = £18
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4)) FH and IK are parallel lines. J K F G E Which angles are alternate exterior angles?
Answer: I couldn't honestly help with that I would if I could
Step-by-step explanation:
if a traingle with all sides of equal legnth has a perimeter of 15x 27 , what is an expression for the legnth of one of the sides
If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).
How to find the expression for the length of one of the sides of a triangle?The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).
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find the smallest positive integer $n$ so that \[\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2}
The smallest positive integer n so that,
$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,
we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.
Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.
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I need help! I need the graph drawn and the steps to how I got the answer but I don’t know it! Please help me!
Answer:
25 computers per hour
Step-by-step explanation:
look ate the point 2 hours corresponding to 50 computers
50/2 = 25/1 or 25 computers per hour
Line A has a gradient of -5. Line B is perpendicular to line A. a) What are the coordinates of the y-intercept of line B? b) What is the equation of line B? S Give your answer in the form y where m and c are integers or fractions written in their simplest form. mx + c,
The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.
What is equation?An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.
Here,
Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.
a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:
y = (1/5)x + c
0 = (1/5)(0) + c
c = 0
Therefore, the y-intercept of line B is (0,0).
b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.
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Mark wants to buy a new pair of sneakers that cost 215. His aunt gave him 100 for the sneakers. Market also lnow sthat he can esrn 16 for each hour that he works at his aunts store how many full hours must mark work to buy the sneakers
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,
therefore, we can say that 215 - 100 = 115
therefore, Mark now needs only 115 for him to buy sneakers and now we need to find how many full hours do Mark need to work to buy sneakers:
therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:
115/16 = 7.2
we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:
8 hours.
Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.
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Arrange the steps to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm in the order. a = 2, m=17 Rank the options below. The ged in terms of 2 and 17 is written as 1 = 17-8.2. By using the Euclidean algorithm, 17 = 8.2 +1. The coefficient of 2 is same as 9 modulo 17. 9 is an inverse of 2 modulo 17. The Bézout coefficients of 17 and 2 are 1 and 8, respectively. a = 34, m= 89 Rank the options below. The steps to find ged(34,89) = 1 using the Euclidean algorithm is as follows. 89 = 2.34 + 21 34 = 21 + 13 21 = 13 + 8 13 = 8 + 5 8 = 5 + 3 5 = 3 + 2 3 = 2+1 Let 34s + 890= 1, where sis the inverse of 34 modulo 89. $=-34, so an inverse of 34 modulo 89 is -34, which can also be written as 55. The ged in terms of 34 and 89 is written as 1 = 3 - 2 = 3-(5-3) = 2.3-5 = 2. (8-5)- 5 = 2.8-3.5 = 2.8-3. (13-8)= 5.8-3.13 = 5. (21-13)-3.13 = 5.21-8. 13 = 5.21-8. (34-21) = 1321-8.34 = 13. (89-2.34) - 8.34 = 13.89-34. 34 a = 200, m= 1001 Rank the options below. By using the Euclidean algorithm, 1001 = 5.200 +1. Let 200s + 1001t= 1, where sis an inverse of 200 modulo 1001. The ged in terms of 1001 and 200 is written as 1 = 1001 - 5.200. s=-5, so an inverse of 200 modulo 1001 is -5.
We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).
How do we find the inverse of a modulus?To find the inverse of a module m using Euclid's algorithm, the steps are as follows:
1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.
2. Let a = GCD * s + m*t, where s is the inverse of a module m.
3. The GCD in terms of a and my is written as 1 = m-s*a.
4. Find s = -a, so the inverse of a module m is -a (or m+s).
For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).
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The average mass of six people is 58kg. The lightest person has a body mass of 43kg. What is the average mass of the other 5 people.
Answer: 61 kg
Step-by-step explanation:
To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:
Find the total mass of all six people:
To find the total mass of all six people, we can multiply the average mass by 6:
Total mass of all six people = 58 kg/person x 6 people = 348 kg
Subtract the mass of the lightest person:
We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:
Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person
Total mass of the other 5 people = 348 kg - 43 kg = 305 kg
Find the average mass of the other 5 people:
Finally, we divide the total mass of the other 5 people by 5 to find the average mass:
Average mass of the other 5 people = Total mass of the other 5 people / 5
Average mass of the other 5 people = 305 kg / 5 = 61 kg
Therefore, the average mass of the other 5 people is 61 kg.
A wire first bent into the shape of a rectangle with width 5cm and lenth 11 cm.then the wire is unbent and reshaped into a square what is the length kf a side of the square
The length of a side of the square is 8 cm.
What do you mean by perimeter of a rectangle and square?
When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.
The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.
Calculating the length of a side of the square:
The length of the rectangle is 11 cm and the width is 5 cm.
Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.
Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.
Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:
[tex]32 = 4s[/tex]
[tex]s = 32/4[/tex]
[tex]s = 8[/tex]
Therefore, the length of a side of the square is 8 cm.
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two fifths of 60 is what number
Answer:
I hope this helps please rate my answer
Step-by-step explanation:
2/5×60
2×12=24
What is the value of x in √1+ 25/144 =1+ /12 ?
The solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6. This was achieved by simplifying the left side of the equation and isolating x on one side.
To solve the equation √(1 + 25/144) = 1 + x/12, we start by simplifying the left side of the equation. The expression inside the square root can be simplified to (144 + 25)/144 = 169/144. Taking the square root of this fraction gives us √(169/144) = (13/12).
Next, we subtract 1 from both sides of the equation to isolate x on one side: (13/12) - 1 = x/12. This simplifies to 1/12 = x/12.
Finally, we multiply both sides by 12 to solve for x: x = (1/12)*12 = 5/6.
So the solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6.
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Can some one help me? It’s three parts but the questions states use the interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. The last question also says topics related to if its constant or not.
The function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)
What exactly are function and example?A function, which produces one output from a single input, is an illustration of a rule. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this.
a) We can see that the function is increasing from approximately x = -3 to x = -1 and from approximately x = 1 to x = 2.5. So, the increasing intervals are (-3,-1) and (1, 2.5)
(b) We can see that the function is decreasing from approximately x = -2 to x = -0.5 and from approximately x = 3 to x = 4. So, the decreasing intervals are (-2, -0.5) and (3, 4)
(c) We can see that the function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)
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Q4 NEED HELP PLEASE HELP
Answer:
D. The electrician charges $23 per hour.
Step-by-step explanation:
C(h)= 23h+30 is in the form y=mx +b
$30 is the initial fee (b)
$23 is the amount charged per hour (h)
16. In Δ ABC and Δ PQR, , AB = PR, BC = RQ and AC = PQ. Δ ABC is congruent to a) Δ RPQ b) Δ QRP c) Δ PQR d) Δ PRQ
In Δ ABC and Δ PQR, if AB = PR, BC = RQ and AC = PQ, then Δ ABC is congruent to Δ PRQ, which means option D is the right answer.
The congruency theorem is used to determine the relation between two similar looking figures in two dimensional space. The word congruent itself means being in harmony. There are different rules which are used to determine the congruency between the triangles.
These rules are given as follows:
All three pairs of corresponding sides are equal = SSS CongruencyTwo pairs of corresponding sides and the corresponding angles between them are equal = SAS congruencyTwo pairs of corresponding angles and the corresponding sides between them are equal = ASA CongruencyIn the given question, it is given that sides AB = PR, BC = RQ and AC = PQ, this implies that the congruency can be setup using SSS rule, which if followed will suggest that Δ ABC will be congruent to Δ PRQ.
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Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Answer:
Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Step-by-step explanation:
To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:
Sn = n/2 [2a + (n-1)d]
where a is the first term, d is the common difference, and n is the number of terms in the sequence.
Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.
In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.
Is this a compound?
First, Gabriel planted the geraniums in a clay pot, and then he placed the pot on a sunny windowsill in his kitchen
A. YES
B. NO
Answer:
yes it is right now you can write it
Tiana has a new beaded necklace. The necklace has 3 blue beads and 17 white beads. What percentage of the beads on Tiana's necklace are blue?
Therefore, 15% of the beads on Tiana's necklace are blue.
What is percentage?Percentage is a way of expressing a fraction or a proportion out of 100. It is denoted by the symbol "%". For example, if we say that 50% of the students in a class are girls, it means that 50 out of every 100 students are girls.
Percentage can be calculated by dividing the given quantity by the total and multiplying by 100. For example, if there are 20 girls out of a total of 40 students in a class, the percentage of girls in the class can be calculated as follows:
Percentage of girls = (number of girls / total number of students) x 100%
= (20 / 40) x 100%
= 50%
by the question.
Tiana's necklace has a total of 3 + 17 = 20 beads.
To find the percentage of blue beads, we need to divide the number of blue beads by the total number of beads and then multiply by 100 to get the percentage:
percentage of blue beads = (number of blue beads / total number of beads) x 100
percentage of blue beads = (3 / 20) x 100
percentage of blue beads = 15
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find the area of a quadrilateral ABCD in each case.
The area of the quadrilateral ABCD for this case is of 4 square units.
How to obtain the area of the quadrilateral ABCD?The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.
The lengths for each diagonal of the diamond are given as follows:
Diagonal AC = 2 - 0 = 2.Diagonal BD = 4 - 0 = 4.The product of the diagonal lengths is given as follows:
AC x BD = 2 x 4 = 8 square units.
Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:
0.5 x 8 square units = 4 square units.
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Elouise finds a woodlouse that is 8 mm long. When she views it under the microscope it
appears 12 cm long.
What is the magnification?
Answer:
Step-by-step explanation:
This can be solved by taking X as the magnification
8*x = 12cm *10
x= 120/8
x= 30/2= 15
the magnification = 15 times
3) One piece of fencing is 71/8 feet long. How long will a fence be that is made up of 9 of these pieces?
Answer:
Step-by-step explanation:
71/8*9 which it 639/8 feet long
3) A lottery ticket says that the chances of winning are 1 in 8. Suppose you buy 10 of these lottery tickets. Find the probability that at least one of them will be a winner
The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.
The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:
(7/8)^10 = 0.362
This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:
P(at least one winner) = 1 - P(no winners)
P(at least one winner) = 1 - 0.362
P(at least one winner) = 0.638
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why does a square root have a plus or minus sign attached to it.
Answer:
To indicate that we want both the positive and the negative square root of a radicand
Answer:
Because a negative number times a negative number has a positive answer
Step-by-step explanation:
The segment of a circle of radius 14 cm has an angle of 135° at the centre. Calculate its perimeter.
Answer: 61
Step-by-step explanation:
explination in image
11. How much time will it take for ₹5000
5618 at 6% per annum
annually?
to become
compounded
Answer:
2.31 Years
Step-by-step explanation:
To calculate the time it will take for ₹5000 to grow to ₹5618 with a 6% annual interest rate when compounded annually, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (₹5618)
P = the principal amount (₹5000)
r = the annual interest rate (6% or 0.06)
n = the number of times the interest is compounded per year (1, since it's compounded annually)
t = the time period in years
Plugging in the values, we get:
5618 = 5000(1 + 0.06/1)^(1t)
Simplifying:
1.1236 = 1.06^t
Taking the natural logarithm of both sides:
ln(1.1236) = ln(1.06^t)
Using the power rule of logarithms:
ln(1.1236) = t ln(1.06)
Solving for t:
t = ln(1.1236) / ln(1.06)
t ≈ 2.31 years
Therefore, it will take approximately 2.31 years for ₹5000 to grow to ₹5618 at a 6% annual interest rate when compounded annually.
a factory was manufacturing products with a defective rate of 7.5%. if a customer purchases 3 of the products , what is the probability of getting at least one that is defective
If a customer purchases 3 of the products, the probability of getting at least one that is defective is 38.59%.
How to determine the probabilityIn order to determine the probability of getting at least one defective product if a customer purchases three products with a defective rate of 7.5%, we can use the concept of complementary probability.
The probability of getting at least one defective product can be calculated as the complement of the probability of getting none defective products.
So, the probability of getting no defective products is:
P(none defective) = (1 - 0.075)³ = 0.6141
Therefore, the probability of getting at least one defective product is:
P(at least one defective) = 1 - P(none defective) = 1 - 0.6141 = 0.3859 or 38.59%
.So, the probability of getting at least one that is defective is 38.59%.
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The terminal ray of angle A, drawn in standard position, passes through the point (-4,
-6). What is the value of sec(A)?
Give your answer in simpliest radical form.
The value of sec A as required to be determined in the task content is; -√13 / 2.
What value represents sec A in the given scenario?As evident from the task content; it follows that the terminal ray of angle A, drawn in standard position, passes through the point (-4, -6).
Therefore, the length that the line from the origin to A has length;
L = √((-4)² + (-6)²)
L = √52.
On this note, it follows that the value of sec A which is represented by; hypothenuse/ adjacent is;
sec (A) = -√52 / 4
sec (A) = -√13 / 2.
Ultimately, the value of sec (A) as required is; -√13 / 2.
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HELPPPP HURRY PLSS………………..
Answer:
C is your answer
Step-by-step explanation:
in my opinion, i think it would be the mode.
