The probability that the system gets damaged is P(AUBUC)=0.76
If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events.
The two events are said to be independent events if the outcome of one event does not affect the outcome of another.
The formula can be defined as:
P(A and B) = P(A)×P(B)P(A and B) = P(A)×P(B)
For independent events U and V we have P(U∩V)=P(U)P(V)
if the viruses are truly independent then the probability that the system gets damaged=
P(AUBUC)=P(A)+P(B)+P(C)-P(AnB)-P(anc)-P(bnc)+P(AnBnC).
0.4+0.5+0.2-0.4*0.5-0.4*0.2-0.5*0.2+0.4*0.5*0.2=1.1-0.2-0.08-0.1+0.04
P(AUBUC)=0.76
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Three forces are acting on the ring in the dlagram.
128 N
128 N
30.0°
64 N
The net force and magnitude is 54°. The solution has been obtained by using trigonometry.
What is trigonometry?
The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle.
We are given that three forces are acting on the ring.
So,
A = -128 N + 64 N
A = -64 N
[tex]A_{x}[/tex] = A cos θ[tex]_{A}[/tex]
[tex]A_{x}[/tex] = (-64 N) (cos 180°)
[tex]A_{x}[/tex] = -64 N
[tex]A_{y}[/tex] = A sin θ[tex]_{A}[/tex]
[tex]A_{y}[/tex] = (-64 N) (sin 180°)
[tex]A_{y}[/tex] = 0 N
B[tex]_{x}[/tex] = B cos θ[tex]_{B}[/tex]
B[tex]_{x}[/tex] = (128 N) (cos 30°)
B[tex]_{x}[/tex] = 111 N
B[tex]_{y}[/tex] = B sin θ[tex]_{B}[/tex]
B[tex]_{y}[/tex] = (128 N) (sin 30°)
B[tex]_{y}[/tex] = 64 N
R[tex]_{x}[/tex] = A[tex]_{x}[/tex] + B[tex]_{x}[/tex]
R[tex]_{x}[/tex] = -64 N + 111 N
R[tex]_{x}[/tex] = 47 N
R[tex]_{y}[/tex] = A[tex]_{y}[/tex] + B[tex]_{y}[/tex]
R[tex]_{y}[/tex] = 0 N + 64 N
R[tex]_{y}[/tex] = 64 N
[tex]R = \sqrt{R_{x}^{2} +R_{y}^{2} }[/tex]
[tex]R = \sqrt{(47 N)^{2} +(64 N)^{2} }[/tex]
R = 79 N
θ = [tex]tan^{-1}(\frac{R_{y} }{R_{x}} )[/tex]
θ = [tex]tan^{-1}(\frac{64 }{47} )[/tex]
θ = 54°
Hence, the net force and magnitude is 54°.
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Since, the question is incomplete, the complete question has been attached below
suppose that we were going to conduct a study to determine if there is an increased risk of getting lung cancer based on whether a person exercises regularly or not. in the group that exercises regularly (1), we find than 2 out of 100 get lung cancer. in the group(2) that does not exercise regularly, we find that 5 out of 100 get lung cancer. what is the sample relative risk? group of answer choices
To calculate the sample relative risk, we compare the proportion of individuals in each group who get lung cancer.where the sample relative risk is 0.4.
What is the sample relative risk? Step 1: Calculate the proportion of individuals in each group who get lung cancer.Group 1 (exercise regularly): 2 out of 100 = 2/100 = 0.02Group 2 (does not exercise regularly): 5 out of 100 = 5/100 = 0.05Step 2: Divide the proportion in group 1 by the proportion in group 2.0.02 ÷ 0.05 = 0.4Step 3: Round the answer to the nearest hundredth.0.4So, the sample relative risk is 0.4.This means that the group of individuals who exercise regularly have a 0.4 times lower risk of getting lung cancer compared to the group who does not exercise regularly.To learn more about relative risk refer:
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A spinner with four equal sectors labeled "purple," "blue," "orange," and "green" is spun 45 times. What is the
probability that the spinner will land on "purple" in fewer than 20% of the spins?
Find the z-table here.
O 0. 212
O 0. 221
0 0. 460
0. 779
One of the four outcomes chosen at random will happen one out of four times, or 25% of the time. Such a result has a 3 to 1 chance of occurring.
While I am unable to see the image, I presume that it is a straightforward, fair spinner with a value indicator when it stops and can only have the outcomes that are listed.
Given that there are four possible outcomes (pink, purple, blue, and green) and only one desired outcome (green), the probability is one-fourth.
One of the four outcomes chosen at random will happen one out of four times, or 25% of the time. Such a result has a 3 to 1 chance of occurring.
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The question seems wrong, the full question:
You spin the spinner shown below once. The spinner has 4 equal sectors colored pink, purple, blue, and green. What is P(green)? If necessary, round your answer to 2 decimal places.
the base of a triangle is 6 meters longer than the height of the triangle. if the area of the triangle is 80 square meters, what are the base and height of the triangle?
The length of the base of the triangle is 16 m and the height of the triangle is 10 m
What is Triangle ?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Use the equation area = 1/2 * base * height to determine a triangle's surface area.
The basic Properties of a triangle :
Three sides and three angles make up a triangle.A triangle's total angles are always 180 degrees.A triangle's outside angles are always a sum of 360 degrees.The total of the parallel interior and exterior angles is additional.Any two sides of a triangle can be added together to have a length larger than the third side. Similar to this, any two triangle sides have length differences between them that are smaller than the length of the third side.Always, the shortest side faces the smallest internal angle. Similar to this, the biggest internal angle is always opposite the longest side.The length of the base = b m
The height of the triangle = b - 6 m
The area of the triangle = 80 m²
Therefore,
(1/2)*b*(b-6) = 80
⇒ b² - 6b = 160
⇒ b² - 6b - 160 = 0
⇒b² - 16b + 10b - 160 = 0
⇒b(b-16) + 10(b- 16) = 0
⇒(b-16)(b =10) =0
The value of b = 16 and b = -10
The value of b is 16 as -10 is negetive and cannot be the length of the triangle.
The height of the triangle = b-6 = 10 m
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A curve is represented by the equation 2y3 + xy - 6x + 3 = 0. Part A: Determine dy dx (10 points) Part B: Evaluate dy at the point (1, 1). (10 points) dx Part C: Determine d°у (10 points) dx2 day Part D: Evaluate at the point (1, 1). (10 points) dx2
The derivative of the equation 2y³ + xy - 6x + 3 at the point (1,1) is 0, and the second derivative is 13.
The derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x. This gives us:
[tex]\frac{dy}{dx} = \frac{x}{2y^2} - 5[/tex]
We can evaluate dy/dx at the point (1, 1) by substituting x = 1 and y = 1 into the equation for dy/dx and calculating the result. This gives us:
[tex]\frac{dy}{dx} = \frac{1}{2} - 6 = -5.5[/tex]
The second derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x twice. This gives us:
[tex]\frac{d^2y}{dx^2} = -\frac{1}{2y^3}[/tex]
We can evaluate d2y/dx2 at the point (1, 1) by substituting x = 1 and y = 1 into the equation for d2y/dx2 and calculating the result. This gives us:
[tex]\frac{d^2y}{dx^2} = -\frac{1}{2} = -0.5[/tex]
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vector → = -6ˆ 8ˆ - 4ˆ. vector → = 5ˆ 7ˆ - 3ˆ. what is →=→−→?
The answer to the given the vector subtraction of these vector question is →=→−→=−11ˆ 1ˆ −7ˆ.
The vector subtraction is a mathematical operation that subtracts two vectors. It is denoted by the symbol →=→−→, where → and → are two vectors. The formula for vector subtraction is →−→=→−(−→).
For the given question, let us consider the vectors →=−6ˆ 8ˆ−4ˆ and →=5ˆ 7ˆ−3ˆ. Applying the formula, the vector subtraction of these vectors can be calculated as follows: →−→=(−6ˆ 8ˆ−4ˆ)−(5ˆ 7ˆ−3ˆ) = (−6ˆ−5ˆ) 8ˆ−(7ˆ−3ˆ)−4ˆ = −11ˆ 1ˆ −7ˆ.
Therefore, the answer to the given question is →=→−→=−11ˆ 1ˆ −7ˆ.
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Challenge 1 - Exp
Enter the equation for the dotted
exponential graph!
Hint: You just need to find the right
base, no shift L/R/U/D necessary!
The exponential function for the graph is obtained as y = 3^x.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
Assume that the plot of a function is in the form -
y =ab^x
where the horizontal asymptote is the x-axis.
To find a, look for the coordinate where the curve crosses the y-axis.
In the plot, it is seen that this happens at (0,1).
So, the value of a = 1.
To find b, look for the coordinate where the curve crosses the vertical line at x = 1.
In the plot, it is seen that this happens at (1,3).
Then, b is the number divided by a -
b = 3/1 = 3.
This plot is the curve -
y = 3^x
Therefore, the exponential function is y = 3^x.
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The sum of three consecutive numbers is 42. What are the three numbers?
Answer:
Step-by-step explanation:
Here's a step-by-step explanation to find the three consecutive numbers whose sum is 42:
Let's call the smallest of the three numbers "x".
Since they are consecutive numbers, we can represent the next two numbers as x+1 and x+2.
The sum of these three numbers can be represented as x + (x + 1) + (x + 2) = 42.
Simplifying this equation, we get 3x + 3 = 42.
Subtracting 3 from both sides, we get 3x = 39.
Dividing both sides by 3, we get x = 13.
So, the three consecutive numbers are 13, 14, and 15.
the ratio of fabric bandages to plastic bandages in each kit is 3 to 9. a small kit has 16 fabric bandages. how many plaastic bandages should a small kit have?
Answer: 48 plastic bandages
Step-by-step explanation:
1. Divide the ratio of 3 fabric bandages to the amount of fabric bandages in the kit
16/3 = 5.33333333 (repeating) or 5 1/3
2. Multiply that amount (5.33333) by 9
5 1/3 x 9 = 48
3. Check your work!
I hope this helped. Leave a comment if there is something wrong! Give me a Thanks if this helped. Thank u!
Use the following function rule to find f(8). f(x) = ( 1 + 2 x ) 2
The solution to the function is 289
How to determine the solution to the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = (1 + 2x)^2
Substitute the known values in the above equation, so, we have the following representation
f(8) = (1 + 2 * 8)^2
Evaluate the product
f(8) = (1 + 16)^2
So, we have
f(8) = 17^2
This gives
f(8) = 289
Hence, the value of the function is 289
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(5)^2/-10 please help
A scatter plot is shown on the coordinate plane.
100 POINTS, HELP ASAP, WILL GIVE BRAINLEIST.
Which two points would a line of fit go through to best fit the data?
(1, 10) and (10, 1)
(1, 7) and (2, 6)
(3, 7) and (7, 4)
(3, 8) and (6, 6)
Answer:D
Step-by-step explanation:
the dots are forming a mixed up line going across the plot. D best fits the line.
PLS HELp! WILL GUVE BRAINLIEST!!
When A'B'C' is reflecting in origin, A" (4, 1), B" (0, -7), and C" are the coordinates of the vertices' pictures (-2, -5).
What is triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry. A triangle with the vertices A, B, and C is referred to as a "triangle ABC."In Euclidean geometry, three non-collinear points result in separate triangles and planes for each point. A triangle is a three-sided polygon since it has three vertices.The end-to-end connections of the three sides at a point define the triangle's angles. The three angles of the triangle add up to 180 degrees.In geometry, triangles are a special kind of polygon because they have three sides and three vertices. It is a two-dimensional figure and has three straight sides. It has a triangle as one of its three sides.The vertices of ABC are A (4, -1), B (0, 7), and C (-2, 5), respectively.
The coordinates of the points for ABC will be A' (-4, -1), B' (0, 7), and C' after reflecting in the y-axis (2, 5).
Once more, when "A'B'C" is reflecting in origin, "A" will be at (4, 1), "B" will be at (0, -7), and "C" will be at (4, 1). (-2, -5).
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10. Express the following function, F(x), as a composition of two functions, f and g: f(g(x)).
F(x)= sqrt(3x-4)
Part I. Find g(x) by identifying the function you are taking the square root of
Part II. Find f(x) by identifying what you are doing to the function you found in Part I. What function is f(x)?
Part III. Verify that
f(g(x))=F(x)
f(g(x))= sqrt(3x-4)
Part I.
g(x) = 3x-4
Part II.
f(x) = √(x)
Part III.
f(g(x)) = f(3x-4) = √(3x-4)
How did we get the values?In Part I, the function F(x) is the square root of 3x-4. Therefore, g(x) is the expression inside the square root: g(x) = 3x-4.
In Part II, the function f(x) is the square root operation applied to its argument, so f(x) = √(x).
Finally, in Part III, we substitute g(x) into f(x) to obtain f(g(x)) = f(3x-4) = √3x-4), which is equal to F(x)
So,
f(g(x))= √(3x-4) = F(x)
Therefore, F(x) = f(g(x)) where f(x) = √(x) and g(x) = 3x-4
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Diff of squares help me out
Answer:
9
Step-by-step explanation:
9 is the correct answer
breifly explain, in your words, how the fundamental theorem of calculus made the precise connection between the indefinite and definite integrals. in other words, what was that connection?
Fundamental Theorem of Calculus made a precise connection between the indefinite and definite integrals by stating that the derivative of the definite integral of a function is equal to the original function.
The Fundamental Theorem of Calculus is a key result in mathematics that connects two branches of calculus - the definite integral and the indefinite integral.
The definite integral is used to calculate the total area under a curve. It is defined as the limit of the sum of rectangles with increasing precision, as the width of each rectangle approaches zero.
The definite integral can be calculated using definite limits, for example, from x = 0 to x = 1, and the result is a definite number.
The indefinite integral, on the other hand, is a function that, when differentiated, will give us the original function.
The Fundamental Theorem of Calculus if we have a definite integral of a function f(x) from a to b, then the derivative of this definite integral will be equal to
=> f(x) at x = b - f(x) at x = a.
This provides us with a precise way of calculating areas under curves, and it has many practical applications in fields such as physics, engineering, and economics.
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Find the area for 5cm 6cm 7cm
33.
60°
C
30°
A supplementary
neither
Are these angles complementary, supplementary or neither?
B
complementary
The angles shown in the figure are complementary angles.
What are angles?The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the shape of the angle can alternatively be used to symbolize the angle, with the middle letter indicating the location of the angle.
Given the angles,
60° and 30°
the sum of both angles is,
60° + 30° = 90°
The sum of two angles is 90° then the angles are known as complementary angles.
Hence the angles are complementary angles.
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-7 1/7*(3 2/5)+ 6 3/5*(-7 1/7)
Answer:
-71.4285714286Y
Step-by-step explanation:
-7 1/7*(3 2/5)+ 6 3/5*(-7 1/7) = 71.4285714286Y or shorter 71.42
Which linear graph represents a proportional relationship?
In Graph the line which passes through the origin represents a proportional relationship.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Linear graph is represented in the form of a straight line.
To show a relationship between two or more quantities we use a graphical form of representation. If the graph of any relation gives a single straight line then it is known as a linear graph.
the graph of a proportional relationship is a straight line through the origin.
In Graph the line which passes through the origin represents a proportional relationship.
Hence, In Graph the line which passes through the origin represents a proportional relationship.
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pls this is urgent this is part b to part one
All the pair of angles are congruent except ∠5 and ∠3 are not congruent.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
Two parallel lines cut by a transversal line.
Then,
∠1 and ∠5 = Corresponding angles.
∠2 and ∠8 = Same-side exterior angles.
∠4 and ∠5 = Alternate interior angles.
From the given choices:
∠5 and ∠3 are not congruent.
Therefore, all the required values are given above.
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what does d' measure
The difference between amount of two proportions is measured by D'.
D' is a metric for comparing differences between two proportions. It serves as a gauge for comparing how far apart the two proportions are from one another. It is determined by multiplying the difference between the two proportions by the sum of the standard deviations of the two proportions. The outcome is a measurement of how many standard deviations there are between the two proportions.
In statistical tests like the Chi-Square test or the Z-test, D' is most frequently employed to calculate the difference between two proportions. It is a helpful way to compare two proportions because it indicates whether or not the difference is statistically significant. Given that it takes into consideration the variability of each sample, it is especially helpful when comparing two proportions when the sample sizes are different. In data-mining applications, where it can be used to find correlations between two proportions, D' is also a helpful measure of the separation between two proportions.
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solve the following equations and identify any extraneous roots where applicable: [6 marks total] a) 4^{x+1} = 5^{3x} [3 marks] b) log2x + log2 (x+2) = 3
a) The solution of equation [tex]4^{x+1} = 5^{3x}[/tex] is x = log4/(3log5 - log4).
b) The extraneous roots of equation [tex]\log_{2}x + \log_{2} (x+2) = 3[/tex] is -4 and 2.
a) The first equation is [tex]4^{x+1} = 5^{3x}[/tex].
Now solving the equation.
To solve the equation we take log on both side.
[tex]\log(4^{x+1}) = \log(5^{3x})[/tex]
Using the formula [tex]\log m^n = n\log m[/tex].
Now the equation is
(x+1) log4 = 3x log5
x log4 + log4 = 3x log5
Subtract x log4 on both side, we get
3x log5 - x log4 = log4
Taking common x
x(3log5 - log4) = log4
Divide by (3log5 - log4) on both side, we get
x = log4/(3log5 - log4)
b) The second equation is [tex]\log_{2}x + \log_{2} (x+2) = 3[/tex]
Now solving the equation.
We can write the equation as
[tex]\log_{2}(x(x+2)) = 3[/tex]
Now eliminating the log
x(x+2) = (2)^3
x(x+2) = 8
Now simplify the bracket
x^2 + 2x = 8
Subtract 8 on both side, we get
x^2 + 2x - 8 = 0
Now factor the equation
x^2 + (4-2)x - 8 = 0
x^2 + 4x - 2x - 8 = 0
x(x + 4) -2(x + 4) = 0
Now the factor of the equation is
(x + 4)(x - 2) = 0
Now equating the factor equal to zero.
x + 4 = 0 x - 2 = 0
x = -4 x = 2
Now the solution of equation is -4 and 2.
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< &
complementary.
If Y measures 32°.
what is the
measure of <?
Therefore , the solution of the given problem of complementary angles comes out to be 29° and 61° QED.
How do complimentary angles work?Two angles are considered complementary when their sum equals 90 degrees. Two angles are considered submissive when their sum equals 180 degrees. For example, the angles of 40 - 60 degrees complement one another. The difference between a supplementary angle and a supplementing angle is that a Triangle angle has two angles joined to produce a 90 degree angle. When two angles add up to 90 degrees, they are said to be complementary. Alternatively, the complementary angles result in a right angle (90 degrees).
Here,
Given :
Allow x to equal the complementary angle.
Given: x plus 32° the opposite angle
Recognized: Complementary angles sum to 90°
=>x + x + 32° = 90° (Adding the two angles) (Adding the two angles)
2x + 32° = 90° (adding the unknown factors) (adding the unknown variables)
=>2x = 90° - 32° (subtract 32 from both sides) (subtract 32 from both sides)
=> 2x = 58° (assess the right side) (evaluate the right side)
=>x = 29° (split both sides by 2) (divide both sides by 2) (One reply)
=> x + 32° = 61° (Add 32 to x) (Add 32 to x) (The other response)
There are two angles: 29° and 61° QED.
Therefore , the solution of the given problem of complementary angles comes out to be 29° and 61° QED.
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The complete question is "The measure of one angle is 32° greater than the measure of its complement. What are the measures of the angles?"
I NEED HELP ASAP what is 4 2/3 divided by 2 1/6?
Answer choices:
- 10 1/9
- 2 2/13
- 1 1/13
- 2 1/13
Answer:
4 2/3 ÷ 2 1/6 is equal to 2 2/13.
Step-by-step explanation:
When dividing 2 1/6 from 4 2/3, you will get 2 2/13 or 2.15.
Help me pls i need help
Answer: 32a^5b^3√b
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors assuming positive real numbers
in florida, approximately what percentage of visitors and residents participate in outdoor recreation? group of answer choices 18% 36% 50% 64% 70%
C) Approximately 50% of visitors and residents in Florida participate in outdoor recreation.
This is an incredibly high rate, given the size and population of the state, and is indicative of the importance of outdoor recreation to the people of Florida. The Florida Department of Economic Opportunity is the main governing body responsible for ensuring visitors are responsible and respectful when participating in outdoor recreation .
This helps to protect the state's natural resources and maintain its beautiful landscapes. Additionally, surveys conducted by the Florida Fish and Wildlife Conservation Commission have found that 64% of Florida residents enjoy participating in outdoor recreation on public lands.
This number is likely higher as many people do not respond to surveys or are unaware of the recreational opportunities available to them. This highlights the importance of outdoor recreation education and outreach programs, which help to inform the public of the resources and activities available to them
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Which point in the diagram at the right had a distance of sq of 130
Answer:
S
Step-by-step explanation:
the distance formula (Pythagoras on the right-angled triangle of the coordinate differences) says that
sqrt²(130) = 130 = (-5 - x)² + (5 - y)²
let's try Q
130 = (-5 - 5)² + (5 - 2)² = (-10)² + 3² = 100 + 9 = 109
no, wrong.
let's try S
130 = (-5 - 4)² + (5 - -2)² = (-9)² + 7² = 81 + 49 = 130
correct !
Find sn for the arithmetic series where a1=5 , n=10, an=−13
The sum of the first 10 terms of the arithmetic sequence is given as follows:
-40.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the equation presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
The sum of the first n terms of the sequence is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In which [tex]a_n[/tex] is the nth term of the sequence.
The parameters for this probelm are given as follows:
[tex]a_1 = 5, a_n = -13, n = 10[/tex]
Hence the sum is given as follows:
S = 10 x (5 - 13)/2
S = 5 x (5 - 13)
S = 5 x (-8)
S = -40.
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HELP pls will mark you the brainliest
Answer: (-5,1)
Step-by-step explanation: