The average time is 7.5. The average is calculated by dividing the total number of values in a given set by the sum of all the values in that set.
How to calculate average ?An average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. Average The arithmetic mean is calculated by adding a set of numbers, dividing by their count, and then taking the result.
If every number in a list is the same number, then that number also serves as the average for the list. Every one of the diverse varieties of average shares this characteristic.
An average of the values in a sample of data can be used to define a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.
Average = Sum / Count
Sum = 7.48 + 7.45 + 7.90 + 7.37 + 7.25 + 7.40 + 7.55 + 7.60
= 60 / 8
= 7.5
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What is represented by P ∨ Q?
The statement [tex]P\land Q[/tex] in Tautology is represented as P and Q , and the symbol "[tex]\land[/tex]" is called as AND operator .
What is Tautology ?
Tautology can be defined as a compound statement which always results in Truth value. It does not matter what individual part consists of, the result in tautology is always true.
AND Operator : The AND is represented by the symbol "[tex]\land[/tex]". When the 2 simple statements are used in forming the compound statement by using AND operator , then it is called as a conjunction of two statements .
The AND operator returns TRUE value only when both the statements P and Q are TRUE , if any one of the statement is FALSE , then it returns FALSE value .
The given question is incomplete , the complete question is
What is represented by [tex]P\land Q[/tex] in Tautology ?
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Mila cuts a sphere with a 13-inch radius in half. Whats the area of the cross section of the sphere in square inches in terms of pi
The area of the cross-section of the sphere in square inches in terms of pi will be 169π inch^2.
The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.
An area is projected onto the plane when a plane slices through a solid object. The axis of symmetry is then perpendicular to that plane. The cross-sectional area refers to its projection.
The cross-section of a sphere is a circle. Hence the area of the cross-section is the area of a circle with a radius of 13, which is given by π*r^2
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2
The scores of seven people playing a card game are listed below.
56, 103, 114, 80, 141, 68, 150
What is the interquartile range of the scores?
OA. 35
OB. 73
O C. 102
OD. 94
Answer:
B. 73
Step-by-step explanation:
An explanation is in the picture if you need it.
road to white house Math
The value of f(4) - g(-5) if function f(x) = 3 / 2x + 2 and g(x) = 2x² - 3 is -39.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x) = 3 / 2x + 2 and g(x) = 2x² - 3
Calculate the value of f(4) and g(-5) as shown below,
f(4) = 3 / 2 × 4 + 2
f(4) = 12 / 2 + 2
f(4) = 6 + 2
f(4) = 8
g(-5) = 2 × (-5)² - 3
g(-5) = 2 × 25 - 3
g(-5) = 50 - 3
g(-5) = 47
Now, calculate the value of f(4) - g(-5) as shown below,
f(4) - g(-5) = 8 - 47
f(4) - g(-5) = -39
Thus, the value of f(4) - g(-5) is -39.
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Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a
30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
0
1
2
W = # of walleye
P(W)
0. 49
0. 42
0. 09
Calculate the mean of W.
walleye
The mean of the walleye 'W' for the given number of walleye and its probability to represent that 30% chances are of walleye is equal to 1.4.
As given in the question,
Let 'W' is the random variable represents the number of walleye.
'P(W)' represents its probability
The values are given as follow:
W : 0 1 2
P(W) : 0.09 0.42 0.49
Mean of the walleye 'W' is given by :
= W₁P(W₁) + W₂P(W₂) + W₃P(W₃)
= ( 0 × 0.09 ) + ( 1 × 0.42 ) + ( 2 × 0.49 )
= 0 + 0.42 + 0.98
= 1.4
Therefore, the mean of the walleye 'W' for the given number of walleye and its probability is given by 1.4.
The above question is incomplete , the complete question is :
Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
W : 0 1 2
P(W) : 0.09 0.42 0.49
Calculate the mean of W.
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based on the data provided, does this algorithm run in a reasonable or unreasonable time? explain your answer
As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.
What exactly is a linear equation?A linear equation is represented by the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "simple formula with 2 factors," where both y and x are variables, is what the previous sentence was referred to as. Calculations with two variables are referred to as "bivariate linear equations." Here are a few illustrations: 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3 are the results. A mathematical equation is considered to be linear if its solution has the format y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Based on how quickly iterations rise as input increases, fair and unreasonable algorithms can be distinguished. Since the algorithm does not grow exponentially, we can infer that it completes in an acceptable amount of time.
assessing the mathematical function that represents the algorithm's growth rate when input is added;
200 = 10k, where k is the proportionality constant.
k = 200/10
k = 20
The function that represents the number of iterations is as a result:
I = input size; n = 20i; represents the number of iterations.
As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.
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Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Constructing a line segment of length 2 and then finding the
midpoint
B. Drawing a perpendicular line segment through a given point on a
given segment
C. Drawing a line through a given point parallel to a given line
D. Drawing a perpendicular line segment from a given point to a
given segment
Answer: Constructions A, B, and D can be accomplished with paper folding.
Construction A involves constructing a line segment of length 2 and then finding the midpoint, which can be done by folding the paper in half.
Construction B involves drawing a perpendicular line segment through a given point on a given segment, which can also be done by folding the paper.
Construction D involves drawing a perpendicular line segment from a given point to a given segment, which can also be done by folding the paper.
Construction C, drawing a line through a given point parallel to a given line, cannot be accomplished with paper folding. To do this construction, you would need a straightedge, such as a ruler.
Step-by-step explanation:
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment. What is construction in mathematics?Constructions are accurate drawings of shapes, angles and lines in geometry. Some basic constructions -
Constructing bisectors of lines and angles.Constructing regular polygons inscribed in circles.Constructing circumcircles and incircles.Constructing a line tangent to a circle.Given is to find which of the following constructions can be accomplished with paper folding.
The following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.Therefore, the following constructions can be accomplished with paper folding -
Drawing a perpendicular line segment through a given point on a given segment.Drawing a line through a given point parallel to a given line.Drawing a perpendicular line segment from a given point to a given segment.To solve more questions on constructions, visit the link-
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And correct the errors in the following mathematical statement
Which statement.........
Kourtney and Kayla are sisters who are taking the same classes this semester: MAT 003, CHM 131/3131A, and ACA 122. If kourtney earns a pee a P in MAT 003, a B in CHM 131A, and an A in ACA, then what will her GPA be?
A. 3. 5
B. 3. 2
C. 2. 58
D. 3. 8
the GPA for the current semester will be 3.5.
What is GPA?
A metric used to assess your performance throughout the course of your complete degree program is your grade point average.
The average grade point average (GPA) is a figure that represents your typical performance in classes over the course of a semester, term, or year. In line with how much you raise your overall grade point average over your time at the university, your typical GPA score will fluctuate (or, in some cases, how much you fall behind).
A pass grade is a P, an A is a grade of excellent performance worth 4 points per credit, and a B is a grade of good performance worth 3 points per credit. The grade averages do not take P grade into account.
MAT 003, CHM 131a, and ACA 122 each have three, one, and two credits. Thus, the final score is 3 + 1 + 1 = 5. P in MAT 003, B in CHM 131a, and A in ACA 122 are the grades she receives.
GPA can be calculated by
GPA = ( 3 × 1 + 4 × 1)/ 5
GPA = ( 3 + 4)/ 5
GPA = 3.5
Hence the GPA for the current semester will be 3.5.
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Does 12 20 and 16 form a Pythagorean triple?
No, 12, 20, and 16 do not form a Pythagorean triple. A Pythagorean triple is a set of three whole numbers, a, b, and c, such that a^2 + b^2 = c^2.
To determine if 12, 20, and 16 form a Pythagorean triple, we can substitute each number into the equation and solve for c.
Start by substituting 12 for a, 20 for b, and 16 for c:
12^2 + 20^2 = 16^2
144 + 400 = 256
544 ≠ 256
Since 544 does not equal 256, the numbers do not form a Pythagorean triple. We can also verify this by calculating the square of c to see if it is equal to the sum of the squares of a and b.
Start by substituting 12 for a, 20 for b, and 16 for c:
a^2 + b^2 = c^2
12^2 + 20^2 = c^2
144 + 400 = c^2
544 = c^2
Taking the square root of both sides:
√544 = √c^2
23.2 ≠ c
Since 23.2 does not equal c, the numbers do not form a Pythagorean triple.
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What is the degree of the polynomial 5x³ 4x² 7x?
The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.
1. Identify the polynomial: 5x³ + 4x² + 7x
2. Count the number of terms: 3
3. Find the highest degree (the largest exponent): 3
4. The degree of the polynomial is 3.
The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term
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A juice container advertises it now contains 20% more juice. Originally, it had 27.5 ounces, how
much juice does it now contain?
Answer:
33 ounces
Explanation:
20% of 27.5 ounces is 5.5 ounces.
To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces
What's the longest UK number 1?
The person who has the most number 1 in UK is Elvis Presley. He has a total of 21 number 1 which is the highest in history.
The UK Singles Chart is a chart which numbers musician on the basis of their songs and their sales and streams it was created in 1969. The records and statistics listed here, however, date back to 1952 .
The song which charted the charts was Old Town Road which was recently remixed and launched by Lil Nas X.
Elvis Aaron Presley or more commonly known as Elvis, was an American singer and actor. He dubbed the "King of Rock and Roll", and is now regarded as one of the most significant cultural figures of the 20th century.
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MEDICINE: Ahmad took 200 mg of a medication. The
function f(t) = 200e 0. 4+ can be used to determine the amount of
medication, f(t), still in his system after t hours. To the nearest hundredth,
after how much time will Ahmad have only 50 mg of medication left in his
system?
A 4. 37 hours
B 7. 47 hours
C
3. 47 hours
D
3. 74 hours
A BH
BO
If Ahmad took 200 mg of medication and the function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .
The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as [tex]f(t) = 200e^{-0.4t}[/tex] ,
we have to find the after how many hours there will be only 50 mg of medication left ;
we need to substitute f(t) as 50 ;
we get ;
⇒ [tex]50 = 200e^{-0.4t}[/tex] ;
⇒ [tex]\frac{50}{200} =e^{-0.4t}[/tex] ;
⇒ [tex]\frac{1}{4} =e^{-0.4t}[/tex]
On solving further ,
we get ;
⇒ [tex]t=3.4657..[/tex] hours ;
So , t≈ 3.47 hours .
Therefore , After 3.47 hours there will be 50 mg of medication left .
The given question is incomplete , the complete question is
Ahmad took 200 mg of a medication. The function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?
(a) 4.37 hours
(b) 7.47 hours
(c) 3.47 hours
(d) 3.74 hours
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PLEASE HELP I will give brainiest Which equation best shows the relationship between x and y? (1 point)
O a
Ob
Oc
Od
y = x + 50
y = 6x + 50
y = 6x + 56
y=x+56
On solving the provided question, we can say that the equation of the expression is given by y = 6x + 50
What is an equation ?Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire? Different graph equations may be used to express the aforementioned graphs.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.
From the table we can see that if the equation be
y = mx + c
for x = 0 y = 50
c = 50
again from x = 1 and y = 56
m = 6
So the equation of the expression is given by y = 6x + 50
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What are the roots of the equation 2x^2 3x 5 0?
The roots of the equation 2x² - 3x - 5 = 0 are 5/2 and -1.
The quadratic formula is a formula that can be used to find the solutions (or roots) of a quadratic equation. For a quadratic equation written in the form ax² + bx + c = 0, where a, b, and c are constants, the quadratic formula is given by:
x = (-b ± √(b²- 4ac))/(2a)
Where x is the solution, a, b, and c are the coefficients of the equation.
Plug in the coefficients of the equation 2x² - 3x - 5 = 0 to the quadratic formula to find the roots.
x = (-b ± √(b²- 4ac))/(2a)
x = (3 ± √((-3)²- 4(2)(-5)))/(2)(2)
x = (3 ± 7)/4
x = 5/2 ; x = -1
Hence, the roots of the equation are 5/2 and -1.
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Charlotte is a customer-satisfaction expert at a large pizza company. She took a random sample of 1{,}0001,0001, comma, 000 delivery orders and constructed a one-sample zzz interval to estimate the proportion of delivery orders that take more than an hour to arrive. She decides to repeat this process, but this time she'll use a sample of 4{,}0004,0004, comma, 000 orders. Assume that the point estimates from each sample are approximately equal.What is true about the margins of error from these two samples
The smaller sample's margin of error will be almost twice as great as the larger sample's margin of error.
Calculating the margin of error for a given sample from a population:
Let the level of significance be and the standard deviation of the population be σ and the sample size be n, then we have:
MOE(Margin of Error)= [tex]z_{a/2}\times\frac{\sigma}{\sqrt n}[/tex]
Using the above formula to calculate the margin of errors for two specified samples
For first sample:
Sample size = n(1) = 1000
MOE(1) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {1000}}[/tex]
For second sample:
Sample size = n(2) = 4000
MOE(2) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {4000}}[/tex]
(since it was given that they have same point estimates, so same standard deviation)
Their ratios are given by
MOE(2)/MOE(1) = [tex]\frac{z_{a/2}\times\frac{\sigma}{\sqrt {4000}}}{z_{a/2}\times\frac{\sigma}{\sqrt {1000}}}[/tex]
MOE(2)/MOE(1) = [tex]\sqrt{\frac{1000}{4000}}[/tex]
MOE(2)/MOE(1) = 1/2
MOE(1) = 2*MOE(2)
Thus, the margin of error from the smaller sample will be about double of the margin of error from the larger sample.
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SOMEONE HELP ME PLSSSS
simplify (pic below)
Answer:
10^11
Step-by-step explanation:
This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.
Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.
10 ^ (8+3)
= 10^11
see image
What is not a polynomial class 10?
A variable-containing expression that divides by a variable, contains fractional or negative exponents, or is enclosed in a radical is not a polynomial.
As long as the polynomial is specified over the real numbers, it is possible for it to have negative coefficients, fractional coefficients, or even radical coefficients.
There cannot be a negative exponent in a polynomial. The exponent of a variable in any term of a polynomial must, by definition, be a nonnegative integer, such as 0, 1, 2, 3, 4, etc. The exponents of variables do not contain fractions, decimals, or negative numbers. There cannot be a variable with a fractional exponent in a polynomial.
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Eden is working on an experiment for her science fair project. She is planting a total of 10 herbs for an herb garden. She is going to plant basil and mint. The basil plants cost $.50 per plant and the mint plants cost $.25 per plant. Eden has a total of $3 to spend on plants because she also has to purchase potting soil and a long planter pot. Write a system of equations and solve either using elimination or substitution.
A system of equations for this problem can be written as:
x + y = 10 (1) equation for the total number of herbs planted
0.50x + 0.25y = 3 (2) equation for the total cost of the herbs
Where x is the number of basil plants and y is the number of mint plants.
Using substitution, we can solve the system of equations.
Solving equation (1) for x, we get x = 10 - y
Substituting this into equation (2) we get:
0.50(10 - y) + 0.25y = 3
5 - 0.50y + 0.25y = 3
5 = 0.75y + 3
0.75y = -2
y = -2/0.75 = -8/3
So, Eden planted -8/3 mint plants, which doesn't make sense, as a fraction of plant are not possible. This implies that either the number of plants or the amount spent are incorrect or something is missing in the problem description.
What is the value of F (- 3 2 where F x )= 4x2 3x 7 2?
The value of F (- 3 2 where F x )= 4x2 3x 72 is:
F ( -3) = - 27 and F (2) = - 62
What is function?In mathematics, function is an expression that shows a relationship between an independent variable and a dependent variable. In other words, a function creates a relation between an input to an output.
As per the given function F(x), x is the independent variable and F (x) is the dependent variables.
generally, we write F(x) = y
What is the value of F ( -3, 2) for the function given in question?given, F (x) = 4x² - 3x -72
F (x) is a function of x
for x = - 3, F ( -3) = 4(-3) ² - 3(-3) -72
F (- 3) = - 27
again, x = 2, we get F (2) = 4(2) ² - 3(2) - 72
F (2) = - 62
from the above calculation, we find (-3, 2) are domain of function F (x) and
(- 27, -62) are ranges of the above function.
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What is a equivalent ratio
Answer:
Step-by-step explanation:
In ratio and proportion , when we compare two ratios or we can say two fractions then they are said to be equivalent when both of them are same.
Use logarithmic table to evaluate 40.79÷0.003949
Answer:
1.033×10⁴
Step-by-step explanation:
You want the quotient 40.79÷0.003949 using log tables.
Log of quotientThe log of a quotient is the difference of logs:
log(a/b) = log(a) -log(b)
Log valuesIt can work well to start by writing the numbers in scientific notation:
log(40.79) = log(4.079×10¹) = 1 +log(4.079) = 1.6106
log(0.003949) = log(3.949×10⁻³) = -3 +log(3.949) = -3 +0.5965
Log of quotientThen the log of the quotient is ...
log(40.79/0.003949) = 1.6106 -(-3 +0.5965) = 4.0141
AntilogThe antilog of this number will be ...
antilog(4.0141) = 10⁴ × antilog(0.0141) ≈ 1.033×10⁴
With our 4-digit log tables, 4 significant figures is the best we can expect.
The quotient is about 1.033×10⁴.
__
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What are the potential solutions to the equation below? 1ln(x+3)=0
A. x = -3 and x = -4
B. x = -2 and x = -4
C. x = 2 and x = -3
D. x = 2 and x = 4
The potential solutions to the equation are x = -2 and x = -4
What is logarithm ?A logarithm is the power to which a number must be raised in order to get some other number .
The given expression is ln(x + 3) = 0
It can be rewritten as
[tex]ln _e (x + 3) = 0[/tex]
[Since base of a natural logarithm is considered as e]
[tex]e^0 = (x + 3)[/tex]
Since in a logarithmic function if log b with base e = c
Then we further solve the expression to get the possible roots.
x + 3 = 1
x = 1-3
x = -2
Therefore, the potential solutions are x = -2 and x = -4
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May someone please help me
The positive value of the distance between the two objects
is [tex]r = + \sqrt\frac{GM_1M_2}{F_g}[/tex]
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Considering the equation for determining the gravitational pull between two items [tex]F_g = \frac{GM_1M_2}{r^2}[/tex], where r is the distance between the objects M is the individual masses and G is the gravitational constant.
The answer to the r in the problem has two values. Since distance cannot be negative, there can only be one positive value, hence we want the positive value.
[tex]F_g = \frac{GM_1M_2}{r^2}[/tex]
[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].
[tex]r = \pm\sqrt\frac{GM_1M_2}{F_g}[/tex]
[tex]r = +\sqrt\frac{GM_1M_2}{F_g}[/tex].
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Jane is building a fence around her garden. For every 4 feet of fencing, the cost is 36 Complete the table below showing the length of the fence and the cost.
The Complete is showing the length of the fence and the cost.
Length of fencing 4 6 7 9 10
Cost: 36 54 63 81 90
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Length of fencing 4 6 7 x 10
Cost: 36 y z 81 w
Now, Using proportion
4/ 36 = 6/y
4y = 36(6)
y = 54
and, 4/36 = 7/z
4z = 36 (7)
z = 63
and, 4/36 = x /81
x = 9
and, 4/36 = 10/w
360 = 4w
w= 90
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If you could take one sample from the mystery bag in order to make a prediction, would you rather draw a sample of 10 marbles or a sample of 20 marbles. Explain your choice by referring to the representations of the two distributions.
I would choose to draw a sample of 20 marbles in order to make a more accurate prediction.
How to illustrate the sample?In general, it is generally better to draw a larger sample if you are trying to make a prediction. This is because a larger sample will provide more information and will therefore lead to a more accurate prediction.
For example, imagine that you are trying to predict the proportion of red marbles in a bag based on the samples that you draw. If you draw a sample of 10 marbles, there is a good chance that the proportion of red marbles in your sample will be different from the true proportion of red marbles in the bag.
However, if you draw a sample of 20 marbles, the proportion of red marbles in your sample will be more likely to be closer to the true proportion of red marbles in the bag.
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Write an equation of the line passing through the point (1,8) and parallel to y=−3x+10
The equation of the line is 3x + y - 11 = 0.
The slope-intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
First we find the slope of the line y=-3x+10 by placing it into slope-intercept form:
y = -3 x + 10
Therefore, the slope of the line is m= -3
Now since the equation of the line with slope m passing through a point
(x₁ ,y₁) is y-y₁ = m(x-x₁)
Here the point is (1,8) and slope is m= -3, therefore, the equation of the line is:
y - 8 = -3(x - 1)
y - 8 = -3x +3
3x + y - 11 = 0
Hence, the equation of the line is 3x + y - 11 = 0.
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In a rhombus MNLP, diagonals intersect each other at point O. If m∠MNL is 120° and the length of the side is 8 in, find m∠MNO, m∠MON, and NP. A (5pts) Find m∠MNO. Answer
In a rhombus, all sides are equal and the diagonals intersect each other at a 90 degree angle and bisect each other.
Diagonal of a rhombus bisects the angles of the rhombus at the vertex.
So as m∠MNL is 120°,
∠MNO = ∠LNO = 120/2 = 60°
The diagonals intersect each other at a 90 degree angle, therefore
m∠MON = 90°
Considering ΔMNO, right angled at O.
cos(∠MNO) = NO/ MN
cos(60) = NO/ 8
NO = 0.5×8 = 4
NP = NO + OP
NP = 2NO
NP = 2×4
NP = 8 in
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The 19th and 15th term of an AP are -5 and -7 1/2 repectively. What i the um of the firt 20 term
The sum of first 20 terms of the AP will be -206.25
As in AP, let us assume that the "a" be the first term and 'd' be the common difference.
So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.
So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)
And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)
Now subtracting (ii) from (i),
We will get,
4d = 2(1/2)
=>4d = 2.5
=>d = (2.5/4) = 0.625
Now putting value of "d" in (i)
We will get,
a+(18*0.625) = -5
a=-5-11.25 = -16.25
We have, the formula for finding the sum of terms:
Sum of terms can be determined by using formula:
Sum = (n/2) × [2a + (n-1)d]
Here, n = 20, a = -16.25, d = 0.625
We will get sum of first 20 terms as:
[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]
10[-32.5+11.875]
=10(-20.625) =-206.25
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