The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k
The given function is f(x)=7x^2.
The given vertex = (3,5)
The equation of the parabola with the vertex of (h,k) is
y=a(x-h)^2+k
On comparing we get; a=7, h=3, k=5
Now putting the value
f(x)=7(x-3)^2+5
Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
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In thi quetion, aume that the car ue the ame amount of petrol for each mile it travel. A car ue 55 litre of petrol to travel 495 mile. How much petrol would the car ue on a trip of 160 mile?
Give your anwer to the nearet litre
The car use 6.67 liters of petrol to travel 160 miles of distance.
Given, the car use the same amount of petrol for each mile it travels.
A car use 55 liters of petrol to travel 495 miles.
we have to find the petrol used to travel 160 miles.
As, 55 liters = 495 miles
495 miles = 55 liters
1 mile = 55/495 liters
Now, 160 miles = 55/495×160 liters
160 miles = 6.67 liters
So, the car use 6.67 liters of petrol to travel 160 miles of distance.
Hence, the car use 6.67 liters of petrol to travel 160 miles of distance.
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PLEASE ANSWER THE QUESTIONS BELOW.. A PICTURE WILL BE PROVIDED ABOVE^^^^^
1: RADIUS FOR NEW TANK?
2. EXISTING VOLUME?
3.SPHERE VOLUME?
4. TOTAL VOLUME?
5. NEW TANK VOLUME?
6. TRIAL OF VALUES FOR R?
1) Radius of the standard tank = 3 feet
2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.
3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.
4)Total volume of the tank is 36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet
5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.
6)Trails of values for r is 4 feet.
What do you mean by Volume?
A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.
What is radius?
A line segment connecting the circumference or boundary surface of a circle or sphere to its center.
Given that;
Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]
[tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]
Volume of new tank = 2 x Volume of standard tank
= 2 x 126π
= 252π
But according to formula, volume of new tank will be;
[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]
where r = radius of new tank
[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]
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the data set has 80 observations and has mean 30 and standard deviation 5. approximately how many observations lie between 20 and 40?
A minimum of 71 observations must fall inside the interval (20, 40).
Define Chebyshev's theorem.It is true that Chebyshev's Theorem holds true for all conceivable data sets. The minimal percentage of measurements that must fall within one, two, or more standard deviations of the mean is described. The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.
Given,
The data set has 80 observations and has mean 30 and standard deviation 5.
Chebyshev's theorem states that for each data set, the proportion (or percentage) of values that lie within k standard deviations of the mean (that is, the interval (x -ks , x +ks) is at least 1-1/k² . where k > 1.
x = 30
s = 5
Three standard deviations are added to and subtracted from the mean to get the interval (10, 40).
(30 - 3.5, 30 + 3.5) = (10, 40)
According to Chebyshev's Theorem, this interval contains at least 1 -1/3² = 8/9 of the data. Given that 8/9 of 80 is 71.11, the interval must include at least 71.11 observations. However, one cannot make a fractional observation, so we draw the conclusion that the interval must contain at least 71 observations.
A minimum of 71 observations must fall inside the interval (20, 40).
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At a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three. If there are 100 in the party, is the data consistent?
Answer:
no because 60+48+36 is 144
Step-by-step explanation:
please mark brainliest
The total number of people is 144. The data is not consistent.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.
The total number of the people in the party,
60+48+36 is 144
But it is given in the question that there are 100 in the party.
Therefore, the total number of people is 144. The data is not consistent.
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solve this equation using the most direct method:
3x(x+6)=-10
Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using (+-) symbol
The solution set for the given quadratic equation is (-0.62, -5.38).
The given equation is 3x(x+6)=-10.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 3x(x+6)=-10
⇒ 3x²+18x=-10
⇒ 3x²+18x+10=0
By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get
a=3, b=18 and c=10
Using quadratic formula x = [-b ± √(b² - 4ac)]/2a
= [-18 ± √(18² - 4×3×10)]/2×3
= [-18 ± √(324 - 120)]/6
= [-18 ± √(204)]/6
= [-18 ± √(204)]/6
= [-18 ± 14.28]/6
= [-18 + 14.28]/6 and [-18 - 14.28]/6
= -0.62 and -5.38
Hence, the solution set for the given quadratic equation is (-0.62, -5.38).
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rove by induction that 3n < n! for all integers n greater than 6. state whether you are using regular or strong induction
We can use both regular and strong induction.
The Fundamentals of Inductive Mathematics (i.e., Regular Induction). If any of the following statements involving a positive number, n, are accurate: The claim is true if and only if n is 1. If the assertion is true for n=k, then it must also be true for n=k+1(x).
In a variation of induction known as strong induction, we make the assumption that the assertion is true for all values before k. This provides us with more information with which to work.
Regular Induction form
N>6 = n=7 in basic case
3n = 37 = 2187
N! = 7! = 5040
For n= 7 3n<n! is true
Induction hypothesis
Let for n= k and k>6
Assume 3k<k! is true
We prove that for k = k+1 the assumption holds true then the assumption must be true for k
K = k+1
3k+1 < (k+1)!
3k. 3 < (k+1) k!
3k < (k+1)/3.k!
For k>6
(k+1)/3 >1 and let (k+1)/3 = p
3k < P.k!
But we assumed that 3k < k! for k > 6 then 3k must be less than p.k1 since P>1
Therefore 3k<k! for k>6
3n < n! for all integers n greater than 6.
Therefore we can use both regular and strong induction
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Flying against the wind, an airplane travels 7680 kilometers in 8 hours. Flying with the wind, the same plane travels 12,420 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.
What is speed?The distance covered in a unit of time is known as speed.
Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.
Therefore, the rate of the airplane against the wind is:
7680/8
= 960 km / hr
The rate of the airplane with the wind is:
12420/9
=1380 km / hr
Let the rate of the airplane in still air be a and the rate of the wind be w.
The net rate while flying against the air is:
a - w = 960 (1)
The net rate while flying with the wind is:
a + w = 1380 (2)
Add equations (1) and (2):
2a = 2340
a = 1170 km/hr
Substitute a = 1170 into equation (1):
1170 - w = 960
1170 - 960 = w
210 = w
Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.
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Find the slope (rate of change) of a line that passes through (-2,-3) and (1, 1).
We have coordinates (-2, -3) and (1, 1)
To find: Slope of a line that passes through these two coordinates
Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)
We will use the formula of Slope :
m = y₂ - y₁ / x₂ - x₁
Where 'm' stands for slope
m = 1 - (-3) / 1 - (-2)
m = 1 + 3 / 1 + 2
m = 4 / 3
The slope of the line is 4/3
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Alana meauring hi dining room table to make a tablecloth the table i zero. 45 m longer than it i wide if it i 1. 06 m wide how long i it?
The length of the table is 1.51 meters.
Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.
Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.
L = 1.06 + 0.45
L = 1.51
Hence, the length of the table is 1.51 meters.
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simplify each expression x = 2x + 48
(please its for today
Solve the following proportion for u. 7/u=3/11 Round to the nearest tenth.
The solution for u in the expression given as 7/u = 3/11 is u = 25.7
How to determine the solution to the variable u in the expression?From the question, the algebraic expression is given as
7/u = 3/11
There is no constant to add to or subtract from the expression
So, the equation remains the same
7/u = 3/11
Multiply both sides of the equation by u
This gives
u * 7/u = 3/11 * u
Evaluate the products
So, we have the following equation
7 = 3/11u
Multiply both sides of the equation by 11/3
This gives
11/3 * 7 = 3/11u * 11/3
Evaluate the products in the above expression
77/3 = u
So, we have
25.6667 = u
Approximate
25.7 = u
Rewrite as
u = 25.7
Hence, the solution is u = 25.7
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on a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes. what is the probability of a waiting time in excess of 25 minutes between successive speeders?
There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.
Define probability.Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes. Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how likely it is that a coin will land heads up after being tossed into the air.
Given,
On a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.
Either the wait is over 25 minutes or it is less than 25 minutes. Decimal 1 represents the total of these events' probabilities. So,
P( X ≤ 25) + P(X > 25) = 1
For P(X > 25):
1 -P(X ≤ 25)
1 - e ⁻⁰⁶⁶⁶⁽²⁵⁾
0.1892
There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.
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9) Willie took a trip to Oman. Upon leaving he decided to convert all of his Rials back into dollars. How many dollars did he receive if he exchanged 12 Rials at the rate of 1 Rial to $3?
10) A rectangle is 2 in wide and 1 in tall. If it is enlarged to a width of 14 in then how tall will it be?
number 9 is 36 12x3 is 36
14 The equation u = 0. 99c shows the value of the U. S. Dollar compared to
the Canadian dollar on one particular day, where c = the value of the
Canadian dollar and u = the value of the U. S. Dollar. The table shows
the value of the U. S. Dollar compared to the Australian dollar on the
same day. Was the U. S. Dollar closer in value to the Canadian dollar or
the Australian dollar that day?
N
t
sed the
the unit
Australian Dollar
1
2
3
4
compare
U. S. Dollar
0. 95
1. 90
2. 85
3. 80
Show your work.
On that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.
Define the term comparison of numbers?In arithmetic, comparing numbers is described as the process or method of determining whether one number is smaller, bigger, or equal to some other number based on their values.The equation u = 0. 99c depicts the value of the US dollar in relation to the Canadian dollar on a specific day.
c = the Canadian dollar's valueu denotes the value of the US dollar.From the equation,
For Australian dollar; (from table)
u = 0.95 c -->
a = 1/0.95 u
a = 20/19 u
(20/19u - u)/ u = 1/19 ....1
For Canadian dollar:
u = 0. 99c
c = 1/0.99 u --> c = 100/99 u
Thus,
(100 u / 99 - u)/ u = 1/99 .....2
From 1 and 2]
1/19 > 1/99
Thus, on that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.
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Graph the parabola
y=3x^2-x-2
A parabola is a bowl-shaped figure. Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
What is a parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface: a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. : something that is bowl-shaped.
Here the given quadratic equation is
[tex]y=3x^{2}-x-2[/tex]
The standard form of the quadratic equation is
[tex]y=ax^{2}+bx+c[/tex]
where [tex]a=3,b=-1,c=-2[/tex]
The axis of symmetry is the x-axis of the vertex
[tex]x=\frac{-b}{2a}\\x=\frac{1}{2(3)}\\x=\frac{1}{6}[/tex]
The y-value of the vertex is determined by substituting [tex]\frac{1}{6}[/tex] for [tex]x[/tex] into the equation and solving it for [tex]y[/tex].
[tex]y=3(\frac{1}{6})^{2}-\frac{1}{6}-2\\y=3(\frac{1}{36})-\frac{1}{6}-2\\y=\frac{3-6-72}{36}\\y=\frac{3-78}{36}\\y=\frac{-75}{36}[/tex]
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
Since [tex]a < 0[/tex] the vertex is the maximum point and the parabola opens downward.
X-intercept values of [tex]x[/tex] when [tex]y=0[/tex]
Substituting [tex]0[/tex] for [tex]y[/tex] and solving for [tex]x[/tex] using the quadratic formula
[tex]0=3x^{2}-x-2\\x=\frac{-b+-\sqrt{b^{2}}-{4ac}}{2a}\\x=\frac{1+-\sqrt{1}-{4(3)(-2)}}{2(3)}\\\\x=\frac{1+-\sqrt({1}+{24})}{6}\\\\\\x=\frac{1+-\sqrt(25)}{6}\\\\\\\\x=\frac{1+-5}{6}\\\\\\x=\frac{1+5}{6} , x=\frac{1-5}{6}\\\x=\frac{1+5}{6},x=\frac{1-5}{6}\\\\\x=1,x=\frac{-2}{3}[/tex]
Y-intercept values of [tex]y[/tex] when [tex]x=0[/tex]
Substituting [tex]0[/tex] for [tex]x[/tex] and solving for [tex]y[/tex] using the quadratic formula
[tex]y=3(0)^{6}-0-2\\y=-2[/tex]
Y-intercept [tex](0,1)[/tex]
Now substitute [tex]3[/tex] for [tex]x[/tex] and solve for [tex]y[/tex]
[tex]y=3(3)^{2}-3-2\\y=3(9)-5\\y=27-5\\y=22[/tex]
So the point is [tex](3,22)[/tex].
Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].
And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].
Since the additional point is [tex](3,22)[/tex]
The parabola is of the form
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a group of people were given a spelling test. the table shows their marks. work out the range of the marks. how many students are in the group. work out the mean mark of the group.
Answer: a) = 4
b) = 30
Step-by-step explanation:
a) They are asking for the range of the marks so you do 10-6 as 10 is the highest mark and 6 is the lowest
b) You find this out by adding the frequency up 10+4+7+4+5 = 30
Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter, what is the total amount she earned?
The total amount of the money earned by Paige will be $1591.92.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.
The total amount of earnings will be,
TA = ( 50 x 30 ) + ( 0.02 x 4596)
TA = 1500 + 91.92
TA = $1591.92
Therefore, the total amount of the money earned by Paige will be $1591.92.
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find the value of the expression when a=2 and b=7
The value of the expression when a=2 and b=7 is 41.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, the expression given is 3a + 5b and we want to find the value of the expression when a=2 and b=7.
This will be illustrated thus:
= 3a + 5b
= 3(2) + 5(7)
= 6 + 35
= 41
The value is 41.
The complete question is given below.
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Complete question
The expression given is 3a + 5b. Find the value of the expression when a=2 and b=7
In triangle ABC, the measure of angle C is 6 times the measure of angle B. 2 times angle A is 20 more than 3 time angle B. Find the measure of each angle in degrees.
Answer:
∠
A
=
x
=
32
∘
∠
B
=
3
x
=
3
⋅
32
=
96
∘
∠
C
=
x
+
20
=
32
+
20
=
52
∘
Step-by-step explanation: Every triangle adds up to 180.
Evaluate x³ if x = 6
Show work pls
Answer:
216
Step-by-step explanation:
x^3
6^3
6x6x6
36x6
216
Hopes this helps pleas mark brainliest
explain how to select a cluster sample of fans. what is the benefit of using a cluster sample in this context?
The cluster sample represents the the characteristic of group of same types objects.
What is the cluster sampling?
A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the entire population.
A researcher intends to carry out a study to evaluate sophomores' abilities in business education across the United States. There is no way to carry out a research study with participants from every university. Instead, the researcher can group the universities from each city into a single cluster by utilizing cluster sampling. The sophomore student population in the United States is then comprised of these clusters. Next, select clusters at random for the research project using either simple random sampling or systematic random sampling. The sophomores from each of these determined groups can then be picked on whom to perform the research study utilizing simple or systematic sampling.
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2(x + 3) = x-4
What is the answer?
Answer:
x=-10
Step-by-step explanation:
2(x+3) = 2x+6
2x+6=x-4
2x+6-6=x-4-6
2x=x-10
2x-x=x-10-x
x=-10
Does the following relation represent a function? {(16,7), (7,26), (15,16), (-7,15), (-8,26)} ?
Yes, No, There is not enough information to answer this question
given a normal distribution with a mean of 50 and standard deviation of 5, what percent of the values are between 40 and 60? enter answer as a percent with no decimals.
For the given normal distribution, 95% of the values lie between 40 and 60.
Let the said distribution be X
Here it is given that X follows a normal distribution and it has a mean of 50 and a standard deviation of 5.
Therefore we can write X~ N(50, 25)
Now we need to find P(40< X< 60)
= P(40< X< 60) = P(X < 60) - P(X<40)
To find this we need to convert it into the form of a standard normal and then look up the p-values from the Z-table.
To do this we need to use the formula
P(X < x) = Φ[(x - μ) / σ]
where,
μ is the mean
σ is the standard deviation
Therefore we get
P(X < 60) - P(X<40) = Φ[(60 - 50) / 5] - Φ[(40 - 50) / 5]
= Φ[2] - Φ[-2]
Φ(-x) = 1 - Φ(x)
Therefore,
Φ[2] - Φ[-2]
= 2Φ(2) - 1
We get the p-value
2 X .97725 - 1
= 1.9545 - 1
= 0.9545
= 95% (approx)
Hence 95% of the values are between 40 to 60.
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2
Select the correct answer.
Which interval describes where the graph of the function is positive?
-8
O
O
O
B.
A. -∞ <<∞
C.
A
D.
N
-∞ < x < -1
-8∞ < < -2
-2 < < -1
Ň
-6
-8
-N
6 8
Option B is the correct answer, the interval in which the graph of the function is positive is -∞ < x < -1.
What do mean by interval?
In mathematics, a (real) interval is a collection of real numbers that includes all real numbers that fall inside any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The set of all real numbers, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton are additional examples of intervals.
As we can see in the graph provided in the question, the graph of function reach the positive side of the y-axis at x = -1, it means one of the two end point of the interval is going to be -1. And, the graph is constantly and slowing increasing it's value as increase in the x-axis therefore, the other endpoint of the interval cab be considered as negative infinity.
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which graph represents a by traveling at a constant rate of 12 mph
There is no graph in your question
in the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a
If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.
The definition of the MoE, or margin of error, is
MoE = sigma ÷ sqrt(n)
The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.
The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.
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Identify the kind of sequence shown: 2,-1,-4, -7, -10, ... *
O Arithmetic
O Geometric
ONeither
Angles ABC and CBD are a linear pair. If m∠CBD=90°, what is m∠ABC in degrees?
NO LINKS OR FILES.
Measurement of ∠ ABC is 90°
What is Linear pair?A linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Given that ∠ CBD and ∠ ABC are linear pairs,
Therefore, m∠ CBD + m∠ ABC = 180°
m∠ ABC = 180° - 90° = 90°
Hence, Measurement of ∠ ABC is 90°
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What’s the answer 60 points plus brainliest also explanation needs to be included
Answer:
both a and b
Step-by-step explanation:
It is because in the elimination method it does not matter whether you eliminate x or y so if you use option a which multiplies -2 by 1st equation so it will become:
-4x+6y=40
4x+6y=8
so the -4x and 4x cancels and a is a valid option.
If you use the b which multiplies the second with 3 it becomes:
2x-3y=-10
4x+3y=24
so -3y and 3y cancel which also makes this a valid option.
Answer: both a and b