Triangle congruence is proved by a sequence of reflections and translations.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Given that, ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17).
By using distance formula, distance =√(x₂-x₁)²+(y₂-y₁)²
AB = 6 units BC = 11 units AC = 12.53 units
∆XYZ X(-10, 5), Y(-12, -2), and Z(-4, 15)
XY = 7.14 units YZ = 18.79 units XZ = 11.66 units
∆MNO M(-9, -4), N(-3, -4), and O(-3, -15).
MN = 6 units NO = 11 units MO = 12.53 units
∆JKL J(17, -2), K(12, -2), and L(12, 7).
JK = 5 units KL = 9 units JL = 10.30 units
∆PQR P(12, 3), Q(12, -2), and R(3, -2)
PQ = 5 units QR = 9 units PR = 10.30 units
So, we have the ∆ABC and the ∆MNO
With all three sides equal are congruent
We have the ∆JKL and the ∆PQR
with all three sides equal are congruent
Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or rotations).
1) If ∆MNO by a sequence of reflections and translation, it can be obtained ∆ABC, then ∆MNO ≅ ∆ABC
a) Reflection (On x-axis)
The coordinate notation for the Reflection is (x,y)→(x,-y)
∆MNO M(-9, -4), N(-3, -4), and O(-3, -15).
M(-9, -4)→ M1(-9,4)
N(-3, -4)→ N1(-3,4)
O(-3,-15)→ O1(-3,15)
B) Reflection (y-axis)
The coordinate notation for the Reflection is (x,y)→(-x,y)
In ∆M'N'O', M'(-9, 4), N'(-3, 4), and O'(-3, 15).
M'(-9, -4)→M"(9,4)
N'(-3, -4)→N"(3,4)
O'(-3,-15)→O"(3,15)
C) Translation
The coordinate notation for the Translation is (x,y)→(x+2,y+2)
∆M"N"O", M"(9,4), N"(3,4), and O"(3, 15).
M"(9, 4) → A(11,6)
N"(3,4)→B(5,6)
O"(3,15)→C(5,17)
So, we have ∆ABC, A(11, 6), B(5, 6) and C(5, 17)
From ∆MNO to ∆M'N'O' reflection, from ∆M'N'O' to ∆M"N"O" reflection, and from ∆M"N"O" to ∆ABC its translation.
2)If ∆JKL, by a sequence of rotation and translation
We obtained ∆PQR
So, ∆JKL ≅ ∆PQR
D) Rotation 90 degree anticlockwise
The coordinate notation for the Rotation is (x,y)→(-y, x)
In ∆JKL, J(17, -2), K(12, -2), and L(12, 7).
J(17, -2)→J'(2,17)
K(12, -2)→K'(2,12)
L(12,7)→L'(-7,12)
E) Translation:
The coordinate notation for the translation is (x, y)→ (x+10, y-14)
Then, ∆J'K'L' has vertices J'(2, 17), K'(2, 12), and L'(-7, 12).
J'(2, 17)→P(12,3)
K'(2, 12)→Q(12,-2)
L'(-7, 12)→R(3,-2)
So, ∆PQR has P(12, 3), Q(12, -2) and R(3, -2)
From ∆JKL to ∆J'K'L' its rotation and from ∆J'K'L' to ∆PQR its translation.
Therefore, ∆JKL ≅ ∆PQR
Hence, triangle congruence is proved by a sequence of reflections and translations.
To learn more about the translation visit:
https://brainly.com/question/17485121.
#SPJ1
Where do I graph the solutions on the number line for both?
Answer:
Step-by-step explanation:
#1 - (−3,9)
#2 - (−∞,−7) and also( −3,∞)
Find the volume of the solid obtained by rotating the region bounded by the graphs y=2, the x- axis, x=10 about x=10. (Give an exact answer. Use symbolic notation and fractions where needed.)
The volume of the solid is -30π cubic units
How did we get the value?The volume of the solid obtained by rotating the region about the x-axis is given by the formula:
V = π * ∫[a,b] (R^2 - (x-c)^2) dx
Where:
a = lower limit of x-coordinate of the region
b = upper limit of x-coordinate of the region
c = axis of rotation
R = distance from the x-axis to the boundary of the region
For the given region, a = 0, b = 10, c = 10, and R = 2.
So the volume of the solid is:
V = π * ∫[0,10] (2^2 - (x-10)^2) dx
= π * ∫[0,10] (4 - (x-10)^2) dx
= π * [2x - (x-10)^2/2 + C] evaluated at x=10 and x=0
= π * [20 - 100/2 + C - 0]
= π * (20 - 50 + C)
= π * (-30 + C)
= π * (-30) = -30π cubic units.
Therefore, the volume of the solid is -30π cubic units
learn more about volume of rotated region: https://brainly.com/question/25756489
#SPJ1
The rate of change of the number of people entering a movie theater is modeled by a logistic differential equation. The capacity of the theater as 500 prole at a certain the number of theater is 100 and is increasing at the rate of 50 per minute. Which of the following differential equatione could describe this situation?
a. dp/dt = 1/8 (500 - P) b. dp/dt = 1/50 P (500-P)
C. dp/dt = 1/500 P (500-P)
d. dp/dt = 1/1200 P (500-P)
The correct answer is d. dp/dt = 1/1200 P (500-P).
What is rate of change?Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period it is commonly used mathematics physics economic and other discipline to make operate of vijay process is a caring rate of changing also known as velocity, derivative or slope.
This differential equation describes the rate of change of the number of people entering a movie theater. It states that the rate of change (dp/dt) is equal to the product of 1/1200 and the current number of people (p) in the theater, multiplied by the difference between the capacity of the theater (500) and the current number of people (p). This equation indicates that the rate of change of people entering the theater is proportional to the difference between the capacity and the current number of people.
To know more about rate of change click-
https://brainly.com/question/25184007
#SPJ1
Company provides to their clients the following products: accidental insurance and
health insurance.
If 55% of male clients opt for accidental insurance and 65% of female clients opt for
health insurance, then what is the probability that health insurance contract is chosen if
60% of the company’s clients are females?
Answer:The probability of a female client choosing health insurance is 65%, and 60% of the company's clients are female, so the probability of choosing health insurance is:
P(health insurance) = 0.65 * 0.60 = 0.39
Therefore, the probability that a health insurance contract is chosen is 0.39.
Step-by-step explanation:
The probability of a female client choosing health insurance is 65%, and 60% of the company's clients are female, so the probability of choosing health insurance is:
P(health insurance) = 0.65 * 0.60 = 0.39
Therefore, the probability that a health insurance contract is chosen is 0.39.
5 STAR AND THANK ME PLS :))
23. The escape velocity from the surface of the Moon is 2.4 × 10³ ms ¹.
(a)
An object is projected from the surface of the Moon with a speed
of 2.0 10³ ms ¹.
Calculate the maximum height reached above the Moon's surface.
The object will reach a maximum height of approximately -89,898.36 meters, or 89.9 kilometers, above the Moon's surface before it falls back down.
What do you mean by escape velocity?Escape velocity is the minimum speed an object must have in order to escape the gravitational pull of a celestial body, such as a planet or moon, and travel into space. It is calculated based on the mass and radius of the celestial body and the distance of the object from its surface. The greater the mass and radius of the celestial body, the greater the escape velocity.
The formula for escape velocity is given by v_escape = √(2GM/R), where G is the gravitational constant, M is the mass of the object, and R is the radius of the object.
In this case, v_escape = 2.4 × 10³ m/s and v_projected = 2.0 × 10³ m/s.
The maximum height can be calculated using the following formula:
h = (v_projected^2 - v_escape^2) / (2g), where g is the acceleration due to gravity.
Since the escape velocity is greater than the projected velocity, the object will not escape the Moon's surface and will eventually fall back down. The maximum height it reaches is given by:
h = (2.0 × 10³ m/s)^2 - (2.4 × 10³ m/s)^2 / (2 * 9.8 m/s^2) = (4.0 × 10^6 - 5.76 × 10^6) m / 19.6 = -1.76 × 10^6 m / 19.6 = -89,898.36 m.
The object will reach a maximum height of approximately -89,898.36 meters, or 89.9 kilometers, above the Moon's surface before it falls back down.
To know more about acceleration visit:
https://brainly.com/question/12550364
#SPJ1
I need help which one????
Answer:
>
Step-by-step explanation:
3^3*3^-2 ? 3^2*3^-3
27*1/9 ? 9*1/27
3 > 1/3
Answer:
3^3 (times)3^-2 < 3^2 (times) 3^-3
Step-by-step explanation:
3^3 (times)3^-2
27 (times) -9
=-243
3^2 (times) 3^-3
9(times)27
=243
The coordinates on a map for San Francisco are
(53, 17) and those for Sacramento are (123, 78).
Note that coordinates represent miles. Find the
distance between the cities to the nearest mile.
I am unsure how to do all of them. Help would be appreciated!
The required distance between the two given cities using the distance formula is 93 miles.
What is the distance?Distance is the sum of an object's movements, regardless of direction.
The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.
The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.
So, we have the points:
(53, 17) and (123, 78)
Distance formula:
d = √(x2-x1)² + (y2-y1)²
Now, calculate as follows:
d = √(x2-x1)² + (y2-y1)²
d = √(123-53)² + (78-17)²
d = √(70)² + (61)²
d = √(4,900) + (3,721)
d = √8,621
d = 92.84
Rounding off: 93 miles
Therefore, the required distance between the two given cities using the distance formula is 93 miles.
Know more about the distance here:
https://brainly.com/question/2854969
#SPJ1
The minute hand of a clock is 6 inches long. How far does the tip of the minute hand move in 35 minutes?
Answer:
22 in
Step-by-step explanation:
It travels 35/60 ths of the complete circumference of a circle with r =6 in
diameter = 12 circumference = pi * d
35/ 60 * pi * 12 = ~22 inches
Which of the following statements are true? I. The sampling distribution of ¯x¯ has standard deviation σ /√n even if the population is not normally distributed. II. The sampling distribution of ¯x¯ is normal if the population has a normal distribution. III. When n is large, the sampling distribution of ¯x¯ is approximately normal even if the the population is not normally distributed. I, II, and III
All three statements are true. The sampling distribution of the sample mean has standard deviation σ/√n even if the population is not normally distributed.
The sampling distribution of the sample mean is normal if the population is normally distributed. Lastly, when the sample size is large, the sampling distribution of the sample mean is approximately normal even if the population is not normally distributed .
The sampling distribution of the sample mean is a probability distribution of the means of all possible samples of a given size from a given population. It is used to describe the behavior of the sample mean in relation to the population mean. The sampling distribution of the sample mean has a mean of μ (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size
Learn more about the sampling distribution:
https://brainly.com/question/30331609
#SPJ4
Please help me with this question.
solve the equation below
Answer:
x = 4cm
Step-by-step explanation:
If the triangle is equilateral, then we already know one of the sides has a length of 3+5 (8).
This, therefore, means the 2 other sides' lengths are also equal to eight, which means all we need to do to find x is subtract 4 from 8, which gives us 4.
Hope this helps
Answer:
[tex]x=\dfrac{20}{3}\; \sf cm[/tex]
Step-by-step explanation:
Side-Splitter TheoremIf a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally.
Applying the side-splitter theorem:
[tex]\implies \dfrac{3}{5}=\dfrac{4}{x}[/tex]
Cross multiply:
[tex]\implies 3 \cdot x=4 \cdot 5[/tex]
[tex]\implies 3x=20[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3}=\dfrac{20}{3}[/tex]
[tex]\implies x=\dfrac{20}{3}[/tex]
Therefore, the value of x is ²⁰/₃ cm
 Look at the steps for solving the equation and choose a true statement.
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
O a
Ob
0 c
0 d
0 e
There is no way to know if there is a solution to this equation.
There are no solutions to the equation.
There are infinitely many solutions to the equation.
The only solution to the equation is -6.
The only solution to the equation is 1.
A finite arrangement of symbols that adheres to context-specific standards and is well-formed is referred to as a mathematical expression.
What is meant by equation?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms. In mathematics, an equation is an equality statement that includes one or more variables or unknowable quantities.
When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. A sentence in math is called an equation.
Let the equations be
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
Therefore, the correct answer is option There are infinitely many solutions to the equation.
To learn more about equation refer to:
https://brainly.com/question/1859113
#SPJ1
Find the equation of the normal line (on the xy-plane) at the point (2, 1) to the ellipse
(x^2) / 4 + y^2 = 2
Answer:
This is the equation of the normal line at the point (2, 1) on the ellipse (x^2)/4 + y^2 = 2.
Step-by-step explanation:
The equation of the ellipse is (x^2)/4 + y^2 = 2. To find the equation of the normal line at the point (2, 1), we first need to find the slope of the tangent line at that point. To do this, we can use the formula for the slope of a tangent line:
slope = -(d/dx)(f(x)) / (d/dy)(f(y))
Where f(x) and f(y) are the equations of the ellipse.
So,
slope = -(x/2)/y = -x/2y
Now we can substitute the point (2, 1) into the equation for the slope:
slope = -(2/2)/1 = -1
We know that the slope of the normal line is the negative reciprocal of the slope of the tangent line, so the slope of the normal line is 1.
To find the equation of the normal line, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Where (x1, y1) is the point on the line and m is the slope.
So,
y - 1 = 1(x - 2)
Simplifying, we get:
y = x - 1
This is the equation of the normal line at the point (2, 1) on the ellipse (x^2)/4 + y^2 = 2.
1/27
2/346
3/34
4/0244
5/24679
6/02
Min=
Q1=
Med =
Q3 =
Max =
Answer: Min=0.02
Q1=0.037037
Med = 0.037037
Q3 = 0.346790
Max = 346
Step-by-step explanation:
To convert the numbers to decimal, we can divide the number before the slash by the number after the slash. So for example, 1/27 becomes 0.037037.
After converting the numbers to decimal and arranging them in ascending order, we get:
0.02, 0.037037, 0.03448, 0.040816, 0.346790, 346
To find the Q1, median (Med), Q3, and other measures of central tendency and spread for this list of numbers, we first need to order the numbers in ascending order:
0.02, 0.03448, 0.037037, 0.040816, 0.346790, 346
Q1 is the value that separates the lowest 25% of the data from the rest of the data. To find Q1, we need to find the median of the lower half of the data set. Since there are 6 numbers in the set and Q1 is the middle value of the lower half, Q1 would be the 3rd number in the ordered set, which is 0.03448.
Med is the middle value of the data set. Since there are 6 numbers in the set, the median would be the 3rd and 4th numbers, which are 0.03448 and 0.037037.
Q3 is the value that separates the highest 25% of the data from the rest of the data. To find Q3, we need to find the median of the upper half of the data set. Since there are 6 numbers in the set and Q3 is the middle value of the upper half, Q3 would be the 5th number in the ordered set, which is 0.346790.
Min is the smallest value of the dataset, which is 0.02
Max is the largest value of the dataset, which is 346
Write this number in scientific notation.
.00000092
[?] ×
]
The number in scientific notation is 9.2 × 10^-7.
How to convert the numberFrom the question, we have the following parameters that can be used in our computation:
Number = .00000092
The number of points from the initial position to a point between 9 and 2 is -7
This means that the coefficient is 9.2 and the power of ten is -7
So, we have
9.2 × 10^-7.
Read more about scientific notation at
https://brainly.com/question/30390146
#SPJ1
Answer:
10^(-7)
Step-by-step explanation:
put first non-zero number, then decimal, then rest of numbers as so
9.2
multiply by +/- depending on where decimal is
9.2*10^(-7)
so 10^(-7)
florida wants to estimate the mean mercury level in the fish from a particular lake. they take a random sample of 56 fish from the lake and record the mercury level of each fish. Fill in the following in the context of this problem: Sample: A sample of 56 fish from a randomly selected Florida lake Variable: Mean mercury level in 56 fish from a randomly selected Florida lake Type of variable: qualitative quantitative continuous quantitative-discrete Mean mercury level in fish of all Florida lakes Parameter of interest: Random sample of 56 fish from the lake Statistic that will be used:
Sample: A sample of 56 fish from a randomly selected Florida lake.
Variable: Mean mercury level in 56 fish from a randomly selected Florida lake
Type of variable: quantitative-discrete
Mean mercury level in fish of all Florida lakes: Parameter of interest
Statistic that will be used: Mean (arithmetic average) of the mercury levels in the sample of 56 fish from the lake.
The Statistic of Florida sampleThe sample of 56 fish from a randomly selected Florida lake represents a portion of the population of fish in all Florida lakes. The mean mercury level in these 56 fish represents a statistic, which is an estimate of the population parameter, the mean mercury level in fish of all Florida lakes.
The mean (arithmetic average) is used as the statistic because it summarizes the data by finding the central tendency of the mercury levels in the sample of 56 fish. It is a suitable measure to describe the typical mercury level in the fish from the lake because it takes into account all the observations in the sample.
Since mercury levels are measured in numerical values, the variable "mean mercury level" is quantitative. Since it is a continuous measurement, it is also a continuous quantitative variable.
In summary, the sample and the mean mercury level in the sample of 56 fish are used to make inferences about the population and its parameter, the mean mercury level in fish of all Florida lakes. The mean is used as the statistic to summarize the data and describe the central tendency of the mercury levels in the sample.
Learn more about The Statistic of Florida sample here:
https://brainly.com/question/16846185
#SPJ4
6x+2y= −4 simplified all fractions
According to the problem the simplified form of the equation is x = -1/2 and y = -3.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions by showing that they have the same value. Equations can be used to describe a variety of physical, chemical and biological processes. They are often used to solve problems in a variety of fields, including engineering, finance and physics.
6x + 2y = -4
This equation can be simplified by combining all like terms on one side of the equation and all constants on the other. In this case, we can combine the 6x and 2y terms to get 8x = -4. We can then divide both sides of the equation by 8 to get x = -1/2. Substituting this value into the original equation, we get 2y = -6. We can then divide both sides by 2 to get y = -3. Therefore, the simplified form of the equation is x = -1/2 and y = -3.
To learn more about equation
https://brainly.com/question/17145398
#SPJ1
Solve the following system of equation. Be sure to show each of your work steps.
The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i
What is Quadratic Equation ?
Quadratic equation can be defined as the equation in which it is in the form of ax^2 + bx + c = 0
where c is a constant.
Given equations,
x^2 - 2x +3 = 0
so, we know that
the roots of a quadratic equation
= (- b + (√ b^2 - 4ac )) / 2a , (- b - (√ b^2 - 4ac )) / 2a
so,
here a = 1 b = -2 c = 3
by substituting the given values,
we get,
= 2+ (√ 4 - 4*1*3 ) / 2 , 2- (√ 4 - 4*1*3 ) / 2
= 2+ (√-8) / 2 , 2- (√-8) / 2
= 2+8i / 2 , 2-8i / 2
= 1 + 4i , 1- 4i
Hence, The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i
To learn more about Quadratic equation from given link.
https://brainly.com/question/30098550
#SPJ1
let be a random variable with pdf f(x) =x2 , x20 .
Find the value of the constant(round off to second decimal place).
The random variable's pdf is f(x) = (3/8) x^2 , x ∈ [0, 2].
Finding the normalizing constant that equals the integral of the pdf over the support of the random variable yields the constant in the pdf (probability density function).
The random variable's support is the interval [0, 2]. The normalizing constant can be calculated as follows:
∫_0^2 x^2 dx = [x^3/3]
_0^2 = (8/3) - (0) = 8/3
So, in the pdf, the constant is 1/(8/3) = 3/8, rounded to the second decimal place.
As a result, the random variable's pdf is:
f(x) = (3/8) x^2 , x ∈ [0, 2].
To learn more about variables.
https://brainly.com/question/29508931
#SPJ4
Hamza found a pattern with some division expressions.
1. Calculate each quotient. (I already did this.)
2. Describe a pattern you see. (I can't find anything :)
The pattern in the following expressions is of square of numbers.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
In given expressions, In divisor the numerator and denominator are square of numerator and denominator in the dividend.
e.g. in (3/5)/(9/25) 9=3^2 and 25=^2
Hence,
The pattern in the following expressions is of square of numbers.
To know more about expressions visit the link
https://brainly.com/question/13947055?referrer=searchResults
#SPJ1
Find the linear function, f (x), passing through the points (-1,-5) and (-8,-5)
we could go ahead and check its slope and so forth, OR we can just take a peek that the y-coordinates are the same -5, hmmmm well, hell that's just a horizontal line, Check the picture below.
Each month, Kim donates the same amount of money to a charity. If she donates $1,800 in one year, how much does she donate each month?
$150 each month
Step-by-step explanation:
1 year=12 months
$1800/12
= $150 each month
Answer:
$150 each month
Step-by-step explanation:
Step 1: take the amount of money she donates in a year and divide it by 12, because there are 12 months in a year. Dividing 1,800 by 12 will tell you how much money she donates each month.
[tex]\frac{1,800}{12}= 150[/tex]
The following expression gives an approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995. 410t+5690 Use this expression to predict what the total average credit card debt was or will be in the year 1998. answer: in the year 1998, the total average credit card debt for a u.s. household will be (or was) ______dollars.
In the year 1998, the total average credit card debt for a U.S. household was approximately 6920 dollars.
As per the data given in the questions,
We have,
The expression for calculating the approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995 is: 410t+5690
So, first we will calculate the value of t
As we have in the year 1998, t = 1998 - 1995 = 3.
So, for determining the value of the total average credit card debt in a u.s. household, we will simply plug in this value into the expression,
Thus, will get it as
410 * 3 + 5690
= 1230 + 5690
= 6920
For more questions on Linear Equation
https://brainly.com/question/2030026
#SPJ4
WHAT IS THE LIMIT OF A CONSTANT?
The limit of a constant function is equal to the constant. The limit of a linear function is equal to the number x is approaching.
What are limits?A limit is defined as a value that a function approaches the output for the given input values.
Limit of a constant :-
We know that the limit of a function exists, only and only if the left-hand limit (LHL) and the right-hand limit (RHL) exists and are equal to one another. And, the value of the limit of that function is equal to the common value, LHL = RHL = f(x).
We need to find the limit of a constant. So, let us assume a function, f(x) = c, where c is a constant. We are assuming that we need to find the limit of this constant function at x = a, i.e. we need to find the value of
[tex]\lim_{x \to \ a} f(x)[/tex]
Plot the graph, y = c, (attached)
Let us calculate the left hand limit first.
LHL = [tex]\lim_{x \to \ -a} f(x)[/tex]
We can see that at x = -a, the value of f(x) is c.
LHL = c.....(i)
Similarly,
For right-hand limit,
We have at x = +a, the value of f(x) is c.
RHL = c....(ii)
Also, Also, the value of our function at a, i.e., f(a) = c
Thus, by equation (i), (ii) and (iii), we can say that
[tex]\lim_{x \to \ a} f(x) = c[/tex]
Hence, we can now say that the limit of any constant is the same constant.
Learn more about limits, click;
https://brainly.com/question/8533149
#SPJ1
21. Probability. is a measure of the ___________________ that a specific event will occur
Probability is a measure of the likelihood that a specific event will occur in a random experiment.
What is the Probability?
The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
In other words, the probability is a number that represents the chance or chance of an event occurring out of all possible outcomes.
It is expressed as a fraction, decimal, or percentage.
For example, if there is a 50% chance of rain, this means that the probability of rain is 0.5 or 1/2.
Probability is important in decision-making, risk assessment, and mathematical modeling. It helps to quantify uncertainty and provides a way to assess the likelihood of different outcomes.
Hence, Probability is a measure of the likelihood that a specific event will occur in a random experiment.
To learn more about Probability visit,
brainly.com/question/24756209
#SPJ1
plaz answer this i beg you
Answer:
I'm not exactly sure, but I'm positive that it's 60 degrees.
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
90 = 30 + (4x)
60 = 4x
x = 60/4 = 15
30° and (4x)° must add up to 90° because they are complementary angles
Electronics The output voltage of an amplifier is calculated by multiplying the input voltage by the voltage gain of the amplifier. Calculate the output voltage, in millivolts (mV), for a circuit if the input voltage is 45 mV and the gain is 30.
The output voltage, in millivolts (mV), for the circuit would be = 1,350 millivolts.
What is an amplifier?An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.
The output voltage of an amplifier= input voltage × gains.
Where;
input voltage = 45 mV
The gain = 30
Therefore the output voltage= 45×30 = 1350millivolts.
Learn more about multiplication here:
https://brainly.com/question/28768606
#SPJ1
the amount of apple juice in a 500 ml can from a certain company is distributed as find the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice (round off to third decimal place).
The probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice is approximately 0.5949 (rounded off to third decimal place).
To find the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice, we need to find the cumulative distribution function (CDF) of a normal distribution with a mean of 500 and standard deviation 4.
Using the Z-score formula, we can calculate the Z-score for 499 ml of juice: (499-500)/4 = -0.25
Next, we use a standard normal table to find the probability of a Z-score less than -0.25, which is 0.4051.
Finally, we use the CDF formula for a normal distribution to find the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice:
P(X < 499) = 1 - P(X >= 499) = 1 - 0.4051 = 0.5949
Therefore, the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice is approximately 0.5949 (rounded off to the third decimal place).
For more questions like Probability visit the link below:
https://brainly.com/question/17023015
#SPJ4
Finish this sequence:
15,20,30,_,65,_,120
pls fill the blanks
Answer:
1st blank = 45
2nd blank = 90
Step-by-step explanation:
this is an quadratic sequence. (an^2 + bn + c)
use of the formulas
2a = (_)
3a + b = (_)
a + b + c = (_)
Find the measure of the complement of a 66° angle.
The measure of the complement of a 66° angle is.
(Simplify your answer. Type an integer or a decimal.)
Please help. Btw it’s only one number
Complementary angles add up to 90°, write an equation using this knowledge and the information provided in the question:
66°+x° = 90°
Subtract 66° from both sides:
x° = 24°
