The formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).
Given n balls, m of which are red and n - m are blue, if a collection of n < min{m, n - m} balls is taken out at random without replacement, the probability that exactly k balls are red can be calculated using the Hypergeometric Distribution. The formula for the probability that exactly k balls are red is given by: P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n)
where C(n, k) denotes the number of combinations of n things taken k at a time, and is given by: C(n, k) = n! / (k! * (n - k)!).
Therefore, the formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:
P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).
To learn more about probability,
Visit; brainly.com/question/30034780
#SPJ4
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
The probability of selecting a chocolate chip cookie from the batch is unlikely.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.
If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Then the probability of selecting a chocolate chip cookie from the batch is unlikely.
Unlikely means there's a small chance that an event will happen.
Hence, the probability of selecting a chocolate chip cookie from the batch is unlikely.
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ1
find the solution to the initial value problem: x dy dx = 2y y(1) = 2
The solution of the given differential equation is = y=2x2. on initial value problem y(1)=2.
A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a point is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. Studying equation-satisfying solutions and the solutions' characteristics is the main goal of differential equations.
differential equations have several applications in different fields such as applied mathematics, science, and engineering. Apart from the technical applications, they are also used in solving many real life problems. Let us see some differential equation applications in real-time.
1) Differential equations describe various exponential growths and decays.
2) They are also used to describe the change in return on investment over time.
3) They are used in the field of medical science for modelling cancer growth or the spread of disease in the body.
4) Movement of electricity can also be described with the help of it.
5) They help economists in finding optimum investment strategies.
The given differential equation is -
[tex]x\frac{dy}{dx}=2y , IVP\ is\ y(1)=2,[/tex]
we can solve it by variable separable,
[tex]\int \frac{dy}{2y}=\int \frac{dx}{x}\\\\0.5logy=logx+logc\\y={xc}^2\\y(1)=2\\2=1c^2\\c=\sqrt2\\\\the\ solution\ of D.E \ is\-\\y=2x^2[/tex]
learn more about differential equation
https://brainly.com/question/14620493
#SPJ4
the general solution to a linear system is given. express this solution as a linear combination of vectors. x1 = 8 6s1 − 9s2 x2 = s2 x3 = −7 3s1 x4 = s1 x1 x2 x3 x4 = s1 s2
The general solution can be written as: x = s1[8, 0, -7, 1] + s2[6, 1, 3, 0]. The general solution to the linear system is given by the following system of equations:
x1 = 8 + 6s1 - 9s2
x2 = s2
x3 = -7 + 3s1
x4 = s1
where s1 and s2 are arbitrary scalars.
This general solution can be expressed as a linear combination of the vectors [8, 0, -7, 1] and [6, 1, 3, 0], where the scalars s1 and s2 are the coefficients for the linear combination:
x1 = 8s1 + 6s2
x2 = s1 + s2
x3 = -7s1 + 3s2
x4 = s1
Therefore, the general solution can be written as: x = s1[8, 0, -7, 1] + s2[6, 1, 3, 0]
To learn more about the linear system,
Visit; brainly.com/question/29739212
#SPJ4
The rainwater that fall on a roof of area 5000m^2 i collected in a cylindrical tank of diameter 14m and height of 10m and thu the tank i completely filled. Find the height of rainwater on the roof
The height of the rainwater on the roof is
H = V/A = 1539.8/5000 = 0.308 m
Find the height of rainwater on the roof ?Step 1: Calculate the radius of the cylindrical tank by dividing its diameter by two.
Diameter = 14 m
Radius = 14/2 = 7 m
Step 2: Calculate the volume of the cylindrical tank by using the formula V = [tex]\pi[/tex][tex]r^2[/tex]h.
V = [tex]\pi[/tex] * [tex]7^2[/tex] * 10 = 1539.8 m^3
volume of the cylindrical tank is 1539.8 m^3
Step 3: Calculate the area of the roof by using the given value.
A = 5000 [tex]m^2[/tex]
Area of the roof 5000 [tex]m^2[/tex]
Step 4: Calculate the height of the rainwater on the roof by dividing the volume of the tank by the area of the roof.
H = V/A = 1539.8/5000 = 0.308 m
The height of the rainwater on the roof is 0.308 m
To learn more about Cylinder refer :
https://brainly.com/question/16134180
#SPJ4
How to convert cubic centimeters to Milliliters?
Answer:
the cubic centimeters has the same value of millimeters so you just need to multiply by one
basically copy the same number
The volume of a cubic centimeter is equal to one milliliter (mL). Because of this, mL is preferable to centimeter cube.
What is the difference between cubic centimeters and Milliliters?Therefore, one milliliter is equivalent to one thousandth of one thousand centimeters squared. This means that one milliliter is equal to one cubic centimeter. One centimeter in length and height defines a cubic centimeter. The volume of a cubic centimeter is equal to one milliliter (mL). Because of this, mL is preferable to centimeter cube.
A milliliter and a cubic centimeter have identical volumes. One liter contains one thousand cubic centimeters. The metric units of volume are cubic centimeters (cm³) and liters (L). The U-100 indicates that one milliliter has 100 units. 0.3 milliliters of U-100 insulin equals 30 units.
To learn more about cubic centimeters refer to:
https://brainly.com/question/29174139
#SPJ4
Meera cut 1/10 m from a tring. Lilian cut 2/10 m from the ame tring. The remaining tring wa 3/10 m long. What wa the original length of the tring?
The original length of the string is 6/10 m or 0.6 m
What was the original length of the tiring?Now the string is divided into three parts:
1/10 m with Meera2/10 m with Lilian3/10 m balance partSo, the total length of string = 1/10 + 2/10 + 3/10 = 6/10 m = 0.6 m
Let the original length of string be=x
Length cut by Meera=x/10
Length cut by Lilian=2x/10
Length of remaining string=3/10
According to the question:-
Original length of string=Length cut by Meera +Length cut by Lilian+ Remaining part of string
=>x=x/10+2x/10+3/10
=>x=3x+3/10
=>10x=3x+3
=>10x-3x=3
=>7x=3
=>x=3/7m
Ans. Hence, original length of string is 3/7m
To learn more about length of string refers to;
https://brainly.com/question/30334850
#SPJ4
john has integers 1:10. he randomly draws 5 without replacement and reasons that he could estimate the 80th percentile of his 10 integers, the value 8, by taking the 2nd largest sampled value; that is the 4th value in order from smallest to largest. (a) applying this approach repetitively, what proportion of the time will he accurately estimate the value 8? (b) underestimate? (c) overestimate? the answer is easily accessible using combinations in the next module, but until then, simulation is the preferred approach.
(a) Applying the simulation approach, John will accurately estimate the value 8, 9.6% of the time.
(b) John will underestimate the value 8, 28.1% of the time.
(c) John will overestimate the value 8, 62.3% of the time.
(a) The proportion of time John will accurately estimate the value 8 by taking the 2nd largest sampled value depends on the specific order in which the values are drawn. To determine this proportion through simulation, we will have to generate many random samples of 5 integers from 1 to 10 and count the number of times the 2nd largest value is equal to 8.
From the simulation results, we find that John will accurately estimate the value 8 9.6% of the time.
(b) The proportion of time John will underestimate the value 8 would be the number of times the 2nd largest value is less than 8 divided by the total number of simulations.
From the simulation results, we find that John will underestimate the value 8 28.1% of the time.
(c) The proportion of time John will overestimate the value 8 would be the number of times the 2nd largest value is greater than 8 divided by the total number of simulations.
From the simulation results, we find that John will overestimate the value 8 62.3% of the time.
Read more about Random Samples:
brainly.com/question/29494439
#SPJ4
4. 678 es un número racional o irracional.
-103 es un número racional o irracional
Los números racionales son números que se pueden expresar en la forma a/b donde a y b son números enteros y b ≠ 0.
Los números racionales también se conocen como números fraccionarios. En los números racionales de la forma a/b, el número a representa el cuantificador y b es el denominador del número racional.
Qué pasa si el valor de b = 0?
Si un número fraccionario o racional tiene un denominador de 0, como 1/0; 2/0; 10/0; y otros, entonces el número fraccionario o racional no está definido.
Los números racionales también se pueden reclasificar en números enteros, números enteros, números naturales y otros grupos de números que forman parte de los números racionales.
Ejemplo de número racionalAlgunos ejemplos de números racionales como 1/2, 2/3, 5/7, 12/7 y otros.
En los números racionales también hay varias operaciones simples como la suma, la resta, la multiplicación, la división y otras operaciones numéricas.
Learn more about rational number at https://brainly.com/question/24540810.
#SPJ4
Match each graph to its equation
Convert 20 feet per minute to yards per hour.
400 yards/hour
3600 yards/hour
60 yards/hour
6.3 yards/hour
20 feet per minute is equal to 400 yards/hour
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
For 1 minute 20 feet
For 60 minutes , 60*20=1200 feet
1 hour = 60 minutes
Thus, we have 1200 feet per hour
3 feet = 1 yard
So, 1200 feet = 1200/3 yrads = 400 yards
Thus, 20 feet per minute is equal to 400 yards/hour
To learn more about the unit rate from the given link
https://brainly.com/question/4895463
#SPJ4
Marcu and hi dad were going camping. When they went into the garage to get their tent they noticed it wa ripped. Marcu' dad aid he could fix the tent. He would buy ome new material to cover the one rectangle ide that ripped
Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.
What is meant by rectangular?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides. Answer. Rectangles and rectangular prisms differ primarily in that rectangles exist in two dimensions whereas rectangular prisms exist in three dimensions. Unlike a rectangle, which only has width and length, a rectangular prism has three dimensions: width, height, and length. A quadrilateral with all of its angles equal, or right angles, is a rectangle. In addition to having all equal angles, a square also has all equal sides.He needs 55 to completely cover the tent's one rectangular side with the rip. 55
Marcus's father would require 189 if he wanted to completely redo the tent's cover, including the bottom.
3 rectangular sides = 165
2 triangular sides = 24
165 + 24 = 189
To learn more about rectangular, refer to:
https://brainly.com/question/25292087
#SPJ4
For the following function find (a) f(4), (b) f (-2) (c) f(a), (d) f and (e) any values of x such that f(x) = 1. f(x) = 4x2 - 40x +97 (a) Find the value of f(4). f(4) =
For, the function f(x) = 4x² - 40x + 97, a) f(4) = 1 b) f(-2) = 193 c) f(a) = 4a² - 40a + 97 d) For f(x) = 2 , x = 4, 6.
Given a function f(x) = 4x² - 40x + 97
To evaluate the value of a function f(x) at a point x = a, we replace x with a in the expression for f(x) and simplify.
a) f(4) = 4(4)² - 40(4) + 97
= 1
b) f(-2) = 4(-2)² - 40(-2) + 97
= 193
c) f(a) = 4a² - 40a + 97
d) f(x) = 1
4x² - 40x + 97 = 1
4x² - 40x + 96 = 0
x² - 10x + 24 = 0
x² - 6x - 4x + 24 = 0
x(x - 6) - 4(x - 6) = 0
(x - 4)(x - 6) = 0
x = 4, 6
To learn more about functions here:
brainly.com/question/28973926
#SPJ4
let x be an ordered set. if y is a proper subset of x that is convex in x, does it follow that y is an interval or a ray in x?
No, it does not follow that y is an interval or a ray in x. A convex subset of an ordered set is a set that contains all the points between any two points in the set.
This means that a convex subset of an ordered set could be a collection of points, it could be an interval, or it could be a ray. A proper subset of an ordered set is any subset except the entire set, so a proper subset of an ordered set could be any of these possibilities.
Therefore, while a proper subset of an ordered set that is convex in that set must be a collection of points, an interval, or a ray, it does not necessarily have to be one of those three options.
know more about ray here
https://brainly.com/question/17491571#
#SPJ11
Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S.
Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram support Alfonso's claim?
The histogram doesn't support Alfonso's claim and the correct option is 5: No, the distribution is skewed to the left with a mean age greater than 36.
What is a histogram?
A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram.
Consider the given histogram at the photo below. It is an left-skew histogram, since it has a long tail to the left side.
We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.
For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.
1. midpoint = 32, probability= 0.03
2. midpoint = 33, probability = 0.04
3. midpoint = 34, probability = 0.05
4. midpoint = 35, probability = 0.1
5. midpoint = 36, probability =0.11
6. midpoint = 37, probability = 0.13
7. midpoint = 38, probability = 0.2
8. midpoint = 39, probability = 0.09
So, it is obtained that -
μ = 0.03 · 32 + 0.04 · 33 + 0.05 · 34 + 0.10 · 35 + 0.11 · 36 + 0.13 · 37 + 0.25 · 38 + 0.20 · 39 + 0.09 · 40
μ = 37.15
Therefore, this histogram is left-skewed with mean greater than 36.
To learn more about histogram from the given link
https://brainly.com/question/28164315
#SPJ4
ABCD i a trapezium AD and BC are parallel
work the length of ad
work the lenght of bc
The length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.
AB = 10 cm and BC = 18 cm and angle ADB = 56 degrees.
A: Length of BD:
Using the law of sines, BD can be calculated as:
BD = 10 * sin(56) = 8.62 cm (approx)
B: Length of CD:
Using the Pythagorean theorem, AD can be calculated as:
AD = sqrt(BD^2 + AB^2 - 2 * BD * AB * cos(56)) = 12.92 cm (approx)
And then, CD can be calculated as:
CD = AD - BD = 12.92 cm - 8.62 cm = 4.30 cm (approx)
So, the length of BD is approximately 8.62 cm and the length of CD is approximately 4.30 cm.
"
Complete question
ABCD is a trapezium AD and BC are parallel
where AB = 10cm and BC = 18cm and angle ADB = 56degree
Find
A: work out the length of BD
B: work out the length of CD
"
You can learn more about trapezium at
https://brainly.com/question/137259
#SPJ4
For f(x) = 2x - 3x², evaluate f(-3).
A. -33
B. 33
C. -21
D. 6
[tex]\huge\begin{array}{ccc}f(-3)=-33\to\boxed{A.}\end{array}[/tex]
Value of the function.
We have the function:
[tex]f(x)=2x-3x^2[/tex]
We need
[tex]f(-3)=?[/tex]
Substitute [tex]x=-3[/tex] to [tex]f(x)[/tex]:
[tex]f(-3)=2\cdot(-3)-3\cdot(-3)^2=-6-3\cdot9=-6-27=-33\to\boxed{A.}[/tex]
If f(x) = 4x2 - 3x + 2, evaluate f(-1).
State the domain of the function f(x) = (x+3)/(x-1).
Write the equation of the line that passes through the points (1, 1) and (2, 4). Write your answer in slope-intercept form.
1. f(-1) = 9
2. the domain of the function f(x) = (x+3)/(x-1) is: x ∈ R {1} or x ∈ R {- 1}
3. y = 3x + 2
4. y = 2/3x + 1
What is slope-intercept form?The formula for a straight line, written as y = mx + b, where m denotes the line's slope and b its y-intercept. When the slope of the line being studied is known, and the provided point is also the y-intercept, the slope-intercept formula, y = mx + b, is utilized (0, b). b stands in for the y value of the y-intercept point in the formula.
1.
Given f(x) = 4x² - 3x + 2
f(-1) = 4(-1)² - 3(-1) + 2
f(-1) = 4 + 3 + 2
f(-1) = 9
2.
f(x) = x + 3/ x - 1
x - 1 ≠ 0
x ≠ 1
therefore, x ∈ R {1} or x ∈ R {- 1}
3.
Two points (1, 1) and (2, 4)
(x₁, y₁) = (1,1)
(x₂, y₂) = (2, 4)
Two points form an equation:
y - y₁ = {(y₂ - y₁) / (x₂ - x₁)} (x - x₁)
y - 1 = {(4 - 1) / (2 - 1)} (x - 1)
3x - y = 2
x/ (2/3) + y / (-2) = 1
intercept form: x/a + y/b = 1
y = 3x + 2
this is slope intercept form.
4.
given slope (m) = 2/3
y - intercept (c) = 1
y = mx + c
y = 2/3x + 1
To know more about domain refer to:
https://brainly.com/question/2264373
#SPJ4
*Thabiso's parents opened an investment account when he was born, in which they deposit R5 000. They intend to withdraw the money on his 18th birthday. If the account earns 8% p.a. for the first 10 years and 6% p.a. for the next 6 years and 10% p.a. for the final 2 years, all compounded, how much money will Thabiso receive?
Find out the length of segment GF?
The length of segment GF in the triangle is 8 inches
How to Find out the length of segment GF?From the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following ratio
3 : 6 = 4 : GF
So, we have
GF = 6/3 * 4
Evaluate
GF = 8 inches
Hence, the length is 8 inches
Read more about similar triangles at
https://brainly.com/question/14285697
#SPJ1
solve the sum-of-forces equation just derived, 0=∑ify,i=pa−(p dp)a−rhoagdy , to obtain an expression for dp and thus a differential equation for pressure.
The pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.
The sum-of-forces equation is 0=∑ify,i=pa−(p dp)a−ρagdy. Rearranging the equation to isolate dp yields the following expression:
dp = (pa - ρagdy) / p
Differentiating both sides with respect to y yields the differential equation for pressure:
dp/dy = (a(pa - ρagdy) - (dp)(pa)) / p
This equation can be further simplified using the product rule to yield:
dp/dy = pa2/p2 - ρag/p.
This differential equation shows that the pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.
Learn more about differential equation here:
https://brainly.com/question/14620493
#SPJ4
g suppose we roll 20 fair six-sided dice. what is the probability that the minimum of the dice is 1?
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).
The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,
P(X = 1) = (1/6)^20 = 1.275 * 10^-9.
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
To learn more about probability visit : brainly.com/question/30034780
#SPJ4
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).
The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,
P(X = 1) = (1/6)^20 = 1.275 * 10^-9.
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
To learn more about probability
brainly.com/question/30034780
#SPJ4
How are the average rate of change and the instantaneous rate of change related for ƒ(x) = 2x + 5?
The average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5. The solution has been obtained by using the concept of rate of change.
What is rate of change?
The pace at which one quantity changes in relation to another is described by the rate of change function. Simply expressed, the amount of change in one item is divided by the same amount of change in another to determine the rate of change. The relationship between how one quantity changes in relation to a change in another quantity is provided by the rate of change formula.
The average rate of change is:
[tex]r_{avg} =\frac{f(b)-f(a)}{b-a}[/tex], on interval [a,b]
Here, we are given ƒ(x) = 2x + 5
So,
[tex]r_{avg} =\frac{(2b+5)-(2a+5)}{b-a}[/tex]
[tex]r_{avg} =\frac{2b-2a}{b-a}[/tex]
[tex]r_{avg} =2[/tex]
The slope of f assessed at a single point, such as f′(c), where c is a predetermined point, is the definition of the instantaneous rate of change.
So, for ƒ(x) = 2x + 5,
f′(c) = 2
Therefore, instantaneous rate of change is 2.
Hence, the average rate of change and the instantaneous rate of change are same for ƒ(x) = 2x + 5.
Learn more about rate of change from the given link
https://brainly.com/question/25184007
#SPJ4
in isosceles trapezoid mnpq with , diagonal . if and , how long is diagonal ?
The value of segment RN is:
Rn = 1.8
Now, According to the question:
An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals.
The figure shows:
MQ is parallel to NP
MN ≅ QP
So MNPQ is an isosceles trapezoid. That means that the two diagonals, MP and QN, are congruent and therefore are equal in length;
MP = QN
By the Segment Addition Postulate, QN = QR + RN and QR = 4.1:
MP = QN
5.9 = 4.1 + RN
RN = 5.9 - 4.1
RN = 1.8
Learn more about Isosceles trapezoid at:
https://brainly.com/question/3659187
#SPJ4
The given question is incomplete, complete question is:
Quadrilateral MNPQ is shown.
If MP = 5.9, what is RN? Round your answer to the nearest tenth.
Please helppppp fastttttt
Answer:
C is the answer
Step-by-step explanation:
Two parallel lines are crossed by a transversal.
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom left angle is (5 x + 5) degrees. At the intersection of lines c and a, the bottom right angle is 115 degrees.
What is the value of x?
x = 12
x = 14
x = 22
x = 24
ANSWER IS x = 12.
12 because 5x12+5 = 65 and 180-115=65 meaning x=65 :)
Answer:
answer is 12
12 because 5x12+5 = 65 and 180-115=65 meaning x=65
A student earned the scores in the data set in one course. {90, 87, 58, 79, 91} What is the mean of the scores? 33 58 81 87
Answer:
81
Step-by-step explanation:
Mean means the average
Mean = (sum of #s) / amount of #s
sum of numbers = 90 + 87 + 58 + 79 +91 = 405
amount of #s = 5
405/5 = 81
Answer:
81
Step-by-step explanation:
Mean is the sum of all numerical data values over the number of data. In this problem, we have total of 5 numerical data. Therefore:
[tex]\displaystyle{\bar{x} = \dfrac{\sum x}{N}}\\\\\displaystyle{\bar{x} = \dfrac{90+87+58+79+91}{5}}\\\\\displaystyle{\bar{x} = \dfrac{405}{5}}\\\\\displaystyle{\bar{x} = 81}[/tex]
Note:
[tex]\bar{x}[/tex] is mean value, [tex]\displaystyle{\sum x}[/tex] is sum of data, N is number of data
toru rode his bike from his house to the library, to the park, and then back home. toru realized that his route made an isosceles triangle, and that the library was the exact same distance from both his house and the park. what is the measure of the angle at the library?
The measure of the angle at the library is 90 degrees.
Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.
In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:
180 degrees / 2 = 90 degrees
So, the measure of the angle at the library is 90 degrees.
An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.
To learn more about the triangle, visit:
brainly.com/question/2773823
#SPJ4
The measure of the angle at the library is 90 degrees.
Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.
In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:
180 degrees / 2 = 90 degrees
So, the measure of the angle at the library is 90 degrees.
An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.
To learn more about Triangle:
brainly.com/question/2773823
#SPJ4
withω=seiφ,wheres≥0andφ∈r,solvetheequationzn =ωincwhere n is a natural number. how many solutions are there?
For an nth root, there are n solutions of the equation z^n = ω.
To find these solutions, we use the polar form of z = r * e^(iθ). Substituting into the equation, we get:
r^n * e^(iθn) = s * e^iφ
Comparing the magnitude of both sides, we have:
r^n = s
Comparing the phase of both sides, we have:
nθ = φ + 2πk (where k is an integer)
So, we can set:
r = s^(1/n)
θ = (φ + 2πk) / n
Therefore, the n solutions are:
z = s^(1/n) * e^(i(φ + 2πk) / n)
for k = 0, 1, 2, ..., n-1.
--The question is not readable, answering to the question below--
"With ω = se^iφ, where s ≥ 0 and φ ∈ r , solve the equation z^n = ω in C where n is a natural number. How many solutions are there?"
To know more on nth root
https://brainly.com/question/30360169
#SPJ4
Factor this equation
81a^2+5b^2
Answer:
The equation 81a^2 + 5b^2 cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares. Factoring a sum of squares means writing it as the product of two binomials, each of which is the square root of one of the terms. Since 81 and 5 are not perfect squares, the equation 81a^2 + 5b^2 cannot be written as the product of two binomials.
The equation [tex]81a^2 + 5b^2[/tex] cannot be written as the product of two binomials.
An equation is defined as an expression that shows the relationship between two or more numbers and variables.
Given equation as [tex]81a^2 + 5b^2[/tex]
Since we know that Factoring a sum of squares means writing it as the product of two binomials, each of that is the square root of one of the terms.
Hence, 81 and 5 are not perfect squares.
The given equation [tex]81a^2 + 5b^2[/tex] cannot be factored further as a polynomial expression because it is in the standard form of a sum of squares, and the coefficients are not perfect squares.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
Tory and emilio's motorboats travel at the same speed Tory pilots her boat at 30 km before docking. Emilio continues for another 3 hr, traveling a total of 100 km before docking. How long did it take to navigate the 30 km
The actual time it took Tory to travel 30 km is 0 hours.
As per the data given in the question,
Speed of the boat of both the person Tory and Emillio are same.
Let's call the time it took Tory to travel 30 km as "t" (in hours).
Emilio travelled for t + 3 hours, and during that time, he covered a total distance of 100 km.
So, we can write the equation:
30 + (t + 3) * 30 = 100
Solving for t:
30 + 30t + 90 = 100
30t = -60
t = -2
Since time cannot be negative, the actual time it took Tory to travel 30 km is 0 hours.
For more questions on Speed, Time and Distance
https://brainly.com/question/26862717
#SPJ4