In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of every binomial formula, such as (x + y)ⁿ.
Explain the term Pascal's triangle?Although it is much older, it bears the name of the French scholar Blaise Pascal from the 17th century. In the eleventh century, the Chinese mathematician Jia Xian created a triangular form for the coefficients.
For instance, the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21), which was first discovered by the mediaeval Italian mathematician Leonardo Pisano ("Fibonacci") in his Liber abaci (1202; "Book of the Abacus"), is produced by drawing parallel "shallow diagonals" and adding the numbers on each line together. Another intriguing characteristic of the triangle is that it will form a fractal understood as the Sierpiski gasket, named for Polish mathematician Wacaw Sierpiski, who lived in the 20th century, if all the positions comprising odd numbers are shaded in black and every positions enclosing even numbers are shaded in white.To know more about the Pascal's triangle, here
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On average, Logan drinks 2/3 of a 6-ounce glass of water in 1 4/5 hours. How much water does he drink, in glasses per hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
PLEASE HELP!!!
On average, Logan drinks (2)/(3) of a 6-ounce glass of water in 1(4)/(5) hours. How much water does he drink, in glasses per hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
The following response has been constructed in a straightforward, step-by-step approach.
Measure: 1 ounce
2/3×6 =4 glass
Considering that a person consumes four glasses every hour.
he Drinks x glasses after one hour.
Reason: Since 21/5x=4,
21x=5×4
Glass 21x=20x=20/21
Answer: So, consume 20/21 glasses in an hour.
The response is a correct fraction.
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Amina has a bag of 6 black balls and 4 green balls. Hamad has a bag of 3 black balls and 5 green balls. If one ball is drawn from each bag, what is the probability that one is black and one is green?
Amina has a bag of 6 black balls and 4 green balls. Hamad has a bag of 3 black balls and 5 green balls. If one ball is drawn from each bag, the probability that one is black and one is green is 0.525.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely is that a proposition is true.
Amina has a bag of 6 black balls (B1) and 4 green balls (G1).
Hamad has a bag of 3 black balls (B2) and 5 green balls (G2).
∴ Probability of getting one black and one green ball
= B1G2 + G1B2
= 6/10 × 5/8 + 4/10 × 3/8
= 30/80 + 12/80
= 0.525
If one ball is drawn from each bag, the probability of getting one black and one green ball is 0.525.
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The probability of getting one black and one green ball if one ball is drawn from each bag is 0.525.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Amina has 6 black balls and 4 green balls in her bag. Hamad has three black balls and five green balls in his bag.
Amina has 6 black balls (B1) and 4 green balls in her bag (G1).
Hamad has 3 black balls (B2) and 5 green balls in his bag (G2).
So, the probability of receiving one black and one green ball:
= B1G2 + G1B2
= 6/10 × 5/8 + 4/10 × 3/8
= 30/80 + 12/80
= 0.525
Therefore, the required probability is 0.525 that one is black and one is green.
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Help I want to convert decimal radian to fractional pi format radian
Eg: how to convert 0.785 rad to pi format
The conversion is 0.785 radian = 141.3 degree.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
A conversion factor is a value or a number that is used to multiply or divide one set of units into another.
Given:
We have to convert 0.785 rad to pi format.
As, we know Radians = Degrees × π/180'
and, 0.785 rad = 0.785 x 180
= 141.3 Degree
Hence, the conversion is 0.785 radian = 141.3 degree.
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Which expression is equal to (8-3i) - (6 + i)?
14-2i
14-4i
2-2i
2-4i
Answer:
2-4i
Step-by-step explanation:
(8-3i)-(6+i)
distribute right side: 8-3i-6-i
8-6: 2-3i-i
So 2-4i
Answer:
2 - 4i
Step-by-step explanation:
Given expression:
[tex](8 - 3i) - (6 + i)[/tex]
Apply the distributive law: -(a + b) = -a - b
[tex]\implies 8 - 3i - 6 -i[/tex]
Collect the real part and imaginary part of the complex number:
[tex]\implies 8 -6- 3i -i[/tex]
Simplify:
[tex]\implies 2-4i[/tex]
determine if the order pair (-4,5) is a solution of the given linear equation -2x -3 write or no as your final answer
please help
Yes ordered pair (-4,5 ) is a solution to this linear equation
What is linear equation?
If an equation is expressed as axe + by + c=0, where a, b, and c are real integers and x and y's coefficients, it is said to be a linear equation in two variables.
Main body:
According to question:
y = -2x-3
point = (-4,5)
so as to find whether this point satisfies the equation or not, we need to put the value of any variable and check whether other value holds true or not.
Now substituting x= -4 in the given equation
⇒ y = -2(-4) -3
⇒y 8-3
⇒y= 5
which is given in the ordered pair
hence (-4,5) are a solution to this equation.
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In order to solve for the variable in the equation 2 (4 x 3) 4 = 3 x minus (2 x 4), giovanni first applies the distributive property. which equation is a result of this step? 8 x 3 4 = 3 x minus 2 x 4 8 x 6 4 = 3 x minus 2 x minus 4 6 x 5 4 = 3 x minus x 3 6 x 3 4 = 3 x minus x 4
In order to solve for the variable in the equation 2 (4 x 3) 4 = 3 x minus (2 x 4), giovanni first applies the distributive property.
The equation is a result is 8x+6+4 = 3x-2x-4.
Given that the distributive property is to multiplying by the numbers outside of the parentheses into the inside of the parentheses
So we now that,
2×4x=8x
2×3=6
8x+6+4
Then do the same thing on the other side also so that Which we gets is equal to the below
3x-2x-4
so the equation we get is
8x+6+4 = 3x-2x-4
Hence the answer is, we get the equation is a result is 8x+6+4 = 3x-2x-4
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you randomly select one card from a standard deck of 52 playing cards find the probability of selecting the six of spades or the nine of clubs
There are 52 cards in the deck.
Picking the 6 of spades or 9 of clubs are two of the possible cards you could pick.
Your probability is 2/52 or 1/26 or 3.8461538461538%.
An equation is shown.
23x = 24
What value of x makes the equation true?
Answer:
all of them are right answers
[tex]x = \frac{24}{23 \\ } [/tex]
or
[tex]x = 1.04[/tex]
or
[tex]x = 1 \frac{1}{23} [/tex]
Use the change of variables formula and an appropriate transformation to evaluate ∫∫g xy dA, where R is the square with vertices (0, 0), (1,1), (2, 0), and (1, -1).
Therefore, the transformation of the double integral can be expressed as follows: ∫∫g(x', y') (x' + 1)(y' - 1) dx' dy' = ∫∫g(x', y') (x' + 1)(y' - 1) |J| dA'
What is the change of variables formula?the alteration of variables A mathematical trick known as a formula is used to switch the variables in an integral from one set of variables to another. The integral is frequently simplified or made easier to solve by doing this. Given a function f(x) and two sets of variables x and y, the integral of f(x) with respect to x may be represented as the integral of a transformed function g(y) with respect to y, where g(y) is connected to f(x) by a functional connection between x and y. For instance, the integral of f(x) with respect to x can be expressed as the integral of f(sqrt(y)) with respect to y if x and y are connected by the equation y = x2.
How to solve?
x' = x - 1
y' = y + 1
∫∫g(x, y) xy dA = ∫∫g(x', y') (x' + 1)(y' - 1) dx' dy'
∫∫f(x, y) dA = ∫∫f(x', y') |J| dA'
|J| = | ∂x'/∂x ∂x'/∂y |
| ∂y'/∂x ∂y'/∂y |
|J| = | 1 0 |
| 1 1 |
Therefore, the transformed double integral can be expressed as follows:
∫∫g(x', y') (x' + 1)(y' - 1) dx' dy' = ∫∫g(x', y') (x' + 1)(y' - 1) |J| dA'
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HIGHSCHOOL GEOMETRY HELP NEEDED ASAP EZ POINTS!
Answer:
x -2x and the y is -2y
Step-by-step explanation:
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The number of students studying abroad in 2001 is 150.38 thousand
The number of students studying abroad in 2018 is 467.53 thousand
What are the number of students?The given equation is known as an exponential equation. An exponential equation is a non-linear equation.
The given exponential equation is 123.1(1.069)^x
Where:
123.1 = initial population in 19981.069 = rate of growthx = number of yearsNumber of students studying abroad in 2001 = 123.1(1.069)^3= 150.38 thousand
Where x = 2001 - 1998 - 3
Number of students studying abroad in 2018 = 123.1(1.069)^20 = 467.53 thousand
Where x = 2018 - 1998 = 20
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packages of sugar bags for sweeter sugar inc. have an average weight of 16 ounces and a standard deviation of 0.2 ounces. the weights of the sugar bags are normally distributed. what is the probability that 16 randomly selected packages will have a sample mean weight in excess of 16.075 ounces?
0.0668 is the probability that 16 randomly selected packages will have a sample mean weight in excess of 16.075 ounces.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
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2x²-14x+1=0
how do i solve?
Answer:
x = 6.928 [tex]x = 0.072[/tex]
Step-by-step explanation:
Use the quadratic formula
[tex]\frac{-b(+-)\sqrt{b^{2 } -4ac} }{2a}[/tex]
[tex]a = 2\\b = -14\\c = 1[/tex]
[tex]\frac{-(-14)(+-)\sqrt{(-14)^{2 } -4(2)(1)} }{2(2)}[/tex]
[tex]\frac{-(-14)(+-)\sqrt{196 -8} }{4}[/tex]
[tex]\frac{14+\sqrt{188} }{4}[/tex] [tex]\frac{14-\sqrt{188} }{4}[/tex]
[tex]x = 6.928[/tex] [tex]x = 0.072[/tex]
What is the measure of an angle if the measure of its supplement is 39 more than twice the measure of its complement?.
The measure of the angle is 39°.
Complementary angles are angles whose sum is equivalent to 90°. On the other hand, supplementary angles are angles whose sum is equivalent to 180°.
Let x be the measure of the angle.
90° - x = complement angle of x
180° - x = supplement angle of x
If the measure of its supplement is 39 more than twice the measure of its complement, then
180° - x = 39 + 2(90° - x)
Simplify and solve for x.
180° - x = 39 + 2(90° - x)
180° - x = 39 + 180° - 2x
x = 39°
Hence, the measure of the angle is 39°.
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A cyclist rides at a constant speed of 15 miles per hour. At this speed, about how long would it take the cyclist to ride from Garden City to Dodge City, Kansas?
Answer: 5.61333333 h
If the length between Garden city to dodge city is 84.2km the answer would be 5.61333333 hours [non-terminating decimal]
Step-by-step explanation:
So ummm, i dunno if the answer is right but yeahh
1h = 15 miles
Distance between GC AND DC = 84.2
84.2 * 15 = 5.6133333
Write Proportion Statement and find the missing sides of the polygon.
The lengths of the sides AN, PM, and MO of the given polygons are 26, 40, and 96, respectively.
We are given two triangles. The vertices of the first triangle are A, N, and T. The vertices of the second triangle are P, O, and M. Both the triangles are right-angled. The triangles are similar to each other. The lengths of the sides AT and TN are 10 and 24, respectively. We will use the Pythagorean theorem to find the length of side AN.
AN = √[(10)² + (24)²] = √(100 + 576] = √676 = 26
Now, as we know the triangles are similar, the lengths of the corresponding sides must be in the same proportion. The ratio is calculated as given below.
r = PO/AN = 104/26 = 4
The length of the side PM is equal to r*AT = 4*10 = 40. The length of the side MO is equal to r*TN = 4*24 = 96.
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Anyone know the slope of this line
Choices are
A. 2
B. 1
C. 1/2
D. 2/3
E. 3/1
Answer: 3
Step-by-step explanation: The dot or the point/exponent lands on 3/1 simplifying as 3
MATH PLEASE HELP!! THANK YOU!
Answer:
Below
Step-by-step explanation:
m = slope
Use two points on the graph to find m
m = ( x1-x2)/(y1-y2) = ( 1- -1) / ( -4 - -2) = 2 / -2 = -1
Perpindicular slope is - 1/m = -1 / (-1) = 1
a. To find 40% of 75, Priya calculates. Does her calculation give the correct
value for 40% of 75? Explain or show how you know.
b. If represents a number, does always represent 40% of that number?
Explain your reasoning.
40 percentage of 75 is 30 and 2/5 of 75 is 30. So, Priya calculated in a correct way.
Given,
To find 40% of 75, Priya calculates 2/5 of 75
We have to find the value of 40% of 75.
Percentage;
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.
Now,
Lets find;
40% of 75
40/100 × 75 = 40/4 × 3 = 10 × 3 = 30
That is,
40% of 75 is 30.
Now,
2/5 of 75
2/5 × 75 = 2 × 15 = 30
That is,
2/5 of 75 is also 30
Therefore,
40 percentage of 75 is 30 and 2/5 of 75 is 30. So, Priya calculated in a correct way
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a. obtain the equation of the estimated regression line and use it to calculate a point prediction of ammonium concentration for a future observation made when ammonium concentration is 25ml/h.
The equation of the regression line is [tex]\bar{y}[/tex]=9.1006+(-0.2157)x and the point prediction of ammonium concentration for 25ml/h is [tex]\bar{y}[/tex]=3.7081
What is meant by regression line?A regression line is an approximation of the line that describes the true, but unknown, linear connection between two variables. The regression line equation is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable.
In statistical modeling, regression analysis is a collection of statistical techniques for estimating the associations between a dependent variable and one or more independent variables.
a) [tex]\bar{y}[/tex]=β₀+β₁x
Where,
β₁=[tex]S_{xy}[/tex]/[tex]S_{xx}[/tex] -------(1)
Where,
[tex]S_{xy}[/tex]= -341.959231
[tex]S_{xx}[/tex]1585.230769
By substituting these values in equation 1 we get,
β₁= -0.2157
β₀= [tex]\bar{y}[/tex]-β₁x
Where,
[tex]\bar{y}[/tex]=∑[tex]y_{i}[/tex]/n
∑[tex]y_{i}[/tex]=52.8
n=13
Then,
[tex]\bar{y}[/tex]=4.0615
[tex]\bar{x}[/tex]=∑[tex]x_{i}[/tex]/n
∑[tex]x_{i}[/tex]=303.7
n=13
[tex]\bar{x}[/tex]=23.3615
β₀=4.0615-(-0.2157)(23.3615)
=9.1006
Therefore, β₀=9.1006
The regression equation is [tex]\bar{y}[/tex]=9.1006+(-0.2157)x
If x=25,
[tex]\bar{y}[/tex]=9.1006+(-0.2157)(25)
[tex]\bar{y}[/tex]=3.7081
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A round fountain has a radius of 86cm. What is the circumstance of the fountain, in meters?
Answer:
The circumference of any circle is 2πr, where r is the radius.
Step-by-step explanation:
For questions 18-20, if l Il m, find the values of x and y.
Step-by-step explanation:
18x + 20y= 38
38xy = 38
xy = 38/38
where x and y = 1
2(-3s+1-5) Pls HELP!
A parabola can be drawn given a focus of ( 0 , − 2 ) and a directrix of x = − 6 . What can be said about the parabola?
The parabola has a vertex at (-3, -2), has a p-value of 3 and it opens up.
How to determine the vertex form of a parabola?Mathematically, the vertex form of a parabola is represented by this mathematical expression:
y = a(x - h)² + k
Where:
h and k represents the vertex of the equation.
In Mathematics, the focus for either a right or left parabola is modeled by this mathematical expression (h + p, k) while its directrix is modeled by this mathematical expression x = h - p;
h + p = 0 ⇒ h = -p
h - p = -6
Solving the set of linear equations simultaneously, we have:
-p - p = -6
-2p = -6
p = 6/2
p = 3
For the value of h, we have:
h = -3.
Additionally, the vertex form of this parabola is given by:
y = a(x - h)² + k
y = a(x - 3)² - 2
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Complete Question:
A parabola can be drawn given a focus of (0, −2) and a directrix of x = −6. What can be said about the parabola?
The parabola has a vertex at ( , ), has a p-value of
and it
-opens up
-opens down
-opens right
-opens left
Write the equation of the line through (-4,9) and (-4,5)
Answer:
x=-4
Step-by-step explanation:
y=mx+b is slope intercept form where m is slope and b is y intercept
To find slope we use y2-y1/x2-x1
5-9/-4-(-4)
-4/0
The slope is undefined
But we can write this as x=-4 since it is a vertical line going straight up
Hopes this helps please mark brainliest
Please help!! (Click on the pic!)
Answer:
[tex]160\sqrt{3}[/tex]
Step-by-step explanation:
Step 1: Know what the question is asking
product ⇒ means to multiplyStep 2: Set up the problem
[tex](8\sqrt{8} )(5\sqrt{24} )[/tex]*Note: Multiplication is commutative ⇒ order doesn't matter, terms can be rearranged and the answer remains the same[tex]8*\sqrt{8} *5*\sqrt{24}[/tex][tex]8*5*\sqrt{8} *\sqrt{24}[/tex][tex]40*\sqrt{8} *\sqrt{24}[/tex]*Note: It is easier to further simplify by simplifying the square roots before multiplying them together.[tex]40*\sqrt{8} *\sqrt{24}[/tex][tex]40*\sqrt{4} *\sqrt{2} *\sqrt{4} *\sqrt{6}[/tex][tex]40*2*\sqrt{2} *2*\sqrt{6}[/tex][tex]40*2*2*\sqrt{2} *\sqrt{6}[/tex][tex]40*4*\sqrt{2} *\sqrt{6}[/tex][tex]80*\sqrt{12}[/tex][tex]80*\sqrt{4} *\sqrt{3}[/tex][tex]80*2*\sqrt{3}[/tex][tex]160\sqrt{3}[/tex]an open-top box is to be constructed from a square piece of cardboard, 3 feet wide, by cutting out a square from each corner and bending up the sides. what is the largest volume that the box can have?
The largest volume that the box can have is 02.
equation for volume :
v = x (3- 2x)²
Differentiating using chain rule and product line:
v' = 1(3 - 2x)² + 2x (3 -2x) (-2)
= 9 - 12x + 4x² -12x +8x²
= 9 - 24x +12x²
Finding the critical value where v' = 0
v' = 0
⇒12x² - 24x +9 =0
⇒3 ( 4x² -8x +3)=0
⇒ 4x² -8x+3 =0
(2x- 3) (2x-1) =0
or, x=3/2 or 1/2
putting the value x= 1/2, we get,
V = 2
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The collection of all input values is the ? of the function. The collection of all output values is the ? of the function.
By definition, we can complete the two sentences as follows:
The collection of all input values is the domain of the function. The collection of all output values is the range of the function.How to complete the statements?A general function can be written as:
y = f(x).
This function "f" takes inputs "x" and transforms them into the outputs "y".
And by definition, the set of all the inputs x is called the domain of the function, while the set of all outputs is called the range of the function.
So the two complete sentences are:
The collection of all input values is the domain of the function.
The collection of all output values is the range of the function.
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Triangle ABC is congruent to triangle DEF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent.
Segment BC is congruent to segment EF,
Angle BAC is congruent to angle EDF,
Angle CBA is congruent to angle DEF.
Given:
Triangle ABC is congruent to triangle DEF.
if two triangles are congruent:
congruent sides are:
AB ↔ DE ,BC↔EF, CA ↔ FD
congruent angles are:
<A ↔ <D , <B ↔ <E, <C ↔ <F.
Therefore Segment BC is congruent to segment EF, Angle BAC is congruent to angle EDF, Angle CBA is congruent to angle DEF are correct.
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(algebra)
Jane and Nina live 480 miles apart. Wanting to surprise each other, they happened to start driving at the same time, and they met 3 hours later. If Nina’s speed was 10 mph faster than Jane’s speed, what was Jane’s speed?
a) 70 mph
b) 75 mph
c) 80 mph
d) 85 mph
e) 90 mph
So, I’m pretty sure the equation will look something like this
10x + 10(x-4) = 1,000
But don’t quote me on that.
