The row of Pascal's triangle that is used to expand the binomial expression (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.
What is a binomial expression?A binomial expression is an expression that contains only two terms.
What is Pascal's triangle?Pascal's triangle is an algorithm for finding the coefficients of a binomial expansion.
How to find the row that is used to expand the binomial expression (2x³ +3y³)⁷?Since we require the expansion of the binomial expression (2x³ +3y³)⁷ using Pascal's triangle, we note that, the power of the binomial expression is always equal to the second and second to the last coefficient of the terms in the Pascal's triangle.
So, we see that the Row eight: 1 7 21 35 35 21 7 1, satisfies this condition.
So, the row of Pascal's triangle that is used to expand the binomial expression (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.
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Please Solve question
The component form of two vectors 2u - v is (10, 0), no magnitude in the second direction.
What is a vector?A vector is a quantity that has both magnitude and direction.
Given are two vectors u = (4, - 1) and v = (-2, - 2).
∴ The value of 2u - v in component form is 2(4, - 1) - (-2, - 2).
2u - v = (8, - 2) - (-2, - 2).
2u - v = (8+2, - 2+2).
2u - v = 10
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find y when x = 10 if y =8 when x = 20
Answer:
ANS:- Y =4
Step-by-step explanation:
x =20 half x =10
y = 8 half y = 4
The area of a rectangle is 105 sq in and the length of one side is 7 in. What is the length of the perimeter?.
The perimeter of the rectangle is 44cm
Given:
Area: [tex]Area = 105cm^{2}[/tex]
width: [tex]w= 7 cm[/tex]
To find the perimeter first we need to find the length of the rectangle.
We find it with the formula for the area of a rectangle:
[tex]Area = width*length[/tex]
so clearing for length:
[tex]length = \frac{area}{width}[/tex]
substituting known values:
[tex]length = \frac{105}{7} \\length = 15 cm[/tex]
And now we can calculate the perimeter:
[tex]perimeter = 2(width + length)\\\\perimeter = 2(7cm + 15cm)\\\\perimeter = 44cm[/tex]
Hence , the perimeter of the rectangle is 44cm
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help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answer:12.9
Step-by-step explanation:
The equation x² - 4x + y2-2y = 16 describes a circle. What is the y-coordinate of
the center of the circle?
Answer:
1
Step-by-step explanation:
→ Complete the square
( x - 2)² - 4 + ( y - 1 )² - 1 = 16
→ Simplify
( x - 2 )² + ( y - 1 )² = 21
→ Find centre
( 2 , 1 )
if the a horizon in a soil sample measures 3 inches, and the rate of top soil for temperate deciduous forest (where the soil was sampled) is 1 in/225 years, how long did it take for this horizon to develop?
The time taken by the horizon to develop is calculated with the half-life which is 675 years.
Organic matter particles have more negatively charged particles, which hold on the positively charged particles.
The organic matter in the soil affects the water holding capacity of the soil. Thus is if there are more organic matter, this means that the organic matter is more. Thus the farmer has to add more organic matter.
In order to reduce the the acidity, the farmers add Calcium oxide, Calsium hydroxide and so on.
The horizon s formed after years of sediment formation. Thus the process can take years.
This is the half-life of the soil and with the formula of half-life we get 225 * 3 = 675 years.
Therefore, the time taken by the horizon to develop is 675 years.
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how far is the end of his shadow from the bottom of the lamppost after 8 seconds. use similar triangles to solve the problem
The Distance from bottom of lamppost is 57.142 ft.
What are similar triangles?Triangles with the same shape but different sizes are called similar triangles. Examples of similar objects include squares with any side length and all equilateral triangles. To put it another way, if two triangles are similar, their angles are the same and their sides are the same size. The "~" symbol indicates the triangular resemblance here.
Given the height of lamp post is 20 ft
height of man is 6 ft
man walking away with speed of 5 ft per sec
distance covered 8 sec is 8 x 5 = 40 ft
let us consider a triangle ΔABC and consider the triangle with man ΔDEC
which is inside ΔABC as shown in figure,
AB = 20 ft, DE = 5 ft and AD = 40 ft
consider ΔABC and ΔDEC
∠BAC = ∠EDC = 90⁰
∠BCA = ∠ECD = common angle
so ΔABC ~ ΔDEC by (AA property)
according to similar triangles
AB/DE = AC/DC
let DC be x and AC is 40 + x
substitute the values
20/6 = (40 + x)/x
20x = (40 + x)6
20x = 240 + 6x
14x = 240
x = 17.142ft
AC = AD + DC = 40 + 17.142 = 57.142 ft
Hence the Distance from bottom of lamp post to the end of shadow is 57.142 ft.
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i need you help mate
Sheila made 51 cookies. Her sister made 27 cookies. Her brother ate 3 cookies. The remaining cookies will be sold in packages containing 5 cookies each. How many packages of cookies will be made?
How many packages of cookies will be made?
15
Step-by-step explanation:
Sheila made 51 cookies… Sister make 27 cookies ( add them )
78…..
Brother ate 3 cookies..
78 - 3 =
75..
75/5 =
15
Your dog has a mass of 45.5 lb. what is the dog’s mass in kilograms? (note: 1 lb = 0.45 kg.)
If the mass of dog is 45.5 lb then the mass in kilogram is 20.475 Kg .
In the question ,
it is given that ,
the mass of the dog is = 45.5 lb ,
we have to convert the given mass of dog into Kilogram .
For that we will need the conversion rate ,
the conversion rate to convert mass from lb to Kilogram is given as , 1 lb is = 0.45 kg ,
So , 45.5 lb in Kilogram will be equal to = 45.5 × 0.45 ,
After multiplication ,
we get ,
mass = 20.475 Kg .
Therefore , the mass in Kilogram is 20.475 Kg .
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One month Ivan rented 9 movies and 7 $74. video games for a total of 3 movies and 5 video games for a total of $40. . Find the rental cost for each movie and each video game.
The rental cost for each movie is $3.75
The rental cost for each video game is $5.75
How to determine the rental costThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
let the cost of renting movies be m and let the cost of video game rental be v
One month Ivan rented 9 movies and 7 video game $74
9m + 7v = $74
3 movies and 5 video games for a total of $40
3m + 5v = $40
The simultaneous equation
9m + 7v = $74
3m + 5v = $40
solving the equation gives
m = $3.75
v = $5.75
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100 Points + brainliest if correct and well explained:
An equation is shown:
−np − 3 = 7(c − 4)
Which of the following solves for n?
n = the quantity 7 times c minus 31 all over negative p
n = the quantity 7 times c minus 25 all over negative p
n = the quantity 7 times c plus 31 all over p
n = the quantity 7 times c plus 25 all over p
The value for n is n = the quantity 7 times c minus 25 all over negative p.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
−np − 3 = 7(c − 4)
Now, solving for n
-np - 3 = 7c - 28
-np = 7c - 28 + 3
-np = 7c -25
-n = 1/p( 7c- 25)
n= 1/ (-p) (7c- 25)
So, the value for n is n = the quantity 7 times c minus 25 all over negative p.
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Grady marks down some $4.09 pens to $3.59 for a week and then marks them back up to $4.09. Find the percent of increase and the percent of decrease to the nearest tenth. Are the percents of change the same for both price changes? If not, which is a greater change? Complete the explanation, and round your percents to the nearest tenth.
The first change was
a decrease
of
0.1
% and the second change was
an increase
of
%. The two percent changes
are not
the same, and the
second
percent change is greater.
The solution is the two percent changes are not the same, and the second percent change is greater
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage
Given data ,
Let the initial value of the pens = $ 4.09
Let the final value of the pens = $ 3.59
So , the percentage change is calculated by
Percentage decrease = ( ( final value - initial value ) / initial value ) x 100
Substituting the values in the equation , we get
Percentage decrease = ( ( 3.59 - 4.09 ) / 4.09 ) x 100
Percentage decrease = ( -0.5 / 4.09 ) x 100
Percentage decrease = -0.122249 %
Therefore , the approximate percentage decrease = -0.1 %
Now ,
The value of the pens is increased to = $ 4.09
So , the percentage change is calculated by
Percentage increase = ( ( final value - initial value ) / initial value ) x 100
Substituting the values in the equation , we get
Percentage increase = ( ( 4.09 - 3.59 ) / 3.59 ) x 100
Percentage increase = ( 0.5 / 3.59 ) x 100
Percentage increase = 0.13927 %
Therefore , the approximate percentage increase = 0.1 %
Hence , the two percent changes are not the same, and the second percent change is greater
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Solve the equation 20 + 0.44x = 19 + 1.69x.
By solving the given equation 20 + 0.44x = 19 + 1.69x we get x=0.8.
What is meant by an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.
Given,
20 + 0.44x = 19 + 1.69x
20-19=1.69x-0.44x
1=1.25x
x=0.8
Therefore, by solving the given equation 20 + 0.44x = 19 + 1.69x we get x=0.8.
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Create a proportion using the form = to represent the following word problem. 78% of what number is 42?.
Therefore the solution to this question of proportion, 78% of what number is 42 is 53.84.
What is proportion?In general, the word "proportion" is used to describe a part, share, or amount that is compared to an entire. Two ratios are in proportion, according to the definition of proportion, when they are equal. Two ratios or fractions being equal is expressed by an equation or a statement.
Here,
If 78% of x (any number) equals 42, then we need to set this up as an equation in order to figure it out.
1) Writing down 78% as a fraction. Taking into account that we refer to a product when we say 78% of some amount (x).
78%=78/100 \s=>78x/100=42
2) Afterward, we can continue:
100*78x/100=42*100
78x=4200
x=4200/78
x=53.84
Therefore the solution of 78% of what number is 42 is 53.84.
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HHHHEeeelllpppPPp
The graph shows the height, y, in meters, of a rocket above sea level in terms of the time
seconds, since it was launched. The rocket landed at sea level.
What does the x-intercept represent in this situation?
A
the height from which the rocket was launched
B the time it took the rocket to return to sea level
C. the total distance the rocket flew while it was in flight
D. the time it took the rocket to reach the highest point in its fight
Emma bought a bag of carrots. There are 5 carrots in the bag, and so far Emma has eaten 4. What percentage of the bag has Emma eaten?
HELP ASAP
Equation in picture
Answer:1/2
Step-by-step explanation:
3/4+(-1/2)-(-1/4)
3/4-1/2+1/4
1-1/2=1/2
5. Use the given process data to construct a control chart for p.
A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected
and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below.
4756831244562
Select the correct lower control limit.
lower control threshold for the data is LCL = -0.007
How does lower control limit work?The lower control limit on a control chart is the value below which any particular data point would be deemed to be out of statistical control owing to specific cause variation. It is represented by a line below the centerline.
The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]
To date,
Size of sample = n
Sample size is 12 samples.
Televisions with defects = X
We have a sample defect = p
p chart week with n = 200
x = 4, 7, 5, 6, 8, 3, 12, 4, 4, 5, 6, 2.
P = x/n
p = 4/200 = 0.02
p = 7/200 = 0.035
p = 5/200 = 0.025
p = 6/200 = 0.03
p = 8/200 = 0.04
p = 3/200 = 0.015
p = 12/200 = 0.06
p = 4/200 = 0.02
p = 4/200 = 0.02
p = 5/200 = 0.025
p = 6/200 = 0.03
p = 2/200 = 0.01
total will be 0.33
p bar = 0.33/12
p bar = 0.0275
The lower control limit formula: LCL = Pbar - [tex]3 \sqrt{p bar (1- p bar)/n}[/tex]
LCL = 0.0275 - 3[tex]\sqrt{ 0.0275 (1- 0.0275/200}[/tex]
LCL = -0.007
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How many solutions does this system of equations have? y=-1/3x+7 y=-2x^3+5x^2+x-2 A. no solution B. 1 solution C. 2 solutions D. 3 solutions
The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution thus option (B) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In other words, the equation must be constrained with some constraints.
As per the given equations,
y = (-1/3)x + 7 and y = -2x³ + 5x² + x - 2
The graph of both equations has been plotted below,
The number of points where both curves cut each other = 1
Thus, the number of solutions = 1
Hence "The system of equations y = (1/3)x + 7 and y = -2x³ + 5x² + x - 2 will have 1 solution".
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Answer:
1 solution
Step-by-step explanation:
Plato/Edmentum
3) Kevin made $9 per hour working as a
lifeguard. How many hours did he work
this week if his weekly pay before
deductions was $288? Define a variable
and write an equation. Solve the equation.
Answer: 9x = 288, 32 hours
Step-by-step explanation:
x can be the variable and it represents the hours he worked. 9 is the amount made each hour, so it is multiplied by x. 288 is the total made, so 9x=288.
9x = 288 Divide by 9 on both sides to isolate x
x = 32 hours. Kevin worked 32 hours this week
Answer:32
Step-by-step explanation: 32x9=288
I WILL MARK AS BRAINLIST PLEASE. Write the equation of the line in fully simplified slope-intercept form
Answer:
y= -5x-8
Step-by-step explanation:
Slope-intercept form equation: y=mx+b
b is where the line meets the y line. So it meets it at the number "-8". Then with the mx in the equation, you find that by doing rise over run. I got 5/-1, which goes to just plain old -5.
I hope this helps!!!
Sunny runs at a steady rate, and Moonbeam runs m times as fast, where m is a number greater than 1. If Moonbeam run to overtake Sunny a head start of h meteres, how many meters must Moonbeam run to overtake Sunny? ( Give your ansewr as an expression in terms of h and m.)
Hint : Let s be Sunny's rate. In terms of m and s, at what rate does Moonbeam catch up to Sunny?
Answer:
4 hours
Step-by-step :
If Sunny runs twice as fast as Moonbeam
Given the assumed data:
Sunny's speed = 12m/h
Moonbeam's speed= 6m/h
Therefore, if they run for 2 hours, Sunny would have covered 12 * 2 = 24 miles
While Moonbeam would have covered 6 *2 = 12 miles in the same 2 hours.
This given illustration shows that given that all parameters are equal, except the x2 speed of Sunny to that of Moonbeam, he would always be 2x faster than Moonbeam.
If they run for 4 hours, Sunny would have covered 12 * 4 = 48 miles
While Moonbeam would have covered 6 *4 = 24 miles in the same 4 hours.
an experiment can be assumed to have internal validity if multiple choice all variables other than the independent variable are kept constant. the dependent variable is valid. confounding variables are present. there is a strong manipulation of the independent variable.
An experiment can be assumed to have internal validity if random assignment and experimental control is employed. So the option c is correct.
The degree to which a study reliably establishes a cause-and-effect link is a sign of its internal validity. The procedures used in the study and the level of care done have a significant impact on this type of validity.
Internal validity is essential because, if proven, it enables alternate explanations for a discovery to be disregarded.
An experiment can be assumed to have internal validity if random assignment and experimental control is employed. So the option c is correct.
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The right question is:
An experiment can be assumed to have internal validity if:
A. the dependent variable is valid.
B. there is a strong manipulation of the independent variable.
C. random assignment and experimental control is employed.
D. confounding variables are present.
Given the graph of the function h(x) below, what is the approximate value of h(2) ?
Answer:
3
Step-by-step explanation:
h(2) we find by looking at what y equals when x is 2
when x is 2 y or h(2) is about 3
hopes this helps please mark brainliest
nothing to hard just please give correct answer!!
The equation of the first graph is
y > 2x - 4
The equation of the first graph is
y ≥ -x + 4
How to get the equations of the linesThe graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m calculating using the points on the graph (0, -4) and (2, 0)
m = (y₀ - y₁) / (x₀ - x₁)
m = (-4 - 0) / (0 - 2)
m = (-4) / (-2)
m = 2
c = y intercept, from the graph
c = -4
The equation of the line is y = 2x - 4
shading above the line is greater than and dotted lines means it does not have equal to
hence y > 2x - 4
for the second graph
the slope, m calculating using the points on the graph (0, 4) and (4, 0)
m = (y₀ - y₁) / (x₀ - x₁)
m = (4 - 0) / (0 - 4)
m = (4) / (-4)
m = -1
c = y intercept, from the graph
c = 4
The equation of the line is y = -x + 4
shading above the line is greater than and solid lines means there is equal to in the inequality
hence y ≥ -x + 4
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3/48
X
у
Find Lx and LY
Answer:
3/48
Step-by-step explanation:
your starting salary at a new company is 35000 and its increases by 2.5 each year
Answer:
35,875
Step-by-step explanation:
35000x(1+2.5%)
35000x1.025%
35,875
(sorry if it's wrong I'm assuming it is the answer because i saw a similar equation and i used the same format..)
The equation for line f can be written as 9x+10y=10. Line g is perpendicular to line f and passes through (– 9,– 7). What is the equation of line g?
Finding line J's slope is the first step.The simplest approach to achieve this is to change the equation's format to y=mx+b, where m represents the slope.
What is the equation of line g?9x-y=10
Take 9x off of both sides.
9x-y-9x=10-9x
Simpllify -y=-9x+10
Divide both sides by (-9x+10)-1, or -1 -y/-1.
Simplify y=9x-10
m=-1/9.
The notation (x1,y1) y-y1=m(x-x1) y-1=-1/9(x- -8) which reduces to y-1=-1/9(x+8)
y-1=-1/9x-8/9
then multiply both sides by 1.
y-1+1=-1/9x-8/9+9/9
(Using 9/9 as 1 makes it easier to use the common denominator to simplify the fractions.)
As the penultimate step, simplify.
y-1/9x+1/9
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a survey is carried out at uiuc to estimate the proportion of students who like to wear costumes on halloween. 1000 students participated in the survey. if you were to create a confidence interval with 98% confidence and a 4% margin of error, what would be the population sd?
The population standard deviation sd would be 0.543 .
Given :
a survey is carried out at uiuc to estimate the proportion of students who like to wear costumes on halloween. 1000 students participated in the survey. if you were to create a confidence interval with 98% confidence and a 4% margin of error .
we know that
margin of error = z * s / [tex]\sqrt{n}[/tex]
Z score at 98% = 2.326
0.04 = 2.326 * s / [tex]\sqrt{1000}[/tex]
0.04 * [tex]\sqrt{1000}[/tex] = 2.326 * s
1.264 = 2.326 * s
s = 1.264 / 2.326
s = 0.543
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