Answer:
[tex]27c^3-27c^2d+9cd^2-d^3[/tex]
Step-by-step explanation:
Binomial Theorem
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
[tex]\textsf{If }(a+b)^n=(3c-d)^3 \: \textsf{ then}:[/tex]
a = 3cb = -dn = 3Substitute the given values into the formula:
[tex]\begin{aligned}(3c-d)^3 & =(3c)^3+\dfrac{3!}{1!(3-1)!}(3c)^{3-1}(-d)+\dfrac{3!}{2!(3-2)!}(3c)^{3-2}(-d)^2+(-d)^3\\\\& =(3c)^3+3(3c)^2(-d)+3(3c)^1(-d)^2+(-d)^3\\\\& =27c^3-27c^2d+9cd^2-d^3\end{aligned}[/tex]
Find the smallest number. 8.9, 9.21, 9.73, 8.2
Answer:
8.2
Step-by-step explanation:
the bigger numbers are 9.21 and 9.73 because they have a higher number and 8.9 and 8.2 are the lower ones but 9 is a bigger number than 2.
Martha bought a 0.35-kilogram bottle of spice. spice. She uses 80 grams a week. Is one bottle of spice enough for 6 weeks? Explain.
Answer:
She has not got enough spice for 6 weeks.
Step-by-step explanation:
Remark
0.35 kg = 0.35 * 1000 grams / kg = 350 grams.
Since she will use 6 * 80 = 480 grams for 6 weeks, and since 350 is less than 480, she does not have enough spice for six weeks.
A refreshment company had declared that their soda drink is 250 oz. A group of students in CNHS wants to prove that the soda is less than advertised. They took 100 of such sodas in their study.
Answer:
200^2
Step-by-step explanation:
what is : 96 x 68.43 ?
Two angles that form a right angle are supplementary is true or false?
which of these numbers: 3,4,18,111,123,340,345,456,555 are divisible by 3 but not 9
Answer:
3
Step-by-step explanation:
3÷3=1
cant be divided by 9 and get a whole number
3÷9=.33333
Here is a list of Numbers:
8 7 12 7 11 10 7 12
Find:
a) median
b) range
c) mode
The median, mode and range of the numbers are 9, 5 and 7 respectively.
How to find median, range and mode?
The median is the middle number when the data is arranged in ascending order.
Therefore,
7, 7, 7, 8, 10, 11, 12, 12
median = 8 + 10 / 2 = 18 / 2 = 9
median = 9
The range is the largest number minus the smallest number.
Therefore,
range = 12 - 7 = 5
range = 5
The mode is the number that appears most. Therefore,
mode = 7
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The kinetic energy (K) that an object has varies jointly with its mass (m) and the square of its velocity (v). The equation that represents this relationship is given by [tex]K=kmv^2[/tex] where k is the kinetic energy constant. If a bowling ball of mass 5 kilograms is traveling at 2 meters per second, its kinetic energy is 10 Joules. What is the kinetic energy of a bowling ball of mass 3 kilograms traveling at 2.6 meters per second?
The kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.
What is Kinetic Energy?Kinetic energy is simply a form of energy a particle or object possesses due to its motion.
It is expressed as;
K = (1/2)mv²
Where m is mass of the object and v is its velocity.
Given that;
Mass of the bowling ball m = 3kgVelocity of the bowling ball v = 2.6m/sKinetic energy K = ?We substitute the given values into the above equation.
K = (1/2)mv²
K = 0.5 × 3kg × (2.6m/s)²
K = 0.5 × 3kg × 6.76m²/s²
K = 10.14kgm²/s²
K = 10.14J
Therefore, the kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.
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Select the correct answer.
Which outcome is an advantage of the SMBO approach?
OA. It takes into consideration the point of view of management.
OB. The customer is the focus of this approach.
OC. It provides motivation to salespeople.
OD. It narrows sales to specific items.
SOE.
It allows for the adoption of multiple and changing sales objectives.
An advantage of the SMBO approach it allows for the adoption of multiple and changing sales objectives.
What is SMBO?SMBO is for Sales Management by Objective and is a selling technique or approach that focuses on achieving a specific set of goals. The entire quantity of products sold is known as the sales volume. It can also be expressed in monitory terms.
An advantage of the SMBO approach it allows for the adoption of multiple and changing sales objectives.
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Select the correct answer from each drop-down menu. use . a boy weighing kilograms is riding a skateboard. he’s moving at 2 meters/second and has 40 joules of kinetic energy. he doubles his speed when he sees his friends ahead of him. his kinetic energy at the faster speed is joules.
If he doubles his speed when he sees his friends ahead of him. his kinetic energy at the faster speed is joules is 160Joules
Kinetic energy of an object.The formula for calculating the kinetic energy of an object is expressed as:
KE = 1/2mv²
where:
m is the mass of an object
v is the velocity
If he’s moving at 2 meters/second and has 40 joules of kinetic energy, the mass is calculated as:
40 = 0.5(2)²m
40 = 2m
m = 20 kg
If he doubles his speed when he sees his friends ahead of him, his kinetic energy will be:
KE = 0.5(20)(4)²
KE = 10*16
KE = 160joules
Hence if he doubles his speed when he sees his friends ahead of him. his kinetic energy at the faster speed is joules is 160Joules
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NEED HELP ASAP
Consider any conic section and discuss an application of the conic that you find most interesting. Include an example of a mathematical equation that models the application. Also, describe why you think this application is relevant and beneficial to society. (Note: To share your equation in the discussion forum, you might need to write your equation as if you were entering it into a graphing calculator.)
Conic sections are shapes that are formed when the surface of a cone intersects with a plane shape
Types of conic sectionThe types include
HyperbolaParabolaEllipseApplication of conic section (Parabola)The parabola can be applied in solving quadratic equations, functions and graph.
The general equation of a parabola is: y = a(x - h)² +k
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Desmond opened a savings account and deposited $600.00 as principal. The account earns
6% interest, compounded annually. What is the balance after 6 years?
Use the formula A = P(1+r/n)^nt
where A is the balance (final amount), P is the principal
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Answer:
$826.28
Step-by-step explanation:
Given:
[tex]P = 600[/tex]
[tex]r = 6% or 0.06[/tex]% or [tex]0.06[/tex]
[tex]t = 6[/tex]
Work:
[tex]A=Pe^{rt}[/tex]
[tex]A=600e^{0.06*6}[/tex]
[tex]A=600e^{0.36}[/tex]
[tex]A=826.28[/tex]
Therefore, the balance after 6 year is 826.28.
What is the product of 0 and any number?
Answer:
It will always be 0 because the rule is anything times 0 is 0
Answer:
0
Step-by-step explanation:
Hey there!
The product of any number and 0 is zero
To explain why this is, just think of it visually
So lets say we are visually explaining 7 x 3
Here is a visual explanation
There are 7 strawberries
You take 7 more strawberries
You take 7 more strawberries again
This means that you are taking 7 strawberries 3 times thereby forming the equation, 7 x 3
Now lets say a numeber [tex]x[/tex] times zero is equal to what
Well we can visualize this again
There are [tex]x[/tex] strawberries in a group
You are taking zero of those groups
Meaning there are no groups
So if there are no groups
There are no strawberries
Meaning [tex]x[/tex] times zero is zero
Since [tex]x[/tex] is any number, the statement, the product of 0 and any number is 0 is true
This is why the product of 0 and any number is 0
#81 will gove brainliest to best answer
To solve this problem, we need to factor both
⇒ numerator: [tex]x^2-4x+4[/tex]
⇒ denominator: [tex]x^2-4[/tex]
Let's factor:
⇒ [tex]x^2-4x+4=(x-2)(x-2)\\[/tex]
⇒ [tex]x^2-4=(x+2)(x-2)[/tex]
Let's put it back into the fraction:
[tex]\frac{x^2-4x+4}{x^2-4}=\frac{(x-2)(x-2)}{(x+2)(x-2)} =\frac{x-2}{x+2}*\frac{x-2}{x-2} =\frac{x-2}{x+2} *1=\frac{x-2}{x+2}[/tex]
Answer: Choice (3) or [tex]\frac{x-2}{x+2}[/tex]
Answer:
[tex]\frac{x-2}{x+2}[/tex]
Step-by-step explanation:
First, let's factor out the fraction into [tex]\frac{(x-2)^2}{(x+2)(x-2)}[/tex], now we can cancel out the [tex]x-2[/tex]. After we do that, our final answer is [tex]\frac{x-2}{x+2}[/tex].
Hope this helps! :)
Find the size of the final unknown exterior angle in a polygon whose other exterior angles are: 51°, 75°, 38°, 47°, 65° and 52º
A vehicle is randomly selected. Let T be the event that
the vehicle is a truck and A be the event that the
vehicle has all-wheel drive. What is the value of P(T°
and A)?
A)0.06
B)0.20
C)0.32
D)0.80
Using it's concept, it is found that the desired probability is given as follows:
B) 0.20.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, out of a total of 165 vehicles, 33 are SUV's with no all wheel drive, hence the probability is given by:
p = 33/165 = 0.2.
Which means that option B is correct.
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Answer:
B) 0.20
Step-by-step explanation:
correct on edge
Round the following numbers
to the nearest len
1)7
2)23
3)1.562
1) 7 = 7.0
2) 23 = 23.0
3) 1.562 = 1.6
Answer:
1) round off 7 to the nearest 10 is 10
2) round off 23 to the nearest 10 is 20
3)round off 1.562 to the nearest 10 is1.6
step by step explanation :
any whole number that is 5 and more can be rounded off to 10 e.g 5, 6 ,7 but numbers that are less than 5 can't be rounded off to 10 so it's becomes 0 e.g 4,2,3
example : round off 12 to the nearest ten
the answer is 10
A ball is projected up into the air from the surface of a platform to the ground below. The height
of the ball above the ground, in feet, is modeled by the function f(t) = -16t2 + 96t + 112, where
t is the time, in seconds, after the ball is projected.
State the coordinates of the vertex. Explain what it means in the context of the problem
The vertex of the quadratic function is of (3,256), which means that a maximum height of 256 feet is obtained after 3 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the height of the ball is given by:
f(t) = -16t² + 96t + 112.
Hence the coefficients are a = -16 < 0, b = 96, c = 112, and the coordinates of the vertex are:
[tex]x_v = -\frac{96}{2(-16)} = 3[/tex][tex]y_v = -\frac{96^2 - 4(-16)(112)}{4(-16)} = 256[/tex]The vertex of the quadratic function is of (3,256), which means that a maximum height of 256 feet is obtained after 3 seconds.
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can i have help with this please if you do it you're a lifesaver
Answer:
1, 2, 5, and 10
Step-by-step explanation:
Factors of 30 :
1, 2, 3, 5, 6, 10, 15, 30
Factors of 20 :
1, 2, 4, 5, 10, 20
what is a venn diagram?a venn diagram is an illustration that uses circles to show the relationship between things or group of things. Circles that overlap share the same traits (in this case numbers) and those that do not overlap dont share the same traits.What numbers go in the shaded overlap?
1, 2, 5, and 10
find the missing side of the right triangle.
Answer :
10.63[tex] \: [/tex]
Step-by-step explanation :
Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.
We'll find the measure of third side with the help of the Pythagorean theorem,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\[/tex]
Here,
The Base is 7The Perpendicular 8The Hypotenuse is x.[tex] \: [/tex]
So, substituting the values in the formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}= (7) {}^{2} + (8 {)}^{2} }}} \\ [/tex]
[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}=49 +64}}} \\ [/tex]
[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}=113 }}} \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x= \sqrt{113} }}} \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x \approx10.63 }}} \\ [/tex]
Therefore,
The measure of the third side (x) is 10.63Which of the following is true of the interquartile range on a box plot?
PLEASE HELPPP i have no clue what to do
Answer:
hope this will help you thank you
it can be also written as 1/5x-5
what least number should 27648 be divided so that the quotient will be a cube number
Pls help will give brainilist
Answer:
$16.37
Step-by-step explanation:
They want to raise $463.72 and they already have $218.22 so if we subtract it
$463.72-$218.22=$245.50
we get $245.50 left to raise.
We have 15 teachers so we do
$245.50/15
we get 16.36 but we round it so we get $16.37.
what is 2.25 x 9 i cant find it loololllooll
Answer:
20.25
Step-by-step explanation:
Answer: [tex]9[/tex] [tex]is[/tex] [tex]your[/tex] [tex]answer :)[/tex]
Step-by-step explanation:
Write the problem as a mathematical expression.
2.25 x 9
The degree is the largest exponent on the variable.
9
Your answer should be (9)
Need done by tonight please! Will mark brainliest just need it done.
Answer:
1. Binary number system only uses 2 digits: 0 and 1.
2. Octal number system uses 8 digits: 0,1,2,3,4,5,6,7 with the base of 8.
3. Decimal number system uses 10 digits: 0,1,2,3,4,5,6,7,8,9 with a base of 10.
4. Hexadecimal number system uses 16 digits and alphabets: 0,1,2,3,4,5,6,7,8,9 and A,B,C,D,E,F with the base of 16.
5. Quinary number system uses 0,1,2,3,4 with 5 as the base.
Absolute value is a number's distance from 0 on the number line.
A prime factor is a number with no factors other than one and itself.
The smallest quantity divisible by every number of the set is known as the least common multiple.
The denominator of a fraction can never be zero since a number divided by zero is not defined.
If the numerator is greater than or equal to the denominator, the fraction is called an improper fraction.
A mixed fraction is the sum of a whole number and a fraction.
To simplify a fraction is to convert it into a form which the numerator and denominator have no common factor other than one.
Step-by-step explanation:
Hope this helps :)
What is the value of x in this figure?
Enter your answer in the box.
A hemispherical tank is filled with water and has a diameter of 10 ft If water weighs 62.4 lb per cubic foot what is the total weight of water and a full tank in the nearest pound
The total weight of water and a full tank in the nearest pound is 16328 lb.
What is the total weight?Volume of a hemisphere = (2/3) x (n) x (r^3)
n = 22/7r = radius = 10/2 = 53.14 x 5³ x 2/3 = 261.67 ft³
Weight = volume x weight per cubic foot
261.67 ft³ x 62.4 = 16328 lb
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The area of a circle is 88.44 cm² find the length of the radius rounded to 2 DP
The radius of the circle is 5.30 cm.
What is a radius?A radius is a line that extends from the center of a circle to any point of the circumference.
To calculate the length of the radius of the circle, we use the formula below.
Formula:
A = πr²......... Equation 1
Make r the subject of the equation
r = √(A/π).................. Equation 2Where:
A = Area of the circler = Radius of the circleπ = PieFrom the question,
Given:
A = 88.44 cm²π = 22/7Substitute these values into equation 2
r = √(88.44/(22/7))r = √(88.44×7/22)r = √(28.14)r = 5.30 cmHence, the radius of the circle is 5.30 cm.
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Can anyone help out with this?? Girl need sum help. Its angles. :D
Answer:
12.8
Step-by-step explanation:
[tex]a^{2} + b ^{2} = c^{2} [/tex]
100+64=c^2
164=c^2
12.8=c
