Answer:
(
t
+
w
)
4
=
t
4
+
4
t
3
w
1
+
6
t
2
w
2
+
4
t
1
w
3
+
w
4
Explanation:
First, you should get to know Pascal's triangle. Here's a small portion of it up to 6 lines. Basically you're just adding the numbers that are beside each other, then writing the sum below them. (For example,
1
+
2
in the third line equals to
3
in the fourth line.) If you want a better explanation for that, feel free to do some more research on it.
Expansion of ( 4- 2z)³ using binomial expansion is equals to
64 - 96z + 48z² - 8z³.
What is binomial theorem?
" Binomial theorem is a way of expanding a binomial expression with exponent n, where n is any positive integer."
Formula used
Binomial Expansion
(a - b) ⁿ = ⁿC₀ aⁿb⁰+ ⁿC₁ aⁿ⁻¹ (-b)¹ + ⁿC₂ aⁿ⁻² + ....... + (-1)ⁿ ⁿCₙ a° bⁿ
According to the question,
Given,
(4 -2z)³
a = 4
b = 2z
Substitute the value in the formula of binomial expansion we have,
= ³C₀ (4)³ (-2z)⁰ +³C₁ (4)² (-2z)¹ +³C₂ (4)¹ (-2z)² + ³C₃ (4)⁰ (-2z)³
= (4)³ - 3 (4)² (2z) + 3 (4) (2z)² -(2z)³
= 64 -96z +48z² -8z³
Hence, expansion of ( 4- 2z)³ using binomial expansion is equals to
64 - 96z + 48z² - 8z³.
Learn more about binomial theorem here
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Find the missing term in the following sequence ? 1, 4, 11, 26, 57, 120, ______
Answer:
247
Step-by-step explanation:
1,4,11,26,57,120. see the pattern that emerges from the series:
4–1 = 3; 3–1 = 2 = 2^1
11–4 = 7; 7 - 3 = 4 = 2^2
26 - 11 = 15; 15 - 7 = 8 = 2^3
57 - 26 = 31; 31 - 15 = 16 = 2^4
120 - 57 = 63; 63 - 31 = 32 = 2^5
so the next number should be 64+63 = 127+120 = 247.
check: 247–120 = 127; 127–63 = 64 = 2^6. correct.
so the next number is 247. 2^n+(n-1)
Given sequence;
1, 4, 11, 26, 57, 120, _
The missing term =?
Solution;
We need to find the relationship between each term and then we can find the missing term;
1, 4, 11, 26, 57, 120, _ ;
let us start with the first two;
3 x 2 + 1 = 7 + 4 = 11
7 x 2 + 1 = 15 + 11 = 26
15 x 2 + 1 = 31 + 26 = 57
31 x 2 + 1 = 63 + 57 = 120
63 x 2 + 1 = 127 + 120 = 247
We see this pattern and can conclude that the missing term is 247
Which of the following shows two equivalent expressions?
A) 3(x - 4) and 3x – 4
B) 2(x + 5) and 2x + 10
C) 3(2x + 6) and 6x + 9
D) 4(2x - 6) and 6x - 24
An elephant weighs about 1.3×10 to the power of 4 pounds a car weighs about 4×10 to the power 3 pounds an elephant weighs about how many times more than the car weighs write your answer in standard notation
Answer:
[tex]\frac{13}{4}[/tex]times
Step-by-step explanation:
Weight of elephant = 1.3 x 10⁴lb = 13000lb
Weight of car = 4 x 10³lb = 4000lb
Unknown:
Number of times the elephant weigh more than the car = ?
Solution:
The number of times = [tex]\frac{Weight of elephant}{Weight of car}[/tex]
Number of times = [tex]\frac{13000}{4000}[/tex] = [tex]\frac{13}{4}[/tex] times
In a class of 40 students, 19 play tennis, 20 play netball and 8 play both of these sports. A student is randomly chosen from the class. Determine the probability that the student plays tennis.
Answer:
19/40 OR 0.475 OR 47.5%
Step-by-step explanation:
The probability of an event is calculated by dividing the total number of 'favorable outcomes' by the number of total outcomes. Here, the number of 'favorable outcomes' is the number of students who play tennis, so 19. The total number of outcomes is 40 as there are 40 students. Therefore the probability a student plays tennis is 19/40, or 0.475 or 47.5%.
Hope this helped!
Solve for y.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
5y +3> -7y + 13
Answer: Y>5/6
Step-by-step explanation: I had this on khan Academy and got this right
The solution to the inequality 5y + 3 > -7y + 13 is y > 5/6.
What is the solution to the inequality?Given the inequality in the question:
5y + 3 > -7y + 13
To solve the inequality 5y + 3 > -7y + 13, combine like terms on both sides and isolate the variable term:
5y + 3 > -7y + 13
Add 7y to both sides of the inequality:
5y + 7y + 3 > -7y + 7y + 13
5y + 7y + 3 > 13
12y + 3 > 13
Next, subtract 3 from both sides of the inequality:
12y + 3 - 3 > 13 - 3
12y > 10
Isolate variable y by dividing both sides by 12:
y > 10/12
Simplifying, we get:
y > 5/6
Therefore, the solution is y > 5/6.
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the gas tanks in a car is 60% full. If the gas tank has 8 gallons in it. How many gallons total does the gas tank hold
Answer:
12
Hope this helps! -xox
i need help with geometry
Answer:
thats soooo easy
Step-by-step explanation:
just do it
Answer:
Angle 5! Hope this helps :)
Step-by-step explanation:
Alternate interior angles.
The sum of three consecutive integers is -90. What is the largest integer
Answer:
Step-by-step explanation:
The sum of three consecutive even integers is 108. What is the largest number? Explanation: Three consecutive even integers can be represented by x, x+2, x+4.
WILL MARK AS BRAINLIEST HELP** NOTE : ANSWER IN FRACTION PLS
Solve -5 x (- 5/2 ) x 4/15
25/4
10/3
20/4
15/2
Step-by-step explanation:
25/2*4/15
100/30
10/3
=0.3
What is the value for x? 8x-13 and 5x+14
Answer:
9
Step-by-step explanation:
8x-13=5x+14
you subtract 5x from both sides and get
3x-13=14
then add 13 to both sides and get
3x=27
then divide 3 from both sides
3/3=x
27/3=9
x=9
Answer:
x = 9
Step-by-step explanation:
8x - 13 = 5x + 14 Subtract 5x from both sides of the equation 3x - 13 = 14 Add 13 to both sides of the equation 3x = 27 Divide by 3 for both sides of hte eqation x = 9
Kelly is recording the temperature of a cooling chemical. Using the table, determine the initial
temperature of the chemical when she poured into the beaker.
Answer:
Initial temperature of the chemical = 97°
Step-by-step explanation:
Time Temperature Difference
4 89.5 -
10 78.25 78.25 - 89.5 = -11.25
16 67.00 67 - 78.25 = -11.25
There is a common difference of -11.25 in each successive term.
Therefore, cooling of a chemical represents a linear function.
Let the function representing temperature is,
f(t) = at + b
Where 'a' = rate of change in temperature
b = initial temperature
t = time
Now 'a' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{78.25-89.5}{10-4}[/tex]
a = -1.875
f(t) = -1.875t + b
For t = 4 and f(t) = 89.50,
89.50 = -1.875(4) + b
b = 97
Therefore, function representing the cooling of chemical is,
f(t) = -1.875t + 97
And the initial temperature of the chemical was 97° when it was poured into the beaker.
3. The light pole is 70 ft. tall and is 1100 ft. from the vanishing point. The fifth light pole is 7 ft. tall, how far from the vanishing point is the fifth light pole?
Answer:
110 ft
70/7=10
1100/10=110
Step-by-step explanation:
Rewrite in simplest terms: (-8x – 9y) + (-X – 5y)
Answer:
-9x - 14y
Step-by-step explanation:
Step 1: Write expression
(-8x - 9y) + (-x - 5y)
Step 2: Combine like terms
-9x - 14y
What is the answer to this question because I don’t know?
Answer:
B.
Step-by-step explanation:
To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.
solve P = P - C for C
Answer:
c=0
Step-by-step explanation:
12. Write the following expression in the form ax? +bx+c, where a, b, and c are real number constants.
(x+6)(x+5)+(x+6)(x-2)
Answer: x=35
Step-by-step explanation: (x+6)(x+5)+(x+6)(x-2) = (x+6) X (2x+3)= 35
((x + 6) • (x + 5)) + (x + 6) • (x - 2)
Pull out x+6
After pulling out, we are left with :
(x+6) • ( 1 * (x+5) - (-1) * (x-2) ))
(x + 6) • (2x + 3)=35
This is 2x²+15x+18 expression in the form ax²+bx+c.
What is expression?
Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
(x+6)(x+5)+(x+6)(x-2)
x²+5x+6x+30+x²-2x+6x-12
2x²+15x+18
Comparing expression to the form ax²+bx+c,
So a = 2, b = 15, and c = 18
Hence, this is 2x²+15x+18 expression in the form ax²+bx+c.
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The price of a box of markers at a retail store is $4.65. Th e price of a box
of markers at the school bookstore is $3.90. How much more do the markers cost at the
retail store? Explain how you can use a quick picture to solve the problem.
Answer:
.75 or 3 quarters
Step-by-step explanation:
4.65 - 3.90 =.75 or 3 quarters
5(x + 4) + 21 ≥ −3 + 4(x − 8)
−5x − 20 + 21 ≥ −3 + 4x − 32
−5x + 1 ≥ 4x − 35
−9x ≥ −36
x ≥ 4
What mistake did Eduardo make in solving the inequality?
please I need HELPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
um on what ?
Step-by-step explanation:
A circle is translated 4 units to the right and then reflected over the x-axis. Complete the statement so that it will always be true of the circle at the new location.
Answer:
The statement is now presented as:
[tex]\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}[/tex]
In other words, this mathematical statement can be translated as:
There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r.
Step-by-step explanation:
Let [tex]C = (h,k)[/tex] the coordinates of the center of the circle, which must be transformed into [tex]C'=(h', k')[/tex] by operations of translation and reflection. From Analytical Geometry we understand that circles are represented by the following equation:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
Where [tex]r[/tex] is the radius of the circle, which remains unchanged in every operation.
Now we proceed to describe the series of operations:
1) Center of the circle is translated 4 units to the right (+x direction):
[tex]C''(x,y) = C(x, y) + U(x,y)[/tex] (Eq. 1)
Where [tex]U(x,y)[/tex] is the translation vector, dimensionless.
If we know that [tex]C(x, y) = (h,k)[/tex] and [tex]U(x,y) = (4, 0)[/tex], then:
[tex]C''(x,y) = (h,k)+(4,0)[/tex]
[tex]C''(x,y) =(h+4,k)[/tex]
2) Reflection over the x-axis:
[tex]C'(x,y) = O(x,y) - [C''(x,y)-O(x,y)][/tex] (Eq. 2)
Where [tex]O(x,y)[/tex] is the reflection point, dimensionless.
If we know that [tex]O(x,y) = (h+4,0)[/tex] and [tex]C''(x,y) =(h+4,k)[/tex], the new point is:
[tex]C'(x,y) = (h+4,0)-[(h+4,k)-(h+4,0)][/tex]
[tex]C'(x,y) = (h+4, 0)-(0,k)[/tex]
[tex]C'(x,y) = (h+4, -k)[/tex]
And thus, [tex]h' = h+4[/tex] and [tex]k' = -k[/tex]. The statement is now presented as:
[tex]\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}[/tex]
In other words, this mathematical statement can be translated as:
There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r.
Answer:
the same area as
Step-by-step explanation:
When a circle is translated and reflected, the center of the circle will change; however, its area, circumference, radius and diameter remain the same.
This is so because, translation and reflection only affect the positioning of the circle not the size.
Considering the above analysis, we can conclude that option d answers the question correctly.
F(n)=2n-5 ;find f (-8)
Answer:
-21
Step-by-step explanation:
f(-8) = 2(-8)-5 = -21
Select all the situations that can be represented by 1/2⋅5. * 1 point Diego lives 5 miles from school, and Elena lives 1/2 as far away as Diego. How many miles does Elena live from school? Jada has 5 bottles that each contain 1/2 liter of water. How many liters of water is that in total? Noah has 5 meters of rope. How many pieces of rope of length 1/2 meter can he cut from it? Lin's goal is to run 5 miles. She ran 1/2 mile. What fraction of her goal is that?
Answer:
Elena lives 2.5 miles away from school.The total liters of water is 2.5 litersHe can cut 10 pieces of rope of length 1/2 meterThe fraction of her goal she ran is 1/10Step-by-step explanation:
From the question,
Diego lives 5 miles from school, and Elena lives 1/2 as far away as DiegoTherefore, Elena lives 1/2 of 5 miles away from school.
1/2 of 5 miles = 2.5 miles
Hence, Elena lives 2.5 miles away from school.
Jada has 5 bottles that each contain 1/2 liter of water.Since each bottle contain 1/2 liter of water, then
The total liters of water is (1/2 × 5) liters
1/2 × 5 = 2.5 liters
Hence, the total liters of water is 2.5 liters
Noah has 5 meters of ropeTo determine how many pieces of rope of length 1/2 meter he can cut,
Number of pieces of rope of length 1/2 meter that can be cut is 5 meter ÷ 1/2 meter
5 meter ÷ 1/2 meter = 10
Hence, he can cut 10 pieces of rope of length 1/2 meter.
Lin's goal is to run 5 miles. She ran 1/2 mile.To determine what fraction of her goal that is,
First, she ran 1/2 mile out of 5 miles.
The fraction of her goal she ran is 1/2 mile ÷ 5 miles
1/2 mile ÷ 5 miles = 1/10
Hence, the fraction of her goal she ran is 1/10.
Answer:
i need points :)
Step-by-step explanation:
Im stuck please help ( use the PEMDAS)
Answer: 2. (4-2) x4 =8
3. (7-1) * 6 = 36
4. 4+ 3+ 4 = 11
5. (15 x2) * -3 = -90
6. 10 * (-3) x19 - 8 = -578
Hope that helps
Step-by-step explanation:
Please Excuse My Dear Aunt Sally
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Someone please help me
(Slope intercept problem)
Answer:
Y=1/2x-2
Step-by-step explanation:
Figures that have the same size and same shape. Their corresponding angles and sides are the same size. whats the answer?
Answer:
prostokąt i kwadrat
Will mark the BRAINLEST!!! 50 points!! If you know any of the answers please help!?!
1.) Bicycles have three types of tires: mountain bike, road touring, and cruising. An experiment is to be conducted to determine whether the mileage before a tire change is needed is the same for all three types of tires. In previous studies, it was determined that bicycle weight (light, normal, heavy) is associated with frequency of tire changes, but bike type (mountain, road, cruising) is not associated with frequency of tire change. How would blocking best be used?
a. By blocking on bicycle type
b. By blocking on mileage
c. Blocking is not suggested.
d. By blocking on tire type
e. By blocking on bicycle weight
2.) From 2010 to 2015, a group of researchers conducted an experiment using two types of pain medication: pill A and pill B. The researchers gave the doctors the pills in unidentified packages so they would not know which package was pill A and which package was pill B. The patients participating did not know which pill they received either. What is this an example of?
a. The effect of a treatment unit
b. The placebo effect
c. A control group study
d. A double-blind study
e. Voluntary response bias
3.) Cocoa plant type 1 yielded 155 bushels per acre last year at a research farm. This year, cocoa plant type 2, planted in the same location, yielded only 123 bushels per acre and there was a major freeze. The researchers do not know whether the difference is the result of the superiority of type 1 or the freeze. What is this an example of?
a. Bias
b. Confounding variable
c. Matched-pairs design
d. The placebo effect
e. Replication
4.) A cell phone company is trying to find a waterproof cell phone case to add to its product line. Company managers know that plastic and silicone will be used. They also know that the depth of the water—less than five feet, between five feet and 20 feet, and more than 20 feet—affects the waterproof case. An experiment will compare all combinations of these choices. The cell phones will be subjected to each treatment, with one group dropped in water without a case, and all phones will be scored for quality. What is the control?
a. Cell phones in the plastic case
b. Cell phones in the silicone case
c. Cell phones in the plastic case dropped in water less than five feet deep
d. Cell phones in the silicone case dropped in water more than 20 feet deep
e. Cell phones with no case
5.) Do children prefer purple juice or yellow juice? Two different supplements, which have no effect on taste, are used on identical juice to produce purple juice or yellow juice. Volunteer children are randomly assigned to either purple juice or yellow juice, and they are asked to rate the juice on a scale from 1 point to 10 points. Is blinding demonstrated in the experiment?
a. No, because the volunteers do not know the color juice they are getting
b. Yes, by having the experimenter in a separate room pick one of the two containers at random and having a juice pulled from that container remotely
c. Yes, by having the statistician analyzing the results not know which volunteer sampled which juice
d. Yes, by having the volunteers wear a blindfold while drinking the juice out of the container, so that they don't know the color juice they are tasting
e. No, because the volunteers know whether they are drinking purple juice or yellow juice
Answer:
1. E
2. A
3. B
4. C
5. E
Step-by-step explanation:
n+q= 8.80
.05n+.25q=68
Answer:
i do not know
Step-by-step explanation:
round 3,989.23655 to the nearest thousandth
Using the segment addition postulate, which is true? What is the measure of AngleDCF? Three lines extend from point C. The space between line C D and C E is 75 degrees. The space between lines C E and C F is 54 degrees. The measure of AngleDCF is degrees.
Answer:
129
Step-by-step explanation:
If three lines CD, CE and CF extend from point C, then the following addition postulate is true;
<DCE + <ECF = <DCF
If the space between line C D and C E is 75 degrees, then <DCE = 75
If the space between lines C E and C F is 54, then <ECF = 54.
Substitute the given values into the expression above will give;
<DCF =<DCE + <ECF
<DCF = 75+54
<DCF = 129
Hence the measure of <DCF is 129°