Answer:
2065.5
Step-by-step explanation:
You have to approximate the following calculation 3.5^6
The binomial theorem is given by:
[tex](a+b)^n=\Sigma_{k=0}^{k=n}\left[\begin{array}{c}n&k\end{array}\right] a^{n-k}b^k[/tex] (1)
You can express the number 3as follow:
[tex]3.5^6=(3+0.5)^6=(3+\frac{1}{2})^6[/tex] (2)
by comparing the equation (1) with the equation (2) you have
a = 3
b = 1/2
To calculate the first three terms of the binomial theorem you use k=3. You replace the values of a, b, n and k in the equation (1):
[tex](3+\frac{1}{2})^6=\Sigma_{k=0}^{k=6}\left[\begin{array}{c}6&k\end{array}\right] (3)^{6-k}b^k[/tex]
You only take the first three terms:
[tex](3+\frac{1}{2}^6)\approx(1)(3)^6(\frac{1}{2})^0+(6)(3)^5(\frac{1}{2})^1+\frac{6\cdot 5}{1\cdot 2}(3)^4(\frac{1}{2})^2\\\\(3+\frac{1}{2}^6)\approx729+729+\frac{1215}{2}=2065.5[/tex]
By using the first three terms of bynomial theorem you obtain 2065.5
I am stuck pls I need help
Answer:
HF is 20 m away from the tower which makes it the base of a triangle
tan 30= opp/adj=PF/HF
PF=tan 30°(20)=11.547
tan 50=T F/20 ⇒ T F=20*tan 50= 23.835
PT= T F-PF= 23.835-11.547=12.288 m
b ) the distance from point H to the power is the hypotenuse
cos 50=adj/hyp
hypo(HT)= 20/cos 50=31.114
(HF at a new angle=40)
tan 40=opp/adj = T F/HF
HF=T F/tan40=23.835/tan 40=28.405
Max must take 10 steps to go the same distance as three of his dad's steps. His dad takes 30 steps to walk down the hall. How many steps must Max take to walk down the same hall?
Max : 10 steps : Dad: 3 steps.
So it you multiply those each by ten, you get
100 steps : 30 steps.
30 Dad steps is 100 Max steps, so you get the answer, which is 100!
The steps taken by Max is 100.
what is arithmetic operators?A mathematical function that performs a calculation on two operands is known as an arithmetic operator. Common arithmetic makes use of them, and the majority of computer languages include a set of such operators that can be used in equations to carry out a variety of sequential calculations.
Given
steps taken by Max = 10
Steps taken by his Dad = 3
both steps of Dad and steps of Max should be in ratio
3/10 …(1)
steps taken by his Dad = 30
let steps taken by Max = x
ratio = 30/x …..(2)
equation 1 equals equation 2
3/10 = 30/x
x = (30 x 10)/3
x = 100
Hence Max must take 100 steps.
Learn more about arithmetic operators;
https://brainly.com/question/25834626
#SPJ5
The volume inside of a sphere is V=4πr33 where r is the radius of the sphere. Your group has been asked to rearrange the formula so that it is rewritten to solve for r. Below are various solutions that your group-mates have arrived at. Select the correct one A) r=3V4π−−−√ B) r=3V4π−−−√3 C) r=3V√34π D) r=4V3π−−−√3
Answer:
Step-by-step explanation:5
The exchange rate for US dollars is £1=$1.62.How many dollars will I get for
a) £3. b)50p. c) £2.60 d) £5.63
Round your answer to 2 decimal places.
Find the value of x:
Step-by-step explanation:
angle (JIF) = 2x°
so angle (FIG) = (180 - 2x)°
Also , IK || EH
So , angle KIG = angle IGF = x°
angle (EFI) = 3x°
angle (IFG) = (180 - 3x)°
In triangle IFG ,
angle IGF + angle IFG + angle FIG = 180°
=> x + 180 - 3x + 180 - 2x = 180
=> 360 - 4x = 180
=> 4x = 360 - 180 = 180
=> x = 180 / 4 = 45°
can someone please help me?
Answer:
-1Option C is the correct option.
Step-by-step explanation:
Let the points be A and B
A ( -2 , 7 ) -----> ( x1 , y1 )
B ( 2 , 3 )-------> ( x2 , y2)
Now, let's find the slope:
Slope = [tex] \frac{y2 - y1}{x2 - x1} [/tex]
plug the values
[tex] = \frac{3 - 7}{2 - ( - 2)} [/tex]
Calculate the difference
[tex] = \frac{ - 4}{2 - (2)} [/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] = \frac{ - 4}{2 + 2} [/tex]
Add the numbers
[tex] = \frac{ - 4}{4} [/tex]
Any expression divided by its opposite equals -1
[tex] = - 1[/tex]
Hope this helps..
Best regards!!
Find the sum. Express your answer in simplest
form.
Answer:
( 3u +12) / (v^2+4)
Step-by-step explanation:
(-u+3) / (v^2+4) + ( 4u+9)/( v^2+4)
Since the denominators are the same, we can add the numerators
((-u+3) + ( 4u+9)) /( v^2+4)
Combine like terms
( 3u +12) / (v^2+4)
Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions
Answer:
c
Step-by-step explanation:
c
Answer:
the answer is C ;D
Step-by-step explanation:
Need help quick quick quico
Answer:
7 batches
Step-by-step explanation:
find the truth set of 2x-6≤5(3-x)
Answer:
x∈(-∞,3]
Step-by-step explanation:
2x-6<=5*3-5x
2x-6<=15-5x
+5x +5x
7x-6<=15
+6 +6
7x<=21
:7 :7
x<=3
x∈(-∞,3]
Please Help ME!! I BEG YALL! Ill give BrAINlIeSt! :) Given the figure below, find the values of x and z.
Answer: [tex]\left \{ {{x=10} \atop {z=63}} \right.[/tex]
Step-by-step explanation:
Vertical Angles states that 9x+27=117
Supplementary Angles states that 117+z=180
[tex]9x+27=117\\Subtract (27)\\9x=90\\Divide(9)\\\left[\begin{array}{c}x=10\end{array}\right] \\\\117+z=180\\Subtract(117)\\\left[\begin{array}{c}z=63\end{array}\right][/tex]
Hope it helps <3
SOMEBODY!!! HEELLLLLLP if you can help me with one question that's fine!
Step-by-step explanation:
Question 1The 20° angle is equal to the angle next you friend.
since they are interior alternate angles
The height of the ballon is 600 feet
Let x be the missing distance we are looking for
sin20° = 600/x switch x and sin 20° x = 600/ sin 20° x=1754.28≈ 1754 ftso the missing distance is 1754 feet
Question 2Here I represented the situation to visualize the problem
Let h be L be the length of the ladder
sin 30° = 7/L switch L and sin 30°L= 7/sin 30° = 14L = 14 ftso the ladder is 14 ft
round off 285 to the nearest ten
Answer:
290
Step-by-step explanation:
Answer:
290
Step-by-step explanation:
I mean you just have to look at a number line and see that 285 is closer to 290 instead of 280...
What is the answer to... 5m+8n-2(3m-n)? Show step by step
Answer:
The answer is
10n - mStep-by-step explanation:
5m+8n-2(3m-n)
Expand the terms in the bracket
That's
5m + 8n - 6m + 2n
Group like terms
We have
8n + 2n + 5m - 6m
Simplify
The final answer is
10n - m
Hope this helps you
If f(x) is the total cost, in dollars, of x candles, which of the following statements best describes the meaning of f(2)=6
Answer: A) The total cost of 2 candies is $6.00.
Step-by-step explanation:
Hi, the question is incomplete, options are :
A) The total cost of 2 candies is $6.00. B) The total cost of 6 candies is $2.00. C) The total cost of 2 candies is $3.00. D) The total cost of 3 candies is $2.00.
So, to answer this question we have to analyze the function given:
f(2)=6
Since the input value x (number of candles) is 2, and the output (cost in dollars ) is $6, the correct option is :
A) The total cost of 2 candies is $6.00.
A pair of parallel lines is cut by a transversal: A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x, and the other part is labeled as 20 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 80 degrees. What is the measure of angle x? 60 degrees 70 degrees 80 degrees 100 degrees
4/5 (x − 20) = 8 solve it
Answer:
30
Step-by-step explanation:
4/5 (x-20)=8
4/5x-4/5*20=8
4/5x-16=8
4/5x=24
x=(24*5)/4
x=30
hope it helps..
In the xy-coordinate plane, a line has a slope of −5/3. If the line crosses the y-axis at (0, b), at what point does it cross the x-axis?
Answer:
([tex]\frac{3}{5}[/tex] b, 0 )
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - [tex]\frac{5}{3}[/tex] and b = b , thus
y= - [tex]\frac{5}{3}[/tex] x + b ← equation of line
The line crosses the x- axis when y = 0, substitute y = 0 into equation and solve for x, that is
- [tex]\frac{5}{3}[/tex] x + b = 0 ( multiply through by 3 to clear the fraction )
- 5x + 3b = 0 ( subtract 3b from both sides )
- 5x = - 3b ( divide both sides by - 5 )
x = [tex]\frac{3}{5}[/tex] b , thus
x- intercept = ( [tex]\frac{3}{5}[/tex] b, 0 )
Answer:
( b, 0 )
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!! A teacher is grading the final exam. He notices that the mean test score is 61, and the standard deviation is 10. The test scores were normally distributed. if there were 450 students in the data sample, how many would have a test score between 61 and 71 *Round your answer to the nearest full value.
Answer:
153.586 close to 154 students
Step-by-step explanation:
mean=61
standard deviation =10
sample 450 students , x between 61 and 71
(x-mean)/deviation for score 61 and 71
61-61/10=0
71-61/10=1
the z-scores is between 0 and 1 ( use calculator)
the percentage is 0.3413 close to 34%
number of students that score between 61 and 71=
450*0.3413= 153.586 close to 154 students
(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the triangle, and (c) determine the area of the triangle. the figure is not drawn to scale.
a. the length of the unknown side is ___
b. the perimeter of the triangle is ___
c. the area of the triangle is ___
Answer:
(A) 40 km
(B) 90 km
(C) 180 km²
Step-by-step explanation:
To find the missing side of this triangle, let's use the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex], assuming that a and b are legs, and c is the hypotenuse.
Assuming the 9km side is a, we need to find the value of b, so we can substitute into the equation.
[tex]9^2+b^2=41^2\\81+b^2=1681\\b^2=1681-81\\b^2=1600\\\\b = \sqrt{1600} \\b=40[/tex]
So, the length of the missing side is 40. Now that we know this piece of information, we can find the perimeter and area of the triangle.
The perimeter is all the sides added together, so [tex]41+9+40 = 90[/tex] km is the perimeter.
The area are the two legs multiplied divided by 2.
So,
[tex]\frac{9\cdot40}{2} \\\\\frac{360}{2}\\\\180[/tex]
So the area of this triangle is 180 cm²
I hope this helped!
|3x+9|= 30
Answer: x=7, -13
Answer:
[tex]\boxed{x=7, \: x=-13}[/tex]
Step-by-step explanation:
[tex]|3x+9|= 30[/tex]
Solve for absolute value.
There are two possibilities.
One possibility:
[tex]3x+9=30\\3x=21\\x=7[/tex]
Second possibility:
[tex]3x+9=-30\\3x=-39\\x=-13[/tex]
Julie gathered data about the numbers of pages and chapters in several books by her favorite author.The equation of the line of best fit is y = 15.261x + 8.83. Based on the line of best fit, approximately how many pages are predicted to be in a book with 8 chapters? A. 113 B. 122 C. 131 D. 193
Answer:
C
Step-by-step explanation:
To get the approximate number of pages in the chapters, what we need to do is to substitute for the value of x in the line of best fit equation.
Thus, we have;
y = 15.261(8) + 8.83 = 122.088 + 8.83 = 130.918
This is approximately equal to 131
HURRY ILL GIVE YOU BRAINLY ;DD
Hi there!! (✿◕‿◕)
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
A.) 4/100
B.) 5,250,000
C.) C. 6/100
Hope this helped!! ٩(◕‿◕｡)۶
Answer:
A) 4/100
B) 5,250,000
C) C) 6/100
Step-by-step explanation:
A) the 4 is in the hundredths place, so it’s worth 4/100.
B) 5,250,000. (250,00 is a quarter million)
C) the 6 is in the hundredths place, so it’s worth 6/100.
Helppppp plzzzz ❤️❤️❤️❤️I’m crying help with my math
Answer:
A
Step-by-step explanation:
I'm certain the answer is this, and I understand that you are in a hurry. I can update it anytime you'd like to see the explanation
Jada and jack are each working during the summer to earn money in addition to their weekly allowance, and they are saving all their money. Jada earns $9 an hour at her job and her allowance is $8 per week. And Jack earns $7.50 an hour and his allowance is $16 per week. How many hours do Jada and Jack need to work in order to save the same amount of money in one week?
The cost of renting a car is $39 plus $0.75 per mile. Which type of
function can represent this situation?
A) linear
B) exponential
Answer:
linear
Step-by-step explanation:
We can write this in the form
y = mx+b
where m is the .75 per mile and b is the 39 dollars
y = .75x + 39
A taste test asks people from Texas and California which pasta they preferred brand a or brand b this table shows the results. A person is randomly selected for those tested. What is the probability that the person is from Texas given that the person prefers Brand b? Round your answer to two decimal places.
Answer: I just did it and the answer is 0.43
Step-by-step explanation:
Using it's concept, it is found that the probability that the person is from Texas given that the person prefers Brand b is given by:
A. 0.43.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 105 people prefer brand B, and of those, 45 are from Texas, hence:
p = 45/105 = 0.43.
Which means that option A is correct.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ2
Hey loves. Again, needing help with a math question.When will this end? Never, or at least until I get it.:). Help is much appreciated
Answer:
Hey there!
SL=KR
We can't prove that the triangles are congruent, but since SL=SK+KL, and KR=RL+LK. We have RL=SK, so we have two lines:
SL=SK+KL
KR=SK+KL
These are clearly congruent, making these two lines congruent.
Hope this helps :)
Add the polynomial
(6s3+9s+10)and(3s3+4s-10)
PLEASE HELP!!! ASAP!!!
Answer:
9s³ ⁺ 13sStep-by-step explanation:
6s³ + 9s + 10 + 3s³ + 4s - 10
Collect like terms
6s³ + 3s³ + 9s + 4s + 10 - 10
Since, two opposites add up to zero, remove them from the expression
6s³ + 3s³ + 9s + 4s
add the like terms
9s³ + 13s
hope this helps..
best regards!!
Answer:
9s^3+13s
Step-by-step explanation:
Add each term:
9s^3+13s
I hope this helps...
And plz mark me brainliest!!
Select the equation that could represent the relationship between f(x) and g(x).
Answer:
C
Step-by-step explanation:
First, f(x) and g(x) are mirror image over the x-axis. so add a -ve in front.
Second, f(x) is about 2x steeper than g(x), that is its slope is doubled. so add a 2 in front.
Thus, f(x) = -2 g(x)