Answer:
Step-by-step explanation:
87°32' = 86°92'
(86°92')/2 = 43°46'
B = 13/(16cos(43°46')) = 1.125
Answer:
Step-by-step explanation:
What is the factored form of the binomial expansion 625x4 – 3,000x3y + 5,400x2y2 – 4,320xy3 + 1,296y4?
(5x – 6y)4
(5x + 6y)4
(25x – 36y)2
(25x + 36y)2
Answer:
(5x – 6y)^4
Step-by-step explanation:
Given
[tex]625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Required
The factored form
Solving (a): (5x – 6y)^4
Expand using pascal triangle;
Exponent 4 is represented as: 1 4 6 4 1. So, we have:
[tex](5x - 6y)^4 = 1 * (5x)^4 + 4 * (5x)^3 * (-6y) + 6 * (5x)^2 * (-6y)^2 + 4 * (5x) * (-6y)^3 + 1 * (-6y)^4[/tex]
Expand:
[tex](5x - 6y)^4 = 1 * 625x^4 + 4 * 125x^3 * (-6y) + 6 * 25x^2 * 36y^2 + 20x * (-216y^3) + 1 * (1296y^4)[/tex]
Remove brackets
[tex](5x - 6y)^4 = 625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Hence, (a) is correct
Anyone willing to help on this worksheet?
Answer:
I am pretty sure it's #2 but wait for more ansawers because im not 100% sure.
Step-by-step explanation:
Answer:
Same I think it's B but I'm not entirely sure
Step-by-step explanation:
Please help me thank you!!!
Answer:
B
Step-by-step explanation:
To solve this use a unit circle (see pic)
Go to the 300 degree
Then look at the y coordinate (y coordinate because it's cosine)
Which matches with answer choice B
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
t > -25
t < -25
t ≤ -25
t ≥ -25
Answer:
t≥-25
Step-by-step explanation:
this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.
Describe a rule for the transformation.
Answer: 90° counterclockwise
Step-by-step explanation:
write your answer in simplest radical form
Answer:
n = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 30 = n / 2 sqrt(3)
2 sqrt(3) tan 30 = n
2 sqrt(3) * sqrt(3)/3 = n
2 = n
We have to find,
The required value of n.
Now we can,
Use the trigonometric functions.
→ tan(θ) = opp/adj
Let's find the required value of n,
→ tan (θ) = opp/adj
→ tan (30) = n/2√3
→ n = 2√3 × tan (30)
→ n = 2√3 × √3/3
→ n = 2√3 × 1/√3
→ [n = 2]
Thus, the value of n is 2.
Consider the series ∑n=1∞5n2+n.
The general formula for the sum of the first n terms is Sn=
. Your answer should be in terms of n.
The sum of a series is defined as the limit of the sequence of partial sums, which means
∑n=1∞5n2+n=limn→∞(
)=
.
Select all true statements (there may be more than one correct answer):
A. Most of the terms in each partial sum cancel out.
B. The series converges.
C. The series is a p-series.
D. The series is a telescoping series (i.e., it is like a collapsible telescope).
E. The series is a geometric series.
(a) Decompose the summand into partial fractions:
[tex]\dfrac5{n^2+n} = \dfrac5{n(n+1)} = \dfrac an+\dfrac b{n+1}[/tex]
[tex]\implies 5=a(n+1)+bn=(a+b)n+a[/tex]
[tex]\implies a+b=0\text{ and }a=5 \implies b=-5[/tex]
[tex]\implies\displaystyle\sum_{n=1}^\infty\frac5{n^2+n} = 5\sum_{n=1}^\infty\left(\frac1n-\frac1{n+1}\right)[/tex]
The n-th partial sum for the series is
[tex]S_n = 5\displaystyle\sum_{k=1}^n\left(\frac1k-\frac1{k+1}\right)[/tex]
which can be simplified significantly by examinging consective terms in the sum:
[tex]\displaystyle S_n = 5\left(1-\frac12\right) + 5\left(\frac12-\frac13\right) + 5\left(\frac13-\frac14\right) + \cdots + 5\left(\frac1{n-1}-\frac1n\right) + 5\left(\frac1n-\frac1{n+1}\right)[/tex]
[tex]\implies S_n = \boxed{5\left(1-\dfrac1{n+1}\right)}[/tex]
(b) Using the result of (a), you then get
[tex]\displaystyle\sum_{n=1}^\infty\frac5{n^2+n} = \lim_{n\to\infty}\boxed{5\left(1-\frac1{n+1}\right)} = \boxed{5}[/tex]
(c) As shown in (a), the partial sum is simplified because of the reasons given in options A and D, and the result of (b) says that B is also correct.
Answer:
Part a. [tex]\displaystyle S_n = 5 - \frac{5}{n + 1}[/tex]
Part b. [tex]\displaystyle \lim_{n \to \infty} (5 - \frac{5}{n + 1}) = 5[/tex]
Part c. A, B, and D
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringPre-Calculus
Partial Fraction DecompositionCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]Sequences
Series
Definition of a convergent or divergent seriesTelescoping Series: [tex]\displaystyle \sum^\infty_{n = 1} (b_n - b_{n + 1}) = (b_1 - b_2) + (b_2 - b_3) + (b_3 - b_4) + ... + (b_n - b_{n + 1}) + ...[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n}[/tex]
Step 2: Rewrite Sum
Factor: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \sum^\infty_{n = 1} \frac{5}{n(n + 1)}[/tex]Break up [Partial Fraction Decomposition]: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{A}{n} + \frac{B}{n + 1}[/tex]Simplify [Common Denominator]: [tex]\displaystyle 5 = A(n + 1) + Bn[/tex][Decomp] Substitute in n = 0: [tex]\displaystyle 5 = A(0 + 1) + B(0)[/tex]Simplify: [tex]\displaystyle 5 = A[/tex][Decomp] Substitute in n = -1: [tex]\displaystyle 5 = A(-1 + 1) + B(-1)[/tex]Simplify: [tex]\displaystyle 5 = -B[/tex]Solve: [tex]\displaystyle B = -5[/tex][Decomp] Substitute in variables: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{5}{n} + \frac{-5}{n + 1}[/tex]Simplify: [tex]\displaystyle \frac{5}{n(n + 1)} = \frac{5}{n} - \frac{5}{n + 1}[/tex]Substitute in decomp [Sum]: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \sum^\infty_{n = 1} \bigg( \frac{5}{n} - \frac{5}{n + 1} \bigg)[/tex]Step 3: Find Sum
Find Sₙ terms: [tex]\displaystyle \sum^\infty_{n = 1} \bigg( \frac{5}{n} - \frac{5}{n + 1} \bigg) = (5 - \frac{5}{2}) + (\frac{5}{2} - \frac{5}{3}) + (\frac{5}{3} - \frac{5}{4}) + (\frac{5}{4} - 1) + ... + ( \frac{5}{n} - \frac{5}{n + 1}) + ...[/tex]Find general Sₙ formula: [tex]\displaystyle S_n = 5 - \frac{5}{n + 1}[/tex]Find Sum [Take limit]: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = \lim_{n \to \infty} S_n[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = 5 + 0[/tex]Simplify: [tex]\displaystyle \sum^\infty_{n = 1} \frac{5}{n^2 + n} = 5[/tex]∴ the sum converges by the Telescoping Series.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Convergence Tests (BC Only)
Book: College Calculus 10e
The line parallel to y = -3x + 4 that passes through (9,-6)
Answer:
y=−3x+21
Step-by-step explanation:
Find the slope of the original line and use the point-slope formula
A particular fruit's weights are normally distributed, with a mean of 344 grams and a standard deviation of 10 grams. If you pick 10 fruit at random, what is the probability that their mean weight will be between 334 grams and 354 grams
Answer:
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 344 grams and a standard deviation of 10 grams.
This means that [tex]\mu = 344, \sigma = 10[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{10}{\sqrt{10}}[/tex]
What is the probability that their mean weight will be between 334 grams and 354 grams?
This is the p-value of Z when X = 354 subtracted by the p-value of Z when X = 334.
X = 354
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{354 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = 3.16[/tex]
[tex]Z = 3.16[/tex] has a p-value of 0.9992.
X = 334
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{334 - 344}{\frac{10}{\sqrt{10}}}[/tex]
[tex]Z = -3.16[/tex]
[tex]Z = -3.16[/tex] has a p-value of 0.0008.
0.9992 - 0.0008 = 0.9984
0.9984 = 99.84% probability that their mean weight will be between 334 grams and 354 grams.
it takes engineer 3 hrs to drive to his brother's house at an average of 50 miles per hour. if he takes same route home, but his average speed of 60 miles per hour, what is the time, in hours, that it takes him to drive home?
Answer:
t2 = 2.5 hours.
Step-by-step explanation:
The distance is the same.
d = r * t
The rates and times are different so
t1 = 3 hours
t2 = X
r1 = 50 mph
r2 = 60 mph
r1 * t1 = r2*t2
50 * 3 = 60 * t2
150 = 60 * t2
150 / 60 = t2
t2 = 2.5
Answer:
Answer: Travel Time is 2 hours & 30 minutes
Step-by-step explanation:
Original Journey Time is 3 hours, Speed is 50 mph, Distance is 150 miles
Original Distance is 150 miles, New Speed is 60 mph.
Also Combined Distance was 300 miles, Combined Time was 5 hours & 30 minutes. therefore: Average Speed for complete round trip is 54. 54 mph
A cube has an edge of 2.25 feet. The edge is increasing at the rate of 1.25 feet per hour. Express the volume of the cube as a function of h, the number of hours elapsed.
Answer:
[tex]V(h)=(1.25h+2.25)^3[/tex]
Step-by-step explanation:
Recall that the volume of a cube is given by:
[tex]\displaystyle V = s^3[/tex]
Where s is the side length of the cube.
The edges of the cube has an original length of 2.25 feet. It increases by 1.25 feet per hour. In other words, the length s after h hours can be modeled by the equation:
[tex]s=1.25h+2.25[/tex]
Substitute. Hence, our function is:
[tex]V(h)=(1.25h+2.25)^3[/tex]
describe how you could use the point-slope formula to find the equation of a line that is perpendicular to a given line and passes through a given point
Answer:
Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.
D
6
5
F
5.5
к.
6.6
What additional information must be known to prove the triangles similar by SSS?
A) No additional information is needed.
B) 2D = LJ
C) The lengths of DG and JL
D) .F.LK
Answer:
C) the length of DG and JL
You start savings a $250 a month for the next 22 years to give us a gift to your daughter when she graduates college if you put the money into a long-term savings account that receives 3.5 interest how much money will you be able to give your daughter
Answer:
$376,475.71
Step-by-step explanation:
FVA Due = P * [(1 + r)n – 1] * (1 + r) / r
FVA Due = 250 * [(1.2916)264 – 1] * (1.2916) / .2916
What is the common denominator of (5/x^2-4) - (2/x+2) in the complex fraction (2/x-2) - (3/x^2-4)/(5/x^2-4) - (2/x+2)
9514 1404 393
Answer:
common denominator: (x² -4)simplified complex fraction: (2x +1)/(9 -2x)Step-by-step explanation:
It is helpful to remember the factoring of the difference of squares:
a² -b² = (a -b)(a +b)
__
Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.
It looks like you want to simplify ...
[tex]\dfrac{\left(\dfrac{2}{x-2}-\dfrac{3}{x^2-4}\right)}{\left(\dfrac{5}{x^2-4}-\dfrac{2}{x+2}\right)}=\dfrac{\left(\dfrac{2(x+2)}{(x-2)(x+2)}-\dfrac{3}{(x-2)(x+2)}\right)}{\left(\dfrac{5}{(x-2)(x+2)}-\dfrac{2(x-2)}{(x-2)(x+2)}\right)}\\\\=\dfrac{2(x+2)-3}{5-2(x-2)}=\boxed{\dfrac{2x+1}{9-2x}}[/tex]
Answer:
c
Step-by-step explanation:
(x+2)^2(x-2)
Are the two figures similar? if they are, solve for the missing side.
Answer:
They are not similar.
Step-by-step explanation:
26 / 13 = 2
24 / 11 = 2.18
They are not proportional which means that they don't have a scale factor and cannot be answered.
1. Prove the following identity:
—> sin^2 theta (1+ 1/tan^2 theta) =1
9514 1404 393
Explanation:
[tex]\sin^2(\theta)\times\left(1+\dfrac{1}{\tan^2(\theta)}\right)=\\\\\sin^2(\theta)\times\left(1+\dfrac{\cos^2(\theta)}{\sin^2(\theta)}\right)=\\\\\dfrac{\sin^2(\theta)\cdot(\cos^2(\theta)+\sin^2(\theta))}{\sin^2(\theta)}=\\\\\cos^2(\theta)+\sin^2(\theta)=1\qquad\text{Q.E.D.}[/tex]
The function ƒ(x) = x−−√3 is translated 3 units in the negative y-direction and 8 units in the negative x- direction. Select the correct equation for the resulting function.
Answer:
[tex]f(x)=\sqrt[3]{x}[/tex] [tex]3~units\: down[/tex]
[tex]f(x)=\sqrt[3]{x} -3[/tex] [tex]8 \: units \: left[/tex]
[tex]f(x+8)=\sqrt[3]{(x+8)} -3[/tex]
----------------------------
Hope it helps..
Have a great day!!
Answer:
its not B that what i put and i missed it
Step-by-step explanation:
$9500 is invested, part of it at 11% and part of it at 8%. For a certain year, the total yield is $937.00. How much was invested at each rate
Answer:
5900 at 11%
3600 at 8%
Step-by-step explanation:
x= invested at 11%
y= invested at 8%
x+y=9500
.11x+.08y=937
Mulitply the first equation by .11
.11x+.11y= 1045
Subtract this and the second equation
(.11x+.11y)-(.11x+.08y)=1045-937
.03y=108
y=3600
SOlve for x
x+3600=9500
x=5900
- Mariah is looking at her bank account and sees that she is in debt $40. She plans to buy dinner
for several friends on Friday at $5 per meal. On Monday she earns $30.25 babysitting and
$25.75 for tutoring several younger students. On Tuesday, she cleans the apartment for her
mom and earns $11 dollars. She spends $2 of those dollars on a candy bar. How many friends
can she buy dinner for on Friday?
Answer: 5 friends
Note: if Mariah pays for her own meal, then it would drop to 4 friends.
===========================================================
Explanation:
Add up the amount she earns:
30.25+25.75+11 = 67
Now add up the amounts that she's either in debt or that she spends money on. Ignore the dinner portion for now.
40+2 = 42
She earns $67 total and has to spend $42, without including the dinner portion just yet. That means Mariah has 67-42 = 25 dollars left over.
-------------------
Let x be the number of $5 meals she can buy
So she can spend a total of 5x dollars here. Set this equal to 25 (the amount left over) and solve for x.
5x = 25
x = 25/5
x = 5
She can buy dinner for 5 friends. Or if Mariah is paying for herself as well, then she can buy dinner for 4 friends. It's not clear which scenario your teacher is after, but I'll assume the first scenario.
Line segment TV is a midsegment of ∆QRS. What is the value of n in the triangle pictured?
A: 6.5
B: 7.6
C: 15.2
D: 3.2
Answer:
D. 3.2
Step-by-step explanation:
Mid-segment Theorem of a triangle states that the Mid-segment in a triangle is half of the third side of the triangle.
Based on this theorem, we have: TV = ½(RS)
TV = 3n - 2
RS = n + 12
Substitute
3n - 2 = ½(n + 12)
Multiply both sides by 2
2(3n - 2) = (n + 12)
6n - 4 = n + 12
Collect like terms
6n - n = 4 + 12
5n = 16
Divide both sides by 5
5n/5 = 16/5
n = 3.2
Plz answer quick!!! Apx Unit 7
What is the following product?
(V12+ V6 (16-V10
6-12-2130+6-2V15
-2 དུ་
6V3-615
31/7- V22+2/3-4
2V3+6-2V15
Answer:
The answer is A: 6√2 - 2√30 + 6 - 2√15
Believe me it right.
What two things have to be true in order to use the Zero Product Property?
A: Both sides of the equations must be zero.
B: One side of the equation must be a factored polynomial, and the other side must be -1.
C: One side of the equation must be a factored polynomial, and the other side must be 1.
D: One side of the equation must be a factored polynomial, and the other side must be zero.
Wrong answers will be reported. Thanks!
Answer:
D - One side is a factored polynomial and the other side is 0.
A - Incorrect; If each side is 0, the equation would be equal since 0 = 0.
B - Incorrect; It cannot be -1 because the property states Zero product which means 0 should be the product.
C - Incorrect; It cannot be 1 because the property states Zero product which means 0 should be the product.
D - Correct; One side is 0, and the other is a factored polynomial, which correctly displays the correct definition of Zero Product Property.
Which of the SMART criteria are NOT met by this data analytics project goal (pay close attention to whether the options are words the SMART acronym stands for)?
Answer:
Specific
Step-by-step explanation:
The data analytics is defined as the study of analyzing the raw data and information so as to make a proper conclusion about the information. It is a process of inspecting, transforming, and modelling the data with the intention of finding useful information and conclusions.
The acronym for S.M.A..R.T is Specific, Measurable, Attainable, Relevant and Time bounding.
The SMAR criteria which do not meet the data analytics project goal in the question is "Specific".
A jewelry box is in the shape of a rectangular prism with an area of 528 cubic inches. The length of the box is 12 inches and the height is 5 1/2 inches. What is the width of the jewelry box? A=LxWxH
please help. :)
how to construct angle 30°
Answer:
Angle ABC = 30°
Step-by-step explanation:
Construct a ray AB, horizontally.Take a compass, keep the pointy edge on the origin of the ray and make an arc passing through AB.Mark the point where the arc cuts AB as XPlace the pointy edge of the compass on X, draw another arc through the existing arc.Mark the point where on arc cuts the other arc as Y.Now from the origin of AB through the point Y draw a straight line.The angle thus formed is 60°.Now make arcs keeping the compass on X and Y.Mark the point where these two arcs meet as Z.Now from the origin of AB through the point Z draw a straight line.The angle formed in this process is a 30°.Question 24… please someone help thank you!
Answer:
72 in^2
Step-by-step explanation:
The area of the square in the middle is
A = s^2 = 6^2 = 36
The area of the triangle on the left is
A =1/2 bh = 1/2 ( 6*6) = 18
The area of the triangle on the right
A = 1/2 bh = 1/2(6*6) = 18
Add the areas together
36+18+18 = 72
Area of the middle square = 6 x 6 = 36
Area of a triangle is 1/2 x base x height:
Area = 1/2 x 6 x 6 = 18
Both triangles have a base of 6 and height of 6 so both triangles have the same area.
Total area = 36 + 18 + 18 = 72 square in.
The answer is D. 72
pls help me in this question it is really needed
Answer:
6 1/8 ×10 2/7= 60
60÷2 1/3= 30
The answer:
30
the fraction a/24reduced by a factor 4, and the result is 5/b. Find a and b
PLEASE HELP MY SISTER
Answer:
A= 20
B= 6
Step-by-step explanation:
A= 5 times 4= 20
B= 24/4= 6
