Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 44:
Because there are 5 terms in the sequence, with each term getting multiplied by 3 having the first term be 3, this equates to the sigma notation [tex]\[ \sum_{n=1}^{5} 3^{n}\][/tex].
Problem 45:
Because there are 5 terms in the sequence, with each term getting multiplied by 1/2 having the first term be 80, this equates to the sigma notation [tex]\[ \sum_{n=1}^{5} 80(\frac{1}{2})^{n-1}\][/tex].
9514 1404 393
Answer:
44. sum[n=1..5](3^n)
45. sum[n=0..3](80·2^-n)
Step-by-step explanation:
The summation symbol is used to collapse all of the plus signs. The argument of the summation symbol is the general term of the series. These are both geometric series, so the general term can be written in the form ...
an = a1·r^(n-1)
where a1 is the first term and r is the common ratio.
The "-1" can be removed from the exponent if the summation starts with n=0 instead of n=1. Sometimes the multiplication by a1 can be accomplished by adjusting the exponent of the exponential term.
__
49. The first term is 3 and the common ratio is 3, so the general term is ...
an = 3·3^(n-1) = 3^n . . . for n starting at 1
There are 5 terms in this series, so it can be written as ...
[tex]\displaystyle S=\sum_{n=1}^5{3^n}[/tex]
__
50. The first term is 80 and the common ratio is 1/2, or 2^-1. Then the general term is ...
an = 80·(2^-1)^(n-1) . . . for n starting at 1
If we let start at 0, then the general term is ...
an = 80·2^-n
There are 4 terms in the series, so it can be written as ...
[tex]\displaystyle S=\sum_{n=0}^3{(80\cdot2^{-n})}[/tex]
Related Questions
Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to solve for
O 3x+ 5x=4
O 3x+4= 5x
О 3x =4+5х
O 3x-4-5x
Answers
BE QUICK GIVING BRAINIEST
A cylinder with a diameter of 24 inches and a height of 8 inches has the same volume as a cone with a diameter of 12 inches.
What is the height of the cone?
A. 4 Inches
B. 16 inches
C. 48 inches
D. 96 Inches
Answers
Answer:
D. 96 inches.
Step-by-step explanation:
Radius of cylinder = 1/2 * 24 = 12 inches.
Radius of the cone = 1/2 * 12 = 6 inches.
Volume of the cylinder = pi r^2 h and volume of the cone = 1/3 pi r^2 h
So pi 12^2 * 8 = 1/3 pi * 6^2 * h
1152 pi = 12 pi h
h = 1152/12
h = 96 inches.
If the height is 24, solve for x. h=-16x^2+8x+48
Answers
Answer:
x=
32
7+
3121
,
32
7−
3121
Step-by-step explanation:
h+16^2-8x-48=0
-7x+16x^2-48=0
x=
32
7+
3121
,
32
7−
3121
Please help me this is for a test. Thank you so much whoever answers this.
Answers
Answer: Pretty sure the answer is 3.
Step-by-step explanation:
[tex]\frac{2(4+7)-7}{5}[/tex]
[tex]\frac{2(11)-7}{5}[/tex]
[tex]\frac{22-7}{5}[/tex]
[tex]\frac{15}{5}[/tex]
A company is making aid badges with personal ID codes on them for each employee. The ID code will consist of two letters followed by 2 digits. Using this scenario, how many possible ID codes are there?
Answers
Answer:
67, 600
Step-by-step explanation:
There are 26 alphabet and 10 digits then the number of the possible ID codes will be 67600.
What are permutation and combination?A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
A company is making aid badges with personal ID codes on them for each employee.
The ID code will consist of two letters followed by 2 digits.
Then the number of ways ID codes are there will be
[tex]\rightarrow 26 \times 26\times 10\times 10\\\\\rightarrow 67600[/tex]
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
reduce to hours and minutes 66000 seconds
Answers
Answer:
18.333333 hours
Step-by-step explanation:
1099.99998 mintunes
Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time it takes her to complete one review.Assume Χ is normally distributed.Let be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.
A. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs. Sketch the graph, labeling
and scaling the horizontal axis. Shade the region corresponding to the probability.
b. P(________________) = _______
C. Find the 95th percentile for the mean time to complete one month's reviews. Sketch the graph.
D. The 95th Percentile =____________
Answers
Answer: i think it would be 20
Step-by-step explanation:
if you do the problem it should show you
Help help help I need help ASAP
Answers
Answer: 54.4
Step-by-step explanation:
Help please i will upload a picture
Answers
HELP ME PLEASE LAWS OF SINES !! IXL !!
Answers
Answer:
f = 19.0
Step-by-step explanation:
By applying sine rule in the triangle given in the figure,
By applying triangle sum theorem,
m∠F + m∠G + m∠H = 180°
110° + m∠G + 40° = 180°
m∠G + 150° = 180°
m∠G = 30°
[tex]\frac{sin(\angle F)}{GH}= \frac{sin(\angle G)}{HF}=\frac{sin(\angle H)}{FG}[/tex]
[tex]\frac{sin(\angle 110^0)}{f}= \frac{sin(\angle 30^0)}{g}=\frac{sin(\angle 40^0)}{13}[/tex]
[tex]\frac{sin(\angle 110^0)}{f}= \frac{sin(\angle 40^0)}{13}[/tex]
[tex]\frac{0.9397}{f}= \frac{0.6428}{13}[/tex]
f = [tex]\frac{13\times 0.9397}{0.6428}[/tex]
f = 19.0
Simplify the following radical expression square root of 20
Answers
Answer:
2 radical 5
Step-by-step explanation:
i am smart
Answer:
[tex]\sqrt{20} =2\sqrt{5}[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt{20}[/tex]
Step 1: Factor out the biggest square number:
[tex]\sqrt{4}\sqrt{5}[/tex]
Step 2: Simplify:
[tex]2\sqrt{5}[/tex]
Therefore, [tex]\sqrt{20} =2\sqrt{5}[/tex]
Please answer, what is x?
Answers
Answer:
ths is the real answer 您同性恋您同性恋您同性恋您同性恋您同性恋
您同性恋您同性恋
Step-by-step explanation:
Choose all the numbers that make 5 × □ < 5 true.
A- 1 1/4 B-3/8 C-10/11 D-4 4/5 E- 4/3 F- 1/4
Answers
Answer:
B, C, F
Step-by-step explanation:
It's asking 5 x (what?) is less than 5.
It has to be less than one to be a correct answer then.
Rationalize the denominator and simplify
Answers
5 points
A circle has a radius of 3 inches. What is the length, in inches, of an arc intercepted by a central angle of 2 radians?
Answers
Answer:
7.5in
Step-by-step explanation:
Helppppp plsssss I will do anything I need to pass this text
Answers
Answer:
(1,1) is the answer
Explanation:
Both lines cross at (1,1)
PLEASE HELP MEEEEEEEEE
Answers
9514 1404 393
Answer:
A, B
Step-by-step explanation:
The equation is equivalent to ...
cos(x -π/7) = -(√2)/2
x -π/7 = arccos(-(√2)/2) = {3π/4, 5π/4} . . . . . cosine is negative in QII and QIII
x = {3π/4 +π/7, 5π/4 +π/7} +2nπ . . . . . matches A and B
A guy wire connects the top of an antenna to a point on level ground at 15ft from the base of the antenna. The angle of elevation formed by this wire is 79. What is the length of the wire and the height of the antenna?
Answers
Answer:
VEFG4KLKB
Step-by-step explanation:
BLB
The length of the guy wire is approximately 74.7 feet, and the height of the antenna is approximately 72.2 feet.
Here, we have,
To find the length of the guy wire and the height of the antenna, we can use trigonometry and the concept of right triangles.
In this scenario, the guy wire represents the hypotenuse of a right triangle, and the height of the antenna represents one of the legs of the triangle.
The angle of elevation formed by the guy wire is given as 79 degrees.
Let's denote the length of the guy wire as h and the height of the antenna as a.
Using the trigonometric function sine (sin), we can relate the angle of elevation and the sides of the triangle:
sin(angle) = opposite/hypotenuse.
In this case, the opposite side is the height of the antenna (a), and the hypotenuse is the length of the guy wire (h).
sin(79°) = a/h.
To solve for h, we can rearrange the equation as:
h = a / sin(79°).
We also have another relationship between the sides of the triangle.
The base of the right triangle is given as 15 feet, and the height of the antenna is a.
Therefore, using the Pythagorean theorem, we have:
h² = a² + 15².
Now we can substitute the expression for h from the first equation into the second equation:
(a / sin(79°))² = a² + 15².
Expanding and simplifying, we get:
a² / sin²(79°) = a² + 225.
Multiplying both sides of the equation by sin²(79°), we have:
a² = sin²(79°) * (a² + 225).
Expanding again, we get:
a² = sin²(79°) * a² + 225 * sin²(79°).
Rearranging the equation, we have:
a² - sin²(79°) * a² = 225 * sin²(79°).
Factoring out a², we get:
(1 - sin²(79°)) * a² = 225 * sin²(79°).
Using the trigonometric identity sin²(θ) + cos²(θ) = 1,
we know that cos²(θ) = 1 - sin²(θ).
Therefore:
cos²(79°) * a² = 225 * sin²(79°).
Taking the square root of both sides, we have:
cos(79°) * a = 15 * sin(79°).
Simplifying, we get:
a = (15 * sin(79°)) / cos(79°).
Using a calculator or software, we find:
a ≈ 72.2 feet (rounded to one decimal place).
Now, to find the length of the guy wire (h), we can substitute the value of a into the first equation:
h = a / sin(79°).
Using a calculator or software, we find:
h ≈ 74.7 feet (rounded to one decimal place).
Therefore, the length of the guy wire is approximately 74.7 feet, and the height of the antenna is approximately 72.2 feet.
To learn more trigonometry click:
brainly.com/question/26719838
#SPJ4
Jill is swimming laps in a pool. The table shows how the total distance she swims depends on the number of laps she does.
Number of Laps - Total Distance (Meters)
5 250
10 500
15 ?
20 1,000
25 1,250
A. 50
B. 75
C. 550
D. 750
Answers
Explanation; because 500 + 250 = 750
Answer:
the expression b/c=b/c is an example of a/an
PLEASE HELP, I WILL GOVE BRAINLIEST. Katrina's cat weighed 12 3/4 pounds at its last visit to the veterinarianSince that visit, the cat has gained 5/8 pound. How much does Katrina's cat weigh now? Show your work
Answers
Answer
13 1/2 pounds
Step-by-step explanation:
welcome ;)
Answer:
the cat now weighs 13 3/8 LBS
Step-by-step explanation:
convert the fractions so you can add them together,
mult 3/4 by two to get common denominators
6/8 + 5/8
the cat gained 11/8 pounds. (1 3/8)
since the numerator is larger we add the mixed number to the 12 pounds.
13 3/8 pounds.
Kathy is building a bed for her dollhouse. She used her real bed as a guide for how to create the dollhouse bed. Her bed is 36 inches wide and 60 inches long. If she wants to scale this down by 1/10, what would be the dimensions of the dollhouse bed? Explain how you got your answer.
*Use the term SCALE FACTOR in your explanation.
Answers
The dimensions of the dollhouse bed are 3.6 inches × 6 inches. By dividing 10 by each dimension, the dollhouse bed's dimensions may be found.
What exactly is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The dimension of real bad;
a = 36 inches
L = 60 inches
Down scale factor = 1/10
The dimensions of the dollhouse bed are obtained by dividing 10 in each dimension;
a'=36/10
a'=3.6 inches
L'=60/10
L'=6 inches
Hence the dimensions of the dollhouse bed are 3.6 inches × 6 inches.
To learn more about dilation, refer to
https://brainly.com/question/13176891
#SPJ1
-7 2/3 + (-5 1/2) + 8 3/4
in faction
Answers
Answer:
= -4.41666666667
Step-by-step explanation:
Answer:
[tex]-7\frac{2}{3} + -5\frac{1}{2} +8\frac{3}{4}\\\\\frac{-23}{3} -\frac{11}{2} + \frac{35}{4}\\\\[/tex]
LCM (3, 2 ,4) = 12
[tex]\frac{(-23*4) -(11*6)+(35*3)}{12} = \frac{-92-66+105}{12} =\frac{-53}{12} = -4\frac{5}{12}[/tex]
Which value for x makes the sentence true?
Answers
One clue to this (if you don’t just multiply 0.22 by 2.95) Is that this is the only value above 1. since the ending equation has a number larger than the original, this is a give away! Hope this helps :)
A company sells cereal in two different-sized boxes: a 17-ounce box for $2.89, and a 24-ounce box for $3.29. How do the unit prices of the two boxes compare?
Answers
pls help (links will get reported)
Answers
Answer:
-938 ft
Step-by-step explanation:
the bird will be going down in elevation. the distance between -422 and -1360
-1360+422= -938
Choose a method you prefer to solve for a system of linear equations.
x+y=0
x-y= -16
Answers
Answer:
Eliminating
Step-by-step explanation:
The given equations are ,
x+y=0x-y= -16Here I would prefer to use Elimination Method. Since there is negative y and positive y in the equations . So we can eliminate y easily and then we can find x. Also , let's solve ,
On addition :-
→ 2x = -16
→ x = -16/2
→ x = -8
Hence the most preferred method is " Elimination Method ".Question- A bakery sells 5 apple muffin for every 2 brand muffins sold. Which table shows this ratio?
No links or you get reported
is my answer correct?
Answers
Answer:
The one on the bottom left corner. I'm not sure what letter that is!
Hope this helped :)
Step-by-step explanation:
PLEASE HELP 20 POINTS
Answers
Answer:
43 3/4 cups of cheese
8 3/4 cups of olives
26 1/4 cups of sausage
Step-by-step explanation:
Answer:
43 3/4 cup of cheese
26 3/4 cups of olives
8 1/3 cups of sausageThe new candy store packed 3 ponds of bubblegum in each of their bags. How many bags would Sam need to bu if he wanted 288 ounces of bubblegum?
Answers
Answer:
NYS Math Module 3 Grade 4 Lesson 32 Concept Development
Problem 1
We all know there are 7 days in a week. How many weeks are in 259 days?
Problem 2
Everyone is given the same number of colored pencils in art class. If there are 249 colored pencils and 8 students, how many pencils does each student receive?
Problem 3
Mr. Hughes has 155 meters of volleyball netting. How many nets can he make if each court requires 9 meters of netting?
Step-by-step explanation:
Answer:
6 bags
Step-by-step explanation:
228 ounces = 18 pounds
18 pounds ÷ 3 pounds
6 bags
-------------------------------------------------------------------------------------------------------------
We all know there are 7 days in a week. How many weeks are in 259 days?
37 weeks
[tex]\frac{1}{7} :\frac{y}{259}[/tex]
y · 7 = 1 · 259
7y = 259
7y ÷ 7 = 259 ÷ 7
y = 37
Everyone is given the same number of colored pencils in art class. If there are 249 colored pencils and 8 students, how many pencils does each student receive?
31 color pencils each and 1 extra pencil
249 ÷ 8 =
31.125 colored pencils each
This rounds to 31 color pencils and 1 extra pencil.
Mr. Hughes has 155 meters of volleyball netting. How many nets can he make if each court requires 9 meters of netting?
7 courts and he will be left with 2 meters of netting
155 ÷ 9
17 and 2/9 volleyball courts
17 courts and he is left with 2 meters of netting.
A study of women’s weights found that a randomly selected sample of 234 women had a mean weight of 157.3 lb. Assuming that the population standard deviation is 15.6 lb., construct a 95% confidence interval estimate of the mean weight of all women.
Answers
Answer:
(155.301 ; 159.299)
Step-by-step explanation:
Xbar = 157.3
Sample size, n = 234
Population standard deviation, σ = 15.6
The confidence interval :
Xbar ± standard Error
Standard Error = Zcritical * σ/√n
Zcritical at 95% = 1.96
Standard Error = 1.96 * (15.6/√234) = 1.999
Lower boundary : 157.3 - 1.999 = 155.301
Upper boundary : 157.3 + 1.999 = 159.299
(155.301 ; 159.299)