Answer:
The opposites of these numbers are -7, 4.5, -3.35, and -712
Step-by-step explanation:
How do you do this question?
Exact value: [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]
Approximate value: c = 0.08387
Round the approximate value however you need to
==============================================
Work Shown:
Let x = 1+c
[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]
We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.
Each new term is found by multiplying the previous term by 1/x.
Assuming -1 < r < 1 is true, the infinite geometric sum is
[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]
Plug in S = 11 and solve for x
[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]
Use the quadratic formula to find the two solutions
[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]
Using these x values, we find that the corresponding r values are
r = 1/x = 1/(1.08387) = 0.92262
r = 1/x = 1/(-0.08387) = -11.92321
The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387
----------------------------------------------
Using the solution that corresponds to x = 1.08387, we find the value of c is
[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]
John's sister is twice his age. In 5 years the sum of their ages will be 31. How old are John and his sister now? Briefly explain how you arrived at your answer.
Like usual, we can solve this question using an equation. Let’s assume that John’s age is x, and his sister’s age is y.
x = 2y
To figure out John’s age, we need to know his sister’s age. He’s 2 times older than his sister.
x + y = 27
The sum of their ages is 27, and we can substitute the value of x here to figure out y.
2y + y = 27
We can now simplify this, and get y by itself.
3y = 27
Now, we can divide by 3 to get the y by itself.
y = 9
We now know that John’s sister is 9.
Now, using our original equation, we can substitute in the value of y.
x = 2(9)
We can simplify this.
x = 18
John’s age is 18!
Hope this helps.
Solve for x in the equation x squared minus 10 x + 25 = 35
Answer:
x=1
Step-by-step explanation:
10x+25=35
10x+25=35
-25 -25
10x=10
10 divided by 10 is 1
Give brainliest answer
Answer:
6
Step-by-step explanation:
if a triangle is reflected, its area stays the same. the height is 3, and the base is 4. the formula for the area of a triangle is 1/2 (b)(h), so that is 1/2 (3)(4) which equals 6 square units.
t Park Junior High, 10%, or 160, of the students, play a musical instrument. How many students attend the school?
A tape diagram. StartFraction part Over whole EndFraction = StartFraction 10 Over 100 EndFraction = StartFraction 160 Over question mark EndFraction
Which statements are correct? Check all that apply.
The total number of students is 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
The percent as a part-to-whole ratio is StartFraction 160 Over 100 EndFraction
There are 1,600 students in the school.
There are 250 students in the school.
Answer:
The total number of students is > 160.
The percent as a part-to-whole ratio is StartFraction 10 Over 100 EndFraction.
There are 1,600 students in the school.
Step-by-step explanation:
got is correct
Answer:
2,3,5 for eg. 2020
Step-by-step explanation:
(3.1 · 10² ) (2 · 10³) Write in Scientific Notation.
Answer:6.03*10^3
Step-by-step explanation:
(3.1 *10^2)(2*10^3)
2*10^3=20*10^2
(3.1*10^2)(20*10^2)
(60.3*10^2)=
6.03*10^3
(Graph attached)
Please show work
What is the average speed of the runner at 4 seconds
A bakery sells, on average, 100 special breads per day and collects with these sales, on average, R $ 300.00. It was found that the quantity of special breads sold daily increases if the price is reduced, according to the equation q = 400 - 100p, in which q represents the quantity of special breads sold daily and p, its price in reais. In order to increase the flow of customers, the bakery manager decided to run a promotion. To do so, it will modify the price of special bread so that the quantity to be sold daily is as large as possible, without decreasing the average daily collection on the sale of this product. The price p, in reais, of the special bread in this promotion should be in the range
a) R $ 0.50 p
b) R $ 1.50 p
c) R $ 2.50 p
d) R $ 3.50 p
e) R $ 4.50 p
If the price is p and the quantity of bread sold is q = 400 - 100p, the average collection, in reais, depending on the price p, is given by R (p) = (400 - 100p). P
For this collection to be R $ 300.00, you must have:
(400 - 100p). p = 300 ⇔ 4p - p² = 3 ⇔ p² - 4p + 3 = 0 ⇔ p = 1 or p = 3
R $ 300.00
The current price is R $ 3.00, as R $ 300,000 / 100 = R $ 3
To maintain the collection, the price must be lowered to R $ 1.00 (R $ 0.50 <R $ 1.00 <R $ 1.50)
ANSWER: letter A
The houses on a city block were thought to be valued at $175,000, $163,000,
$142,000, $135,000, $191,000, $122,000, and $147,000, respectively. But a
public assessor has determined that the value of each house is actually
$20,000 higher than previously thought. According to the public assessor,
what is the median value of the houses?
O A. $162,000
O B. $167,000
O c. $155,000
O D. $147,000
SUBMIT
Answer:
$167,000
Step-by-step explanation:
THAT'S THE ANSWER.COM
The median value of the houses is $167,000.
MedianWhat is median value?The middle number in a collection of numbers is known as the median.
How median is calculated?Check to see if 'n' is an even number of values.Find the two numbers that are in the centre of the table of data. Adding the two middle numbers together and dividing the result by two will yield the average of the two numbers.The median is the outcome of this average.Calculation for the median of the houses:The initial value of the 7 houses were,
$175,000, $163,000, $142,000, $135,000, $191,000, $122,000, and $147,000.
As, the value of each house were increased by $20,000.
The value of houses after increment,
$195,000, $183,000, $162,000, $155,000, $211,000, $142,000, and $167,000.
Arrange the values in the increasing order.
$142,000, $155,000, $162,000$, 167,000, $183,000, $195,000, $211,000.
Since, the given data has 7 values which is a odd number. So, values come in the middle is $167,000.
Therefore, the median value of the houses is $167,000.
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In an experiment, college students were given four quarters
Answer:
What is the question?
Step-by-step explanation:
I don't see a question.
A well is 20ft deep. A snail at the bottom of the well climbs upto 4ft each day and slips back 2ft every night.how many days the snail to reach the too
Answer:
10 days
Step-by-step explanation:
4ft-2ft= so the snail moves 2ft every 24hrs
20ft÷2ft= takes the snail 10 days
Answer:
Defining Variables:
Let the number of days the snail takes to climb = x days
Total distance climbed in x days = x*4
Total distance slipped in x days = 2*x
Solving for the number of days:
Since the total distance the snail climbs is 20ft (depth of well)
The total distance climbed - total distance slipped = 20
replacing the variables
4x - 2x = 20
2x = 20
x = 10
Therefore, it will take the snail 10 days to reach the top
A couch and coffee table cost a total of $1156. The cost of the couch is three times the cost of the coffee table find the cost of each item.
Answer:
The couch is 867 and the coffee table is 289
Step-by-step explanation:
The question states that the couch is 3 times the cost of the coffee table. This means this includes the cost of the couch and the coffee table. So I would do 1156= x+3x, which equals 1156=4x. X is the cost of the coffee table. 3x is the cost of the couch. I'd divide 1156 by 4 and get 289. Now you take 289 and plug it in the equation, 1156=x+3x. X would equal to 289, and 3x would equal to 867.
Think about the proportion and the cross products for this problem:
Shelley sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20.
Answer:
The ratios are equivalent
The ratios are a proportion
prin ce insusiri se remarca sfantul si dreptul simeon
Answer:
Nu știu scuze
Step-by-step explanation:
5.) You are working for a car dealership. You are doing an inventory of the lot. You counted 34
trucks. 15 cars, and 8 SUVs. What is the ratio of SUVs to total vehicles on the lot?
Answer: 8 SUVs to 57 total
Step-by-step explanation: You add 34 + 15 + 8 which gives you 57 Then you see there are 8 SUVs. So the answer is 8 to 57.
Sorry. I kinda got ahead of myself and excited. Guess mistakes happen. I was right the first time. I'm just so tired right now
If the odds for a certain event are 5 to 12, what is the probability of the event occuring? Write your answer
as a simplified fraction.
Answer:
5/12
Step-by-step explanation:
Isn't this just a ratio?
Mrs. Balcon owes the dentist $342. She wants to have her payments taken from her checking account over the next 7 1/2 months. By what amount will her account change each month for the first 7 months?
Answer:
$45.60 per month
Step-by-step explanation:
She owes the dentist $342.00
you take $342.00 divided by 7.5(the amount of months)
and get $45.60 per month
Given the linear function 2x - y= 5 what is the slope? And As x increase does y increase or decrease and as x decreases does y increase or decrease
Answer:
The slope is 2. As x increase y is increase and as x decrease y decrease
The two triangles shown are similar. Find the value of a/b
Answer:
[tex] \frac{a}{b} = 1.5 [/tex]
Step-by-step explanation:
Given that both ∆s are similar, therefore the ratio of their corresponding sides will be the same.
This means: [tex] \frac{2.1}{a} = \frac{1.4}{b} [/tex].
Since this equation is true, rewrite so that you have [tex] \frac{a}{b} [/tex]
[tex] \frac{2.1}{a} = \frac{1.4}{b} [/tex]
Cross multiply
[tex] a*1.4 = b*2.1 [/tex]
Divide both sides by 1.4
[tex] a = \frac{b*2.1}{1.4} [/tex]
Divide both sides by b
[tex] \frac{a}{b} = \frac{2.1}{1.4} [/tex]
[tex] \frac{a}{b} = 1.5 [/tex]
The value of [tex]\dfrac{a}{b}[/tex] is [tex]1.5[/tex].
Given:
Two triangles in the given figure are similar.
To find:
The value of [tex]\dfrac{a}{b}[/tex].
Explanation:
The corresponding sides of two similar triangles are proportional.
[tex]\dfrac{a}{2.1}=\dfrac{b}{1.4}[/tex]
It can be rewritten as:
[tex]\dfrac{a}{b}=\dfrac{2.1}{1.4}[/tex]
[tex]\dfrac{a}{b}=1.5[/tex]
Therefore, the value of [tex]\dfrac{a}{b}[/tex] is [tex]1.5[/tex].
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The area of a square sports arena is 10,000 m² what are the dimensions of the sports arena on the map.
Answer:
Step-by-step explanation:10,000square you have to multiply them my all squares to get the answer
Simplify the expressions by distributing and combining like terms 5/8x-2(7-1/4x)
find the value of x.
(6x+8)
(7x-7)
Answer:
ITS 95
Step-by-step explanation:
TRY CALCULATING IT
sorry i don't know
sbhwgwvhwhev
Please help what is -0.5 divided by -1/5
A hotel manager is buying wallpaper for the rooms in his
hotel. Each roll of wallpaper costs $48. If he spent $5,568,
how many rolls of wallpaper did the hotel manager buy?
1,017
106
1,016
116
11. Mark builds 3 Lego towers. Each tower is made of 5 square layers
which have a width and length of 5 Lego pieces. Suddenly, Mark's little
brother breaks one and runs off with 45 pieces. Use the expression to show
how many pieces Mark is left with.
Answer:
Step-by-step explanation:
in the real world humans hear sound as an analog signal. this means the signal is a continuous waveform which is completely processable by human ears. however machines 'hear' sound a little differently as they process sound digitally which is a discrete waveform. when sound is recorded or transmitted electronically the continuous (analog) waveform is sampled to convert it to a discrete (digital) sequence. sampling is the process of reducing a continuous time signal to a discrete-time signal. as the sampling rate increases the sound quality of the recording or transmission will improve. the graphs below represent two different samples of pure tone. sample one is taken 8 times per unit of time. sample two is taken 16 times per unit of time. a) why would sample 2 reproduce a better replication of the pure signal? b) write a sinusoid model for sample 2
Answer:
y=7.75cos(pi/8(x)) + 7.75
Step-by-step explanation:
A= 15.5 - 0 = 15.5/2 = 7.75 (Max Y - Min Y)
P = 16-0 (Distance between Max x and next Max x)
F= Pi/8
Midline= 7.75
Vertical Shift = Midline = 7.75
Answer for A since the other person answered only B
Sample 2 would reproduce a better replication of the pure signal because it records more frequently, meaning that it would be closer to being a continuous waveform when compared to sample 1.
If he drank 80% of his water on his entire hike, how much did he drink?
Not enough information is given to answer this question. If there was 100% water at the beginning of the hike and now there is 80% it would be 20% but without the information, you cant know.
use a number line to solve the sum
2+5
Answer:
"7" Would be your answer.
Step-by-step explanation:
If three times a number is at least four or more than eight times the number, which of the following is true? A-The number is at least negative four-fifths.
B- the number is at most four-fifths.
C-The number is at least four-fifths.
D-The number is at most negative four-fifths .
Answer:
I believe A...
Step-by-step explanation:
Sorry if i'm wrong):
Option (A) The number is at least negative four-fifths. is correct because x is at least -4/5.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
If three times a number is at least four or more than eight times the number,
Let x be the number
Mathematically, it can be written as:
3x is at least 4 + 8x
3x - 8x is at least 4
- 5x is at least 4
x is at least -4/5
Thus, option (A) The number is at least negative four-fifths. is correct because x is at least -4/5.
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have a random argument with yourselves
Answer:
ok
Step-by-step explanation: