What is the sum of the numbers in the series? 15 + 11 + 7 + . . . + (–129)

A. -2,124
B. -2,109
C. -2,052
D. -1,995

Answers

Answer 1
Using Gauss's method
Total number of terms = [15-(-129)]/4+1=36+1=37
Add
S=15+11+7+....-125-129
S=-129-125-...+7+11+15
--------------------------------
2S=-114-114-114...(37 times)
=>
sum=S=(1/2)*(-114)*37=-2109


Using AP, T(n)=15+11+7+....-129
T(n)=19-4n  => T(1)=15, T(37)=-129
S(n)=(1/2)(37)(T(1)+T(37)=(1/2)37(15-129)=2109

Related Questions

a radio commercial for a loan company states: "you only pay for each $500 borrowed." If you borrow $1959 for 251 days, what amount will you repay, and what annual interest rate is the company actually charging? ( assume a 360- day year.)

Answers

well... hmmm so.. for 500 bucks you only pay a rate of say "r", and it comes down to only 28cents, or $0.28.

If 500 is say the 100%, what percentage is 0.28?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 500&100\\ 0.28&p \end{array}\implies \cfrac{500}{0.28}=\cfrac{100}{p}\implies p=\cfrac{0.28\cdot 100}{500} \\\\\\ p=0.056\%\implies p=\cfrac{56}{1000}\%[/tex]

now, we're assuming the company is charging and APR, so you pay that at the end of the year.  We're also assuming the year is only 360 days.

so, if you borrow 1959 on simple interest for 251 days out of 360 days, how much are you repaying?

[tex]\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$1959\\ r=rate\to 0.056\%\to \frac{0.056}{100}\to &0.00056\\ t=years\to &\frac{251}{360} \end{cases} \\\\\\ A=1959\left(1+0.00056\cdot \frac{251}{360} \right)[/tex]

and surely you can do that one... which is just 1959 and a few pennies.

Five sandwich rings are each cut into four pieces you then cut each of the pieces into three servings how many servings do you have

Answers

You would have 48 servings

an appliance store sold 360 microwave ovens last year. Of that amount, 3/8 were apartment-sized models. The number of apartment-sized models sold for the year was what?

Answers

3/8 of 360...." of " means multiply

3/8(360) = 1080/8 = 135....so 135 were apartment-sized

multiply:

360 * 3/8 = 360*3 =1080

1080/8 = 135 were apartment sized

Is a measure of dispersion that indicates how much scores in a sample vary around the mean of the sample?

Answers

The measure of dispersion that indicates how much scores in a sample vary around the mean of the sample is the standard deviation.
The measure is called STANDARD DEVIATION.
Standard deviation is a mathematical measure that is used to evaluate the difference between the mean value of a set of number and each value in the group. It is calculated as the square root of variance by determining the variation between each data point relative to the mean.

Find examples of decimals in a news paper or magazine,on television,or on the internet.write a real word problem in which multiplies decimals

Answers

Sally buys 5 shirts which each cost $8.50 cents. How much did she pay in total?
Final answer:

Decimals can be found in various sources including the internet, and they are used in everyday activities like shopping online. The word problem involves a book sale where a discount is given in decimal form.

Explanation:

Decimals are usually found in various sources such as newspapers, magazines, television, and predominantly on the internet. For example, when we read about the latest international currency exchange rates or the percentage rates in the stock market, we encounter decimals.

Let's create a real-world problem involving decimals: Sam is browsing a popular online bookstore. He found a book he wanted to buy for $5.49. However, there is a pop-up stating that for today only, all books are discounted by 0.15 (or 15%). How much would the book cost after the discount?

To find the solution, subtract the discount from the original price in decimal form i.e., $5.49 * 0.15 = $0.82 (approx). Then subtract this amount from the original price, $5.49 - $0.82 = $4.67. So, Sam will pay $4.67 for the book after discount.

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Write an equation in​ slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.

​(−5​,−7​); y=−2x+1

Write an equation for the line in​ slope-intercept form.

Answers

Parallel lines have the same slope. Hence, using the base equation of y=mx+b, plug in the given value for y and the given value for x into the equation y=-2x+b to solve for b:
-7=-2(-5)+b
-7=10+b 
b=-17
Hence the equation would be y=-2x-17

Answer:

y=-2x-19

Step-by-step explanation:

this is the right answer , i tried the other answer for this and it said it was wrong so

What is the standard form of 14 ten thousands + 12 thousands

Answers

140000 + 12000 = 152000

hope this helps

The sum of three consecutive numbers is 72. What is the largest of these numbers?

Answers

3 consecutive numbers....x, x + 1 and x + 2

x + x + 1 + x + 2 = 72
3x + 3 = 72
3x = 72 - 3
3x = 69
x = 69/3
x = 23

x + 1 = 23 + 1 = 24
x + 2 = 23 + 2 = 25

so ur numbers are 23,24,25 with 25 being the largest

25  Is the largest number too add up to the sum.

Assuming that this is a complete, if scrambled, record of Ronald’s May spending and that any overdraft fees incurred do not affect the running total, how many times did Ronald overdraw his account in May

Answers

The answer is C, Ronald overdrew his account twice

how many times larger is the value of the 8 in 80,351 than the value of the 8 in 95,852

Answers

I believe it is 100 times larger as it is in the hundreds place for one, and the ten thousands place for the other
10000/100= 100
The 8 in 80,351 is 100 times larger than the value of the 8 in 95,852 because the 8 in 95,852 is in the hundreds place and the 8 in 80,351 is in the ten thousands place. 800x100 is 80,000.

Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule.

Answers

[tex]\bf f(x)=(x^2)^3(x^2+2)^6\impliedby \textit{product rule on the factors} \\\\\\ \cfrac{df}{dx}=[ 3(x^2+1)^2(2x)][(x^2+2)^6]~+~(x^2+1)^3[6(x^2+2)^5(2x)] \\\\\\ \cfrac{df}{dx}=[6x(x^2+1)^2(x^2+2)^6]~+~[12x(x^2+1)^3(x^2+2)^5] \\\\\\ \cfrac{df}{dx}=\stackrel{\textit{common factor}}{6x(x^2+1)^2(x^2+2)^5}[(x^2+2)+2(x^2+1)] \\\\\\ \cfrac{df}{dx}=6x(x^2+1)^2(x^2+2)^5[3x^2+4][/tex]

1.4t-0.4(t-3.1)=5.8

What is T?

Answers

1.4t-.4t+1.24=5.80

t+1.24=5.80

t=4.56

Write the number 63 in four different ways

Answers

 63 in four different ways
1) 63 ones
2) 6 tens and 3 ones
3) 3 tens and 33 ones
4) 4 tens and 23 ones

Solution:

we have been asked to write the number 63 in four different ways. It can be done as follows

[tex]63=60+3[/tex]

Here we are just adding 3 to 60 and finally we get 63.

[tex]63=6\times10+3[/tex]

This one of the many way of writing 63.

[tex]63=70-7[/tex]

Here we have used the concept of subtraction to write 63.

[tex]63=7\times10-7[/tex]

Concept of subtraction and multiplication to write the number 63.

Hence  the four ways have been written.


Estimate sin pi/3 if sin pi/2 = 1 and sin 0 = 0 and sin pi = 0

Answers

hello :  
sin(π/3) = √3 / 2 
Final answer:

To estimate the value of sin pi/3, which is roughly 1.047 or 60 degrees, we can use standard trigonometric values. Since pi/3 is closer to pi/2 than pi, where sin achieves its maximum of 1, the value of sin pi/3 should be closer to 1 than 0. Standard trigonometric values confirm that sin pi/3 = sqrt(3)/2 = 0.866.

Explanation:

To estimate sin pi/3, we can make use of some standard values in trigonometry. Pi is roughly 3.14, hence pi/3 is roughly 1.047. The sin function gives a result of 1 at pi/2 (or 90 degrees), 0 at 0, and again 0 at pi (or 180 degrees). Thus, it achieves its maximum at pi/2 and then decreases to 0 at pi. Intuitively, since pi/3 (or 60 degrees) is closer to pi/2 than to pi, the sin value at pi/3 should be closer to 1 than to 0. From the standard trigonometric values, we know that sin pi/3 = sqrt(3)/2 which is roughly 0.866.

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Joe is playing a game with a regular die.  If the number that turns up is   even, he will gain 5 times the number that comes up.  If it is odd, he will  lose 10 times the number that comes up.  He tosses a 3. Express the   results as an integer.

Answers

3 is odd
So by the question he will lose 10 times the number that comes up
3*10=-30

Q=3X+9XZ solve for X

Answers

The required solution is X=Q/3+9Z.

It is required to find the solution is X.

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The given expression is

Q=3X+9XZ

We move all terms to the left side and equate to find the value of x we have.

Q=X(3+9Z)

By taking common to x and divide and move each term to left side, we have

X=Q/3+9Z

Therefore, the required solution is X=Q/3+9Z.

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True or false: the standard deviation is the square root of the variance.

Answers

Why not look up "standard deviation" yourself, to be sure?  But yes, the std. dev. is the sqrt of the variance.

Answer:

True. The standard deviation is indeed the square root of the variance.

Explanation:

The standard deviation measures the dispersion or spread of data points around the mean in a dataset. It quantifies the average distance of data points from the mean. Mathematically, it's the square root of the variance, which is the average of the squared differences between each data point and the mean. By taking the square root, we return to the original scale of the data, making the standard deviation more interpretable. A higher standard deviation indicates greater variability, while a lower standard deviation suggests that the data points are closer to the mean, signifying less variability within the dataset.

A restaurant uses 44 pounds of potatoes for a party of 1212 people. If they are cooking potatoes for a party of 60 people, what should they do?

Answers

use 5 times more potatoes

what interest rate is needed for $9,500 to earn $900 in 19 months?

Answers

Answer:

The interest rate is 5.98%.  

Step-by-step explanation:

To find : What interest rate is needed for $9,500 to earn $900 in 19 months?

Solution :

The formula of interest is given by,

[tex]I=P\times R\times T[/tex]

Where,

I is the interest amount I=$900

P is the principle P=$9500

T is the time T=19 months= [tex]\frac{19}{12}[/tex] year.

R is the interest rate

Substitute the value in the formula,

[tex]900=9500\times R\times \frac{19}{12}[/tex]

[tex]R=\frac{900\times 12}{9500\times 19}[/tex]

[tex]R=\frac{10800}{180500}[/tex]

[tex]R=0.0598[/tex]

The rate of interest in percentage is [tex]R=0.0598\times 100=5.98\%[/tex]

Therefore, The interest rate is 5.98%.

To earn $900 from $9,500 in 19 months, an annual interest rate of approximately 5.97% is needed.

To determine the interest rate needed for $9,500 to earn $900 in 19 months, we can use the simple interest formula:

Simple Interest Formula: SI = P × R × T

SI: Simple Interest ($900)

P: Principal ($9,500)

R: Annual Interest Rate (as a decimal)

T: Time (in years)

Convert 19 months into years: 19 months / 12 months/year = 1.5833 years.Substitute the values into the formula: $900 = $9,500 × R × 1.5833.Isolate R: R = $900 / ($9,500 × 1.5833).R = 0.0597, which is approximately 5.97% per year.

13. Apply the rules for order of operations to simplify 2 + 3 − 4 + (5 × 4). A. 9 B. 24 C. 22 D. 21

Answers

Work: 2+3-4+(5×4)
Parenthesis
2+3-4+20
Add or subtract whichever comes first
5-4+20
Add or subtract whichever comes first
1+20
Add
21
Answer: 21 or D

julia has just gotten a new job paying 80,000 a year . what would be her estimated federal taxes?


Answers

0.28*80 000=22 400
She would pay $22 400 in federal taxes

Julia estimated federal taxes will be $ 22,400.

What is Percentage?

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Julia has just gotten a new job paying 80,000 a year .

From the figure the tax will be of 28%.

So, Julia estimated federal taxes will be

= 80,000 x 28/100

= 800 x 28

= $ 22,400

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find two consecutive odd integers whose product is 1 less than 6 times their sum. Domain for the smallest : {-1, 1, 11}

Answers

Let x be the 1st odd number, and x+2 the second odd consecutive number:

(x)(x + 2) = 6[((x) + (x+2)] -1
x² + 2x = 6(2x + 2) - 1

x² + 2x = 12x +12 - 1
And x² - 10x - 11=0

Solve this quadratic expression:

x' = [+10 +√(10²- 4.(1)(-11)]/2  and x" = [+10 -√(10²- 4.(1)(-11)]/2

x' = [10 + √144]/2      and  x" = [10 - √64]/2

x' = (10+12)/2    and x" = (10-12)/2

x = 11 and x = -1

We have 2 solutions that satisfy the problem:

1st for x = 11, the numbers at 11 and 13
2nd for x = - 1 , the numbers are -1 and +1
If you plug each one in the original equation :(x)(x + 2) = 6[((x) + (x+2)] -1
you will find that both generates an equlity


19. What are the extremes of the following proportion? 3⁄15 = 12⁄60

Answers

4 is your answer

3 x 4 = 12
15 x 4 = 60

so 4 is the amount 
hope this helps

How many elements are in the set (A,B,C)

Answers

The answer is:
A has 25 elements
B has 30 elements
C has 35 elements
the answer to this question is 1 I believe 

The ends of a pipe when measured with a tape measure that has marks every millimeter are exactly at the 0 mark and the 15 meter mark. how would you record this measurement keeping the correct number of significant figures.

Answers

If the ends span from the 0 to the 15 meter mark, then the length of the pipe is 15 meters. However, you should report it using the right amount of significant figures. It is mentioned in the problem that millimeter marks are calibrated between meters. Since millimeter is 1/1000 of a meter, you should add three decimal places to the 15 meters. Hence, you should report it as 15.000 meters.

what percent of 1600 is 20?

Answers

Set up a proportion like so. Remember that percent means per 100.

20/1600= x/100

Cross multiplication:
100*20=2000
2000/1600= 1.25=x

Final answer: 1.25%

20 is 1.25% of 1600.

(Part / Whole) * 100 = Percentage

20 by 1600:

20 / 1600 = 0.0125.

Multiply the result by 100 to get the percentage:

0.0125 * 100

= 1.25%.

So, 20 is 1.25% of 1600.

When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm . part a what is the flea's acceleration as it extends its legs?

Answers

The flea's acceleration is 1,000 m/s².

Further explanation

The problem we overlook this time is about uniformly accelerated motion.

The list of variables to be considered is as follows.

[tex]\boxed{u \ or \ v_i = initial \ velocity}[/tex]

[tex]\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}[/tex]

[tex]\boxed{a = acceleration \ (constant)}[/tex]

[tex]\boxed{d = distance \ travelled}[/tex]

Given that a take-off speed of 1.0 m/s over a distance of 0.50 mm.  

The initial speed was zero from rest.  It was asked about flea's acceleration when she extends her legs.

The formula we follow for this problem are as follows:

[tex]\boxed{ \ v^2 = u^2 + 2ad \ }[/tex]

a = acceleration (in m/s²)u = initial velocity = 0 m/sv = take off speed = 1.0 m/sd = distance travelled = 0.50 mm

Converted 0.50 mm to meters: [tex]\boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}[/tex]

Steps:

We set the formula so that the acceleration becomes the subject.

[tex]\boxed{ \ v^2 = u^2 + 2ad \ }[/tex]

[tex]\boxed{ \ v^2 - u^2 = 2ad \ }[/tex]

[tex]\boxed{ \ 2ad = v^2 - u^2 \ }[/tex]

[tex]\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }[/tex]

Substitute all data into equations.

[tex]\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }[/tex]

[tex]\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }[/tex]

[tex]\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }[/tex]

[tex]\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }[/tex]

We get the flea's acceleration, i.e., 1,000 m/s².

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Keywords: flea, when jumping, rapidly extends its legs, take-off speed, initial velocity, distance, acceleration, uniformly accelerated motion, convert

The Flea acceleration as it extends its leg is [tex]\fbox{\begin\\\ 1000\ m/s^{2}\\\end{minispace}}[/tex].

Further explanation:

Given:

The takeoff speed of the flea is [tex]1.0\ \text{m/s}[/tex].

The distance cover by flea is [tex]0.50\ \text{m/s}[/tex].

To find:

The acceleration of the flea as it extended it legs.

Formula used:

The acceleration of the flea can be obtained by the given formula.

[tex]\fbox{\begin\\\ \math v^{2}=u^{2}+2as\\\end{minisapce}}[/tex]  ....(1)

Here, [tex]v[/tex] is the final velocity of flea, [tex]u[/tex] is the initial velocity of flea, [tex]a[/tex] is the acceleration of the flea, [tex]s[/tex] is the distance cover by the flea.

Calculation:

The initial velocity of flea is [tex]0[/tex].

The final velocity of flea is [tex]1.0\text{m/s}[/tex].

The distance cover by flea is in millimeter.

Convert millimeter into meter as follows.

[tex]\fbox{\begin\\\ \begin{aligned}0.50 \text{ mm}&=\dfrac{0.50}{1000}\text{ m}\\&=0.0005\text{ m}\end{aligned}\\\end{minispace}}[/tex]

Now substitute [tex]0[/tex] for [tex]u[/tex], [tex]1.0[/tex] for [tex]v[/tex] and [tex]0.0005[/tex] for [tex]s[/tex] in equation (1) to obtain the value of acceleration.

[tex]\begin{aligned}1^{2}&=0^{2}+(2a\times(0.0005))\\1&=0.001a\\a&=\dfrac{1}{0.001}\\a&=1000\end{aligned}[/tex]

Therefore, the acceleration of the flea is as it extends its leg is [tex]\fbox{\begin\\\ 1000\ m/s^{2}\\\end{minispace}}[/tex].

Learn more:

1. Solution of linear equation: //brainly.com/question/1682776

2. Magnitude of the acceleration https://brainly.com/question/1597065

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Speed and distance

Keywords:  Flea, jump, legs, takeoff speed, acceleration , distance cover, 0.05 mm, 1000 meter per second square. Initial velocity, Final velocity

What do March 16, 1948, Feb. 25, 1950, and Aug. 8, 1964 have in common??

Answers

the product of the month and the day is equivalent to the years last two digits

subtract the quotient of 15/3 from the sum of 33 and 7

Answers

quotient is division

 so 15/3 = 5

sum is addition so 33+7 = 40

40-5 = 35

solve the following equation for 2 + √4y -3 = 11

Answers

2+√4y-3=11
2+√4y=11+3=14
√4y=14-2=12
root 4y=2y
2y=12,divide both side by 2
y=6

Final answer:

To solve the equation 2 + √(4y - 3) = 11 for y, subtract 2 from both sides, square both sides to remove the square root, then solve for y to find that y = 21.

Explanation:

The question asks to solve the equation 2 + √(4y - 3) = 11 for y. To solve for y, follow the steps below:

First, subtract 2 from both sides of the equation to isolate the square root term: √(4y - 3) = 9.

Now, square both sides of the equation to eliminate the square root: (√(4y - 3))^2 = 9^2, which simplifies to 4y - 3 = 81.

Add 3 to both sides of the equation to isolate the term with y: 4y = 84.

Finally, divide both sides by 4 to solve for y: y = 21.

Therefore, the solution to the equation is y = 21.

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