The sum of 5 consecutive integers is 505

Answers

Answer 1

505/5 = 101

so 101 is the middle number, now add the 2 below it and the 2 above it


99 + 100 + 101 + 102 +103 = 505


Related Questions

0.75 = log x raise each side of the equation as power

Answers

Hi there!


0.75 = logx
I always flip them so that I can make sure I don't forget anything. FYI, this is one of the trick they used to force you make the mistake so make sure you always flip the equation (omg I talked too much)

--------------------------------------------------------------------------------
0.75 = logx
Flip it
logx = 0.75
We need to solve for the logarithm
log(x)= 0.75
Take exponent of both sides
10^logx =10^0.75
x = 10^0.75
x= 5.623413


I hope that helps!

on every 3rd day Ivan goes to the gym. On every fifth day Gavin goes to the gym. What day will Ivan and Gavin will see each other.

Answers

they will see each other on the fifteenth day

Find the least common multiple. It would be 15, so on the 15th day.

Answer ALL if u cant see all the answers it don't matter all u need is the question

Answers

I'm probably wrong but I think A.

2. If you have budgeted 12% of your monthly income for groceries, how much can you spend on groceries if you earn $950 bi-weekly?

Answers

bi weekly means you get paid every 2 weeks ( 2 times a month)

950*2 = 1900 per month for pay

1900*0.12 = 228 a month for food

Answer:

if you earn $950 bi-weekly, you earn 2 x 950 = $1900 per month. If you have budgeted 12% of your monthly income for groceries you need to find 12% of $1900: (1900 / 100) x 12 = 228. Answer: you can spend $228 a month on groceries.

The sum of 74 and four times a number is 258. Find the number

Answers

74 + 4x = 258
4x = 258 - 74
4x = 184
x = 184/4
x = 46  ←  the number

The unknown number is 46.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Let the number be x.

The sum of 74 and four times a number is 258,

⇒ [tex]74+4x=258[/tex]

⇒ [tex]4x=258-74[/tex]

⇒ [tex]x=\frac{184}{4}[/tex]

⇒ [tex]x=46[/tex]

Hence we can conclude that the unknown number is 46.

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In italy about 74 of every 100 people use celular telephones. Write the fraction of celular phone users in italy. Then write it as a decimal.

Answers

74 out of every 100...
74/100 reduces to 37/50 = 0.74

Module 04.03 Exponential Functions and Models: Essential Questions:
1) How do the properties of exponents apply to exponential functions?
2)How are key features of graphs and tables used to model relationships between two quantities?
3)How can the average rate of a change be identified for a function?
*PLEASE HELP! NEED TO KNOW THIS.*

Answers

Final answer:

Properties of exponents are used to simplify and manipulate exponential functions. In graphing, growth rate, intercept, and asymptotes model relationships. The average rate of change for a function is calculated based on changes in output divided by input changes over an interval.

Explanation:Understanding Exponential Functions and Models

Exponential functions are mathematical expressions where a constant base is raised to a variable exponent. The properties of exponents, such as product, quotient, and power rules, apply to these functions and are used to simplify and manipulate expressions.

When modeling relationships between two quantities using graphs and tables, key features like the growth rate, y-intercept, and asymptotes are important. The growth rate can be understood from the steepness of the graph or how quickly the y-values increase as x increases. The y-intercept represents the starting value of the quantity being modeled when x equals zero.

The average rate of change for a function is identified by calculating the change in the function's output values (y-values) divided by the change in the input values (x-values) over the interval of interest. For exponential functions, this rate of change is not constant, but increases or decreases at a rate proportional to the function's current value.

An example of exponential growth in a natural population might be the rapid increase in a bacteria population in an ideal lab condition, where it doubles every fixed amount of time. In contrast, a logistic growth pattern occurs when the growth rate decreases as the population reaches carrying capacity, such as the population of sheep in a field with limited grass for food.

Exploring the Exponential Distribution

The exponential distribution is typically used to model the time between events in a memoryless process, where the probability of an event occurring is the same at any moment. In an exponential distribution, outcomes are not equally likely as not all intervals of time are equally likely to occur before the next event. The mean (m), often referred to as the expected value, and the standard deviation can be derived from the rate parameter, which is the reciprocal of the mean.

Understanding how to manipulate a linear equation, as well as interpret and compute growth rates, is foundational in various applications including those in economics, biology, and environmental science. The ability to read and manipulate graphs is crucial for clearly presenting data and drawing accurate conclusions.

How to simplify the expression 60/(-4)

Answers

Hey!

We could rewrite the problem as: [tex]\frac{60}{-4}[/tex]
Since we have a negative number, we could rewrite the fraction like this. 
[tex]=-\frac{60}{4}[/tex]
Let's simplify it...
[tex]-\frac{60}{4}=-15[/tex]
Our answer would be:
[tex]=-15[/tex]

Thanks!
-TetraFish

Solve the equation for the letter L: A=LW

L = AW
L equals W over A
L = A − W
none of the above

Answers

[tex] \frac{L}{A} =LW[/tex] ⇒ Multiply both sides by A
[tex] \frac{LA}{A}=LWA [/tex] ⇒ The terms 'A' on the LHS cancel each other
[tex]L=LWA[/tex] ⇒ Divide both sides by 'L'
[tex] \frac{L}{L}= \frac{LWA}{L} [/tex] ⇒ The terms 'L' on the LHS cancel each other to '1' and the terms 'L' on the RHS will also cancel each other
[tex]1= WA[/tex]

The correct answer is the last option = none of the above

11 POINTS GUYS PLZ
Answer 12 and 14

Answers

12) 10.77 + 2.09 + 0.75 = 13.61

13.61 x 1.07 = $14.56

 total amount = $14.56


14) C shows the possible combinations

can someone help with this

Answers

Hey There! :)

Solve for g. 
[tex]g/20=12/48 [/tex]
Isolate the variable; Multiply both sides by 20.
[tex](g/20)*20=(12/48)*20 [/tex]
[tex]g=240/48 [/tex]
[tex]g=5[/tex]

Hope this helps.
-Benjamin


If there are 11 apples and I eat one and split half of the rest with my friend. How many do i have?

Answers

The answer to this my friend is 5. If you ate one that means there are 10 left. Then if you split 10 in half that equals 5. hope this helps!
It's 5... cuz 10/2 equal 5

Select the factors of 6ab + 3ay − 2bx − xy.

A. (3a − x)(2b + y)
B. (3a − y)(2b + x)
C. (2a − x)(3b + y)
D. (2a − y)(3b + x)

I need the answer I don't get it ...and this is a really long test ..but so far I only need help on this one . thanks to whoever helps me and give correct answer

Answers

answer
A. (3a − x)(2b + y)

cause

 (3a − x)(2b + y) = 6ab + 3ay -2bx -xy (expand by using distributive property)

Answer:

The factors of given expression is (3a-x)(2b+y)

A is correct

Step-by-step explanation:

Given: [tex]6ab+3ay-2bx-xy[/tex]

We need to factor the given expression.

First we make two group

[tex]\Rightarrow (6ab+3ay)+(-2bx-xy)[/tex]

Factor each group

[tex]\Rightarrow 3a(2b+y)-x(2b+y)[/tex]

[tex]\Rightarrow (3a-x)(2b+y)[/tex]

So, we get two factor (3a-x) and (2b+y)

Hence, The factors of given expression is (3a-x)(2b+y)

The height of a ball thrown directly up with a velocity of 10 feet per second from a initial height of of 100 feet is given by the equation h(t) = -16tsquared + 10t + 100, where t is the time in seconds and h is the ball’s height, measured in feet. When will the ball hit the ground? Round your answer to the nearest tenth.

Answers

The ball will hit the ground when h(t)=0 so:

-16t^2+10t+100=0

Using the quadratic equation:

t=(-10±√6500)/-32, and since t>0

t≈2.8 seconds (to nearest tenth of a second)


Answer:

The ball will hit at 2.83 seconds.

Step-by-step explanation:

It is given that,

Velocity with which a ball is thrown up is, v = 10 ft/s

Initial height, h = 100 ft

The equation for the height of an object as a function of t is given by :

[tex]h(t)=-16t^2+10t+100[/tex]...............(1)

Where

t is the time in seconds

h is the ball's height measured in feet

We have to find the time when the ball hits the ground. It can be calculated by solving the quadratic equation of equation (1). On solving we get the value of t as :

t = 2.832 seconds

So, at 2.83 seconds the ball will hit the ground. Hence, this is the required solution.                        

if O represents number of integers between 10,000 and 100,000 all of whose digits are odd, and E represents number of integers between 10,000 and 100,000 all of whose digits are even, what is the value of O - E?

Answers

i) 
fist let's find O, that is the number of all numbers between 10,000 and 100,000, whose all digits are odd.

so we have to count: 11,111;       11,113;       ... 99,999

we notice that all these numbers are 5 digit, and they are made up of the odd digits {1, 3, 5, 7, 9} with repetition allowed.

so there are in total [tex]5*5*5*5*5= 5^{5} [/tex] such numbers.

ii) 

E is the total number, of 5-digit numbers formed from the set{0, 2, 4, 6, 8} with repetition allowed, and the first digit not equal to 0.

so [tex]E=4*5*5*5*5= 4*5^{4}[/tex]


iii) [tex]O-E=5^{5}-4*5^{4}=5^{4}(5-4)=5^{4}=625[/tex]


Answer: 625

how to write place value 35 thousand,26hundredand 16 tens and 12 ones

Answers

35 thousand=35,000
26 hundred=2,600
16 tens=160
12 ones=12
I think the answer is 37772. 35 thousand=35000. 26 hundred=2600. 16 tens=160. And 12 ones is 12. Add them together, you get 37772. Hope this helped

Simplify the following expression: 2x − 6y + 3x2 + 7y − 14x. 3x2 + 12x + y 3x2 − 12x − y 3x2 − 12x + y 3x2 − 12x − 13y

Answers

3x2 − 12x + y  would be your answer 

The required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.

Given that,
To simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

= 2x − 6y + 3x² + 7y − 14x.
= 3x² + 2x -14x + 7y -6y
= 3x² -12x + y

Thus, the required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.

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Solve the equation by completing the square. Round to the nearest hundredth if necessary? X^2+3x=24

Answers

x^2+3x=24, halve the linear coefficient, square it, and add it to both sides

In this case (3/2)^2=2.25

x^2+3x+2.25=26.25 now the left side is a perfect square...

(x+1.5)^2=26.25  take the square root of both sides

x+1.5=±√26.25  subtract 1.5 from both sides

x=-1.5±√26.25

x=-1.5-√26.25 and -1.5+√26.25

x≈ -6.62 and 3.62

c+1/c-2 = 4/7 please show how you got the answer

Answers

C = 3 while c = 9

C + 1 = 4
c - 2 = 7

4 - 1 = C
C = 3

2+ 7 = c
c = 9


hope this helps
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o graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
a.-5/2
b.-2/5
c.2/5
d.5/2

Answers

2x + 5y = 10
Change to y = mx + b
subtract 2x from both sides
5y = -2x + 10
divide both sides by 5
y = -2/5x + 2
slope = -2/5
LETTER B

we have

[tex] 2x + 5y = 10 [/tex]

we know that

the formula to calculate the slope is equal to

[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]

Let

[tex] A( 5,0)\\B( 0,2) [/tex]

Step [tex] 1 [/tex]

Find the slope AB

[tex] mAB=\frac{(2-0)}{(0-5)} \\ \\ mAB=-\frac{2}{5} [/tex]

therefore

the answer is the option B

[tex] -\frac{2}{5} [/tex]

the graph in the attached figure

When the factors of a trinomial are (x - p) and (x - q) then the constant term of the trinomial is:

A. The quotient of -p and -q
B. The product of -p and -q
C. The difference of -p and -q
D. The sum of -p and -q

Answers

its the product of -p and -q

that is b.

The constant term will be the product of -p and -q.

What is a trinomial?

A trinomial is an algebraic expression that has three non-zero terms and has more than one variable in the expression.

Given that the factors of a trinomial are (x - p) and (x - q) we need to determine the constant term of the trinomial:

We know that a trinomial in its factors form can be written as,

x² + (α+β)x + αβ, where α and β are factors.

So, here the constant term of the trinomial will be (-p) × (-q) = pq.

Hence the constant term will be the product of -p and -q.

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Which of these expressions is equal to 6 + (2 + 3) × 5

Answers

6 + (2+3) x 5
6 + (5) x 5
6 + 25
31

Order of operations: PEMDAS
Parenthesis
Exponents
Multiply Divide
Addition 
Subtraction
if one of the choices is 31 then thats your answer


For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.

During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .

Answers

To answer we let x be the amount of money that Sam invested during the first year. 

Below are the expressions translated from the given word forms for the amount invested.

Sam:
2nd year :   amount = 5x/2 - 2000
3rd year  :   amount = x/5 + 1000

The sum of money invested by Sam is:
  x + (5x/2 - 2000) + (x/5 + 1000)

Similarly, we derive the expressions that we use for the amount that Sally invested.
Sally
1st year  :    amount  = 3x/2 - 1000
2nd year :    amount = 2x - 1500
3rd year :     amount = x/4 + 1400

The total amount that Sally invested is, 
        total = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)

Equating the two equations:
 (x) + (5x/2 - 2000) + (x/5 + 1000) = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)

 Solving for x,
               x = 2000
For Sally's investment in the third year:
    amount = x/4 + 1400 = (2000/4 + 1400) = 1900

ANSWERS: 
  Sam's first year = $2000
  Sally's third year = $1900

Please help me :) Thanks!

Answers

x^2+12x+5 = (x+6)^2 -31,

So the minimum value is y = -31. Dunno if -31 or you have to type =-31, I guess just '-31'?

With derivatives:

y' = 2x+12=0, x = -6, then y(-6) = 36-72+5 = -36+5 =-31

Just to be sure!!!! lol
The minimum value for y in the equation y = x² + 12x + 5 is (-6,-31). Here's how I figured it out:

Step 1: Figure out if the parabola is going up or down. If "a" is positive, the parabola will go up. If "a" is negative, the parabola will go down. In your case...

a = 1
Positive
Up
____________________________________________________________

Step 2: Find the Axis of Symmetry.

Formula:      -b             -12               -12
                 --------- =  ------------ =  ------------- = -6
                    2a            2(1)                 2

The axis of symmetry is x = -6.
____________________________________________________________

Step 3: Plug in the value you found for the axis of symmetry for x into your original equation.

f(-6) = -6² + 12(-6) + 5
f(-6) = 36 - 72 + 5
f(-6) = -36 + 5
f(-6) = -31

The minimum gets written as an ordered pair: (-6,-31).
⊕ The axis of symmetry is the first number in the coordinate pair.
⊕ The answer that you get to step 3 is the second number in the pair.
____________________________________________________________

I hope that my answer helps you! This is the method that I use to solve these types of problems, but there are also other methods.


 

What is the area of the polygon shown below?

Answers

(22*10)+(0.5*10*7) = 255 cm^2

22x10= 220 for the area of the rectangle because basexheight= area and then take the triangle separately which is 7x10 multiplied by a half because the equation for the area of a triangle is base x height / 1/2

If the family has three pets, what is the theoretical probability that they have three dogs or three cats?

Answers

The probability helps us to know the chances of an event occurring. The theoretical probability that they have three dogs or three cats is 0.25.

What is Probability?

The probability helps us to know the chances of an event occurring.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

As it is given that the pet can either be a dog or a cat, therefore,

The probability that all the three pets are dogs is:

[tex]\rm P(X= 3\ dogs) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]

The probability that all the three pets are cats is:

[tex]\rm P(X= 3\ Cats) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]

Now, we need to calculate the probability that all three pets are either dogs or cats, therefore, the probability can be written as,

[tex]\rm P(3\ Dogs\ or\ 3\ Cats) = P(X = 3\ dogs) + P(X = 3\ cats)[/tex]

                                [tex]= \dfrac{1}{8}+\dfrac{1}{8}\\\\=\dfrac{2}{8}\\\\ = \dfrac{1}{4} = 0.25[/tex]

Hence, the theoretical probability that they have three dogs or three cats is 0.25.

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jackson bikes 2 miles in 15 minutes. At this rate, how many miles will he bike in 45 minutes?

Answers

He will ride 6 miles in 45 minutes.

Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}. What is A ∩ B? (2 points)

Answers

A = {odd numbers between 0 and 100}
A = {1, 3, 5, 7,...., 95, 97, 99}

B = {numbers between 50 and 150 that are evenly divisible by 5}
B = {50, 55, 60, 65, ..., 140, 145, 150}

The notation A ∩ B means the set of items that are in set A and also in set B. In terms of venn diagrams, it's the overlapping region between circle A and circle B

In this case, the following values are found in both set A and set B
{55, 65, 75, 85, 95}

So that's why 
A ∩ B = {55, 65, 75, 85, 95}
which is the final answer

Erika and Rita have added a 1-mile walk to their daily exercise schedule. The table lists the time each of them took to walk the 1-mile distance over the past five days. Erika’s Time (in minutes) Rita’s Time (in minutes) 20 21.25 21.5 24.75 22.75 23 23.25 23 20.25 20.75 On average, it takes Erika about minute(s) per mile less than Rita.

Answers

There are two sets of data: Erika's and Rita's. Now, we have to find the average values for each of both and compare them. I would assume that the order of the presentation of data points is alternating, first for Erika followed by Rita. To illustrate what I mean, let's say in Day 1, Erika's time is 20 and Rita's time is 21.25. In Day 2, Erika's time is 21.5 and Rita's is 24.75. And so on and so forth. The complete tabulation is shown in the picture.

Erika's average = (20+21.5+22.75+23.25+20.25)/5 = 21.55
Rita's average = (21.25+24.75+23+23+20.75)/5 = 22.55

On average, Erika is much slower than Rita by 1 minute.


Find the value of X in the problem below. Geometry

Answers

(3x+10) +14x = 180

17x +10 = 180

17x=170

x = 170/17 = 10

 x = 10

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