Use the upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y = 1 − x2.

Answer:

[tex]\lim_{x \to 5^{-}} f(x)= 54[/tex]

[tex]\lim_{x \to 5^{+}} f(x) = -17[/tex]

Step-by-step explanation:

+ means we are approaching from the right

- means we are approaching from the left

We are given that if x < 5, it is x² + 5x + 4

So to find [tex]\lim_{x \to 5^{-}} f(x)[/tex] we would plug in 5 into that piecewise function part:

5² + 5(5) + 4 = 54

We would be approaching y = 54 if we approach from the left.

We are given that x > 5, it is -4x + 3

So to find [tex]\lim_{x \to 5^{+}} f(x)[/tex] we would plug in 5 into that piecewise function part:

-4(5) + 3 = -17

We would approach y = -17 if we approached from the right.

Answer:

[tex]\lim_{x \to 5^-}f(x)=54\\\lim_{x \to 5^+}f(x)=-17[/tex]

Step-by-step explanation:

So, we have the function:

[tex]f(x)=x^2+5x+4,x<5\\f(x)=8,x=5\\f(x)=-4x+3,\text{ otherwise}[/tex]

And we want to show that this has a jump discontinuity.

As directed, calculate the limit at x=5 from the left and from the right. Thus:

[tex]\lim_{x \to 5^-}f(x)[/tex]

To calculate this, since we're coming from the left, x is less than 5. So, use the first equation:

[tex]\lim_{x \to 5^-}f(x)\\= \lim_{x \to 5^-}(x^2+5x+4)\\[/tex]

Use direct substitution:

[tex]=(5)^2+5(5)+4\\=25+25+4\\=54[/tex]

Thus, as the limit approaches f(5) from the left, the function approaches 54.

Now, calculate the limit at x=5 from the right. Since we're coming from the right, use the third equation:

[tex]\lim_{x \to 5^+}f(x)\\= \lim_{x \to 5^+}(-4x+3)[/tex]

Direct substitution:

[tex](-4(5)+3)\\=-20+3\\=-17[/tex]

Thus, as the limit approaches f(5) from the right, the function approaches -17.

As you can picture, there's a huge gap between y=54 and y=-17. The limits are not equal and both of the limits do exist. Thus, we have jump discontinuity.

Answer:

$21

Step-by-step explanation:

Multiply 7 by 3, since it increased $3 each week for 7 weeks:

7(3)

= $21

So, the total change in the price of a share of stock was $21

Answer:

  see below

Step-by-step explanation:

You can try the answer choices to see which one works. Since the amount repaid is greater than the amount borrowed, you can be pretty sure that the multiplier of x will not be 4/5 (a value less than 1).

You can see right away that

 y = 5/4x

does not work for x=100, because it gives y=(5/4)(100) = 125, and the table value is 135. Note that 135 is 10 more than 125, so we expect that ...

  y = 5/4x +10

will be correct. Trying that function on the other table values shows it fits exactly:

  5/4(200) +10 = 250 +10 = 260

  5/4(500) +10 = 625 +10 = 635

  5/4(800) +10 = 1000 +10 = 1010

_____

You can also use the table values to create the relation equation. One possible method uses the 2-point form of the equation for a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (260 -135)/(200 -100)(x -100) +135

  y = 125/100(x -100) +135 . . . . simplify a bit

  y = 5/4x -125 +135 . . . . . . . . . simplify more

  y = 5/4x +10 . . . . . . . . . . . . . . simpler yet; matches 3rd choice

Answer: 11, 56, 168

Step-by-step explanation: order of operations:

1+10=11.

3+11=14. 14x4=56.

3x56=168

Answer:

Step-by-step explanation:

Collin initially have  14

Step-by-step explanation:

Let

x------> money that Brian had initially

y------> money that Collin had initially

we know that

x/y=7/2

solve for x

x=7/2y -------> equation A

y-39=y-4 ------> equation B

substitute equation A in equation B

7/2y-39=y-4

7/2y-y=39-4

5/2y=35

y=14

Answer:

£49.

Step-by-step explanation:

Let the ratio of  brain's money to Colin's is 7x : 2x.

From the given info:

7x - 39  = 2x - 4

5x = -4 + 39 = 35

x = 7

So initially Brian had 7*7 = £49.

Colin had £14.

Answer:

c

Step-by-step explanation:

Given

sinN = [tex]\frac{a}{b}[/tex] ( multiply both sides by b ) , then

a = bsinN → (a)

And

sinM = [tex]\frac{a}{y}[/tex] ( multiply both sides by y ), then

a = ysinM → (b)

Thus a is both (a) and (b)

Answer:

360

Step-by-step explanation:

.0 is less than .5 so round down

Answer:

360

Step-by-step explanation:

[tex]360.048 = 360[/tex]

0 to 4 = 0(round down)

5 to 9 =1 (round up)

Answer:

Step-by-step explanation:

[tex]\left(\dfrac{143}{4}-\dfrac38\right)+\left(\dfrac{207}{8}-\dfrac38\right)=\dfrac{286}{8}-\dfrac38+\dfrac{204}{8}=\dfrac{283}{8}+\dfrac{204}{8}=\dfrac{487}{8}[/tex]

Step-by-step explanation:

what concepts of functions can you associate with the picture

The concepts of functions that can be associated with the pictures are :

attached below is the missing diagram.

A concept is general idea about a Thing which can be represented in different forms. It can be visual or non-visual. therefore some of the concept of  function represented in the pictures includes ; money, Financial Accounts, savings.  e.t.c.

Hence from the pictures attached below the concepts that are represented in them includes ; Money, Account, Revenue and Savings.

learn more : https://brainly.com/question/1103669

Answer:

Step-by-step explanation:

We will use the combination rule to solve this questions since it bothers selection. Combination has to do with selection.

If r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

If there are Eight committee members meeting in a room that has twelve chairs, the number of ways they can sit in the chair can be done in 12C8 number of ways.

12C8 = 12!/(12-8)!8!

12C8 = 12!/4!8!

12C8 = 12*11*10*9*8!/4*3*2*8!

12C8 =  12*11*10*9/4*3*2

12C8 = 11*10*9/2

12C8 = 11*5*9

12C8 = 495

Hence the committee can sit in the chairs in 495 different ways

Answer:

The least number of days it  will take each person to save the same amount of money is 36 days.

Step-by-step explanation:

We are given that Steve can save 9 dollars every day while Maria can save 12 dollars.

And we have to find the least number of days it will take each person to save the same amount of money.

Whenever we talk about the least common value, the LCM or Least common multiple comes into account.

Here also; the least number of days it  will take each person to save the same amount of money will be the LCM or Least common multiple of 9 and 12.

LCM of 9 and 12 is calculated as;

2 = 9 , 12    

2 = 9 , 6

3 = 9 , 3

3 = 3 , 1

      1 , 1

Here, the second line means that 12 is divisible by 2 at 6, i.e; 2 [tex]\times[/tex] 6 = 12 and so on.

So, the LCM of 9 and 12 = [tex]2\times 2 \times 3 \times 3[/tex] = 36

Hence, the least number of days it  will take each person to save the same amount of money is 36 days.

Answer:

Step-by-step explanation:

(A).

No' of siblings           Frequency           Rel. frequency     Cumm. frequency

0                                     51                          0.2429                       51

1                                      37                          0.1762                        51 + 37 = 88

2                                     34                          0.1619                        122

3                                     41                         [tex]\frac{41}{169}=0.2426[/tex]                163

4                                     47                           0.2238                     210

(B).

Percent of people having exactly one sibling = [tex]\frac{\text{Frequency}}{\text{Total frequency}}\times 100[/tex]

                                                                           = [tex]\frac{37}{210}\times 100[/tex]

                                                                           = 17.62%

Answer:

$1136.88 So she earned more than $1135

Step-by-step explanation:

$8.50 an hour.

31.25 week 1 = 265.625

33.75 week 2 = 286.875

36 week 3 = 306

32.75 week 4 = 278.375

In all - 1136.88 (rounded)

1136.875 (not rounded)

Answer:

Hey there!

5760/480000=x/600000

Solving for x, we get the answer is $7200.

Let me know if this helps :)

Answer:

$7200

Step-by-step explanation:

We can start by finding out the tax rate by dividing the property tax by assessed value.

$5760/$480,000 = 0.012

From this, we learn the tax rate is 1.2%

Now, we can multiply the assessed value of $600,000 by the tax rate.

$600,000*0.012 = $7200

The property tax on a house with the assessed value of $600,000 is $7200.

Answer:

Step-by-step explanation:

[tex]6x-10=-8+3x\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\6x-10+10=-8+3x+10\\\\\mathrm{Simplify}\\6x=3x+2\\\\\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}\\6x-3x=3x+2-3x\\\\Simplify\\3x=2\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3x}{3}=\frac{2}{3}\\\\Simplify\\x=\frac{2}{3}[/tex]

Answer:

x = 2/3

Step-by-step explanation:

This equation can be solved by using conventional algebraic techniques.

We firstly want to make sure to get our constants on one side of the equation and then get our variables on the other.

6x - 10 = -8 + 3x Subtract 3x from both sides of the equation.

3x - 10 = -8 Add 10 to both sides of the equation.

3x = 2 Divide by 3 on both sides of the equation.

x = 2/3

Then, you can voluntarily check your answer.

6(2/3) - 10 = -8 + 3(2/3)

4 - 10 = -8 + 2

-6 = -6

Answer: 250 words in 5 minutes

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

This equation can be solved three steps, classifying it as a multi-step equation.

To solve, you need to get the constants on one side and the variables on the other and then isolate the variable. These steps are illustrated below.

3y + 2 = 2y + 4 Subtract 2y from both sides of the equation.

y + 2 = 4 Subtract 2 from both sides of the equation.

y = 2

Answer:

81

Step-by-step explanation:

The area of a square is its side length squared so 9^2 is 81

Answer:

Zero

Step-by-step explanation:

Zero

Answer

To fill in the blank, it would be zero

Step-by-step explanation:

Answer:

x>0

Step-by-step explanation:

We want to solve for x in the inequality:

4^x > 1

ln(4^x)=xln(4) > ln(1)=0

x > 0/ln(4) =0

x>0

So for any value of x greater than 0, you will have 4^x be greater than 1.

Answer:

They are some side interior angles. Angle A measures 55 degrees.

Step-by-step explanation:

Angle A is accuse so it can’t be 90 or more, so that narrows you’re options down by two. From there it’s fairly easy to distinguish.

Answer:

Question Answer

I am a number whose prime factors are all the prime numbers between 6 and 15 no factor is repeated what number am i? 1001

The number is 1001 if a number whose prime factors are all of the prime numbers between 6 and 15.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

We have:

I am a number whose prime factors are all of the prime numbers between 6 and 15.

The prime number between 6 and 15:

As we know, the prime number is the number that is divisible by 1 and itself.

Prime number = {7, 11, 13}

= 7×11×13

= 1001

Thus, the number is 1001 if a number whose prime factors are all of the prime numbers between 6 and 15.

Learn more about the number here:

brainly.com/question/17429689

#SPJ2

Answer:

[tex]x=7,y=16[/tex]

Step-by-step explanation:

The tick marks you see on the sides denote congruence. If they have the same number of tick marks, then their side length are congruent.

And, recall that congruent side lengths have the same measure.

So, look at the sides with 2 tick marks. They are congruent. Therefore:

[tex]2x+5=x+12[/tex]

Subtract x from both sides:

[tex]x+5=12[/tex]

Subtract 5 from both sides:

[tex]x=7[/tex]

So, x is 7.

Now, look at the sides with only 1 tick mark. Again, they are congruent. Thus:

[tex]y-4=x+5[/tex]

We already know x is 7. So:

[tex]y-4=(7)+5[/tex]

Add:

[tex]y-4=12[/tex]

Add 4 to both sides:

[tex]y=16[/tex]

So, y is 16.

Answer:

1. Number of boys in A is 52028.

2. Number of girls in B is 46510.

3. Town B has more number of girls.

Step-by-step explanation:

1. [tex]95364 - 43336 = 52028[/tex]

2. [tex]100005-53495=46510[/tex]

3. [tex]43336<46510[/tex] (A < B)

Answer:

33 x 15.80

521.40 x 50= 26,070

B 26,070

Hope this helps! （づ￣3￣）づ╭❤～

Answer a=3f+g/b+x

Step-by-step explanation:

Let's solve for a.

a(x+b)=g+3f

Step 1: Factor out variable a.

a(b+x)=3f+g

Step 2: Divide both sides by b+x.

a(b+x)/b+x=3f+g/b+x

a=3f+g/b+x

Answer:

  point G

Step-by-step explanation:

Find the referenced points on the diagram and notice the lines between them. The point at the intersection of those lines is what is wanted.

It is point G.

The correct answer is Josh has 240 points and his brother has 180 points

Explanation:

The ratio 4:3 means for every four points Josh has, his brother has three points. Now, to find how many points each boy has if there are 420 points, follow this process:

1. Use the ratio to write the equivalent fraction

4 : 3 = [tex]\frac{4}{3}[/tex]

2.  Find the total number of parts

4 + 3  = 7

3. Divide the total number into the parts

420 ÷ 7 = 60 (each of the part is equivalent to 60)

4. Multiply the value of each part by each section of the ratio

4 × 60 = 240 - This represents the number of points Josh has if there are 420 points

3 × 60 = 180 - This represents the points Josh's brother has

This means Josh has 240 points and his brother has 180 points

Answer:

Josh has 240 points and his brother has 180 points\

I hope this helps. Have a nice day :D

Answer:

13 is a prime number, not divisible by any number greater than 1 or less than 13. So the prime factorisation of 78 is: 78 = 2 ⋅ 3 ⋅ 13 This can also be represented by a factor tree:

Step-by-step explanation:

Answer:

78 = 2 ⋅ 3 ⋅ 13

Step-by-step explanation:

78  ends with an even digit, so is divisible by  2 and we find:  78 = 2 ⋅ 39

39  ends with an odd digit, so is not divisible by  2 .

The digits of  39  add up to a multiple of  3 , namely  3 + 9 = 12 . So we can tell that  39  is divisible by  3 : 39 = 3 ⋅ 13

13  is a prime number, not divisible by any number greater than  1  or less than  13 .

So the prime factorization of  

78  is:

78= 2 ⋅ 3 ⋅ 13