Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x = 0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
I error l ≤

Answer:

[tex]x = 2[/tex]

[tex]y = -2[/tex]

Step-by-step explanation:

Given

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

[tex]2x + 2y = 0[/tex]

Required

Solfe for x and y

Subtract both equations

[tex]2x- 2x + y - 2y = 2 -0[/tex]

[tex]-y = 2[/tex]

Divide by -1

[tex]y = -2[/tex]

Substitute [tex]y = -2[/tex] in [tex]2x + 2y = 0[/tex]

[tex]2x+2 *-2 = 0[/tex]

[tex]2x-4 = 0[/tex]

[tex]x - 2 = 0[/tex]

Collect like terms

[tex]x = 2[/tex]

Answer:

You can go ahead with option D

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

The directrix of a parabola is the vertical line found by subtracting

p from the x-coordinate h

of the vertex if the parabola opens left or right.

x=h-p

Substitute the known values of

p and h

into the formula and simplify.

x=7

Answer:

See Explanation

Step-by-step explanation:

Required

Proportion problems

An example is:

y is directly proportional to x such that: y=4 when x = 2;

Derive the equation

For direct proportions, we have:

[tex]y\ \alpha\ x[/tex]

This gives:

[tex]y = kx[/tex]

Make k the subject

[tex]k = y/x[/tex]

So:

[tex]k = 4/2 =2[/tex]

So, the equation is:

[tex]y = kx[/tex]

[tex]y = 2x[/tex]

Assume the above question is for inverse proportion

The variation will be:

[tex]y\ \alpha\ \frac{1}{x}[/tex]

This gives:

[tex]y\ = \frac{k}{x}[/tex]

Make k the subject

[tex]k =x*y[/tex]

[tex]k =2* 4 = 8[/tex]

So, the equation is:

[tex]y\ = \frac{k}{x}[/tex]

[tex]y = \frac{8}{x}[/tex]

Answer:

C

Step-by-step explanation:

x + 2 < -5

x < - 5 - 2

x < - 7

Answer:

{x| x R, x<-7}

Step-by-step explanation:

=> x+2<-5

=> x<-5-2

=> x<-7

Answer:

False

Step-by-step explanation:

A field book is a private notepad used by a surveyor to record measurements and notes.

Basically, the size of a field book is 200 millimeters × 120 millimeters (20 centimeters × 12 centimeters) and it's typically opened lengthwise. There are two (2) main types of field book and these includes;

I. Double-line field book.

II. Single-line field book.

As a general rule, it's best that all findings, entries (notes) and observations are recorded or made into a field book after each and every measurement have been taken by a surveyor.

In conclusion, a field book is considered to be a legal document used by surveyors to keep records of accomplished field work or work done in the field. Thus, it's not a private notepad used by a surveyor to transcribe notes.

Answer:

False

Step-by-step explanation:

A field book is a private notepad used by a surveyor to transcribe notes and is not considered a legal document is False.

Answer:

[tex]\sigma_1 = 0.08[/tex] --- Location 1

[tex]\sigma_2 = 0.34[/tex] --- Location 2

Step-by-step explanation:

Given

See attachment for the given data

Required

The standard deviation of each location

For location 1

First, calculate the mean

[tex]\bar x_1 =\frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x_1 =\frac{30.40+30.20+30.30+30.40+30.30}{5}[/tex]

[tex]\bar x_1 =\frac{151.60}{5}[/tex]

[tex]\bar x_1 =30.32[/tex]

The standard deviation is calculated as:

[tex]\sigma_1 = \sqrt{\frac{\sum(x - \bar x_1)^2}{n-1}}[/tex]

[tex]\sigma_1 = \sqrt{\frac{(30.40 - 30.32)^2+(30.20 - 30.32)^2+(30.30 - 30.32)^2+(30.40 - 30.32)^2+(30.30 - 30.32)^2}{5-1}}[/tex]

[tex]\sigma_1 = \sqrt{\frac{0.028}{4}}[/tex]

[tex]\sigma_1 = \sqrt{0.007}[/tex]

[tex]\sigma_1 = 0.08[/tex]

For location 2

First, calculate the mean

[tex]\bar x_2 =\frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x_2 =\frac{30.10+30.90+30.20+30.70+30.30}{5}[/tex]

[tex]\bar x_2 =\frac{152.2}{5}[/tex]

[tex]\bar x_2 =30.44[/tex]

The standard deviation is calculated as:

[tex]\sigma_2 = \sqrt{\frac{\sum(x - \bar x_2)^2}{n-1}}[/tex]

[tex]\sigma_2 = \sqrt{\frac{(30.10-30.44)^2+(30.90-30.44)^2+(30.20-30.44)^2+(30.70-30.44)^2+(30.30-30.44)^2}{5-1}}[/tex]

[tex]\sigma_2 = \sqrt{\frac{0.472}{4}}[/tex]

[tex]\sigma_2 = \sqrt{0.118}[/tex]

[tex]\sigma_2 = 0.34[/tex]

Answer:

$375.25

Step-by-step explanation:

[tex]===========================================[/tex]

Withdrew- taking out money (-)

Deposit- putting in money (+)

[tex]===========================================[/tex]

Ray started off with 153.75. He withdraws (-) 71.

[tex]153.75-71=82.75[/tex]

Then he deposits (+) 292.5.

[tex]82.75+292.5=375.25[/tex]

That's your answer!

I hope this helps ❤

Answer:

216

Step-by-step explanation:

y=k÷x

k=xy

k=9×24

k=216

Answer:

(a) A = 20(1.6)^t

(b) 210 rabbits

Step-by-step explanation:

Initial number of rabbits = 20

rate of growth, R = 60 % annually

(A) The general equation is  

[tex]A = P \left ( 1+\frac{R}{100} \right )^t\\\\A = 20\left ( 1+\frac{60}{100} \right )^t\\\\A = 20 (1.6)^t[/tex]

(B) Let the time, t = 5 years

So, the population after 5 years is

[tex]A = 20 (1.6)^5\\\\A = 209.7 = 210 rabbits[/tex]

Answer:

78%

Step-by-step explanation:

the chance of rain

P(R) = 0.9

the chance of wind and rain

P(R∩ W) = 0.7

The probabilities of windy weather is

P(W) = [tex]\frac{P(RW)}{P(R)} =\frac{0.7}{0.9} =0.78[/tex]

The correct answer is B) 78%

Answer:

[tex]Drink = 354.882\ mL[/tex]

Step-by-step explanation:

Given

[tex]Drink = 12oz[/tex]

Required

Equivalent in mL

We have:

[tex]1\ oz = 29.5735\ mL[/tex]

So:

[tex]Drink = 12 * 29.5735mL[/tex]

[tex]Drink = 354.882\ mL[/tex]

Answer:

A and F

Step-by-step explanation:

A and F both represent instances of division of 14/5

B represent multiplication

C represent the reciprocal of the problem, 5/14

D represent addition

Answer:

Step-by-step explanation:

I assume that you mean y = x²/(x²+1), not y = x²/x²+1.

x²+1 = 0

x² = -1

x = ±√(-1) = ±i

deleted: deleted by user

Answer:

n>2 2/3

Draw a filled dot at a little more than 2 1/2 and continue the line to the right.

Step-by-step explanation:

Subtract 1/3 from both sides to get

2 2/3

Flip the inequality

n> 2 2/3

I hope this helps!

Answer

13

Step-by-step explanation:

We are essentially being asked to find f(10), so let's evaluate this function at 10 by plugging this in for x.

f(10)=10/2+8=5+8=13

Answer:

f(x) = 40

Step-by-step explanation:

f(x) = x / 2 * 8

x = 10

f(x) = (10 / 2) * 8

     = 5 * 8

     = 40

Answer:

Your answer is C. X = 29/8c

Step-by-step explanation:

2/3(cx + 1/2) - 1/4 = 5/2

2cx/3+1/3-1/4=5/2

2cx3+1/12=5/2

2cx/3=5/2-1/12

2cx/3=29/12

(3)2cx/3=29/12(3)

2cx= 31/4

(2c)2cx=29/4(2c)

X=29/8c

Your answer is C. X = 29/8c

Answer:

WHAT IS THE FACTOR?

Step-by-step explanation:

Answer:

Step-by-step explanation:

first speed --- x mph

return speed -- x+16 mph

6/x + 6/(x+16) = 1

times each term by x(x+16)

6(x+16) + 6x = x(x+16)

x^2 + 4x - 96 = 0

(x-8)(x+12) = 0

x = 8 or x is a negative

her first speed was 8 mph

her return speed was 24 mph

check:

6/8 + 6/24 = 1 , that's good!

Answer:

8 and 6

Step-by-step explanation:

Two numbers are such that their difference, their sum, and their product are to

each other as 1:7:24. Their product must equal what number?

:

Two numbers a & b

Let x = the multiplier

:

a - b = 1x

a + b = 7x

a * b = 24x

:

Add the 1st two equations

a - b = x

a + b = 7x

2a = 8x

a = 4x

or

x = .25a

:

a * b = 24x

Replace 24x; a = 4x therefore:

a * b = 6a

b = 6

;

Using the 1st equation

a - b = 1x

Replace b with 6 and x with .25a

a - 6 = .25a

a - .25a = 6

.75a = 6

a =

a = 8

:

Find the multiplier

a - b = x

8 - 6 = 2

:

Check this

a - b = 2 (1*2)

a + b = 14; (7*2)

a * b = 48: (24*2)

:

The numbers are 8 and 6; their products = 48

Answer:

x = 960.4

Step-by-step explanation:

980 = 1000[tex]e^{kt}[/tex]

.98 = [tex]e^{10 k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

~~~~~~~~~~~~~~

x = 1000[tex]e^{20 *-.00202}[/tex]

x = 960.4

The amount of the material right after 20 years will be x = 960.4.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

Given that radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now.

The amount of the material will be calculated as,

980 = 1000

[tex]0.98 = e^{10k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

The value after 20 years will be,

[tex]x = 1000e^{20\times 0.00202}[/tex]

x = 960.4

Therefore, the amount of the material right after 20 years will be x = 960.4.

To know more about an exponential expression follow

https://brainly.com/question/2456547

#SPJ5

Answer:

B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.

Step-by-step explanation:

The proportion of male golfers is less than 0.6.

At the null hypothesis, we test if the proportion is of at least 0.6, that is:

[tex]H_0: p \geq 0.6[/tex]

At the alternative hypothesis, we test if the proportion is of less than 0.6, that is:

[tex]H_1: p < 0.6[/tex]

Fail to reject the null hypothesis.

This means that there is not sufficient evidence to conclude that the proportion is less than 0.6, and thus the correct answer is given by option B.

Answer:

[tex]\sqrt{97} \\ \sqrt{9^{2}+4^{2} }[/tex]

Step-by-step explanation:

9514 1404 393

Answer:

  66.5 cm²

Step-by-step explanation:

A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...

  A = LW + 1/2(b1 +b2)h

  A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²

  A = 66.5 cm² . . . . area of the figure

Answer:

See edit

A 20 km / hour

Step-by-step explanation:

The exact answer is 30 km / 172 which is less than 1 km / hr. Since that answer isn't offered, I suspect there is something wrong with the question. If there is a decimal after the 1 in 172 you would get 17.44 km / hr. That's roughly A.

If the decimal is not there, I think you should either resubmit the question or answer A.

Edit

The note said (below) that the ship went 30 km in 1 1/2 hours.

Rate = distance / time

distance = 30 km

time = 1 1/2 hours = 1.5 hours

rate = 30 / 1.5 = 20 km / hr

9514 1404 393

Answer:

  Kim

Step-by-step explanation:

The ratio of Kim's distance to Adrian's distance is ...

  (9/10)/(3/5) = (9/10)/(6/10) = 9/6 = 3/2 = 1.5

__

You need to be very careful with the wording here. Kim ran 1 1/2 times as far as Adrian. That is, she ran Adrian's distance plus 1/2 Adrian's distance.

If we take the wording "1/2 times farther" to mean that 1/2 of Adrian's distance is added to Adrian's distance, then Kim is correct.

_____

In many Algebra problems, you will see the wording "k times farther" to mean the distance is multiplied by k. If that interpretation is used here, neither claim is correct, as Kim's distance is 1 1/2 times farther than Adrian's.

On the other hand, if the value of "k" is expressed as a percentage, the interpretation usually intended is that that percentage of the original distance is added to the original distance. Using this interpretation, Kim's distance is 50% farther than Adrian's. (Note the word "times" is missing here.)

__

Since Adrian ran 1 5/10 the distance Kim ran, Adrian's claim is incorrect regardless of the interpretation. If you require one of the two to be correct, then Kim is.

Answer:

B. No, the two triangles don't have

corresponding sides marked congruent.