Use Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the value of the error. (Round your answers to three significant figures.)
sinh(0.4) ≈ 1 − (0.4)^2 / 2! + (0.4)^2 / 4!
R4 ≤
R4 =
Specifically what does R4 equal.

Answer:

Hey there!

We have two equations, x-2y=6, and y=2x-21.

Thus, we can substitute all y's in the first equation for 2x-21.

x-2(2x-21)=6

x-4x+42=6

-3x+42=6

-3x=-36

3x=36

x=12

y=2(12)-21

y=24-21

y=3

x=12, and y=3.

Hope this helps :)

Answer:

[tex]\boxed{x=12, y=3}[/tex]

Step-by-step explanation:

[tex]x-2y=6\\y=2x-21[/tex]

Plug y as 2x-21 in the first equation.

[tex]x-2(2x-21)=6\\x-4x+42=6\\-3x+42=6\\-3x=-36\\x=12[/tex]

Plug x as 12 in the second equation.

[tex]y=2(12)-21\\y=24-21\\y=3[/tex]

Answer:

[tex]\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}}[/tex]

Step-by-step explanation:

Hello,

[tex]a=bc^2+d \\ \\ <=> a-d=bc^2+d-d=bc^2 \ \text{ subtract d }\\ \\ <=> c^2=\dfrac{a-d}{b} \ \text{ divide by b, assuming b is different from 0}\\ \\<=>\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}} \ \ \text{ take the root of both parts}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

Using elimination method:

2x - y = 7

3x + y = 3

--------------

5x = 10

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{10}{5} [/tex]

Calculate

[tex]x = 2[/tex]

Now, substitute the given value of X in the equation

3x + y = 3

[tex]3 \times 2 + y = 3[/tex]

Multiply the numbers

[tex]6 + y = 3[/tex]

Move constant to R.H.S and change it's sign

[tex]y = 3 - 6[/tex]

Calculate

[tex]y = - 3[/tex]

The possible solution of this system is the ordered pair ( x , y )

---------------------------------------------------------------------

Check if the given ordered pair is the solution of the system of equation

[tex]2 \times 2 - ( - 3) = 7[/tex]

[tex]3 \times 2 - 3 = 3[/tex]

Simplify the equalities

[tex]7 = 7[/tex]

[tex]3 = 3[/tex]

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Step-by-step explanation:

a).

It is given that rate at which the population increases is directly proportional to size of the population. Thus we have,

[tex]\frac{dP}{dt}\propto P[/tex]

It is given in the question that the population increases by 2% in one day. Now we know that the time in days is a continuous variable, so we have

2% of P = [tex]$\frac{2}{100}\times P$[/tex]

[tex]$\therefore \frac{dP}{dt}=0.02 P $[/tex]

b).

It is given that the population is harvested by 4 % in one day

[tex]$\therefore \frac{dP}{dt} =0.02P-0.04P$[/tex]

(Since 4% of the P is harvested.)

[tex]$\therefore \frac{dP}{dt}=-0.02P$[/tex]

c).

It is given that 1000 fish are being harvested or removed in one day.

[tex]$\therefore \frac{dP}{dt}= 0.02 P-1000$[/tex]

d).

The threshold is given by

[tex]$0.02 P_{eq}-1000=0$[/tex]

[tex]$\therefore P_{eq}=\frac{1000}{0.02}$[/tex]

or  [tex]$P_{eq}=5\times 10^4$[/tex]

Answer:

x=60

Step-by-step explanation:

We know that when two secant lines, or a secant line and a tangent line, intersect at a point outside the circle, the measure of the angle formed at the point of intersection is half the difference between measures of the intercepted arcs.

So, we can set up the equation [tex]55=\frac{1}{2} (170-x)[/tex], which will come out to [tex]x=60[/tex].

hope this helps!

Answer: Helen is 8 years old.

Step-by-step explanation:

Given: Helen’s age is a multiple of 4.

i.e. Choices for Helen’s age = 4, 8 , 16, ...

Helen’s older brother is now 19.

That means Helen's age < 19

Choices for Helen's age left = 4, 8, 16

Next year it’ll be a multiple of 3.

That is only possible if Helen's age = 8

Because next year her age = 8+1 = 9 years which is divisible by 3.

Hence, Helen is 8 years old.

Answer:

the parabola opens down

Step-by-step explanation:

The quadratic equation is

ax^2 + bx + c

When a < 0 the parabola opens down

          a > 0 it opens up

since a  = -2 the parabola opens down

Answer:

The correct answer to this question is C: (72,24).

Step-by-step explanation:

We are given that:

The cost of 1 cap is $5 each

The cost of 1 t-shirt is $10 each

Let x be the number of caps sold

Let y be the number of t-shirt sold

In the context we are given that the drama club needs to raise at least $500 to go on the trip.

So based on this information we can create a inequality as:

the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500

Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.

Next we need to figure out how many caps and t-shirt were sold.

- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)

Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )

B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500

YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!

C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.

So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.

Answer: C

Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.

First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.

Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.

So, (8,5) is a valid solution in the context of the situation.

Answer: m = - 2200

Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.

The year a car is bought and its price means:

f(0) = 31,500

Five years later, the price is $20,500, i.e.:

f(5) = 20,500

With these two pairs of value, slope is calculated as:

[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]

[tex]m = \frac{20500-31500}{5-0}[/tex]

[tex]m = \frac{- 1100}{5}[/tex]

m = - 2200

The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.

Answer:

[tex]\frac{109}{122}[/tex]

Step-by-step explanation:

Well first we need to find the total amount of Winter Olympic medals won.

550 + 540 + 130

= 1220

Now we need to find the amount won from the Western and Northern Europe.

550 + 540

= 1090

Now we can make the following fraction,

1090/1220

Simplify

= 109/122

Thus,

the answer is [tex]\frac{109}{122}[/tex].

Hope this helps :)

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

Northern Europe: 550 medals

Western Europe: 540 medals

550 + 540 = 1,090

Northern Europe and Western Europe: 1,090

Other: 130

1,090 + 130 = 1,220

European Regions: 1,220 medals

1,090/1,220 = 109/122

Hope this helped!!  ٩(◕‿◕｡)۶

Answer:

36 cups of Chex total.

Step-by-step explanation:

Well, he will obviously be using 12 cups of pretzels, so let's set that aside. For every cup of pretzels, there are 3 cups of chex. So, multiply 3x12. That will give you how much chex you will need.

sine(X) = opposite side / hypotenuse

sine(X) = (2√11) / (4√11)

sine(X) = (2/4)

sine(X) = 0.5

X = arcsine(0.5)

X = 30°  

Answer: m∠x = 30°

Step-by-step explanation:

In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°

∠x is the smallest one, so  m∠x = 30°

It is possible to figure the sine and get the angle from that, but in this case it might not be necessary.  ;-)

Answer:

Sample size 'n' = 1067

Step-by-step explanation:

Explanation:-

Given margin of error of the true proportion

M.E  = 0.03

The margin of error is determined by

                   [tex]M.E =Z_{\alpha } \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]

Level of significance = 0.95

The critical value Z₀.₀₅ = 1.96

 The margin of error is

                   [tex]0.03 =1.96 \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]

we know that

             [tex]\sqrt{p(1-p} \leq \frac{1}{2}[/tex]

                [tex]0.03 =\frac{1.96 X\frac{1}{2} }{\sqrt{n} }[/tex]

    on cross multiplication , we get

                √n  = 32.66

Squaring on both sides, we get

               n = 1066.6≅1067

Answer:

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  43 out of a random sample of 100 people said they pick their noses at red lights.

sample proportion

                           [tex]p^{-} = \frac{x}{n} = \frac{43}{100} = 0.43[/tex]

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

95% of confidence interval of the proportion of all people who pick their noses at red lights

[tex](p^{-} -Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } ,p^{-} +Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.43 -1.96 \sqrt{\frac{0.43(1-0.43)}{100} } ,0.43 +1.96 \sqrt{\frac{0.43(1-0.43)}{100} })[/tex]

( 0.43 -  0.0958 , 0.43 + 0.0958)

(0.3342 , 0.5258)

Conclusion:-

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)

Answer:

c. $50.37

Step-by-step explanation:

Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.

Answer:

c.50.37

Step-by-step explanation:

Answer:

P = 0,3749       or    P = 37,49 %

Step-by-step explanation:

17 girls play football  10 boys do   ⇒ 27 students

24 girls running  3 boys do   ⇒ 27 students

then  6 girls play tennis  and  12 boys do ⇒ 18 students

Probability of student running P is equal to P1 (probability of student (boy) running ) plus P2 (probability of student (girl) running )

P = P1  +  P2

P1 (probability of girl running ) is equal to choose a girl out of 72 students, times the probability of the girl running

Probability of girl   47/72      =   0,6528

Probability of running is equal to 24/47  = 0,5106

Then the probability of girl running is equal to

P2 = 0,6528*0,5106  =  0,3333    or   33,33 %

P2 = 0,3333    or     P2 = 33,33 %

Now we have 72 students 25 boys, then the probability of choosing a boy is  = 25/72    =  0,3472

And the probability of running is 3/25 = 0,12

Then

P1 = 0,3472*0,12

P1 = 0,04166   and

P = P1 + P2

P = 0,04166 + 0,3333

P = 0,3749       or    P = 37,49 %

Answer:

Option D is correct.

Angle C = 70°

Step-by-step explanation:

The sum of angles in a triangle = 180°

So,

(Angle A) + (Angle B) + (Angle C) = 180°

(Angle A) = 67°

(Angle B) = 43°

(Angle C) = ?

67° + 43° + (Angle C) = 180°

Angle C = 180 - 67 - 43 = 70°

Angle C = 70°

Hope this Helps!!!

Answer: 4 years after the original investment, it is approximately $1,093.

Step-by-step explanation:

Hi, to answer this question we have to apply the simple interest formula:  

I = p x r x t

Where:  

I = interest

P = Principal Amount  

r = Interest Rate (decimal form)  

t= years

Replacing with the values given  

I = 1000x (2.25/100) x t

I = 1000x (2.25/100) x 3 =67.5

1000+67.5 = 1067.5

I = 1000x (2.25/100) x 4 =90

1000+90 = $1090

I = 1000x (2.25/100) x 10 =225

1000+90 = $1225

Feel free to ask for more if needed or if you did not understand something.

Answer:

Step-by-step explanation:

The height of the house, the ground and the ladder forms a right angle triangle, with the following parameters stated below.

1. the hypotenuse is the length of the ladder which is 30 feet

2.the opposite is the height of the house, which is 25 feet

3. the adjacent is the distance of the ladder away from the building, this is the parameter we are solving for.

Since we have two sides of the triangle given, we can employ Pythagoras theorem to solve for the third side of the triangle

let the the opposite be x

we know that

[tex]hyp^2= opp^2+adj^2\\\\ 30^2= x^2+25^2\\\\ 900= 625+x^2\\[/tex]

Solving for x we have

[tex]x^2= 900-625\\\\X^2= 275\\\\x=\sqrt{275} \\\\x= 16.58[/tex]

Hence the maximum distance away from house that he can place

the ladder is 16.6 ft to the nearest foot

Answer:

95% confidensce interval of the mean (two-tail) =  [132.2, 139.2]

Step-by-step explanation:

Given:

N = size of sample = 61

m = sample mean = 135.7

s = sample standard deviation 13.7

Need 95% confidence interval

Solution.

alpha (95% confidence interval) = 0.05

(1-alpha/2) = 0.975   [two sided]

Equation for confidence interval of the mean

= m +/- t(1-alpha/2,N-1) * s / sqrt(N)

= 135.7 +/- 2.0003 * 13.7 / sqrt(60)

= [132.16, 139.24]

Answer:

The value of the cosine function at 37º is 0.80. A. 0.80

Step-by-step explanation:

The correct statement is: "If the secant of 37º is 1.25, the cosine value to the hundredths degree is:"

Secant and cosine functions are related by the following trigonometric identity:

[tex]\sec 37^{\circ} = \frac{1}{\cos 37^{\circ}}[/tex]

[tex]\cos 37^{\circ} = \frac{1}{\sec 37^{\circ}}[/tex]

[tex]\cos 37^{\circ} =\frac{1}{1.25}[/tex]

[tex]\cos 37^{\circ} = 0.80[/tex]

The value of the cosine function at 37º is 0.80. The right answer is A.

Answer:

r = 90/30

r = 3

T12 = 10 × 3¹¹

T12 = 1771470

Answer:

a) the K-map is in the attachment

f = Σm(0,1,2,3,6,10,14,15)

b) from the k-map, the minimum sum of products is

F = A'B' + CD' + ABC

c) the minimum product of sums is

F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')

Step-by-step explanation:

A Karnaugh map (K-map) is a pictorial framework used to limit the Boolean expressions without utilizing Boolean algebra theorems and equation controls.

a) the given function is f(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’

expanding the function as four variable terms

f(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’

= A'B'(C + C')(D + D')+(A + A')(B + B")CD' + ABC(D + D') + A'B'CD' + ABCD'

= A'B'CD + A'B'CD' + A'B'C'D' + ABCD' +AB'CD' + A'BCD' + A'B'CD' + ABCD +ABCD' + A'B'CD' + ABCD'

=A'B'CD + A'B'CD' + A'B'C'D + A'B'C'D' + ABCD' + AB'CD' + A'BCD' +ABCD

f = Σm(0,1,2,3,6,10,14,15)

note: diagram is in the attachment

b) the minterms for the minimum sum of product are

f = Σm(0,1,2,3,6,10,14,15)

simplifying the K-map(done in the attachment)

from the k-map, the minimum sum of products is

F = A'B' + CD' + ABC

c) the maxterms for the minimum product of sums are

f = ПM(4,5,7,8,9,11,12,13)

plot the K-map to find minimum product of sums(done in the attachment)

the minimum product of sums is

F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')

Answer: The required number of heads = 30

Step-by-step explanation:

Given, Total tosses = 50

The theoretical probability of getting head = [tex]\dfrac{1}{2}[/tex]

As per given,

Experimental probability = Theoretical probability + 20% of Theoretical probability

= [tex]\dfrac{1}{2}+\dfrac{20}{100}\times\dfrac{1}{2}[/tex]

= [tex]\dfrac{1}{2}+\dfrac{1}{10}=0.5+0.1=0.6[/tex]

Required number of heads = (Experimental probability) x (Total tosses )

= 0.6 x 50

= 30

Hence, the required number of heads = 30

For example: {(1,2), (3,4), (2,3), (4,1))}

Answer:

35 is the Answer

Answer:

The final price to be paid after the 2% discount has been made will be $ 16,645.30.

Step-by-step explanation:

Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:

16,985 x 2/100 = X

33,970 / 100 = X

339.70 = X

Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.

Answer:

P(success at first attempt) = 0.1353

Step-by-step explanation:

This question follows poisson distribution. Thus, the formula is;

P(k) = (e^(-G) × (G)k)/k!

where;

G is number of frames generated in one frame transmission time(or frame slot time)

Let's find G.

To do this, we need to find number of frames generated in 1 slot time which is given as 50 ms.

Now, in 1000 ms, the number of frames generated = 50

Thus; number of frames generated in 50 ms is;

G = (50/1000) × 50

G = 2.5

To find the chance of success on the first attempt will be given by;

P(success at first attempt) = P(0) = e^(-G) = e^(-2) = 0.1353

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

Answer:

d) d(x)

Step-by-step explanation:

Derivative Rules

Answer:

2 minutes

Step-by-step explanation:

You need to first subtract 9 from 11 and you get 2 minutes.

11 minutes will it take to fill the tub by both hot and cold water faucets.

What is Time?

Time as the progression of events from the past to the present into the future.

Given that,

the cold water faucet can fill the tub in 9 minutes

The hot water faucet can fill the tub in 11 minutes.

If both the faucets are used together then it takes 11 minutes to fill the tub because it takes longer time for hot water faucet to fill the tub.

Therefore it takes 11 min to fill the tub together.

To learn more on Time click:

https://brainly.com/question/28050940

#SPJ5

Answer:

(x-1)²=-10(y-0.5)

Step-by-step explanation: