Find constants b and c in the polynomial p (x )equals x squared plus bx plus cp(x)=x2+bx+c such that ModifyingBelow lim With x right arrow 4 StartFraction p (x )Over x minus 4 EndFraction equals 10limx→4 p(x) x−4=10. Are the constants​ unique?

Answer:

10 oz

Step-by-step explanation:

there are 16 oz in a pound. 4 * 16 = 64 so she needs 64 oz in all. she has 26 oz of walnuts and 28 oz of cashews. add these together and subtract it from 64 to find how many oz of peanuts she needs.

26 + 28 = 54

64 - 54 = 10

she needs 10 oz of peanuts

The dimension of pen is 42 feet by 36 feet

Solution:

Let "x" be the width of pen

Let "y" be the length

Farmer wants each side of the pen to be at least 20 feet long

[tex]x\geq 20[/tex]

The farmer has 120 feet of fence to enclose an area of 1512 square feet

The amount of fencing is equal to the perimeter of fence which is 2 times the width plus only one length since the other side (length) is along the barn

2x + y = 120

Therefore,

y = 120 - 2x

The area of barn is given as 1512 square feet

The area of rectangle is given as:

[tex]Area = length \times width[/tex]

[tex]1512 = x \times y\\\\1512 = x \times (120-2x)\\\\1512 = 120x - 2x^2\\\\2x^2-120x + 1512 = 0[/tex]

Divide the entire equation by 2

[tex]x^2-60x + 756 = 0[/tex]

Factor the left side of equation

[tex]x^2-60x+756 = 0\\\\(x-18)(x-42) = 0[/tex]

Therefore, we get two values of "x"

x = 18 or x = 42

Since, [tex]x\geq 20[/tex]

Therefore, x = 42 is the solution

Thus, width = x = 42 feet

Length = y = 120 - 2x

y = 120 - 2(42)

y = 120 - 84

y = 36

Thus the dimension of pen is 42 feet by 36 feet

The area of a shape is the amount of space it occupies.

The dimension of the pen is 42 by 36 feet.

The perimeter is given as:

[tex]\mathbf{P = 120}[/tex]

Because one of the sides does not need fencing, the perimeter would be:

[tex]\mathbf{P = 2x + y}[/tex]

Make y the subject

[tex]\mathbf{y = P - 2x}[/tex]

Substitute 160 for P

[tex]\mathbf{y = 120 - 2x}[/tex]

The area of a pen is:

[tex]\mathbf{A = xy}[/tex]

Substitute [tex]\mathbf{y = 120 - 2x}[/tex]

[tex]\mathbf{A = x(120 -2x)}[/tex]

Substitute 1512 for Area

[tex]\mathbf{x(120 -2x) = 1512}[/tex]

Open brackets

[tex]\mathbf{120x -2x^2 = 1512}[/tex]

Rewrite as:

[tex]\mathbf{2x^2 -120x + 1512 = 0}[/tex]

Divide through by 2

[tex]\mathbf{x^2 -60x + 756 = 0}[/tex]

Expand

[tex]\mathbf{x^2 -18x - 42x + 756 = 0}[/tex]

Factorize

[tex]\mathbf{(x -18)(x - 42) = 0}[/tex]

Solve for x

[tex]\mathbf{x =18 \ or\ x = 42}[/tex]

The dimension must be at least 20.

So, we have:

[tex]\mathbf{x = 42}[/tex]

Recall that:

[tex]\mathbf{y = 120 - 2x}[/tex]

This gives:

[tex]\mathbf{y = 120 - 2 \times 42}[/tex]

[tex]\mathbf{y = 36}[/tex]

Hence, the dimension of the pen is 42 by 36 feet.

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Answer: This relation is reflexive, antisymmetric and transitive so it is a partial order relation.

Step-by-step explanation: A relation is called a partial order relation if and only if it is reflexive, antisymmetric and transitive. We will check these three characteristics for the given relation.

Reflexive: We need to have that for all [tex]x\in\mathbb{N}[/tex], [tex]xRx[/tex]. This is obviously true since each prime factor of [tex]x[/tex] is certainly a factor of [tex]x[/tex].

Antisymmetric: We need to show that for all [tex]x,y\in\mathbb{N}[/tex] if both [tex]xRy[/tex] and [tex]yRx[/tex] then it must be [tex]x=y[/tex]. To show this suppose that two, otherwise arbitrary, natural numbers [tex]x[/tex] and [tex]y[/tex] are taken such that [tex]xRy[/tex] and [tex]yRx[/tex]. The first of these two says that every prime factor of [tex]x[/tex] is a factor of [tex]y[/tex]. The second one says that every prime factor of [tex]y[/tex] is a factor of [tex]x[/tex]. This means that every prime factor of [tex]x[/tex] is also the prime factor of [tex]y[/tex] and that every prime factor of [tex]y[/tex] is the prime factor of [tex]x[/tex] i.e. that [tex]x[/tex] and [tex]y[/tex] have the same prime factors meaning that they have to be equal.

Transitive: The relation is called transitive if from [tex]xRy[/tex] and [tex]yRz[/tex] then it must also be [tex]xRz[/tex]. To see that this is true of the given relation take some natural numbers [tex]x,y[/tex] and [tex]z[/tex] such that [tex]xRy[/tex] and [tex]yRz[/tex]. The first condition means that each prime factor of [tex]x[/tex] is the factor of [tex]y[/tex] i.e. that all the prime factors of [tex]x[/tex] are contained among the prime factors of [tex]y[/tex]. The second condition means that each prime factor of [tex]y[/tex] is a factor of [tex]z[/tex] i.e. that all the prime factors of [tex]y[/tex] are contained among the prime factors of [tex]z[/tex]. So we have that all of the prime factors of [tex]x[/tex] are contained among the prime factors of [tex]y[/tex] and they themselves are contained among the prime factors of [tex]z[/tex]. This means that certainly all of the prime factors of [tex]x[/tex] are contained among the prime factors of [tex]z[/tex] meaning by the given definition of [tex]R[/tex] that [tex]xRz[/tex] which is what we needed to show.

416.67 pounds of food should be given all five lions each day

Solution:

Given that, three adult lions together eat 250 pounds of food a day

Thus, 3 adult lions = 250 pounds of food per day

Two more adult lions joined the group and ate food at the same rate as the original three

Now number of adult lions = 3 adult lions + 2 adult lions = 5 adult lions

Let "x" be the food ate by 5 adult lions

Thus we can say,

3 adult lions = 250 pounds of food per day

5 adult lions = "x" pounds of food per day

This forms a proportion and we can solve the sum by cross multiplying

[tex]\frac{3}{5} = \frac{250}{x}\\\\3 \times x = 250 \times 5\\\\3x = 1250\\\\x = 416.67[/tex]

Thus 416.67 pounds of food should be given all five lions each day

Answer:

0.0079 cm.

Step-by-step explanation:

We have been given that the last page of a book is numbered 764. The book is 3.0 cm thick, not including its covers.

We know that each page is marked on both sides, so we will find total number of pages by dividing 764 by 2 as:

[tex]\text{Total number of pages}=\frac{764}{2}[/tex]

[tex]\text{Total number of pages}=382[/tex]

To find the average thickness of each page, we will divide thickness of book by total number of pages as:

[tex]\text{Average thickness of each page}=\frac{3.0}{382}[/tex]

[tex]\text{Average thickness of each page}=0.0078534031413613[/tex]

We can see that there are 3 significant figures in 764 and 2 significant digits in 3.0.

We know that the result of a multiplication or division is rounded to the number of significant figures equal to the smallest number of significant figures among the numbers being multiplied/divided. So we need to round our answer to 2 significant digits.  

[tex]\text{Average thickness of each page}\approx 0.0079[/tex]  

Therefore, the average thickness of each page is approximately 0.0079 cm.

Answer:

34.8

Step-by-step explanation:

1. Convert percent to decimal

40.00/100=.4

2.Multiply decimal by subtotal

87*.4=34.8

Peter will save $34.80 on the coat.

Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is often denoted by the symbol "%".

If the coat is on sale for 40% off, Peter will only need to pay 60% of the original price.

60% of $87 can be calculated as follows:

= 60/100 x $87

= $52.20

Therefore, the amount that Peter will save on the coat is:

= $87 - $52.20

= $34.80

So, Peter will save $34.80 on the coat.

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Answer: 0.031 .

Step-by-step explanation:

The standard error of the sample proportion is given by :-

[tex]SE_p=\sqrt{\dfrac{p(1-p)}{n}}[/tex]

, where p= Sample proportion and n is the sample size.

As per given , we have

In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery.

i.e. p= 0.25 and n= 200

Then , the  standard error of the sample proportion [tex]=\sqrt{\dfrac{0.25(1-0.25)}{200}}[/tex]

[tex]=\sqrt{\dfrac{0.25\times0.75}{200}}=\sqrt{0.0009375}\\\\=0.0306186217848\approx0.031[/tex]

Hence, the standard error of the sample proportion is approximately 0.031 .

Final answer:

The standard error of the sample proportion is approximately 0.0306.

Explanation:

The standard error of a sample proportion can be calculated using the formula:

Standard Error = √((p)(1-p)/n)

where p is the proportion of the sample and n is the sample size. In this case, the proportion is 0.25 (since 25% of the sample is strongly opposed to having a state lottery) and the sample size is 200. Plugging these values into the formula:

Standard Error = √((0.25)(1-0.25)/200) = √(0.1875/200) = √(0.0009375) = 0.0306

So, the standard error of the sample proportion is approximately 0.0306.

Answer:

a) Number of calories burned in [tex]x[/tex] hours of cycling [tex]600x[/tex] and Number of calories burned in [tex]y[/tex] hours of Swimming is [tex]400y[/tex].

b)The equation in general form that relates number of hours of cycling and swimming carols needs to perform to loose 5 pounds is [tex]6x+4y=160[/tex].

Step-by-step explanation:

Given:

5 pounds of body fat = 16000 calories

Number of calories burn in 1 hour of cycling = 600

Number of calories burn in 1 hour of swimming = 400

Part a:

We need to find number of calories will Carol burn in [tex]x[/tex] hours of cycling and number of calories will Carol burn in [tex]y[/tex] hours of swimming.

Solution:

Now we know that;

1 hr of cycling = 600 calories burned

[tex]x[/tex] hr of cycling = Number of calories burned in [tex]x[/tex] hours of cycling.

By using Unitary method we get;

Number of calories burned in [tex]x[/tex] hours of cycling = [tex]600x[/tex]

Also we know that;

1 hr of swimming= 400 calories burned

[tex]y[/tex] hr of swimming = Number of calories burned in [tex]y[/tex] hours of swimming.

By using Unitary method we get;

Number of calories burned in [tex]y[/tex] hours of Swimming = [tex]400y[/tex]

Hence Number of calories burned in [tex]x[/tex] hours of cycling [tex]600x[/tex] and Number of calories burned in [tex]y[/tex] hours of Swimming is [tex]400y[/tex]

Part b:

We need to write equation in general form that relates number of hours of cycling and swimming carols needs to perform to loose 5 pounds.

Solution:

Now given;

5 pounds = 16000 calories.

So we can say that;

Total number of calories to be burn is equal to sum of Number of calories burned in [tex]x[/tex] hours of cycling  and Number of calories burned in [tex]y[/tex] hours of Swimming.

framing in equation form we get;

[tex]600x+400y=16000[/tex]

Now dividing both side by 100 we get;

[tex]\frac{600x}{100}+\frac{400y}{100}=\frac{16000}{100}\\\\6x+4y=160[/tex]

Hence the equation in general form that relates number of hours of cycling and swimming carols needs to perform to loose 5 pounds is [tex]6x+4y=160[/tex].

Answer:

Step-by-step explanation:

So 8 times more than 2/3

The total ascension of the swimmer can be calculated by multiplying the distance ascended each time by the number of ascents, resulting in 5 and 1/3 meters.

The total ascension of the swimmer can be calculated by multiplying the distance ascended each time by the number of ascents. In this case, the swimmer ascended 2/3 meters 8 times.

Total ascension = 2/3 meters * 8 ascents = 16/3 meters = 5 and 1/3 meters.

Therefore, the distance representing the swimmer's total ascension is 5 and 1/3 meters.

Answer:

The answer to your question is a) y = x - 1  b) the point is not on the line

Step-by-step explanation:

Data

A ( -1, -2)

B (4, 3)

C ( 3, 1)

Process

1.- Find the slope of the line (m)

Formula

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

Substitution

m = [tex]\frac{3 + 2}{4 + 1} = \frac{5}{5} = 1[/tex]

2.- Find the equation of the line

Formula

    y - y1 = m(x - x1)

Substitution

    y + 2 = 1(x + 1)

Solve for y

   y = x + 1 - 2

   y = x - 1

- Prove that the point (3, 1) is on the line

  1 = 3 - 1

  1 = 2

The point is not on the line because  1 ≠ 2

Answer:

a) The probability is %55

b) The probability is %0.15

c) The probability is %9.15

d) The probability is %91.85

Step-by-step explanation:

a) We need to basically subtract probability of 0 type blood from 1:

P=1-0.45=0.55

b) The probability of one person that is having A blood type is %11. Then probability of four persons that are having A blood type will be:

(0.11)^4=0.00015

c) We need to approach to this question same as B. Probability of having not 0 type of blood is %55. Then probability of four persons that are not having 0 type of blood will be:

(0.55)^4=0.0915

d) To find the probability we can simply subtract probability of four persons that are having 0 type blood from 1:

1-0.0915=0.9185

Answer:

Option 2) A binomial variable with 25 independent trials                  

Step-by-step explanation:

We are given the following in the question:

Sample size = n

R: the number of people from the sample who answer yes to the question whether they have read a novel in the past year.

[tex]var(R) = 6[/tex]

[tex]p =0.40[/tex]

Then, the random variable R follows a binomial distribution:

[tex]var(R) = npq\\6 = n(0.4)(1-0.4)\\\\n = \dfrac{6}{0.4\times 0.6}\\\\n = 25[/tex]

Thus, R is a binomial variable with 25 independent trials.

Answer:

A binomial variable with 25 independent trials

Answer:

Mathematical modeling

Step-by-step explanation:

Mathematical modeling is defined as translating the problems from an application area using the mathematical formulas.

The numerical analysis and theoretical analysis gives an insight and answers or guidance which is useful for the originating application.

It provides with the precision and direction for the solution of the problem.

Answer:

The linear equation representing cost after using coupon is [tex]y=x-18[/tex].

Step-by-step explanation:

Given:

Value of coupon = $18

Let the cost of the calculator be 'x'.

And the Cost after redeeming the coupon be 'y'.

We need to write a linear equation to represent using the coupon.

Solution:

Now we can say that;

Cost after redeeming the coupon will be equal to cost of the calculator minus Value of coupon.

framing in equation form we get;

[tex]y=x-18[/tex]

Hence The linear equation representing cost after using coupon is [tex]y=x-18[/tex].

Answer: the correct option is D

Step-by-step explanation:

Note: the chapter summary can be found in chapter 22 of the Pearson Education,Inc. (PDF format).

In the chapter, a single slit aperture diffraction and a circle aperture diffraction was discussed.

A circle aperture diffraction occurs when light pass through a tiny hole or aperture to produce a circular disc image. This disc is called Airy's disc.

To calculate the aperture diameter,d we can use the formula below;

d= m× λ/ sin θ. ------------------------------------------------------------------------------(1).

The single slit aperture diffraction is when light pass through a single slit to produce. The wavelength, λ is greater than the width of the aperture.

Answer:

Italian style = 19,000 packages

French style = 13,000 packages

Oriental style = 53,000 packages

Step-by-step explanation:

let the number of packages of Italian style = x

let the number of packages of French style = y

let the number of packages of Oriental style = z

See the attached table which summarize the problem

Using the table we can get the following system of equations:

0.4x + 0 * y + 0.2z = 18,200

0.3x + 0.5y + 0.3z = 28,100

0.3x + 0.5y + 0.5z = 38,700

Solving the 3 equations together to find x , y and z

Using the calculator

x = 19,000

y = 13,000

z = 53,000

Answer:

  A.  $12

Step-by-step explanation:

For a quadratic of the form ax²+bx+c, the axis of symmetry is given by ...

  x=-b/(2a)

For your quadratic function, the axis of symmetry is ...

  s = -(2400)/(2(-100)) = 12

The function has its extreme value on the axis of symmetry. Here, the leading coefficient is negative, so the parabola opens downward. That means the extreme value is a maximum.

Profit will be a maximum at a selling price of $12.

Answer:

275 people more attended the play on Saturday then on Friday.

Step-by-step explanation:

Given:

number of people attended play on Friday = 537

Number of people attended play on Saturday = 812.

We need to find how many people more attended the play Saturday then on Friday.

Solution:

Now we can say that;

To find Number of people more attended the play on Saturday then on Friday can be calculated by subtracting the number of people attended play on Friday from Number of people attended play on Saturday.

framing in equation form we get;

Number of people more attended = [tex]812-537 = 275[/tex]

Hence 275 people more attended the play on Saturday then on Friday.

There are 659 blocks

Solution:

The number in ones place is 9

Let's denote number in the tens place with x

The number in the hundreds place is one more then the tens place

Therefore,

The number in hundreds place is 1 + x

Those two numbers equal 11

Which means tens place number and hundreds place number sums up to 11

tens place + hundreds place = 11

x + 1 + x = 11

2x = 11 - 1

2x = 10

x = 5

Thus number in tens place = x = 5

Number in hundreds place = 1 + x = 1 + 5 = 6

The number is represented as:

Number = (Number in hundreds place)(number in tens place)(number in ones place)

Number = 659

Thus 659 blocks are there

Answer:

4.41 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a man flies a kite at a height of 16 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. We are asked to find how fast must he let out the string when the kite is flying on 34 ft. of string.

We will use Pythagoras theorem to solve for the length of side x as:

[tex]x^2+16^2=34^2[/tex]

[tex]x^2=34^2-16^2[/tex]

[tex]x^2=900\\\\x=30[/tex]

Now, we will use Pythagorean theorem to relate x and y because we know that the vertical side (16) is always constant.

[tex]x^2+16^2=y^2[/tex]

Let us find derivative of our equation with respect to time (t) using power rule and chain rule as:

[tex]2x\cdot \frac{dx}{dt}+0=2y\cdot \frac{dy}{dt}[/tex]

We have been given that [tex]\frac{dx}{dt}=5[/tex] , [tex]y=34[/tex] and [tex]x=30[/tex].

[tex]2(30)\cdot 5=2(34)\cdot \frac{dy}{dt}[/tex]

[tex]300=68\cdot \frac{dy}{dt}[/tex]

[tex]\frac{dy}{dt}=\frac{300}{68}[/tex]

[tex]\frac{dy}{dt}=4.4117647058823529[/tex]

[tex]\frac{dy}{dt}\approx 4.41[/tex]

Therefore, the man must let out the string at a rate of 4.41 feet per second.

To find the point at which the total cost of rental is the same for both companies, set the cost functions C(m) and T(m) equal to each other and solve for m. In this case, the car needs to be driven approximately 273 miles.

To determine the number of miles, m, that a car needs to be driven in a day to equal the total cost at both rental companies, we need to find when C(m) is equal to T(m).

C(m) = $41 + $0.10m

T(m) = $0.25m

Setting these two equations equal to each other gives the equation $41 + $0.10m = $0.25m. Solve this equation to find the value of m.

Subtract $0.10m from both sides, leaving: $41 = $0.15m. Next, divide both sides by $0.15 to obtain the value of m, which is m = $41/$0.15 = 273.33. Therefore, the car needs to be driven approximately 273 miles for the rental cost to be the same at both companies.

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Answer:

Harry had $90 and Kayla had $120 at the beginning.

Step-by-step explanation:

Given:

Initial amount of Harry's money = 75% of Kayla's initial amount.

Harry earned $30 and Kayla earned 25% more.

Harry's final amount = 80% of Kayla's final amount.

Let the initial amount of Kayla be 'x'.

As per question:

Initial amount of Harry's money = 75% of Kayla's initial amount.

Initial amount of Harry's money = 75% of [tex]x[/tex]

Initial amount of Harry's money = [tex]0.75x[/tex]

Now, Harry earned $30 more. So, total amount of Harry is given as:

Final amount of Harry's money = [tex]0.75x+30[/tex]

Kayla also earned 25% more of her money. So, final amount of Kayla's money is given as:

Kayla's final amount = [tex]x+25\%\ of\ x=x+0.25x=1.25x[/tex]

Now, again as per question:

Harry's final amount = 80% of Kayla's final amount.

[tex]0.75x+30=0.80\times 1.25x[/tex]

[tex]0.75x+30=1x[/tex]

[tex]1x-0.75x=30[/tex]

[tex]0.25x=30[/tex]

[tex]x=\frac{30}{0.25}=\$120[/tex]

Therefore, initial money Kayla had = $120

Initial money Harry had = [tex]0.75x=0.75\times 120=\$90[/tex]

Hence, Harry had $90 and Kayla had $120 at the beginning.

To find the height of the football field at a distance of 35 feet from the side, you plug x=35 into the equation h=-0.00025x^2 + 0.04x, resulting in a height of 1.1 feet after rounding to the nearest tenth.

To find the height of the football field a distance of 35 feet from the side, we will substitute the value of x into the given quadratic equation h = -0.00025x2 + 0.04x. We can follow these steps:

Question is Incomplete; Complete question is given below;

Chase purchased a sweatshirt from the clearance rack. The price of the sweatshirt after the discount is represented by the expression ​0.75x, where ​x  represents the original price of the sweatshirt.

Which expression also represents the discounted price of the sweatshirt?

A  (0.75​ −​ 0.25)x  

B  ​(0.75​ +​ 0.25)x  

C  x​ –​ 0.25x  

D  ​x​ +​ 0.25x

Answer:

C . [tex]x-0.25x[/tex]

Step-by-step explanation:

Given:

Expression representing price of the sweatshirt after the discount = [tex]0.75x[/tex]

[tex]x[/tex] ⇒ original price of sweatshirt

We need to find the expression which also represents the discounted price of the sweatshirt.

Solution:

Form the given expression we can see that after discount we are paying only 75% of the original amount of sweatshirt.

So we can say that;

The discount price was 25% of the original price i.e [tex]0.25x[/tex]

So now we can say that;

Price after discount is equal to difference of original price and discounted price.

framing in equation form we get;

Price after discount = [tex]x-0.25x[/tex]

Hence the equivalent expression for the given discounted price of sweatshirt is  [tex]x-0.25x[/tex].

Answer:

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

12 a 2 in box # 1

4-6a for box # 2

2a*2+8a box # 3

12a*2- 8 a box # 4

have a good day hope this helps

Answer:

The answer to your question is  below

Step-by-step explanation:

Remember that the greatest common factor of a set of numbers is the greatest factor common to all the numbers.

              Greatest common factor        Factor           Expression

                           2a²  + 8a                  2a(a + 4)                2a

                          12a² - 8a                 4a(3a - 2)                4a

                            4a + 8                     4(a + 2)                    4

                            4 - 6a                      2(2 - 3a)                  2

Step-by-step explanation:

We have equation for volume of a sphere

             [tex]V=\frac{4}{3}\pi r^3[/tex]

where r is the radius

Differentiating with respect to time,

            [tex]\frac{dV}{dt}=\frac{d}{dt}\left (\frac{4}{3}\pi r^3 \right )\\\\\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}[/tex]

Given that

           Radius, r = 24 cm

           [tex]\frac{dr}{dt}=0.3cm/s[/tex]

Substituting

           [tex]\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi \times 24^2\times 0.3\\\\\frac{dV}{dt}=2171.47cm^3/min[/tex]

At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.

Answer:

[tex]y=4e^{-(x+1)}[/tex] will be the solutions.

Step-by-step explanation:

The given equation is [tex]y=C_{1}e^{x}+C_{2}e^{-x}[/tex]

Therefore, for x = -1

[tex]4=C_{1}e^{-1}+C_{2}e^{1}[/tex] ------(1)

Now y'(-1) = -4

y'(x) = [tex]C_{1}e^{x}-C_{2}e^{-x}[/tex] = -4

[tex]C_{1}e^{-1}-C_{2}e^{1}[/tex] = -4 -----(2)

By adding equation (1) and (2)

[tex]2C_{1}e^{-1}=0[/tex]

[tex]C_{1}=0[/tex]

From equation (1),

[tex]4=0+C_{2}e^{1}[/tex]

[tex]C_{2}=4e^{-1}[/tex]

By placing the values in the parent equation

y = [tex]4e^{-1}\times e^{-x}[/tex]

y = [tex]4e^{-(x+1)}[/tex]

Answer:

Stephen's wife got £354 more than his son.

Step-by-step explanation:

Given:

Amount of Lottery = £2950

Now Given:

Stephen & Richard share a lottery amount in the ratio 2 : 3

Let the common factor between them be 'x'.

So we can say that;

[tex]2x+3x=2950\\\\5x = 2950[/tex]

Dividing both side by 5 we get;

[tex]\frac{5x}{5}=\frac{2950}{5}\\\\x = 590[/tex]

So we can say that;

Stephen share would be = [tex]2x =2\times 590 = \£1180[/tex]

Now Given:

Stephen then shares his part between himself, his wife & their son in the ratio 3 : 5 : 2.

Let the common factor between them be 'y'.

So we can say that;

[tex]3y+5y+2y=1180\\\\10y=1180[/tex]

Dividing both side by 10 we get;

[tex]\frac{10y}{10}=\frac{1180}{10}\\\\y=118[/tex]

So Stephen's wife share = [tex]5y = 5\times 118= \£590[/tex]

And Stephen's son share = [tex]2y=2\times118 =\£236[/tex]

Now we need to find how much more her wife got then her son.

To find how much more her wife got than her son we will subtract Stephen's son share from Stephen's wife share.

framing in equation form we get;

Amount more her wife got than her son = [tex]590-236 = \£354[/tex]

Hence Stephen's wife got £354 more than his son.

Answer:

heres your answers

Step-by-step explanation:

George Washington  was defeated  when he went to fight the French in the Ohio River Valley.

The British then sent a trained army to attack the French Fort Duquesne.

The British suffered a defeat in the first battle of the French Indian War.

Answer:

Step-by-step explanation:

A nickel is worth 5 cents. Converting to dollars, it becomes

5/100 = $0.05

A dime is worth 10 cents. Converting to dollars, it becomes

10/100 = $0.1

Let x represent the number if nickels.

Let y represent the number of dimes.

He has no more than 19 coins. This means that

x + y ≤ 19

He has no less than $1.30 combined. This means that

0.05x + 0.1y ≥ 1.3

If Nolan has 5 nickels, then, substituting x = 5 into x + y ≤ 19, it becomes

5 + y ≤ 19

y ≤ 19 - 5

y ≤ 14

substituting x = 5 into 0.05x + 0.1y ≥ 1.3, it becomes

0.05 × 5 + 0.1y ≥ 1.3

0.25 + 0.1y ≥ 1.3

0.1y ≥ 1.3 - 0.25

0.1y ≥ 1.05

y ≥ 1.05/0.1

y ≥ 10.5

Therefore, all possible values for the number of dimes that he could have would be

10.5 ≤ y ≤ 14