The fish store is filling their 5 1/2 gallon tanks for a speacial fish display.They have filled 4 1/2 tanks so far.How many gallons of water have they used?

Answer:

65.83

Step-by-step explanation:

The total amount Mr. And Mrs. Kingsley have to leave if Their dinner bill came to $57.24, If they wish to leave, a 15% tip is $65.83.

As it is clear from the term per cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

The dinner bill is $57.24,

The tip percentage = 15%,

Calculate the amount of the tip as shown below,

The amount of the tip = 15% of 57.24

The amount of the tip = 15 / 100 × 57.24

The amount of the tip = 0.15 × 57.24

The amount of the tip = 8.586

Hence, total amount = tip amount + bill amount

Total amount = 57.24 + 8.586

Total amount = 65.83

Thus, the total amount is $65.83.

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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:

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.

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:

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: 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.

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

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.

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:

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.

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:

August D is the fastest rapper. XD

Step-by-step explanation:

Answer:

Based on this info I would say that Mark Lee does because he is at 90.0 sps.

Step-by-step explanation:

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:

a). 170 miles

b). Planes will be 500 miles apart after 1.1 hours.

Step-by-step explanation:

a). Two planes heading towards North and South when passed each other were 80 miles apart.

Distance between these planes after 20 minutes or [tex]\frac{1}{3}[/tex] hours.

From the figure attached,

In right angle triangle DEC,

DE = 80 miles

BE = (Speed × duration) = [tex]300\times \frac{1}{3}=100[/tex] miles

Similarly, BC = [tex]150\times \frac{1}{3}=50[/tex] miles

By Pythagoras theorem,

DC² = EC² + DE²

       = (EB + BC)² + DE²

       = (100 + 50)² + (80)²

       = 28900

DC = √28900 = 170 miles

b). Now we have to evaluate the duration after which distance between the planes is 500 miles.

Let after t hours planes will be 500 miles apart.

Then EB = 300t

BC = 150t

Therefore, EC = EB + BC = 450t

It's given that DC = 500 miles

By Pythagoras theorem again,

DC² = EC²+ DE²

(500)²=  (450t)²+ (80)²

250000 = 202500t² + 6400

2500 = 2025t² + 64

2025t² = 2436

t² = 1.20297

t = 1.097 hours ≈ 1.1 hours

Therefore, both the planes will be 500 miles apart after 1.1 hours.

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 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:

2.

Step-by-step explanation:

Healthy baby.

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:

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.

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

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.

Final answer:

The total weight of books on the last book cart is 216 pounds, found by dividing the total number of books by the number of carts and then multiplying by the weight per book.

Explanation:

The question involves dividing the total number of math books evenly among book carts and then determining the total weight of books on one cart. Here's a step-by-step solution:

First, divide the total number of books, which is 288, by the number of book carts, which is 8, to find the number of books per cart: 288 \/ 8 = 36 books per cart.

Next, since each book weighs 6 pounds, multiply the number of books per cart by the weight per book to get the total weight on one book cart: 36 books x 6 pounds/book = 216 pounds.

Therefore, the total weight of books on the last book cart is 216 pounds.

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:

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: the cost of one adult ticket is $8

the cost of one kid ticket is $4

Step-by-step explanation:

Let x represent the cost of one adult ticket.

Let y represent the cost of one kid ticket.

They sold 64 adult tickets (x) and 132 kid tickets (y) and made $1040. This means that

64x + 132y = 1040 - - - - - - - - - - -1

An adult ticket is double the cost of a kid's ticket. This means that

x = 2y

Substituting x = 2y into equation 1, it becomes

64 × 2y + 132y = 1040

128y + 132y = 1040

260y = 1040

y = 1040/260 = 4

x = 2y = 2 × 4

x = 8

If the quantity demanded, q, of a product when the price is p dollars is given by the equation p = 462 − 5q, the equilibrium price and quantity are 132 dollars and 66.

An equation is a combination of expressions in a meaningful manner in terms of variables.

The given equation between the quantity demanded, q, of a product and the price, p dollars, is as follows:

p = 462 - 5q ...(1)

The quantity supplied is given by the equation as follows:

p = 2q ...(2)

Substitute p = 2q in the equation (1),

2q = 462 - 5q

2q + 5q = 462

7q = 462

[tex]q = \dfrac{462}{7}[/tex]

q = 66

The equilibrium quantity is 66.

Put q = 66 in equation (2),

p = 2 × 66

p = 132

The equilibrium price is 132 dollars.

Thus, the equilibrium price and quantity are 132 dollars and 66.

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The equilibrium quantity is 66 units, and the equilibrium price is $168.

To find out the equilibrium price and quantity, we must make the quantity demanded equal to the quantity supplied. This essentially means that we need to solve the system of equations defined by the two product price functions therefore set 462 - 5q = 2q.

The next step is grouping the 'q' terms on one side and the constants on the other which gives us: 7q = 462. Dividing by 7 on both sides, we get q = 66, which is the equilibrium quantity.

Finally, by substituting q = 66 into either of the original equations (but be consistent, for this case I'll use the first equation: p = 462 - 5q), we find out that the equilibrium price is p = 462 - 5*66 = $168.

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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

Explanation

Lets use congruence

For the square of an integer lets use congruence module 3

Thus, the square of an integer has the form 3k (the congruence is 0) or 3k+1 (the congruence is 1).

For the cube, lets use congruence module 9

With the argument given above, we obtain that the congruence module 9 of the cube of a number is always 0,1 ir 8, thus, the cube of an integer has the form 9k, 9k+1 or 9k+8.

As for the fourth power, we take congruence module 5:

In any case, the congruence of the fourth power module 5 is either 0 or 1, as a result, the fourth power has the form 5k or 5k+1.

Final answer:

Using the Division Algorithm, we show that the square of an integer is in the form of 3k or 3k+1, the cube is in the form of 9k, 9k+1, or 9k+8, and the fourth power is in the form of 5k or 5k+1.

Explanation:

The Division Algorithm states that if we divide any integer n by a positive integer d, there are unique integers q and r such that n = dq + r and 0 ≤ r < d. Using this and thinking about integers as being of the form 3q, 3q + 1, or 3q + 2 we can prove the following statements:

(a) The square of any integer:

Any integer can be written as 3k, 3k + 1, or 3k + 2. Squaring these forms:

In each case, the square of an integer is either of the form 3k or 3k + 1.

(b) The cube of any integer:

Cubing the three forms:

The cube is of the form 9k, 9k + 1, or 9k + 8.

(c) The fourth power of any integer:

For 3k and 3k + 1, the fourth powers are:

For 3k + 2, because 2⁴ = 16 is already a multiple of 5, (3k + 2)⁴ will also have the form 5m or 5m + 1. Therefore, the fourth power of an integer is either of the form 5k or 5k + 1.

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.