A four-foot tree was planted. It will grow 2.5 feet each year. The relationships between x, the number of years since the tree has been planted, and y, the projected height of the tree is a linear relationship.

Write an equation to represent this relationship.

The number of proper subsets contained in P if P={x| x is an odd, positive integer and x < 20} is 1023.

It should be noted based on the information, the value of P will be:

= P(x is an odd, positive integer and x < 20}

P = (1, 3, 5, ,7, 9, 11, 13, 15, 17, and 19)

Therefore, it should be noted that there are 10 numbers.

Therefore, the number of subsets will be:

= 2^n - 1

= 2^10 - 1

= 1023

Therefore, the number of proper subsets contained in P if P={x| x is an odd, positive integer and x < 20} is 1023.

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Determine the number of proper subsets contained in P if P={x| x is an odd, positive integer and x < 20}.

Answer:   Maricella has a bag containing 35 nickels and quarters. The ...

Jun 11, 2018

Bag of Nickles and Quarters | Wyzant Ask An Expert

Step-by-step explanation:

The volume of a cone with a height of 6 cm and a radius of 4 cm is:

V =  100.5 cm³

If the volume of a cone varies jointly as its height, and the square of its radius, then we can write the equation:

V = R²*H*k

Where:

R = radius

H = height

k = constant of the variation.

Here we know that if R = 2cm and H = 8cm, the volume is 33.5 cm³, then we can replace that to get:

33.5 cm³ = (2cm)²*8cm*k

The value of k is:

(33.5 cm³)/(  (2cm)²*8cm ) = k = 1.046875

Then the formula for the volume is:

V = R²*H*1.046875

Now if the radius is 4cm and the height is 6cm, the volume will be:

V = (4cm)²*(6cm)*1.046875 = 100.5 cm³

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The equation of a line perpendicular to y = x that passes through the point (8,2) is y = -x + 10

The equation of the line is given as

y = x

Rewrite the equation as

y = x

A linear equation is represented as

y = mx + c

Where

Slope = m

So, we have

m = 1

The slopes of perpendicular lines are opposite reciprocals

This means that

m2 = -1/m1

So, we have

m = -1/1

Evaluate

m = -1

The equation of the perpendicular line is then calculated as

y = m(x - x1) + y1

Where

(x1, y1) = (8, 2)

This gives

y = -1(x - 8) + 2

Evaluate

y = -x + 8 + 2

Evaluate the sum and the difference

y = -x + 10

So, the equation of a line perpendicular to y = x that passes through the point (8,2) is y = -x + 10

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Answer:

Step-by-step explanation:

Greetings !

The union of two sets is a set containing all elements that are in A or in B (possibly both). For example, {1,2}∪{2,3}={1,2,3}. Thus, we can write x∈(A∪B) if and only if (x∈A) or (x∈B). Note that A∪B=B∪A.

Hope it helps!!

The length of rectangle is 25 feet and the width  of rectangle is 135 feet.

The perimeter of a rectangle  can be calculated by making use of the formular that will be written below which is

P = 2(l + b)

But if we are to interpret the question, then we will have

2(L + W) = 320 after the simplification

and from the above simplification , we will have

L+ W=160

But according to the question, Odd integers that follow each other with a difference of 2, hence we will have  x  as the  odd integer, then  go in a  consecutive odd integers manner we will have

W = 5(x+2)

Then if we substitute, we have

[x+5x+10=160]

Then simplify we have

6x=150

x=25

Then input x into the width equation, then, width will be  135 feet.

Therefore, The length of rectangle is 25 feet and the width  of rectangle is 135 feet.

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Answer:

Prime Factors of 545 are 5, 109, and usually expressed as 5 x 109. 4.

hope this is right! :) -liaa

The total ticket were sold this year is 39  tickets.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

The circle graph shows last year's ticket sales with a total of 842 tickets.

Adults =4%

Students =17%

Children Under 12 =55%

Seniors =24%

This year 22 more tickets were sold to seniors.

According to given question we have

Ticket sold to the senior

=24% *842

= 202.08  tickets.

Tickets were sold this year

= 202.08/12  tickets.

=16.84  tickets.

This year 22 more tickets were sold to  seniors

=16.84  tickets+22 tickets

=38.84 ≈39  tickets

Therefore, the total ticket were sold this year is 39  tickets.

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Answer:

96 people

Step-by-step explanation:

Per 5 students 1 adult goes:

80÷5=16

So, 16 adults went.

Total number of Students and Adults combined=The number of people that went on the trip:

80+16=96

Answer:

2.29x8=18.32

20 an hour because 160÷8=20

31.16 more than part a+b

Step-by-step explanation:

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The required value of x is 12.5 when y = 87.5

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

300x + 500/7y = 10,000

Now for the value of x put the value of y which is 87.5 in the given equation we get,

300x + 500/(7*87.5) = 10,000

Solving we get,

300x + 500/612.5 = 10,000

Simplifying the fraction we get,

300x + 43,750/7 = 10,000

Dividing the fraction we get

300x + 6,250 = 10,000

Subtract 6,250 from both sides

300x + 6,250 - 6,250 = 10,000 - 6,250

Solving we get,

300x = 3,750

Divide both sides by 300

x = 3,750/300

Solving we get

x = 12.5

this is the required value of x when y = 87.5

Thus, the required value of x is 12.5 when y= 87.5

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The correct question is attached.

Answer:

Step-by-step explanation:

The each side of the square will be 8.

Therefore, the area of ​​a rectangle with a height of 4 cm  and a length of 16 cm is 64 cm². Since a square is a rectangle with equal height and width, we need to find a number that when multiplied by itself equals 64... which is  the square root of 64. That's 8.8x 8 = 64.

A square is a two-dimensional planar object in geometry that has four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are fairly comparable, however a rectangle only has its opposing sides equal. Therefore, a rectangle is only referred to as a square if its four sides are of the same length.

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

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The projected weight overstated is 86.92 lbs.

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics.

Given:

Baggage weight projected was 2,182 1/4 lbs = 2182.25 lbs

The actual weight is 2,095 1/3 lbs = 2095.33 lbs

So, the overstated weight is

=2182.25 -  2095.33

=86.92 lbs

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Answer:

x=5

Step-by-step explanation:

-x + 8 = 3

-x = 3 - 8

-x = -5

x = 5

Hope this helps :)

Have a nice day!

The inequality will be:

6.2 + v ≥ -4.7

And it can solved to get:

v ≥ -10.9

Here we have the mathematical sentence:

"The sum of a number v and 6.2 is at least -4.7"

The sum is written as:

6.2 + v

And that is equal to or more than -4.7, then we need to use the symbol ≥, with that, we can write the inequality:

6.2 + v ≥ -4.7

Solving that four our number v, we get:

v  ≥ -4.7 - 6.2

v ≥ -10.9

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Given that  F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.the line integral ∫F.dr = 355¹/₃ units

Line integrals are integrals evaluated along a curve. It is given by I = ∫F.dr

where dr = dxi + dyj

Given that F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.

So, we need to find the line integral ∫F.dr

Since

So, ∫F.dr = ∫[(7xy)i + (2y²)j.(dxi + dyj)] = ∫(7xydx + 2y²dy)

We integrate y from 0 to 8 and x from 0 to 1 and susbstitute y = 8x² into the equation. So, we have

∫F.dr = ∫(7xydx + ∫2y²dy)

= ∫(7x(8x²)dx + ∫2y²dy)

= ∫56x³dx + ∫2y²dy

= 56∫₀¹x³dx + 2∫₀⁸y²dy

= 56[x⁴/4]₀¹ + 2[y³/3]₀⁸

= 56[1⁴/4 - 0⁴/4] + 2[8³/3 - 0³/3]

= 56[1/4 - 0] + 2[512/3 - 0]

= 56[1/4} + 2[512/3]

= 14 + 1024/3

= (42 + 1024)/3

= 1066/3

= 355¹/₃ units

So, given that  F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.the line integral ∫F.dr = 355¹/₃ units

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Nate's restaurant sold the greater amount of coffee.

The least common multiple of two numbers is the smallest number that is a multiple of both of them.

Given:

Nate's Diner coffee sold = 7/8

and, at Jeremiah's Pie shop

coffee sold = 528 / 606

= 176 / 202

=88/101

Now, making denominator equal by taking LCM(8, 101) which is 808.

So, Nate's coffee's sold = 707 / 808

and, Jeremiah's coffee sold =  704/808

Hence, Nate's restaurant sold the greater amount of coffee.

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The amount of money that is invested in the account that yields an 8% interest is $6,050.

The amount of money that is invested in the account that yields a 4% interest is $4,650.

Given these two equations:

x = y + 1400

x - y = 1400 equation 1

0.08x + 0.04y = 670 equation 2

take the following steps to determine the amount of money invested at each interest rate:

Multiply equation 1 by 0.08

0.08x - 0.08y = 112 equation 3

Subtract equation 3 from equation 2

0.12y = 558

Divide both sides by 0.12

y = 558 / 0.12

y = $4,650

x =  $4,650 + 1400

x = $6,050

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The fraction that is equivalent to the given fraction is -5/3

From the question, we are to determine the equivalent form of the given fraction

The given fraction is 5/-3

From one of the properties of fractions, we have that

-x/y = x/-y

Thus,

We can write that 5/-3 is equivalent to -5/3 by the above property.

Hence, the fraction that is equivalent to the given fraction is -5/3

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Indira is having 34 tulips, 68 daffodils and 102 hyacinths , altogether 204 flowers in her spring garden.

Given, In Indira's springtime garden, there are three times more hyacinths than tulips and half as many daffodils as tulips.

let the number of tulips be = x

    the number of daffodils be = y

    the number of hyacinths be = z

hence according to the question,

tulips are (x) = 1/2 (y) = y/2

hyacinths are (z) = 3(x) = 3x

therefore, total flowers = 204

tulips ₊ daffodils ₊ hyacinths = 204

y/2 ₊ y ₊ 3x = 204

substitute x value in the above equation.

y/2 ₊ y ₊ 3(y/2) = 204

take LCM

y ₊ 2y ₊ 3y = 408

6y = 408

y = 408/6

y = 68

hence the number of daffodils is 68.

now substitute y value in x = y/2

x = 68/2

x = 34

now substitute x value in z= 3x

z = 3(34)

z = 102

hence we get the number of tulips,daffodils and hyacinths as 34 , 68 and 102 respectively.

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Based on the number of times Drew dropped the thumbtack and the number of times it landed point up, the probability that the thumbtack lands points up is 27.6%

The probability that the thumbtack lands points up can be found by the formula:

= Number of times the thumbtack lands points up  / Number of total times the thumbtack was dropped by Drew x 100%

Solving for the probability of a thumbtack landing points up gives:

= 62 / 225 x 100%

= 0.2755556 x 100%

= 27.6%

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The answer is 17/48

If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

based on the given conditions , formulates

1×(325-240)÷240

calculate the sum or difference 85/240

cross out the common factor 17/48

so therefore the answer will be 17/48

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Answer:

$567.88

Step-by-step explanation:

Start with the beginning balance.

Add all the mounts of checks and subtract the total from the beginning balance.

Add the amount of the deposit to the balance.

Beginning balance: $887.43

Withdraw: $435, $58.27, $127.96

Total withdrawals:  $435 + $58.27 + $127.96 = $621.23

Deposit: $301.68

Final balance = beginning balance - total of checks + amount of deposit

Final balance: $887.43 - $621.23 + $301.68 = $567.88

Answer: $567.88

The photograph is 6 inches wide and 15 inches long.

Answer: 220

Step-by-step explanation: 395-175=220

Answer:

e=570

Step-by-step explanation:

570-395=175