One year, the population of a city was 117,000. Several years later it was 136,890. Find the percent increase.

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Explanation:

The given equation y = -4x+5 has a slope of -4. Compare it to y = mx+b and m is the slope.

Parallel lines have equal slopes, but different y intercepts. The answer will have a slope of -4.

The point we want the answer to go through is (x1,y1) = (0,4)

We'll plug the following values

into the point slope formula below. Solve for y.

y - y1 = m(x - x1)

y - 4 = -4(x - 0)

y - 4 = -4x

y = -4x+4 which is choice A

The 2 ft 3 in. semicircular section of the window and the 4 ft 6 in. by 4 ft 6 in. of the square section gives;

a. The area of the semicircular pane is approximately 1145.1 in.²

b. The square section is 2916

c. The entire window has a perimeter of approximately 354.82 inches

a. The given radius of the semicircular pane, r = 2 ft. 3 in. = 27 in.

The area of the semicircular pane is therefore;

A = 0.5 × π × 27² ≈ 1145.1

b. The area, A, of the 9 panes of glass, disregarding the window trim is found using the equation for the area of a square, as follows;

A = Side × Side

The area of the 9 panes is therefore;

A = 4 ft. 6 in. × 4 ft. 6 in.

Which gives;

A = 54 in. × 54 in. = 2916 in.²

c. The perimeter of the entire window, P, is given by the sum of the perimeter of the semicircular pane, P1, and the perimeter of the 9 square window panes, P2, as follows

P1 = 54 + π×27

P2 = 4 × 54

Which gives;

P = 54 + π × 27 + 4 × 54 ≈ 354.82

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Answer:

∠ B = 23°

Step-by-step explanation:

vertical angles are congruent , so

∠ B = ∠ A , that is

5x - 17 = x + 15 ( subtract x from both sides )

4x - 17 = 15 ( add 17 to both sides )

4x = 32 ( divide both sides by 4 )

x = 8

Then

∠ B = 5x - 17 = 5(8) - 17 = 40 - 17 = 23°

Vertically opposite angles are equal

[tex]x + 15 = 5x - 17 \\ 15 + 17 = 5x - x \\ 32 = 4x \\ x = 8[/tex]

[tex] \sf \: \angle \: a = x + 15 = > 8 + 15 = 23 \degree[/tex]

[tex] \sf \: \angle \: b= 5x - 17 = > 5 \times 8 - 17 = > 40 - 17 = 23 \degree[/tex]

Answer: 296 with a remainder of 1 (I'm guessing this by mental math, btw, why not just use a calculator, the calc is your best chance for a right answer anyway)

Edit: Used calc, was close lol, 296.5 is the exact answer

Step-by-step explanation:

P.S: Question, is that supposed to be divided or square rooted?

Anyway, I'll explain it since I can't leave it hanging:

2*2 = 4 so 5-4 = 1 and bring 9 down, after that 2*9 = 18, so it becomes 1, and then bring down 3 for 13, and 6*2 = 12, so 13-12 = 1, and that is 296 with a remainder of 1.

The sum of any number and zero is the original number: Identity property

When two numbers are added, the sum is the same regardless of the order of addends: Commutative property

When three or more numbers are added, the sum is the same regardless of how the addends are grouped: Associative property

A + B = B + A if A and B are any two whole numbers.

In other words, the sum of two whole numbers is true regardless of how the addends—or real numbers—are arranged.

Any order will work for adding the numbers. Even if the numbers are rearranged, the sum of the two numbers remains the same.

When an is a whole number, A + 0 equals 0 + A.

In other words, the number itself is equal to the sum of any whole number and zero. In other words, zero is the only whole number that when added to, does not alter the value (identity) of the original number.

The additive identity or identity element for the addition of whole numbers is the integer 0 (zero).

When zero is added to a number, the result is unchanged.

If any three whole numbers are A, B, and C, then (A + B) + C = A + (B + C)

In other words, whole number addition is associative.

Any group or placement of the numbers has no effect on the sum when three or more are added.

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The total number of SUVs sold = 195

and the total number of passenger cars were sold = 115

For given question,

Let x be the total number of SUVs and y be the total number of passenger cars sold.

For a recent year,80 more SUVs were sold than passenger cars.

So we get an equation,

x = y + 80                .............(1)

A total of 310 vehicles were sold.

So we get an equation,

x + y = 310              .............(2)

Substitute the value of x from (1) in an equation (2),

(y + 80) + y = 310  

2y + 80 = 310

2y = 230

y = 115

This means, total 115 passenger cars were sold.

Substitute the above value of in equation (1),

x = 115 + 80

x = 195

This means, total 195 SUVs were sold.

Therefore, the total number of SUVs sold = 195

and the total number of passenger cars were sold = 115

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Answer:

2/10 or 20

Step-by-step explanation:

the only one i could figure out was the reduced fraction and the whole

Part (a)

r = radius

h = height = 5r

SA = Surface area of a cylinder

SA = 2pi*r^2 + 2pi*r*h

SA = 2pi*r^2 + 2pi*r*5r

SA = 2pi*r^2 + 10pi*r^2

SA = (2pi+10pi)*r^2

SA = 12pi*r^2

====================================================

Part (b)

r = radius

h = height = 5r

V = volume of a cylinder

V = pi*r^2*h

V = pi*r^2*5r

V = 5pi*r^3

Set this equal to the stated volume of 1715pi cubic cm and solve for r.

The pi terms cancel

So,

V = 5pi*r^3

1715pi = 5pi*r^3

1715 = 5r^3

r^3 = 1715/5

r^3 = 343

r = CubeRoot(343)

r = 343^(1/3)

r = 7

Answer:

y = 3/4x -2

Step-by-step explanation:

We first find the slope of the line using two points

(0,-2) and (8,4)

m = ( y2-y1)/(x2-x1)

m = ( 4---2)/(8 - 0)

   = (4+2)/(8)

   = 6/8

   = 3/4

We can write the equation in slope-intercept form using

y = mx+b  where m is the slope and b is the y-intercept

b is where it crosses the y axis.  It crosses at -2

y = 3/4x -2

Answer: the width of the rectangle is 14 units

Let's denote the length of the rectangle to be x and the width to be y.

The first sentence tells us that the length, x , is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. x = 2y - 4.

In the question given that the perimeter of the rectangle is 76 units

Perimeter of a rectangle is 2( length + breadth )

According to the question :

76 = 2(x + y)

76 = 2(2y – 4 + y)

76 = 2(3y – 4 )

76 = 6y – 8

84 = 6y

y = 14 units

putting the value of in x = 2y – 4

x = 2(14) – 4

x = 24 units

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Answer:

log(m) - log(n) + 1/2 log(p)

log(m/n) + log(√p)

log[(m*√p)/n]

The distance from earth to the sun is 387.5 times greater than the distance from the earth to the moon.

Given Data;

The distance from earth to the sun = 9.3 x 10⁷ miles

The distance from the earth to the moon = 2.4 x 10⁵ miles

The distance ES to EM

Then we need to divide the distance from earth to the sun by the distance from the earth to the moon

=  9.3 x 10⁷ miles / 2.4 x 10⁵ miles

= 387.5 times is greater.

Therefore, The distance from earth to the sun is 387.5 times greater  than the distance from the earth to the moon.

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Answer:

The distance between both numbers is 3.2.

Step-by-step explanation:

How to find the answer is to:

1. Subtract the 9 and 7 to get 2.

2. Place your decimal point behind the 2 to make .2

3. Do 5 minus 2 to get 3.

Your answer is 3.2.

The value of 't' that is nearest entire year is

18 years

Ian made a vehicle investment of $2500.

that would ensure an annual interest rate of 4%.

the function for this  A(t)=2500(1.04).

Find the value of t that makes the equation A(t)=5000 true, to the nearest whole year, using the tables on your calculator.

Give numerical support for your response.

Ian invested $2500

yearly interest 4%

function is A(t)=2500(1.04)

equation A(t)=5000.

[tex]A(t)=2500\times(1.04)^t[/tex]

A ( t ) = 5000

[tex]5000=2500\times(1.04)^t[/tex]

[tex](1.04)^t=5000:2500[/tex]

[tex](1.04)^t=2[/tex]

t = 17.68 ≈ 18

The value of t is 18 years.

Therefore, The value of 't' that is nearest entire year is

18 years

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Answer:

A

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

A y = [tex]\frac{1}{2}[/tex] x+ 2 ← has slope m = [tex]\frac{1}{2}[/tex]

B y = - [tex]\frac{1}{2}[/tex] x + 7 ← has slope m = - [tex]\frac{1}{2}[/tex]

C y = 2x + 4 ← has slope m = 2

D y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{4}[/tex] ← has slope m = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

• the product of the slopes of perpendicular lines = - 1

- [tex]\frac{1}{2}[/tex] × 2 = - 1

then lines B and C are perpendicular

Answer:

12

Step-by-step explanation:

This is a ratio problem where 3 is to 8 as x is to 32.  Set up as fractions and solve:

3/8 = x/32 solve for x

The error was the use of just a line on each name instead of a line with an arrow head pointing to the right. It should be: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex]are opposite rays.

To name two rays that are opposite each other, start the name of each of the rays with the letter of the endpoint that connects both rays together, then use the letter of the point where each of the rays extend to infinity.

The line on top both of the letters of the rays must have an arrow head, "→" that points to the right.

In problem 26, the letters used in naming the opposite rays were correct, but, the line on each letter that was used had no arrows pointing to the right. They are wrong.

The correct way of naming the opposite rays is: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex].

Therefore, we can conclude that, the error was the use of just a line on each name instead of a line with an arrow head pointing to the right. It should be: [tex]\overrightarrow{\rm YC}[/tex] and [tex]\overrightarrow{\rm YE}[/tex]are opposite rays.

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The state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.

We are given that:

The rate of tax on sales for South Salt Lake is = 7.05 %

That is:

Sale tax rate = r = 7.05 %

Now, we are given that the selling price of a car = $ 21,900

Selling price = $ 21,900

Now we need to find the sales tax amount that will be imposed on the car.

For this, we will calculate the percentage.

Sales tax = 7.05 % of $ 21,900

Sales tax = 7.05 % × $ 21,900

Sales tax = 7.05 / 100 × $ 21,900

Sales tax = 7.05 × $ 219

Sales tax = $ 1543.95

Therefore, we get that the state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.

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Answer:

8i

Step-by-step explanation:

[tex] \sqrt{ {4}^{2} - 4(2)(10)} [/tex]

[tex] \sqrt{16 - 80} [/tex]

[tex] \sqrt{ - 64} = 8i[/tex]

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

First I'd like to convert the fractions into decimals.

2 1/2 = 2.5

3 1/4 = 3.25

Now, multiply each number by how many days that distance was reached.

2.5 x 5 = 12.5

3.25 x 5 = 16.25

We add our products:

28.75 (28 3/4)

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

Good luck! :)

(Consider leaving a Brainliest if this helped!)

~pinetreee

Answer:

d,c,a,b

Step-by-step explanation:

The total possible ways of arranging 30 students in two groups of sizes 4 and 6 respectively are 6309453150, which is obtained by using the prerequisite knowledge of combinations.

What is the combination?

A combination is a mathematical procedure that deduces the number of feasible selections in a collection of articles in which the order of the selection does not matter. In combinations, you can choose any items in any order. Its formula is given by C(n,r) = n! / (n - r)! r!)

Calculation of the total possible ways of arranging two focus groups of students with sizes 4 and 6 respectively

Given a group of 30 students

Two focus groups are to be arranged in sizes 4 and 6 respectively

Total number of possible ways to arrange the two focus groups = C(30,4) × C(26,6)

Using the formula for combination, we get,

T.F.O = [30! / (26! 4!)] × [26! / (20! 6!)]

T.F.O = 27405 × 230230

         = 6309453150

Hence, the required possible ways to arrange two groups are given by 6309453150.

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By definition of perpendicularity, plane, point and line, we find that two lines are perpendicular if they intersect at a right angle. (Correct choice: C)

According to Euclidean geometry, two pairs of opposite angles are created by generating two lines with different slopes on the same plane. Two lines with same slope never cross on the plane and are known as parallel lines.

Opposite angles have the same measure and the two lines are perpendicular to each other if and only if each pair of opposite angles are right angles. Right angles have a measure of 90° (π / 2 radians), then each of the four angles must have a measure of 90° (π / 2 radians).

In summary, two lines set on a plane are perpendicular to each other if they intersect at a right angle.

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Answer: What are the values of sin, cos and tan?

Sin Cos Tan Chart

Angles (in degrees) 0° 60°

Sin θ 0 √3/2

Cos θ 1 1/2

Tan θ 0 √3

Cot θ ∞ 1/√3

Step-by-step explanation:  hope this helps a little!!!!

Answer: How do you write a population growth equation?

The annual growth of a population may be shown by the equation: I = rN (K-N / K), where I = the annual increase for the population, r = the annual growth rate, N = the population size, and K = the carrying capacity.

Step-by-step explanation: hope this helps!!!

Answer:

Step-by-step explanation:

The annual growth of a population may be shown by the equation: I = rN (K-N / K), where I = the annual increase for the population, r = the annual growth rate, N = the population size, and K = the carrying capacity.

Based on the percentage of those who love running and those who don't,  the total percentage of the athletes who do not enjoy cycling is 24.5%.

The percentage who don't enjoy cycling are:

= Percentage who enjoy running and but not cycling + Percentage who don't enjoy running or cycling

Solving gives:

= ((1 - 70%) x 45%) + ( (1 - 45%) x (1 - 80%))

= (30 % x 45%) + (55% x 20%)

= 24.5%

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The lateral area of the right octagonal prism is 672 square inches

The formula for lateral area of a right octagonal prism is expressed as;

Lateral area = 8ah

Where;

Substitute the values into the formula

Lateral area = 8 × 7 × 12

Multiply through

Lateral area = 672 square inches

Thus, the lateral area of the right octagonal prism is 672 square inches

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He has enough money to buy all the paving stone for the rectangular garden.

The garden path is rectangular.

He wants to cover the path with a paving stone. The paving stone is square in shape and have side of 40 cm.

Therefore,

area of the square stone = l²

where

Therefore,

area of the square stone = 40²

area of the square stone = 1600 cm²

area of the rectangular garden = lw

where

Therefore,

area of the rectangular garden = 800 × 120

area of the rectangular garden = 96000

area of the rectangular garden = 96000 cm²

Therefore,

number of paving stone required = 96000 / 1600

number of paving stone required = 60

Hence,

cost of covering the path = 4.50 × 60 =  £ 270

Therefore, he has enough money to buy all the paving stone for the rectangular garden.

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