another scale drawing of Jimmy's living room is shown below:

If each 2 cm on the scale drawing equals 8 feet, what are the actual dimensions of the room?

Length = 8 feet, width = 6 feet
Length = 12 feet, width = 8 feet
Length = 18 feet, width = 16 feet
Length = 24 feet, width = 16 feet

Answer:

a) 28 units

b) 0.0262 seconds

c) Minimum height of the nail = 1.923 units

Step-by-step explanation:

a) From the given equation, f(x) = -14×cos(720(t - 10)) + 14 comparing with the equation for periodic function, y = d + a·cos(bx - c)

Where:

d = The mid line

a = The amplitude

The period  = 2π/b

c/b = The shift

Therefore, since the length of the mid line and the amplitude are equal, the diameter of the bike maximum f(x) = -14×-1 + 14 = 28

b) Given that three revolution = 6×π, we have;

At t = 0

cos(720(t-10) = cos(720(0-10))  = cos(7200) = 1

Therefore, for three revolutions, we have

720(t - 10) = 720t - 7200

b = 720

The period = 2π/b = 6·π/720 = 0.0262 seconds

c) The minimum height of the nail is given by the height of the wheel at t = 0, as follows;

f(x) = -14×cos(720(t - 10)) + 14

At t = 0 gives;

f(x) = -14×cos(720(0 - 10)) + 14

Minimum height of the nail = -14×cos(-7200) + 14 = -14×0.863+14 =1.923

Minimum height of the nail = 1.923

Answer:

No

Step-by-step explanation:

0.99 is not a repeating decimal because it terminates, meaning that it "ends". We know this because there are no more digits after 9 and there is no "..." at the end of the decimal.

Answer:

40

Step-by-step explanation:

area is length times width for 2d shapes. do 4x10 the are is 40

Answer:

7182

Step-by-step explanation:

All you shoud do is to replace x by 9

● y = 10 * 9^3 -12*9

● y = 7182

Answer:

Increase.

Step-by-step explanation:

Let's say p=25.

50/25=2

If p decreased and we turned the 25 into a 2, then 50/2=25.

The answer increased.

I hope this is what you were looking for!! <3

Answer:

a) [tex]1,000,000 \times (1.06)^{t}[/tex]

b) The function is recursive

c) The benefits includes;

1) Simplification of information

2) Faster data access

3) Lesser storage requirement

4) Good for forecasting

5) Simplifies information analysis.

Step-by-step explanation:

The given information are;

The current population = 1,000,000

The rate of increase of the population = 6%

a) With the standard function notation is [tex]P_f[/tex]  = [tex]P_p[/tex] × [tex](1 + r)^{t}[/tex]

Where;

[tex]P_f[/tex] = Future population

[tex]P_p[/tex] = Present population

r = Rate of population increase

t = The number of years

Therefore, we have;

[tex]P_f[/tex]  = 1,000,000 × [tex](1 + 0.06)^{t}[/tex] = 1,000,000 × [tex](1.06)^{t}[/tex]

The population increases by a factor of [tex](1.06)^{t}[/tex] given the number of years, t

b) The function is recursive as it takes account of the number of years and the previous population to calculate the future population

c)  The benefits includes;

1) Simplification of the relationship of a given data with time

2) Provides a more faster way to access data that is recursive than using complex regular function with more variables

3) Reduces data storage space for statistical calculations as several particular data can be accessed using one function

4) Provides improved forecasting

5) Enables detailed information analysis.

Answer:

Z=7.9

Step-by-step explanation:

20.4 + 20.4 = 40.8  

56.6 - 40.8 = 15.8

15.8/2 = 7.9

Answer:

z=7.9 cm

Step-by-step explanation:

So, what we have to do is gather all the information we already have. The length of the rectangle is 20.4 cm, and the perimeter is 56.6. To find the perimeter, you always add all the sides up. So 20.4+20.4 is 40.8. since 4+4 is 8, and 20+20 is 40. Then, you subtract that from the perimeter to get what is 2z(both sides). 56.6-40.8 is 15.8. So we know 2z is 15.8. To find z, we divide 15.8 by 2 which is 7.9. You can do this with a calculator or write it down.

z=7.9 cm

Answer:

writing the answer would be confusing so i went on and wrote it on the page click image the attached to see the answers    

Answer: [tex]\dfrac{1}{6840}[/tex]

Step-by-step explanation:

According to the permutations:

The arrangement of n things in an order = n!

If we fix that the first, second, and third person for skating, then we to arrange only 17 of the skaters.

Number of ways to arrange rest of 17 skaters = 17!

Number of ways that Christie, Taylor, and Jona will  skate first, second, and third, respectively = 1 x 17!=17!

Number of ways to arrange all 20 skaters = 20!

Now, the required probability = [tex]\dfrac{\text{favourable outcomes}}{\text{total ways}}[/tex]

[tex]=\dfrac{17!}{20!}\\\\=\dfrac{1}{20\times19\times18}\\\\=\dfrac{1}{6840}[/tex]

Hence, the required probability = [tex]\dfrac{1}{6840}[/tex]

Answer:

Step-by-step explanation:

it is ASA

by definition if two pairs of corresponding angles and the side between them are known to be congruent, the triangles are congruent. This shortcut is known as angle-side-angle (ASA)

Answer:

Approximately 13.9 units.

Step-by-step explanation:

First, note that ΔTVW is a right triangle.

Since we are given that ∠UTV is 112°, this means that ∠WTV is 68° because 180-112 is 68°.

Now that we know ∠WTV is 68°, we can use the basic trigonometric ratios to solve for VW. VW is the side opposite ∠WTV. We also know the hypotenuse. So, we would use sine. Recall that:

[tex]\sin(\theta)=opp/hyp[/tex]

Plug in 68° for theta, VW for the opposite, and 15 for the hypotenuse:

[tex]\sin(68)=VW/15\\VW=15\sin(68)\\VW\approx13.9078\approx13.9[/tex]

Answer:

The board game store

Step-by-step explanation:

Just divide the store price by 4 and online by 5

Answer:

Toy store

Step-by-step explanation:

Let's find the unit rates for the toy store and the online store. To find the unit rate, divide the price by the number of board games.

price/board games

Toy Store

price/board games

The toy store sells 4 board games for $25.84

$25.84 / 4 board games

25.84/5

6.46

Online Store

price/ board games

The online store sells 5 board games for $32.15

$32.15 / 5 board games

32.15/5

6.43

At the toy store, a board game costs $6.46. Online, it costs $6.43.

6.46 is greater than 5.43, therefore, the toy store has the higher price for a board game.

Answer:

Simply subtract the sum of the the three angles given from 360° in order to get the measure of the fourth angle!

Step-by-step explanation:

Answer:

c     15

Step-by-step explanation:

Tangent AB is tangent to circle D at point A. The angle made by a tangent to a circle and a radius of the circle at the point of tangency is a right angle. That means that angle is a right angle, and triangle ABD is a right triangle.

We can use the Pythagoren theorem.

a^2 + b^2 = c^2

x^2 + 20^2 = (x + 10)^2

x^2 + 400 = (x + 10)(x + 10)

x^2 + 400 = x^2 + 10x + 10x + 100

400 = 20x + 100

20x = 300

x = 15

Answer:

see explanation

Step-by-step explanation:

2πr (230/360) = 2(3.142)(40) = 160.59 cm = circumference

160.59 = 2πr

base radius = 25.56 cm

Use pythagorean formula for semi-vertical height

40² = h² + 25.56²

h = 30.77 cm

volume = 1/3πr²h

V = 1/3(3.142)(25.56)²(30.77) = 21,053.98 cm³

Answer:

  see below

Step-by-step explanation:

You can work this based only on the domain. You don't need to figure the volume, though you can if you want to check the answer further.

x represents the length of the box, which has a restriction that it can be no greater than 6 ft. This tells you x ≤ 6. However, the width is 5 ft shorter than the width, so its value is x-5. But we know the width must be greater than zero:

  0 < x -5

  5 < x

So, the constraints on the domain of x are ...

  5 < x ≤ 6 . . . . . . only matches the last choice, (5, 6]

___

Checking the volume

The height is 3 more than the width, so the volume is ...

  V = LWH = (x)(x -5)(x -5 +3) = x(x -5)(x -2) = x(x^2 -7x +10)

  V = x^3 -7x^2 +10x

Answer:

x = 3 and x = -3

Step-by-step explanation:

/x/ - 8 = -5

Add 8 to both sides

/x/ -8 + 8 = -5 +8

/x/ = 3

/ x / will be always positive as it is absolute value of x. So, x = 3 & x= -3

Answer:

Based on the function, the growth rate is 4.5%

Step-by-step explanation:

In this question, we are given the exponential equation and we are told to deduce the growth rate.

Mathematically, we can rewrite the exponential equation as follows;

S(t) = 152(1.045)^t = 152(1 + 0.045)^t

What we see here is that we have successfully split the 1.045 to 1 + 0.045

Now, that value of 0.045 represents the growth rate.

This growth rate can be properly expressed if we make the fraction given as a percentage.

Thus the issue here is converting 0.045 to percentage

Mathematically, that would be;

0.045 = 4.5/100

This makes is 4.5%

So the growth rate we are looking for is 4.5%

Answer: S = 8.9 or just 9

Step-by-step explanation:

Answer:

Sacramento

Step-by-step explanation:

S 11+9+14+12+8=54

SF 11+8+8+9+12=48

The statement that is true about the information in the table is that the data is non-linear.

The easier way to study the table is by graphing it. Here we have the points:

(11, 11), (12, 9), (9, 8), (8, 8), and (14, 12).

The graph of these points can be seen below, there you can see that the data in the table is clearly non-linear, as we can't draw a line that contains the points on the table.

So the correct option is non-linear.

If you want to learn more about tables, you can read:

https://brainly.com/question/7301139

A hexagon is composed of 6 congruent equilateral triangles. Each equilateral triangle has interior angle of 60 degrees. Adding 6 such angles together gets you to 360 degrees. So we've done one full rotation and covered every bit of the plane surrounding a given point. Extend this out and you'll be able to cover the plane. A similar situation happens with rectangles as well (think of a grid, or think of tiles on the wall or floor)

In contrast, a regular pentagon has interior angle 108 degrees. This is not a factor of 360, so there is no way to place regular pentagons to have them line up and not be a gap or overlap. This is why regular pentagons do not tessellate the plane. The same can be aside about decagons and octagons as well.

Answer:

x=7/5

Step-by-step explanation:

Original dimensions

Length=11 meters

Width=5 meters

Each dimension reduced by x meters

L=11-x

W=5-x

Length/width=ratio of length/ratio of width

11-x/5-x = 8/3

Cross product

(11-x)3 =( 5-x)8

33-3x=40-8x

-3x+8x=40-33

5x=7

x=7/5

Check:

11-7/5=55-7/5

=48/5

5-7/5=25-7/5

=18/5

48/5÷18/5

=48/5*5/18

=240/90

=24/9

=8/3

Length: width=8:3

Answer:

216

Step-by-step explanation:

Find each angle's value. This is a pentagon, so 360/5 = 72. Now, to get from A to D, you have to go 3 spaces counter-clockwise. This'll get you 72 x 3 = 216.

Answer:

216

Step-by-step explanation:

Find each angle's value. This is a pentagon, so 360/5 = 72. Now, to get from A to D, you have to go 3 spaces counter-clockwise. This'll get you 72 x 3 = 216.

Answer:

172.83 kg

Step-by-step explanation:

A cylindrical container has a radius (r) of 0.3 meter and a height (h) of 0.75 meter and density of 815 kg/m³.

The density of a substance is the mass per unit volume, it is the ratio of the mass of a substance to the volume occupied. The density is given by the formula:

Density = Mass / volume

The volume of a cylinder is given as:

V = πr²h

V = π × (0.3)² × 0.75 = 0.212 m³

Density = Mass/ volume

Mass = Density × Volume

Mass = 815 kg/m³ × 0.212 m³

Mass = 172.83 kg

Answer:

The answer is 173

Step-by-step explanation:

The other guy's answer was correct, but he forgot to round up to the nearest whole number so just in case you didn't notice the question saying that!

Answer: x = 2

Step-by-step explanation:

First, Distribute

-2+8x=3x+8

Then, Subtract 3x

-2 + 5x=8

Then, Add 2

5x=10

Then, Divide by 5

x=2

Hope it helps <3

Answer:

-2(1-4x)=3x+8

distributive property

-2+8x=3x+8

subtract 8 on both sides

-2-8+8x=3x=-10+8x

now subtract 8x on both sides which equal: -10=-5x

now it part of the step and divide -5 on both sides to leave x or solve for x

-10/-5=x=2=x

x=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the question ( 4x + 7)° and [5(x - 4)]° are vertically opposite

Since vertically opposite angles are equal we can equate them to find x

That's

4x + 7 = 5(x - 4)

4x + 7 = 5x - 20

Group like terms

5x - 4x = 20 + 7

Hope this helps you

Answer:

Step-by-step explanation:

If a group of hikers finished hiking at an elevation of -5 the group started hiking at an elevation of 8, their initial feet will be -5 and their final feet will be 8.

Change in feet of the groups elevation = final feel - initial feet

Final feet = 8 feet

Change in feet of the groups elevation = 8 -(-5)

Change in feet of the groups elevation = 8+5

Change in feet of the groups elevation = 13

Answer: probability of getting two 5s =0.04

probability of getting at least one 5 =0.36

probability of getting a total score greater than 5 =0.6

Step-by-step explanation:

Total outcomes on 1 spinner = 5

Then , total outcomes of spinning it 2 times=  [tex]5\times5 = 25[/tex]

Number of outcomes for getting two 5's = 1

Then, the probability of getting two 5s [tex]=\dfrac{\text{Favorable outcomes of getting two 5's }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{25}=0.04[/tex]

Number of outcomes for getting at least one 5 [ {(1,5),(2,5),(3,5),(4,5),(5,5), (5,1), (5,2), (5,3), (5,4)} ] =9

Then, the probability of getting at least one 5[tex]=\dfrac{\text{Favorable outcomes of getting at least one 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{9}{25}=0.36[/tex]

Number of outcomes for getting a total score of 5, [ {(1,4),(4,1),(2,3),(3,2)} ] =4

Then, the probability of getting a total score of 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score of 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{4}{25}[/tex]

Number of outcomes for getting a total score greater than 5 [ {(1,5),(5,1),(2,4),(4,2),(2,5), (5,2), (3,4),(4,3), (3,5), (5,3), (3,3), (4,5), (5,4), (4,4), (5,5)} ] =15

Then, the probability of getting a total score greater than 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score greater than 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{15}{25}=\dfrac{3}{5}=0.6[/tex]

Answer:

3/4

Step-by-step explanation:

Since, angles θ and α are complementary.

Therefore,

θ + α = 90°

θ = 90° - α

Taking sin both sides.

sin θ = sin (90° - α)

sin θ = cos α (sin (90° - θ) = cos θ)

Since, sin θ = 3/4.....(given)

Hence, cos α = 3/4

Answer:

B: 2²

Step-by-step explanation:

3(7+2²) - 5

PEMDAS says parentheses first

Then we do the order of operations inside the parentheses

Exponents are the first thing inside the parentheses