On the day after my birthday this year, I can truthfully say: "The day after tomorrow is a Monday". On which day is my birthday?

Answer:

The height of the rider as a function of time is [tex]h(t) = 15 + 82.5\cdot (1-\cos 0.168t) \,[ft][/tex], where time is measured in seconds.

Step-by-step explanation:

Given that Ferris wheel rotates at constant rate and rider begins at the bottom of the wheel, the height of the rider as a function of time is modelled after this expression:

[tex]h(t) = h_{bottom} + (1-\cos \omega t)\cdot r_{w}[/tex]

Where:

[tex]h_{bottom}[/tex] - Height of the bottom with respect to ground, measured in feet.

[tex]\omega[/tex] - Angular speed of the ferris wheel, measured in radians per second.

[tex]t[/tex] - Time, measured in seconds.

[tex]r_{w}[/tex] - Radius of the Ferris wheel, measured in feet.

The angular speed of the ferris wheel, measured in radians per second, is obtained from the following expression:

[tex]\omega = \frac{\pi}{30}\cdot \dot n[/tex]

Where:

[tex]\dot n[/tex] - Angular speed of the ferris wheel, measured in revolutions per minute.

If [tex]\dot n = 1.6\,rpm[/tex], then:

[tex]\omega = \frac{\pi}{30}\cdot (1.6\,rpm)[/tex]

[tex]\omega \approx 0.168\,\frac{rad}{s}[/tex]

Now, given that [tex]h_{bottom} = 15\,ft[/tex], [tex]r_{w} = 82.5\,ft[/tex] and [tex]\omega \approx 0.168\,\frac{rad}{s}[/tex], the height of the rider as a function of time is:

[tex]h(t) = 15 + 82.5\cdot (1-\cos 0.168t) \,[ft][/tex]

Answer:

The width is 23.5 ft and the length is 47 ft

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w)

141 = 2(l+w)

The length is twice the width

l = 2w

141 = 2 ( 2w+w)

141 = 2( 3w)

141 = 6w

Divide each side by 6

141/6 = 6w/6

23.5 = w

l = 2w = 2(23.5) = 47

The width is 23.5 ft and the length is 47 ft

Answer:

[tex]\boxed{Width = 23.5 \ feet}[/tex]

[tex]\boxed{Length = 47 \ feet}[/tex]

Step-by-step explanation:

Let Length be l and Width be w

Perimeter = 2(Length) + 2(Width)

Condition # 1:

2l+2w = P

=> 2 l + 2 w = 141

Condition # 2:

=> l = 2w

Putting the second equation in the first one

=> 2(2w)+2w = 141

=> 4w + 2w = 141

=> 6w = 141

Dividing both sides by 6

=> Width = 23.5 feet

Given that

=> l = 2w

=> l = 2(23.5)

=> Length = 47 feet

Answer:

x = 56 degrees

y = 62 degrees

Step-by-step explanation:

Given TS || PR

x = 56    ................. corresponding angles TS, PR parallel sides of trapezium.

VSK = x ...................... correspoinding angles given TU || SV

y = 118 - VSK          .......... given VSR = 118

= 118 - 56

= 62

Answer:

0

Step-by-step explanation:

Answer: it's C. 0

Also Happy early Christmas

Answer:

233.37

Step-by-step explanation:

so between each gondola is 20.95 so you will multiply it by 35 not 36 (because between the first you go round and come back to the same first you started so no space between first and last) then get circumference as 733.25 using

[tex]c = \pi \: d[/tex]

you get diameter

Answer:

ABC≅DEF

x = 2

CB = 3

FE = 4

y = 5

ED = 6

FD = 7

AB = 8

AC = 9

In triangle ABC=

Side AC= 9 cm

Side CB= 3 cm

Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]

        =13.5 cm^2

In triangle DEF=

Side FE= 4 cm

Side FD= 7 cm

Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]

        =14 cm^2

Answer:

The answer is 45 inches².

Step-by-step explanation:

First, you have to find the area of each triangle:

[tex]area = \frac{1}{2} \times base \times height[/tex]

[tex]let \: base = 3 \\ let \: height = 6[/tex]

[tex]area = \frac{1}{2} \times 3 \times 6[/tex]

[tex]area = \frac{1}{2} \times 18[/tex]

[tex]area = 9 \: \: {inches}^{2} [/tex]

Assuming that the formula for surface area of pyramid is Surface area = base area(area of square) × 4(area of triangle):

[tex]base \: area = 3 \times 3 = 9[/tex]

[tex]area \: of \: triangle = 9[/tex]

[tex]s.a = 9 + 4(9)[/tex]

[tex]s.a = 9 + 36[/tex]

[tex]s.a = 45 \: \: {inches}^{2} [/tex]

Answer:

if it takes 4 people for 2 days

4+4= 8

so it would only take 8 people for 1 day

Answer:

1 day

Step-by-step explanation:

4 people = 2 days

→ Work out how long 1 person takes

4 people = 2 days

( ÷ 4 )            ( × 4 )

1 person = 8 days

→ Work out how long 8 people can do it

1 person = 8 days

( × 8 )            ( ÷ 8 )

8 people = 1 day

Answer:

Step-by-step explanation:

–3(6 – 2x) ≥ 4x + 12

Expand the terms in the bracket

We have

- 18 + 6x ≥ 4x + 12

Group like terms

that's

6x - 4x ≥ 12 + 18

2x ≥ 30

Divide both sides by 2

x ≥ 15

Hope this helps you

Step-by-step explanation:

no worries

if u multiply by a negative number the sign changes

so it can -18 + 6x <= 4x + 12

take x to one side and others to other side

6x - 4x <= 18 + 12

2x <= 30

x<= 15

so solutions can be from ....-2,-1,0,1,2,3....

Answer:

0.09

0.55

Step-by-step explanation:

to write least to greatest firstly, start comparing both number

so the answer will be=0.09,0.55

it least to greatest or in assending order.

Answer:

$24 will be the cost of tennis racquet with weight 25 oz.

Step-by-step explanation:

Given that Price of racquet is inversely proportional to its weight.

i.e.

[tex]Price \propto \dfrac{1}{Weight}[/tex]

We can replace the proportional sign with a constant of proportionality.

[tex]Price = \dfrac{C}{Weight}[/tex]

Where C is a constant named as constant of proportionality.

Given that cost of 20 oz. racquet is $30.00

Putting both the values :

[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]

So, the equation becomes:

[tex]Price = \dfrac{600}{Weight}[/tex]

Now, we have to find the price of 25 oz. racquet.

Putting Weight = 25 oz and finding Price:

[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]

So, $24 will be the cost of tennis racquet with weight 25 oz.

4/25

Step-by-step explanation:

16/100, 8/50, 4/25

Answer:

cos C

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos C = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

Answer: 24 units

Step-by-step explanation:

MO, NO and LO are radii.

If MO = 13, THEN LO = NO = 13

IF NO = 13 and NP = 8, THEREFORE,

PO = NO - NP

PO = 13 - 8 = 5

USING PYTHAGORAS, WE CAN FIND MP:

MP = Sqrt(MO^2 - PO^2)

MP = sqrt(13^2 - 5^2)

MP = sqrt(169 - 25)

MP = sqrt(144)

MP = 12 units

P is the midpoint of Segment ML,

THEREFORE,

MP = PL

ML = MP + PL

ML = 12 + 12

ML = 24 units

Answer: 24

Step-by-step explanation:

edge

Answer:

A

Step-by-step explanation:

Answer:

x = 3

y = -2

Step-by-step explanation:

x + 2y + 1 = 0

2x - 3y - 12 = 0

Multiply first equation by -2.

-2x + -4y + -2 = 0

2x - 3y - 12 = 0

Add equations.

0x + -7y - 14 = 0

Solve for y.

-7y = 14

y =-2

Put y as -2 in the first equation and solve for x.

x+2(-2)+1=0

x + -4 + 1 = 0

x = 0 + 4 - 1

x = 3

Answer:

[tex]\boxed{x = 3, y = -2}[/tex]

Step-by-step explanation:

[tex]x+2y +1 = 0[/tex]

=> [tex]x+2y = -1[/tex] -------------------(1)

[tex]2x-3y-12 = 0[/tex]

=> [tex]2x-3y = 12[/tex] -------------------(2)

Multiplying (1) by 2

=> [tex]2(x+2y) = 2(-1)[/tex]

=> [tex]2x+4y = -2[/tex] ------------------(3)

Subtracting (3) from (2)

=> [tex]2x-3y+2x-4y = 12+2[/tex]

=> -3y-4y = 14

=> -7y = 14

Dividing both sides by -7

=> y = -2

Now, Put y = -2 in Eq (1)

=> x+2(-2)+1 = 0

=> x -4+1 = 0

=> x - 3= 0

Adding 1 to both sides

=> x = 3

Answer:

(3,2)

Step-by-step explanation:

Just took the test

Answer:

i need help this too

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

x = 5

Now, let's find the value of C

[tex]c = 3x - 2[/tex]

plug the value of x

[tex] = 3 \times 5 - 2[/tex]

Multiply the numbers

[tex] = 15 - 2[/tex]

Calculate the difference

[tex] = 13[/tex]

Hope this helps..

Best regards!!

Answer:

0.8185 or 81.85%

Step-by-step explanation:

The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.

The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive  and if the raw score is below the mean the z sore is negative. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.

For 8 inches:

[tex]z=\frac{x-\mu}{\sigma}=\frac{8-11}{1.5}=-2[/tex]

For 12.5 inches:

[tex]z=\frac{x-\mu}{\sigma}=\frac{12.5-11}{1.5}=1[/tex]

From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1)  - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%

Answer:

25p^2 + 4 + 20p

Step-by-step explanation:

(5p + 2)^2 = (5p)^2 + (2)^2 + 2 × 5p × 2

= 25p^2 + 4 + 20p

Answer:

20

Step-by-step explanation:

20 + (75% × 20) =

20 + 75% × 20 =

(1 + 75%) × 20 =

(100% + 75%) × 20 =

175% × 20 =

175 ÷ 100 × 20 =

175 × 20 ÷ 100 =

3,500 ÷ 100 =

35;

Answer:

For the first one, answer is dilation of 2

Step-by-step explanation:

you see the coordinates for triangle A'B'C' are all doubled the coordinates of triangle ABC

Answer:

y = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 5 when x = 7, then

5 = [tex]\frac{k}{7}[/tex] ( multiply both sides by 7 )

35 = k

y = [tex]\frac{35}{x}[/tex] ← equation of variation

When x = 70, then

y = [tex]\frac{35}{70}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

ADB and ADC

Step-by-step explanation:

SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.

Answer:

ABD and ECD

Step-by-step explanation:

EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.

Answer:

You havent showed us the pattern

Answer:

b. Contains four right angles.

Step-by-step explanation:

A parallelogram has two pairs of opposite sides that are both congruent and parallel, as does a rectangle.

A parallelogram usually does NOT have four right angles, but a rectangle does. b Contains four right angles is the difference between a parallelogram and a rectangle.

The diagonals of a parallelogram bisect each other, and so do the rectangle's diagonals.

The opposite angles of parallelograms are congruent, and all four angles of a rectangle are congruent, so this is a similar aspect of both a parallelogram and a rectangle.

Hope this helps!

Answer:

19.5 km

Step-by-step explanation:

the actual distance between Harry and the Sea view:

if 24 km is 5 cm on map

24*4/5= 19.5 km

Explanation:

The flat horizontal portion S is where the distance (y) does not increase or decrease. So Ted is stationary during this time frame.

In terms of speed, we would say speed = distance/time = (change in y)/(change in x). Note how this is the slope.

Rise = 0 because the horizontal line does not go up or down. The run is any positive number, though convention usually has Run = 1. Therefore, slope = rise/run = 0/1 = 0. All flat horizontal lines have a slope of 0 to indicate no upward or downward movement.

Answer:

what expressions?

Step-by-step explanation:

Answer:

The coordinates are;

For reflection over the x-axis

A'(-8, 2)

B'(-4, 3)

C'(-2, 8)

D'(-10, 6)

For reflection over the y-axis;

A''(8, 2)

B''(4, 3)

C''(2, 8)

D''(10, 6)

Step-by-step explanation:

When a point (x, y) is reflected over the x, axis, we have;

Coordinates of the pre-image = (x, y)

Coordinates of the image after reflection = (x, -y)

Therefore, for the points A, B, C, D we have;

Pre-image A(-8, -2), Image A'(-8, 2)

Pre-image B(-4, -3), Image B'(-4, 3)

Pre-image C(-2, -8), Image C'(-2, 8)

Pre-image D(-10, -6), Image D'(-10, 6)

When a point (x, y) is reflected over the y, axis, we have;

Coordinates of the pre-image = (x, y)

Coordinates of the image after reflection = (-x, y)

Therefore, for the points A', B', C', D' we have;

Pre-image A'(-8, 2), Image A''(8, 2)

Pre-image B'(-4, 3), Image B''(4, 3)

Pre-image C'(-2, 8), Image C''(2, 8)

Pre-image D'(-10, 6), Image D''(10, 6).