Ferris wheel has a 108-foot diameter and the center of the Ferris wheel is 58 feet above the ground. The Ferris wheel rotates in the CCW direction at a constant angular speed of 6 radians per minute. Chance boards the Ferris wheel at the 3-o'clock position and rides the Ferris wheel for many rotations. Let t represent the number of minutes since the ride started.

Required:
a. Write an expression (in terms of t) to represent the number of radians Justin has swept out from the 3-0'clock position since the ride started.
b. How long does it take for Justin to complete one full revolution (rotation)?
c. c. Write an expression (in terms of t) to represent Justin's height above the center of the Ferris wheel (in feet)

Answer:

True

Step-by-step explanation:

If a is negative then the shape of the graph is an upside down U, which intersects the x-axis. If a is positive it will never cross the X axis.

It is true that f(x)=[tex]a^{x}[/tex]+4 will never cross the x axis if a is positive.

Function is relationship between two or more that are variables expressed in equal to form. In a function each value of x must have a corresponding value of y.

We have been given that f(x)=[tex]a^{x} +4[/tex] and we have to find whether it will cross x axis or not.

when a line crosses the x axis the value of y becomes negative. We have to first check at y=0.

[tex]a^{x}+4[/tex]=0

[tex]a^{x}[/tex]=-4

taking log both sides,

log [tex]a^{x}[/tex]=log(-4)

x log a=0.602059991+1.3437635i

x=(0.602059991+1.3437635i)/log a

when we put the value of x in f(x) the value of f(x) cannot be negative so it cannot crosses the x axis.

Hence it is true that f(x)=[tex]a^{x}[/tex]+4 will never cross the x axis if a is positive.

Leaarn more about function at https://brainly.com/question/10439235

#SPJ2

Answer:

[tex]S = \{PRC, PRI,PAC,PAI,PDC,PDI,BRC, BRI,BAC,BAI,BDC,BDI\}[/tex]

Step-by-step explanation:

Given

[tex]Restaurant = \{P,B\}[/tex]

[tex]Movies = \{R,A,D\}[/tex]

[tex]Post-movie = \{C,I\}[/tex]

Required

List out the sample space

To do this, we simply pick 1 item in each category, without repetition.

So, we have:

[tex]S = \{PRC, PRI,PAC,PAI,PDC,PDI,BRC, BRI,BAC,BAI,BDC,BDI\}[/tex]

Answer:

Step-by-step explanation:

the graph will move 3 units to the right

graph 4 I think, although cannot see the picture well

Answer:

Step-by-step explanation:

The -3 translates the graph of x^3 3 units to the right.

Answer:

40 yards

Step-by-step explanation:

Pythagorean theorem: a² + b² = c²

Using this, let's set the length as x.

42² + x² = 58²

Simplify.

1764 + x² = 3364

Subtract 1764 from both sides.

x² = 1600

Take the square root.

x = 40

Thus, the length she would swim would be 40 yards.

Answer:

40

Step-by-step explanation:

Answer:

[tex]P(t) = 29816591(1.025)^{t-5}[/tex]

Step-by-step explanation:

Equation:

The equation for the population of California, in t years after 1990, is given by:

[tex]P(t) = 29816591(1.025)^t[/tex]

In which 29816591 is the initial population, that is, the population in 1990.

From 1995:

First, we have to find the population in 1995(5 years after 1990), which is P(5), which we will consider as the initial value in the equation.

So

[tex]P(5) = 29816591(1.025)^5 = 33734736[/tex]

So

Since t is still given in years after 1990, we have to subtract t by 1995 - 1990 = 5 in the exponent. So

[tex]P(t) = 29816591(1.025)^{t-5}[/tex]

Answer:

210.

Step-by-step explanation:

10.5 x 20 = 210

i hope that helps!!!

Answer:

The possible values of X are 0,1 or 2.

Step-by-step explanation:

In this question:

Two number cubes are going to be rolled.

X is the number of odd numbers that show up on the two cubes.

For each cube, there is one number, which can be even, or odd.

Thus, there can be no odd numbers, one odd number or two odd numbers, and the possible values of X are 0,1 or 2.

Answer:

x = -3, y = -3

Step-by-step explanation:

Solve the following system:

{-y + 2 x = -3 | (equation 1)

3 y + 4 x = -21 | (equation 2)

Swap equation 1 with equation 2:

{4 x + 3 y = -21 | (equation 1)

2 x - y = -3 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{4 x + 3 y = -21 | (equation 1)

0 x - (5 y)/2 = 15/2 | (equation 2)

Multiply equation 2 by 2/5:

{4 x + 3 y = -21 | (equation 1)

0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:

{4 x + 3 y = -21 | (equation 1)

0 x+y = -3 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{4 x+0 y = -12 | (equation 1)

0 x+y = -3 | (equation 2)

Divide equation 1 by 4:

{x+0 y = -3 | (equation 1)

0 x+y = -3 | (equation 2)

Collect results:

Answer: x = -3, y = -3

Answer:

Amount of shampoo in a bottle = 30 \frac{1}{2} 30

2

1

ounces

Amount of shampoo Nico uses in one bathe for his dog = 1 \frac{1}{4} 1

4

1

Since 3 ounces of shampoo is spilled out, the amount of shampoo left in the bottle will be = 27 \frac{1}{2} 27

2

1

If Nico can Bathe his dog x times using this bottle, the value of x can be written as:

x= \frac{27 \frac{1}{2} }{ 1\frac{1}{4} } x=

1

4

1

27

2

1

Using this equation we can find the number of times Nico can use the shampoo to Bathe . The value of x comes out to be 22.

Thus, Nico can Bathe his dog 22 times using the bottle

Nico dropped the brand new bottle of dog shampoo and 3 ounces spilled out. He measures 1 1/4 ounces each time he shampoos his dog and the bottle of shampoo originally contained 30 1/2 ounces. Which is the correct equation and value of x, the number of times Nico can bathe his dog using this one bottle?

mark as brainliest

Answer: 2 primes 1 disinct

Step-by-step explanation:

Answer:

m=−57/92,x=−43/4

Step-by-step explanation:

Given:

The function is:

[tex]f(x)=-4(2)^x[/tex]

The graph of the function [tex]g(x)=f(x)+k[/tex] is given.

To find:

The value of k.

Solution:

We have,

[tex]f(x)=-4(2)^x[/tex]

[tex]g(x)=f(x)+k[/tex]

Using these two functions, we get

[tex]g(x)=-4(2)^x+k[/tex]

From the given graph it is clear that the graph of g(x) passes through the point (0,2). It means the point (0,2) satisfies the function g(x).

Substituting [tex]g(x)=2[/tex] and [tex]x=0[/tex] in the above function, we get

[tex]2=-4(2)^0+k[/tex]

[tex]2=-4(1)+k[/tex]

[tex]2=-4+k[/tex]

[tex]2+4=k[/tex]

[tex]6=k[/tex]

Therefore, the value of k is 6.

Answer:

volume = 7/8 cubic units

Step-by-step explanation:

[tex]volume = base \ area \times height = \frac{1}{2} \times \frac {7}{4} = \frac{7}{8} units^3[/tex]

Answer:

Find the amplitude which is half the distance between the maximum and minimum.

Find the period of the function which is the horizontal distance for the function to repeat. If the period is more than 2π then B is a fraction; use the formula period = 2π/B to find the exact value.

Find any phase shift, h.

Step-by-step explanation:

Answer:

there is no graph maybe post again

tan( 20 ) + 4 Sin( 20 ) =

( Sin( 20 ) / Cos( 20 ) ) + 4 Sin( 20 ) =

Sin( 20 ) + 4 Sin( 20 ).Cos( 20 ) / Cos( 20 ) =

Sin( 20 ) + 2 × 2 Sin(20).Cos(20)/ Cos(20) =

Sin( 20 ) + 2 × Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Cos( 50 ) / Cos ( 20 ) =

Sin( 20 ) + 2Cos( 20 + 30 ) / Cos( 20 ) =

________________________________

2 × Cos( 30 + 20 ) =

2 × [ Cos(30).Cos(20) - Sin(30).Sin(20) ] =

2 × [ √3/2 × Cos(20) - 1/2 × Sin(20) ] =

√3 Cos(20) - Sin(20)

_________________________________

Sin( 20 ) + 2Cos ( 20 + 30 ) / Cos( 20 ) =

Sin( 20 ) + √3 Cos(20) - Sin(20) / Cos(20) =

Sin(20) - Sin(20) + √3 Cos(20) / Cos(20) =

0 + √3 Cos(20) / Cos(20) =

√3 Cos(20) / Cos(20) =

Cos(20) simplifies from the numerator and denominator of fraction

√3 × 1 / 1 =

√3

And we're done ....

Answer:

A. For every 1 inch of mercury the pressure increases, the boiling point is expected to increase by 1.9°F

Step-by-step explanation:

A regression model is in the form :

y = mx + c

With m being the slope = rate of change

In regression, the value of the slope gives the rate of change in y value per unit increase in the value of x

The slope in the question above is 1.9, this means for every unit increase in mercury pressure, then boiling point, y increases by 1.9°F

Answer:

7.14%

Step-by-step explanation:

A fair number cube has 6 sides while a normal spinner has 7 different colors. In order to find the probability of Jack getting a number less than 4 and lands on blue, we need to find the probability of each individual event and multiply them together. Since the cube has six sides and 3 options that are less than 4 then the probability of getting less than 4 is 3/6. On the wheel there are 7 colors and only one is blue, therefore, the probability is 1/7. Now we multiply these fractions together.

[tex]\frac{3 * 1}{6 * 7} = \frac{3}{42}[/tex] or 0.0714 or 7.14%

Therefore, the probability of this event happening is 7.14%

The probability of this event is 7.14%.

A fair number cube has 6 sides.

While a normal spinner has 7 different colors.

In order to find the probability of Jack getting a number less than 4 and lands on blue,

we have to find the probability of each individual event and then multiply them together.

The cube has six sides and 3 options that are less than 4 then the probability of getting less than 4 is 3/6.

On the wheel there are 7 colors and only one is blue.

Therefore, the probabilitiy is 1/7.

Now we multiply these fractions together.

[tex]\frac{3\times 1}{6\times 7} =\frac{3}{42}= 0.0714[/tex]

[tex]\frac{ 0.0714 }{100}=7.14\%[/tex]

Therefore, the probability of this event is 7.14%.

To learn more about the probability visit:

https://brainly.com/question/24756209

Answer:

i dont know your answer but plz can u help me in my maths question plz

Answer:

See Below

Step-by-step explanation:

The fibonacci sequence is a recursive type sequence where each term is the sum of the two previous terms. The sequence starts out as:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811...

The fibonacci sequence can be found in nature quite often. For example, it is found in "the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bract". It can also be found in the number of tree branches in each row.

Another cool place it can be found is in the diagonals of pascals triangle (shown in the image attached)

*Disclaimer: I do not own any of the images

Answer:

(2x+1) +x = -35

3x= -36

x= -12

Step-by-step explanation:

Answer:

i think false

Step-by-step explanation:

The elevation of the city with an elevation opposite Seeley's is -45 feet. The correct option is A.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles, and the calculations based on these relationships. It specifically focuses on the ratios between the sides of a right-angled triangle.

The elevation of a city with an elevation opposite of Seeley's can be found by taking the opposite of Seeley's elevation, which is 45 feet, to get the answer.

Therefore, the elevation of the city with an elevation opposite of Seeley's is:

A) -45 feet

To know more about trigonometry follow

https://brainly.com/question/17571933

#SPJ2

Answer:

$42

Step-by-step explanation:

less than 8 is supposed to be 7 or less 6×7=$42

Answer:

C.) 87

Step-by-step explanation:

if you look at it from the other side, its counting down from 91 from the left.

Answer: 87

No explanation :)

Answer:

64

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

A.)

Vehicle speeds on highway (9 vehicles) 74, 82, 67, 73, 65, 41, 74, 49, 85

Ordered data :

41, 49, 65, 67, 73, 74, 74, 82, 85

Sample size, n = 9

Median = 1/2 * (n +1) th term

Median = 1/2 * 10 = 5th term

Median value = 73

Midrange = (Maximum + minimum) / 2

Midrange = (85 + 41) / 2 = 126 / 2 = 63

Geometric mean : √(x1*x2*.. xn)^1/n

Geometric Mean:

(41*49*65*67*73*74*74*82*85)^1/n

= 66.19

B.)

Sodium grams in canned soup (8 varieties)

X = 4.22, 3.60, 2.68, 2.75, 2.70, 4.17, 2.72, 4.29

Ordered data:

2.68, 2.70, 2.72, 2.75, 3.60, 4.17, 4.22, 4.29

Sample size, n = 8

Median = 1/2 * (n +1) th term

Median = 1/2 * 9 = 4.5th term

Median value = (2.75+ 3.6) / 2 = 3.175

Midrange = (Maximum + minimum) / 2

Midrange = (4.29 + 2.68) / 2 = 3.485

Geometric mean : √(x1*x2*.. xn)^1/n

Geometric Mean:

(2.68*2.70*2.72*2.75*3.60*4.17*4.22*4.29)^1/8

= 3.32

C.)

Campus health center visits (12 students)

X : 1, 5, 6, 13, 2, 3, 1, 3, 3, 1, 4, 3

Ordered data :

1, 1, 1, 2, 3, 3, 3, 3, 4, 5, 6, 13

Sample size, n = 12

Median = 1/2 * (n +1) th term

Median = 1/2 * 13 = 6.5th term

Median value = 3

Midrange = (Maximum + minimum) / 2

Midrange = (1 + 13) / 2 = 7

Geometric mean : √(x1*x2*.. xn)^1/n

Geometric Mean:

(1*1*1*2* 3*3*3*3*4* 5*6*13)^1/12

= 2.82

9514 1404 393

Answer:

Step-by-step explanation:

1 m is 100 cm, so the volume is ...

  V = LWH

  V = (100 cm)(50 cm)(4 cm) = 20,000 cm³ . . . volume

__

The mass is ...

  (20,000 cm³)(2.7 g/cm³) = 54,000 g = 54 kg

The mass of the block is 54 kg.