The express elevator in the Empire State Building in New York City travels nonstop from
the ground floor to the top floor at a rate of 1,400 feet per minute.
The express elevator in the John Hancock Center in Chicago travels nonstop from the
ground floor to the observatory on the top floor at a rate represented by the equation
y = 30x, where y is the height, in feet, and is the number of seconds
Graph the two relationships on the grid below to compare the rates of the
two elevators,
ELEVATOR RATES
I
Height (feet)
1,000
900
800
700
600
500
400
300
200
100
0
10
40
50
20 30
Time (seconds)
Which elevator travels at a faster rate?
Using the information from the graph, explain how you got your answer.

The Express Elevator In The Empire State Building In New York City Travels Nonstop Fromthe Ground Floor

Answers

Answer 1

The elevator of  John Hancock Center in Chicago travels at a faster rate.

The standard equation of a line is y = m + bm is the slope or rate of changeb is the y-intercept.

For the equation represented by the height of the elevator of  John Hancock Center in Chicago given as y = 30x, the rate of change is 30 ft/s which is equivalent to 1800 per minute.

Since the express elevator in the Empire State Building in New York City travels nonstop from  the ground floor to the top floor at a rate of 1,400 feet per minute, hence the elevator of  John Hancock Center in Chicago travels at a faster rate.

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Related Questions

solve for x -

[tex] x^{2} + 5x + 6 = 0 \\ \\ [/tex]

ty! :)​

Answers

Hello,

x² + 5x + 6 = 0

a = 1 ; b = 5 ; c = 6

∆ = b² - 4ac = 5² - 4 × 1 × 6 = 25 - 24 = 1 > 0

2 solutions :

[tex] x_{1} = \frac{ - b - \sqrt{\Delta} }{2a} = \frac{ - 5 - 1}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]

[tex]x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 5 + 1}{2 \times 1} = \frac{ - 4}{2} = - 2[/tex]

S = { -3 ; -2}

Consider the following pair of equations:

y = x + 4
y = −2x − 2

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Source
StylesFormatFontSize

Answers

Answer:

(-2, 2)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=x+4\\y=-2x-2 \end{cases}[/tex]

To solve by substitution, substitute the first equation into the second equation:

[tex]\implies x+4=-2x-2[/tex]

Add 2x to both sides:

[tex]\implies x+4+2x=-2x-2+2x[/tex]

[tex]\implies 3x+4=-2[/tex]

Subtract 4 from both sides:

[tex]\implies 3x+4-4=-2-4[/tex]

[tex]\implies 3x=-6[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3}=\dfrac{-6}{3}[/tex]

[tex]\implies x=-2[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\implies y=-2+4[/tex]

[tex]\implies y=2[/tex]

Therefore, the solution to the given system of equations is (-2, 2).

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Substitute y value from first eqn in second equation

y=-2x-2x+4=-2x-23x=-6x=-2

Put in first one

y=-2+4=2

(-2,2) is the solution

A movie ends at 7:45 P.M. The next movie begins 50 minutes later. What time does the next movie begin?

Answers

Answer:

8:35 PM

Step-by-step explanation:

First, subtract 15 from 50.

50-15=35

Add that 15 taken from 50 to 7:45.

7:45 + 0:15 = 8:00

Add 35 to 8:00

8:00 + 0:35 = 8:35

The next movie will start at 8:35 PM.

Hope this helps!

3\sqrt(6)*6\sqrt(6)
Please quick reply!

Answers

Answer: 3

Step-by-step explanation:

Multiply the numerator to get 3 x 6 is 18

Multiply the denominator to get √6 x √6 = 6

Divide 18 by 6 to get the answer is 3


A chemist wants to make 45 ml of a 17% acid solution by mixing a 13% acid solution and a 19 % acid solution. How many milliliters of each solution should the chemist use?

Answers

Answer:

22 millilitres of 13% solution

23 millilitres of 19% solution

Step-by-step explanation:

A + B = 45

13A + 19B = 45 x 17 = 765

-13A - 13B + 13A + 19B = -650 + 765 = 115

5B = 115

B = 23

22 + 23 = 45

A = 22

At 3:20, what is the measure in degrees of the lesser angle formed by the hour hand and the minute hand

Answers

Answer: 30 degrees

Step-by-step explanation:

Which triangles are similar to ABC? Explain.

Answers

NMP, the mesures of the sides of NMP are half the length of the mesures of the sides on ABC

Answer: △JKL & △ MNP

Step-by-step explanation:

△JKL is similar because:

5 x 1.6 = 8

2.5 x 1.6 = 4

3.75 x 1.6 = 6

△MNP is also similar because:

4 x 2 = 8

2 x 2 = 4

3 x 2 = 6

find the value of x from the figure

Answers

Answer:

x = 30

Step-by-step explanation:

110 and 3x - 20 are supplementary angles, sum to 180° , then

110 + 3x - 20 = 180

90 + 3x = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer:

x = 30

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

For this question, you must be clear of the angle properties.

z + 110 = 180 (Sum of Angles on a straight line)

z = 180 - 110 = 70

z = 3x - 20 (Corresponding Angles)

3x - 20 = z

3x - 20 = 70

3x = 70 + 20

3x = 90

x = 90 / 3 = 30

What addition/subtraction equation should I put?

Answers

Answer:

7 - 10

Step-by-step explanation:

Because it is -3 and 7 - 10 = -3

A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.

A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°

Answers

The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

What is a right angle triangle?

A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore, angle of depression from the helicopter can be found as follows:

tan x = opposite / adjacent

where

x = angle of depression

Hence,

tan x = 660 / 280

tan x = 2.35714285714

x = tan⁻¹ 2.35714285714

x = 67.1231281953

x = 67°

Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

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Answer:

D = 67

Step-by-step explanation:

A population of a particular yeast cell develops with a constant relative growth rate of 0.4311 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 5 hours. (Round your answer to one decimal place.)

Answers

A population of a particular yeast cell develops with a constant relative growth rate of [tex]0.4311[/tex] per hour. The initial population consists of [tex]3.9[/tex]million cells. Find the population size (in millions of cells) after 5 hours. Population size after [tex]5hrs[/tex]  is  [tex]33.6million[/tex].

How can we find the population size ?

The projection of population growth in yeast is given by

[tex]N=N_{0} e^{rt}[/tex]

Where [tex]N_{0}[/tex]=initial population which is [tex]3.9million[/tex]

[tex]r[/tex]=intrinsic rate of natural increases which is [tex]0.4311million per hour[/tex]

N is population size

Substitute the values

[tex]N=N_{0} e^{rt}\\N=3.9(e^{0.4311*5} )\\\\N=33.6 million[/tex]

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Let k be a positive integer. In how many ways can one select three distinct numbers from the set {1,2,..., 3k} such that their sum is divisible by 3

Answers

Reduce the numbers in the list modulo 3 to get the set

{1, 2, 0, 1, 2, 0, …, 1, 2, 0}

containing [tex]k[/tex] copies each of 1, 2, and 0.

Take any 3 elements from the list. Their sum is divisible by 3 if those elements' residues also sum to 3 ≡ 0 (mod 3). To get a sum of 0, we must make one of the following choices:

3 elements each with the same residue, so

0 + 0 + 0 ≡ 0 (mod 3)

1 + 1 + 1 ≡ 3 ≡ 0 (mod 3)

2 + 2 + 2 ≡ 6 ≡ 0 (mod 3)

1 element each with different residues, so

0 + 1 + 2 ≡ 3 ≡ 0 (mod 3)

There are

[tex]\dbinom k3 \dbinom k0 \dbinom k0 = \dfrac{k(k-1)(k-2)}6[/tex]

ways of choosing 3 elements with a given residue and 0 elements with any other residue, hence

[tex]3\dbinom k3\dbinom k0\dbinom k0 = \dfrac{k(k-1)(k-2)}2[/tex]

ways of choosing any 3 elements with the same residue, and there are

[tex]\dbinom k1 \dbinom k1 \dbinom k1 = k^3[/tex]

ways of choosing any 3 elements with distinct residues.

So, the total number of ways of making the selection is

[tex]3\dbinom k3\dbinom k0^2 + \dbinom k1^3 = \boxed{\dfrac32 k^3 - \dfrac32 k^2 - k}[/tex]

The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3

Answers

1a) f(x) = -1/3(x + 12)² + 9

1b) f(x) = -1/3x² - 8x - 39

Lets simplify it,

Expand by FOIL (First Outside Inside Last)

Standard Form: ax² + bx + c = 0

Transformations Graph: f(x) = a(bx - c)² + d

Reflected down and vertically stretched by 1/3:   a = -1/3

Shifted vertically by 9 units:   d = 9

Shifted horizontally by -12 units:   c = -12

Vertex Form:

 f(x) = a(bx - c)² + d

 f(x) = -1/3(x + 12)² + 9

Standard Form:

f(x) = -1/3(x + 12)² + 9

f(x) = -1/3(x² + 24x + 144) + 9

f(x) = -1/3x² - 8x - 48 + 9

f(x) = -1/3x² - 8x - 39

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2+8+32+128…..,n=9
Evaluate each geometric series described

Answers

The value of 2+8+32+128…..,n=9 is 174762

How to evaluate the series?

The series is given as:

2+8+32+128…..,n=9

Start by calculating the common ratio (r)

r = 8/2

r = 4

The sum of the series is then calculated as:

[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]

This gives

[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]

Evaluate the difference

[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]

Evaluate the quotient

[tex]S_9 = 174762[/tex]

Hence, the value of 2+8+32+128…..,n=9 is 174762

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10 points please help me!!!

Answers

Step-by-step explanation:

16-19 -> 3 (16, 17, 19)20-23 -> 1 (21)24-27 -> 3 (24, 26, 26)28-31 -> 4 (28, 29, 30, 31)32-35 -> 5 (32, 33, 34, 34, 35)

Write y=5x-9 in standard form
Will give brainliest!

Answers

Answer:

5x - y = 9

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = 5x - 9 ( subtract 5x from both sides )

- 5x + y = - 9 ( multiply through by - 1 )

5x - y = 9 ← in standard form

A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. Her work is shown below. What is Amies error

Answers

Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

In the question, we are given that a sphere and a cylinder have the same radius and height.

We assume the radius of the sphere to be r, and its height to be h.

Now, the height of a sphere is its diameter, which is twice the radius.

Thus, the height of the sphere, h = 2r

Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.

The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.

Thus, the volume of the given sphere using the formula is (4/3)πr³.

The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.

Now, to compare the two volumes we take their ratios, as

Volume of the sphere/Volume of the cylinder

= {(4/3)πr³}/{2πr³}

= 2/3.

Thus, the volume of the sphere/the volume of the cylinder = 2/3,

or, the volume of the sphere = (2/3)*the volume of the cylinder.

Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.

Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

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For the complete question, refer to the attachment.

For the geometric series 1 - 2/3 + 4/9 - 8/27....
find s8

Answers

Answer:

Step-by-step explanation:

The sum of an alternating geometric series SUM((-1)^n*ar^n) = a/(1+r). The given series has r=2/3 and a=1. The sum will be 1/(1+2/3)= 3/5

Hello,

We have s0 = 1 and q = -2/3

[tex]S _{n} = S _{0} \times q {}^{n} = 1 \times ( - \frac{2}{3} ) {}^{n} [/tex]

[tex]S _{8} = ( - \frac{2}{3} ) {}^{8} = \frac{2 {}^{8} }{3 {}^{8} } = \frac{256}{6 561} [/tex]

The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. Group of answer choices mean: 1.39; standard deviation: 0.80 mean: 1.18; standard deviation: 0.64 mean: 1.39; standard deviation: 0.64 mean: 1.18; standard deviation: 1.30

Answers

The value of the Mean & Standard deviation is 1.30 and 1.18.

According to the statement

we have a given that the random variable x represents the number of computers that families have along with the corresponding probabilities.

And we have to find the mean and standard deviation from the given data which is related to the probabilities values

So, according to the given data

The formula to compute the mean is:

Mean = summation [x*p(x)]

Compute the mean as follows:

Mean = summation [x*p(x)]

Mean = summation [0*0.49 + 1* 0.05 + 2*0.32 + 3*0.07 + 4*0.07]

Mean = 0 +0.05 + 0.64 + 0.21 + 0.28

Mean = 1.18

The mean of the random variable x is 1.18.

And after calculating the variance from the formula get

The value of standard deviation is 1.30

So, The value of the Mean & Standard deviation is 1.30 and 1.18.

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Study the illustration. Write the ratio
of flowers to bees. Complete the sentence.
For every 5 flowers there are _______
bees.

Answers

Answer: 6 bees

Step-by-step explanation:

The picture has 12 bees and 10 flowers. Thus, the ratio of flowers to bees is 10 to 12, which simplifies to 5 to 6.

Therefore, for every 5 flowers, there are 6 bees.

16. c= vλ. If c = 2.998 x 10^8 m/s, v= 4.41 x 10¹4 s-¹; find a value for λ.

Answers

Answer:

6.80 x 10⁻⁷ m

Step-by-step explanation:

You can find the value of λ by inserting the given values into the equation and simplifying.

c = vλ                                                            <----- Given equation

2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ               <----- Insert values

6.80 x 10⁻⁷ m = λ                                          <----- Divide both sides by 4.41 x 10¹⁴

A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72m2, what is the length of the pool?

Answers

The length of the square pool is 8. 49cm

How to determine the area

Note that the formula for finding the area of a square is given as;

Area = length^2

We have

Area = 72 m²

Substitute into the formula

I^2 = 72

Find the square root of both sides

I= √72

I = 8. 49cm

The length of the square pool given as I is 8. 49cm

Thus, the length of the square pool is 8. 49cm

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check out the pic first

Answers

Answer: (0, 16)

Step-by-step explanation:

y = mx + c

c is the y intercept

from the equation, c = 16

(it's not exactly mx but you don't need to solve for x)

Given the right triangle, use the pythagorean theorem to find "a" (one of the legs) when c=85 and b= 53. (round answer to nearest tenth).

Answers

Answer:

a= 100.2

Step-by-step explanation:

You solve it like you ate looking for the hypotenuse

Which of the following is an equivalent form of the equation of the graph shown in the xyxyx, y-plane above, from which the coordinates of vertex AAA can be identified as constants in the equation

Answers

The equivalent form of the equation y=[tex]x^{2} -2x-15[/tex]given is y=(x+3)(x-5).

Given an equation y=[tex]x^{2}[/tex]-2x-15 and we are required to find the equivalent form of the equation.

Equation is like a relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or any other equation  depending on the powers of the variable.

To find the equivalent equations we are required to form factors of the equation. Equivalent equation are those equations which when solved gives the same solution as the equation when solved gives.

y=[tex]x^{2}[/tex]-2x-15

y=[tex]x^{2}[/tex]-5x+3x-15

y=x(x-5)+3(x-5)

y=(x+3)(x-5)

Hence the equivalent form of the equation y= [tex]x^{2}[/tex]-2x-15 given is

y=(x+3)(x-5).

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Question is incomplete as question should includes the equation

y= [tex]x^{2}[/tex]-2x-15.

Read the following description of a relationship:
Ron is making a banner by stringing letters on a cord. The cord weighs 8
ounces, and each letter weighs 10 ounces.
Let n represent the number of letters and w represent the weight of the banner.
This relationship can also be shown in a table. Complete the equation that represents the
relationship between n and w

Answers

The equation that represents the relationship between n and w is w = 10n + 8.

How to illustrate the expression?

From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8

ounces and each letter weighs 10 ounces.

Let represent the number of letters

Let w represent the weight of the banner.

In this case, when n = 6, w = 68 and when n = 7, w = 78.

Therefore, the relationship will be:

w = 10n + 8

To confirm let's use n = 6

10n + 8

10(6) + 8

= 68

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Answer:

Step-by-step explanation:

w=10n+8

mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees

Answers

Answer:

Below in bold.

Step-by-step explanation:

That would be 4/15 * 360   as there are 360 degrees in a circle

= 96 degrees.

Please please help me. It’s due right now! it would mean a lot :))<3 Pls show work!!!

Answers

Answer: 9 triangles.

Step-by-step explanation:

Just make a dot in the middle and make lines and connect each line to an edge or bend.

Solve:

2a + 6 = 12

a =

Answers

Answer:

8

Step-by-step explanation:

because hhhhhh

gghhhh

jkkkkk

lllll

vvvvv

dddfff

oooooo

eeeerer

kkkkkk

lllll.ssss

A bag contains lettered tiles. the theoretical probability of choosing a vowel is 40%. the bag contains 78 consonants. how many tiles are in the bag?

Answers

The total number of ties present in the bag are 130.

What is probability?

Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."

Formula for probability is -

Probability(Event) = Favourable Outcomes/Total Outcomes

It P(E) is the probability for occurring any event.

'x' be the favourable outcome.

'n' be the total outcome.

Then,

P(E) = x/n.

Calculation for the total tiles present the bag.

The probability of choosing a vowel is 40% = 0.4.

Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.

Let P(E) be the probability of the occurrence of the consonants.

Then,

P(E) = total number of consonants/total tiles in the bag.

Let 'T' be the total tiles in the bag.

0.6 = 78/T

T = 78/0.6

T = 130

Therefore, the total tiles present in the bag are 130.

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