A train is travelling at a constant speed. The distance travelled is proportional to the time taken. In 5 minutes the train travels 13 kilometers. Complete the table with the graph.

Answer:

Step-by-step explanation:

resources. This includes fostering the wisest use of our land and water resources, ... Back Cover: Geologist John B. Mertie exploring the Brooks Range, April 1924. ... I would like to thank Lynn Horvath for her wise counsel and ... focuses more broadly on exploration as a his- ... he paused several times to meet with Eskimo.

Answer:

u = 6/35

Step-by-step explanation:

w = k * u

w = ku

Where

k = constant of proportionality

if w=5 when u= 3

w = ku

5 = k * 3

5 = 3k

k = 5/3

find u when w is =2/7​

w = ku

2/7 = 5/3 * U

2/7 = 5/3u

u = 2/7 ÷ 5/3

= 2/7 × 3/5

= (2*3)/(7*5)

= 6/35

u = 6/35

answer:B. 90 good luck I hope you pass

The answer is B which is 90

The range of the function (f+g)(x) = x² - 1 will be ( -1, ∞ ). The correct option is B.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

Given that the function is f(x) = x²+2x-5. The function g(x) will be calculated by the data given in the table.

x           -6    -3     -1    4

g(x)       16    10    6   -4

The function g(x) will be:-

g(x) = mx + c

m = ( 10 - 16 ) / ( -3 + 6 )

m = -6 / 3

m = -2

c = y - mx

c = 10 - 6

c = 4

g(x) = -2x + 4

The function ( f + g)(x) will be:-

( f + g)(x) = f(x) + g(x)

( f + g)(x) = x²+ 2x - 5 - 2x + 4

( f + g)(x) = x² - 1

At x = 0, the value ( f + g)(x) is -1. The range of the function is ( -1, ∞).

To know more about domain and range follow

https://brainly.com/question/2264373

#SPJ1

Answer:

34.69 years for the first part.

Step-by-step explanation:

I got it right

The volume of the solid is 4/5π.

The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.

In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by

V = ∫0 1 π(y)2dy

= ∫0 1 πx6dx

= π/7

= 4/5π

The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.

Learn more about volume here

https://brainly.com/question/16134180

#SPJ4

A.  The event "the student could run a mile in less than 7.72 minutes" can be written as Y < 7.72.

B. The probability that a randomly chosen student can run a mile in less than 7.72 minutes is approximately 0.7937.

(a) The event "the student could run a mile in less than 7.72 minutes" can be written as Y < 7.72.

(b) We need to find the probability that a randomly chosen student can run a mile in less than 7.72 minutes.

Using the standard normal distribution with mean 0 and standard deviation 1, we can standardize Y as follows:

z = (Y - mean)/standard deviation

z = (7.72 - 7.11)/0.74

z = 0.8243

We then look up the probability of z being less than 0.8243 using a standard normal table or calculator. This probability is approximately 0.7937.

Therefore, the probability that a randomly chosen student can run a mile in less than 7.72 minutes is approximately 0.7937.

Learn more about  probability   from

https://brainly.com/question/30390037

#SPJ11

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$11250\\ r=rate\to 3.45\%\to \frac{3.45}{100}\dotfill &0.0345\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}\)

\(A=11250\left(1+\frac{0.0345}{1}\right)^{1\cdot 5} \implies A \approx 13329.23 ~\hfill \underset{interest~paid}{\stackrel{13329.23~~ - ~~11250}{\approx\text{\LARGE 2079.23}}}\)

Answer: 6\(\sqrt{2}\)

Step-by-step explanation: why the process of elimination is because 9 is sticking like a sore thumb and the last one is too big the first one and the third one are similar but the third one has a square root of 3 so it would be THE  FIRST ONE.

The number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.

In a farm, there is food to feed 300 rabbits for 60 days.

Let x be the number of rabbits that must be sold if they want to be fed for 15 more days.

From the given data, we have the following equation:

300 * 60 = (300 - x) * 75

The equation represents the amount of food for 300 rabbits that can last 60 days is equal to the amount of food for 300 - x rabbits that can last 75 days.

Solving for x, we get:

x = 150 rabbits

Hence, the number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.

For more such questions on rabbits, click on:

https://brainly.com/question/378897

#SPJ8

The required length of the curve with the specified limits is calculated to be  23,423 units.

The curve r(t) is given as (5 t, 2 sin t, 2 cos t) where −4 ≤ t ≤ 5.

The expression to find the arc length of a parametric vector curve, we use,

Arc length = ∫√[ (dx/dt)² + (dy/dt)² + (dz/dt)²]

The above expression is derived from the Pythagoras theorem.

Applying the formula on the above curve, we have,

dx/dt = d/dt (5t) = 5

dy/dt = d/dt (2 sin t) = 2 cos t

dz/dt = d/dt (2 cos t) = -2 sin t

Arc length = ∫√[ 5² + (2 cos t)² + (-2 sin t)²]

Arc length = ∫ √[ 25 + 4 cos² t + 4 sin² t]

⇒ 2/3 [25 + 4 cos² t + 4 sin² t]^(3/2) × (25t + sin2t/4 + t/2 + t/2 - sin 2t/4)

⇒ 2/3  [25 + 4 cos² t + 4 sin² t]^(3/2) × (25t)

⇒ 50t/3  [25 + 4 cos² t + 4 sin² t]^(3/2)

⇒ 50t/3  [25 + 4(1)]^(3/2) = 50t/3 (29)^(3/2) = 156.16 × 50t/3

⇒ 156.16 × 50t/3 (the limits are from -4 to 5)

⇒ 13,013 - (-10,410)

⇒ 23,423 units.

Thus, the length of the given curve is 23,423 units.

To know more about arc length:

https://brainly.com/question/16833144

#SPJ4

Answer:

30.

Step-by-step explanation:

first term = a

3r term = ar^2

So here ar^2/ a  = r^2

r^2 = 5/180 = 1/36

r = 1/6

So missing term = 180 * 1/6 = 30.

First, determine the number of miles covered per day:

Her car already has 45,300 miles on it.

(a)The total number of miles, f(x), Stefanie's car will have been driven after x more days will be:

(b) Stephanie works 4 days a week.

After 3 weeks, the number of days worked = 4 x 3 = 12 days

Therefore, when x=12:

No, Is it not possible for A and B to be in- dependent events yet satisfy A = B?

Actually if two events are mutually exclusive it is only in a special case that they can be independent. The definitions state that two events A, B are mutually exclusive iff: P (A ∩ B) = 0, i.e. A ∩ B = ∅, independent iff: P (A ∩ B) = P (A) P (B). Assume know that A, B are both mutually exclusive and independent.

Two events A and B can be independent and yet satisfy A = B. In this case, the two events are identical, for example 'getting a head on the first flip' and they are always independent of themselves.

Yes, it is possible for events A and B to be independent and yet satisfy A = B. In probability theory, two events are considered independent if the probability of both events occurring is the product of the probabilities of each event occurring separately. If A = B, it merely means that the two events are identical. For instance, flipping a coin twice, the event A could be 'getting a head on the first flip' and event B could also be 'getting a head on the first flip'. Here, A = B and every event is independent of itself.

Answer:

the answer is 4.344

Step-by-step explanation:

hope this helps :)

Answer:

G(x) = x^3 - 3

Step-by-step explanation:

I'd used desmos

y=-2x(squared)+3x-7

the 2x is squared

hope that helped

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

Learn more about Congruent polygons here:

https://brainly.com/question/2096633

#SPJ1

Answer:

Your answer is C) 1.92

Hope this helps ^_^

Answer:

Sales tax is $1.92 or 192 cents.

Step-by-step explanation:

Given the price of a DVD is $24.00 plus 8% sales tax.

we have to find the sales tax on this DVD in dollars and cents.

The sales tax is 8% can be calculated as

8/100 X $24

1.92

In cents

as one dollar equals 100 cents

∴ 1.92 dollar = $1.92 = 192 cents

Hence, sales tax is $1.92 or 192 cents.

So your answer is C!!

i ⁴³⁵ = i ⁴³²⁺³ = i ⁴³² • i ³

i ⁴³⁵ = i ⁴³² • i ³

i ⁴³⁵ = (i ⁴)¹⁰⁸ • i ³

i ⁴³⁵ = 1¹⁰⁸ • (-i)

i ⁴³⁵ = -i

The value of the imaginary number i⁴³⁵ is : i ⁴³⁵ = -i.

Here, we have,

To evaluate the expression i⁴³⁵, we need to understand the properties of the imaginary unit, denoted by i.

The imaginary unit i is defined as the square root of -1, meaning i² = -1.

When raising i to an exponent, we can use the pattern of powers of i to simplify the expression.

The pattern of powers of i repeats every four exponents:

i¹ = i

i² = -1

i³ = -i

i⁴ = 1

Since i⁴ = 1, we can divide the exponent 435 by 4 to find the remainder:

435 divided by 4 gives a remainder of 3.

Therefore, i⁴³⁵ is equivalent to i³.

Using the pattern of powers of i, we know that i³= -i.

So, i⁴³⁵ = -i.

i.e. we get,

i ⁴³⁵ = i ⁴³²⁺³ = i ⁴³² • i ³

i ⁴³⁵ = i ⁴³² • i ³

i ⁴³⁵ = (i ⁴)¹⁰⁸ • i ³

i ⁴³⁵ = 1¹⁰⁸ • (-i)

i ⁴³⁵ = -i

To learn more on complex number click:

brainly.com/question/19467739

#SPJ6

Answer:

Step-by-step explanation:

Part A: Based on the given graph, we can observe that as the temperature of the city increases, the number of people at the swimming pool generally tends to increase as well. This suggests a positive correlation between temperature and the pool's population. In other words, when it gets hotter, more people are likely to visit the swimming pool. The relationship is not strictly linear, but it shows a general trend of increasing pool population with increasing temperature.

Part B: To determine the line of best fit, we can calculate the approximate slope and y-intercept using the given data points. Let's select two points from the data, such as (2.5, 1) and (12, 12):

Slope (m) = (change in y) / (change in x)

= (12 - 1) / (12 - 2.5)

= 11 / 9.5

≈ 1.16

To find the y-intercept (b), we can choose one of the points and substitute the values into the slope-intercept form (y = mx + b). Let's use the point (2.5, 1):

1 = 1.16 * 2.5 + b

1 = 2.9 + b

b ≈ -1.9

Therefore, the approximate slope of the line of best fit is 1.16, and the approximate y-intercept is -1.9.

The sum of the first n terms \($S_n$\) in the given sequence is equal to the n-th harmonic number \($H_n$\).

The sequence \($\{a_n\}$\) is defined as follows:

\($$a_n = \begin{cases}1 & \text{if } n = 1 \\\frac{1}{n} & \text{if } n > 1 \\\end{cases}$$\)

We need to find the value of  \($S_n = \sum_{k=1}^{n} a_k$\)

Let's calculate the first few terms to observe a pattern:

\(S_1 &= a_1 = 1 \\\\\)

\(S_2 &= a_1 + a_2 = 1 + \frac{1}{2} = \frac{3}{2} \\\)

\(S_3 &= a_1 + a_2 + a_3 = 1 + \frac{1}{2} + \frac{1}{3} = \frac{11}{6} \\S_4 &= a_1 + a_2 + a_3 + a_4 = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{25}{12} \\\)

Based on the observed pattern, it appears that \($S_n$\) can be expressed as a fraction. To find a general formula for \($S_n$\), let's express each term \($a_k$\) with a common denominator:

\(S_1 &= 1 = \frac{1}{1} \\S_2 &= 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \\S_3 &= 1 + \frac{1}{2} + \frac{1}{3} = \frac{6}{6} + \frac{3}{6} + \frac{2}{6} = \frac{11}{6} \\S_4 &= 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{12}{12} + \frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{25}{12} \\\)

From the observations, we can deduce that \($S_n$\) can be represented as:

\($$S_n = \frac{n}{n} + \frac{n}{2n} + \frac{n}{3n} + \dots + \frac{n}{nn} = \frac{1}{n} \left(\frac{n}{1} + \frac{n}{2} + \frac{n}{3} + \dots + \frac{n}{n}\right)$$\)

Notice that the expression in the parentheses is the harmonic series \($H_n = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}$\), but multiplied by \($n$\). Therefore, we have:

\($$S_n = \frac{1}{n} \cdot n \cdot H_n = H_n$$\)

So, the sum of the first \($n$\) terms \($S_n$\) is equal to the \($S_n$\)-th harmonic number \($H_n$\).

Learn more about sequence here: https://brainly.com/question/30262438

#SPJ11

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

are you in preschool?

Answer:

it will take her 15 minutes (1/4 hour) to get from F to G

Step-by-step explanation:

distance formula:  d = r * t     Distance = Rate * Time

10 = 40t

t = 10/40 = 1/4 = 14 of 60 minutes; thus, 15 minutes

Answer:

The expression equivalent to 3( x - 9) Is

3(x) - 3(9)

3x-27

3(x)-3(9)= 3x-27

Answer:18

Step-by-step explanation:

The scale factor of the drawing to the real statue is 4

From the question, we have the following parameters that can be used in our computation:

The table

The scale factor is calculated as

Scale factor = Statue/Drawing

Substitute the known values in the above equation, so, we have the following representation

Scale factor = 36/9

Evaluate

Scale factor = 4

Hence, the scale factor is 4

Read more about scale factor at

https://brainly.com/question/15891755

#SPJ1

The difference in distance traveled by the two particles is 2√(2)π - 2π.

(a) To find the difference in distance traveled by the two particles, we need to calculate the arc length of their respective curves. The arc length of a curve ~r(t) = f(t)i + g(t)j + h(t)k over an interval [a, b] is given by the formula:

∫[a,b] √(f'(t)^2 + g'(t)^2 + h'(t)^2) dt

For the first particle's curve ~r1(t) = costi + sin tj + tk, we have f(t) = cos(t), g(t) = sin(t), and h(t) = t. Taking the derivative of each component gives us f'(t) = -sin(t), g'(t) = cos(t), and h'(t) = 1.

Plugging these values into the arc length formula, we get:

∫[0,2π] √((-sin(t))^2 + (cos(t))^2 + 1^2) dt

= ∫[0,2π] √(sin^2(t) + cos^2(t) + 1) dt

= ∫[0,2π] √(2) dt

= √(2) ∫[0,2π] dt

= √(2) * [t] evaluated from 0 to 2π

= √(2) * 2π

= 2√(2)π

For the second particle's curve ~r2(s) = i + tk, we have f(s) = 1, g(s) = 0, and h(s) = s. Taking the derivative of each component gives us f'(s) = 0, g'(s) = 0, and h'(s) = 1.

Plugging these values into the arc length formula, we get:

∫[0,2π] √(0^2 + 0^2 + 1^2) ds

= ∫[0,2π] 1 ds

= [s] evaluated from 0 to 2π

= 2π

Therefore, the difference in distance traveled by the two particles is 2√(2)π - 2π.

To know more about distance traveled refer here:

https://brainly.com/question/12696792

#SPJ11