A train starts from rest and accelerates uniformly until it has traveled 5.6 km and acquired a velocity of 42 m/s. What is the approximate acceleration of the train during this time?

Answer:

-443 is the 90th term

Step-by-step explanation:

n=90th

Given: 7-5n

> 7-5(90)

> 7-450

> -443

The legitimate probability distribution for the discrete random variable X whose possible values are 0, 3, 4, 5 and 6 is: P(X=0) = 0.2, P(X=3) = 0.2, P(X=4) = 0.3, P(X=5) = 0.2, and P(X=6) = 0.1.

For a probability distribution to be legitimate, the probabilities of all the possible values of a random variable need to add up to 1. So, in this case, the sum of all the probabilities must be equal to 1.

For the given values, we can assign the probability of 0.2 to the values 0 and 3, 0.3 to the value 4 and 0.1 to the value 6, so that the sum of all the probabilities is 1.

Therefore, the legitimate probability distribution for the given discrete random variable X is as follows:

| Value (x) | P(X=x) |

|---|---|

| 0 | 0.2 |

| 3 | 0.2 |

| 4 | 0.3 |

| 5 | 0.2 |

| 6 | 0.1 |

The legitimate probability distribution for the discrete random variable X whose possible values are 0, 3, 4, 5 and 6 is: P(X=0) = 0.2, P(X=3) = 0.2, P(X=4) = 0.3, P(X=5) = 0.2, and P(X=6) = 0.1.

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-19.99; The line of best fit underpredicts the student's science test score.

So correct option is A.

A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.

The predicted science score for the student with IQ 100 can be calculated using the line of best fit:

ŷ = −20.3 + 0.7489 * 100 = 71.59

The residual is the difference between the actual science test score and the predicted science score:

residual = actual score - predicted score = 52.6 - 71.59 = -19.99

So the line of best fit underpredicts the student's science test score by 19.99 points.

Therefore, the residual is:

-19.99; The line of best fit underpredicts the student's science test score.

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Answer:

A) Yes; AA Similarity

Step-by-step explanation:

Yes; AA Similarity

The differentiated form of the function with respect to x will be e³ˣ³.9x².

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range. The exponential function is that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x where a is a constant and a>1.

It is given that the function is,

y=e³ˣ³

Differentiate the function with respect to x.

\(=\frac{dy}{dx} \\\\ =\frac{d}{dx}\left(\left(e^3\right)^{x^3}\right) \\\\ =e^{3x^3}\frac{d}{dx}\left(3x^3\right) \\\\ =e^{3x^3}\cdot \:9x^2\)

Thus, the differentiated form of the function with respect to x will be e³ˣ³.9x².

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Answer:

It's true

Step-by-step explanation:

Answer:

5ft

Step-by-step explanation:

Given parameters:

Length of the pool  = 25ft

Width of the pool  = 15ft

Volume of water the pool can hold = 1875ft³ of water

Unknown:

Depth of the pool = ?

Solution:

The pool is in the shape of a cuboid.

The volume of a cuboid is given as;

        Volume of a cuboid  = L x width x depth

Insert the parameters and solve for the depth;

        1875  = 25 x 15 x depth

         depth = \(\frac{1875}{25 x 15}\)   = 5ft

The value of x is (-∞, -5) ∪ (1, ∞).

Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),

Solving for x,

Factors =

\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)

Therefore,

\(\left(x-1\right)^3\left(x+5\right) > 0\)

\(x < -5\quad \mathrm{or}\quad \:x > 1\)

Hence the value of x is (-∞, -5) ∪ (1, ∞).

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The height of the tree after 6 years can be expressed as "3 feet + 6f feet."

The correct answer is A. 3f + 6 feet.

To determine the current height of the tree in terms of "f,"

let's analyze the given information.

We know that the tree was initially 3 feet tall when it was planted 6 years ago.

Since the tree grows every year, we can assume that its growth rate is consistent.

Let's denote the current height of the tree as "h" (in feet).

After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").

Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."

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Add 7 to both sides.

Add −4 and 7 to get 3.

Multiply both sides by 3, the reciprocal of 1/3 . Since 1/3 is >0, the direction of inequality remains the same.

Multiply 3 and 3 to get 9.

The equation for the cost y birr in terms of the distance X driven is y = 20 + 2x.

When the car is leased for 5 days, the cost is 100 + 2x.

From the information, the car rental company leases automobiles for a charge of 20 birr / day plus 2birr/km.

The equation for the distance x will be:

= 20 + (2 × x)

= 20 + 2x.

When the car is leased for 5 days, this will be:

= 5(20) + 2x.

= 100 + 2x

= 100 + 2x

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The area of the net of the solid figure is 96 square inches

The image that completes the question is added as an attachment

From the image, we have:

Squares = 6

Length = 4

The area of the net is then calculated as:

Area = Squares * Length^2

This gives

Area = 6 * 4^2

Evaluate

Area = 96

Hence, the area of the net of the solid figure is 96 square inches

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Answer:

Step-by-step explanation:

In order to calculate the 40% of 95, multiply 40/100 by 95:

(40/100)(95) = 38

To determine the associated percentage to 9 of 45, proceed as follow:

(x/100)(15) = 9

x = (100/15)(9)

x = 60

Answer:

5

Step-by-step explanation:

plug everything in:

48+4h=68

-48      -48

4h=20

divide by 4 to isolate h

h=5

Answer:

H=5

Step-by-step explanation:

S=68, L=6, w=2, H=?

68=4x6x2+2x2xH

68=48+4H

68-48=4H (collect like terms)

20=4H (divide both side by the coefficient of H)

H=5

Answer:

5cm

Step-by-step explanation:

Given data

volume = 225π cm³

Height= 9cm

r= ???

Volume of cylinder

v=πr^2h

substitute

225π= π*r^2*9

225= r^2*9

r^2= 225/9

r^2= 25

r= √25

r= 5cm

Hence the radius is 5cm

The remaining amount of salt that Tom needed to pour was 67.59 grams.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The group's total number of items decreases or becomes lower when we subtract from it.

As per the given,

The total amount that Tom needs to pour = 84.99 grams

Amount poured = 17.4 grams

Remaining = 84.99 grams - 17.4 grams = 7.59 grams

Hence "The remaining amount of salt that Tom needed to pour was 67.59 grams".

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The probability of observing heads when tossing either coin is P(h) = 0.5*P(f) + 0.6*P(b), and the probability of observing tails is P(t) = 0.5*P(f) + 0.4*P(b).

Let's denote the probability of observing heads when tossing the fair coin as P(h|f) and the probability of observing tails when tossing the fair coin as P(t|f). Similarly, we can denote the probability of observing heads when tossing the biased coin as P(h|b) and the probability of observing tails when tossing the biased coin as P(t|b).

In this experiment, the probability of tossing the fair coin is P(f) and the probability of tossing the biased coin is P(b). We can calculate the probability of observing heads as:

P(h) = P(h|f)*P(f) + P(h|b)*P(b)

= 0.5*P(f) + 0.6*P(b).

Similarly, the probability of observing tails is:

P(t) = P(t|f)*P(f) + P(t|b)*P(b)

= 0.5*P(f) + 0.4*P(b).

The probability of observing heads when tossing either coin is P(h) = 0.5*P(f) + 0.6*P(b), and the probability of observing tails is P(t) = 0.5*P(f) + 0.4*P(b).

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"Nathan rolls a number cube and records the result of each roll in the table" is a true statement. Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

"He spun a 4 five times." is not a valid statement, as it is not clear what "he" or "a 4" refers to.

A valid probability distribution is a set of possible outcomes of a random event, along with the corresponding probabilities of those outcomes occurring. For example, if we roll a number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6, and the probability of each outcome occurring is 1/6.

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The graph of the piecewise function is the one in option D-

First, we know that:

f(x) = 4  when x ≤ 3

So, we want to have a horizontal line in the left side of the graph, such that it ends in a closed circle at x = 3 (we need to have a closed circle because the symbol ≤ is used).

From the given graphs, the only one with that form is D.

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The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.

Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).

(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get

P(t)=40

(50(1+0.05t))/(2+0.01t)=40

Cross multiply both sides, we get

50(1+0.05t)=40(2+0.01t)

Apply the distributive property a(b+c)=ab+ac, we get

50+2.5t=80+0.4t

Subtract 0.4t and 50 from both sides, we get

50+2.5t-0.4t-50=80+0.4t-0.4t-50

2.1t=30

Divide both sides with 2.1, we get

t=14.29 months

(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get

\(\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end\)

(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.

Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.

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Answer:

just sayin x=4

Step-by-step explanation:

\(\textit{arc's length}\\\\ x = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =\frac{\pi }{3} \end{cases}\implies x=10\cdot \cfrac{\pi }{3}\implies x\approx 10.47\)

Answer:

the savings is 6000

Step-by-step explanation:

We are told that the ratio of savings to expenditure is 2: 8, that is, that person saves 2 when he spends 8.

They tell us to find the savings when the cost is 24,000, so we are left with:

24000 * 2/8 = 6000

which means that when 24000 are spent the savings is 6000

3900000×18% = 702000

702000÷2500 = 280.8 per share dividend

450×280.8 = 126360

Answer:

Same I also like numbers

Answer:

yeah numbers are funnnnnnnn

Answer:

(a) 0.0000245

(b) 0.000025

Step-by-step explanation:

The complete question is:

Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000 shipped. The probability that the first chip randomly selected is defective is  50 /10,000  = 0.005.  Compute the probability that two randomly selected chips are defective under the assumption of independent events.

Solution:

(a)

In this case we need to compute the conditional probability of selecting two defective chips, i.e. the selection of the second defective chip is dependent on the first defective chip.

The probability of selecting the first defective chip is:

\(P(1D)=\frac{50}{10000}=0.005\)

Now there are 9999 chips left and 49 defective chips among them.

The probability of selecting the second defective chip is:

\(P(2D)=\frac{49}{9999}=0.0049\)

Compute the probability that two randomly selected chips are defective using conditional probability as follows:

P (Two defective chips) \(=P(1D)\times P(2D)=0.005\times 0.0049=0.0000245\)

Thus, the answer is 0.0000245.

(b)

Compute the probability that two randomly selected chips are defective under the assumption of independent events as follows:

The above statement implies that the selection was done with replacement.

The probability is:

P (Two defective chips) \(=P(1D)\times P(2D)\)

                                      \(=\frac{50}{10000}\times \frac{50}{10000}\\\\=0.005\times 0.005\\\\=0.000025\)

Thus, the probability that two randomly selected chips are defective under the assumption of independent events is 0.000025.

The slope of the line is -0.8.

The formula for distance  is...

y2−y1                                5−1

______=                       ________    

  x2−x1                            −9− −4

And so when simplified we  get

4

__

-5

Giving us -0.8.

Answer:B

Step-by-step explanation:

Step-by-step explanation:

This is a circle with center, h,k = 3,2 and radius = 2

   circle equation is   ( x-h)^2 + (y-k)^2 = r^2

so:

(x-3)^2 + (y-2)^2 = 4