Q2. A train travels at a constant speed of 45 m/s. a) Calculate the distance travelled by the train in:
i) 30 s
ii) 2 minutes.​

Answer:

The third one as they have no links really

The number of decorative pillows did the realtor arrange on each twin bed and queen bed is 6 and 9 respectively.

let

x + y = 15

2x + y = 21

From equation (1)

x = 15 - y

2x + y = 21

2(15 - y) + y = 21

30 - 2y + y = 21

- 2y + y = 21 - 30

-y = -9

y = 9

Substitute y = 9 into

x + y = 15

x + 9 = 15

x = 15 - 9

x = 6

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[tex]y = 2x {}^{2} - 4x - 16 \\ \delta = b {}^{2} - 4ac \\ \delta = ( - 4) {}^{2} - 4(2)( - 16) \\ \delta = 16 + 128 \\ \delta = 144 > 0 [/tex]

[tex]x = \frac{ - b + \sqrt{ \delta} }{2a} = \frac{4 + 12}{2 \times 2} = \frac{16}{4} = 4[/tex]

[tex]x = \frac{ - b - \sqrt{ \delta} }{2a} = \frac{4 - 12}{2 \times 2} \frac{ - 8}{4} = - 2[/tex]

[tex]x = 4 \: \: \: \: \: or \: \: \: \: x = - 2 \\ (x - 4) = 0 \: \: \: \: \: or \: \: \: \: \: (x + 2) = 0[/tex]

Answer:

B

Step-by-step explanation:

Answer:

  ln(5/3)

Step-by-step explanation:

The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.

We can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.

  [tex]\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}[/tex]

From the given similar triangles we can conclude that the length of Side SQ is; 4

We are given that;

PQ is parallel and congruent to MT.

Now, from the concept of similar triangles , we can say that;

PS/TS = QS/MS

From the given triangle we see that;

PS = 3 - 2x

QS = 6x - 1

MS = 30

TS = 10

Thus;

(3 - 2x)/10 = (6x - 1)/30

Cross multiply to get;

3(3 - 2x) = 6x - 1

9 - 6x = 6x - 1

Rearranging gives;

6x + 6x = 9 + 1

12x = 10

x = 10/12

x = 5/6

Thus;

SQ = 6(5/6) - 1

SQ = 4

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Answer:

Step-by-step explanation:

Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM.  9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM.  60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.

Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.

Here is the five-number summary, range and interquartile range:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the data. The  minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.

Median = 25

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Answer:

Step-by-step explanation:

The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.

Answer:

680

Step-by-step explanation:

x = total number

.6x  = bus riders = 408              (.6 is decimal for 60%)

.6x = 408

x = 408/.6 = 680

The points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).

Given:

f(x) = -0.5x+2

g(x) = x³ - 5x² + 3

The point of intersection exists the point where f(x) = g(x)

x³ - 5x² + 3 = - 0.5x + 2

x³ - 5x² + 3 + 0.5x - 2 = 0

x³ - 5x² + 0.5x + 1 = 0

Factorize and estimate the value of x

Let x = 0.53 and 4.85

substitute the value of x = 0.53

f(0.53) = -0.5(0.53) + 2

f(0.53) = -0.265 + 2

f(0.53) = 1.375

If x = 4.85

f(4.85) = -0.5(4.85) + 2

f(4.85) = -2.425 + 2

f(4.85) = -0.245

Therefore, the points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).

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360° ÷ 10 ÷ 2 = 18°

So the length of the decagon side is:

10 × tan18° × 2 = 20 × tan18°

The area is: ½ × 20 × tan18° × 10 × 10 = 1000 × tan18°

≈ 324.9

.: 324.9 is the final answer.

I hope this helps.

The line of best-fit that represents the relationship between velocity and time is:

v = 2.19t + 6.7.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (t,v) are given as follows:

(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).

Hence, inserting these points into a calculator, the equation is given by:

v = 2.19t + 6.7.

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The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

To find the minimum value of 10x (3y/5):

Given - y = 3/(2x)

So, we want the bare minimum of,

Take the derivative to obtain:

When you set it to zero, you get:

So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.

Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.

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Answer:

irrational,  it can't be written as a fraction

Step-by-step explanation:

Answer:

Euler's Formula = F+V=E+2

F=9

V=14

So, 9+14=E+2

23=E+2

23-2=E

21=E

Hence, E (edges) = 21

Step-by-step explanation:

Using the permutation formula, the number of different options for the top three finishers is given as follows:

[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]

The order in which the players are chosen is important, as A, B, C is a different outcome than C,B,A for example, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 students will be chosen from a set of 14, hence the number of ways is:

[tex]P_{14,3} = \frac{14!}{11!} = 2184[/tex]

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The correct option is the third one.

y = -√(x - 5) + 3

Remember that a square root can only be evaluated in values equal or larger than zero.

So, if we want the domain to be x > 5, then we must have:

√(x - 5)

Now we also want the range to be equal or smaller than 3, then we should have a constant term equal to 3, and a negative coefficient before the square root, then we get:

y = -√(x - 5) + 3

So the correct option is the third one.

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Answer:

Is there more information?  There is not enough to find the slope of a line.  I'll answer with an equation that works, but I suspect it won't be correct.

Step-by-step explanation:

If the only requirement is to have a line that goes through (4,3).  Then one could simply say:

y = 4

This is a horizonal line that goes through (3,4), and will always produce a y value of 4 regardless of x.  No, it will not pass through (4,3) since y is aleways 4, regardless of x.

If you wanted to get fancier, we could write a needlessly more complex equation:

y = (4/3)x

When x = 3, y = 4, so (3,4) is on this line.  But (4,3) is not.  y = (4/3)(4) means y = (16/3), not 4.

Answer:

not linear since all first differences are not equal

Step-by-step explanation:

To find the first differences, subtract each y value from the next y value.

Use only y values.

here are the 4 first differences you need to calculate.

1 - 0 = 1

4 - 1 = 3

9 - 4 = 5

16 - 9 = 7

Now you place them in the appropriate column in the table.

x   y      first difference

0   0       1

1   1         3

2   4       5

3   9       7

4   16

If the first differences were all equal, the function would be a linear function.

In this case, the first differences are all different, 1, 3, 5, 7, so the function is not linear.

The correct answer is option (C) median.

The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.

The mean, median, and mode are the three most commonly used measures of central tendency for populations that do not have much data, that is, they do not need to be grouped.

The mean, also known as average, is the value obtained by dividing the sum of a cluster of numbers by the number of them.

When arranging the numbers from least to largest, the median sits exactly in the middle of the values that are above. The median is a set that is a value that is in the middle of the other values.

The number that appears most frequently in a set of numbers is called the mode.

So, The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.

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Hi :)

Let's use some Algebra skills to find w ^•^

First off, let's subtract both sides by 6

[tex]\longrightarrow\darkblue\sf{-9-6 > 5w}[/tex]

[tex]\longrightarrow\darkblue\sf{-15 < 5w}[/tex]

Divide both sides by 5

[tex]\longrightarrow\sf{-3 < w}[/tex]

Or

[tex]\longrightarrow\sf{w > -3}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

A regular hexagon inscribed in a circle is the construction that requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments. Option D. This is further explained below.

Generally, any of the pieces into which something may be separated or which naturally separates over time. a section that is removed from a figure (such as a circle) using a line or plane as the cutting tool. a segment of a straight line that includes the territory between two points.

In conclusion, For the construction of a regular hexagon that is inscribed inside a circle, it is necessary for the ends of the diameter as well as the locations at which the arcs meet the circle to be linked, in the correct sequence, by line segments.

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Complete Question

Which construction requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments?

If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.

Given that m∠ABF=41° and BF is an angle bisector.

We are required to find the angle m∠BCE if BF is an angle bisector.

Angle bisector basically divides an angle into two parts.

If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.

In this way ∠ABC=2*∠ABF

∠ABC=2*41

=82°

In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.

∠BCE+∠CEB+EBC=180  (Sum of all the angles in a triangle is 180°)

∠BCE+90+82=180

∠BCE=180-172

∠BCE=8°

Hence if BF is an angle bisector then angle m∠BCE=8°.

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The coordinates for P and Q are as follows,

P = (a, a)

Q = (0, a)

Finding the Missing Coordinates:

Triangle OPQ is an isosceles triangle, hence two of its legs are equal.

Since the coordinates of the end point of the leg OQ lies on the y-axis, and OP is parallel to x-axis, OQ ⊥ QP ............ (1)

Also, it indicates that the x- coordinate of point Q is 0.

⇒ The coordinates of point Q are (0, a)

From (1), we can infer that,

OP = OQ [∵ OP is the hypotenuse]

⇒ The distance of point P from x-axis = a

The distance of point P from y-axis =a

Hence, the coordinates of point P are given as (a, a).

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Answer: A. V: x = –4; H: y = 4

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

First step is to find the slope of the line given

y = -x - 2

y = mx + c where m is the slope of the line so the slope of the line is -1

If 2 lines are perpendicular to one another, the product of the slopes is -1 so the slope of the perpendicular line is -1/-1 = 1

y = 1x + c or y = x + c

As the line passes through the coordinate (-5,10), we can substitute the x and y value of the coordinates into the equation

10 = -5 + c

c = 15

So the equation of the line is y = x + 15

0.9544 = 95.44% of scores lie between 220 and 380 points.

Normal distribution problems can be solved using the Z-score formula.

With a set of means and standard deviations, the Z-score for measure X is given by: After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is less than X. H. Percentile of X. Subtract 1 from the p-value to get the probability that the value of the measure is greater than X.

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

We are given mean 300, standard deviation 40.

This means that µ= 300, σ = 40

What proportion of scores lie between 220 and 380 points?

This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.

X = 380

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

Z= (380-300)/40

Z= 2

Z=2 has a p-value of 0.9772.

X=300

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

Z= (220-380)/40

Z=-2

Z=-2 has a p-value of 0.9772.

0,9772 - 0,0228 = 0,9544

0.9544 = 95.44% of scores lie between 220 and 380 points.

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Answer:

you need all of them?

Step-by-step explanation:

Answer:

Step-by-step explanatio