A sports centre has a seating capacity of 600. Seventy-five percent of the seats are occupied. How many seats are unoccupied?

Answer:

c=80

Step-by-step explanation:

Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.

So let's see that characteristic equation:

20⁢r^2+c⁢r+80⁢=0

The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.

a=20

b=c

C=80

c^2-4(20)(80)

We want this to be 0.

c^2-4(20)(80)=0

Simplify:

c^2-6400=0

Add 6400 on both sides:

c^2=6400

Take square root of both sides:

c=80 or c=-80

Based on further reading damping equations in form

a⁢y′⁢′+b⁢y′+C⁢y=0

should have positive coefficients with b also having the possibility of being zero.

N is the midpoint of MO and NO is 5, so MN would also be 5

MP = MN + NP = 5 + 9 = 14

Answer:50

Step-by-step explanation:(40x100):80

Answer: 50 workers

Let the ratio be

(40×100):80

= 400/80

= 50

Therefore 50 workers will complete the same work in 80 hours.

Must click thanks and mark brainliest

Answer:

10610

Step-by-step explanation:

Given,

T=6years

R=3.2%

A=86125

Now,

CA=P[1+R/10]^T

or,P=86125/[1+3.2/10]^6

=86125/5.29

=10610

Step-by-step explanation:

angle of a triangle is 180, therefore to get the remaining one, subtract the sum of the two knows from 180, also for the second one; angle on a straight line is as well 180, since you have fine the interior one, subtract it from 180 to get the second answer

Answer:

so angles in a triangle add up to 180,

32+50+m<MQP=180

82+m<MQP=180

m<MQP=180-82

=98°

and angles on a straight line add up to 180 therefore

m<MQR=180-m<MQP

=180-98

=82

I hope this helps and if you don't understand feel free to ask

The standard deviation for the given data items is 2.6

The standard deviation of the given data items can be calculated by taking the square root of the variance.

Variance is a measure of variability and it is calculated by taking the average of squared deviations from the mean.

Hence, we will first determine the mean of the given data items.

Mean is simply the average of the numbers.

Therefore mean of the given data items is

[tex]Mean = \frac{9+11+11+16}{4}[/tex]

[tex]Mean = \frac{47}{4}[/tex]

Mean = 11.75

Now, for the variance of the data

[tex]Variance = \frac{(9-11.75)^{2}+(11-11.75)^{2}+(11-11.75)^{2}+(16-11.75)^{2} }{4}[/tex]

[tex]Variance = \frac{(-2.75)^{2}+(-0.75)^{2}+(-0.75)^{2}+(4.25)^{2} }{4}[/tex]

[tex]Variance = \frac{7.5625+0.5625+0.5625+18.0625}{4}[/tex]

[tex]Variance = \frac{26.75}{4}\\[/tex]

∴ Variance = 6.6875

But,

Standard deviation [tex]= \sqrt{Varinace}[/tex]

∴Standard deviation  [tex]=\sqrt{6.6875}[/tex]

Standard deviation = 2.586

Standard deviation ≅ 2.6

Hence, the standard deviation for the given data items is 2.6

Learn more on standard deviation here: https://brainly.com/question/18562832

The 3rd one

Step-by-step explanation:

Reason being that it has no factors, meaning it cannot be simplified any further, but quadratic method can be used to attain factors.

hope it makes sense :)

Answer:

The answer is B. 3

Step-by-step explanation:

The right angle points at side C which is the biggest side of a triangle and the smallest side is half of what side C is which is 3

Answer:

9 − (3 x 2) ÷ 3 + 6 is the answer

Answer:

5+4 = 9

6+4 = 10

7+4 =11

Step-by-step explanation:

Answer:

(5,9)

(6,10)

(7,11)

Step-by-step explanation:

w = m + 4

when m = 5,

w = 5 + 4 = 9

when m = 6

w = 6 + 4 = 10

when m = 7

w = 7 + 4 = 11

Answer:

48

Step-by-step explanation:

We need to find the multiples of 8

8,16,24,32,40,48

48 is between 45 and 50 so he must have bought 48

Answer:

6 bottles

Step-by-step explanation:

For this question we need to know the multiple of 8 which are:

8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40

8 x 6 = 48

8 x 7 = 56

There is only one multiple, which is greater than 45 but less than 50, which is 8x6 l.

This means he bought 6 bottles.

Answered by g a u t h m a t h

Answer:

The answer is A

Step-by-step explanation:

The answer needs to be in slope-intercept form or y=mx+b because the amount of carpet being cleaned every minute is a constant decrease of 9 square feet.

So our b value (or how much carpet cleaned at 0 minutes) is 220

And our m value (or slope or how much carpet is being cleaned every minute) is 9

So if we plug the variables with the tangible numbers we get A(t) = -9x+220 or A(t) = 220-9x.

provided by gauth math

Answer:

y - 9 = 2 (x - 2)

Step-by-step explanation:

y2 - y1 / x2 - x1      9 - 3 / 2 - (-1)      6/3    = 2

y - 9 = 2 (x - 2)

Answer:

The mean is the average number of a data set gotten by adding all the numbers then dividing by two.

the median is the middle number in a sorted set of data,either sorted in ascending order or descending order.

I hope this helps

To calculate mean:

• add up all the numbers,

• then divide by how many numbers there are.

Example:

Data: 5, 6, 10, 1

Add these all together, which is 22, then divide by 4 (because that is how many numbers there are), so:

the mean is 5.5

To calculate median:

Arrange your numbers in order.

Cross off numbers until you get to the middle.

If there is an even number of data, then find the two in the middle and find the middle of that.

Example:

Data: 5, 6, 10, 1

Arrange: 1, 5, 6, 10

So, the middle 2 are 5 and 6. In between these would be 5.5, so that is the median.

If the data was: 1, 5, 6, 8, 10,

then the median would be 6.

Answer:

The ratio of the perimeters of the first nonagon to the second is 3.6 to 1.

Step-by-step explanation:

Given that a regular nonagon has an area of 90 square feet, and a similar nonagon has an area of 25 square feet, to determine what is the ratio of the perimeters of the first nonagon to the second, the following calculation must be performed:

25 = 1

90 = X

90/25 = X

3.6 = X

Therefore, the ratio of the perimeters of the first nonagon to the second is 3.6 to 1.

A number has fixed number of factors but infinite number of multiples

Ex:-

Take a number 12

It has factors 1,2,3,4,6,12

It is fixed.

But

It has multiples 12,24,36,48,60...

It is infinite

9514 1404 393

Answer:

Step-by-step explanation:

Reflection over the x-axis changes the sign of the y-coordinate. Reflection over the y-axis changes the sign of the x-coordinate. We can summarize the transformations as ...

  preimage point ⇒ reflection over x ⇒ reflection over y

A(−8,−2) ⇒ A'(-8, 2) ⇒ A"(8, 2)

B(−4,−3) ⇒ B'(-4, 3) ⇒ B"(4, 3)

C(−2,−8) ⇒ C'(-2, 8) ⇒ C"(2, 8)

D(−10,−6) ⇒ D'(-10, 6) ⇒ D"(10, 6)

Answer:

12/55

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that the bag contains 8 red balls and 3 white balls, the probability of picking a red ball

p(r) = 8/(8+3) = 8/11

Probability of picking a white ball

= 3/11

when a red ball is picked first, the total number of balls reduces to 10 hence the probability that the second ball is white, given that the first ball is red

=8/11 * 3/10

= 24/110

= 12/55

Answer:

(a)

[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]

(b)

[tex]P(2) = 640[/tex]

(c)

[tex]Length= 16[/tex]

[tex]Width = 8[/tex]

[tex]Height =5[/tex]

(d)

[tex]Volume = 640[/tex]

Step-by-step explanation:

Given

[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]

Solving (a): The prism dimension

We have:

[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]

Factor out 8x

[tex]P(x) = 8x(6x^2 + 7x + 2)[/tex]

Expand 7x

[tex]P(x) = 8x(6x^2 + 4x + 3x + 2)[/tex]

Factorize

[tex]P(x) = 8x(2x(3x + 2) +1( 3x + 2))[/tex]

Factor out 3x + 2

[tex]P(x) = 8x(3x + 2)(2x + 1)[/tex]

So, the dimensions are:

[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]

Solving (b): The volume when [tex]x = 2[/tex]

We have:

[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]

[tex]P(2) = 48 * 2^3 + 56 * 2^2 + 16 * 2[/tex]

[tex]P(2) = 640[/tex]

Solving (c): The dimensions when [tex]x = 2[/tex]

We have:

[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]

Substitute 2 for x

[tex]Length=8*2[/tex]

[tex]Length= 16[/tex]

[tex]Width = 3*2+2[/tex]

[tex]Width = 8[/tex]

[tex]Height = 2*2 + 1[/tex]

[tex]Height =5[/tex]

So, we have:

[tex]Length= 16[/tex]

[tex]Width = 8[/tex]

[tex]Height =5[/tex]

Solving (d), the volume in (c)

We have:

[tex]Volume = Length * Width * Height[/tex]

[tex]Volume = 16 * 8 * 5[/tex]

[tex]Volume = 640[/tex]

Answer:

y = - [tex]\frac{2}{3}[/tex] x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (- 4.5, 0 ) ← coordinates of intercepts

m = [tex]\frac{0-(-3)}{-4.5-0}[/tex] = [tex]\frac{0+3}{-4.5-0}[/tex] = [tex]\frac{3}{-4.5}[/tex] = - [tex]\frac{2}{3}[/tex]

The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - [tex]\frac{2}{3}[/tex] x - 3 ← equation of line

Answer:

25%

Step-by-step explanation:

Formula to calculate the percent change :-

Change in distance from $12 per hour to $15 per hours = 15-12=3 per hour

Previous value = $12 per hour

Now, the percent change will be :_

Hence,  the percent change for  from $12 per hour to $15 per hour= 25%

(I copied this answer from JeanaShupp from question-11653373 [no links])

9514 1404 393

Answer:

  B. 6

Step-by-step explanation:

The diagonals of a parallelogram intersect at their midpoints, so ...

  DE = BE

  4y -8 = y +10

  3y = 18 . . . . . . . add 8-y

  y = 6 . . . . . . . . divide by 3

__

Additional comment

The value of x is found the same way:

  2x = x+2   ⇒   x = 2

Answer:

12

Step-by-step explanation:

Answer:

A) [tex]\$\ 2932.5[/tex]

Step-by-step explanation:

One is given that a certain amount of money was allotted to be spent on supplies. However, there was a discount applied to the purchase. One is asked to find the amount of money actually spent on the supplies.

$3450 was the initial price that was to be spent on supplies, however, a (15%) discount was applied to this price. Subtract (15) from (100) to find the percent value that was actually spent on supplies.

[tex]100-15=85[/tex]

(85%) of the allotted money was actually spent on supplies. Now one has to find out the numerical value of the amount spent. Divide (85) by (100) and then multiply it by the amount of money allotted to the purchase, to fin the amount actually spent on the purchase.

[tex]3450*(\frac{85}{100})\\\\=3450*0.85\\\\=2932.5[/tex]

Answer:

96

Step-by-step explanation:

Surface area=2*Area of triangle+Area of different rectangular strips

Surface area=2*(1/2)*(48)+2*8+2*6+2*10=48+48=96