8. (10 pts) A square plate is being heated so that the length of a side increases at a rate of 0.08 cm/min. How fast is the area increasing when the length of a side is 12cm?

Answer: 30 units^2

Step-by-step explanation:

[tex]\mathrm{From \ the \ figure \ we \ know \ this \ is \ a \ right \ triangle. \ The \ area \ of \ the \ triangle}:[/tex]

[tex]A = \frac{1}{2}bh \\= \frac{1}{2} \times 6 \times 10\\= 30 \ units^2[/tex]

(Formula for area of right triangle: Half of the product of two right edges)

Therefore, the area of the triangle is 30 units^2

The rate which the walk-in guest is how fast a guest needs a room

The rate which the walk-in guest pay for the night is $189.75

The given parameters are:

Average rate = $165 per night

The walk-in guest is 15% greater than the average rate.

So, the rate of the walk-in guest is:

Walk-in = 165 * (1 + 15%)

Evaluate the product

Walk-in = $189.75

Hence, the rate which the walk-in guest pay for the night is $189.75

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Answer:

x= -13.5

Step-by-step explanation:

X-3x+(-6)=21

-2x-6=21

-2x=27

2x=-27

x=-13.5

Answer:

Step-by-step explanation:

Working with the top equation, subtract 2x from both sides.

y = 9 - 2x

Put this value for y in the second equation

3x - 4(9 - 2x) = 8                 Remove the brackets

3x -36 + 8x = 8                   Add 36 to both sides

3x + 8x = 8 + 36                 Combine

11x = 44                               Divide by 11

x = 4

2x + y = 9

2*4 + y = 9                          

8 + y = 9                              Subtract 8 from both sides

y = 9-8

y = 1

Answer:

You can solve this by setting up an exponential growth equation.

Now we solve for b

Now that we have found b, we can use the equation  to predict how many bacteria will be present after 10 hours.

t = 10

Answer = 4732

Step-by-step explanation:

Answer:

I believe a is equal to -54

Answer: the slope is 0

Step-by-step explanation:

Answer:

B. 4

Step-by-step explanation:

To undo multiplication (which is what is being asked of us) you must divide. 28 divided by 7 is 4

so

4 x 7 is 28

If Brianna is taking care of 7 chickens, Tamara is taking care of 4 times the number of chickens because she is taking care of 28

the answer for this would be 20 percent

Answer:

9

Step-by-step explanation:

Add all numbers together: 36

divide by the amount of numbers in the list: 9

                                      :)

As 12 visitors went down a water slide 4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11 and 1 times, the average number of times each visitor went down is 11.41.

To reach that answer, the following calculation must be performed:

Therefore, each visitor went down, on average, 11.41 times.

Learn more about averages in https://brainly.com/question/897199

To find area of square one :-

Given :

To find :

We know :

Area of square = side²

Therefore:-

→Area of square = 9²

→Area of square = 9 × 9

→Area of square = 81 (unit)²

To find area of square two :-

Given :

To find :

We know :

Area of square = side²

Therefore:-

→Area of square = 11²

→Area of square = 11 × 11

→Area of square = 121 (unit)²

Now it's clearly visible that the whole figure is also. a square .

Therefore AE = CP

Which means area of square three = 81 (unit)²

Now area of shaded figure :-

The question asked by Troy is a statistical question because there would be variability in the answers he get fro the 12 maths teachers.

A statisical question is a question that can only be answered through the collection of data. Thhere would be variablility in the results gotten from the data.

A non- statistical question is a question that has only one answer. For example, how old are you? is a non-statistical question.

To learn more about a statisitcal question, please check: https://brainly.com/question/21508412

Answer:

16,

Step-by-step explanation:

1) Put numbers in ascending order

15, 16, 17, 17, 19, 19, 23, 24

2) Find the middle numbers use n+1/2

n = the amount of numbers in the sequence

8+1/2 = 4.5

3) The answer is 18 because that's the number between 17 and 19

Answer:

Me thinks its 18

Answer:

Box 4

Step-by-step explanation:

negative divided by negative is positive so both negatives cancel out and u get (5/6) / (1/3)

Answer:

Length: 20, Width=34

Step-by-step explanation:

Say the length of the width is w, and the length of the length is l. Then, we can establish an equation of W=2L-6. Since the area of a rectangle is W*L, we can substitute W with 2L-6. If we multiply 2L-6 and L, we get [tex]2L^{2} -6L[/tex]=680. We can simplify this equation by dividing everything by 2. We then get [tex]L^{2}-3L=340[/tex]. If we solve for L, we get 20. Now, we plug 20 into the equation, W=2L-6. Since W=2(20)-6, which simplifies to W=40-6 which is 34, we get a width of 34.

Hope this helps

Answer:

83

Step-by-step explanation:

first add whatever is in the 1's place so for 38, 8 is in the 1's place and for 45, 5 is in the 1's place

so first it will be 8+5 which is 13 so you are going to carry the 1 over to the tens place so now it will be 30 + 40 + 10 and that equals 80 so you add 80 and 3 which looks like 80+3 and that equals 83

Answer:

D is d because when You have to do they graph You have multiplicar

Answer:

706.5m^2

Step-by-step explanation:

The sign is a circle

Area of a circle is (pi)r^2

d = 30 in -> r = d/2  = 30/2 = 15

Area = 3.14 x (15)^2 = 706.5m^2

Answer:

about 706.5 or 706.86

Step-by-step explanation:

to find this answer we need to use the area formula of a circle which is A = πr ^2

we know the diameter is 30, and the radius is half the of diameter, so we take 30 and divide it by 2, which should give us 15 for the radius. ( 30/2 = 15, so r = 15)

depending on how your teacher wants u to answer this you can use π on a calculator or use 3.14

now just plug in your numbers to formula

A = 3.14 * 15^2 or A = π * 15^2

and should equal about 706.5 or 706.86 (depending on if you use 3.14 or π)

Answer:

69

Step-by-step explanation:

To do this, you want to first find how many pages he has read

So, to get that you want to multiply 230 by 70% or 0.7 (70% = 0.7 because to get the percent, you multiply the number by 100)

230 * 0.7 = 161

BUT, since you want to find how many pages he has left, you subtract the amount of pages he has read by how many pagest here are in total like so:

230 - 161 = 69 pages left

If you have any questions feel free to ask in the comments, and if this helped it would be appreciated if you left a brainliest :)

Step-by-step explanation:

I hope its helped ! studied well.

Answer:

a: The tape diagram represents the story because there’s 5 boxes representing the 5 weeks and x-2 in each box since x represents the amount Andre’s neighbor will pay him weekly to mow the lawn. This all equals 40 because that’s how much money he has to save.

B: Andre’s neighbor pays him 10 dollars each week to mow the lawn.

Step-by-step explanation:

b: For this part you have to make an equation combining all the five weeks which would be 5x-10. Then you would make it equal 40 because that’s how much he needs to save 5x-10=40. The you solve to find x by adding 10 to both sides of the equation and get 5x = 50. Then if you divide 5 on both sides you get 10!
You can check you work by plugging in 10 as x into the diagram.

Using proportions, it is found that she spent 25.76 hours at Yoga.

A proportion is a fraction of a total amount.

Researching the problem on the internet, it is found that the circle graph shows that she spent 28% of her time of 92 hours on yoga, hence:

h = 0.28 x 92 = 25.76.

Hence, she spent 25.76 hours at Yoga.

More can be learned about proportions at https://brainly.com/question/24372153

Answer

90

Step-by-step explanation

600 divided by 100

600 / 100 (5+10)

[tex]\cfrac{6}{5}~~ + ~~\boxed{?}~~ = ~~\cfrac{27}{10}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{6}{5}~~ + ~~\boxed{?} \right)~~ = ~~10\left( \cfrac{27}{10} \right)}\implies 12+10\boxed{?}=27 \\\\\\ 10\boxed{?}=15\implies \boxed{?}=\cfrac{15}{10}\implies \boxed{?}=\cfrac{3}{2}[/tex]

P + Q = 180

43 + Q = 180

Q = 180 - 43

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#LibreAngMatuto

[tex]\boxed{\bold{x = 2, 3}}[/tex]

Stepwise Solving:

[tex]\rightarrow \sf x^2-5x + 6 = 0[/tex]

[tex]\sf use \ the \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]

Identify the coefficients:

Solve for x:

[tex]\dashrightarrow \ \sf x=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4 \ x \ 1 \ x \ 6}}{2 \ x \ 1}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{\left25-24}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{1}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right+ 1}{2} \ , \dfrac{\left5\right- 1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{6}{2} \ , \ \dfrac{4}{2}[/tex]

[tex]\dashrightarrow \ \sf x= 3, \ 2[/tex]

Answer:

1/7 and 1/2

Step-by-step explanation:

The probability of orange marble is 1/7

Probability of tails is 1/2

If you need to add this, then it'll be 1/14

7 x 2 = 14

1 x 1 = 1

The expression (3a + 2b)^7 is a binomial expression;

The coefficient of the fourth term is 15120

The equation is given as:

(3a + 2b)^7

The above expression is a binomial expression;

Assume the expression is:

(x + y)^n

The equation of the expansion is:

[tex](x + y)^n = ^nC_r * x^{n-k} * y^k[/tex]

When the expression is expanded, the parameters of the fourth term are

n = 7

r = 4

x = 3a

y = 2b

So, we have:

(3a + 2b)^7 = 7C4 * (3a)^(7-4) * (2b)^4

Evaluate each factor

(3a + 2b)^7 = 35 * (3a)^3 * (2b)^4

Evaluate the powers

(3a + 2b)^7 = 35 * 27a^3 * 16b^4

Evaluate the product

(3a + 2b)^7 = 15120a^3b^4

The coefficient of the above expression is 15120

Hence, the coefficient of the fourth term is 15120

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Answer:

10

Step-by-step explanation:

The Interquartile Range (IQR) is the difference between Q3 and Q1.

From the diagram we see that Q1 = 40, and Q3 = 50

IQR = Q3-Q1 = 50 - 40 = 10

Step-by-step explanation:

a)

we have 400 people. that is 10/10 of the whole group.

7/10 of the whole group drink tea. that is

400 × 7/10 = 40 × 7 = 280

that leaves 3/10 of the whole group not drinking tea

400 × 3/10 = 40 × 3 = 120

from the 280 tea drinkers 20% drink at lay e cups of tea each day. that is

280 × 20/100 = 28 × 2 = 56

because 20 out of 100 is the meaning of 20%.

and the remaining 80% of the tea drinkers drink less then 3 cups each day.

280 × 80/100 = 28 × 8 = 224

b)

out of the 400 people 56 drink at least 3 cups of tea each day. that is

56/400 = 7/50