Sarah hired a painter to paint her bedroom walls and ceiling. Each of the four bedroom walls is 18 ft. long and 8 ft. high. Two walls each have one door,and both doors measure 3 ft. by 7 ft. One wall has a window that is 3 ft. by 5 ft. The doors and window do not have to be painted
What is the area of the wall space that has to be painted?

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Answer 1

Answer:

Step-by-step explanation:

519 I believe

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Laws have been instituted in Florida to help save the manatee. To establish the number of manatees in Florida, manatees were tagged. A new sample was taken later, and among the manatees in the sample, were tagged. Approximate the number of manatees in Florida. brainly

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Answer:

It think this should be the complete question: Laws have been instituted in Florida to help save the manatee.To establish the number of manatees in Florida, 150 manatees were tagged. A new sample was taken later, and among the 40 manatees in the sample, 3 were tagged. Approximate the number of manatees in Florida.

The approximate number of manatees in Florida is 2,000

Step-by-step explanation:

To solve this problem, we will use the formula

N= (C*R)/M

Where N is the toal estimated population

C is the total first capture

R is the total recapture after the first

M is the total tagged from recapture

Thus, we have:

N = (150*40)/3

N = 6000/3

N= 2,000

So, the approximate manatee is $2000$ .

Ratio and Proportion:

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of $a:b$ , then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are the two important concepts, and it is the foundation to understand the various concepts in mathematics as well as in science. the proportion is represented by,

$(a)/(b)=(c)/(d)$ .

Let us assume $x$ represents the unknown observed manatee, which is actually total manatees so the proportion is, $(40)/(3)=(x)/(150)$ .

Now, cross multiplying the given proportion as,

$3x=40* 150\nx=(40* 150)/(3) \nx=2000$

Learn more about the topic Proportion: brainly.com/question/24320792

The table on the left is that of a linear function, and the one on the right is that of an exponential function. Can you tell which function has the higher rate of growth? How?

Answers

The correct answer is D.

As you can see, the exponential function grows by doubling the previous output with each increment of the input: start with 1, you double it to get 2, then you double it to get 4, 8 and so on.

On the other hand, the linear function adds 7 with each step. This means that the exponential function will eventually reach and pass the linear one, and will definitely be grater from that point on. In fact, if we continue the table, we get

$\begin{array}{c|c|c}\text{x value}&\text{linear}&\text{exponential}\n4&28&8\n5&35&16\n6&42&32\n7&49&64\n8&56&128\n9&63&256\end{array}$

and you can see how the exponential growth is much faster than the linear one.

Find the length of the curve. R(t) = 2 i + t2 j + t3 k, 0 ≤ t ≤ 1

Answers

Length of a curve is the length of its plot its curve. The length of the given curve for given range of t is: L = 1.44 units approx.

How to find the length of a curve?

If the curve has position vector p(x) for value of x ranging from x = a to x = b,

then, the curve's length is calculated as:

$L = \int_a^b ||p'(x)||dx\n$ units.

For the given case, we have:

Position vector = $R(t) = 2\hat i + t^2 \hat j + t^3 \hat k$

Its differentiation gives:

$R'(t) = 2t\hat j + 3t^2\hat k$

Its non negative magnitude is: ||R'(t)|| = $√((2t)^2 + (3t^2)^2) = t√(4+9t^2)$

Thus, as t ranges from a = 0 to b = 1, thus, length of the curve is:

$L = \int_0^1 (t√(4+9t^2))dt\n\n\text{Let v = 4+9}t^2, \text{then dv = 18tdt}\nand\nt=0\implies v = 4\nt=1 \implies v = 13\nThus,\nL = \int_4^(13)((√(v))/(18))dv = (1)/(18) [(2(v)^(3/2))/(3)]^(13)_4 \approx (38.87)/(27) \approx 1.44 \: \rm units$

Thus,

The length of the given curve for given range of t is: L = 1.44 units approx.

Learn more about length of the curve here:

brainly.com/question/4464059

curve equation is

$\n \vec{R}\left ( t \right ) = 2\hat{i}+t^(2)\hat{j} + t^(3)\hat{k}$ ,0≤ t≤ 1

now taking the differentiation

$\n{R}'t = 2t\hat{i} + 3t^(2)\hat{j}$

now taking the modulus

$\left \| {R}'(t) \right \|=$ $\sqrt{4t^(2) +9t^(4)}$

= $\sqrt{4 + 9 t^(2) } .t$

now taking the integration

length of the curve = $\n\int t\sqrt{4 + 9 t^(2)} dt\n$

now put the value v= 4 + 9t²

dv= 18 tdt

now put this value in the above equation

we get

length of the curve = $\n(1)/(18)\int √(v)dv\n$

now taking integation we get and put the value of the v

we get

= $(1)/(18)$ × $(2)/(3)$ × $(4 + 9t^(2) )^{(3)/(2) }$

= $(1)/(27) ( 4 + 9 t^(2) )^{(3)/(2) }$

now find out the length of the curve in the interval from 0 to 1.

length of the curve $= (1)/(27) (13^{(3)/(2)} -4^{(3)/(2)} )\n=(1)/(27) (13√(13) -8)$

Hence proved

The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time in the store. What is the null and alternative hypothesis for this scenario? (Ch10)A. H0: m =7.5 and H1:m ? 7.5

B. H0: m <=7.5 and H1:m > 7.5

C. H0: m >=7.5 and H1:m < 7.5

D. H0: m <7.5 and H1:m >=7.5

E. H0: m >7.5 and H1:m <= 7.5

Answers

Answer: C . $H_0:\mu\geq7.5$ and $H_a:\mu<7.5$

Step-by-step explanation:

Definition:

Null hypothesis $(H_0)$ is a statement about the population parameter according to the objective raised by the researcher . It contains '=' , '≤' and '≥' signs.