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3 years ago

14

a student used his place value chart to show a number after the teacher instructed him to divide his number by 100 the chart sho

wed 28.003. draw a picture of what the place value looked like at first

1 answer:

Anna35 [415]3 years ago

8 0

<span>A student divided the given number by 100 that resulted to 28.003 in his chart. So what we are looking for this situation is the value of the number before it was divided by 100.
To get the value, simply multiply the result by 100
=> 28.003 x 100
=> 2800.3
by dividing 100 to the given number, we simply move the value to the right in a value of hundreds.
See attached Image.

</span>

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A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t

Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be $F=L+2W$ .

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

$LW=80,000...(1)$

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be $C=20L+5(2W)\Rightarrow 20L+10W$ .

From equation (1), we will get:

$L=\frac{80,000}{W}$

Upon substituting this value in cost equation, we will get:

$C=20(\frac{80,000}{W})+10W$

$C=\frac{1600,000}{W}+10W$

$C=1600,000W^{-1}+10W$

To minimize the cost, we need to find critical points of the the derivative of cost function as:

$C'=-1600,000W^{-2}+10$

$-1600,000W^{-2}+10=0$

$-1600,000W^{-2}=-10$

$-\frac{1600,000}{W^2}=-10$

$-10W^2=-1,600,000$

$W^2=160,000$

$\sqrt{W^2}=\pm\sqrt{160,000}$

$W=\pm 400$

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

$C''=-2(-1600,000)W^{-3}$

$C''=3200,000W^{-3}$

$C''=\frac{3200,000}{W^3}$

Now, we will substitute $W=400$ in 2nd derivative as:

$C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05$

Since 2nd derivative is positive at $W=400$ , therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting $W=400$ in $L=\frac{80,000}{W}$ , we will get:

$L=\frac{80,000}{400}\\\\L=200$

Therefore, the side parallel to the river will be 200 feet.

4 0

3 years ago

Karim began his day by drinking 1 cups of milk at breakfast. By the end of the day, he drank a total of 2

uranmaximum [27]

Answer:

Equation:

21 = 1 + m

Solution:

20 = m

Step-by-step explanation:

What we know:

Karim drank 1 cup of milk at breakfast
Karim drank a total of 21 cups of milk
m = the amount of milk, in cups, Karim drank after breakfast

We know that Karim drank 21 cups of milk in a day. In an equation, that would look like this:

21 =

What does 21 equal?

The amount of milk Karim drank at breakfast plus the amount of milk Karim drank after breakfast.

21 = milk at breakfast + milk after breakfast

Let's substitute what we know into this equation:

21 = milk at breakfast + milk after breakfast

21 = 1 + m

Now that we have our equation, let's solve.

21 = 1 + m

-1 -1

20 = m

Therefore, Karim drank 20 cups of milk after breakfast.

4 0

3 years ago

Please help anybody?!???

hjlf

180-50= 130 so x=130 or 360-100=260 then 260/2=130 so x=130

7 0

3 years ago

PLEASE HELP ME ANSWER! im so desperate bro !!

sergey [27]

a)13

b) skewed

c) IQR

d)Sam's observation is correct

e)6.17

Step-by-step explanation:

Step 1 :

From the histogram we can infer that

0 to 2 texts has been sent by 1 student

2 to 4 texts has been sent by 3 student

4 to 6 texts has been sent by 4 student

6 to 8 texts has been sent by 4 student

8 to 10 texts has been sent by 5 student

Step 2:

a)

From step 1 , we can see that there are total of 17 students represented by the histogram

Step 3:

b)

This is a skewed histogram because we have all large values of students on the right of the histogram and smaller values on the left of the histogram.

In symmetrical histogram, there would be large values on the center and the smaller values on both sides.

Step 4:

c)

IQR would be better recommendation for this as this is a skewed histogram

Standard deviation would be recommended for a symmetrical histogram

Step 5:

d)

Total number of students is 17

Number of students who text between 8 to 10 messages is 5

Hence the students who text between 8 and 10 messages is 5/17

which is nearly 1/3 rd of the total students.

Hence Sam's observation is correct

Step 6:

e)

Mean amount of the texts = (1 * 3 + 3* 3 + 5*4 +7*4 + 9* 5) /17 = 6.17

6 0

3 years ago

The vector ab has a magnitude of 20 units and is parallel to the<br> vector 4i + 3j.<br> find ab.

stepladder [879]

The vector ab has a magnitude of 20 units and is parallel to the

vector 4i + 3j. Hence, The vector AB is 16i + 12j.

<h3>How to find the vector?</h3>

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

Given;

The vector ab has a magnitude of 20 units and is parallel to the

vector 4i + 3j.

magnitude

$\sqrt{4^2 + 3^2} \\\\\sqrt{16 + 9} \\\\= 5$

Unit vector in direction of resultant = (4i + 3j) / 5

Vector of magnitude 20 unit in direction of the resultant

= 20 x (4i + 3j) / 5

= 4 x (4i + 3j)

= 16i + 12j

Hence, The vector AB is 16i + 12j.

Learn more about vectors;

brainly.com/question/12500691

#SPJ1

7 0

1 year ago