Janna is making a prediction of the frequency of a key that is 12 keys from middle C. A 2-column table with 5 rows. The first column is labeled number of keys above middle c with entries 0, 1, 2, 4, 8. The second column is labeled frequency (hertz) with entries 277. 18, 293. 66, 311. 13, 249. 23, 440. 0. Which best describes her prediction? interpolation, because a key that is 12 keys from middle C is within the data set interpolation, because a key that is 12 keys from middle C is outside the data set extrapolation, because a key that is 12 keys from middle C is within the data set extrapolation, because a key that is 12 keys from middle C is outside the data set.

The volume of the box is the amount of space in it.

The dimension of the postcard is:

[tex]\mathbf{Length = 10}[/tex]

[tex]\mathbf{Width = 18}[/tex]

Let x represents the length of the cut.

So, the dimension of the box is:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

(a) The function that represents the volume of the box

This is calculated as:

[tex]\mathbf{V(x) = Length \times Width \times Height}[/tex]

So, we have:

[tex]\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}[/tex]

Expand

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Hence, the volume function is: [tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

(b) The dimension that maximizes the volume

We have:

[tex]\mathbf{V(x) = 180x - 56x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V'(x) = 180- 112x + 12x^2}[/tex]

Set to 0

[tex]\mathbf{180- 112x + 12x^2 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{x = 7.3,2.1}[/tex]

The value x = 7.3 is greater than the dimension of the box.

So, we have:

[tex]\mathbf{x = 2.1}[/tex]

Recall that:

[tex]\mathbf{Length = 10 -2x}[/tex]

[tex]\mathbf{Width = 18 -2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, we have:

[tex]\mathbf{Length = 10 -2 \times 2.1 = 5.8}[/tex]

[tex]\mathbf{Width = 18 -2 \times 2.1 = 13.8}[/tex]

[tex]\mathbf{Height = 2.1}[/tex]

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

[tex]\mathbf{Volume = 5.8 \times 13.8 \times 2.1}[/tex]

[tex]\mathbf{Volume = 168.1}[/tex]

Hence, the maximum volume of the box is 168.1 cubic inches

Read more about volumes at:

https://brainly.com/question/17056191

Answer:

1 - quarts of juice for 5.82 (the first one)

2 - 9.84 for a 12 pack of batteries (the second one)

3 - 24-pack of pencils for 2.64 (the first one)

4 - $2.46 for a 12-ounce jar of jam (the first one)

Step-by-step explanation:

Have a nice day

[tex]n = - 1[/tex]

[1] Complementary means the angles will add up to 90 degrees

 () Blank one is BOC

 () Blank two is 90

 () Reason blank I am unsure as I do not know the wording that is being looked for, but it is either "given," "complementary angles" or something similar

[2] Since AOC is equal too BOC + 30, we can decide the following is true

 () First blank is BOC

 () Second blank is 30

[3] 30°

 () BOC + BOC + 30 = 90 [Given]

    2(BOC) = 60 [Subtract 30 from both sides & combine like terms]

    BOC = 30 [Divide by 2]

[4] 60°

 () 90 - 30 = 60

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

4200

hope helpful <3 !!!!!!!!!!!!!

Answer:

i think you need to add all that up

Step-by-step explanation:

You may begin by calculating the slope's angle, then marking the slope's midway point, or 0, then the left end, -1, and finally the right end, 1.

Answer:

4.5 + 19.75 = 24.25

Find your missing digits with the equation above

Step-by-step explanation:

4 1/2 = 9/2

so, the calculation is simply how often 3/4 fits into 9/2.

and that is done by division :

9/2 / 3/4

and as we know, to divide by a fraction is the same as to multiply with the upside-down fraction.

so,

9/2 / 3/4 = 9/2 × 4/3 = (9×4)/(2×3) = 3×2/1 = 6

so, without any breaks the teacher can schedule 6 lessons each night.

Answer:

b

Step-by-step explanation:

The change from the first quarter to the second quarter is +357,000. Therefore, the correct answer is option D.

Given that, the money made by company in first quarter = $700,000 and in the second quarter = $343,000.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

The difference in money made by company from first quarter to second is

700,000-343,000

= +357,000

Therefore, the correct answer is option D.

Learn more about the subtraction here:

brainly.com/question/2346316.

#SPJ4

Answer:

55 degrees

Step-by-step explanation:

if u and v are parallel and cut by the transversal in the middle the two angles would be congruent or equal to each other , therefore the angle in question is also 55

Answer:

Step-by-step explanation:

what is the question

Answer:

710

Step-by-step explanation:

81+74+72+66+67+72+66+66+72+65+71= 701

701 rounded to the nearest tenth is 710

Answer:

They are similar by AA

Step-by-step explanation:

Angle B and C are similar as well as angle ABE and DCE are similar

16-8=8

Step-by-step explanation:

Answer:

6 time

Step-by-step explanation:

97÷14=6•928

=6 or round it up to 7

Answer:

6

Step-by-step explanation:

97÷14=6.928

6 or round it up to 7

Answer:

Step-by-step explanation:

[tex]\frac{6}{4.5}=\frac{4}{x}[/tex]

6x = 4 × 4.5

6x = 18

x = 3

Answer:

whats the question

Step-by-step explanation:

Answer:

Simplify:

[tex]\frac{( {x}^{2} + 6x + 9) }{x - 3} [/tex]

Factoring:

[tex] {x}^{2} + 6x + 9[/tex]

The first term is, x2 its coefficient is 1 .

The middle term is, +6x its coefficient is 6 .

The last term, "the constant", is +9

Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9

Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is 6 .

-9 + -1 = -10

-3 + -3 = -6

-1 + -9 = -10

1 + 9 = 10

3 + 3 = 6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3

[tex] {x}^{2} + 3x + 3x + 9[/tex]

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+3)

Add up the last 2 terms, pulling out common factors :

3 • (x+3)

Step-5 : Add up the four terms of step 4 :

(x+3) • (x+3)

Which is the desired factorization.

Multiply (x+3) by (x+3)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+3) and the exponents are :

1 , as (x+3) is the same number as [tex](x+3) {}^{1}[/tex]

and 1 , as (x+3) is the same number as[tex](x + 3) {}^{1} [/tex]

The product is therefore, [tex](x + 3) {}^{(1 + 1)} = (x + 3) {}^{2} [/tex]

Step-by-step explanation:

check the attached file

Answer:

the left side is the answer

Answer:

180

Step-by-step explanation:

Answer:

I and IV

Step-by-step explanation:

based on the unity circle 0 and 360 is on the same plane..hope it's answerd

[tex] \: \: \: \: \: \: [/tex]

[tex] = 432[/tex]

Step-by-step explanation:

[tex] {6}^{3} + {6}^{3} [/tex]

[tex]2 \times {6}^{3} [/tex]

[tex]2 \times 216[/tex]

[tex] = 432[/tex]

[tex] \: \: \: \: \: \: [/tex]

Step-by-step explanation:

So we are given 2 coordinates.

so in a linear equation, we have the given function:

y=mx+b

thus we should have an x value and a y value.

So let's set x to be the hours and y be the cost

With 2 sets of coordinates, we can solve for the slope (m in the function) of the function using rise/run or y1-y2/x1-x2

so with that being said,

7.75-5.5/7-4=m

2.25/3=m

.75=m

This is our slope.

Our formula will look like this: y=0.75x

Now we can determine how much it will cost in 3 hours by changing x to be 3 since x is the number of hours parked

y=0.75(3)

y=2.25

The cost to park for 3 hours will be $2.25

Hope This Helps :D

Answer:

this is the correct answer happy

Answer:

The requirements for taking out a loan tend to be very strict, and therefore, an impressive internship program would not be something that can meet the requirements to obtain a loan of $6500.

Step-by-step explanation:

1. If you were trying to decide whether to take out an auto loan for $6500 to buy your first car, thereby allowing you to commute for an impressive summer internship program next year, that loan would not meet the requirements.

Is it necessary?

No, travelling can be done by other means.

Do the monthly payments fit in your budget?

Maybe

Could you save instead of borrow?

Yes saving for the whole year is better than borrow.

Is it worth the added interest?

No, its not worth the added interest.

All of the answers indicate that the loan does not meet the requirements.

Paying a huge amount of interest for something which is not that necessary is useless.

https://brainly.com/question/1658653

https://brainly.com/question/9302251

Answer:

3x^2+15x-1=0

Step-by-step explanation:

4/(3x+15)=4x

4=12x^2+60x

12x^2+60x-4=0

3x^2+15x-1=0

Please solve after that, I cannot do everything for you