You want to make a rectangular box, open at the top, by cutting the same size square corners out of a rectangular sheet of cardboard and then folding up the sides. The cardboard measures 11 in. by 14 in. What are the dimensions of the box that will have greatest volume if the possible corner cuts measure 1 in., 2 in., 3 in., or 4 in.?

Answer:

4200 divided by 10

Step-by-step explanation:

To make 4200 a multiple of ten after dividing it by a multiple of ten, we first find the number of 5's in 4200 to see how many 10's go into 4200. Since 4200 = 6*7*2*2*5*5, we see that there are 2 fives. This means that there are two tens too. Since we have to keep 4200 a multiple of ten after dividing it by another 10. So the only possible way to do that is dividing 4200 by 10.

Dividing 4200 by the power of 10, 100, results in the quotient 42, which is also a multiple of 10. This is achieved by moving the decimal point two places to the left in the number 4200 due to the two zeros in the power of 10.

In this mathematics problem, you are asked to divide 4200 by a multiple of 10 such that the result, or quotient, is also a multiple of 10. The key to this problem lies in understanding the concept of dividing by powers of 10.

When you divide a number by a power of 10, you move the decimal point to the left by as many places as there are zeros in the power of 10. So if you wanted to divide 4200 by a multiple of 10 so that the result is also a multiple of 10, you might choose 100 (10^2) as your divisor. Why? Because there are two zeros in the power of 10, which means you move the decimal point two places to the left in the number 4200.

So when you divide 4200 by 100, you get 42 which is a multiple of 10. Therefore, 4200 divided by a multiple of 10 (100 in this case) gives a quotient (42) that is also a multiple of 10.

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Answer:

A) exponential

Step-by-step explanation:

It is in a curving pattern which indicates exponential. Linear is a straight line.

The best-fitting regression model for the considered data plot is given by: Option A: Exponential.

When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.

The considered plot is not forming a straight line(so no linear fitting), but we can see that a smooth curve can be fitted in the considered data. Since the exponential functions' graph approximately goes the same way (for positive exponent, and increasing value of output).

Thus, the best-fitting regression model for the considered data plot is given by: Option A: Exponential.

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Answer:

y > –5x + 3

Step-by-step explanation:

we know that

1) The solution of the inequality is the shaded area above the dashed line

so

The linear inequality could be

y > –5x – 3

y > –5x + 3

y > –3x + 5

2) The slope of the dashed line is negative ----> the three options have slope negative

3) The y-intercept of the dashed line is (0,3)

therefore

The linear inequality is

y > –5x + 3

Answer:

[tex]y>-5x+3[/tex]

Step-by-step explanation:

To find the linear inequality , Let pick two points from the graph

Lets pick (0,3) and (1,-2)

Lets find out slope using the points

[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]slope =\frac{-2-3}{1-0}=-5[/tex]

Slope m= -5

y intercept b= 3

Equation of the line is y=mx+b

[tex]y=-5x+3[/tex]

Now we look at the shaded part. we use test point (0,0)

(0,0) is not in the shaded region

[tex]y=-5x+3[/tex]

[tex]0=-5(0)+3[/tex]

0 >3 is false

[tex]y>-5x+3[/tex]

Answer:

let the past stay in the past

Step-by-step explanation:

Answer:

a. 17 x 10 = 170

b. 24 x 100 = 2,400

c. 6 x 1000 = 6000

Step-by-step explanation:

Answer:

a. 170

b. 2,400

c. 6,000

Step-by-step explanation:

You need to make the multiplications that are indicated in each option:

Option a: you only need to multiply the first factor (17) by the digit that is not zero (1) of the second factor (10), and then write all the zeros that has the second factor:

 [tex]17*10=170[/tex]

Option b: you need to multiply the first factor (24) by the digit that is not zero (1) of the second factor (100), and then write all the zeros that has the second factor:

 [tex]24*100=2,400[/tex]

Option c: you have to multiply the the first factor (6) by digit that is not zero (1) of the second factor (1000), and then write all the zeros that has the second factor:

 [tex]6*1,000=6,000[/tex]

I think it's C but don't quote me on that I don't know

Answer:x2_>16 B.

Step-by-step explanation:

For this case we will show that the correct option is option C.

[tex]x ^ 2 \leq16[/tex]

We find the value of the variable "x":

We apply root to both sides of the equation to eliminate the exponent:

[tex]x \leq \pm \sqrt {16}\\x \leq \pm4[/tex]

We found the first solution with the positive value:

[tex]x \leq4[/tex]

We use the negative value to find the other solution. Since it is an inequality, the sign of the inequality changes in the negative portion of the solution.

[tex]x \geq-4[/tex]

So, the roots are:

[tex]x_ {1} \geq-4\\x_ {2} \leq + 4[/tex]

The solution is given by the values of "x" greater than or equal to -4 and less than or equal to 4

Answer:

Option C

Replace x with 3 and solve for Y.

If y equals 8 in both equations, then it is a solution.

y = -5(3) +1 = -15+1 = -14

-14 does not equal 8 , so it is not a solution.

No because -5• 3 +1 does not equal 8 makings it impossible for it to work for that equation. Then 3•3-2 doesn’t equal 8 either so (3,8) is not a solution for these equations

Answer:

1

Step-by-step explanation:

sec(x)*cos(x) + cos(x)-1/(sec(x))

We know that sex(x) = 1/(cos(x))

substitute it in our expression.

1/(cos(x)) * cos(x) + cos(x) - 1/(1/cos(x)) = 1+cos(x) - cos (x)= 1

ANSWER

A. 1

EXPLANATION

The given trigonometric expression is

[tex] \sec(x) \cos(x) + \cos(x) - \frac{1}{ \sec(x) } [/tex]

Recall and use the following reciprocal identities.

[tex] \frac{1}{ \sec(x) } = \cos(x) [/tex]

and

[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]

When we apply these identities, we get

[tex] \frac{1}{ \cos(x) } \times \cos(x) + \cos(x) - \cos(x) [/tex]

This simplifies to:

[tex]1 + 0 = 1[/tex]

The correct choice is A

Answer:

Every 20 days.

Step-by-step explanation:

I just did 5 times 4 to get the answer

In 20 days there will be both lessons on the same day again.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given:

Violin class= 4th day

singing lesson= 5th day

So, the possible number of days on which we have both violin and singing class

=4 x 5

=20 days

Hence,  20 days there will be both lessons on the same day again.

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Answer:

option D

8√2

Step-by-step explanation:

Given in the question a right angle triangle,

hypotenuse = x

height = 8

We can use trigonometry identity to solve x

we know that,

sinФ = opposite / hypotenuse

sin(45) = 8 / x

x = 8 / sin(45)

x = 8√2

The required weight of Carmen's rabbit is given as 5 pounds and the equation is given as 9 = 2x -1.

As mentioned in the question,
Angelos's pet rabbit weighs 1 pound less than twice the weight of Carmen’s pet rabbit. Angelos rabbit weighs 9 pounds.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the weight of the Carmen's be x,
According to the question,
Angelos pet rabbit weighs,
9 = 2x -1
x = 5

Thus, the required weight of Carmen's rabbit is given as 5 pounds.

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To find the weight of Carmen's pet rabbit, an equation is set up: 2w - 1 = 9, where w represents the unknown weight of Carmen's rabbit. Solving the equation, we find that Carmen's rabbit weighs 5 pounds.

To find the weight of Carmen's pet rabbit, we first need to translate the given information into a mathematical equation. The problem states that Angelo's pet rabbit weighs 1 pound less than twice the weight of Carmen's pet rabbit and Angelo's rabbit weighs 9 pounds. Let's denote the weight of Carmen's rabbit as w. The relationship can be written as:

2w - 1 = 9

To solve for w, we add 1 to both sides of the equation:

2w - 1 + 1 = 9 + 1

2w = 10

Now, we divide both sides by 2 to get the weight of Carmen's rabbit:

2w / 2 = 10 / 2

w = 5

Therefore, Carmen's pet rabbit weighs 5 pounds.

Answer: A

Step-by-step explanation:

For this case we must simplify the following expression:

[tex]\sqrt [5] {224x ^ {11} * y ^ 8}[/tex]

We follow the steps below:

We rewrite 224 as the product of: 32 * 7

[tex]\sqrt [5] {32 * 7 * x ^ {11} * y ^ 8} =[/tex]

We rewrite [tex]32\ as\ 2 ^ 5, x^{11}\ as\ x * x^{10}:[/tex]

[tex]\sqrt [5] {2 ^ 5 * 7 * x ^ {10} * x * y ^ 8} =[/tex]

We rewrite [tex]x^{10}[/tex] as [tex](x ^ 2) ^ 5,[/tex] we also rewrite [tex]y ^ 8[/tex] as [tex]y ^ 5 * y ^ 3:[/tex]

[tex]\sqrt [5] {2 ^ 5 * 7 * (x ^ 2) ^ 5 * x * y ^ 5 * y ^ 3} =[/tex]

We reorder:

[tex]\sqrt [5] {2 ^ 5 * (x ^ 2) ^ 5 * y ^ 5 * 7 * x * y ^ 3} =\\\sqrt [5] {(2 * x ^ 2 * y) ^ 5 * (7 * x * y ^ 3)} =[/tex]

We take the terms of the radical considering that: [tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

[tex]2 x ^ 2y \sqrt [5] {7 x y ^ 3}[/tex]

Answer:

Option A

Answer:

Plain rolls: $16

Shinny rolls: $20

Step-by-step explanation:

So, we have 2 equations to start with, let p = plain rolls and s = shinny rolls:

1)  8p + 10s = 328

2) 9p + 2s = 184

We need to isolate one variable, usually I go for the one with the lowest multiplicative... so let's go for the '2s' and isolate the s from equation 2.

2s = 184 - 9p

3) s = (184 - 9p) / 2

And let's place that s equivalent into the first equation:

8p + 10 (184 - 9p)/2 = 328

8p + 5(184 - 9p) = 328

8p - 45p + 920 = 328

-37p = -592

p = 16

Then we go into any of the 3 equations to get the value of s.  Let's take the 3rd equation, it will be simpler:

s = (184 - 9p) / 2 = (184 - 9*16) / 2

s = (184 - 144)/2 = 40/2 = 20

Then last step, we enter the values for s and p in one of the first equations to validate it.  We haven't worked with first equation, so let's use that one:

8p + 10s = 328

8 (16) + 10 (20) = 328

128 + 200 = 328

328 = 328

Confirmed!

Answer: 7w

Step-by-step explanation:

In one week, Ash recycles 7 * 1 = 7 bottles

In two weeks, Ash recycles 7 * 2 = 14 bottles

So, in w weeks, he recycles 7 * w = 7w bottles!

Hope this helps!

Answer:

7w is the correct answer

Step-by-step explanation:

Answer:

5-4(x+2)=3

1(x+2)=3

1x+2=3

3-2=1

Step-by-step explanation:

x=1

Answer:

D

Step-by-step explanation:

because it seem to be correct

D is the answer.....!!!!!

Answer:

2(x-8)=8

x=12

Step-by-step explanation:

The equation for the given statement is 2(x-8)=2.

The given statement "Twice the difference of a number and 8 is equal to 2 ​

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, the difference between a number and 8 can then be written as 'x-8'. Twice that amount would be 2(x-8). If it's equal to 2, you can say 2(x-8)=2.

Therefore, the equation for the statement is 2(x-8)=2.

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Answer:

b.the graph of g(x) is the graph of f(x) compressed vertically

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2[/tex]

and

[tex]g(x)=\frac{2}{5}x^2[/tex]

This is a transformation in the form

[tex]y=a*f(x)[/tex] where [tex]a=\frac{2}{5}[/tex]

Since 0<a<1, the graph of f(x) is compressed vertically by a factor of

[tex]\frac{2}{5}[/tex]

A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.

A function assigns the value of each element of one set to the other specific element of another set.

When the graph of the two function f(x) and g(x) is plotted, then it can be observed that the graph of g(x) is the graph of f(x) compressed vertically.

Hence, the correct option is B.

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Answer:

[tex]4\pi[/tex]

or

12.57

Step-by-step explanation:

I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make

Essentially, you are attempting to find the area of a circle with a radius of 2 meters.

The formula for an area of a circle is [tex]\pi r^2[/tex], or pi times radius squared.

Plugging in 2 meters as your radius, that gets your answer to be [tex]4\pi[/tex], or 12.57 in decimal.

Answer:

$100

Step-by-step explanation:

To find out how much money Gayle initially had, we solved the two equations provided by the problem: G + 20 = 2(J + 20) and J + 20 = G + 20 - 50. Solving these equations, it was found that Gayle initially had $90.

The question is asking us to figure out how much money Gayle had before their mother gave them each $20. Let's denote the amount of money Jerry initially had as J and the amount of money Gayle initially had as G. According to the problem, after the mother gave them $20 each, Gayle had twice the amount of Jerry's, which mathematically translates to G + 20 = 2(J + 20). Likewise, Jerry had $50 less than Gayle, which can be written as J + 20 = G + 20 - 50. Thus we are given a system of two equations that we can solve simultaneously.

Both equations can be simplified to G = 2J + 20 and J = G - 50. By substituting J = G - 50 in the first equation, we can solve for G to get G = 2(G - 50) + 20 which further simplifies to G = $90. Thus, Gayle initially had $90.

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Answer:

[tex]\frac{1}{ab^{2} }[/tex] (a³ - 6b)

Step-by-step explanation:

[tex]\frac{-6}{ab} + \frac{a^{2} }{b^{2} }[/tex]

= [tex]\frac{-6b + a^{3} }{ab^{2} }[/tex]

= [tex]\frac{1}{ab^{2} }[/tex] (a³ - 6b)

Answer:

Step-by-step explanation:

abs(x)>0

This statement is false because what happens when x = 0? For all other instances, the statement is true, but not for 0.

Zero is not greater than itself.

Answer:

[tex]\boxed{\text{[2, 33]}}[/tex]

Step-by-step explanation:

The range is the spread of the y-values (minimum to maximum distance travelled).

The minimum is 2 mi, and the maximum is 33 mi, so the range is from 2 to 33.

In interval notation, the range is [tex]\boxed{\textbf{[2, 33]}}[/tex]

Answer:

31

Step-by-step explanation:

31

The range is the difference between the largest and smallest number.

range = biggest − smallest = 33 − 2 = 31

Answer:

IT would be 6 because 10 X 6 = 60 just take away the 0

Step-by-step explanation:

Answer:

cscθ = [tex]\frac{1}{y}[/tex]

Step-by-step explanation:

cscθ = [tex]\frac{Hypotenuse}{opposite}[/tex]

For a unit circle, radius = 1

hence, hypotenuse = 1

opposite = y

cscθ = [tex]\frac{1}{y}[/tex]

Answer:

D

Step-by-step explanation:

The tenth column value is the first after the decimal point, that is 3

To round the required value of 3

• If the value following 3  ≥ 5, round 3 up to 4

• If the value following 3 < 5 , then leave as 3

Here the value following 3 is 5 so round 3 up to 4

All other digits remain unchanged.

Thus

3, 295.351 ≈ 3, 295.4 → D

Answer:

the answer is B: 3

Step-by-step explanation:

you look at the verticle line on the left side of the box which represents the lower quartile then to the right of the verticle line represents the upper quartile

To find the interquartile range, subtract the lower quartile, 9.5, from the upper quartile, 12.5

12.5 - 9.5 = 3

[tex] \frac{27}{30} \times 100\% \\ = 90\%[/tex]

Approximately 90 percent voted for her