Suppose you wanted to make an open-topped box out of a flat piece of cardboard that is 25 inches long
by 20 inches wide. You cut a square out of each corner, all the same size, then fold up the flaps to form
the box. If the box has a volume of 750 in), which could be the side length of the square that was cut
out of each corner?

Answer:

-26 sqrt(3)

Step-by-step explanation:

-12 sqrt(12) - 2 sqrt(3)

Rewriting

-12 sqrt(4*3) - 2 sqrt(3)

We know sqrt(ab) = sqrt(a)sqrt(b)

-12 sqrt(4)sqrt(3) - 2 sqrt(3)

-12 (2) sqrt(3) - 2 sqrt(3)

-24 sqrt(3) - 2 sqrt(3)

-26 sqrt(3)

Answer:

2²=4 is square root and 3³=9 is cube root

Step-by-step explanation:

because 3×3×3=3³and 2×2=2²

Answer:

[tex]55[/tex]

Step-by-step explanation:

We'll be using case-work to solve this problem. Let's call the ones digit of the telephone number [tex]B[/tex] and the tens digit [tex]A[/tex]. Each telephone number can be represented as [tex]AB[/tex].

Since the question states that numbers that are smaller when their digits are reversed are not used, we have the following inequality:

[tex]B\geq A[/tex]

This is because if [tex]A>B[/tex], the number would become smaller when [tex]A[/tex] and [tex]B[/tex] are switched in [tex]AB[/tex]. However, if [tex]A=B[/tex] or [tex]B>A[/tex], the number will not become smaller.

Let's work our way up starting with [tex]A=0[/tex]. If [tex]A=0[/tex], there are 10 other numbers (0-9) that we can choose for [tex]B[/tex] that adhere to the condition [tex]B\geq A[/tex]:

[tex]0B,\\01, 02, 03,...[/tex]

Therefore, there are 10 possible telephone numbers when the tens digit is 0.

Repeat the process, now assigning [tex]A=1[/tex]. Now, we only have the digits 1-9 to choose from for [tex]B[/tex], since [tex]B[/tex] needs to be greater than or equal to A. Therefore, there are 9 possible telephone numbers when the tens digit is 1.

This pattern continues. As we work our way up through the cases (when increasing [tex]A[/tex] by 1), the number of possible telephone numbers decreases by 1, since there becomes one less option for [tex]B[/tex].

The last case would be [tex]A=9[/tex] in which case there would only be one option for [tex]B[/tex] and that would be 9.

Since there are 10 cases (0-9), add up the possible telephone numbers for each case:

[tex]\displaystyle \sum_{n=1}^{10}n=1+2+3+4+5+6+7+8+9+10=\boxed{55}[/tex]

Alternatively, recall that the sum of this series can be found using [tex]\frac{n(n+1)}{2}[/tex], where [tex]n[/tex] is the number of values in the set. In this case, [tex]n=10[/tex], and we have:

[tex]1+2+3+4+5+6+7+8+9+10=\frac{10(11)}{2}=\frac{110}{2}=\boxed{55}[/tex]

Answer:

56

Step-by-step explanation:

Since 3 is between -6 and 9 we use the first definition

f(3) = 6 x^2 +2

     = 6(3)^2+2

    = 6(9) +2

   = 54+2

    = 56

Answer:

x = 55°

Step-by-step explanation:

The sum of the angles in a triangle is 180°.

x + 75 + 50 = 180

x + 125 = 180

x = 55

Therefore, x = 55°.

Answer:

x = 55

Step-by-step explanation:

the angles of a triangle add up to 180 degrees. So far we have 125 taken up.

We do 180 - 125 = 55.

x = 55

Answer:

85 i guess

Step-by-step explanation:

The mean of the distribution is 70 and the standard deviation of the distribution is 4.

The shaded area in the distribution below represents approximately 95% of the data. This means that the shaded area is equal to 1.96 standard deviations from the mean.

The 68-95-99.7 rule states that 95% of the data in a normal distribution falls within 2 standard deviations of the mean. So, the shaded area in the distribution below represents the area between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.

The mean of the distribution is the center of the shaded area. The standard deviation of the distribution is the distance from the mean to the edge of the shaded area.

In this case, the mean of the distribution is approximately 70. The standard deviation of the distribution is approximately 4.

Here is a step-by-step explanation of how to find the mean and the standard deviation:

Identify the shaded area in the distribution.

Remember that the shaded area represents 95% of the data.

Use the 68-95-99.7 rule to determine that the shaded area is between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.

Find the mean by averaging the two points on the distribution that are 1.96 standard deviations from the mean.

Find the standard deviation by subtracting the mean from one of the points on the distribution that is 1.96 standard deviations from the mean.

Therefore, the mean of the distribution is approximately 70 and the standard deviation of the distribution is approximately 4.

To learn more about standard deviation here:

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First go to the y intercept (or the b in y=mx+b) look for the slope and plot the points on the graph they're talking about e.g. #23 the y-intercept is 6 go to the 6 on the y axis, and then look at the slope (x), so it goes up and over to the right since it's positive by 1

Answer:

nacho taco Guadalupe Juan ching chong

Step-by-step explanation:

Noob

Answer:

4, 8, 16, 32, 64

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

Given

a₇ = 256 and a₁₀ = 2048 , then

a₁ [tex]r^{6}[/tex] = 256 → (1)

a₁ [tex]r^{9}[/tex] = 2048 → (2)

Divide (2) by (1)

[tex]\frac{a_{1}r^{9} }{a_{1}r^{6} }[/tex] = [tex]\frac{2048}{256}[/tex]

r³ = 8 ( take the cube root of both sides )

r = [tex]\sqrt[3]{8}[/tex] = 2

Substitute r = 2 into (1)

a₁ × [tex]2^{6}[/tex] = 256

a₁ × 64 = 256 ( divide both sides by 64 )

a₁ = 4

Then

a₁ = 4

a₂ = 2a₁ = 2 × 4 = 8

a₃ = 2a₂ = 2 × 8 = 16

a₄ = 2a₃ = 2 × 16 = 32

a₅ = 2a₄ = 2 × 32 = 64

Answer:

x=1

Step-by-step explanation:

log_4(x + 3) + log_4x = 1

We know that loga(b) + loga(c) = loga(bc)

log_4(x + 3)x = 1

Raise each side to the base of 4

4^log_4(x + 3)x = 4^1

(x+3)x = 4

x^2 +3x = 4

Subtract 4 from each side

x^2 +3x -4 = 0

Factor

(x+4) (x-1) =0

Using the zero product property

x= -4  x=1

But x cannot be negative since logs cannot be negative

x=1

Answer:

A..  x = 1.

Step-by-step explanation:

log_4(x + 3) + log_4x = 1

log_4 x(x + 3) = log_4 4

Removing the logs:

x(x + 3) = 4

x^2 + 3x - 4 = 0

(x + 4)(x - 1) = 0

x = 1, -4.

We can ignore the -4 as there is no log of a negative.

Answer:

[tex]x = \frac{3y-4}{y-1}[/tex]

Step-by-step explanation:

y(x-3) = (x-4)

yx -3y = (x-4)

yx - x = 3y -4

x(y-1)= 3y -4

[tex]x = \frac{3y-4}{y-1}[/tex]

Answer:

Below!

Step-by-step explanation:

To find the volume of a cylinder, you can use this formula : v = πr^2h

r = 12km , h = 7 km

v = π(12km)^2(7)

  = 3166.72539

Round to the nearest 10th

  = 3166.7 km^3

Hope this helps! Best of luck <3

Answer: B

Step-by-step explanation:

Its written in slope intercept form not standard

Given:

The data set is:

0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

To find:

The correct statement that represents the box plot of the data correctly.

Solution:

We have,

0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

Divide the data in 2 equal parts.

(0, 1, 1, 1, 2), 3, (4, 4, 6, 6, 9)

Divide each parenthesis in 2 equal parts.

(0, 1), 1, (1, 2), 3, (4, 4), 6, (6, 9)

Here,

Minimum value = 0

First quartile = 1

Median = 3

Third quartile = 6

Maximum value = 9

A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 1 to 6. A line divides the box at 3.

Therefore, the correct option is D.

Answer:

its d

Step-by-step explanation: my yt Tray Clayps

Answer:

1. D

2.C

3. E

4.A

Step-by-step explanation:

the guy above or below me is incorrect.

Answer:

18.45

Step-by-step explanation:

I used a calculator

Answer:

Step-by-step explanation:

0 is the correct answer

Answer:

0

Step-by-step explanation:

The natural numbers are numbers that you can count on your fingers

1,2,3,4,5.......

Whole numbers include 0

0,1,2,3,4.....

Answer:

average speed = distance/ time

711/9

79km/h

Answer:

I've attached the graph with it, the intersection point is,

x = 3, y = 2

Answer:

x = 1

Step-by-step explanation:

5x - (4x - 1) = 2

Let's get rid of the parenthesis

Multiply whatever is in the parenthesis by -1 since there is a minus sign before it

5x - 4x + 1 = 2

Move common terms to one side, so subtract 1 from both sides

5x - 4x + 1 = 2

           -  1  - 1

5x - 4x = 1

Subtract the 5x by 4x

x = 1

Answer:

x = 1

Step-by-step explanation:

5x - (4x - 1) = 2

5x - 4x + 1 = 2  {Distribute property  (-1) is distributed with 4x  and (-1)}

Combine like terms

x + 1 = 2

Subtract 1 from both sides

x = 2 - 1

x = 1

Answer:

Starting with the first one, we need to convert both of the equations into slope-intercept form. y = -2x + 5 is already in that form, now we just need to do it to 4x + 2y = 10.

2y = -4x + 10

y = -2x +5

Since both equations give the same line, the first one has infinite solutions.

Now onto the second one. Once again, the first step is to convert both of the equations into slope-intercept form.  

x = 26 - 3y becomes

3y = -x + 26

y = -1/3x + 26/3  

2x + 6y = 22 becomes

6y = -2x + 22

y = -1/3 x + 22/6

Since the slopes of these two lines are the same, that means that they are parallel, meaning that this one has no solutions.  

Now the third one. We do the same steps.  

5x + 4y = 6 becomes

4y = -5x + 6

y = -5/4x + 1.5

10x - 2y = 7 becomes

2y = 10x - 7

y = 5x - 3.5

Since these two equations are completely different, that means that this system has one solution.

Now the fourth one. We do the same steps again.  

x + 2y = 3 becomes

2y = -x + 3

y = -0.5x + 1.5

4x + 8y = 15 becomes

8y = -4x + 15

y = -1/2x + 15/8

Once again, since these two lines have the same slopes, that means that they are parallel, meaning that this one has no solutions.  

Now the fifth one.  

3x + 4y = 17 becomes

4y = -3x + 17

y = -3/4x + 17/4

-6x = 10y - 39 becomes

10y = -6x + 39

y = -3/5x + 3.9

Since these equations are completely different, there is a single solution.  

Last one!

x + 5y = 24 becomes

5y = -x + 24

y = -1/5x + 24/5

5x = 12 - y becomes

y = -5x +12

Since these equations are completely different, this system has a single solution.

Step-by-step explanation:

hope this helps you out:)

Answer:

i think you just extend the coordinates to the side, except the right point, by 3, and then the bottom ones go down by 3, and the top one goes up by 3

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

if u divide two fractions, it is same as multiplying with its reciprocal

Answer:

what do you need to find? Area? perimeter?

Step-by-step explanation:

Answer:

$2/ hat

Step-by-step explanation:

Find the unit rate:

$ to hats

8 to 4

Divide by four to get the unit rate; over 1

2 to 1

So, $2 per hat

Hope this helps!

Answer:

The additive inverse of -61 is 61. For additive inverse just reverse the sign.

Answer:

b or d

Step-by-step explanation:

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Answer:

A

Step-by-step explanation:

A mode is the value that appears most frequently in the data set because there is not more than one of any number the data set has no mode.

Answer: its going to be 3 dollars and 67 cents

Step-by-step explanation:

In the diagram, ∠5 is adjacent to ∠EHD.

Angle

Angles are formed when two rays intersect at a point. An angle is also formed when to lines intersect each other, thereby the two lines share a common endpoint.

Adjacent angles are two angles that have a common side and a common vertex (corner point). They are placed side by side to each other.

In the diagram, ∠5 is adjacent to ∠EHD.

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