An open box is made by cutting squares from the corners of a piece of
metal that is 16 inches by
20 inches, as shown in the figure. The edge of each cut-out square is x inches. Find V(x), the
volume of the box in terms of x.

Answer:

The answer is  6.88.

Step-by-step explanation:

The mean absolute deviation for the given data will be equal to 6.9.

The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection.

It is a statistical summary of statistical variability or dispersion.

The formula used to calculate MAD is given below:-

MAD = 1/n ∑ |xi-m|

The given data set is 32, 43, 38, 28, and, 51. First, calculate the mean of the given data.

Mean = ( 32 + 43 + 38 + 28 + 51 ) / 5

Mean = 192 / 5 = 38.4

The MAD will be calculated as below:-

MAD = ( 1 / 5) [ | ( 32 - 38.5 ) | + | ( 43 - 38.5 ) | + | ( 38 - 38.5 ) | + | ( 28 - 38.5 ) + | ( 51 - 38. 5 ) | ]

MAD = ( 6.5 + 4.5 + 0.5 + 10.5 + 12.5 + ) / 5

MAD = 6.9

Therefore, the mean absolute deviation for the given data will be equal to 6.9.

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Answer:

26, 18, -1, -25

Step-by-step explanation:

for easier understanding just draw a number line with integers for easier clarification.

... -5, -4, -3, -2, -1, 0, 1, 2 , 3 , 4 ...

26,18,-1,-25 is the answer from greater to least

Answer:

1400< 350d (its less than or equal to, but i cant put the bar under.

Answer:

I hope this helps you

Step-by-step explanation:

50.2654824574

Answer:

Y divided by 3.99 = X

Step-by-step explanation:

Answer:

67.5

Step-by-step explanation:

7.5 (the lenght of the pencil) multiplied by 9 (the number of pencils) is 67.5

Answer:

7in

Step-by-step explanation:

The difference between the distances 43.82 feet and 50.02 feet is 6.2 feet.

How to find the difference between two numbers?

Subtract the greatest from the smallest value of two numbers to determine the difference between them. The difference between the two numbers is the sum's product.

Given,

The two distances:

x = 43.82 feet

y = 50.02 feet

We have to determine the difference between x and y.

That is,

y – x. This is because y > x.

y – x = 50.02 feet – 43.82 feet = 6.2 feet.

Therefore,

The difference between the distances 43.82 feet and 50.02 feet is 6.2 feet.

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Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.75 x 10⁵ ) / (2.25 x 10² )= (2.75 / 2.25) x 10⁵⁻²= 1.2 x 10³ times .(That's 1,200 times as many.)

Answer:

Merry Christmas!!!! :D

Step-by-step explanation:

The awnser is 1 :D

Answer:

x=1

Step-by-step explanation:

15x=5(4-x)

15x=20-5x

20x=20

x=1

Happy Holidays! Please give me brainliest!

Answer:

x=1/5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

I think it's 62 :D

Step-by-step explanation:

52 - (-10)= 62

Answer:

a) [tex]-16t^{2}+64t\geq40[/tex]

b)[tex][2-\frac{\sqrt{6}}{2} , 2+\frac{\sqrt{6}}{2}][/tex]

(see attached picture for the number line)

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) [tex]h_{max}=64ft[/tex]

d) t=2s

Step-by-step explanation:

a)

Basically the ball will disappear when it is higher than 40 ft, so we can build the inequality like this:

[tex]-16t^{2}+64t\geq40[/tex]

this is because the function represents it's height, so when the function is greater than or equal to 40, then the ball will disappear.

b) to solve the inequality, first we need to turn the ≥ symbol to an = symbol and solve for t, so we get:

[tex]-16t^{2}+64t =40[/tex]

we can move the 40 to the other side of the equation so we get:

[tex]-16t^{2}+64t-40=0[/tex]

we can factor the equation so it's easier to solve, so we get:

[tex]-8(2t^{2}-8t+5) =0[/tex]

which simplifies to:

[tex]2t^{2}-8t+5=0[/tex]

and we can use the quadratic formula to solve this equation, so we get:

[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]

so we get:

[tex]t=\frac{-(-8)\pm\sqrt{(-8)^{2}-4(2)(5)}}{2(2)}[/tex]

which yields:

[tex]2\pm \frac{\sqrt{6}}{2}[/tex]

and next we need to test the posible intervals to see which one makes the inequality true, the possible intervals are:

[tex](-\infty, 2-\frac{\sqrt{6}}{2}][/tex]  for a test value of 0

[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex] for a test value of 1

[tex][2+\frac{\sqrt{6}}{2},\infty)[/tex] for a test value of 4

so next we test each of the values in the original inequality and see if the inequality is true:

[tex](-\infty, 2-\frac{\sqrt{6}}{2}][/tex] for a test value of 0

[tex]-16(0)^{2}+64(0)\geq40[/tex]

[tex]0\geq40[/tex] false

so this is not an answer.

[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex] for a test value of 1

[tex]-16(1)^{2}+64(1)\geq40[/tex]

[tex]48\geq40[/tex]

true, so this is an answer.

[tex][2+\frac{\sqrt{6}}{2}, \infty)[/tex] for a test value of 4

[tex]-16(4)^{2}+64(4)\geq40[/tex]

[tex]-16(16)+64(4)\geq40[/tex]

[tex]-256+256\geq40[/tex]

[tex]0\geq40[/tex]

false, so this is no answer.

So the answer is the interval:

[tex][2-\frac{\sqrt{6}}{2},2+\frac{\sqrt{6}}{2}][/tex]

This interval means that from about 0.78s to about 3.22s the ball will not be visible because it will be higher than 40 feet high.

c) In order to find how high Penelope kick the football, we must find the vertex of the parabola which is gotten when graping the given function (see attached picture)

so we can use the following formula to find the t-value for this maximum height:

[tex]t=-\frac{b}{2a}[/tex]

so we substitute the corresponding values:

[tex]t=-\frac{64}{2(-16)}[/tex]

which yields:

t=2s

next, we can substitute this time into the original function to find the maximum height, so we get:

[tex]h=-16(2)^{2}+64(2)[/tex]

which yields:

h=64 ft

d) We found the answer for d on the previous part where we got that t=2s

Answer:

liner Y=9(2x)  Y=5x-3

Step-by-step explanation:

Y=9(2x) and y = 5x - 3 are linear equations while others are non-linear.

The standard linear equation is in the form y = mx + b

Other equations are non-linear in nature since they have a degree of 2 or more.

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Answer:

Please check explanations for answer

Step-by-step explanation:

Here, we want to check the given list and state the true values;

1. This is true

Compound interest has the exponent nt; simple interest has no exponent

2. This is false

Simple interest is only earned on the principal which is the amount deposited

3. True

Due to its multiplication chain, it earns more money as we can compound more than once within the given time frame

4. This is false; check explanations above

5. This is true

Its value is only based on the amount invested originally

6. This is false

simple interest earns the same amount annually based on rate

7. This is false

Both considers the time factor t in their formulas

8. This is true

The interest and principal forms the principal for another compounding time

Answer:

12 feet

Step-by-step explanation:

Sometimes, a simple drawing is a great way to start! In the attached drawing, the red line represents the ladder, the brown represents the ground, and the black represents the building!

We want to find the side of the triangle from where the ladder meets the building to where the building meets the ground. This can be found using trigonometric identities, namely sine:

[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]

Plug in known values:

[tex]sin(74^o)=\frac{x}{12}[/tex]

Rearrange to isolate the variable:

[tex]x=12sin(74^o)[/tex]

Simplify!

[tex]x=11.535140... ft[/tex]

Round to the nearest foot:

[tex]x=12ft[/tex]

Answer:

7% of 100 is 7 so 100 + 7 = 107

Step-by-step explanation:

Answer:

Huh??

Step-by-step explanation:

6x10=60/12=5×2=10??????

[tex] \underline{\underline{\sf{ \color{purple}{Given :} }}} [/tex]

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

[tex] \underline{\underline{\sf{ \color{purple}{To\:Find :} }}} [/tex]

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

[tex]\underline{\underline{\sf{ \color{purple}{Solution :} }}}[/tex]

[tex]\underline{\tt{As\:we\:know\:that,}}[/tex]

[tex]\star\:{\boxed{\sf{\purple{Area \: of \: circle} = 2 \times Area \: of \: semicircle}}}[/tex]

[tex] : \: \implies \sf{Area \: of \: circle = 2 \times 77cm^{2} }[/tex]

[tex]: \: \implies \sf{Area \: of \: circle =154 \: {cm}^{2} }[/tex]

━━━━━━━━━━━━━━━━━━━━━

[tex]\underline{\tt{Now, \: we\:know\:that,}}[/tex]

[tex]\star\:{\boxed{\sf{\purple{Area \: of \: circle} = \pi r^{2}}}}[/tex]

[tex] : \: \implies \sf{ 154 = \dfrac{22}{7} \times {r}^{2} }[/tex]

[tex] : \: \implies \sf{ 7 \times 7 = {r}^{2} }[/tex]

[tex] : \: \implies \sf{ 49 = {r}^{2} }[/tex]

[tex] : \: \implies \sf{ {r}^{2} = 49 }[/tex]

[tex] : \: \implies \sf{ {r} = \sqrt{ 49} }[/tex]

[tex] : \: \implies \sf{ {r} = { 7 cm} } [/tex]

━━━━━━━━━━━━━━━━━━━━━

[tex]\underline{\tt{Now, \: we\:know\:that,}}[/tex]

[tex]\star\:{\boxed{\sf{\purple{Perimeter} = \pi r + 2r }}}[/tex]

[tex] : \: \implies \sf{ Perimeter = \dfrac{22}{7} \times 7 + 2 \times 7 }[/tex]

[tex] : \: \implies \sf{ Perimeter = 22 + 14 }[/tex]

[tex] : \: \implies \sf{ Perimeter = 36 }[/tex]

[tex]\sf \therefore \: perimeter \: of \: the \: circle \: is \: 36cm[/tex]

━━━━━━━━━━━━━━━━━━━━━

Answer:

A , one solution.........

Answer:

FM = 22

Step-by-step explanation:

Centroid of a triangle divides the median in the ratio 2 : 1

Therefore, AM : FM = 2 : 1

Let AM = 2x and FM = x

Since, AM = 44

Therefore, 2x = 44

x = 44/2

x = 22

FM = 22

The least number of pages Yao must read per hour to finish reading the book is 26 pages per hour. which is the correct answer would be an option (B)

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

Calculate the total number of hours Yao has left to finish reading the book by subtracting the number of hours he has already spent reading from the total number of hours he has available:

8 hours - 1 hour = 7 hours.

The number of pages Yao has left to read : 300 pages - 120 pages = 180 pages.

The number of pages Yao must read: 180 pages / 7 hours = 25.7 pages/hour.

Round up the number of pages Yao must read per hour to the nearest whole number. The least number of pages Yao must read per hour is 26 pages/hour.

Therefore, the minimum number of pages Yao must read each hour to finish the book is 26 pages per hour.

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Both the garden are in the shape of rectangles.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

The dimension of the two gardens are given as:

6 ft ×3 ft and 6 ft × 4 ft

From the dimension, we can conclude that the gardens are in the shape of a rectangle.

For the first garden 6 ft ×3 ft,

The length of the garden is l = 6 ft and;

The breadth of the garden is b = 3 ft.

Similarly,

For the second garden  6 ft × 4 f,

The length of the garden is l = 6 ft and;

The breadth of the garden is b = 4 ft.

The models for the two gardens:

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Answer:

y=-x-2 this is the answer