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3 years ago

Greatest integer of x < -3

Mathematics

1 answer:

Irina18 [472]3 years ago

8 0

Answer:

-4

Step-by-step explanation:

Here, we want to get the greatest integer less than -3

The integer less than -3 that is the greatest is -4

It is the internet directly after it to the left of the number line

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The sum of the circumference of a circle and the perimeter of a square is 24. Find the dimensions of the circle and square that

lyudmila [28]

Answer:

The radius of the circle is $r=1.68\ units$

The length of the square is $x=3.36\ units$

Step-by-step explanation:

we know that

The circumference of a circle is equal to $C=2\pi r$

The perimeter of the square is equal to $P=4x$

$24=2\pi r+4x$

Simplify

$12=\pi r+2x$

$x=(12-\pi r)/2$ -----> equation A

The area of a circle is equal to $A=\pi r^{2}$

The area of a square is $A=x^{2}$

The total area is equal to

$At=\pi r^{2}+x^{2}$ -----> equation B

substitute equation A in equation B

$At=\pi r^{2}+[(12-\pi r)/2]^{2}$

This is a vertical parabola open upward

The vertex is the minimum

The x-coordinate of the vertex is the radius of the circle that produce a minimum area

The y-coordinate of the vertex is the minimum area

Solve by graphing

The vertex is the point (1.68, 20.164)

see the attached figure

therefore

The radius of the circle is

$r=1.68\ units$

Find the value of x

$x=(12-\pi r)/2$

assume

$\pi =3.14$

$x=(12-(3.14)*(1.68))/2$

$x=3.36\ units$

8 0

3 years ago

Darren wants to grow tomatoes and herbs so he can make his own fresh pizza sauce. Darren's planter box is seven feet long and fo

n200080 [17]

Answer:

The volume of soil in Darren's planter box is 56 feet³

Step-by-step explanation:

The formula of the volume of a rectangular box is V = l × w × h, where l is its length , w is its width and h is its height

∵ Darren's planter box is seven feet long and four feet wide

∴ l = 7 feet

∴ w = 4 feet

The volume of the soil is equal to the volume of the box using the height of the soil, because the soil takes the shape of the box, so they have the same dimensions of the base

∵ Darren fills the planter box with soil to a height of two feet

∴ h = 2 feet

- Substitute the values of l, w and h in the formula of the volume

∵ V = 7 × 4 × 2

∴ V = 56 feet³

The volume of soil in Darren's planter box is 56 feet³

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3 years ago

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the length of a rectangular frame is 15 inches and the width of 8 inches. what is the length of a diagonal of this Fram inches

Rashid [163]

Answer:

using the phytogaran theory we get 17 inch as the length of the diagonal

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3 years ago

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Find the next term in the sequence. Simplify completely. 3 3,3 3, 3, [?]

FrozenT [24]

3 or 9 could be an answer

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3 years ago

In a survey of 1,532 former UF students, 84% said they were still in love with Tim Tebow. The survey's sampling error was 2%. Us

nalin [4]

Answer:

confidence interval for the proportion of all former UF students who are still in love with Tim Tebow.

(0.79 , 0.89)

Step-by-step explanation:

step 1:-

Given sample survey former UF students n = 1532

84% said they were still in love with Tim Tebow

p = 0.84

The survey sampling error

$= \sqrt{\frac{p(1-p)}{n} }$

Given standard error of proportion = 2% =0.02

Step 2:-

The 99% of z- interval is 2.57

The 99% of confidence intervals are

p ± zₐ S.E (since sampling error of proportion = $\sqrt{\frac{pq}{n} }$

$(0.84 - 2.57X0.02 , 0.84 + 2.57X0.02)$

on simplification , we get

(0.84 - 0.0514 , 0.84 + 0.0514)

(0.79 , 0.89)

conclusion:-

confidence interval for the proportion of all former UF students who are still in love with Tim Tebow.

(0.79 , 0.89)

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3 years ago