A bird picks up a golf ball and drops it while flying 81 feet above the ground. The ball hits the top of a 32-foot-tall pine tree then bounces down to the ground. After how many seconds does the ball hit the tree?

Final answer:

Sarah has 1 1/5 cups of nuts and must add 2/5 cup of dried fruit to make a total of 1 3/5 cups of trail mix.

Explanation:

Imagine Sarah is making a trail mix for a hiking trip. She already has 1 1/5 cups of nuts and wants to add more dried fruit to reach a total of 1 3/5 cups of trail mix. To find out how much dried fruit she should add, we can set up the equation:

1 1/5 + x = 1 3/5

Converting mixed numbers to improper fractions gives us:

6/5 + x = 8/5

Subtracting 6/5 from both sides, we find that x (the amount of dried fruit to be added) is:

x = 8/5 - 6/5

x = 2/5

Therefore, Sarah needs to add 2/5 cup of dried fruit to the nuts to make 1 3/5 cups of trail mix.

This figure is made up of a rectangle BDFE and parallelogram ABCD.

The area of this figure= Area of BDFE+Area of ABCD

Area of parallelogram=base*height and Are of rectangle= length*Width

So, Area of ABCD= CD*BH

And, Area of BDFE=BD*DF

area of this figure= BD*DF+CD*BH

From the figure CD=4 and BH=3

To find BD, Let us apply Pythagorean theorem, [tex] hypotenuse^{2} =adjacent^{2}+ opposite^{2} [/tex], to ΔBHD

[tex] BD^{2} =HD^{2}+ BH^{2} [/tex]

HD=2 and BH=3

[tex] BD^{2} =2^{2}+ 3^{2} [/tex]

[tex] BD^{2} =4+ 9=13 [/tex]

[tex] BD=\sqrt{13} [/tex]

To find DF, Let us apply Pythagorean theorem, [tex] hypotenuse^{2} =adjacent^{2}+ opposite^{2} [/tex], to ΔBHD

[tex] DF^{2} =DG^{2}+ GF^{2} [/tex]

DG=6 and GF=9

[tex] DF^{2} =6^{2}+ 9^{2} [/tex]

[tex] DF^{2} =36+ 81=117 [/tex]

[tex] BD=\sqrt{117}=3\sqrt{13} [/tex]

[tex] BD=\sqrt{13} and DF=3\sqrt{13} [/tex]

area of this figure= BD*DF+CD*BH

area of this figure= [tex] \sqrt{13} [/tex]*3[tex] \sqrt{13} [/tex]+4*3

area of this figure=13*3+12

area of this figure=39+12=51

Area of this figure=51 square units

We are given

total number of dolls =5

and there are five spaces only to be arranged in

In first space:

Any five dolls can be put in

so, number of ways of putting dolls in first space is 5

In Second space:

One doll is already put in first space

so, only four dolls can be put in

so, number of ways of putting dolls in second space is 4

In Third space:

One doll is already put in second space

so, only three dolls can be put in

so, number of ways of putting dolls in third space is 3

In Fourth space:

One doll is already put in third space

so, only two dolls can be put in

so, number of ways of putting dolls in fourth space is 2

In Fifth space:

One doll is already put in fourth space

so, only one dolls can be put in

so, number of ways of putting dolls in fifth space is 1

so, total number of ways five dolls can be arranged

[tex] =5*4*3*2*1 [/tex]

[tex] =120 [/tex].................Answer

Answer:

120

Step-by-step explanation:

just a simple awnswer for those imapatient peeps    

Final answer:

The expression 2d(3) is simplified by multiplying 2 by 3, yielding 6, and then by d, resulting in 6d.

Explanation:

To simplify the expression 2d(3), you simply need to multiply the variable d by the number 2 and then multiply the result by the number inside the parentheses, which is 3. This is straightforward multiplication, similar to the distributive property used in algebra to simplify expressions.

The simplified form of the expression is found by multiplying 2 by 3, giving us 6, and then multiplying that result by d. Hence, 2d(3) simplifies to 6d.

The value of the expression ¹²P₃ and ¹⁰C₄ will be 1,320 and 210, respectively.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

The value of the expression ¹²P₃ is given as,

¹²P₃ = 12! / (12 - 3)!

¹²P₃ = 12 x 11 x 10 x 9! / 9!

¹²P₃ = 1,320

The value of the expression ¹⁰C₄ is given as,

¹⁰C₄ = 10! / [(10 - 4)! x 4!]

¹⁰C₄ = 10 x 9 x 8 x 7 x 6! / (6! x 4 x 3 x 2 x 1)

¹⁰C₄ = 10 x 3 x 7

¹⁰C₄ = 210

The value of the expression ¹²P₃ and ¹⁰C₄ will be 1,320 and 210, respectively.

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

#SPJ6

Here are a bunch of CORRECT answers. Your answer is in the first pic. I got number 3 wrong, but it still showed the correct answer.

Answer:

1/4

Step-by-step explanation:

Final answer:

The fraction of free throws Marcela made in simplest form is 1/4.

Explanation:

Marcela made 4 out of 16 free throws. To express this fraction in simplest form, we divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor. In this case, the greatest common divisor of 4 and 16 is 4.

To simplify the fraction:

Therefore, the fraction of free throws Marcela made in simplest form is 1/4.

Answer:

e

Step-by-step explanation:

Final answer:

Tamara needs 5 boxes of tiles to complete her bathroom wall border. The calculations involve finding the total area of the border, the area covered by one tile, and then determining the total number of tiles and boxes required.

Explanation:

To determine how many boxes of tiles Tamara needs for her bathroom wall border, we first calculate the total area of the border and then divide that by the area of an individual tile. The area of the border is obtained by multiplying its length by its width. Then, knowing that each box contains 6 tiles, we calculate how many boxes she needs.

First Equation

Area of border = 9 × \(1/3\) = 3 square feet.

Second Equation

Number of tiles = 3 / (\(1/3\) × \(1/3\)) = 3 / \(1/9\) = 27 tiles.

Therefore, the number of boxes needed = 27 / 6 = 4.5.

Since Tamara cannot purchase half a box, she would need to round up to 5 boxes in total to complete the border.