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4 years ago

Prove that 3n< n! if n is an integer greater than 6.

1 answer:

4 0

Let $n=7$ . Then

$3(7)=21$

Assume the inequality holds for $n=k$ , so that $3k$ . Then for $n=k+1$ , you have, for $k>7$ ,

$3(k+1)$

so the statement is true.

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Sally is planning a trip for 225 students

Gala2k [10]

Answer: 75 students.

Step-by-step explanation:

In the data set we have a total of 10 + 8 + 7 + 5 = 30 students.

of those, 10 want to go to the park, the percentage is:

(10/30)*100% = 33.3%

Then, out of the 225, we can expect that a 33.3% (or 0.333 in decimal form) want to go to the park, this is:

N = 225*0.333% = 74.925

We can roud it up, and get N = 75

So Sally can expect that 75 students want to go to the park

4 0

3 years ago

If u can explain please :)

zhannawk [14.2K]

Answer:

it would be c because 12+8 = 20 and 24 is closer to 20

7 0

3 years ago

the area of a rectangle is 30 to the square root of 3750 square inches, and the length is 3 to the square root of 250 inches. wh

uranmaximum [27]

<h3>Answer:</h3>

$\sf { width =10 \sqrt{15} \:inches}$

<h3>Solution:</h3>

We are given that:

Area of rectangle is 30√3570
Length of the rectangle is 3√250

Area of rectangle is given by:

$\implies\quad{\pmb{ \sf{Area = length\times width}} }$

Hence, putting the values in the formula:

$\implies\quad \sf{ A = l\times w}$

$\implies\quad \sf{ 30\sqrt{3750}=3\sqrt{250}\times w}$

$\implies\quad \sf{3\sqrt{250}\times w = 30\sqrt{3750} }$

$\implies\quad \sf{ w =\dfrac{30\sqrt{3750}}{3\sqrt{250}}}$

$\implies\quad \sf{ w =10\dfrac{\sqrt{3750}}{\sqrt{250}}}$

$\implies\quad \sf{ w = 10\times\sqrt{\dfrac{3750}{250}}}$

$\implies\quad \underline{\underline{\pmb{\sf{ w =10\sqrt{15}}}}}$

8 0

3 years ago

Find the value of each variable

aniked [119]

Answer:

Answer d)

$a= 10*\sqrt{3}$ $b=5*\sqrt{3}$ , $c=15$ , and $d=5$

Step-by-step explanation:

Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".

So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:

$b=10*sin(60^o)= 10*\frac{\sqrt{3} }{2} = 5*\sqrt{3}$

where we use the fact that the sine of 60 degrees can be written as: $\frac{\sqrt{3} }{2}$

We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:

$d=10*cos(60^o)=10* \frac{1}{2} = 5$

In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:

$sin(30^o)= \frac{b}{a} \\a=\frac{b}{sin(30)} \\a=\frac{5*\sqrt{3} }{\frac{1}{2} } \\a= 10*\sqrt{3}$

where we used the value of the sine function of 30 degrees as one half: $\frac{1}{2}$

Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:

$c=10*\sqrt{3} * cos(30^o)=10*\sqrt{3} *\frac{\sqrt{3} }{2} \\c= 5*3=15$

Therefore, our answer agrees with the values shown in option d)

6 0

3 years ago

What is the meaning of the word indiced

grin007 [14]

Basically means “ to succeed in persuading or influencing someone to do something “

6 0

3 years ago

Read 2 more answers