In how many ways can we pick three different numbers out of the group:
1, 2, 3, ..., 100
such that the largest number is larger than the product of the two smaller ones? (The order in which we pick the numbers does not matter.)

9514 1404 393

Answer:

  70

Step-by-step explanation:

If we consider the terms to have decreasing powers of x, then the middle term is the one with x^4y^4 as its variables. The full value of that term is ...

  (8C4)(2x)^4(3y)^4 = 70(6xy)^4

Substituting for x and y, this is ...

  70(6(1/3)(1/2))^4 = 70(1^4) = 70

The middle term is 70 when (x, y) = (1/3, 1/2).

_____

The value of nCk is n!/(k!(n-k)!). Then 8C4 is 8!/(4!)^2 = (8·7·6·5)/(4·3·2·1) = 70.

Answer:

Area = 80

Step-by-step explanation:

area = a^2 = 4^2 = 16 = square

area = wl = 12*8 = 96 = rectangle

rectangle - square

96 - 16 = 80

Answer:

A. 75 km²

Step-by-step explanation:

The area of a triangle

A =1/2 ab sin C  where a and b are the lengths of the sides and C is the included angle

A = 1/2 (14)(11) sin (77)

A = 75.0264949885

{x = 2y

{x + y = 9

{x = 2y

{2y + y = 9

{x = 2y

{3y = 9 / : 3

{y = 3

{x = 2 · 3

x = 6 and y = 3

2cos2x=y

dy/dx(2cos2x)=-4sin2x

d/du cosu= u'×cos'u=-u'×sinu

d/du sinu= u'×sin'u= u'×cosu

d/du tanu = u'×(1+tan²u)

d/du cotu = u'×-(1+cot²u)

proof for cosu :

cos2x= 1-2sin²x

or 2cosx²-1

or cos²x-sin²x

we will one of this fro example let's take the first one

d/dx 1-2sin²x=0-2×2(sinx)×cosx=-2sin2x

and we have 2 in the begining so its -4sin2x

Answer:

first question: reflection on the y axis

second question: reflection on the x axis

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

If P is the perimeter of the larger triangle, then 3/5P will be the perimeter of the smaller one. The difference in perimeters is ...

  P -3/5P = 40 in

  2/5P = 40 in

  P = (5/2)(40 in) = 100 in

  3/5P = 3/5(100 in) = 60 in

The smaller triangle perimeter is 60 in; the larger is 100 in.

Answer:

B

Step-by-step explanation:

it simplifies to [tex]x^{4}[/tex]

9514 1404 393

Answer:

  3 in

Step-by-step explanation:

Ratios of corresponding sides are equal, so we have the proportion ...

  x/(5 in) = (6 in)/(10 in)

  x = (5 in)(6/10) = 3 in

The missing side (x) is 3 in.

Answer:

[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]

Or, their exact solutions:

[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle 2\sec^2 \theta = 4\tan \theta + 1[/tex]

For 0° ≤ θ ≤ 360°.

Recall that tan²(θ) + 1 = sec²(θ). Substitute:

[tex]\displaystyle 2\left(\tan^2 \theta + 1\right) = 4\tan \theta + 1[/tex]

Distribute:

[tex]\displaystyle 2\tan^2\theta + 2 = 4\tan\theta + 1[/tex]

Isolate:

[tex]\displaystyle 2\tan^2\theta - 4\tan\theta + 1 = 0[/tex]

This is in quadratic form. Thus, we can solve it like a quadratic. Let u = tan(θ). Hence:

[tex]\displaystyle 2u^2 - 4u + 1=0[/tex]

The equation is not factorable. Therefore, we can consider using the quadratic formula:

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

In this case, a = 2, b = -4, and c = 1. Substitute and evaluate:

[tex]\displaytstyle \begin{aligned} u &= \frac{-(-4)\pm\sqrt{(-4)^2 - 4(2)(1)}}{2(2)} \\ \\ &= \frac{4\pm\sqrt{8}}{4} \\ \\ &= \frac{4\pm2\sqrt{2}}{4} \\ \\ &= \frac{2\pm\sqrt{2}}{2}\end{aligned}[/tex]

Therefore:

[tex]\displaystyle u = \frac{2+\sqrt{2}}{2} \approx 1.7071\text{ or } u = \frac{2-\sqrt{2}}{2}\approx 0.2929[/tex]

Back-substitute:

[tex]\displaystyle \tan\theta = \frac{2+\sqrt{2}}{2} \text{ or } \tan \theta = \frac{2-\sqrt{2}}{2}[/tex]

Take the inverse tangent of both equations. Hence:

[tex]\displaystyle \theta = \arctan\frac{2+\sqrt{2}}{2} \approx 59.6388^\circ\text{ or } \theta = \arctan\frac{2-\sqrt{2}}{2}\approx 16.3249^\circ[/tex]

The same value of tangent occurs twice in every full rotation. Hence, by reference angles, the other two solutions are:

[tex]\displaystyle \theta = 180^\circ + \arctan\frac{2+\sqrt{2}}{2} \approx 239.6388^\circ \\ \\ \theta = 180^\circ + \arctan\frac{2-\sqrt{2}}{2} \approx 196.3249^\circ[/tex]

In conclusion, the four solutions are:

[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]Or, approximately:

[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]

Answer:

{6, 8, 10, 12, 14, 16, 18, 20, ...}

Step-by-step explanation:

even natural numbers >/= 6.

Thus this has no upper limit and the set is thus infinite.

The set of even natural numbers greater than or equal to 6 is

" The natural numbers are those numbers used for counting and ordering. Numbers used for counting are called cardinal numbers."

We know the natural numbers are:

{1, 2, 3, 4, 5, 6, 7,..........}

Now, the set of even natural numbers are:

{2, 4, 6, 8, 10...........}

Therefore, the set of even natural numbers greater than or equal to 6 is

{6, 8, 10, 12,..............}

Learn more about natural numbers here: https://brainly.com/question/8102087

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Answer:

0.48

Step-by-step explanation:

[tex]0.6*0.8 = 0.48[/tex]

When both quantities in a rate are fractions, the strategy to write the rate as a unit rate is to divide both the numerator and denominator of the rate by their greatest common factor (GCF) to simplify the fraction.

To write the rate as a unit rate:

1. Identify the rate, which is a fraction with a numerator and a denominator.

2. Find the greatest common factor (GCF) of the numerator and denominator.

3. Divide both the numerator and denominator by the GCF to simplify the fraction.

4. The resulting simplified fraction is the unit rate.

For example, if the rate is 3/6, the GCF of 3 and 6 is 3. Divide both the numerator and denominator by 3:

3/6 ÷ 3/3 = 1/2

So, the unit rate of 3/6 is 1/2.

By converting the rate to a unit rate, we make it easier to compare the rate for a single unit of one quantity to a single unit of the other quantity, making it more convenient for comparison and analysis.

To know more about quanity:

https://brainly.com/question/32582242

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Answer:

D

Step-by-step explanation:

im thinking its d, because prime factorisation is a way of expressing a number as a product of its prime factors.

a isn't correct since 9 isn't is a prime number.

b isn't correct because you wouldn't use decimals typically.

c isn't correct because 1 is not a prime number.

d is the only correct solution since all the numbers listed are prime numbers.

Step-by-step explanation:

500 divided by 3 __

__ + 3645 = __

__ - 240 = __

Answer:

n | 0 | 0 1

| y 2 | 2 y 3 | 3 años

Step-by-step explanation:

[tex] - 15 + 8x = x + 3 \\ 8x - x = 3 + 15 \\ 7x = 18 \\ \\ x = \frac{18}{7} \\ \\ x = 2.571[/tex]

We put the unknown on one side, and the other end is empty of the unknown , When it turns to the other side, its sign changes.

As for the number with the unknown, it becomes the denominator with the number without the unknown.

I hope I helped you^_^

Answer:

60

Step-by-step explanation:

5(x + 7)

when x is equal to 5, then

Here, we want to solve for the number of servings 10 pounds of egg whites can make

Number of servings 10 pounds of egg whites can make is approximately 27 servings

1 pound = 16 ounce

10 pounds = 160 ounce

Quantity of egg whites available = 10 pounds

Quantity of egg whites per serving = 6 oz

Number of servings 10 pounds can make = Quantity of egg whites available / Quantity of egg whites per serving

Recall,

10 pounds = 160 oz

= 160 oz / 6 oz

= 26.67

Approximately,

27 servings

https://brainly.com/question/24443164

Answer:

11

Step-by-step explanation:

(y+5)-(y-6)

y+5-y+6(opening the bracket)

5+6

11

Answer:

11

Step-by-step explanation:

(y+5) - (y-6) = y + 5 - y + 6 =

0y + 11 = 11

Remember, y - y = 1y - 1y = 0y or 0,  and - (y-6) = -1 (y-6) = -y + 6

Answer:

The answer is option 1

Step-by-step explanation:

For the linear inequality on the top line of the system, it's saying that the y-value must be greater than or equal to 1.  This is verified by the graph because all y-values that fit the criteria of the linear inequality are shaded.  The graph is also showing for the dotted line that the area is shading all points where, if you subtract an x-value from a y-value, the difference will always be greater than 0.  Note that this does not apply for points ON the line, as it cannot be equal to 0.  This matches with the linear inequality on the bottom line of option 1.

Answer:

x = 1

Step-by-step explanation:

Vertical angles are opposite angles formed by two lines.

Both the angles are equivalent

65x - 12 = 43x + 10

Subtract 43x from both sides

22x - 12 = 10

add 12 from both sides

22x = 22

Divide each side by 22

x = 22/22

x = 1

If my answer is incorrect, pls correct me!

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Answer:

5(n+7)=8

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Simply plug 3 into the equation and follow the order of operations.

2(3 - 4) + (3(3)) - (3^2)

2(-1) + (9) - (9)

= -2

Answer:

2

Step-by-step explanation:

2 pounds of fudge ÷ 1 pounds servings = 2 servings

If my answer is incorrect, pls correct me!

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-Chetan K

Answer: 8

Step-by-step explanation:

Step-by-step explanation:

the correct aanswer is 3 is correct answermark me bbrainleast plz

Answer:

d is the answer

Step-by-step explanation:

mark me as brilliant

Answer:

Yes. It is a rational number.

Answer:

1.60934 per hour

please mark me brainliest

Answer:

1.60934 per hour

plz mark my answer brainliest answer plz