Clara says that if you square the number 4 and then divide the result 2, you end up with 4. Is Clara correct? Explain.

Answer:- 512

Explanation:-

We know that [tex](m+1)^{th},\ (T_{m+1})[/tex] in the binomial expansion [tex](p+q)^n[/tex] is given by

[tex]T_{m+1}=^nC_m\ p^{n-m}q^m[/tex]

Assume that [tex]x^9y[/tex] occurs in the [tex](m+1)^{th}[/tex] term of the expansion of [tex](2y+4x^3)^4=(4x^3+2y)^4[/tex]

[tex]T_{m+1}=^4C_m\ (4x^3)^{4-m}(2y)^m[/tex]

Comparing power of x and y in  [tex]x^9y[/tex]  we get m=1

Thus term for m=1 [tex]=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y[/tex]

Thus the coefficient of [tex]x^9y[/tex] is 512.

The equation of a line with a given slope and passing through a point can be found using the point-slope formula.

To find the equation of a line with a given slope (m) passing through a point (a, c), we can use the point-slope formula. The point-slope formula is given by:

y - c = m(x - a)

where (x, y) represents any point on the line. This equation represents a line with slope m passing through the point (a, c).

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Answer:

y<3

Step-by-step explanation:

Do you do rsm lol

y<3 is the value.

In mathematics, an inequality is a relation that makes a non-equal assessment between two numbers or different mathematical expressions. Its miles are used most often to evaluate numbers at the quantity line by means of their size. There are several unique notations used to represent exceptional types of inequalities:

The notation a < b means that a is less than b.

The notation a > b approach that a is greater than b.

The range of y which will satisfy this inequality will result in the first fraction of a larger value as compared to the second fraction.

Multiplying both sides of an inequality by 12, we get:

12×10>12×3y-7/12

2(7-2y)>3y-7

14-4y3y-7

14+7>3y+4y

21> 7y

3>9

y<3

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You can go on a maximum of 5 rides with $16 after paying for the $5 admission at the amusement park, where each ride costs $2.

The amusement park charges $5 for admission and $2 for each ride. We can write an expression for the total cost as C = 5 + 2r, where C is the total cost and r is the number of rides. To find out how many rides you can go on with $16, we would set up the equation 16 = 5 + 2r.

Step-by-step solution:

Since you cannot go on half a ride, you could go on a maximum of 5 rides with your $16.

the square root of a negative number needs to end in I

 so find the square root of 36 and add an I

 sqrt(36) = 6

 so sqrt(-36) = 6i

3F=-8.5

F = -8.5 / 3 =-2.8333333

round answer as needed

In order to find the reciprocal of a number, we should just flop it over, like so:-

[tex]\sf{The~reciprocal~of~a~is~\frac{1}{a}}[/tex]

According to the formula, the reciprocal of 60 is:-

[tex]\bigstar{\boxed{\pmb{\frac{1}{60}} \longleftarrow\sf{reciprocal~of~60}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

The number of low and high resolution pictures that can be taken with a 512 megabyte memory card is determined by the equation 4L + 8H = 512, where L represents low resolution pictures and H represents high resolution pictures.

To determine the number of low and high resolution pictures that can be taken with a 512 megabyte memory card, we can set up an equation based on the storage requirements of each type of picture. Let's use L to represent the number of low resolution pictures and H to represent the number of high resolution pictures.

Because each low resolution picture requires 4 megabytes and each high resolution picture requires 8 megabytes, we can write the equation as:

4L + 8H = 512

This equation shows that the total memory used by L low resolution pictures and H high resolution pictures cannot exceed 512 megabytes, the capacity of the memory card.

Carly has 2 dimes and 4 nickels in her pocket.

Let's assume Carly has x dimes in her pocket. Since Carly has 2 more nickels than dimes, she would have x + 2 nickels. The value of x dimes is 10x cents and the value of (x + 2) nickels is 5(x + 2) cents. Since Carly has 40 cents in total, we can set up the equation: 10x + 5(x + 2) = 40.

Simplifying the equation gives us: 10x + 5x + 10 = 40. Combining like terms gives us: 15x + 10 = 40. Subtracting 10 from both sides gives us: 15x = 30. Dividing both sides by 15 gives us:
x = 2.

Therefore, Carly has 2 dimes and 4 nickels.

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Given that 20% of students are studying Physics and 25% Chemistry, the rest, which is 55% are studying Biology. In the simplest case, where the total of students is 100, the smallest number of Biology students would be 55.

The question asks us to identify the smallest possible number of students studying biology. Given that 20% of students study Physics and 25% study Chemistry, we can emphasize that the rest are studying Biology. In the simplest situation, the total number of science students could be 100 because percentages are based on 100. Therefore, for this case, 20 students are studying Physics, 25 are studying Chemistry, and the rest which is 55, are studying Biology. Thus, the smallest possible number of Biology students can be 55.

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Answer:

theheckisthis thing

Step-by-step explanation:

Answer:

the range will be 248 ≤ x ≤ 370

Step-by-step explanation:

The given inequality models the range of amount of gems.

132 ≤ 1/2x + 8 ≤ 193

So we have to solve the inequality for the value of x.

132 ≤ [tex]\frac{1}{2}x[/tex] + 8 ≤ 193

Now we subtract 8 from the inequality.

132 - 8 ≤ ([tex]\frac{1}{2}x[/tex] + 8) - 8 ≤ 193 - 8

124 ≤ [tex]\frac{x}{2}[/tex] ≤ 185

Now we multiply the inequality by 2

124 × 2 ≤ [tex](\frac{x}{2})[/tex] × 2 ≤ 185 × 2

248 ≤ x ≤ 370

So the range will be 248 ≤ x ≤ 370