A cafeteria sells 30 drinks every 15 minutes.How many drinks would they sell in 1 hour?

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 student made mistake in step 2

The correct answer is an option (B)

"It is a mathematical statement which consists of equal symbol between two mathematical expressions."

"It is a value of the variable which makes equation true."

For given question,

We have been given an equation [tex]x^{2} +14x+45=0[/tex]

A student performed the following steps to find the solution to the equation [tex]x^{2} +14x+45=0[/tex]

Step1: factor the polynomial into (x+5) and (x+9)

Step2: x+5=0 and x-9=0

Step 3: x=-5 and x=9

Now we solve given equation.

[tex]\Rightarrow x^{2} +14x+45=0\\\\\Rightarrow x^{2} +9x+5x+45=0\\\\\Rightarrow x(x+9)+5(x+9)=0\\\\\Rightarrow (x+9)(x+5)=0\\\\\Rightarrow x+9=0~~and~~ x+5=0\\\\\Rightarrow x=-9~~and~~ x=-5[/tex]

We can observe that the student made mistake in step 2.

In stead of factor (x + 9), he wrote (x - 9)

Therefore, the student made mistake in step 2

the correct answer is an option (B)

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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.

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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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.

Answer:

theheckisthis thing

Step-by-step explanation:

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.

3F=-8.5

F = -8.5 / 3 =-2.8333333

round answer as needed

Answer:

2.5 or 2.500

Step-by-step explanation:

Equivalent decimals are that decimal which is equal.

If we put zero on the right side of digit after decimal then it is said to be equivalent digits.

2.50 is called as 250 hundredth

2.5 is called as 25 tenth

2500 is called as 2500 thousandth

All 2.50, 2.5 and 2.500 are equal.

The two numbers that are equivalent to 2.50 are 2.5 and 2.50.

We have,

When we write a decimal number, the trailing zeros after the decimal point do not change the value of the number.

Thus, 2.5 and 2.50 represent the same value of 2.50.

The first decimal, 2.5, is the simplified or standard form of the number.

It is commonly used when the exact level of precision is not required or when rounding is involved.

In this case, 2.5 provides sufficient information about the number without the need for the trailing zero.

The second decimal, 2.50, includes the trailing zero.

This format is often used when a specific level of precision is desired or when the number is part of a larger set of numbers with consistent decimal places.

The trailing zero helps to maintain a consistent number of decimal places and can be useful in situations where exactness is important.

Thus,

Both 2.5 and 2.50 represent the same value of 2.50, with the second decimal including a trailing zero for added precision or formatting purposes.

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