square root of 12 is between

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.

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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9/5 = 54/30

1/6 = 5/30

54/30 - 5/30 = 49/30 = 1 19/30

The difference is as follows:

  [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{49}{30}[/tex]

We are given two fractions and we are asked to find there difference.

The expression is as follows:

   [tex]\dfrac{9}{5}-\dfrac{1}{6}[/tex]

( since, the denominator of two fractions is different hence we take the least common multiple of the denominators.

i.e. lcm{5,6}=30 )

Now, we proceed as follows:

   [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{9\times 6-1\times 5}{30}[/tex]

i.e.

   [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{54-5}{30}[/tex]

i.e.

   [tex]\dfrac{9}{5}-\dfrac{1}{6}=\dfrac{49}{30}[/tex]

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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As per linear equation, the value of 'c' equals 3/4.

A linear equation is an equation that contains one or multiple variable with the highest power of the variable is one.

Given, (3 - 5c) is 1 less than the value of (1 - c).

Therefore, (1 - c) - 1 = (3 - 5c)

⇒ - c = 3 - 5c

⇒ 4c = 3

⇒ c = 3/4

Hence, the value of 'c' is 3/4.

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3F=-8.5

F = -8.5 / 3 =-2.8333333

round answer as needed

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 four-digit number that fits all the given conditions is 4710. It ends in 0 to be divisible by 5 and by 6, has a hundreds digit of 7, tens and ones digits that sum to 1, and has a total digit sum of 12, while being less than 5000.

Finding the Four-Digit Number

To find this four-digit number, we need to follow the given conditions closely:

The number is divisible by 5, which means the last digit must be either 0 or 5.

It is also divisible by 6, which means the number must be divisible by both 2 and 3. Since the last digit is 0 or 5, to be divisible by 2, it must end in 0.

The sum of its digits is 12.

The hundreds digit is 7.

The sum of the hundreds, tens, and ones digits is 8, but since the hundreds digit is 7, the tens and ones must add up to 1.

The tens and ones digits must have a difference of 1.

Only one of its digits is divisible by 3, which must be the hundreds digit, 7.

It is less than 5000.

Considering all of the above, let's start by deciding the tens and ones digits. They must add to 1, and their difference must be 1. This means the tens digit is 1 and the ones digit is 0.

With a hundreds digit of 7, tens digit of 1, and ones digit of 0, the sum of the digits so far is 8. To make the total sum 12, the thousands digit must be 4.

The complete number following all these conditions is 4710.

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 :)

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.