an architectural drawing lists the scale as 1/4"=1'. if a bedroom measures 2 1/2" by 3 3/4" on the drawing, how large is the bedroom?

The proportion is solved and the cost of 18 bumper stickers is $ 12.96.

Given data:

To find out how much 18 bumper stickers cost, use a proportion since the cost of bumper stickers is directly proportional to the number of stickers.

Cost of 12 bumper stickers / Number of 12 bumper stickers = Cost of 18 bumper stickers / Number of 18 bumper stickers

On simplifying the proportion:

$8.64 / 12 = x / 18

Now, solve for x (the cost of 18 bumper stickers):

x = ($8.64 / 12) * 18

x = $12.96

Hence, 18 bumper stickers cost $12.96.

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The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]  is 82

The function is given as:

[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]

Substitute 6 for x

[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]

Evaluate the difference

[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]

Evaluate the exponents

f(6)=2 * 36 + 5 * 2

Evaluate the sum of products

f(6) = 82

Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]  is 82

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Answer:

[tex]x^2+8x-65=0[/tex]

Step-by-step explanation:

Side length of square = 4 inches

Let x be the increase in length

So, New length = x+4

Area of square = [tex]Side^2[/tex]

Area of enlarged square = [tex](x+4)^2[/tex]

Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]

Area of enlarged square = [tex]x^2+16+8x[/tex]

We are given that The final area needs to be 81 square inches.

So,  [tex]x^2+16+8x=81[/tex]

[tex]x^2+16+8x-81=0[/tex]

[tex]x^2+8x-65=0[/tex]

So, Option C is true

Hence  equation can be used to solve for x, the increase in side length of the square in inches is  [tex]x^2+8x-65=0[/tex]

Answer: 64

Step-by-step explanation:

i put it into math-way

Answer:  The required value is

[tex](f-g)(x)=x^2+8.[/tex]

Step-by-step explanation: The given functions are:

[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]

We are given to find the value of [tex](f-g)(x).[/tex]

We know that, if s(x) and t(x) are any two functions of a variable x, then we have

[tex](s-t)(x)=s(x)-t(x).[/tex]

Therefore, we have

[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]

Thus, the required value is

[tex](f-g)(x)=x^2+8.[/tex]

Answer:

3x2 - 6   its the answer

1 kg = 2.25 pounds

5*2.25 = 11.25 pounds

11.25/5 = 2.25 bags

 so you would need 3 bags

Answer: The expression that represents the number of hours the mountaineer climbed is given by

[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]

Step-by-step explanation:

Since we have given that

Distance covered by mountaineer = 1000 feet

Speed at which he climbed = x feet per hour

Time taken by him would be

[tex]\dfrac{1000}{x}[/tex]

Additional distance covered by him = 5000 feet

Speed at which he climbed this time = 2x-10

So, Time taken is given by

[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]

Hence, the expression that represents the number of hours the mountaineer climbed is given by

[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]

Answer:

$,37 dollars per ounce of strawberries

Step-by-step explanation:

We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:

5,92/16= ,37

SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.

Final answer:

The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.

Explanation:

The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:

[tex]\( \int \frac{1}{x} dx = \ln(|x|) + C \)[/tex]

The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.

0.8x – 12

The sale price is (x-15). After the 20% discount, the final price is 0.80 times the sale price, so is ...

... final price = 0.80×(x -15) = 0.80x -12

Answer:

The correct option is B.

Step-by-step explanation:

Let the original price of the jacket be x.

A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases.

The price of jacket after $15 off is [tex]x-15[/tex].

Then 20% discount is applied, so the final price of the jacket is

[tex]P=(x-15)(1-\frac{20}{100})[/tex]

[tex]P=(x-15)(1-0.2)[/tex]

[tex]P=(x-15)(0.8)[/tex]

[tex]P=0.8x-12[/tex]

The final price of the jacket during this sale is 0.8x-12. Therefore the correct option is B.

I am not quite sure what the choices are, but the answer to that problem is:

If p is a positive integer, then p(p+1)(p-1) is always divisible by “an even number”.

The explanation to this is that whatever number you input to that equation, the answer will always be an even number. This is due to the expression p(p+1)(p-1) which always result in a even product.

For example if p=3, then (p+1)(p-1) becomes (4)(2) giving you a even number.

And if for example if p=2, then (p+1)(p-1) becomes (3)(1) which gives an odd product, but we still have to multiply this with p therefore 2*3 = 6 which is even product. The outcome is always even number.

Answer: From the choices, select the even number

Final answer:

If p is a positive integer, p(p+1)(p-1) is always divisible by 3.

Explanation:

If p is a positive integer, then p(p+1)(p-1) is always divisible by 3.

This can be proven by applying the property of divisibility by 3. According to this property, a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

In the expression p(p+1)(p-1), the three terms p, (p+1), and (p-1) represent three consecutive numbers. Since the sum of the digits of any consecutive numbers is always divisible by 3, the expression is always divisible by 3.

Final answer:

To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.

Explanation:

Susan has invested $x at 4% interest rate and $2x at 8% interest rate.

Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.

Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.

The probability that the mean leg length is less than 20 cm is practically 0.

To find the probability that the mean leg length is less than 20 cm, we can use the sampling distribution of the sample mean. The sampling distribution of the sample mean is approximately normal when the sample size is large enough. In this case, the sample size is 9, which is smaller than 30 but still reasonably large, so we can assume that the sampling distribution of the sample mean follows a normal distribution.

We can standardize the sample mean using the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

Substituting the given values:

z = (20 - 43.7) / (4.2 / sqrt(9))

z = -23.7 / (4.2 / 3)

z = -23.7 / 1.4

z ≈ -16.93

Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score less than -16.93 is practically 0. Therefore, the probability that the mean leg length is less than 20 cm is practically 0.