On average, the merchandise shop sells 80 CDs for every 1 vinyl record. Estimate how many vinyl records they are likely to sell if the merchandise shop sells 760 CDs.

To solve this problem, let us first find for the binary equivalents of the numbers. They are:

Decimal --> Binary

+ 29 --> 00011101

+ 49 --> 00110001

- 29 --> 11100011

- 49 --> 11001111

Now we apply the normal binary arithmetic to these converted numbers:

(+ 29) + (- 49) ---> 00011101 + 11001111 = 11101100 ---> - 20 (TRUE)

(- 29) + (+ 49) ---> 11100011 + 00110001 = 00010100 ---> + 20 (TRUE)

(- 29) + (- 49) ---> 11100011 + 11001111 = 10110010 ---> - 78 (TRUE)

The probability of a woman being pregnant if a home pregnancy test yields a negative result can be calculated using conditional probabilities and Bayes' theorem. From the provided probabilities, we can substitute into Bayes' theorem to calculate this probability.

The subject of this question is based on conditional probabilities. From the question we know that:

From the above, we can find the probability of a woman being pregnant even though the test results are negative. To find this we need to use Bayes' theorem, which states:

P(A|B) = P(B|A) * P(A) / P(B)

So, to calculate the probability of a woman being pregnant given a negative test result P(Pregnant|Negative), we need the probability of getting a negative result when pregnant P(Negative|Pregnant), the probability of a woman actually being pregnant P(Pregnant), and the total probability of getting a negative test result P(Negative).

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The total number of books in the library are 75.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Let the total number of books in the library be x.

The equation formed by using given information will be [tex]\frac{x}{3} +15+15+\frac{x}{5}+ 5=x[/tex]

Collect the like terms,

[tex]\frac{x}{3} +35+\frac{x}{5}=x[/tex]

On solving the equation for x we get x=75.

Therefore, the total number of books in the library are 75.

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The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]

For example;

                    =  1/2 x base x height

For example;

In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm

Therefore, we use the Heron's formula;

Area= [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

 [tex]s =\frac{(a+b+c)}{2}[/tex]

[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]

Therefore;

Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]

       = [tex]22.5\sqrt{22.5(22.5-15)(22.5-10)(22.5-20)}[/tex]

       =[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]

[tex]= 72.618 mm^{2}[/tex]

Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.

Level: Middle school

Subject; Mathematics  

Topic: Area

Sub-topic: Area of a triangle

The area under the standard normal curve between z = −2.57 and z = 1.27 is, 0.8929

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to give that,

To find the area under the standard normal curve between z = −2.57 and z = 1.27.

Now, the area under the standard normal curve is between z = −2.57 and z = 1.27 is,

P(-2.57 ≤ Z ≤ 1.27) = P(Z ≤ 1.27) - P(Z ≤ -2.57)

Since, P(Z ≤ 1.27) = 0.8980

And, P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57)

= 1 - 0.99488

= 0.00512

Hence,

P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512

= 0.89288

= 0.8929

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The selling price of a product with a 35% markup on a cost of $15 is calculated by adding the markup amount of $5.25 to the cost, resulting in a selling price of $20.25.

To calculate the selling price of a product using a variable percentage markup, you first need to determine the amount of markup by converting the percentage to a decimal and multiplying by the cost of the product. In this case, with a 35% markup on a product that costs $15, the calculation is as follows:

$15 × 0.35 = $5.25

This $5.25 represents the amount of markup on the product. To find the selling price, you simply add the markup to the cost:

$15 + $5.25 = $20.25

Therefore, the selling price of the product would be $20.25.

formula for volume of a sphere is V=4/3 x pi x R63

if diameter = 16 than radius = 16/2 = 8

 so the equation would be 4/3 x pi x 8^3

To translate situations into inequalities, use context clues and keywords. Start by understanding the relationships and factors involved. Then, represent the situation with variables and create an inequality based on the context clues. For example, if Bob earns $10 more than Alice, the inequality would be 'a < a + 10'.

In order to use context clues and keywords to translate situations into inequalities, it's important to understand the relationships and factors involved. Let's take an example:

Scenario: Suppose you have two friends, Bob and Alice. Bob earns $10 per hour more than Alice. In this case, we can use the following context clues:

We can now translate this situation into an inequality:

By using the context clues and the keywords (earnings, difference), we were able to translate the situation into the inequality 'a < a + 10'.

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Answer:

C.  randomization

Step-by-step explanation:

We are told that the study randomly selects participants in the study to sleep in either a dark room or a room with light.  This means that randomization is part of the study.