what does a^2+b^2=C^2 mean

Answer:

D. Mean: 10, Median: 12, Mode: 12, Range: 14

Step-by-step explanation:

3, 6, 7, 12, 12, 13, 17

Mean: 3 + 6 + 7 + 12 + 12 + 13 + 17 = 70/7 = 10

Median: 12

Mode: 12

Range: 17 - 3 = 14

Final answer:

The exact probability that you win the first prize and your friend wins the second prize in a raffle with 18 participants is 1/306.

Explanation:

To calculate the exact probability that you win the first prize and your friend wins the second prize in a raffle, we need to look at the total number of possible outcomes and the number of favorable outcomes. Assuming that there are 18 tickets in total (yours, your friend's, and 16 others), the chance that you win the first prize is 1 in 18. After you win, there are 17 tickets left, so your friend's chance of winning the second prize is 1 in 17. To find the combined probability, we multiply these individual probabilities:

The probability that you win first prize = 1/18
The probability that your friend wins second prize given you've won first = 1/17

Combined probability = (1/18) x (1/17) = 1/306

The exact probability that you win the first prize and your friend wins the second prize is 1/306.

The exact probability that you win the first prize and your friend wins the second prize is[tex]\( \frac{1}{306} \).[/tex]

To determine the probability that you win the first prize and your friend wins the second prize in the raffle, we need to calculate the total number of possible outcomes and the number of favorable outcomes where this specific event occurs.

Total number of participants: You and your friend are among 18 people who bought raffle tickets.

Total number of outcomes: There are 18 people in total, so there are

( 18 ) possible winners for the first prize and ( 17 ) remaining people eligible for the second prize after the first winner is chosen.

Therefore, the total number of outcomes where one person wins the first prize and another wins the second prize is:

[tex]\[ 18 \times 17 = 306 \][/tex]

This represents all possible ways the first and second prize can be awarded to two different individuals.

Favorable outcomes (desired event): There is exactly ( 1 ) way for you to win the first prize and ( 1 ) way for your friend to win the second prize.

So, the number of favorable outcomes where you win the first prize and your friend wins the second prize is:

[tex]\[ 1 \times 1 = 1 \][/tex]

Probability calculation: The probability ( P ) that you win the first prize and your friend wins the second prize is given by the ratio of the number of favorable outcomes to the total number of outcomes:

[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{306} \][/tex]

Therefore, the exact probability that you win the first prize and your friend wins the second prize is [tex]\( \frac{1}{306} \).[/tex]

Answer:

Hes wrong trust me its C or three more than the quotient of nine and a number cubed, decreased by two; 3 +  9 Over n cubed minus 2 I trusted him and got it wrong

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     x^2-(16/25)=0 

 2.1   Subtracting a fraction from a whole 

Rewrite the whole as a fraction using  25  as the denominator :

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

 2.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 2.3      Factoring:  25x2 - 16 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  25  is the square of  5 
Check : 16 is the square of 4
Check :  x2  is the square of  x1 

Factorization is :       (5x + 4)  •  (5x - 4) 

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

Now, on the left hand side, the  25  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   (5x+4)  •  (5x-4)  = 0

 3.2    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

 3.3      Solve  :    5x+4 = 0 

 Subtract  4  from both sides of the equation : 
                      5x = -4 
Divide both sides of the equation by 5:
                     x = -4/5 = -0.800 

 3.4      Solve  :    5x-4 = 0 

 Add  4  to both sides of the equation : 
                      5x = 4 
Divide both sides of the equation by 5:
                     x = 4/5 = 0.800 

The first step in solving the equation [tex]\rm x^2-\dfrac{16}{25}=0[/tex] is adding and subtracting 4\5x in the equation.

The quadratic formula helps to evaluate the solution of quadratic equations by replacing the factorization method.

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are real numbers, also called “numeric coefficients”.

The given quadratic equation is;

[tex]\rm x^2-\dfrac{16}{25}=0\\\\x^2-\dfrac{4^2}{5^2}=0\\\\ x^2+ \dfrac{4}{5}x-\dfrac{4}{5}x - \dfrac{4^2}{5^2}=0\\\\\left (x-\dfrac{4}{5} \right ) \left (x+\dfrac{4}{5} \right )=0[/tex]

Hence, the first step in solving the equation [tex]\rm x^2-\dfrac{16}{25}=0[/tex] is adding and subtracting 4\5x in the equation.

Learn more quadratic equations here;

https://brainly.com/question/16932064

#SPJ3

Final answer:

The cross-sectional area of a cylinder is found using the formula πr², and the external surface area is calculated by adding twice the area of the ends (2πr²) with the area of the side (2πrh). For volume, use V = πr²h. It's important to use consistent units throughout the calculations.

Explanation:

Finding the Area of a Cylinder

To find the cross-sectional area of a cylinder, you need to calculate the area of the circular base. The formula for the area of a circle is πr², where π is approximately 3.142 and r is the radius of the cylinder. To find the external surface area of a cylinder, you need to calculate the area of both circular ends and the rectangular side that wraps around the cylinder. The formula for that is 2πr² for the ends, plus 2πrh for the side, where h is the height of the cylinder.

If you want to find the volume of the cylinder, use the formula V = πr²h. This formula tells us that the volume is the area of the base times the height of the cylinder. This exemplifies the idea that understanding geometry can help calculate different geometric quantities such as cross-sectional area, the area of different parts, and volume effectively.

Remember to use consistent units in all calculations to ensure the correct solutions. For instance, if you're working in the metric system, keep all measurements in meters or centimeters.

1. BC/CD = AC/CE 1. Given

2. <BCA is congruent to <ECD 2. Vertical angles are congruent

3. Tr.ACB is congr to Tr.ECD 3. SAS Similarity

Answer:

ANSWERS LOL

Step-by-step explanation:

SS Geometry B: Unit 3: Similarity

1. A

2. B

3. A

4. B

5. C

6. A

7. A

8. C

9. C

10. B

11. C

12. ESSAY

13. ESSAY

To find (g o h)(0), first calculate h(0) which is -4, then apply this result to g(x), leading to a final result of -8.

The student's question asks to find (g o h)(0), which means to find the value of g(h(0)). This involves two functions, g(x) = 2x and h(x) = x2 - 4. First, we need to find h(0), which is 02 - 4 = -4. Then, we use this result as the input for g(x), resulting in g(-4) = 2*(-4) = -8. Therefore, (g o h)(0) = -8.

Answer:

C - All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Step-by-step explanation:

got it correct on edge

Final answer:

After increasing and then decreasing a number by 10%, the final result is less than the original number because the decrease is calculated from a higher number, resulting in a net decrease.

Explanation:

When a number, let's call it xx, increases by 10%, this can be represented as xx plus 10% of xx, which is xx + 0.10xx or 1.10xx. Then, if this new number decreases by 10%, we need to take 10% off this new value, so we calculate 10% of 1.10xx which is 0.10 × 1.10xx. The resulting value is 1.10xx - 0.11xx, which simplifies to 0.99xx.

Thus, after an increase and a subsequent decrease of 10%, the final value is less than the original since 0.99xx is 99% of the original value xx.

Answer:  The correct options are

(B) [tex]\dfrac{9^x.3^x}{9^x}[/tex]

(C) [tex] 3^x[/tex]

(E) [tex]\left(\dfrac{27}{9}\right)^3.[/tex]

Step-by-step explanation:  The given expression is

[tex]E=\dfrac{27^x}{9^x}.[/tex]

We are to select the correct expressions that are equivalent to the expression "E".

We will be using the following properties of exponents:

[tex](i)~a^x.b^x=(ab)^x,\\\\(ii)~\dfrac{a^x}{b^x}=\left(\dfrac{a}{b}\right)^x.[/tex]

We have

[tex]E\\\\\\=\dfrac{27^x}{9^x}\\\\\\=\dfrac{(9\times 3)^x}{9^x}\\\\\\=\dfrac{9^x.3^x}{9^x}\\\\\\=3^x.[/tex]

Also,

[tex]E=\dfrac{27^x}{9^x}=\left(\dfrac{27}{9}\right)^x.[/tex]

Thus, (B), (C) and (E) are the correct options.

Answer:

Let your monthly income = $ x

As, Mortgage payment does not exceed 28% of the total monthly income.

Monthly mortgage payment = $1,125.98

So, 28% of x=1125.98

[tex]=\frac{28x}{100}=1125.98\\\\x=\frac{112598}{28}\\\\ x=4021.3571[/tex]

So, Your monthly income should be $ 4021.36 (approx) to stay within acceptable housing expense limits.

Final answer:

The number of calories burned on a 5 km run are 375 calories burned.

Explanation:

The question involves burning calories relative to the distance run by a runner. To find out how many calories would be burned on a 5 km run, we need to set up a proportion since the relationship is assumed to be linear.

Let's start by examining the given data: a runner burns 120 calories for a 1.6 km distance. If we divide the number of calories burned by the distance, we get the rate of calories burned per kilometer:

120 calories / 1.6 km = 75 calories/km.

Now, we can find the total calories burned for a 5 km run:

75 calories/km x 5 km = 375 calories.

Therefore, the runner would burn 375 calories on a 5 km run.

To calculate Beth's age, we use the equation 29 = 6B + 5, where 29 is Emma's age, B represents Beth's age, and then solve for B, resulting in Beth being 4 years old.

To find Beth's age, we need to set up an equation based on the information provided. We know that Emma is 29 years old and that she is 5 years older than 6 times Beth's age. This relationship can be described with the equation E = 6B + 5, where E is Emma's age and B is Beth's age.

Plugging Emma's age into the equation, we get 29 = 6B + 5.

Next, we solve for B by first subtracting 5 from both sides of the equation, which gives us 24 = 6B. Then, we divide both sides by 6 to find Beth's age: B = 24 / 6.

Finding the value of B tells us that Beth is 4 years old.

Therefore, the equation is 29 = 6B + 5.

The estimated probability of the basketball player making the next free throw is 0.8 or 80%, calculated by dividing the number of successful throws by total attempts (160/200).

The student's question involves estimating the probability of a basketball player making the next free throw based on past performance. Given the player made 160 out of 200 free throws, the estimated probability is calculated by dividing the number of successful throws by the total number of throws attempted. Therefore, the estimated probability is:

   P(successful free throw) = Number of successful free throws / Total free throws attempted
   P(successful free throw) = 160 / 200 = 0.8 or 80%

Probability lessons often use sports examples to explain concepts because they provide clear, real-world instances of chance and outcomes. To further understand the concept, one can look at various situations, such as Helen's basketball free throw practice where P(C) = 0.75 and P(D) = 0.75 for her making each shot, or Carlos's soccer goal shooting with a probability of 0.65 for each shot, and special situations like streak shooting where probabilities may change after a successful event.

In mathematics, the logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication. That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number. In the most simple case the logarithm counts repeated multiplication of the same factor; e.g., since 1000 = 10 × 10 × 10 = 103, the "logarithm to base 10" of 1000 is 3. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1. The logarithm of x to base b, denoted logb (x) (or logb x when no confusion is possible), is the unique real number y such that by = x. For example, log2 64 = 6, as 64 = 26.

The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering. The natural logarithm has the number e (≈ 2.718) as its base; its use is widespread in mathematics and physics, because of its simpler derivative. The binary logarithm uses base 2 (that is b = 2) and is commonly used in computer science.

Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors:

provided that b, x and y are all positive and b ≠ 1. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century.

Logarithmic scales reduce wide-ranging quantities to tiny scopes. For example, the decibel (dB) is a unit used to express log-ratios, mostly for signal power and amplitude (of which sound pressure is a common example). In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals. They help describing frequencyratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting.

In the same way as the logarithm reverses exponentiation, the complex logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant; it has uses in public-key cryptography.

Final answer:

The logarithm of a number is the exponent to which a base must be raised to get that number. Common logarithms use base 10, while natural logarithms use the constant e as the base. An example of a logarithm is log10(1000) = 3, whereas a non-example is the logarithm of a negative number, which is undefined in real numbers.

Explanation:

Definition of Logarithm

The logarithm of a number is the power to which a given base must be raised to obtain that number. In the case of common logarithms, the base is 10. As an example, the common logarithm of 100 is 2, because 10 raised to the power of 2 is 100.

Facts about Logarithms

Example of a Logarithm

An example is the logarithm of the number 1000 in base 10, which is 3, because 10 to the power of 3 equals 1000.

Non-example of a Logarithm

A non-example would be stating that the logarithm of a negative number in the common logarithm system, as logarithms of negative numbers are undefined in real numbers.