Tom separated the rectangle shown below into 8 equal parts what fraction shows the area of one of the parts

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 : a person born in a certain place or country

the word 'native' means "of indigenous origin or growth".

John James was of French origin although he was born in America.So, his native country would be France to which he finally shifted when he was 25 years old.

Answer:

Option C

Step-by-step explanation:

The given expression is[tex]\frac{8.9\times 10^{8}}{3.3\times 10^{4}}[/tex]

Now we have to solve this.

[tex]\frac{8.9\times 10^{8}}{3.3\times 10^{4}}[/tex]

[tex]=\frac{8.9}{3.3}\times \frac{10^{8}}{10^{4}}[/tex]

= 2.70 × 10⁽⁸⁻⁴⁾

= 2.70 × 10⁴

≈  3 × 10⁴

Therefore, Option C is the answer.

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 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 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.

If you want to solve this problem using formulas, there are two important formulas:

t1  =  first term  =  -5          

tn  =  nth term  =  last term  =  -5

n  =  numbr of terms

Sn  =  sum of the n terms

tn  =  t1 + (n - 1)d     --->     65  =  -5 + (n - 1)(5)

                                          65  =  -5 + 5n - 5

                                          65  =  -10 + 5n

                                          75  =  5n

                                            n  =  15

Sn  =  n(t1 + tn)/2     --->     Sn  =  15(-5 + 65)/2

                                          Sn  =  450

So ur answer rounds up to 450

Letter c

:)

hope i helped 

~Luis

The sum of the arithmetic series is 450, option c. Calculation: (15/2) * (first term + last term).

To find the sum of a finite arithmetic series, we can use the formula:

[tex]\[ S_n = \frac{n}{2} \times (a_1 + a_n) \][/tex]

where:

- [tex]\( S_n \)[/tex] is the sum of the series,

- [tex]\( n \)[/tex] is the number of terms in the series,

- [tex]\( a_1 \)[/tex] is the first term of the series, and

- [tex]\( a_n \)[/tex] is the last term of the series.

First, we need to find the number of terms, [tex]\( n \)[/tex]. The series is an arithmetic sequence with a common difference of [tex]\( 5 \)[/tex]. The first term is [tex]\( -5 \)[/tex], and the last term is [tex]\( 65 \)[/tex].

To find the number of terms, we can use the formula for the [tex]\( n^{th} \)[/tex] term of an arithmetic sequence:

[tex]\[ a_n = a_1 + (n - 1) \times d \][/tex]

where [tex]\( d \)[/tex] is the common difference.

Given [tex]\( a_n = 65 \)[/tex], [tex]\( a_1 = -5 \)[/tex], and [tex]\( d = 5 \)[/tex], we can solve for [tex]\( n \)[/tex]:

[tex]\[ 65 = -5 + (n - 1) \times 5 \][/tex]

[tex]\[ 65 = -5 + 5n - 5 \][/tex]

[tex]\[ 65 = 5n - 10 \][/tex]

[tex]\[ 75 = 5n \][/tex]

[tex]\[ n = 15 \][/tex]

So, there are [tex]\( 15 \)[/tex] terms in the series.

Now, we can use the formula for the sum of a finite arithmetic series:

[tex]\[ S_n = \frac{n}{2} \times (a_1 + a_n) \][/tex]

Plugging in the values:

[tex]\[ S_{15} = \frac{15}{2} \times (-5 + 65) \][/tex]

[tex]\[ S_{15} = \frac{15}{2} \times 60 \][/tex]

[tex]\[ S_{15} = \frac{15}{2} \times 60 = \frac{15 \times 60}{2} \][/tex]

[tex]\[ S_{15} = \frac{900}{2} \][/tex]

[tex]\[ S_{15} = 450 \][/tex]

So, the sum of the series is [tex]\( 450 \)[/tex], which corresponds to option [tex]\( c \)[/tex].

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

Answer: 1) The answer is -4x^8, you just have to subtract 7 from 3 to get -4

Step-by-step explanation:

Answer:

You have to follow the landlord/owner's rules. For example, if you are renting an apartment and want to have a pet, but your landlord says no then you can't get a pet, or you'll be kicked out.

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.

Answer:

There are 4,925,250 to 7,223,700 insect species worldwide.

Step-by-step explanation:

Supposing that there are 67 butterfly species for every 22,000 insect species and there are 15,000 to 22,000 species of butterflies worldwide, in order to know how many insect species are there we have to do the following calculation:

22,000 (insect species) / 67 (butterfly species) = X (relation of butterfly and insect species)

22,000 / 67 = X

328.35 = X

There are 328.35 insect species for every butterfly species.

So, as there are 15,000 to 22,000 species worlwide, we have to multiply those numbers by 328.35 to know the total amount of insect species:

15,000 x 328.35 = 4,925,250

22,000 x 328.35 = 7,223,700

There are 4,925,250 to 7,223,700 insect species worldwide.