5/If AB is 12, what is the
length of A' B'?

The number of pairs that must be randomly selected from the set {1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 16 is 5.

In the given set {1,3,5,7,9,11,13,15}, there are four pairs that sum up to 16, which are (1,15), (3,13), (5,11), and (7,9). Let k numbers be picked from the set. Consider k = 5, then using the pigeonhole principle, for one of the pairs described above, both of the endpoints must have been picked. Hence, if 5 numbers are picked from the set, then there exists a pair with a sum of 16.

To learn more about the pigeonhole principle and probability theorem,

https://brainly.com/question/24491336

#SPJ4

Answer: T= 1

Step-by-step explanation:

The value is 5/2 and 35/2 pounds.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.

Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire.

The ratios of  the given table

Table 10,

[tex]\begin{aligned}&\Rightarrow \frac{5}{3}=\frac{1}{x} \\&\Rightarrow x=\frac{3}{5} \\&\Rightarrow \frac{5}{3}=\frac{12}{x}=\frac{12+3}{15} \\&\Rightarrow x=\frac{12}{5}\end{aligned}[/tex]

Table 9,

[tex]\begin{aligned}&\frac{10}{4}=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{1} \\&x=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{7} \\&x=\frac{35}{2}\end{aligned}[/tex]

[tex]\begin{array}{rccc}\text { 9) pounds } & 10 & \frac{5}{2} & \frac{35}{2} \\\text { Weeks } & 4 & 1 & 7 \\\text { 10) tons } & 5 & 1 & 12 \\\text { days } & 3 & \frac{3}{5} & \frac{12}{5}\end{array}[/tex]

To learn more about ratio refer to

brainly.com/question/2914376

#SPJ1

The probability that a randomly selected tire will have a life of at least 38,100 miles is 0.9115.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

Let, the life expectancy of a particular brand of tire is normally distributed with a mean of 30,000 and a standard deviation of 6,000 miles.

So, μ = 30000, σ = 6000, x = 38100.

Therefore,

z  = (x - μ) / σ

   = (38100 - 30000) / 6000

   = 8100 / 6000

   = 81 / 60

z  = 1.35

Now,

P(X = 38100) = P(z = 1.35) = 0.9115

Hence, the probability that a randomly selected tire will have a life of at least 38,100 miles is 0.9115.

To know more about the probability, click on the link

https://brainly.com/question/24756209

#SPJ4

Answer:

4/9

Step-by-step explanation:

Area of a triangle is 1/2*base*height

1/2*2/3*4/3 = 8/18 = 4/9

The value of the fraction 28/63 in the simplest form is 4/9.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, we want to reduce 28/63 yo the simplest term. This will be illustrated thus:

= 28/63

= (7 × 4) / (9 × 7)

= 4 / 9

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

If in a class of 25 students, 14 are boys and 11 are girls. On a unit test, 6 boys and 6 girls made an A grade. If a student is chosen at random from the class, The probability of choosing a boy or an A student 4 / 5

From the question, we have the following data

Total number of students = 25

The total number of boys = 14

The students that are A male students = 6

Then we would have probability of having an A male student to be:

Total boys + A male students / total

= 14 + 6 / 25

= 4 / 5

Hence the probability is 4 / 5

Read more on probability https://brainly.com/question/24756209

#SPJ1

It is possible that the ball may reach a height of 5 meters in accordance with the quadratic formula.

The height of the ball as a function of time is represented by a quadratic equation, in which we must determine if the ball may reach a height of 5 meters. First, substitute the height in the quadratic equation:

- 5 · t² + 9 · t + 2 = 5

5 · t² - 9 · t + 3 = 0

Second, use the quadratic formula to determine the roots of the resulting quadratic equation:

t = - (- 9) / (2 · 5) ± [1 / (2 · 5)] · √[(- 9)² - 4 · 5 · 3]

t = 9 / 10 ± (1 / 10) · √(81 - 60)

t = 9 / 10 ± √21 / 10

t = (9 ± √21) / 10

Since all roots of the quadratic equations are real, then the ball can reach a height of 5 meters above the ground.

To learn more on quadratic formula: https://brainly.com/question/9300679

#SPJ1

Answer:

a is right (prime number is always a even number)

Answer:

A.

a prime number may be an even or an odd number

Answer:

tan 25° = b / 8 m

Step-by-step explanation:

You need to know what the ratios are.

sin X = opp/hyp

cos X = adj/opp

tan X = opp/adj

For angle B, the opposite leg is b, ad the adjacent leg is 8 m.

The hypotenuse is AB.

sin B = sin 25° = opp/hyp = b/AB

tan B = tan 25° = opp/adj = b / 8 m

a) The percentage of students who passed the exam, given that they completed the exam review is of 73%.

b) The percentage of students who passed the exam, given that they did not complete the exam review, is of 27%.

c) There is a positive association between passing the exam and completing the exam review.

A percentage is obtained by the division of the desired amounts by the total amounts, multiplied by 100%.

For item a, these amounts are given as follows:

Hence the percentage is of:

p = 55/75 = 0.73 = 73%.

For item b, these amounts are given as follows:

Hence the percentage is of:

p = 20/75 = 0.27 = 27%.

There is a positive association between passing the exam and completing the exam review, as the percentage of students who passed completing the review, found in item a, is greater than the percentage of students who passed without completing the review, found in item b.

More can be learned about percentages at https://brainly.com/question/843074

#SPJ1

The numbers of hours per week teenagers spend playing a sport or outdoor game is 2.4 or 2[tex]\frac{1}{15}[/tex] hours.

What is Averaging?

This refers to the mean value, which is equal to the ratio of all the numbers added and divided by the number of a given set of values present in the set of values.

Average= x₁+x₂+x₃+x₄..........xn

                        n

Where,

x₁+x₂+x₃+x₄..........xn = Given set of values

                             n= Number of a given set of values

From the question:

The number of hour per week spent playing a port or a game outdoors:

3; 2; 0; 6; 3; 3; 3; 1; 1; 2

number of teenagers,n =10

Average= 3+ 2+ 0+ 6+3+3+3+ 1+ 1+2

                                  10

               =2.4 or 2[tex]\frac{1}{15}[/tex] hours.

Learn more about average on

https://brainly.com/question/17000651

#SPJ1

Answer:

enter a function and from there you approximate hope it helps

the slope of the given point is m=−3/4

Answer:

3.82%

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Each coordinate is six times the corresponding coordinate in the preimage.

Answer:

1/2

Step-by-step explanation:

(-6-(-4)/(3-7)

(-6+4)/-4

-2/-4

1/2

Answer:

4 metters por el significado

The perimeter of the smaller square would be = 12feet. That is option B.

Perimeter can be defined as the summation of all the sides and edges of an object.

Scale factor is also defined as the ratio of difference between an original object and a newly formed object.

A square has four sides and it's perimeter = 24 ft

This means that the sides of the square= 24/4 = 6ft.

If the original (smaller square) dialted by a factor of 1/2 to have 6 ft as its sides, it means that it's original side of the small square is 3ft.

This is because to form the bigger square, 1/2 × 6 = 3ft.

Therefore, the perimeter of small square = 3+3+3+3 = 12ft.

Learn more about scale factor here:

https://brainly.com/question/28339205

#SPJ1

Answer: The number of no votes is 1876 votes.

What is the ratio?

"The ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another".

For the given situation,

Let x be the number of votes.

The ratio of yes votes : no votes = 3x:2x

Total = 5x

Total votes = 4690 votes

⇒

Divide by 5 on both sides,

⇒

Thus the number of no votes =

⇒

⇒

Hence we can conclude that the number of no votes is 1876 votes.

Learn more about ratios here

brainly.com/question/13016636

#SPJ2

Step-by-step explanation:

The statement that best compares the graph of G(x) with the graph of F(x) is the graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 7 units to the left.

According to the question,

We have the following information:

F(x) = x² and G(x) = -1/4 (x+7)²

Now, the graph of G(x) will be the graph of F(x) but there will be certain changes in the graph according to its function.

Now, in this function, 7 is added to x then it means that it will shift 7 units to left.

There is a negative sign before the function which says that is flipped over the x-axis.

Now, the factor 1/4 in the multiplication says that it has been compressed.

Hence, the correct option is D.

To know more about graph of G(x) here

https://brainly.com/question/2120300

#SPJ1

Since in the question we reject the alternative hypothesis hence type II error occurs.

What is Type I error?

When the null hypothesis is true but rejected in hypothesis testing, type 1 errors often confused with false positives occur. A general assertion or default attitude that there is no connection between two measurable phenomena is known as the null hypothesis.

What is Type II error?

Type II errors take place when you fail to reject the null hypothesis even though it is untrue.

The average number of insect parts per 100 gm in this problem is 75. This number cannot be demonstrated by the test to be larger than 75. This indicates that the test is producing a "false negative" since it is not detecting these insect parts.

Hence, this is a Type II error.

To learn more about hypothesis testing:

https://brainly.com/question/4232174

#SPJ4

The nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex]

Given that:

the given sequence is 4,9,16,25,36

nth term of quadratic sequence is [tex]an^{2}+bn+c[/tex]

Now lets find out the value of each variable a,b,c

a = second difference divide by 2

lets find out second difference

4,9,16,25,36

the first difference between the terms are

5,7,9,11

The second difference between the terms

2,2,2

the value of a = second difference / 2

[tex]a = \frac{2}{2} = 1\\[/tex]

a = 1

Now we find the value of b

3a + b = first term of first difference

3a + b = 5

3(1) + b = 5

3 + b = 5

b = 5 - 3

b = 2

Now find the value of c

a + b + c = first term

a + b + c = 4

1 + 2 + c = 4

3 + c = 4

c = 1

Now we replace all the values to find the nth term

 [tex]an^{2}+bn+c\\ \\n^{2}+2n+1[/tex]

Hence the answer is the nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex].

To learn more about sequence click here https://brainly.com/question/6561461

#SPJ9

Circumference = pi x d

Circumference = 3.14 x 24 =  75.36

I hope this helps!

Answer:

x = 13  x = 1

Step-by-step explanation:

(13-7) = 6

6^2 = 36

1-7 = -6

(-6)^2 = 36

The length of x is 4.1.

Given:

Base = 9 + 4.5 = 13.5

From figure:

= [tex]\sqrt{9^{2}+5^{2} }[/tex]

= [tex]\sqrt{81+25}[/tex]

= [tex]\sqrt{96}[/tex]

= 9.797

4.5 opposite is equal to 4.5.

5 opposite equal to 5 and remaining to x - 5.

According to pythagorean theorem:

= [tex]\sqrt{4.5^{2}+(x-5)^{2} }[/tex]

[tex]13.5^{2} +x^{2} =(\sqrt{96}+\sqrt{4.5^{2} +(x-5)^{2} })^{2}[/tex]

[tex]\sqrt{13.5^{2} +x^{2} }[/tex] - [tex]\sqrt{96} = \sqrt{20.25+x^{2} +25 -10x}[/tex]

squaring on both sides

182.25 + [tex]x^{2}[/tex] - 96 = [tex]x^{2}[/tex] - 10x + 45.25

10x = 45.25 + 96 - 182.25

10x = 41

x = 4.1.

Therefore the value of x is 4.1.

Learn more about the length here:

https://brainly.com/question/8552546

#SPJ1

1353 numbers of minutes he has used his phone in a month.

What do you mean by algebraic expression?

In mathematics, an algebraic expression is an expression composed of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by exponents that are rational numbers).

Algebraic equations are equations that contain only algebraic expressions.

Algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual value. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.

It is given that Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use.

Let m be the additional minutes

Then charge for additional minutes is $0.07m

Now , it is also given that least he has been charged in a month is

$121.71.

⇒ 0.07m + 27 = 121.71

⇒ 0.07m = 121.71 - 27

⇒ 0.07m = 94.71

⇒ m = 94.71/0.07 = 1353

Therefore, 1353 numbers of minutes he has used his phone in a month.

To learn more about the algebraic expression from the given link.

https://brainly.com/question/28036476  

#SPJ1