Draw a rectangle that has a diagonal twice as long as its width. Then write an equation to find the length of the rectangle.

Answer:

Minimum 1/4 Hour Maximum 1/2 Hour

Speed is the ratio of distance and time.

The maximum number of hours the boat will cruise is 1/2 hours.

The minimum number of hours the boat will cruise is 1/4 hour.

Speed is the ratio of distance and time.

It tells us how fast a body is moving.

We have,

Boat speed = 24 miles per hour.

Speed = distance / time

Distance = 9 miles

Time = distance / speed

Minimum number of hours:

Distance = 9 - 3 = 6 miles

Time = Distance / Speed = 6 / 24 = 1/4 hours

Maximum number of hours:

Distance = 9 + 3

Time = Distance / Speed = 12 / 24 = 1 / 2 hours

Thus,

The maximum number of hours the boat will cruise is 1/2 hours.

The minimum number of hours the boat will cruise is 1/4 hour.

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The number of ways that a book can be chosen from all the books can be determined by using combination.

Combination is a method of choosing items from a set in a way that order of selection does not matter. It refers to the combination of n items taken k at a time without repetition. From example, selection of food, menu, subjects, etc.

A combination is the selection of r items from a set of n items without replacement and where order is unimportant.

nCr=n!/r!(n-r)!

Where n! = 1*2*3*….*n

In the given situation, r = 1(number of books to be chosen) and n=10(total number of books)

10C1=10!/1!(10-1)!

10C1=10!/1!(9)!

10C1=(10*9!)/1!(9)!

10C1=10

The number of ways to choose a book from the ten books is 10.

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Answer:

f(g(x)) = x² - 6x + 8

Step-by-step explanation:

to evaluate f(g(x)) , substitute x = g(x) into f(x)

f(x² - 6x + 13)

= x² - 6x + 13 - 5 ← collect like terms

= x² - 6x + 8

The solution fo the equation by completing the square is x = 12.544 or -4.544

Completing the square method is a method of solving quadratic equations in which the equation is converted into a perfect square binomial.

Given (x - 12)(x + 4) = 9

Expanding the brackets, we have

x² - 12x + 4x - 48 = 9

x² - 8x - 48 = 9

x² - 8x - 48 - 9 = 0

x² - 8x - 57 = 0

To complete the square, we add half the square of the coefficient of x to both sides. so,

x² - 8x - 57 = 0

x² - 8x - 57 + (-8/2)² = 0 + (-8/2)²

x² - 8x - 57 + (-4)² = 0 + (-4)²

x² - 8x + (-4)² - 57  = 0 + (-4)²

(x - 4)² - 57 = 16

(x - 4)² = 16 + 57

(x - 4)² = 73

Taking square roots, we have

x - 4 = ±√73

x - 4 = ±8.544

x = 4 ± 8.544

x = 4 + 8.544 or x = 4 - 8.544

x = 12.544 or -4.544

So, the solution fo the quadratic equation by completing the square is x = 12.544 or -4.544

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Answer:

Step-by-step explanation:

x=+/-square root 73

If an infinite geometric series is a convergent series then it must have a sum.

What is a convergent series?

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Answer:

1/4 or 25% or 0.25

Step-by-step explanation:

d= 17/2 is the solution of the given equation 43-3 d=d+9.

According to the given question.

We have a linear equation in one variable 43 -3d = d + 9.

Since, we have to solve the above linear equation in one varible 43 -3d = d + 9, which means we have to solve the above equation for d.

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofore, the solution of the given linear equation in one variable 43 -3d = d + 9 is given by

43 -3d = d + 9

⇒ 43 - 9 -3d = d          (subtracting 9 from both the sides)

⇒ 34 = d + 3d      (adding 3d both the sides)

⇒ 34 = 4d

⇒ d = 34/4

⇒ d = 17/2

Now, we will check whether d = 17/2 is the solution of the given equation or not.

Thereofore,

LHS

= 43 - 3(17/2)

= 43 - 51/2

= 86 - 51/2

= 35/2

RHS

= 17/2 + 9

= 17 + 18/2

=35/2

Here, LHS = RHS for d = 17/2

Hence, d= 17/2 is the solution of the given equation 43-3 d=d+9.

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The slope of the line that contains the points (4,3) and (-2,-5) is 4/3

In this question,

we need to find the slope of the line that contains the points (4,3) and (-2,-5).

We know that the slope of the line passing though points (x1, y1), (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

Let (x1, y1) = (4, 3),

(x2, y2) = (-2, -5)

Using the formula of the slope,

m = (y2 - y1) / (x2 - x1)

m = (-5 - 3) / (-2 - 4)

m = -8 / (-6)

m = 4/3

Therefore, the slope of the line that contains the points (4,3) and (-2,-5) is 4/3

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The coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)

The given parameters are

A = (-1, 5)

B = (6, 5)

Ratio, m : n = 1 : 2

The coordinates of point m are calculated using

M = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

M = 1/(1 + 2) * (1 * 6 + 2 * -1, 1 * 5 + 2 * 5)

Evaluate the sum of products

So, we have

M = 1/3 * (4, 15)

Evaluate the product

M = (4/3, 5)

Hence, the coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)

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3x^4-5x³

Step-by-step explanation:

Answer: 3720087

Step-by-step explanation:

n=term number

an=term value

terms: 7, 21, 63...

term number: 1, 2, 3, ...

7 is 1st term. 21 is 2nd term. 63 is 3rd term.

21/7=3

63/21=3

Common change in each term is multiplication by 3

Hence, the formula can be expressed in exponents.

an=3^(n-1) * 7 where n is the term number, an is the term value, and 7 is the 1st term in the sequence.

an=3^(13-1) * 7

an=3^12 * 7

an=531441 * 7

an=3720087

The least preferable and reliable method of selecting people to participate in a research study is convenience sampling.

Convenience sampling is a type of sampling in which you include people who are easy to reach. Convenience sampling is included in non-probability sampling because it doesn't include a random selection of the participants. Convenience sampling can be used when you need to conduct a study quickly or when you are on a shoestring budget as it is inexpensive compared to other methods of sampling.

It is the least preferable method because of the inability to generalize the result of the survey to the population as a whole. In addition to this, there is a possibility of under or over-representation of the population as a whole. The biggest problem with convenience sampling is dependence as the sample items are connected to each another in some way. This dependency interferes with statistical analysis.

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If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.

According to the inscribed angle theorem, an angle inscribed in a circle is half the central angle 2 that subtends the same arc on the circle.

The central angle has the same length as the intercepted arc. As can be seen, if a central angle and an inscribed angle intersect the same arc, the central angle is twice as large as the inscribed angles. Similarly, the inscribed angle equals half of the central angle.

An inscribed angle is one that has its vertex on a circle and its sides are chords. The intercepted arc is the arc that is contained within the inscribed angle and has its endpoints on the angle.

If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.

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Answer:

a 50% chance of getting tails

but about the spinner It depends on what kind of spinner it is and how many sides/numbers/etc

does it have

The length of the organism in millimeters is 200 ч 1000 or 0.2 mm.

In the given situation, the organism's length in millimeters is 200 ч 1000 or 0.2 mm.

Therefore, the length of the organism in millimeters is 200 ч 1000 or 0.2 mm.

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   The given function y = x- 2(x+5), is a linear function.

 A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.

   A function can be linear or quadratic, this is evidenced by the higher exponential degree.

   We rewrite the function and reduce it to its minimum expression:
y = x- 2(x+5)

y = x + (-2x - 10)

y = x - 2x - 10

y = -x - 10 ,   linear function.

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Answer:

Her age is 15.

Step-by-step explanation:

13 + 14 + 15 = 42

Julia is the oldest and 15 is the greatest of the 3 numbers

therefore Julia is 15

The 20 randomly generated pairs for the numbers 1 to 6 is (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6) and  the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.

Sum of the number:

When we add two or more numbers, the result or the answer we get can be defined as the SUM. The numbers that are added are called addends.

For example if we add the numbers 2 and 7 then we get the um as 9.

Given,

Here we need to generate the 20 pairs of integers between 1 and 6 . And also we have to record the sum of each pair.

The 20 pairs by using the number 1 to 6 are,

Listed as,

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6).

Now the sum of these 20 pairs are,

(1,1) = 1 + 1  = 2

(1,2) = 1 + 2 = 3

(1,3) = 1 + 3 = 4

(1,4) = 1 + 4 = 5

(1,5) = 1 + 5 = 6

(1,6) = 1 + 6 = 7

(2,2) = 2 + 2 = 4

(2,3) = 2 + 3 = 5

(2,4) = 2 + 4 = 6

(2,5) = 2 + 5 = 7

(2,6) = 2 + 6 = 8

(3,3) = 3 + 3 = 6

(3,4) = 3 + 4 = 7

(3,5) = 3 + 5 = 8

(3,6) = 3 + 6 = 9

(4,4) = 4 + 4 = 8

(4,5) = 4 + 5 = 9

(4,6) = 4 + 6 = 10

(5,5) = 5 + 5 = 10

(5,6) = 5 + 6 = 11

Therefore, the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.

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Answer:

Step-by-step explanation:

x+4x+1=76 is the answer

The function's domain and range as represented either by set of ordered pairs:

Domain = (-13 , -7 , 5 , 11)

Range = (9 , -5 , 14 , 11)

Range and domain The domain of something like a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the collection of values  that the function can take. This is the set of values that the function returns after we enter an x value.

The set of ordered pairs = {(-13, 9), (-7,-5), (5, 14), (11,-10)}.

(x,y)

x=input

y=output

As a result, the domain consists only of the first numbers.

range refers to all of the second numbers.

x=domain

y=range

So,

Domain = (-13 , -7 , 5 , 11)

Range = (9 , -5 , 14 , 11)

The function's domain and range as represented either by set of ordered pairs:

Domain = (-13 , -7 , 5 , 11)

Range = (9 , -5 , 14 , 11)

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Answer:

Step-by-step explanation:

The statements 6 covers the operation:

This is the reflection of the distributive property of multiplication.

The matching answer choice is B.

The value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344

Chi-square Distribution:

The chi-square distribution is a continuous probability distribution. It is skewed to the right or positively skewed for low degrees of freedom but shifts towards the symmetric distribution as the degrees of freedom are increased.

Given,

Degree of freedom = 8

Area of the left = 0.05

Here we need to find the value X² of the chi-square distribution.

The value of X² of the chi-square distribution is calculated through the formula,

X² = X²₍₁ ₋ₓ₎,y

Where

x represents the area of the given tails

y represents the degree of freedom

Apply the values on the formula,

=> X² = X²₍₁ ₋₀.₀₅₎,8

=> X² = X²₍₀.₉₉₅₎,8

Now, based on the Chi square distribution table,

The value of

=> X² = 1.344

Therefore, the value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344

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The multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.

It should be noted that multiples simply mean the answer that one gets when the number of multiplied by any whole number.

Therefore, the multiples will be:

= 5/4 × 2 = 2 1/2

= 5/4 × 3 = 3 3/4

= 5/4 × 4 = 5

Therefore, the multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.

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Considering the definition of an equation and the way to solve it, each cupcake cost $0.85.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:

Being "x" thecost of the cupcake, and knowing that:

the equation in this case is:

Amount spent by Michele= Amount spent by Myka

12.75 + 9x= 24x

Solving:

12.75= 24x - 9x

12.75= 15x

12.75÷ 15= x

0.85=x

Finally, each cupcake cost $0.85.

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Combination is the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects, where order of selection is not important.

The formula for combination is given by:

C = N! / n!(N - n)!

where N is the set of objects

and n is the number of objects to be selected from N

example: If the order doesn't matter, how many ways can 3 girls be selected from a group of 5 girls?

C = N! / n!(N - n)!

where N = 5 and n = 3

C = 5! / 3!(5 - 3)!

C = 120/(6)(2)

C = 10

Hence, there are 10 ways to select 3 girls from a group of 5 girls.

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Answer: –1, 9, 19, 29, … (1 point)

38, 37, 32

40, 51, 62

39, 49, 59

38, 47, 56.

Step-by-step explanation: tried

The domain of the given function is a 180.62 to 355.55.

According to the statement

We have to find that the linear equation domain.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The total cost to buy gloves for the football team can be found using the function \(p=24.99g+5.69\), where \(g)\ is the number of gloves bought. If there are at least \(7\) players but no more than \(14\) players on the football team

Then

p=24.99g+5.69

Now find the value of the g is

p=24.99g+5.69

Here the domain of the g]function is a From 1 to 14.

Then

For 7

p=24.99(7)+5.69

p=174.93+5.69

p = 180.62.

And for 14

p=24.99(14)+5.69

p=349.86+5.69

p = 355.55.

So, The domain of the given function is a 180.62 to 355.55.

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The inverse of the function is f-1(x) = √1/7(x - 8)

The function is given as

h(x) = 7x^2 + 8

Express h(x) as y

So, we have

y = 7x^2 + 8

Swap the positions of x and y

So, we have

x = 7y^2 + 8

Rewrite as

7y^2 = x - 8

Divide by 7

y^2 = 1/7(x - 8)

Take the square roots

y = √1/7(x - 8)

Hence, the inverse of the function is f-1(x) = √1/7(x - 8)

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Answer:

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

Step-by-step explanation:

[tex]0.5*\frac{10}{10} = \frac{5}{10} = \frac{1}{2}[/tex]