Which equation is represented by the table ?

Step-by-step explanation:

The wheel has a diameter of 250 feet, so its circumference is:

C = 2πr = πD

C = 250π feet

It makes one revolution in 30 seconds, or half a minute, so the linear speed of the passenger is:

v = d / t

v = 250π / 0.5

v = 500π ft/min

v ≈ 1571 ft/min

This is about the same as 17.9 mph.

Final answer:

The linear speed of a passenger on the original Ferris wheel with a diameter of 250 feet, making one revolution every 30 seconds, was approximately 1570.8 feet per minute.

Explanation:

The question asks to calculate the linear speed of a passenger on the edge of the first Ferris wheel, which was 250 feet in diameter, and made one revolution every 30 seconds. To find the linear speed, we first need to determine the circumference of the Ferris wheel, which can be done by using the formula for the circumference of a circle, C = πd, where d is the diameter.

For the first Ferris wheel:

Diameter (d) = 250 feet

Circumference (C) = π * 250 feet = 785.398163 feet (approximately)

Time for one revolution = 30 seconds

Since the question requires the speed in feet per minute, we need to convert the time for one revolution to minutes:

30 seconds = 0.5 minutes

The linear speed (v) can be found using the formula v = C / time. Substituting our values in:

v = 785.398163 feet / 0.5 minutes = 1570.79633 feet per minute

Therefore, the linear speed of a passenger at the edge of the Ferris wheel was approximately 1570.8 feet per minute.

Answer:

14.08 m

Step-by-step explanation:

Start by finding the area of the fence and the area of the garden. Garden- 10.1*4.2=42.42   Fence-11.3*5=56.5

Now subtract the two values. 56.5-42.42=14.08

Linear data is data lying across a straight line. The runner which kept the most consistent pace was runner B.

Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.

For the given case, the second runner(runner B)'s data is almost forming a linear trend, whereas, for the first runner, its more spread, and the third graph, its a quadratic trend.

For non-linear trends like in third graph(runner C), we use polynomial regression to fit polynomial curves of higher degrees.

Thus, as the runner B's data set is lying more near to a line than other runners, thus,

The runner which kept the most consistent pace was runner B.

Learn more about linear regression here:

https://brainly.com/question/18854090

Answer:

3 1/3

Step-by-step explanation:

8 1/6 - 4 5/6    Borrow 1 or 6/6 from the 8 so you have something to subtract.

7 7/6 - 4 5/6    Subtract the whole numbers.

7 - 4 = 3           Subtract the fractions.

7/6 - 5/6          Do the subtraction

2/6                   Reduce

2/6 = 1/3          Put the two parts together.

3 1/3

the result of subtracting the two mixed numbers is  [tex]3\frac{1}{3}[/tex]

To subtract the mixed numbers [tex]8\frac{1}{6}[/tex] and [tex]4\frac{5}{6}[/tex] we need to first understand how to subtract it. To subtract mixed numbers we need to first convert them to improper fraction. For the new fraction, the denominator remains same but new numerator is calculated by finding the product of whole number and denominator and then adding it to the numerator. This can be done as follows:

[tex]8\frac{1}{6} = \frac{ 8 \times 6 +1}{6} = \frac{49}{6}[/tex]

[tex]4\frac{5}{6} = \frac{ 4 \times 6 +5}{6} = \frac{29}{6}[/tex]

Now we subtract them as follows:

[tex]\frac{49}{6} - \frac{29}{6} = \frac{20}{6} = \frac{10}{3}[/tex]

To convert this back into mixed fraction we divide 10 by 3 and the quotient becomes the whole number while the remainder becomes numerator and 3 remains as denominator

[tex]\frac{10}{3} = 3\frac{1}{3}[/tex]

Therefore, the result of subtracting the two mixed numbers is  [tex]3\frac{1}{3}[/tex]

Answer:

X int : 5

Y int : 15

Step-by-step explanation:

y=15

-

3x=15

3/3 15/3

x=5

Answer:

y-intercept=15 and x-intercept = 5

Step-by-step explanation:

We have the following equation:

3x + y = 15.

To find the x-intercept and y-intercept we have to do the following:

1. To find the y-intercept we need to make x=0, and solve for 'y' as follows:

3x + y = 15 ⇒ 3(0) + y = 15 ⇒ y=15

2. To find the x-intercept we need to make y=0, and solve for 'x' as follows:

3x + y = 15 ⇒ 3x + (0) = 15 ⇒ 3x = 15  ⇒ x=5

Therefore, the y-intercept=15 and x-intercept = 5

Answer:

[tex]5x\leq30[/tex]

Step-by-step explanation:

Let

x -----> the number of ice cream

we know that

[tex]5x\leq30[/tex]

Solve for x

Divide by 5 both sides

[tex]x\leq30/5[/tex]

[tex]x\leq 6\ ice\ cream[/tex]

therefore

The maximum number of ice cream is 6

Answer:

f(6)  =  68

Step-by-step explanation:

f(6)

f(n+1)=f(n)-8

n = 5, so

f(6)=f(5)-8

and with n = 4

f(5)=f(4)-8 , so

f(4) = f(3) - 8

f(3) = f(2) - 8 = 100 - 8 = 92

f(3)  = 92

Then, we can go and find the result

f(4) =[92] - 8  = 84

f(5)=[84] - 8 = 76

f(6)  = [76] -8 = 68

[tex]f(n+1)=f(n)-8\\f(2)=100\\\\f(3)=100-8=92\\f(4)=92-8=84\\f(5)=84-8=76\\f(6)=76-8=68[/tex]

Answer:

b. 3

Step-by-step explanation:

In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].

30°-60°-90° Triangles

x√3 → long side

x → short side

2x → hypotenuse

45°-45°-90° Triangles

x → two legs

x√2 → hypotenuse

I am joyous to assist you anytime.

Answer:

[tex]x=15.56[/tex]

Step-by-step explanation:

We can use the law of sines here. However, we will first need to solve for the missing angle.

The interior angles of a triangle add up to 180.

Therefore,

[tex]35+90+x=180[/tex]

where [tex]x[/tex] is the missing angle.

[tex]35+90+x=180[/tex]

[tex]x+125=180[/tex]

[tex]x=55[/tex]

So the missing angle is 55 degrees.

Now we can use the law of sines to set up a proportion.

[tex]\frac{19}{sin(90)}=\frac{x}{sin(55)}[/tex]

Now simplify the equation.

[tex]x=15.56[/tex]

Rounded to the nearest hundredth.

Answer:

x ≈ 19.6

Step-by-step explanation:

Since the triangle is right use the cosine ratio to solve for x

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{19}[/tex]

Multiply both sides by 19

19 × cos35° = x, hence

x ≈ 19.6 ( to 1 dec. place )

Answer:

Multiply 9 by 6

Step-by-step explanation:

7:9 is the ratio

We multiply the first term by 6.

What we do to one side, we do to the other

7*6=42

9*6 = 54

That way we keep the ratio in the same proportion

42:54

Answer: Multiply 9 by 6.

Step-by-step explanation:

Answer:

(2x-9)(2x+9)

Step-by-step explanation:

This is a difference of squares because it can be written as (2x)^2-9^2

The formula for factoring a difference of squares is a^2-b^2=(a-b)(a+b)

So replace a with 2x and b with 9 giving us

4x^2-81=(2x-9)(2x+9)

Answer:

(x - 15)(x + 3)

Step-by-step explanation:

Consider the factors of the constant term (- 45) which sum to give the coefficient of the x- term (- 12)

The factors are - 15 and + 3, since

- 15 × 3 = - 45 and - 15 + 3 = - 12, hence

x² - 12x - 45 = (x - 15)(x + 3)

Answer:

18

Step-by-step explanation:

First you need to plug in the numbers for each variable.

3(3)+(5+2(8))-12

Now you solve

3(3)+(21)-12

9+21-12

18

Answer:

acute

Step-by-step explanation:

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Answer:

acute and obtuse

Step-by-step explanation:

In an obtuse triangle, one angle is greater than a right angle—it is more than 90 degrees. An obtuse triangle may be isosceles or scalene. In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. Please mark me as branliest. Thank you :3

Answer:

Distribute the -9 into the values in the parentheses.

STEP BY STEP

-9(-2x-3)

-9*-2x=18x

-9*-3=27

Therefore, the equation then becomes: 18x+27.

The answer is the first choice, or A.

For this case we have that the variable "x" represents the number of hours that Leticia uses to take care of children on Saturday.

IF on Friday I use 4 hours ($ 8 each) and on Saturday "x" hours ($ 8 each) obtaining a profit of $ 72, we have the following equation:

[tex]8 (4 + x) = 72[/tex]

We apply distributive property:

[tex]32 + 8x = 72\\8x = 72-32\\8x = 40\\x = \frac {40} {8}\\x = 5[/tex]

So, on Saturday she spent 5 hours.

Answer:

[tex]8 (4 + x) = 72\\x = 5[/tex]

Answer:

Option A.

Option  C.

Step-by-step explanation:

Let be "x" the amount of hours  Leticia babysat on Saturday.

We know that she charges $8 per hour to babysit, she babysat Friday night for 4 hours and the total amount of money she earned on those two days was $72. Knowing this, we can set up the followin equation models this situation:

[tex]8(4+x)=72[/tex]

Finally, we must  solve for "x":

[tex]8(4+x)=72\\\\32+8x=72\\\\8x=72-32\\\\8x=40\\\\x=\frac{40}{8}\\\\x=5[/tex]

a box plot is drawn with end points at 10 and 35. The box extends from 13 to 30 and a vertical line is drawn inside the box at 21.

Answer:

Step-by-step explanation:

Perimeter= 2L+2W. If L=3W(three times the width) then 2(3W)+2W=112. Or 6W+2W=112 which is equal to 8W=112. To solve for the width, divide both sides by 8 and find 112/8=14, therefore W=14.

Answer:

14 cm

Step-by-step explanation:

Given the length is 3 times the width

If each width is denoted by W, then each length is L = 3W

Perimeter (add up all lengths and widths),

= L + L + W + W

= 3W + 3W + W + W

= 8W

Given that the max perimeter is 112cm

hence 8W = 112,

W = 14 cm at most

Divide 45 by 3 ( the quantity of consecutive numbers) This will give you the middle number, then use the number higher and lower.

45/3 = 15

14 + 15 + 16 = 45

The 3 numbers are 14, 15 and 16

Answer:

its (5x+8)(25x^2-40x+64

Step-by-step explanation:cuz

The equivalent expression to 4 √6 divided by 3 √2 is 4/3 × √3. This is achieved by expressing the square roots as fractional exponents and simplifying.

The student is asking which expression is equivalent to the following mathematical expression: √(4 √6) / (3 √2).

To simplify this expression, we'll use the properties of exponents and radicals.

The square root of a number x can be written as x raised to the power of 0.5, so:

√6 = 60.5

√2 = 20.5

The given expression thus becomes:

(4 × 60.5) / (3 × 20.5) = 4/3 × 60.5/20.5

Since the exponents are the same, we can simplify the radicals by dividing the numbers inside the radicals:

4/3 × (6/2)0.5 = 4/3 × (3)0.5

And as (3)0.5 is the square root of 3:

4/3 × √3

Therefore, the equivalent expression is 4/3 × √3.

Answer:

x = 11/6

Step-by-step explanation:

You need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

Please mark brainliest and have a great day!

Answer:  [tex]\bold{x=-\dfrac{4}{3}\qquad x=5}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{x-2}+\dfrac{7}{x^2-4}=\dfrac{5}{x}\\\\\\\text{Multiply each term by the LCD x(x-2)(x+2) to clear the denominator:}\\\dfrac{2}{x-2}[x(x-2)(x+2)]+\dfrac{7}{x^2-4}[x(x-2)(x+2)]=\dfrac{5}{x}[x(x-2)(x+2)]\\\\\\\text{Simplify - cross out like terms:}\\2[x(x+2)]+7[x]=5[(x-2)(x-2)]\\\\\\\text{Distribute:}\\2x^2+4x+7x=5x^2-20\\\\\\\text{Set equation equal to zero and Add like terms:}\\0=5x^2-2x^2-7x-4x-20\\0=3x^2-11x-20\\\\\text{Factor, set each factor equal to zero, and solve for x:}[/tex]

[tex]0=(3x+4)(x-5)\\0=3x+4\qquad 0=x-5\\\large\boxed{x=-\dfrac{4}{3}\qquad x=5}[/tex]

Answer: 24

Step-by-step explanation:

Break down the numbers until they have no way to be broken down anymore

8 = 4*2 = 2*2*2

24 = 6*4 = 3*2*2*2

The one that has more products is 24, so, it is 24.

Answer:

Im boutta fail my final

Step-by-step explanation:

1 like= 1 prayer

Answer:

$720

Step-by-step explanation:

1 hour of tutoring  =  $45

16 hours of tutoring = $45 x 16 hours = $720

Answer:

$720

Step-by-step explanation: just multiply 45 and 16 together, boom theres your answer

Answer:

The equation has infinity solutions

Step-by-step explanation:

3( x - 4 ) + 5 - x = 2 x - 7

⇒ Expand brackets

3 x - 12 + 5 - x = 2 x - 7

⇒ Simplify

2 x - 7 = 2 x - 7

Answer:

False

Step-by-step explanation:

a^2+b^2=c^2 so the biggest number would be c and that would be 11 9^2=81 4^2=16 adding these together gets 97. 97=/=11^2 which is 121

Answer:

A. True.

Step-by-step explanation:

We have been given lengths of three segments. We are asked to determine whether the given segments could form a triangle or not.

Triangle inequality theorem states that sum of two sides of triangle must be greater than third side of the triangle.

Using triangle inequality theorem, we will get:

[tex]9+4>11[/tex]

[tex]13>11[/tex] True

[tex]9+11>4[/tex]

[tex]20>4[/tex] True

[tex]4+11>9[/tex]

[tex]15>9[/tex] True

Since our given segments satisfies triangle inequality theorem, therefore, the given segments could form a triangle.

ANSWER

b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward

EXPLANATION

The given polynomial function is

[tex]f(x) = - {x}^{4} + 1[/tex]

The degree of this function is even which is 4.

The function extends in the same direction at both ends.

In other words both ends continue in the same direction.

Since the coefficient of the leading term is negative, the graph extends to negative infinity at both ends.

The correct answer is B