Ratios are these equivalent : 11/7 and 77/63 , 3/5 and 45/75 , 1/8 and 10/80 , and 2/9 and 18/81

The force acting on the adult and the student, both stuck to the wall, is determined by their weight and the centripetal force acting on them.  This means that the net force acting on both of them must be equal to zero.

The quadratic equation in LaTeX:

$ax^2 + bx + c = 0$

The weight of an object is proportional to its mass, and the centripetal force acting on an object is proportional to its mass and the square of its velocity.

Therefore, the ratio of the force acting on the adult to the force acting on the student will be equal to the square of the ratio of their masses and the square of the ratio of their velocities.

Let the mass of the student be 'm' and the mass of the adult be '2m'. Then, the ratio of the forces acting on them will be (2m) / m * (v_adult / v_student)^2, where 'v' represents velocity.

Since the ride remains stationary against the wall for both the student and the adult, this means that the net force acting on both of them must be equal to zero, i.e. their weight must be balanced by the centripetal force acting on them.

Thus, (2m) / m * (v_adult / v_student)^2 = 1.

This equation shows that the mass of the rider does not determine if the ride will remain stationary against the wall while rotating. The ride's velocity and the distribution of mass on the ride will determine whether it remains stationary or not, not the mass of the rider.

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Answer:

104.12 > 104.002

Step-by-step explanation:

Answer:

62.8 inches

Step-by-step explanation:

C=2pir= 62.8

Answer: -15

Step-by-step explanation:

First, calculate exponents.

-3 * -3 is 9.

Then multiply 2 and 9 which is 18.

3-18 is -15.

Part (a)

The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.

\(C(x)=500+1.25x\)

Part (b)

The revenue is the number of slushies sold multiplied by the amount charged per slushie.

\(R(x)=3.50x\)

Answer:
A the answer is A

Step-by-step explanation:

The area of the rectangular figure with two semicircles on the opposite side is  36.56 sq cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A rectangle with two semicircles on two opposite sides.

The length of the rectangle is 6cm and the width of the rectangle is 4cm.

The two given semicircles have a diameter of 4cm seems obvious.

∴ The area of the total figure is an area of the rectangle added to the area of 2 semicircles which makes up to a circle with a radius 2 cm.

∴ (4×6) + π(2)² sq cm.

= 24 + 4π sq cm.

= 24 + 12.56 sq cm.

= 36.56 sq cm.

The area which is not taken up in the rectangle and two circle questions are

(area of the rectangle - 2 times the area of a circle).

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The values of the composite functions are

(r * q)(5) = 96

(q * r)(5) = 96

From the question, we have the following functions that can be used in our computation:

q(x) = x² + 7

r(x) = √(x + 4)

The composite functions are given as

(r * q)(5) and (q * r)(5)

The base functions of the above composite functions are

(r * q)(x) and (q * r)(x)

And they are calculated using

(r * q)(x) = r(x) * q(x)

(q * r)(x) = q(x) * r(x)

Substitute the known values in the above equations

So, we have the following equations

(r * q)(x) = (x² + 7) * (√(x + 4))

(q * r)(x) = (√(x + 4)) * (x² + 7)

Substitute 5 for x

(r * q)(5) = (5² + 7) * (√(5 + 4))

(q * r)(5) = (√(5 + 4)) * (5² + 7)

Evaluate the equations

(r * q)(5) = 96

(q * r)(5) = 96

Hence, the solution of the composite functions is 96

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g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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Answer:

A. 2Fe + 3CI2 - 2FeCI3 ........

Answer:

So first you do 47 -20=27, So x=27

The answer 27 is X =

Answer:57.5

Step-by-step explanation:

057

6 345

0

34

30

 45

 42

   3

u have a remainder of 3 so u add .5 to 57

Answer:

3/4 = 0.75

Have a beautiful day!

The area of the triangle is 97.07 units².

Given is a triangle we need to find the area,

So, let the triangle be ABC and the altitude be AD.

Using the trigonometric ratios,

Sin 52° = AB / AD

Sin 52° = 9 / AD

AD = 9 / Sin 52°

AD = 11.42

Now,

Tan 26° = DC / AD

Tan 26° = DC / 11.42

DC = 5.56

Also,

Cos 26° = AD / AC

Cos 26° = 11.42 / AC

AC = 12.7

BC = 11.42 + 5.56

BC ≈ 17

Now, the sides are BC = 17, AC = 12.7 and AB = 9,

The area of the triangle = 1/2 x BC x AD = 1/2 x 17 x 11.42

= 5.71 x 17

= 97.07

Hence the area of the triangle is 97.07 units².

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The percentage of the employees at the water slides are temporary​ is 88%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

To find the percentage of the employees that are temporary

66/75 x 100/1

=88%

Hence, 88% is the percentage of the employees at the water slides are temporary​

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Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

The data correlation in the scatter plot above include the following: B. positive.

In Mathematics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.

By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation between the x-values and y-values because they both increase simultaneously.

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The length of the arc is 1 unit.

The distance that runs through the curved line of the circle making up the arc is known as the arc length.

length of an arc is expressed as;

l = tetha/360 ×2πr

the circumference of circle is expressed as ;

C = 2πr

6 = 2×3.14 × r

r = 6/6.28

r = 0.955 units

Therefore length of the arc

= 60/360 × 6

since 2πr is the circumference,

l = 360/360 = 1 unit

therefore the length of the arc is 1 unit.

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Answer:

What is the angle of rotation for this counterclockwise rotation about the origin?

answer:

270°

Step-by-step explanation:

Answer:

(d) and (e) are true

Step-by-step explanation:

Given

\(Food = 23\ oz\)

See attachment for proper presentation of question

Required

Select all true statements

For any option to be true, it must satisfy the following condition.

\(Days * Food = 23\)

Option (a):

\(Days = 6\)

\(Food = 4\frac{1}{6}\) per day

So, we have:

\(Days * Food = 6 * 4\frac{1}{6}\)

\(Days * Food = 6 * \frac{25}{6}\)

\(Days * Food = 25\)

This is not true because: \(25 \ne 23\)

Option (b):

\(Days = 10\)

\(Food = 2\frac{2}{23}\) per day

So, we have:

\(Days * Food = 10 * 2\frac{2}{23}\)

\(Days * Food = 10 * \frac{48}{23}\)

\(Days * Food = \frac{480}{23}\)

\(Days * Food = 21\) --- approximated

This is not true because: \(21 \ne 23\)

Option (c):

\(Days = 8\)

\(Food = 3\frac{1}{8}\) per day

So, we have:

\(Days * Food = 8 * 3\frac{1}{8}\)

\(Days * Food = 8 * \frac{25}{8}\)

\(Days * Food = 25\) --- approximated

This is not true because: \(25 \ne 23\)

Option (d):

\(Days = 11\)

\(Food = 2\frac{1}{11}\) per day

So, we have:

\(Days * Food = 11 * 2\frac{1}{11}\)

\(Days * Food = 11 * \frac{23}{11}\)

\(Days * Food = 23\) --- approximated

This is true because: \(23 = 23\)

Option (e):

\(Days = 7\)

\(Food = 3\frac{2}{7}\) per day

So, we have:

\(Days * Food = 7 * 3\frac{2}{7}\)

\(Days * Food = 7 * \frac{23}{7}\)

\(Days * Food = 23\) --- approximated

This is true because: \(23 = 23\)

The minimum length of the box to hold the smaller mirror is 10 inches for largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror.

What is proportion ?

In mathematics, proportion refers to the equality of two ratios. Two ratios are said to be proportional if they have the same relative size, meaning they represent the same relationship between quantities.

For example, if we have two ratios, such as 2/3 and 4/6, they are proportional because they represent the same relationship between two quantities. We can say that 2 is to 3 as 4 is to 6, and we can simplify both ratios by dividing the numerator and denominator of each by their greatest common factor, which in this case is 2.

Since the smaller mirror is similar in proportion to the larger mirror, the ratio of their corresponding sides is the same. Therefore, the width of the smaller box is half of the width of the larger box (9 inches is half of 18 inches).

To find the minimum length of the smaller box, we need to use the same ratio of sides. The length of the larger box is 20 inches, so the length of the smaller box should be half of 20 inches, which is 10 inches.

Therefore, the minimum length of the box to hold the smaller mirror is 10 inches.

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Answer:

no

Step-by-step explanation:

most people go through mid school cheating

Answer:

probably not cause same lol

Step-by-step explanation:

The expression can be simplified to: \(tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))\)

We can simplify the expression as follows:

tan(x) + cot(x)/sec(x) = tan(x) + 1/tan(x) / 1/cos(x) = tan(x) + cos(x) / tan(x) * cos(x) = tan(x) + cos^2(x) / tan(x)

Using the identity: tan(x)^2 + 1 = sec^2(x), we can simplify further:

tan(x) + cos^2(x) / tan(x) = tan(x) + cos^2(x) / (sqrt(sec^2(x) - 1)) = tan(x) + cos^2(x) / sqrt(tan^2(x) + 1 - 1) = tan(x) + cos^2(x) / sqrt(tan^2(x))

Using the identity sin^2(x) + cos^2(x) = 1, we can simplify further:

\(tan(x) + cos^2(x) / \sqrt(tan^2(x)) = tan(x) + (1 - sin^2(x)) / \sqrt(tan^2(x)) = tan(x) + \sqrt(1 - sin^2(x)) / \sqrt(tan^2(x)) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))\)

Therefore, the expression can be simplified to:

\(tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))\)

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Answer:

x=70

Step-by-step explanation:

Due to the law of alternate interior angles, we can see that one of the angles in the triangle is equal to 35 degrees as well (please see the picture attached).

We're given that one of the exterior angles of the triangle is equal to 105. The exterior angle of a triangle will always be equal to the sum of the two opposite interior angles. Knowing this, we can write:

x+35=105

Subtract both sides by 35

x+35-35=105-35

x=70

Therefore, the value of x is 70 degrees.

I hope this helps!

Step-by-step explanation:

yes, the step is correct.

a² = cx | multiply by c

ca² = c²x

I am just not sure how that simplified the equation.

what do you want to achieve ? what's the goal here ?

to solve the equation for x it would be to divide both sides by c, which gives

a²/c = x

We are given the following equation

We need to substitute the (-7, -9) into the equation to find out whether it satisfies the equation or not.

x = -7

y = -9

As you can see, -9 is not equal to 9

This means that the point (-7, -9) doesn't satisfy the given equation.

the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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