A double ferris wheel is pictured below. A large rotating arm with diameter 20 is centered 14 meters off the ground, and completes one rotation every 11 minutes. At the end of each side of the large arm is a smaller wheel with diameter 6 meters, which completes one rotation about its center every 6 minutes.
If you board the ferris wheel at point P at time t = 0, and each wheel rotates in the direction shown by the arrows, find an equation for your height, H above ground after t minutes.

For the exponential function:

g(x) = 14*(2)^x

We can see that:

a = 14, and b = 2.

A general exponential function is written as:

y = a*(b)^x

Where a is the inital value of the exponential function and b is the base.

Here we have the exponential function:

g(x) = 14*(2)^x

Comparing that to the general one, we can see that the initial value is 14 and the base is 2.

Then:

a = 14

b = 2

The correct option is the second one.

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A residual is the difference between an observed value and the predicted value from a regression line.

A negative residual indicates that the observed value lies below the regression line. This can be expressed mathematically using the formula [tex]y = mx + b[/tex], where y is the observed value, m is the slope, x is the independent value, and b is the y-intercept of the line.

For example, if the observed value is y = 3, the predicted value is y = 5, and the slope and intercept of the line are m = 2 and b = 1, respectively, then the residual can be calculated as [tex]y = 3 - (2*1 + 1) = -1.[/tex] Since the residual is negative, this indicates that the observed value lies below the regression line.

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Answer:

(a) The height of the cubiod is 5cm.

(b) The volume of metal not used in making these spheres is 172cm^3.

Step-by-step explanation:

(a) 12*10= 120

     600/120= 5cm

(b) volume of 1120 spheres= (4/3*π*0.45^3)(1120)

                                              = 428cm^3 (to 3 s.f.)

    600-428= 172cm^3

Answer:

about 23,000 usd

Step-by-step explanation:

If you want a quick way to translate yen to usd, take the yen amount and take away two zeros. So 3 mil yen would be 30,000. This method is a bit off but is quick and easy.

1 us dollar is about 130 yen

Answer:

Step-by-step explanation:  1133.5.

The measure of ∠U= 80°, ∠B=44°, ∠Q= 93° respectively which indicates the angle of each triangle.

First take the Triangle TUV:

⇒∠T+∠U+∠V=180°

⇒37°+∠U+63°=180°

⇒∠U+100°=180°

⇒∠U=80°

Now, take triangle ABC:

⇒∠A+∠B+∠C=180°

⇒46°+∠B+90°=180°

⇒∠B+136°=180°

⇒∠B=44°

Finally take triangle PQR:

⇒∠P+∠Q+∠R=180°

⇒51°+∠Q+36°=180°

⇒∠Q+87°=180°

⇒∠Q=93°

Therefore, measure of the indicated angle in each triangle are 80°, 44 and 93° respectively.

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From the given  information provided, by converting the units there are 0.001 milliliters in 1 microliter.

This means that if you have 1 microliter of liquid, it is equal to 0.001 milliliters of liquid.

The conversion factor between milliliters (mL) and microliters (μL) is:

1 mL = 1000 μL

Therefore, to convert microliters to milliliters, you divide the number of microliters by 1000.

For example, if you have 500 μL of liquid, you can convert it to milliliters by dividing 500 by 1000:

500 μL / 1000 = 0.5 mL

So, 500 microliters of liquid is equal to 0.5 milliliters of liquid.

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The formula of the given exponential function whose graph passes through the points (3, 2.8) and (4, 5.6) is :

   y = 0.35* (2)ˣ

What is an exponential function?

When the input variable x appears as an exponent in the formula

f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. It is mostly used to determine exponential growth or decay.

When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. In exponential decay, the quantity initially falls very quickly and then gradually. Over time, the rate of change slows. As time goes on, change happens at a slower rate.

The general formula of an exponential function is:

y = abˣ

It is said that points (3, 2.8) and (4, 5.6) are present on the graph of the given exponential function.

W can substitute these value values in the above formula.

2.8 = ab³

5.6 = ab⁴

Dividing the above equations,

2.8 /5.6 = b³/b⁴

1/2 = 1/b

b = 2

Now substituting this value in one of the equations to find the value of a.

2.8 = a. (2)³

a = 2.8/8 = 0.35

Therefore the formula of the given exponential function is :

   y = 0.35* (2)ˣ

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The solution is, the equation of the line that passes through the point (5,0) and has a slope of 6/5 is , y=6/5*x - 6

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

the line that passes through the point (5,0) and has a slope of 6/5

now, w know, the point slope form of straight line is,

y-y1=m(x-x1)

so, putting the values , we get,

y-0=6/5(x-(5))

y-0=6/5(x-5)

y=6/5*x- 30/5

y=6/5*x- 6

Hence, The solution is, the equation of the line that passes through the point (5,0) and has a slope of 6/5 is , y=6/5*x - 6

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Translation: 2 units left and 1 unit down. Q(0,-1), D(-2,2), V (2,4), J(3,-3)

New coordinates are respectively, (-2, -2), (-4, 1), (0, 3), (1, -4)

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given the points Q(0,-1), D(-2,2), V (2,4), and J(3,-3),

we can see that each point has been translated 2 units to the left and 1 unit down.

This is because each x-coordinate has decreased by 2 and each y-coordinate has decreased by 1.

So, the translation of 2 units left and 1 unit down has moved each point along the plane in the negative x-direction and the negative y-direction.

the points are respectively (-2, -2), (-4, 1), (0, 3), (1, -4)

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The next term is -25.

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers. In Maths, number patterns are the patterns in which a list number that follows a certain sequence. usaually, the patterns establish the relationship between two numbers. It is known as the sequences of series in numbers.

Given;

The pattern20,−10,5,___

Here, first term is 20, second is -10

Difference=20+10

=30

Now,

=5-30

=-25

Therefore, the answer of the given pattern will be -25.

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No , it is not possible to form a triangle with side lengths 3.5, 3.5, and 9 , because of the rule that sum of any two sides must be greater than other side. So, Option D is correct.

A triangle is a two-dimensional shape formed by three line segments connecting three points. In order to form a triangle, a necessary and sufficient condition is that the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.

If the sum of the lengths of any two sides is less than or equal to the length of the third side, then the three line segments will not be able to form a closed shape, and therefore cannot form a triangle.

In the case of the triangle with side lengths 3.5, 3.5, and 9, the sum of the lengths of the first two sides is 7, which is less than the length of the third side, 9. Hence, these three side lengths do not satisfy the triangle inequality theorem, and therefore cannot form a triangle.

In general, to determine the type of triangle that can be formed with three given side lengths, it is necessary to compare the lengths of the sides and check if any two sides are equal in length (isosceles), or if all three sides are equal in length (equilateral). If none of the sides are equal, then the triangle is called scalene.

In this case, since it is not possible to form a triangle with the given side lengths, it is not possible to determine the type of triangle that would be formed.

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"Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all" is the true statement.

This a problem on addition and subtraction of fractions

Since Hope's dad gives her 7/8 of a chocolate bar one day and then gives her 6/12 of a chocolate bar the next day. Hope received approximately 1 chocolate bar. Total chocolate  received will be:

Total chocolate received = 7/8  + 6/12 = 1 3/8

This statement is not true

Since Dee has 10/12 of a cake and gives 4/8 to her neighbor. Dee has approximately 1 cakes left. The cakes left will be:

cakes left = 10/12 - 4/8 = 1/3

This statement is not true

Since Joe ran 8/15 of a mile on Thursday. He ran 4/5 of a mile on Friday. Joe ran approximately 1/2 mile in all. The total mile ran will be:

total mile ran =  8/15 + 1/2 = 2 1/10

This statement is not true

Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all.

mile swam =  9/16 +  1 5/8 = 2 3/16

This statement is true

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Answer:

SInce 2 is 2 less than 4, the value of x+2 is 4 less than 31. So x+2=29

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since 2 is 2 less than 4, the value of x + 2 is 2 less than 31.

So, x + 2 = 29.

The length of the missing side in the given triangle is equal to option c. 5.

Figure is attached.

In the attached figure of a right angle triangle,

Let the triangle be named as ABC.

AC is the hypotenuse of a triangle.

AB is the altitude of a triangle.

BC is the base of a triangle.

Form the attached figure

Length of altitude AB = 3

Length of base BC = 4

Using Pythagoras theorem we have,

Hypotenuse² = Altitude² + Base²

⇒ AC² = AB² + BC²

Substitute the value we get,

⇒ AC² = 4² + 3²

⇒AC = √ 16 + 9

⇒ AC = √25

⇒ AC = 5

Therefore, the length of the missing side in the given triangle is equal to option c . 5.

The above question is incomplete, the complete question is:

Find the length of the missing side. Leave your answer in simplest radical form.

The triangle is not drawn to scale.

A.) 25

B.) 144

C.) 5

D.) Square root of 5

Figure is attached .

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The probability of picking a factor of 10 is 1/4 or 0.25 as a decimal.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
To calculate the probability of picking a factor of 10, we need to count the number of cards that are factors of 10 and divide that by the total number of cards.

The factors of 10 are 1, 2, 5, and 10. Out of the given cards, only 2 is a factor of 10.

Therefore, the probability of picking a factor of 10 is 1/4 or 0.25 as a decimal.

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The correct answer is P and T directly varies with V and N, and P and N inversely varies with T and V respectively.

It is the mathematical relationship between two variables which can be expressed by an equation in which one variable is equal to a constant times the other.

Given that, the equation pT = kVN, where k is a constant.

pT = kVN

If we remove constant, then,

pT ∝ VN

or

p 1/∝ T

V 1/∝ N

Hence, the correct answer is P and T directly varies with V and N, and P and N inversely varies with T and V respectively.

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The domain and range of the function for the given graph is -

The range of values which we're permitted to enter into our function is known also as domain of a function.

Thus, the domain and range of the function for the given graph is -

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Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean according to the z-score table.

The statistical measurement known as the Z-score describes the relationship between a value and the mean of a group of values. Z-score is quantified by the standard deviations from the mean. The mean score and the data point's score are equal when the Z-score is 0. The Z-score for a value that deviates by one standard deviation is 1.0. Z-scores are binary, with a positive value denoting a score above the mean and a negative value denoting a score below the mean.

Equation of the z-score: z = ( x - μ ) / σ

Get the value corresponding to one decimal place of the z-score by first looking at the left side column of the z-table.

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The solution of system of equation  y= -2x-4 and  y=2/5x + 16/5 is (-3, 2).

Two or more expressions with an Equal sign is called as Equation.

The system of equations are  y= -2x-4

and y=2/5x + 16/5

By substitution method let us find the solution.

2/5x + 16/5=-2x-4

2/5x+2x=-4-16/5

12x/5=-20-16/5

12x=-36

Divide both sides by 12

x=-3

Now plug in x value in any of the equation

y=-2(-3)-4

y=6-4

y=2

Hence, the solution of system of equation  y= -2x-4 and  y=2/5x + 16/5 is (-3, 2).

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Due to the fact that they are both increased to the same power, the two functions are exponential. Both functions have distinct constants and rates.

A unit of code known as a function carries out a particular task. A function in mathematics is a relationship between a set of allowable inputs and outputs, having the condition that each input is connected to exactly one output.

As illustrated in the graphic that represents the posed question, the two functions that we are considering are all such that we can see that they are exponential in nature.

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The scale factor for the dilation that maps △ABC to △DEF is 0.75.

A triangle is a geometric shape that consists of three line segments that connect to form three angles. These angles always add up to 180 degrees. A triangle has three sides and three vertices (corners). Triangles can have different shapes and sizes, and they are often classified based on the length of their sides or the size of their angles. Some common types of triangles include equilateral triangles (where all sides are equal in length and all angles are equal to 60 degrees), isosceles triangles (where two sides are equal in length), and right triangles (where one angle is a right angle, or 90 degrees). Triangles have many properties and are an important part of geometry and mathematics.

Here,

To determine the scale factor for the dilation that maps △ABC to △DEF, we need to find the ratio of the corresponding side lengths of the two triangles.

Since △ABC ∼ △DEF, we know that the corresponding angles of the two triangles are congruent. Therefore, angle B in △ABC corresponds to angle E in △DEF, and angle A in △ABC corresponds to angle D in △DEF.

Using the Pythagorean theorem, we can find the length of the missing side of △DEF:

DF² = DE² + EF²

6² =DE² + 4²

DE=√20

DE=2√5 units

3/4=2/2√5=√13/6=0.75

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Answer:

1298/3 is the answer

Step-by-step explanation:

Answer:

1296

Step-by-step explanation:

Let the unknown number be x.

If 432 is the result of x being decreased by 66²/₃%, then 432 is 33¹/₃% of x since 100% - 66²/₃% = 33¹/₃%.

Therefore:

[tex]\implies 33\frac{1}{3}\%\;\textsf{of}\;x=432[/tex]

[tex]\implies \dfrac{33\frac{1}{3}}{100} \cdot x=432[/tex]

[tex]\implies \dfrac{33\frac{1}{3}x}{100} =432[/tex]

Multiply both sides of the equation by 100:

[tex]\implies 33\frac{1}{3}x =43200[/tex]

Rewrite 33¹/₃ as an improper fraction:

[tex]\implies \dfrac{100}{3}x =43200[/tex]

Multiply both sides by 3:

[tex]\implies 100x=129600[/tex]

Divide both sides by 100:

[tex]\implies x=1296[/tex]

Therefore, the number that when decreased by 66²/₃% is 432, is 1296.

Answer:

[tex]117500[/tex]

Step-by-step explanation:

[tex]500 \times 235=100\times (5\times 235)=1175 \times 100=117500[/tex]

Answer: 117,500

Step-by-step explanation: 500 x 235 = 117,500

Answer:can u take a picture that is a bit more closer

Step-by-step explanation:

please submit a closer picture

At (0.958, 0.287, 5) and (0.958, -0.287, -5) points, the helix r(t) = sin(t), cos(t), t intersect the sphere x^2 + y^2 + z^2 = 26.

The sphere x^2 + y^2 + z^2 = 26 is a sphere with center at the origin and radius sqrt(26).

The helix r(t) = sin(t), cos(t), t is parameterized by sine and cosine functions, which oscillate between -1 and 1.

To find the points at which the helix intersects the sphere, we need to find the values of t such that the distance between r(t) and the origin is equal to sqrt(26).

The distance between a point (x, y, z) and the origin is given by the formula:

d = sqrt(x^2 + y^2 + z^2)

So, substituting the values from r(t), we have:

d = sqrt(sin^2(t) + cos^2(t) + t^2)

Setting d equal to sqrt(26), we have:

sqrt(sin^2(t) + cos^2(t) + t^2) = sqrt(26)

Squaring both sides, we have:

sin^2(t) + cos^2(t) + t^2 = 26

Recall that sin^2(t) + cos^2(t) = 1, so we have:

1 + t^2 = 26

Subtracting 1 from both sides, we have:

t^2 = 25

Taking the square root of both sides, we have:

t = ±5

So, the two points of intersection are (sin(5), cos(5), 5) and (sin(-5), cos(-5), -5).

Rounding the results to three decimal places, we have:

(sin(5), cos(5), 5) = (0.958, 0.287, 5)

(sin(-5), cos(-5), -5) = (0.958, -0.287, -5)

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The probability that a student studied for 1 hour will be 0.10. Then the correct option is D.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The table is given below.

Number of hours               Total number of students

            0                                                 1

            1                                                  3

            2                                                 2

            3                                                 5

            4                                                 9

            5                                                 7

            6                                                 3

The total number of students is given as,

Total = 1 + 3 + 2 + 5 + 9 + 7 + 3

Total = 30

Then the probability that a student studied for 1 hour is given as,

P = 3 / 30

P = 0.10

The probability that a student studied for 1 hour will be 0.10. Then the correct option is D.

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For the given similar triangles, the length of the missing side in the second triangle is 20.

To solve for the length of the missing side in the pair of similar triangles, we can use the SSS similarity theorem. The theorem states that 'if all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar'. Since the triangles are similar, the ratio of their corresponding sides will be equal.

The given measurements of the first triangle are 12, 18, and 24, and the measurements of the second triangle are 10, 15, and x. To solve for x, you can use the ratio of corresponding sides of similar triangles. The ratio for the sides of the first triangle are 12:18:24 and for the second triangle are 10:15:x. The ratio of the corresponding sides is 10:12, 15:18, and x:24.

We can set up a proportion using the given dimensions and solve for x.

The proportion will look like this:

12/10 = 18/15 = 24/x

Cross-multiplying and simplifying, we get:

12x = 240

x = 20

Therefore, the length of the missing side in the second triangle is 20.

Note: The question is incomplete. The complete question probably is: Solve for length of the missing side in the pair of similar triangles. The dimensions of one triangle are 12, 18, and 24, and the dimensions of the second triangle is 10, 15, and x. (These are corresponding measurements).

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