At the start of an experiment, the temperature of a solution was -12°C. During the expirament

The equation expressing the height as a function of elapsed time for the provided Ferris wheel scenario is: h = 35 cos 2π (t - 30) / 60 + 36. This assumes the highest point is reached halfway through the rotation and uses a cosine function to map the cycle.

The subject of this question is mathematics, specifically it's about trigonometric functions and their applications to real world scenarios. The question is seeking for an equation that can express the height of a point on a Ferris wheel as a function of elapsed time.

Here's the solution: The highest height will be the radius of the Ferris wheel (35m) plus the height of the wheel's center above the ground (36m), which is a total of 71m. This height will be reached halfway through the rotation period of the wheel (30s). So, as the function of time, height can be represented by a cosine function shifted to the right by 30s with a period of 60s. Therefore, the equation to represent this scenario correctly is:

In this equation, 'h' stands for height, 't' represents time, 'cos' is the cosine function, 'π' is pi, and '35', '60', '30', and '36' are specific constants representing the radius of the Ferris wheel, the period of rotation, the time shift, and the wheel's center height respectively.

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Answer:

D:Point A and point B are the same distance from the origin.

Step-by-step explanation:

hope this helps :)

Answer:

D

Step-by-step explanation:

Hit the THANKS button pls >.<

  V

  V

  V

Answer:

110 1/3 or 100.33 degrees (to the nearest hundredth).

Step-by-step explanation:

There are 60 ' (minutes) in a degree.

So 20' = 20/60 = 1/3 of a degree.

Answer:

110 1/3°

Step-by-step explanation:

Recall that 1° = 60'.  Then 20' is 1/3 of 1°, or (1/3)°.

Then 110° 20' = 110° + (1/3)° = 110 1/3°.

Answer:

Part 1) option a. [tex]y=(x+1)^{2}[/tex]

Part 2) option c. [tex]y(x)=10x+1[/tex]

Part 3) option a. Yes , d=-2

Part 4) option b.  [tex]y=2x+4[/tex]

Part 5) option b. [tex]m=-2[/tex]

Part 6) option c. [tex]y=4x+14[/tex]

Part 7) option c. [tex]y=4x+5[/tex]

Part 8) option a. y=2x-1 and y=x+1

Step-by-step explanation:

Part 1)

we know that

If a ordered pair satisfy a function, then the function pass through the ordered pair

Verify each function with the points (1,4), (2,9) and (3,16)

case a) we have

[tex]y=(x+1)^{2}[/tex]

For x=1, y=4

[tex]4=(1+1)^{2}[/tex]

[tex]4=4[/tex] ----> is true

For x=2, y=9

[tex]9=(2+1)^{2}[/tex]

[tex]9=9[/tex] ----> is true

For x=3, y=16

[tex]16=(3+1)^{2}[/tex]

[tex]16=16[/tex] ----> is true

therefore

The function pass through the three points

case b) we have

[tex]y=(x+3)^{2}[/tex]

For x=1, y=4

[tex]4=(1+3)^{2}[/tex]

[tex]4=16[/tex] ----> is not true

therefore

The function not pass through the three points

case c) we have

[tex]y=7x-5[/tex]

For x=1, y=4

[tex]4=7(1)-5[/tex]

[tex]4=2[/tex] ----> is not true

therefore

The function not pass through the three points

Part 2)

Let

y------> the number of laps

x-----> the number of hours

we know that

The linear equation that represent this situation is

[tex]y(x)=10x+1[/tex]

Part 3) we have

{4,2,0,-2,-4,-6,...}

Let

a1=-4

a2=2

a3=0

a4=-2

a5=-4

a6=-6

we know that

a2-a1=2-4=-2 -----> a2=a1-2

a3-a2=0-2=-2 ----> a3=a2-2

a4-a3=-2-0=-2 -----> a4=a3-2

a5-a4=-4-(-2)=-2----> a5=a4-2

a6-a5=-6-(-4)=-2----> a6=a5-2

therefore

Is an arithmetic sequence, the common difference is -2

Part 4) we know that

The y-intercept of the graph is (0,4)

The x-intercept of the graph is (-2,0)

therefore

the function is [tex]y=2x+4[/tex]

because

For x=0 -----> y=2(0)+4 -----> y=4

For y=0 ----> 0=2x+4 --------> x=-2

Part 5) we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]A(3,5)\ B(2,7)[/tex]

substitute the values

[tex]m=\frac{7-5}{2-3}[/tex]

[tex]m=-2[/tex]

Part 6) we know that

The equation of the line into slope point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=4[/tex]

[tex]point(-3,2)[/tex]

substitute the values

[tex]y-2=4(x+3)[/tex]

Convert to slope intercept form

[tex]y=4x+12+2[/tex]

[tex]y=4x+14[/tex]

Part 7) we know that

If two lines are parallel, then their slopes are the same

The equation of the given line is [tex]y=4x-2[/tex]

so

The slope of the given line is [tex]m=4[/tex]

therefore

The line [tex]y=4x+5[/tex] is parallel to the given line

Because the slope is equal to [tex]m=4[/tex]

Part 8) we know that

If a ordered pair is a solution of a system of equations, then the ordered pair must satisfy both equations of the system

Verify each case for (2,3)

case a)

y=2x-1 -----> equation 1

y=x+1 -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

Verify equation 1

3=2(2)-1

3=3 -----> is true

Verify equation 2

3=2+1

3=3 -----> is true

therefore

The point (2,3) is a solution of the system of equations case a

case b)

y=2x+1 -----> equation 1

y=x-1 -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

Verify equation 1

3=2(2)+1

3=5 -----> is not true

therefore

The point (2,3) is not a solution of the system of equations case b

case c)

y=4x-5 -----> equation 1

y=2x -----> equation 2

Substitute the value of x and the value of y in each equation and then compare the results

Verify equation 1

3=4(2)-5

3=3 -----> is true

Verify equation 2

3=2(2)

3=4 -----> is not true

therefore

The point (2,3) is not a solution of the system of equations case c

[tex]\boxed{d=2\sqrt{107}}[/tex]

For a rectangular prism whose side lengths are [tex]a,\:b\:and\:c[/tex] the internal diagonal can be calculated as:

[tex]d=\sqrt{a^{2}+b^{2}+c^{2}}[/tex]

So here, we know that:

[tex]a=l=18 \\ \\ b=w=10 \\ \\ c=h=2[/tex]

So:

[tex]d=\sqrt{l^{2}+w^{2}+h^{2}} \\ \\ d=\sqrt{18^{2}+10^{2}+2^{2}} \\ \\ d=\sqrt{324+100+4} \\ \\ d=\sqrt{428} \\ \\ \boxed{d=2\sqrt{107}}[/tex]

Answer : The value of diagonal of the rectangular solid is, 20.69 unit.

Step-by-step explanation :

First we have to calculate the side AC.

Using Pythagoras theorem in ΔABC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

Given:

Side AB = l = 18

Side BC = w =  10

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(18)^2+(10)^2[/tex]

[tex]AC=\sqrt{(18)^2+(10)^2}[/tex]

[tex]AC=\sqrt{324+100}[/tex]

[tex]AC=\sqrt{424}[/tex]

Now we have to calculate the side AD (diagonal).

Using Pythagoras theorem in ΔACD :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](AD)^2=(AC)^2+(CD)^2[/tex]

Given:

Side AC = [tex]\sqrt{424}[/tex]

Side CD = h =  2

Now put all the values in the above expression, we get the value of side AD.

[tex](AD)^2=(\sqrt{424})^2+(2)^2[/tex]

[tex]AD=\sqrt{(\sqrt{424})^2+(2)^2}[/tex]

[tex]AD=\sqrt{424+4}[/tex]

[tex]AD=\sqrt{428}[/tex]

[tex]AD=20.69[/tex]

Thus, the value of diagonal of the rectangular solid is, 20.69 unit.

Answer:

A is the closest one

Step-by-step explanation:

Remark

The general formula is

V = V_2 cones + V_cylinder.

Formula

That turns out to be

V = 2*(1/3)*pi*r^2*h1 +  pi*r^2*h

Givens

r = 7 feet

h = 22 feet

h1 = 12 feet

pi = 3.14

Solution

V = 2*(1/3)*3.14 * 7^2*12  +   3.14* 7^2 * 22

V = 1231.5 ft^3 + 3384.92

V = 4616.42

Answer:

4618.1 ft3

Step-by-step explanation:

That's the exact correct answer :)

Answer:

See below

Step-by-step explanation:

The given rational function is;

[tex]y=\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}[/tex]

The given function is not continuous where the denominator is equal to zero.

[tex](x+4)(x-4)(x+2)=0[/tex]

The function is discontinuous at [tex]x=-4,x=4,x=-2[/tex]

b) The point at x=-2 is a removable discontinuity(hole) because (x+2) is common to both the numerator and the denominator.

The point at x=-4 and x=4 are  non-removable discontinuities(vertical asymptotes)

c) The equation of the vertical asymptotes are x=-4 and x=4

To find the equation of the horizontal asymptote, we take limit to infinity.

[tex]\lim_{x\to \infty}\frac{(x-3)(x+2)}{(x+4)(x-4)(x+2)}=0[/tex]

The horizontal asymptote is y=0

Answer:

k.lkkkkkkkkkkkkk

200 ft because 8x25 is 200

Answer:

x=18

Step-by-step explanation:

The two triangles are similar. The ratio of the sides are the same.

20/20=40/(40+x)

Cross multiply and solve. Hint: the easiest way to solve is to simplify, then solve.

Answer:

  D. a constant function divided by the sum of a constant function and an exponential function

Step-by-step explanation:

It's all about the meaning of the math symbols used to create the function. The exponential function is called that because the variable (t) is in the exponent of the expression.

The "numerator" is the part of the expression above the "divided by" line. The "denominator" is the part below that line. When describing a fraction like this, we say, "<the numerator> divided by <the denominator>."

The numerator is a number with no math symbols or variables: it is a constant. The same is true of the left term of the denominator.

The plus sign between the denominator terms indicate these terms are added together. The result of that addition is called a "sum." The terms either side of the plus symbol are those that the symbol is indicating the sum of.

So, we can describe the expression as ...

  a constant function divided by the sum of a constant function and an exponential function

The logistic equation is a model of population growth, correctly described as a constant function divided by the sum of a constant function and an exponential function. This matches option D from the choices provided.

The logistic equation is a model of population growth where the growth rate decreases as the population approaches its carrying capacity. The equation structure is generally given as a constant function divided by the sum of a constant function and an exponential function. Thus, the correct description from the options provided would be D. A constant function divided by the sum of a constant function and an exponential function.

As an example, the basic form of a logistic function is P(t) = c / (1 + ae-bt). Here c is the constant function representing the maximum achievable population and ae-bt is an exponential function that models the population growth over time 't'.

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The answer is 4 hours and 49 minutes HERE IS MY WORK

4 hours and 49 minutes

Answer: The lower quartile is Q1) is your minimum & your maximum is quartile Q3) bc is the larger one

Step-by-step explanation:

c

a

e

b

d

is none of your answer.

Answer:

person above is correct

Step-by-step explanation:

show them some love

2:6 so simplify it 1:3. This means the scale ratio is 1:3 for the figures. To find w, sub in the 3 from the smaller figure to the ratio so 3×3=9, 3:9 w=9

Answer:

w = 9

Step-by-step explanation:

Since the 2 polygons are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{2}{6}[/tex] = [tex]\frac{3}{w}[/tex] ( cross- multiply )

2w = 18 ( divide both sides by 2 )

w = 9

Answer:

0.22

Step-by-step explanation:

The point estimate is the average of the upper and lower bounds of the interval.

Answer:

Step-by-step explanation:

You can't answer c. There is not enough information.  Other than there are 14 boys that went, you know nothing about how many went.

Girls going = (3/5) * 20 = 12

Girls not going = 20 - 12 = 8

Answer:

  it depends

Step-by-step explanation:

If the tradeoff between giants and elves is linear, then about 76 elves can be admitted. If it is non-linear, we need more information about the tradeoff.

For example, elves may fit in the spaces between giants in such a way that they take up proportionately less room. Or, elves may repel giants in such a way that they take up proportionately more room.

See the attached graph for some possibilities.

_____

The linear equation can be written as ...

  g/160 + e/240 = 1

Then for g=109, we can solve for "e" as ...

  109/160 + e/240 = 1

  240(1 -109/160) = e = (3/2)(51) = 76.5

If the tradeoff is linear, 76 elves can be admitted.

Answer: 4.59

sin(35)=x/8

8*sin(35)=x

x=4.59

The value of x in the given triangle round to the nearest hundredths is:

                           4.59

From the given triangle we observe that the side x is the opposite side corresponding to angle 35°.

i.e. we will use sine trignometric ratio in the triangle to get the value of x.

We know that:

[tex]\sin 35=\dfrac{x}{8}ddd[/tex]

Since the sine of an angle is the ratio of opposite side to the hypotenuse of the right angled triangle.

i.e.

[tex]x=8\times \sin 35\\\\i.e.\\\\x=8\times 0.5736\\\\i.e.\\\\x=4.588[/tex]

which is approximately equal to 4.59  units.

There were 3 different fish caught, Salmon, Herring and Flounder.

4/9 were Herring, 2/9 were Salmon, 4/9 +2/9 = 6/9

This means 3/9 were Flounders ( 3/9 + 6/9 = 9/9 = 1)

3/9 can be reduced to 1/3.

1/3 of the fish were Flounders.

Divide the amount of flounders by the portion caught:

12 / 1/3 = 12 * 3/1 = 36 total fish.

Now you have total number of fish, multiply the total by each portion for each type of fish.

Total fish = 36

Herring = 4/9 x 36 = 16

Salmon = 2/9 x 36 = 8

Answer:

8.4

Step-by-step explanation:

hope it helped

Check the picture below.

Answer:

False

Step-by-step explanation:

Using the trigonometric identities

• sin²x + cos²x = 1

• secx = [tex]\frac{1}{cosx}[/tex]

Consider the left side

sec²x(1 - sin²x)

= [tex]\frac{1}{cos^2x}[/tex] × cos²x = 1

The correct identity is

sec²x(1 - sin²x) = 1

Answer:

102 students

Step-by-step explanation:

Note that 65% and 71% are both 1 standard deviation from the mean (71%).  According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.

68% of 150 students would be 0.68(150 students) = 102 students

68% of 150 students would be 0.68 (150 students) is, 102 students.

According to the question:

65% and 71% are both 1 standard deviation from the mean (71%).

According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.

68% of 150 students would be 0.68(150 students) = 102 students.

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A destructive earthquake happens once per year.

The exponential equation would be f(x) = 1-e^-x

The probability of going 3 months out of a year would be

P(X≥3/12)  ( divide 3 months by 12 months per year).

Now x equals 3/12

Now you have

P = 1-(1-e^-3/12)

= e^-1/4

= 0.7788

The probability that at least 3 months elapse would be 0.7788

(Round answer as needed).

The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is; 0.7788

We are told that a destructive earthquake happens once per year.

Thus, the exponential equation in this scenario is;

f(x) = 1 - e⁻ˣ

Thus, the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is given as;

P(X ≥ ³/₁₂)  since 12 months make a year

This will be;

P(X ≥ ³/₁₂) = 1 - (1 - e^(⁻³/₁₂))

P(X ≥ ³/₁₂) = e^-1/4

P(X ≥ ³/₁₂)= 0.7788

In conclusion, the probability that at least 3 months elapse would be 0.7788

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Answer:

C

Step-by-step explanation:

Since we are dealing with recursive equations, we can use a simple format.

[tex]a_{1}=x \\ \\ a_{n}=a_{n-1}+y[/tex]

x is the starting value and y is the change.

We can see that the change is -5.6 since 5.6 is being subtracted from each term each time.

So the equation would be

[tex]a_n=a_{n-1}-5.6[/tex]

We can check this by plugging in the numbers.

Let's see if -8.3 works, which is the 2nd term in the equation.

[tex]a_2=a_{2-1}-5.6 \\ \\ -8.3=a_{1}-5.6 \\ \\ -8.3=-2.7-5.6 \\ \\ -8.3=-8.3[/tex]

Therefore, the recursive rule is the third one.

Answer:

The picture where the red image is the skinniest

Step-by-step explanation:

The graph P(x) is the parent graph for all absolute functions. It has a vertex of (0,0) and has the following points:

x      f(x)

-2      2

-1       1

0       0

1         1

2       2

The image of l(x) = 12P(x) changes the points of the function to

x      f(x)

-2      24

-1        12

0       0

1        12

2       24

This makes the graph much skinnier. The graph with the skinniest red graph is the graph.

Answer:

Step-by-step explanation:

The parent function is

[tex]P(x)=|x|[/tex]

(Remember, a parent function refers to the simplest function of its type)

The image function is

[tex]I(x)=12P(x)[/tex]

Which is [tex]I(x)=12|x|[/tex].

Observe in the image attached, the image function is vertically stretched by a factor of 12.

Therefore, the right answer is the second graph.

ANSWER

[tex]x ^{2} = - 4(y - 1).[/tex]

EXPLANATION

Since the parabola has the (0, 0) and the directrix at y=2.

The equation is of the form

[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]

where (h,k) is the vertex.

The vertex is half way between the directrix and the focus.

The vertex will be at (0,1)

and is the distance from the vertex to the focus which is 1.

[tex]{(x - 0)}^{2} = - 4(1)(y - 1)[/tex]

[tex]x ^{2} = - 4(y - 1)[/tex]

There are two possible ways for X=1: first light is green and second is red OR first light is red and second is green. The probabilities for these two options are to be summed: 0.6*0.4 + 0.4*0.6 to give the probability of exactly one light being green, namely 0.48.

P(X = 1) = 0.48

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

"It is a probability distribution that gives only two possible results in an experiment, either success or failure. "

[tex]P(x)=n_C_x\times (p)^{x}\times (q)^{n-x}[/tex], here n is the total number of outcomes, 'p' is the probability of success and 'q' is the probability of failure

For given example,

The probability that traffic lights on a certain road will be green is 0.6

This means, the probability  of success (p) = 0.6

So, the probability of failure (q) = 1 - p

q = 0.4

When a driver on that road approaches two traffic lights in a row, X is the number of traffic lights that are green.

here, n = 2, p = 0.6, q = 0.4, x = 1

Using the formula of Binomial distribution the required probability is,

[tex]P(x=1)=2_C_1\times (0.6)^{1}\times (0.4)^{2-1}\\\\P(x=1)=\frac{2!}{1!\times (2-1)!}\times 0.6\times 0.4^1\\\\P(x=1)=2\times 0.6\times 0.4\\\\\bold{P(x=1)=0.48}[/tex]

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Answer:

Step-by-step explanation:

[tex]\sum\limits_{n=1}^{42}2n-3\\\\a_n=2n-3\\\\a_{n+1}=2(n+1)-3=2n+2-3=2n-1\\\\a_{n+1}-a_n=(2n-1)-(2n-3)=2n-1-2n+3=2=constant\\\\\text{Therefore it's an arithmetic sequence with first term}\\\\a_1=2(1)-3=2-3=-1\\\\\text{and common difference}\\\\d=2[/tex]

[tex]\text{The formula of a sum of terms of an aithmetic sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{Substitute:}\\\\n=42,\ a_1=-1,\ d=2:\\\\S_{42}=\dfrac{2(-1)+(42-1)(2)}{2}\cdot42=[-2+(41)(2)](21)=(-2+82)(21)\\\\=(80)(21)=1680[/tex]

Answer:

h = 10.92 m.

Step-by-step explanation:

The small triangle on the left is similar to the whole triangle, so:

12/20 = h/18.2

h = 12*18.2 / 20

h = 10.92 m.

Answer:

The maximum number of turns is 3

Step-by-step explanation:

The given function is

[tex]f(x)=x^4-x^3+3x+1[/tex]

The degree of this polynomial is 4.

If the degree of a given polynomial is n, then the polynomial has at least n-1 turns.

Therefore the number of turns of this 4th degree polynomial is at least 3.