The graph shows the distance y, in centimeters, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x.

How many seconds are required for the pendulum to swing from its position furthest to the right to its position furthest to the left?

Answer:

B

Step-by-step explanation:

360/6

6 is number of sides

You get 60

Rotate twice to reach 120

Moving F Counter clockwise twice is where B was

The image of point F after the rotation of 120°, r(120°), will be point B.

So, we need to rotate point F a total angle of 120°.

As you can see, in the image we have 6 sections, and equally distributed in these 6 sections we will have an angle of 360° (a complete rotation). So each section has an angle of:

360°/6 = 60°.

Then a rotation of 120°  (two times 60°) will rotate the point F two sections counterclockwise. Then the image of the point after the rotation will be point B.

If you want to learn more about rotations, you can read:

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Answer:

The answer is B) 3

Step-by-step explanation:

The reason why is because 1 is less than OR equal to x and 3 is less than or equal to x and is x = 3 then it fits both descriptions the best.

Answer:

-3

Step-by-step explanation:

3 is the average rate of change for the exponential graph shown over the interval 1 ≤ x ≤ 3.

Start by determining the two distinct points: (1, 2) and (3, −4).

Therefore,  

Δf(x)

Δx

=  

−4 − 2

3 − 1

=  

−6

2

= −3

Answer:

The 24th Customer is the first to get two gift certificates.

Since, 2 x 2 x 2 x 2 x 3 = 24

The first customer to receive two gift certificates is the customer at the 24th position in the sequence of customers.

The LCM of 8 and 6 is 24. This means that the first customer to receive two gift certificates will be the one who appears at the 24th position in the sequence.

To calculate the position of this customer, we can consider the multiples of 24:

24, 48, 72, and so on.

The 24th customer is the first to receive two gift certificates, as they satisfy both the every-8th and every-6th customer criteria.

The Greatest Common Factor (GCF) and the Least Common Multiple (LCM) are fundamental concepts in number theory. The GCF of two or more numbers is the largest positive integer that divides all the given numbers without leaving a remainder. On the other hand, the LCM of two or more numbers is the smallest positive multiple that is divisible by all the given numbers.

In this scenario, the GCF and LCM were used to determine the customer who would receive two gift certificates. The GCF was not explicitly required to solve this particular problem, but it is a useful concept in various mathematical contexts.

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Complete Question:

To celebrate its grand opening, a store is giving -customers gift certificates. Which customer is the first to get two gift certificates? Every 8 th customer gets Every 6th customer gets a $10 gift certificate. 200 4-2 Find Greatest Common Factor and Least Common Multiple

Answer:

a) 43 m b) 55 m

Step-by-step explanation:

a) From question at t = 0, initial velocity [tex]V_{o}[/tex] = 15 m/s

   Using equation of motion, [tex]S = V_{o}t + \frac{1}{2} at^{2}[/tex] ; at t = 2 secs , a = 4 m/[tex]s^{2}[/tex]

    S = (15 x 2) + (0.5 X 4 x [tex]2^{2}[/tex])

    S = 30 + 8 = 38 m , Therefroe;

  car is (38 + 5)m from the sign post

  car is 43 m from the sign post at t = 2 secs

b) Also from equation of motion, [tex]V^{2} = V_{o} ^{2} + 2aS[/tex]

    [tex]25^{2} = 15^{2}[/tex] + (2 x 4 x S)

     625 - 225 = 8S

S = 50 m

 Car is (50 + 5) m from the sign post

Car is 55 m from the sign post at V = 25 m/s

At t=2s, the motorcyclist is at position 29m east of the signpost with a velocity of 23m/s. When his velocity is 25m/s, he is at a position 38.75m east of the signpost.

Given that the motorcyclist starts 5 m east of the signpost with an initial velocity of 15 m/s and a constant acceleration of 4.0 m/s2, we can use the equation of motion to find his position and velocity at any given time.

(a) At t=2s, the motorcyclist's position (x) and velocity (v) can be determined using the following two equations respectively:

(b) When the velocity is 25 m/s, the time can be calculated using the equation v = v0 + a*t. By setting v=25m/s, v0=15m/s, and a=4.0m/s2, we get t = (25m/s-15m/s) / 4.0m/s2 = 2.5s. Substituting this time into the position equation gives x = 5m + 15m/s*2.5s + 0.5*4.0m/s2*(2.5s)2, which results in the motorcyclist being at position 38.75 m.

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Answer:

Wm = 43.2 pounds

Step-by-step explanation:

If the ratio of the weight of an object on Mars to its weight on Earth is 9 to 25, this means that what on Mars weighs 9 units on earth weighs 25 units, therefore:

Data

ratio = 9/25

Weight on Mars (Wm) = ?

Weight on Earth (We) = 120 pound

Wm = (9/25)*120 pound = 43.2 pounds

Answer:

Constant of proportionality = 24

Equation: [tex]y=24x[/tex]

Step-by-step explanation:

Given:

'x' and 'y' are proportional to each other.

At [tex]x=3,y=72[/tex]

Now, for a proportional relationship, the constant of proportionality is given as the ratio of the two values of the two variables that are in proportion.

Here, 'x' and 'y' are in proportion. So, the constant of proportionality is given as:

[tex]k=\frac{y}{x}\\\\k=\frac{72}{3}=24[/tex]

Therefore, the constant of proportionality is 24.

Now, a proportional relationship in 'x' and 'y' is given as:

[tex]y=kx[/tex]

Now, plug in the given value of 'k' and complete the equation. This gives,

[tex]y=24x[/tex]

Therefore, the equation that relates 'x' and 'y' is [tex]y=24x[/tex]

Answer:

For the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

Hence the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let [tex]a_1=\frac{-2}{3}[/tex] ,[tex]a_2=-4[/tex] ,[tex]a_3=-24[/tex],...

First find the common ratio

[tex]r=\frac{a_2}{a_1}[/tex] here  [tex]a_1=\frac{-2}{3}[/tex] and,[tex]a_2=-4[/tex]

[tex]=\frac{-4}{\frac{-2}{3}}[/tex]

[tex]=\frac{4\times 3}{2}[/tex]

[tex]=\frac{12}{2}[/tex]

[tex]r=6[/tex]

[tex]r=\frac{a_3}{a_2}[/tex] here  [tex]a_2=-4[/tex] and [tex]a_3=-24[/tex]

[tex]=\frac{-24}{-4}[/tex]

[tex]=6[/tex]

[tex]r=6[/tex]

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

[tex]a_n=a_1r^{n-1}[/tex]

The formula which describes the given geometric sequence is

[tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...

[tex]=\frac{-2}{3}6^{x-1}[/tex] for x=1,2,3,...

Now verify that [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of [tex]a_1[/tex] in [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...

we get [tex]f(1)=-\frac{2}{3}(6)^{1-1}[/tex]

[tex]=-\frac{2}{3}(6)^0[/tex]

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

Therefore [tex]f(1)=-\frac{2}{3}[/tex]

put x=2 we get [tex]f(2)=-\frac{2}{3}(6)^{2-1}[/tex]

[tex]=-\frac{2}{3}(6)^1[/tex]

[tex]=-\frac{12}{3}[/tex]

Therefore [tex]f(2)=-4[/tex]

put x=3 we get [tex]f(3)=-\frac{2}{3}(6)^{3-1}[/tex]

[tex]=-\frac{2}{3}(6)^2[/tex]

[tex]=-\frac{2(36)}{3}[/tex]

Therefore [tex]f(3)=-24[/tex]

Therefore the sequence is f(1),f(2),f(3),...

Therefore  the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

Hence the formula [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence

Answer:

a

Step-by-step explanation:

Answer:

(x⁻¹)(x⁻⁵) = x⁻⁶

Step-by-step explanation:

When multiplying number with the same base, you add up their exponent.

(x⁻¹)(x⁻⁵) =

= x⁽⁻¹⁾ ⁺ ⁽⁻⁵⁾

= x⁻⁶

you can also write x⁻⁶ as 1/x⁶. The negative sign in the exponent just flip the numerator and denominator with each others.

Answer:

The answer to your question is   x⁻⁶ or 1/x⁶

Step-by-step explanation:

Multiplying exponents

-To multiply exponents they must have the same base and the result will be the base and the exponents will add.

Ex

              (a³)(a²)

base = a

exponents = 3 and 2

result     a³ ⁺ ²  = a⁵

In your question

             (x⁻¹)(x⁻⁵) = x⁻¹⁻⁵ = x⁻⁶ = 1/x⁻⁶

Answer:

Step-by-step explanation:

total height, H = 113 inches

height of each stair case, h = 7.25 inches

Number of stair case, n = total height / height of each stair case

n = 113 / 7.25 = 15.6

Answer:

Step-by-step explanation:

Simplify.

4n + 12 + 7n  

16n + 7

23n

11n + 12

4n + 19

Answer with Step-by-step explanation:

We are given that

DE

[tex]x''+x=2e^t[/tex]

Function:[tex]x=C_1sint+C_2cost+e^t[/tex]

We have to show that given function is  a solution of the equation for all values of the constants.

If given function is  solution of DE then it satisfied the given DE.

Differentiate  function w.r.t.t

[tex]x'=C_1cost-C_2sint+e^t[/tex]

Again differentiate w.r.t. t

[tex]x''=-C_1sint-C_2cost+e^t[/tex]

Substitute the values in the given DE

[tex]-C_1sint-C_2cost+e^t+C_1sint+C_2cost+e^t=2e^t[/tex]

LHS=RHS

Given function satisfied the given DE.Therefore, it is solution of given DE for all values of the constants.

Answer:

The data claims that 90% of the seeds are viable meaning that 90% of the seeds are likely to germinate and grow into healthy plants under good conditions.90% 0f 1000seeds gives 900seeds,and 903seeds germinated so the claim is true

Step-by-step explanation:

Total number of seeds=1000

Seeds that germinate =903

90% of 1000=>90/100×1000 =900seeds.

Bob can buy 15 cupcakes for the price of 18 cookies.

Step-by-step explanation:

Answer:

Additive inverses for complex numbers are just like they are for real numbers: they mean the number you'd add to get back to 0. Just like real numbers, this means that you change the signs. Thus, the additive inverse of -4+7i is 4-7i

hope it helps

Step-by-step explanation:

Answer:

Fractional form = [tex]\frac{95}{100}=\frac{19}{20}[/tex]

Percent form = 95%

Trisha got 95% of her problems correct.

Step-by-step explanation:

Given:

Total number of questions (N) = 100

Number of correct questions (C) = 95

Therefore, the ratio of the correct answers to the total number of problems is given by dividing the the number of correct questions by the total number of questions. This is given as:

Ratio expressed as a fraction = [tex]\frac{C}{N}=\frac{95}{100}=\frac{95\div 5}{100\div 5}=\frac{19}{20}(Simplest\ form)[/tex]

Now in order to express this ratio in percentage form, we need to multiply the given ratio by 100. This gives,

Ratio expressed as a percent = [tex]\frac{C}{N}\times 100=\frac{95}{100}\times 100=95\%[/tex]

Therefore, Trisha got 95% of her problems correct.

Answer:

1: the first one

2:the third one

3:the third one

Step-by-step explanation:

Tens is the correct answer

Answer:

i think it' =-8abc(a+b-c)

Step-by-step explanation:

Final answer:

In a time series, an explainable one-time variation is known as an outlier. Outliers can be important for understanding data, but they differ from inexplicable random components which include variations not explained by trend, cyclical, or seasonal patterns.

Explanation:

In the context of data patterns in a time series, a one-time variation that is explainable is usually referred to as an outlier. An outlier can be a potential key to understanding the data or it may be due to some abnormality or error. In a time series, data is analyzed over time to determine components such as the trend, cyclical, seasonal, and random components.

Trend component displays the long-term progression of the series, the cyclical component deals with fluctuations occurring at non-fixed intervals, the seasonal component reflects regular variations within a specific period, like quarters within a year, and the random component comprises those elements that cannot be attributed to the trend, cyclical, or seasonal patterns.

It's essential to distinguish outliers from the random components, which are, by definition, inexplicable variations. However, if an outlier can be explained by a particular event or change, it's not part of the random component but a distinct deviation from the expected pattern.

Answer:

Correct answer is (a). Simple random sampling

Step-by-step explanation:

Simple random sampling (SRS) is a statistical techniques used in choosing subset of members of the population randomly without given special priority to anyone to be chosen. It gives every members of the population equal chance.

By randomly selecting 6060 customers from the customer's database, Maytag has employed Simple Random Sampling method of survey.

Answer :

The required number is 2.

Step-by-step explanation:

Given : The sum of six fifths and six times a number is equal to four fifths subtracted from seven times the number.

To find : The number ?

Solution :

Let the number be 'x'.

The sum of six fifths and six times a number i.e.  [tex]\frac{6}{5}+6x[/tex]

Four fifths subtracted from seven times the number i.e. [tex]7x-\frac{4}{5}[/tex]

According to question,

[tex]\frac{6}{5}+6x=7x-\frac{4}{5}[/tex]

[tex]7x-6x=\frac{6}{5}+\frac{4}{5}[/tex]

[tex]x=\frac{10}{5}[/tex]

[tex]x=2[/tex]

The required number is 2.

answer is C: [tex]\frac{EF}{DF}[/tex]

Answer:option C is the correct answer

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle,

DF represents the hypotenuse of the right angle triangle.

With m∠θ as the reference angle,

EF represents the adjacent side of the right angle triangle.

DE represents the opposite side of the right angle triangle.

To determine Cos ∠θ, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos θ = EF/DF

Answer:

The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.

Step-by-step explanation:

We have attached the division for your reference.

Given:

Dividend = [tex]6x^3 + 11x^2 - 4x -4[/tex]

Divisor= [tex]3x - 2[/tex]

Explaining the division we get;

Step 1: First when we divide the Dividend [tex]6x^3 + 11x^2 - 4x -4[/tex] with divisor [tex]3x - 2[/tex] we will first multiply [tex]2x^2[/tex] with the divisor then we get the Quotient as [tex]2x^2[/tex] and Remainder as [tex]15x^2-4x-4[/tex]

Step 2: Now the Dividend is [tex]15x^2-4x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply [tex]5x[/tex] with the divisor then we get the Quotient as [tex]2x^2+5x[/tex] and Remainder as [tex]6x-4[/tex]

Step 3: Now the Dividend is [tex]6x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply 2 with the divisor then we get the Quotient as [tex]2x^2+5x+2[/tex] and Remainder as 0.

Hence The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.

Answer:

3/2

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

9 to 6 means  

                                                          [tex]\dfrac{9}{6}[/tex]

Now we will cancel that fraction - we will divide numerator and denominator both by 3:

9 divided by 3 equals 3

6 divided by 3 equals 2

Hence,

                                        [tex]\dfrac{9}{6} = \dfrac{3\cdot 3}{2\cdot 3} = \dfrac{3}{2}[/tex]

Answer:

a. Form B would be better because statistical methods can be applied to the ordinal data.

Step-by-step explanation:

Ordinal data can be ranked. This teacher evaluation can be ranked on a scale of 1-10 for example. Ordinal data can  provide good information about the choice of the person who is responding. And these informations are quantitative in nature.

Answer:

The length of the room in the drawing is 5 inches.

Step-by-step explanation:

Given:

Kenneth measured a hotel and made a scale drawing the scale he used was 1 inch= 4 feet.

The actual length of a room in the hotel is 20 feet.

Now, to find the length of the room in the drawing.

Let the length of the room in the drawing be [tex]x.[/tex]

The actual length of the room = 20 feet.

The scale used in drawing is 1 inch = 4 feet.

As, 1 inch is equivalent to 4 feet.

Thus, [tex]x[/tex] is equivalent to 20 feet.

Now, to get the length of the room in the drawing we use cross multiplication method:

[tex]\frac{1}{4} =\frac{x}{20}[/tex]

By cross multiplying we get:

[tex]20=4x[/tex]

Dividing both sides by 4 we get:

[tex]5=x[/tex]

[tex]x=5\ inches.[/tex]

Therefore, the length of the room in the drawing is 5 inches.

Answer:

x = 9

Step-by-step explanation:

if the perimeter os square JKLM is 48  

each side has 48/4

so each side has 12

now if JK is x + 3 = 12

we only need to solve that

x + 3 = 12

x = 12 -3

x = 9

Answer:

B. 9

Step-by-step explanation:

Answer:

11/92

Step-by-step explanation:

G = 11

R = 7

B = 6

P(b) = 6/24 = 1/4

P(g) = 11/23

P(blue first and then green(without replacement)) = 1/4 * 11/23

= 11/92

The probability of randomly selecting a blue marble followed by a green marble from a jar of 24 marbles (6 blue, 7 red, 11 green) is 11/92.

The number of outcomes considered favorable or desired is compared to the total number of outcomes possible. In this situation, we're interested in choosing a blue marble first, then a green marble. The total number of marbles is 11 green + 7 red + 6 blue = 24 marbles.

Initially, the probability of selecting a blue marble is 6/24 = 1/4

because there are 6 blue marbles out of a total of 24.

After taking one marble out (assuming it's blue), you have 23 marbles left, with 11 of them being green. So, the probability of selecting a green marble next is 11/23.

Therefore, the probability of both of these events happening (selecting a blue marble followed by a green marble) is found by multiplying these two probabilities together, which gives (1/4) * (11/23) = 11/92.

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Answer:

View graph

Step-by-step explanation:

we have that at constant speed the student and the pet must travel equal distances in equal times, so they must be in the middle of the distance with the same travel time

As can be seen in graph 2 the distance of P = -15 m, and that of S = 15, the sign is due to the orientation, P goes to the left and S to the right

Answer:

Step-by-step explanation:

An arc is a portion of the circle's circumference bounded by 2 radii

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle or angle which the 2 radii subtends at the center of the circle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 5 inches

θ = 170 degrees

Therefore,

Length of arc = 170/360 × 2 × π × 5

Length of arc = 4.7222π feet

rounding up to 2 decimal places, it becomes

4.72π feet