Choose the best definition for the following term: variable

Answer:

The height of the plank after the π/3 rotation motion is 8.464 ft

Step-by-step explanation:

The radius of the wheel = 4 ft

The elevation of the bottom of the wheel from the bottom = 1 foot

The angle to which the wheel is rolled = π/3 radians

The height of a rotating wheel is given by the following relation

f(t) = A·sin(B·t + C) + D

Where;

D = Mid line =  4 + 1 = 5 feet

B·t = π/3

C = 0

A = The amplitude = 4

Which gives;

f(t) = 4×sin(π/3) + 5 = 8.464 ft

The height of the plank after the π/3 rotation motion = 8.464 ft.

Answer:7 ft

Step-by-step explanation:

C

Answer:

B and C

Step-by-step explanation:

1/5 prefer apple juice

T = prefer orange juice

9/20 prefer apple or oranger juice

First, we can subtract 1/5 from 9/20 to get 1/4 (simplified)

Equation = 9/20  - 4/20 = 5/20 = 1/4

Plug it in:

A. 9/20 + 1/4 =1/5 (Incorrect)

B. 1/5 + 1/4 = 9/20 (Correct

C. 1/4 + 1/5 = 9/20 (Correct)

D. 1/4 - 1/5 = 9/20 (Incorrect)

Answer:

1/5 + t = 9/20

t + 1/5 = 9/20

Step-by-step explanation:

1/5 are apple + unknown for orange = apple + orange

1/5  + unknown = 9/20

Let t = unknown

1/5 + t = 9/20

order doesn't matter on the left side since we are adding

t+1/5 = 9/20

Answer: 161/13

Step-by-step explanation: 1. Multiply the denominator by The number

2. add the answer from step one to the numerator

3. Write the answer from step 2 over the denominator

Answer:

C. 1.01,1.01¯¯¯¯,2119

Step-by-step explanation:

1.01,1.01¯¯¯¯,2119

Is arranged from the least number to the greatest number.

It shows the numbers with decimals, and it showed the number with Dec again.

Then gave a space in between then the highest number in the least follows

So option c is the answer

-17 is a rational number

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Rational numbers have finite or recurring decimal expansions. Irrational numbers are numbers that can not be expressed as the ratio or fraction of two integers. Irrational numbers have non-terminating and non-repeating decimal expansions.

Whereby -17 can be expressed as the value -17/1, based on the definition of a rational number, -17 is a rational number

Learn more on rational numbers here: https://brainly.com/question/16933806

#SPJ6

Answer:

the answer is going to be A. -6x - 14 x+ 6

Answer:

20.96 m/s is the final speed.

Step-by-step explanation:

Given that:

Initial speed of the car = 8 m/s

Acceleration of the car = 1.8 m/[tex]s ^{2}[/tex]

Time for which the car accelerates = 7.2 seconds

To find:

The speed of car after accelerating for 7.2 seconds at an acceleration of 1.8 m/[tex]s ^{2}[/tex] = ?

Solution:

First of all, let us have a look the formula given for the final velocity of an object with given initial speed, acceleration and time:

[tex]v=u+at[/tex]

Where [tex]v[/tex] is the final speed of object

[tex]u[/tex] is the initial speed of an object

[tex]a[/tex] is the acceleration of object and

[tex]t[/tex] is the time

Here, [tex]u = 8\ m/s[/tex]

[tex]a = 1.8\ m/s^{2}[/tex] and

[tex]t = 7.2\ seconds[/tex]

To find:

[tex]v = ?[/tex]

Let us put all the given values in the formula:

[tex]v =8+1.8 \times 7.2\\\Rightarrow v =8+12.96\\\Rightarrow \bold{v =20.96\ m/s}[/tex]

So, the answer is:

20.96 m/s is the final speed.

Answer: x=-6

Step-by-step explanation:

Undefined slopes are vertical lines, so there's no y variable in the equation. so you look at the point (-6, -8) and take out the y, which is negative eight. So your answer is negative six.

The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Then the equation of the line that passes through the point (-6, -8) and has an undefined slope will be

y + 8 = m (x + 6)

The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer:

- 19

Step-by-step explanation:

Let's consider the equation as ;

y = 3x + c

( 6, -1 ) satisfies the equation ;

-1 = 3( 6) + c

c = - 18 - 1

c = -19

So the slope - intercept is (- 19)

Answer:

16 mi

Step-by-step explanation:

To find how many miles you could travel with one gallon, you want to multiply both sides of the equation by 64. This will make '1/64' to 1, so the answer should be 1/4 * 64 = 16.

Answer:

C

Step-by-step explanation:

3-(-5=8

3+5=8

They are on the same x axis so all you have to do is add 3 and 5 together.

Answer:

c) Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.

Step-by-step explanation:

a) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.

b) Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.

c) Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.

d) Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8

Answer:

[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

[tex]\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}[/tex]

In order to estimate the point along the shore, x meters from B, the runner should  stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

=[tex]\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0[/tex]

[tex]-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0[/tex]

[tex]\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]

[tex]\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]

[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}[/tex]

[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}[/tex]

squaring both sides; we get

[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}[/tex]

[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}[/tex]

By cross multiplying; we get

[tex]49x^2 = 25(54^2+x^2)[/tex]

[tex]49x^2 = 25 \times 54^2+ 25x^2[/tex]

[tex]49x^2-25x^2 = 25 \times 54^2[/tex]

[tex]24x^2 = 25 \times 54^2[/tex]

[tex]x^2 = \dfrac{25 \times 54^2}{24}[/tex]

[tex]x =\sqrt{ \dfrac{25 \times 54^2}{24}}[/tex]

[tex]x =\dfrac{5 \times 54}{\sqrt{24}}[/tex]

[tex]x =\dfrac{270}{\sqrt{4 \times 6}}[/tex]

[tex]x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}[/tex]

[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]

Answer:

x = - 12

Step-by-step explanation:

2                5

--- x - 2 =   --- x

3                6

2x             5

---  - 2 =  ------ x

3             3 * 2

(2x) - 3 * 2          5x

----------------  =  --------

       3               2 * 3

x = - 12

Answer:

volume = 33965.39

Step-by-step explanation:

Attached below is a detailed solution of the problem and the required sketch

volume of this solid is calculated integrating about the axis of : 5,3

Y = In x = x = e^y

the shaded region in the sketch represent the region where the rotating takes place.

Answer:

Researcher B

Step-by-step explanation:

Power of statistics is the probability that a test will correctly reject a false null hypothesis.

This probability is more accurate with greater sample size as it is better representation of the population.

Therefore researcher B has more power to detect an effect since he has nearly twice sample size (40 vs 22)

Answer:

Q  has coordinates (qx+5, qy-5)

Step-by-step explanation:

Q  has coordinates (qx, qy)

we move 5 units to the right so add 5 to the value of x

Q  has coordinates (qx+5, qy)

we move 5 units down so subtract 5 from the value of y

Q  has coordinates (qx+5, qy-5)

==================================================

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(x) = 5/12

x = arccos(5/12)

x = 65.375681647836 which is approximate

x = 65.4 after rounding to one decimal place

Make sure your calculator is in degree mode. The arccosine function is the same as the inverse cosine function (shortened to [tex]\cos^{-1}[/tex] ).

Answer:

There is an accident ahead, which often causes traffic to slow.

Step-by-step explanation:

Looking at the question closely, we understand that the traffic jam occurred at a time that is not generally regarded as a rush hour.

A traffic jam due to road repair is not really an option because roads are closed during repairs. Shop malls announce their special sales days ahead of time so that many people will hear about it.

However, it is likely that an accident occurred. An road accident may suddenly occur on an otherwise less busy road. This often leads to an unusual delay in traffic irrespective of the hour of the day when it occurs.

Answer:

D

Step-by-step explanation:

3x - 4 < 8

Add 4:

3x - 4 + 4 < 8 + 4

3x < 12

Divide by 3:

3x / 3 < 12 / 3

x < 4

Answer:

D. x<4

Step-by-step explanation:

3x-4<8

3x<8+4

3x<12

x<4

Hope this helps ;) ❤❤❤

Answer:

m = -3

b = 0

equation of line

y = -3x

Step-by-step explanation:

in the  the equation in the form y = mx +b

m is the slope

b is the y intercept.

__________________________________________________

given slope = -3

thus,

m = -3

the required equation of line is

y = mx +b  

put m = -3

y = -3x + b

to find b , we put x = -2, y = -6 as this equation contains point (-2,-6).

-6 = -3*-2 + b

=> -6 = -6 + b

=> b = -6 + 6 = 0

thus. m = -3

b = 0

equation of line

y = -3x

Answer:

x = -1/2

Step-by-step explanation:

Step 1: Write out equation

9 - 8x - 8 - 2x = 4

Step 2: Combine like terms (x)

9 - 10x - 8 = 4

Step 3: Combine like terms (constants)

-10x - 1 = 4

Step 4: Add 1 to both sides

-10x = 5

Step 5: Divide both sides by -10

x = -5/10

Step 6: Simplify

x = -1/2

Answer:

divide both sides by 23

making it to be 0.26

The value of x from the equation 23x =6 is x= 6/23.

To solve for the value of x in the equation 23x = 6, we need to isolate x on one side of the equation.

Divide both sides of the equation by 23:

(23x) / 23 = 6 / 23

Simplifying:

x = 6 / 23

Therefore, the value of x is 6 divided by 23, which can be left as a fraction or decimal depending on the desired form.

Learn more about Equation here:

https://brainly.com/question/29538993

#SPJ6

Answer:

A) P_n = 1.06(P_(n-1)) - 80

B) 887 fishes

Step-by-step explanation:

A) We are told that the lake initially contains 1000 fishes.

Thus, P_o = 1000

Now, the number of fishes increases by 6% each month

Thus, after n months, we have;

P_n = P_(n-1) + 0.06P_(n-1)

P_n = 1.06P_(n-1)

Where P_(n-1) is the population of fish in the previous month.

We are told that 80 fishes are lost each month.

Thus;

P_n = 1.06(P_(n-1)) - 80

B) We want to find out how many fishes we have after 5 months.

Thus;

P_5 = 1.06(P_(5-1)) - 80

P_5 = 1.06(P_4) - 80

We don't know P_4,thus;

P_o = 1000

P_1 = 1.06(1000) - 80 = 980

P_2 = 1.06(980) - 80 = 958.8

P_3 = 1.06(958.8) - 80 = 936.328

P_4 = 1.06(936.328) - 80 = 912.50768

Thus,

P_5 = 1.06(912.50768) - 80 = 887.2581408 ≈ 887

Answer:

The mean is 7.1

The median IS NOT 1.6 (its 8)

The mode IS NOT 0 (its 8)

Step-by-step explanation:

The true statement is , The mean is 7.1.

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

The median is the middle value when a data set is ordered from least to greatest.

The mode is the number that occurs most often in a data set.

here, we have,

given data, group of numbers (8, 12, 4, 8, 6, 0, 9, 11, 3, 10)

now, we get,

The mean is 7.1.

The median IS NOT 1.6 (its 8)

The mode IS NOT 0 (its 8).

hence, The true statement is , The mean is 7.1.

To learn more on mean, median, mode click:

https://brainly.com/question/13829039

#SPJ2

Answer:

10

Step-by-step explanation:

This expression uses the idea of exponential edition.  The basis is, when you have the same base number being multiplied, you can add the exponentials.  

Consider the case of 2 * 2.  We know this to be 4.  When writing 2 * 2, you can write this as 2^1 * 2^1 == 2^(1+1) == 2^2 == 4.  See how we added the powers to get the new exponential?

We will apply this same idea here.

10^(1/2) * 10^(1/2) == 10^(1/2 + 1/2) == 10^(1) == 10.

So, the simplified expression is 10.

Cheers.

Answer:

25/36

Step-by-step explanation:

Solved in steps:

Simplest fraction is 25/36

Answer:

lines CD, AE, and BD are half the length of CD

Step-by-step explanation:

All circles will have the same radius "r"

then CD = 4r

½CD = 2r

CB = AE = BD = 2r

The line CD has two circles which are equidistant from the points C and D and both meet at point B.

Point B is the midpoint of Line CD dividing line CD into two equal halves.

The line segments AE , CB and BD are line segments that are half of the length of line CD.

CB and BD form the diameters of the circles.

A diameter is a line that divides the circle into 2 equal halves. It passes through the center of the circle and joins one end point to another.

A radius is the distance from the circumference to the center of the circle.

A diameter is made up of two radius.

In the figure two equal diameters divide the line segment into two equal parts.

The third circle has the diameter AE which has radius AB and AE which are also the radius of the other two circles.

Hence the three circle are equal .

Hence the line segments AE , CB and BD are line segments that are half of the length of line CD.

https://brainly.com/question/15379859

https://brainly.com/question/15441177

Answer:

1.37

Step-by-step explanation:

The student can give only 0.139 % answer correctly.

The first and second questions have four answer choices,

Probability of first and second question answer correctly is,

                [tex]P_{1}=\frac{1}{4}*\frac{1}{4} =\frac{1}{16}[/tex]

The third and fourth questions have three answer choices,

Probability of third and fourth question answer correctly is,

           [tex]P_{2}=\frac{1}{3} *\frac{1}{3}=\frac{1}{9}[/tex]

The last question has five answer choices.

Probability of fifth question answer correctly is,

              [tex]P_{3}=\frac{1}{5}[/tex]

The probability of corrected answer is,

        [tex]P=P_{1}*P_{2}*P_{3}\\\\P=\frac{1}{16} *\frac{1}{9}*\frac{1}{5}=\frac{1}{720}[/tex] = 0.139 %

Hence, The student  can give only 0.139 % answer correctly.

Learn more:

https://brainly.com/question/10734660

Answer:

50

Step-by-step explanation:

first you plug in 4 for x and -3 for y. then you solve

Answer: 50 and 5, respectively

Step-by-step explanation:

For this problem, we are given x and y. With the x and y value given, all we have to do is to plug them into the expressions and solve.

5(x-2y)                        [plug in x=4 and y=-3]

5((4)-2(-3))                 [combine like terms by using order of operations]

5(4+6)

5(10)=50

-----------------------------------------------------------------------------------------------------------

2x+y                            [plug in x=4 and y=-3]

2(4)+(-3)                     [combine like terms by using order of operations]

8-3=5

Now that we have plugged in x=4 and y=-3 into the two expressions, we get 50 for the first expression and 5 for the second equation.

Answer:

56 different ways

Step-by-step explanation:

This is a combination question since it deals with selection. For example, if n objects is to be selected from a pool of r objects, this can be done in nCr different ways.

nCr = n!/(n-r)!r!

According to the question, If the police have 8 ​suspects, the different number of ways 5 can be selected for a line up is expressed as 8C5

8C5 = 8!/(8-5)!5!

8C5 = 8!/(3!)!5!

8C5 = 8*7*6*5!/3*2*5!

8C5 = 8*7*6/3*2

8C5 = 8*7

8C5 = 56 different ways

Hence, the selection of picking 5 for a line up out of 8 suspects can be done in 56 different ways.