(Subtracting rational coefficients-Mixed numbers)

Simplify by combining like terms:

1/3k - 8 3/4k

[?] ?
_k
?

Answer:

18.8 inches

Step-by-step explanation:

The circumference is [tex]\displaystyle{C = 2\pi r}[/tex]. The diameter is two times of radius which can be expressed as [tex]\displaystyle{d = 2r}[/tex].

We can rewrite the equation of circumference as [tex]\displaystyle{C = \pi d}[/tex]. Thus, substitute d = 6 in:

[tex]\displaystyle{C = 6\pi}\\\\\displaystyle{C = 18.849}[/tex]

Rounding to the nearest tenth, we will get:

[tex]\displaystyle{C = 18.8 \ \sf \ inches}[/tex]

Hence, the circumference is 18.8 inches.

Terminal point: (0, 1); sinФ = 1 ⇒ A

On a unit circle Ф = 90°

Using the second rule listed above

The terminal point is (0, 1)

sinФ = 1

Terminal point: (0, 1); sinФ = 1

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The value of the stock a year ago is $7778

The given parameters are:

Depreciation rate, r = 10%

Value of investment today, V(t) = $7000

The value of the stock a year ago is then calculated as:

Value of investment today = Value of investment last year * (1 - Depreciation rate)

Substitute the known values in the above equation

7000 = Last year * (1 - 10%)

Evaluate the difference of 1 and 10%

7000 = Last year * (90%)

Divide both sides by 90%

Last year = 7778

Hence, the value of the stock a year ago is $7778

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Answer:

Step-by-step explanation:

98-7=91

165-9=156

(91/156)/13=7/12

Answer = 13

It is divided by a positive integer a, which will equal the number 13.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the data provided by the question,

The number are 98 and 165.

The remainders are 7 and 9.

So, the actual number is,

98 - 7 = 91 and,

165 - 9 = 156

They are divided by the number 13, so the value of a will be equal to 13.

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Step-by-step explanation:

we know from the laws of motion that in the equation

h = 20t - 1.86t²

the gravitational acceleration is in the factor of the t² term.

h = v0t + 1/2 × g × t²

v0 being the initial velocity (20 m/s).

and we can therefore see, that the gravitational acceleration "a" on Mars is 2×1.86 = 3.72 m/s²

(a)

the velocity v after 2 seconds is (first law of motion)

v = v0 + at = 20 - 3.72×2 = 12.56 m/s

gravity pulling down, so negative acceleration.

(b)

first we need the time when the rock is at 25 m.

25 = 20t - 1.86t²

0 = -1.86t² + 20t - 25

the solution to a quadratic equation is always

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -1.86

b = 20

c = -25

t = (-20 ± sqrt(400 - 4×-1.86×-25))/(2×-1.86) =

= (-20 ± sqrt(214))/-3.72

t1 = (-20 + 14.62873884...)/-3.72 =

= 1.443887409... s ≈ 1.44 s

t2 = (-20 - 14.62873884...)/-3.72 =

= 9.308800763... s ≈ 9.31 s

that means, on its way up the rock reached 25m after

1.44 s.

on its way down the rock reached 25 m after

9.31 s.

velocity 0 (the rock came to a stop before falling back down) was after

0 = 20 - 3.72t

3.72t = 20

t = 20/3.72 = 5.376344086... s

that means the rock was falling after this point back to the ground and was gaining speed again.

that accelerating phase until the rock was again at 25 m was

9.308800763... - 5.376344086... = 3.932456677... s

long

the velocity at these points was

v-up = 20 - 3.72×1.443887409... = 14.62873884... m/s ≈

≈ 14.63 m/s

v-down = 0 + 3.72×3.932456677... = 14.62873884... m/s ≈

≈ 14.63 m/s

as expected : the rock did a perfectly symmetric flight path between the two 25 m marks.

so time and speed on both sides had to be identical.

but we have proven it.

Answer:

a)  12.56 m/s

b) up:  14.63 m/s (2 d.p.)

   down:  -14.63 m/s (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^{-1}$ (meters per second)\\v = final velocity in m s$^{-1}$ (meters per second)\\a = acceleration in m s$^{-2}$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}[/tex]

The average gravitational acceleration on Mars is 3.721 m/s² (about 38% of that of Earth).  The fact that the rock is thrown from the surface of Mars rather than the surface of Earth is of no consequence when using the equations of constant acceleration (SUVAT equations) as long as acceleration is not used in the calculations.

Given:

[tex]s=20t-1.86t^2, \quad u=20, \quad t=2[/tex]

[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies 20(2)-1.86(2)^2 & = \dfrac{1}{2}(20+v)(2)\\\\32.56 & = 20+v\\\\v & = 32.56-20\\\\v & = 12.56\:\: \sf m/s\end{aligned}[/tex]

Therefore, the velocity of the rock after 2 s is 12.56 m/s.

Find the time when the height of the rock is 25 m:

[tex]\begin{aligned}20t-1.86t^2 & = s\\\implies 20t-1.86t^2 & = 25\\1.86t^2-20t+25 & = 0\end{aligned}[/tex]

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]a=1.86, \quad b=-20, \quad c=25[/tex]

[tex]\implies t=\dfrac{-(-20) \pm \sqrt{(-20)^2-4(1.86)(25)} }{2(1.86)}[/tex]

[tex]\implies t=\dfrac{20 \pm \sqrt{214}}{3.72}[/tex]

[tex]\implies t=9.308800763..., 1.443887409...[/tex]

Therefore, the height of the rock is 25 m when:

To find the velocity (v) of the rock at these times, substitute the found values of t into the equation, along with s = 25 and u 20 m/s:

[tex]\begin{aligned}\textsf{Using }\: s&=\dfrac{1}{2}(u+v)t\\\\\implies v & = \dfrac{2s}{t}-u\\\\v & = \dfrac{2(25)}{t}-20\\\\v & = \dfrac{50}{t}-20\\\\\end{aligned}[/tex]

When t = 1.443887409...s

[tex]\implies v=\dfrac{50}{1.443887409...}-20=14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]

When t = 9.308800763...s

[tex]\implies v=\dfrac{50}{9.308800763...}-20=-14.63\:\: \sf m/s \: \:(2\:d.p.)[/tex]

Therefore, the velocity of the rock when its height is 25 m is:

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Hello,

The triangle be right only if : 18² = 8² + 12²

We have : 18² = 18 × 18 = 324

and 8² + 12² = 8 × 8 + 12 × 12 = 208

324 ≠ 208 → the triangle can not be a right triangle

The probability that a randomly selected study's participant was less than 4 is 0.2266.

Given that:

mean = 5.8

standard deviation = 2.4

a) P(x < 4) = P[(x - mean ) /sd < (4 - 5.8) / 2.4]

= P(z < -0.75)

Using z table,

= 0.2266

b) P(4 < x < 6) = P[(4 - 5.8)/ 2.4) < (x - \m ) /sd < (6 - 5.8) / 2.4) ]

= P(-0.75 < z < 0.08)

= P(z < 0.08) - P(z < -0.75 )

Using z table,

= 0.5319 - 0.2266

= 0.3053

c) P(x > 8) = 1 - p( x< 8)

=1- p P[(x - \m ) / sd< (8 - 5.8) / 2.4]

=1- P(z < 0.92)

Using z table,

= 1 - 0.8212

= 0.1788

Lastly, there are no unusual events because all the probabilities are greater than 0.05.

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Answer: 5 times

Step-by-step explanation: The distance from his house to school and back is 0.4 km. Since he traveled 2km in a week, we have to divide 2 by0.4. 0.4x5 = 2 so he went to school 5 times a week.

[tex]\stackrel{\stackrel{total~amount}{goal}}{481}~~ = ~~22(lawn)\implies \cfrac{481}{22}=lawn\implies \stackrel{rounded}{22}\approx lawn[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

[tex]\qquad \sf  \dashrightarrow \: 2b = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = 6[/tex]

length of conjugate axis is :

[tex]\qquad \sf  \dashrightarrow \: 2a = 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 4[/tex]

Equation of hyperbola ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]

plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]

Answer:

[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Step-by-step explanation:

Standard form equation of a vertical hyperbola

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]

[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Answer:

1/19

Step-by-step explanation:

The number in the set that are a multiple of both 4 and 6 is 12.

This is one number out of the 19 numbers in the set, so the probability is 1/19.

Answer:

  $264.78

Step-by-step explanation:

The government pays the interest on Briana's loan while she is in school. Her monthly payments will be for a loan of $26,000. The amount of the payment can be found from the amortization formula, or using a calculator or spreadsheet.

For a loan of principal amount P at annual rate r for t years, the monthly payment is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t)) = $26000(0.04125/12)/(1 -(1 +0.04125/12)^(-120)) = $264.78

Briana's monthly payment after she graduates is $264.78.

simple interest= principal x time x rate/100

Answer:

25

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence:

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

where:

Given values:

Substitute the given values into the formula and solve:

[tex]\implies a_5=400(0.5)^{5-1}[/tex]

[tex]\implies a_5=400(0.5)^{4}[/tex]

[tex]\implies a_5=400(0.0625)[/tex]

[tex]\implies a_5=25[/tex]

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Answer:

45 405 415 425 435 445

Step-by-step explanation:

this are the pattern of 6 numbers multiplying by number 5 to get the number starts with 4

Answer:

4,20,100,500,1500,8500.

Step-by-step explanation:

Answer: If one angle of a parallelogram is a right angle, then all other angles would also be right angles and the parallelogram would be a rectangle.

The answer to the question is B. The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.

This is the plot that shows the relationship between two different variables along a straight line. All of the points that are known to have a relationship between these variables would fall under this line. Other parts that fall outside the line are regarded as the outliers in the plot.

In this particular question, the outlier is seen to be outside of the critical values so we have to conclude that the solution is B. We fail to reject the null hypothesis.

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Answer: tan 1 radians = 1.557, tan 1 degrees = 0.017

Answer:

4days atlases in the week

Quantity             day

  25------------------1

 1000---------------x

We solve

                  [tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]

Answer: To spend $1,000 it will take 40 days.

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Hey there!

8!
= 8(7)(6)(5)(4)(3)(2)(1)

= 56(6)(5)(4)(3)(2)(1)

= 336(5)(4)(3)(2)(1)

= 1,680(4)(3)(2)(1)

= 6,720(3)(2)(1)

= 20,160(2)(1)

= 40,320(1)

= 40,320

Therefore, your answer should be:

40,320

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

From the given functions, of the cost, c(x) = 300 + 260•x, and revenue, r(x) = 300•x - x², we have;

First part;

The values of x to break-even are;

x = 30, or x = 10

Second part;

The profit function, P(x) is presented as follows;

P(x) = x•(40 - x) - 300

Third part;

The cost is c(x) = 300 + 260•x

Revenue is r(x) = 300•x - x²

First part;

At the break even point, we have;

Which gives;

300 + 260•x = 300•x - x²

x² + 260•x - 300•x + 300 = 0

Factoring the above quadratic equation gives;

x² - 40•x + 300 = (x - 30)•(x - 10) = 0

At the break even point, x = 30, or x = 10

The values of x at the break even point are;

Second part;

Profit = Revenue - Cost

The profit function, P(x), is therefore;

P(x) = r(x) - c(x)

Which gives;

P(x) = (300•x - x²) - (300 + 260•x)

P(x) = 300•x - x² - 300 - 260•x

P(x) = 300•x - 260•x - x² - 300

P(x) = 40•x - x² - 300

The profit function is therefore;

Third part;

When 10 more units are sold than the break even point, we have;

x = 30 + 10 = 40 or x = 10 + 10 = 20

The profit at x = 40 or x = 20 are;

P(40) = 40•(40 - 40) - 300 = -300

When the number of units sold, x = 40, the profit is, P(40) = -($300) unexpected loss

At x = 20, we have;

P(20) = 20•(40 - 20) - 300 = 100

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Answer:

shown below

Step-by-step explanation:

Look at the white squares, count them. 1, 2, 3. the next will be 4 and 5. draw 4 white squares, then house it in black squares like the others. to know if u did it right, count the black squares, there should be 8, then 9.

This count is a discrete random variable (option A).

A discrete random variable is a variable that contains integers that can only be a limited number of possible values.  A discrete random variable is can contain only a finite set of numbers .

An example of discrete random variable is the number of students in the first period class. It is impossible for the number of students in the class to go on indefinitely.

Discrete random variable has the following properties:

A continous random variable is a variable that has an infinite number.

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Answer:

5.5 hours

Step-by-step explanation:

I am going to assume that a helmet is necessary prerequisite for renting the bike.

I also am assuming that the hourly rate can be turned into a sub hourly rate if the full hour isn’t used.

10+4.25h=33.38

4.25h=23.38

h=23.38/4.25

h=5.5

Answer:

37°

Step-by-step explanation:

• recall that the sum of the interior angles of a triangle

  is equal to 180°

Then

The measure of the two other angles :

= 180 - 106

= 74°

The measure of each of the equal angles :

= 74 ÷ 2

= 37°

Answer:

the 2 angles r 37

Step-by-step explanation:

the angles of triangle sums up to 180, and lets call the unknown angle x, since they're both equal, x+x=2x

so when 3 angles of triangle adds up, we get 180

106+2x=180

2x=180-106
2x=74, divide both sides by 2 to get x

x=74/2

x=37

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Answer:

Los números son 23 y 35.

Step-by-step explanation:

Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?

Set the numbers as x and y. Using the given information, we have two equations:

x+y=58

x=y+12

Solving using substitution, we have:

y+y+12=58 -> y=23

Substituting, x=23+12=35

The numbers are 23 and 35.