You traveled 35 minutes at 21k(m)/(h) speed and then you speed up to 40k(m)/(h) and maintained this speed for certain time. If the total trip was 138km, how long did you travel at higher speed? Write your answer in minutes.

We can write the given statement as expression -

- 5 + (1/2)x = 3

Given is the statement -

"-5 increased by one-half of a number is a maximum of 3"

We can write it as an expression -

- 5 + (1/2)x = 3

Therefore, we can write the given statement as expression -

- 5 + (1/2)x = 3

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Answer:

3

Step-by-step explanation:

\( \frac{ {3} - 5 }{8 + 2} = \frac{ - 2}{1 0} = \frac{ - 1}{5} \)

The values are calculus in the vectors,

r(t)= <4t, 6t², 2t³>

r'(t)= <4, 12t, 6t²>

r''(t)= <0, 12, 12t>

T(1) = <4, 12t, 6t²>/13

r'(t)×r''(t) =<72t²,-48t, 48>

Given that,

The r(t)= <4t, 6t², 2t³>

We have to find r'(r),t(1), r''(t) and r'(t)×r''(t).

We know that,

Calculus is the mathematical study of change, much as geometry is the study of shape and algebra is the study of operations and how they are used to problem-solving.

r(t)= <4t, 6t², 2t³>

r'(t)= <4, 12t, 6t²>

r''(t)= <0, 12, 12t>

T(1) = r'(1)/||r'(t)||

T(1) = <4, 12t, 6t²>/√4²+12²+6²

T(1) = <4, 12t, 6t²>/√16+144+36

T(1) = <4, 12t, 6t²>/√136

T(1) = <4, 12t, 6t²>/13

r'(t)×r''(t) = \(\left[\begin{array}{ccc}i&j&k\\4&12t &6t^{2} \\0&12 &12t\end{array}\right]\)

=i(144t²-72t²)-j(48t-0)+k(48-0)

=72t²i-48tj+48k

=<72t²,-48t, 48>

Therefore, The values are calculus in the vectors,

r(t)= <4t, 6t², 2t³>

r'(t)= <4, 12t, 6t²>

r''(t)= <0, 12, 12t>

T(1) = <4, 12t, 6t²>/13

r'(t)×r''(t) =<72t²,-48t, 48>

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Answer:

Step-by-step explanation:

Given that the previous cost is

$216 per month

she expects an increase of 5% of the previous cost

therefore 5% of $216 is given as

=(5/100)*216

=0.05*216=10.8

Therefore she should be expected to pay extra $10.8 and the previous amount

hence the expected utilities each month is

=10.8+216=

=$226.8

Answer:

226.80 dollars

Step-by-step explanation:

VERY IMPORTANT

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

AOPS does not accept 226.8 dollars as an answer as I have tried. The solution that the system accepts is 226.80 dollars.

Answer:

80*5.2= 416

D: 416 miles

\( \frac{1}{ \sqrt{3} - 1 } \\ = \frac{1}{ \sqrt{3} - 1} \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } \\ = \frac{ \sqrt{3} + 1}{( \sqrt{3})^{2} - (1)^{2} } \\ = \frac{ \sqrt{3} + 1 }{3 - 1} \\ = \frac{ \sqrt{3} + 1}{2} \)

\( \frac{ \sqrt{3} + 1}{2} \)

Answer:

x=0

y=-3

Step-by-step explanation:

The Fourier series representation of the output y(t) is;

(a) y(t) = 0.097 cos(3πt - 67)

(b) y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

Given;

A causal continuous-time LTI system whose input x(t) and output y(t) are related by the following differential equation;

\(\frac{d}{dt}y(t) + 4y(t) = x(t)\)

By taking Laplace's Transform;

sY(s) + 4Y(s) = X(s)

Y(s)/X(s) = H(s) = 1/(s + 4)

(a) When input x(t) = cos3πt

∵ ω = 3π

H(jω) = 1/(jω + 4)

H(jω₁) = 1/\(\sqrt{w^2+4^2}\) = 0.097

∠H(jω) = -tan⁻¹(ω/4) = -67° = Ф₁

y(t) = H(jω₁)*cos(3πt + Ф₁)

→ y(t) = 0.097 cos(3πt - 67)

(b) When input x(t) = sin3πt + cos(6πt + π/4)

∵ ω = 6π

H(jω) = 1/(jω + 4)

H(jω₂) = 1/\(\sqrt{w^2+4^2}\) = 0.051

∠H(jω) = -tan⁻¹(ω/4) = -78° = Ф₂

y(t) = H(jω₁) * sin(3πt + Ф₁) +  H(jω₂) * cos(6πt + π/4 + Ф₂)

→  y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

The Fourier series representation of the output y(t) is;

y(t) = 0.097 cos(3πt - 67)

y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

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Answer:

hope this helps you out

it's 21 a or b

you can choose witch one you want to use

Step-by-step explanation:

there is 2 possible answers

To determine if x and y are proportional, we need specific values or a proportional relationship equation.

To determine whether x and y are proportional, we need to compare the ratio of their values. If the ratio of x to y remains constant as x and y vary, then they are proportional.

Mathematically, if x/y = k, where k is a constant, then x and y are proportional. However, without specific values or equations, it is not possible to ascertain their proportionality.

Without further information, we cannot determine whether x and y are proportional. Additional context, such as specific values or an equation relating x and y, is needed to make a conclusive statement about their proportionality.

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Diameter = 30

30/2 = 15 15 is the radius

To find area:

3.14 x 15 x 15 = 706.5

706.5 is the answer

The value of x and y in the angles are 15.6 and 10.5 respectively.

When parallel lines are cut by a transversal lines, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, line XD, TZ, YF and LP are parallel to each other.

WC is the transversal line.

Hence,

m∠CNL = 6x - 17.6

m∠FBH = 12y - 22

m∠THR = 3x + 29.2

Hence,

180 - (12y - 22) = 6x - 17.6(corresponding angles)

Corresponding angles are congruent

180 - 12y + 22 = 6x - 17.6

6x + 12y = 180 + 22 + 17.6

6x + 12y = 219.6

Therefore,

180 - (3x + 29.2) = 12y - 22 (alternate angles)

Alternate angles are congruent .

180 - 3x - 29.2 = 12y - 22

180 + 22 - 29.2 = 12y + 3x

172.8 = 3x + 12y

combine the equation

6x + 12y = 219.6

3x + 12y = 172.8

subtract equation(ii) from equation(i)

3x = 46.8

x = 46.8 / 3

x = 15.6

12y = 219.6 - 6(15.6)

12y = 219.6 - 93.6

12y = 126

y = 126 / 12

y = 10.5

Therefore,

x = 15.6

y = 10.5

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Given:

Greg wants to estimate the percentage of people who lease a car. He surveys 340 individuals and finds out that 90 lease a car

Required:

What is the sample propoertion for the success?

Explanation:

Total individual =340

Individual who lease car=90

Now,

90 out of 340 people lease car.

Fraction of people leasing car

Percent of people leasing car

Answer:

26.471 is the answer.

The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.

(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.

(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.

(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.

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The complete question is:

A kindergarten teacher has five books to distribute to 20 children in her class.

(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?

(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.

(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?

Answer:We know that 0 = tan-¹(0.52).

The tangent function gives the ratio of the opposite side to the adjacent side of a right-angled triangle. Therefore, we can use the inverse tangent function to find the angle when the opposite and adjacent sides are given.

So, we can write this equation as:

tan(0) = 0.52

To solve for 0, we need to take the inverse tangent of both sides of the equation:

tan-¹(tan(0)) = tan-¹(0.52)

0 = tan-¹(0.52) ≈ 27.4° (rounded to 1 decimal place)

Therefore, the value of 0 is approximately 27.4 degrees to 1 decimal place.

Step-by-step explanation:

Answer:

Commutative Property of Addition

Step-by-step explanation:

The commutative property states that you can change the order of the addends. For example, 4 + 7 = 7 + 4.

It is not the addition property of equality because this property states that whatever is added to one side of the equal sign must be added on the other side as well. For example, x - 5 = 8 is the same as x = 13 because we added 5 to both sides of the equation.

It is not the associative property because that states that you can change the grouping of the addends. For example, 3 + (7 + 29) = (3 + 7) + 29.

It is not the identity property because that states that a number plus 0 is still that number. For example, 54 + 0 = 54.

In the problem "3/5 + (-7/8) + 4/5 = 3/5 + 4/5 + (-7/8)" we are simply switching the 4/5 and the -7/8, so it is illustrated by the commutative property.

Answer:

B. (1.5, 2)

Step-by-step explanation:

Hope it helps!

Answer:

B

Step-by-step explanation:

The intersection of the two lines looks to be about (1.5 , 2)

Using the simplex method, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

To solve the linear program using the simplex method, we start by converting the problem into standard form with all constraints in the form of inequalities and non-negative variables. The initial tableau for the problem is as follows:

 |   x1  |   x2  |   s1   |   s2   |   b   |

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

z |  -3   |   6   |   0    |   0    |   0   |

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

s1|   5   |   7   |   1    |   0    |   35  |

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

s2|  -1   |   2   |   0    |   1    |   2   |

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

Next, we perform the simplex iterations to improve the objective function value. After performing the necessary row operations, we arrive at the final tableau:

 |   x1  |   x2  |   s1   |   s2   |   b   |

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

z |   0   |   1   |  3/2   |  -1/2  |   14  |

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

s1|   0   |   0   |   4    |   3    |   5   |

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

s2|   1   |   0   |  -1/2  |   5/2  |   3   |

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

From the final tableau, we can see that the optimal solution is z = 14, with x1 = 0 and x2 = 5. The decision variable x1 is at its lower bound, indicating that it is non-basic. Therefore, there are no alternative optimal solutions in this case.

In summary, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

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The equation of plane will be x+y-2z=4.

A plane in geometry can go on forever in two dimensions. The absence of width. An illustration of coordinate geometry is a plane. The coordinates of a point in a plane determine its position.

In mathematics, a plane is a two-dimensional, flat surface that never ends. A plane is a two-dimensional equivalent that includes three spatial dimensions, a line, and a point. In some higher-dimensional environments, planes can resemble subspaces, as though the room's walls had been greatly extended. These walls possess a distinct existence all their own, just as in the framework of Euclidean geometry.

The equation of plane can be used to represent a plane surface in three dimensions. There are numerous methods that can be used to find the equation for a plane depending on the input values given. The equation for the plane can be expressed in either cartesian form or vector form.

Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0

Now,

The solution is provided in image.

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Answer:

A scale factor of 2 could be in fact 4 because you can factor 2 twice to give you 4

Step-by-step explanation:

Answer:

≈ 44°

The correct answer is the second one

Step-by-step explanation:

Use trigonometry:

\( \cos(x°) = \frac{15}{21} \)

Use the reverse function (SHIFT, cos) on your calculator to find x:

\(x≈44°\)

Check the picture below.

\(\cos(x )=\cfrac{\stackrel{adjacent}{15}}{\underset{hypotenuse}{21}}\implies \cos(x)=\cfrac{5}{7}\implies x=\cos^{-1}\left( \cfrac{5}{7} \right)\implies x\approx 44^o\)

Make sure your calculator is in Degree mode.

Answer:

m = 2

Step-by-step explanation:

The number of cups of  marshmallows, m, needed for r  cups of Rice Krispy r is described by  the equation :

r= 1.5m ...(1)

We need to find the no. of marshmallows  are needed to mix with 3 cups of  Rice Krispies.

Pu r = 3 in equatin (1) :

\(m=\dfrac{r}{1.5}\\\\m=\dfrac{3}{1.5}\\\\m=2\)

So, there are 2 cups of marshmallows .

Answer:

the answer is 66feet

Step-by-step explanation:

can i get a brainliest plz

The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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Answer:

salary after 10: 66,000$

Step-by-step explanation:

43,000 + 2,500 x 10

Answer:

Salary after 10 years: 68000

Salary after t years: 25000

Step-by-step explanation: i just did it and got it right

Answer:

50 percent

Step-by-step explanation:

100 percent divided by 6 (the amount of data) is 16 2/3.

Each number represents 16 2/3 percent.

3 of the numbers are either 2 or 9.

16 2/3x3=50.001

The final answer is a 50% probability.

I think

Answer:

The two teachers are 26 meters apart. To calculate this, you can use the Pythagorean Theorem, which states that the distance between two points is equal to the square root of the sum of the squares of the differences between the coordinates of the two points. In this case, the coordinates of the math teacher are (10, 0) and the coordinates of the science teacher are (0, 24), so the distance between them is the square root of [(10-0)^2 + (0-24)^2] = √(100 + 576) = √676 = 26 meters.

We can use the Pythagorean theorem to solve this problem. Let's draw a diagram:

A (Amy)

/|

/ |

/ |10 meters

/ |

/____|

B C (science teacher)

We have a right triangle ABC, where AB = 10 meters and BC = 24 meters. We want to find the length of AC, which is the distance between the two teachers.

Using the Pythagorean theorem:

AC^2 = AB^2 + BC^2

AC^2 = 10^2 + 24^2

AC^2 = 676

AC = sqrt(676)

AC = 26 meters

Therefore, the two teachers are 26 meters apart.

As the age of the bus increases, the annual maintenance cost generally increases as well. Therefore, the estimated regression model is: y = a + bx = 883.5 + 253.17x where y is the annual maintenance cost and x is the age of the bus.

(a) The correct scatter chart is (i) which has age of bus as the independent variable. The scatter chart indicates there may be a linear relationship between age of bus and annual maintenance cost.

(b) To develop an estimated regression equation, we can use the following steps:

X = (1+2+2+2+2+3+4+4+5+5)/10 = 3

Y = (350+370+480+520+590+550+750+800+790+950)/10

= 643

Calculate the deviations of age of bus (x) and annual maintenance cost (y) from their respective means (X and Y).

x - X: -2, -1, -1, -1, -1, 0, 1, 1, 2, 2

y - Y: -293, -273, -163, -123, -53, -93, 107, 157, 147, 307

Calculate the sum of the product of the deviations of x and y.

∑[(x - X)(y - Y)] = (-2)(-293) + (-1)(-273) + (-1)(-163) + (-1)(-123) + (-1)(-53) + (0)(-93) + (1)(107) + (1)(157) + (2)(147) + (2)(307)

= 4,557

Calculate the sum of the squared deviations of x.

∑[(x - X)²] = (-2)² + (-1)² + (-1)² + (-1)² + (-1)² + 0² + 1² + 1² + 2² + 2²

= 18

Calculate the estimated slope of the regression line, b.

b = ∑[(x - X)(y - Y)] / ∑[(x - X)²]

= 4,557 / 18

= 253.17

Calculate the estimated intercept of the regression line, a.

a = Y - bX

= 643 - (253.17)(3)

= 883.5

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