4 times 1/6 in fraction.​

Answer:

$26 dollars

Step-by-step explanation: when you divide 156 divided by 6 you get 26

Answer:

26 dollars per ticket

Step-by-step explanation:

156/6=26

26x6=156

Answer:

30 Leaps

Step-by-step explanation:

A kangaroo chases a rabbit that starts 150 feet ahead of the kangaroo.

Let's say After x  Leap  kangaroo catches up to the rabbit

1  Leap of Kangaroo  = 12 foot

x leap of Kangaroo = 12x  foot

1  Leap of Rabbit =7 foot

x leap of Rabbit =7x  foot

The rabbit starts 150 feet ahead of the kangaroo. Hence 150 feet  extra by the kangaroo

12x  = 7x  + 150

5x = 150

x = 30

Kangaroos have to make 30 Leaps to catch up to the rabbit

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if \($a \neq b$\),\($f(n)$\)and \($g(n)$\) will not have the same growth rate. It is not true that \($\forall a, b \in \mathbb{N}, f(n) = a^n, g(n) = b^n$ implies $f \in \Theta(g)$\).

To determine whether $f(n) = a^n$ and $g(n) = b^n$ satisfy $f \in \Theta(g)$, we need to evaluate their growth rates and see if there exist constants $c_1$, $c_2$, and $n_0$ such that $c_1 \cdot g(n) \leq f(n) \leq c_2 \cdot g(n)$ for all $n \geq n_0$.

Let's analyze the growth rates of $f(n)$ and $g(n)$ separately:

1. $f(n) = a^n$:

  - When $a > 1$, $f(n)$ grows exponentially with $n$. For example, if $a = 2$, $f(n)$ doubles with each increment of $n$.

  - When $a = 1$, $f(n)$ is constant and does not grow with $n$.

  - When $0 < a < 1$, $f(n)$ converges to 0 as $n$ increases. For example, if $a = 0.5$, $f(n)$ halves with each increment of $n$.

2. $g(n) = b^n$:

  - When $b > 1$, $g(n)$ also grows exponentially with $n$.

  - When $b = 1$, $g(n)$ is constant.

  - When $0 < b < 1$, $g(n)$ converges to 0 as $n$ increases.

In general, if $a \neq b$, $f(n)$ and $g(n)$ will not have the same growth rate. Therefore, we cannot conclude that $f \in \Theta(g)$ for arbitrary $a$ and $b$.

Thus, it is not true that $\forall a, b \in \mathbb{N}, f(n) = a^n, g(n) = b^n$ implies $f \in \Theta(g)$.

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Answer:

p = -4, q = -3

Step-by-step explanation:

y = -2x +4  ... (1)   perpendicular bisector of AB, slope = -2

slope of AB = 1/2

Line AB pass (8,3): (y-3) / (x-8) = 1/2

AB equation: y-3 = 1/2(x-8)      y = 1/2x - 1  ... (2)

(2)-(1): 5/2 x = 5      x = 2

y = 0       (2,0) intercept of bisector and AB, it is midpoint of A (8,3) and (p,q)

(8+p)/2 = 2

p = -4

(3+q)/2 = 0

q = -3

The values of p and q from the perpendicular bisector are;

p = -4 and q = -3

We are given coordinates of A and B as;

A(8, 3) and B(p, q)

Bisector of AB is y = -2x + 4

Thus, from y = mx + c, Slope of the bisector is -2.

Since the bisector is perpendicular to AB, then slope of AB = -(1/-2) = 1/2

Thus, slope of the line from point A to the point of the bisector on AB is;

(y - 3)/(x - 8) = 1/2

y - 3 = ¹/₂(x - 8)

y - 3 = ¹/₂x - 4

y = ¹/₂x - 1

Putting ¹/₂x - 1 for y in the bisector equation gives;

¹/₂x - 1 = -2x + 4

2x + ¹/₂x = 4 + 1

2.5x = 5

x = 5/2.5

x = 2

Thus;

y = -2(2) + 4

y = 0

Thus, the coordinate of the midpoint of AB is (2, 0)

Now, this means that;

(8 + p)/2 = 2

8 + p = 4

p = 4 - 8

p = 4

Also; (3 + q)/2 = 0

3 + q = 0

q = -3

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Answer:

140°

Step-by-step explanation:

The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)

20 + 120 = 140

Answer:

y= 140

Step-by-step explanation:

first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.

Answer:

37 years

Step-by-step explanation:

Answer:

36 years

Step-by-step explanation:

it would take 36 years to reach the height of 40 feet. I know this because it is already 4 feet and needs to grow 36 feet and if it is growing at a rate of 1 foot per year then it would take 36 years

Answer:

C. -1.7

Step-by-step explanation:

-4.2 - x = -2 2/4

-2 2/4 = -10/4 = -2.5

-4.2 - x = -2.5

-x = 1.7

x = -1.7

So, the answer is C. -1.7

Answer:

2

Step-by-step explanation:

that is the least common denominator

lcd is 2...............

You can just try out all the answers but I'll give you a solution.

We will expand out the middle term to 5x^2 - 30x - 6x + 36, then we group the first 2 terms together, and the last 2 terms together.

= 5x (x - 6) - 6(x - 6)

And we put x-6 out : (x-6)(5x-6) = 0

Now, we can just set the value of one bracket to 0 and find out the value of x, and do the same for the other one

x - 6 = 0 -> x = 6
5x - 6 = 0 -> x = 6/5

Because 6 is not a possible option, the answer is x = 1.2

Carlos harvests cassavas at a constant rate. He needs 353535 minutes to harvest a total of 151515 cassavas.

The ratio of the change in dependent values or outputs to the change in independent values or inputs is known as the rate of change. The change, which also refers to the function's slope, represents the shift in values between two points on a coordinate plane. The formula for the rate of change is (y2 - y1)/, where y stands for the dependent variable and x for the independent variable (x2 - x1).

Given:

Carlos gives  353535 minutes to harvest a total of 151515 cassavas.

Find:

We have to find the total number of cassavas.

Solution:

Carlos harvests cassava at constant rate is 353535 minutes per 151515 cassavas

= 151515/353535

= 0.429

A formula for the quantity of cassava (C) that Carlos harvests each time (T).

This means that after 353535 minutes, 151515 cassavas have been harvested, after 700000 minutes, 300000 cassavas, and so on.

Hence, the required constant rate is 0.429T.

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The ratio of letter size paper to Legal size paper is 3 : 1

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained.

Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

If a copier contains letter size paper = 75%

Legal size paper = 25%

thus the ratio will be 75 : 25= 3 : 1

The latter is being obtained from the former by dividing both the quantities by 25. Therefore, we can write 3 : 1 equally.

The ratio of letter size paper to Legal size paper is 3 : 1

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Answer:

x≥−3

Step-by-step explanation:

−4x−10≤2

Add 10 to both sides.

−4x≤2+10

Add 2 and 10 to get 12.

−4x≤12

Divide both sides by −4. Since −4 is negative, the inequality direction is changed.

x≥12/-4

Divide 12 by −4 to get −3.

x≥−3

The time that the object hits the ground is given as follows:

B. t=5.

The equation giving the height of the object after t seconds is given as follows:

h(t) = -16t² + 80t.

The object hits the ground when:

h(t) = 0.

Hence the time is obtained as follows:

-16t² + 80t = 0

16t² - 80t = 0

16t(t - 5) = 0.

Hence the non-zero time is given as follows:

t - 5 = 0

t = 5 seconds.

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Answer:

A, b, d

Step-by-step explanation:

Answer:

b+2=b-2

Step-by-step explanation:

The first step to solving this equation is subtract b from both sides. After you do that, you get 2=-2. 2 does not ever equal -2 and that statement is false. Therefore that equation has no solution.

False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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Answer:

y = 6.5

Step-by-step explanation:

Using a ratio

10           13

-----    = -----------

10+5      13+y

10           13

-----    = -----------

15        13+y

Using cross products

10(13+y) = 13*15

10(13+y) = 195

130+10y = 195

Subtract 130 from each side

10y = 65

Divide by 10

y = 65/10

y = 6.5

The existence and uniqueness theorem in the ordinary differential equations are explained below.

(a) "Existence" in the context of the existence and uniqueness theorem for ordinary differential equations (ODEs) refers to the guarantee that a solution to the ODE exists for a certain interval or range of values.

(b) "Uniqueness" means that there is only one solution to the ODE that satisfies certain initial conditions or constraints. It ensures that there are no multiple solutions that meet the given criteria.

(c) The equation x' = f(t, x) represents a first-order ODE, where the derivative of the function x with respect to t is equal to the function f, which depends on both t and x.

(d) The notation x(to) = xo represents the initial condition of the ODE. It specifies the value of the function x at a particular initial time to, which is equal to xo.

(e) The graph of R = {(t, x): 0 ≤ |t - to| ≤ a, 0 ≤ |x - xo| ≤ b} represents a rectangular region in the t-x plane. It includes all points (t, x) that satisfy the conditions: the absolute difference between t and to is less than or equal to a, and the absolute difference between x and xo is less than or equal to b. The point (to, xo) is included in this region.

(f) The symbol u(t) is not mentioned in the given context. Without additional information, it is not possible to provide a specific interpretation or meaning for u(t).

(g) "On some interval |t - to| < h contained in |t - to| < a" implies that there exists a smaller interval, represented by |t - to| < h, which is fully contained within the larger interval |t - to| < a. The value of h represents the size or length of the smaller interval. In the graph, h can be added as a smaller length within the interval defined by a.

The relationship between a and h is that h is a subset of a. This means that h is smaller or equal to a and is fully contained within a. In other words, h represents a sub-interval of the larger interval a.

(h) The significance of the existence and uniqueness theorem in layman's terms is that it provides a mathematical assurance that a specific type of differential equation has a unique solution that satisfies certain conditions. It gives confidence that a solution exists and is unique within a specified range or interval. This is valuable for various scientific and engineering applications, as it allows for the prediction and understanding of systems described by differential equations.

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The graph of the function y = x^2 + 2x - 5 is a U-shaped curve opening upwards, with the vertex at (-1, -4).

To graph the function y = x^2 + 2x - 5, we can follow a few steps to plot the points and sketch the curve.

Step 1: Determine the vertex of the parabola.

The vertex of the parabola occurs at the minimum or maximum point. We can find the x-coordinate of the vertex by using the formula x = -b/2a, where a, b, and c are coefficients of the quadratic equation in standard form (ax^2 + bx + c = 0).

For our function, a = 1, b = 2, and c = -5.

Plugging these values into the formula, we get x = -2/2(1) = -1.

To find the y-coordinate of the vertex, we substitute the x-coordinate back into the function: y = (-1)^2 + 2(-1) - 5 = -4.

Therefore, the vertex is at (-1, -4).

Step 2: Find additional points.

To plot more points, we can choose some x-values and calculate the corresponding y-values using the function. Let's select x-values of -3, 0, and 2.

For x = -3, y = (-3)^2 + 2(-3) - 5 = 9 - 6 - 5 = -2.

For x = 0, y = (0)^2 + 2(0) - 5 = 0 + 0 - 5 = -5.

For x = 2, y = (2)^2 + 2(2) - 5 = 4 + 4 - 5 = 3.

Step 3: Plot the points and sketch the curve.

Plot the points (-3, -2), (0, -5), (2, 3), and the vertex (-1, -4) on a coordinate plane.

The vertex (-1, -4) is the lowest point, so the parabola opens upwards.

Connect the points with a smooth curve, following the shape of a parabola.

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Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

The statement (p ∧ ~q) ∨ r means "either p and not q are true, or r is true." the truth value of the statement (p ∧ ~q) ∨ r is true under both conditions.

a) If p is true and q is true, then ~q is false. So, (p ∧ ~q) is false. Since r is also true, the entire statement becomes true: (false ∨ true) = true.

b) If p is false and q is true, then (p ∧ ~q) is false (both p and ~q need to be true for this part to be true). However, since r is true, the entire statement becomes true: (false ∨ true) = true.

So, the truth value of the statement (p ∧ ~q) ∨ r is true under both conditions.

Let's evaluate the truth value of the statement (p ∧ ~q) ∨ r under the given conditions:

a) p is true, q is true, and r is true.
(p ∧ ~q) ∨ r = (True ∧ ~True) ∨ True = (True ∧ False) ∨ True = False ∨ True = True
The statement is true under these conditions.

b) p is false, q is true, and r is true.
(p ∧ ~q) ∨ r = (False ∧ ~True) ∨ True = (False ∧ False) ∨ True = False ∨ True = True
The statement is true under these conditions as well.

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Answer:

27

Step-by-step explanation:

Width = w

length = l

w=1/3 * l

or, l=3w

perimeter=2l+2w=24

2(l+w)=24

2(3w+w)=24

2*4w=24

8w=24

w=3

l=9

Area=3*9=27

Answer:

\(-\frac{17}{4}\\-3.95\\-\sqrt{15}\\-3\frac{6}{7}\\-3\frac{1}{4}\\-3.2\)

Step-by-step explanation:

From smallest to largest:

\(-\frac{17}{4}\\-3.95\\-\sqrt{15}\\-3\frac{6}{7}\\-3\frac{1}{4}\\-3.2\)

Solution: Any value for a variable that makes the equation true.

Reciprocal: Focuses on the use of multiplication and division

Coefficient: A number that is multiplied by a variable in an algebraic expression is a coefficient

Term: A term of an algebraic expression is a number, variable, or product of numbers and variables

Base: The base of a power is the factor that is multiplied repeatedly in the power.

Hope this helps, and have a great day!

Answer:

Solution: any value for a variable that makes an equation true

Reciprocal: focuses on use of multiplication and division

Coefficient: A number being multiplied by a variable in an algebraic expression

Base: the base of a power is a factor that is multiplied repeatedly in power

u got the term definition right

Step-by-step explanation:

The equation \(\(ax^2 + by^2 + cz^2 + d = 0\)\) does not represent any of the provided conics.

Thus, option (d) is correct.

The equation \(\(ax^2 + by^2 + cz^2 + d = 0\)\) represents an equation of a surface in three-dimensional space.

(a) An ellipsoid:

      An ellipsoid is defined by an equation of the form \(\(\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1\)\),

      where a, b, and c are positive constants.

    The given equation \(\(ax^2 + by^2 + cz^2 + d = 0\)\) is not in the form of an    

    ellipsoid equation.

(b) A hyperboloid of one sheet:

    A hyperboloid of one sheet is defined by an equation of the form

    \(\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} - \dfrac{z^2}{c^2} = 1\)\), where a, b, and c are positive constants.

     The given equation \(\(ax^2 + by^2 + cz^2 + d = 0\)\) does not have a

     subtraction of terms involving \(\(z^2\)\).

(c) A hyperboloid of two sheets:

   A hyperboloid of two sheets is defined by an equation of the form

  \(\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} - \dfrac{z^2}{c^2} = -1\)\), where a, b, and c are positive constants.

    The given equation \(\(ax^2 + by^2 + cz^2 + d = 0\)\) is not in the form of a    

    hyperboloid of two sheets equation.

(d) None of the above:

    This option seems to be the correct choice since the given equation    

    does not match the standard forms of ellipsoid or hyperboloid

    equations.

Thus, option (d) is correct.

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The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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(a) A motor is the device that converts electrical energy to mechanical energy. (b) The kinetic energy of the antelope is nine times greater than before.

(a)A motor is an electrical device that uses the principle of electromagnetic induction to convert electrical energy into mechanical energy. It consists of coils, magnets, and a rotating shaft. When an electric current is passed through the coils, it creates a magnetic field that interacts with the magnetic field of the permanent magnets, causing the shaft to rotate and thus converting electrical energy to mechanical energy. Motors are commonly used in various applications such as appliances, vehicles, and industrial machinery.

(b)The kinetic energy of an object is given by the equation KE = (1/2)mv^2, where KE represents kinetic energy, m represents mass, and v represents velocity. When an object's speed is tripled, the new kinetic energy is calculated by substituting the new velocity into the equation. Since the velocity is squared, tripling the velocity results in a nine-fold increase in the kinetic energy. Therefore, the kinetic energy of the antelope is nine times greater than before when its speed is tripled.

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Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3