Jack pours 1/3 gallon of fruit juice in 1 and 1/2 minutes. Assume that he bores at a constant rate. What fraction of a gallon of fruit juice does he pour in one minute?

Answer:

\(r=4.38\)

Step-by-step explanation:

Step 1: Arrange the equation so that you are calculating rate (divide both sides by t)

\(\frac{d}{t} = \frac{rt}{t}\)

\(t\) cancels out on the right side.

Step 2: Substitute in the numerals

\(r=\frac{d}{t}\)

\(r=\frac{5.7}{1.3}\)

Step 3: Divide

\(r=4.38\) \(mph\)

There's your answer!

Hope this helps you!

AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.

In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.

Therefore, we can conclude as saying:

C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

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Answer:

4/9 or 44%

Step-by-step explanation:

4 + 5 = 9

Probability: 4/9 or 44%

DFS can be used because the graph is directed and all of the edge weights are positive.

What is Algorithms?

An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially. All aspects of IT employ algorithms extensively.

Steps can be taken. There may be a path from v to z* but not from z* to v or different from each with different weights, so we just need to apply DFS, dijkstras twice, starting with vertex v, to find the path length until z*. Then we need to add the path weights.

The problem is clear in that we need to find path weight from v to z* and z* to v. There may be more than one path that leads from v to z*, thus we must locate them all and store some of them because each loop will require a time complexity of O(V+E).

where, in the given graph, E stands for edges and V for vertex. When a graph is complete, meaning there is a path connecting every vertex to every other vertex, we must execute this technique V times to determine the total number of paths. As a result, the time complexity is O(V(V+E)).

Then we must repeat the process from z* to v, but this time we must choose every path whose weights satisfy the specified condition. In the worst case, we must repeat this process (V-1) times, thus the time complexity will be the same as before. As a result, our time complexity will be O(V(V+E)) overall.

Since the graph is directed and every edge weight is positive, DFS may be used.

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Answer:

20

Step-by-step explanation:

lol

The time that it will take, to the nearest year, for the value of the account to reach $2,310 for this case is 20 years.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

\(CI = P(1 +\dfrac{R}{100})^T - P\)

The final amount becomes:

\(A = CI + P\\A = P(1 +\dfrac{R}{100})^T\)

For this case, we're provided that:

Let the time be 'T' years after which this investment becomes $2310

Then, by the formula stated above, we get:

\(A = P\left(1 +\dfrac{R}{100}\right)^T\\\\2310 = 920\left(1 +\dfrac{4.7}{100}\right)^T\\\\\\2310 = 920\times(1.047)^T\\\\(1.047)^T = \dfrac{2310}{920}\\\\\\T = \log_{1.047}\left( \dfrac{2310}{920} \right)\\\)

Using calculator, we get:

\(T \approx 20.0446 \approx 20 \: \rm years\) (as unit of time in rate of interest was assumed to be yearly)

Thus, the time that it will take, to the nearest year, for the value of the account to reach $2,310 for this case is 20 years.

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Answer:

i think is A

Step-by-step explanation:

Answer: probability of won=

no. of won match=21

no. of total match=28

so they cut and made 3/4

probability of lost match=

no. of lost match=7

no. of total match=28

so they cut and made 1/4

HOPE THIS HELPS

Answer:

8.60cm

Step-by-step explanation:

a/sinA=b/sinB

15/sin90⁰=x/sin35⁰

cross multiply

15sin35⁰=xsin90⁰

8.6036=x

x=8.60cm

Answer:

16+31=31+16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$15.02

Step-by-step explanation:

Given data

Total cost= $16

tax= 6.5%

let the actual cost of the slippers be x

6.5/100*x+ x= 16

0.065x+x= 16

1.065x= 16

divide both sides by 1.065

x= 16/1.065

x= 15.02

Hence the actual cost of the slippers is $15.02

Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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A rectangle has a perimeter of 60 feet. The rectangle's length is four times its width. The area of rectangle is 144 square feet.

Given that,

A rectangle has a perimeter of 60 feet.

The rectangle's length is four times its width.

We have to find the area of rectangle.

Let us take length as x

The width will be 4x

The perimeter =2(4x+x)

2(4x+x)=60

4x+x=60/2

5x=30

x=30/5

x=6

The length will be 6.

The width will be 4×6=24.

The area of rectangle is length×width

=6×24

=144 square feet.

Therefore, the area of rectangle is 144 square feet.

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Answer:

d) 1/12

Step-by-step explanation:

Answer:

0.501

Step-by-step explanation:

On solving the provided question we can say that - here in trigonometry \(v^2x - 2u - 3 = 0\) = (u-3)(u+1)

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

\(sin^2x - 2 sinx - 3 = 0\\u= sinx\\u^2 = sin^2x\\v^2x - 2u - 3 = 0\\\\\)

factors are = -3 and 1

(u-3)(u+1)

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Answer:

2/3

this question doesn't make sense

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

Answer:

  0.012t + 28 = 30

Step-by-step explanation:

The depth starts at 28 meters. The amount of increase in t minutes will be 0.012t, so the total depth after t minutes is ...

  0.012t +28

We want to find when that is equal to 30, so the appropriate equation is ...

  0.012t +28 = 30

Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

Answer:

x is 12

Step-by-step explanation:

Answer:

c=pie r squared is the equations and the answer is 50.27

Step-by-step explanation:

The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.

How to solve and what is angle?

An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.

Any angle coterminal with 8° can be expressed as:

θ = 8° + 360°k

where k is an integer.

Therefore, the expression describing all the angles that are coterminal with 8° is:

θ = 8° + 360°k, where k is an integer.

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.

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Answer:

560

Step-by-step explanation:

The reasonable constraint so the function is at least 600 would be A. 0 ≤ x ≤ 20.

Given the function y = -2x² + 40x + 600, we want to find the constraint for x so that the function's value is at least 600.

Since the parabola opens downward (as a is negative), the function will be at least 600 for all values of x within the interval where the parabola is above y = 600. The vertex of the parabola is at its maximum value, so we should look for the interval around the vertex (10, 800).

Looking at the given constraints, the option "0 ≤ x ≤ 20" is a reasonable constraint that ensures the function is at least 600. The parabola starts at a value of 600 at x = 0, reaches its maximum value at the vertex, and then returns to a value of 600 at x = 20.

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Answer:

1080

Step-by-step explanation:

All you have to do is simple multiply

Answer:

1080 copies in 12 minutes

Step-by-step explanation:

12 divided by 4 = 3

so, 360 x 3 = 1080

Therefore the value of x is less than 4 when x is in the inequality 3x + 2 < 14 and greater than -3 when x is in the inequality 2 x-5> -11

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.

Expressions are carried out, or evaluated, in order to yield a value. In an evaluation process, values of expressions can be employed as components of surrounding expressions.

To solve for x in the inequality 3x + 2 < 14, we can begin by subtracting 2 from both sides to get 3x < 12. Then, dividing both sides by 3 gives x < 4.

To solve for x in the inequality 2 x-5> -11, we can begin by adding 5 to both sides to get 2x> -6, then divide both sides by 2 to get x > -3

So x can be any number greater than -3 and less than 4

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Answer:

Two examples of points that satisfy this condition is (0,5) and (0,-5).

Step-by-step explanation:

Suppose we have two points:

\(A = (x_{1}, y_{1})\)

\(B = (x_{2}, y_{2})\)

The distance between these points is:

\(D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)

In this question:

B(0,0)

A(x,y)

We have to find x and y.

We have that:

\(\sqrt{(x-0)^{2} + (y-0)^{2}} = 5\)

\(\sqrt{x^{2} + y^{2}} = 5\)

\((\sqrt{x^{2} + y^{2}})^{2} = 25\)

\(x^{2} + y^{2} = 25\)

One example of a point:

I will say that x = 0. So

\(0^{2} + y^{2} = 25\)

\(y = \pm \sqrt{25}\)

\(y = \pm 5\)

So two examples of points that satisfy this condition is (0,5) and (0,-5).

The distance formula is a formula that is used to find the distance between two points.

The coordinate of point A is (0, 5)  or   (0, -5).

Let us consider that, coordinate of point A is (x, y).

The distance between (0,0) and (x, y) is computed as by using distance formula.

                 \(Distance=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\5=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\x^{2} +y^{2}=25\)

All values that satisfies above equation, will be the coordinate of point A.

When x = 0,  

                \(y=\sqrt{25} =\pm 5\)

The coordinate of point A is (0, 5)  or   (0, -5).

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Answer:

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

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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