Cual es el valor de la fracción 11/14 como un número decimal redondeado a la décima más cercana

If someone wins 2 blue balls and loses 3 red balls every day for 5 days, and ends up with the same number of blue and red balls, then they must have started with 25 red balls.

Explanation:

Let x be the number of red balls the person started with. After 5 days, they would have won 2 × 5 = 10 blue balls and lost 3 × 5 = 15 red balls. So, the person would have a total of (x - 15) red balls and (10 + 2 × 5) = 20 blue balls. We know that the person ends up with the same number of blue and red balls, so we can set up the equation:

x - 15 = 20

Solving for x, we get:

x = 35

Therefore, the person started with 35 red balls. However, this does not satisfy the condition that the person ends up with the same number of blue and red balls, since 35 - 15 = 20 ≠ 20 blue balls. So, we made a mistake in our assumption that the person started with x red balls. Let's try again:

Let y be the number of red balls the person started with. After 5 days, they would have won 2 × 5 = 10 blue balls and lost 3 × 5 = 15 red balls. So, the person would have a total of (y - 15) red balls and 20 blue balls. We know that the person ends up with the same number of blue and red balls, so we can set up the equation:

y - 15 = 20

Solving for y, we get:

y = 35

Therefore, the person started with 35 red balls and ended up with 20 blue balls and 20 red balls, satisfying the given condition. So, the answer is that the person started with 25 red balls.

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The diagram given is a sector, and from the diagram

Radius(r) = 9 in

The amount that would be owed after seven years is $3824.40

EXPLANATION

Given:

Principal(P)= 3100

rate (r) =0.03

Time (t) = 7

Using the formula below (since it is continuously compounded):

Substitute the values into the formula and evaluate.

Hence, the amount that will be owed is $3824.40

Answer:

The inequality for x is x > 36

(In interval notation form it is (36, ∞)

Step-by-step explanation:

Multiply to remove the fraction, then set equal to zero and solve.

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The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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Since 1 dozen = 12, 12 cupcakes = 1 1/4 cups of flour

36/12 = 3

36 = 1 1/4(3)
36 cupcakes = 3 3/4 cups of flour

Answer:

8 1/4 cups

Step-by-step explanation:

You multiple 11/4 by 3 and change the answer to a mixed fraction

9514 1404 393

Answer:

  162.46 square units

Step-by-step explanation:

The area of a sector of arc b (in radians) is ...

  A = 1/2r²b

  A = (1/2)(9.6²)(202·π/180) = 162.46 . . . square units

128 ÷3=42.66

it doesn't say if they have to pay the money back but if they do it's

128-35= 43

43÷3= 14.33

The number of fishes in the Goff family is represented by a bar graph

Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. Sometimes referred to as a column chart, a vertical bar graph.

Discrete, continuous, or categorical data are typically organized into class intervals in bar charts. They are made up of a set of marked horizontal or vertical bars and an axis.

Given data ,

Let the bar graph be represented as A

Now , the value of A is

Let the total number of fishes in the Goff family be n = 18 fishes

Let the number of black fishes = 10 fishes

Let the number of white fishes = 5 fishes

Let the number of gold fishes be = 3 fishes

Now , the total number of fishes in the Goff family is represented by a bar graph

And , it is a continuous categorical data

Hence , the bar graph is plotted

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Answer:

it is possible because the fact provided says X is greater than or equal to -7.

the word 'equal' means -7 could be a possible solution

Answer: 48 dollars

Step-by-step explanation:

Las coordenadas de la escuela (rojo) son (4,3), las coordenadas de mi casa (rosado) son (6,5) las coordenadas del supermercado (verde) son (11,4) y las coordenadas del restaurante (amarillo) son (9,8).

Se refiere a una expresión, valor o magnitud sobre el plano cartesiano que muestra la ubicación de un punto o referencia.

Siempre se deben tener los valores de ambos ejes: el eje y (vertical)  y el eje x (horizontal). Para esto primero escriba el valor del eje x luego añada una coma y escriba el valor de y.

De acuerdo a lo anterior, los lugares ubicados en el mapa tiene las siguientes coordenadas:

(4,3)

(6,5)

(11,4)

(9,8)

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

h(5) = 20

Step-by-step explanation:

Assume that '2' is an exponent.

So the question for you should be:-

\( \displaystyle \large{h(x) = {x}^{2} - x}\)

We want to find h(5); we substitute x = 5 in.

\( \displaystyle \large{h(x) = {5}^{2} - 5}\)

5^2 is 5•5 = 25.

\( \displaystyle \large{h(x) = 25 - 5} \\ \displaystyle \large{h(x) = 20}\)

Therefore, h(5) is 20.

Answer:

87

Step-by-step explanation:

9 + [ 6 x (9 + 4) ]

= 9 +  [6 x 13]

= 9 + 78

= 87

So, the answer is 87

Answer:

87

Step-by-step explanation:

9 + [ 6 x (9 + 4) ]

= 9 +  [6 x 13]

= 9 + 78

= 87

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The polar equation for this curve is: theta = pi/3 (or any angle that satisfies tan(theta) = sqrt(3))

To find the polar equation for the curve represented by the given Cartesian equations, we can use the conversion formulas between Cartesian and polar coordinates.

\(x^2 + y^2 = 25:\)

In polar coordinates, the conversion formulas are:

x = r cos(theta)

y = r sin(theta)

Substituting these values into the equation \(x^2 + y^2 = 25:\)

\((r cos(theta))^2 + (r sin(theta))^2 = 25\)

\(r^2 (cos^2(theta) + sin^2(theta)) = 25\)

\(r^2 = 25\)

The polar equation for this curve is simply:

r = 5

\(x^2 + y^2 = -8y:\)

In polar coordinates:

x = r cos(theta)

y = r sin(theta)

Substituting these values into the equation \(x^2 + y^2 = -8y:\)

\((r cos(theta))^2 + (r sin(theta))^2 = -8(r sin(theta))\)

\(r^2 (cos^2(theta) + sin^2(theta)) = -8r sin(theta)\)

\(r^2 = -8r sin(theta)\)

The polar equation for this curve is:

r = -8 sin(theta)

y = sqrt(3) x:

In polar coordinates:

x = r cos(theta)

y = r sin(theta)

Substituting these values into the equation y = sqrt(3) x:

r sin(theta) = sqrt(3) (r cos(theta))

r sin(theta) = sqrt(3) r cos(theta)

tan(theta) = sqrt(3)

The polar equation for this curve is:

theta = pi/3 (or any angle that satisfies tan(theta) = sqrt(3))

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Answer:

Step-by-step explanation:

6x + 8

take common. 2 is the common number because it is the highest number that exactly divides both a and 8.So,if we take two common from two terms

2(3x + 4)

therefore the GCF is 2.

= 6x + 8

= 2(3x + 4)

GCF is the greatest common factor. As you can see, 2 is the highest common factor of the value 6x + 8.

Therefore, GCF = 2.

Answer:

Step-by-step explanation:

These are all the same types of questions so I will explain how you solve these and answer question #1 to get you started :)

for #1, y=3x+4

your first x value is -2.

You plug in the x value (which is -2 for the first box) into the equation (y=3x+4)

and you should get your first y value.

x=-2

y=3x+4

y=3(-2) + 4

y=-6+4

y= -2

therefore, #1 your first value of y is -2

The next x value is -1

Just plugin again!

y=3x+4

y=3(-1) + 4

y=-3+4

y= 1

Your second y value for #1 is -1

The third x value for #1 is 0

Same process: we plugin 0

y=3x+4

y=3(0) +4

y= 0+4

y=4

Your third y value for #1 is 4

Last x value for #1 is 2

Again, we plugin!

y=3x+4

y=3(2) +4

y= 6+4

y=10

Last y value for #1 is 10

I hope this helped! reach out if you need further explanation with questions 2-6!

Answer: -5

Step-by-step explanation:

When x = 8, y = -5.

An exponential function is a mathematical function in which the output of the function increases (or decreases) at a rate that is proportional to the current value of the output.

Exponential functions have an “asymptote”, which is a line that the graph approaches but never crosses. This asymptote is often a horizontal line, and it can be used to identify exponential functions.

To determine if a graph is an exponential function, look for a curve that rises or falls steeply and then levels off. The curve should be smooth and symmetrical, and the points should lie along a straight line when plotted on a logarithmic scale. The equation for the graph should also have an exponential form, such as y=ab^x. If these characteristics are present, then the graph is an exponential function.

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Considering the zeros, the graph for the sinusoidal function is:

\(F(x) = \sin{\frac{\pi}{7}(x-3)}\)

The sine function is given by:

\(F(x) = A\sin{Bx}\)

In which:

In this problem:

\(\frac{2\pi}{B} = 14\)

\(B = \frac{2\pi}{14}\)

\(B = \frac{\pi}{7}\)

Thus:

\(F(x) = \sin{\frac{\pi}{7}x}\)

Like this, the zeros are at \(x = -14\) and \(x = 0\). We want it at \(x = -11, x = 3\), thus, we shift the function 3 units to the right, that is, the function is:

\(F(x) = \sin{\frac{\pi}{7}(x-3)}\)

The graph is sketched at the end of this answer, and has the desired behavior, which are points (-11,0) and (3,0).

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Answer:

Yes

Step-by-step explanation:

To determine whether the sequence \(\(a_n = \frac{1}{3n^4}\)\) is increasing, decreasing, or not monotonic, we can analyze the behavior of the terms as \(\(n\)\)increases.

Let's calculate the values of \(\(a_n\)\) for a few values of \(\(n\)\) to observe any patterns:

\(\(a_1 = \frac{1}{3(1)^4} = \frac{1}{3}\)\)

\(\(a_2 = \frac{1}{3(2)^4} = \frac{1}{48}\)\)

\(\(a_3 = \frac{1}{3(3)^4} = \frac{1}{243}\)\)

\(\(a_4 = \frac{1}{3(4)^4} = \frac{1}{768}\)\)

We can see that as \(\(n\)\) increases, the values of \(\(a_n\)\) are decreasing. This indicates that the sequence is decreasing.

To formally prove this, we can compare the terms \(\(a_n\)\) and \(\(a_{n+1}\)\) for any \(\(n\)\) :

\(\(a_n = \frac{1}{3n^4}\)\)

\(\(a_{n+1}\) = \(\frac{1}{3(n+1)^4}\)\)

To determine if \(\(a_n\)\) is less than \(\(a_{n+1}\)\) , we can simplify and compare the fractions:

\(\(\frac{1}{3n^4} < \frac{1}{3(n+1)^4}\)\)

Cross-multiplying and simplifying:

\(\(3(n+1)^4 < 3n^4\)\)

Expanding the binomial and further simplifying:

\(\(n^4 + 4n^3 + 6n^2 + 4n + 1 < n^4\)\)

Since the left side of the inequality is positive and the right side is \(\(n^4\)\) (which is positive for all \(\(n\))\) , we can see that the inequality is not true for any \(\(n\).\) Therefore, \(\(a_n\)\) is always less than \(\(a_{n+1}\)\) , indicating that the sequence is decreasing.

In conclusion, the sequence \(\(a_n = \frac{1}{3n^4}\)\)  is a decreasing sequence.

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Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.

To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:

Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.

Proof:

Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:

      M _______N

       |\      |

       |  \    |

       |    \  |

       |      \|

      O--------P

            A

We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.

Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.

Since MNOP is a trapezium, the area of trapezium is given by:

Area of trapezium MNOP = (1/2)(MN+OP) × height

Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.

Therefore, the area of trapezium MNOP can be written as:

Area of trapezium MNOP = (1/2)(MN+OP) × height

= (1/2)(MA+AP+OP) × height

= (1/2)(MA+MP) × height (Since AP = NO/2 = height)

So, we have proved that:

Area of trapezium MNOP = (1/2)(MA+MP) × height

Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,

Area of triangle MAP = (1/2) × Area of triangle MAP

Substituting the above in the expression for the area of trapezium, we get:

Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP

= (3/2) × Area of triangle MAP

Therefore, we have:

Area of triangle MAP = (1/2) × Area of trapezium MNOP

Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.

The standard form of the quadratic inequality represented by the description is; y <  -2x² + 160x - 2400

An inequality with a quadratic expression is referred to as a quadratic inequality.

It is of the form y = ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.

Let's assume that the equation is y = a(x - h)² + k

Where (h, k) is the coordinate of the vertex. Thus;

y = a(x - 40)² + 800

Put the point (60, 0) in the equation

0 = a(60 - 40)² + 800

0 = a(20)² + 800

-800 = 400a

a = -800/400

a = -2

Thus, the equation is;

y = -2(x - 40)² + 800

The inequality is a dashed line and shaded below the parabola and is;

y <  -2(x - 40)² + 800

= y <  -2(x² - 80x + 1600) + 800

y <  -2x² + 160x - 3200 + 800

y <  -2x² + 160x - 2400

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