Ron deposits $2,000 into an account that receives 3.1% interest compounded continuously. How much money is in the account after 9 years?

Answer:

\(x=\frac{1}{2}\)

Step-by-step explanation:

equation of a circle:  \((x - h)^2+(y-k)^2=r^2\)

where (h, k) = center and r = radius

From inspection, we can see that the center of the circle = (0, 0)

and the radius = 1

\(\implies (x - 0)^2+(y-0)^2=1^2\)

\(\implies x^2+y^2=1\)

Substitute \(y=\frac{\sqrt{3}}{2}\)  into  \(x^2+y^2=1\)  and solve for \(x\):

\(\implies x^2+(\frac{\sqrt{3}}{2})^2=1\)

\(\implies x^2+\frac{3}{4}=1\)

\(\implies x^2=\frac{1}{4}\)

\(\implies x=\pm \sqrt{\frac{1}{4}}\)

\(\implies x=\pm\frac{1}{2}\)

As point P is in quadrant 1, \(x\) is positive, so \(x=\frac{1}{2}\)

The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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The domain of the function obtained from the graph of the function indicates that the correct option is the second option

{x | x ≤ 0}

The domain of a function is the set of the possible x-values of the function.

The graph of the function indicates that the as the x-value approaches x = 0, the function approaches ∞

Similarly, as the x-value of the function approaches -∞, the function approaches f(x) = 0, therefore;

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Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

Answer:

I think that's 11,8

Step-by-step explanation:

Hope its right

Answer:

Question is missing

Step-by-step explanation:

Question missing

Answer:

25a-20

Step-by-step explanation:

15a+10a-20=

25a-20

Answer:

A.  4

Step-by-step explanation:

Given inequality:

\(x+9 < 4x\)

Rearrange the inequality to isolate x.

Subtract x from both sides of the inequality:

\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)

Divide both sides of the inequality by 3:

\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)

So the values of x that make the inequality true are:

Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.

To check this, substitute x = 4 into the inequality:

\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)

As 13 is less than 16, the inequality is true when x = 4.

Answer: 1/6 of a pie

Step-by-step explanation: each friend receives 1/6 of a pie because there are 2 pies being distributed to 12 friends. 2/12 = 1/6

Answer:

1/6 of the pie.

Step-by-step explanation:

We Know

Two pies are shared among 12 friends.

How much did each friend receive?

We take

2 / 12 = 1/6 of the pie

So, each friend receives 1/6 of the pie.

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Answer:

*50

Step-by-step explanation:

Sum of the interior angle

(n - 2) 180

From the question n is 3.

=(3 - 2) 180

=(1) 180

=180

The value of x

x + (x + 5) + (x + 25) 180

=x + x + x + 5 + 25 = 180

=3x + 30 = 180

=3x = 180 - 30

=3x = 150

=3x/3 = 150/3

x = 50

Therefore the value of x is 50.

Answer:

Two lines are parallel if their slopes are equal.

Step-by-step explanation:

I think the actual equation you meant to write was 5x⁴ + 7x³ - 2x² - 3x + c.

You're going to equate the whole equation to 0 and replace x for -1( because x + 1 is a factor)

= 5(-1)⁴ + 7(-1)³ - 2(-1)² - 3(-1) + c = 0

= 5 - 7 - 2 + 3 + c = 0

= - 1 + c = 0

Therefore c = 1

(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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Answer:

r≤-11+20

r≤9

r≤9 is the answer

We are given the following rule.

The values of y are given and the values of x are missing.

We can simply substitute the values of y into the rule and solve for the values of x.

For y = 5:

For y = 4:

For y = 2:

Therefore, the complete table is

Answer:

the last one

Step-by-step explanation:

(clustered around 1 and 3)

Answer:

The data are clustered from 1 to 3, so most teams won 1 to 3 games.

Step-by-step explanation:

There is only 1 dot at 8 and more near 1-3

Answer:

  x < 4  or  6 < x

Step-by-step explanation:

You want the compound inequality that describes the number line graph with open circles at 4 and 6, and shading everywhere except between them.

The left line segment has all values less than 4 shaded. The corresponding inequality is ...

  x < 4

The right line segment has all values greater than 6 shaded. The corresponding inequality is ...

  x > 6

These do no overlap, so the compound inequality uses "or" to combine them:

  x < 4 or x > 6

__

Additional comment

Sometimes it is helpful to have the relationship between the shading and the limit values a little more obvious in the inequality. That will be the case if you always use left-pointing inequality symbols: < or ≤. By writing the compound inequality as ...

 x < 4 or 6 < x

we see that shading is outside (left or right of) the interval [4, 6].

The symbol without the "or equal to" bar is used when the circle is an open circle. A filled dot would signify the limit value is part of the interval of interest, and the ≤ (or ≥) symbol would be used.

Answer:

we need more info to answer this question

Answer:

A.

Step-by-step explanation:

12 divided by 4 equals 3. So if he gets 3 dollars a week by the fourth week he should have 12 dollars. It could also be 4 times 3 equals 12.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

What is inequality?

An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.

c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).

d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.

Hence,

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

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The percentage of the sodas that was served which were regular would be = 18%

The quantity of regular sodas served = 18

The quantity of diet soda served = 82

The total number of soda served = 18+82 = 100

Therefore the percentage of soda that were regular would be;

= 18/100 × 100/1

= 18%

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Answer:

Step-by-step explanation:

125.

Answer:

In mathematics, a rational number is a number such as −3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1.

In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.

Step-by-step explanation:

hope it helps :)))

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

Here, we have,

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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Our vertex has an x-coordinate of 0, so the axis of symmetry for our function is x = 0. Now, let's consider the zeros of our function. Graphically, the zeros of a function are the x-coordinates of the points where the function crosses the x-axis. This occurs where y = 0.

The required piecewise linear relations are f(x) = 4 if [0, 2), and f(x) = -2x + 8 if [2, 4).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = 2x + 4 if [-2, 0]

This the sub-function define between the interval [-2, 0].

f(x) = 4 if [0, 2)

This the sub-function define between the interval [0, 2).

f(x) = -2x + 8 if [2, 4)

This the sub-function define between the interval [2, 4).

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under 21 years of age= 40     25         20  tot= 85

between 21 and 40=     35     20         30  tot = 85

       over 40=               20     30         35   tot = 85

If one of the 255 subjects is randomly selected

P (over 40) = 85/255 = 1/3

Hope this helps!