Show that phi(n) = c/x + 4, -infinity explicit solution for 0 x(dy/dx)+y=4
is the equation linear?

Answer:

around 1.92

cause 2.5 divided by 1.3 gives you the amount of minutes hank picked to match tom in 1 minute

Hank picked at least as many pounds of berries as Tom in 4.8 minutes.

What is algebraic expression ?

An algebraic expression in mathematics is made up of variables, constants and operations such as addition, subtraction, etc.

Given that Hank picked 1.3 pounds of berries at rate 0.75 pounds per minute , whereas Tom picked 2.5 pounds of berries at rate 0.5 pounds per minute.

Assume the time taken is x minutes.

Hank : 1.3 + 0.75 x

Tom : 2.5 + 0.5 x

Keeping both equations equal we get ,

1.3 + 0.75x = 2.5 + 0.5x

Let's move x term on one side and constant terms on another side.

0.75 x - 0.5 x = 2.5 - 1.3

0.25 x = 1.2

x = 1.2 ÷ 0.25

x = 4.8

Therefore , Hank picked at least as many pounds of berries as Tom in 4.8 minutes.

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Answer:

the values of x and y, based on the figure on the right is of b

x=76°,y=48°

Answer:

The answer is -8x-10

Step-by-step explanation:

-4(2x+3)-2

you will use the -4 to open the bracket

-8x-12-2

-8x-10

a) The average rate of change over the interval [−2,2] is 4.

b) The instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4).

A) To find the average rate of change of g(x) over the interval [-2,2], we need to calculate the slope of the line passing through the points (-2,g(-2)) and (2,g(2)).

g(-2) = (-2)³ - 6 = -8 - 6 = -14

g(2) = (2)³ - 6 = 8 - 6 = 2

Therefore, the slope of the line passing through these two points is:

(g(2) - g(-2))/(2 - (-2)) = (2 - (-14))/(2 - (-2)) = 16/4 = 4

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivative of g(x):

g'(x) = 3x²

At x=-2, the instantaneous rate of change of g(x) is:

g'(-2) = 3(-2)² = 12

At x=2, the instantaneous rate of change of g(x) is:

g'(2) = 3(2)² = 12

We can see that the instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4). This is because the function g(x) is not a straight line and its rate of change varies across the interval.

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To determine which of the following ordered pairs are found on the graph of the inverse function, we first need to find the inverse function. We can do this by switching the x and y values in each ordered pair and solving for y.

Original table:

| x | y |
|---|---|
| 1 | 4 |
| 2 | 5 |
| 3 | 6 |
| 4 | 7 |
| 5 | 8 |

Switching x and y values:

| y | x |
|---|---|
| 4 | 1 |
| 5 | 2 |
| 6 | 3 |
| 7 | 4 |
| 8 | 5 |

Now we can solve for y:

y = 1 if x = 4
y = 2 if x = 5
y = 3 if x = 6
y = 4 if x = 7
y = 5 if x = 8

So the inverse function is:

f^-1(x) = x - 3

Now we can check which of the following ordered pairs are found on the graph of the inverse function:

(-2, f^-1(-2)) = (-2, -5) is on the graph of the inverse function
(2, f^-1(2)) = (2, -1) is not on the graph of the inverse function

Therefore, the ordered pair (-2, 2) is found on the graph of the inverse function. To determine if the given ordered pair (-2, 2) is found on the graph of the inverse function, we'll need to follow these steps:

1. Identify the ordered pairs from the table of values for the original function.
2. Find the inverse of the ordered pairs by swapping the x and y coordinates.
3. Check if the given ordered pair (-2, 2) is among the inverse ordered pairs.

Unfortunately, you haven't provided the table of values for the original function. Please provide the table of values, and I'll be happy to help you determine if the given ordered pair is found on the graph of the inverse function.

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lim sin(pi/3+h) - sin(pi/3)/ h as h approaches 0 is  Non existent. The correct answer is option e.

To evaluate the limit, we can use the formula for the derivative of sin(x), which is:

lim f(x+h) - f(x) / h as h approaches 0 = f'(x)

where f(x) = sin(x).

So, in this case, we have:

lim sin(pi/3+h) - sin(pi/3) / h as h approaches 0

which can be rewritten as:

lim [sin(pi/3+h) - sin(pi/3)] / h as h approaches 0

Using the identity for the difference of two sines, we can simplify this expression to:

lim [2cos(2pi/6+h/2)sin(h/2)] / h as h approaches 0

Now, we can cancel out the factor of sin(h/2) in the numerator and denominator, and we are left with:

lim 2cos(2pi/6+h/2) / h as h approaches 0

We can evaluate the limit using direct substitution, and we get:

2cos(pi/3) / 0

Since the denominator is 0, the limit does not exist. Therefore, the answer is option E: Nonexistent.

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Answer:

B.) About 200 minutes napping

Step-by-step explanation:

74+56+128+38=296

500-296=204

204 is about 200

Two solutions:

1. x =(100-√2160)/2=50-6√ 15 = 26.762

2. x =(100+√2160)/2=50+6√ 15 = 73.238

Answer:

An equilateral triangle has all side lengths the same, and all angles are 60 degrees. Using this we can split the triangle along its altitude to get two right triangles with a hypotenuse of length 10 and a base of 1/2 of the original length, so 5. Now we can either use the Pythagorean theorem (a^2+b^2=c^2) or the fact that it is a 30 60 90 triangle (angles measure at 30 60 and 90 degrees) Pythagorean theorem is probably easier.

It stated that the squares of the two legs of a right triangle add to the square of the hypotenuse. So a(the altitude)^2+5(the base)^2=10(the hypotenuse)^2

A^2+5^2=10^2

A^2+25=100

A^2=75

A=sqrt(75)

A=5*sqrt(3)

Final answer:

The altitude of an equilateral triangle with side length 10 is 5sqrt(3), or about 8.66

Step-by-step explanation:

Please give the brainliest, really appreciated.

Based on the 1.5 × IQR rule for outliers, there is no evidence to support the student's claim because there is only one outlier at 58 minutes.

The interquartile range is the difference between upper and lower quartiles. The semi-interquartile range is half the interquartile range. When the data set is small, it is simple to identify the values of quartiles.

Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

The following interquartile ranges was calculated by using Excel:

Q₃ = 31.5

Q₁ = 20.5

Now, the interquartile range (IQR) is given by:

IQR = Q₃ - Q₁

IQR = 31.5 - 20.5

IQR = 11

Based on the 1.5 × IQR rule for outliers, we have:

1.5 × IQR = 1.5 × 11 = 16.5

Therefore, our fences will be 16.5 points below Q₁ and 16.5 points above Q₃:

Lower fence = 20.5 - 16.5 = 4.5

Upper fence = 4.5 + 31.5 = 36.

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Answer:

a: (2, -3)

b: 20

c: 24

Answer:

exponent law a^m x a^n = a^m+n

4^11 x 4^-8 = 4^11-8 = 4^3

hope that answers your question

Step-by-step explanation:

Answer:

4^3

Step-by-step explanation:

When multiplying monomials with exponents you add them together.

Answer:

\(y=\dfrac{2}{7}x-12\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Given:

The y-intercept is the y-value when x = 0.

Substitute the slope and y-intercept into the formula to create the equation of the line in slope-intercept form:

\(\implies y=\dfrac{2}{7}x-12\)

a. the solutions for \(\theta\): \[\theta = \frac{\pi}{6} + \pi k, \frac{5\pi}{6} + \pi k\]

b. the solutions within the interval \([0, 2\pi)\) are \(\theta = \frac{\pi}{6}\) and \(\theta = \frac{5\pi}{6}\).

(a) To find the solutions of the equation \(2 \cos(2\theta) - 1 = 0\), we can start by isolating the cosine term:

\[2 \cos(2\theta) = 1\]

Next, we divide both sides by 2 to solve for \(\cos(2\theta)\):

\[\cos(2\theta) = \frac{1}{2}\]

Now, we can use the inverse cosine function to find the values of \(2\theta\) that satisfy this equation. Recall that the inverse cosine function returns values in the range \([0, \pi]\). So, we have:

\[2\theta = \frac{\pi}{3} + 2\pi k, \frac{5\pi}{3} + 2\pi k\]

Dividing both sides by 2, we get the solutions for \(\theta\):

\[\theta = \frac{\pi}{6} + \pi k, \frac{5\pi}{6} + \pi k\]

where \(k\) is an integer.

(b) To find the solutions in the interval \([0, 2\pi)\), we need to identify the values of \(\theta\) that fall within this interval. From part (a), we have \(\theta = \frac{\pi}{6} + \pi k, \frac{5\pi}{6} + \pi k\).

Let's analyze each solution:

For \(\theta = \frac{\pi}{6} + \pi k\):

When \(k = 0\), \(\theta = \frac{\pi}{6}\) which falls within the interval.

When \(k = 1\), \(\theta = \frac{7\pi}{6}\) which is outside the interval.

When \(k = -1\), \(\theta = -\frac{5\pi}{6}\) which is outside the interval.

For \(\theta = \frac{5\pi}{6} + \pi k\):

When \(k = 0\), \(\theta = \frac{5\pi}{6}\) which falls within the interval.

When \(k = 1\), \(\theta = \frac{11\pi}{6}\) which is outside the interval.

When \(k = -1\), \(\theta = -\frac{\pi}{6}\) which is outside the interval.

Therefore, the solutions within the interval \([0, 2\pi)\) are \(\theta = \frac{\pi}{6}\) and \(\theta = \frac{5\pi}{6}\).

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Step-by-step explanation:

x -2 -1 2 7

y -6 -6 -2 3

All y are in under root

Answer:

y = mx + b

m being the slope

b being the y intercept

Step-by-step explanation:

Answer:

Point slope formula is as follows:

Answer:

B) 333.

Step-by-step explanation:

The discriminant of ax^2 + bx + c = 0

is b^2 - 4ac

So here we have:

(-9)^2 - 4*7*-9

= 81 + 252

= 333.

Answer:

Theusage is 585 minutes of call duration..

Explanation:

Fixed plan cost is M=$.39.95

Charge for first 500 minutes call: Free

Charge for call exceeding 500 minutes: $.0.35/minutes.

Let x minutes be the total call duration.

The bill is P=$.69.70 i.e. more than $.39.95, which indicates

call duration is more than 500 minutes.

The rule states that bill for call exceeding 500 minutes is

P=M+(x−500).0.35 or

69.70=39.95+(x−500).0.35 or (x−500).0.35=69.70−39.95 or

(x−500).0.35=29.75 or (x−500)=

0.35

29.75

or

(x−500)=85 or x=500+85=585 minutes.

The usage is 585 minutes of call duration .

Step-by-step explanation:

hope this helps

Answer:

242 ft²

Step-by-step explanation:

8X18=144

7X14=98

144+98=242

Answer:

corresponding angles

To find the relationship between the volume of a prism and a pyramid with congruent bases and equal heights, we need to consider their formulas.  
The volume of a pyramid is given by the formula V = (1/3)Bh,

where B represents the area of the base and h represents the height. Since the bases of the prism and pyramid are congruent and their heights are equal, we can write the equation:

Volume of Prism = 2 × Volume of Pyramid Using the formulas mentioned earlier, we can substitute the expressions for the volumes:

Bh = 2 × (1/3)Bh
Simplifying this equation, we can cancel out the B's:

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The statement "a prism and a pyramid have congruent bases and equal heights, and the volume of the prism is twice the volume of the pyramid" is FALSE.

To understand why, let's consider a simple example. Imagine we have a triangular prism and a triangular pyramid with congruent bases and equal heights. The base of both shapes is a triangle, and their heights are the same.

The volume of a prism can be calculated by multiplying the area of its base by its height. Similarly, the volume of a pyramid can be calculated by multiplying the area of its base by one-third of its height.

Since the prism and the pyramid have congruent bases and equal heights, the only difference in the volume calculation is the factor of 1/3 for the pyramid.

This means that the volume of the pyramid is one-third the volume of the prism, not half. Therefore, the statement that the volume of the prism is twice the volume of the pyramid is false.

Therefore, the statement is incorrect, and the volume of the prism is not twice the volume of the pyramid, but rather three times as much.

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Answer:

58°

Step-by-step explanation:

X is a geometric random, its variable is constant and equal to p.

To show that if X is a geometric random variable, its failure rate is constant and equal to p, we will use the definition of the geometric distribution and the failure rate formula.

As the expression for z(x) does not depend on x, the failure rate is constant and equal to p/(1-p). However, we need to show that it is equal to p.
Recall that p is the probability of success. Since failure and success are complementary events, the probability of failure is q = 1-p.

Observe that the failure rate z(x) equals the probability of success p when divided by the probability of failure q. Since the failure rate for a geometric random variable only depends on the probability of success p and the probability of failure q, it is constant and equal to p.

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The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

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The value of Nicholas' property in the market, considering a market capitalization rate of 5.75% compounded annually, is approximately $346,581.15 rounded to the nearest cent.

To calculate the value of Nicholas' property in the market, we need to determine the present value of the rental payments using the market capitalization rate of 5.75% compounded annually.

The value of Nicholas' property can be calculated using the formula for present value of an annuity:

PV = P * (1 - (1 + r)^(-n)) / r,

where PV is the present value, P is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is $3,000 per month, the interest rate is 5.75% (or 0.0575) per year, and we need to calculate the present value over the entire holding period of the property.

To convert the interest rate to a monthly rate, we divide it by 12. So, the monthly interest rate is 0.0575 / 12 = 0.0047917.

Next, we need to determine the number of periods. Assuming Nicholas plans to hold the property for a certain number of years, we multiply the number of years by 12 to get the number of months.

Let's say Nicholas plans to hold the property for 10 years. The number of periods would be 10 * 12 = 120.

Plugging the values into the formula, we have:

PV = 3000 * (1 - (1 + 0.0047917)^(-120)) / 0.0047917.

Evaluating this expression, we find that the present value of the rental payments is approximately $346,581.15.

Therefore, the value of Nicholas' property in the market would be approximately $346,581.15 rounded to the nearest cent.

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Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Answer:

For example, the position of a planet is a function of time. ... A function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the codomain of the function.

Step-by-step explanation:

Problem 2, Part (a)

A = event elevator's 1st stop at the 2nd floor

P(A) = 3/4

Since the elevator needs to go up one floor

B = event elevator has its 2nd stop at the 3rd floor

P(B given A) = probability event B happens given event A happened

P(B given A) = 3/4

-----------

P(A and B) = P(A)*P(B given A)

P(A and B) = (3/4)*(3/4)

P(A and B) = 9/16

-----------

===============================================================

Problem 2, Part (b)

A = event elevator's 1st stop at the 2nd floor

P(A) = 3/4

B = event elevator has its 2nd stop at the 3rd floor

P(B given A) = 3/4

C = event elevator has its 3rd stop at 4th floor

P(C given (A and B)) = 3/4

-----------

P(A & B & C) = P(A)*P(B given A)*P(C given (A and B))

P(A & B & C) = (3/4)*(3/4)*(3/4)

P(A & B & C) = 27/64

-----------

===============================================================

Problem 2, Part (c)

A = event elevator's 1st stop at the 2nd floor

x = P(A) = 3/4

B = event elevator has its 2nd stop at the 3rd floor

y = P(B given A) = 3/4

C = event elevator has its 3rd stop at 2nd floor

z = P(C given (A and B)) = 1/4

D = event elevator has its 4th stop at 1st floor

w = P(D given (A & B & C)) = 1/4

-----------

P(A & B & C & D) = x*y*z*w

P(A & B & C & D) = (3/4)*(3/4)*(1/4)*(1/4)

P(A & B & C & D) = 9/256

-----------