A person places $8440 in an investment account earning an annual rate of 9.2%, compounded continuously. Using the formula v=pe^rt where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 8 years.

The graph of this function would be a straight line passing through the point (0, c) with a slope of m.

What is the function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

If the function increases at a constant rate of m and has a y-intercept of (0, c), then its equation can be written as:

f(x) = mx + c

The graph of this function would be a straight line passing through the point (0, c) with a slope of m.

Here's an example of the graph of f(x) = 2x + 3:

Attachment

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The number of students who watched the games = (2/3)x = [2/3 * Total number of students] = [2/3 * x] = (2/3) x 150 = 100 students.

Let's assume that the total number of students in the school stadium is x. So,1/5 of the students were basketball players => (1/5)x2/15 of the students were soccer players => (2/15)x

So, the rest of the students watched the games => x - [(1/5)x + (2/15)x]

Let's simplify the given expressions=> (1/5)x = (3/15)x=> (2/15)x = (2/15)x

Now, we can add these fractions to get the value of the remaining students=> x - [(1/5)x + (2/15)x]

=> x - [(3/15)x + (2/15)x]

=> x - (5/15)x

=> x - (1/3)x = (2/3)x

Students who watched the games are (2/3)x

.Now we have to find out how many students watched the game. So, we have to find the value of (2/3)x.

We know that, the total number of students in the stadium = x

Hence, we can say that (2/3)x is the number of students who watched the games, and (2/3)x is equal to [2/3 * Total number of students] = [2/3 * x]

Therefore, the students who watched the game are (2/3)x.

Hence the solution to the given problem is that the number of students who watched the games = (2/3)x = [2/3 * Total number of students] = [2/3 * x] = (2/3) x 150 = 100 students.

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Answer:

47.5 per 1 lamp

Step-by-step explanation:

First, we can ignore the info about the department store because it is useless. Now, for the appliance store, we now that it sells lamps for 95 dollars per 2 lamps. 2 lamps equal 95, and it is asking how much does 1 cost. We can simply divide. So, 95/2= 47.5 dollars

Answer: 1320 ways.

Step-by-step explanation:

For this problem you should use the formula for variations in combinatorics. You use this when choosing a few objects from a group in which the order of the objects is of importance:

\(P^{12} _{3}=\frac{12!}{(12-3)!}=\frac{12 \cdot 11\cdot 10\cdot ...\cdot 1}{9 \cdot 8 \cdot ... \cdot 1} = 12 \cdot 11 \cdot 10 = 1320\)

where ! stands for factorial.

Answer:

Negative

Step-by-step explanation:

Answer:

Negative

Step-by-step explanation:

A positive divided by a negative is a negative.

Answer:

opposite operation

Step-by-step explanation:

divide 35 by 5 so x=7

The  given expression can be written as a single logarithm:

log ap - log29 + 2 log ar = log ((a * p * r^2)/29)

So, the correct answer is (d) log_a((p * r^2)/q).

We can use the following logarithmic identities to simplify the given expression:

log a - log b = log (a/b)
n log a = log (a^n)

Using the first identity, we can write:

log ap - log29 + 2 log ar = log (ap/29) + log (ar^2)

Using the second identity, we can simplify the second logarithm:

log (ap/29) + log (ar^2) = log ((ap/29) * (ar^2)) = log ((ap * ar^2)/29)

Using the distributive property of multiplication, we can simplify this expression further:

log ((ap * ar^2)/29) = log ((a * p * r^2)/29)

Therefore, the given expression can be written as a single logarithm:

log ap - log29 + 2 log ar = log ((a * p * r^2)/29)

So, the correct answer is (d) log_a((p * r^2)/q).

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Answer: 0.00034

Step-by-step explanation: 10^-4 would move the decimal left four times.

A real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

It should be noted that an equation is used to show the relationship between the variables that are illustrated.

In this case, a real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

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Answer:

B) (-2,6)

Step-by-step explanation:

Where do the two lines intersect? That is where the solution is.

Hope this helps

Answer:

I believe the answer B ( I think)

Answer:x is6 y is 3

Step-by-step explanation:

Answer:

She spends 45 hours practicing her culinary skills in 5 weeks.

The slope of the line AB is 2 when the AB line is perpendicular to the BC line with slope -1/2.

Given that,

In the picture we have a circle,

The circle is O.

AC is the diameter of the circle.

The slope of line BC is -1/2.

We have to find the slope of the line AB.

We can see in the diagram.

The AB line is perpendicular to the line BC.

We know that,

If two lines are perpendicular to each other then the slope of the lines will be

m₁×m₂=-1

So,

-1/2×m₂=-1

1/2×m₂=1

m₂=2

Therefore, The slope of the line AB is 2 when the AB line is perpendicular to the BC line with slope -1/2.

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Answer:

2

Step-by-step explanation:

Angle B is an inscribed angle which intercepts an arc of 180°.

The measure of an inscribed angle is half the measure of the intercepted arc.

Therefore, m<B = 90°.

Lines BC and AB are perpendicular lines.

The product of the slopes of perpendicular lines is -1.

m[BC] × m[AB] = -1

m[BC] = -1/2

-1/2 × m[AB] = -1

m[AB] = 2

Answer: 2

Answer:

Step-by-step explanation:

Step one:

given data

intial pay= $11 per hour

final pay= $16 per hour

Required

% increase

Step two:

%increase= final-initial/initial*100

substitute

%increase= 16-11/11*100

%increase=5/11*100

%increase= 0.45*100

%increase= 45%

Hence the percent raise is 45%

Answer:

the second graph in the picture shows the equation

Step-by-step explanation:

Answer:el segundo grafico muestra la equation

Step-by-step explanation:

Answer:

( x + 5 )² + ( y - 3 )² = 52

Step-by-step explanation:

Let find the equation of the line going through A( - 11, 7 ) and B( - 9, - 3 )

m = \(\frac{-3-7}{-9+11}\) = - 5

y - 7 = - 5( x + 11 )

y = - 5x - 48

Now, let find the equation of the line passing through midpoint of the segment AB

Coordinates of that midpoint is ( \(\frac{-11-9}{2}\) , \(\frac{7-3}{2}\) ) = ( - 10 , 2 )

Slope of the perpendicular line is \(\frac{1}{5}\) ( opposite reciprocal of ( - 5 )

y - 2 = \(\frac{1}{5}\) ( x + 10 )

y = \(\frac{1}{5}\) x + 4 ........... (1)

Coordinates of an intersection of two lines (1) and x = - 5 are coordinates of the center of the circle

y = \(\frac{1}{5}\) ( - 5 ) + 4 = 3 ⇒ y = 3

O( - 5 , 3 ) is the center

The last!! RADIUS which is OA or OB

r = \(\sqrt{(-5+11)^2 +(3-7)^2}\) = √52

( x + 5 )² + ( y - 3 )² = 52

The possible number of ways of selection by using combination formula is 3060.

What is combination?

A grouping of items where the order in which they were chosen is irrelevant is known as combination.

Given that the number of people in the group is 18. Only 4 people will be member of the council.

The formula of combination is \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\) , where r number of objects are selected from n objects.

In the given question the value of n is 18 and the value of r is 2.

Substitute the value of n and r in \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\).

\(^{18}C_{4}=\frac{18!}{4!(18-4)!}\)

Solve the above expression:

18^C_4 = 18x17x16x15x14/4x14

18^C_4 = 18x17x16x15/4x3x2x1

3060 18^C_4 = 3060

The number of ways such selection is 3060.

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Answer:

1550m3

Step-by-step explanation:

7750m3 ×1/5=1550m3

Answer:

1550m^3

Step-by-step explanation:

Volume of the prism= 7750m^3

Factor of dilated prism= 1/5

So,

7750×1/5= 1550m^3

The diameter of the bike's tire is 2.325 inches.

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.  If we open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in units, such as cm or unit m.

A mountain bike tire completes 15 revolutions and travels 146 feet.

Now,

1 revolution of a tire is equal to the circumference of the tire.

Since we have 15 revolutions, we should take 15C=146

where C=πd where π is pi (use 3.14 or the pi symbol).

Our equation is:

20πd=146.

Then solve for d:

20 × 3.14 × d = 146

62.8d = 146

d = 146/62.8

d = 2.325 inches.

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Answer:

97 oz.

Step-by-step explanation:

1 lb.=16oz

3+2 lbs = 5 lb's which equals to 80 oz.

then add the extra ounces 7+10 = 17

80 + 17 = 97 oz.

Answer:

D.

Step-by-step explanation:

There are 16 ounces in one pound.

3 X 16 = 48 + 7 = 55 ounces for the first book.

2 X 16 = 32 + 10 = 42 ounces for the second book.

55 + 42 =  97 ounces.

Answer: 49x^14

Step-by-step explanation:

Answer:

18°

Step-by-step explanation:

x + 140° + 22° = 180° { being sum of angles of triangle }

x + 162° = 180°

x = 180° - 162°

x = 18°

Hope it will help :)

get x = 128 is not a step

The critical point q = 1 is a relative minimum for the function \(p(q) = q^2 - 2q - 9\).

To find the critical points of the function \(p(q) = q^2 - 2q - 9\), we need to determine the values of q where the derivative of p(q) is equal to zero or undefined.

First, let's find the derivative of p(q):

p'(q) = 2q - 2

Next, we set p'(q) equal to zero and solve for q:

2q - 2 = 0

2q = 2

q = 1

So, q = 1 is a critical point.

To determine the nature of this critical point, we can examine the second derivative of p(q):

p''(q) = 2

The second derivative is a constant, which means it doesn't change with q. Since p''(q) is positive (2 > 0) for all q, this indicates that the critical point q = 1 is a relative minimum.

Therefore, the critical point q = 1 is a relative minimum for the function \(p(q) = q^2 - 2q - 9\).

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Answer: \(x=-1 \pm \sqrt{15}\)

Step-by-step explanation:

\((x+1)^2 =15\\\\x+1 =\pm \sqrt{15}\\\\x=-1 \pm \sqrt{15}\)

Given the function is \(\[f(x)=2(x+1)^3-5\]\) The parent function of the given function is\[y=x^3\]

Transformations of the given function from the parent function are as follows.

1. Vertical stretching by a factor of 2.

2. Horizontally shifted left by 1 unit.

3. Vertical shift down by 5 units.

Graph of the function and identifying its key characteristics: Graph:

Observations:

1. The function has a cubic shape.

2. The function intersects the x-axis at (-1.44, 0) and has a zero at -1.

3. The function has a local minimum at (-1, -7)

4. The function is increasing to the right of the minimum and decreasing to the left of the minimum.

5. The range of the function is all real numbers.

6. The function has no symmetry.

Hence, the key characteristics of the given function\(\[f(x)=2(x+1)^3-5\]\)are:

Vertical stretching by a factor of 2,

Horizontally shifted left by 1 unit,

Vertical shift down by 5 units.

The function has a cubic shape. The function intersects the x-axis at (-1.44, 0) and has a zero at -1. The function has a local minimum at (-1, -7).

The function is increasing to the right of the minimum and decreasing to the left of the minimum. The range of the function is all real numbers. The function has no symmetry.

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Answer: p is greater than or equal to 8

Step-by-step explanation:

To isolate the variable (p) you divide both sides of the equation by 6 to get p by itself and the answer comes out clean because 48 is a multiple of 6.

Answer:

Divide both sides by the same factor

6p > 48

6p > 48

---     ---

6  >   6

result

p > 8

The side length of the triangle (y) will be 45.88 units.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The angle of a triangle is 42° and its opposite side is 31. And the angle of a triangle is 85° and its opposite side is y. Then by the sine law, the equation is written as,

y / sin82° = 31 / sin42°

Simplify the equation, then the value of the variable 'y' is calculated as,

y / sin82° = 31 / sin42°

y = 31 x  sin82° / sin42°

y = 31 x 1.4799

y = 45.88 units

The side length of the triangle (y) will be 45.88 units.

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