A car was valued at $34,000 in the year 1991. The value depreciated to $15,000 by the year 2006.

A) What was the annual rate of change between 1991 and 2006?
=
Round the rate of decrease to 4 decimal places.

B) What is the correct answer to part A written in percentage form?
=
%.

C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2011 ?
value = $
Round to the nearest 50 dollars.

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer:

24

Step-by-step explanation:

It is a meaning of GCF(greatest common factor.)

Both 6 and 8 can multiply to become 24.

Answer:

b

Step-by-step explanation:

n

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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A=prt

A=2000×7%×4

=560

Answer:

8%of 14000=1120

14000-1120=12880 is the final price

Answer:

12,800

Step-by-step explanation:

14000 × 8 ÷ 100 = 1,120

14000 - 1,120 = 12,800

Step-by-step explanation:

since b = 8, it has to be

y = 2x + 8

that was the whole point of the exercise, as the general slope-intercept form is

y = mx + b

you determined m = 2 and b = 8, so there is your answer. I am not sure where your problem was, as you solved the actual important part yourself.

Answer:

Less than

Step-by-step explanation:

The span of student ones box plot is going farther in the negatives then student two

Answer:

less than

Step-by-step explanation:

student 1 is 64 and student 2 is 65

Answer:

Domain: 0, 1, 2, 3, 4,

Range: 1, 2, 3, 4, 5,

Step-by-step explanation:

Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5,  therefore, the answer is:

Answer:

ok first we can simplyfy 4 3/6 to 4 1/2 and 5 4/8 to 5 1/2 so

4 1/2* 5 1/2

now we need to convert into improper fractions so

9/2*11/2=99/4 then we need to simplfy

24 3/4

Hope This Helps!!!

9514 1404 393

Answer:

  1. 6.1 to 10.3

  2. 9.6 hours

  3. 7.5 hours

Step-by-step explanation:

1. The empirical rule or the supplied chart will tell you that μ ±3σ of the distribution is within 99.7% of the mean. Here, that is ...

  8.2 ±3(0.7) = 8.2 ±2.1 = [6.1, 10.3]

The range of hours is 6.1 to 10.3 hours.

__

2. 2.5% of the distribution is above μ +2σ, or ...

  8.2 +2(0.7) = 9.6 . . . hours

__

3. The bottom 16% of the distribution is below μ -σ, or ...

  8.2 -0.7 = 7.5 . . . hours

Answer:

(a) If A is the area of a circle with radius and the circle expands as time passes, find dA/dt in terms of dr/dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spills increases at a constant rate of 1m/s, how fast is the area of the spill increasing when the radius is 30m

Answer:

A) 410 ≤ x ≤ 450 AND 68 ≤ y ≤ 70

B) 410 ≤ x ≤ 450 AND 0.6 ≤ x ≤ 1.1

Step-by-step explanation:

In the first statement we are told that the ball should weigh between 410–450 g (14–16 oz), with a circumference of 68–70 cm (27–28 in).

If the weight is x, it means we have the inequality as;

410 ≤ x ≤ 450

If the circumference is denoted as y, we have;

68 ≤ y ≤ 70

Compound inequality is when we join two inequalities with the word "OR" or the word "AND.

Thus, the compound inequality is;

410 ≤ x ≤ 450 AND 68 ≤ y ≤ 70

Similar to he first statement, in the second statement, we have;

410 ≤ x ≤ 450

If the inflated pressure is denoted by z, then we have;

0.6 ≤ x ≤ 1.1

Like in the first statement, the compound inequality can be represented as;

410 ≤ x ≤ 450 AND 0.6 ≤ x ≤ 1.1

Multiply 15 and 6.8. So speed * time = distance

So the answer is 102

The solutions to the trigonometric equation in this problem are given as follows:

Two angles are said to be complementary angles when the sum of their measures is of 90º.

For complementary angles, we have that the sine of one of the angles is the cosine of the other angle, hence in this problem we have that 2θ and θ are complementary angles.

Then the value of θ is obtained as follows:

2θ + θ = 90

3θ = 90

θ = 30º.

θ = π/6.

The equivalent angles, which are also solutions to the equation, are given as follows:

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Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

Answer:

3.5

Step-by-step explanation:

total pretzel=10 1/2 or10.5

no. of brother = 3

now,

10.5 pretzel for each borther= 10.5/3

=3.5 ans

Answer:

120 degress

Step-by-step explanation:

The domain restrictions for (f/g)(x) are (c) x = 0, 6

From the question, we have the following parameters that can be used in our computation:

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−2

hope this is what your looking for

Answer:

x = -2

Step-by-step explanation:

\(-4+x=\frac{3}{4}x-\frac{9}{2}\)

\(\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\)

\(-4+x+4=\frac{3}{4}x-\frac{9}{2}+4\)

\(Simplify\)

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

\(\mathrm{Subtract\:}\frac{3}{4}x\mathrm{\:from\:both\:sides}\)

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

\(\frac{1}{4}x=-\frac{1}{2}\)

\(\mathrm{Multiply\:both\:sides\:by\:}4\)

\(4\cdot \frac{1}{4}x=4\left(-\frac{1}{2}\right)\)

\(x=-2\)

~lenvy~

Where F_pivot is the magnitude of the force exerted on the pivot point.

What are perpendicular lines?

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, if you draw a line perpendicular to another line, the two lines will form four right angles at the point where they intersect.

(a) The torque applied by the adult rider (on the left) can be calculated as the product of the force applied by the rider and the perpendicular distance from the pivot to the force. Let F_a be the force applied by the adult rider and let r_a be the perpendicular distance from the pivot to the force. Then, the torque applied by the adult rider is:

τ_a = F_a * r_a

The perpendicular distance r_a can be calculated using the Pythagorean theorem:

r_a = sqrt((L/2 - d)^2 + Xoffset^2)

Therefore, the torque applied by the adult rider is:

τ_a = F_a * sqrt((L/2 - d)^2 + Xoffset^2)

(b) Similarly, the torque applied by the child rider (on the right) can be calculated as:

τ_c = F_c * sqrt((L/2 + d)^2 + Xoffset^2)

where F_c is the force applied by the child rider and r_c is the perpendicular distance from the pivot to the force, which can be calculated using the Pythagorean theorem.

(c) The torque applied by the board can be calculated as the sum of the torques applied by the two riders:

τ_b = τ_a + τ_c

Substituting the expressions for τ_a and τ_c, we get:

τ_b = F_a * sqrt((L/2 - d)^2 + Xoffset^2) + F_c * sqrt((L/2 + d)^2 + Xoffset^2)

(d) To determine the distance d in terms of given quantities and variables, we can use the condition for static equilibrium, which requires that the sum of the torques about the pivot point is zero:

τ_a + τ_c = 0

Substituting the expressions for τ_a and τ_c and simplifying, we get:

F_a * (L/2 - d) = F_c * (L/2 + d)

Solving for d, we get:

d = (F_a/F_c - 1) * L/4

Substituting F_a = Mg and F_c = mg, where M is the mass of the adult rider, m is the mass of the child rider, and g is the acceleration due to gravity, we get:

d = (M/m - 1) * L/4

(e) The magnitude of the force exerted on the pivot point by the see-saw while in use can be calculated using the condition for static equilibrium, which requires that the sum of the forces in the vertical direction is zero:

F_a + F_c = Mg + mg

Substituting F_a = Mg and F_c = mg, we get:

F_pivot = Mg + mg

Therefore, where F_pivot is the magnitude of the force exerted on the pivot point.

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Answer:

The polynomial function from number 2 is:

f(x) = 4x^3 - 5x^2 + 2x - 1

To write this in standard form, we need to arrange the terms in descending order of degree:

f(x) = 4x^3 - 5x^2 + 2x - 1

f(x) = 4x^3 + (-5x^2 + 2x - 1)

f(x) = 4x^3 - 5x^2 + 2x - 1

So the standard form of the polynomial function is:

f(x) = 4x^3 - 5x^2 + 2x - 1

The average weight of a male Florida panther rounded to the nearest whole number is 53 kg

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Average weight = 52.6 kg

52.6

The number after decimal point is 6 which is more than 5.

So add  1 to the 52, we get 53

Thus, the average weight of a male Florida panther rounded to the nearest whole number is 53 kg

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Joel has 3/8 gallon of paint left after painting the ceiling and the wall.

Joel used a total of 1/4 + 3/8 = 5/8 gallon of paint to paint the ceiling and the wall.

To find out how much paint he has left, we can subtract the amount of paint used from the original gallon of paint:

1 gallon - 5/8 gallon = 8/8 gallon - 5/8 gallon = 3/8 gallon.

The method used to solve this problem is subtraction of fractions.

First, we added the fractions 1/4 and 3/8 to find the total amount of paint used.

Then, we subtracted the total amount of paint used from the original one gallon of paint to find how much paint was left.

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Answer:

You aren't allowed to post tes questions, oh well I will help though. The answer is going to be 3/8 miles I believe.

Step-by-step explanation:

3/4 - 3/8 = 6/8 - 3/8 = 3/8

Answer:

1.2 trains for $25.

Step-by-step explanation:

For 50 dollars, you could get 2.4 trains with the $25 dollar option.

For 90 dollars (an extra 40 dollars!) you only get 0.2 more trains.

If you add another $25 to the current $50 on the other option, you get 3.6 trains.

So, 1.2 trains for $25 must be the better option as you can get an extra 1 train for 15 dollars less!

Hope this helps!

Also, who buys 0.2 or 0.6 of a train? -_-

Answer:

Step-by-step explanation:

I forgot to add the last reason is AAS (two angles one side are congruent = triangles are congruent)

S.

1.Given

2. AE = EC

3. <AEB = <CED

4. <CDE = <ABE

5. triangles congruent

R.

1. Given

2. Segment bisector theorem

3. Vertical angles theorem

4. PAI Theorem

Hope this helps!

Step-by-step explanation:

nasa picture po yunv sagot

#HOPE IT HELPS