Mathematics High School

The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?
93
-7
50
7

Answers

Answer 1
P(t) = 5,000 (1-r)t
P(t) = 5,000 (1-7%)t
P(t) = 5,000 (0.93)t

The annual depreciation rate is 7%
Answer 2

Answer:

Option 4 - 7%

Step-by-step explanation:

Given : The function [tex]P(t) = 5000 (0.93)^t[/tex] is the value of a motor scooter t years after it is purchased.

To find : Which of the following values show the annual depreciation of the value of the motor scooter?

Solution :

We are given a function p(t) which is represented as:

[tex]P(t) = 5000 (0.93)^t[/tex]

Where, p(t) is the value of a motor scooter t years after it is purchased.

Depreciation is the amount that has been deducted from the cost of an item.

The rate of change is 1-0.93=0.07 i.e. 7%.

So, The function P(t) has 7% of the amount has been deducted each year and the value of the motor scooter is 93% of the amount of the previous year.

Therefore, The annual rate of depreciation is 7%.

So, option 4 is correct.

Related Questions

How to factor out the greatest common factor in a polynomial?

Answers

Hello,

To find something COMMON, we must at least have 2 things!

So , we can find the greatest common factor of 2 polynomials!

Final answer:

To factor out the GCF in a polynomial, identify the highest common factor, write it outside the parentheses, divide each term by the GCF, and write the quotients inside the parentheses.

Explanation:

To factor out the greatest common factor (GCF) in a polynomial, follow these steps:

First, identify the highest common factor that is present in each term of the polynomial.Write down this factor outside of a set of parentheses.Divide each term of the polynomial by the GCF, and place the resulting quotient inside the parentheses. This step can be seen as dividing both sides by the same factor to turn polynomial terms into integers, if that is easier to understand.Check your answer to see if it simplifies further and whether it is reasonable.

For example, for the polynomial 6x³ + 9x², the GCF is 3x2. Factoring out the GCF gives us:

3x²(2x + 3)

The products inside the parentheses are the result of dividing the original terms by the GCF. Remember, by finding the GCF, we simplify the algebra and may check the work by expanding the factored form back out to verify it equals the original polynomial.

How can an expression or process be determined for an arithmetic sequence?

Answers

an aritmetic sequcne is represented as

[tex]a_n=a_1+d(n-1)[/tex]

where
an=nth term
a1=first term
d=common differnce, or how much each term increases by
n=which term



example

1,3,5, etc
first term is 1
common difference is 2 because it increases by 2 each time
so the formula would be
[tex]a_n=1+2(n-1)[/tex]

if we had
5,3,1
first term s 5
common difference is -2 since it goes up by -2 each time
so formula is
[tex]a_n=5-2(n-1)[/tex]



hope this helps

A system of linear equations includes the line that is created by the equation y=0.5x-1 and the line through the points (3, 1) and (–5, –7), shown below.

What is the solution to the system of equations?

a. (–6, –4)
b. (0, –1)
c. (0, –2)
d. (2, 0)

Answers

The answer is (2,0). If you graph the lines, it shows that the intersection occurs right there.

Answer: Solution is,

d. (2, 0)

Step-by-step explanation:

Since, the equation of line that passes through points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

[tex](y-y_1)=\frac{x_2-x_1}{y_2-y_1}(y-y_1)[/tex]

Thus, the equation of line through the points (3, 1) and (–5, –7) is,

[tex](y-1)=\frac{-7-1}{-5-3}(x-3)[/tex]

[tex](y-1)=\frac{-8}{-8}(x-3)[/tex]

[tex]y - 1 = x - 3[/tex]

[tex]\implies y = x - 2------(1)[/tex],

Equation of second line is,

[tex]y = 0.5x - 1 -----(2)[/tex],

By equation (1) and (2),

x - 2 = 0.5x - 1 ⇒ 0.5x = 1 ⇒ x = 2,

From equation (1),

We get, y = 0,

Hence, the solution of line (1) and (2) is (2,0).

Determine the interest rate in order to Dublin investment in nine years assuming interest is compounded continuously

Answers

Set up the equation 2P=Pe^9r since you are doubling your money in nine years and it is continuous interest. Divide everything by P, so 2=e^9r, then take the ln of each side so ln2=9r. Now divide by 9 to get your interest. 

Find the value of x.

A.
25
B.
32.5
C.
37.5
D.
65

Answers

The answer is A. 25.
Hope this helped!

Answer:  The correct option is (A) 25.

Step-by-step explanation:  We are given to find the value of x from the figure shown.

From the figure, we note that there are two parallel lines and a transversal.

Also, the angles with measurements (x + 40)° and (3x - 10)° are corresponding angles.

Since the measures of two corresponding angles are equal, so we must have

[tex](x+40)^\circ=(3x-10)^\circ\\\\\Rightarrow x+40=3x-10\\\\\Rightarrow 3x-x=40+10\\\\\Rightarrow 2x=50\\\\\Rightarrow x=\dfrac{50}{2}\\\\\Rightarrow x=25.[/tex]

Thus, the required value of x is 25.

Option (A) is CORRECT.

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −6y2 − 9y = −1

Answers

[tex]-6y^2 - 9y = -1 [/tex]

[tex]y= \dfrac{-9+ \sqrt{9^2-4*-6} }{2*6}, \dfrac{-9-\sqrt{9^2-4*-6}}{2*6} [/tex]


[tex]y= \dfrac{-9+ \sqrt{105} }{12}, \dfrac{-9- \sqrt{105} }{12} [/tex]

Joe the trainer has two solo workout plans that he offers his clients: Plan A and Plan
b. Each client does either one or the other (not both). On Monday there were 2 clients who did Plan A and 3 who did Plan
b. On Tuesday there were 4 clients who did Plan A and 8 who did Plan
b. Joe trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 17 hours. How long does each of the workout plans last?

Answers

Let workout Plan A last a hours, and Plan B last b hours.

we are assuming personal training for each client.

i)
"On Monday there were 2 clients who did Plan A and 3 who did Plan"

the total time spent is : 2*a + 3*b =2a+3b

ii)
"On Tuesday there were 4 clients who did Plan A and 8 who did Plan B"

the total time spent was 4*a+8*b=4a+8b

iii) "Joe trained his Monday clients for a total of 7 hours"

so 2a+3b = 7

iv)

"Joe trained his Tuesday clients for a total of 17 hours"

so 4a+8b=17

v) thus we have the following system of equations:

2a+3b = 7
4a+8b=17

multiply the first equation by -2, and then add both equations, to eliminate a:

-4a-6b=-14
4a+8b=17
-------------------
2b=3, so b=3/2

2a+3b = 7
2a+3(3/2)=7
2a+9/2=7
multiply by 2:
4a+9=14
4a=5
a=5/4

Answer :

Plan A lasts 5/4=1.25 h
Plan B lasts 3/2=1.5 h


Divide 6 feet 6 inches by 5

Answers

6 ft 6 in....
1 ft = 12 inches, so 6 ft = (12 * 6) = 72 inches...+ the other 6 inches = 78 inches

78 / 5 = 15.6 inches


Final answer:

To divide 6 feet 6 inches by 5, convert the length to inches, divide by 5, then convert back to feet and inches, resulting in 1 foot 3 inches per section.

Explanation:

To divide 6 feet 6 inches by 5, first convert the entire length to inches. Since there are 12 inches in 1 foot, 6 feet equals 72 inches (6 feet x 12 inches/foot). Adding the additional 6 inches gives us a total of 78 inches. Now, divide 78 inches by 5 to find the length of each section.

78 inches ÷ 5 = 15.6 inches per section.

To convert this back to feet and inches, remember that there are 12 inches in a foot. Therefore, 15 inches is 1 foot 3 inches, and the remaining 0.6 inches can be expressed as a fraction of an inch (0.6 x 12 = 7.2, which is approximately 7 inches). So, each section is 1 foot 3 inches.

Suppose the vertex of a parabola is in the first quadrant and the parabola opens upwards. What can be determined about the value of a and the discriminant?

Answers

A parabola is the graph of a quadratic function, 

that is the graph of [tex]f(x)=a x^{2} +bx+c[/tex], where a is not 0.

from a, b and c we can derive the following informations about the shape of a parabola:

if a>0, the parabola opens upwards.
if a<0, the parabola opens downwards.

Consider the discriminant [tex]D= b^{2} -4ac[/tex]

If D>0, the parabola intersects the x-axis at 2 points.
If D=0, the parabola intersects the x-axis at 1 point.
If D<0, the parabola does not intersect the x axis.

"the vertex of a parabola is in the first quadrant and the parabola opens upwards."

the vertex is in the first quadrant means that the vertex is above the x-axis, and it opens upwards, so the parabola does not intersect the x-axis.

This means that:

Answer: a>0, the discriminant D<0

Final answer:

A parabola in the first quadrant opening upwards implies a positive 'a' value and a discriminant that, if not negative, yields real roots with positive values.

Explanation:

When a parabola has its vertex in the first quadrant and it opens upwards, we can determine specific values for a and the discriminant. The coefficient 'a' in the quadratic equation ax²+bx+c = 0 must be positive for the parabola to open upwards. Concerning the discriminant (calculated as b²-4ac), if the vertex is in the first quadrant, the parabola either does not intersect the x-axis at all (discriminant < 0), or it intersects the x-axis at one point (discriminant = 0) or two points (discriminant > 0) that both have positive x values.

The discriminant plays a key role in determining the nature of the roots of the quadratic equation. For quadratic equations constructed on physical data, they usually have real roots. Practical applications often deem the positive roots significant.

Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y. Which two figures have the same volume?
Choices:
Prism M
Cylinder p
Cone Z
And
Pyramid N
Prism Q
Cylinder Y

Answers

V=1/3*π*R²*H
Сone Z and Cylinder Y have the same volume. 

If a car is $27,000 and loses 15% of its value each year what will be the value in 5 years

Answers

$27,000

10%- $2,700.
5%- $1,350.

$2,700+ $1,350 = $4,050.

$4,050 × 5 = $20,250.

$27,000 - $20,250 = $6,750.

the value will be $6,750.

Need help. Thank you

Answers

The answer is D.
The side lengths aren't the same and you can tell by calculating the hypotenuses of sides AB and sides BC.
For AB 2^2+5^2= 29 The length is root 29.
For BC 2^2+4^2=20 The length is root 20.
A square must have equal side lengths, which this figure does not

Use the graph below for this question:

graph of parabola going through negative 3, negative 3 and negative 4, negative 1.

What is the average rate of change from x = −3 to x = −4?

3
4
−3
−2

Answers

average rate of change is just the slope betwen the points
that is just the slope between (-3,-3) and (-4,-1)

slpe between (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

so slope between (-3,-3) and (-4,-1) is (-1-(-3))/(-4-(-3))=(-1+3)/(-4+3)=2/-1=-2

the average rate of change is -2
I believe it's going to be -2

Calculate the average rate of change for the graphed sequence from n = 2 to n = 4. graphed sequence showing point 1, negative 3, point 2, negative 3.5, point 3, negative 6.75, point 4, negative 10.125, point 5, negative 15.1875, and point 6, negative 22.78125

Answers

 I believe the given sequence is in the tabular form of:

n             value

1              - 3

2              - 3.5

3              - 6.75

4              - 10.125

5              - 15.1875

6              - 22.78125

 

Now to find for the average rate of change from n1 = 2 to n2 = 4, we simply have to use the formula:

average rate of change = (value2 – value1) / (n2 – n1)

Substituting:

average rate of change = (- 10.125 – (-3.5)) / (4 – 2)

average rate of change = (- 6.625) / (2)

average rate of change = -3.3125

 

Therefore the average rate of change from n=2 to n=4 is -3.3125.

Answer:

B or −3.3125

Step-by-step explanation:

flex point 2023

In the triangle below, b = _____. If necessary, round your answer to two decimal places.

Answers

The Law of Sines is applicable here for quick calculation...

b/sin(180-42-41.5)=37/sin42

b/sin96.5=37/sin42

b=37sin96.5/sin42 units

b≈54.94 units (to nearest hundredth of a unit)


Answer: The value of b is approximately 54.94 .

Explanation:

In the given figure two angles are given and according to the angle sum property the sum of interior angles of a triangle is 180 degree.

[tex]\angle A+\angle B+\angle C=180[/tex]

[tex]42+\angle B+41.5=180[/tex]

[tex]\angle B=180-83.5[/tex]

[tex]\angle B=96.5[/tex]

According to the law of sine,

[tex]\frac{a}{\sin A} =\frac{b}{\sin B} =\frac{c}{\sin C}[/tex]

From given figure, [tex]\angle A=42,a=37[/tex]

[tex]\frac{37}{\sin (42^{\circ})}= \frac{b}{\sin (96.5^{\circ})}[/tex]

[tex]\frac{37}{0,66913} =\frac{b}{0.99357}[/tex]

[tex]b=54.94018[/tex]

[tex]b\approx 54.94[/tex]

Therefore, the value of b is 54.94.

A carnival game allows a group of players to each draw and keep a marble from a bag. The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles.

A player wins a large prize for drawing a gold marble and a small prize for drawing a silver marble. There is no prize for drawing a red marble.

At the start of the game, the probability of winning a large prize is 0.05 and the probability of winning a small prize is 0.25.

1. Suppose that the first player draws a silver marble and wins a small prize. What is the probability that the second player will also win a small prize?

2. If a group of four plays the game one at a time and everyone wins a small prize, which player had the greatest probability of winning a large prize?

3. How could the game be made fair for each player? That is, how could you change the game so that each player has an equal chance of winning a prize?

Answers

5 gold marbles,
25 silver marbles, and
70 red marbles.
------------------------------

100 total marbles

large prize: drawing a gold marble
small prize: drawing a silver marble.

At the start of the game,

probability of winning a large prize = positive outcoumes / total possible outcomes = 5 gold marbles / 100 total marbles =  0.05

probability of winning a small prize = positive outcomes / total possible outcomes = 25 silver marbles / 100 total marbles = 0.25.

1. Suppose that the first player draws a silver marble and wins a small prize. What is the probability that the second player will also win a small prize?

Answer:

numer of silver marbles / number of total marbles = (25 -1 ) / (100 - 1) = 24 / 99 ≈ 0.24

2. If a group of four plays the game one at a time and everyone wins a small prize, which player had the greatest probability of winning a large prize?

Answer:

First player: 0.25

Second player: 5 gold marbles / ( 100 - 1) total marbles = 5 /99 ≈ 0.0505

Third player: 5 gold marbles / (99 - 1) total marbles = 5 / 98 ≈ 0.051

Fourth player: 5 gold marbles / ( 98 - 1) total marbles = 5 / 97 ≈ 0.0515

So, the probability of winning a big prize increases as more balls different of gold marbles are extracted from the bag, and so, in this case, the fourth player has a greater chance to win a large prize.

3. How could the game be made fair for each player? That is, how could you change the game so that each player has an equal chance of winning a prize?

Answer: All the players would have equal chance of winning a prize if the balls were replaced in the bag after each play.

A spherical scoop of ice cream is placed on top of a hollow ice cream cone. the scoop and cone have the same radius. the ice cream melts completely and it fills the cone to the top. how many times greater is the height of the cone than the radius of the cone?

Answers

The figure shown below illustrates the problem.

The volume of the empty cone is
V₁ = (1/3) π r²h

The volume of the sphere is
V₂ = (4/3) π r³

Because the melted ice cream completely fills the cone, therefore
V₁ = V₂
(1/3) π r² h = (4/3) π r³
Divide each side by (1/3) π r².
h = 4r

Answer:
The height of the cone is 4 times greater than the radius f the cone.

Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is 1/2. What is the probability that the next child born to the same familiy will also be a girl?

Answers

for both children to be girls, the probability is 1/4

probability is 1/4 (b)

Step-by-step explanation:

WHICH ONE IS IT?////

Answers

The answer is:  [B]:  " (3.69/10) = 12/x " .
______________________________________________


Joe multiplies a number by 4, adds 1, and then divides by 3, getting a result of 7. sue divides the same original number by 3, adds 1, and multiplies by 4. what result does she get? express your answer as a common fraction.

Answers

Final answer:

Sue divides the initial number (which is 20/3 in this case) by 3, adds 1, and then multiplies by 4. Simplifying this we find her result to be 80/9 or 8 8/9.

Explanation:

Let's denote the initial number as 'x'. If Joe multiplies 'x' by 4, adds 1 and then divides by 3, getting 7, we can say that (4x+1)/3 = 7. Solving this equation, we find that x = 20/3.

Now let's apply this value to Sue's operations. Sue divides the initial number (which is 20/3) by 3, adds 1, and then multiplies by 4. Therefore, Sue's result is 4*((20/3)/3 + 1). Simplifying this expression, we obtain that Sue's result is 80/9 or 8 8/9.

Learn more about Number Operations here:

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A junior basketball has a diameter of approximately 7 in., and a regulation basketball has a diameter of approximately 9.5 in. about how many times as great is the volume of the regulation basketball as the volume of the junior basketball?

Answers

scale factor  = 9.5 / 7
the ratio of the volumes will be 9.5^3 / 7^3

=  2.5  to nearest thousandth

So the volume the regulation ball is  2.5 times the volume of the junior one.

Solve the system by the elimination method.
x + y - 6 = 0
x - y - 8 = 0
When you eliminate y , what is the resulting equation?

Answers

Since we have a positive y in one equation and a negative y in the other, we can simple add the two together to eliminate y...

2x-14=0

2x=14

x=7, which makes x+y=6 become:

7+y=6

y=-1, so the solution to the system of equations is the point:

(7, -1)

Answer: 2x = 14

Step-by-step explanation:

Solving the equation us in elimination method,

x + y - 6 = 0...1

x - y - 8 = 0...2

From 1,

x+y = 6...3

x-y = 8...4

To eliminate y, we will add equation 3 and 4 since both the signs attached to y are different.

2x=6+8

2x = 14 (This will be the resulting equation)

To get the variables x, we will divide both sides of the resulting equation by 2

x = 14/2

x = 7

Substituting x = 7 into eqn 3

7 + y = 6

y = -1

(15 POINTS) A card is drawn from a deck of 52. What is the probability of drawing either a diamond or a seven?
A) 6/13
B) 17/52
C) 19/52
D) 4/13

Answers

that would be a 6/13

Answer:

The correct answer is 4/13

Step-by-step explanation:

The events "drawing a diamond or a seven" are inclusive events since there is a seven of diamonds. Follow the rule for inclusive events.

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Hope this helps! :)

You invest $500 in an account with an annual interest rate of 1.1%, compounded continuously. How much money is in the account after 15 years? Round your answer to the nearest whole number.

Answers

The formula is
A=p e^rt
A future value?
P present value 500
E constant
R interest 0.011
T time 15 years
A=500×e^(0.011×15)
A=589.7

Determine the slope and y-intercept of the line.
y =  5x + 4

a.
Slope = 4, y-intercept is (0, 5)
c.
Slope =  5, y-intercept is (0, 4)
b.
Slope = -5, y-intercept is (0, 4)
d.
Slope =  4, y-intercept is (0, -5)




 

Please select the best answer from the choices provided

A
B
C
D

Answers

The answer is C. Slope = 5, y-intercept is (0,4)

AB is tangent to circle O at B. what is the length of the radius r? Round to the nearest tenth. Look at image attached.

Answers

check the picture below.

A circle is a curve sketched out by a point moving in a plane. The radius of the given circle is 8.4 units. The correct option is D.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

In a circle, a tangent is always perpendicular to the radius of the circle. Therefore, in the given figure the triangle formed will be a right angled triangle.

Now, in a right angle triangle, using the Pythagoras theorem the relation between the different sides of the triangle can be written as,

AO² = AB² + OB²

(9.8)² = 5² + r²

96.04 = 25 + r²

r² = 96.04 - 25

r² = 71.04

r = √(71.04)

r = 8.4

Hence, the radius of the given circle is 8.4 units.

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K is the midpoint of line segment lm. the coordinates of k are (5, 12) and the coordinates of l are (2, 6), find the coordinates of m.

Answers

midpoint (K) is (5,12)

L = (2,6)
M = (x2,y2)

midpoint = (x1 + x2)/2 , (y1 + y2) / 2
m = (2 + x2) / 2 , (6 + y2)/2

(2 + x) / 2 = 5
2 + x = 5 * 2
2 + x = 10
x = 10 - 2
x = 8

(6 + y) / 2 = 12
6 + y = 12 * 2
6 + y = 24
y = 24 - 6
y = 18

so M = (8,18) <==

The population of current statistics students has ages with mean muμ and standard deviation sigmaσ. samples of statistics students are randomly selected so that there are exactly 4242 students in each sample. for each​ sample, the mean age is computed. what does the central limit theorem tell us about the distribution of those mean​ ages?

Answers

We are told that the population has a mean of μ and standard deviation of σ.

From each sample of 42, we can compute a mean value of [tex]\Bar{x}[/tex].
We do not know the distribution for any sample.

According to the Central Limit Theorem, the distribution of the sample means will follow a normal distribution, regardless of the distribution of the individual samples.

Answer:
The distribution of sample means is normally distributed, and [tex]\Bar{x} \Rightarrow \mu[/tex],

Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.
Please help!!

Answers

check the picture below

thus then

[tex]\bf \qquad \textit{internal division of a line segment}\\\\ R(-2,4)\qquad S(18,-6)\qquad ratio1=3\qquad ratio2=7\qquad 3:7\\ \quad \\ \quad \\ \cfrac{RQ}{QS}=\cfrac{ratio1}{ratio2}\implies \cfrac{R}{S}=\cfrac{3}{7} \implies 7R=3S \\\\\\ 7(-2,4)=3(18,-6)[/tex]

[tex]\bf {{ Q=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}\\ \quad \\ \qquad thus\qquad \\ \quad \\ Q=\left(\cfrac{(7\cdot -2)+(3\cdot 18)}{3+7}\quad ,\quad \cfrac{(7\cdot 4)+(3\cdot -6)}{3+7}\right)[/tex]

Of five letters (a, b, c, d, and e), two letters are to be selected at random. how many possible selections are there

Answers

You can use C(5,2) which is [tex]5*4/2[/tex] which makes 10!
Other Questions
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