The value of a car that costs $30,000 and depreciates at 6.5% annually will be $22,530 after 5 years, calculated using exponential decay.
The value of a car is $30,000 and it loses 6.5% of its value each year. To calculate the value of the car after 5 years, we can apply the concept of exponential decay. The value after one year would be the initial value minus 6.5% of the initial value. Mathematically, we can express this as:
V1 = V0 (1 - 0.065),
where V1 is the value after one year and V0 is the initial value. To find the value after 5 years, we would apply this formula iteratively or use the formula for exponential decay:
Vn = V0 x (1 - 0.065)ⁿ,
where Vn is the value after n years. Therefore:
V5 = $30,000 x (1 - 0.065)⁵,
V5 = $30,000 x (0.935)⁵,
V5 = $30,000 x 0.7510,
V5 = $22,530.
After 5 years, the value of the car will be $22,530.
The circumference of a circular frisbee is 20 centimeters. If
we multiply the radius of the frisbee by 5, what will be the
circumference of the new frisbee?
OA) 981 cm
OB) 100 cm
OC) 1451 cm
OD 2007 cm
Answer:
100cm
Step-by-step explanation:
since the circumference is 20cm and formula for finding a circumference of a circle is c=2(pi)r, where r is radius and pi is constant value which is equivalent to 22/7. so the radius of 20cm circumference is 3.1847 by using this eqn c/2(pi)=r. now the calculated radius will b multiply by 5 to get 15.92cm which is put in cirumference formula i.e. c=2(pi)r we get 100cm circumference.
Jake swims a distance from one end of a 50 meter pool to the other end in 25 seconds. What is his average speed?
Answer:
2 meters/ second
Step-by-step explanation:
Speed is equal to distance divided by time
Speed = 50 meters / 25 seconds
= 2 meters/ second
If gasoline costs $47.86 for 12.5 gallons of gasoline, how much does it cost for 8 gallons?
Round your answer to the nearest cent.
Answer:
8 gallons of gasoline costs $30.63.
Step-by-step explanation:
Set up a proportion to solve for x, or the cost of 8 gallons of gasoline. The $47.86 goes on top of the first ratio, and 12.5 goes on top of the second. This is because the $47.86 is the cost of the 12.5 gallons of gasoline. Next, put x on the bottom of the first ratio and 8 on the bottom of the second ratio. This is because the amount of money you are trying to find, x, is the cost of the 8 gallons of gasoline. The proportion should look like this: [tex]\frac{47.86}{x} = \frac{12.5}{8}[/tex]
To solve the proportion, use cross multiplication. To do that, multiply 8 by 47.86 to get 382.88. Then, divide 382.88 by 12.5. The answer is 30.6304, so round to the nearest cent to get a total of $30.63.
I hope this helps! ☺
WHICH SENTENCE IDENTIFIES THE Y INTERCEPT AND ORDERED PAIR OF THE POINT ON THE GRAPH
What is the angle of a triangle if one angle is 68 and the other is 52
Answer:
The last angle is 60 degrees
Step-by-step explanation:
All triangles add up to 180 degrees
Step 1: Make an equation
What is the angle of a triangle if one angle is 68 and the other is 52.
68 + 52 + x = 180
Step 2: Combine like terms
68 + 52 + x = 180
120 + x = 180
Step 3: Subtract 120 from both sides
120 + x - 120 = 180 - 120
x = 60
Answer: The last angle is 60 degrees
The sum of the angles in a triangle will be equal to 180°.
68 + 52 = 120°
180 - 120 = 60° (This is the 3rd angle)
Best of Luck!
between the time Iko woke up and lunchtime, the temperature rose by 11°. Then by the time he went to bed, the temperature dropped by 14 °. Write an addition expression for the temperature relative to when Iko woke up.
Answer:
x + (11) + (-14) [x being temperature when Iko woke up]
Step-by-step explanation:
Let the temperature be "x" when Iko woke up
Then,
Temperature ROSE 11° in lunch
The temp in lunch was: x + 11
Then the temperature DROPPED 14° when he went to bed, relative to lunch temperature, so we can say:
(x + 11) - 14
So, the final temperature that end of day was:
x + 11 - 14
As addition expression, it will be:
x + (11) + (-14)
The manufacturer of cell phones spends $320 to make each cell phone and sells them for 440 . The manufacturer also has fixed costs each month of $11400 .
Answer:
x=95
Step-by-step explanation:
320x+11400=440x
320*95+11400=440*95
30,400+11,400=41,800
41,800=41,800
The manufacturer needs to sell approximately 95 cell phones to cover its fixed costs of $11,400 per month. The profit per month depends on the number of units sold, with a contribution margin of $120 per unit after covering variable costs.
To analyze the manufacturer's costs and profitability, we can break down the information provided:Cost to Make Each Cell Phone: $320 per unitSelling Price of Each Cell Phone: $440 per unitFixed Costs: $11,400 per monthFirst, let's calculate the variable cost per unit, which is the cost to make each cell phone:Variable Cost per Unit = Cost to Make Each Cell Phone = $320Now, we can calculate the contribution margin per unit, which is the amount each phone contributes to covering fixed costs and generating profit:Contribution Margin per Unit = Selling Price - Variable Cost per UnitContribution Margin per Unit = $440 - $320 = $120Next, calculate the break-even point in units, which is the number of units the manufacturer needs to sell to cover its fixed costs:Break-Even Point (in units) = Fixed Costs / Contribution Margin per UnitBreak-Even Point (in units) = $11,400 / $120 ≈ 95 unitsSo, the manufacturer needs to sell approximately 95 cell phones to cover its fixed costs.To determine the profit, we can calculate the profit per month after covering fixed costs:Profit per Month = (Selling Price - Variable Cost per Unit) * Number of Units Sold - Fixed CostsSuppose the manufacturer sells "X" cell phones per month. Then:Profit per Month = ($440 - $320) * X - $11,400Now, you can calculate the profit for any given number of cell phones sold.For more questions on profit -
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You are riding your bicycle. It takes you 9min to go 2.5 mi. If you continue traveling at the same rate, how long will it take you to go 7 mi?
Answer:
Step-by-step explanation:
To find out how many miles you are going per minute you would find the unit rate. The unit rate is 3.6
You are going at 3.6 minutes per mile.
So you would multiply 3.6 by 7 to get 25.2 minutes.
5x - 1= 3х + 9
Find x
Answer:
X=5
Step-by-step explanation:
[tex]5x - 1 = 3x + 9 \\ 5x - 3x = 9 + 1 \\ 2x = 10 \\ x = 5[/tex]
5x-1=3x+9
collect like terms
5x-3x=9+1
2x=10
divide both sides by 2
x=5
Find the distance from the point (3,2) to the line 2y + 3x = 5. Round your answer to the nearest tenth.
Answer:
(8/13)√13 ≈ 2.2
Step-by-step explanation:
The distance from point (x, y) to line ax+by=c can be found using the formula ...
d = |ax +by -c|/√(a²+b²)
Filling in the given values, we find the distance to be
d = |3·3 +2·2 -5|/√(3² +2²) = 8/√13
d = (8√13)/13 ≈ 2.2 . . . . . after rationalizing the denominator
Use rounding to estimate the product.
8.24 × 5.88
40
45
48
85
Answer:
Its 48.4512 and rounded it is 48 :)
Which best describes the graphs of the line that passes through (−12, 15) and (4, −5), and the line that passes through (−8, −9) and (16, 21)?
A)
They are parallel lines.
B)
They are vertical lines.
C)
They are perpendicular lines.
D)
They are intersecting lines.
Answer:
C) They are perpendicular lines.
Step-by-step explanation:
We first need to find the slope of the graph of the lines passing through these points using:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
The slope of the line that passes through (−12, 15) and (4, −5) is
[tex] m_{1} = \frac{ - 5 - 15}{4 - - 12} [/tex]
[tex]m_{1} = \frac{ - 20}{16} = - \frac{5}{4} [/tex]
The slope of the line going through (−8, −9) and (16, 21) is
[tex] m_{2} = \frac{21 - - 9}{16 - - 8} [/tex]
[tex] m_{2} = \frac{21 + 9}{16 + 8} [/tex]
[tex]m_{2} = \frac{30}{24} = \frac{5}{4} [/tex]
The product of the two slopes is
[tex]m_{1} \times m_{2} = - \frac{4}{5} \times \frac{5}{4} = - 1[/tex]
Since
[tex]m_{1} \times m_{2} = - 1[/tex]
the two lines are perpendicular.
Answer:D) They are intersecting lines.
Step-by-step explanation: that other answer was wrong .
Which statement show equivalent expressions? PLEASE HELP ME ASAP
A 5(x−2)=5x−3
B 3(x+6)+x=4x+9
C 8(2x+3)=16x+24
D 4(5x+2)−6=20x+14
Answer:
c.
Step-by-step explanation:
8(2x+3) = 16x + 24
8(2x) + 8(3) = 16x + 24
Answer:
C)
Step-by-step explanation:
C) 8(2x+3)=8*2x+8*3=16x+24 true
[]: what is 20056x345
Answer:
6,919,320
Step-by-step explanation:
20056 * 345
6919320
Answer: 6,919,320
Answer:
6,919,320.00
Step-by-step explanation:
a pair of running shoes costs $37 less than twice the cost of a pair of basketball sneakers. The sneakers cost $48.50. How much do the running shoes cost?
Answer:
11.5
Step-by-step explanation:
Sneakers = 48.50
Expression for cost of running shoes = 2(sneakers) - 37
Plug in value of sneakers and solve:
2(48.50) - 37
97 - 37
$60
The running shoes cost $60.
Hope this helps!! :)
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees. What is the measure of Angle A B C ? 36° 43° 72° 144°
Answer:
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°.
Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees.
What is the measure of Angle A B C ?
36° *****
43°
72°
144°
Step-by-step explanation:
its 36°
Applying the central angle theorem, the measure of angle ABC is: a. 36°
What is the Central Angle Theorem?The central angle theorem states that the angle measure of a central angle equals the measure of the intercepted arc.Inscribed angle = half the intercepted arc.Given:
m∠ADC = (7x + 2)° (central angle)
measure of intercepted arc AC = (8x - 8)°
Therefore:
(7x + 2)° = (8x - 8)°
Solve for x7x + 2 = 8x - 8
8 + 2 = 8x - 7x
10 = x
x = 10
Thus:
m∠ABC is an inscribed angle = half of measure of intercepted arc AC
Therefore:m∠ABC = 1/2(8x - 8)°
Plug in the value of xm∠ABC = 1/2[8(10) - 8]
m∠ABC = 36°
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Which expressions are equivalent to
2 In a + 2 In b - In a?
Check all that apply.
Answer:
ln ab^2
ln a + 2 ln b
ln a^2 + ln b^2 - ln a.
Step-by-step explanation:
2 ln a + 2 ln b - ln a
= ln a^2 + ln b^2 - ln a
= ln (a^2/a) + ln b^2
= ln a + 2 ln b
= ln a + ln b^2
= ln ab^2.
Yo sup??
2lna+2lnb-lna
=lna²+lnb²-lna
=lna²b²/a
=lnab²
correct answer is option E
Hope this helps
0.009 times 0.07
show how you got the answer
Answer:
63/100000 or 0.000063
Step-by-step explanation:
0.009*0.07 is the same as 9/1000*7/100 which is 63/100000 when you multiply numerator with numerator and denominator with denominator.
So your answer is 63/100000 or 0.000063
9.0758 to 2 significant figures.
Answer w/ explanation:
The answer is 9.1
To round to 2 significant figures, we have to find the first significant figure. We find the first sig fig by looking for the first nonzero digit in the number (it can be before or after the decimal point), which is "9"
The next digit is "0". This will also be a significant figure in our answer.
It may seem we are done now since we found the two significant figures. However, let's look at the digit after "0" to see if we need to round up or down.
The digit after "0" is "7". Since 7 is greater than 5, we round up the "0" to a "1" in our final answer, making the answer 9.1
Side note:
The definition and concept of significant figures can be very confusing overall, so please continue to ask questions if you are still struggling with them.
Let me know if you need any clarifications, thanks!
~ Padoru
A number 9.0758 to 2 significant figures is, 9.1
We have to give that,
A number is,
⇒ 9.0758
Since There are 5 significant numbers.
Hence, A number 9.0758 to 2 significant figures is,
⇒ 9.0758
Since 7 is greater than 5.
Hence,
9.0758 ≈ 9.1
So, The solution is, 9.1
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slope:
y-intercept:
equation:
We can conclude -
m = -A/B → unit rate of change of [y] with respect to [x].c = - C/A → the point where the graph cuts the [y] axis.Equation → y = mx + cWhat is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
Given is a straight line.
The equation of a straight line is written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Now, from this we get -
m = -A/B {Slope}
c = - C/A {y - intercept}
So, the equation will be -
y = mx + c
We can also calculate slope by -
m = (y₂ - y₁)/(x₂ - x₁)
Therefore, we can write -
m = -A/B → unit rate of change of [y] with respect to [x].
c = - C/A → the point where the graph cuts the [y] axis.
Equation → y = mx + c
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Sales tax in Pennsylvania is 6%. Carlos bought a mountain bike that costs $125.50 before tax. What was the cost of the new bike including sales tax?
Answer:
$878.50
Step-by-step explanation:
it's asking about new bike cost including sales tax.
Strawberries cost $2.14 per pound and Annie purchased 1.3 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?
A. $2.78
B. $2.79
C. $27.82
D. $27.90
Answer:
A. $2.78
Step-by-step explanation:
You would multiply the cost per pound, $2.14, by the amount of pounds bought, 1.3. Then round to the nearest hundredth.
2.14 x 1.3 = 2.782
2.782 rounded to the nearest hundredth is $2.78
Answer:
I think it is 2.78 sorry if it’s not
Step-by-step explanation:
what’s the relationship? linear, exponential, or neither?
Answer:
This relationship is linear
Step-by-step explanation:
As x goes up by 5, y goes up 3. Since this is a constant rate, this relationship is, therefore, linear
1. Find the x-intercept of the line: 5x - y = 10
2. Find the y-intercept of the line: 9x + 3y = -18
3. What are the x- and y- intercepts of the graph of 6x - 4y = -12
Final answer:
The x-intercept of the line 5x - y = 10 is (2, 0), the y-intercept of the line 9x + 3y = -18 is (0, -6), and the equation 6x - 4y = -12 has an x-intercept at (-2, 0) and a y-intercept at (0, 3).
Explanation:
To find the x-intercept of a line, we set the value of y to zero and solve for x. For the equation 5x - y = 10, we set y to 0:
5x - (0) = 10
5x = 10
x = 2
The x-intercept is therefore the point (2, 0).
To find the y-intercept of a line, we set the value of x to zero and solve for y. For the equation 9x + 3y = -18, we set x to 0:
(0) + 3y = -18
3y = -18
y = -6
The y-intercept is therefore the point (0, -6).
For the equation 6x - 4y = -12, the x-intercept and y-intercept can be found similarly. Let's start with the x-intercept. Set y to 0:
6x - (0) = -12
6x = -12
x = -2
The x-intercept is the point (-2, 0). Now, for the y-intercept, we set x to 0:
(0) - 4y = -12
-4y = -12
y = 3
The y-intercept is the point (0, 3). Thus, for 6x - 4y = -12, the intercepts are x = -2 and y = 3.
Look at the image used by the author of "Heads Up on
Sports Safety
Look at the image used by the author of "Heads Up on
Sports Safety
The author most likely included this image from an outside
resource to show how
stadiums have changed.
photographic technology has changed.
football uniforms have changed.
football strategies have changed.
The author most likely included this image to show how football uniforms have changed.
Why the image is added?
The thesis of "Heads Up on Sports Safety" is, as the name implies, sports safety.
The image shows some kids, all of them with their correspondent football equipment (protective equipment).
So, what is being presented in the image, is in some way how the "football uniforms have changed." In a way in which the safety of the players is a priority.
So that is the correct option.
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PLS HELP
What is the volume of the right rectangular prism shown?
A. 8 un3
B. 20 un3
C. 24 un3
D. 12 un3
Answer:
12 UN 3
Step-by-step explanation:
ok i hope this is right answer
find x and y?????????
Answer:
[tex]a)\\x=12\\y=12\sqrt{3}[/tex]
Step-by-step explanation:
The angle without a numerical value is 30°
Using the 30-60-90 rule:
x = a24 = 2ay = [tex]a\sqrt{2}[/tex]Since we know that 2a is the side with length 24
[tex]2a=24\\a=24/2\\a=12\\x=12[/tex]
To find y
[tex]y=a\sqrt{3}\\a=12\\y=12\sqrt{3}\\[/tex]
Which point approximates the square root of 15
Option B:
Point B approximates [tex]\sqrt{15}[/tex].
Solution:
Let us first find the approximate value of [tex]\sqrt{15}[/tex].
[tex]\sqrt{15}=3.87[/tex]
In the number line 3.87 lies between 3 and 4.
So that [tex]\sqrt{15}[/tex] lies between 3 and 4.
Look at the given number line.
Point B lies between 2 and 4.
Hence point B approximates [tex]\sqrt{15}[/tex].
Option B is the correct answer.
Which fraction can be expressed as a terminating decimal? 1/9, 3/11, 5/8, 2/3
Answer:
2/3 can be expressed as 0.6666666666666666666666 repeating
Step-by-step explanation:
Answer:
1/3 there is no 2/3
Step-by-step explanation:
If I have 30 vegetables and 2 of the vegetables are beans. What percentage of vegetables are beans
Answer:
6%
Step-by-step explanation:
.02 times 30
.6=6%