Answer: a) , where 'A' is the value of car after 't' years.
b) $12446.784
Step-by-step explanation:
Given: A new car that sells for $21,000 depreciates (decreases in value) 16% each year.
Then a function that models the value of the car will be
, where 'P' is the selling price of car, 'r' is the rate of depreciation in decimal, 't' is the time in years and 'A' is the value of car after 't' years.
Thus after substituting given value, the function becomes
To find the value after 3 years, substitute t=3 in the above function.
Hence the value of car after 3 years=$12446.784
The value of a car such as the 2017 Honda Civic decreases approximately 7% per year after manufacture. This is an example of exponential decay. After the first year, the car's value would be close to $18,172.
Explanation:The value of a car declining annually after its manufacture is an example of exponential decay in mathematics. In the case of the 2017 Honda Civic costing $19,540, the value decreases by approximately 7% each year. To calculate this, we can use the formula for exponential decay which is A = P(1 - r), where A is the final amount, P is the initial amount (price of the car), r is the rate of decrease (in decimal form), and n is the number of time periods (years in this case).
Now, if you want the value of the car after its first year, replace P with $19,540, r with 0.07, and n with 1. When calculating this, you should get a value close to $18,172, which is the approximate value of the car one year after it was manufactured.
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A cone and cylinder have the same height and the same base radius. If the volume of the cylinder is 81 cm^3 what is the volume of the cone in cm^3?
A) 9
B) 27
C) 78
D)243
Answer:
The volume of the cone is [tex]27cm^3[/tex]
Step-by-step explanation:
We know that formulas
Volume of cylinder is
[tex]V_1=\pi r^2 h[/tex]
Volume of cone is
[tex]V_2=\frac{1}{3}\pi r^2 h[/tex]
we are given
A cone and cylinder have the same height and the same base radius
So, both will have same radius and height
now, we can find ratios
[tex]\frac{V_2}{V_1}=\frac{\frac{1}{3}\pi r^2h }{\pi r^2h}[/tex]
now, we can simplify it
[tex]\frac{V_2}{V_1}=\frac{1}{3}[/tex]
we are given
the volume of the cylinder is 81 cm^3
so, [tex]V_1=81[/tex]
now, we can plug it and solve for V2
[tex]\frac{V_2}{81}=\frac{1}{3}[/tex]
[tex]81\times \frac{V_2}{81}=81\times\frac{1}{3}[/tex]
[tex]V_2=27[/tex]
So, the volume of the cone is [tex]27cm^3[/tex]
The volume of the cone, which has the same height and base radius as the cylinder with a volume of 81 cm³, is one-third that of the cylinder, equating to 27 cm³.
For a cone with the same height and base radius as the cylinder, the volume formula is V = ⅓πr²h, which is one-third of the volume of the cylinder. Given that the volume of the cylinder is 81 cm³, the volume of the cone can be found by dividing this value by 3, resulting in a volume of 27 cm³ for the cone. Therefore, the correct answer is B) 27 cm³.
solve for x
1 = − 4 + x
Answer: x = 5
Step-by-step explanation:
1 = -4 + x
We have to isolate x, and remember, what we do to one side we do to the other.
1 + 4 = -4 + 4 + x
5 = x
Check:
-4 + 5 = 1
1=1
Find the sum of 10(E)(i=3) 2i-9
The sum represented by the notation [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex] is 32
How to determine the sum represented by the notation
From the question, we have the following parameters that can be used in our computation:
[tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]
This means that we determine the value of the expression from i = 3 to i = 9 and then add them up
So, we have
2(3) - 9 = -3
2(4) - 9 = -1
2(5) - 9 = 1
2(6) - 9 = 3
2(7) - 9 = 5
2(8) - 9 = 7
2(9) - 9 = 9
2(10) - 9 = 11
Evaluate the sum
Sum = -3 - 1 + 1 + 3 + 5 + 7 + 9 + 11
Sum = 32
Hence, the sum represented by the notation is 32
Question
Find the sum of [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]
Kelli is running a mile in gym class. She runs at a pace of 6 minutes per mile. What's the dependent variable in the situation?
A. The length of the race
B. The amount of time passed
C. The distance Kelli has run
D. The speed at which Kelli runs
If you know this can you help me
[tex] log_24 + log_216 - log_232[/tex]
Answer: 1
Step-by-step explanation:
Method #1: Using the log rules (+ → x and - → ÷)
log₂4 + log₂16 - log₂32
= log₂[tex](\frac{4*16}{32})[/tex]
= log₂[tex](\frac{64}{32})[/tex]
= log₂2
= 1
Method #2: Using log rules to simplify each expression
log₂4 = x log₂16 = x log₂32 = x
4 = 2ˣ 16 = 2ˣ 32 = 2ˣ
2² = 2ˣ 2⁴ = 2ˣ 2⁵ = 2ˣ
2 = x 4 = x 5 = x
log₂4 = 2 log₂16 = 4 log₂32 = 5
2 + 4 - 5 = 1
The perimeter of a triangle is 28 feet. The sides of the triangle measure 10 feet, 9 feet, and x feet. Write and solve an equation to find the length of the missing side.
Kayson mixes 300 milliliters ( mL ) (mL) of spinach, 200mL of berries, and 42mL of dressing to make a salad. There are s s milligrams ( mg ) (mg) of vitamin C per milliliter of spinach, b mg bmg per milliliter of berries, and d mg dmg per milliliter of dressing. Which expressions can we use to describe how many milligrams of vitamin C are in the salad?
Answer:
X= (300 s + 200 b + 42 d )mg
Step-by-step explanation:
Amount of spinach=300 ml
Amount of berries =200 ml
amount of dressing = 42 ml
Vitamin C in one ml of spinach = s mg
Vitamin C in 300 ml of spinach = 300 s mg
Vitamin C in one ml of berries=b mg
Vitamin C in 200 ml of berries = 200 b mg
Vitamin C in one ml of dressing = d mg
Vitamin C in 42 ml of dressing = 42 d mg
Let total vitamin C be = x
Then
X= (300 s + 200 b + 42 d )mg
is the required expression
Which value is equivalent to (see attachment)
10/9
20/3
100/9
700/3
Point Q is the opposite of point P. Determind the location of point Q on the number line
Answer:
With a number line with two points opposite from each other on a number line, the middle of it is always going to be 0. Therefore, both points are the same distance away from 0 just in opposite directions. That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.
This method only works when it is specifically stated that the two points are opposite from each other.
Hope this helps!
xx,
myara
The location of Point Q on the number line is the opposite of the location of Point P. If Point P is at +a, then Point Q is at -a, and vice versa.
Explanation:In order to determine the location of Point Q, we first need to know the location of Point P on the number line. If we assume that point P is positive and located at +a, then Point Q, being the opposite of Point P, would be located at -a on the number line. Conversely, if Point P was negative and located at -a, the opposite, Point Q, would be on the +a location on the number line. The important thing to remember here is that opposite points on a number line are simply reflection of each other with respect to the origin (0).
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chris has 5 stack of dvd each stack has10 dvds if chris add 2 more identical stacks of dvds to the shelves how many dvds will chris have
what is the y intercept of the line y-14=6(x-2.5)
Answer:
The y intercept is -1
Step-by-step explanation:
y-14=6(x-2.5)
We need to get the equation in the form y = mx+b where b is the y intercept
Distribut the 6
y-14 = 6x -15
Add 14 to each side
y-14+14 = 6x-15+14
y = 6x-1
The y - intercept is -1
Answer:
(0, -1)
Step-by-step explanation:
y-14=6(x-2.5)
Distributive property:
y-14 = 6 * x - 6*2.5
y-14= 6x-15
Add 14 on each side:
y-14+14=6x-15+14
Simplify:
y=6x-1
In the form y=mx+b (slope-intercept form, as shown above), the y-intercept is (0, b). b is -1.
PLEAE HELP IM SO CONFUSED!An experiment involves selecting a numbered chip, some black and some white, from a bag of chips. The probability of selecting a black chip with an even number is 12 . The probability of selecting a black chip is 35 . What is the probability of selecting a chip with an even number given that the chip is black?
Answer: The probability of selecting a chip with an even number given that the chip is black = 5/6
Step-by-step explanation:
Let B represents the event of getting black chip,
While E represents the event of getting even chip.
So, according to the question,
It is given, The probability of selecting a black chip with an even number is,
[tex]P(B\cap E)=\frac{1}{2}[/tex]
And, The probability of selecting a black chip is,
[tex]P(B)=\frac{3}{5}[/tex]
Thus, the probability of selecting a chip with an even number given that the chip is black,
[tex]P(\frac{E}{B} )= \frac{P(B\cap E)}{P(B)} = \frac{1/2}{3/5}[/tex] ( By the conditional property )
⇒ [tex]P(\frac{E}{B} )= \frac{5}{6}[/tex]
Martina filled a 100mL container Simone filled a 1.2 liter container how much more water does Simone have than Martina
Answer:
divide 100 ml and 1.2 liter
Step-by-step explanation:
You will get the answer in percent
Answer:
10
Step-by-step explanation:
Please help need this answer
A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
(2, 0), (-3, 3), (9, 1), (-3, 5) NOT
(9, 1), (-3, 4), (2, 1), (9, 2) NOT
(2, 4), (-3, 2), (9, 1), (-7, 2) YES
(2, 4), (-3, 6), (2, 3), (-7, 2) NOT
Consider the piecewise-defined function given by the graph. What are these values?
A) f(–3) =
B) f(–1) =
C) f(3) =
Answers:
f(-3) = -1
f(-1) = 2
f(3) = 5
======================================
Explanations:
Draw a vertical line through -3 on the x axis. Make sure this vertical line crosses the orange graph. Mark this point of intersection and then draw a horizontal line from this point to the y axis. You should find that it touches -1 on the y axis. Check out the attached image to see this process in action.
Those steps basically say that x = -3 leads to y = -1. Since y = f(x), this means f(-3) = -1
Through similar steps, you should find that f(-1) = 2 and f(3) = 5
Note that the open hole/circle does not count. So if you land on an open hole, just keep going until you hit a closed circle on the other piece of the graph.
A) f (–3) = -1
B) f (–1) = 2
C) f (3) = 5
Further explanationStraight-line equations are mathematical equations that are described in the plane of cartesian coordinates
General formula
y-y1 = m (x-x1)or
y = mx + c
Where
m = straight-line gradient which is the slope of the line
x1, y1 = the Cartesian coordinate that is crossed by the line
c = constant
The formula for a gradient (m) between 2 points in a line
m = Δy / Δx
or we can use:
[tex]\rm \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}[/tex]
Piecewise Functions: functions that have different equations based on the input (x) value
We look for 3 pieces of function from the graph
1. graph 1 is a straight line that passes through 2 points : (-4.0) and (-1, -3) so that the straight line equation:
[tex]\rm \dfrac{y-0}{-3-0}=\dfrac{x+4}{-1+4}\\\\\dfrac{y}{-3}=\dfrac{x+4}{3}\\\\3y=-3(x+4)\\\\3y=-3x-12\\\\y=-x-4\Rightarrow \:for\:x<-1[/tex]
2. graph 2 is a straight line with the equation: \
[tex]\rm y=2\Rightarrow \:for\:-1\leq x<3[/tex]
3. graph 1 is a straight line that passes through 2 points, (3.5) and (5.1) so that the straight line equation :
[tex]\rm \dfrac{y-5}{1-5}=\dfrac{x-3}{5-3}\\\\\dfrac{y-5}{-4}=\dfrac{x-3}{2}\\\\2(y-5)=-4(x-3)\\\\2y-10=-4x+12\\\\2y=-4x+22\\\\y=-2x+11\:\Rightarrow for\:x\geq 3[/tex]
A function made up of 3 pieces:
a solid dot means "including",
an open dot means "not including"
[tex]\rm y=-x-4\:for\:x<-1[/tex]
[tex]\rm y=2\:for\:-1\leq x<3[/tex]
[tex]\rm y=-2x+11\:for\:x\geq 3[/tex]
A) f (–3) =
Because -3 <-1, the function used is y = -x-4, so
f (-3) = - (- 3) -4
f (-3) = 3-4
f (-3) = -1
B) f (–1) =
Because x = -1, the function used y = 2, so
f (-1) = 2
C) f (3) =
Because x = 3, the function used is = -2x + 11, so
f (3) = -2 (3) +11
f (3) = -6 + 11
f (3) = 5
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an 8 in. by 10 in. photo is reduced so that the width (the shorter dimension) is 3 in. what is the length of the reduced photo
Answer:
Step-by-step explanation:
The length can be found by setting up a proportion. If the width is reduced by some ratio, then the length will share the same ratio.
3 / 8 = x / 10 Multiply both sides by 10.
3 * 10 / 8 = x Multiply first
30/8 = x Divide next. You don't need to do it in this order.
3 6/8 Simplify
3 3/4 Give another choice
3.75
The length = 3.75 inches
If none of these are correct, please leave a note with your choices.
Answer:
The length = 3.75 inches
Step-by-step explanation:
Use the following flowchart to determine if the family qualifies for bankruptcy. Their yearly income is 58,000- the median annual income is $47,778 and the family has a monthly expenses of $4,600.
Answer:
Do not qualify
Step-by-step explanation:
Yearly income = $58000
Monthly income = [tex]\frac{58000}{12}[/tex] = $4833.33
Median annual income = $47778
Monthly expenses = $4600
Income < Median Income ? 58000 < 47778 -> No
x = (Monthly income - expenses) * 60
= (4833.33 - 4600) * 60
= 233.33 * 60
= 13999.8
x < 10000 ? 13999.8 < 10000 -> No
So, Do not qualify
Answer:
The family does not qualify for bankruptcy
Step-by-step explanation:
Expenses=$4,600
Yearly income=$58,000
Monthly income=Yearly income / 12
Monthly income=$58,000/12
Monthly income=$4,833.333333
Rounded to the nearest cent:
Monthly income=$4,833.33
Flowchart
No
Mean test. Calculate
Income=$58,000<$47,778=Median → (Monthly income - expenses)*60
Income ($4,833.33-$4,600)*60
($233.33)*60
$13,999.80
Call this number X. No
X=$13.999.80 < $10,000 → Do not
qualify
The family does not qualify for bankruptcy
what is the midpoint of mn?
First off, the length of MN is 2√10, not 8. This is because using Pythagorean Theorem, you get that MN=√4+36=2√10, which is (3).
The midpoint of MN can be found by finding the average of the coordinates of M and N. Therefore, our first part to solving this question is to find the coordinates of M and N. M is (2,5) and N is (4,-1). Finding the average of the x-coordinates gives us 3. Finding the average of the y-coordinates gives us 2, Therefore, the midpoint of MN is (3,2), or answer choice (3).
How many milliliters can fit into 5 liters.
Answer:
5000.
Step-by-step explanation:
1000 milliliter is one liter. So if you have 5 liters 5 x 1000 can fit inside.
I need HELP guys i can't really figure these two out
Answer:
m=1
Boys: Girls
2:1
Step-by-step explanation:
To find the slope from 2 point we use the formula
m = (y2-y1)/(x2-x1)
m = (-13--10)/(3-6)
= (-13+10)/(3-6)
= -3/-3
= 1
Boys: Girls
16:8
We can divide each number by 8
16/8: 8/8
2:1
Boys: Girls
2:1
The diagram shows two parallel lines cut by two transversals. Which statement is NOT true?
A. Angle c is congruent to angle e.
B. The measures of angles a, d, and e sum to 180°.
C. Angles a, b, and c are the interior angles of a triangle.
D. Angle b is congruent to angle e.
Answer:
D
Step-by-step explanation:
A) True. Alternate interior angles are congruent so
[tex]\angle c\cong \angle e[/tex]
B) True. Considering the sum of these three angles is equal to a straight angle. Since ∠a+∠d supplementary to ∠e
[tex]\angle a+\angle e+\angle d=180[/tex]
C) True. Since the line segments form a triangle having a (black) line as triangle base.
D) False. ∠b is congruent to its corresponding angle, and ∠e is not its corresponding angle. The corresponding angle of ∠b is the angle vertex opposed to ∠d (not identified).
If x-1/3 = k and k = 3, what is the value of x ?
A) 2
B) 4
C) 9
D) 10
Answer:
None of the above
Step-by-step explanation:
x-1/3 = k
We know that k=3, so we can substitute that into the equation
x-1/3 = 3
Add 1/3 to each side
x-1/3 + 1/3 = 3+1/3
x = 3 1/3 or as an improper fraction 10/3
which is greater 23/44 or 33/64
Answer:
23/44 < 33/64
Step-by-step explanation:
if you don't want to get common denominators multiply the denominator of the second fraction by the numerator of the first (1,427) and the denominator of the first one to the numerator of the second (1,452) the bigger number is greater. 1,427 < 1,452
By converting both fractions into decimals (23/44 becomes 0.5227; 33/64 becomes 0.5156), it is clear that 23/44 is greater than 33/64.
Explanation:To compare which fraction, 23/44 or 33/64, is greater, you need to find a common denominator and then compare the numerators. The calculation can be simplified by converting these fractions into decimals. To do so, divide the numerator by the denominator. Therefore, 23/44 becomes 0.5227 and 33/64 becomes 0.5156. Therefore, 23/44 is greater than 33/64.
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-7/10 divided by 2/5 in it's simplest form
To divide fractions, multiply the first fraction (-7/10) by the reciprocal of the second one (5/2). This gives -35/20 which simplifies to -7/4 or -1 3/4.
Explanation:When dividing fractions, the conventional method is to multiply the first fraction, which is the dividend, by the reciprocal of the second fraction, which is the divisor. In this case, let's take the content loaded -7/10 divided by 2/5.
The reciprocal of 2/5 is 5/2. So, to divide -7/10 by 2/5, we instead multiply -7/10 by the reciprocal of 2/5.
-7/10 * 5/2 = -35/20.
Finally, we simplify this to its simplest form, by reducing to the lowest terms. We find that, -35/20= -7/4 or -1 3/4 if expressed as a mixed number.
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There are 36 female performers in a dance recital. The ratio of men to women is 5:6. How many men are in the dance recital?
point A lies in plane B how many planes can be drawn perpendicular to plane B through point A
1) one
2)two
3) zero
4) infinite
Answer:
4
Step-by-step explanation:
Only one plane can be drawn perpendicular to plane B through point A in three-dimensional space. The correct answer is option 1) that is One.
The question at hand involves geometric concepts, specifically the relationship between planes and lines in three-dimensional space. If point A lies in plane B, then there can be one and only one plane drawn perpendicular to plane B through point A; this is because in three-dimensional space, a point defines a line and only one perpendicular plane can contain that line.
This principle is similar to how any three points not on a single straight line determine a plane and how two lines intersect at a single point or not at all. The perpendicular plane would form a 90-degree angle along every line in plane B that passes through point A.
The correct answer is option 1) that is One
You have two exponential functions. One function has the formula g(x) = 3 x . The other function has the formula h(x) = 2-x. Which option below shows the graph of k(x) = g(x) - h(x)?
Answer:
k(x) = 4x - 2
Please refer attachment for the graph.
Step-by-step explanation:
Given :
g(x) = 3x
h(x) = 2- x
k(x) = g(x)-h(x)
k(x) =3x -(2-x) = 3x -2 +x =4x -2
∴k(x) = 4x - 2
Which of the lines graphed has a slope of 1 and a y-intercept of -3?
Answer:
C
Step-by-step explanation:
The line has a positive slope which means it slopes upwards from left to right
A and B slope downwards so can be excluded
C and D have the correct upward slope but C has the y-intercept of - 3
Thus C is the required line
Ed has 28 blocks. Sue has 34 blocks who has more blocks? How many more?
Answer:
Sue // 6 More blocks
Step-by-step explanation:
Sue has more blocks because 34>28.
34-28 is 6 so sue has 6 more.