A naomi's car exponentially depreciates at a rate of 8% per year. if nina bought the car when it was 4-years old for $16,500, . what the approximate original of the car?
The original price of the car before 4 years will be $23,032.
What is an exponent?Consider the function:
y = P (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, P = original amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %
A Naomi's car exponentially depreciates at a rate of 8% per year.
If Nina bought the car when it was 4 years old for $16,500.
Then the original price will be
16500 = P(0.92)⁴
16500 = 0.716P
P = $ 23,032
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A map has the scale 1 : 200,000 and the distance between two villages on the map is 8 cm. What is the distance in metres between the towns in real life?
The distance in metres between the towns in real life is 1600000 meters
How to determine the distance in real life?The scale ratio is given as:
Scale = 1 cm : 200000 m
The map distance of 8cm implies that:
8 cm : Real = 1 cm: 200000 m
Express as fraction
Real/8 = 200000 m/1
Multiply both sides by 8
Real = 1600000 m
Hence, the distance in metres between the towns in real life is 1600000 meters
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Pythagorean theorem. How do I solve this?
Answer:
By using the pythsgorean theorem! simple
Answer:[tex]\sqrt{155}[/tex]
Step-by-step explanation:
Oh god pythagorean triples got thrown out the window for this one. This will be a bit ugly.
First, we find the other side length of the rectangle using the pythagorean theorem.
Then, we use that side length in ANOTHER pythagorean theorem to get our answer.
Well, we know that the side length is [tex]\sqrt{5^{2}+9^{2} }[/tex]
We'll use whatever that number is, let's call it x for now, in our other expression:
[tex]\sqrt{x^{2}+7^{2}}[/tex]
So we can do this in one clean equation by substituting our first equation as x in the second one.
Or do them separately. Your choice.
Anyways, try to solve this one now that you know what to do. If you need more help then message.
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who does not have a dog has a cat?
Has a cat Does not have a cat
Has a dog 8 6
Does not have a dog 7 3
The probability that a student who does not have a dog has a cat is 7/10.
What is the probability?Probability determines the chances that a random event would happen. The odds that the random event would happen lies between 0 and 1.
The probability that a student who does not have a dog has a cat = number of students that do not have a dog but has a cat / total number of students that do not own a dog
= 7/10.
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Area of the shaded segment=
The area of the entire sector is [tex](\pi)(6^{2}) \left(\frac{60}{360} \right)=6\pi[/tex]
The area of the triangle OAB is [tex]\frac{\sqrt{3}}{4}(6^{2})=9\sqrt{3}[/tex].
So, the area of the segment is [tex]\boxed{6\pi-9\sqrt{3}}[/tex]
HELP PLEASEEE GEOMETRY
What is the scale factor of the dilation of line segment ba? one-fifth one-fourth 4 5
The scale factor of the dilation of line segment BA is 1/5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Dilation is the increase or decrease in the size of a figure.
From the diagram:
scale factor of BA = AC / CA' = 4 / (4 + 16) = 1/5
The scale factor of the dilation of line segment BA is 1/5.
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Answer:
B
Step-by-step explanation:
I do believe
how to workout that i need the way of how to work it out not the answer
Simplify the following radical expression.
√20
OA. 2√5
OB. 5√2
OC. 4√5
D. 10√5
OO
The solution of the given radical expression√20 using factorization is [tex]2 \sqrt{5}[/tex]. Therefore, the correct option for the radical expression√20 is option A, i.e [tex]2 \sqrt{5}[/tex].
A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression.
Example = 4y, 3x+4.
An expression containing the values in the form of square root, cube root is called a radical expression.
The breaking of a number into its own factors, so that they multiply to give the same number again, is called factorization.
Given expression, √20
The solution of the expression can be obtained by the factors of 20.
[tex]\sqrt{20} = \sqrt{2\times2\times5}[/tex]
[tex]\sqrt{20}[/tex] = [tex]2 \sqrt{5}[/tex]
Here, 2 and 5 are factors of 20.
Thus, the value of the radical expression [tex]\sqrt{20}[/tex] is [tex]2 \sqrt{5}[/tex].
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What is the simplified form of 3 over x squared all over 1 over x-cubed ? (1 point)
A. x/3
B. 1/3x
C. 3x
D. 3/x
The answer is 3x. C is correct.
Help me out please asap
a boat sails due south from a port at a steady speed of 9 km/h.
the wind blows the boat due west at a speed of 3 km/h. how far is the boat from the port after 1 h?
give your answer to 1 decimal place.
The distance travelled by boat after 1 hour will be 10km.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
The distance will be calculated as:-
a²+b²=c²
9² + 3 ²= c ²
81+9 = c²
100 = c²
c = 10 km / hour
The distance travelled after one hour will be calculated as:-
Distance = Speed x Time
Distance = 10 x 1 = 10 Km
Therefore the distance travelled by boat after 1 hour will be 10km.
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Simplify: square root of 81+18[tex]\sqrt{7}[/tex]+7
[tex] \sqrt{81 \: + \: 18 \sqrt{7} \: + \: 7} [/tex]
Factor the indicated expression:[tex] \sqrt{(9 \: + \: \sqrt{7} ) ^{2} } [/tex]
Simplified the index, the root and also the exponent using the number 2.[tex] \boxed{ \bold{9 \: + \: \sqrt{7} }}[/tex]
MissSpanishConvert 3678 grams to kilograms
Answer:
3.678 Kilograms
Answer:
3678/1000
=3.678kg
the answer is 3.678kg
A shipment of 14 smartphones contains 8 with cracked screens. if they are sold in a random order what is the probability that the 1st 3 sold have cracked screens? (without replacement)
Answer:
4/7 or 57 percent rounded up
Step-by-step explanation:
initially, you put 8/14 as a fraction then divide both the top and bottom by 2 to get 4/7 as that's the lowest you can get the number reduced.
help im being timed plssss
The value of cos 45 in a right angle triangle is 1/√2.
What is the trigonometry ratio?The trigonometry ratios are ratios that can be used to determine the side and angles of a triangle depending on the known parameter. The basic trigonometry ratios are denoted by the acronym: SOH CAH TOA
i.e.
Sin θ = opp/hypCos θ = adj/hypTan θ = opp/adjFrom the given diagram, we are to find the Cos 45°
i.e.
θ = 45°
Let's recall the angle 45 45 90 theorem that states that right angles have the following values for the sides:
hypotenuse = √2opposite = 1adjacent = 1Since
Cos θ = adj/hyp
Cos 45 = 1/√2
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Archimedes was asked by his king to figure out a way of telling if people were giving him fake gold objects. That was when Archimedes discovered his famous principle: an object placed in water displaces the same volume of water as the object’s volume. Explain how Archimedes used this to solve his problem.
Answer:
The Archimedes Principle
Step-by-step explanation: He took the 5 kg crown and dipped it in a vessel full of water. He calculated the displaced water.
Then he took 5 kg pure gold bricks and dipped it in a vessel full of water. He then calculated the displaced water and he found that the vessel with pure gold bricks displaced more water than the vessel with the crown. This is the Archimedes principle which states that the body at rest in a fluid is acted upon by a force pushing upward called the buoyant force, which is equal to the weight of the fluid that the body displaces.
Hope it helps you:))))
Have a good day
Answer:
Archimedes Principle
Step-by-step explanation:
Archimedes used the principle of buoyancy, which states that an object immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. By applying this principle, Archimedes was able to determine the density of an object and distinguish between real gold and fake gold objects.
To solve his problem, Archimedes first measured the weight of the suspect gold object on a scale. He then filled a container with water and recorded the amount of water displaced when the object was submerged. According to the principle of buoyancy, the weight of the water displaced by the object is equal to the weight of the object itself.
Next, Archimedes compared the weight of the object to the weight of an equivalent volume of pure gold. Since the density of gold is known, he could calculate the expected weight of a genuine gold object with the same volume as the suspect object. If the weight of the suspect object matched the expected weight, it was likely made of real gold. However, if the weight was significantly different, it indicated that the object was made of a less dense material, such as a gold alloy or another metal.
By using the principle of buoyancy and comparing the weight of objects to the weight of the water they displaced, Archimedes devised a method to identify fake gold objects and ensure the integrity of the king's treasure. This principle is known as Archimedes' principle and has since become a fundamental concept in physics.
20 points! Which graph represents two functions that are decreasing on all points across the domain that is common to both functions?
Answer:
Its C or D, I would say C tho
Step-by-step explanation:
I took the test and both A and B are wrong
a) What type of triangle is triangle ABC? Isosceles b) Give reasons for your answer.
I know it’s an isosceles triangle I just need help explaining :p
Answer:
It is isosceles by the base angles theorem. It states that when the base angles are equal, the triangle is isosceles.
Step-by-step explanation:
unknown measure : 50°
James paid off the loan on his motorboat in the year 2006. He originally borrowed $6500 to buy the boat, but with simple annual interest, he discovered that he paid a total of $8775 over the life of the loan. If James’s annual interest rate was 7%, in what year did his loan begin?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The number of years for which James took the loan is 5.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
Amount after T years = P + SI
SI = PRT
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
James paid off the loan on his motorboat in the year 2006. He originally borrowed $6500 to buy the boat, but with simple annual interest, he discovered that he paid a total of $8775 over the life of the loan. Also, the annual interest rate is 7%. Therefore,
A = P + (PRT)
8775 = 6500 + (6500×0.07×T)
2275 = 6500×0.07×T
T = 5
Hence, the number of years for which James took the loan is 5.
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Answer: 2001
Step-by-step explanation:
The temperature was 73 degrees at noon. The temperature then changed because -2 degrees F each hour for 4 consecutive hours. What was the resulting temperature?
Step-by-step explanation:
73° starting temperature.
every hour -2° for 4 hours.
that means -2×4 = -8° during 4 hours.
so, the resulting temperature is
73 - 8 = 65°
Audrey takes a sheet of paper and makes a diagonal cut from one corner to the opposite
corner, making two triangles. The cut she makes is 87 inches long and the width of the paper
is 60 inches. What is the paper's length?
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Solution:}}}}}}[/tex]
Let us take the width of the paper as base, the cut she made be hypotenuse and the paper's length be perpendicular.
Here,
Hypotenuse (H) = 87 inch
Base (B) = 60 inch
Perpendicular (P) = [To be calculated]
As, we can use Pythagoras theorem to find. So by using Pythagoras theorem :
H² = P² + B²
[tex] {87}^{2} = {P}^{2} + {60}^{2} \\ \\ \implies \: 7569 = {P}^{2} + 3600 \\ \\ \implies \: 7569 - 3600 = {P}^{2} \\ \\ \implies3969 = {P}^{2} \\ \\ \implies \: P = \sqrt{3969} \\ \\ \implies \: P = 63[/tex]
The length of the paper is 63 inches.
[tex] \boxed{ \frak \pink{BrainlyDamurai}}[/tex]
Leslie buys a new pair of sneakers for
$43 and several pairs of laces, I, that
cost $6 each. Write an algebraic
expression to represent the total
amount she will spend.
Answer:
$43 + $6l
Step-by-step explanation:
Hello!
She spends $43 and bus several $6 laces.
We don't know how many she buys, but we know that we can represent that number using l.
That means she spends $43 + $6l.
The algebraic expression is $43 + $6l.
We can determine the price if we know the number of laces she buys. We can simply plug in the number of laces she bought, and we can plug it in for l in the equation.
Answer:
43= 6(x)
Explanation:
43 is the total, and each of them are 6$ each. X is the variable that we don't know.
What is the value of x? Do not round your answer.
Answer:
x = 3
Step-by-step explanation:
Setup a proportion
[tex]\frac{CB}{CA} =\frac{DB}{DA} \\\frac{4}{3} =\frac{x}{2.25} \\3x=9\\\frac{3x}{3} =\frac{9}{3} \\x=3[/tex]
What is the difference of a surface area and a volume
Surface area is all the area of all sides while volume is the amount of space (a substance) occupies in a solid.
For example:
A cube has a length,breadth and height of 5cm,find:
a) surface area of the cube;
b) and the volume of the cube.
a) area of one side of the cube = 5 x 5
= 25cm²
Total surface area = 25cm x 6 (a cube has 6 sides)
= 150cm²
b) volume of cube = length x breadth x height
= 5 x 5 x 5
= 125cm³
Hope this helps you :]
p.s. can you mark me as the brainliest? <3
How do I simplify this (w²+6)-(3w² + 4w)
Answer:
6-2w(w+2)
Step-by-step explanation:
6-2w²+4w
6-2w(w+2)
PQRS is a rhombus. Find QR.
Will give points!!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
As we know, all sides of a Rhombus are equal to each other ~ so we can conclude that :
[tex]\qquad \sf \dashrightarrow \:4x - 16 = 2x + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:4x - 2x = 6 + 16[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 22[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 22 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 11[/tex]
Now, plug in the value of x in any equation to get the side length of rhombus ~
[tex]\qquad \sf \dashrightarrow \:2x + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:2(11) + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:22 + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:28 \: \: units[/tex]
Side PS = Side QR = 28 units
5x- 4y +2z when x= 8,y =3 and z =3
34
Step-by-step explanation:
=5x-4y+2z
=5×8-4×3+2×3
=40-12+6
=46-12
=34
Evaluate the numerical expression.
9 × [(25 − 4) − (4 + 6)]
The value of the expression is
Answer:
firstly the inner brackets are simplified followed by the outer brackets, and finally the value we got from simplifying brackets is multiplied with 9
Simplify.
√50
OA. 10√5
OB. 2√5
OC. 5√2
OD. 25√2
Decomposition in factors of 50: 2 · 5².
[tex]\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \:a\ge 0 ,\:b\ge 0[/tex]
[tex]\sqrt{2\cdot \:5^2}=\sqrt{2}\sqrt{5^2}[/tex]
[tex]\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \sqrt{a^2}=a,\:\quad \:a\ge 0[/tex]
[tex]\sqrt{5^2}=5[/tex]
[tex]=\sqrt{2}\cdot \:5[/tex]
[tex]\bf{=5\sqrt{2} \ === > \ Answer }[/tex]
Option C
↓
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{MyHeritage} \end{gathered}$}}}[/tex]
The diagram shows a rectangle. The area of the rectangle is 310 m². Work out the value of w when 5x-9 is the length and 3x+7 is the another length
Answer:
w = 10
Step-by-step explanation:
First we take the two values for the breadth of the rectangle
So:
5x - 9 = 3x + 7
now we solve this equation as follows:
5x - 3x = 9 + 7
2x = 16
x = 8
now that we have found the value for x, we can substitute it in the equation, 5x - 9,or in the equation, 3x + 7.
when we substitute x in any of these equations, we get
5(8) - 9 = 31
3(8) + 7 = 31
now that we have the value for the breadth we can form the following equation:
31 × w = 310
31w = 310
w = 310/31 = 10
Answer:
10
Step-by-step explanation:
Firstly, we find the value of X
since 5X-9 and 3X+7 are lenghts
5X-9= 3X+7
5X-3X= 7+9
2X = 16
dividing bothsides by 2
2X/2= 16/2
X = 8
Hence,
5X-9= 5(8)-9= 40-9 = 31
3X+7=3(8)+7= 24+7= 31
To find the width
Area= lenght×width
310= 31×w
31w= 310
w= 310/31
W= 10