a. The type of sequence we have here is a Geometric Progression.
b. The common ratio of the sequence is 7/10.
c. iPhone 10 will cost $83 in 2025.
What is a geometric progression?In a particular kind of progression called a Geometric Progression, each succeeding term has a fixed ratio known as a common ratio.The term "GP" is also frequently used. The general form of the GP is written as a, ar, ar²,..., where a denotes the first term and r denotes the common ratio of the progression.The common ratio can be both positive and negative numbers.Given sequence is:
$1000, $700, $490, $343, $240
a. To determine the type of sequence we find the common ratio between terms:
700/1000 = 7/10
490/700 = 7/10
All terms differ by a common ratio hence it is a geometric progression.
b. From above,
1000 × 7/10 = 700
700 × 7/10 = 490
490 × 7/10 = 343
343 × 7/10 = 240
Hence, the common ratio of G.P is 7/10.
c. The next terms in the given G.P is:
240 × 7/10 = 168
So, iPhone 10 will cost $168 in 2023.
168 × 7/10 = 118
So, iPhone 10 will cost $118 in 2024.
118 × 7/10 = 83
So, iPhone 10 will cost $83 in 2025.
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help i need help with this maths question
x add 3 = 8
Answer:
i guess X=5 because 3+5=8?
Step-by-step explanation:
order the following rational and irrational numbers from least to greatest
1.25,square root of 2,1 3/8, and 1 3/5
The ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.
How to illustrate the information?It should be noted that ✓2 = 1.414
It should be noted that 1 3/8 = 1.375
It should be noted that 1 3/5 = 1.6
The other numbers given are 1.25 and 1.875
Therefore, the ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.
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Do the math: the price of iron ore can be measured per ton. a ton is about the
weight of a cow. if the price of 1 ton of iron ore starts at $104 per ton with a
quantity demanded of 90 tons, then rises to $211 per ton, what is the new quantity
demanded at this price? assume the slope of the demand curve is -3.2 and the
y-intercept is $392. round your answer to the nearest tenth of a ton.
Answer:
Step-by-step explanation:
56.6 tons.
Based on the slope of the demand curve and the new price of iron ore, the new quantity demanded at the new price of $211 is 49.60 tons
What is the new equilibrium quantity demanded?The equation given will allow us to find the new quantity demanded:
y = Mx + c
y = new quantity demanded
m = slope of the demand curve
x = change in price of iron ore
c = y intercept
Solving for the new quantity demanded at the new price gives:
= -3.2 x (211 - 104) + 392
= -342.40 + 392
= 49.60 tons
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PLEASE HELP!! DUE TODAY!! WILL MARK BRAINLIEST IF MULTIPLE PEOPLE RESPOND RIGHT AND FAST!
Question: The sets of numbers 6, 8, 10 and 5, 12, 13 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples! (5 points)
We know that 6, 8, 10 and 5, 12, 13 are Pythagorean triples.
The formula to see if a set of three numbers is a pythagorean triple is:
[tex]a^{2} +b^{2} =c^{2}[/tex]
For the first one, we can do
6^2 + 8^2 = 10^2 and see if it is true.
36 + 64 = 100, so this works.
The next one, we can do
5^2 + 12^2 = 13^2
25 + 144 = 169
This also works.
So in conclusion, using the formula, we can prove that they are both Pythagorean triples.
I hope this is clear to you, have a great day! :)
a = y² - x²
b = 2xy
c = x² + y²
where x and y are positive integers y > x
→ In Pythagorean triple number set 6,8,10
c² = a² + b²(10)² = (6)² + (8)²100 = 36 + 64100 = 100→ In Pythagorean triple number set 5,12,13
c² = a² + b²13² = 5² + 12²169 = 25 + 144169 = 169At a baseball game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team. If 735 people attending the game supported the home team, what was the total number of people attending the game?
Answer:
1300
Step-by-step explanation:
455 divided by 35%
= 455 x 100/35
= 455 x 20/7
= 65 x 20
= 1300
The total number of people attending the game is 2100.
Given that, at a baseball game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the total number of people attending the game be x.
Given, 735 people attending the game supported the home team.
Now, 35% of x=735
⇒ 35/100 × x=735
⇒ 35x=73500
⇒ x=73500/35
⇒ x=2100
Therefore, the total number of people attending the game is 2100.
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Write each expression as a single logarithm.
log₃4 + log₃y + log₃8 x
The expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
Given that the expression is log₃4 + log₃y + log₃8 x.
We are told to write the expression as a single logarithm.
Change of base theorem is basically used when we have to find the log values having different bases from 10 as we have tables which tell the log values with base 10. We know that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex] and
log mn=log m+log n.
The expression is log₃4 + log₃y + log₃8 x.
log₃4 + log₃y + log₃8x=[tex]log_{3}[/tex] (4*y)+ [tex]log_{3}[/tex] 8x
=[tex]log_{3}[/tex] (4*y*8x)
=[tex]log_{3}[/tex] 32xy
Hence the expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
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Expand each logarithm.
log m³/n⁴ p⁻²
After expanding logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]\frac{log_{10} m^3}{n^4 \\ p^-2} \\[/tex]
apply formula log a^x = x log a
[tex]= > \frac{3 log_{10} (m)}{\frac{n^4}{p^2} }\\ \\= > \frac{3 log_{10} (m) p^2}{{n^4} }[/tex]
Thus, after expanding the logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
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Please help me please help me
Answer:
Step-by-step explanation:
90 degree
Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 333 marbles into a marble jar. when the jar has 100100100 or more marbles, the students have a party. right now, the jar has 242424 marbles. write an inequality to determine the number of additional times, rrr, mrs. morton could reward the class in order for the students to have a party. will the students have a party if mrs. morton rewards them 313131 additional times?
Yes the students have a party is mrs. Morton reward them 313131 additional times.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most of the time, size comparisons between two numbers on the number line are to be made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a > b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since a is apparently less than or solely greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
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Show that k=(4 + 3j)/(5-j) can be rearranged to j =(5k - 4)/(3 + k)
Answer: f(x)=4
f(x)=√3x−4
f(x)=4x−5
Step-by-step explanation:
30 POINTS! Question is on the attachment below :D
A. 35 in. x 17 in.
B. 36 in. x 18 in.
C. 35 in. x 18 in.
D. 36 in. x 17 in.
Answer:
B
Step-by-step explanation:
35 [tex]\frac{3}{4}[/tex] ≈ 36 ( to the nearest whole number
17 [tex]\frac{5}{6}[/tex] ≈ 18 ( to the nearest whole number )
then 36 in × 18 in
Which of the following interpretations for the given expression is correct
(x+y)^n/2
The correct interpretation for the given expression is the sum of x and y raised to the power of half n
How to determine the correct interpretations for the given expression?The expression is given as
(x + y)^n/2
To interpret the expression, we start by evaluating the expression in the bracket and the exponent
So, we have
(x + y): The sum of x and yn/2: n divided by 2Hence, the correct interpretation for the given expression is the sum of x and y raised to the power of half n
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Let f(x)=3 x²-4 and g(x)=x-2 . Calculate (f ⁰ g⁻¹)(x) for x=-3 .
If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.
If x = -3 then (f ⁰ g⁻¹)(x) is 23.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Let the two functions be f(x) = 3x² - 4 and g(x) = x - 2
(g⁻¹)(x) = 1 - 2
(g⁻¹)(x) = -1
substitute (g⁻¹)(x) value in (f ⁰ g⁻¹)(x)
(f ⁰ g⁻¹)(x) = (f ⁰ ) (-1)
then f(x) equation is 3 x² - 4 substitute -1 in x
f(-1) = 3(-1)² - 4
f(-1) = -1
Now when x = -3 the (f ⁰ g⁻¹)(x) value is
f(-3) = 3(-3)² - 4
f(-3) = 23
Therefore, the value of (f ⁰ g⁻¹)(x) for x = -3 is 23.
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Please help!
Rebecca has twice as much money as Rachel. If Rebecca gives Rachel $60, then the two of them will have the same amount of money. How much money did Rebecca have originally?
A.
B.
C.
D.
E.
Answer:
Rebecca originally had 240 dollars.
Step-by-step explanation:
Let's set B as Rebecca's money and C as Rachel's.
Rebecca has twice as much money as Rachel
B = 2C
If Rebecca gives Rachel $60, then the two of them will have the same amount of money
B - $60 = C + $60
let's combine the 2 by subtracting the second from the first
B - (B - $60) = 2C - (C + $60)
$60 = C - $60
$120 = C
so Rachel had 120 dollars.
Rebecca had twice as much, so 240 dollars.
If Rebecca gives $60 to Rachel, they have $180 each. Everything checks out.
Write each equation in exponential form.
log₆6=1
Answer:
The answer to the given question is 6
Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.
A logarithmic equation includes a logarithm in the variable x.
An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.
For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.
In the given problem, b = 6, x = 6 and y = 1
b = 6
x = 6
y = 1
Substituting the values of b, x and y into the equation b^y = x;
6^(1) = 6
therefore, the value of the given equation log₆6=1 is 6
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What is the simplest form of the quotient √72 x⁵ y³ z⁸ / √3 x y²z² ?
(A) √24 x⁴ y z⁶
(C) 24 x⁴ y z⁶
(B) 2 x² z³ √6y
(D) 12 x² y z⁶
The simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.
What do we mean by simplest form?When the numerator and denominator have no common factors other than one, the fraction is in its simplest form. When the top and bottom cannot be any smaller while still being whole numbers, the fraction is in its simplest form. To simplify a fraction, divide the top and bottom numbers by the largest number that divides both numbers exactly (they must stay whole numbers).So,
Given: 72x⁵y³z⁸/√3xy²z²Then,
72x⁵y³z⁸/√3xy²z²Simplify the radical by dividing it into a product of known factors and assuming positive real numbers, which gives us:2x²z³√6yTherefore, the simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.
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In a science lab, a number of rock samples are weighed. If the scientist finds one of the rocks to weigh 6 pounds and this is 38.7% of the total weight of all of the rocks, what is the weight of all of the rocks? If necessary, round your answer to the nearest tenth.
10.5 lb
2.3 lb
232.2 lb
15.5 lb
Answer:
15.5
Step-by-step explanation:
We are trying to find out:
38.7% of what number is 6?
38.7% as a decimal is .387
.387x = 6 Divide both sides by .387
x = 15.503875969
Round 15.5
A florist buys a dozen roses for $12.96 and sells them for $48.48. Find the amount of markup on a single rose.
The amount of markup on a single rose is $2.96
What is profit?Profit = Selling Price – Cost Price.
We have,
We can consider the cost price as:
Bought amount = $12.96
We can consider the selling price as:
Selling amount = $48.48
Now,
Markup price can be considered as the profit:
Profit = Sellin price - Cost price
Profit = $48.48 - $12.96
Profit = $35.52
Since in a dozen we have 12 roses the markup price for each rose is:
= $35.52 / 12
= $2.96
Thus the amount of markup on a single rose is $2.96
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A tortoise moves
at about 0.05
meters per
second. How
many
centimeters per
second does a
tortoise move?
Answer:
0.05 metrs = 5 cetimeters
Step-by-step explanation:
1 meter = 100 centimeters
0.05 meters = 0.05 * 100 = 5 centimeters
An elephant charged 13.3 meters on 15 seconds. At this rate, how far would the elephant go in one minute? (20 seconds = 1/3 minute)
Answer: 53.2 meters
Step-by-step explanation:
Since 15 seconds is 1/4 of 1 minute, multiply 13.3 by 4 to get 53.2.
how many gallons are in a liter again i forgot
Answer:
The exact conversion rates between Liters and Gallons is as follows...
1 Liter = 0.264 Gallons
and
1 Gallon = 3.785 Liters
Choose Yes or No to tell if the equation is true.
I'll give u brainliest and i'll do anything this is really important
Answer:
true,true,false,false
Step-by-step explanation:
true it's the amount of decimal places
true: same with this true
false: if it was 10^5 then yes but it's not
false: there is one too many 10s
Find the sum: 1/3+1/4
Answer:
7/12
Step-by-step explanation:
i used lowest common denomator
Answer:
answer is 7/12
Step-by-step explanation:
hope this helps
write the number below (81) as a power with a base of 3 and a base of 9
Answer:
base of 3 --> 3^4 (three to the fourth); base of 9 --> 9^2 (nine squared)
Step-by-step explanation:
3 x 3 = 9 x 3 = 27 x 3 = 81 = 3^4
You multiply 3 by itself 4 times.
9 x 9 = 81 = 9^2
You multiply 9 by itself 2 times.
(2x² + 3x³ - 3x²-
3x - 4x-3)÷(x-2)
The simplified form of the expression [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex] is [tex]\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}[/tex]
As per the question statement, we are provided with an expression [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex].
We are supposed to simplify the above mentioned expression.
To solve this question, let us simplify the expression, part by part, i.e., first, let us consider the numerator part which is
[2x² + 3x³ - 3x² -3x -4x - 3].
Here, it is clearly visible that the numerator expression consists of terms having same same variable but with different coefficients, such as
[2x², -(3x²)] and [-(3x), -(4x)]. Therefore, we can perform the mentioned operations on the like terms and thus simplify our numerator.
[tex][2x^{2} +(-3x^{2} )]=(2x^{2} -3x^{2} )=-(x^{2})\\[/tex]
And, [tex][(-3x) + (-4x)]=-(3x+4x)=-x(3+4)=-(7x)[/tex].
Hence, [tex](2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(2x^{2} -3x^{2})-(3x+4x)-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(-x^{2} )-7x-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=(+3x^{3}-x^{2}-7x-3)\\[/tex]
And our denominator is (x - 2). Since, [2x² + 3x³ - 3x² -3x -4x - 3] does not equate to Zero for (x = 2), there (x - 2) is not a factor of the numerator, i.e., the numerator cannot be exactly divided by the denominator.
Therefore, the simplest form of our expression [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex] is [tex]\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}[/tex].
Expressions: These are mathematical statements, that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.Like Terms: Terms having the same variable.To learn more about expressions, click on the link below.
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Solve each equation. Round to the nearest ten-thousandth. 5x +3=12
the value of the given equation 5x +3=12 Round to the nearest ten-thousandth = 1.8000
What is rounding off?In a given base, a round number is a number that ends with one or more "0s." So, 590 is more round than 592, but less round than 600. A round number is frequently interpreted in both technical and casual language to stand for a value or values close to the nominal value represented.
According to the given data:given:- 5x +3=12
simplifying:
5x +3=12
5x = 12 - 3
5x = 9
x = 9/5
x = 1.8000
the value of the given equation 5x +3=12 Round to the nearest ten-thousandth = 1.8000
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Every Tuesday so far, I noticed that
Casey wears yellow to class. This
Tuesday she will probably wear yellow to
class. Is it inductive or deductive or a detachment or syllogism
Answer:
inductive
Step-by-step explanation:
vbkugu stottlxd5xlhlhclxylyyldydpdyxyo
if p and q are the robots of the equation 3x^2 _ 16x + 2 = 0, find the value of p+q(1+ p).
Step-by-step explanation:
3x² - 16x + 2 = 0
ax² + bx + c = 0
a = 3 , b = -16 , c = 2
= p + q.(1 + p)
= p + q + p.q
= -b/a + c/a
= -(-16)/3 + 2/3
= (16 + 2)/3
= 18/3
= 6
d(n)=-5(1/2)n-1 what is the third term in the sequence
Answer: d3 = - 17/2
correction: This is an explicit formula
All we have to do is plug n = 3 in the formula to find the 3rd term.
2. d(3)=-5(1/2)3-1
= -5/4
Step-by-step explanation:
An item is regularly priced at $30. It is now priced at a discount of 70%
off the regular price. What is the price now?
If something is priced at 30$,then 70% off would make it 9.00$!