Given the graph, description or sequence values create both an explicit and a recursive function.
Answers
Looking at the table, the values differ by a common ratio. This means that the values are increasing in geometric proportion. The common ratio, r is 8/4 = 16/8 = 2
The value of the first term on the table, a is 4
We can see that the next term is the product of the previous term and the common ratio
If n represents the number of terms, each consecutive term would be (n - 1) * r
Therefore, the expression for the recursive function is
\(^{an-1\text{ }\times r}\)an - 1 represents the previous term
For the explicit funtion, the formula for a geometric sequence is expressed as
\(\begin{gathered} Tn=ar^{n\text{ - 1}} \\ Tn=4(2)^{n\text{ - 1}} \end{gathered}\)Related Questions
The circle graph below represents the opinions of 100 students about their favorite sports. Each student chose exactly one of these four options: Basketball, Hockey, Football, and Other. The following statements are true about the graph:
The number of students who chose Basketball is three times the number of students who chose Other.
Ten more students chose Football than chose Hockey.
The percent of students who chose Basketball plus the percent of students who chose Football equal 65.
What percent of the students chose Basketball?
Answers
Answer:
Yo…what’s the graph?
Step-by-step explanation:
help please it's due tomorrow
Answers
\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)
\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)
where, n denotes to number of elements in set .
Since, given set contains 4 elements .
Thus , 2⁴ {2 raise to power 4} .
\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)
\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)
\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)
\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)
Therefore, Required subsets are 16.
They are , Namely;
\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)
_____________________________
Additional Information:-If n is the number of elements in the set then,
No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).
Let's take another example, {1,2}
Here, n = 2
subsets =2^2 =4
Subsets = ϕ, {1}, {2},{1,2}
Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set
A. a scientist is studying the change in population for two species of fish in a lake. The table shows how the numbers of each species changed during a 4-year period.
YEAR: 1; 2; 3; 4
FISH A: 500; 520; 540; 560; 580
FISH B: 400; 430; 460; 490; 520
The scientist uses a linear model to predict future populations of both fish. Explain why, given the data in the table, population of fish A and the population of fish B can be modeled using linear equations.
Answers
Answer:
The data can be modeled using linear equatins, because there's the same amount of population for fish A (+20 per year) and fish B (+30 per year) every year.
As a gift for your hard-earned victory in defense of the kingdom, the king gives you a reward. One penny with the promise to double it every day for the next 25 days. What would a reasonable range be in this situation? How many pennies will you have on the 25th day?
Answers
can you explan transformation
Answers
Transformation is the process of changing one form or structure into another. Here are some key points about transformation:
• Physical transformations involve changing the physical properties of an object, like shape, size, state of matter, etc. Some examples are cutting, bending, melting, freezing, dissolving, combining substances, etc.
• Chemical transformations involve changing the chemical composition of a substance, forming new substances with different properties. Some examples are chemical reactions that produce new compounds, oxidation reactions, decomposition, synthesis reactions, etc.
• Biological transformations occur within living organisms through processes like development, growth, metabolism, adaptation, and evolution. These changes occur over time and at the cellular or molecular level.
• Mathematical transformations involve applying operations or functions to mathematical objects like numbers, vectors, matrices, etc. to produce new outputs. Common transformations include translation, rotation, reflection, scaling, and projection.
• Information transformations occur when data is manipulated, organized, or changed. Examples are data compression, encryption, encoding, classification, and filtering of information.
• Conceptual transformations refer to changes in a person's knowledge, understanding, perspectives, beliefs, attitudes, or behavior. Things like experiences, education, and realizations can cause conceptual transformations.
The key aspects of any transformation are that there is an initial state or form that undergoes some change process resulting in an altered final state or form. There are often changes to properties, composition, structure, or relationships involved.
Hope this explanation of transformation helps! Let me know if you have any other questions.
Transformation can refer to a marked change in form, nature, or appearance. It can also refer to a process by which one figure, expression, or function is converted into another one of similar value.
Solve y = ax² + c for x.
O x
x= ± √ay-c
O
O
x = ±₁
X=
X=
у-с
a
y
y + c
a
Answers
In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)
A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.
To find the value of x
Assuming \(a\neq o\)
First, subtract c from both the sides to get:
\(y-c=ax^{2}\)
then, divide both sides by \(a\) and transpose to get:
\(x^{2} =\frac{y-c}{a}\)
So, \(x\) must be a square root of \(\frac{y-c}{a}\) and we can deduce:
\(x=\) ± \(\sqrt \frac{y-c}{a}\)
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Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
Answers
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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A cube has a depth of 9 dm. What is the volume of the cube?
Answers
The volume of the cube is 729 dm³
How to find the volume of the cube?Remember that all the dimensions on a cube are the same ones, then we have:
Length = Width = Depth.
And for any prism, the volume is the product between the 3 dimensions, then for any cube the volume is:
V = Length*Width*Depth.
In this case we know that the depth is 9dm, then also is the length and the width, and thus, the volume of this cube is:
V = 9dm*9dm*9dm = 729 dm³
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Problem-work-interest-total
Rita needs to take out a loan for a new
car. Her loan is for $25,000. The interest
rate on the loan is 6%, and is
compounded yearly. She plans to pay off
the loan in 5 years. What will she owe
after she factors in interest?
Answers
The amount that she owes after she factors in interest will be $33,455.64.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.
Then the amount is given as,
A = $25,000 x (1 + 0.06)⁵
A = $25,000 x (1.06)⁵
A = $25,000 x 1.3382
A = $33,455.64
The amount that she owes after she factors in interest will be $33,455.64.
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2. Lara collects shark's teeth. She has 72 teeth. She wants to put them in special cases. Each case can hold 10 teeth. How many cases should Lara buy? Draw a picture to find the answer. Then explain how you know your answer is correct.
Answers
Answer:
Lara should buy 8 boxes
Step-by-step explanation:
To start we would need to do
72/10
since 72 isn't a multiple of ten we can round it down to 70, then do
70/10=7
since we still have two teeth, we can put them in their own box so
7+1=8
3 to the power of 5 = 243. Explain how to use that fact to quickly evaluate 3 to the power of 6
Answers
Step-by-step explanation:
3^6 = 3 * 3^5
= 3 * 243 = 729
Random simple service of voters were taken in three different regions of a county that has a voter population of 55,000. On average 42 out of 100 voters supported issue seven and 58 oppose it estimated number of voters in the county who support the issue.
Answers
Answer: 23100 voters
Step-by-step explanation:
42*55000=2310000
2310000/100=23100 voters
The graph represents the piecewise function: f (x) ={ , if -3
Answers
The domain and the range of the function are
Domain = (-∝, ∝)Range = (0, ∝)How to determine the domain and range of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph is a piecewise function
When combined gives an absolute function
The rule of a function is that
The domain is the set of all real numbers
This means that the input value can take all real values
However, the range is greater than the constant term
In this case, it is 0
So, the range is y > 0
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Question
The graph represents the piecewise function:
f(x) =
What is the domain and range of the function
The length of a rectangle is four times its width. The length is 4 2/3 feet. What is the area of the rectangle?
Answers
Answer:
4.687225
Step-by-step explanation:
help me please I really need help
Answers
Answer:
25.46
Step-by-step explanation:
6.7X3.8
solve pls brainliest
Answers
I hope this is correct
Answer:
-8^2=1/64 and -3^3=1/27
Step-by-step explanation:
I appreciated if you mark me as brainliest
GIVING OUT BRAINLIST ASAP
The Spanish Club sells hot pretzels as a fundraiser. The pretzels normally sold for $2.00, but near the end of the sale the price was reduced by 25% How much is the price of the pretzel being reduced by? Round your answer to the nearest cent (hundredths place)
Answers
Answer: 1.50
Step-by-step explanation:
Answer
25% of 2.00$ is 50 cents
Step-by-step explanation:
2. Find two numbers for such that the distance between (2, -1) and (t, 3) equals 7.
Answers
The two numbers such that the distance between (2, -1) and (t, 3) equals 7 are
t = 2 + √33 and t = 2 - √33What is the distance between two points?The distance between two points (x, y) and (x', y') is given by
d = √[(x' - x)² + (y' - y)²]
Since we need to find two numbers for such that the distance between (2, -1) and (t, 3) equals 7., then
(x, y) = (2, -1), (x', y') = (t, 3) and d = 7So, substituting the values of the variables into the equation, we have that
d = √[(x' - x)² + (y' - y)²]
7 = √[(t - 2)² + (3 - (-1))²]
√[(t - 2)² + (3 + 1)²] = 7
√[(t - 2)² + 4²] = 7
√[(t - 2)² + 16] = 7
Squaring both sides, we have that
[(t - 2)² + 16] = 7²
(t - 2)² + 16 = 49
(t - 2)² = 49 - 16
(t - 2)² = 33
Taking square root of both sides, we have that
t - 2 = ±√33
t = 2 ± √33
So, t = 2 + √33 and t = 2 - √33
So, the two number are
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Granite was formed slowly as magma cooled.
What is the result of this slow cooling?
fine grains
a smooth texture
air pockets
large crystals
Answers
Answer:
Step by step explanation:
A smooth textureAre you able to help again with this one? And could you explain how you came to the answer like the steps behind it?
Answers
Solution:
Given:
\(\frac{\sqrt{16\times 10^{20}}}{4\times 10^{-4}\times 10^5}\)Splitting the numbers under the root sign as a perfect square;
\(\begin{gathered} \frac{\sqrt{16\times10^{20}}}{4\times10^{-4}\times10^5}=\frac{\sqrt{4^2\times(10^{10})^2}}{4\times10^{-4}\times10^5} \\ =\frac{4\times10^{10}}{4\times10^{-4}\times10^5} \\ Cancelling\text{ out the common term;} \\ =\frac{10^{10}}{10^{-4}\times10^5} \end{gathered}\)Applying the law of exponents;
\(\begin{gathered} x^a\times x^b=x^{a+b} \\ \\ Hence, \\ \frac{10^{10}}{10^{-4}\times10^5}=\frac{10^{10}}{10^{-4+5}} \\ =\frac{10^{10}}{10^1} \\ \\ Also\text{ applying the law of exponents below;} \\ \frac{x^a}{x^b}=x^{a-b} \\ \\ Hence, \\ \frac{10^{10}}{10^1}=10^{10-1} \\ =10^9 \end{gathered}\)In scientific notation, the solution is;
\(1\times10^9\)if you could help that would be greatly appreciated
Answers
Answer: search
Step-by-step explanation: look up the question on your browser and the answer will pop up
find the 9th term of the geometric sequence. 12,36,108,...
Answers
The 9th term of the given sequence is 78732.
The given sequence is 12, 36, 108... is a geometric sequence with a common ratio of 3.To find the 9th term of the given sequence, we will use the formula for the nth term of a geometric sequence, which is given by:
aₙ = a₁rⁿ⁻¹
Here, a₁ = 12 and r = 3.
Therefore, the formula for the nth term becomes:
aₙ = 12(3)ⁿ⁻¹
Now, we need to find the 9th term of the sequence. Hence, n = 9. Substituting the values of a₁ and r, and n in the formula, we get:
a₉ = 12(3)⁹⁻¹= 12(3)⁸= 12(6561)= 78732
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solve the expression
(x2-9)
Answers
Answer:
This equals (2x-9), you cannot simplify it more because it's a variable and number. They have to both be numbers without variables or both variables to simplify.
Step-by-step explanation:
? This makes no sensibility.....
how do I do this ? Need help
Answers
Which fraction is equivalent to
-(7/8)?
Answers
Answer:
Step-by-step explanation:
\(-\frac{35}{40} =-\frac{7}{8}\)
Answer:
i think it will be -7/8
Step-by-step explanation:
5. Ms. Sellers flew out to Utah to take her sons to college. If she flew 245.6
miles in 5.4 hours. How far did she fly in 1 hour?*
Answers
Answer:
Step-by-step explanation:
distance flown in 5.4 hours = 245.6 miles
distance flown in 1 hour = 245.6/5.4
= 45.481 miles
Hope this helps
plz mark as brainliest!!!!!
Answer: 49.12 miles
Step-by-step explanation:
You have to divide 245.6 by 5.4
Suppose that 11 inches of wire costs 44 cents. At the same rate, how many inches of wire can be bought for 16 cents?
Answers
Answer:
4 inches
Step-by-step explanation:
of 11 inches of wire costs 44 cents, then 1 inch of wire costs 4 cents because 44 cents ÷ 11 inches = 4 cents per inch. (44 ÷ 11 = 4)
So, if 1 inch is 4 cents, 16 cents is 4 inches because 16 ÷ 4 = 4
select the solution of the inequality y>-3x+2
Answers
The shaded region shows the possible set of solutions.
What is inequality? Differentiate between equation and expression?inequality : An inequality is used to make unequal comparisons between two expressions or numbers.
expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.
equation : A mathematical equation is used to equate two expressions.
Given is the inequality as -
y > -3x + 2
The inequality is -
y > -3x + 2
Refer to the graph attached. It shows the possible set of solutions under the shaded region.
Therefore, the shaded region shows the possible set of solutions.
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In a large school, it was found that 69% of students are taking a math class, 70% of student are taking an English class, and 50% of students are taking both.
A. True
B. False
Answers
Answer:
P(Math or English) = 0.89
Step-by-step explanation: This solution will only be applicable if finding the probability that a randomly selected student is taking a math class or an English class.
Lets study the meaning of or , and on probability. The use of the word or means that you are calculating the probability
that either event A or event B happened
Both events do not have to happen
The use of the word and, means that both event A and B have to happened
The addition rules are: # P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
The union is written as A ∪ B or “A or B”.
The Both is written as A ∩ B or “A and B”
Lets solve the question
The probability of taking Math class 69%
The probability of taking English class 70%
The probability of taking both classes is 50%
P(Math) = 69% = 0.69
P(English) = 70% = 0.70
P(Math and English) = 50% = 0.50
To find P(Math or English) use the rule of non-mutually exclusive
P(A or B) = P(A) + P(B) - P(A and B)
P(Math or English) = P(Math) + P(English) - P(Math and English)
Lets substitute the values of P(Math) , P(English) , P(Math and English)
in the rule P(Math or English) = 0.69 + 0.70 - 0.50 = 0.89
P(Math or English) = 0.89
P(Math or English) = 0.89
This solution will only be applicable if we are to find the probability that a randomly selected student is taking a math class or an English class.
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, what would the same 30 second commercial have cost during the first Super Bowl in 1967, when the CPI was 33.4? Round your answer to the nearest hundred dollars.
Answers
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.
To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).
The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.
Given data:
Cost of a 30-second commercial in 2021 = $5.6 million
CPI in 2021 = 271.4
CPI in 1967 = 33.4
To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:
Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)
Cost in 1967 = ($5.6 million) * (33.4 / 271.4)
Cost in 1967 ≈ $0.689 million
To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:
Cost in 1967 ≈ $68,900
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