The cost of an adult ticket is $9 and the cost of a student/child ticket is $7. The solution was found by solving a system of two equations, where the variables x and y represent the costs of the two types of tickets.
Let's assign variables for the unknowns
x = cost of adult tickets
y = cost of student/child tickets
From the given information, we can create two equations
Equation 1 Friend, mom, and little sister paid a total of $23
x + 2y = 23
Equation 2 Another family paid $39 for two adults and three students
2x + 3y = 39
We now have two equations with two unknowns, which we can solve using substitution or elimination.
Here, using substitution
Solve for x in Equation 1
x = 23 - 2y
Substitute the value of x into Equation 2
2(23 - 2y) + 3y = 39
Simplify and solve for y
46 - 4y + 3y = 39
-y = -7
y = 7
Substitute the value of y into Equation 1 to solve for x
x + 2(7) = 23
x = 9
Therefore, the cost of adult tickets is $9 and the cost of student/child tickets is $7.
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Ms. Griffin has 0. 8 liters of hot tea and 4 teacups. She will divide the tea evenly among the cups. Which model represents 0. 8 divide by 4
The model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.
To find the amount of tea in each teacup, you need to divide the total amount of tea (0.8 liters) by the number of teacups (4). The model for this is 0.8 ÷ 4. Follow these steps:
1. Divide 0.8 by 4:
0.8 ÷ 4 = 0.2
2. Interpret the result:
Each teacup will have 0.2 liters of hot tea.
So, the model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.
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Find all solutions of the equation in radians.
sin(2x)sin(x)+cos(x)=0
Answer:
[tex]x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n[/tex]
Step-by-step explanation:
Given equation:
[tex]\sin(2x)\sin(x)+\cos(x)=0[/tex]
Rewrite sin(2x) using the trigonometric identity sin(2x) = 2sin(x)cos(x):
[tex]\implies 2\sin(x)\cos(x)\sin(x)+\cos(x)=0[/tex]
[tex]\implies 2\sin^2(x)\cos(x)+\cos(x)=0[/tex]
Factor out cos(x):
[tex]\implies \cos(x)\left[2\sin^2(x)+1\right]=0[/tex]
Applying the zero-product property:
[tex]\textsf{Equation 1:}\quad\cos(x)=0[/tex]
[tex]\textsf{Equation 2:}\quad2\sin^2(x)+1=0[/tex]
Solve each part separately.
[tex]\underline{\sf Equation \; 1}[/tex]
[tex]\begin{aligned}\cos(x)&=0\\x&=\arccos(0)\\x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n\end{aligned}[/tex]
[tex]\underline{\sf Equation \; 2}[/tex]
[tex]\begin{aligned}2\sin^2(x)+1&=0\\\sin^2(x)&=-\dfrac{1}{2}\;\;\;\;\;\;\leftarrow\;\textsf{No solution}\end{aligned}[/tex]
Therefore, the solutions of the equation in radians are:
[tex]\boxed{x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n}[/tex]
The ratios of successive numbers in the Fibonacci sequence eventually get closer to which number?
a.
1. 61
c.
2. 3
b.
1. 46
d.
1
The ratios of successive numbers in the Fibonacci sequence eventually get closer to a. 1.61
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1 (0, 1, 1, 2, 3, 5, 8, 13, ...). When you take the ratio of successive numbers in the sequence (e.g., 5/3 or 8/5), it converges to approximately 1.618, also known as the Golden Ratio or Phi.
The closest option in your list is 1.61, which is option (a).
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What is the scale factor for the similar figures below?
The scale factor of the similar figure is 2.
What is scale factor?
Scale factor is the ratio of the length of a new object to the original object.
To calculate the scale factor of the similar figures, we use the formula below
Formula:
S.F = New length/Original length.................. Equation 1Where:
S.F = Scale factorFrom the diagram,
Given:
New length = 14Original length = 7Substitute these values into equation 1
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Luis created a spreadsheet of his expenses for three months. Which of Luis's expenses are variable expenses
utility bill
Expenses Jan Feb Mar
rent
$1,250,00 $1,250,00 $1,250,00
$124. 11 $108. 72 $121. 69
car loan payment $384. 00 3384,00 $384. 00
Insurance payment 397. 18 597. 18 $97. 18
groceries
$315,43 $367. 25 $341. 04
clothing
$72. 18 $152. 74 $0. 00
fuel
$108. 71 $117. 46 $127. 34
Variable expenses are expenses that fluctuate from month to month, and are typically not a fixed amount. Examples of variable expenses include groceries, fuel, clothing, and entertainment. These expenses can be influenced by various factors such as personal choices, seasonality, and external events.
In Luis's expenses, the following expenses are variable expenses:
Groceries: The amount spent on groceries changes from month to month depending on the types of food Luis purchases and the quantity he buys.Clothing: This expense is variable because Luis only spent money on clothing in January and February, and did not spend anything on clothing in March.Fuel: The amount spent on fuel changes from month to month depending on how often Luis drives and the price of gasoline.On the other hand, the following expenses are fixed expenses:
Rent: This expense is fixed because Luis pays the same amount for rent every month.Car loan payment: This expense is fixed because Luis is required to pay the same amount for his car loan every month.Insurance payment: This expense is fixed because Luis is required to pay the same amount for his insurance every month.Utility bill: The utility bill could be either a variable or fixed expense, depending on the type of utility. For example, if the utility bill is for electricity, it may be a variable expense because the amount of electricity used can fluctuate from month to month. However, if the utility bill is for a fixed service such as internet, it would be a fixed expense.To learn more about “utility” refer to the https://brainly.com/question/14729557
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Answer:
groccieries is the answer for plato 2023
The value of a car that depreciates over time can be modeled by the function
G(t) = 24000(0.95)2t. Write an equivalent function of the form G(t) = abt
An equivalent function of the given function in the form G(t) = [tex]ab^t[/tex] is G(t) = 24000[tex](0.9025)^t[/tex].
The given function for the value of a car that depreciates over time is G(t) = 24000[tex](0.95)^{2t[/tex]. To write an equivalent function of the form G(t) = [tex]ab^t[/tex], we need to rewrite the function using exponent rules.
First, we can rewrite [tex](0.95)^{2t[/tex] as [tex][(0.95)^{2}]^{t[/tex], which simplifies to [tex](0.9025)^t[/tex]. Therefore, we have:
G(t) = 24000[tex](0.9025)^t[/tex]
Next, we need to express 24000 as a product of two factors, a and b. We can choose a = 24000 and b = 0.9025, so we have:
G(t) = 24000[tex](0.9025)^t[/tex] = 24000[tex](0.9025)^t[/tex]
This function gives the value of the car at time t, where t is the number of years after the initial purchase, with a starting value of 24000 and a depreciation rate of 9.75% per year.
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AC B Round your answer to the nearest hundredth.
Answer:
4.28
Step-by-step explanation:
To find what the length of AC is, we can use the tangent of angle A, which is 35°. Here's the equation:
tan(35)=3/x
multiply both sides by x
x·tan(35)=3
divide both sides by the tangent of 35
x=4.28 (rounded to the nearest hundredth)
This means that AC=4.28
Hope this helps! :)
In a circle, an angle measuring 2.2radians intercepts an are of length 11.9.Find the radius of the circle to the nearest
10th.
The radius of the circle to the nearest 10th is 5.4
Showing how to calculate radiusThe formula for calculating the length of an arc of a circle is:
length of arc = radius x angle in radians
l = rθ
where
r = radius of the circle
l = length of arc
θ = angle in radians
From the question, we are given:
length of arc = 11.9
angle in radians (θ) = 2.2radians
The we can plug in the values
11.9 = r x 2.2
make r the subject of the formula
r = 11.9/2.2
r = 5.41 (to 2 decimal places)
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A piece of wire of length 50 is out, and the resulting two pieces are formed to make a corde and a square. Where should the wre be cut to day minance and provimine the continet water who? (e) To minimize the combined area, the wire should be cut so that a length of 25.964 used for the circle and a longen er 3.04 es lo quem (Round to the nearest thousandth as needed) (1) To maximize the combined uros, there should be cut so that a length of used for the circle and we canned tere dere (Round to the nearest thousandth as needed) Evaluate the following limit. Use Thôpitals Rule when it is convenient and applicable Iim cox How should the given timt be evaluated? Select the correct choice below and, if necessary, in the answer box to complete your choice A. U topitals Rule more than once to rewrite the imtin ta final fomas tim 9. Multiply the expension by a una traction to obtain im (1) OG UTHopitals Rule exactly once to rewrite the imit im OD. Vse direction Evaluate the limit imetype an exact answer
To minimize the combined area of a circle and a square made from a wire of length 50, you should cut the wire so that 25.964 units are used for the circle (as the circumference) and 24.036 units are used for the square (as the perimeter).
To maximize the combined areas, the optimal cutting point cannot be determined due to the lack of information provided in the question. For the limit evaluation, it's not clear which limit should be evaluated, as the question has some typos and irrelevant parts. If you can provide the correct limit expression, I will be happy to help you evaluate it using the appropriate method, such as Hsopital's Rule or other techniques.
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Suppose a friend or family asked you how it could be possible that an annual interest rate is higher than 100%. write out an explanation of what you might say to them
If someone asked me how it could be possible for an annual interest rate to be higher than 100%, I would explain that it is actually quite common in certain situations, particularly in the case of loans with very short terms or loans with high fees.
For example, let's say you borrowed $100 from a lender and agreed to pay back $110 in one week. The lender is essentially charging you 10% interest for the one-week loan period, but if you annualize that rate, it comes out to over 520%. This is because the lender is charging you a very high interest rate for a very short period of time.
Another example would be if you took out a payday loan, which typically have very high fees attached to them. For instance, you might borrow $500 and have to pay back $575 in two weeks. The interest rate on this loan might be calculated as the $75 fee divided by the $500 borrowed, which comes out to 15%. However, if you annualize that rate, it comes out to over 390%.
In both of these examples, the interest rate is very high because the loan term is very short and/or the fees are very high. It's important to note that borrowing at such high interest rates can be extremely costly and can lead to a cycle of debt, so it's generally recommended to avoid loans with high interest rates whenever possible.
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In a right triangle, angle λ has a measure of 19º. If the hypotenuse of this right triangle has a measure of 24 feet, what is the measure of the side adjacent to angle λ?
Answer:
22.69 ~ = 23 feet
Step-by-step explanation:
cos 19 = adj/24
24cos 18 = adj
adj = 22.69~= 23
Given that MNPQ is a rectangle with vertices M(3, 4), N(1, -6), and P(6, -7), find the coordinates Q that makes this a rectangle
Given that MNPQ is a rectangle with verticles M(3, 4), N(1, -6), and P(6, -7), to find the coordinates of point Q, we can use the fact that opposite sides of a rectangle are parallel and have equal lengths.
First, let's find the vector MN and MP:
MN = N - M = (1 - 3, -6 - 4) = (-2, -10)
MP = P - M = (6 - 3, -7 - 4) = (3, -11)
Now, let's add the vector MN to point P:
Q = P + MN = (6 + (-2), -7 + (-10)) = (4, -17)
Therefore, the coordinates of point Q that make MNPQ a rectangle are Q(4, -17).
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find the missing side length
Answer:
Step-by-step explanation:
[tex]x^{2}[/tex]=a²+b²
x²=6²+2.5²
x²=36+6.25
x²=42.25
√x=√42.25
x=6.5
Answer:
6.5
Step-by-step explanation:
6^2 + 2.5^2 = c^2
•36 + 6.25 = c^2
•42.25 = c^2
• find square root of 42.25 = 6.5
• 6.5 = C
7 Plot (6,2) on the grid.
My teacher never thought us this and this was on my homework I give you 59 points if you give me a answer
Answer:Go to the 6 number on the bottom line.Then go up until you reach 2
Step-by-step explanation:
|
|
|
|
| .
|______
Should look like that-ish
Answer:
Step-by-step explanation:
Put the point to the right 6 times and up two times
On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set.
The solution to the system of equations shown above is the ordered pairs [-2, -9] and [3, -4].
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = -x² + 2x - 1 ......equation 1.
2x - 2y = 14 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pairs (-2, -9) and (3, -4).
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To meet the company’s sales goals, the sales director for the pet food company decided to provide training for some of the sales representatives in the Midwest and Northeast regions. After conducting a one-month training program, the sales director analyzed the effectiveness of the program by conducting a statistical study.
Question 1
The purpose of the sales director’s study is to determine whether attending the training program caused an increase in sales for representatives from the two regions. So the sales director collected sales data from both groups (those receiving training and those receiving no training) for three months after the one-month program and compared the number of orders secured by those who attended the training program with the number of orders secured by those who didn’t attend.
Part A
Question
Select the correct answer from each drop-down menu.
The sales director conducted _______ because a treatment _____ applied to the sales representatives. This is the best statistical study for this situation because the sales director is trying to establish _______.
1. ) An experiment
An observational
A survey
2. ) was
was not
3. ) causality
correlation
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A bee flies for 4.0 min at 32.5 in/min find the bees distance in ft
The distance that the bees cover in feet is 10.84 feet.
The speed at which the bees travel is given in the unit inches per min but the required solution is in feet so we need to convert the unit from in/min to ft/min using the unit conversion method.
We know that
1 inch=1/12feet.
so 32 inches/min=32.5 *(1/12) feet/min.
which is roughly equal to 2.71 feet/min (rounded to two decimal places).
Now by using the speed, distance, and time formula which is:
distance=speed*time
we can calculate the distance covered by bees at the given speed and time.
Substituting the values in the equation.
distance=2.71 feet/minute * 4.0 minutes.
=10.84 feet
Therefore, the bee's distance in feet will be 10.84 feet (rounded off to 2 digits).
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Help guys asap i need correct answers only!! find the volume of the cylinder. find the volume of a cylinder with the same radius and double the height.
the volume of the cylinder in^3?
the volume of with the same radius and double the height is
To find the volume of the cylinder, we need to use the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
If we have a cylinder with radius r and height h, and another cylinder with the same radius r but double the height (2h), the volume of the second cylinder is:
V' = πr^2(2h) = 2πr^2h
So, to answer the questions:
The volume of the cylinder is V = π(5 cm)^2(8 cm) = 100π cubic cm, which is approximately 314.16 cubic cm rounded to two decimal places.
The volume of the cylinder with the same radius and double the height is V' = 2π(5 cm)^2(8 cm) = 200π cubic cm, which is approximately 628.32 cubic cm rounded to two decimal place
solve for x:
6x+26=16x
Step-by-step explanation:
[tex]6x + 26 = 16x\\ 16x - 6x = 26 \\ 10x = 26 \\ x = 2.6[/tex]
x+y=112
y=x-58
using elimination
PLEASE HELP ME!!!!
Answer:
x=85
y=27
;)
Step-by-step explanation:
x+y=112
y=x-58
add 58 to the other side
58+y=x
Subtract y
x-y=58
x+y=112
Now if we add these we get
2x=170
x=85
Then if we substitute 85 in x+y=112
85+y=112
112
-85
____
27
Check your Answer on
y=x-58
27=85-58
27=27
This is the Answer
Please DM me if I should reexplain THANK YOU!
Hope this helps!
A company estimates that 0. 5% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $500. 0. If they offer a 2 year extended warranty for $33. 00, what is the company's expected value of each warranty sold? Please format your answer using a dollar sign and two decimal points for the cents. For example, if the expected value was 50, please enter it as $50. 0
The expected value of each warranty sold is $2.47.
The expected value of each warranty sold can be calculated by subtracting the cost of the warranty from the expected value of the potential savings on replacement costs.
Let's assume that the company sells 1000 warranties. Then, the expected number of products that will fail within 2 years is:
0.5% of 1000 = 0.005 x 1000 = 5
The expected cost of replacing these products is:
5 x $500 = $2500
Therefore, the expected value of the warranty is:
($2500 - $33 x 1000) / 1000 = $2.47
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You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test your suspicion, you rolled the die in question 200 times and obtained the following frequencies for each of the six possible outcomes of the die:
Number Frequency 1 2 3 4 5 6 45 39 35 25 27 29
Can you conclude that the die is loaded? Use a 0. 05 as the significance level and perform a hypothesis test. Remember to state the null and alternative hypothesis
Based on the hypothesis test, with a significance level of 0.05, there is no evidence to suggest that the die is loaded, as the p-value is greater than the significance level. The null hypothesis that the die is fair is failed to rejected.
To determine if the die is loaded, we need to perform a hypothesis test.
Null Hypothesis (H0) The die is fair; all outcomes are equally likely.
Alternative Hypothesis (Ha) The die is loaded, and not all outcomes are equally likely.
We will use a significance level of 0.05.
To test the hypothesis, we can use a chi-square goodness-of-fit test.
First, we need to calculate the expected frequencies for each outcome, assuming that the die is fair. Since there are six possible outcomes, each with an expected frequency of 200/6 = 33.33.
Number Observed Frequency (O) Expected Frequency (E) (O - E)² / E
1 45 33.33 3.48
2 39 33.33 0.87
3 35 33.33 0.07
4 25 33.33 1.83
5 27 33.33 0.99
6 29 33.33 0.44
The test statistic is the sum of (O-E)² / E, which is 7.68.
The degrees of freedom for this test are (number of categories - 1) = 5.
Using a chi-square distribution table or calculator, we find that the p-value associated with a test statistic of 7.68 and 5 degrees of freedom is approximately 0.177.
Since the p-value is greater than our significance level of 0.05, we fail to reject the null hypothesis. We cannot conclude that the die is loaded based on this data alone.
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(65 points) ASAP!!! Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.
Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)
Part B: Explain how you know the equation from Part A is correct. (1 point)
Part C: Solve the equation from Part A. Show every step of your work. (2 points)
Answer:
Total wood = 4.5 Left over wood = 0.7 let 1 piece of wood = x
hence we have 5x+0.7=4.5
5x=4.5 - 0.7
5x = 3.8 x= 3.8/5 = 0.76 ft
Step-by-step explanation:
Answer:
A: 5x + 0.7 = 4.5
B: You know the equation is correct because it takes into account that Warren cut five pieces of wood that are equal in length from a 4.5 feet long piece of wood. The total length of the five pieces of wood should equal the length of the original piece of wood, minus the leftover wood he has. In other words, 5x represents the total length of the five pieces of wood cut, and 0.7 represents the amount of wood left over after the cutting.
C: 0.76 feet
Step-by-step explanation:
Part A:
Let x be the length of each of the five pieces of wood cut from the 4.5 feet long piece of wood. The equation that could be used to determine the length of each piece is:
5x + 0.7 = 4.5
Part B:
You know the equation is correct because it takes into account that Warren cut five pieces of wood that are equal in length from a 4.5 feet long piece of wood. The total length of the five pieces of wood should equal the length of the original piece of wood, minus the leftover wood he has. In other words, 5x represents the total length of the five pieces of wood cut, and 0.7 represents the amount of wood left over after the cutting.
Part C:
5x + 0.7 = 4.5
5x = 4.5 - 0.7
5x = 3.8
x = 3.8/5
x = 0.76
Therefore, each of the five pieces of wood that Warren cut is 0.76 feet long.
PLS HELP ME WITH THIS 50 POINTS!
Answer: The transformation is up one and to the left 5
(-5, 1)
Step-by-step explanation:
Please Give brainliest, have a great night!
Answer: h(x) = g(x+5)+1
Step-by-step explanation:
h(x) = g(x+5)+1
You went 5 in the negative direction x direction; take the opposite sign
Also went up 1 in the y direction so add 1 to equation
What is the perimeter of the triangle?
?? units.
Answer:
36 units
Step-by-step explanation:
You want to know the perimeter of the right triangle with leg lengths 9 units and 12 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides. We can count squares to find the lengths of the horizontal and vertical legs. The length of the hypotenuse can be found using the Pythagorean theorem:
c² = a² +b²
c² = 9² +12² = 81 +144 = 225
c = √225 = 15 . . . . length of the hypotenuse
Then the perimeter is ...
P = a +b +c = 9 +12 +15 = 36 . . . units
The perimeter of the triangle is 36 units.
__
Additional comment
The leg lengths have the ratio 9:12 = 3:4, telling you this is a 3:4:5 right triangle. This means you know the side lengths are 3:4:5 = 9:12:15, and their sum is 9+12+15 = 36.
It is handy to memorize a few of the Pythagorean triples that often show up in algebra, trig, and geometry problems: {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.
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solve this problem:
Suppose that you are headed toward a plateau 50 m high. If the angle of elevation to the top of the plateau is 20 , how far are you from the base of the plateau?
Answer:
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's call the distance from the base of the plateau to our position "x". We can then use the tangent function to find x:
tan(20°) = opposite / adjacent
In this case, the opposite side is the height of the plateau (50 m) and the adjacent side is x. So we can write:
tan(20°) = 50 / x
To solve for x, we can rearrange this equation:
x = 50 / tan(20°)
Using a calculator, we get:
x = 143.45 meters (rounded to two decimal places)
Therefore, if the angle of elevation to the top of the plateau is 20 degrees, and the plateau is 50 meters high, we are approximately 143.45 meters away from the base of the plateau.
Answer:
The distance is 137.3739 feet.
Step-by-step explanation:
I hope this answer is right.
The area of a rectangle park is 53 square mile. The length of the park is 87 mile. What is the width of the park? URGENTTT PLS ANSWER STEP BY STEP
What is the recursive formula for the sequence -1, -3, -9, -33 ...
The recursive formula for an, the nth term of the sequence is a(n) = a(n - 1) * 2 where a(1) = -1
How to determine the recursive formula of the sequenceFrom the question, we have the following parameters that can be used in our computation:
-1, -3, -9, -3³ ...
The above definitions imply that we simply multiply 3 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a(n) = a(n - 1) * 3
Where
a(1) = -1
Hence, the sequence is a(n) = a(n - 1) * 2 where a(1) = -1
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Rosita is writing an explicit function for the geometric sequence:
80, 40, 20, 10, \dots80,40,20,10,…80, comma, 40, comma, 20, comma, 10, comma, dots
she comes up with t(n)=160\left( \dfrac12 \right)^nt(n)=160(
2
1
)
n
t, left parenthesis, n, right parenthesis, equals, 160, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript.
what domain should rosita use for ttt so it generates the sequence?
The domain of the function is the set of all positive integers, since the sequence starts with the first term and continues indefinitely. Therefore, Rosita should use the domain of positive integers for her function to generate the given sequence.
An explicit function is a mathematical expression that directly relates an independent variable to a dependent variable. In the case of Rosita's function, t(n) represents the nth term in the geometric sequence and is dependent on the value of n, the term number.
The explicit function that Rosita came up with is t(n)=160(1/2)^n, which can be simplified to t(n)=80(1/2)^(n-1). This function represents the relationship between the term number and the corresponding value in the sequence.
To determine the domain of the function, we need to consider the values of n that generate the given sequence. Looking at the sequence, we can see that the first term is 80 and each subsequent term is half of the previous term. This means that the sequence is generated by multiplying 80 by (1/2) raised to a power. We can write this as:
80(1/2)^(n-1)
where n is the term number. The domain of the function is the set of all positive integers, since the sequence starts with the first term and continues indefinitely. Therefore, Rosita should use the domain of positive integers for her function to generate the given sequence.
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You pick a card at random. (1234)
What is P(greater than 1 or divisor of 2)?
The probability of picking a number greater than 1 or a divisor of 2 is 3/4.
Calculating the probability P(greater than 1 or divisor of 2)?The numbers greater than 1 or divisor of 2 in the set {1, 2, 3, 4} are {2, 3, 4}.
Therefore, the probability of picking a number greater than 1 or a divisor of 2 is:
P(greater than 1 or divisor of 2) = P(2 or 3 or 4) = P(2) + P(3) + P(4)
Since there are four equally likely outcomes, the probability of each individual outcome is 1/4. Thus, we have:
P(greater than 1 or divisor of 2) = 1/4 + 1/4 + 1/4 = 3/4
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