The next term is double the previous term, so that the [tex]n[/tex]-th term is given recursively by
[tex]\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}[/tex]
This rule tells us that
[tex]a_2=2a_1[/tex]
[tex]a_3=2a_2=2^2a_1[/tex]
[tex]a_4=2a_3=2^3a_1[/tex]
and so on, with the explicit rule
[tex]a_n=2^{n-1}a_1=2^{n-1}[/tex]
for [tex]n\ge1[/tex].
If 512 is the [tex]k[/tex]-th term in the sequence, then
[tex]512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10[/tex]
Final answer:
In the geometric progression 1, 2, 4, ..., the 9th term is 512, determined by the formula for the nth term of a geometric progression.
Explanation:
The question asks us to find the term in a geometric progression where the value is 512. A geometric progression (GP) is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the ratio. In the given geometric progression 1, 2, 4, ..., each term is obtained by multiplying the previous term by 2. To find which term is 512, we can use the formula for the nth term of a GP, which is a_n = a_1 × r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.
Since a_1 is 1 and r is 2, we have: 512 = 1 × 2^(n-1). Simplifying this gives us 2^9 = 512, which means the 9th term of the sequence is 512. Therefore, 512 is the 9th term in the given geometrical progression.
Solve for X. Each figure is a parallelogram.
Answer:
x = 3
Step-by-step explanation:
m < T = m < R (Because they are opposite angles of a parallelogram). Therefore:-
40x + 2 = 122
40x = 120
x = 120/40
x = 3
Parallelogram is the closed shaped quadrilateral which has opposite site equal and the opposite angle are equal. The value of the x is 3 units.
Given-For the parallelogram angle T is (40x+2) degrees.
The angle R is 122 degrees.
To solve this the it should be known about the angle of the parallelogram.
Parallelogram-Parallelogram is the closed shaped quadrilateral which has opposite site equal and the opposite angle are equal.
As in the given figure the angle T and angle R is the opposite angle. Thus angle T and angle R will be equal to the each other. Thus,
[tex]\angle T= \angle R[/tex]
Put the values of the angle in the above equation. Thus,
[tex]40x+2=122[/tex]
[tex]40x=122-2[/tex]
[tex]40x=120[/tex]
[tex]x=\dfrac{120}{40}[/tex]
[tex]x=3[/tex]
Hence the value of the x is 3.
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you are making scarves for presents each scarf needs 3/4 yards of fabric how many yards of fabric do you need for 6 scarves
Answer: 8/1
Step-by-step explanation: 6/1 x 3/4= 24/3( divide both numbers by 3) and you get 8/1 yards of fabric.
Answer:
18/4
Step-by-step explanation:
3/4 per scarf
6 scarfs
6*(3/4)=(18/4)=4.5 yards
Which equation represents a non-proportional situation? y = 6x y = –2x + 14 y = –3x y = 14x
The equation of proportional situation is y = ax.
Therefore your answer is y = -2x + 14
Brainliest + Points! Need help and please show work :)
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Assuming it hits the target, what is the probability that a dart will land in the blue region?
A.
0,25
B.
0.33
C.
0.67
D.
0.75
Answer:
B. 0.33
Step-by-step explanation:
The probability will be given by the amount of space in the target area, blue, compared to the total amount of space, the red square.
The size of the blue square is 64 and the size of the red square is 196; this gives us a probability of
64/196 = 16/49 = 0.3265 ≈ 0.33.
The required probability that a dart will land in the blue region is 0.33. Option B is correct.
Given that,
A target is made of a blue square inside of a red square. The blue square has an area of 64 square units, and the red square has an area of 196 square units.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total sample space = 196
Total favorable space = 64
The probability that a dart will land in the blue region is given as.
probability = 64 / 196 ≈ 0.33
Thus, the required probability that a dart will land in the blue region is 0.33. Option B is correct.
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there are 24 students at the class picnic if 3/4 of the class is at the picnic how many students are in the class
Answer:
32
Step-by-step explanation:
To find the number of students in the class, use the equation 3/4x = 24 and solve for x.
Explanation:To find the number of students in the class, we can set up the equation 3/4x = 24, where x represents the total number of students in the class.
To solve for x, we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of 3/4, which is 4/3.
3/4x * 4/3 = 24 * 4/3
x = 32
Therefore, there are 32 students in the class.
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Equation in standard form
8x=-5y+3
Answer:
8x + 5y = 3
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given 8x = - 5y + 3 ( add 5y to both sides )
8x + 5y = 3 ← in standard form
Which expressions are equivalent to (5⋅x)⋅3 ? Drag and drop the equivalent expressions into the box.
3⋅(5⋅x)
5⋅3+x⋅3
5⋅(x⋅3)
15x
5⋅3⋅x⋅3
Answer:
3⋅(5⋅x)
5⋅(x⋅3)
15x
Step-by-step explanation:
As the values are inside the brackets, it does not matter what side the (x3) is on, so 3⋅(5⋅x) is equivalent.
Multiplying the contents of the brackets in the third one (x * 3) by 5 gives the same value as 3 * (x * 5) so 5⋅(x⋅3) is also equivalent.
On multiplying the brackets out:
5 * x = 5x
5x * 3 = 15x
So 15x is also equivalent.
Answer:
B
Step-by-step explanation:
The volume of a sphere is 36π in³. What is the radius of the sphere? Enter your answer in the box. in.
Answer:
3 inches
Step-by-step explanation:
⇒r3=36π×3/4π
or r3=27
Taking cube root of both sides
r=3 inch
A recipe calls for 12 cups of blueberries to make 7 jars of blueberry jam.
What is true about the number of cups of blueberries in each jar?
Each jar has 7/12 cup of blueberries.
Each jar has 1/12 of 7 cups of blueberries.
Each jar has 12/7 cups of blueberries.
Each jar has 1 5/12 cups of blueberries.
Answer:
Each jar has 12/7 cups of blueberries.
Step-by-step explanation:
To find out how many cups of blueberries per jar, we take the number of cups of blue berries and divide by the number of jars
12 cups/7 jars
12/7 cups of blueberries per jar
Each jar has 12/7 cups of blueberries.
Answer:
Step-by-step explanation:
GEOMETRY HELP PLEASE!!!!!!! Josh is building an enclosure with recycled cardboard for his collection of model cars his design is as shown below:
What is the length of side BC in inches?
A) 14
B) 43
C) 49
D) 63
the results of a survey showed that 7 tenths of the housholds surveyed used a computer what fraction of the household surveyed did not use a computer
What is the volume of this cylinder use 3.14 for pie
72
200.96
204.53
226.08
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
W have r = 3cm and H = 8cm. Substitute:
[tex]V=\pi(3)^2(8)=\pi(9)(8)=72\pi\ cm^3[/tex]
[tex]\pi\approx3.14\to V=72(3.14)=226.08\ cm^3[/tex]
Answer: 226.08 cm³.heelp will give brianliest
Answer:
256
Step-by-step explanation:
4(7)^2 + 30(2)
196 + 60 = 256
PLZ HELP ONE MORE TIME LAST QUESTION
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future, however, its value depreciates monthly. The expression below shows the depreciated sales value of the gadget: 2020 – 22m What does the second term of the expression represent?
A. The number of months Megan will wait to sell the gadget.
B. The original value of the gadget.
C. The monthly depreciation value of the gadget.
D. The total depreciation value of the gadget.
Answer: C
Step-by-step explanation: The word problem says that the value depreciates monthly, which means that -22m is how much Megan's gadget depreciates because m stands for months.
Options B and D are not true because the value has a variable, which indicates that it is decreasing by number of months according to the minus sign and not at a fixed amount.
Option A is not true because the word problem says that the expression shows the monthly depreciated sales value of the gadget, not the amount of time Megan will wait to sell the gadget.
If 2/3 of the 600 seeds sprouted, how many seeds did not sprout?
By calculating 2/3 of 600, we find that 400 seeds sprouted, which means 200 seeds did not sprout.
Explanation:To determine how many seeds did not sprout, we start by calculating the number of seeds that did sprout. Given that 2/3 of the 600 seeds sprouted, we multiply 600 by 2/3:
600 × (2/3) = 400
So, 400 seeds sprouted. Next, we subtract this number from the total number of seeds to find out how many did not sprout:
600 - 400 = 200 seeds
Therefore, 200 seeds did not sprout.
Slope 8/5;y-intercept(0,-9)
Answer:
y = 8/5x - 9
Step-by-step explanation:
That would be your equation.
Final answer:
The question pertains to finding the equation of a straight line with a given slope of 8/5 and a y-intercept of (0,-9), which can be represented in slope-intercept form as y = (8/5)x - 9.
Explanation:
The question involves constructing the equation of a line with a given slope and y-intercept.
To find the equation of a line, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Given the slope of 8/5 and a y-intercept of (0,-9), the equation of the line would be y = (8/5)x - 9.
The slope tells us that for every increase of 5 units in the horizontal direction (-axis), the line rises 8 units in the vertical direction (-axis). Meanwhile, the y-intercept indicates that the line crosses the y-axis at -9.
Paws at play made a total of $1234 grooming 22 dogs. Paws at Play charges $43 to groom each small dog and $75 for each large dog.
a. Write a system of equations that can be used to determine the number of small and large dogs that were groomed.
b. How many large dogs did Paws at Play groom?
Answer:
Answer (a):
s + l = 22 ... (i)
43s + 75l = 1234 ... (ii)
Answer (b)
9 large dogs.
Step-by-step explanation:
Paws at Play made a total of $1234 grooming 22 dogs.
Paws at Play charges $43 to groom each small dog and;
$75 for each large dog.
Let the number of small dogs be 's'
And the number of large dogs be 'l'
A system of equations will be:
s + l = 22 ... (i)
43s + 75l = 1234 ... (ii)
Solving this set of simultaneous equations by elimination, we simply multiply (i) by 43 to get;
43s + 43l = 946 ... (i)
43s + 75l = 1234 ... (ii)
Subtracting (i) from (ii) we get;
32l = 288 , l = [tex]\frac{288}{32}[/tex] = 9
So there are 9 large dogs.
How do I find the perimeter of the shapes
Answer:Here is the answer
Step-by-step explanation: You first break the shape into two different shapes.Then add them side by side. Determine the length for each side. Then add them together. Add both of the perimeters of the shapes.
18 - t/20= -9 what does t equal?
18 - t/20 = -9 what does t equal?
Answer:
t = 540
Step-by-step explanation:
18 - t/20 = -9
Subtract 18 from both sides.
-t/20 = -27
Multiply both sides by -20.
t = 540
What is the zero in the quadratic function f(x)= 9x^2-54x-19?
Answer:
6.33... and 0.333...
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}[/tex]
We will now solve for the plus and the minus.
The plus,,,
[tex]x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3[/tex]
and the minus...
[tex]x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...[/tex]
X varies directly and inversely with z. X=20 when y=8 and z=4 . Find x when y=4 and z =8
Answer:
Value of x = 5 .
Step-by-step explanation:
Combined variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others.
Given: x varies directly with y and inversely with z.
i.e [tex]x \propto y[/tex] and [tex]x \propto \frac{1}{z}[/tex]
then we have the combined variation as;
[tex]x = k\frac{y}{z}[/tex] ......[1] where k is the constant variation.
Substitute the value of x =20 when y =8 and z = 4 to solve for k;
[tex]20 = k\frac{8}{4}[/tex]
Simplify:
[tex]20 = 2k[/tex]
Divide both sides by 2 we get;
[tex]k = 10[/tex]
Now, substitute k =10 , y =4 and z = 8 to find x;
Using [1] we have;
[tex]x = 10 \times \frac{4}{8} = 10 \times \frac{1}{2} = 5[/tex]
Therefore, the value of x is, 5
The problem involves the concept of direct and inverse variation. From the given conditions, a constant of variation 'k' is calculated as 1.6. Using this 'k', x is found to be 20 when y is 4 and z is 8.
Explanation:This question involves the concept of direct and inverse variation. When it is stated that 'x varies directly and inversely with z', it implies a relationship which can be written in the form of y = kx/z, where k is a constant of variation.
To find the constant, we plug in the provided values for x, y, and z into our equation. Hence, using the known values (x=20, y=8, and z=4), our equation becomes 8 = 20k/4. Simplifying this gives us k = 1.6.
Now, to find the value of x when y=4 and z=8, we substitute these into the equation giving us 4 = 1.6x/8. Solving for x, we find that x = 20.
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PLEASE HELP!!!!!!
Which number(s) below belong to the solution set of the inequality? Check all that apply.
“9x>117”
A. 13
B. 19
C. 6
D. 14
E. 8
F. 12
If I understand the question corrects it’s asking which numbers work in the inequality so you just plug in each number where x is.
B and D
Seymour is twice as old as Cassandra. If 16 is added to Cassandra’s age and 16 is subtracted from Seymour’s age, their ages will be equal. What are their present ages?
Answer:
The age of Cassandra is 32 years and Seymour is 64 years old.
Step-by-step explanation:
Let the age of Cassandra be x.
The age of Seymour = 2x
If 16 is added to Cassandra’s age and 16 is subtracted from Seymour’s age, their ages will be equal.
x + 16 = 2x - 16
2x - x = 16 + 16
x = 32 years
x = 32 years
The age of Seymour = 2x = 2 × 32 years = 64 years
The age of Cassandra is 32 years and Seymour is 64 years old.
For a certain spinner, if we expect to win a prize four times in sixty tries, what is the theoretical probability of winning a prize?
Answer:1/15
Take 60/4=15
The theoretical probability of winning a prize is 1/15.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, given data;
Total trials = 60
Expect to win = 4
Probability = favorable outcomes/total outcomes
= 4 / 60
= 1/15
Thus, The theoretical probability of winning a prize is 1/15.
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Chole bought 4 movie tickets. Each ticket cost $6. What was the total cost of the movie tickets
Answer:
$24
Step-by-step explanation:
So, Basically you multiply 4 times 6 because you have 4 tickets that cost $6
and you would get 24 and add a dollar sign you should be good.
Evaluate the expression below, -0.25 -(-1/5)+0.2+(-1/4)
Answer:
0.4
Step-by-step explanation:
-1/5 = -2/10 = -0.2, -1/4 = -25/100 = -0.25
-0.25-(-1/5)+0.2+(-1/4) = -0.25+0.2+0.2+0.25 = -0.25+0.25+0.2+0.2 = 0.4
Answer:
0.0016
Step-by-step explanation:
Find the quotient. 1,458/26
1458/26 = 56.0769230769
Hope this helps! <3
The quotient is 56, and there is a remainder of 2.
The quotient of 1,458 divided by 26 is 56. In long division, you would set up the problem as follows:
56
__________
26 | 1,458
You start by asking how many times 26 can fit into 145 (the first two digits of 1,458). The answer is 5 (5 times 26 equals 130).
You write the 5 above the line and subtract 130 from 145, leaving you with 15.
Then, you bring down the next digit, which is 8, making it 158. You repeat the process, finding that 26 goes into 158 six times (6 times 26 equals 156).
Write the 6 above the line, and you're left with a remainder of 2. So, the quotient is 56, and there is a remainder of 2.
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Distinguish between the situations that can be modeled with a linear function, an exponential functions or neither
Answer:
Examples of linear functions would be relationships that represent a constant rate of change, such as 20 miles per gallon of gas. Exponential functions would be relationships that represent a growth or decay the increases or decreases by an exponential amount, such as a bacterial growth that doubles each hour. Examples of situations that would be neither linear or exponential would be absolute value functions or quadratic functions.
Step-by-step explanation:
Situations, or relationships between data, that can be modeled with a linear function must show a constant increase or decrease in rate. For example, we could control the rate of temperature in a water bath by two degrees every ten minutes. For exponential functions, these can be modeled in situations where there is a significant growth or decay of a material. For instance, the radioactivity of an element will decrease by one-half every year. This would represent an exponential decay. For other types of situations, such as changes in body temperature (absolute value) or the speed of a kayaker (quadratic), these would not be modeled using either linear or exponential functions.
A linear function can model constant rate of change, exponential function can model constant growth or decay, and some situations do not fit into these mathematical models.
Explanation:A linear function can model situations where there is a constant rate of change between two variables. For example, if the cost of a movie ticket increases by $2 for every additional hour of the movie, you can represent this relationship with a linear function.
An exponential function can model situations where there is constant growth or decay. For example, if the value of an investment doubles every year, you can represent this relationship with an exponential function.
There are situations that cannot be modeled with either a linear or exponential function. For example, unpredictable events or situations with multiple complex factors may not fit into these mathematical models.
What is the written form of the decimal number 0.954?
Answer:
nine hundred fifty-four thousandths
Step-by-step explanation:
If you mean written as in a form in words:
To the first decimal place means tenths because it is out of ten
To the second place, it's hundredths because 100 = 10^2
3rd is 1000, and so on
A fraction (as in two out of five), is expressed in words as "two fifths"
So 954 out of 1000 would be nine hundred fifty-four thousandths
if the domain of f(x) = x^2 + 1 is limuted to {0,1,2,3} what is the maximum value of the range?
Answer: 10
Plug in the given x values and see which result is the largest
Plug in x = 0 ---> x^2+1 = 0^2 + 1 = 1
Plug in x = 1 ----> x^2 + 1 = 1^2 + 1 = 2
Plug in x = 2 ----> x^2 + 1 = 2^2 + 1 = 5
Plug in x = 3 ---> x^2 + 1 = 3^2 + 1 = 10
The range is therefore {1, 2, 5, 10} which is just the set of possible outputs.
We see that y = f(x) = 10 is the largest output of the range if the domain is restricted to the set {0, 1, 2, 3}