The given sequence 48, 12, 3, .... written in the explicit formula is as follows:
aₙ = 48·(1/4)^(n-1)
What is the explicit formula?The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.
An arithmetic sequence has the explicit formula aₙ = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms.
The nth term of arithmetic, geometric, or harmonic series is usually the explicit formula.
So, the sequence we have is as follows:
48, 12, 3, ....
The common ratio of the terms is 1/4, and the first term is 48.
The universal equation for a geometric sequence's n-th term is:
aₙ = a1·r^(n-1)
This is true when r = 1/4 and a1 = 48:
aₙ = 48·(1/4)^(n-1)
Therefore, the given sequence 48, 12, 3, .... written in the explicit formula is as follows:
aₙ = 48·(1/4)^(n-1)
Know more about the explicit formula here:
https://brainly.com/question/24198356
#SPJ1
Which of the following problems would NOT have a solution? Group of answer choices 10 divided by 2. 10 divided by 5. 10 divided by 0. 0 divided by 10.
10 divided by 0 problem would NOT have a solution.
Given:
a. 10 divided by 2
b. 10 divided by 5
c. 10 divided by 0
d. 0 divided by 10
We know that ,
Integer divided by an integer is an integer
Therefore (a) and (b) will have a proper solution
We also know that ,
Zero divided by anything is Zero
Therefore (d) also have a unique answer that is zero
Now , We know that
Any numeric value divided by Zero tends to infinity .
Hence, 10 divided by 0 problem would NOT have a solution.
Learn more about infinity at:
https://brainly.com/question/903340
#SPJ1
1. Draw a scaled copy of either Figure A or B using a scale factor of 3.2. Draw a scaled copy of either Figure C or D using a scale factor of 1/2
For a Scaled copy multiply each side length by the scale factor
1.
A
Multiply each side by 3 , and then connect the missing side:
C. figure C
Multiply each side length by 1/2
A high school is voting on a new mascot. Lion Eagle Bee Ninth Grade 45% 32% 23% Tenth Grade 36% 40% 24% Eleventh Grade 50% 28% 22% Twelfth Grade 40% 25% 35% Match the two-way table to the segmented bar graph.
The steps to create a bar graph are explained below.
To match the two-way table to the segmented bar graph, we need to create a segmented bar graph that represents the data in the table. The table shows the percentage of students in each grade who voted for each mascot option.
Here is how we can match the two-way table to the segmented bar graph:
For the Lion mascot option, the segmented bar graph would have the largest segment for 11th grade, followed by 9th grade, 10th grade, and 12th grade.For the Eagle mascot option, the segmented bar graph would have the largest segment for 10th grade, followed by 11th grade, 9th grade, and 12th grade.For the Bee mascot option, the segmented bar graph would have the largest segment for 12th grade, followed by 9th grade, 10th grade, and 11th grade.By creating a segmented bar graph that represents the data in the two-way table, we can visually compare the percentage of students who voted for each mascot option across different grade levels.
Learn more about graphs here:
https://brainly.com/question/17267403
#SPJ1
32, 25, 18, 11..... Next 3...
18, 25, 32
4, -3, -10
7, 14, 21
39, 46, 53
Answer:
you subtract by 7 everytime
Iris is a working freelancer and has been tracking her monthly income for the last four months she found out that she made $2700 $4600 $3550 and $1700 when making her budget what income value should she use
Iris should use an income value of approximately $3,137.50 when making her budget.
When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.
To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:
$2700 + $4600 + $3550 + $1700 = $12,550
Next, dividing the total income by four (the number of months), we find:
$12,550 / 4 = $3,137.50
Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.
It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.
For more such questions on value,click on
https://brainly.com/question/843074
#SPJ8
The probable question may be:
Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?
iota z^3 -8 =0 find |z|
plzz tell fast mode
z btana h
Answer:
thats 8 with the power of three or a fraction of 3 and if your subtracting 8 the so called "hidden" number is 8 meaning that it would equal 0
Step-by-step explanation:
Write an expression that represents the area of just the portrait (white rectangle)
the area of the rectangle will be 1.5w².
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
The given length of the rectangle is w
The width will be 1.5w
So the rectangle of the white figure is Area = w*1.5w = 1.5 w²
hence the area of the rectangle will be 1.5w².
Learn more about rectangular by following the link below.
brainly.com/question/25292087
#SPJ1
The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
it is 4.5 miles from moulton to filby via Burnham and denton how far is it between denton and filby
Answer: I think that the answer is 3/4 miles
Step-by-step explanation:
50 Points! Multiple choice algebra question. If r(x)=x^3-2x+1, find r(2a^3). Photo attached. Thank you!
Answer:
D
Step-by-step explanation:
Answer:
D. \(8a^{9} -4a^{3} +1\)
Step-by-step explanation:
Given \(r(x)=x^{3} -2x+1\) and find \(r(2a^{3} )\) :
\(r(2a^{3} )\) is the same as saying \(x=2a^{3}\)So, we have \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1\)Solve for \(r(2a^{3} )\) :
1. \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1\)
Start with simplifying \((2a^{3})^{3}\)\((2a^{3})^{3}=2^{3}*(a^{3})^{3}=8*a^{3*3}=8a^{9}\)When you have a quantity raised to a power, or an exponent, you have to distribute the exponent to each term multiplied.When you multiply two terms that are raised to a power, you add the powers.When you divide two terms that are raised to a power, you subtract the power in the numerator from the power in the denominator.When you have a power raised to a power, you multiply the powers.2. \(r(2a^{3} )=8a^{9} -2(2a^{3})+1\)
Simplify \(2(2a^{3})\)Multiply two times the quantity\(2(2a^{3})=4a^{3}\)3. \(r(2a^{3} )=8a^{9} -4a^{3}+1\)
Answer:
So, if \(r(x)=x^{3} -2x+1\), then \(r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1\).
Then the answer is D. \(r(2a^{3} )=8a^{9} -4a^{3}+1\)
Carl button airline ticket two weeks ago the cost of this flight was $300 what is the percent increase
Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
The exponential function that can model the county population, y, x decades after Tiana was born, is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
\(y = a(b)^x\)
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 when y = 600000, hence:
\(y = 641000(0.99)^x\)
\(600000 = 641000(0.99)^x\)
\((0.99)^x = \frac{600000}{641000}\)
\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)
\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)
\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)
x = 6.6 decades.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
Find sin theta if cos theta is 4/5
Answer:
Step-by-step explanation:
hello :
cos²θ +sin²θ = 1 and cosθ =4/5
(4/5)² + sin²θ = 1 so : sin²θ = 1 - 16/25
sin²θ = 9/25 = (3/5)²
sinθ = 3/5 or sinθ = - 3/5 because : (3/5)²= (- 3/5)²= 9/25
Use two unit multipliers to convert 145 centimeters to kilometers (show work)
Answer:
0.00145 km or 1.45×\(10^{-3}\) kmStep-by-step explanation:
We know:
1 km = 1000 m1 m = 100 cmConvert cm to km:
1 cm = 1/100 m = 1/100* 1/1000 km = 1/100000 km145 cm = 145/100000 km = 0.00145 km or 1.45×\(10^{-3}\)It cost the Wilson children $55 to make lemonade. How many glasses must they sell at 75¢ each to make a profit?
Answer:
Step-by-step explanation: x=number of glasses sold
55<0.75x
55/0.75<x
x>73 ⅓
they have to sell at least 74
Draw a triangle with an area of 21 square units in a coordinate plane where the vertices are not all in the same quadrant?
The graph of the triangle is on the image at the end.
How to draw the triangle?Remember that the area of a triangle of base B and height H is:
A = B*H/2.
Here we want to have an area of 21, then we can use:
B = 6
H = 7
Then:
A = 6*7/2
A = 3*7 = 21
So we must have a base of 6 units and a height of 7 units, then the vertices that we can have are:
(-3, 0), (3, 0), (-3, 7)
So we will have a right triangle such that the vertices are on the first and second quadrant, the graph of the vertices is below.
Learn more about triangles at:
https://brainly.com/question/2217700
#SPJ1
URGENT!!! Elementary school students were given a geometry assignment. They were to measure the area of several rectangles and to measure the diagonal of the rectangle as shown in the table.
The equation of the least-squares regression line is
ŷ = 3.6 + 0.113x, where ŷ is the diagonal and x is the area of the rectangle. Which shows the residual plot?
The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.
Please find attached the graph of the residual plot for the data created with MS Excel
What is a residual plot?A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.
The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158
The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;
Area (in²) \({}\) Residuals
x-value
5 \({}\) -1.0178
10 \({}\) -0.2718
24 \({}\) 0.605
46 \({}\) 0.7874
53 \({}\) 0.7018
78 \({}\) 0.0758
84 \({}\) -0.129
100 \({}\) -0.7538
The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option
Learn more on residual values of a set of data here: https://brainly.com/question/31687998
#SPJ1
Please help with this !! ASAP
Answer:
B) 12
Step-by-step explanation:
These two angles are known as same-side interior angles. These angles add up to 180°. Use this to solve for y:
9y + 7 + 7y - 19 = 180
16y - 12 = 180
16y = 192
y = 12
What is 2(a +8) pls help me I want to pass
Answer:
2a+16
Step-by-step explanation:
Your first distribute 2(a+8) and get 2a+16.
Whenever a number is in front of a group of numbers in parenthesis, then it is always multiplying. You have to multiply both numbers, and that's how I got 2a+16. Hopefully this helps!
QUESTIONS
A salt is packed in jars containing 32 grams. How many jars can be filled from 15kg of the salt? [
Answer:
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
Step-by-step explanation:
Given:
Amount of salt containing in jar = 32 gram
Total amount of salt in jar = 15 kg
Find:
Number of jars can be filled from 15kg of the salt
Computation:
Total amount of salt in jar = 15 kg
Total amount of salt in jar (in grams) = 15 x 1000 g
Total amount of salt in jar (in grams) = 15,000 g
Number of jars can be filled from 15kg of the salt = Total amount of salt in jar (in grams) / Amount of salt containing in jar
Number of jars can be filled from 15kg of the salt = 15,000 / 32
Number of jars can be filled from 15kg of the salt = 468.75
Number of jars can be filled from 15kg of the salt = 468 or 469 jars (Approx.)
I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS 7
A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides. Given that there are 30 meters of fencing available, determine the dimensions that would create the garden of maximum area. What is the maximum possible area?
The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters
What is measurement?
Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.
Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.
Since we have 30 meters of fencing available, the total length of wire fencing used is:
L + 2W = 30 - W
Simplifying this equation, we get:
L = 30 - 3W
The area of the garden is:
A = LW
Substituting the expression for L from the previous equation, we get:
A = W(30 - 3W)
Expanding the expression, we get:
A = 30W - 3W²
To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:
dA/dW = 30 - 6W = 0
Solving for W, we get:
W = 5
Substituting this value back into the expression for L, we get:
L = 15
Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:
A = 5(15) = 75 square meters
To know more about measurement visit:
brainly.com/question/4804936
#SPJ1
Determine the x- and y- intercepts for the graph defined by the given equation.
y = x + 8
a. x-intercept is (0,8)
c. x-intercept is (-8, 0)
y-intercept is (-8, 0)
y-intercept is (0,8)
b. x-intercept is (0, -8)
d. x-intercept is (8,0)
y-intercept is (8,0)
y-intercept is (0, -8)
Answer:
Y-intercept is (0,8)
Step-by-step explanation:
The line of an equation is y=mx+b. M in this case is 1 and "b" is the y intercept. since in the place of b is positive 8 the y-intercept is 8
Can someone help me?Solve the equation , check for extraneous solutions
Answer:
0
Step-by-step explanation:
\(2\sqrt[3]{(1-3x)} =6-4=2\\\sqrt[3]{(1-3x)}=\frac{2}{2} =1\\\sqrt[3]{(1-3x)}^{3} =1^{3} \\(1-3x)=1\\-3x=0\\x=0\)
given the following matrices, if possible, determine A+B+C. if not, state “not possible”
Given:
\(\begin{gathered} A=\begin{bmatrix}{-5} & {1} & {} \\ {4} & {1} & {} \\ {4} & {-3} & {}\end{bmatrix} \\ B=\begin{bmatrix}{-2} & {10} & {} \\ {6} & {-3} & {} \\ {-7} & {-1} & {}\end{bmatrix} \\ C=\begin{bmatrix}{8} & {-1} & {} \\ {8} & {-10} & {} \\ {-3} & {-5} & {}\end{bmatrix} \end{gathered}\)Required:
To find A+B+C.
Explanation:
Now the addition of given matrix is possible.
\(A+B+C=\begin{bmatrix}{-5} & {1} & {} \\ {4} & {1} & {} \\ {4} & {-3} & {}\end{bmatrix}+\begin{bmatrix}{-2} & {10} & {} \\ {6} & {-3} & {} \\ {-7} & {-1} & {}\end{bmatrix}+\begin{bmatrix}{8} & {-1} & {} \\ {8} & {-10} & {} \\ {-3} & {-5} & {}\end{bmatrix}\)\(=\begin{bmatrix}{-5-2+8} & {1+10-1} & {} & {} \\ {4+6+8} & {1-3-10} & {} & {} \\ {4-7-3} & {-3-1-5} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}\)\(=\begin{bmatrix}{1} & {10} & {} \\ {18} & {-12} & {} \\ {-6} & {-9} & {}\end{bmatrix}\)Final Answer:
\(A+B+C=\begin{bmatrix}{1} & {10} & {} \\ {18} & {-12} & {} \\ {-6} & {-9} & {}\end{bmatrix}\)find the area and circumference of a circle with a radius 5 m. use the value 3.14 for radius, and do not round your answers. Be sure to include the correct units in your answers.
Area and circumference of the circle are 78.5 m² and 31.4 m respectively.
What is a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that, a circle have a radius 5 m
Area of a circle = π × radius²
Circumference = 2π×radius
Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²
Circumference = 3,14 × 2 × 5 = 31.4 m
Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.
Learn more about circle, click;
https://brainly.com/question/29142813
#SPJ1
Solve: 2x -3 =6
Hey can someone please help me with this?
Hey there!
\(Answer:\boxed{x=\frac{9}{2}}\)
\(Explanation:\)
\(2x-3=6\)
\(2x-3+3=6+3\\2x=9\) Add 3 to both sides.
\(\frac{2x}{2}=\frac{9}{2}\) Divide both sides by 2.
\(x=\frac{9}{2}\)
Hope this helps!
\(\text{-TestedHyperr}\)
\(\text {Hi! Let's Solve this Problem!}\)
\(\text {The First Step is to Add 3:}\)
\(2x-3+3=6+3\\2x=9\)
\(\text {The Final Step is to Divide 2:}\)
\(\text 2x/2=9/2\)
\(\text {Your Answer would be:}\)
\(\fbox {x=9/2 or as a decimal x=4.5}\)
\(\text {Best of Luck!}\)
\(\text {-LimitedX}\)
If h(x) = -2x + 6, find x if h(x) = 12.
\(-2x+6=12\\2x=-6\\x=-3\)
8. The first three terms of a geometric sequence are ( x-6), 3x, and y. If the common ratio is 6, then the value of y is.
Answer:
The value of y is 216
(and the value of x is 12)
Step-by-step explanation:
The general formula for a geometric sequence is,
\(a_n = a_1(r)^{n-1}\)
Where n represents the nth term, a_1 is the first term and r is the common ratio,
we see that,
r = 6,
the first term is,
a_1 = (x-6)
the 2nd term is,
a_2 = 3x,
the 3rd term is,
a_3 = y, finding y,
first we find x, using the above given formula we have,
\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)
x = 12,
Now, for y we can use the relation between a_3 and a_2,
\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)
y = 216
How can u find a geometry-big circle mAB=56 mBC=59 mCD=63 mDE=63 mEF= 31
To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.
We are given the following measures:
\(\sf\:m\angle AB = 56 \\\)
\(\sf\:m\angle BC = 59 \\\)
\(\sf\:m\angle CD = 63 \\\)
\(\sf\:m\angle DE = 63 \\\)
\(\sf\:m\angle EF = 31 \\\)
To find the measure of the geometry-big circle, we add up these measures:
\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)
Substituting the given values:
\(\sf\:56 + 59 + 63 + 63 + 31 \\\)
Simplifying the expression:
\(\sf\:272 \\\)
Therefore, the measure of the geometry-big circle is 272.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)