Given the sequence:
1, 1, 2, 6, 24
Let's fill in the sequence.
Here, we can see that the nth term is equal to the pprevious term multiplied by n.
First term: 1 x 1 = 1
Second term: 1 x 2 = 2
Third term: 2 x 3 = 6
Fourth term: 6 x 4 = 24
Fifth term: 24 x 5 = 120
Sixth term: 120 x 6 = 720
Seventh term: 720 x 7 = 5040
8th term: 5040 x 8 =40320
Hence, the sequence is:
1, 1, 2, 6, 24, 120, 720, 5040, 40320
The explicit formula of the sequence is:
[tex]a_n=a_{n-1}\ast n[/tex]For example to find the 6th term, we have:
[tex]\begin{gathered} a_6=a_{6-1}\ast6 \\ \\ a_6=a_5\ast6 \\ \\ a_6=120\ast6 \\ \\ a_6=720 \end{gathered}[/tex]We can see the 6th term is 720.
For the recursive formula, we have:
[tex]\begin{cases}a_1=1 \\ \\ n\ge2_{} \\ \\ a_n=a_{n-1}\ast n\end{cases}[/tex]ANSWER:
Sequence: 1, 1, 2, 6, 24, 120, 720, 5040, 40320
Explicit formula:
[tex]a_n=a_{n-1}\ast n[/tex]
Recursive formula:
[tex]\begin{cases}a_1=1 \\ \\ n\ge2_{} \\ \\ a_n=a_{n-1}\ast n\end{cases}[/tex]
Choose the coefficient closest to 0.Choose the coefficient with the least value.
Explanation:
In the given graph f(x) = a |x| .
The coefficient ''a'' increases the graph of the function will shrink and it will goes to zero.
And when coefficient ''a'' decreases the graph will expands.
The graph in the option C represents the graph below x-axis and the coefficient of |x| will be negative so it will be least value.
Answer: Option C.
Consider the first three terms of the arithmetic sequence 9,14,19Determine d , the common difference Find the nth term, TnDetermine T9, the 9th term in the sequence
The common difference, d = 5
[tex]\begin{gathered} T_n=5n+4 \\ T_9=49 \end{gathered}[/tex]Explanation:The given sequence is:
9, 14, 19
The common difference is the difference between the consecutive terms of the sequence.
The common difference, d = 14 - 9 or d = 19 - 14
Therefore, the common difference, d = 5
The nth term of an Arithmetic sequence is given by the formula:
[tex]T_n=a+(n-1)d[/tex]where the first term, a = 9
The common difference, d = 5
Substitute a = 9, and d = 5 into the nth term formula above
[tex]\begin{gathered} T_n=9+5(n-1) \\ T_n=9+5n-5 \\ T_n=5n+4 \end{gathered}[/tex]The 9th term in the sequence is calculated by substituting n = 9 into the nth term gotten above
[tex]\begin{gathered} T_n=5n+4 \\ T_9=5(9)+4 \\ T_9=45+4 \\ T_9=49 \end{gathered}[/tex]A club is selling snacks at a track meet. Oranges cost $1 each and protein bars cost $4 each. They sell 100 items and collect 304. Describe what the solution means in the context of the situation. Explain your thinking
By writing and solving a system of equations, we will see that the club sold 32 oranges and 68 bars.
What the solution means?Here the solution will be the number of oranges and protein bars sold.
Let's define:
x = number of oranges.
y = number of bars.
We know that they sell 100 items and win a total of $304, then we can write the system of equations:
x + y = 100
x*$1 + y*$4 = $304
Isolating x on the first equation we get:
x = 100 - y
Replacing that in the other equation we get:
(100 - y)*$1 + y*$4 = $304
$100 - y*$1 + y*$4 = $304
y*$3 = $304 - $100 = $204
y = $204/$3 = 68
y = 68
And the value of x is:
x = 100 - y = 100 - 68
x = 32
That is the solution, x = 32 and y = 68.
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Find the price of one candy bar if sixteenth candy bars cost $128
sixteen candy bars cost $128
Divide the cost by 16 to get the price of one candy bar.
[tex]\frac{128}{16}=8[/tex]Therefore the answer is $8
Answer:
$8 per candy bar
Step-by-step explanation:
128/16 = 8
This shows a scale drawing of Javier's room. The scale of his room is 1 cm = 2 ft. 5 cm 6.5 cm How much carpet does Javier need to purchase to completely cover his floor? A 130 square feet B. 120 square feet C. 111 square feet
Answer:
A 130 ft²
Step-by-step explanation:
if I understand this right, then the scale is 1 cm on a drawing is 2 ft in reality.
the room in the drawing measures 5 cm × 6.5 cm.
the question about how much carpet is needed is the question about the area of the floor of the rectangle room.
first e need to get the real measurements :
5 cm = 5×1 cm = 5 × 2 ft = 10 ft
6.5 cm = 6 5×1 cm = 6.5×2 ft = 13 ft
so, the real room is 10 ft × 13 ft.
and the area is therefore 130 ft².
Help mee pleasee!!
thank you <3
As a function, the cost C(x) of publishing the newsletter would be C(x) = 75.00 + 0.25x, where the number of copies printed is x.
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
We have been given that the cost of producing a newsletter is an initial charge of $75.00 for formatting and editing plus $0.25 for printing each copy.
Let the number of copies printed x and the cost C(x) of printing the newsletter as a function
As per the given data, the function would be as:
C(x) = 75.00 + 0.25x
Therefore, the cost C(x) of printing the newsletter as a function expressed would be C(x) = 75.00 + 0.25x.
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(18−4²+2)²1÷4⋅1/2 please help
Answer:
70 8/9
Step-by-step explanation:
I think that is correct answer. I don't know if it is correct.
help meeeeeeeeee pleaseee
Answer:
I think this would convert to (-infinity,-4).
Step-by-step explanation:
Forgive me if I'm wrong, but this is the best i could remember from when I was learning this.
Find the values at the 25th and 60th percentiles for the data set. The value at the 25th percentile is_____.
Answer:
25th percentile: 5
60th percentile: 12
Explanation:
To find the percentile, we need to organize the data from lowest to greatest, so
1 3 4 4 5 6 6 7 8 8 9 12 14 15 17 17 19 20 20 20
Therefore, there are 20 values in the data set.
The position of the 25th percentile can be calculated as:
[tex]\frac{25(n)}{100}=\frac{25(20)}{100}=5[/tex]Then, the position of the 25th percentile is 5th. In this case, the number in this position is 5 so the 25th percentile is 5
In the same way, we can calculate the position for the 60th percentile as follows:
[tex]\frac{60(n)_{}}{100}=\frac{60(20)}{100}=12[/tex]Then, the position of the 60th percentile is the 12th. In this case, this value is 12, so the 60th percentile is 12.
So, the answers are:
25th percentile: 5
60th percentile: 12
U = {1,2,3,4,5,6,7,8}, A={2,4,5}, B = {1,4,7,8}, C = {3,6,8}. (Use the roster method to write the set. enter EMPTY for the empty set) A U (B U C)
U = {1,2,3,4,5,6,7,8}, A={2,4,5}, B = {1,4,7,8}, C = {3,6,8}. (Use the roster method to write the set. enter EMPTY for the empty set)
A U (B U C)
step 1
Find out B U C
we have
B = {1,4,7,8}, C = {3,6,8}
so
B U C={1,4,7,8} U {3,6,8}={1,3,4,6,7,8}
step 2
Find out A U (B U C)
A U (B U C)={2,4,5} U {1,3,4,6,7,8}={1,2,3,4,5,6,7,8}=set U
therefore
the answer is
{1,2,3,4,5,6,7,8}Solve this or I will eat all of your pickles
Also I will mark brainliest :)
4y + 12 = 0Find two points on the line to be graphed
Given the line:
[tex]4y+12=0[/tex]We simplify to have:
[tex]\begin{gathered} 4y=-12 \\ y=-\frac{12}{4} \\ y=-3 \end{gathered}[/tex]The line y=-3 is a horizontal line passing through y=-3.
Two points on the line that can be graphed are:
[tex]\begin{gathered} (1,-3) \\ (5,-3) \end{gathered}[/tex]You can pick any value of x. The value of y has to remain constant.
. When you are translating a number from scientific notation to standard form, what does the
exponent tell you?
O the number of zeroes to add to the end of the original number
O the number to multiply by the first factor
O the number of places to move the decimal point
O the number of times to multiply the first factor by itself?
Answer:
A. The number of zeroes to add to the end of the original number
Step-by-step explanation:
I got stuck with my math homeworkI was trying to figure these equations for 2 HOURS STRAIGHT (i gave up )
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]1-5\left(x-1\right)=2\left(2x-1\right)-x[/tex]STEP 2: Simplify the equation
Expand the two sides of the equation
[tex]\begin{gathered} 1-5(x-1)=2(2x-1)-x \\ 1-5x+5=4x-2-x \end{gathered}[/tex]STEP 3: Simplify both sides
[tex]\begin{gathered} -5x+6=3x-2 \\ \mathrm{Subtract\:}6\mathrm{\:from\:both\:sides} \\ -5x+6-6=3x-2-6 \\ -5x=3x-8 \\ \mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides} \\ -5x-3x=3x-8-3x \\ -8x=-8 \\ \mathrm{Divide\:both\:sides\:by\:}-8 \\ \frac{-8x}{-8}=\frac{-8}{-8} \\ \\ \therefore x=1 \end{gathered}[/tex]Hence, the value of x is 1
.name three fractions that are equivalent to 2/5
Answer:
4/10, 20/50, and 40/100
Hope this is helpful
1 The midpoint of AB is M. If the coordinates of A are (2,-6) and the coordinates of Mare (5, -1), find the coordinates of B.
The midpoint of two points is given as
(x1 + x2)/2, (y1 + y2)/2
Given that the coordinates of the midpoint are (5, -1), let the coordinates of point B be x2 and y2
(2 + x2)/2 = 5
2 + x2 = 10
x2 = 10 - 2
x2 = 8
(-6 + y2)/2 = -1
-6 + y2 = -2
y2 = -2 + 6
y2 = 4
The coordinates of B are (8,4)
On a math test, a group of students received the following scores:68, 98, 86, 75, 86, 94, 75, 81,75Find the MEAN of the test scores.
Answer
Mean of the score is 82
Explanation
Given the following set of data
68, 98, 86, 75, 86, 94, 75, 81, 75
Mean = summation of all the data / frequency of the data
Frequency = n
n = 9
Mean = 68 + 98 + 86 + 75 + 86 + 94 + 75 + 81 + 75 / 9
Mean = 738 / 9
Mean = 82
Therefore, the mean of the score is 82
Answer:
82
Step-by-step explanation:
68+98+86+75+86+94+75+81+75=738
738/9=82
what is the distance between points (4,0) and (0,3)1 unit 5 unit7 unit25 unit
We want to find the distance between the points:
[tex](4,0)\text{ and }(0,3)[/tex]For doing so, we remember the formula of the distance between two points:
[tex]d(P,P^{\prime})=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Where P(x₁,y₁) and P'(x₂,y₂). Applying the formula we get:
[tex]\begin{gathered} d=\sqrt[]{(4-0)^2+(0-3)^2} \\ =\sqrt[]{4^2+3^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5 \end{gathered}[/tex]This means that the distance between the points (4, 0) and (0, 3) is 5 units.
The function f(x) = 3|x| is translated to create the function g(x) = 3|x| + 4. What is the vertex of g(x)?
The function f(x) = 3|x| is translated to create the function g(x) = 3|x| + 4.
the vertex of g(x) is (0,4)
This is further explained below.
What is the vertex?Generally, The equation for the function given is mathematically given as
g(x)=3|x|+4
To find the x coordinate of the vertex, set the inside of the absolute value x equal to 0 .
In this case, x=0. x=0
Replace the variable x with 0 in the expression.
y=3|0|+4
Simplify 3|0|+4
y=4
In conclusion, The absolute value vertex is (0,4).
(0,4)
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A booth at the State Fair recorded the number of items sold in the chart below. What is the ratio of lemonade and sodas sold to the number of candy bars sold?
Answer:
7:6
Step-by-step explanation:
add the amount of lemonade and soda together, that is 42.
so you have 42:36.
you need to simplify it, so you divide 42 / 2 = 21
then you divide 36 / 2 = 18.
so now you have 21:18.
then you divide 21 / 3 = 7
then you divide 18 / 3 = 6.
so therefore, your answer is 7:6.
hope this helped:)
Help me to answer the second question with a more detailed process, thank you.
Hence the answer is
Quotient is
[tex]x^2+2x-4[/tex]remainder is 9
What is the area of triangle ABC?The area of triangle ABC is___ in²
ANSWER:
187.5 in^2
STEP-BY-STEP EXPLANATION:
We know that the area of a triangle is equal to the base times the height divided by 2
In the figure we have these values
The base is 3 squares that is 15 inches and the height is 5 squares that is 25 inches since each square measures 5 inches
The area is
[tex]A=\frac{b\cdot h}{2}=\frac{15\cdot25}{2}=\frac{375}{2}=187.5[/tex]The area of the triangle is 187.5 square inches
Randall wants to mix 54 Ib of nuts worth $1 per lb with some nuts worth $5 per Ib to make a mixture worth $4 per lb. How many pounds of $5 nuts must he use?
Let:
x = no. of lb of $5 nuts required.
resulting mixture = x + 54
Hence:
[tex]54\times\text{\$1}+\text{ \$5x}=(x+54)\times\text{\$4}[/tex]Solving for x:
[tex]\begin{gathered} 54+5x=4x+216 \\ 5x-4x=216-54 \\ x=162 \end{gathered}[/tex]ANSWER
Randall must use 162 lb of $5 nuts
Find c if a=2.93 mi,b=3.95 mi and c=40.3 degrees C=Round your answer to 3 decimal places
Using the law of cosines, we have the following relation between the measures of this triangle:
[tex]c^2=a^2+b^2-2ab\cos C[/tex]Plugging the given values, we have:
[tex]c^2=(2.93)^2+(3.95)^2-2(2.93)(3.95)\cos40.3^o[/tex]Solving for c, we have our answer:
[tex]c\approx2.556[/tex]The measure of c is 2.556 miles.
Question in picture answer correct
The reason for the statements for the algebraic proof is as follows;
Multiplication property of equalityDivision property of equalityHow to solve equation with reasons?The equation given is as follows:
3x / 6 = 4 . This equation is given.
Therefore,
3x / 6 = 4
Using multiplication property of equality, we will multiply both sides of the equation by 6.
3x / 6 × 6 = 4 × 6
3x = 24
The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
Hence,
3x = 24
Using division property of equality, we divide both sides by 3.
3x / 3 = 24 / 3
x = 8
The Division Property of equality says that dividing both sides of an equation by the same number does not affect the equation.
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Select the type of equation
The type of equation is equivalent.
What are equivalent equation?Equation systems that have the same solutions are said to be equivalent. A useful skill in both algebra class and daily life is the ability to recognize and solve comparable equations. View several illustrations of comparable equations, learn how to solve them for one or more variables, and consider how you may apply this knowledge outside of the classroom.
Algebraic equations with equal solutions or roots are said to be equivalent.An equation is equivalent if the same quantity or expression is added to or subtracted from both sides.An analogous equation is created by multiplying or dividing both sides of a non-zero equation by the same number.To know more about equivalent equations ,visit:
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What is the equation of the line that is parallel to the line y = x + 4 and passes through the point (6, 5)?y = x + 3y = x + 7y = 3x – 13y = 3x + 5
You have to find a line that is parallel to y=x+4 and passes through the point (6,5)
Parallel lines always have the same slope.
The slope of the line is the coefficient that multiplies the x term, in this case, there is no number multiplying "x" but that does not mean that the line has no slope, turns out that the line has a slope equal to "1" when the variables (letters in an equation) are "alone" the coefficient is 1
So for both lines, the slope is
[tex]m=1[/tex]Using the slope and the known point of the line, you can determine the equation of said line by using the "point-slope" form
[tex]y-y_1=m(x-x_1)[/tex]Where
(x₁,y₁) are the coordinates of a point of the line
m is the slope
Replace the coordinates of the point and the slope in the formula
[tex]y-5=1(x-6)[/tex]Next is to solve for y to express it in slope-intercept form
[tex]\begin{gathered} y-5=1\cdot x-1\cdot6 \\ y-5=x-6 \\ y-5+5=x-6+5 \\ y=x-1 \end{gathered}[/tex]The equation for a line parallel to y=x+4 that passes through point (6,5) is
[tex]y=x-1[/tex]Find the equation of the given line,Find the equation of the line passing through (2, 1) with slope 3.у =
Tori, this is the solution to the exercise:
Step 1: Let's remember that this is a case that we can solve using the following equation form:
y = mx+b, where m is the slope and b is the y-intercept.
Step 2: Solving for b:
y = mx + b
We replace x and y with the coordinates:
1 = 3 * 2 + b
1 = 6 + b
b = 1 - 6
b = - 5
Step 3: Therefore, the equation of the line that passes through the point (2,1) with a slope of 3 is:
y = 3x - 5
I have a partial sum question for a geometric sequence picture included
Solution
The partial sum of the arithmetic sequence with a = 3, d = 8
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex][tex]\begin{gathered} S_{13}=sum\text{ of the arithmetic sequence where n = 13} \\ S_{13}=\frac{13}{2}(2(3)+(13-1)8) \\ S_{13}=6.5(6+12(8)) \\ S_{13}=6.5(6+96) \\ S_{13}=6.5(102) \\ S_{13}=663 \end{gathered}[/tex]Therefore the partial sum of the arithmetic sequence = 663
Tina has a pet sitting business. She charges a flat service fee of $20, plus $15 per day for each animal. If one of her customersspent less than $110 on one animal, which of the following inequalities could be used to solve for x, the number of days thecustomer paid for pet sitting?
If the initial fee is $20 and additionally $15 is charged per day, then the total amount is given by:
[tex]A=20+15x[/tex]Where "x" is the number of days and "A" the total amount to pay. Since the total amount is less than $110, then we have the following inequality:
[tex]20+15x\le110[/tex]This is the inequality that can be used to determine the value of "x".
