Given that the recursive formula for a sequence is [tex]a_n=a_{n-1}+2n[/tex]
The first term of the sequence is [tex]a_1=4[/tex]
We need to determine the first four terms of the sequence.
Second term:
The second term of the sequence can be determined by substituting n = 2 in the recursive formula.
Thus, we have;
[tex]a_2=a_{2-1}+2(2)[/tex]
[tex]a_2=a_{1}+2(2)[/tex]
[tex]a_2=4+4[/tex]
[tex]a_2=8[/tex]
Thus, the second term of the sequence is 8.
Third term:
The third term of the sequence can be determined by substituting n = 3 in the recursive formula.
Thus, we have;
[tex]a_3=a_{3-1}+2(3)[/tex]
[tex]a_3=a_{2}+2(3)[/tex]
[tex]a_3=8+6[/tex]
[tex]a_3=14[/tex]
Thus, the third term of the sequence is 14.
Fourth term:
The fourth term of the sequence can be determined by substituting n = 4 in the recursive formula.
Thus, we have;
[tex]a_4=a_{4-1}+2(4)[/tex]
[tex]a_4=a_{3}+2(4)[/tex]
[tex]a_4=14+8[/tex]
[tex]a_4=22[/tex]
Thus, the fourth term of the sequence is 22.
Hence, the first four terms of the sequence is 4, 8, 14, 22.
Brenda invests $4500 in the savings account earning 5.5% interest compounded quarterly. What will the account balance be after seven years?
The account balance will be $6642 after seven years.
Step-by-step explanation:
It is given that, Brenda invests $4500 in the savings account.The interest rate is 5.5% interest compounded quarterly.To find the amount after seven years, a certain formula is used.
Amount = [tex]P( 1+r/n)^{n\times t}[/tex]
where,
P is the principal amount that is invested in the account.
Therefore, P = 4500 dollars.
r is the rate of interest. (r = 5.5 %)
Therefore, r = 5.5/100 = 0.055
n is the number of time the interest is compounded per year which is n= 4.
t is the time period which is t = 7 years.
Now, substituting all the above values in the formula,
Amount = [tex]4500(1+0.055/4)^{4\times 7}[/tex]
⇒ [tex]4500(4.055/4)^{28}[/tex]
⇒ [tex]4500(1.014)^{28}[/tex]
⇒ [tex]4500\times1.4759[/tex]
⇒ 6641.55 (which is approximately equal to 6642)
⇒ 6642 dollars.
The account balance after 7 years is $6642.
Combine the like terms to simplify the polynomial. Show any work. Put your answers in standard form.
(5x^4-3x^3+2x^2-15x+27)+(7x^4+5x^3-x^2+8x-13)
Answer:
12x⁴ + 2x³ + x² - 7x + 14
Step-by-step explanation:
(5x^4-3x^3+2x^2-15x+27) + (7x^4+5x^3-x^2+8x-13)
(5+7)x⁴ + (-3+5)x³ + (2-1)x² + (-15+8)x + (27-13)
12x⁴ + 2x³ + x² - 7x + 14
What is the mad of this set 0,3,6,9,11,13,14
Answer:
When I calculated this I got: 4.2857142857143 but I don't know if that's the correct answer.
Step-by-step explanation:
Look at the following graph of the given equation. Determine whether the equation is a function. Explain why or why not.
y= 2x+2
+ • 2.6)
+ (1.4)
(0.2)
The equation [tex]y=2x+2[/tex] is a function
Explanation:
Given that the graph contains the coordinates [tex](-1,0)[/tex], [tex](0,2)[/tex] , [tex](1,4)[/tex] and [tex](2,6)[/tex]
We need to determine whether the equation [tex]y=2x+2[/tex] is a function.
To determine the equation is a function, let us substitute the coordinates in the equation and check whether it satisfies the equation.
Let us substitute the coordinate [tex](-1,0)[/tex] in the equation [tex]y=2x+2[/tex]
Thus, we have,
[tex]0=2(-1)+2[/tex]
[tex]0=-2+2[/tex]
[tex]0=0[/tex]
Thus, the coordinate [tex](-1,0)[/tex] satisfies the equation [tex]y=2x+2[/tex]
Substituting the coordinate [tex](0,2)[/tex] in the equation, we have,
[tex]2=2(0)+2[/tex]
[tex]2=2[/tex]
Thus, the coordinate [tex](0,2)[/tex] satisfies the equation [tex]y=2x+2[/tex]
Substituting the coordinate [tex](1,4)[/tex] in the equation [tex]y=2x+2[/tex]
[tex]4=2(1)+2[/tex]
[tex]4=4[/tex]
Thus, the coordinate [tex](1,4)[/tex] satisfies the equation [tex]y=2x+2[/tex]
Substituting the coordinate [tex](2,6)[/tex] in the equation, we get,
[tex]6=2(2)+2[/tex]
[tex]6=6[/tex]
Thus, the coordinate [tex](2,6)[/tex] satisfies the equation [tex]y=2x+2[/tex]
Hence, the coordinates [tex](-1,0)[/tex], [tex](0,2)[/tex] , [tex](1,4)[/tex] and [tex](2,6)[/tex] satisfies the equation [tex]y=2x+2[/tex]
Thus, the equation [tex]y=2x+2[/tex] is a function.
Four times a divided by two equals 5.2
Initial equation:
4a / 2 = 5.2
Multiply both sides by 2:
4a = 10.4
Divide both sides by 4:
a = 2.6
Hope this helps!! :)
Answer:
Step-by-step explanation:
2.6 becuase 4a/2= 5.2
4a=10.4
a=2.6
The length of a certain rectangle is 15cm more than three times its width. If the perimeter of the rectangle is 94cm, what is the area.
Answer:
Step-by-step explanation:
Let w be the width
Length = 3w +15
Perimeter = 94 cm
2*(length + width) = 94
2*(3w+15 + w) = 94
2*( 4w + 15) = 94
4w + 15 = 94/2
4w +15 = 47
4w = 47 -15
4w = 32
w = 32/4
w = 8 cm
Length = 3w +15 = 3*8 + 15 = 24 +15 = 39
Length = 39cm
Area = length * width = 39*8 = 312
Area = 312 cm²
The area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]
Step 1
Let's denote the width of the rectangle as w cm.
According to the problem, the length of the rectangle is [tex]\( 15 \)[/tex] cm more than three times its width. So, the length [tex]\( l \)[/tex] can be expressed as [tex]\( 3w + 15 \)[/tex]cm.
The perimeter P of a rectangle is given by:
[tex]\[ P = 2(l + w) \][/tex]
Given that the perimeter of the rectangle is [tex]\( 94 \)[/tex] cm, we can write the equation:
[tex]\[ 94 = 2((3w + 15) + w) \][/tex]
Step 2
Now, let's solve for [tex]\( w \)[/tex]:
[tex]\[ 94 = 2(4w + 15) \]\[ 94 = 8w + 30 \]\[ 8w = 94 - 30 \]\[ 8w = 64 \]\[ w = \frac{64}{8} \]\[ w = 8 \][/tex]
Step 3
Now that we have found the width of the rectangle to be [tex]\( 8 \)[/tex] cm, we can find its length:
[tex]\[ l = 3w + 15 \]\[ l = 3(8) + 15 \]\[ l = 24 + 15 \]\[ l = 39 \][/tex]
Step 4
Now that we have the width [tex]\( w = 8 \)[/tex] cm and the length [tex]\( l = 39 \)[/tex] cm, we can calculate the area A of the rectangle:
[tex]\[ A = l \times w \]\[ A = 39 \times 8 \]\[ A = 312 \][/tex]
So, the area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]
can someone pls answer this question for me
Answer:
the height is 3
the with is also 3 because
1.5+1.5=3
What size are the intervals on the histogram?
6 4 7 5
To construct a histogram, you must decide on your interval size by dividing the data range by your desired number of intervals. Then, sketch the graph with scaled axes and intervals consistently to accurately represent the data.
Explanation:To construct a histogram, you need to determine the interval size for your bins. The interval size depends on the range of your data and the number of intervals you want to use. For instance, if you have data ranging from 32.5 to 100.5 and you want to create five intervals, you subtract the smallest value from the largest and then divide by the number of intervals. So it would be (100.5 - 32.5) ÷ 5, which equals 13.6. This means each interval would be 13.6 units wide.
When constructing the actual histogram, the x-axis would cover from 32.5 to 100.5 and the y-axis would cover the frequency of the data within each interval. An interval's endpoints can be determined successively by adding the interval width to the previous endpoint, starting with 32.5. Moreover, for data with a small range like 1 to 6, you could create six intervals ranging from 0.5 to 6.5 to ensure all data points are included, with a 1 unit interval size for clarity.
Sketch the graph using a ruler and pencil, and carefully scale the axes to accurately reflect the range and intervals for the data you're representing. Consistency in interval size is key when placing data values into each bin.
Final answer:
A histogram is constructed by determining the number of intervals, with a common range being five to 15 intervals. Calculate the interval width by dividing the total range of data by the chosen number of bins. Use a ruler and pencil for a scaled and precise histogram representation.
Explanation:
To construct a histogram, you need to decide on the number of intervals, also known as classes or bins. In this case, the data provided suggests we need to create five to six intervals. The x-axis for our histogram might range from 32.5 to 100.5, representing the data values, and the y-axis records the frequency of the data points.
To calculate the width of each interval, take the range of the data (100.5 - 32.5 = 68) and divide it by the number of intervals (5). This gives us an interval width of 13.6. When scaling the axes, use a ruler and pencil for precision.
For example, if your data set ranges from a smallest value of 1 to a largest value of 6, you might set your bins to start at 0.5 and end at 6.5 to ensure that all values are included. With this range of 6 (6.5 - 0.5), and deciding on six bins, the bin size or interval size would be 1. This is explained in Solution 2.10.
Remember to consistently apply the same method when placing data values within intervals to enable comparability and clarity in your histogram.
what is between 1 1/2 and 2 1/2
Answer:
4
Step-by-step explanation:
we add them then divide 2
(11/2+2 1/2)/2
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
15 mm
Not drawn to scale.
What is the surface area of the prism?
Answer:
The answer should be 45
Step-by-step explanation:
To get the whole are you would have to multiply the lenght with the Width and then take that answer and multiply it with the height
BUT
because you want the surface area, it would be just the lenght and width
15x3=45
so 45 is your answer.
The probability
The number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3,5,8, and 9 is _. The probability that both the first digit and the last digit of the three-digit number are even numbers is _.
Probability of distinct 3-digits is 1/6.
Probability of both the first digit and the last digit are even numbers is 1/5.
Step-by-step explanation:
Given set of numbers {1,2,3,5,8,9} = 6
Total number of 3-digits can be formed = 6[tex]\times[/tex]5[tex]\times[/tex]4 = 120.
Probability of the three-digit numbers with distinct digits :
The number of 3-digit numbers with distinct digits = (6[tex]\times[/tex]5[tex]\times[/tex]4) / (3[tex]\times[/tex]2[tex]\times[/tex]1) = 20.
P(distinct 3-digits) = no. of distinct 3-digits / Total no.of 3-digits
⇒ 20/120
⇒ 1/6
Probability that both the first digit and the last digit of the three-digit number are even numbers :
The even numbers in the set are 2 and 8 = 2 possibilities.
The number of 3-digits with 1st and 3rd digit are even = (2[tex]\times[/tex]6[tex]\times[/tex]2) = 24.
P(1st and 3rd digits even)= no. of 1st and 3rd digit even/Total no. of 3-digits.
⇒ 24/120
⇒ 1/5
Consider the sequence of steps to solve the equation:
5(x - 3) =
7x
2
Step 1 ⇒ 10(x - 3) = 7x
Step 2 ⇒ 10x - 30 = 7x
Step 3 ⇒ 3x - 30 = 0
Step 4 ⇒ 3x = 30
Step 5 ⇒ x = 10
Identify the property of equality which yields Step 3.
A) Division Property
B) Addition Property
C) Subtraction Property
D) Multiplication Property
Answer:
C
Step-by-step explanation:
Subtraction Property
10x - 30 = 7x
Subtract 7x from both sides.
3x - 30 = 0
Use the distributive property to write an equivalent expression: 4(x -3)
Answer:
4x - 12
Step-by-step explanation:
Distribute the 4 to the x and -3.
4 × x = 4x
4 × -3 = -12
4x - 12
x2 + y2 + 12x + 2y – 1 = 0
Answer:
This question would be related to slopes so the answer is [tex]y=-\frac{7}{2}x+\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope-Intercept\:form\:of}\:\\x2+y2+12x+2y-1=0:\quad y=-\frac{7}{2}x+\frac{1}{4}[/tex]
[tex]\mathrm{Domain\:of\:}\:-\frac{7}{2}x+\frac{1}{4}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Range\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Parity\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{Neither\:even\:nor\:odd}[/tex]
[tex]\mathrm{Axis\:interception\:points\:of}\:\\-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{14},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:\frac{1}{4}\right)[/tex]
[tex]\mathrm{Inverse\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad -\frac{4x-1}{14}[/tex]
[tex]\mathrm{Slope\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad m=-\frac{7}{2}[/tex]
Hope this helps you!
Have a good night!
A spinner has 6 equal sections : purple,yellow,blue,green,orange,and red. What is the probability of landing on a section that is NOT orange (in fraction form)
Convert 746% to a mixed number
Answer: 373/50
Step-by-step explanation:
Step 1: convert to a fraction
746% = 746 ÷ 100 = 7.46
7.46 = 373/50
Step 2: Write the number as a fraction of one: 7.46 = 746/100
Step 3: use a common divisor of 2 to reduce the numbers, we have
(746÷2)= 373
(100÷2)=50
when reduced to the simplest form= 373/50
Therefore, 746/ 100 = 373/50 when expressed as a mixed number.
Answer: 373/50
Step-by-step explanation:
Step 1) Since 746% is a percent, it is written over the denominator of 100. So first convert it to a fraction, which would be 746/100.
Step 2) Find the GCF (greatest common factor). In order to find the GCF start by writing all the factors of
100:
1, 2, 4, 5, 10, 20, 25, 50, 100
Step 3) Now test every number there and see if any go into 746. Start at the highest number, which in this case is 100. (Example, ask yourself, “does 100 go into 746? No.” Then try with 50, and continue until you get to a number that goes into 746 evenly.)
Step 4) The GCF from the previous step is 2. So now divide 746 by 2 (answer is 373) and 100 by 2 (answer is 50).
Step 5) Now put 373/50 and that’s your answer! Congratulations you finished it!
What is the volume, in cubic feet, of a cylinder with a height of 16 feet and a base radius of 3 feet, to the nearest tenths place?
Answer:
452.39 feet³
Step-by-step explanation:
In the attached file
Answer:
452.4
Step-by-step explanation
π·r²·h
π·3²·16
π·9·16
π·144
452.38
round that up to the tenths place it's 452.4
If the policy premium on a 30 year $1,000,000 term life policy for a 35-year-old female is increased to $714, what is the percent increase in price?
A) 3%
B) 5%
C) 6%
D) 7%
3. In a carnival game, players are given three darts and throw them at a set of balloons on a wall.
Suppose there are eight balloons on the wall. Five of the eight balloons have slips of paper in
them that say 'Winner' while three of the eight balloons have slips of paper that are blank.
Suppose you pop a balloon with each of your three darts. If all three balloons have 'Winner'slips,
you win the grand prize. If all three balloons have blank slips, you win the consolation prize.
What is the probability that:
a) you win the grand prize?
b) you win the consolation prize?
The chances of winning the grand prize in this game are approximately 0.089, whereas the chances of winning the consolation prize are 0.01.
Explanation:The subject of this question is Probability, which is a branch of Mathematics. To calculate the probability, we'll need to determine the total number of outcomes and the count of the favorable outcomes.
a) To win the grand prize, all three balloons popped have to have 'Winner' slips. The probability of each dart hitting such a balloon will decrease as the total number of balloons decreases. First dart probability would be 5/8 (5 'Winner' balloons out of 8 total), the second one 4/7 (as one 'Winner' balloon is already popped), and 3/6 for the third. Multiply these probabilities together to get the overall probability: (5/8) * (4/7) * (3/6) = 0.089 (rounded to the third digit).
b) Similarly, for the consolation prize, we would have to hit all three balloons with blank slips. The process is equivalent, resulting in a probability of (3/8) * (2/7) * (1/6) = 0.01 (rounded to the third digit).
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Step by step please :)
Answer:
Step-by-step explanation:
a) (5,5) ; (10,6); slope = 1/5
(x1,y2); (x2,y2)
y-y1 = m (x-x1)
[tex]y-5=\frac{1}{5}*(x-5)\\\\y-5=\frac{1}{5}*x-\frac{1}{5}*5\\\\y-5=\frac{1}{5}x-1\\y=\frac{1}{5}x-1+5\\\\y=\frac{1}{5}x+4[/tex]
d) (√2,7) ; (√2,-7)
(x1,y1) ; (x2,y2)
[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-7-7}{\sqrt{2}-\sqrt{2}}\\\\=\frac{-14}{0}=0[/tex]
Equation: y =7 or y = -7
if 2a+b=3,find the value of 8a³+b³+18ab
Answer:
531.
Step-by-step explanation:
Let's assume 2(1) + 1 = 3
a = 1 and b = 1
Now we can plug that in
8(1)^3 + (1)^3 + 18(1)(1)
Then we need to multiply together
8^3 + 1^3 + 18
Then do the powers
512 + 1 + 18
Then add them together
531
Hope this helped!
Answer:
27
Step-by-step explanation:
A sum of cubes factors as
a³ + b³ = (a + b)(a² - ab + b²)
Factor the sum of cubes 8a³ + b³
8a³ = (2a)³, thus
8a³ + b³
= (2a)³ + b³
= (2a + b)(4a² - 2ab + b²)
We now have the right side as
(2a + b)(4a² - 2ab + b²) + 18ab ← substitute 2a + b = 3
= 3(4a² - 2ab + b²) + 18ab
= 12a² - 6ab + 3b² + 18ab ← collect like terms
= 12a² + 12ab + 3b² ← factor out 3 from each term
= 3(4a² + 4ab + b²) ← perfect square
= 3(2a + b)² ← substitute 2a + b = 3
= 3 × 3²
= 3 × 9
= 27
what is the probability of rolling a 4 on a single sided die and then rolling a 6?
Answer:
If it is a six-sided die then it has the probability of 1/6 or .16
Step-by-step explanation:
What is the value of 10^3 x 0.006?
Answer:
6
Step-by-step explanation:
10^3 = 1000
1000 x 0.006 = 6
abby buys 4 pencils and 2 erasers for $3.58. Micheal buys 1 pencil and 6 erasers for $2.49
what is the cost of 1 pencil and 1 eraser ?
Answer:
1 pencil = $0.75
1 eraser = $0.29
Step-by-step explanation:
4p+2e=3.58 1p+6(0.29)=2.49
1p+6e=2.49 1p+1.74=2.49
p=2.49-6e 1p=0.75
4(2.49-6e)+2e=3.58 p=0.75
9.96-24e+2e=3.58
9.96-22e=3.58
-22e=-6.38
e=0.29
question 3 - open up to see pic
(12, 11):
2((12) + 3) - (11) = 7 + (12)
2 • 15 - 11 = 19
2 • 4 = 19
8 [tex]\neq[/tex] 19
(1, 0):
2((1) + 3) - (0) = 7 + (1)
2 • 4 = 8
8 = 8
(-5, 1):
2((-5) + 3) - (1) = 7 + (-5)
2 • -2 - 1 = 2
2 • -3 = 2
-6 [tex]\neq[/tex] 2
Hope this helps.
Hi I just have a question what is 23+4189
Answer:
4,212
Step-by-step explanation:
Step 1: Add
23 + 4189
4,212
Answer: 4,212
What is the solution to the equation? k – 7 = -24
Answer: k = -17
Step-by-step explanation:
K -7= -24
k= -24 + 7
k = -17
What is the rate of change for the equation y = 4x +60?
The rate of change is .
The slope represents the rate of change. Then the rate of change will be 4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
y = 4x + 60
The slope is 4 and the y-intercept is 60.
The slope represents the rate of change. Then the rate of change will be 4.
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The rate of change in the equation y = 4x + 60 is 4, which is the coefficient of x. This means for each unit increase in 'x', 'y' will increase by 4 units.
Explanation:In mathematics, the rate of change in an equation like y = 4x + 60 is represented by the coefficient of the variable x. This is because, in such an equation which is in the form of y = mx + b (a standard linear equation), 'm' represents the rate of change or the slope of the line.
So, in your specific equation y = 4x + 60, the rate of change or slope is 4. This means that for each increment of 1 in 'x', 'y' will increase by 4 units. This value - 4 - is your rate of change in this case.
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A circle has a diameter of 30 yd. What is it’s circumference?
Use 3.14 for PIE, and don’t your answer.
Circumference of the circle = 94.2 yd
Solution:
Given data:
Diameter of the circle = 30 yd
The value of π = 3.14
To find the circumference of the circle:
Circumference of the circle = πd
Substitute the diameter value in the formula, we get
Circumference of the circle = 3.14 × 30
= 94.2
Circumference of the circle = 94.2 yd
Please help me!!! Thank you!!
Answer:
Part A - 4x + 8 dollars
Part B - $45
Step-by-step explanation: