If a_1=7a
1
=7 and a_n=a_{n-1}+5a
n
=a
n−1
+5 then find the value of a_5a
5
The final value of a_5 is 27a.
The equation a_n=a_{n-1}+5a is a recursive formula that gives the value of a_n in terms of the value of a_{n-1}. To find the value of a_5, we need to apply this formula repeatedly, starting with the given initial value of a_1=7a.
Using the recursive formula:
a_2 = a_1 + 5a = 7a + 5a = 12a
a_3 = a_2 + 5a = 12a + 5a = 17a
a_4 = a_3 + 5a = 17a + 5a = 22a
a_5 = a_4 + 5a = 22a + 5a = 27a
so a_5 = 27a
This is the final result and no need to calculate more.
Thus the final value of a_5 is 27a.
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A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use. In Plan B, the customer pays a monthly fee of $26.30 and then an additional 4 cents per minute of use. For what amounts of monthly phone use will Plan A cost no more than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.
34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
In Plan A, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use
20+7m
In Plan B, the customer pays a monthly fee of $26.30 and then an additional 4 cents per minute of use
26.3+4m
We need to find the amounts of monthly phone use will Plan A cost no more than Plan B
20+7m<26.3+4m
7m-4m<26.3-20
3m<6.3
m<2.1
Hence, 34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.
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A $73 ceramic vase costs $78.84 after sales tax is figured in. What is the sales tax percentage?
Answer:
8%
Step-by-step explanation:
78.84 - 73 = 5.84
Tax = $5,84
5.84 / 73 = 0.08
0.08 * 100 = 8%
Answer:
8%
Step-by-step explanation:
1. Set up the equation represented
[tex]$78.84 = \frac{x}{100}(73) + 73[/tex]
x is the sales tax percentage. hence, we have to solve for x.
[tex]$78.84 = \frac{x}{100}(73) + 73[/tex]
[tex]$78.84 = \frac{73x}{100} + 73[/tex]
[tex]5.84 = \frac{73x}{100}[/tex] . . . . . . . . . . . . . . subtract both sides of the equation by 73
[tex]584 = 73x[/tex] . . . . . . . . . . . . . . multiply both sides by 100
[tex]8 = x[/tex] . . . . . . . . . . . . . . . . . . divide both sides by 73
∴ There was an 8% sales tax on the ceramic vase.
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What does exponential growth look like on a logarithmic graph?
Exponential growth on a logarithmic graph looks like a straight line. On a regular graph, the line would appear to be curved, but when plotted on a logarithmic graph, the line appears to be a straight line.
Exponential growth on a logarithmic graph appears as a straight line. This is because the logarithmic scale is a compressed scale, meaning that it takes a large range of values and compresses them into a smaller range. This makes the data easier to read and understand. The straight line occurs because the logarithmic scale is designed to fit the data points more closely, making the line appear linear. This is in contrast to the regular scale, where the line appears curved due to the large range of values being plotted. Thus, exponential growth appears as a straight line on a logarithmic graph.
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hey! please help i’ll give brainliest
Answer: The answer is -ing (D)
Step-by-step explanation:
Which would be an appropriate display for the data shown in the table?
scatter plot
histogram
circle graph
line graph
Answer:
circle graphs work well to illustrate percentages
Step-by-step explanation:
{1/4096, 1/1024, 1/256, 1/64}
Find the common ratio
Answer:
None of them are the same
If AnB= {2,4}
AnB'= {0,1}
AUB= {0,1,2,3,4,5}, Then what is B\A?
Answer:
I don't know I'm just a grade 6 girl
The perimeter of a rectangle is 54cm. If the length of rectangle is 18cm,find its area
Answer:
162cm squared
Step-by-step explanation:
The perimeter of a rectangle can be calculated by length+length+width+width.
We know the length is 18, so our equation of finding the width is:
54-(18*2) divided by 2.
54-36=18.
18/2=9.
The area of a rectangle can be calculated by length * width. We already have the length, and now we have the width.
18*9=162
WHAT?
Never in my life have I ever wanted to kill math
Answer:
Y-intercept: 15
Slope: 1.3
Equation: y = 1.3x + 15
Step-by-step explanation:
Base on the table:
# of haircuts = x
Cost ($) = y
Knowing that;
y-intercept = The starting point (y)
Thus, based on the table the y-intercept is 15.
Y-intercept: 15.
To find the slope.
We first have to pick two points on the line & determine their coordinates.
Then subtract y-coordinates of these two points and also subtract x-coordinates for these two points.
After that divide the y by the x.
Shown below:
I'm going to use;
(0,15) and (1,20.5)
0 = x₁
15 = x₂
1 = y₁
20.5 = y₂
Now we do;
20.5 - 1 = 19.5
15 - 0 = 15
19.5 / 15 = 1.3
Hence, Slope = 1.3
Slope: 1.3
The equation - y = mx + b
Knowing that;
b = y-intercept
m = Slope
Substitute it in we have;
y = 1.3x + 15
Equation: y = 1.3x + 15
RevyBreeze
How do I solve/graph 2x + 3y <12
The graph has plotted and attached below
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
2x + 3y <12.
Here The graph have plotted and attached below.
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HELPPPPPPP MEEEEE
If a trapezoid has an area of 135cm^2 and it’s height is 10cm and one base is 12 cm, find the other base length.
thxxx <333
The length of other base is 15 cm.
The area of a trapezoid can be found by using the formula:
Area = (b1+b2) * h / 2 where b1 and b2 are the lengths of the bases, and h is the height.
Given that the area of the trapezoid is 135 cm^2, the height is 10 cm, and one base is 12 cm, we can substitute these values into the formula to find the length of the other base.
Area = (b1+b2) * h / 2 = 135cm^2
We can solve for the other base length by isolating b1
b1 = 2*Area/h - b2
b1 = 2*135/10 - 12 = 27 - 12 = 15
So, the other base length is 15 cm.
Therefore, The length of other base is 15 cm.
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Vanessa draws one side of equilateral AABC on the coordinate plane at points A(-2, 1) and B(4,1). What are the possible coordinates of vertex C? Select all that apply.
Answer:
Step-by-step explanation:
Answer E is the only one that is close
At Hunter Elementary School, 73% of students buy their lunch. In a randomly selected first grade class of 19 children, find the probability that at least 12 buy their lunch. Round to 3 decimal places.
The probability that at least 12 buy their lunch = 0.887
Given that 73% of students buy their lunch.
⇒ p = 0.73
And q = 1-p
q = 0.27
sample size (the number of student selected) n = 19
We need to calculate the probability that at least 12 buy their lunch.
i.e., P(x ≥ 12)
We use binomial distribution formula, P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
P(X ≥ 12)
= P(X= 12) + P(X= 13) + P(X= 14) + P(X= 15) + P(X= 16) + P(X= 17) + P(X= 18) + P(X= 19) [tex]=~ ^{19}C_{12}(0.73)^{12}(0.27)^{7} + ^{19}C_{13}(0.73)^{13}(0.27)^{6}+ ^{19}C_{14}(0.73)^{14}(0.27)^{5} + ^{19}C_{15}(0.73)^{15}(0.27)^{4} + ^{19}C_{16}(0.73)^{16}(0.27)^{3} + ^{19}C_{12}(0.73)^{17}(0.27)^{2}+ ^{19}C_{12}(0.73)^{18}(0.27)^{1}+ ^{19}C_{12}(0.73)^{19}(0.27)^{0}[/tex]
= 0.1207 + 0.1757 + 0.2036 + 0.1835 + 0.1240 + 0.0592 + 0.0178 + 0.0025
= 0.887
The required proability is 0.887
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Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. G
The necessary probabilities are 3/8, 1/3, 9/64, and 37/64.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
S = { G1, G2, G3, Y1, Y2, Y3, Y4, Y5 }
G = { G1, G2, G3 }
P(G) = 3/8
E = { G2, Y2, Y4 }
P(G|E) = 1/3
P(G and E) = P(G)*P(E) = (3/8)*(3/8) = 9/64
P(G or E) = P(G) + P(E) - P(G and E) = (3/8) + (3/8) - (9/64) = (6/8) - (9/64) = (48/64) - (9/64) = 37/64
The required probability is 3/8, 1/3, 9/64 and 37/64.
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F(x)=Sin2x ,x0=pi:3
f(x)=3x-x^2 ,x0=-1
Pleae help and if omeone ha dicord erver to help olve math problema pleae give me invite
The given equation 1 value of F(x) is 0.109 and in equation 2 F(x) is -4 respectively.
What in mathematics is trigonometric?Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle. This concept is given by the Greek mathematician Hipparchus.
Trigonometry is the study of angles and the angular relationships between planar and three-dimensional figures. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.
if x⁰=π in eq1
then [tex]f(x)= sin\ 2 \pi[/tex]
[tex]f(x) = 0.109[/tex]
if x⁰= -1 in eq2
then [tex]f(x)=3(-1)-(-1)^2[/tex]
[tex]f(x) = -4[/tex]
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One-sixth of a certain number is four more
than one-twelfth the number. Find the number. a. 6 b. 18 C. 36 d. 48
Answer:
d) 48
Step-by-step explanation:
1/6n = 4 + 1/12n
2/12n = 4 + 1/12n
subtract 1/12n from each side to get:
1/12n = 4
cross-multiply:
n = 48
Which angle measures are correct? Select three options.
O m 2= 125°
m 3 = 55°
O m 8= 55°
O m 12= 100°
O m14 = 100°
Answer:
Step-by-step explanation:
analyze the graph, we found ∠1=∠5,∠2=∠6,
one.because ∠5+∠6=180, so ∠2=∠6=180-∠5=180-55=125
two.∠3=∠2=125
three.∠8=∠5=55
four.∠12=∠9=80
five.∠14=∠10=180-∠9=100
so, the three options are ∠2,∠8,∠14
11. Use the information to answer the questions.
A video streaming
company offers on-demand programming without a monthly contract. The company charges a connection fee plus a charge for each hour of video
streaming. The table shows the cost for up to three hours of video streaming for one connection fee.
Cost of Video Streaming
Video
Streaming 0 1
(hours)
$0.75 $1.25 $1.75 $2.25
N
3
Cost
How much is the connection fee for video streaming?
Answer: $
Answer:
0.75
Step-by-step explanation: 2 weeks late >_<
(1,46) (2,40) (3,39) (4,35) (5,30) (6,27) equation line of best fit
Answer:
ertyghujikol
Step-by-step explanation:
3456t7ujn
anyone know how to solve these
Answer:
amogus
Step-by-step explanation:
B)
The volume of a cylinder is 1,0291 cubic centimeters. The height of the cylinder is 21 centimeters. What is the radius, to the nearest centimeter, of the cylinder?
Answer:
12.49 = r
13 = r to the nearest cm.
Step-by-step explanation:
The formula to calculate the volume is:
V = π*r^2*h
We know that V = 10291 cm^3 and Height (h) = 21cm
V = π*r^2*h
10291 = π*r^2*21
Divide both side by 21
10291/21 = (π*r^2*21)/21
490.05 = π*r^2
Now divide both side by π
490.05/π = (π*r^2)/π
155.99 = r^2
Now square root both side
√155.99 = √(r^2) Note: square and square root cancel eachother out.
12.49 = r or,
13 = r
can you guys help me with this its due today and if you get it correct I will give brainliest
Darius has a cylindrical can that is completely full of sparkling water. He also has an empty cone-shaped paper cup. The height and radius of the can and cup are shown.
Darius pours sparkling water from the can into the paper cup until it is completely full. Approximately, how many centimeters high is the sparkling water left in the can?
Answer: 6.2
Step-by-step explanation:
Find the lowest common denominator of 1/3 and 2/5
Answer:
The lowest ccommon denominator (or LCD) of 1/3 and 2/5 is 15.
Step-by-step explanation:
The lowest multiple of 3 and 5 is 3*5 = 15.
In terms with the LCD, 1/3 now equals 5/15; and 2/5 now equals 6/15.
Hope this helps :)
A cylindrical cooler ha a diameter of 30 inche and a height of 24 inche. Runner in
a marathon can ue cone haped cup to get a drink from the cooler. If the cup have a
diameter of 3 inche and a height of 4 inche, how many full cup would be able to
be filled from the cooler?
So, 600 full cup would be able to be filled from the cooler. This can be solved using the concept of volume of cylinder.
What is volume of cylinder?The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centers of the circular bases cross each other. The measure of space within a cylinder is measured by its volume. Find it by dividing the base area by the height. V = πr²h is the formula for the volume of a cylinder with base radius "r" and height "h."
Given that,
diameter of cylinder = 30 inch
diameter of cup = 3 inch
height of cylinder = 24 inch
height of cup = 4 inch
Calculate the volume of the cylinder:
Volume = πr²h
putting the values we get:
Volume = (3.14)(30/2)²(24)
Volume = (3.14)(15)²(24)
Volume = (3.14)(225)(24)
Volume = 16959 in³
Calculate the volume of the cup:
Volume = (3.14)(3/2)²(4)
Volume = (3.14)(1.5)²(4)
Volume = (3.14)(2.25)(4)
Result
Volume = 28.26 in³
Divide the volume of the cylinder by the volume of the cup, we get:
Number of full cups = 16959 in³ / 28.26 in³
Number of full cups = 600
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What are tractable and intractable problems?
As a result, the provided problem of tractable problem has the following outcome: As a result, a problem is said to be tractable if a polynomial-time algorithm exists to solve it.
Define tractable problem.An algorithm that can solve a tractable problem in a polynomial amount of time. Polynomial describes the upper bound. An intractable problem is one that cannot be resolved in a polynomial amount of time. Exponential is the lower bound.
Here,
Tractable refers to "manageable," hence the word is used to indicate issues that can be resolved in a reasonable amount of time.
This leads to the definition of a problem as tractable as the existence of a polynomial-time algorithm that can solve it.
Unabating: Intractable. As an illustration, intractable pain and intractable diarrhea are both conditions that are untreatable despite the use of medication.
As a result, the provided problem of tractable problem has the following outcome: As a result, a problem is said to be tractable if a polynomial-time algorithm exists to solve it.
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Teresa wrote this expression to describe the total distance she was going to swim during two swim classes s+3 which situation could be described by this expression
The correct answer of expression 's+3' is (c) Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class. She used the sign "+" instead of "x" or any other notation.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression is (Number/variable, Math Operator, Number/variable)
The answer here should be Option C, as she used the sign "+" instead of "x" or any other notation. She wanted to add something.
And as it is very clear that she wanted to write the information about two classes, so that makes the second term for second class and first term for first class.
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The complete Question is:
Teresa wrote this expression (s+3) to describe the total distance she was going to swim during two swim classes. Which situation could be described by this expression?
A. Teresa wasn't sure how far she would swim during the first class. She would swim 3 fewer laps during the second class.
B. Teresa wasn't sure how far she would swim during the first class. She would swim the same distance for 3 classes.
C. Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class.
D. Teresa wasn't sure how far she would swim during the first class. She would swim 3 times farther during the second class.
what is the area of the triangle
Answer:
The area of the triangle is 27
05. Divided by 26.75
Answer:
use this link
Step-by-step explanation:https://www.calculatorsoup.com/calculators/math/math.php