Answer:
[tex]f(n) = 1.9 +0.6n[/tex]
Step-by-step explanation:
The nth term of the arithmetic sequence is given by:
[tex]a_n = a_1+(n-1)d[/tex] ....[1]
where
[tex]a_1[/tex] is the first term
d is the common difference and n is the number of terms.
Here, f(n) represent diameter in centimeters and n the term number in the sequence.
Given the sequence represents the diameters of circles used to create an art project:
2.5 cm, 3.1 cm, 3.7 cm , 4.3 cm
This sequence is an arithmetic sequence with
[tex]a_1[/tex] = 2.5 and d = 0.6
Since,
3.1-2.5 = 0.6,
3.7-3.1 = 0.6
4.3-3.7 = 0.6
Substitute the given values in [1] we have;
[tex]f(n) =2.5+(n-1)(0.6)[/tex]
Using distributive property, [tex]a\cdot (b+c) = a \cdot b+ a\cdot c[/tex]we have;
[tex]f(n) = 2.5+0.6n-0.6[/tex]
Simplify:
[tex]f(n) = 1.9 +0.6n[/tex]
Therefore, the equation represents the sequence of diameters is, [tex]f(n) = 1.9 +0.6n[/tex]
Marie worked 2 weeks during her college she earned $280 the first week and 245 the second week. If 1/2 of her total earnings went to taxes and 1/4 went to college tuition how much money did she have left
Marie's total earnings for the two weeks were $525. She paid $262.5 to taxes and $131.25 to college tuition, leaving her with a balance of $131.25.
Explanation:To find out the amount left, we need to first calculate Marie's total earnings for the two weeks by adding what she earned each week. $280 for the first week plus $245 for the second week gives her a total earnings of $525.
Marie gave half of her earnings to taxes, which is 0.5 * $525 = $262.5. After that, she spent one-fourth of her earnings on college tuition, which equals 0.25 * $525 = $131.25. Summing up both amounts, we find that she spent $262.5 + $131.25 = $393.75 on taxes and tuition.
To find out the amount Marie has left, we subtract the total expenses from her total earnings. Thus, $525 - $393.75 = $131.25 is the total amount she has left after paying her taxes and tuition.
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After calculating her total earnings, subtracting the amounts for taxes and tuition, Marie had $131.25 left. Her total earnings were $525. 1/2 went to taxes, and 1/4 went to tuition.
First, find her total earnings for the two weeks:
Total Earnings = $280 + $245 = $525
Next, calculate how much went to taxes. Since 1/2 of her total earnings went to taxes:
Taxes = 1/2 x $525 = $262.50
Then, calculate how much went to college tuition. Since 1/4 of her total earnings went to tuition:
College Tuition = 1/4 x $525 = $131.25
Finally, subtract the amounts for taxes and tuition from her total earnings to find out how much money she had left:
Money Left = $525 - $262.50 - $131.25 = $131.25
Marie had $131.25 left after paying taxes and college tuition.
If the probability of an event is 2/7, what must be the probability of its complement?
Answer:
[tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Let
x------->the probability of its complement
we know that
The Complement Rule states that the sum of the probabilities of an event and its complement must equal [tex]1[/tex]
so
in this problem
[tex]\frac{2}{7}+x=1[/tex]
solve for x
Adds [tex]-\frac{2}{7}[/tex] both sides
[tex]x=1-\frac{2}{7}[/tex]
[tex]x=\frac{5}{7}[/tex]
The probability of its complement is 5/7
What is the complement of a probability event?The complement of a probability event is the event that contains all of the universal elements of the event but is not found in the provided event.
From the given information:
The provided event (x) = 2/7The complement of an event is mathematically calculated as:
P(C') = 1 - (x)
P(C') = 1 - 2/7
P(C') = 5/7
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Add each pair of monomials and match it to the correct sum.
Tiles
-15u3 + 5u3
10u3 + (-5u3)
10u3 + 5u3
5u3 + (-10u3)
Answer:
-10u^3
5u^3
15u^3
-5u^3
Step-by-step explanation:
Given tiles
-15u^3+5u^3
10u^3+(-5u^3)
10u^3+5u^3
5u^3+(-10u^3)
Monomial : that type of polynomial in which only one term .
Adding of polynomial : when we add two polynomial then the coefficient of like terms will be added and sum of unlike terms remain . There is no change in the power of like terms and unlike terms.-15u^3+5u^3coefficient of like terms means same viable with same power -15 and 5 .
Therefore, coefficient of these two terms added and no change in power of u^3
-15u^3+5u^3=-10u^3Similarly, 10u^3+(-5u^3)=5u^310u^3+5u^3=15u^35u^3+(-10u^3)=-5u^3I need help with this question:
3c + 17, for c=5
The variable c = 5 meaning we can replace the value of c in the equation with 5. Solve the equation now as you normally would.
3 (5) + 17 = 15 + 17 = 32
The answer is 32 and if this helps please give brainliest to help me reach expert ;)
For how many positive integer values of N will the expression 18/N + 2 be an integer?
N can have 6 different positive integer values.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
The expression is :
18/N +2
An integer is a whole number that includes all positive numbers, negative numbers and zero.
An integer cannot be a fraction.
The value of N has to be determined for the expression such that, the value of the expression is a positive integer.
For the expression to be positive integer, the 18/N should be an integer value, so the number N should completely divide 18.
The factors of 18 is 1,2,3,6,9,18.
If N is any value among these, it will divide 18 to give a integer and the value of the expression will be a positive integer value.
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PLEASE HELP!! IM REALLY CONFUSED
If the radius of a circle is multiplied by 3 what happens to the area of a circle
Help me with this plz
HELP NEEDED!!
Calculate the side lengths a and b to two decimal places.
A. a = 16.23 and b = 17.99
B. a = 16.23 and b = 18.83
C. a = 17.99 and b = 16.23
D. a = 4.81 and b = 5.33
E. a = 5.33 and b = 4.81
Will thank rate five stars and give brainlist anser to first person to answer!
Answer:
A. a = 16.23 and b = 17.99
Step-by-step explanation:
The addition of the three angles of the triangle is equal to 180°. So,
C + 64° + 85° = 180°
C = 180° - 64° - 85°
C = 31°
The law of sine states:
sin(A)/a = sin(B)/b = sin(C)/c
where c is the side opposite to angle C
Taking angles A and C, and sides a and c, we get
sin(A)/a = sin(C)/c
sin(64°)/a = sin(31°)/9.3
sin(64°)*9.3/sin(31°) = a
a = 16.23
Taking angles B and C, and sides b and c, we get
sin(B)/b = sin(C)/c
sin(85°)/b = sin(31°)/9.3
sin(85°)*9.3/sin(31°) = b
b = 17.99
What is the height of an airplane as it descends to an airport runway
Final answer:
The height of an airplane during its descent to an airport runway is influenced by factors like approach angle, stall speed, and descent rate.
Explanation:
The height of an airplane as it descends to an airport runway is determined by various factors such as approach angle, stall speed, and glide slope.
During descent, the pilot manages corrections for side-winds, updrafts, and downdrafts to aim for a specific touchdown point on the runway.
Typically, the descent rate of an aircraft during landing is about 500 feet per minute, translating to approximately 8 mph.
what is the domain of the function on the graph?
a. all real numbers
b. all real numbers greater than or equal to - 2
c. all real numbers greater than or equal to - 5
d. all real numbers greater than or equal to 0
Answer:
Option a is correct.
Step-by-step explanation:
The given graph is of the function f(x)=|x|-2
Domain are the values that x will take in the given function x can take all the values whether fraction, integer the function will always be defined.
Hence, the domain of the function is all real numbers.
Therefore, Option a is correct.
Answer: Domain are all real number [a].
Step-by-step explanation:
Given : graph .
To find : what is the domain of the function on the graph.
Solution : We have given that a graph of function f(x) : |x| - 2.
Domain : The domain of a function is the set of its possible inputs,that is the set of input values where for which the function is defined.
Therefore, the domain are all real number [a].
1. What shape is the graph?
2. What direction does the graph open?
3. Where is the graph increasing/decreasing?
4. What are the intercepts?
5. Are there any special points?
6. Is there a line of symmetry?
1. Triangular, 2. Upwards, 3. (- ∞, 3),(3, ∞), 4. (-1, 0) and (-3, 0), and (0, 1),
5. (-3, -1), 6. symmetry is along the x-axis.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A modulus function | x + 2 | - 1.
The shape of the graph is triangular.
The graph opens in the upwards direction positive y-axis.
The graph is decreasing at the interval (- ∞, 3) and it is increasing at an interval (3, ∞).
The x-intercepts of the graph is (-1, 0) and (-3, 0), and The y-intercepts of the graph is (0, 1).
The special point of the graph is (-3, -1) where the graph is increasing from decreasing.
Yes, the line of symmetry is along the x-axis.
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The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −5 g(x)
0 −1 g(x) = 4x + 3
1 3
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Determine the slope of the line that contains the given points. t(6,3),v(8,8)
The slope of the line that contains the given points T(6, 3) and V(8, 8) will be 2.5.
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 slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given below.
T(6, 3) and V(8, 8)
The slope is given as,
m = (8 - 3) / (8 - 6)
m = 5 / 2
m = 2.5
The slope of the line will be 2.5.
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Coins are marked with the letters A-G. What is the probability of selecting a coin with a vowel on it?
a. 28.6%
b. 16.7%
c. 33.8%
d. 18.9%
The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 64 miles due north of the warehouse.
A truck traveled from the warehouse to the airport and then to the factory. What is the total number of miles the truck traveled?
48 miles
56 miles
104 miles
128 miles
warehouse location (24,-32)
airport location (-24,32)
distance = sqrt((x2-x1)^2 +(y2-y1)^2)=
Sqrt(24--24)62 +(32--32)^2) =
sqrt(48^2 +64^2) =80
then distance from airport to the factory = -24 to 24 = 48
80+48 = 128 miles total
The ideal width of a certain conveyor belt for a manufacturing plant is 50 in. an actual conveyor belt can vary from the ideal by 7/32 in. find the acceptable widths for this conveyor belt. CHECK ALL THAT APPLY
a) x>=49 24/32
b)x<=50 7/32
c)49 25/32<=x<=50 7/32
d)x+7/32<=50
e)absolute value of x-50 <=7/32
In March Tom had -£165 in his bank account. In April he had -£156.
In which month did he have the least amount of money in his account?
Answer:
March.
Step-by-step explanation:
We have been given that in March Tom had -£165 in his bank account. In April he had -£156.
We know that the a biggest negative number has least value as biggest negative numbers lie on the extreme left on the number line.
Since -£165 is more negative than -£156, so -£165 is the least amount.
Therefore, Tom had least amount of money in his account in March.
Jason is a used-car salesman who sells domestic and foreign cars. He earns $7,000 for each domestic car sold and loses $3,500 for each foreign car sold. Due to certain business commitments, Jason has to sell at least 10 foreign cars each month. He needs to make at least $17,000 each month to cover his expenses. Which graph shows the number of cars he has to sell each month to at least cover his expenses?
If the federal reserve decreases the reserve rate from 7% to 5%, how does this affect the amount of money that would result because of fractional-reserve banking from an initial deposit into a bank of $30,000?
Answer:
The total affect of the decrease in the interest rate = $29400
Step-by-step explanation:
The initial amount of money which has been deposited into the account = $30000
The rate at which the initial money was deposited = 7%
But it is given that the federal reserve decreases the reserve rate from 7% to 5%
Now, we need to find the affect of this decrease on the deposited money
The rate of change in the interest rate = 7 - 5 = 2%
So, The affect of this decrease = 2% of 30000
= $600
So, The money becomes = 30000 - 600
Therefore, The total affect of the decrease in the interest rate = $29400
Jimmy set his score for his math test. After the math teacher returnee his paper to him, he realized that if he increased his target by 10%, he would need 1 more mark to reach his actual score. If he increased his target by 15%, this target would exceed his actual test marks by 3. What is his actual test score.
On Tuesday, Pizza Hut sold 60 plain pizzas at $5 each; 20 meatball pizzas at $8 each; 25 Sicilian pizzas at $9 each; and 33 large crust supremes at $10 each. What were the total dollar sales for Pizza Hut on Tuesday? A. $790 B. $1,015 C. $1,115 D. $1,511
Match the graph with the correct equation.
y – 1 = –4(x + 5)
y + 1 =-1/4 (x + 5)
y – 1 =-1/4 (x + 5)
y – 1 =-1/4 (x – 5)
The first term of a geometric series is a/b^2, and the common ratio is b/a^2. Find the next five terms of the geometric sequence.
Answer:
the next five terms are:
[tex]\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }[/tex]
Step-by-step explanation:
A geometric serie is a succession of terms on which every terms is the result of the last term multiply to a common ratio. for example, a geometric serie with inicial terms equal to 2 and the common ratio is 3, the four first numbers of the serie is given by
2, 6, 18, 54
Where every term is calculate as:
first term = 2
second term = first term x common ratio = 2 * 3 = 6
third term = second term x common ratio = 6 * 3 = 18
fourth term = third term x common ratio= 8 * 3 = 54
Then, with this exercise we have the same situation, the first term is [tex]\frac{a}{b^{2} }[/tex] and the common ratio is [tex]\frac{b}{a^{2} }[/tex], so we get:
first term = [tex]\frac{a}{b^{2} }[/tex]
second term = first term * common ratio = [tex]\frac{a}{b^{2} } *\frac{b}{a^{2} } = \frac{1}{ab}[/tex]
third term = second term * common ratio = [tex]\frac{1}{ab} *\frac{b}{a^{2} } =\frac{1}{a^{3} }[/tex]
fourth term = third term * common ratio = [tex]\frac{1}{a^{3} } *\frac{b}{a^{2} } = \frac{b}{a^{5} }[/tex]
fifth term = fourth term * common ratio= [tex]\frac{b}{a^{5} } *\frac{b}{a^{2} } = \frac{b^{2} }{a^{7} }[/tex]
sixth term = fifth term * common ratio= [tex]\frac{b^{2} }{a^{7} } *\frac{b}{a^{2} } = \frac{b^{3} }{a^{9} }[/tex]
so, the next five terms are:
[tex]\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }[/tex]
What's the verbal expression for the algebraic expression 15+r ?
Solve for a:
3/5a = 1/4
When writing an equation in exponential form , how can you tell by the number in parentheses if it's exponential growth or exponential decay?
About 145 out of 300 students prefer walking instead of riding the bus to school. About what percent of the students prefer walking?
The equation a=640s gives the relationship between s square miles and acres. Pam owns 7.5 square miles of farmland. How many acres does she own
Answer:
4800 acres.
Step-by-step explanation:
We have been given an equation [tex]a=640s[/tex], which gives the relationship between s square miles and acres.
To find the number of acres Pam owns we will substitute [tex]s=7.5[/tex] in our given equation.
[tex]a=640\times 7.5[/tex]
[tex]a=4800[/tex]
Therefore, Pam owns 4800 acres.
Which of the relations given by the following sets of ordered pairs is not a function?
a. {(5,2),(4,2),(3,2),(2,2),(1,2)}{(5,2),(4,2),(3,2),(2,2),(1,2)}
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}{(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
Answer:
The answer is the B)
Step-by-step explanation:
By the definition, in a function, a value in the first set of numbers only have a value in the second set of numbers, so for every pair of numbers, we have to review if the first number for this pair only appears one time in all the function.
All the set ot values agrees with this definition except the B, because the third and fourth pair have the same first value (3)