The answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
What is a sequence?
A sequence is defined as an arrangement of numbers in a particular order.
A sequence is given ; -1/5, 2/6, -3/7, 4/8.....
Part A
From inspection of the sequence, the pattern is:
i) Add 1 to the numerator of the previous term.
ii) Add 1 to the denominator of the previous term.
iii) Make every other term negative.
Therefore, The next four terms are -5/9, 6/10, -7/11, 8/12
Part B
From inspection of the sequence, we can see that the numerator is the position of the term (n) in the sequence. So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.
The denominator is 5 more than the position of the term in the sequence. So when n = 2 the denominator is 2 + 4 = 6, and when n = 4 the denominator is 4 + 4= 8.
Hence, the rule can be,
f(n) = n/(n+4)
If n is even, then f(n) is positive.
If n is odd, then f(n) is negative.
Part C
56 is an even number.
As the function f(n) is positive when n is even, the sign of f(56) is positive.
Therefore, the answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.
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Use the Distributive property to solve the equation 2(x-3)+3=6x-5
Answer:
x = -2
Step-by-step explanation:
Isolate the variable by dividing each side b factors that don't contain the variable.
A doctor has 2 doses of flu protection vaccine left. He has 5 women and 8 men who want the medication. If the
names of 2 of these people are selected at random, determine the probability that 2 men's names are selected
The problem is to be done without replacement. Use combinations to determine the probability.
The required probability for the 2 men's names are selected is 0.358.
Given that,
A doctor has 2 doses of flu protection vaccine left. He has 5 women and 8 men who want the medication.
The names of 2 of these people are selected at random, determining the probability that 2 men's names are selected is to be determined,
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
The number of ways to select 2 men = 8C2 = 28
The number of ways to select 2 people from 13 = 13C2 = 78
The probability of the 2 men's names being selected = 28 / 78 = 0.358
Thus, the required probability for the 2 men's names are selected is 0.358.
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"Match the expression and its value to the value of x that gives the expression its value by filling in the box in the correct column.
Evaluate the expression 4 n-5 r for n=-2 and r=3
(A) 23
(C) 7
(B) -7
(D) -23
The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h, where s is the side length of the square h is the height of the prism. What is the surface area in square feet rectangular prism when s=4 feet and h=6feet?"
Value of the expression 4n - 5r when n = -2 and r = 3 is -23.
The surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given expression:
4n - 5r
When n = -2 and r = 3
The value of the expression become,
4(-2) - 5(3)
= -8 - 15
= -23
Hence, option D is correct.
Now, it is given that the surface area for a rectangular prism with a square base is given by the expression 2s²+4sh, where s is the side length of the square h is the height of the prism.
The surface area in square feet rectangular prism when s=4 feet and h=6feet is
2[tex](4)^{2}[/tex] + 4(4)(6)
= 2(16) + 96
= 32 + 96
= 128 square feet
therefore, the surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.
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Which ordered pair is a solution of the inequality?
y ≥ 4x - 5
O (3,0)
O (1, 1)
O (2, 1)
O (3, 4)
Answer:
3_0
Step-by-step explanation:
Let f(x) be a polynomial with a leading coefficient of 6 and a constant term of 5. Which of the following cannot be true?
====================================================
Reason:
The leading coefficient is 6, which is the coefficient of the leading term (aka the first term). The constant is 5, which is the last term.
Here are some examples of what f(x) could be.
[tex]f(\text{x}) = 6\text{x}^2+\text{x}+5\\\\f(\text{x}) = 6\text{x}^3+2\text{x}^2-7\text{x}+5\\\\f(\text{x}) = 6\text{x}^5+4\text{x}^3-81\text{x}^2+5[/tex]
The middle terms don't matter and neither does the exponent on the leading term.
So this is what the general template would look like
[tex]f(\text{x}) = 6\text{x}^{n}+\ldots+5\\\\[/tex]
where n is a positive integer.
If we were to plug in x = 0, then all of the terms involving x go to zero. They cancel out. The only thing left standing would be the "5" at the very end.
So,
[tex]f(\text{x}) = 6\text{x}^{n}+\ldots+5\\\\f(0) = 6*0^{n}+\ldots+5\\\\f(0) = 0+0+\ldots+0+0+5\\\\f(0) = 5\\\\[/tex]
In short, the constant value is the y intercept of the polynomial curve. It allows us to quickly spot it without having to do much (or any) math.
This is why choice B is a false statement.
The other answer choices cannot be proven true or false since we don't have enough information about this particular function.
Liam spent $5.76 on 12 pounds of potatoes. How much did he spend per pound? How to solve this step by step
He spend 0.48 per pounds
What is division ?
Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
A group is divided into equal portions. Division can be used to divide a class into equal groups for a game or activity, or even to divide a pizza among a group of friends in equal quantities. Partitive division and quotative division are the two types of division.
As it is $5.76 for 12 pounds
∴ for one pound
5.76 / 12
= 0.48 pounds
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can anyone explain these 3 questions to me in detail and how the answer is found
The solution to the first and the second equation are 28.648 and 183.5 respectively.
What is a radical expression?A radical expression is an expression consisting of a square root or nth root.
(1) The given equation is [tex]-5\sqrt[4]{x-1}=12[/tex].
Solve the equation as follows:
[tex]-5\sqrt[4]{x-1}=12\\\\\sqrt[4]{x-1}= -\frac{12}{5}\\\\(x-1) = (-\frac{12}{5})^4\\x-1 = 27.648\\x = 28.648[/tex]
(2) The given equation is [tex]-2\sqrt[6]{4x-5}+9 =3[/tex].
Solve the equation as follows:
[tex]-2\sqrt[6]{4x-5}+9 =3\\ \\2\sqrt[6]{4x-5}= 9-3\\\\\sqrt[6]{4x-5}=3\\\\4x-5=3^6\\\\4x=729+5\\\\x=734/4\\\\x=183.5[/tex]
The third equation is the same as the first equation.
Hence, the solution to the first and the second equation are 28.648 and 183.5 respectively.
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I’ll mark you BRAINLIST please help!!
I'm sorry i don't know :(
Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.
(20 POINTS!!!!!!!! SHOW YOUR WORK PLEASE!!!!)
Answer:
y = 3x - 1
y = 3x + 2
Step-by-step explanation:
Here Is The Right Lined Up Answer,
If You Expected It As A Photo Lined For An
Easier Review I Don't Have The 'Capture Photo' Button
But I Can Reuse/Repost, Here It Is:
There You Are, I Hope This Helped You Out
Don't Get Stressed You WILL Get 100%
By: LocalLesMara
K
Factor the trinomial.
b²-13b+40
Answer: (b-8)(b-5)
Step-by-step explanation:
Find the multiple of 40 that adds up to -13 while being mutiplied by multiples of b^2
1*-5=-5
1*-8=-8
-8-5=13
-8*-5=40
(b-8)(b-5)
if n is an integer,what is the sum of the next three consecutive even integers greater than 2n
The sum of the next three consecutive even integers greater than 2n, where n is an integer, is: Sum = 6n + 12
What is the sum of the next three consecutive even integers?We know that n is an integer number, we want to find the sum of the next three consecutive even integers greater than 2n2n is already an even integer, and consecutive even integers are given by adding 2 to the smaller one.
Then the 3 consecutive integers larger than 2n are:2n + 22n + 42n + 6
The sum of these 3 gives:(2n + 2) + (2n + 4) + (2n + 6)3*(2n) + 2 + 4 + 66n + 12
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10 points cause it not thay hard for yall
Answer:
6,63,9 and 90
Step-by-step explanation:
The slope of the table is 9.
36/4 is equal to 9.
54/9 = 6
7*9=63
81/9=9
10*9=90
PLEASE HURRY ASAP I NEED TO FINISH!!
Pete was building a doghouse for his dog, Chip. He made the door 32 inches tall. The height of the door was four times the height of the window in the doghouse.
Write an equation to determine the height of the window.
A. 32 equals h over 4
B. 32 = 4h
C. 32 = 4 + h
D. 32 = h − 4
Answer:
Step-by-step explanation:
B
Question 2 of 15
Is this relation a function? Justify your answer.
the only criteria, really, to be a function is to assign exactly 1 y-value to every valid x-value. not 2 or 0 y-values.
we see here, x = 2 has one assigned y-value : y = 3.
x = 4 has y = 9.
x = 6 has y = 10.
x = 9 has y = 5.
there is no indication that there are more valid x-values.
each x-value used has exactly 1 y-value.
so, the criteria is fulfilled. it is a function.
Rajani is carrying 9.725 kg of vegetables and Mamta is carrying 8.50 kg of vegetables. Who is carrying more and how much?
Answer:
Step-by-step explanation:
let Rajani be carrying r = 9.725kg
let Mamata be carrying m = 8.500kg
difference = r - m = 9.725 - 8.500 = 1.225kg
hence Rajani is carrying 1.225kg more than Mamata
O
Yaritza made 25% of her free throws over the season. If she shot 160 free throws, how
many did she make?
Divide/scale down to solve for the missing percent.
attempts
percent
Submit Answer
25
BB
A
160
100
0
attempt 1 out of 2 by
Yaritza made 25% of her free throws over the season. If she shot 160 free throws, 40 many did she make. Using the concept of percentage.
What is Percentage?When a fraction of a whole is represented as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
When the denominator is 100, percentages are really just fractions. The percent sign (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
An easy way to solve this problem is by first finding 50%.
To find 50% of 160
= 160 × (50/100)
= 80
So, 160.0 becomes 80.
Then, because 25% is half of 50% to find the answer divide 80 by 2.
Therefore, Yaritza made 40 of her 160 free throws.
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Two questions show work
1. What is 0.00526 in scientific notation?
2. What is 0.00639 in scientific notation?
1. To convert 0.00526 into scientific notation, follow these steps:
Move the decimal 3 times to right in the number so that the resulting number, m = 5.26, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -3
Write in the scientific notation form, m × 10n
= 5.26 × 10-3
Therefore, the decimal number 0.00526 written in scientific notation is 5.26 × 10-3 and it has 3 significant figures.
2. To convert 0.00639 into scientific notation also known as standard form, follow these steps:
Move the decimal 3 times to right in the number so that the resulting number, m = 6.39, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -3
Write in the scientific notation form, m × 10n
= 6.39 × 10-3
Therefore, 0.00639 in scientific notation is 6.39 × 10-3 and It has 3 significant figures. In scientific e-notation it is written as 6.39e-3.
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Find the solution to the following system by substitution
y=2 x-1
y=5 x-7
A. (2,3)
B. (6/7), (5/7)
C. (-2,-5)
D. (1,1)
the correct answer is a=(2,3)
Write equation of hyperbola from key features
Check the picture below, so the hyperbola looks more or less like so.
the center of the hyperbola is half-way between the foci, so namely at (-2 , -1) as you see there, since we know the covertices, half that distance is the "b" component, so all we're really missing is the "a" component, but we know what "c", since it's just the distance from a foci to the center, so
[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-2\\ k=-1\\ b=15 \end{cases}\implies \cfrac{( ~~ x- (-2) ~~ )^2}{ a^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1[/tex]
[tex]\stackrel{\textit{we know that}}{c=17}\qquad 17=\sqrt{a^2+15^2}\implies 17^2=a^2+15^2\implies 17^2-15^2=a^2 \\\\\\ \sqrt{17^2-15^2}=a\implies \sqrt{64}=a\implies 8=a \\\\[-0.35em] ~\dotfill\\\\ \cfrac{( ~~ x- (-2) ~~ )^2}{ 8^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1\implies {\Large \begin{array}{llll} \cfrac{(x+2)^2}{64}-\cfrac{(y+1)^2}{225}=1 \end{array}}[/tex]
Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week
The sales Jamie made for the week is $530
How to find Jamie sales for the weekinformation from the problem
Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales
Jamie makes $229.50 in one week, her sales for that week = ?
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
15% = 15 percent
= 15 / 100
= 0.15
Let Jamie's sales for the week be x
total earning = 150 + 0.15x
229.50 = 150 + 0.15x
229.50 - 150 = 0.15x
0.15x = 79.5
x = 79.5 / 0.15
x = 530
The sales for the week is $530
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A DVD costs $18.99 plus 6.5% sales tax. What is the total cost if the DVD?
Answer:
Step-by-step explanation:
To determine the total cost of the DVD, you need to calculate the amount of sales tax and add it to the cost of the DVD.
The sales tax is equal to the cost of the DVD multiplied by the sales tax rate:
Sales tax = $18.99 * 6.5% = $1.23
To determine the total cost, you need to add the cost of the DVD to the sales tax:
Total cost = $18.99 + $1.23 = $20.22
So the total cost of the DVD is $20.22.
Fun fact-
Washington Sales Tax. State Sales Tax: 6.5%
A large university accepts 70% of the students who apply. Of the students university, 25% actually enroll. If 20,000 students apply, how many enroll?
Answer:
350 enrolled
Step-by-step explanation:
.7 x 20000 = 1400
.25 x 1400 = 350
Answer:
3500
Step-by-step explanation:
20000 * 0.70 = 14000
14000 * 0.25 = 3500
Use the number line to explain why 2 is 10 times the value of 2.0
on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.
What is the number line?
The number line is a visual representation of the set of all real numbers, which are the numbers that can represent any value on the continuous number scale, including fractions and decimals. On the number line, each point corresponds to a specific real number.
The number 2 is represented by a point on the number line, as is the number 2.0. These two numbers are different because 2.0 is a decimal number, while 2 is a whole number.
2 is 10 times the value of 2.0 if you multiply 2.0 by 10. This is because multiplying a number by 10 shifts its decimal point one place to the left, which increases its value by a factor of 10. For example, if you multiply 2.0 by 10, you get 20.0, which is 10 times the value of 2.0.
Hence, on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.
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In which direction does the parabola defined by the equation y = 4x + 4 open?
Hence, given parabola is defined in Negative Y direction. -Y direction
Which of the several equation types are there?Either identity equations or conditional equations classify an equation. Every value of the variables has a corresponding identity. Only particular values of the variables are valid for a conditional equation. The equals symbol ("="), which divides two expressions, denotes an equation.
Here,
Given : y = 4[tex]x^{2}[/tex] + 4
Thus,
General Guidance The answer provided below has been developed in a clear step by step manner.
Step: 1 Given parabola equation is,
=> y = -4[tex]x^{2}[/tex]+4
=>y-4=-4x2 -4x2 =
=> (y-4) == y-4 = 4
This is the equation of a downward parabola. Hence this parabola is defined in negative Y direction.
Explanation: Upward parabola is given by [tex]x^{2}[/tex] = 4AY, And downward parabola is [tex]x^{2}[/tex] = - 4Ay
Hence, given parabola is defined in Negative Y direction. -Y direction
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Write and graph the inverse of y=-x²+9
Write the inverse of y=-x²+9
y=
(Simplify your answer. Use a comma to separate answers as needed.)
The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]
What is Inverse of a Function ?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.
The output of a function is returned by the inverse function, which also returns the initial value.
If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.
For instance, f(x) = 2x + 5 = y
Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).
The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.
A function is said to be an inverse function if its own inverse is represented by the symbol f-1.
[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex] is the inverse of y=-x²+9
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Need help with this question.
580 lb to kg
(Round to the nearest hundredth as needed)
Answer:
264 kg.
Step-by-step explanation:
To convert from pounds to kilograms, divide the number of pounds by 2.20462. In this case, we have:
580 lb / 2.20462 = 263.74 kg
So, rounded to the nearest hundredth, the answer is 264 kg.
someone please answer this question and give the right answer please!
The area of the rectangle is 4 (7-2) unit².
What is rectangular shape?A rectangle is a quadrilateral with four equal vertices and parallel sides of equal length.
Given, the sides of the rectangle are 4 and 7.
And in the diagram,
The rectangle overshadowed by the rectangle having the sides 4 and 2.
So, the sides of the shaded rectangle are 4 and (7-2).
So, the area of the rectangle
= length x width
= 4 x (7-2)
= 4 (7-2)
Therefore, the area is 4 (7-2) unit².
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Use quadratic regression to find a model for the following data set. (Round the terms to four decimal places.) f(x)=___________________________________x 1 3 5 6 8f(x) 2.1 7.4 28.4 34.9 64.4
Use quadratic regression a model for the following data set is [tex]y=1.96 x^2-5.2 x+5.33[/tex].
What is quadratic regression?
A statistical method called quadratic regression is used to identify the parabola equation that best fits a given collection of data. Finding the equation of the straight line that most closely fits a collection of data is the goal of this sort of regression, which is an extension of simple linear regression.
The equation of the parabola that best fits a collection of data is the process of a quadratic regression. As a consequence, we arrive at the equation y=ax2+bx+c where a≠0. The least squares approach is the most effective way to manually locate this equation.
[tex]$$\begin{aligned}& x=1, f(x)=2.1 \\& x=3 \quad f(x)=7.4 \\& x=5 \quad f(x)=20 \cdot 4 \\& y=a x^2+b x+c \\& \text { Print (1) } \\& 2 \cdot 1=a(1)^2+b \times 1+c \\& 2.1=a+b+c \\& \text { Point(2) } \\& 7.4=a(3)^2+b \times 3+c \\& 7.4=9 a+3 b+c \\& \text { Poin (3) } \\& 28.4=a(5)^2+b \times 5+c \\& 28 \cdot 4=25 a+5 b+c \\& \text { by solving (4) (5) (6) } \\& a=1.96 \\& b=-5.2 \\& c=5.33 \\&\end{aligned}$$[/tex]
so, quadratic equation -
[tex]y=1.96 x^2-5.2 x+5.33[/tex]
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Kyle buys last years best selling hardcover for $19.50 . This is with a 25% discount from the original price. What was the original price of the novel ,
Use variable x to set up an equation to solve the given problem. DONT TAKE STEPS TO SOLVE
The answer to your problem is $26
PLEASE ANSWER CLEARLY WITH THE EQUATION
A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 5 people and each large car can hold 7 people. The students rented 2 more small cars than large cars, which altogether can hold 46 people. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.
There were 6.75 small cars rented and 1.75 large cars total were rented.
How to find the Equation?Let x represent the quantity of little cars rented, and y represent the quantity of big cars rented.
The system of equations below is based on the statements that have been provided:
5x + 8y = 51
x = y + 5
If we replace (1) with the value of x from (2), we get
5(y+5) + 7y = 46
5(y) + 5(5) + 7y = 46
5y + 25 + 7y = 46
12y = 46 -25
12y = 21
y = 1.75
Adding the value of y to (2) yields x = 1.75 + 5 = 6.75.
There were 6.75 small cars rented.
1.75 large cars total were rented.
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