Answers
Answer:
[tex]-9,-18,-27,-36[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-9[/tex] and the common difference is [tex]-9[/tex], then each successive term in the sequence is [tex]9[/tex] less than the previous term:
[tex]a_n=-9n[/tex]
Therefore, the first term is [tex]-9[/tex], followed by [tex]-18[/tex], [tex]-27[/tex], and [tex]-36[/tex].
Related Questions
In a school of 320 children, 45% of the children speak a language other
than English at home.
(i) Calculate the number of children in the school who speak a
language other than English at home.
(ii) Of the children who speak a language other than English at home,
24 speak Polish. Write the number of children who speak Polish as
a fraction of the number of children who speak a language other than English at home.
Give your answer in its simplest form.
Answers
The number of children in the school who speak a language other than English at home is 144.
The fraction of children who speak Polish is 1/6.
How many children speak a language other than English?Percentage is the ratio of a quantity expressed as a number out of 100. Percentage is a measure of frequency. The sign that is used to represent percentage is %.
Number of children in the school who speak a language other than English at home = Percentage of the students who speak a language other than English x number of children
Number of children in the school who speak a language other than English at home = 45% x 320
Number of children in the school who speak a language other than English at home = 0.45 x 320 = 144
A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.
Fraction of the students who speak Polish = number of students that speak Polish / total number of students who speak a language other than English.
Fraction of the students who speak Polish = 24 / 144 = 1/6.
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How do I solve this question
Answers
The partial fraction form of the given fraction [x+5/(x-7)(x-5)] is
[A/(x-7)+B/(x-5)].
What is decomposition to partial fractions?For a rational fraction to be partially decomposed or expanded in algebra, the fraction must be expressed as the product of a polynomial and one or more fractions with a simpler denominator.Partial fraction decomposition is the process of taking a rational expression and breaking it down into smaller rational expressions that we can combine or divide to recover the original rational expression.So, the fraction is:
x+5/(x-7)(x-5)We know that:
px + q/(x-a)(x-b), a≠b ⇒ A/(x-a) + B/(x-b)Use the same identity to get the partial fraction of the given fraction as follows:
x+5/(x-7)(x-5)A/(x-7) + B/(x-5)Therefore, the partial fraction form of the given fraction [x+5/(x-7)(x-5)] is [A/(x-7) + B/(x-5)].
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One spring day, Harper noted the time of day and the temperature, in degrees
Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 58° F. For the
next 3 hours, the temperature rose 4° per hour. For the next 5 hours, it rose 1° per
hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the
temperature dropped 1° per hour. The temperature then dropped steadily until the
temperature was 70° at midnight. On the set of axes below, graph Harper's data.
Answers
The graph that shows Harper's data about temperature and time is shown below .
The graph is a relation that represents the relationship between two variables on the x and y axis .
In the question ,
Harper's data of time of day and the temperature, in degrees Fahrenheit is given,
the temperature at 6 a.m. = 58° F
for the next 3 hours the temperature rose 4° each hour means
in 3 hours it will rise 12°
So , the temperature at 9 a.m. = 70° F
For the next 5 hours, it rose 1° per hour which means
in 5 hours it will rise 5°
So , the temperature at 2 p.m. = 75° F
The temperature then stayed steady until 6 p.m. which means
temperature at 6 p.m. = 75° F
For the next 2 hours, the temperature dropped 1° per hour , which means
temperature at 8 p.m. = 73° F
the temperature at midnight = 70° F
So , from the above data the graph is shown below .
Therefore , The graph that shows Harper's data about temperature and time is shown below .
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x-3y = 3
2x - 6y = -24
Substitution.
Answers
With the help of substitution the answer to the equation is - (-9/2 , 5/2)
What is substitution method?The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.. We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y. The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions.acc to our question -
Subtract 3y from both sides of the equation.Replace all occurrences of x with 3−3y in each equation.Replace all occurrences of x in 2x+6y=6 with 3−3y.2(3−3y)+6y=6x=3−3yHence,The solution to the equation is (-9/2, 5/2) using substitution.
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consider the line y= 5/2x+5
1. find the equation of the line that is perpendicular to this line and passes through the point (-5,6)
2. find the equation of the line that is parallel to this line and passes through the point (-5,6)
Answers
Answer:
Step-by-step explanation:
1
y-6 = -2/5(x-(-5)
y - 6 = -2/5(x+5)
y -6 = -2/5 x -2
y = -2/5 x -2 + 6
y = -2/5 x + 4
2
y-6 = 5/2 (x-(-5)
y-6 = 5/2 (x+5)
y - 6 = 5/2 x + 25/2
y = 5/2 x + 25/2 + 6
y = 5/2 x + (25+12)/2
y = 5/2 x + 37/2
Dave’s Furniture Store is having a 35% off sale on tables. Robert paid $195 for a table that was on sale. What was the original price of the table?
Answers
Answer:
557.143
Step-by-step explanation:
195 / 35% = 557.14
A person deposits $8,000 into a savings account at an interest rate of 6.5%. The interest is compounded quarterly. If no other money is deposited into the account, what will the balance be after 12 years? Round to the nearest cent.
Answers
If a person deposits $8,000 into a savings account at 6.5% interest compounded quarterly for 12 years, the balance (future value) will be $17,342.70.
What is the future value?The future value is the compounded present value of an investment for a future period.
The future value can be computed using the FV formula, table, or an online finance calculator as below.
N (# of periods) = 48 quarters (12 years x 4)
I/Y (Interest per year) = 6.5%
PV (Present Value) = $8,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $17,342.70
Total Interest = $9,342.70
Thus, the future value of a present investment of $8,000 at 6.5% interest compounded quarterly for 12 years is $17,342.70.
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f(x) = -x³ + 3x² +9
x=4
Answers
[tex]{ \pink{ \boxed{ \red{ \sf{f(4) = - 7}}}}}[/tex]
Step-by-step explanation:
[tex]{ \green{ \sf{f(x) = { - x}^{3} + 3 {x}^{2} + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = ( { - 4})^{3} + 3( {4})^{2} + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = - 64 + 3(16) + 9}}}[/tex]
[tex]{ \green{ \sf{ f(4) = - 64 + 48 + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = - 64 + 57}}}[/tex]
[tex]{ \blue{ \boxed{ \orange{ \sf{f(4) = - 7}}}}}[/tex]
0.1098 round to nearest hundredth
Answers
Given (0.25 x 12.3) x 8, which two numbers are compatible, and which
property would you use to calculate this mentally?
4a) Two numbers
4b) Property
Answers
The two numbers that are compatible are 0.25 and 8. The property which helps to calculate it is commutative property.
What is the commutative property?
This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution.
Given numerical expression is (0.25 x 12.3) x 8.
First remove the parenthesis from the numerical expression:
(0.25 x 12.3) x 8 = 0.25 x 12.3 x 8
Now apply commutative property:
(0.25 x 12.3) x 8 = (0.25 x 8) x 12.3
(0.25 x 12.3) x 8 = 2.00 x 12.3
(0.25 x 12.3) x 8 = 24.6
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Y =-3x + b solve for b
Answers
Answer:
b=3x+y
Step-by-step explanation:
y=-3x+b
get b by itself on one side
y+3x=b
The rearranged equation, [tex]b = Y + 3x[/tex], allows us to determine the value of b based on the given values of Y and x.
Rearranging an equation involves manipulating the terms and variables in order to isolate a specific variable or simplify the equation. The goal is to rewrite the equation in a different form while maintaining equality.
In the context of solving the equation [tex]Y = -3x + b[/tex] for b, rearranging the equation means moving the terms around so that b is isolated on one side of the equation. This is done by performing inverse operations on the equation.
Starting with [tex]Y = -3x + b[/tex], we want to isolate b. To do this, we need to move the [tex]-3x[/tex] term to the other side of the equation.
By subtracting [tex]-3x[/tex] from both sides, we can eliminate the -3x term on the right-hand side. The equation becomes [tex]Y - (-3x) = b[/tex].
Simplifying further, [tex]Y + 3x = b[/tex]. Now, b is isolated on one side of the equation.
Therefore, the rearranged equation, [tex]b = Y + 3x[/tex], allows us to determine the value of b based on the given values of Y and x.
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Classify the following number: 4. Choose all that apply.
Answers
Answer: real number, integer, whole number, rational #
Step-by-step explanation:
Look at a chart about rational numbers vs irrational numbers.
What is the product of 1.45 and 0.34 rounded off to one decimal place
Answers
Answer: 0.5
Step-by-step explanation:
1.45*0.34 = 0.493
Rounded to the tenth place is 0.5
Construct a polynomial function with the following properties: third degree, 2 is a zero of multiplicity 1, −4 is the only other zero, leading coefficient is 2.
Answers
The polynomial in standard form is equal to 2 · x³ + 12 · x² - 64.
How to derive a cubic equation
Cubic equations have three roots. In this problem we need to derive a cubic equations whose three real roots (r₁, r₂, r₃) and leading coefficient (a) are given. The procedure consists in substituting on factor form of a cubic polynomial and expanding the resulting expression until standard form is obtained.
First, substitute on the factor form of the cubic equation:
y = 2 · (x - 2) · (x + 4)²
Second, expand the polynomial until its standard form is found:
y = 2 · (x - 2) · (x² + 8 · x + 16)
y = 2 · (x³ + 8 · x² + 16 · x - 2 · x² - 16 · x - 32)
y = 2 · (x³ + 6 · x² - 32)
y = 2 · x³ + 12 · x² - 64
The polynomial is equivalent to 2 · x³ + 12 · x² - 64.
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calculate the length of a scarf with sections if each section is 1/2 foot long
Answers
Answer:
depends on how many sections there are
Step-by-step explanation:
if there were 2 then it would be one foot 4 sections equal 2 and so on. the ratio for this 2:1 meaning there has to be 2 sections for there to be one foot.
Tonia hit 65% of the 20 pitches thrown to her at softball practice. Fill in the missing information and determine how many pitches Tonia hit.
Answers
Answer: 13
Step-by-step explanation:
20(.65) = 13
Hope that helps!
A speed of 60 mph is equal to 88 ft/sec. Find the speed to the nearest mile per hour of an aircraft that travels 1000 ft/sec.
Answers
The speed of the aircraft is 682 mph
How to determine the speed of the aircraft to the nearest mile per hour?Given that: A speed of 60 mph is equal to 88 ft/sec
If an aircraft travels at a speed of 1000 ft/sec, the speed to the nearest mile per hour can be calculated by using the unit ratio of
of mph to ft/s, that is:
60/88 = m/1000
m = 6x1000/ 88 = 60000/88 = 682 mph
Therefore, the speed of the aircraft to the nearest mile per hour is 682 mph
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Hey can someone please explain this to me I’m a bit confused. Thank you I appreciate it!
Answers
The area of given figure is 93mm².
Which of the following is the inverse of f(x) =
2x+4/3
Answers
By using the concept of function, it can be calculated that
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, the function is
[tex]f(x) = 2x + \frac{4}{3}\\[/tex]
Let f(x) = y
[tex]2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\[/tex]
6x + 4 = 3y
6x = 3y - 4
[tex]x = \frac{3y - 4}{6}[/tex]
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
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PLS PLS PLS HELP!!!!!
Answers
The triangle in option (a) is an equilateral triangle in option (b) is isosceles and the triangle in option (c) is a scalene triangle.
What is a triangle?A triangle is a 3-sided shape occasionally referred to as a triangle. Every triangle has three sides and three angles, some of which may be the same.
An equilateral triangle is a triangle whose all sides are equal.
As below the triangle in option (a) with the purple marks has all sides are same thus it will be equilateral.
An isosceles triangle is a triangle whose two sides are the same.
In option (b) triangle the (blue marked) has two equal sides thus it will be isosceles.
A scalene triangle is a triangle with all unequal lengths in option (c) (green mark) all sides are unequal.
Hence "The triangle in option (a) is an equilateral triangle in option (b) is isosceles and the triangle in option (c) is a scalene triangle".
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Please Help 2
Find (fxg)(x) if f(x)=x2+2+4 and g (x)=x-2
Answers
Answer:
x³ - 8
Step-by-step explanation:
1.94 million is what percent of 2.16 million
Answers
89.81% of 2.16 million is 1.94 million.
What percentages are there?In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. After dividing a number by its whole, multiply it by 100 to determine its percentage. As a result, the percentage refers to a component per 100. The word "percent" denotes a percentage of 100.
To calculate a group's share of the total in terms of 100, use the percentage formula. Using this method, you may represent a number as a fraction of 100. You'll see that the approach below may be used to rapidly calculate each of the the percentages:
(Value/Total Value) x 100 = %
According to the question,
(x/100) 2.16 = 1.94
x = 1.94 (100)/ 2.16
x = 194/ 2.16
x = 89.81 %
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The approximate volume in milliliters, m, for a volume of f fluid ounces is equal to
29.57 times the value of f. Which table represents this relationship?
Answers
The table that represents this relationship regarding the volume is table D.
How to illustrate the information?From the information, the approximate volume in milliliters, m, for a volume of f fluid ounces is equal to 29.57 times the value of f.
Therefore, when f is 1, the millimeters will be:
= 1 × 29.57
= 29.57
When f is 2, the millimeters will be:
= 2 × 29.57
= 59.14
When f is 3, the millimeters will be:
= 3 ×29.57
= 88.71
When f is 4, the millimeters will be:
= 4 × 29.57
= 118.28
Therefore the correct option is table D.
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please find the difference 7(2x+4)-5x
Answers
Answer:
9x+28
Step-by-step explanation:
7(2x+4)_5x
14x+28-5x
9x+28
You can tell that is an irrational number because it has a what?
Answers
Answer:
Can't be written as fraction
Step-by-step explanation:
Irrational Numbers are Real Numbers which are not rational , which means that it can't be written as fraction
The problem is sketch the graph of each line
Answers
The required sketch graph of given straight line is shown below in the image.
Explain the concept of equation of line.
The general equation of line is written as Y = mx + c where, m is the gradient of straight line, c is the point where the line cut y-axis.
According to the question:we have, line y = x - 1
So, slope of line is 1 and y-intercept is -1
Thus,required graph of straight line is
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The average cost per night of a hotel room in New York City is $273 (Smart Money, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.
Show all work for each solution
a. With 95% confidence, what is the margin of error?
b. What is the 95% confidence interval estimate of the population mean?
c. Two years ago the average cost of a hotel room in New York City was $229. Discuss the change in cost over the two-year period.
Answers
With 95% confidence, the margin of error is 19.523, population mean is (253.477, 292.523) and the change in cost over the two-year period is 19.21%.
In the given question,
The average cost per night of a hotel room in New York City(y) = $273
Number of rooms in hotel(n) = 45.
The sample standard deviation(s) = $65
(a.) Now finding the margin of error, with 95%(0.95) confidence.
The formula of margin of error is
ME= [tex]z_{\alpha /2}\times \frac{s}{\sqrt n}[/tex]
Now find the value of [tex]z_{\alpha /2}[/tex].
[tex]\alpha[/tex] = 1-0.95
[tex]\alpha[/tex] = 0.05
[tex]\alpha[/tex]/2 = 0.05/2
[tex]\alpha[/tex]/2 = 0.025
Now the value of [tex]z_{\alpha /2}[/tex]
[tex]z_{\alpha /2}=z_{0.025}[/tex]
From the standard table of z is 2.015.
Now putting the value in formula
ME= 2.015 × 65/√45
ME= 2.015 × 65/6.708
ME= 2.015 × 9.689
ME= 19.523
Hence, with 95% confidence, the margin of error is 19.523.
(b) Now finding .the 95% confidence interval estimate of the population mean.
Population Mean = y ± ME
Population Mean = 273 ± 19.523
Population Mean = {(273-19.523), (273+19.523)}
Population Mean = (253.477, 292.523)
(c) Now two years ago the average cost of a hotel room in New York City was $229 then the change in cost over the two-year period is
The change in cost = difference between the cost/old cost
The change in cost = (273-229)/229 *100
The change in cost = 44/229 *100
The change in cost = 0.1921 *100
The change in cost = 19.21%
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Which value of a makes the following equation true?
(³) = 125
a = 1
No value of a will work.
a=3
a = 2
Answers
Answer:
No value of a will work.
Step-by-step explanation:
let me explain,
given values of a are1,2,3
checking these values of a ,
(1)³=125
1=125 (not true)
(2)³=125
8=125 (not true)
(3)³=125
27=125 (not true)
the correct value of a which makes this equation true is 5. let me make you clear,
(5)³=125
125=125 (true).
i. Can you
3. Two cards are randomly dealt from a deck. Find the probability that the first is a king and the
second is a 7. Find the probability that the first is a king and the second is a spade.
Answers
The Total Probability is 4/663 and 35/2652
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. An event's probability is a number between 0 and 1.
Solution:
We know that there are 52 cards in a deck of cards.
So, probability of getting a king = 4/52 = 1/13
And probability of getting a 7 after drawing a king is 4/51,
this is because one card is drawn out from the deck and there are only 51 cards left in the deck.
Total Probability = 1*4/13*51 = 4/663
In the secon case, there are two possibilities,
It can be the kling drawn might be of spade or not
Case 1: When King drawn is of Spade
Probaility of drawing a King of Spade = 1/52
Probability of drawing a Spade after King of Spade is drawn = 11/51
Total Probaility = 1*11/52*51 = 11/2652
Case 2: When King drawn is not of Spade
Probability of drawing a King not of Spade = 2/52
Probability of drawing a Spade after drawing the King = 12/51
Total Probability = 2*12/51*52 = 24/2652
Total Probability of drawing a king and spade = 11/2652 + 24/2652 = 35/2652
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A surveywas giben to people who awned a cerrain type of car what percent of the people surveyd were completely satisfief with the car?
Answers
Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.
A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes.
In this problem, researching in the internet, it is found that:
A total of 1260 + 650 + 180 = 2090 people were surveyed.
Of those, 1260 were completely satisfied.
Hence:
60.29% of the people surveyed were completely satisfied with the car.
