What is the next term in the sequence −10,−17,−24,−31,
Answer:
-38
Step-by-step explanation:
The sequence is decreasing by 7 everytime
-10 to -17 decrease of 7
-17 to -24 decrease of 7
-24 to -31 decrease of 7
Ann Dyslecki is buying a sports car. She financed $ 5590 at her
bank and agreed to repay it in four years. Her monthly payment
was $ 149,60. Find the total amount to be repaid and the finance
charge.
Answer:
5590-149,60
Step-by-step explanation:
sum completed
A motel has 200 rooms. Those with a window view rents for $50 a night. Those without a window view rent for $40 a night. When the motel is 100 percent occupied the motel earns $8,500 for the night. How many rooms does the motel have that have a window view? How many rooms does the motel have that don't have a window view? Rooms with window view: Rooms without window view:
Answer:
Window view rooms is 50, no window view rooms is 150.
Step-by-step explanation:
I just multiplied the prices times random number of rooms until they added together to 8,500$. It was purely by chance that I discovered the answer ngl to you lol
At a college, the cost of tuition increased by 10%. Let b represent the former cost of tuition. Use the expression b+0.10b for the new cost of tuition.
a. Write an equivalent expression by combining like terms.
b. If the cost increases by 10%, you can multiply the former cost by %.
The equivalent expression by combining like terms is 1.10b and
If the cost increases by 10%, you can multiply the former cost by 110%
How to determine the equivalent expression by combining like terms.From the question, we have the following parameters that can be used in our computation:
Expression of 10% raise = b + 0.10b
Evaluate the like terms in the above expression
So, we have the following representation
Expression of 10% raise = 1.10b
Hence, the expression is 1.10b
How to complete the blankRecall that we have the mathematical statement to be
If the cost increases by 10%, you can multiply the former cost by %.
In this case, the factor is calculated as
factor = 1 + 10%
So, we have
Factor = 110%
So, the missing expression in the statement 110%
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A population of 50 foxes in a wildlife preserve doubles in size every 14 years. The function y = 50.2*, where x is the number of 14-year periods, models the population
growth. How many foxes will there be after 42 years?
After 42 years there will be foxes. (Type a whole number.)
Answer:
400
Step-by-step explanation:
You want to know the number of foxes predicted after 42 years by y = 50·2^x, where x is measured in 14-year periods.
Periods42 years is 42/14 = 3 14-year periods. Using x=3 in the equation, we predict ...
y = 50·2^3 = 50·8 = 400
foxes.
After 42 years, there will be 400 foxes.
__
Additional comment
It is often convenient to use time measured in 1-year periods. In that case, the equation could be written ...
y = 50·2^(t/14)
Then t/14 is the number of 14-year periods when t is in years.
A pinball machine which normally sells for $1999 is on sale for $1750. Find the discount and the rate of discount.
HELP ME THIS IS DUE TODAY!!
Answer: 12.5%
Step-by-step explanation:
Take 1750 divided by 1999, then time 100% = 87.5%
100% - 87.5% = 12.5%
The rate of discount is 12.5%
A population of chipmunks moves into a new region at time t=0 months. At time t (in months), the population size is given by
P(t) = 100[1+0. 3t+(0. 04)t^2].
How long does it take for this population to double its initial size P(0)? Include the units in your answer.
What is the average rate of population change between time t=0 and time t=20? Include the units in your answer.
What is the instantaneous rate of growth of the population when the population size is P=200? Include the units in your answer
Part a: Time taken to double the population of chipmunks is 5/2 months.
Part b: Population at population size; P = 200 is 50.
Explain the term average rate of population change?the country, region, or geographic area's average yearly rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and indeed the overall population for that year.Part a: Time taken to double the population of chipmunks;
P(t) = 100[1 + (0.3)t + (0.04)t²].
P(0) = 100[1 + 0 + 0] = 100
P(t) = 200 = 100 + 30t + 4t²
4t² + 30t − 100 = 0
2t² + 15t − 50 = 0
(2t − 5)(t + 10) = 0
t = 5/2
It will take 5/2 months population to double its initial size P(0).
Part b: Population at population size; P=200
P'(t) = 0 + 30 + 8t
P = 200 when t = 5/2
P'(200) = 30 + 8(5/2)
P'(200) = 30 + 20
P'(200) = 50
Thus, the instantaneous rate of growth of the population when the population size is P=200 is 50.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
3,12,48,...
This is __ sequence and the ____ is equal to.
| |
Arthmatic, geomatric commom ratio, commom difference
Answer:
3
12
12
48
48
192
192
768
768
I hope I helped you
Rule: Start at ? Subtract 6 then multiply by 2 each time
? 22- 32- 52
Step-by-step explanation:
let the number be x
So,
(x - 6) × 2 = 22
2x - 12 = 22
2x = 34
x = 17
Thus, the answer is 17
Find the slope of the line that passes through (2, 14) and (10, 5).
Answer:
m=-12/5
Step-by-step explanation:
yes
Scott has a bag containing plain chocolate pieces and another bag containing peanut chocolate pieces. The bag with plain chocolate pieces contains 6 blue, 1 yellow, 3 green, and 2 red candies. The bag with peanut chocolate pieces contains 3 blue, 1 yellow, and 4 green candies. Scott will randomly select 1 candy from each bag. What is the probability that Scott will select a green candy from each bag?
Answer: 35%
Step-by-step explanation:
The total amount of candy is 20, and there is 7 green candy, so we got 7/20. Then we multiplied 20 and 7 by 5, so we got 100 and 35, so we got 35/100, which is 35%
5. What are the real and complex solutions of the polynomial equation? (1 point)
x-8=0
01+i3, and 1-i√√3
O2,-1+13, and-1-i√√3
O2, 1+2i √√3, and 1-2i √√3
02, 2+2i √√3, and 2-2i
The real and complex solutions of the polynomial equation [tex]x^{3} - 8[/tex] = 0 is 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i. option 2 is correct.
Polynomial equation: what is it?Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree. By factoring polynomials according to their degree and the variables in the equation, we may find their solutions.
Our equation is [tex]x^{3} - 8[/tex]
and we know that: [tex]x^{3} = 8[/tex]
then we can write our equation as: [tex]x^{3} - 2^{3}[/tex]
And using the identity: [tex]a^{3} - b^{3} = (a-b) *(a^{2} +ab+b^{2} )[/tex]
where a = x and b = 2, then our equation is:
them, if x = 2 the first part is zero, so x = 2 is a solution, and now we need to see the second part in order to find the complex solutions.
[tex]x^{2} + 2x +2^{2}[/tex] = 0
Here we need to use.
a[tex]x^{2}[/tex] + bx + c = 0 if for a, b and c constants, then:
x = [tex]-b +-\sqrt{b^{2} - 4ac } /2a[/tex]
in our problem we have:
x = -2 +-[tex]\sqrt{4 - 16}[/tex] /2
x = -1 +-[tex]\sqrt{-3}[/tex]
x = -1 +-[tex]\sqrt{3}[/tex] i
So here we have two complex solutions: -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
So the value of x are 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
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I think you mean
What are the real and complex solutions of the polynomial equation? (1 point)
[tex]x^{3} - 8[/tex] = 0
( the equation is [tex]x^{3} - 8[/tex] = 0 and not x-8 =0)
Daniela notices
a pattern in her scrapbook. The leaves on the first page
are green. The second page has yellow leaves. The third
page has green leaves. The next page has yellow
leaves. Is this a repeating or growing pattern
Answer:
I think it's repeating pattern
im not sure I'm very very bad at math
Answer:
Step-by-step explanation:
for the first car 374/17 = 22 m per second
for bus 414/23 = 18 m per second
so the car is moving faster
car is moving faster than (22-18)=4 m per second from the bus
Answer: Car: 22 meters per second, Bus: 18 meters per second. The bus travels faster at 4 meters per second.
Step-by-step explanation: First, you should write a proportional relationship for meters per second so the car would be 374/17 and the bus would be written as 414/23. This is so you can know that you divide 374 by 17 to get 18, and 374 by 17 to get 22. So, you had it backward, the bus is faster by 4 meters per second, I hope this helped, for me (a 7th grader) this was review math, so I hoped this helped you.
please help me i need it before tomorrow if possible. i need all 4 answered
The answer to this Question based on Thales Theorem is x = 8
What is Thales Theorem?
It says that when we join the mid points of two sides of a triangle the line is parallel to third side of triangle then the length of this joined line is half of length of third side
Here in Question given figure is like trapezium but we can extend it to make a triangle then by thales theorem we need to apply on other two sides hence joined line is parallel to third lines hence will be half of it
Solution:
1/2(x) = 2x - 12
x = 2(2x-12)
x = 4x - 24
24 = 3x
x = 8
Hence required value of x is 8
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Jack broke apart 5x216 a 5x200 5x16 to multiply mentally what trategy did Jack ue?
In the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.
What is distributive property?The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
So, in this instance, the multiplication is as follows:
5 * 216
This multiplication can be rewritten as follows:
5*(200+16)
We then put the distributive property to use. So, we have:
(5*200) + (5*16)
Therefore, in the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.
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Correct question:
Jack broke apart 5x216 as (5x200)+(5x16) to multiply mentally. What strategy did Jack use?
In four middle schools, the teacher to student ratio is equivalent. How many teachers and students are at each school? Enter the correct answers in the boxes in the table.
As the teacher-to-student ratio is equivalent in all schools, the number of students in school B is 506, the number of teachers in school C is 25 and the number of students in school D is 792 respectively.
What are ratio and proportion?
An equation known as proportion shows that the two ratios presented are equal to one another. A ratio is the comparative or condensed form of two quantities of the same type. The majority of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers.
Given, the teacher-to-student ratio is equivalent for all schools.
For school A, ratio of teacher-to-student = 15/330 = 1:22
Then, for school B, the number of students = 23*22 = 506
For school C, the number of teachers = 550/22 = 25
For school D, the number of students = 36*22 = 792
Hence, these are the required number of students and teachers for the respective schools.
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what does side b equal?
Answer: 8.6
same side s C and B
Answer: 7.2
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem to solve for side b.
Pythagorean theorem: a²+b²=c²
Since the side length opposite the right angle is the hypotenuse we plug 11.2 in for C
(8.6)² + b²=(11.2)²
73.96 + b² = 125.44
b²=51.48
b = 7.17495644586
b=7.2
our school's girls volleyball team has $14$ players, including a set of $3$ triplets: alicia, amanda, and anna. in how many ways can we choose $6$ starters with no restrictions? (the triplets are treated as distinguishable.)
There are 990 ways to select 6 starters from a possible 14 using precisely two of the three triplets.
= C(3,2) = 3! / ( 2! x 1! ) = 3
To select the final 4 starters out of the 11 players ,
= C(11,4) = 11! / (4!7!)
= 330
There are a total of 6 ways to select starters.
= 3*330 = 990
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.
The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
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Hi pls help me and explain
The linear model representing the information is y = 600x + 1500.
To produce 12 solar heaters it cost $8,700.
The domain of the linear model is [1, 80].
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
10 solar heaters = $7500
20 solar heaters = $13,500
The linear model can be in the form of y = mx + c
m = (13,500 - 7500)/(20 - 10)
m = 6000/10
m = 600
Now,
(10, 7500) = (x, y)
7500 = 600 x 10 + c
c = 7500 - 6000
c = 1500
Now,
The linear model is y = 600x + 1500.
Where y is the cost of x solar heaters.
Now,
x = 12,
y = 600 x 12 + 1500
y = 7200 + 1500
y = 8700
Now,
y ≤ 50,000
We see that,
x = 81
y = 600 x 81 + 1500 = 48600 + 1500 = 50,100
x = 80
y = 600 x 80 + 1500 = 48000 + 1500 = 49,500
The domain is from x = 1 to x = 80.
Thus,
The linear model is y = 600x + 1500.
$8,700 is the cost to produce 12 solar heaters.
The domain is [1, 80].
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Abha is climbing a mountain. While cvering 20 yards of horizontal distance. Abha's elevation increases by 40 yards. consider Abha's climb as a linear function. 1. what is the slope her climb,? 2. does the line 54y=13x pass through the origin? daliyah is given one point on a like as (3,-1) and the slope of the line as -5. 3. what is the y-intercept of the line?and 4. how to write the equation of the line?
1. The slope of Abha's climb is 2 (rise/run).
2. No, the line 54y=13x does not pass through the origin.
3. The y-intercept of the line is 5.
4. The equation of the line is y = -5x + 3.
What does linear function mean?A linear function is one that has one or two variables and no exponents, according to the definition given in mathematics. It is a graphing function that produces a straight line.
How is a linear function determined?To finish the graph, use a straightedge to draw a line through the two points as two points decide a line. The formula for a linear function is f(x)=mx+b, where m and b are real values representing the slope. Set f(x)=0 and work out the value of x to determine the x-intercept, if one exists. We can use y and f(x) interchangeably because y=f(x).
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Consider the line y = 9x - 3.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Zero is the slope of a line parallel to this line.
-1/9 is the slope of a line perpendicular to this line.
What is slope?According to linguists, the Middle English adverb aslope, which meaning "at an angle," is where the term slope is said to have originated. A steep hill or the ramp in a parking garage are examples of things that are at an angle or on a slope and may be described using the word's noun form.
The ratio of the vertical change between two places is referred to as the slope. A line's slope is another indicator of how steep it is. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The line becomes: y = 9x - 3
line is in the Slope-Intercept form : y = mx + c
Now comparing this two and we get slope, (m) = 9
So, The line perpendicular will have slope (m') = -1/m
or, m' = -1/9
The line parallel to this line will have slope (m'') = 0
because here the two lines are parallel, so they have no slope.
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An arithmetic sequence has a 2nd term of -2 and a 7th term of 18.
1. What is the 10th term in the sequence? 2. Write an explicit formula for the sequence.
3. Write a recursive formula for the sequence.
4. What is the sum of the first 10 terms?
The arithmetic sequence has a 2nd term of -2 and a 7th term of 18 has the following answers.
What is arithmetic progression?
An progression or arithmetic sequence may be a sequence of numbers specified the difference between the consecutive terms is constant.
Main body:
General formula for arithmetic sequence
a + (n-1)d = aₙ
arithmetic sequence has a 2nd term of -2 , which means
a+d = -2
a = -(d+2) ---------(1)
7th term of 18 , which means
a+ 6d = 18
substituting value from equation 1,
-(d+2) +6d = 18
-d -2 +6d = 18
5d = 20
d = 5
using d= 5 in equation 1,
a = -(5+2)
a =-7
A) 10th term
=a +9d
= -7+9*5
= 38
B) recursive formula for the sequence = aₙ+1=aₙ+d .
Hence for the given sequence , it is
a₃ = a₂ +d
a₃ = -2+5
a₃ = 3
C) sum of first 10 terms
Sₙ = n/2{2a+ (n-1)d}
S₁₀ = 5 {2*-7 + 9*5}
S₁₀ = 5[ -14 +45]
S₁₀ = 5*31
= 105
Hence the sum of the first 10 terms is 105.\
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HELP i need help asap
The inequality that is used to find the domain of the function would be B x - 3 ≥ 0
What is the domain of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The given function is f(x) = √x - 3
Here we have to find the inequality that is used to find the domain of the function.
Therefore, the function (x - 3) must be greater than or equal to 0
That is;
x - 3 ≥ 0
We will use the above inequality to find the domain of the function.
When we solve the above inequality, we get the domain of the function then;
x - 3≥0
Now add 3 on both sides, we get;
x - 3 + 3 ≥ 0 + 3
x ≥ 3
Therefore, the answer is x - 3 ≥ 0
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Judi Imhoff's previous balance was $717.52. She received $4.36 in interest and had $125.00 and $276.95 in deposits and $90.00 in withdrawals. What is her new balance?
After checking Judi Imhoff's account statement her new balance is $1003.83
What is an account statement?
A statement of accounts is a document that lists all the transactions you have with a certain client during a specific time period. In order to inform their clients of the amount they owe for purchases made during that time period on credit, company owners typically issue statements of accounts to their clients. The manual explains the statement of accounts' contents and demonstrates how to file it for clients.
Your bank may send you a monthly or annual statement if you have a savings account.
account statement for the quarter. All deposits are reflected on the account statement,
withdrawals, as well as interest that is added to your account.
The new balance = Previous Balance + Interest + Deposits - Withdrawals
The new balance = $717.52 + $4.36 + ($125.00 + $276.95) - $90.00
So, the new balance of Judi Imhoff is $1003.83
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can you please help me with my sisters homework ?
Answer:
Bro you require a protector to measure angle
Answer:
A. 45 degrees
B.90 degrees
Step-by-step explanation:
convenience sampling allows for generalizations to a larger population, and probability sampling does not. group of answer choices true false
Probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.
Explain the term convenience sampling?Convenience sampling is any non sampling technique where units are chosen for the sample based on their accessibility to the researcher.
This may be as a result of close proximity geographically, availability at a specific moment, or willingness to take part in the study. Convenience sampling, sometimes known as inadvertent sampling, is a non-random sampling technique.Research projects in qualitative and medical fields frequently employ convenience sampling.In medical science, convenience sampling frequently entails choosing clinical cases or volunteers who are accessible nearby (such as at a hospital) or from a database of medical information.Convenience sampling is frequently employed in qualitative research in the social sciences and in education where it is practical to use which was before groups, including such students.Thus, probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.
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What value for a in the system of equations below would yield no solutions for the system? Explain how you obtained your answer.
ax+12y=−6
2x−6y=4
a=
After solving the provided question, The value for a in the system of equations below would yield no solutions for the system is [tex]= > a = 18 - 20\frac{y}{x}[/tex]
A system of equations is what?several equations at once, multiple equations In algebra, you must work together to solve two or more equations (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, there must be an equal number of equations and unknowns.
When there are two variables and you are given two pieces of information about how those variables are related, a system of equations is used. To address a number of typical problems, a system of equations can be employed.
[tex]3x-5y=15\\multiply with 6\\18x -30y = 90\\compare the equation with \\ax-10y=90\\then \\18x -30y = ax-10y\\ax = 18x + 10y -30y\\ax = 18x-20y\\a= (18x -20 y) / x\\[/tex]
[tex]= > a = 18 - 20\frac{y}{x}[/tex]
x≠o
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Determine the domain of (g ∘ f)(x) if f (x) = x2 + 2x − 4 and g of x is equal to 1 over the quantity x plus 1 end quantity period
{x ∈ ℝ}
{x ∈ ℝ| x ≠ −1}
{x ∈ ℝ| x ≠ −3, 1}
{x ∈ ℝ| x ≠ −3, −1, 1}
The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.
Given that, f(x)=x²+2x-4 and g(x) =[tex]\frac{1}{(x+1)}[/tex].
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, (g·f)(x) can be determined as follows
(g·f)(x)=g(x)×f(x)
= [tex]\frac{1}{(x+1)} \times x^2+2x-4[/tex]
Find the domain by finding where the expression is defined.
Interval Notation:
(-∞,-1)∪(-1,∞)
Set-Builder Notation:
{x∈ℝ|x ≠ -1}
The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.
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You are considering taking some courses at your local community college on a part-time basis for the upcoming school year. For a student who carries fewer than twelve credits (the full-time minimum), the tuition is $155 for each credit hour taken. All students, part-time or full-time, must pay a $20 parking fee for the semester. This fixed fee is added directly to your tuition and is included in your total bill. Write an equation to determine the total bill , t, for a student carrying fewer than twelve credit hours. Use n to represent the number of hours taken for the semester. Then, determine the total bill if you take nine credit hours. A. T + 20 = 155 n; $1395 b. T = 155 n + 20; $1395 c. T = 155 n + 20; $1415 d. T + 20 = 155 n; $1415.
The total bill if the student takes nine credit hours at the community college is T = $1415.
What are linear equations?One or more variables can be present in a linear equation, but their maximal possible power is only one. The graph of a linear equation will thus always be a straight line. Y = mx + b, where m denotes the line's slope and b its y-intercept, or point of intersection with the y-axis, is how linear equations are expressed. Many real-world situations, such as the connection between two variables or the distance travelled at a constant pace, may be modelled using linear equations. In order to obtain the value of the variable(s) necessary to make the equation true, one must use algebraic methods.
How to solve?
The total bill, t, for a student carrying fewer than twelve credit hours is given by,
T = 155 n + 20, where n represents the hours taken for semester.
The total bill if the student takes nine credit hours is T = 155(9) + 20 = $1415.
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