Answers
We will take a look at how we go about with arithmatic progressions.
Arithmmetic sequences are caetgorized by the following two parameters:
[tex]\begin{gathered} a\text{ = First term} \\ d\text{ = common difference} \end{gathered}[/tex]Where,
[tex]\begin{gathered} \text{The value of the first term is called ( a )} \\ \text{The common difference between each and every successive value in a sequence is called ( d )} \end{gathered}[/tex]We are given the following arithmetic sequence:
[tex]3\text{ , -1 , -5 , }\ldots[/tex]Now we will try to determine the values of the two parameters ( a and d ) from the given sequence as follows:
[tex]\begin{gathered} a\text{ = 3 }(\text{ first term value )} \\ d\text{ = (-1 ) - ( 3 ) = (-5 ) - ( -1 ) = -4 ( common difference )} \end{gathered}[/tex]Now to determine the value of any term number ( n ) in an arithmetic sequence we use the following formula:
[tex]a_n\text{ = a + ( n - 1 )}\cdot d[/tex]Where,
[tex]n\text{ is the term number}[/tex]So if we plug in the values of arithmetic sequence parameters into the general equation above we get:
[tex]\textcolor{#FF7968}{a_n}\text{\textcolor{#FF7968}{ = 3 + ( n - 1 ) }}\textcolor{#FF7968}{\cdot}\text{\textcolor{#FF7968}{ ( -4 )}}[/tex]Now we are to determine the values of term numbers ( n = 4 ) and ( n = 5 ). We will evaluate the ( an ) for each term number as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 4}} \\ a_4\text{ = 3 + ( 4 - 1 )}\cdot(-4\text{ )} \\ a_4\text{ = 3 - 12} \\ \textcolor{#FF7968}{a_4}\text{\textcolor{#FF7968}{ = -9}} \\ \\ \text{\textcolor{#FF7968}{For n = 5}} \\ a_5\text{ = 3 + ( 5 - 1 )}\cdot(-4\text{ )} \\ a_5\text{ = 3 - 1}6 \\ \textcolor{#FF7968}{a_5}\text{\textcolor{#FF7968}{ = -}}\textcolor{#FF7968}{13} \end{gathered}[/tex]Hence, the next two consecutive numbers in the arithmetic sequence would be:
[tex]3\text{ , -1 , -5 ,}\text{\textcolor{#FF7968}{ -9}}\text{ , }\text{\textcolor{#FF7968}{-13}}[/tex]Related Questions
Sharon's house, the library, and Lisa's house are all on the same straight road. Sharon has to ride her bike 1 3/5 miles to get from her house to the library and another 2 3/4 miles to get from the library to Lisa's house. How far does Sharon live from Lisa? Explain how you got your answer.
Answers
Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .
In the question ,
it is given that
distance between Sharon and Library is [tex]1\frac{3}{5}[/tex] miles .
distance between Library to Lisa's house is [tex]2\frac{3}{4}[/tex] miles .
So according to the question
distance between Sharon's house and Lisa's house = (distance between Sharon and Library) + (distance between Library to Lisa's house) .
On substituting the values from above ,
we get ,
distance between Sharon's house and Lisa's house = [tex]1\frac{3}{5}[/tex] + [tex]2\frac{3}{4}[/tex]
= (5+3)/5 + (8+3)/4
= 8/5 + 11/4
taking LCM as 20 and solving further we get
= 32/20 + 55/20
= 87/20
= [tex]4\frac{7}{20}[/tex]
Therefore , Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .
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Terry invested $2,200 in the stock market for 2 years. If the investment earned 12%, how muchmoney did Terry earn in 2 years?
Answers
We will have that $2200 represent the 100%, then how much money does 12% represent.
In order to solve for the ammount of money we multiply the invested ammount ($2200) times the percentage we want to know (12%) and divide it by 100%, that is:
[tex]m=\frac{2200\cdot12}{100}\Rightarrow m=264[/tex]Here we can see, he earned $264 in those 2 years.
Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
Answers
Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
The expression (222)(x?) is equivalent to z What is the value of p?
Answers
SOLUTION;
Step 1:
[tex]undefined[/tex]Xavier wants to compare two websites based on customer ratings in order to decide on which website to make a big purchase. He creates a boxplot for each website with the same number of ratings. (look at the graph)What can Xavier NOT include?A. Website A has a higher median rating B. Website A has a larger interquartile range C. Website A has larger rangeD. Website A has a lower median rating E. Website A has a lower first quartile value
Answers
D.
Since the median of the blue box is upper from the orange one we conclude that the median is higher in website A.
Therefore, the wrong statement is D.
Hi, can you help me answer this question please, thank you!
Answers
From the problem we have
[tex]\begin{gathered} n_1=50 \\ n_2=30 \\ \bar{x_1}=2.31 \\ \bar{x_2}=2.02 \\ s_1=0.89 \\ s_2=0.61 \end{gathered}[/tex]We replace in t
[tex]\begin{gathered} t=\frac{(2.31-2.02)}{\sqrt[]{\frac{(0.89)^2_{}}{50_{}}+\frac{(0.61)^2_{}}{30_{}}_{}}} \\ t=\frac{0.29}{\sqrt[]{0.028245_{}_{}}} \\ t=1.725 \\ t=1.73 \end{gathered}[/tex]The answer is t=1.73Segment RS is translated by (x+1, y-2) and then reflected over the x-axis. The resulting segment R" S" has coordinates R" (7,3) and
S" (2,7). What are the coordinates of the segment RS?
can someone pls help meee
Answers
The coordinates of segment RS are obtained as R(6, -1) and S(1, -5) for the given translation.
What is termed as the reflection over the axis?The line of reflection is the point at which the image satisfy the axis of reflection. There are two kinds of reflections: x-axis reflections and y-axis reflections. Vertical reflections are reflections that cross the x-axis. Horizontal reflections are reflections that cross the y-axis.For the given question;
Segment RS is translated by (x+1, y-2).
Then, the image formed is again reflected over the x-axis to form R" S" has coordinates R" (7,3) and S" (2,7).
To find the measure of R and S, first find the x -axis reflection of R" S".
R" (7,3) = R'(7, -3)and S" (2,7) = S'(2, -7)As, RS was translated by (x+1, y-2).
Then, subtract 1 and add 2 to its coordinates.
R'(7, -3) = R (7 - 1, -3 + 2) = R(6, -1)S'(2, -7) = S(2- 1, -7 + 2 ) = S(1, -5)Thus, the coordinates of segment RS are obtained as R(6, -1) and S(1, -5).
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the equation 5x+7=4x+8+x-1 is true for all real numbers substitute a few real numbers for x to see that this is so and then try solving the equation
Answers
The equation 5x+7 = 4x+8+x-1 is true for all real numbers.
Solution for the equation is 5x + 7 = 5x + 7.
Given,
The equation; 5x+7 = 4x+8+x-1
We have to find the solution for this equation.
Here,
5x + 7 = 4x + 8 + x - 1 = 5x + 7
The equation is true for all real numbers;
Lets check;
x = 65 x 6+7 = 4 x 6 + 8 + 6 - 1
30 + 7 = 24 + 13
37 = 37
x = 155 x 15 + 7 = 4 x 15 + 8 + 15 - 1
75 + 7 = 60 + 22
82 = 82
That is,
The equation 5x + 7 = 4x + 8 + x - 1 is true for all real numbers.
The solution for the equation is 5x + 7 = 5x + 7.
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The sides of triangle ABC are: AB = 6 cm,BC = 12 cm, AC = 10cm. K, M and P arethe midpoints of the sides AB, BC and AC respectivelyare the midpoints of the sides and the midpoints of the sides. Calculate the perimeter of KMP.
Answers
Answer: By inspecting the triangle we can come up with the following relationships, using the proportionality:
[tex]\begin{gathered} \frac{12}{10}=\frac{6}{x}\rightarrow(1) \\ \frac{12}{6}=\frac{6}{y}\rightarrow(2) \\ \frac{6}{12}=\frac{3}{z}\rightarrow(3) \end{gathered}[/tex]Solving the three equations, (1) (2) and (3) gives the answer for x,y,z which are the three sides of the smaller triangle, the steps are as follows:
[tex]\begin{gathered} x=KM=5 \\ y=MP=3 \\ z=KP=6 \end{gathered}[/tex]Therefore the perimeter is as follows:
[tex]\begin{gathered} P=x+y+x=5+3+6=14 \\ P_{(KMP)}=14 \end{gathered}[/tex]3) An experiment is designed to compare the average salaries in a particular Position in two competing companies. The null hypothesis is assumed to be that there is no difference in the average salaries of empoty employees in a particular position in the two companies. What is the alternative hypothesis?
Answers
Given:
There are two competing companies.
Required:
We need to find the alternative hypothesis
Explanation:
If the null hypothesis assumes equal average salaries (i.e. no difference), then the alternative can take on three cases:
A)
One mean is greater than the other
B)
One mean smaller than the other
C)
The means are not equal
Now here A and B sound the same, so I shoukd be more precise,
Please help me
I give brainliest
worth 15 points
The amount of money in a bank account is given by the function y = 200(1+0.05), where y is in dollars and t is measured in months since the account was opened.
What is the percent rate of growth of the bank account?
Enter your answer in the box.
Answers
Answer:
60% annual rate
Step-by-step explanation:
Your equation is incorrect
It should be Y = 200 (1+.05)^t
T is the number of compounding periods per year (12 to a year)
.05 is the periodic interest rate ( 1/12 th of the annual)
.05 * 12 = .6 Which is 60% <=====REALLY high annual rate!
Which of the following is a valid application of the distributive property?
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
ONeither A nor B
OB only
O A only
O Both A and B
Answers
5 2+3=5 (2) +5. (3) is a valid application of the distributive property.
What is a distributive property?
According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given that,
A. 5.2+3=5 (2+3)
B. 5 2+3=5 (2) +5. (3)
Distributive property
a*(b+c) = a*b+a*c
In option A the RHS part is not correct.
In option B both part is correct.
5*(2+3)= 5*2+5*3
5*5 = 10+15
25 = 25
LHS = RHS
Hence, Option B is correct.
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Multiply. (−5 2/5)⋅3 7/10. −19 49/50. −15 7/25. −9 1/10. -1 7/10
Answers
To perform this multiplication, first, we have to transform the mixed numbers into fractions as follows:
[tex]-5\frac{2}{5}=-\frac{5\cdot5+2}{5}=-\frac{27}{5}[/tex][tex]3\frac{7}{10}=\frac{3\cdot10+7}{10}=\frac{37}{10}[/tex]Substituting these values into the multiplication, we get:
[tex]\begin{gathered} (-5\frac{2}{5})\cdot3\frac{7}{10}= \\ =(-\frac{27}{5})\cdot\frac{37}{10}= \\ =-\frac{27\cdot37}{5\cdot10}= \\ =-\frac{999}{50} \end{gathered}[/tex]This result can be expressed as a mixed number as follows:
[tex]-\frac{999}{50}=-\frac{950+49}{50}=-(\frac{950}{50}+\frac{49}{50})=-(19+\frac{49}{50})=-19\frac{49}{50}[/tex]
I am having so much trouble with my assignment. can you please help me with number 8 and 10.
Answers
We have to solve this system of equations by substitution.
8) First, we find the value of one of the variables in function of the other using one of the 2 equations (first equation, in this case). Then, we use the other equation and replace the variable we just cleared (x, int his case) and solve for the other variable (y).
Then, after calcualting y, we can use the first equation to calculate x.
[tex]\begin{gathered} x+4y=0 \\ x=-4y \end{gathered}[/tex][tex]\begin{gathered} 3x+2y=20 \\ 3(-4y)+2y=20 \\ -12y+2y=20 \\ -10y=20 \\ y=\frac{20}{-10} \\ y=-2 \end{gathered}[/tex][tex]\begin{gathered} x=-4y=-4(-2) \\ x=8 \end{gathered}[/tex]Answer: x=8, y=-2.
10)
[tex]\begin{gathered} x-3y=-2 \\ x=3y-2 \end{gathered}[/tex][tex]\begin{gathered} 10x+8y=-20 \\ 10(3y-2)+8y=-20 \\ 30y-20+8y=-20 \\ 38y=-20+20 \\ 38y=0 \\ y=0 \end{gathered}[/tex][tex]x=3y-2=3\cdot0-2=0-2=-2[/tex]Answer: x=-2, y=0
A triangular road sign has a base of 30 inches and a height of 40 inches. What is it’s area?
Answers
Answer:
600ft
Step-by-step explanation:
Because a triangle is half of a rectangle, the area can be found by taking the base times height and dividing by 2.
A = (b * h)/2
A = (40 * 30)/2
A = 1200/2
A = 600ft
A point is chosen at random in the square shown below. Find the probability that the point is in the shaded circular region. Each side of the square is 6in, and the radius of the circle is 3in.Use the value 3.14 for π. Round your answer to the nearest hundredth.
Answers
We will have the following:
First, we determine the area of the square and of the shaded region, that is:
[tex]\begin{gathered} A_s=6in^2\Rightarrow A_s=36in^2 \\ \\ A_c=\pi(3)^2\Rightarrow A_c=9\pi in^2 \end{gathered}[/tex]Now, we will have that the probability will be of:
[tex]P=\frac{9\pi}{36}\Rightarrow P=\frac{\pi}{4}\Rightarrow P\approx0.79[/tex]So, the probability is approximately 79%.
1. Caitlyn is going away to college and will need to rent a truck to helpmove. The cost of the truck is $35 plus $0.79 per mile. If her collegeis 85 miles away and she budgeted $100 for the rental, will she haveenough money?
Answers
1. Caitlyn is going away to college and will need to rent a truck to help
move. The cost of the truck is $35 plus $0.79 per mile. If her college
is 85 miles away and she budgeted $100 for the rental, will she have
enough money?
we know that
The equation in slope intercept form of this situation is
y=mx+b
where
m=$0.79 per mile
b=$35
y -----> is the total cost
x -----> the number of miles
so
y=0.79x+35
so
For x=85 miles
substitute
y=0.79(85)=35
y=$102.15
we have that
102.15 > 100
therefore
she not have enough moneyPLEASE HELP I WILL MARK BRAINLIEST!!Which of the following equations is a linear function?A) 2x + 3y = 6B) y = x^2 + 1C) y=x^3D) x^2 + y^2 = 9
Answers
Given data:
The given sets of equations.
The polynomial in which degree of the variable is 1 is said to be linear expression.
The first option 2x+3y=6 is only linear function.
Thus, the option (A) is correct.
A periodic deposit is made into an annuity with the given terms. Find how much the annuity will hold at the end of the specified amount of time. Round your answer to the nearest dollar.Regular deposit:$1300Interest rate:4.2%FrequencyannuallyTime:17 yearsFuture value: $
Answers
SOLUTION
We will use the formula
[tex]FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack[/tex]Where FV represents the future value annuity
P = Periodic payment = 1300
r = interest rate = 4.2% = 0.042
n = number of periods = 17 years.
So we have
[tex]\begin{gathered} FV=P\lbrack\frac{(1+r)^n-1}{r}\rbrack \\ FV=1300\lbrack\frac{(1+0.042)^{17}-1}{0.042}\rbrack \\ FV=1300\lbrack\frac{(1.042)^{17}-1}{0.042}\rbrack \\ FV=31,341.485 \end{gathered}[/tex]Hence, the answer becomes $31,341 to the nearest dollar
The answers available are SSS SAS CPCTC and definition of congruence
Answers
Solution
The diagram below will be of help
From the above, we have two sides to be equal and an angle to be equal
Therefore, the answer Side, Angle, Side (SAS)
y 4 7(x-6)
x-intercept:
y-intercept:
PLEASE ANSWER FAST.
Answers
Answer: y-4=7(x-6)
x-intercept(s): (38/7,0)
y-intercept(s): (0,−38)
I believe this is right hope this helps
Step-by-step explanation:
10Estimate the solution to the following system of equations by graphingOA (1,7)OB. (-1,1)OC.OD. (-1,-1)
Answers
we have the system of equations
-4x + 5y =8
6x - y = 11
Using a graphing tool
Remember that
the solution is the intersection point of both lines
The answer is the option A6. ΔABC is mapped onto ΔA'B'C' by a dilation at D. Complete the statement: The dilation of 4/3 is _____. a. a reduction b. an enlargement
Answers
Dilation involves adjusting the size of an object or a figure, without altering its shape.
The object can be increased or decreased depending on its scale factor.
A scale factor less than 1 results in a figure of reduced dimensions whereas, a scale factor greater than 1 results in a figure or an object of enlarged dimensions.
In the ΔABC, a dilation of 4/3, which is greater than 1, will thus result into an enlargement.
The correct option is B.
The owner of a movie theater was countingthe money from 1 day's ticket sales. He knewthat a total of 150 tickets were sold. Adulttickets cost $7.50 each and children's ticketscost $4.75 each. If the total receipts for theday were $891.25, how many of each kind ofticket were sold?
Answers
65 adult's ticket and 85 children's ticket was sold
Explanation:Let the number of tickets for children = x
Let the number of adults ticket = y
Total tickets = 150
x + y = 150 ....equation 1
The cost of tickets per child = $4.75
The cost of tickets per adult = $7.50
Total revenue from tickets = $891.25
Total revenue from tickets = The cost of tickets per child × number of children ticket +
The cost of tickets per adult * number of adults ticket
891.75 = 4.75(x) + 7.5(y)
891.75 = 4.75x + 7.5y ...equation 2
x + y = 150 ....equation 1
891.75 = 4.75x + 7.5y ...equation 2
Using substitution method by making x the subject of formula in equation 1:
x = 150 - y
Substitute for x in equation 2:
891.25 = 4.75(150 - y) + 7.5y
891.25 = 712.5 - 4.75y + 7.5y
891.25 = 712.5 + 2.75y
891.25 - 712.5 = 2.75y
178.75 = 2.75y
y = 178.75/2.75
y = 65
Substitute for x in equation 1:
x + 65 = 150
x = 150 - 65
x = 85
Hence, 65 adult's ticket and 85 children's ticket was sold
In 2001, Rodney Hampton earned $75,200 as a self-employed worker. He also earned $41,350 as an employee. How much FICA tax did he pay for both earnings? Note:Self-employed tax rate is 15.3% and the employee tax rate is 7.65%.$14,668.88$14,577.25$14,324.09$14,225.50None of these choices are correct.
Answers
Step 1: Rodney Hampton earned $75,200 as a self-employed worker
% tax rate for self employed = 15.3%
[tex]\begin{gathered} =15.3\text{ \% of \$75200} \\ =\frac{15.3}{100}\text{ x \$75200} \\ =11505.6 \\ =\text{ \$11505.6} \end{gathered}[/tex]Step 2: Rodney Hampton earned $41,350 as a employee worker
%tax rate for employee = 7.65%
[tex]\begin{gathered} =\text{ 7.65\% of \$41350} \\ =\text{ }\frac{7.65}{100}\text{ x \$41350} \\ =\text{ 3163.3} \\ =\text{ \$3163.3} \end{gathered}[/tex]Step 3: FICA tax paid for both earnings = $11505.6 + $3163.3
= $14668.875
=$14668.88
Hence FICA tax paid for both earnings = $14668.88
Circumference of a circleThe radius of a circle measures 16 m. What is the circumference of the circle?Use 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Solution:
Given:
[tex]\text{radius of a circle, r = 16m}[/tex]The circumference (C) of a circle is given by;
[tex]\begin{gathered} C=2\pi r \\ \text{where;} \\ C\text{ is the circumference of the circle} \\ r\text{ is the radius} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} r=16m \\ \pi=3.14 \\ C=\text{?} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times16 \\ C=100.48m \end{gathered}[/tex]Therefore, the circumference of the circle is 100.48m
A quadrilateral has two angles that measure 110° and 120°. The other two angles are in aratio of 6:7. What are the measures of those two angles?andSubmit
Answers
From the problem, two angles in a quadrilateral are 110 and 120 degrees.
Note that the sum of interior angles in a quadrilateral is 360 degrees.
Then the sum of the other two angles will be :
[tex]360-(110+120)=130[/tex]And the angles are in a ratio of 6 : 7.
Multiply the ratio by a common factor "x"
[tex]6x\colon7x[/tex]Then take the sum and equate it to 130 degrees.
[tex]6x+7x=130[/tex]Solve for x :
[tex]\begin{gathered} 13x=130 \\ x=\frac{130}{13} \\ x=10 \end{gathered}[/tex]Now, substitute x = 10 to the ratio.
[tex]\begin{gathered} 6(10)\colon7(10) \\ 60\colon70 \end{gathered}[/tex]Therefore, the other two angles are 60 and 70 degrees.
ANSWER :
60 and 70 degrees
Two numbers sum to 61. Twice the first subtracted from the second is 1. Find the numbers.
Answers
x + y = 61
y - 2x = 1
y = 2x + 1
x + (2x + 1) = 61
3x + 1 = 61
3x = 60
x = 20
y = 61 - 20 = 41
Which number line shows the correct solution to 4y - 82-20 ? H 4 -3 -2 -1 0 1 2 3 4 5 HHH O > & -3 -2 -1 0 1 2 3 4 5 HH H -4 -3 -2 -1 0 1 1 2 3 4 5 H → -3 -2 -1 0 1 2 3 4 5
Answers
To find which of the lines represent the solution we first need to solve the inequality:
[tex]\begin{gathered} -4y-8\ge-20 \\ -8+20\ge4y \\ 12\ge4y \\ \frac{12}{4}\ge y \\ 3\ge y \end{gathered}[/tex]the last line is equivalent as:
[tex]y\leq3[/tex]Now that we have the solution we can look at the line that represents it. The solution tells us that y is less or equal to 3, this means that the solutions are to the left of the number 3. Now, since the inequality is not an exact one that means that the 3 is also a solution, which also means that the circle over the 3 has to be a solid one.
With this in mind we conclude that the line representing the solution is the third option.
Find the solutions of the given system of equations: x2 + y2 = 68 and y = 4x.
Answers
Given the system of equations:
[tex]\begin{gathered} x^2+y^2=68 \\ y=4x \end{gathered}[/tex]We can solve it by substituting the second equation into the first as follows:
[tex]\begin{gathered} x^2+(4x)^2=68 \\ \\ Operating: \\ \\ x^2+16x^2=68 \\ 17x^2=68 \end{gathered}[/tex]Dividing by 17:
[tex]x^2=\frac{68}{17}=4[/tex]Applying square root on both sides:
[tex]\begin{gathered} x=\pm\sqrt{4} \\ x=\pm2 \end{gathered}[/tex]There are two solutions for x and they produce two solutions for y.
For x = 2
y = 4*2 = 8
For x = -2
y = 4*(-2) = -8
Thus, the solutions are:
(2,8) and (-2, -8)