Answer:
n = 17
Step-by-step explanation:
Method 1The difference between the 5th and 6th terms is 13 - 11 = 2
Therefore, the next term can be found by adding 2 each time.
If we continue with this sequence, we get:
5 = 11
6 = 13
7 = 13 + 2 = 15
8 = 15 + 2 = 17
9 = 17 + 2 = 19
10 = 19 + 2 = 21
So n = 17
-------------------------------------------------------------------------------------
Method 2Arithmetic sequence
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven terms of the sequence:
[tex]a_5=11\\a_6=13\\a_8=n\\a_{10}=21[/tex]
The common difference can be found by subtracting one term from the next term:
[tex]d=13-11=2[/tex]
To find a, substitute the found value of d into the equation for one of the given terms:
[tex]\begin{aligned}a_5 =a+(5-1)2 & =11\\ a+8 & =11\\ a & = 3\end{aligned}[/tex]
Therefore, the formula to find the nth term is:
[tex]\implies a_n=3+(n-1)2[/tex]
[tex]\implies a_n=2n+1[/tex]
So, the 8th term is:
[tex]\implies a_8=2(8)+1=17[/tex]
Lets form a equation
(5,11)(6,13)Slope:-
m=13-11/6-5=2Equation:-
y-11=2(x-5)So
Put x=8
n-11=2(8-5)n-11=2(3)n-11=6n=17select the equivalent expression (3^3*6^6)^-3
Answer:
[tex]\textsf{B)} \quad \dfrac{1}{3^9 \cdot 6^{18}}[/tex]
Step-by-step explanation:
[tex](3^3 \cdot 6^6)^{-3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{(3^3 \cdot 6^6)^3}[/tex]
[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^c \cdot b^c:[/tex]
[tex]\implies \dfrac{1}{(3^3)^3 \cdot (6^6)^3}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{1}{3^9 \cdot 6^{18}}[/tex]
[tex]\\ \rm\Rrightarrow (3^3.6^6)^{-3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{(3^36^6)^3}[/tex]
(a^n)^m=a^mn[tex]\\ \rm\Rrightarrow \dfrac{1}{3^96^{18}}[/tex]
Option B
M is the point (3, -3) and N is the point (7,5). P is a point on the line MN such that MP = 1/3MN. - (a) Find the position vector of P. (b) Calculate the magnitude of MN
Answer:
[tex]P=\left(\dfrac{13}{3},-\dfrac{1}{3}\right)[/tex]
[tex]|\overrightarrow{MN}|=4\sqrt{5}[/tex]
Step-by-step explanation:
Part (a)
[tex]x_P=\dfrac13(x_N-x_M)+x_M=\dfrac13(7-3)+3=\dfrac{13}{3}[/tex]
[tex]y_P=\dfrac13(y_N-y_M)+y_M=\dfrac13(5-(-3))+(-3)=-\dfrac13[/tex]
[tex]\implies P=\left(\dfrac{13}{3},-\dfrac{1}{3}\right)[/tex]
Part (b)
The magnitude of MN is the distance between points M and N.
Using the distance between two points formula, where
[tex](x_1,y_1)=(3,-3)[/tex] and [tex](x_2,y_2)=(7,5)[/tex]
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\implies |\overrightarrow{MN}|=\sqrt{(7-3)^2+(5-(-3))^2}[/tex]
[tex]\implies |\overrightarrow{MN}|=4\sqrt{5}[/tex]
What is the perimeter of the parallelogram?
Please help! Will mark brainlyest.
Answer:
58
Step-by-step explanation:
B=base
A=side
X=2(a+b)=2·(13+16)=58
Step-by-step explanation:
58 maybe coz I got 58 so??
A survey was done where boys and girls were asked if they would prefer to play inside or outside. The results of the survey are shown in the two-way frequency table.
Play inside Play outside
Boy 0.252 0.329
Girls 0.203 0.216
What percent of the boys surveyed prefer to play inside?
Enter your answer to the nearest tenth of a percent in the box.
%
Answer:
25.2% of the boys want to play inside
Step-by-step explanation:
Answer:
1/125 probability for each student so, a 0.8 percent probably of winning per student.
Step-by-step explanation:
What is the solution to the equation below?
Help Me please Its on inequality’s
Answer:
Yes
Step-by-step explanation:
y > 3x + 6
-8 > 3(-5) + 6
-8 > -15 +6
-8 > -9
-8 is greater than -9
find the mean weight of 3,2,26,9
Answer:
10
Step-by-step explanation:
Add all the numbers : 3+2+26+9 = 40
Divide the total with the number of data you have which is 4 so 40÷4= 10
The following two-way table represents data from a survey asking students whether they have visited alaska, hawaii, or both. a 4-column table with 3 rows. the first column has no label with entries hawaii, not hawaii, total. the second column is labeled alaska with entries 6, 8, 14. the third column is labeled not alaska with entries 15, 21, 36. the fourth column is labeled total with entries 21, 29, 50. what is the relative frequency for students who have been to alaska? what is the relative frequency for students who have been to hawaii but not alaska? what is the relative frequency for students who have not been to alaska or hawaii?
Relative frequency is frequency relative to some quantity, usually the marginal or total frequency. The needed relative frequencies are: 14/50, 15/50, and 44/50 respectively.
How to find the relative frequency?Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).
The two way table given is:
Alaska Not Alaska Total
Hawaiii 6 15 21
Not Hawaii 8 21 29
Total 14 36 50
Calculating the needed relative frequencies one by one:
Case 1: The relative frequency for students who have been to Alaska
Total students who went to Alaska= 14Total number of students in survey = 50Thus, the relative frequency for students who have been to Alaska (relative to total count) is 14/50
Case 2: The relative frequency for students who have been to Hawaii but not Alaska
Total students who went to Hawaii but not Alaska= 15Total number of students in survey = 50Thus, the relative frequency for students who have been to Alaska (relative to total count) is 15/50
Case 3: The relative frequency for students who have not been to Alaska or Hawaii
Total students who haven't been to Alaska or Hawaii = total students's count - those who have been to both Hawaii and Alaska = 50 - 6 = 44Total number of students in survey = 50Thus, the relative frequency for students who have been to Alaska (relative to total count) is 44/50
Thus, the needed relative frequencies are: 14/50, 15/50, and 44/50 respectively.
Learn more about relative frequency here:
https://brainly.com/question/8358304
what is 55-22 asap I USED MY HANDS BUT -_-
Answer:
33 there you go
Step-by-step explanation:
Expand and fully simplify 3(x + 1) + 2(3x + 4)
Answer:
[tex]\Large\boxed{\sf{9x+11}}[/tex]Step-by-step explanation:
Given:
Isolate the term of x from one side of the equation.
Use the distributive property.
DISTRIBUTIVE PROPERTY:
[tex]\Longrightarrow: \sf{A(B+C)=AB+AC}[/tex]
Each term within the parentheses can be multiplied by a factor outside the parentheses.
3(x+1)
3*x=3x
3*1=3
Rewrite the expression down.
3x+3
3x+3+2(3x+4)
Multiply expand.
2(3x+4)
2*3x=6x
2*4=8
6x+8
3x+3+6x+8
Combine like terms.
3x+6x+3+8
Add the numbers from left to right.
3+8=11
3x+6x+11
Add.
Solutions:
3x+6x=9x
[tex]\Longrightarrow: \boxed{\sf{9x+11}}[/tex]
Therefore, the final answer is 9x+11.I hope this helps. Let me know if you have any questions.
Scientists have determined that the amount of carbon dioxide in the atmosphere can be modeled by the equation y = 2x + 368, where x is the number of years since the turn of the century and y is the amount of carbon dioxide in parts per million. Which of these statements are correct according to the model? Select all that apply.
A Every year the amount of carbon dioxide in the atmosphere increases by 2 parts per million.
B Every 2 years the amount of carbon dioxide in the atmosphere increases by 1 part per million.
C 10 years from now there will be 5 more parts per million of carbon dioxide in the atmosphere than there are now.
D 10 years from now there will be 20 more parts per million of carbon dioxide in the atmosphere than there are now.
E 10 years from now there will be 373 parts per million of carbon dioxide in the atmosphere.
F 10 years from now there will be 388 parts per million of carbon dioxide in the atmosphere.
Answer:
A and D
Step-by-step explanation:
A true
B false
C false
D true
E false
F false ==> 10 years from now is 32 years since turn of century = x
there will be 2 (32) + 388 = 452 ppm
please please please help meee
Answer:
-5 ≤ x ≤ 5
Step-by-step explanation:
If x^2 = 25
x = -5 or 5
BUT inequality
IF x is POSITIVE 5
You can square root both sides
x ≤ 5
IF x is NEGATIVE 5
You can divide both sides by -5
BUT switch inequality sign
This is because basically dividing both sides by negative
x ≥ -5
FINAL INEQUALITY
-5 ≤ x ≤ 5
MATH
NATION
Which of the following statements are true? Select all that apply.
The correlation coefficient gives us information as to how strong the linear association is between two qualitative variables ?
Answer:
1,3
Step-by-step explanation:
The value of y varies directly with x, and when x = y = 25. What is the value of
HELP A GIRL OUT
Answer:
A 233.3 or 233 1/3
Step-by-step explanation:
X =1/4
Y =25
1/4 X 100= 25
2 1/3 X 100= 233.3
lol
Name:
Unit 10: Circles
Date:
Per
Homework 9: Standard Form of a Circle.
** This is a 2-page document! **
Directions: Graph each circle and identify its center and radius.
1. (7-6) + (x - 1) = 9
2. (x-2) + ( + 3) = 36
I
do
Furn
ѕ соmn
Center:
Center:
st ccm
en
Radius:
Radius:
M
3.8+(+2) - 64
4. (x + 4)' +(3-5) = 25
Center
Center
The centers and radius for the equations are:
1) (1, 6) and radius 32) (2, -3) and radius 63) (-4, 5) and radius 5And the circles are in the graph below.
How to identify the center and radius of a circle?
A general circle equation centered at the point (a, b), with a radius of R, is written as:
(x - a)^2 + (y - b)^2 = R^2
Then for the given equations we have:
1) (y-6)^2 + (x - 1)^2 = 9
So the center is at (1, 6) and the radius is 3.
2) (x-2)^2 + (y + 3)^2 = 36 = 6^2
So the center is at (2, -3) and the radius is 6.
3) (x + 4)^2 +(y-5)^2 = 25 = 5^2
So the center is at (-4, 5) and the radius is 5.
The graphs of the 3 circles can be seen below. Green is the first circle, blue is the second circle, and red is the last circle.
If you want to learn more about circles, you can read:
https://brainly.com/question/1559324
Answer:
Step-by-step explanation:
0/1 Hannah went to the store and spent $14. 69 on a book, $20. 99 on a shirt, and $5. 99 on a pack of pencils. If she paid with a $50 bill, what would be her change? Do not use a calculator. Don't forget a Dollar Sign $!
Answer:
$8.33
Step-by-step explanation:
$14.69 50.00
+ $20.99 - 41.67
=35.68 = $8.33
+5.99
=$41.67
I would really like some help with this problem, if anyone can help me with this problem I will appreciate it, thank you advance.
HELP ASAP!!! Reflect the triangle across the dashed line and enter the new coordinates. Enter the number that belongs in the green box. ALL ANSWERS PLEASE!!! WILL MARK BRAINLIEST!!!
Answer:
Step-by-step explanation:
The triangle is being reflected over the y-axis.
The rule for a reflection over the y-axis is (x, y) → (x, -y)This means that the x-values stay the same while the y-values change.A(x, y) → (x, -y)
A(1, 4) → (1, -4)
A'(1, -4)
B(x, y) → (x, -y)
B(4, 3) → (4, -3)
B'(4, -3)
C(x, y) → (x, -y)
C(2, 1) → (2, -1)
C'(2, -1)
Hope this helps!
jorden linvested $800 in a savings account. The intest rate id 6%per. Find the simple intrest earned in 3 years. then find the total prinabal plus interst
Answer:
interest: $144principal plus interest: $944Step-by-step explanation:
The amount of interest is found using the simple interest formula. That is added to the principal to find the total account balance.
__
InterestI = Prt . . . . . P = principal, r = annual rate, t = number of years
I = $800·0.06·3 = $144
The simple interest earned in 3 years is $144.
__
Principal plus interestAdding that to the principal gives ...
$800 +144 = $944
The total principal plus interest is $944.
Select the correct answer from each drop-down menu. using the distributive property to factorize the equation 3x2 24x = 0, you get . the solution of the equation is .
Using the distributive property to factorize the equation 3x² + 24x = 0, you get 3x(x + 8) = 0 and the solution of the equation is x = -8
How to factorize the expression?The expression is given as:
3x² + 24x = 0
Factor out 3x
3x(x + 8) = 0
Divide both sides by 3x
x + 8 = 0
Subtract 8 from both sides
x = -8
Hence, the solution of the equation is x = -8
Read more about factorized expressions at:
https://brainly.com/question/7438300
Answer:
3x(x + 8) = 0 and x = -8
Step-by-step explanation:
It was correct for me
1323 flowers, each vase has to have exactly 8 flowers, how many vase
Answer:
Step-by-step solving
Step-by-step explanation:
Looking at this problem you are going to need to divide the numbers already given to firgure out how many flower vases fit exactly 8 flowers-
1323 divided by 8= the answer I got was a decimal(165.375) you could always round or re-look at the problem, but you can't have a half of a vase so you would need to round to a whole number. Maybe insert a picture of the problem just incase you might of not added some things in the question. hope this helps.
What is true about the solution(s) to this system of linear equations?
On a coordinate plane, the same line has equation y = one-fourth (x minus 4) and y = one-fourth x minus 1).
The solution is (4,0).
There is no solution.
The solution is (0,−1).
There are infinitely many solutions.
The options that are true about the system of linear equations are;
A) The solution is (4,0).
C) The solution is (0,−1).
D) There are infinitely many solutions.
What is the solution to the linear equation graph?From the given linear equation graph, we see that the linear equation that is graphed is given by;
y = ¹/₄x - 1
Now, the solution to the given equation will be the value of x that corresponds with the value of y when traced on the graph.
Let us access (4, 0)
At x = 4, we have;
y = ¹/₄(4) - 1
y = 0
Thus, (4, 0) is a solution of the graph.
Let us access (0, -1)
At x = 0, we have;
y = ¹/₄(0) - 1
y = -1
Thus, there are many solutions to the graph
Read more about linear equation graph at; https://brainly.com/question/26148595
#SPJ1
How much lower is -124 than 2,194
Answer: -124 - 2,194= -2408
(I think this is right, but if not i'm sorry!)
Answer: 2318
Step-by-step explanation: 2194- (-124)=
2318
|2x-5|=9 please awnser i need this for math
Answer:
7
Step-by-step explanation
2x = 14
divide by 2
90 over 7 EndFraction divided by 1 and three-fourths
Answer:
7[tex]\frac{17}{49}[/tex]
Step-by-step explanation:
[tex]\frac{90}{7}[/tex]÷1 [tex]\frac{3}{4}[/tex]
= [tex]\frac{90}{7}[/tex]×[tex]\frac{7}{3}[/tex] ( keep change flip )
= [tex]\frac{360}{49}[/tex]
=7[tex]\frac{17}{49}[/tex]
I’m struggling with this question need some help
The heights of 100 people in an office building were recorded and the results were normally
distributed. Which histogram shows a normal distribution that could represent this data?
Answer:
d
Step-by-step explanation:
In money in a savings account earned 8.5% intrest per annum, how much interest would be earned on $200.00 over two years?
Answer:
$1305.91
Step-by-step explanation:
To solve this, we can use the geometric sequence formula
[tex]\alpha _n=a_1*r^n^-^1[/tex]
If we plug in our values we get [tex]\alpha _n=200*1.085^2^3[/tex]
Thus, leaving us with 1305.91
Hope this helps
What is the value of x?
10
X
8
Answer:
ans = 6
Step-by-step explanation:
using pythoras theorem:
Hyp^2 = Opp^2 + Adj^2
10^2 = x^2 + 8^2
100 = x^2 + 64
x^2 = 100 - 64
x^2 = 36
x = √36
x = 6.
Hope this helps .
How many minutes should I spend on each question with a 75 question test and a 3 and a half hour time limit?
you should try to keep it under 5 minutes.
since there will be easier ones and harder ones, its ok to take up to 10 minutes on a test as long a you try to get the easy ones done first. if you can skip questions then go back to them later, do the hardest ones first thengo back and do the easier ones afterwards.
Try to take your time when you need to. if you get stuck, think about what it says. Try to think of it another way. You also want to get as much done as you can, this is because if you miss 5-10 questions, the grade could be seriously decreased, as you might have gotten a few other questions wrong.
Make sure to do a "QC" as I call it; or a "Quick Check." If it looks good and it's reasonable then you are fine to move on. it it doesnt look right, retrace your steps. Then rewrite it if you got something else on your next try for the QC.
I hope you do good!
May luck be with you!