Answer:
The general rule for the nth term of this sequence will be:
[tex]a_n=3na+9a[/tex]
Step-by-step explanation:
Given the sequence
12a, 15a, 18a, 21a, 24a,...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
Here,
a₁ = 12a
computing the differences of all the adjacent terms
d = 15a-12a = 3a, d = 18a-15a=3a, d=21a-18a=3a, d=24a-21a=3a
using the nth term formula
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting a₁ = 12a, d = 3a
[tex]a_n=12a+\left(n-1\right)3a[/tex]
[tex]=12a+3na-3a[/tex]
[tex]=3na+9a[/tex]
Therefore, the general rule for the nth term of this sequence will be:
[tex]a_n=3na+9a[/tex]
A class has average height of 68 inches and a standard division of 2 inches what height do you need to be taller than 90% of the class please round your answer to the nearest thousandth.
Answer:
65.426
Step-by-step explanation:
Given that:
Mean height (m) = 68 inches
Standard deviation (s) = 2 inches
Height required to be taller than 90% of the class :
P(Z > x) = 0.9
The corresponding Zscore is - 1.282 (Z probability calculator)
Using the Zscore relation :
Zscore = (x - m) / s
-1.282 = (x - 68) / 2
-1.282 * 2 = x - 68
-2.564 = x - 68
-2.564 + 68 = x
x = 65.436
I need help bad I will mark you as king or what every pkz get it right I can’t get it right plz help
Answer:
d=6c it looks like. good luck
A car is traveling at a rate of 41 miles per hour. At this rate, how many miles will the car will travel in 30 minutes? Pls it will make my christmas
Answer:
41/2=20.5
Step-by-step explanation:
Susan can solve 8 math problems in 20 minutes while Betsy can solve the same 8 math problems at a rate of 1 problem per 5 minutes. Who works faster? Show your work.
Seven pounds of grapes cost $10.43. How much would 4 pounds cost?
Answer:
5.96
Step-by-step explanation:
2. Sandra has earned 284 out of 300 points in Math class. What grade did Sandra
make in her math class? (Round your answer to the nearest whole percent)
Answer:
95%
Step-by-step explanation:
300/284 = 0.946666... rounded the the whole percent is 95%
300 * 95% = 285
Can some one help me plz
Answer:
1b
1
Step-by-step explanation:
A student survey asked: "How tall are you (in inches)?" Here's the data:
67, 72, 73, 60, 65, 86, 72, 69, 74
Give the five-number summary.
A. 60, 67, 72, 73, 74
B.0, 60, 70. 89. 74, 100
C. Median 73 mean: 70.89, interquartile range (IQR): 5, min: 60, max: 74
D. 60, 66, 72. 73.5. 86
Answer:
a
Step-by-step explanation:
Select the statement that indicates that the triangles in each pair are congruent. 50 points
Answer:
C) ΔEFG ≅ΔLMN
Step-by-step explanation:
C) ΔEFG ≅ΔLMN
Please help me I don’t understand.
An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tiles has a length 1/2 inch and width 1/6 inch. The actual tiles have a length 1/3 ft and width 1/9 ft. What is the area of a tile in the model to the area of the actual tile?
Answer:
1 : 64
Step-by-step explanation:
Model:
1/2 in * 1/6 in = 1/12 in^2
Real:
1/3 ft * 1/9 ft = 1/3 * 12 in * 1/9 * 12 in = 16/3 in^2
model : real
1/12 / 16/3 = 1/12 * 3/16 = 3/192 = 1/64
model : real = 1 : 64
Rank in Oder 4/9,2/3,7/12,5/6
Answer:
The sorted inputs in order from least to greatest is:
4/9 < 7/12 < 2/3 < 5/6
Step-by-step explanation:
Using the given inputs:
4/9,2/3,7/12,5/6
The least common denominator (LCD) is: 36
Rewriting as equivalent fractions with the LCD:
4/9, 2/3, 7/12, 5/6
16/36, 24/36, 21/36, 30/36
Sorting this table by the numerators of the equivalent fractions in order from least to greatest:
4/9 7/12 2/3 5/6
16/36 < 21/36 < 24/36 < 30/36
Therefore, the sorted inputs in order from least to greatest is:
4/9 < 7/12 < 2/3 < 5/6
An athlete's target heart rate, in beats per minute, is $80\%$ of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from 220. To the nearest whole number, what is the target heart rate of an athlete who is 26 years old
Answer:
155
Step-by-step explanation:
Since the question states that;
Maximum heart rate= 220 - athletes age
If athletes age = 26 years
Maximum heart rate= 220 - 26 = 194
Again;
athlete's target heart rate= 80% × Maximum heart rate
Athlete's target heart rate= 0.8 × 194= 155
RIGHT TRIANGLES & TRIGONOMETRY MATH
TOMMOROW DUE PLZZZ
Answer:
sin d= 20/29
cos d= 21/29
tan d= 20/21
sin e= 21/29
cos e= 20/29
tan e= 21/20
7) x=47 (25tan(62))
8) x=25.1 (11/sin(26))
9) x=23.8 (32sin(48))
10) x=29.6 (29/cos(12))
11) x=21 degrees (invcos(14/15))
12) x=39.6 degrees (invtan(19/23))
13) x=58 degrees (invcos(9/17))
14) x=72.9 degrees (invsin43/45))
Step-by-step explanation:
good luck m8 it gets harder trust me
also srry if something is wrong im so exhausted thxbye
Please help. First correct answer I’ll mark as brainliest
Answer:
AA similarity, triangle CBA is congruent to triangle CST
Step-by-step explanation:
angle ACB and angle TCS are congruent by the vertical angles theorem
The picture marks that angle B and angle S is congruent
since 2 angles are congruent, the triangles are similar by the AA similarity
There are 15 applicants for four jobs : Computer Programmer , Software Tester , Manager , and Systems Engineer
IS THIS A PERMUTATION OR COMBINATION ?
Answer:
it Permutation 32760
Step-by-step explanation:
it permutation because the order is matter
15p4=32760
This is the case of a combination and the possibility of arrangement is 1365.
What is the combination?The combination is the process of choosing items or things from a bigger group where the order is irrelevant. The combination formula aids in determining the number of possible combinations that can be created by selecting a portion of a bigger set of objects.
Given There are 15 applicants for four jobs: Computer Programmer, Software Tester, Manager, and Systems Engineer.
From the difference between permutation and combination:
A permutation is a method of arranging all the members in order. The combination is a selection of elements from a collection.
Since the order is not asked thus this is the case of a combination
and total arranging possibility = ⁿCₓ
total arranging possibility = ¹⁵C₄
total arranging possibility = 15! /( 11! * 41)
total arranging possibility = 1365
therefore, This is a combination case, and the number of possible arrangements is 1365.
Learn more about combination here:
https://brainly.com/question/17512033
#SPJ2
I dont understand this problem
Answer:
64 ; 8
Step-by-step explanation:
a² ± 2ab + b² = (a ± b)²
x² + 2(8)(x) + 8² =
x² + 16x + 64 =
(x + 8)²
I need help with this!!
Answer:
14 burgers
Step-by-step explanation:
3 1/2 ÷ 1/4 = 14
The following shape is a rhombus. Find the measure of each unknown angle:
90
52
38
46
72
Answer:
63 42
53
53
52
Jdjdjdjfh
Properties of a rhombus:Diagonals of a rhombus intersect each other at 90°. Sum of two adjacent angles of a rhombus is 180°.Diagonals bisect opposite angles.
By using property - 1,
m∠APD = m∠DPC = m∠BPC = m∠APB = 90°
Apply triangle sum theorem in ΔAPD,
m∠DAP + m∠APD + m∠DPA = 180°
52° + 90°+ m∠DPA = 180°
m∠DPA = 38°
By using property - 3,
m∠PDC = m∠DPA = 38°
m∠PAB = 52°
By using property - 2,
m∠ADC + m∠DCB = 180°
2(38°) + m∠DCB = 180°
m∠DCB = 104°
Therefore, m∠PCD = m∠PCB = [tex]\frac{104}{2}[/tex] = 52°
m∠DAP = m∠BAP = 52°
Since, m∠ADC = m∠ABC = 76°
Therefore, mABP = m∠CBP = [tex]\frac{76}{2}=38^\circ[/tex]
Hence, m∠APD = m∠DPC = m∠BPC = m∠APB = 90°, m∠DPA = 38°, m∠PAB = 52°, m∠PCD = m∠PCB = 52°, m∠BAP = 52°, mABP = m∠CBP = 38°.
Learn more about rhombus here,
https://brainly.com/question/11812488?referrer=searchResults
Determine the largest integer value of x in the solution of the following inequality.
3x+9 < -13
Answer:
-7
Step-by-step explanation:
an open top box with a square base and a volume of 4m^3 is to be constructed what should the dimensions of the box be to minimize the surface area of the box?
Answer:
Dimensions of the box:
x = 1,26 ( the side of the square base )
h = 2,52 the heigh of the cube
Step-by-step explanation:
V(b) = x² *h x is the side of the square base, and h the heigh of the cube
The surface area of such cube is:
Area of the base A(b) = x²
Lateral area is 4*x*h
A(c) = x² + 4*x*h
Now x² * h = v = 4 m³ ⇒ h = 4/x² and
A(x) = x² + 4/x
Tacking derivatives on both side of the equation:
A´(x) = 2*x - 4/x²
A´(x) = 0 2*x - 4/x² = 0 ⇒ 2*x³ - 4 = 0
x³ = 2
x = 1,26 m
And h = 4/(1,26)² ⇒ h = 2,52 m
How do we know the value of x = 1,26 is for a minimum value of A(x)
We find the second derivative of A(x)
A´´(x) = 2 - (-4*2*x/x⁴)
A´´(x) = 2 + 8/x³ is positive A´´(x) > 0
Then function A(x) has a minimum value at x = 1,26
What's this? I don't know
Answer:
it's a quadratic formula
Step-by-step explanation:
in the formula, substitute the value of a as 1, b as 2 and c as -8
then, you will get ur answer
The point (5,0) is a solution of 3 x - y > 4.
true or false ?
Answer:
false
Step-by-step explanation:
its not correct
A bag contains 100 marbles. Some are blue, and the rest are white. There are 24 blue
marbles for every 1 white marble. How many blue marbles are in the bag?
Explain your reasoning.
Answer:
there would be 96 blue marbles and 4 white ones
Step-by-step explanation:
theres 100 marbles. every 24 marbles is 1 white marble. 24+1=25 25×4=100 24×4=96 1×4=4
Answer:
96 blue
Step-by-step explanation:
There are 24 blue for every 1 white so
24+1 = 25 blue marbles
25x4 = 100 or the total amount
100(total)-4 (white)
= 96 blue marbles
Number of doctors and lawyers asked whether they prefer to watch medical dramas or court dramas on TV according to the table below the percent of a lawyer surveyed preferred medical dramas
Answer:
Although doctor-centric dramas can be entertaining, they're usually filled with a number of inaccurate portrayals of the medical field.
To see where which popular shows get the details right and which ones are loaded with problems, Insider consulted with real doctors and nurses.
Here's how the experts really feel about popular medical shows.
Note: The Entertainment Value and Medical Accuracy scores on each slide are the averages of the scores (out of 10) that the experts provided for each show.
Step-by-step explanation:
please mark me as brainlest answer hope this helps
An electrician charges a $100 flat fee, plus $75 per hour to work on a house.
Answer:
y=75x+100
Step-by-step explanation:
If F(x)= logx, which statement best describes the transformation (0.5(x-3)) + 12
Given a point A(-3,-14, it is dilated by some scale
factor to A' (-9,-3). If the same dilation is applied
to B(-1,-5), what are the coordinates of B'?
The question was rewritten because it has an obvious mistype.
Answer:
The coordinates of B' are (-3,-15)
Step-by-step explanation:
We are given the point A(-3,-1) and we know it was dilated to the point A'(-9,-3) by some scale factor.
The scale factor can be found by dividing each coordinate of A' by the same coordinate of A. Let's call the factor as k:
k = -9/(-3) = 3
k = -3/(-1) = 3
Thus the scale factor is 3.
If we apply the same factor to B(-1,-5), we get the coordinates of B' as:
B'( 3*(-1) , 3*(-5) ) = B'(-3,-15)
The coordinates of B' are (-3,-15)
A football team loses 7 yards on each of 2 consecutive plays. Find the total change in yards from where the team started.
I NEED HELP ASAP
Which equation represents the situation below?
Bry's account was overdrawn by $11.85, so he deposited $11.85 into his account.
A.
(-11.85) + (-11.85) = 0
B.
(-11.85) – 11.85 = 0
C.
11.85 – (-11.85) = 0
D.
(-11.85) + 11.85 = 0
Answer:
D
Step-by-step explanation:
overdrawn = =negative so -11.85+11.85 or option D
Hope this helps plz hit the crown ;D
25 35 47
17 5 61
11 72 ??
Answer:
There is no pattern to it.
Step-by-step explanation: