Answer:
100
Step-by-step explanation:
We have the sum of first n terms of an AP,
Sn = n/2 [2a+(n−1)d]
Given,
36= 6/2 [2a+(6−1)d]
12=2a+5d ---------(1)
256= 16/2 [2a+(16−1)d]
32=2a+15d ---------(2)
Subtracting, (1) from (2)
32−12=2a+15d−(2a+5d)
20=10d ⟹d=2
Substituting for d in (1),
12=2a+5(2)=2(a+5)
6=a+5 ⟹a=1
∴ The sum of first 10 terms of an AP,
S10 = 10/2 [2(1)+(10−1)2]
S10 =5[2+18]
S10 =100
This is the sum of the first 10 terms.
Hope it will help.
[tex]\sf\underline{\underline{Question:}}[/tex]
If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.
$\sf\underline{\underline{Solution:}}$
$\sf\bold\purple{||100||}$$\space$
$\sf\underline\bold\red{||Step-by-Step||}$
$\sf\bold{Given:}$
$\sf\bold{S6=36}$ $\sf\bold{S16=255}$$\space$
$\sf\bold{To\:find:}$
$\sf\bold{The \: sum\:of\:the\:first\:ten\:numbers}$$\space$
$\sf\bold{Formula\:we\:are\:using:}$
$\implies$ $\sf{ Sn=}$ $\sf\dfrac{N}{2}$ $\sf\small{[2a+(n-1)d]}$
$\space$
$\sf\bold{Substituting\:the\:values:}$
→ $\sf{S6=}$ $\sf\dfrac{6}{2}$ $\sf\small{[2a+(6-1)d]}$
→ $\sf{36 = 3[2a+(6-1)d]}$
→$\sf{12=[2a+5d]}$ $\sf\bold\purple{(First \: equation)}$
$\space$
$\sf\bold{Again,Substituting \: the\:values:}$
→ $\sf{S16}$ $\sf\dfrac{16}{2}$ $\sf\small{[2a+(16-1)d]}$
→ $\sf{255=8[2a + (16-1)d]}$
:: $\sf\dfrac{255}{8}$ $\sf\small{=31.89=32}$
→ $\sf{32=[2a+15d]}$ $\sf\bold\purple{(Second\:equation)}$
$\space$
$\sf\bold{Now,Solve \: equation \: 1 \:and \:2:}$
→ $\sf{10=20}$
→ $\sf{d=}$ $\sf\dfrac{20}{10}$ $\sf{=2}$
$\space$
$\sf\bold{Putting \: d=2\: in \:equation - 1:}$
→ $\sf{12=2a+5\times 2}$
→ $\sf{a = 1}$
$\space$
$\sf\bold{All\:of\:the\:above\:eq\: In \: S10\:formula:}$
$\mapsto$ $\sf{S10=}$ $\sf\dfrac{10}{2}$ $\sf\small{[2\times1+(10-1)d]}$
$\mapsto$ $\sf{5(2\times1+9\times2)}$
$\mapsto$ $\sf\bold\purple{5(2+18)=100}$
$\space$
$\sf\small\red{||Hence , the \: sum\: of \: the \: first\:10\: terms\: is\:100||}$
_____________________________
Hey guys please help me please and thank you
Answer:
B
Step-by-step explanation:
No matter how many times you multiply 1 by itself, it will always be 1 which makes A and D incorrect.
x is a power. The question is 1/4 * 1/4 * 1/4 which is 1/64
Answer: B
Step-by-step explanation:
[tex]f(x)=(\frac{1}{4})^x\\f(3)=(\frac{1}{4})^3\\f(3)=(\frac{1}{4})(\frac{1}{4})(\frac{1}{4})\\f(3)=\frac{1}{64}[/tex]
need help solving this equation right now please
9514 1404 393
Answer:
(5, -6)
Step-by-step explanation:
x-coordinates measure the distance to the right of the y-axis. Moving a point 4 units to the right adds 4 to its x-coordinate.
y-coordinates measure distance up from the x-axis. Moving a point 4 units down subtracts 4 from its y-coordinate.
(1, -2) +(4, -4) = (1 +4, -2 -4) = (5, -6) . . . . image of translated point
In a clinical trial of a certain drug, 17 subjects experience headaches among the 221 subjects treated with the drug. Construct a 95% (Wald) confidence interval estimate for the proportion of treated subjects who experience headaches.
a. Find the best point estimate of the population proportion.
b. Identify the value of the margin of error E.
c. Construct the confidence interval.
d. write a statement that correctly interprets the confidence interval.
Solution :
Given :
n = 221
x = 17
a). [tex]$p=\frac{17}{221}$[/tex]
= 0.076
b). At the 95 confidence interval
Value of z = 1.96
Margin of error
[tex]$=1.96 \times \sqrt{\frac{p(1-p)}{n}}$[/tex]
[tex]$=1.96 \times \sqrt{\frac{0.076(1-0.076)}{221}}$[/tex]
[tex]$=1.96 \times \sqrt{\frac{0.076\times 0.924 }{221}}$[/tex]
= 1.96 x 0.017
= 0.03332
c). confidence interval
= ( 0.076-0.033, 0.076+0.033)
= ( 0.043, 0.109 )
d). The confidence interval does not contain null value, so it is significant.
a test for diabetes results in a positive test in 95% of the cases where the disease is present and a negative test in 07% of the cases where the disease is absent. if 10% of the population has diabetes, what is the probability that a randomly selected person has diabetes, given that his test is positive
Answer:
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Person has diabetes.
Probability of a positive test:
0.95 out of 0.1(person has diabetes).
0.007 out of 1 - 0.1 = 0.9(person does not has diabetes). So
[tex]P(A) = 0.95*0.1 + 0.007*0.9 = 0.1013[/tex]
Probability of a positive test and having diabetes:
0.95 out of 0.1. So
[tex]P(A \cap B) = 0.95*0.1 = 0.095[/tex]
What is the probability that a randomly selected person has diabetes, given that his test is positive?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.095}{0.1013} = 0.9378[/tex]
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
60°
8
30°
х
Determine the value of x.
Answer:
4 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = x / 8
8 sin 60 = x
8 ( sqrt(3)/2) = x
4 sqrt(3) =x
look at the image below
The table shows a linear function.
Which equation represents the function?
x f(x)
-6 -1
-3 4
0 9
3 14
A. f(x)= -5/3x+9
B. f(x)= -5/3x-9
C. f(x)= 9x+5/3
D. f(x)= 5/3x+9
Answer:
D.
Step-by-step explanation:
Try A:
x = -6, f(x) = -1:-
f(-6) = -5/3(-6) + 9
= 10 + 9 = 19 NOT A.
Try B:
f(-3) = -5/3(-3) - 9
= 5 - 9 = -4 NOT B
Try C:
9(0) + 5/3 = 5/4 NOT C
Try D:
f(3) = 5 + 9 = 14
f(0) = 9, f(-6) = -1 and f(-3) = 4
Write the equation of the line in fully simplified slope-intercept form.
From the graph, we can write that
The equatuon of line passes through (0,4) and
(-8,0) points.
So
[tex] \sf \: slope \: \: m = \frac{4 - 0}{0 - ( - 8)} = \frac{4}{8} = \frac{1}{2} \\ \therefore \green{\sf \: m = \frac{1}{2} }[/tex]
Intercept of Y-axis c = 4
So equation is :
[tex] \bf \: y = mx + c \\ \bf = > y = \frac{1}{2} x + 4 \\ \bf = > 2y = x + 4 \\ \bf= > \orange{ \boxed{ \bf \: x - 2y + 4 = 0}}[/tex]
a grocery store cashier packed 2 carts of groceries equally into 12 paper bags. what fraction of a cart is in each bag?
Answer:
Step-by-step explanation:
(2 carts)/(12 bags) = (⅙ cart)/bag
Need the help thanks guys
Answer:
x=−5+√29 or x=−5−√29
Step
Let's solve your equation step-by-step.
x2+10x+10=14
Step 1: Subtract 14 from both sides.
x2+10x+10−14=14−14
x2+10x−4=0
For this equation: a=1, b=10, c=-4
1x2+10x+−4=0
Step 2: Use quadratic formula with a=1, b=10, c=-4.
x=
−b±√b2−4ac
2a
x=
−(10)±√(10)2−4(1)(−4)
2(1)
x=
−10±√116
2
x=−5+√29 or x=−5−√29
The length of a rectangle is (x+1) cm, and its width is 5 cm less than its length.
a) Express the area of the rectangle, A cm^2 , in terms of x.
b) The area of the rectangle is 24 cm^2. Calculate the length and width of the rectangle.
Answer:
a) x^2-3x-4(you also can express it as (x+1)(x-4))
b)The length is 8 cm, the width is 3 cm
Step-by-step explanation:
a) The length is x+1
The width is (x+1-5)= x-4
The area is the product of the length and the width
(x+1)(x-4)= x^2-3x-4
b) The formula for counting the area is x^2-3x-4
It is equal to 24
S0 x^2-3x-4=24
x^2-3x-28=0
a=1 b=-3 c=-28
D= b^2-4ac= 3^2-4*(-28)= 9+112= 121
sqrtD= 11
x1= (-b-sqrtD)/2a=(3-11)/2=-4 The length is -4+1=-3<0, but the length must be positive, this root isn't suitable.
x2= (-b+sqrtD)/2a=(3+11)/2=7 The length is 7+1=8 (it is suitable)
8-5=3 - The width
Mai is kayaking on a river that has a current of 2 miles per hour. If r represents her rate in calm water, then (r + 2) represents her rate with the current, and (r – 2) represents her rate against the current. Mai kayaks 2 miles downstream and then back to her starting point. Use the formula for time,
t
=
d
r
t=
r
d
, where d is the distance, to write a simplified expression for the total time it takes Mai to complete the trip.
4
(
r
+
2
)
(
r
−
2
)
h
o
u
r
s
(r+2)(r−2)
4
hours
4
r
(
r
+
2
)
h
o
u
r
s
(r+2)
4r
hours
4
r
(
r
+
2
)
(
r
−
2
)
h
o
u
r
s
(r+2)(r−2)
4r
hours
4
(
r
−
2
)
h
o
u
r
s
(r−2)
4
hours
Answer:
Plese explain your answer properly
Step-by-step explanation:
Answer:what is the answer
Step-by-step explanation:
The vertex form of the equation of a parabola is y =
standard form of the equation?
Y=1/2(x - 4)^2 +13. What is the
O A. y-2x2-8x+29
O B. y=zx2 - 4x +21
O C. y=1* -8x+21
O D. y - 4x2 - 4x +29
Answer:
Step-by-step explanation:
y = ½(x-4)² + 13
y = ½(x² - 8x + 16) + 13
y = ½x² - 4x + 21
Cho hệ vectơ:
X1=(2;1;0;1); X2=(1;1;0;-1); X3=(0;-1;2;2); X4=(1;0;2;1)
a) Xét xem hệ vectơ trên độc lập tuyến tính hay phụ thuộc tuyến tính.
b) Biểu diễn vectơ X 4 qua các vectơ còn lại.
Answer:
i dont no the ans
Step-by-step explanation:
Dr. Kingston predicted that swearing can help reduce pain. In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeatedly yelled their favorite curse words while their hands were in the water. In the other condition the participants repeated a neutral word. The table below presents the amount of time that participants kept their hand in the ice in each condition.
Swear Words
Neutral Words
98
56
70
61
52
47
87
60
46
32
120
92
72
53
41
31
1. Calculate the mean for the Swear Words condition:_______________
Answer:
Step-by-step explanation:
First, we add them all up.
98+70+52+87+46+120+72+41 = 586
Now, we divide 586 by the number of things there are. 586 / 8 = 73.25.
The mean of the swear words condition is 73.25.
In the figure, triangles ABC and DEF are congruent.
Find the measure of DF.
a. 13m
b. 13m
c. 7m
d. 13.928m
Please show work to help me understand.
since the two triangles are congruent..
AB=ED
AC=FD(side opposite to the right angle)
FD=AC
•°•FD=13m
Add the first 79 terms of this sequence:
-8,-1, 6, 13, 20, ...
Answer:
Sum is 20,935.
Step-by-step explanation:
This is an arithmetic progression.
Sum:
[tex]S = \frac{n}{2} (2a + (n - 1)d) [/tex]
n is the number of terms, n = 79
S is the sum
a is the first term, a = -8
d is common difference, d = -1-(-8) = 7
substitute:
[tex]S = \frac{79}{2} (2 \times - 8 + (79 - 1) \times 7)) \\ \\ S = \frac{79}{2} ( - 16 + 546) \\ \\ S = \frac{79}{2} (530) \\ S = 20935[/tex]
find the principal argument z= -2i
9514 1404 393
Answer:
-π/2
Step-by-step explanation:
The number lies on the negative imaginary axis, at an angle of -π/2 radians from the positive real axis.
__
The principal argument is the angle in the interval (-π, π].
What type of equation is 9x-3y=27
Answer:
a first degree equation
A survey is conducted to determine the percentage of students at state universities who change their major at least once. In a study of 100 students 78% indicated that they graduated with a major different from the one with which they entered college. Determine a 90% confidence interval for the percentage of students who change their major.
Answer:
Step-by-step explanation:
Confidence Level - "P" values
90% 1.645
Confidence Interval - "P" values
(0.7119 , 0.8481 )
Based on the equation 6x + 2y = 30, what is the missing value in the table?
Answer:
x =5
Step-by-step explanation:
hope this helps you
please mark as brainliest
Answer:15
Step-by-step explanation:6x +2y=30
2(3x+y) =30
3x+y=30÷2
3x+y=15
Pauline mixed 0.32 liter of syrup with 12 times as much water to make orange squash.She split 1.28 liter of orange squash.Then she poured the remaining orange squash equally into 4 bottles.How much orange squash were there in each bottle.Give your answer in Liters.
Answer:
0.72 litres
Step-by-step explanation:
Litres of syrup = 0.32 litres
Litres of water = 12 times the amount of syrup = 12 * 0.32 = 3.84 litres
Litres of orange squash = litres of syrup + litres of water
Litres of orange squash = (0.32 + 3.84) = 4.16 litres
Amount of orange squash litres split = 1.28 litres
Amount of orange squash left = (4.16 - 1.28) = 2.88 litres
Splitting the amount of squash left equally into 4 :
2.88 litres / 4 = 0.72 litres
Need help please due in 1 hour and 30 mins
Answer:
the answer of that is number C
(52+2)-3x -6
help me with thanks
Answer:
48 - 3X
Step-by-step explanation:
( 52+2) - 3x - 6
54 - 3x - 6 So first we deal with the numbers in brackets and that is 52 + 2 giving us 54.
54 - 6 - 3x Then you simplify the expression that is collecting like terms so then we subtract 6 from 54
48 - 3x This is the final expression after simplifying
HOPE THIS HELPED
sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0
Recall the angle sum identity for cosine:
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))
Then rewrite the equation as
sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0
1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0
1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0
sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0
-sin(5x) (sin(4x) + sin(2x)) = 0
sin(5x) (sin(4x) + sin(2x)) = 0
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
Rewrite the equation again as
sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0
sin(5x) sin(2x) (2 cos(2x) + 1) = 0
sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0
sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2
sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ
… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π
… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5
sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ
… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π
… … … … … ==> x = nπ or x = (2n + 1)π/2
cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ
… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ
… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ
(where n is any integer)
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
5,20,80,320
Step-by-step explanation:
a1 = 5
an = 4 an-1
Let n = 2
a2 = 4 * a1 = 4*5 = 20
Let n = 3
a3 = 4 * a2 = 4*20 = 80
Let n = 4
a4 = 4 * a3 = 4*80 = 320
I need help guys thanks so much
Answer: A & C
Step-by-step explanation:
[tex]i=\sqrt{-1}[/tex]
[tex]\sqrt{-1} *\sqrt{4} =\sqrt{-4}[/tex]
You can also simplify the above by taking the -4 out of the radical
It becomes 2 x [tex]\sqrt{-1}[/tex], which can be simplifed to C
Need help on polynomial expressions
Answer:- 10[tex]m^{2}[/tex] + 3m -9
Step-by-step explanation: Given ;
A= -3 -m
B= 3m -5[tex]m^{2}[/tex]
2B + 3A
solution
2B + 3A
substitute A and B in the formula
2(3m - 5[tex]m^{2}[/tex]) + 3(-3 -m)
6m - 10[tex]m^{2}[/tex] - 9 - 3m group like terms
- 10[tex]m^{2}[/tex] + (6m -3m) -9
- 10[tex]m^{2}[/tex] + 3m -9
Find the length of the segment indicated.
A. 16.4
B. 11.4
C. 12.1
D. 13.3
using Pythagorean triplet
[tex]\\ \sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \sf\longmapsto x^2=19.6^2-15.4^2[/tex]
[tex]\\ \sf\longmapsto x^2=384.16-237.16[/tex]
[tex]\\ \sf\longmapsto x^2=147[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{147}[/tex]
[tex]\\ \sf\longmapsto x=12.1[/tex]
Answer:
C.) 12.1
Step-by-step explanation:
I got it correct on founders edtell
which of the following are ordered pairs for the given function f(x)=1+x.? (1,2) (3,3) (0,2) (1,0) (0,1)
Answer:
no,
(
1
,
0
)
is not an ordered pair of the function
f
(
x
)
=
1
+
x
.
Step-by-step explanation:
Ordered pairs are usually written in the form
(
x
,
y
)
by tradition.
so usingthe function,
f
(
x
)
=
1
+
x
we can rewrite it as,
y
=
1
+
x
any pair of x and y that satisfy this equation are solutions to the equation.
so subbing in
(
1
,
0
)
,
0
=
1
+
(
1
)
0
=
2
which is not true so the point does not make the function true.
It might be easier to see graphically,
graph{1+x [-10, 10, -5, 5]}
any combination of x and y on this line make the equation true and as such are an ordered pair of the function.
Answer:
Step-by-step explanation:
