Answer: [tex]17.67[/tex]
Step-by-step explanation:
Given
Sample of 12 measurements has a mean of 16.5 and
a sample of 15 measurements has a mean of 18.6
Take [tex]\bar{x_1},n_1[/tex] be the mean and no of measurements
and [tex]\bar{x_2},n_2[/tex] be the mean and no of measurements in second case
[tex]\therefore \bar{x_1}=\dfrac{\sum a_1}{n_1}\\\\\Rightarrow \sum a_1=\bar{x_1}\times n_1\\\\\Rightarrow \sum a_1=198\quad \ldots(1)[/tex]
Similarly,
[tex]\therefore \bar{x_2}=\dfrac{\sum a_2}{n_2}\\\\\Rightarrow \sum a_2=\bar{x_2}\times n_2\\\\\Rightarrow \sum a_2=279\quad \ldots(2)[/tex]
Mean of 27 measurements
[tex]\Rightarrow \bar{x_3}=\dfrac{\sum a_1+\sum a_2}{n_1+n_2}\\\\\Rightarrow \bar{x_3}=\dfrac{198+279}{12+15}\\\\\Rightarrow \bar{x_3}=\dfrac{477}{27}\\\\\Rightarrow \bar{x_3}=17.67[/tex]
I wil Mark BRANLIEST!! HELP!!!! Consider the graphs of linear function f(x) = 3x, quadratic function g(x) = 3x2, and exponential function h(x) = 2x. Which statement about the functions f, g, and h is correct?
A. As x increases, the value of f(x) will eventually exceed the values of g(x) and h(x).
B. As x increases, the value of g(x) will eventually exceed the values of f(x) and h(x).
C. As x increases, the value of h(x) will eventually exceed the values of f(x) and g(x).
D. As x increases, the values of both f(x) and g(x) will eventually exceed the value of h(x).
Here the Graph: https://www.savvasrealize.com/community/proxy/assessment/68bd51a0599744be92849bd2e08be180/images/bdbcc6b2-8670-4ddc-95a2-a48b6d6da348
Answer:
option C
Step-by-step explanation:
Given :
[tex]f(x) = 3x \\\\g(x) = 3x^2\\\\h(x) = 2^x[/tex]
We will just put values for x and check the function :
Let x = 1
f(x) = 3
g(x) = 3
h(x) = 2
Let x = 10,
f(x) = 30
g(x) = 300
h(x) = 1024
Let x = 100
f(x) = 300
g(x) = 30000
h(x) = [tex]1.27 \times 10^{30}[/tex]
Clearly , as x increases value of h(x) exceeds the value of f(x) and g(x).
What is the gradient of the blue line
Answer:
1/4
Step-by-step explanation:
1) Find two points of the line
(4,2) and (8,3)
Gradient = (y2 - y1)/(x2-x1)
(3-2)/(8-4) = 1/4
CAN ANYONE HELP ME WITH THIS QUICKKKKK!
Step-by-step explanation:
You can mention the main values like N = 50 , Efm= 2640 in the answer box and put the formula for calculating mean Efm/N and simply show the answer. Goodluck
help meeeeeeeeeeee (25 points)
Answer:
239 mm^2
Step-by-step explanation:
We will split the figure into 3 pieces
The bottom rectangle
A = l*w = 7*3 = 21 mm^2
The top rectangle
A = l*w = 5*10 = 50 mm^2
The right triangle
A = 1/2 b*h = 1/2 ( 16) * (16+5) = 8 * (21) = 168 mm^2
The total area is 21+50+168 =239
What is the area of a circle with a radius of 3.5cm
Answer:
A≈38.48cm²
Step-by-step explanation:
Answer:
38.48 cm²
Step-by-step explanation:
Area of a circle goes by the formula πr²
Substitute in the value of r;
area = π(3.5)²
= 38.48451 cm²
~ 38.48 cm² (2 d.p.)
Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars
Complete Question
Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars
a) Determine the total amount they will pay for their house
b) How much of the cost will be interest?
c) How much of the first payment on the mortgage is applied to the principal?
Answer:
a) [tex]X=\$289800[/tex]
b) [tex]I=\$169800[/tex]
c) [tex]Y=\$116[/tex]
Step-by-step explanation:
From the question we are told that:
Time [tex]T=25years =>300 months[/tex]
Initial Mortgage [tex]N=140,000[/tex]
Mortgage [tex]N'=120,000[/tex]
Rate [tex]r=8.5\%=>0.085[/tex]
Monthly Mortgage payment P=\%966
a)
The total amount Payable X is mathematically given as
[tex]X=Monthly\ Mortgage\ payment*Number\ of\ months[/tex]
[tex]X=966*300[/tex]
[tex]X=\$289800[/tex]
b)
Generally the equation for Interest I is mathematically given by
[tex]Interest= Total\ amount\ Payable -Mortgage N'[/tex]
[tex]I=289800-120000[/tex]
[tex]I=\$169800[/tex]
c)
Generally the equation for Interest I is mathematically given by
[tex]I=Ptr[/tex]
Where
[tex]t= Month +.1month=>1/12[/tex]
Therefore
[tex]I=120000*1/12*0.085[/tex]
[tex]I=850[/tex]
Therefore the first payment on the mortgage is applied to the principal is
[tex]Y=\$966-850[/tex]
[tex]Y=\$116[/tex]
What is the value of g(3)
Answer:
f(3)=2 (from the right table). g(f(3))=g(2)=-3.
Step-by-step explanation:
lemme get Brainliest please
(125^2 +25^2) (5^2-1) is divisible by 3
Answer:
See Below.
Step-by-step explanation:
We want to prove that the expression:
[tex](125^2+25^2)(5^2-1)[/tex]
Is divisible by three.
We can simplify the second factor:
[tex]=(125^2+25^2)(25-1)\\\\ = (125^2+25^2)(24) \\\\ = (125^2+25^2)(8\cdot 3)[/tex]
Since the second factor is being multiplied by three, we can conclude that the entire expression is divisible by three.
Answer:
It is divisible by 3.
Step-by-step explanation:
(125² + 25²)(5² - 1) ÷ 3
(15625 + 625)(25 - 1) ÷ 3
(16250)(24) ÷ 3
390000 ÷ 3
130000
Adar, Chi, and Melissa each left the party by themselves. In how many different orders can they leave?
A. 5
B. 6
C. 7
D. 9
Pls help me I don’t understand how they got 6 on the first one let alone the rest of the questions. -due tomorrow- will give brainliest—thanks
Answer:
(x, y)
-2, 0
-1, -4
1, -6
2, -4
3, 0
Work:
x^2 - x - 6
(-3)^2 -(-3) - 6
9 + 3 - 6 = 9 - 3 = 6
Just substitute the x values, and solve for y
Answer:
Step-by-step explanation:
[tex]substitute x=-3\\ x^{2} -x-6=(-3)^{2} -(-3)-6=9+3-6=12-6=6[/tex]
The factors of x cube -10x square -53x-42
Answer:
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]
Step-by-step explanation:
[tex]x^3 - 10x^2 -53x - 42[/tex]
The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42
Using trial and error method we will find the first root of the polynomial.
1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42
1 - 10 - 53 - 42 ≠ 0
Therefore 1 is not a root
-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42
- 1 - 10 + 53 - 42
53 - 53 = 0
Therefore - 1 is a root of the polynomial.
Therefore ( x + 1) is a factor.
Now by long division or by using synthetic division we can find other factors.
Synthetic Division :
-1 | 1 -10 -53 - 42
| 0 - 1 11 42
|______________________
1 - 11 - 42 0
Therefore ,
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)[/tex] ------ ( 1 )
Next further factorize x² - 11x - 42
x² - 11x - 42
= x² - 14x + 3x - 42
=x(x - 14) + 3 (x - 14)
=(x + 3 )(x - 14)
Therefore ,
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]
In the diagram below
Answer:
Step-by-step explanation:
Given RT bisects QTS, so
3x+9 = 5x-3
9+3 = 5x-3x
2x = 12
x = 6
Check:
3(6) + 9 = 27
5(6)-3 = 27
checks
78.4 divided by 0.56
78.4 ÷ 0.56 = 140
I just used an online calculator like you could do. But, here you go.
how many whole numbers starting with 1 and ending with 1000 are perfect squares?
Answer:
There are 31 perfect squares between 1 and 1000
Hope it helps❤️
Find the value of (2x-1) -(y+3) when x=3 and y=1
Answer:
1
Step-by-step explanation:
(2*3-1)-(1+3)
(6-1)-4
5-4
1
If this helps you mark as brainlist
Answer:
putting the Given values in equation
(3*3-1)-(1+3)
=8-4
=4
what is (x+2)(x-2) equal ?
Answer:
x^2 - 4
Step-by-step explanation:
since it is in the form of
a^2 - b^2 = (a + b)(a - b)
u can directly write x^2 - 2^2
=x^2 - 4
process :
(x + 2)(x - 2)
=x(x - 2) + 2(x - 2)
=x^2 - 2x + 2x - 4
=-2x and plus 2x gets cancel
=x^2 - 4
Please solve this equation. Thank you!
38x-12y = (6+2n)x + (4-n)y
Step-by-step explanation:
the answer is in the above image
Answer:
39x -12y = (6n+2n)X+(4-n)y
6+2n=38
2n=38-6
2n=32
n=32÷2
n= 16
Evaluate:
will give brainliest
Answer:
80
Step-by-step explanation:
S4 = 2(3°+3¹+3²+3³)
= 2(1+3+9+27)
= 2(40)
= 80
2 consecutive postive nos are such that the sum of their squares is 113. Find the 2 numbers
Answer:
7,8
Step-by-step explanation:
n^2+(n+1)^2=113; this is the information we are provided in the question.
n^2+n^2+2n+1=113 ; just expanding the numbers
2n^2+2n-112=0 ; moving everything to the same side
n^2+n - 56= 0 ; divide everything by two
(n-7)(n+8)=0 : factor the polynomial
so answers for n are: 7 and -8. since the questions asks for positive numbers -8 cannot be correct.
so n=7
n+1 = 8
Paul wants to buy a bicycle that costs $86.50. He has saved $60. He earns $5.30 an hour working after school and can save half of his total earnings. How many hours will he have to work to buy the bicycle?
Answer:
10 hours
Step-by-step explanation:
86.50-60=26.50
5.30/2=2.65
2.65*10=25.50
so 10 hours of work to buy the bicycle
What is the general equation for direct
variation?
Answer:
☆ y=kx
Example: if we have x= 3 and y= 15
Find y?
y= kx
*We know that y= 15 and x= 3
So,
15=k(3)
15=3k
*divide 3 from both sides
K=5
y=5x
y=5(5)=25
☆▪☆▪☆▪☆▪☆
Hope it helps..
Have a great day!!
ABCD is a square. Square A B C D is shown. The length of A B is x + 6 and the length of B C is 2 x minus 1. What is the length of line segment DC? 5 units 7 units 11 units 13 units
Answer:
DC = 13units
Step-by-step explanation:
For a square, all the sides are equal, hence;
AB = BC
x+6 = 2x-1
x-2x = -1-6
-x = -7
x =7
Also DC =AB
DC = x+6
DC = 7+6
DC = 13units
Hence the length of DC is 13units
Answer: 13 units
Step-by-step explanation:
DC = 13 units
Step-by-step explanation:
For a square, all the sides are equal, hence;
AB = BC
x+6 = 2x-1
x-2x = -1-6
-x = -7
x =7
Also DC =AB
DC = x+6
DC = 7+6
DC = 13 units
Hence the length of DC is 13 units
⚠️TEST QUESTION PLEASE HELP DUE IN 5 MINUTES⚠️
Answer:
Step-by-step explanation:
The letter c
A car travels at a speed of s miles per hour. It covers 126 miles in 3 hours.
The equation that can be used to find the value of s is
× s = ??
The speed of the car is ??
miles per hour.
PLEASE HELP (also thanks for the answers on the last couple of questions yall)
Answer:
Step-by-step explanation:
This is a distance = rate times time problem where you are calling the rate "speed" instead. So our formula for distance then is distance = speed times time which is
d = st
The distance traveled in 126 miles and the time it took to do this was 3 hours. Filling in those values gives us
126 = s3 or
126 = 3s since multiplication is commutative. Solve for s by dividing both sides by 3 to get
s = 126/3 which is
s = 42 miles per hour
URGENT: Click on the graph to choose the correct answer to the equation.
x > 2
(Choose one of the pictures as the answer)
Answer:
The first graph.
Step-by-step explanation:
The equation is x is greater than 2. Therefore, the graph needs to shade anything greater than 2, but not 2.
Each pair of figures is similar find the missing sie
Answer:
x = 3
Step-by-step explanation:
since they are similar use these ratios
x/9 = 1/3
do cross multiplication
9*1 = 3*x
9/3 = x
3 = x
80 PTS PLS ANSWER WILL AWARD BRAINLIEST
Answer:
I think it’s A B B A and the last one is D is believe
Step-by-step explanation:
Answer:
2. A
3. A
4. D
5. A
6.
a) 180-n = m
b) 180-40 = 140
7. a) 161-(38+80)=a
b)38+80=118
b)161-118 = 43, a = 43
8. a) NMQ, and NQR
b) NMR and NPR
Step-by-step explanation:
Remember, two vertical angles are always congruent or the same. Complimentary angles equal 90 degrees and supplementary angles equal 180 degrees.
What the car monthly payment?? Show work plz
Answer:
$656.25
p=35000
t=5
r=2.5
interest=ptr/100
=35000x5x2.5/100
=4375
amount=p+i
=35000+4375
=39375
now,
5 yr= 5x12months = 60 months
$39375/60=$656.25
i think so...
what is 65 divded by 487
Answer:
0.13347022587
Step-by-step explanation:
Answer:
7 R 32
Step-by-step explanation:
0 0 7
6 5 4 8 7
− 0
4 8
− 0
4 8 7
− 4 5 5
3 2
Expand and simplify (x - 1)(x + 2)(x - 1)
Answer:
[tex](x - 1)(x + 2)(x - 1)=(x-1)^{2}(x+2)[/tex]
Step-by-step explanation:
Use the product rule [tex]x^{a} x^{b}=x^{a+b}[/tex]
Answer:
x^3 -3x + 2
Step-by-step explanation:
(x - 1)(x - 1) =
x^2 -2x + 1 (x+2) =
x^3 + 2x^2
-2x^ - 4x
x + 2
----------------------------
x^3 -3x + 2