A sample of 12 measurements has a mean of 16.5, and a sample of 15 measurements has a mean of 18.6. Find the mean of all 27 measurements

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

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

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]

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

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.

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

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.

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

Answer:

Step-by-step explanation:

The letter c

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

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...

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]

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

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

Answer:

80

Step-by-step explanation:

S4 = 2(3°+3¹+3²+3³)

= 2(1+3+9+27)

= 2(40)

= 80

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

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

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).

Answer:

There are 31 perfect squares between 1 and 1000

Hope it helps❤️

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 ÷ 0.56 = 140

I just used an online calculator like you could do. But, here you go.

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

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

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

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]

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.)

Answer:

f(3)=2 (from the right table). g(f(3))=g(2)=-3.

Step-by-step explanation:

lemme get Brainliest please

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

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!!