Calculate the sample standard deviation of data from Question 1
76,45,64,80,92

24nk

n=6

k=8

24 × (6) × (8)

24 × (48) = 1152

Answer:

24nk=1152

Step-by-step explanation:

24nk

Substituting the values in the equation

24*6*8

In order to evaluate these values we have to simply multiply the numbers

144*8

I hope it will help you

1152 is the answer

Work Shown:

sec(80) = 1/cos(80) = 5.75877048314363 which rounds to 5.76

Make sure your calculator is in degree mode.

Answer:

3 divided by 10.

Step-by-step explanation:

I'm slightly confused as to what you're asking about, but I could only assume that you want me to represent that fraction as a division problem. In that case, I have listed the answer above. If you want it in decimal form, it is 0.3.

Answer:

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Answer:

15

Step-by-step explanation:

f(x)=5x+40

so f(5)=5(-5)+40

f(5)= -25+40

f(5)=15

Answer:

13.5

Step-by-step explanation:

In triangle ABC, DE || AC

Therefore by basic proportionality theorem:

[tex] \frac{BD}{DA} = \frac {BE}{EC} \\\\

\therefore \frac{4}{8} = \frac {BE}{9} \\\\

\therefore \frac{1}{2} = \frac {BE}{9} \\\\

\therefore BE = \frac{9}{2} \\\\

\therefore BE = 4.5\\

\because BC = BE + EC \\

\therefore BC = 4.5 + 9\\

\huge \red {\boxed {\therefore BC = 13.5}} \\[/tex]

Answer:A D and E

Step-by-step explanation:

Answer:

Step-by-step explanation:

A, D, and E.

The value of x must be equal to 1000

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as

For x > 0 , a > 0, and a ≠1,

y= logₐ x if and only if x = a^y

Then the function is given by

f(x) = logₐx

Given here  log x= 3 ⇒x=10³

                                 ⇒x=1000

Hence, The value of x must be equal to 1000

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Answer:

C. 58 tables

Step-by-step explanation:

If there are 460 people, and each table seats 8 people, then we divide 460 by 8, giving us 57.5 tables. We cannot have a half of a table, so the answer is 58 tables.

Answer:

4 + (-3) = 1

hope this helped :3

4 + (-3) = 1 this is the right answer

Answer:

21

Step-by-step explanation:

You subtract 17 (x - 17) and multiply the answer by 8 (8(x - 17)).  This is equal to 32.  Solve for x

8(x - 17) = 32

8x - 136 = 32

8x = 168

x = 21

Answer: x² + 5x = 3

Step-by-step explanation:Step-by-step explanation:

The rectangle has been divided into a square and three rectangles.

The area of

a square = (x)(x) = x²

a rectangle #1 = (2)(x) = 2x

a rectangle #2 = (3)(x) = 3x

a rectangle #3 = (2)(3) = 6

The area of a large rectangle is the sum of the square area and three rectangles, and is 9 cm². Therefore we have the equation:

x² + 2x + 3x + 6 = 9     subtract 6 from both sides

x² + 5x + 6 - 6 = 9 - 6

x² + 5x = 3

The equation is proven.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The rectangle has been divided into a square and three rectangles.

The areas are;

square = (x)(x) = x²

rectangle 1 = (2)(x) = 2x

rectangle 2 = (3)(x) = 3x

rectangle 3 = (2)(3) = 6

The area of a large rectangle is the sum of the square area and three rectangles, and is 9 cm². Therefore, we have the equation:

x² + 2x + 3x + 6 = 9

x² + 5x + 6 - 6 = 9 - 6

x² + 5x = 3

Hence, proved.

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Answer:

C

Step-by-step explanation:

SA=pi*r^2+pi*r*s

SA=3.14*3^2+3.14*3*8

SA=3.14*9+3.14*24

SA=103.62

SA= about 104 inches

Aubrey included the base (you can't put on a hat that has a bottom), the right work should be:

SAhat=pi*r*s

SAhat=3.14*3*8

SAhat=3.14*24

SAhat=75.36

SAhat= about 75

Thus, answer is C

Answer:

144 p

Step-by-step explanation:

It was due to be returned on 26 November but she returned it on 12 December.

She was therefore with it for an extra 16 days.

The fine is 9p per day. Therefore, she will pay a fine of:

9 * 16 = 144 p

Answer:

Amelia rented a DVD and it was due to be returned on 26 November. She actually returned it to the shop on 12 December. The rental shop applies a fine of 9p for every day the DVD is overdue.

Work out the total fine paid by Amelia. Give your answer in £

Answer:

9.90 inches

Step-by-step explanation:

Area of a triangle is equal to base times height divided by 2.

[tex]bh/2[/tex]

Base and height is x.

[tex]xx/2=49[/tex]

Solve for x.

[tex]x^2=49 \times 2[/tex]

[tex]x^2=98[/tex]

[tex]x=\sqrt{98}[/tex]

[tex]x=9.899495[/tex]

Answer: 1p/5

Step-by-step explanation:

Answer:

Gina will eat  pound cheese for lunch each day

Explanation

Amount of cheese bought = 1 pound and the amount of cheese used =  pound

So, the remaining amount of cheese

As this  pound cheese is splitting into 5 equal parts, so the amount of each part will be:  ÷ 5 =  ×  =  pound

So, Gina will eat  pound cheese for lunch each day.

Step-by-step explanation:

Answer:

D) 5

Step-by-step explanation:

The smaller triangle is similar to the big triangle with the big triangle with a scale factor of 1.8.

5x × 1.8 = 45

Divide both sides by 1.8

5x = 25

Divide both sides by 5

x = 5

Answer:

[tex]x+y+z \Rightarrow 2+2+6 = 10[/tex]

Step-by-step explanation:

First we have to factor the equation:

[tex]6xyz+30xy+21xz+2yz+105x+10y+7z=812[/tex]

The commom factor of first three terms and [tex]105x[/tex] is [tex]3x[/tex]. Note that [tex]105x=3x(35)[/tex]

[tex]3x(2yz+10y+7z+35)+2yz+10y+7z=812[/tex]

[tex]3x(2yz+10y+7z+35)+(2yz+10y+7z)=812[/tex]

In order to have two equal factors add 35 both sides:

[tex]3x(2yz+10y+7z+35)+(2yz+10y+7z+35)=847[/tex]

Let's factor [tex](2yz+10y+7z+35)[/tex]

[tex](2yz+10y+7z+35) \Rightarrow 2y\left(z+5\right)+7\left(z+5\right) \Rightarrow \left(z+5\right)\left(2y+7\right)[/tex]

Now we have:

[tex]3x(z+5)\left(2y+7\right)+\left(z+5\right)\left(2y+7\right)=847[/tex]

[tex](3x + 1) (2y + 7) (z + 5) = 847[/tex]

Now it is the interesting part: You have to figure out that 3 numbers multiplied by each other will result in 847.

We have [tex]847 = 7 \cdot 11 \cdot 11[/tex]

Let's try

[tex]2y+7=7\\2y=0[/tex]

I will stop right here. This is not true.

Let's try then

[tex]2y+7=11\\2y=4\\y=2[/tex]

Now let's try

[tex]z+5 = 11\\z=6[/tex]

Now let's try

[tex]3x+1=7\\3x=6\\x=2[/tex]

Note that in this case I didn't considered [tex]3x+1=11[/tex] because it would not be an integer.

Therefore,

[tex]x+y+z \Rightarrow 2+2+6 = 10[/tex]

Answer:

G(x)=-(x+3)+6

Step-by-step explanation:

f(x) means that whatevers in the parentheses is x. In g(x) x is equal to x+3

Answer:

If f and h are inverses, then:

f (h(x) ) = x   and also

h( f(x) ) = x

Step-by-step explanation:

Inverse function: The function f(x) goes from domain to range and the inverse function f^{-1} goes from Range to domain

Option C is correct

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Answer:

30 days

Step-by-step explanation:

There are 6 * 7 = 42 days in 6 weeks.

There are 2 * 6 = 12 weekends in 6 weeks.

42 - 12 = 30

Answer:

30 days

Step-by-step explanation:

Answer:

f(x) = x² - 81 = ( x+ 9)(x - 9) Difference of two squares

g(x) = x+9/x-9

g(x) . f(x) = x + 9/ x - 9 × (x+9)(x - 9)

= ( x + 9)(x +9)

= ( x + 9)²

= x² + 18x + 81

Hope this helps.

Answer:

2). Volume = 14400 feet³

3). Volume = 157.5 ft³

Step-by-step explanation:

Both the figures given in the sheet attached are a rectangular pyramid and a triangular prism.

2). In this part of the question solid given is in the shape of an rectangular pyramid.

Volume of this oblique pyramid = [tex]\frac{1}{3}(\text{Base})(\text{Height})[/tex]

Here 'B' = area of the base

h = height of the pyramid

Volume = [tex]\frac{1}{3}(25\times 36)\times 48[/tex]

             = 14400 cubic feet

4). Volume of a triangular cone = (Area of the triangular base)×(height)

                                                    = [tex][\frac{1}{2}(\text{Base})(\text{height})]\times {\text{height of the prism}}[/tex]

                                                    = [tex]\frac{1}{2}(7\times 9)\times {5}[/tex]

                                                    = 157.5 ft³

Answer:

31.

Step-by-step explanation:

1. Write out the problem.

6w-19 + k; w=8 and k=2

2. Figure out the first part of the problem.

So, if w=8 and 6 and w are next to each other, we should multiply 6*8, which is 48. Next, it says to subtract 19. 48-19=29.

3. Find out what the last part of the problem is.

Since the first part of the problem is 29 and k=2, we should add 29+2=31, which is the final answer.

Hope this helped :)

Answer:

3) 10^12

4) 0.99^4

8) x^12

9) 3/4^6

Step-by-step explanation:

10^(6+5+1)

0.99^(3+1)

x^(6+2+4)

3/4^(2+2+2)

3) 10^12=1000000000000

4)0.99^4=0.96059601

8)x^12

9)(3/4)^6=0.1779...

Answer:

x = 6

Step-by-step explanation:

3 ln x = ln 216

Rewrite 216 as 6^3

3 ln x = ln 6^3

We know that ln a^b = b ln a

3 ln x = 3 ln 6

x = 6

Answer:

C

Step-by-step explanation:

2 units right and 3 units up

Answer:

(x + 6 )(x + 6 )

2 numbers to add to 12 but also multiply to get 36

Answer:

(x+6)(x+6)

Step-by-step explanation:

x^2 + 12x + 36

What 2 numbers multiply to 36 and add to 12

6*6 =36

6+6 =12

(x+6)(x+6)

Answer:

a) g(f(x)) = (sqrt(x - 5))^2 + 1 = x - 5 + 1 = x - 4

b) For f(x), domain is x - 5 >= 0, or x >= 5, so for g(f(x)), the domain is

x >= 5

The  solutions of the equation 2x²+7x+3=0 are x=-1/2 and x=-3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation is 2x²+7x+3=0

Two times of x square plus seven times of x plus three equal to zero is the form of quadratic.

We can solve the quadratic equation  2x²+7x+3=0 using factoring

Let us find two numbers whose product is 2x²+7x+3=0 and

whose sum is 7.

We can see that 2x²+7x+3=0

Let us factor by grouping

2x²+6x+x+3=0

2x(x+3)+(x+3)

=(2x+1)(x+3).

x=-1/2 and x=-3

Therefore, the solutions are x=-3 and x=-1/2.

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