Which theorem does it offer proof of?

Answer:

2.5

Step-by-step explanation:

"Four different positive integers have a mean (average) of 100"

The total of the 4 numbers is then 4* 100 = 400

"the positive difference between the smallest and largest of these integers is as large as possible"

to get the greatest difference the first 3 numbers must be

1, 2 and 3 which totals 6

the 4th number is then 400 - 6 = 394

the four numbers are 1, 2, 3 and 394

The greatest difference is between 1 and 394

"the average of the other two integers"

(2 + 3)/2 = 2.5

The average of the other two integers is 1.5.

An integer is an whole number. An example of an integer is 20.

If the mean of the four integers is 100. It means that the sum of the integers must be 400. If the integers are 0,1,2, 397. The largest number is 397 and the smallest number is 0. The average of the other two integers is (1 + 2 ) / 2 = 1.5

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Answer:

£60 per day

Step-by-step explanation:

1 week = 5 days

Dan earned = £300

therefore 1 day = 300 ÷ 5 = £60 per day

Answer:

x = 5

Step-by-step explanation:

24 - 8x = -16

Subtract 24 from both sides.

-8x = -40

Divide both sides by -8.

x = 5

Answer:

5

Step-by-step explanation:

24 - 8x = -16

24 + 16 = 8x

8x = 40

x = 40/8

= 10/2

= 5

Answer:

see explanation

Step-by-step explanation:

The following statements are true

The domain of f(x) is all real numbers

The range of f(x) is all real numbers

f(2) = 4

locate x = 2 on the x- axis, go vertically up to meet the line at (2, 4 ) , then

f(2) = 4

Answer:

7.22 x 10^5

Step-by-step explanation:

Remember that the decimal is always to the right of the ones place.

1. Move it one place to the left and multiply by 10 to compensate.

2. Move it two places to left and multiply by 10^2.

3. Move the decimal point three times and multiply 10^3 to compensate, and the pattern continues until you reach the very last digit, the 7.

4. Numbers after the 7 that are not zeros will be after the decimal point.

so, 7.22 x 10^5

Answer:

M = -2 1/4

Step-by-step explanation:

You can use the formula y2 - y1 / x2 - x1 to get your answer.

y2 is 18 and y1 is 9. x2 is 6 and x1 is 10 so plugging that into the formula above you will get 18 - 9 / 6 - 10.

18 - 9 is 9 and 6 - 10 is -4

9/-4 = M (M is short for slope)

M = -2 1/4

Hope this worked for you.

3 cases /3= $11 /3

1 case x 2= 11/3 x2

2 case = 22/3 = (round to the hundreth) $7.33

Answer:

my suggestion to you is that you use a ruler and a piece of paper to draw out the graph then plot the point down and draw the line.

(I hope this helps you!)

Answer:

2400

Step-by-step explanation:

60(customers/day) x40(days) = 2400 customers in 40 days

Step-by-step explanation:

sum of 2 angles on a straight line = 180°

therefore,

y + 120 = 180

y = 180 - 120 = 60

y = 60°

now apply angle sum property of triangle

now,

50 + x + y = 180

50 + x + 60 = 180

110 + x = 180

x = 180 - 110

x = 70

therefore, x = 70 & y = 60

hope this answer helps you dear! take care

Answer:

x = 70°

y = 60°

Step-by-step explanation:

hope it helps u

plzz plzz pLZZ MARK AS BRAINLIEST

Answer:

>

Step-by-step explanation:

Squares eventually get bigger then when you multiply

Answer:

A & B

Step-by-step explanation:

A rational number is a number that can be written as a fraction or a terminating or repeating decimal. An irrational number is one that cannot be written as a fraction, or one that goes on forever without terminating or repeating in any way. Let's check all of our options and find the ones that are irrational.

Our first option (A) looks irrational! The "..." shows us that it goes on forever, and it doesn't look like it repeats. So this option is irrational.

Our next option is B, the square root of 24. What is the square root of 24? Well, if we look it up on a calculator, we get 4.89897948557..., and it looks like this one doesn't terminate or repeat either. So option B is also irrational.

Option C is the square root of 121. The square root of 121 is 11, which can be written as a fraction (11/1) and is a terminating decimal. So it's rational.

Our last option is D, and it is written already as a fraction, so we know for sure that it's rational. If we divide it out, we get 0.44444... with the 4 going on forever. It's a repeating decimal, and repeating decimals are rational.

So our final answers for which are irrational are A & B.

we have 9x - 7 ≤ 28 + 4x

⇔9x - 4x ≤ 28 +7

⇔5x ≤ 35

⇔x ≤ 7

ok done. Thank to me :>

Answer:

(4 + d) × 2

Step-by-step explanation:

Answer:

  £2.76

Step-by-step explanation:

The cost of Amy's purchase is ...

  16×(£0.14) = £2.24

Her change from £5.00 is ...

  £5.00 -2.24 = £2.76 . . . . Amy's change

Using similar triangles formed by the fence, and the house, the top of which the property line passes, the height of the house can be determined.

Reasons:

The given parameters are;

Height of the fence = 12 foot

Length of the shadow cast by the fence = 25 foot

Distance of the house from the property line = 60 feet

The maximum allowable height for the house.

Solution:

Using similar triangles, we have;

[tex]\displaystyle \frac{Height \ of \, fence}{Length \ of \ fence \ shadow} = \mathbf{\frac{Height \ of \, house}{Distance \ of \ house\ from \ property \ line}}[/tex]

Which gives;

[tex]\displaystyle \frac{12}{25} = \mathbf{\frac{Height \ of \, house}{60}}[/tex]

[tex]\displaystyle Height \ of \ house = \frac{12}{25} \times 60 = 28.8[/tex]

The height of the house = 28.8 feet

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Please find attached the drawing of the question created with MS Visio, obtained from a similar question online.

Answer:

EZ

Step-by-step explanation:

A. 15 Percent

B. 40 Percent

Answer:

A) 15% B) 40%

Step-by-step explanation:

Answer:

1st , 2nd , and 4th

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

so we know m<3=70

m<2=90

m<2+m<1=m<4

try 50?

let me know if it is wrong

Answer:

You can make as many as you want, infinitely smaller but you need to specify the size of the brownies

Step-by-step explanation:

Answer:

500: starting amount

(1 + 0.02): interest/growth rate

x: time

Step-by-step explanation:

Answer:

2 months

Step-by-step explanation:

To solve this equation create an expression for the cost of each club. Use the slope-intercept form of y=mx+b where m is the monthly fee and b is the flat fee. So the 2 expressions would be A) 29x+14 and B) 22x+28. Since we want to find when these are equal, set the expressions equal to each other. This gives the equation 29x+14=22x+28. Then, solve for x.

When solved, x=2. This means that after 2 months the cost of each will be the same.

Answer:

C=66, C=25 1/7

Step-by-step explanation:

i

C=pi(d)

C=22/7*21

C=66

ii

C=pi(d)

C=22/7*16

C=25 1/7

Answer:

(2;5)

Step-by-step explanation:

Elimination:

Let's first multiply the first by 2 to clear fractions and write them both in standard form:

[tex]\left\{ {x-2y=-8} \atop {2x+y=9}} \right. \\[/tex]

Eliminate x: Multiply the first by 2, then subtract the equations:

[tex]2I-II: 2x-4y-2x-y=-16-9\\-5y=-25 \rightarrow y= 5[/tex]

Eliminate y: Multiply the second by 2, then add equations:

[tex]I+2II: x-2y +4x+2y = -8+18\\5x=10 \rightarrow x=2[/tex]

Subtsitution

Solve the first for y (oh, what a coincidence, it's done already!) and replace the value in the second.

[tex]\frac12x +4 = -2x+9 \rightarrow \ x+8=-4x+18\\x+4x = 18-8 \rightarrow 5x=10 \rightarrow x=2[/tex]

Then let's plug this value into a convenient one - let's say, the first - and find y from there:

[tex]y=\frac12\cdot 2 +4\rightarrow y =1+4 \rightarrow y=5[/tex]

If anyone tries saying it's not substitution, bring the system in standard form, as you did for the elimination method, then solve again for y.

The value of [tex]x[/tex] is 29.

The formulae for the surface area ([tex]A_{s}[/tex]) and volume ([tex]V[/tex]) are, respectively:

[tex]A_{s} = 2\cdot (h\cdot l + w\cdot l + h\cdot w)[/tex] (1)

[tex]V = w\cdot h \cdot l[/tex] (2)

Where:

According to the statement, we must equalize (1) and (2) and substitute the remaining variables:

[tex]2\cdot (h\cdot l + w\cdot l + h\cdot w) = w\cdot h\cdot l[/tex]

[tex]2\cdot h\cdot l + 2\cdot w \cdot l + 2\cdot h\cdot w = w \cdot h \cdot l[/tex]

[tex]2\cdot \log_{2}x\cdot \log_{4}x+2\cdot \log_{3}x\cdot \log_{4}x+2\cdot \log_{2}x\cdot \log_{3}x = \log_{2}x\cdot \log_{3}x\cdot \log_{4}x[/tex]

By applying logarithm properties, we simplify the expression:

[tex]2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right) = \log_{2}x \cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right)[/tex]

[tex]2\cdot \left[\frac{1}{\log_{2}4}+\frac{1}{\log_{2}3\cdot \log_{2}4}+\frac{1}{\log_{2}3}\right] = \left(\frac{1}{\log_{2}3\cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]

[tex]2\cdot \left(\frac{\log_{2}3+\log_{2}4+1}{\log_{2}3\cdot \log_{2}4} \right) = \left(\frac{1}{\log_{2}3 \cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]

[tex]\log_{2}x = 2\cdot (\log_{2}3 + \log_{2}4+1)[/tex]

[tex]\log_{2}x = \log_{2}9 + \log_{2}16 +2[/tex]

[tex]x = 9 + 16 + 4[/tex]

[tex]x = 29[/tex]

The value of [tex]x[/tex] is 29.

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Nota - The statement of this question presents typing mistakes and is also incomplete, the corrected form is presented below:

A right rectangular prism whose surface area and volume are numerically equal has edge lengths [tex]\log_{2} x[/tex] (height), [tex]\log_{3}x[/tex] (width) and [tex]\log_{4}x[/tex] (length). What is [tex]x[/tex]?

To solve this issue, first we have to match the denominators, for this we have to take the LCM from the denominators 5.6, Then just solve the fraction normally, See:

[tex]\sf \dfrac{4x}{5}+\dfrac{5x}{6}\to LMC~(5,6)=30\\\\\\\sf =\dfrac{24x}{30}+\dfrac{25x}{30}\\\\\\\sf =\dfrac{24x+25x}{30}\\\\\\\boxed{\sf \frac{49x}{30}}[/tex]

Hi there!

a. A stratified sample can be used by dividing the tenants into two groups: those who have children and those who do not have children. Then, a Sample Random Sample FROM EACH stratum can be conducted for a total of 16 tenants surveyed.

b. Using a cluster sample in this situation could introduce undercoverage or selection bias if there is a distinction between those on some floors and those on others. For example, tenants on lower floors might be more opposed to a playground  (ex: noise, crowd, etc.) in comparison to those on higher floors.

[tex]\\ \sf\longmapsto (x-2)(x+1)[/tex]

[tex]\\ \sf\longmapsto x(x+1)-2(x+1)[/tex]

[tex]\\ \sf\longmapsto x^2+x-2x-2[/tex]

[tex]\\ \sf\longmapsto x^2-x-2[/tex]