Which of the following systems of equations is an example of one where substitution is the best method?

Answer:

(1) N or n = 20

(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4

(3) σ = 9.78 and s = 10.04.

Step-by-step explanation:

We are given with the following data set below;

{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}

(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.

(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;

        Mean  =  [tex]\frac{\sum X}{n}[/tex]

              =  [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]

              =  [tex]\frac{868}{20}[/tex]  = 43.4

So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.

(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;

        Standard deviation, [tex]\sigma[/tex] =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]

             =  9.78

Similarly, the formula for calculating sample standard deviation (s) is given by;

        Sample Standard deviation, s =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]

             =  10.04

Answer:

Look below

Step-by-step explanation:

8 boxes of toothpicks were given to at LEAST 25 students but 15 threw them out

8x= 8 boxes

At least 25= no less than 25 students

-15= the 15 that threw them out

x=boxes

the people= All real numbers

HOPE THIS HELPS!!!

Answer:

1 2 3 4

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Let us take the breadth as 'x'

breadth = x

length = 3 + x

perimeter = 38m

perimeter of a rectangle = 2 ( l + b )

= 2( x + x + 3 ) = 38

4x + 6 = 38

4x = 38-6

x = 32/4

x = 8

breadth = 8

length = 11

Answer:

I think it's A but I could be wrong

Answer: B

Step-by-step explanation:

A graph or table is a function if it passes the vertical line test. That means, each x and only 1 y. One x cannot have more than 1 y because, that means it does not pass the veritcal line test. In the vertical line test, the vertival line only passes through 1 point, not 2. Since we know that this graph does not pass the vertical in test, we can eliminate C and D. We can eliminate A because 2 y-values can be the same as lone as there have different x. B fits the description of what we see on the table. Therefore, the answer is B.

Answer:

The third and fourth options.

Step-by-step explanation:

You simplify the inequality first...

-6x + 15 < 10 - 5x

-x < -5

x > 5

The first option is incorrect since it is less than.

The second option is basically -5x < 15; x > -3; that's incorrect.

The third option is basically -x < -5; x > 5; that is correct!

The fourth option is correct since it shows more than 5.

The fifth option is incorrect because it shows less than -5.

Hope this helps!

Answer: The answer is C and E

Step-by-step explanation:

Hope this helps;)

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}=?\\\\1)\sqrt{8^2+15^2}=\sqrt{289}=17\\2)\sqrt{9^2+40^2}=\sqrt{1681}=41\\3)2\times17=34\\4)\sqrt{34+41}=5\sqrt{3}[/tex]

All Done!

Answer:

Your correct answer is 8.660254

Step-by-step explanation:

√2√82 + 152 + √92 + 402 = 8.660254

Answer: 5x + 1

Step-by-step explanation:

f(x) - g(x)

(3x + 2) - (-2x + 1)       Here you distribute the negative sign to (-2x + 1)

3x + 2 + 2x - 1            Here you combine like terms

5x + 1                         This is the answer.

Answer:

6/7 ÷ 3/14

= 6/7 × 14/3

= 2/7 × 14           (we cancelled 3 with 6)

=  2×2                (we cancelled 7 with 14)

= 4

hope it helps

Step-by-step explanation:

Answer:

[tex]\frac{6}{7} / \frac{3}{14} = \frac{6}{7} x \frac{14}{3} = (6)(14) / (7)(3) =\frac{84}{21} = 4[/tex]

Step-by-step explanation:

Hope this helps you!! ( BTW this means / Divide ).

Answer:

x^2 - 10 = (p - 9)(x)

Step-by-step explanation:

Please indicate exponentiation with the symbol " ^ ":  p(x) = x^2 - 1.

To obtain (p - 9), start with p(x) = x^2 - 1 and subtract 9:

(p - 9)(x) = x^2 - 1 - 9 = x^2 - 10 = (p - 9)(x)

Answer:

Park Q has greatest percentage of pink butterflies.

Step-by-step explanation:

Butterfly Park Survey Park           P     Q      R       S

No, of Pink Butterflies                  25    35   37      23

Total Number of Butterflies          53    64   75     55

Now we are supposed to find which park had the greatest percentage of pink butterflies

So, Percentage of pink butterflies in park P =[tex]\frac{25}{53} \times 100=47.169\%[/tex]

Percentage of pink butterflies in park Q =[tex]\frac{35}{64} \times 100=54.68\%[/tex]

Percentage of pink butterflies in park R= [tex]\frac{37}{75} \times 100=49.33\%[/tex]

Percentage of pink butterflies in park S= [tex]\frac{23}{55} \times 100=41.81\%[/tex]

So, Park Q has greatest percentage of pink butterflies.

So, Option B is true

Hence Park Q has greatest percentage of pink butterflies.

Answer:

≈ 5.8

Step-by-step explanation:

Step 1: Round the fractions

29 1/5 = 146/5 = 29.2 ≈ 29

4 6/7 = 34/7 = 4.85714 ≈ 5

Step 2: Divide

29/5 = 5.8

The answer is under

Answer:

f(x) = (x - (-5))^2 + (-18)

Step-by-step explanation:

Given:

f(x) = x^2 + 10x + 7

Rewrite f(x) in vertex form

Solution:

f(x) = ax^2 + bx + c is a quadratic function.

The vertex form of f(x) is a(x - h)^2 + k, where (h, k) is the vertex.

=> f(x) = x^2 + 10x + 7

          = x^2 + 10x + 25 - 18

          = (x + 5)^ - 18

          = (x - (-5))^2 + (-18)

=> f(x) can be rewritten in form of a(x - h)^2 + k, where (h, k) is the vertex, with a = 1, h = -5, k = -18

Answer:

The correct option is:

14 inches

Step-by-step explanation:

The question is incomplete because the picture of the flap is not shown in the question nor the measurements are given. First lets complete the question. The figure was this question is attached below.

We can see that the bottom width of the trapezoid is 9 inches, the top width of the trapezoid is 5 inches, and it has a height of 2 inches.

The area of trapezoid is given as:

Area = ((Top width + Bottom width)/2) · h

Area = ((9+5)/2) · 2

Area = (14/2) · 2

Area = 7 · 2

Area = 14 inch²

Answer:

14

Step-by-step explanation:

Answer:

3.625 is ans

Step-by-step explanation:

4.5+0.25_+1.125=3.625

Step-by-step explanation:

this is your answer sis ...

Answer:

19.625 cm^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = 3.14 * 5^2 * .25

V =19.625 cm^2

Answer:

price paid of speakers= £40.5

price paid of headphones=£ 5.6

price paid of book=£6.65

price paid of mobile phone=£42

price paid of mouse=£ 15.75

price paid of DVD=£11.05

solution,

1. Cost of speakers:

Discount percent=10 %

Marked price=£45

discount amount= discount % of MP

=10% of 45

=£4.5

Selling price= MP - discount amount

=£45-£4.5

=£ 40.5

2. cost of headphones:

discount amount= discount% of MP

=20% of 7

=£1.4

Selling price= MP- Discount amount

=£7-£1.4

=£ 5.6

3. cost of books:

discount amount= discount percent of MP

= 30% Of 9.50

=£ 2.85

selling price= MP- Discount amount

= £ 9.50-£2.85

=£ 6.65

4. cost of mobile phone:

discount amount= discount% of MP

=40% of 70

=£ 28

selling price= MP- Discount amount

=£70-£28

=£ 42

5. cost of mouse:

discount amount= discount% of MP

= 25% of 21

=£ 5.25

selling price= MP- Discount amount

=£21-£5.25

=£ 15.75

6. cost of DVD:

discount amount= discount % of MP

= 15% of 13

= £ 1.95

selling price= MP- discount amount

=£ 13 -£ 1.95

=£ 11.05

Hope this helps...

Good luck on your assignment..

Answer:

D

Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

Answer:

the interest is 5.42

Step-by-step explanation:

Answer:

Interest = 5.42

Step-by-step explanation:

Answer: −22+3

Step-by-step explanation:

Answer:

−22+3

Step-by-step explanation:

Answer:

See Explanation Below

Step-by-step explanation:

Given

[tex]-3(-3 + 2) - 6[/tex]

Required

Drag the steps

Note that not all steps in the given diagram will be used;

Step 1: Perform Multiplication; 9 + -6 - 6

Step 2: Simplify: -3

Further Explanation:

Step 1 is gotten by opening the bracket;

[tex]-3(-3 + 2) - 6[/tex]

[tex]9 +-6 - 6[/tex]

Step 2 is gotten by solving step 1 further

[tex]9 +-6 - 6[/tex]

[tex]9 - 6 - 6[/tex]

[tex]9 - 12[/tex]

[tex]-3[/tex]

Answer:

You can verify if lines are parallel if they have the same slope and different y-intercepts and if they don't intersect each other. You can also graph the 2 equations to see if they ever intersect.

Step-by-step explanation:

Answer:

C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right

Step-by-step explanation:

270 degree counterclockwise rotation around the origin

=============================================================

Check out the diagram below. In the diagram, I only focus on points A and A'.

We have A = (-3,4) move to A ' = (4, 3). We see the x and y coordinates swap places. Then the new second coordinate -3 becomes positive, or it has flipped sign. So the rule applied here is [tex](x,y) \to (y,-x)[/tex] which describes a 90 degree clockwise rotation; which is equivalent to a 270 degree counterclockwise rotation

The other points follow the same idea.

Answer:

c

Step-by-step explanation:

Answer:27.5

Step-by-step explanation:

Answer:

B. 27.5

Step-by-step explanation:

37 is the Q2, which is the median,

Q1 is 27 + 28 / 2 = 27.5

Answer:

a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]

b)  [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]

d)  [tex]\alpha\approx 53.1^o[/tex]

Step-by-step explanation:

a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

[tex]cos(\alpha)=-\frac{3}{5}[/tex]

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:

[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]

Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]

Then:

[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]

d)

Since [tex]sin(\alpha)=\frac{4}{5}[/tex]

then  [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]

Answer:

4*5*5*2=200 numbers

Step-by-step explanation:

this is because 2,4,6,8 can be the first digit.

2,4,6,8,0 can be the second same for the third.

2 digits can be divisible by 5 which are 5, 0. If it has a 0 at the end it is divisible by 10 which means it is divisible by 5.

Answer:

100 numbers

Step-by-step explanation:

Since there are four digits, the answer will be the product of four numbers. The first digit has to be either 2,4,6, or 8 because it is a four digit number with all even digits. Same for the next two numbers, but zero is also a possibility. The question asks for a number divisible by 5, so the last digit must be a 0 in order to qualify as an even number. So the answer would be 4*5*5*1 (number of possible digits) which is 100.

Answer:

32% of the students did not have a pet.

Step-by-step explanation:

From the total students (100%):

Answer:

70 000 200, 7 030 400, 790 300, 709 400, 78 300, 70 800

Step-by-step explanation:

Greatest is always the number with the most digits.

Answer:

70 000 200, 7 030 400, 790 300, 709 400, 78 330, 70 800

Step-by-step explanation:

To answer this I simply needed to know the orders of numbers from ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, tens of millions, and hundreds of millions. You must also know which digits hold the most value.

[tex]1\\10\\100\\1,000\\10,000\\100,000\\1,000,000\\10,000,000\\100,000,000[/tex]

Answer:

The answer is given below

Step-by-step explanation:

Let the number of passengers that boarded the bus at the interchange be x.

At the first  bus stop, 1/4 of the passengers alighted the bus and 6 people boarded the  bus.

Therefore The number of passengers when the bus left the first bus stop = [tex]x-\frac{1}{4}x +6=\frac{3}{4}x+6[/tex]

At the 2nd bus stop, 8/15 of the passengers alighted and 10 passengers  boarded the bus.

Therefore The number of passengers when the bus left the second bus stop

[tex]=\frac{3}{4}x+6-\frac{8}{15}( \frac{3}{4}x+6)+10=\frac{3}{4}x+6-\frac{8}{20}x-3.2+10\\\\=\frac{7}{20}x+12.8[/tex]

Given that there were 24 passengers on the bus when it left the  2nd bus stop

[tex]\frac{7}{20}x+12.8=24\\7x+256=480\\7x=480-256\\7x=224\\x=32[/tex]

Therefore 32 passengers boarded the bus at the interchange