Given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3

Answer:

[tex]\huge \boxed{x=12}[/tex]

Step-by-step explanation:

Let the unknown number be x.

12+24=2(6+x)

Switch sides.

2(6+x)=12+24

Expand brackets.

12+2x=12+24

Subtract 12 from both sides of the equation.

12+2x-12=12+24-12

2x=24

Divide both sides of the equation by 2.

(2x)/2=24/2

x=12

12+24=2(6+x )

36=2(6+ )

36\2=(6+x)

18=(6+x)

18-6=x

12=x

the answer is 12

Answer:

Yes

Step-by-step explanation:

Because a - - - - - - - - - - b

Same as b-----------------a

Answer:

x=19

Step-by-step explanation:

2(x+6)=3(x-4)+5

2x+2*6=3x-3*4+5

2x+12=3x-12+5

12+12-5=3x-2x

19=x

Answer:

distribute 2 to (x+6) and 3 to (x-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the original trail be x

From the question 150% of the trail is

12 mile

That's

150% of x = 12

So we have

[tex] \frac{150}{100} x = 12 \\ \\ \frac{3}{2} x = 12[/tex]

Multiply through by 2

That's

[tex]2 \times \frac{3}{2} x = 12 \times 2[/tex]

We have

3x = 24

Divide both sides by 3

We have the final answer as

x = 8

Therefore the length of the original trail is

Hope this helps you

56.347..........

just simply put the value 3175 under division root and make pairs of 31 and 75.Now think of a number whose square will be nearest to 31 and that ll be 5.Now write 5 in the quotient and 5 also 5 under the divider.Now by multiplying 5 with the 5 in the quotient you ll get 25 write this under 31.And by adding 5 in the divider 5 youll get 10.write this under the divider.no by subtracting 25 from 31 you ll get 6 and by bringing 75 down it ll be 675.Now think of a number again and write it with 10.Like 6 into 6 is 36 and when you multiply 6 with 106 you ll get nearest number to 675 that ll be 636.Now because its giving a remainder just add a .0 in the question and continue to solve it the same way.And as it ll be a continuous answer so just add continuty dots........ or just round it off to nearest whole number

Answer:

56.347138347923

Step-by-step explanation:

Answer:

Everyday mathematics would include lower-level math skills and comprehension, such as adding 5 cups of flour and 2 cups of sugar to some batter. Academic mathematics would include more complex math skills and comprehension, such as quadratic equations and interval notation.

Step-by-step explanation:

Everyday mathematics would include lower-level math skills and comprehension, such as adding 5 cups of flour and 2 cups of sugar to some batter. Academic mathematics would include more complex math skills and comprehensions, such as quadratic equations and interval notation. With one, you could pick up such skills just by living life. With the other, there is a higher chance that attending an educational institute would bestow such skills and understanding.

Answer:

???

Step-by-step explanation:

???

Answer:

27720

Step-by-step explanation:

So let's assume that in any arrangement we are not able to distinguish the balls having the same colour, so only different orders of the colours involved are counted.

If we number these balls we have 12 different numbers, 3 of which belong to the white balls, 4 belong to the blue balls and the final 5 belong to the red balls. They could be arranged in 12! different ways. Pick any of these arrangements.

The white balls in this arrangement are now ordered because I gave these balls a number. But I specifically stated in the first alinea that we were not interested in all these possible orders of the white balls within a sequence of 12 balls. So we must correct for these orders, there are 3! of these, each one leading to exactly the same visual order of white balls. The other colours lead to a correction of 4! and 5!. Moreover, these corrections are independent of each other. I can change the position of the white balls without interrupting the order of the colours of the remaining balls. So we should divide by the product of 3!,4! and 5!.

Total number of arrangement = 3,628,800

Given that;

Number of red ball = 5

Number of white ball = 2

Number of blur ball = 3

Find:

Total number of arrangement

Computation:

Total number of balls = 5 + 2 + 3

Total number of balls = 10

Total number of arrangement = 10!

Total number of arrangement = 3,628,800

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Answer:

5

Step-by-step explanation:

15/3=5 when the y are 3 it division

Answer:

What the other guy said

Step-by-step explanation:

Answer:

4x + 3y

Step-by-step explanation:

Answer:

4x+3y

Step-by-step explanation:

Answer:

7.7 seconds

Step-by-step explanation:

t = √(h / 4.9)

t = √(290.57 / 4.9)

t = √59.3

t ≈ 7.7

Answer/Step-by-step explanation:

Length of rectangle = [tex] l [/tex]

Width of rectangle = [tex] \frac{1}{3} of l - 1 = \frac{1}{3}l - 1 = \frac{l}{3} - 1 [/tex]

A. Expression for finding area of the rectangle:

Area of rectangle is given as [tex] length*width [/tex]

[tex] Area = l(\frac{l}{3} - 1) [/tex]

Or

[tex] Area = l*\frac{l}{3} - l*1 [/tex]

[tex] Area = \frac{l^2}{3} - l [/tex]

b. Expression for finding perimeter:

Perimeter of rectangle is given as [tex] 2(Length + Width) [/tex]

[tex] Perimeter = 2(l + (\frac{l}{3} - 1)) [/tex]

Or

[tex] Perimeter = 2(l) + 2(\frac{l}{3} - 1) [/tex]

[tex] Perimeter = 2l + \frac{2l}{3} - 2) [/tex]

c. Quotient of Perimeter divided by area:

[tex] 2(l + (\frac{l}{3} - 1)) [/tex] ÷ [tex] l(\frac{l}{3} - 1) [/tex]

[tex]2(l + (\frac{l}{3} - 1))[/tex] ÷ [tex]\frac{l^2 - 3l}{3}[/tex]

Change the ÷ to × and flip the fraction on your right upside down.

[tex]2(l + (\frac{l}{3} - 1)) * \frac{3}{l^2 - 3l}[/tex]

[tex]2l + 2(\frac{l}{3} - 1) * \frac{3}{l^2 - 3l}[/tex]

Answer:

Step-by-step explanation:

Hello,

Let's develop both expressions and try to re factorise.

[tex]\forall (a,b,x,y) \in \mathbb{R}^4 \\ \\ (a^2+b^2)(x^2+y^2)=(ax+by)^2\\ \\<=>(ax)^2+(ay)^2+(bx)^2+(by)^2=(ax)^2+(by)^2+2(ax)(by)\\ \\<=> (ay)^2+(bx)^2-2(ay)(bx)=0\\ \\<=> (ay-bx)^2=0\\ \\<=> ay-bx=0\\ \\<=> \boxed{\sf \bf ay=bx}[/tex]

Thanks

Answer:

Σ( xi ) / n ; $29

Step-by-step explanation:

Given the following data:

X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26

Number of observations (n) = 12

Mean formula (m) = ( Σ xi ) / n

Where i = each individual value in X

Mean water bill for the years is thus :

m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12

m = 348 / 12

m = 29

Hence, the mean water bill for the year is $29

Answer:

Here we have two points R and S.

How many lines pass through both R and S?

Well, we can have only one line that passes through both R and S.

Because we are working with lines, we can only see a plane X-Y here.

Then the points R and S can be written as:

R = (x1, y1) and S = (x2, y2)

Now, a line or a  linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now, let's suppose that we have two different lines that pass through points R and S.

From above, both lines must have the same slope, because they pass through the same points.

y1 = a*x + b

y2 = a*x + c

So the only thing that our lines can have different is the y-intercept, but the y-intercept acts as a vertical shift.

This means, if we have different values in the y-intercept, we will have two parallel lines.

And two parallel lines can never pass through the same points, which means that we can not have different values for the y-intercept.

Then the two lines must be identical.

Then there is only one line that passes through points S and R at the same time,

Answer:

answer below

Step-by-step explanation:

from the question the

mean = ∑x/n

∑x = 317

n = 16

mean = 19.8125

x           x-Ц           x-Ц²

19       -0.8125      0.66015625

20       0.1875      0.03515625

19          -0.8125      0.66015625

20         0.1875      0.03515625

18         -1.8125       3.28515625

21          1.1875        1.41015625

17           -2.8125      7.91015625

19           -0.8125      0.66015625

24           4.1875       17.53515625

23            3.1875      10.16015625

21           1.1875        1.41015625

21            1.1875        1.41015625

17             -2.8125      7.91015625

20          -0.8125      0.66015625

20           -0.8125      0.66015625

18            -1.8125       3.28515625

∑(x-Ц)² = 56.44

s.d = 1.9

b.

19.81 + 2*1.9= 23.61

19.81-2*1.9 = 16.01

=

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

Explanation:

The slope of f(x) is 4, since the equation y = 4x+2 has slope m = 4. Compare this to y = mx+b.

The slope of g(x) is 5. Note how if we started at (0,-2) on the red line and moved up 5 and to the right 1, we arrive at (1,3) which is another point on the red line. You could use the slope formula

m = (y2-y1)/(x2-x1)

to get the same result.

Since the slope of f(x) is 4 and the slope of g(x) is 5, we see that g(x) has a larger slope. The g(x) line is steeper compared to f(x).

Answer:

x=4

Step-by-step explanation:

In order to solve for x, we must isolate x on one side of the equation.

x+3x+5=21

First, combine like terms. x and 3x are both terms with variables, and can be combined.

(x+3x) + 5=21

4x + 5=21

5 is being added to 4x. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.

4x+5-5= 21-5

4x= 16

x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.

4x/4=16/4

x= 16/4

x=4

Let's check our solution. Plug 4 in for x and solve.

x+3x+5=21

4+3(4)+5=21

4+12+5=21

16+5=21

21=21

This solution checks out, so we know our answer is correct.

x is equal to 4, x=4.

Answer:

x = 4

Step-by-step explanation:

x + 3x + 5 = 21

4x + 5 = 21

4x = 21 - 5

4x = 16

x = 16/4

x = 4

verify:

4 + 3*4 + 5 = 21

4 + 12 + 5 = 21

Answer:

x=26

y=9

Step-by-step explanation:

5x-17+3x-11=180

8x=180+17+11

8x=208

x=26

3(26)-11=78-11=67

2y+5=90-67

2y=90-67-5

2y=18

y=9

Answer:

0.82

Step-by-step explanation:

The question says that three percent (3 out of 100) of the rackets (racquets) produced by the company are found to be defective.

First thing to calculate is the probability that 1 in a box of 6 rackets are defective.

That probability is gotten by cross multiplying, as illustrated below;

3 - 100

x - 6

x = (6×3)/100 = 18/100 = 0.18

Since the probability of having/finding 1 defective racket in a box of 6 is 0.18, the probability of finding more than 1 (minimum of 2 and maximum of all six) defective rackets in same box would be (1 - 0.18) = 0.82

Answer:

maybe : 1,2,5,6,9,10,13,14,17,

Step-by-step explanation:

I think it's in odd/even number pattern but it'll always skip a number???

or it's just in +1 then +3 pattern

The next terms of the pattern 1,2,5,6,9 are 10, 13,14,17,18,21.

Sequence is a collection of terms which are related in some way which is common to all the terms or some of the terms.

The pattern is given as 1,2,5,6,9 and we have to find the next terms of the pattern.

The First term is 1, the second term is 2. The difference between them is 1.

Second term is 2 and the third term is 5. The difference between them is 3.

Third term is 5 and the fourth term is 6. The difference between them is 1.

Fourth term is 6 and fifth term is 9. The difference between them is 3.

If we observe pattern in them them we can find that in first term they have added 1 , in second term 3 , in third term 1, in fourth term 3. It means first add 1 and then 3.

The next terms will be :

9+1=10

10+3=13

13+1=14

14+3=17

17+1=18

18+3=21.

Hence the next terms of the pattern 1,2,5,6,9 are 10,13,14,17,18,21.

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Answer:

272 thats the umm..never mind heheh

Answer:

0.1998

Step-by-step explanation:

This is a conditional probability question.

We solve this question using Bayes's Theorem of conditional probability.

P(A|B) = [P(B|A) × P(A)] ÷ [(P(B|A) × P(A))+ (P(B|A') × P(A'))]

Based on the information in the question, we have the following values.

Suppose it snows in Greenland once every 27 days.

Probability (it snows) = P(A) = 1/27

= 0.037037037

Approximately = 0.0370

Probability ( it doesn't snow) = P(A') = 1 - 0.0370 = 0.963

Probability ( that when it snow, glaciers grow) = P(B|A) = 26% = 0.26

Probability( that is doesn't snow , glaciers grow) = P(B|A)' = 4% = 0.04

Using the Bayes's Theorem of conditional probability

Probability that it is snowing in Greenland when glaciers are growing is =

P(A|B) = [P(B|A) × P(A)] ÷ [(P(B|A) × P(A))+ (P(B|A') × P(A'))]

= [0.26 × 0.0370] ÷ [(0.26 × 0.0370) + (0.04 × 0.963)]

= 0.00962 ÷( 0.00962 + 0.03852)

=0.00962 ÷ 0.04814

= 0.199833818

Approximately to 4 decimal places ≈ 0.1998

Therefore, probability that it is snowing in Greenland when glaciers are growing is 0.1998

Answer:

74

Step-by-step explanation:

60,000 + 14,000

ANS 14%

ANSWER: 74

The project's IRR is approximately 13.45%.

We have,

To calculate the project's internal rate of return (IRR), we need to find the discount rate at which the net present value (NPV) of the project's cash flows is equal to zero.

Given:

Initial cost (C0) = $60,000

Net cash inflow per year (CF) = $14,000

Number of years (n) = 9

Cost of capital (r) = 14% = 0.14

To calculate the IRR, set up the equation:

[tex]0 = C0 + (CF / (1 + r)^1) + (CF / (1 + r)^2) + ... + (CF / (1 + r)^n)[/tex]

[tex]0 = 60,000 + (14,000 / (1 + r)^1) + (14,000 / (1 + r)^2) + ... + (14,000 / (1 + r)^9)[/tex]

By using a financial calculator or software, the IRR for this project is found to be approximately 13.45% when rounded to two decimal places.

Therefore,

The project's IRR is approximately 13.45%.

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Answer:

The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].

Step-by-step explanation:

The average value of a function over an interval is represented by this integral:

[tex]\bar y = \frac{1}{b-a}\cdot \int\limits^{b}_{a} {f(x)} \, dx[/tex]

Where:

[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds of the interval, dimensionless.

[tex]f(x)[/tex] - Function, dimensionless.

If [tex]a = -1[/tex], [tex]b = 4[/tex] and [tex]f(x) = 6 - x^{2}[/tex], the average value of the function is:

[tex]\bar y = \frac{1}{4-(-1)}\int\limits^{4}_{-1} {6-x^{2}} \, dx[/tex]

[tex]\bar y = \frac{6}{5}\int\limits^{4}_{-1} \, dx - \frac{1}{5}\int\limits^{4}_{-1} {x^{2}} \, dx[/tex]

[tex]\bar y = \frac{6}{5}\cdot x |_{-1}^{4} - \frac{1}{15}\cdot x^{3}|_{-1}^{4}[/tex]

[tex]\bar y = \frac{6}{5}\cdot [4-(-1)]- \frac{1}{15}\cdot [4^{3}-(-1)^{3}][/tex]

[tex]\bar y = \frac{5}{3}[/tex]

The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].

Answer:

The answer is below

Step-by-step explanation:

The graph used to estimate the consumption (in billions) in the United States for the years 1900 to  2007 is attached.

The year is plotted on the x axis and the number of cigarettes is on the y axis. To estimate the number of cigarattes smoked in year 2000, we have to find the y coordinate that corresponds to an x coordinate of 2000. This is done by drawing a line vertically to touch the graph from the point 2000 on the x axis. The point it touches the graph is then traced to the y axis to get the consumption as shown in the graph attached.

From the graph  the number of cigarettes smoked in 2000 is about 420 billion cigarettes

Step-by-step explanation:

Let coordinates of B be ( x , y )

X coordinate of B = (-1 + x) / 2 = - 3

Y coordinate of B = (-1 + y) / 2 = -3

Therefore, coordinates of B are ( - 5, - 5 ).

Answer:

28.60×.35=10.01

10.01+28.60=$38.61

Answer:

2<∛13<3      1<∛6<2

Step-by-step explanation:

Lets find the integers a and b  ∛13 lies between.

a<∛13<b

a³<13<b³

=> a=2 so 2³=8   and b=3 so 3³=27    8<13<27

Similarly     a<∛6<b

a³<6<b³

a=1    and b=2