Use the following rules/intervals: Function 1: (-∞, -5) Function 2: [-5, 0) Function 3: [0,5) Function 4: [5, ∞) If the function is undefined over a given interval then pick another function and include an explanation as to why the original function did not work. Make one of the functions linear, one of the functions square root, one of the functions absolute value, and the last function either exponential, quadratic or square root (one that you will be able to graph).

Answer:

2a.

Step-by-step explanation:

6 = 2 * 3

8 = 2 * 2 * 2   - 2 is common to both sets of factors.

So the GCF of 6 and 8 is 2.

For the 2 a's it is a.

Answer:

3

Step-by-step explanation:

4.5x 2 = 9

[tex]\sqrt{9}[/tex]= 3

this is an example of linear equations is one variable

Answer:

4)8 goats, 3 hens.

Step-by-step explanation:

8*4=32

3*2=6

32+6=38

Answer:

396

Step-by-step explanation:

It's a square.

That means that all four sides are equal.

So the two expressions you have been given are equal.

2.5x + 76.5 = 12x - 9            Subtract 2.5x from both sides.

-2.5x               -2.5x  

          76.5 = 9.5x - 9          Add 9 to both sides

           9                 9

          85.5 = 9.5x              Divide by 9.5

       85.5/9.5 = x

x = 9

That is just the value for x. It is not the answer

Side = 12x - 9

Side = 12*9 - 9

Side = 108 - 9

Side = 99

The perimeter = 4 * Side

The perimeter = 4 * 99

Perimeter = 396

this figure can be divided into three parts one is rectangle other one is semicircle and the third one is one fourth of the circle .so let's find the area of each figure one by one. For the rectangle 12×8 =96

for semicircle that is on the top it has the radius 6 which is a half of 12

so area of the semicircle is

[tex] \frac{1}{2} \pi \: r {}^{2} \\ \frac{1}{2} \times 3.14 \times 6 {}^{2} \\ 3.14 \times 18 \\ 56.52[/tex]

no that's fine. 80 of the 1/4 of the other Circle

[tex] \frac{1}{4} \pi {}^{2} \\ \frac{1}{4} 3.14 \times 8 {}^{2} \\ 3.14 \times 16 \\ 50.24[/tex]

add all these areas

96+56.52+50.24 =202.76

Max is participating at a school bake sale. Each cookie he sells costs 50 cents. Unfortunately, it took 6 dollars to buy the materials for the cookies. Find how much money would it take for Max to break even.

Answer:

Step-by-step explanation:

4 years ago when Mary was 6, she was one half the age of her brother.  

 How old is her brother now?

Solution :

Let brother's age be = x

Four years ago, brothers age was = (x - 4)

Four years ago Mary was = 6

She was half the age of her brother

                                                   [tex]6 = \frac{1}{2} (x - 4)[/tex]

Answer:

it says round to the nearest 10th so it wouldn't be 81, it would be 81.8%

Answer:

Buses - 43 people

Vans - 12 people

Answer:

0.2&4

Step-by-step explanation:

There are 60 minutes in one hour, so 12 divided by 60 is the answer.

0.2   kilometers * 20 = 4

Answer:

20°

Step-by-step explanation:

perpendicular from the center on a chord of a circle always bisects the chord.

AR=BR

∴m arcAC=m arc BC=20°

Answer:

Median: The median is the middle value of the data set when the data is arranged in ranking order. It always lies at the center of the data set and not affected by the extreme values or outliers. For the calculation of median, the variable should be measured at least at the ordinal level.

Answer:

See the answers below

Step-by-step explanation:

Name two characteristics of the Fibonacci Series that you observed. ​

If we take a closer look at the Fibonacci series, we will notice the following characteristics

1.The next number is the sum of the two preceding numbers

2. Another interesting characteristic is evidenced in the convergence of the sequence

Answer:

a) 2 nonsingular 2 by 2  matrices are not closed when added together hence it is not a vector space( i.e. their sum = singular and not nonsingular )

b) 2 singular 2 by 2 matrices is not  closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )

Step-by-step explanation:

a) Prove that nonsingular 2 by 2 matrices is not a vector space

2 nonsingular matrices are not closed when added together hence it is not a vector space ( i.e. their sum = singular and not nonsingular )

vector A = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]    +  vector B =  [tex]\left[\begin{array}{ccc}0&1\\1&0\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&1\\1&1\\\end{array}\right][/tex] ( singular vector )

b) Prove that singular 2 by 2 matrices is not a vector space

2 singular 2 by 2 matrices is not  closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )

Vector C = [tex]\left[\begin{array}{ccc}1&0\\0&0\\\end{array}\right][/tex]  + vector D = [tex]\left[\begin{array}{ccc}0&0\\0&1\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( nonsingular vector )

Answer:

379

Step-by-step explanation:

a23 = 27 + (23-1)(16)

= 27 + (22)(16)

= 27 + 352

= 379

Answer:

(a+b)²=a²+b²+2ab

Step-by-step explanation:

The square of sum of two terms is equal to the squared plus squared plus times product of and . In mathematics, the plus whole squared algebraic identity is called in three ways. The square of sum of two terms identity.

Answer:

4.53

Step-by-step explanation:

Given the data :

4, 5, 10, 11, 15

The mean = 9

The standard deviation of a sample :

s = √[Σ(x - mean)²/(n-1)]

s = √[((4-9)² + (5-9)²+(10-9)² + (11-9)² + (15-9)²) / (5-1)]

s = √(25+16+1+4+36)/4

s = √20.5

s = 4.527

s = 4.53

Answer:

4.5

Step-by-step explanation:

5.1.3

Answer:

4. (2, 3)

5. (0, 1)

7. (-1, 2)

Step-by-step explanation:

I hope this helps! Have a nice dayy! :)

You're very close. Choices D and E are two of the three answers. The third answer is choice G (-1,2)

If you plug the coordinates of the points into the inequality, you should get a true statement.

For instance, let's try the coordinates of choice G

[tex]-2x + 3y\ge 3\\\\-2(-1) + 3(2)\ge 3\\\\2 + 6\ge 3\\\\8\ge 3\\\\[/tex]

Which is true since 8 is indeed greater than 3. That verifies point G is a solution point. A similar story happens with points D and E as well.

----------

If you tried something like choice A, then,

[tex]-2x + 3y\ge 3\\\\-2*(2) + 3(-3)\ge 3\\\\-4 - 9\ge 3\\\\-13\ge 3\\\\[/tex]

Which is false because -13 is not greater than 3, and -13 is not equal to 3 either. So choice A is a non-answer. You should find that choices B, C, and F are also non-answers.

----------

The graph is below. Notice how points D, E and G are either in the blue shaded region or on the boundary. The boundary line is solid (due to the "or equal to" as part of the inequality sign), so points on the solid boundary line are part of the solution set. The graph is a quick way to visually confirm the answers. I used GeoGebra to make the graph.

So that's why the 3 answers are D, E and G.

Answer:

s(t) = 160/3  ( 1 - e^(-3t / 200) )

Step-by-step explanation:

volume of pure water in tank  = 1000 L

Brine contains 0.04kg of salt/L

Inflow rate of Brine containing 0.04kg of salt/L = 5L/min

Brine containing 0.06 kg of salt/L

Inflow rate of Brine containing 0.06 kg of salt/L = 10L/min

Solution is thoroughly mixed and drains from tank at 15L/min

a) Determine the amount of salt is in the tank after t minutes

rate of salt entering = 0.2 + 0.6 = 0.8 kg/min

rate of salt leaving = s/1000 * 15

amount of salt at time (t) = s(t)

initial condition s( 0 ) = 0

ds/dt = 0.8 - 15s/1000 = 0.8 - 3s/200

200 ds/dt = ( 160 - 3s )

-200/3  In ( 160 - 3s ) = t + c

Given that ;  t = 0 , s = 0    

c =  - 200/3  In ( 160 )

∴  -200/3  In ( 160 - 3s ) = t - 200/3  In ( 160 )

- 200/3  [ In ( 60 - 3s ) - In ( 160 ) ] = t

therefore:  

In ( 160 - 3s / 160 ) = -3t/200

= ( 160 - 3s / 160 ) = e ^ (-3t/200 )

Hence amount of salt in tank after t minutes

s(t) = 160/3  ( 1 - e^(-3t / 200) )

The answers are as follows part A = 30m+15  part B =3m+15+27m

and partC = 30m+15

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.

Part A:- Two expressions that are equivalent to the given expressions are:-

3m   +   15   +   27m

30m  +   15

Part B:  Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties.

3  (  m   +   5    +   9m   )

Open the bracket by multiplying 3 by what is in the bracket

3m   +   15   +   27m

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m.

3   (  m    +   5   +   9m  )

Open the bracket by multiplying 3 by what is in the bracket

3m    +    15    +     27m

Collect like terms together

3m    +     27m  +   15

=   30m   +    15

To know more about Expression follow

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

4

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻  

[tex]\boxed{\text{Calculating the Answer...}}\\\\8^{\frac{2}{3}}\\-----------\\\text{Recall the Exponent Rule: }} a^{\frac{b}{c}} = \sqrt[c]{a^b}\\\\\rightarrow {\frac{\text{Power}}{\text{Root Index}}\\\\[/tex]

[tex]-----------[/tex]

[tex]\rightarrow 8^{\frac{2}{3}}\\\\\rightarrow \sqrt[3]{(8^2)}\\\\\rightarrow\sqrt[3]{64}\\\\\rightarrow \boxed{4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

4

Step-by-step explanation:

[tex]8^{\frac{2}{3} }[/tex]

=[tex](2)^3*\frac{2}{3}[/tex]

=[tex](2)^\frac{3*2}{2}[/tex]

=[tex](2)^\frac{6}{3}[/tex]

=[tex]2^2[/tex]

=4

Answer:

Y=x

Step-by-step explanation:

The y and x values are the same

Answer:

y = x

Step-by-step explanation:

a 45° line with the origin passing through the origin has the equation y=x.

Have a nice day.

Answer:

For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on.

Step-by-step explanation:

You can figue out the rest.

Answer:

0% probability that the mean of the sample taken is less than 2.2 feet.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 2.5 feet and a standard deviation of 0.2 feet.

This means that [tex]\mu = 2.5, \sigma = 0.2[/tex]

Sample of 41

This means that [tex]n = 41, s = \frac{0.2}{\sqrt{41}}[/tex]

Find the probability that the mean of the sample taken is less than 2.2 feet.

This is the p-value of Z when X = 2.2 So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}[/tex]

[tex]Z = -9.6[/tex]

[tex]Z = -9.6[/tex] has a p-value of 0.

0% probability that the mean of the sample taken is less than 2.2 feet.

Answer:

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.

The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Answer:

x = 1, y = 2 , z = 3

Step-by-step explanation:

[tex]6x\:+\:2y\:-4z\:=\:-2 \ \ \ \ \ \ \ \ \ -----( 1 ) \:\\\\-3x-4y\:+2z\:=\:-5 \ \ \ \ \ \ ------( 2 ) \:\\\\4x-\:6y\:+3z\:=\:1 \ \ \ \ \ \ \ \ \ \ \ \ ------- ( 3 ) \\\\( 2 ) \times 2=> -6x -8y + 4z = -10 \ \ \ \ \ \ \ -----( 4)[/tex]

Now add ( 1 ) and  (4)

[tex]6x +2y -4z = - 2\\\\-6x-8y - 4z = -10\\\\=>0x -6y + 0 = - 12\\\\-6y = -12[/tex]

y = 2

Now multiply ( 1 ) by  2 and (3) by 3

[tex](1) \times 2 => 12x + 4y -8z = -4\\\\(3) \times 3 => 12x -18y +9z = 3\\\\Subtract \ the \ equation : ( 1) - ( 3) => 0x +22y -17z = -7[/tex] ------ ( 5 )

Substitute y = 2 in ( 5 ) :

[tex]22(2) - 17z = - 7\\\\ 44 - 17z = - 7\\\\ -17z = - 7 - 44\\\\ -17z = -51\\\\[/tex]

z = 3

Substitute z = 3 and y = 2 in ( 1 ) :

[tex]6x + 2y - 4z = - 2\\\\6x + 2( 2) -4( 3) = -2\\\\6x + 4 - 12 = -2\\\\6x - 8 = - 2\\\\6x = - 2 + 8 \\\\6x = 6\\[/tex]

x = 1

9514 1404 393

Answer:

  182 lbs

Step-by-step explanation:

You can write the proportion for the required patient weight (w) as ...

  weight/medicine = w/(174.72 mg) = (150 lb)/(144 mg)

  w = (150 lb)(174.72/144) . . . . . multiply by 174.72 mg

  w ≈ 182 lb

The patient's weight is 182 pounds.

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

∴ x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

∴ x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

Learn more about word problems leading on simultaneous equations here:

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There are 12 month in a year :

6360 ÷ 12 = 530

Thus the labour earns Rs 530 in a month .

To find this out we will divide 6360 by 12 (as there are 12 months in an year) 6360/12 = 530 . Therefore answer = rs 530

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