solving systems by Substitution
x-4y=15=3x-12y=12

a) Natural number: [tex]12[/tex]

b) Integer that is not a natural number:[tex]-8[/tex]

c) Rational number that is not an integer: [tex]\frac{5}{10} or 0.5[/tex]

d) An Irrational number: [tex]\sqrt{3}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5,6[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or [tex]0[/tex]. Examples of integers are: [tex]-5,0,1,5,10.[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]-\frac{1}{2},\frac{3}{4},0.75, etc.[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi (3.14), \sqrt{2}, etc.[/tex]

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a) Natural number: 12

b) Integer that is not a natural number:-8

c) Rational number that is not an integer: [tex]\frac{5}{10}[/tex]

d) An Irrational number: [tex]\sqrt{5}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or 0. Examples of integers are: [tex]-1,5, etc[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]\frac{1}{2} ,0.5[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi ,\sqrt{6}[/tex]

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The function g(x) = √x + 4 is the result of a vertical translation 4 units up of the function f(x) = √x. (Right choice: B)

In this problem we find the definition of a function f(x) and its image g(x). Both f(x) and g(x) are radical functions and we need to determine the transformation rule to obtain the latter function. By direct inspection, g(x) is the result of applying a vertical translation, whose definition is shown below:

g(x) = f(x) + k

Where:

Please notice that k indicates a translation in the +y direction. k > 0 indicantes a vertical shift k units up.

Then, g(x) is the result of a vertical translation (4 units up) on f(x).

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The percentage of total hours was spent skiing is 10%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, total number of hours =5+20+10+5+10 =50

Number of spent on skiing is 5

Now, percentage is 5/50 ×100

=10%

Therefore, percentage of hours spent on skiing is 10%

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"Your question is incomplete, probably the complete question/missing part is:"

What percentage of total hours were spent skiing?

Soccer 5

Jogging 20

walking 10

skiing 5

football 10

The probability that all adjacent points differ in color is given as follows:

1/10. (second option).

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the total outcomes, we have an arrangement of 6 elements, due to the six points, with 3 and 3 repetitions, as 3 are green and 3 are red, hence the number of total outcomes is calculated as follows:

[tex]T = A_6^{3,3} = \frac{6!}{3!3!} = 20[/tex]

For the desired outcomes, there are two, given as follows:

This means that the probability that all adjacent points differ in color is calculated as follows:

p = 2/20 = 1/10.

Hence the second option is the correct option.

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The answer that is entirely correct based on the sales of popcorn is;

A: Jorge will raise more money because he is selling the popcorn for $3 per bag, and Alan is selling the popcorn for $2 per bag.

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, For Alan, we are told that her popcorn sales can be represented by the equation; y = 2x

where;

x is the number of bags of popcorn sold.

y is the amount of money raised.

Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $2

Now, for Jorge, looking at the graph, we can see that;

y -intercept = 0

Slope = (15 - 6)/(5 - 2)

Slope = 3

Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $3.

Looking at the options, the correct one are Options A,

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The probability that Republicans and Democrats come from the same party is 7/15.

For the stated question-

P = P(DD) + P(RR)

There are a total of four ways to choose both from same party:

4C2 + 6C2 = 4 + 15

= 21

There are various methods for selecting a candidate from the entire pool, so

P = 21/ 10C2

P = 21/45

P = 7/15

Thus, the probability that Republicans and Democrats come from the same party is 7/15.

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The complete question is-

Six Republicans and four Democrats have applied for two open positions on a planning committee. Since all the applicants are qualified to serve, the City Council decides to pick the two new members randomly. What is the probability that both come from the same party?

Answer: B, D, E (2^-1; subtract exponents)

Step-by-step explanation:

B > 1/2 = 2^-1

D > 2^-1 = 2^-1

E > Add exponents 2 + -5 = -1

By using percentage, it can be calculated that

2% of the product of 19 and the average of 63,500, 65,000 and 66,500 = 24700

What is percentage?

Suppose, there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example, 7% means [tex]\frac{7}{100}[/tex]. Here, 7 is expressed as a percentage of 100.

This is a problem on percentage

The numbers are 63,500, 65,000 and 66,500

Average = [tex]\frac{63500 + 65000 + 66500}{3}[/tex] = 65000

Product of 19 and 65000 = 65000 [tex]\times[/tex] 19 = 1235000

2% of 1235000 = [tex]\frac{2}{100} \times 1235000[/tex] = 24700

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If it is important to detect a mean difference in score of one point with the probability of at least 0.90 , then the number of pairs that should be used is  10 .

What is a Probability ?

The term probability of an event  is defined as ⇒ number of favorable outcomes / total number of outcomes  .

It is given that ,

the probability is at least 0.90 ,

So , in the paired t test ,

testing mean paired difference is = 0

alpha = 0.05 , the assumed standard deviation of paired difference = 0.441

So the output is

Difference = 1 , Size = 5 power(probability) = 0.90 ,

So , the actual probability is = 0.95190

From the output above , the required sample size is n = 5 .

We observe that , under the given conditions the sample size is = 5 .

but the researcher  considered 10 pairs ,

So , the sample size 10 is used for this study .

Therefore , 10 pairs should be used .

The given question is incomplete ,the complete question is

It is important to detect a mean difference in score of one point with a probability of at least 0.90. how many pairs should have been used ?

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(a) if 20 cards are defective, then the probability that at least 1 defective card is in the sample is 0.964​

(b) if 5 cards are defective, then the probability that at least 1 defective card appears in the sample is 0.543​

Probability:

In statistics, probability refers the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Given,

Here we have a printed circuit cards are placed in a functional test after being populated with semiconductor chips. a lot contains 190 cards, and 20 are selected without replacement for functional testing.

And we need to find the following probability.

Here we have to recall the formula for probability mass function of the hypergeometric random variable X with the parameters

N = 190

n ​= 20​

and the parameter K.

And it is the following expression:

f(x) = [(K x) (140 - k 20 - x)] / (140 20)

Now, we have to Set K=20 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.964​

And then Set K=5 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.543​

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The difference between the two confidence intervals is given as follows :

Width of confidence interval is directly proportional to confidence level.

This is because,  width is directly proportional to critical value (z or t), which is directly proportional to confidence level.

Now, width is inversely proportional to square root of sample size.

But if sample size is same for both levels of confidence. Then, sample size would have same effect.

Hence, the appropriate answer here is,

The 95 percent confidence interval will not be as wide as the 99 percent confidence interval.

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The simplified expression, when using the Quotient rule is b. 1 / 8⁴.

The Quotient Rule allows us to be able to carry out operations on quotients. The rule is such that when dividing quotients with the same base, you should subtract the quotients. For multiplication, you add the quotients.

8 ⁵ / 8 ⁹ will therefore be:

= 8 ⁵ ⁻ ⁹

= 8 ⁻⁴

8 ⁻⁴  is the equivalent of  1 / 8⁴ because when a number is taken to a negative power, then that number becomes a denominator to 1.

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Answer: decimal 0.03 fraction 3/10

Step-by-step explanation:

26 points are scored in the fifth game.

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

First four games, a netball team scores an average of 31 points per game.

x/4=31

Let x represents four games

x=124

After the fifth game, the average for the first five games is 30

y/5=30

Let y represents five games

y=150

We need to find the number of points scored in fifth game.

x-y

124-150

26

Hence, 26 points are scored in the fifth game.

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Answer:

Below

Step-by-step explanation:

( Your question asks for m^2 discharge......I think you need m^3 discharge per minute)

Find the volume of a cylinder that is 8 meters long with radius of 8cm ( .08 m)

area = pi r^2 = pi (.08)^2 = .0201 m^2

    area * 8 m   = volume PER SECOND

        volume PER SECOND  *  60 = volume per minute

                 .0201   * 8 * 60 = 9.65 m^3 / min  discharge

The formula for an exponential function is y = 45/8x + 57/8.

Here we have to find the formula for an exponential function that passes through the points.

Given data:

The two points are (-1, 3/2) and (3, 24).

We need to find the slope of the line. So,

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

m = (24 - 3/2) / ( 3+ 1)

   = 45/ 8

The general equation of a line:

y = mx + c

Now putting the value of x and y as -1 and 3/2 and m = 45/8.

3/2 = -1 × 45/8 + c

c = 57/8

Now we get the equation:

y = 45/8x + 57/8

Therefore the equation is y = 45/8x + 57/8.

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Answer:

m-2

Step-by-step explanation:

to start simplify

-3(7/2-2/3m)+17/2-m

-21/2+6/3m+17/2-m

-21/2+17/2+2m-m

-4/2+m

-2+m

m-2

hopes this helps

Answer:

Step-by-step explanation:

So basically you can always use bodmas( Brackets of division multiplication addition substractions)

or if it is like 5-4=8+9

then u can   5= 8+9+4

so.................. 5= 21

then................ 21-5=16

A system of linear equations has one solution when the graphs intersect at a point.

A system of linear equations has no solution when the graphs are parallel.

A system of linear equations has infinite solutions when the graphs are on the exact same line.

The graphs attached below show the linear equations that have one solution, multiple solutions, and no solutions.

A linear equation in two variables of the form axe + by + c = 0, where a, b, c R, a 0, and b 0. By comparing the coefficients of the equations while taking the system of linear equations into consideration, we may determine how many solutions there are. Additionally, we can use a graphical way to determine whether the equation system has a single solution or an infinite number of solutions.

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Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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The true statements regarding the construction are statement 2) and statement 5)

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

Given that, A design began from the construction of a regular hexagon.

The true statements made on the construction is;

2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.

5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.

Hence, The true statements regarding the construction are statement 2) and statement 5)

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Answer:

Step-by-step explanation:

i need points goodluck tho

Answer:

t ≈ 7.7

Step-by-step explanation:

                   r         ^nt

A = P ( 1 + ------- )

                  n

A = 3000

P = 1500

n = 12

r = 0.09

t = ?

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

                               12

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

÷1500  ÷1500         12

              0.09        

2 =  ( 1 + ------- ) ^(12)(t)

               12

Change into logs and divide

  log 2

----------------------    =   12t

              0.09

log (1 + ----------)

               12

multiply both sides by (1/12)

                 log 2

(1/12) ----------------------    =   12t (1/12)

                    0.09

      log (1 + ----------)

                     12

7.7304805 = t

7.7 ≈ t

I hope this helps!

At the significance level, 0.01

p-Value=0.973 > 0.01 which implies fail to reject null hypothesis and no evidence to support the claim.

So, there is no reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes.

We have given that,

A study conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction.

x₁-bar = 8.8 micromoles

Standaard deviations, s₁= 1.2

x₂-bar = 7.5 ; s₂ = 1.5

n₁ = 12 ; n₂ = 15

significance level = 0.01

Consider the Null hypothesis and alternative hypothesis othesis

H₀ : μ = 0.5

Hₐ : μ > 0.5

Consider,

Pooled Standard Deviation = √(((n₁ - 1)s₁² + (n₂- 1)s₂²)/(n₁ + n₂-2))

plugging all known values

= sqrt(((12-1)(1.2²) + (15 -1)(1.5²))/(12+15-2))

Sp = 1.3761

Now , test statistic :

t =((x₁-bar - x₂-bar) - 0.5) / (Sp×√(1/n₁+ 1/n₂))

substitute all known values we get,

= ((8.8 - 7.5) - 0.5) / (1.3761× sqrt(1/12 + 1/15))

=> t = 1.5

Degree of freedom = n₁+ n₂ - 2

= 12 + 15 - 2

= 25

Now the p-value corresponding to t = 1.5 & df = 25 is 0.073

Here p-value > 0.01 (significance level) thus, we fail to reject null hypothesis.

So there is no enough evidence to support the claim.

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We found that after simplifying , He have 13 dimes and 10 quarters.

Given,

A man has 23 coins in his pocket.

The total value of his change is 380 cents.

Now,

23 = x + y

23 - x = y

As we know that

A dime=10 cents

So the cost of x dime is 10x.

A quarter=25 cents

so the cost of y quarters is 25y.

380 = 10x + 25y

Substitute the first equation, so

389 = 10x + 25 (23 - x)

380 = 10x + 575 - 25x

15x = 195

x = 13 dimes

Therefore,

y = 23 - 13 = 10 quarters

y = 10 quarters

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(2, 1,985.5) is not a solution of the equation y = 2200(0.95)x.

What is solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Consider, the given equation

y = 2200(0.95)x

And the point given is, (2, 1985.5).

From this x = 2, y = 1985.5

Plug x = 2 in the above equation,

y = 2200(0.95)(2)

y = 4180 ≠ 1985.5

Hence, the given point (2, 1985.5) is not a solution to the equation

y = 2200(0.95)x.

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