-3x+y=2
-x+y-4=0
solving a system of linear equations by substitution

Correct option is C

The plot of normal distributions A and B

A has the larger standard deviation

Standard Deviation

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The name standard deviation for SD came from Karl Pearson. I would guess no more than that he wanted to recommend it as a standard measure. If anything, I guess that references to standardization either are independent or themselves allude to SD.

Mean

In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set. The mean, median and mode are the three commonly used measures of central tendency.

Normal Distribution

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a bell curve.

The plot of normal distributions A and B

A has the larger standard deviation

Correct option is C

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The equality property that is used to prove the statement is the addition property of the equality.

Let's start with the general equation

A = B

That we assume is a true equation.

There is a property called the addition property of the equality, it says that we can add the same number in both sides of the equation.

Then if we add a number C in both sides, we will get:

A + C= B + C

And that equation is still true.

Ok, let's go to our equation:

x - 2 = 9

We can add the same number in both sides which is 2, then we get:

x - 2 + 2 = 9 + 2

x = 11

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The statement that correctly compares -9 and 2 is A. -9 < 2 because 9 is to the left of 2 on a number line.

In arithmetic, a number line is a depiction of a graduated straight line which functions as a graphic representation of real numbers. It is presumed that every number line point and every real number correspond to one another.

Horizontal straight lines termed number lines have integers along them spaced equally apart. All of the numbers in a series can be shown on a number line. This line extends indefinitely at both ends.

In this case, -9 is on the left of a number line since it's negative. In conclusion, the correct option is A

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Jane's share in the profit as per the amount invested by her is $39,375.

A ratio shows us the number of times a number contains another number.

Given that Capital balances were $100,000 for John, $75,000 for Sally and $225,000 for Jane. Therefore, the ratio of the capital invested by three can be written as,

John : Sally : Jane = $100,000 : $75,000 : $225,000

John : Sally : Jane = 4 : 3 : 9

Now, the profit will be shared as per the capital invested, therefore, as per the capital invested. Thus, we can write,

4x + 3x + 9x = $70,000

16x = $70,000

x = $70,000 / 16

x = $4,375

Further, Jane's share can be written as,

Jane's share = 9x

                     = 9 × $4,375

                     = $39,375

Hence, Jane's share is $39,375.

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Answer:

8 x 7 is the same as 7 x 8.

An expression that is equal to 8 x 7 would also be an expression that has the same solution.  

7 x 8 = 56

4 x 14 = 56

2 x 28 = 56

1 x 56 = 56

The expression could also have division instead of multiplcation, for example, 7 x 8 = 56 could also be written as 56 ÷ 8 = 7, or 56 ÷ 7 = 8

I hope this helps :)

Answer: x = 3

Step-by-step explanation:

The value of x in the absolute value equation |3x + 12| = 0 is -4

From the question, we have the following parameters that can be used in our computation:

|3x + 12| = 0

The above equation is an absolute value equation

So, we start by removing the absolute brackets

So, we have the following representation

3x + 12 = 0

Evaluate the like terms

This gives

3x = -12

Divide both sideso of the equation by 3

x = -4

Hence. the solution is -4

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If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

Given that,

The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.

We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.

We know that,

Let

Length= Breadth =x

Height=y

Volume can be written as

V=x²y

Now,

Combined length and girth is

7x+y=171

y=171-7x

V(x)=x²(171-7x)

V(x)=171x²-7x³

Differentiating with respect to x.

V'(x)=343x-21x²

The maximum value

V'(x)=0

343x-21x²=0

7x(49-3x)=0

x=0

and

49-3x=0

3x=49

x=49/3

Once again differentiating with respect to x.

V''(x)=343-42x

V''(x)=343-42(0)=343>0(min)

V''(x)=343-42(49/3)=-343<0(max)

The maximum volume is

Vmax=V(49/3)=(49/3)(171-7(49/3))

Vmax=925

Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

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The given expression can be simplified to obtain the quotient and remainder as 3x + 4 and -4 respectively.

The polynomial p(x) divided by the other polynomial g(x) gives remainder r(x) and quotient as q(x) such that degree of r(x) is not greater than g(x).

The given expression is (3x²+ 22x + 27)/(x+6).

The division can be done as follows,

First take the quotient as 3x so that that the remainder is,

3x²+ 22x - 3x(x + 6)

= 4x

Now, the new dividend is 4x + 6.

Take the quotient as 4 to get the remainder as,

4x + 6 - 4(x + 6)

= -18

It cannot be further divided because the degree of -18 is less than x + 6.

Which implies that the quotient is 3x + 4 and the remainder is -18.

Hence, the quotient and remainder for the given division of polynomials is 3x + 4 and -4 respectively.

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The Future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly is $10263.734 ..

The future value of an annuity is the value of a group of regular payments at some point in the future. It assumes a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.

P = PMT× ((1+r)ⁿ −1)/r

where:

P---> Future value of an annuity stream

PMT---->Dollar amount of each annuity payment

r -->Interest rate (also known as discount rate)

n--->Number of periods in which payments will be

We have given that

Present value for an Annuity = $200

compounded rate , r = 13%

but compounded quarterly, then, r = 13%/4

= 0.13/4 = 0.325

Number of years , n = 2 + 1/2 = 5/2

then change into quarterly, n = 5/2 × 4 = 10

Future value formula ,

F.V = PMT ( (1+i)ⁿ - 1)/r

=> Future value = 200((1+0.325)^10/0.325)

=> F.V = 10263.734

Hence, the future value of an annuity is $10263.734..

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Answer:

-20

Step-by-step explanation:

We see the number line is counting by 5's so let's count down by 5's until we get to the blue dot!

5

0

-5

-10

-15

-20!

We moved down 3 points from -5 on the number line!

Answer:-20

Step-by-step explanation:

If On December 31, a corporation determines that they have income taxes expense of $20,000, with $15,000 currently due. the journal entry is Debit Income taxes expense $20,000, Credit income taxes payable $15,000 Credit Deferred income tax liability $5,000.

Based on the given information the appropriate journal entry to record the transaction is"

Journal entry

Debit Income taxes expense $20,000

Credit income taxes payable $15,000

Credit Deferred income tax liability $5,000

($20,000 -$5,000)

(To record income taxes)

Therefore the entry is Debit Income taxes expense ,Credit income taxes payable and Credit Deferred income tax liability.

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The RAM of the larger server is 30GB and the RAM of the small server is 20GB.

The first step is to form a system of equations:

2L + 4S = 100 equation 1

L + 3S = 60 equation 2

The elimination method would be used to determine the required values:

In order to determine the value of S, multiply equation 2 by 2

2L + 6S = 120 equation 3

Subtract equation 1 from equation 3 :

2S = 20

Divide both sides of the equation by 2:

S = 20 / 2 = 10

Substitute for s in equation 1 :

2L + 4(10) = 100

2L + 40 = 100

2L = 100 - 40

2L = 60

L = 60 / 2

L = 30

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The answer choice which corrects justifies the step as described is; Choice B; addition property of equality.

It follows from the task content that the answer choice which corrects justifies the step as given is to be determined.

Since the starting step is;

2x + 3 = -5x - 1

By adding 5x to both sides of the equation;

2x + 5x + 3 = -5x - 1 + 5x

7x + 3 = -1

Recall that; the addition property of equality postulates that;

if x = y;

Then, x + a = y + a.

On this note, the property which justifies the step is; Choice B; Addition property of equality.

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Answer: -26/27

Step-by-step explanation:

The material that she has left after the cut of 1/2 yard of the material is 2/5 yards left

While I show you how to solve this problem, I would like to highlight some of the words and how they convert into a mathematical equation.

"She cut 1/3 yard off the material."

 This means you multiply whatever you are starting with by 1/3.

 So in this case Mineko begins with 3/5 yards.

 So,

3/5 • 1/3 = 1/5

She used 1/5 yard to make the pillow.

This will translate to Mineko having left

Therefore 3/5-1/5

She has 2/5 yards left.

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The base case in a recursive solution to the problem of finding the factorial of a number is n = 0 .

Given :

the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! .

Base case :

The base case is the condition to stop the recursion. The recursive case is the part where the function calls on itself .

we know that ,

def func ( n ) :

     if   n == 0 :

return 1

Here the base case is clearly n = 0

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The value of the expression; 6 × 10 + 4³ as given in the task content is; 124.

It follows from the task content that the value of the expression given in the task content; 6 × 10 + 4³ is to be determined.

Hence, the value of the expression can be evaluated using PEMDAS guidelines as follows;

Since the given expression is;

6 × 10 + 4³

Since the exponent, so that we have;

6 × 10 + 64

Next, solve the multiplication, so that we have;

60 + 64

= 124.

On this note, the value of the expression is; 124.

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The age of the bones from the skeleton of s fish is 2000 years.

The formula to be used for calculation of age is-

ln (N/No) = - kt, where N/No represents remaining time, k represents constant of proportionality and t refers to the age or time period.

The remaining time = 100 - 22

Remaining time = 78% or 0.78

Keep the values in mentioned formula to find the time.

ln 0.78 = - 0.000124t

Keeping the value of ln 0.78 on Left Hand Side of the equation

- 0.248 = - 0.000124t

Negative sign will be cancelled as it is present on both sides of the equation

t = 0.248/0.000124

Performing division on Right Hand Side of the equation

t = 2000

Hence, the age is around 2000 years.

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The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number be represented as A

Now , the value of A is calculated as

Five subtracted from the product of 6 and a number is at most -25

So , the inequality equation will be

And , substituting the values in the equation , we get

6A - 5 ≤ -25   be equation (1)

Now , adding 5 on both sides of the equation , we get

6A ≤ -25 + 5

6A ≤ -20

Divide by 6 on both sides of the equation , we get

A ≤ -3.33

Therefore , the value of A is -3.33

Hence ,

The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33

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If the bucket is allowed to fall, then its linear acceleration is 8.687 m/s^2.

From the given question,

We have to solve, if the bucket is allowed to fall, then its linear acceleration

Mass of Pulley(M)= 0.692 kg

Radius of pulley(r)= 0.131 m

Mass of bucket(m)= 2.70 kg

Net torque on pulley,

[tex]\Sigma[/tex] r = rT = Iα

T = Iα/r

T= tension on string(connecting pulley and bucket)

I= moment of inertia of pulley

α= angular acceleration of pulley

linear acceleration of bucket(a),

a = rα

α = a/r

Pulley is disc shaped so

I = 1/2 Mr^2

Now, T= Iα/r = (1/2 Mr^2) (a/r)/r

T = 1/2 Ma

Now considering the motion of bucket

ma = mg-T

ma = mg-1/2 Ma

ma+1/2 Ma = mg

a = m/(m+1/2 M) g

Now putting the value

a = (2.70)×9.8/ (2.70+1/2 (0.692))

After solving

a = 8.687 m/s^2

If the bucket is allowed to fall, then its linear acceleration is 8.687 m/s^2.

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The right question is;

A 2.70 kg bucket is attached to a disk-shaped pulley of radius 0.131 mm and mass 0.692 kg . If the bucket is allowed to fall, What is its linear acceleration.

If n is a multiple of 8, then n is even, according to commutativity. However, n is not an even number. As a result, n is not a multiple of 8.

Commutativity is a mathematical term that explains sums that can be shifted about and still produce the same solution.

'Commutative' is derived from the term 'commute,' which means to move and go around; thus, commutative equations feature integers that can be moved within the equation.

In mathematics, commutative law is one of two laws relating to number operations of addition and multiplication that are symbolically written as

a + b = b + a and ab = ba.

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Answer:

35:1 because that is the most likely answer

The two consecutive positive integers as detailed in the question are;

15 and 16

Let the two consecutive integers be;

x and (x + 1).

We are told that the product of two consecutive positive integers is greater than their sum by 209.

Thus, the expression for this is;

x(x + 1) - 209 = x + x + 1

x² - x - 210 = 0

Using quadratic equation formula, we get;

x = -(-1) ± √((-1)² - 4(1 * -210))]/2(1)

x = (3 ± √(9 + 840)]/2

x = 15

Thus, the second number is; x + 1 = 15 + 1 = 16

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As a result, the second table agrees with the formula y= 3x -3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

-3x - 3 = -6

y= 3x -3

Therefore, the second table matches the equation y= 3x -3.

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Answer:

Step-by-step explanation:To calculate the total cost of the cement manufacturing company, you need to consider the unit variable cost, the commission, and the fixed costs.

First, calculate the total variable cost per day by multiplying the unit variable cost by the number of tons of cement produced per day: $80/ton * 5000 tons/day = $400,000/day

Then, calculate the total commission cost by multiplying the total variable cost by the commission rate: $400,000/day * 5% = $20,000/day

Next, calculate the total fixed cost per day by dividing the monthly fixed cost by the number of days in a month: $12,000/month / 30 days/month = $400/day

Finally, add the total variable cost, the total commission cost, and the total fixed cost to calculate the total cost per day: $400,000/day + $20,000/day + $400/day = $420,400/day

To calculate the break-even revenue, divide the total cost by the difference between the sales price and the unit variable cost, then multiply by the number of tons of cement sold per day: ($420,400/day) / ($150/ton - $80/ton) * 5000 tons/day = $600,000/day

This means that the cement manufacturing company needs to generate at least $600,000 in revenue per day in order to break even.

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Answer:

[tex]\begin{aligned}\textsf{1.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{2.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{3.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

Step-by-step explanation:

Root Multiplicity

Odd multiplicity → the graph will cross the x-axis at the root.

Even multiplicity → the graph will touch the x-axis at the root (but will not cross the x-axis).

Given function:

[tex]p(x)= \dfrac{2}{3}(3x - 6)(x + 2)(x - 3)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  

Therefore, the x-intercepts are:

Therefore, the graph of the given function has 3 turning points.

Given function:

[tex]p(x)=(x - 3)^2 (x + 2) (2x + 7)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  Therefore, the x-intercepts are:

Therefore, the graph of the given function has 4 turning points.

Given function:

[tex]p(x)=(x - 5)(x + 2)(x - 1)-30[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The graph has 2 turning points.

Answer: 6,845.9, or to whole number 6,846

Step-by-step explanation:

Step-by-step explanation:

this is a combined event.

a probability is always the ratio

desired outcomes / totally possible outcomes

in our experiment with rolling 2 dice we have totally 6×6 = 36 different outcomes.

from these 36 total possibilities we desire the following (sum is less than or equal to 8, one die has to show a 6) :

6 1

6 2

1 6

2 6

that is 4 desired outcomes.

and the probabilty for this is

4/36 = 1/9 = 0.111111111...

in mathematical terms we could say :

one possible scenario is one die is 6, and the other is either 1 or 2.

the probability for one die to show 6 is

1/6

the probability for one die to show 1 or 2 is

2/6.

the probabilty for the combination is then

1/6 × 2/6 = 2/36 = 1/18

how many different combinations can we have ?

well, with 2 dice we have 2 such possible combinations.

therefore, the probability is

2 × 1/18 = 2/18 = 1/9.

Centroid and Incentre always lie inside the triangle.

The centroid is the center point of the object. The point in whereby the three medians of the triangle intersect is called the centroid of a triangle. It is also described as the point of intersection of all the three medians. The median is a line which joins the midpoint of a side and the opposite vertex of the triangle.

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be described as the point in which the internal angle bisectors of the triangle cross.

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