The single equivalent discount rate of the trade discount 6/4/2 is:

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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a²b is the same thing as ba²

b and a are two separate variables lets pretend a is 2 and b is 3

2² * 3 = 4 * 3 = 12

3 * 2² = 3 * 4 = 12

this is the commutative property of multiplication

An expression is defined as a set of numbers, variables, and mathematical operations. The two of the given expressions a²b and ba² are the same.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The two of the given expressions a²b and ba² are the same because if the two of the expressions are expanded then the value of the two expressions will be equal to each other.

Therefore, the two expressions are expanded as shown below,

a²b = a × a × b

ba² = b × a × a

Therefore, the two of the given expressions a²b and ba² are the same.

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Answer:

C / 15%

Step-by-step explanation:

Answer:

6.05

Step-by-step explanation:

12 and a half percent of 48.4 = 6.05 because you can put .125 in your calculator and it is the same at 12.5% so you do .125 * 48.40 and you get 6.05

Answer:

no

Step-by-step explanation:

Answer:

y = x - 10

Step-by-step explanation:

slope - intercept form: y = mx + b

y2 - y1         -4 - ( -8 )            4

---------   =   -------------   =   --------   =   1

x2 - x1           6 - 2               4

---------------------------------------------------------

y = mx + b

y = 1x + b

pick whichever point you want to use, for this I'll use (2, -8)

-8 = 1( 2) + b

-8 = 2 + b

-2   -2

-10 = b

y = 1x - 10 or y = x - 10

I hope this helps!

Answer:

5040 is the right answer

Step-by-step explanation:

5040/1=5040

5040/2=2520

5040/3=1680

5040/4=1260

5040/5=1008

5040/6=840

5040/7=720

5040/8=630

5040/9=560

5040/10=504

9514 1404 393

Answer:

  m = -6/7

Step-by-step explanation:

The sum of an infinite geometric series with first term a1 and common ratio r is ...

  S = a1/(1 -r)

Here we have the first term (3) and the sum (27/7) and we want to find r.

  27/7 = 3(1 -r)

  9/7 = 1 -r

  r = 1 -9/7 = -2/7

Then the value of m is 3r = 3(-2/7) = -6/7.

Answer:

z=2

Step-by-step explanation:

The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer:

The maximum probability for each of the components in a system to fail, for you to still achieve your objective, is 0.008992

Step-by-step explanation:

- There are 1,000 different components in each system.

- The Objective:

Each system should have a 0.999 probability of functioning properly. In other words, your department (or you) expects that each system will have a high probability of functioning properly, hence the closeness of 0.999 to 1.

- Each system is such that at most 8 components out of 1,000 can be bad, for it to still function.

- Question:

What must be the maximum probability for each component in a system to fail, for the system to still have a 0.999 probability of functioning properly?

ANSWER:

When the question says maximum, you need to assume that for each system, 8 components are actually bad!

1000 - 8 = 992

So with 992 components (at least or minimum) functioning, a system will still function.

Next Step:

Since the objective (the expected probability) for a system to function is 0.999, the probability of each of the minimum 992 components to function (which is same as the maximum probability for each of the 1,000 components to function) is

992/1000 × 0.999    

=0.992 × 0.999

=0.991008

Now, remember that the question says fail, not succeed. So, if the figure above is the maximum success rate for each of the 1,000 component parts (same as the success rate for each of the minimum of 992 component parts), then the failure rate or probability is (1 - 0.991008 = 0.008992).

FINAL ANSWER:

The maximum probability for each of the components in a system to fail, for you to still achieve your objective, is 0.008992

Answer:

F, J, and K

Step-by-step explanation:

The others are negative so they can't be exponential

The exponential function can't be negative or irrational, so options A, D, and E are correct.

The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras. The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.

As we discussed above, the exponential function can't be negative or irrational  so, look at the options only,

f(x) = 10(1/7)ˣ,

j(x) = 8(4.13)ˣ,

k(x) = 12(8)ˣ are the exponential functions, whereas

g(x) = 4(-3)ˣ,

h(x) = 4(-13)ˣ are negative, so they can't be exponential functions.

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Answer:

D 0.89275

Step-by-step explanation:

\(\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+2} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\stackrel{\textit{one intercept}}{\textit{\underline{one solution}}}\qquad \\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 4^2-4(2)(2)\implies 16-16\implies 0\)

The value of the given expression, -50 + 5/13p, when p = -26 is -60

From the question, we are to evaluate the given expression for the given value of p

The given expression is

-50 + 5/13p

and

The given value of p is p = - 26

Substitute the given value of p into the given expression

That is,

-50 + 5/13p

When p = -26, the expression becomes

-50 + 5/13(-26)

Simplify

-50 + 5(-2)

-50 - 10

= - 60

Hence, the value of the expression is -60

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Answer:

P = 37 units

Step-by-step explanation:

Answer:

1436.026667 cubic yd

Step-by-step explanation:

given :

radius = 7 yards

pie = 3.14

we have ,

Volume of sphere = 4/3 × pie × r

=4/3 × 3.14 × 7

=1436.026667 cubic yards

You answered 6,9 and 10,13. The correct answer is 6,9 and 7,13 to find the equation of the linear model.

(a) The two points you selected are (6,9) and (10,13). This is correct.

(b) To find the slope of the linear model, we can use the formula: slope = (change in y) / (change in x). By using the points (6,9) and (10,13), we have (13-9) / (10-6) = 4/4 = 1. So, the slope is indeed 1. This is correct.

(c) The equation of the linear model in point-slope form is given as: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (6,9) as the point and 1 as the slope, we get y - 9 = 1(x - 6). This simplifies to y - 9 = x - 6. This is not the same as the equation you provided. It seems you made a mistake here.

(d) The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To convert the equation y - 9 = x - 6 to slope-intercept form, we can add 9 to both sides: y = x - 6 + 9, which simplifies to y = x + 3. This matches the equation you provided. So, this is correct.

(e) The equation for the least squares regression line is in the form y = bx + a, where b is the slope and a is the y-intercept. In this case, the slope is 1, and we need to find the y-intercept.

We can use the point (6,9) and the slope-intercept form equation y = x + 3 to find the y-intercept: 9 = 6 + 3. Solving this equation, we find that the y-intercept is 3.

Therefore, the equation for the least squares regression line is y = x + 3. This does not match the equation you provided. It seems you made a mistake here.

(f) Based on the correct equation from part (d) (y = x + 3), the correct equation for the least squares regression line is y = 1x + 3. When rounded to three decimal places, this would be y = 1.000x + 3.000.

The equation you provided (Y = 1.028x + 2.271) is slightly different, so it appears you made a mistake in the calculations or rounding.

To summarize, your answers in parts (a) and (b) are correct. However, there are mistakes in parts (c), (e), and (f). The corrected answers are:

(c) The equation of the linear model in point-slope form: y - 9 = x - 6.

(d) The slope-intercept form of the equation: y = x + 3.

(e) The equation for the least squares regression line: y = 1x + 3.

(f) When rounded to three decimal places, the equation is: y = 1.000x + 3.000.

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The required values are,

x = 3

y = 5.

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero

Now in the given question,

we have two equations,

3x - 2y = -1                                 ......(1)

3x + y = 14                                 .......(2)

subtract (2) from (1), we get

-3y = -15

divide both sides by -3, we get

y = 5

now put this value of y in (2),

3x + 5 = 14

subtarct both sides by 5, we get

3x = 9

divide both sides by 3, we get

x = 3

Hence, the required values are,

x = 3

y = 5

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Answer: 408

Step-by-step explanation:

The present worth of Rs 2040 is due 4 years hence reckoning interest at 5% per annum will be Rs 2448.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

Simple interest has a constant principal amount, as opposed to compound interest, which multiplies the interest from the principal of previous years to calculate the interest of the subsequent year.

Given,

Principle amount =  Rs 2040

Time period = 4 years

Rate of interest = 5 %

Simple interest = PRT/100

Simple interest = 2040 × 5 × 4/100 = Rs408

Present worth =  Principle amount + Interest

Present worth = 2040 + 408

Present worth = Rs 2448.

Hence present worth of the amount of Rs2040 in 4 years will be Rs 2448.

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Answer:

d) y= -2/3x+3 1/2

Step-by-step explanation:

Points on the graph: ( -4, 6) and ( -7, 8)

Slope:

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

m=(8-6)/(-7+4)

m= 2/(-3)

m= -2/3

Slope-intercept:

y - y1 = m(x - x1)

y - 6 = -2/3(x + 4)

y - 6 = -2/3x - 8/3

y = -2/3x + 3 1/2

Answer: 270

Step-by-step explanation:

2+5 = 5 times 54 = 270

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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Answer:

x=-12,y=3

Step-by-step explanation:

1/2x+6y=12

y=x+15

since y=x+15

substitute y in first equation, we have

1/2x+6(x+15)=12

open the bracket

1/2x+6x+90=12

1/2x+6x=12-90

x/2+6x= -78

13x/2=-78

13x=2×-78

x=-12

Now x=-12, put x=-12 in the second equation, we have

y=x+15

y=-12+15

y=3

hope it helps

Answer:

x=-8, y=2

Step-by-step explanation:

if 1/2x+6y=12 then 1/2x+y=2 and x+y=1 and y=1-x..if y=1-x then 1-x=x=15 and 2x=16 so x=8 if x=8 then 1/2(8) +6y=12 or 4=6y=12.. then 2y=4 and y=2

Answer:

it is 2.021978 or 184/91

heart if this helps

It's 2.021978 or 184/91

The equation of the line passing through two points (0, 0) and (4, -2) is y = -x/2

The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers.

Given is a line passing through two points (0, 0) and (4, -2), we need to find the equation of the line,

We know that the equation of the line, passing through two points (x₁, y₁) and (x₂, y₂), is given by:

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here, (x₁, y₁) and (x₂, y₂) are (0, 0) and (4, -2), putting the values to finding the equation,

y-0 = -2-0 / 4-0 (x-0)

y = -1/2(x)

y = -x/2

Hence, the equation of the line passing through two points (0, 0) and (4, -2) is y = -x/2

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Answer:

6. .0001

7. .0123

Step-by-step explanation:

Plug in the values in place of x.

6. 10^-4=.0001

7. 2(6)^-1(3)^-3 = .0123

Answer: To write the given values A = 4, B = -2, and C = 7 in standard form, we arrange them in the standard form equation:

4x - 2y = 7

In the standard form of a linear equation, the variables are on the left side of the equation, the coefficients are integers, and the constant term is on the right side.

Step-by-step explanation:

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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The probability of buying 3 tires is 0.05 and the cumulative probability distribution table is created.

What is meant by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

     Percentage of people who buys 4 tires = 50%

      Percentage of people who buys 2 tires = 32%

      Percentage of people who buys less than 2 tires = 13%

    Percentage of people who buys none = 6%

a) Prob(X=0) = 0.06

    Prob(X=2)  = 0.32

   Prob(X=4)  = 0.50

 Prob(X < 2) = Prob(X=0) + prob(X=1) = 0.06+ prob(X=1)

   prob(X=1) =   Prob(X < 2) - 0.06  = 0.13 - 0.06 = 0.07

Therefore prob(X = 3) = 1 - ( 0.5+0.32+0.07+0.06) = 1 - 0.95 = 0.05 = 5%

b) Cumulative probability distribution is as given in the figure.

Therefore the probability of buying 3 tires is 0.05 and the cumulative probability distribution table is created.

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