L'expression -6x + 8 est la forme réduite de :
-3x + 3x + 2 *4 ou 2x - 8x *5 + 3 ou 2x - (5x - 6) + (-3x + 2) ou - (3x + 5) + (-2x + 3) - x

Answer:

60 years old

Step-by-step explanation:

A=Ashu's age. M=Ashu's Mother's Age

M=A*3

M/3 = (A*3)/3  ==> divide 3 on each side to solve for A

A = M/3

A+5 = M/3 + 5  ==> A+5=25 since that'll be Ashu's age 5 years from now

25 = M/3 + 5  => plug in 25 for A+5

25-5 = M/3 + 5 - 5 ==> solve for M

20 = M/3

M = 20 * 3

M = 60 years old

Answer:

Solutions: -1, 4, and 0

Step-by-step explanation:

f= -4.5

2f - 8 ≤ 6f + 4

2 (-4.5) -8 ≤ 6 (-4.5) + 4

-9 - 8 ≤ -27 + 4

-17 ≤ -23

Not True

f= -8

2f - 8 ≤ 6f + 4

2 (-8) - 8 ≤ 6 (-8) + 4

-16 - 8 ≤ -48 + 4

-24 ≤ -44

Not true

f= -1

2f - 8 ≤ 6f + 4

2 (-1) - 8 ≤ 6 (-1) + 4

-2 - 8 ≤ -6 + 4

-10 ≤ -2

True

f= 4

2f - 8 ≤ 6f + 4

2 (4) - 8 ≤ 6 (4) + 4

8-8 ≤ 24 + 4

0 ≤ 28

True

f= 0

2f - 8 ≤ 6f + 4

2 (0) - 8 ≤ 6 (0) + 4

0 - 8 ≤ 0 + 4

-8 ≤ 4

True

The range of the starting salaries is 53,000

Given,

The box and whisker plot below shows the starting salaries

The number of graduates in a small college = 120

We have to find the range of the starting salaries;

Range of a data;

The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.

Here,

Lowest value = 19,000

Highest value = 72,000

Then,

Range of the set = 72,000 - 19,000 = 53,000

That is,

The range of the given data set is 53,000

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The total Number of miles she biked, was 216.

In the given question, over 18 days, Sophia rode her bike an average of 12 miles each day.

We have to find the total number of miles she biked.

As we know that average is the sum of all numbers divide by total numbers.

As from the question, there is a total average of 18 days.

So the total number of days is 18.

The average distance of her bike for one day is 12 miles.

So we have to find the total number of miles that she biked.

We can find the total number of miles by multiplying the total number of days with the average speed of one day. So;

Total Number of Distance = Total Days × Average Speed of One Day

Total Number of Distance = 18 × 12

Total Number of Distance = 216 miles.

So, the total Number of Distance she biked, was 216 miles.

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The van der Pol equation which is a second-order differential equation is given by

d²x/dt² - μ(1 - x²)dx/dt + x = 0

Here we are asked to convert it to a two-dimensional system.

Here we need to set y = dx/dt, where y represents the system's velocity.

Hence we will rewrite it as

d²x/dt² = μ(1 - x²)y + x

Now if we set the derivatives of x and y with respect to time to be equal to different variables we get

dx/dt = y

dy/dt = μ(1 - x²)y + x

Hence we get the above systems of equations as the 2-dimensional representation of the Van der Pol equation where x and y represent the system's position and velocity respectively.

If we set μ = 1 and x = 0, then we get

dx/dt = y

dy/dt = y

Hence we get the system of differential equations representing the behavior of the van der Pol equation with μ = 1 and x = 0 in two dimensions.

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The final distance is 31 km.

Time, t = Distance, d/Velocity, v

Let's assume the ambulance drives a distance of x along the road, which leaves us 50-x on the road, after which it has reached the road.

It forms a triangle, after which we can use Pythagoras Theorem.

Using it, we get distance down the hill, d1, and we can calculate distance on the road remaining till the hospital, d2.

t = d1/v1 + d2/v2

 = [tex]\frac{\sqrt{x^{2} + 30^{2} } }{30} + \frac{50 - x}{120}[/tex]

We need to minimise t. Therefore, we have to differentiate.

On differentiating and equating it to 0, we get the value of x as [tex]\sqrt{60} = 7.75[/tex]

How far down the road should the vehicle aim to reach the road to reach the hospital at the minimum time?

[tex]= \sqrt{900 + 7.75^{2} } = 31 km[/tex]

Thus, the final distance is 31 km.

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C. The point estimate of the difference between the two population means is 2.

D. The 90% confidence interval estimate of the difference between the two population means is (1.748, 0.867)

Given that:

Sample 1 mean (x1) = 9

Sample 2 mean (x2) = 7

Sample 1 standard deviation (σ1^2) = 2.28

Sample 2 standard deviation (σ2^2) = 1.79

C. To find point estimate of the difference between the two population   means.

sample mean(x1) - sample mean(x 2)

 = 9 - 7

= 2

Therefore, point estimate = 2

D. To find 90% confidence interval estimate of the difference between the two population means

90% confidence for 't'

df = (n1 + n2) - 2

   = 12-2

   = 10

90%  confidence with df = 10 is t

t = 1.812

point estimate + 1 - t * [tex]\sqrt{\frac{s^2_{1} }{n_{1} } + \frac{s^2_{2} }{n_{2} } }[/tex]

2 + 1 - 1.812*[tex]\sqrt{\frac{2.28^2}{6} + \frac{1.79^2}{6} }[/tex]

3 - 1.812 *[tex]\sqrt{0.866 + 0.534}[/tex]

1.188 * 0.9305 + 0.7307

(1.748, 0.867)

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86

Step-by-step explanation:

Answer:

The width would be 5, and the length would be 15.

Step-by-step explanation:

To solve this problem, first look at the perimeter. If the perimeter of the rectangle is 40m, then we can now solve the problem.

Since we don't know the width or the length, first, say that the width is w.

Width=w

Now, since the length is three times the width, we can write 3w for the length.

Length=3w.

Now, combine like terms.

w+3w+w+3w=40

8w=40

Divide by 8 on both sides.

40/8=5

w=5.

Since now we know that the width is 5, plug in 5 for w.

3(5)=15

w=5

The width would be 5, and the length would be 15.

Hope this helps! Have a great day! :D

Answer:

Step-by-step explanation:

Let us assume that,

→ Perimeter = 40 m

→ Width = x

→ Length = 3x

Perimeter of rectangle formula,

→ P = 2(l + w)

Forming the equation,

→ 2(3x + x) = 40

Now the value of x will be,

→ 2(3x + x) = 40

→ 2(4x) = 40

→ 8x = 40

→ x = 40/8

→ [ x = 5 ]

Then the length and width is,

→ Width = x = 5 m

→ Length = 3x = 3(5) = 15 m

Hence, these are the answers.

The solution to the inequality, 2/3z > 4/5, is calculated as z > 1.2. See attachment for the graph of the solution.

The solution to an inequality is determined by finding he value of the variable in the inequality that will make it true.

Given the inequality, 2/3z > 4/5, isolate the variable z to one side to determine its value:

2/3z > 4/5 [given]

Multiply both sides by 3/2:

2/3z × 3/2 > 4/5 × 3/2

z > (4 × 3) / (5 × 2)

z > 12 / 10

Simplify further:

z > 6/5

z > 1.2

The solution is z > 1.2. The graph of the solution is shown in the image that is given in the attachment below.

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Answer:

y = -1/2 x - 1

Step-by-step explanation:

A (-2,0)

B (0,-1)

slope = (-1-0)/(0-(-2)

-1/2

y intercept = -1

y = -1/2 x - 1

Answer:

  y = e^(-1/2x -1)

Step-by-step explanation:

You want the equation for y(x), which is graphed as a straight line on a semi-log scale.

Let z = ln(x). The graph shows a straight line with a z-intercept of -1 and a slope of "rise"/"run" = -1/2. That means the slope-intercept equation for this line can be written as ...

  z = -1/2x -1

Using z = ln(y), we can find the equation for y by taking antilogs:

  ln(y) = -1/2x -1

  y = e^(-1/2x -1)

__

Additional comment

The attached graph shows y = f(x) and the line ln(y).

a) The joint density of Y1 and Y2 is f(y1, y2) = 1, for 0 ≤ y1, y2 ≤ 1.

b) The marginal density for Y1 is f(y1) = 1, for 0 ≤ y1 ≤ 1.

Explanation:

(a) The joint density of Y1 and Y2 is found by multiplying the two individual densities together. Since Y1 and Y2 are independent, this is simply the product of the two densities.

The density for U1 is the same for all values of U1 on the interval (0,1), which is 1. The density for U2 is also the same for all values of U2 on the interval (0,1), which is also 1.

Therefore, the joint density of Y1 and Y2 is:

f(Y1,Y2) = f(U1U2,U2)

= f(U1) x f(U2)

= 1 x 1

= 1

(b) The marginal density for Y1 is the density of Y1 without regard to Y2. Since Y2 is uniform on (0,1), we can integrate the joint density over the interval (0,1) to obtain the marginal density of Y1:

f(Y1) = ∫f(Y1,Y2)dY2

= ∫1dY2

 Y2 = 1

Therefore, the marginal density of Y1 is 1

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Count the average-case number of + operations performed by the following pseudocode segment. The average-case number of + operations performed is 6.67.

The pseudocode segment is a while loop that runs from t=0 to t=101. For each iteration, it adds Xi to the value of the variable liri. Since the preconditions list X as a set of five integers (10, 20, 30, 40, 50, 60) in increasing order, the variable Xi will take on each of these values in turn. Thus, the loop will perform + operations six times (once for each value of Xi). The average-case number of + operations performed is 6.67 (6 operations in total divided by the number of iterations, i.e. 101).

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A bond quote of 75.65 is equal to  $75.65 in dollars. The correct option is B.

A bond quote is the most recent price at which a bond traded, converted to a point scale and expressed as a percentage of par value. Par value is typically set at 100, or 100% of a bond's $1,000 face value. If a corporate bond is quoted at 99, for instance, it is currently trading at 99% of its face value. In this instance, each bond costs $990 to purchase.

The most recent price at which a bond traded is referred to as a bond quote.

Bond quotes are converted to a point scale and expressed as a percentage of par (face value). The standard par value is 100, which equals 100% of a bond's $1,000 face value. Bond quotes can include fractional values.

Therefore, based on the information given, the correct option is B.

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Answer:

the probability of selecting one red marble, one yellow marble, and a blue marble is 1/52. This can also be expressed as a percentage by dividing the probability by 1 and multiplying by 100%, which gives a probability of approximately 1.9%.

Step-by-step explanation:

The graph of the given proportional relation shows that the line passes through the point (0, 0) and continues through the point (15, 5). The relation is represented by the equation y = -0.33x. So, option A is correct.

The given table shows the x and y coordinates of a line.

So, we can find the relationship among them by writing an equation from the given points as

y - y₁ = {(y₂ - y₁)/(x₂ - x₁)} × (x - x₁)

Here we have (x₁, y₁) = (15, 5); (x₂, y₂) = (9, 3)

⇒ y - 5 = (3 - 5)/(9 - 15) × (x - 15)

⇒ y - 5 = (-2)/(-6) × (x - 15)

⇒ y - 5 = 1/3 × (x - 15)

⇒ 3y - 15 = x - 15

⇒ 3y = x + 0

∴ y = 0.33x

Thus, the equation for the given proportions is y = 0.33x.

Since the line is in the form of y = mx, it passes through th point (0, 0) and continues through the point (15, 5).

So, option A is correct.

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The solution of the algebraic expression   (3x + 2y)³ is

[tex]\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now, algebraic expressions are of different types. They are-

Monomial, Binomial and trinomial.

Algebraic expression with only one term is called monomial

Algebraic expression with two terms are called binomial

Algebraic expressions with three terms are called trinomial.

Algebraic expressions with more than three terms are called polynomial.

Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on

Algebraic expression of degree one is called linear

Algebraic expression of degree two is called quadratic

Algebraic expression of degree one is called cubic

The given algebraic expression is  (3x + 2y)³

Now,

[tex](3x +2y)^3\\(3x)^3 + 3 \times (3x)^2 \times (2y) + 3 \times 3x \times (2y)^2 + (2y)^3\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]

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The nominal rate investment ranges from 4.90%, 4.92%, 4.95%, and 4.96%.

Part (c), or IV, III, II, and I, is therefore the right response to the question.

We must now determine the effective interest rate [tex]R_{e}[/tex] , we'll use the formula:-

[tex]R_{e} = (1 + i)^{k} - 1[/tex]

where, i = r / k

Here,

r = interest rate,

I = the nominal interest rate,

k = is the number of times that interest is compounded annually.

(i) 4.87% compounded quarterly

Then i = (4.87 / 100) * 4 =

i = 0.0487 * 4 = 0.012

So, [tex]R_{e}[/tex]  = (1 + 0.012)⁴ - 1

[tex]R_{e}[/tex] = 0.0496 = 4.96 %

Therefore, the effective Interest Rate = 4.96%

(ii) 4.85% compounded monthly

Then i = (4.85 / 100) * 12

i = 0.0485 * 12 = 0.0040

So, [tex]R_{e}[/tex]  = (1 + 0.0040)⁴ - 1

[tex]R_{e}[/tex] =0.04959 = 4.95 %

(iii) 4.81% compounded daily (365 days)

Then i = (4.81 / 100) * 365

i = 0.0481 * 365 = 0.00013

So, [tex]R_{e}[/tex]  = (1 + 0.00013)⁴ - 1

[tex]R_{e}[/tex] = 0.0492 = 4.92 %

(iv) 4.79% compounded continuously

Then i = (4.79 / 100)

i = 0.0479

So, [tex]R_{e}[/tex]  = (1 + 0.0479)⁴ - 1

[tex]R_{e}[/tex] =  0.0490 = 4.90 %

Therefore, the nominal rate investment is as follows: 4.90%, 4.92%, 4.95%, and 4.96%.

The right response to the question is section (c), which is IV, III, II, and I.

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Answer:

$126,000

Step-by-step explanation:

The net cash flow for the year is $103, 000.

After all debts have been settled, net cash flow can represent either a gain or a loss in money over a time period. A company is said to have positive cash flow if, after paying all of its operational expenses, it still has cash left over.

We have,

Sales for the year = $ 218, 000

Cash expenses = $92, 000

Depreciation Expenses = $23, 000

So, the Net cash flow is

= 218,000 - (92, 000 + 23, 000)

= $ 103, 000.

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Answer:

x=-6.-3.0.3.6

y=6.3.0.-3.-6

Step-by-step explanation:

So in this problem you're given the table at the top for your values of X is going across their corresponding P of X values and their corresponding Q of X values. So in part A we want to find P fq of X. So first off we're gonna start when X is equal to zero. So that would mean we want to find p. of Q. of zero. So remember you start with your inside function. Well Q of zero is equal to zero. So now we need to find P. Of zero which is equal to three. Alright so next we want to find when X is one. So we have P of Q of one. Well Q of one is equal to one and I'm sorry that would leave us with PS one and PS one happens to also be one. So that'll be value for one. Next for one. X. is to so api of Q of two. Well Q two is equal to four and then P. Of four. That would leave us a pr four and pr four is equal to five. So that will be our answer for the next one. It will be five. Alright, next for three. So we have p. of Q. of three. So we have two of three which is equal to two. So now sorry that should be a P. Then we find P. F two which is also to So that'll be the answer to the 3rd 1 Next we need it for four. So we're looking for p of Q of four. Well looking according to our thing. Q4 is equal to five and then we have to find P. Of five which is zero. And lastly for five. So first we'll start with p. of Q. of five. So Q. A. Five we're told is three. So then we have to find pf three which is equal to four. So that's how you would find your first values. Okay, So now part B. We want to find sfx but no, this is the opposite way this time it's Q. A. P. Of X. So when X zero, we're going to be looking for Q. Of P. Of zero. Well no this P. Of zero is equal to three. So then we have to find Q. of three which is equal to two. It'll be our first answer. Next we'll do one. So we're gonna have Q. Of P. Of one. Well p. of one is equal to one. So then we find Q. Of one which is also one. So bring that down. All right, so now for two. First we're gonna start with Q. A. P. F. Two. Well P. F two is two. So that means we're essentially just finding Q. Of two which is four. Alright, next for three. So you're gonna have cute Of p. of 3? Well p of three is equal to four And Q four is equal to five. So I'll be your answer there. I'll do a new color because I think we're running out of room here. So next we're doing for, so I'm gonna go right here. So we're gonna have Q. A. P. Of four. Well if you four is equal to five, so that means we have to find Q. Of five which is three. And lastly for five. So we're gonna have Q. A. P. Of five. So first we'll find PFE which is zero. So that means now we need Q. Of zero which is zero. And now we filled out both of your tables.

The compositions of the two given functions are:

g(f(x)) =   √(2*x + 29) - 2

f(g(x)) = √(2*x  + 25)

Here we have the two functions:

f(x) = √(2x + 29)

g(x) = x - 2

We want to find the compositions:

f(g(x))

So we just need to evaluate f(x) on g(x), we will get:

f(g(x)) = √(2*g(x) + 29)

Now we can replace g(x) there:

f(g(x)) = √(2*(x - 2) + 29)

f(g(x)) = √(2*x - 2*2 + 29)

f(g(x)) = √(2*x  + 25)

The other composition is:

g(f(x)) = f(x) - 2

g(f(x)) =   √(2*x + 29) - 2

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Answer:

every week jill is going to make 5.20 dollars then you do 5.20 x 1095 days in 3 years = $5694 a year  

Step-by-step explanation:

Answer:

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

Since the triangles CAT and DOG overlap, their corresponding parts are congruent.

As we are looking for ASA congruency, we need to select two angles and the included side.

Let's review the given options, considering names of triangles and the order of vertices in those names.

A. ∠ A ≅ ∠ T  

B. CA ≅ DO

C. AT ≅ OG

D. CT ≅ DG

E. ∠ A ≅ ∠ O

F. ∠ C ≅ ∠ D

So we have corresponding angles A and C and the included side must be AC.

Looking, at the options, we can get ASA with combination of options B, E and F.

Answer:

$130.84

Step-by-step explanation:

If a 7% sales tax is applied, the cost of the item (including tax) will be 107% of the original price.

To calculate how much Emma can spend if she has $140 cash to spend, divide $140 by 107%:

[tex]\implies \dfrac{140}{107\%}[/tex]

[tex]\implies \dfrac{140}{\frac{107}{100}}[/tex]

[tex]\implies 140 \times \dfrac{100}{107}[/tex]

[tex]\implies \dfrac{14000}{107}[/tex]

[tex]\implies 130.84[/tex]

Therefore, Emma can spend $130.84 on items if there is a 7% sales tax.

Relations in the options (a), (b) and (e) are the Equivalence relations as, the relations are reflexive, symmetric and transitive all.

Given, five relations as,

a) {(a, b) | a and b are the same age}

b) {(a, b) | a and b have the same parents}

c) {(a, b) | a and b share a common parent}

d) {(a, b) | a and b have met}

e) {(a, b) | a and b speak a common language}

we have to find which of them are equivalence relations

a) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.

So, R = {(a, b) | a and b are the same age} is an equivalence relation.

b) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.

So, R = {(a, b) | a and b have the same parents} is an equivalence relation.

c) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.

So, R = {(a, b) | a and b share a common parent} is not an equivalence relation.

d) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.

So, R = {(a, b) | a and b have met} is not an equivalence relation.

e) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.

So, R = {(a, b) | a and b speak a common language} is an equivalence relation.

Hence, the relations in options (a) , (b) and (e) are the equivalence relations.

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The meaning when LA Lakers had a PCT of 58.3 in the 2020-21 season is that the percentage of winning is 58.3%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information given, the LA Lakers had a PCT of 58.3 in the 2020-21 season. It should be noted that PCT simply means percentage. Therefore, it denotes 58.3 percent.

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Complete question

The LA Lakers had a PCT of 58.3 in the 2020-21 season. What does this mean in practical terms