Which of the following equations shows a directly proportionate relationship?
y = -4x
y = 3x - 1
y = 2.75x - 3
y = 7x

6 hours will it take another train to travel the same distance .

What is speed?

Average speed = Total distance/Total time

A train travels 3 hours at 20km per hour.

 train travels 20 km in 1 hours.

      then in 3 hours train travels = 3 * 20 = 60 km

 total speed = 10 km/hr

          t = distance/speed

           = 60/10 = 6 hours

Learn more about Speed

brainly.com/question/28224010

#SPJ13

Answer: 13,8 litres

Step-by-step explanation:

£1.45 ------------ 1 L

 £20 ------------- ?

?= [tex]\frac{20 *1}{1.45} = 13,79310345 L[/tex] = 13,8 L

The solution of the system of equation by substitution is x = 3 and y = -1.

System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method

Therefore,

3x + 2y = 7

x = 3y + 6

Substitute equation(ii) in equation(i)

3(3y + 6) + 2y = 7

9y + 18 + 2y = 7

9y + 2y + 18 = 7

11y = 7 - 18

11y = -11

y = -11 / 11

y = -1

Hence, let's find x

x = 3(-1) + 6

x = -3 + 6

x = 3

learn more on system of equations here: bhttps://brainly.com/question/10716108

#SPJ1

Answer:In this item, I take it that we are to get  the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.

   -64 = (-4)(-4)(-4)

Then,

  x6 = x2 (x2) (x2)

and,

   y9 = (y3)(y3)(y3)

If we take the cube root, we consider only one item per product. Thus, the answer is,

   -4x²y³

Step-by-step explanation:

The answer to be entered in the boxes for the area model is 17, 0 and 17

An area model is a rectangular diagram or model used for solving multiplication and division problems, in which the quotient and divisor define the length and width of the rectangle

Given:

    ....60.....1.............

36|2160 | 36 | 17

2160 ÷ 36 = 60 R 0

36 ÷ 36 = 1 R 0

17  ÷ 36 =  0 R 17

Note:  (0 x 36) + 17 = 17

Therefore, the answer to be entered in the boxes is 17, 0 and 17 respectively

Learn more about  area model on:

https://brainly.com/question/41837

#SPJ

Answer:

5/8 - 1/4 = 3/8

Step-by-step explanation:

1 x 2 = 2, 4 x 2 = 8, so we're left with 2/8

Answer:

3/8

Step-by-step explanation:

5/8 - 1/4

to be able to compare fractions or add/subtract them directly, we need to bring them all to the same denominator (the bottom part of the fractions).

it is usually easier to bring the smaller to a larger number than the other way around, because of the existing numerators (the top part of a fraction).

since we are dealing with fractions (divisions !), the best way to manipulate them is by multiplying or dividing them by a factor.

so, what do we need to multiply with 4 to get 8 (the other denominator) ?

2, as 4×2 = 8.

aha.

but now careful, we cannot just multiply the denominator by 2. that would change the value of the whole original fraction.

we have to multiply denominator AND numerator by the same factor. that way the original value of the fraction remains the same, because we are essentially multiplying the whole fraction just by 1.

so,

1/4 × 2/2 = 2/8

and now we can easily use it in a calculation with other 8ths :

5/8 - 2/8 = 3/8

the 2 values X(19.8,30.2)  is value will 15% of the observations be below .

by hypothesis .

What is hypothesis ?

Here, Mean(\mu) and Standard Deviation (\sigma)= 5. You need to find the 2 values of which the smallest has 15% of the values below it i.e (Z<x)= 0.15 and the largest has 15% of the values above it i.e(Z>y)= 0.15.

Now we need to refer to the Z tables and see which value of x corresponds to 0.15, and we see that -1.04 is = 0.149 \sim 0.15

Now we know that the Z value is given by Z = X - μ/σ

Substituting we get

  -1.04= (X-25)/5

therefore -5.2= X-25 or X= 19.8

Now let us get the value of X for (Z>y)=0.15`. Since Z tables give values for Z<a only, hence we can write that

Z>y=0.15 is the same as Z<y= 1-0.15= 0.85. We now check the Z tables and see which value of Z corresponds to 0.85, and we get 0.850 = +1.04

Again, substituting Z in the equation Z = X - μ/σ

we get

+1.04= (X-25)/5

Therefore 5.2= X-25, therefore X= 30.2

From the 2 values X(19.8,30.2)

Learn more about hypothesis

brainly.com/question/17173491

#SPJ4

Answer:

182 minutes

Step-by-step explanation:

0.09x+5=21.38

         -5.   -5

0.09x=16.38

/0.09.   /0.09

  X=182

182 minutes

Hopes this helps please mark brainliest

The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.

The equation, in vertex form, of a absolute value function is expressed as y = a|x – h| + k, where:

From the graph, we know that:

Vertex (h, k) = (3, 5)

Substitute h = 3 and k = 5 into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). To find the value of a, substitute x = 5 and y = 7 into the equation y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = 2a + 5

7 - 5 = 2a + 5 - 5 [subtraction property of equality]

2 = 2a

Divide both sides by 2

2/2 = 2a/2 [division property of equality]

Substitute a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5 [equation of the absolute value function]

Learn more about equation of absolute value function on:

https://brainly.com/question/25290500

#SPJ1

In a one-period binomial model of an option value, the probabilities of an up-move and a down-move are "calculated from the model inputs."

The number of survivors, x, in n independent tests is described by a binomial model. The number of tests must be predetermined, the results—success or failure—must be statistically independent for each test, and the survival probability—p—must be constant throughout the tests. When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of observing a specified number of "successes."

To know more about binomial model,

https://brainly.com/question/27575903?referrer=searchResults

#SPJ4

The simplified expressions for the questions will be, 1) 3w, 2) 8x, 3) 10p, 4) 8b.

The simplification of an algebraic expression generally means breaking the equation into a smaller form for easier calculation with the help of formulas or using the rule of BODMAS.

Here, all the questions can be solved by using the BODMAS rule.

1) 7w + 2w - 6w

= (7w + 2w) - 6w

= 9w - 6w

= 3w.

2) 9x - 3x + 2x

= (9x + 2x) -3x

= 11x - 3x

= 8x.

3) 8p + 3p - p

= (8p + 3p) - p

= 11p - p

= 10p.

4) 6b - 3b + 5b

= (6b +5b) - 3b

= 11b -3b

= 8b.

To know more about algebraic expressions:

https://brainly.com/question/19864285

Step-by-step explanation:

[tex]7w + 2w - 6w \\ 9w - 6w \\ = 3w[/tex]

[tex]9x - 3x + 2x \\ 6x + 2x \\ = 8x[/tex]

[tex]8p + 3p - p \\ 11p - p \\ = 10p[/tex]

[tex]6b - 3b + 5b \\ 3b + 5b \\ = 8b[/tex]

The equation of a line on a point (-2,2) is y = -2x-2. That option A is correct.

Here we have to find the equation of a line.

The given data:

Point = ( -2, 2)

Slope(m) = -2

Equation of a line:

y = mx + c

Now putting the values as

y = 2

x = -2

m = -2

We will get the y-intercept.

So we have:

2 = -2 × -2 + c

c = 2 - 4

  = -2

So, y = -2x -2

Therefore we get the equation of line as y = -2x -2.

To know more about the equation of a line refer to the link given below:

https://brainly.com/question/18831322

#SPJ4

Answer:

1,070 g

Step-by-step explanation:

Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 15 minutes. After 45 minutes, then, the amount of radioactive atoms is halved three times. Therefore:

1st half-life: 8,560 ÷ 2 = 4,280 g

2nd half-life: 4,280 ÷ 2 = 2,140 g

3rd half-life: 2,140 ÷ 2 = 1,070 g

The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)

Information gotten from the question include

a slope of -2/3

points (1, -7)

A linear function consists of functions where the variables has exponents of 1.

The equation of a line in point- slope form is expressed in the form.

(y - y₁) = m (x - x₁)

Definition of variables

(y and y₁) = refers to variables in the y direction

m = slope

x and  x₁ = refers to variables in the x direction

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

Learn more about linear functions at:

https://brainly.com/question/29213643

#SPJ1

154.5

Step-by-step explanation:

left triangle and right triangle has the same degree.

M to Q 107/2 = P to R 53.5

O to N 110/2 = R to Q 55

Find X

M to N 92/2 = P to Q 46

Perimeter- 53.5+ 55+ 46= 154.5

Answer:

2-3/-6-(-8)

= -1/2

A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

So we know that the perimeter of rectangle is

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

As we know the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

To learn more about perimeter and area of rectangle link is here

brainly.com/question/16572231

#SPJ1

Step-by-step explanation:

The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.

2028 - 1995 = 33 years, so t = 33

D = 401t + 5940

D = 401(33) + 5940

D = 13,233 + 5940  

D = 19,173

Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173

For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years.

As given in the question,

The formula given to us is A = P[tex]e^{rt}[/tex] where

A = accumulation value

P = principal money

t = time period

r = interest rate compounded

P = 9500

A = 2*9500

r = 0.12

By applying it in the given formula we get

19000 = 9500 * [tex]e^{0.12t}[/tex]

2 =    [tex]e^{0.12t}[/tex]

Take natural log on both sides

㏑(2) = 0.12t

0.6931 = 0.12t

t = 5.775

Therefore , For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years after rounding it off to one place after decimal.

Learn more about interest rate here

brainly.com/question/11339060

#SPJ1

Answer:

b

Step-by-step explanation:

the right side base angle and 80° are vertically opposite angles and are congruent, both 80°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

123° is an exterior angle of the triangle , then

x + 80 = 123 ( subtract 80 from both sides )

x = 43

Since it is labeled that this triangle has two equal sides, it is isosceles. Isosceles triangles' acute angles are always congruent, so we can infer that there are two angles with a measurement of 29 degrees. Knowing that all of the angles in a triangle add up to 180 degrees, we can set up this equation:

2*29 + 11x - 65 = 180

58 + 11x - 65 = 180

-7 + 11x = 180

11x = 187

x = 17

Knowing that "x = 17" we can find the measurement of the obtuse angle:

11*17 - 65

= 187 - 65

= 122

The type of function best models Mrs. Robinson’s data is A. exponential function.

The formula f(x) = a^x defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x. Where an is greater than zero and less than one. x can be any actual number.

Mrs. Robinson created the table, which shows the number of cells in a biology experiment after a certain number of days. The independent variable, or x-value, in an exponential function is the exponent, while the base is a constant.

In this case, we can see that:

2 days = 2² = 4

3 days = 2³ = 8

4 days = 2⁴ = 16

This is an exponential function.

Learn more about exponential function on:

https://brainly.com/question/2456547

#SPJ1

The balance in Marie saving account in week 20 will be $408  .

In the question ,

it is given that

the amount in Marie's saving account in week 1 is $180 .

amount of money deposited every week is = $12 .

to find the balance in week 20 means , she deposited money for 19 weeks .

the amount deposited in 19 weeks = 19 × 12 = $228

the equation to represent the balance after w weeks = 180 + 12*w

putting w = 19 in the equation , we get

the balance in saving account in week 20 = 180 + 12*19

the balance in week 20 = 180 + 228

= $408

Therefore , The balance in Marie saving account in week 20 will be $408  .

Learn more about Equation here

https://brainly.com/question/20917911

#SPJ1

The commission that thereal estate agency gets is $16885.

The commission that the agent gets is $76750

The selling price for a house = $ 307,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 25 %

So, the commission which real estate agency gets:

= 5.5 % of $307,000

= 0.055 × $ 307,000

= $16885

The commission which agent get:

= 25% of $ 382,000

= 0.25 × $ 307,000

= $76750

Learn more about real estate on;

https://brainly.com/question/13960098

#SPJ1

The range of scores that Marjorie's can receive in the final exam to earn a C in the course is 67 to 82  .

in the question ,

it is given that

the Marjorie's score in the tests are 67 , 78 , 75 , 78 .

let the score in the final exam be "x"

it is given that the final exam score is worth 6 test scores , which means

the score in final exam is = 6x

and the total number of tests = 6+4 = 10

given that to get the grade C minimum average is = 70

that is  (67 + 78 + 75 + 78 + 6x)/10 = 70

67 + 78 + 75 + 78 + 6x = 700

298 + 6x = 700

6x = 700 - 298

6x = 402

x = 402/6

x = 67

given that to get the grade C maximum average is = 79

that is  (67 + 78 + 75 + 78 + 6x)/10 = 79

67 + 78 + 75 + 78 + 6x = 790

298 + 6x = 790

6x = 790 - 298

6x = 492

x = 492/6

x = 82

the range of scores is 67 to 82 .

Therefore , The range of scores that Marjorie's receive in the final exam to earn a C in the course is 67 to 82  .

Learn more about Average  here

https://brainly.com/question/12191218

#SPJ1

Answer:

3/5

Step-by-step explanation:

Given problem,

→ (1/10) + (1/2)

Let's solve the problem,

→ (1/10) + (1/2)

→ (1/10) + (5/10)

→ 6/10

→ 3/5 {simplest form}

Thus, answer is 3/5.

the equation of the line passing through the given points is y = 3

What is an equation of the line?

An expression which is satisfied by every point on the line is known as equation of the line. generally it is given in y = mx + c form where m is the slope and c is the y-intercept

We are given two point (-7,3) and (5,3)

We first find the slope of the lines passing through the given points

Slope = [tex]\frac{3-3}{5+7}[/tex]

Slope = 0

Substituting the value in the equation we get

y = c

Now the value of y in both the cases is 3

Substituting that we get c = 3

Hence y = 3 is the required equation of the line

To learn more about equation please refer the following link

https://brainly.com/question/22688504

#SPJ1

We can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.

Given, that there are 3 boxes and we have to put 8 balls in them such that no box is empty.

Let, a + b + c = 8, where a , b , c represent three different boxes.

The equation be reduced by allotting 1 ball to each box so that no box remains empty.

Hence, a + b + c = 5

Now, using the formula of "no. of ways in which 'n' objects can be grouped into 'r' groups" i.e. C(n+r-1 , r-1)

So, the required number of ways = C(5+3-1 , 3-1) = C(7 , 2)

Calculating, C(7 , 2) = (7×6)/2 = 21

Hence, we can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.

Learn more about Permutation and Combination here https://brainly.com/question/1216161

#SPJ4