A freight train travels 50 miles per hour. Write a linear function that describes the distance the train travels over time. Then make a graph to show the distance the train travels in 5 hours.

Answer:

Table C

Step-by-step explanation:

Given

Table A to D

Required

Which shows a proportional relationship

To do this, we make use of:

[tex]k = \frac{y}{x}[/tex]

Where k is the constant of proportionality.

In table (A)

x = 2, y = 4

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{4}{2}[/tex]

[tex]k = 2[/tex]

x = 4, y = 9

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{9}{4}[/tex]

[tex]k = 2.25[/tex]

Both values of k are different. Hence, no proportional relationship

In table (B)

x = 3, y = 4

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{4}{3}[/tex]

[tex]k = 1.33[/tex]

x = 9, y = 16

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{16}{9}[/tex]

[tex]k = 1.78[/tex]

Both values of k are different. Hence, no proportional relationship

In table (C):

x = 4, y = 12

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{12}{4}[/tex]

[tex]k = 3[/tex]

x = 5, y = 15

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{15}{5}[/tex]

[tex]k = 3[/tex]

x = 6, y = 18

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{18}{6}[/tex]

[tex]k = 3[/tex]

This shows a proportional relationship because all values of k are the same for this table

(a) w(x) = 5u(x) + 8v(x)

Differentiating with the sum rule gives

w'(x) = 5u'(x) + 8v'(x)

so that

w' (-5) = 5u' (-5) + 8v' (-5)

… = 5×2 + 8×4 = 42

(b) w(x) = u(x) v(x)

Differentiate using the product rule:

w'(x) = u'(x) v(x) + u(x) v'(x)

Then

w' (-5) = u' (-5) v (-5) + u (-5) v' (-5)

… = 2×6 + (-5)×4 = -8

(c) w(x) = u(x) / v(x)

Quotient rule:

w'(x) = (u'(x) v(x) - u(x) v'(x) ) / v(x) ²

Then

w' (-5) = (u' (-5) v (-5) - u (-5) v' (-5) ) / v (-5)²

… = (2×6 - (-5)×4) / 6² = 32/36 = 8/9

(d) w(x) = u(x) / (u(x) + v(x) )

Chain and quotient rule:

w'(x) = (u'(x) (u(x) + v(x)) - u(x) (u(x) + v(x))' ) / (u(x) + v(x) )²

… = (u'(x) (u(x) + v(x)) - u(x) (u'(x) + v'(x))) / (u(x) + v(x) )²

Then

w' (-5) = (u' (-5) (u (-5) + v (-5)) - u (-5) (u' (-5) + v' (-5))) / (u (-5) + v (-5) )²

… = (2×((-5) + 6) - (-5)×(2 + 4)) / ((-5) + 6)²

… = (2×1 + 5×6) / 1² = 32

Answer:

14

Explanation: 2/9x 63= 2x 63/9= 2x7

Answer:

14

Step-by-step explanation:

i believe so....

Answer: 38

step by step

deltamath

Answer:

38

Step-by-step explanation:

Answer:

I believe the answer is c) 3

Step-by-step explanation:

f(x) = (x + 3)(x - 1)(2x + 2)

x(x) + x(-1) + 3(x) + 3(-1)

f(x) = (x^2 - x + 3x - 3)(2x + 2)

f(x) = (x^2 + 2x - 3)(2x + 2)

2x(x^2) + 2x(2x) + 2x(-3) + 2(x^2) + 2(2x) + 2(-3)

f(x) = (2x^3 + 4x^2 - 6x + 2x^2 - 6)

f(x) = (2x^3 + 6x^2 - 6x - 6)

Answer:

B

Step-by-step explanation:

If you look at 3 on the X-axis and go down 4 then you will get point B as your answer.

Answer:

E is the correct answer because A is (-4,-3), B is (-4,3), C is (5,1), D is (4,-3), E is (3,-4), and F is (-2,-4)

Hi there! Your answer to this question would be 90%..

Step By Step Explanation:

So we know that 100% is the average grade for an correct for an entire test.

But how can we find 90%?

Let think like this. 10=100%.

Well if 10 is 100% then 9 would be 90% since every 1 of 10 is 10%.

Final Result: 90%

Answer:

D. -12x + 18

Step-by-step explanation:

f(x) = -6x +5; g(x) = 2x + 8

[g o f](x) = g(f(x))

this means that in g(x), everywhere there's an x, f(x) replaces it. [g o f](x) is represented at the following: (f(x) is in bold)

g(f(x)) = 2(-6x +5) + 8                  distribute the 2 to (-6x + 5)

g(f(x)) = -12x + 10 + 8                   combine like terms

g(f(x)) = -12x + 18

Answer:

A, D,

A.) He decides to give all male athletes Gatorade and the female athletes eitherPowerade or Vitaminwater.

D.) He has some of the athletes drink the sports drink two hours beforerunning,others one hour before running, and the rest 30 minutes beforerunning.

Step-by-step explanation:

Confounding variables could be described as variables which introduces elements that causes unwanted relationship between measured variables in data. Such that observed relationship is actually not as a result of the independent variable.

The confounding variables in the options chosen are gender and timing of the consumption and when the athletes eventually ran.

As for gender, male athletes are expected to put up a better running speed and energy than women and Hence would finish the rate faster based on these fact. Hence, it will be wrong to conclude that Gatorade has Better effect on performance.

As for timing, those who run shortly after taking an energy drink are more likely to be boosted that those who take much later and this the effect may not necessarily be in the type of energy drink consumed.

Confounding variables are the variables which are not related to the experiment.

Confounding variables are the variables which are not related to the experiment. Confounding variables provides the affects the useless results and affects the experiment.

Given information-

The total number of meters the athletes runs is 400 meters.

The sports drink given to athletes are Powerade, Gatorade and Vitamin water.

The given options are,

Hence,

learn more about the confounding variable here;

https://brainly.com/question/10458420

Answer:

z = 4/5

Step-by-step explanation:

Answer:

121 feet

Step-by-step explanation:

Equation:

484 / 4 = 121

Word Explanation:

If there are 4 sides in a square and the total of all 4 sides is 484, We have to divide 484 by 4 and get 121 feet.

The perimeter of the square fence is P = 88 feet and Tyrone needs 22 feet of fence on each side

The perimeter of a square is given by four times the length of its each side

The equation for the perimeter of the square with the side 'a' is given by

Perimeter of Square = 4a

Given data ,

Let the perimeter of the square be represented as P

Now , the equation will be

Let the side length of the square be a²

The area of the square is A = 484 feet²

Taking square roots on both sides of the equation , we get

A = a²

a² = 484

a = 22 feet

Now , perimeter of the square P = 4a

Substituting the values in the equation , we get

Perimeter of the square P = 4 x 22

Perimeter of the square P = 88 feet

Hence , the perimeter of the square is 88 feet

To learn more about perimeter of square click :

https://brainly.com/question/11495285

#SPJ6

9514 1404 393

Answer:

  A.  (2, 0)

Step-by-step explanation:

The x-intercept is the point where the line crosses the x- (horizontal) axis. The coordinates there are (2, 0).

Answer:

x= 2y - 3/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x=2y - 3/2

Step-by-step explanation:

Answer:

this is an example

Step-by-step explanation:

There are a few different ways to approach this problem, including the following two methods.

1) Find 20% of the original price, then subtract that amount from the original price. 

    To find a percentage of a number, you multiply the number by the percentage.  (You are finding a part of a whole.)

                   20% = 20/100 = 1/5    or   20% = 0.20

    Original Price: $24   Find 20% of $24.                         (Note: "of" is taking part of a whole, so you multiply.)

                    0.20 x 24 = 4.80            This is the mark down, or the amount you subtract from original price.

    Sale Price = Original Price - Mark Down   

                   =   24.00 - 4.80

                   =   19.20

2) If you save 20%, you are still paying 80%. (100-20 = 80) Therefore the sale price is 80% of the original price.

                    80% = 80/100 = 4/5     or    80% = 0.80

     Sale Price = 80% of Original Price

                    = 0.80 x 24

                    = 19.20

Answer:

640

Step-by-step explanation:

Using the Central Limit Theorem, it is found that the researcher should use a sample size of 640.

Hence, for the standard deviation to be cut be half, the sample size has to be multiplied by 4, which means that it should be of 4 x 160 = 640.

To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/25581475

Answer:

The third one

Step-by-step explanation:

mP is not correct

Answer: (-8,0) (0,4)

Step-by-step explanation: graphing it would be for coordinate one (-8,0) and for the second coordinate it would be (0,4.) and for the x y chart it goes for x's it goes -8 and then next is 0 and for the y's, it's 0 then next is 4. give me brainliest thankssss

Answer:

18

Step-by-step explanation:

you have to multiply 5 and 3(which gives you 15) first, then move on to16 times 1/4 which gives you 4 then just add 7 and your done.

Answer:

237 = m + 137

this is the equation showing the relationship

Answer:

The average speed at which Nimes drove his car was 50 miles per hour.

Step-by-step explanation:

Given that Nimes was driving to the hotel at 1:30 p.m., being 65 miles away from it, and finally arriving at its destination at 2:48 p.m., to determine the average speed at which the circle should be made. following calculation:

14:48 - 13:30 = 1:18

60 = 100

18 = X

(18 x 100) / 60 = X

1,800 / 60 = X

30 = X

65 / 1.30 = X

50 = X

Therefore, the average speed at which Nimes drove his car was 50 miles per hour.

Answer:

When x = 2.4, we have y = 10.8

Step-by-step explanation:

A direct variation of two variables, x, and y, can be written as:

y = k*x

Where k is a constant, called the constant of variation.

We know that y = 7.2, when x = 1.6

Then we can replace these two in the above equation to get:

7.2 = k*1.6

Now we can solve this for k:

7.2/1.6 = k = 4.5

Then our relation is:

y = 4.5*x

Now we want to find the value of y, when x = 2.4

Then we just need to replace x by 2.4 in the above equation:

y = 4.5*(2.4) = 10.8

y = 10.8

Answer:

12

Step-by-step explanation:

[tex]F \alpha \frac{1}{d^{2} }[/tex]

[tex]F = \frac{K}{d^{2} }[/tex]

When F = 18; d = 2

[tex]18 = \frac{K}{2^{2} }[/tex]

[tex]18 = \frac{K}{4}[/tex]

Cross multiply;

18 x 4 = K

72 = K

There the equation connecting F and [tex]d^{2}[/tex] is

[tex]F = \frac{72}{d}[/tex]

Now, Find F when d = 6

All you do is to substitute d = 6 in to [tex]F = \frac{72}{d}[/tex]

[tex]F = \frac{72}{6}[/tex]

Therefore;

F = 12

Please mark me brainiest if correct.

Answer:

8 is not in the solution set

Step-by-step explanation:

Given, -y + 7 < -4

To find out if 8 is in the solution set, substitute y = 8 in the inequality and solve to see if the statement would be true.

Thus:

-8 + 7 < -4

-1 < -4

This -1 is less than -4. This is actually not TRUE. -1 is rather greater than -4.

Therefore, 8 is not in the solution set.

Answer:

ANSWER IS D

Step-by-step explanation:

forgive me if is wrong

Answer:

x = 84

Step-by-step explanation:

1. Solve for m<R

The sum of angles in a triangle is 180 degrees, regardless of each individual angle measure in the triangle. One can apply that to triangle QRS by stating that;

m<SQR + m<R + m<QSR = 180

Substitute

68 + 3x + m<R = 180

Inverse operations,

m<R = 112 - 3x

2. Solve or m<PSR

Verticle angles theorem states that when two lines intersect, four angles are formed. The angles that are opposite each other are congruent. Using this, one can concluce that;

m<TSU = m<PSR = 4x

3. Solving for x

Now all one has to do is apply the sum of angles in a triangle theorem for triangle PSR

m<P + m<R + m<PSR = 180

Substitute,

x + 112 - 3x + 4x = 180

Simplify

2x + 112 = 180

Inverse operations

2x + 112 = 180

     -112      -112

2x = 168

/5       /5

x = 84

Answer:

The correct answer should be A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Given:

The polynomial function is

[tex]F(x)=4x^3-6x^2+9x+10[/tex]

To find:

The possible roots of the given polynomial using rational root theorem.

Solution:

According to the rational root theorem, all the rational roots and in the form of [tex]\dfrac{p}{q}[/tex], where, p is a factor of constant and q is the factor of leading coefficient.

We have,

[tex]F(x)=4x^3-6x^2+9x+10[/tex]

Here, the constant term is 10 and the leading coefficient is 4.

Factors of constant term 10 are ±1, ±2, ±5, ±10.

Factors of leading term 4 are ±1, ±2, ±4.

Using rational root theorem, the possible rational roots are

[tex]x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}[/tex]

Therefore, the correct options are A, C, D, F.

Answer:

a.) 0.5

b.) 0.66

c.) 0.83

Step-by-step explanation:

As given,

Total Number of Batteries in the drawer = 10

Total Number of defective Batteries in the drawer = 4

⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6

Now,

As, a sample of 3 is taken at random without replacement.

a.)

Getting exactly one defective battery means -

1 - from defective battery

2 - from non-defective battery

So,

Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ =  [tex]\frac{4!}{1! (4 - 1 )!}[/tex] × [tex]\frac{6!}{2! (6 - 2 )!}[/tex]

                                                                            = [tex]\frac{4!}{(3)!}[/tex] × [tex]\frac{6!}{2! (4)!}[/tex]

                                                                            = [tex]\frac{4.3!}{(3)!}[/tex] × [tex]\frac{6.5.4!}{2! (4)!}[/tex]

                                                                            = [tex]4[/tex] × [tex]\frac{6.5}{2.1! }[/tex]

                                                                            = [tex]4[/tex] × [tex]15[/tex] = 60

Total Number of possibility = ¹⁰C₃ = [tex]\frac{10!}{3! (10-3)!}[/tex]

                                                        = [tex]\frac{10!}{3! (7)!}[/tex]

                                                        = [tex]\frac{10.9.8.7!}{3! (7)!}[/tex]

                                                        = [tex]\frac{10.9.8}{3.2.1!}[/tex]

                                                        = 120

So, probability = [tex]\frac{60}{120} = \frac{1}{2} = 0.5[/tex]

b.)

at most one defective battery :

⇒either the defective battery is 1 or 0

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 0 , then 3 non defective

Possibility   = ⁴C₀ × ⁶C₃

                   =  [tex]\frac{4!}{0! (4 - 0)!}[/tex] × [tex]\frac{6!}{3! (6 - 3)!}[/tex]

                   = [tex]\frac{4!}{(4)!}[/tex] × [tex]\frac{6!}{3! (3)!}[/tex]

                   = 1 × [tex]\frac{6.5.4.3!}{3.2.1! (3)!}[/tex]

                   = 1× [tex]\frac{6.5.4}{3.2.1! }[/tex]

                   = 1 × 20 = 20

getting at most 1 defective battery = 60 + 20 = 80

Probability = [tex]\frac{80}{120} = \frac{8}{12} = 0.66[/tex]

c.)

at least one defective battery :

⇒either the defective battery is 1 or 2 or 3

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 2 , then 1 non defective

Possibility   = ⁴C₂ × ⁶C₁

                   =  [tex]\frac{4!}{2! (4 - 2)!}[/tex] × [tex]\frac{6!}{1! (6 - 1)!}[/tex]

                   = [tex]\frac{4!}{2! (2)!}[/tex] × [tex]\frac{6!}{1! (5)!}[/tex]

                   = [tex]\frac{4.3.2!}{2! (2)!}[/tex] × [tex]\frac{6.5!}{1! (5)!}[/tex]

                   = [tex]\frac{4.3}{2.1!}[/tex] × [tex]\frac{6}{1}[/tex]

                   = 6 × 6 = 36

If the defective battery is 3 , then 0 non defective

Possibility   = ⁴C₃ × ⁶C₀

                   =  [tex]\frac{4!}{3! (4 - 3)!}[/tex] × [tex]\frac{6!}{0! (6 - 0)!}[/tex]

                   = [tex]\frac{4!}{3! (1)!}[/tex] × [tex]\frac{6!}{(6)!}[/tex]

                   = [tex]\frac{4.3!}{3!}[/tex] × 1

                   = 4×1 = 4

getting at most 1 defective battery = 60 + 36 + 4 = 100

Probability = [tex]\frac{100}{120} = \frac{10}{12} = 0.83[/tex]

Answer: 140

Step-by-step explanation:

6(8) = 48

4(23) = 92

48 + 92 = 140

Because of this, 6(8) + 4(23) = 140.

Answer: 41 i think

Step-by-step explanation: