1. A train travels at 80 miles per hour. What equation that compares the time (t) with the distance (d)?
d = 80t
t = 80d
t = d + 80
d = t + 80

Answer:

93.73

Step-by-step explanation:

72.1

x 1.3

_____

93.73

The derivative of f(x) = (1 - 3x)^(1/3) is  f'(x) = - (1 - 3x)^(-2/3). The  *(-3) comes from the derivative of (1 - 3x) with respect to x, due to the chain rule.

Chain rule:  dy/dx = dy/du. du/dx

Suppose we have f(g(x)), then its derivative is: f'(g(x)) . g'(x)

In the problem:

f(x) = (1 - 3x)^(1/3)

Let u = 1 - 3x

then f(u) = u^(1/3)

and f'(u) = 1/3 u^(-2/3)

That part only the derivative of f with respect to u. We still need to take the derivative of u with respect to x. That is:

u(x) = 1 - 3x

u'(x) = -3

Hence, the complete derivative is:

f'(x) = f'(u) . u'(x)

     = 1/3 u^(-2/3) . (-3)

     = -  u^(-2/3)    ( substitute back u = 1 - 3x )

     = - (1 - 3x)^(-2/3)

Hence the *(-3) comes from the derivative of (1 - 3x) with respect to x, due to the chain rule.

Learn more about chain rule here

https://brainly.com/question/17035616

#SPJ4

Based on the discount to be applied by the online store when an order totals below $50 and $50 and above, the correct statement is C. A purchase of 2 pots at $20 each and 1 pan at $35 will be charged at $56.25.

The discount for orders above $50 is 25%.

When a person buys 2 pots for $20 each and then 1 roasting pan for $35, the amount they'll pay normally is:
= (2 x 20) + 35

= 40 + 35

= $75

The amount the person will pay after the 25% discount is applied is:

= 75 x (1 - 25%)

= 75 x 75%

= $56.25

Find out more on promotional discounts at https://brainly.com/question/20827376

#SPJ1

Answer:200 in^2

Step-by-step explanation:

Answer:x=-13+1/5

Step-by-step explanation:

10x-18=15x+48

We move all terms to the left:

10x-18-(15x+48)=0

We get rid of parentheses

10x-15x-48-18=0

We add all the numbers together, and all the variables

-5x-66=0

We move all terms containing x to the left, all other terms to the right

-5x=66

x=66/-5

x=-13+1/5

The inequalities that model each situation are given as follows:

a. w ≤ 20, meaning that vehicles with two axles can weight at most 20 tons.

b. w ≤ 30, meaning that vehicles with three axles can weight at most 30 tons.

c. w ≤ 40, meaning that vehicles with four axles can weight at most 40 tons.

In each inequality, the plotted numbers are the numbers to the left, with a closed circle, hence:

In item a, we have that for vehicles with 2 axles, the upper weight limit is of 20 tons, hence the inequality is:

w ≤ 20.

In item b, we have that for vehicles with 3 axles, the upper weight limit is of 30 tons, hence the inequality is:

w ≤ 30.

In item c, we have that for vehicles with 4 axles, the upper weight limit is of 40 tons, hence the inequality is:

w ≤ 40.

More can be learned about inequalities at https://brainly.com/question/24372553

#SPJ1

The likely terms that are the same based on the information include 3/4a³ and 0.75a³.

It should be noted an equation is used to show the relationship between the variables that are given.

In the question, the likely terms that are given include: 3d, 3/4a³, -6ad, and 0.75a³.

It should be noted that the expressions that are the same include 3/4a³ and 0.75a³. This is because 3/4 is the same as 0.75 in decimal.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

1cm:2km

Step-by-step explanation:

you ratio both of the answers which shows that 1cm on the map represents 2km in reality.

Answer:

x could be 10 or -10

Step-by-step explanation:

10 x 10  = 100

and

(-10) x (-10) = 100  A negative times a negative is a positive.

Answer: their difference in elevation is 188 feet

Step-by-step explanation:

The solution for x in the equation is x = 2b/(2a - c)

The equation is given as

2ax - b = cx + b

Collect the like terms in the above equation

So, we have the following equation

2ax - cx = b + b

Evaluate the like terms in the above equation

So, we have the following equation

2ax - cx = 2b

Factor out x from the equation

x(2a - c) = 2b

Divide both sides by 2a - c

x = 2b/(2a - c)

Hence, the solution for x is x = 2b/(2a - c)

Read more about subject of formula at

https://brainly.com/question/10643782

#SPJ1

When counting the number of successes in n trials, the (D) binomial distribution should be used if the success probability, p, stays constant from trial to trial.

As it is given in the descrip[tion itself that the probability of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Therefore, when counting the number of successes in n trials, the (D) binomial distribution should be used if the success probability, p, stays constant from trial to trial.

Know more about binomial distribution here:

https://brainly.com/question/9325204

#SPJ9

The complete question is given below:

Which distribution is appropriate when counting the number of successes in n trials if the probability of success p remains constant from trial to trial?

(A) Normal Distribution

(B) Power Normal Distribution

(C) Extreme Value Type Distribution

(D) Binomial Distribution

option a , c and d are the correct statement or is a proper interpretation of a 95% confidence interval 95% of the population values will fall within this variable

What is the 95% confidence interval for a population mean?

It means that for any given number of samples, 95% of them will fall within 2 standard errors of the true mean of the population the sample is derived from.

a. In 95% of all samples, the sample mean will fall within 2 standard errors of the true population mean.

c. In 95% of all samples, the true population mean will be within 2 standard errors of the sample mean.

d. 95% of the population values will lie within 2 standard errors of the sample mean.

therefore option a , c and d are correct

learn more about of mean here

https://brainly.com/question/24071798

#SPJ4

By comparing the fractions, we see that 7/9 is larger than 5/8, thus, Jamal has the better record.

We know that Jamal made 7/9 of his free throws while Brian made 5/8 of his free throws.

To see which player has the better record, we need to see which one of the two fractions is larger.

To do so we can write both of the fractions as decimals, we will get:

7/9 = 0.77...

5/8  =0.625

There we can see that 7/9 is larger, thus, we can conclude that Jamal has a better record.

Learn more about fractions:

https://brainly.com/question/11562149

#SPJ1

Answer: d ≥ 825-405

You're Welcome

The algebraic equation that represents the given sentence is:

g - 15 = 67.

We have to look at the description of the sentence, and then formulate expressions that represent this sentence.

The difference between two numbers x and y is represented by the following expression.

x - y.

Gail's age is represented by the following variable:

g.

Hence the difference of Gail's age and 15 is represented by:

g - 15.

The numeric value of this expression is of 67, hence the equation is:

g - 15 = 67.

A similar problem, also about algebraic equations and sentences, is given at https://brainly.com/question/28036476

#SPJ1

Answer:

[-5 3] [-5 6]

Step-by-step explanation:

Answer:

Your answer is on the pic...mate

Solving a system of equations we can see that Lucy is 30 years old.

Let's define the variables:

L = Lucy's age.

F = father's age.

We know that when Lucy turns 15, her father was 3 times her age, so:

if L = 15

then F = 15*3 = 45

So her father is 30 years older than Lucy.

So we can write the linear relation:

F = L + 30

Now we know that this year, her father has exactly twice Lucy's age, then we have the system of equations:

F = L + 30

F = 2*L

Replacing the other equation here we get:

L + 30 = 2*L

30 = 2*L - L = L

30 = L

Lucy is 30 years old.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Considering the numeric value of the function f(x), the test average for your math class after completing test 2 was of 80.8.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

For this problem, the function is given by:

f(x) = 79 + 0.9x.

The average after test 2 is represented by the numeric value when x = 2, hence we replace the lone instance of x on the function to find the average as follows:

f(2) = 79 + 0.9(2) = 80.8.

The problem asks for the test average for your math class after completing test 2.

The function that gives the average after test x is:

f(x) = 79 + 0.9x.

More can be learned about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Answer:

x<3

Step-by-step explanation:

4x<5+7

4x<12

x=12÷4

x=3

Answer:3.8 square meters

Step-by-step explanation: hope this helps!

Answer:

t = 10.09

Step-by-step explanation:

Answer in the picture below!

Answer:

1

Step-by-step explanation:

Not sure how to answer it but here's the correct answer i believe

Answer:

[tex]f {}^{ - 1} (x) = - x - 2[/tex]

Answer:

Exact Form:

37/16

Decimal Form:

2.3125

Mixed Number Form:

2 5/16

Step-by-step explanation:

The equation of the graph using the format y= a*|x-h|+k is y=|x+4|-5 .

In the question ,

From the graph we can see that the vertex of the graph is (-4,-5) ,

The absolute value equation of the graph is denoted by y=a*|x-h|+k ,

where (h,k) are the vertex of the graph .

Since (-4,-5) is the vertex , So h= -4 and k= -5 ,

Substituting the values of h and in the absolute value equation , we get

y=a*|x-(-4)|+(-5)

y=a*|x+4|-5

Take any point that lies on the graph ,

Selecting the point (1,0) which lie on the graph ,

Substituting the value as x=1 and y=0 , we get

0=a*|1+4|-5

5=a*|1+4|

5=5a

a=1 ,

Substituting the values of a=1 , h= -4 and k=-5 in the absolute value equation , we get y=|x+4|-5

Therefore , the equation of the graph using the format y= a*|x-h|+k is y=|x+4|-5 .

Learn more about Graphs here

https://brainly.com/question/5218738

#SPJ1

Considering when a triangle is formed given three sides, the code for the puzzle is given as follows:

BBBACC

In a triangle, the sum of the lengths of the two smaller sides of the triangle has to be greater than the length of the greater side of the triangle.

For the first letter, we have two sides, hence there are many possible values for the third side x, as long as 2.5 + x > 8, for x < 8 or x < 10.5, for x > 8, hence the first letter of the code is of B.

For the second letter, 4 + 7 < 19, hence no triangle can be formed with these dimensions and the letter is of B.

For the third letter, 2 + 4 > 5, hence one unique triangle can be formed with all the dimensions given and the letter is of B.

For the fourth letter, 6 + 8 > 12, hence one unique triangle can be formed with all the dimensions given and the letter is of A.

For the fifth letter, we have two sides, hence there are many possible values for the third side x, as long as 1 + x > 2.4, for x < 2.4 or x < 3.4, for x > 2.4, hence the letter is of C.

For the sixth letter, 5 + 9 > 13, hence one unique triangle can be formed with all the dimensions given and the letter is of C.

More can be learned about the lengths of the sides of a triangle at https://brainly.com/question/25401493

#SPJ1

Answer:

False

Step-by-step explanation:

Answer:

[tex]621 = {3}^{3} \times 23[/tex]

Step-by-step explanation:

[tex]621 \div 3 = 207[/tex]

[tex]207 \div 3 = 69[/tex]

[tex]69 \div 3 = 23[/tex]

[tex]621 = 3 \times 3 \times 3 \times 23 = {3}^{3} \times 23[/tex]