Rationalizing factor of cube root 5

Answer:

x<3

Step-by-step explanation:

4x<5+7

4x<12

x=12÷4

x=3

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.

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Answer:

93.73

Step-by-step explanation:

72.1

x 1.3

_____

93.73

Answer:

1cm:2km

Step-by-step explanation:

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

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.

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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]

Answer:

Exact Form:

37/16

Decimal Form:

2.3125

Mixed Number Form:

2 5/16

Step-by-step explanation:

Answer:

[-5 3] [-5 6]

Step-by-step explanation:

Answer:

Your answer is on the pic...mate

If your train travels at 65 miles per hour for 3.5 hours, it go 227.5 miles.

What is Speed ?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.

Given:

Speed S = 65 miles per hour

Time T = 3.5 hours

We know that,

S= D/T  Where D is the distance traveled.

Therefore,

65 miles per hour = D/ 3.5 hours

D = 65 x 3.5 miles

=227.5 miles

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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.

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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

Answer:

False

Step-by-step explanation:

Answer:3.8 square meters

Step-by-step explanation: hope this helps!

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 range for both groups are the same, therefore: C. The variability in students’ heights of both groups is the same.

To find the mean of a data set, sum all data points given together and divide what you get by the number of data points that is given in the data set.

The range of a data gives us an idea of the spread of a data, which is a measure of variability. The larger the range, the more the variability that exist in the data set.

Given, Group A: 51, 53, 60, 64, 55, and Group B: 50, 55, 58, 63, 52, find the mean of each data set

Mean for Group A = (51 + 53 + 60 + 64 + 55)/5 = 283/5 = 56.6

Mean for Group B = (50 + 55 + 58 + 63 + 52)/5 = 278/5 = 55.6

Range for Group A = 64 - 51 = 13

Range for Group B = 63 - 50 = 13

This means that variability in students’ heights is the same for both group A and B.

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Answer:

t = 10.09

Step-by-step explanation:

Answer in the picture below!

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

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Answer:

1

Step-by-step explanation:

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

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.

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.

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Answer:200 in^2

Step-by-step explanation:

Answer: their difference in elevation is 188 feet

Step-by-step explanation:

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

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The degree measure of one angle of a 30 sided regular polygon is 168°​

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.

The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.

We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is

(Side - 2) × 180°

(30 - 2) × 180°

= 5040°

Measure of each angle of 30-gon

= 5040°/30

= 168°​

Thus, the degree measure measure of One angle of a 30 sided regular polygon is 168°​

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Answer: 168

Step-by-step explanation: did the test

Answer:

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

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.

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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.

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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.

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