What’s the relationship between the number of
$4 lunches
you buy with a $100 school
lunch card and the money remaining on
the card

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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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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Answer:

t = 10.09

Step-by-step explanation:

Answer in the picture below!

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)

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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:3.8 square meters

Step-by-step explanation: hope this helps!

Ava's age is 26 years when Ava and Olivia's ages are consecutive even integers and the sum of Ava's age and 2 times Olivia's age is 74.

According to the question,

Ava and Olivia's ages are consecutive even integers.

Now, let's take Olivia's age to be x years.

So, Ava's age would be (x+2) years because their ages are consecutive even integers. (Even numbers are the number which are divisible by 2.)

We have the sum of Ava's age and 2 times Olivia's age is 74.

So, we have the following expression:

(x+2+2x) = 74

3x+2 = 74

3x = 74-2

3x = 72

x = 72/3 (3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)

x = 24 years

So, Olivia's age is 24 years.

Now, we have:

Ava's age = (x+2) years

Ava's age = (24+2) years

Ava's age = 26 years

Hence, Ava's age is 26 years.

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Answer: Patrisha robbed 20+ banks

Bob has farted 30 times

Mary and John have 55 combined

Step-by-step explanation:

First one: She robbed 20 banks and then robbed more, giving 20+

Second one: 6 times a day for 5 days - 6x5=30

Third one:  25+30=55

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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Answer:

[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]

Step-by-step explanation:

Given points:

Standard equation of a horizontal hyperbola (opening left and right):

[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]

where:

Points (5, 0) and (-1, 0) are the vertices of the hyperbola.

The center (h, k) is midway between the vertices.  Therefore:

[tex]\implies h=\dfrac{5-1}{2}=2[/tex]

[tex]\implies k=0[/tex]

Substitute the found values of h and k into the formula:

[tex]\dfrac{(x-2)^2}{a^2}-\dfrac{y^2}{b^2}=1[/tex]

Substitute point (5, 0) and solve for a²:

[tex]\implies \dfrac{(5-2)^2}{a^2}-\dfrac{0^2}{b^2}=1[/tex]

[tex]\implies \dfrac{3^2}{a^2}=1[/tex]

[tex]\implies \dfrac{9}{a^2}=1[/tex]

[tex]\implies 9=a^2[/tex]

Substitute one of the (2±3√2, ±2) points and the found value of a² and solve for b²:

[tex]\implies \dfrac{(2+3\sqrt{2}-2)^2}{9}-\dfrac{2^2}{b^2}=1[/tex]

[tex]\implies \dfrac{(3\sqrt{2})^2}{9}-\dfrac{4}{b^2}=1[/tex]

[tex]\implies \dfrac{18}{9}-\dfrac{4}{b^2}=1[/tex]

[tex]\implies 2-\dfrac{4}{b^2}=1[/tex]

[tex]\implies \dfrac{4}{b^2}=1[/tex]

[tex]\implies 4=b^2[/tex]

Substitute the found values of a² and b², together with the values of h and k, into the formula to create the equation of the hyperbola:

[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]

yes you want to know about math then you will tell answer d

Answer:

3.2 x 105

Step-by-step explanation:

its simple

Answer:

The answer is

[tex]a < - 7 \: or \: a > 15[/tex]

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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The team has enough money that will be used to buy 11 baseball uniforms.

The information illustrated that the baseball team has $1,400 to buy baseball uniforms and each uniform costs $124.

It was also stated that the team needs to buy 11 uniforms. In this case, the cost of 11 uniforms will be the multiplication of the coat of each pair of uniform by the number of uniforms that will be bought.

This will be illustrated as:

= Amount of each uniform × Number of uniform

= $124 × 11

= $1364

Therefore, the total amount is $1364. Therefore, since the baseball team has $1400, the amount is enough.

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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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270 counter clockwise

Step-by-step explanation:

look at the rotation

Answer:

False

Step-by-step explanation:

Answer: their difference in elevation is 188 feet

Step-by-step explanation:

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.

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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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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.

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The solution of the algebraic expression for the variable M is given as follows:

M = (4π²a³)/(T²G)

To solve an algebraic expression for a variable, we have to isolate this variable, as a function of the other variables in the expression.

In the context of this problem, the expression which we want to solve for M is given as follows:

T² = 4π²a³/GM

Applying cross multiplication to remove the fraction, we have that:

T²GM = 4π²a³

To isolate M, we apply the division, which is the opposite operation of the multiplication, as T²G are multiplying M, hence the simplified expression for M is given as follows:

M = (4π²a³)/(T²G)

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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.

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 .

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The slope of the line is 2.

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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: d ≥ 825-405

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