Ari thinks the perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream. Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice cream.
What will Ari think about Freeze Zone's milkshakes?
Choose 1 answer:



A
They have too much caramel.


B
They have too little caramel.


C
They are just right.

Answer:

u + m ≥ 25

25u + 40m ≤ 1000

Step-by-step explanation:

WRUF 103.7 FM is giving away tickets to a concert. Tim, the general manager of the radio station, plans to give away upper-level and mid-level seats that cost $25 and $40, respectively. Tim wants to give away at least 25 tickets, but he has a budget constraint of $1,000.

Write a system of two inequalities that describes this situation

Solution

Let

u = number of upper level tickets

m = number mid level tickets

Cost of upper level tickets = $25

Cost of mid-level tickets = $40

Tim wants to give away at least 25 tickets

He has a budget constraint of $1,000

Equation for the amount of tickets given away

u + m ≥ 25

Equation for the cost of tickets

25u + 40m ≤ 1000

Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

Answer: \((x+2)(x+8)\)

Step-by-step explanation:

1) First, we need to see which number multiplies to 16 and adds up to 10.

By looking at the factors of 16, we can see that only 2 and 8 will work.

2) Now, we need to arrange them in the factorized equation, which is always

(x+r)(x+q).

3) This will give us our final equation:

\((x+2)(x+8)\)

If you want the roots, just do the negation of r and q and you will get it!

Let's solve the equation w/4 + 16 = 7 step by step:Step 1: Begin by isolating the variable term on one side of the equation. In this case, we want to isolate w/4. To do that, we can subtract 16 from both sides of the equation:

w/4 + 16 - 16 = 7 - 16

This simplifies to:

w/4 = -9

Step 2: Now, to solve for w, we need to get rid of the division by 4. We can do this by multiplying both sides of the equation by 4:

4 * (w/4) = 4 * (-9)

On the left side, the 4s cancel out, leaving us with:

w = -36

Step 3: We have found the solution for w, which is -36. To confirm, we can substitute this value back into the original equation to verify its correctness:

(-36)/4 + 16 = 7

Simplifying the left side:

-9 + 16 = 7

This further simplifies to:

7 = 7

Since the equation is true when w is -36, we can conclude that -36 is the solution to the equation w/4 + 16 = 7.

In summary, the equation is solved by subtracting 16 from both sides to isolate the variable, then multiplying both sides by 4 to eliminate the division by 4. The final solution is w = -36, which satisfies the equation.

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Answer:

e=-2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

-1 / 2 = -0.5

1/-2 = -/0.5

Answer:

b

Step-by-step explanation:

both the top and bottom are negative so there fore the whole fraction is negative.

Answer:

137174211/100000000000

Step by Step Explanation:

First, find the answer of 9^(-3), which would be 0.00137174211. Then, convert that into fraction form. Which would be 137174211/100000000000. Then simplify, which in order to simplify a fraction, there must be: 1. A number that will divide evenly into both the numerator and denominatior so it can be reduced. No such number exists for 137174211 and 100000000000. or 2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. 137174211 is not greater than 100000000000, also meaning, this fraction is in it's simplest form.

Answer:

10=.50n+1.50

Step-by-step explanation:

The total cost, c, of n chicken wings can be represented by a system of equations as follows c = 0.50n + 1.50

c = total cost

n = number of chicken wings

Therefore,

The cost of chicken wing at restaurant Z is $0.50 per wings plus a one time $1.50 charge for sauce.

The system of equation that represent the system is as follows:

c = 0.50n + 1.50

The one time fee for sauce is just like a constant in the equation.

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Therefore, the formula for converting 35 liters to milliliters is 35000, with a conversion factor of 1000.

This is further explained below.

Generally,  The amount that is supplied in liters must be multiplied by 1000 in order to be converted to milliliters.

A conversion factor is a number that may be multiplied or divided to shift the units of measurement used for one set to another.

In situations when a conversion is required, the correct conversion factor that results in the same value must be used. For the purpose of converting inches to feet, for instance, the correct value for the conversion is 12 inches equaling 1 foot.

In conclusion, Therefore 35 liters to milliliters is given as 35000, conversion factor of 1000

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Answer:

1000ml and 1 liter

Step-by-step explanation:

a) The free variables of the given lambda-calculus term are {x, y}.

b) The normal form of the given lambda-calculus term is (λ. t) s.

c) In lambda calculus, calculating the free variables, renaming bound variables, and avoiding variable capture are crucial steps to accurately reduce terms and obtain the normal form.

In lambda calculus, calculating the free variables, renaming bound variables, and avoiding variable capture are crucial steps to accurately reduce terms and obtain the normal form.

(a) To calculate the free variables of the lambda-calculus term (λx. λy. y x) (λ. y), we can use the FV function. The FV function recursively checks the variables in a lambda term, excluding the ones bound by lambda abstractions. Here are the steps to calculate the free variables:

Start with the given term: (λx. λy. y x) (λ. y)

Apply the FV function to each subterm:

FV((λx. λy. y x)) = FV(λx) ∪ FV(λy. y x) = {x} ∪ (FV(λy) ∪ FV(y x)) = {x} ∪ ({y} ∪ (FV(y) ∪ FV(x))) = {x} ∪ {y} ∪ {y, x} = {x, y}

FV((λ. y)) = FV(λ) ∪ FV(y) = ∅ ∪ {y} = {y}

Take the union of the free variables from the previous steps:

FV((λx. λy. y x) (λ. y)) = {x, y} ∪ {y} = {x, y}

Therefore, the free variables of the given lambda-calculus term are {x, y}.

(b) Now let's reduce the term to its normal form by renaming the bound variables:

Start with the given term: (λx. λy. y x) (λ. y)

Rename the bound variables:

(λx. λy. y x) (λ. y) [Rename x to z] (λz. λy. y x) (λ. y) [Rename y to w] (λz. λw. w x) (λ. y) [Rename x to v] (λz. λw. w v) (λ. y) [Rename y to u] (λz. λw. w v) (λ. u) [Rename u to t] (λz. λw. w v) (λ. t) [Rename v to s] (λz. λw. w s) (λ. t)

Perform the reductions:

(λz. λw. w s) (λ. t) [Apply (λz. λw. w s) to (λ. t)] (λw. w s)[z := (λ. t)] [Substitute z with (λ. t)] (λw. w s) [Substitute w with (λ. t)] (λ. t) s [Substitute s with (λ. t)]

The term (λ. t) s is in normal form because there are no more reducible expressions.

Therefore, the normal form of the given lambda-calculus term is (λ. t) s.

(c) If we did not rename bound variables during reduction, we could encounter variable capture or unintentional variable collisions. Variable capture occurs when a variable bound in a lambda abstraction clashes with a free variable in the context it is being substituted into, leading to incorrect results. By renaming bound variables, we ensure that each variable remains distinct and does not interfere with other variables in the expression. This allows us to correctly perform reductions and reach the desired normal form without any unintended side effects.

Therefore, In lambda calculus, calculating the free variables, renaming bound variables, and avoiding variable capture are crucial steps to accurately reduce terms and obtain the normal form.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

The slope of a linear line (or a linear equation) can be found by simply taking 2 values for x and y and then using the slope formula which is \(\frac{dy}{dx}\) or:

\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Example:

Let's say you're give this table:

x: 1, 2

y: 1, 2

Following the steps which I gave, you take 1 value for the y (preferably the larger one) which in this cause will be 2 and then another y from the table which would be 1

Do the same for x

Now plug the values taken in the slope formula and you get:

\(\frac{2 - 1}{2 - 1}\)

\(\frac{1}{1} = 1\)

Therefore the slope is 1.

Answer:

Rise/run

Rise over run.

Step-by-step explanation:

To find the slope pick two perfect spots on the line when the coordinates are not decimals.

Then, take those  two points and figure out the distance. You will use rise/run.

so rise is how much you either go up or down and run is how much you either go right or left. so how much you'll go up or down? how much will you move right or left?

Lets say you have to go up 5 and then left 7 to get to the coordinate.

That's your slope! you went up so it's positive and you went left so it's negative. Rise over run : rise 5 left 7 so, 5 and -7 which is 5/-7 and that's your slope!

Answer:

k=84

Step-by-step explanation:

k= 4 x 21

K= 84

This is self explanatory.

Given:

K = 4 TIMES 21

Which means -

K = 4*21

  = 84

which is equal to 84

Answer: 3 weeks

Step-by-step explanation:

We have to note firstly that 12 inches = 1 foot.

The equation given to represent the height in the question, h = 3w + 3.

The number of weeks that it will take the plant to reach one foot will then be:

h = 3w + 3

12 = 3w + 3

3w = 12 - 3

3w = 9

w = 9/3

w = 3

It'll take 3 weeks

Answer:

EF = 58

Step-by-step explanation:

Find the diagram of the question attached.

According to the addition postulate;

DE+EF = DF

Given

DE = 47

EF = 3x+10

DF = 9x-39

Substitute into the addition postulate formula and get x

47+3x+10= 9x-39

Collect like terms

3x-9x = -39-10-47

-6x = -96

x = -96/-6

x = 16

Next is to evaluate EF:

EF = 3x+10

EF = 3(16)+10

EF = 48+10

EF = 58

Hence the measure of EF is 58

Answer:

F(x) = $6.50x + $48

Step-by-step explanation:

Answer:

f(x)= 6.5x + 48

From 1976 until 1987, red M&Ms were removed from packets owing to a research associating the food dye used to color them to cancer.

Arithmetic is defined as working with numbers through addition, subtraction, multiplication, and division. Adding two and two to produce four is an example of arithmetic. Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. Arithmetic (derived from the Greek word arithmos, "number") relates to the fundamental components of number theory, arts of mensuration (measuring), and numerical computing (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

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Answer:

The one you picked

Step by Step explanation

Answer: 15 dimes 12 nickels 12 pennies 7 quarters?

Step-by-step explanation:

Answer:

1/13

Step-by-step explanation:

There are 4 cards that are a "3" in a deck of cards

3 of hearts, 3 of spades, 3 of clubs, 3 of diamonds

P( 3) = number of cards that are a "3" / total number of cards

P(3) = 4/52 = 1/13

Answer:

\(\frac{1}{13}\) (one thirteenth)

1/13

Step-by-step explanation:

There's 4 of the card 3 in a deck. (3 of hearts, 3 of diamonds, 3 of clubs, 3 of spades.)

This means 4 of 52 cards are a 3, which makes the fraction \(\frac{4}{52}\). This is the probability.

This fraction can be simplified to \(\frac{1}{13}\) by dividing the top and bottom by four. This is the final answer, since it is in the simplest form.

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Work Shown:

r = 6 = radius

V = volume of a sphere of radius r

V = (4/3)*pi*r^3

V = (4/3)*pi*6^3

V = 904.77868423386

V = 904.8

I used my calculator's stored version of pi (instead of something like pi = 3.14)

The units "cubic meters" can be abbreviated to m^3 or \(m^3\)

The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.

         The volume of a sphere can be calculated using the formula:

V = \(4/3 * \pi * r^3\),

Where V is the volume and r is the radius of the sphere.

\(\pi\) = 3.14

The radius of the sphere (r) = 6m

Plugging in the given radius of 6m into the formula, we get:

V = (4/3) * \(\pi\) * (6^3)

V = 1.333 * \(\pi\) * 216

V = 1.333 * 3.14 * 216

V = 4.1866 * 216

V = 904.8 cubic meters

Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8  cubic meters.

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Answer:

46

Step-by-step explanation:

let that number x

so \(\frac{23}{50} =\frac{x}{100}\)

I do cross multiplication so 23*100=2300 and 50*x=50x

so 50x=2300 divide both by 50

x=46

Answer:

46

Step-by-step explanation:

since 100 is 50×2 you just do the same thing to 23 and multiply it by 2.

Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

Step-by-step explanation:

(x^2 -x)=(5^2-5)

=25-5 =20

Answer:

(x²-x)=(5²-5)

=(25-5)

=(20)ans..............

The graphs that show functions with direct variation are Graph One, Graph Two, and Graph Three. Options A, B and D are correct responses.

In direct variation, as one variable increases, the other variable also increases proportionally, or as one variable decreases, the other variable also decreases proportionally. In Graph One, as x increases, y increases proportionally. In Graph Two, as x decreases, y decreases proportionally. In Graph Three, the line passes through the origin (0,0), indicating a direct variation relationship between x and y. On the other hand, Graphs Four and Five do not exhibit direct variation as the relationship between x and y is not consistent or proportional.

Therefore, the correct options are A. Graph Two, B. Graph Three, and D. Graph One.

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Functions with direct variation are those that vary directly, and their graphs are line graphs that pass through the origin.

That means a direct variation is a relation that connects two variables and is expressed algebraically in the form y=kx where k is the constant of variation. Let's look at the given graphs to determine which ones exhibit direct variation.

Graph One is not a direct variation since it does not pass through the origin; therefore, it is not one of the correct answers. The same is true for Graph Two and Graph Three.

Graph Four shows a direct variation, but its graph is not a straight line; therefore, it is not a direct variation. Graph Five is the only straight line that passes through the origin, which means it is a direct variation. Thus, the correct answer to this question is C. Graph Five.

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Answer: 1/27

Step-by-step explanation:

(1/3)^3 = 1/27