Aubrey can run at a pace of six miles per hour. running at the same rate how many miles can she run in ninety minutes

Answer: 640 fluid ounces

Step-by-step explanation:

We assume that the fluid ounces in jar is directly proportional to the number of servings.

Given : A jar holds 128 fluid ounces of juice. The label says the jar has 16 servings.

Ratio of  fluid ounces of juice to number of servings =[tex]\dfrac{128}{16}[/tex]  (1)

Let x denotes the fluid ounces are needed for 80 servings.

Ratio of  fluid ounces of juice to number of servings =[tex]\dfrac{x}{80}[/tex]   (2)

From (1) and (2) , we have

[tex]\dfrac{x}{80}=\dfrac{128}{16}[/tex]   [in direct variation ration  remains constant.]

[tex]x=\dfrac{128\times80}{16}=640[/tex]

Hence, 640 fluid ounces are needed for 80 servings.

Answer:

A

Step-by-step explanation:

a) people have heard it  by 3 p.m is 800 people

b) people have heard it  by 12.30 p.m is 141 people

c) people have heard it  by 1.45 p.m is 530 people

Let's analyze this rumor spread problem. Each person who hears the rumor is assumed to spread it to exactly two other people.

a) By 3 p.m.: The rumor spreads for 3 hours after noon. Starting with 100 people at noon, by 3 p.m. it would be 100 * 2^3 = 100 * 8 = 800 people.

b) By 12:30 p.m.: The rumor spreads for half an hour after noon. That's 30 minutes or 0.5 hours. Since the rumor spreads exponentially, in half an hour, the number of people who hear it doubles once. So, by 12:30 p.m., it would be 100 * 2^0.5 = 100 * √2 ≈ 100 * 1.41 ≈ 141 people.

c) By 1:45 p.m.: The rumor spreads for 1 hour and 45 minutes after noon, which is 1.75 hours. So, by 1:45 p.m., it would be 100 * 2^1.75 ≈ 100 * 5.3 ≈ 530 people.

In summary:

a) 800 people

b) 141 people

c) 530 people

Answer:

The required number in the fraction is x=11

Step-by-step explanation:

Given : The repeating decimal, 0.27..., is converted to the fraction  [tex]0.27....=\frac{3}{x}[/tex]            

To find : What is the value for x in the fraction ?

Solution :

Let [tex]y=0.272727...[/tex] ....(1)

Multiply both side by 100,

[tex]100y=27.2727...[/tex] .....(2)

Subtract (1) and (2),

[tex]100y-y=(27.2727....)-(0.272727...)[/tex]

[tex]99y=27[/tex]

[tex]y=\frac{27}{99}[/tex]

[tex]y=\frac{3}{11}[/tex]

On comparing with [tex]0.27....=\frac{3}{x}[/tex]

The value of x is 11.

Therefore, The required number in the fraction is x=11.

Answer:

Ted should write the amount in the PAYMENT column of the checkbook register.

Step-by-step explanation:

When we want to withdraw money from the account then we need to mention the amount in the WITHDRAWAL column of the checkbook register.

When we want to deposit money to the account then we need to mention the amount in the DEPOSIT column of the checkbook register.

When we want to pay money to the someone else's  account then we need to mention the amount in the PAYMENT column of the checkbook register.

So, Ted must write the amount in the PAYMENT column of the checkbook register.

The ordinary number for the given Scientific notation is 0.00000000000007085.

Given that, [tex]7.085\times10^{-14}[/tex].

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.57\times10^7[/tex].

The given number can be written as [tex]\frac{7.085}{10^{14}}[/tex]

= 0.00000000000007085

Therefore, the ordinary number for the given Scientific notation is 0.00000000000007085.

To learn more about the Scientific notation visit:

https://brainly.com/question/18073768.

#SPJ5

The required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).

As per the question we have to determine the derivative of the f(x) = (x⁴ + 9x² − 5)⁴.

A derivative is defined as the rate of change of the function with respect to the respective variables.

Here,
According to the question,
f(x) = (x⁴ + 9x² − 5)⁴
Differentiate both sides with respect to x.
f'(x) = d[(x⁴ + 9x² − 5)⁴] / dx
f'(x) = 4 (x⁴ + 9x² − 5)³ × (4x³ + 9×2x)
f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x)

Thus, the required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).

Learn more about derivatives here:
https://brainly.com/question/25324584
#SPJ2

In this case, the final temperature of the two nails will be an average of their initial temperatures, which is 55 °C.

When two objects at different temperatures come into contact, heat is transferred from the object with higher temperature to the object with lower temperature until they reach thermal equilibrium.

In this case, the heated iron nail at 95 °C will transfer heat to the cooled iron nail at 15 °C when they are placed in the coffee cup calorimeter.

The final temperature of the two nails will be an average of their initial temperatures, which is (95 °C + 15 °C) / 2 = 55 °C.

To maximize the area of the rectangular field, express the area in terms of one variable, derive the area function, and set it to zero for solving. The sides of the field yielding the maximum area are obtained using these calculations.

This question involves optimization in calculus, specifically related to finding the maximum area of a rectangle. In such a problem, the first step is to express the area (A) of the rectangle in terms of one variable. Given a fence that is 1000 ft in length, if we name the side perpendicular to the stream as 'x', and the side parallel to it (bounded by the fence) as 'y', the perimeter of the field is 2x + y = 1000.

We can express y in terms of x: y = 1000 - 2x. The area of the rectangle, A = x*y = x*(1000 - 2x).

To find the maximum area, we find the first derivative of A with respect to x, set it to zero and solve for x. The second derivative test will confirm if it's a maximum. Based on the solutions, the maximum area is achieved with the dimensions of the rectangular field being specific values of x and y that you compute.

https://brainly.com/question/33322941

#SPJ3

Answer:

Step-by-sstep explanation:

Remove unnecessary parenthesis.

-5k 3 - 6k +1 - 6k 2 + 5k (simplify each term) -15k - 6k + 1 - 12k +5k = -28k +1

Answer: 28k + 1

Step-by-step explanation:

−5k

3

−6k

2

−k+1

The fractions 9/6 and 21/14 are proportional because both simplify to the same value, which is 1.5. Cross-multiplication also confirms their proportionality as the cross products are equal.

To determine if the fractions 9/6 and 21/14 are proportional, we can simplify each fraction or cross-multiply to see if we end up with an equivalent value. If two ratios are proportional, this means they are equivalent to each other when reduced to simplest form, or the cross products are equal.

Simplifying 9/6, we get 1.5, and simplifying 21/14, we also get 1.5. Since both simplified fractions result in the same value, 9/6 and 21/14 are indeed proportional.

We can also cross multiply to verify: (9×14) should be equal to (6×21). This results in 126 = 126, confirming that both ratios are indeed proportional.

Final answer:

The ratios 9/6 and 21/14 are proportional because both simplify to the same ratio 3/2, and cross-multiplication yields equal products, confirming proportionality.

Explanation:

To determine if the ratios 9/6 and 21/14 are proportional, we simplify each ratio. The ratio 9/6 simplifies to 3/2 and the ratio 21/14 simplifies to 3/2 as well. Since both simplified ratios are equal, we can confirm that 9/6 and 21/14 are indeed proportional ratios.

Another way to check for proportionality is to cross-multiply and see if the products are equal. Multiplying 9 times 14 and 6 times 21 gives us 126 in both cases, which reaffirms our conclusion. Thus, based on these methods, the given ratios are proportional.

This question is all about doubles. The given bottom cards 5 2 3 4 and the top cards are 1 4 3 2.

The problem is asking to match the top cards to the bottom ones then adding 1 to get the doubles.

So 1 should be corresponding to two. Since 1 + 1 = 2

4 should be corresponding to 5. Since 4 + 1 = 5

3 should be corresponding to 4. Since 3 + 1 = 4

And lastly, 2 should be corresponding to 3. Since 2 + 1 = 3