You weigh a gallon of 2% milk in science class and learn that it is approximately 8.4 pounds. You pass the milk to the next group, and then realize that you teacher wants it in kilograms, not pound. Explain how you can adjust your answer without weighing the milk again. Then give you the weight in kilograms.

Barbara Mack owes approximately $2543.78 at the end of 4 years with 6% interest compounded continuously.

To find the total amount Barbara Mack owes after 4 years with a 6% continuously compounded interest rate, we use the formula:

A = P[tex]e^{rt}[/tex]

with P = $2000,

r = 0.06, and

t = 4

A = 2000 x [tex]e^{0.06 * 4}[/tex].

When we calculate e(0.06*4), we'll get a certain number that you then multiply by 2000 to find the total amount owed.

A= 2000 x [tex]2.71828 ^{0.24}[/tex]

A= 2543.78 ( approx)

So, Barbara Mack owes approximately $2543.78 at the end of 4 years with 6% interest compounded continuously.

Answer:

5 people

Step-by-step explanation:

Let

The total cost was $1400, which was to be divided equally among the members going. Then,

y = 1400 / x [1]

Prior to the trip, 3 members decided not to go. The cost per person increased by $105.

y + 105 = 1400 / (x - 3)

(y + 105) . (x - 3) = 1400 [2]

We replace [1] in [2],

(1400/x + 105) . (x - 3) = 1400

1400 - 4200/x + 105x -315 = 1400

- 4200/x + 105x = 315

(- 4200 + 105x²)/x = 315

- 4200 + 105x² = 315 x

105x² - 315x - 4200 = 0

When we solve this quadratic equation using the quadratic formula, we get x₁ = 8 and x₂ = -5. Only the positive x has sense.

The people that went to the expedition was x - 3 = 8 - 3 = 5.

The point that is closest to the point (3, 0) can be found by finding the

minimum value for the function of the distance between points.

The closest point on the hyperbola  x·y = 8 to the point (3, 0) is the point [tex]\underline{(4, \ 2)}[/tex]

Reasons:

The equation of the hyperbola is x·y = 8

The given point = (3, 0)

Therefore;

[tex]y = \dfrac{8}{x}[/tex]

The distance of a point from a line, [tex]d = \mathbf{ \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}}[/tex]

Where;

(x₁, y₁) = (3, 0)

(x₂, y₂) = The closest point on the hyperbola

We get;

[tex]d = \sqrt{\left (y-0 \right )^{2}+\left (x-3 \right )^{2}}[/tex]

Which gives;

[tex]d = \sqrt{\left (\dfrac{8}{x} -0 \right )^{2}+\left (x-3 \right )^{2}} = \mathbf{ \sqrt{\left (\dfrac{8}{x}\right )^{2}+\left (x-3 \right )^{2}}}[/tex]

At the minimum distance, using an online app, we have;

[tex]\dfrac{d}{dx}d = \dfrac{d}{dx} \left( \sqrt{\left (\dfrac{8}{x}\right )^{2}+\left (x-3 \right )^{2}} \right) = \dfrac{-64 + x^3 \cdot (x - 3)}{x^2 \cdot \sqrt{x^2 \cdot (x - 3)^2 + 64} } = 0[/tex]

Which gives;

x³·(x - 3) - 64 = 0

Using a graphing calculator, we get;

(x - 4)·(x³ + x² + 4·x + 16) = 0

Therefore;

A solution for the closest or point of minimum distance is x = 4

Which gives;

[tex]y = \dfrac{8}{4} = 2[/tex]

Therefore, the closest point on the hyperbola  x·y = 8 to the point (3, 0) is the

point [tex]\underline{(4, \ 2)}[/tex]

Learn more here:

https://brainly.com/question/4279271

The calories in a 21-oz iced tea that is originally 78 calories in a 13-oz serving, multiply the calories per ounce by the new serving size for a total of 126 calories.

The 13-oz iced tea contains 78 calories. To find the calories in a 21-oz iced tea:

Calculate the calories per ounce: 78 calories ÷ 13 oz = 6 calories/oz

Multiply the calories per ounce by the 21-oz serving size: 6 calories/oz × 21 oz = 126 calories in a 21-oz iced tea

Answer:

5%

Step-by-step explanation:

to work out what percent 17 is out of 340 we can formulate an equation

so 340(x%)=17

when we solve for x we get 5

we have that

[tex] f(x) =x^{2} + x - 9 [/tex]

Using a graph tool

see the attached figure

The function represent a vertical parabola that open up

the vertex is a minimum-------> is the point [tex] (-0.5,-9.3) [/tex]

The x-intercepts are the points when the y coordinate is equal to zero

The x-intercepts are the points [tex] (-3.5,0) [/tex] and [tex] (2.5,0) [/tex]

so

the function cross the negative x-axis at point [tex] (-3.5,0) [/tex]

therefore

the answer is

(–4, 0) and (–3, 0)

Final answer:

Ava can capture the chip on square 72 by using the +30 change card once to reach 66, and then the +1 change card six times to reach the final value of 72.

Explanation:

Ava's game piece is on square number 36, and she wants to capture a chip on square number 72. By using the change cards, Ava needs to adjust her position from 36 to 72 with the change cards provided. The change cards are: -10, +30, -1, +1, and -2. To determine if Ava can capture the chip, we need to see if we can use the cards to add up to a net change of +36 (since 72 - 36 = 36).

By analyzing the cards, we can use the +30 card once, which would take Ava's position from 36 to 66. Next, she can use the +1 card six times to go from 66 to 72. Ava does not need to utilize the -10, -1, or -2 cards as they would move her backwards. Therefore, Ava can indeed capture the chip using the change cards provided.

The steps Ava should follow are:

Use the +1 card six times to move from 66 to 72.

Answer: Amount she earn on the sale is $42.9.

Step-by-step explanation:

Since we have given that

A furniture salesperson sells a couch for $1560.

Percentage of commission she receive on the sale of the couch = 2.75%

So, Amount she earn on the sale is given by

[tex]2.75\%\ of\ 1560\\\\=\frac{2.75}{100}\times 1560\\\\=0.0275\times 1560\\\\=\$42.9[/tex]

Hence, amount she earn on the sale is $42.9.

It will take her 13 weeks to save enough money for a trip to the Six Flags amusement park

Comparison is an effort to compare two or more objects in terms of shape or size, or number  

Proportional Comparisons / Directly proportional are comparisons of two or more numbers where one number increases, the other numbers also increase at the same rate  

 Can be formulated  

[tex]\displaystyle \frac {x1} {y1} = \frac {x2} {y2}[/tex]

 so that if:  

 x = 2  

 then  

[tex]\displaystyle y ={ \frac {y} {x} \times \: 2}[/tex]

 While the reversal value comparison / inversely proportional is the comparison of two or more numbers where one number increases, the other number decreases in value  

or when one value decreases at the same rate that the other increases  

Can be formulated  

[tex]\displaystyle \frac {x1} {y2} = \frac {x2} {y1}[/tex]

so that if:  

 x = 2  

 then  

[tex]\displaystyle y = \frac {x} {y} \times \: 2[/tex]

Michelle wants to save $150

she saves $12 each week

the number of weeks needed to save money

every weeks , she save $12 or we can make equation 1:

1 weeks = $12

the amount of money needed to travel to the six flags amusement park

= $150

we can make equation 2

? weeks = $150

Because this includes Proportional Comparisons / Directly proportional,

from two equation above , we can make comparison :

[tex]\displaystyle \frac{1\:weeks}{\$12} =\frac{x\:weeks}{\$150}[/tex]

[tex]\displaystyle x\:weeks=\frac{\$150\times1\:weeks}{\$12}[/tex]

[tex]\large{\boxed{x\:weeks= 12.5}}[/tex]

or we round up to :

[tex]\large{\boxed{\bold{13\:weeks}}}[/tex]

1,092 flowers are arranged into 26 vases  

https://brainly.com/question/2713244  

dividing 878 by 31  

https://brainly.com/question/839496  

round trips  

https://brainly.com/question/10739583  

Keywords: save money,a trip to park, Proportional Comparisons / Directly proportional

There are 1001 different choices of 10 questions.

d. Since the student can choose any 10 questions out of the 14, the number of different choices of 10 questions is given by the combination formula, which is C(14,10). Using the formula for combinations, we have:

C(14,10) = 14! / (10!(14-10)!)

= 14! / (10!4!)

= (14*13*12*11) / (4*3*2*1) = 1001

Therefore, there are 1001 different choices of 10 questions.

https://brainly.com/question/30646507

#SPJ11

To find the length of the ladder, we can use the property of right triangles. The length of the ladder is 10 feet.

To find the length of the ladder, we can use the property of right triangles. Let's assume the length of the ladder is 'L'.

According to the given information, the distance from the ground to the top of the ladder is 2 feet less than the length of the ladder. So, the height of the triangle formed by the ladder, the building, and the ground is L - 2.

The distance from the bottom of the ladder to the building is given as 6 feet. Using the Pythagorean theorem, we can set up the following equation: (L-2)^2 + 6^2 = L^2

Simplifying the equation, we get L^2 - 4L + 4 + 36 = L^2, which simplifies further to 40 = 4L. Dividing both sides by 4, we get L = 10.

Therefore, the length of the ladder is 10 feet.

To complete the partial worksheet for Bill's Company, you need to record the appropriate adjusting entries using the given data. Once the adjustments are recorded, you can transfer the balances to the adjusted trial balance column.

To complete the partial worksheet for Bill's Company, we need to record the appropriate adjusting entries using the given data. Let's go step by step:

Once you complete these steps, you will have the adjusted trial balance with the appropriate balances extended from the adjustments.

To write an equation relating the total cost to the number of tickets purchased with a fixed fee, set up a system of equations using the given information and solve for the variables.

To write an equation relating the total cost to the number of tickets purchased, we need to determine the cost of one ticket and the fixed fee added by the ticket agency. Let's assign the ticket price as x and the fixed fee as y. Based on the given information, we can set up two equations:

5x + y = 93

3x + y = 57

Now, we can solve this system of equations to find the values of x and y and write the final equation relating the total cost to the number of tickets purchased.

https://brainly.com/question/32790022

#SPJ2

The length of the rectangle with a perimeter of 36 meters and a length that is 2 meters more than three times the width is 14 meters.

The perimeter of a rectangle is twice the sum of its length and width. According to the question, the perimeter of the rectangle is 36 meters, and the length (L) is 2 meters more than three times the width (W). We can express this relationship as follows: L = 3W + 2.

The formula for the perimeter (P) of a rectangle is P = 2L + 2W.

Using the given perimeter of 36 meters, we can set up the equation as 2(3W + 2) + 2W = 36.

Simplifying this equation, we find that 8W + 4 = 36, and thus W = 4 meters.

Substituting the value of W back into the equation for L gives us L = 3(4) + 2, which means the length of the rectangle is 14 meters.