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Creative Capacities

Part 1
Directions: Use the information in the chart to answer the questions. Show your
work and include equations to show how you solved each problem. Refer to the unit
glossary terms to remind yourself of the measurement conversions.

Mandy wants to buy a variety of beverages for her brunch party. She
wants to make sure she has enough to drink for all her friends, so she
decides to buy 10 liters of beverages. She also wants to buy at least
one of each beverage.

1. Complete the table to record the amount of each beverage in liters. Show
your work in the space below.
(Hint: 1 liter = 1,000 milliliters

2. If she buys one container of each beverage, how many liters of beverage
will she have

3. What combination of beverages can she buy to equal exactly 10 liters?

Part 2
Directions: Use the information in the chart to answer the questions.

1. Complete the table to record the amount of each beverage in liters.
Show your work in the space below.
(Hint: 1 liter equals 1,000 milliliters

Answer:

Step-by-step explanation:

For Keiko's trend line equation, we have t = 0.95a + 59. Plugging in a = 16, we get t = 0.95(16) + 59 = 74.2. Rounding to the nearest whole number, we get t ≈ 74.

For Eric's trend line equation, we have t = 0.55a + 90. Plugging in a = 16, we get t = 0.55(16) + 90 = 98.8. Rounding to the nearest whole number, we get t ≈ 99.

Therefore, a 16 year old would send approximately 74 texts per day based on Keiko's trend line equation and approximately 99 texts per day based on Eric's trend line equation. So, the answer is Keiko = 74, Eric = 99.

The solution is, a 16 year old would send approximately 74 texts per day based on Keiko's trend line equation and approximately 99 texts per day based on Eric's trend line equation.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

For Keiko's trend line equation,

we have t = 0.95a + 59.

Plugging in a = 16,

we get t = 0.95(16) + 59 = 74.2.

Rounding to the nearest whole number, we get t ≈ 74.

and, we have,

For Eric's trend line equation,

we have t = 0.55a + 90.

Plugging in a = 16,

we get t = 0.55(16) + 90 = 98.8.

Rounding to the nearest whole number, we get t ≈ 99.

Therefore, a 16 year old would send approximately 74 texts per day based on Keiko's trend line equation and approximately 99 texts per day based on Eric's trend line equation.

So, the answer is Keiko = 74, Eric = 99.

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Answer:

Triangles: 4(1/2)(5)(12) = 120 square feet

Square: 5 × 5 = 25 square feet

Total surface area = 120 + 25 = 145 square feet

Answer:

Original box costs less than the new box.

Step-by-step explanation:

A). original box has a surface are of 216 sq in

2(10x6)+2(6x3)+2(10x3) = 216sq in

216sq in/144sq in = 1.5sq ft

1.5 sq ft x .22 = .33 per sq ft

B) new box has a surface area of 434 sq in

2(15x11) + 2(11x2) + 2(15x2) = 434 sq in

434sq in/144 sq ft = 3.01sq ft

3.01 sq ft x .15 = .45 per sq ft

Answer:

Step-by-step explanation:

Answer: D. 56 units

Step-by-step explanation:

   To find the perimeter, we will count the units all around the outline of the outside of the figure. See attached.

➜ Note that the scale of this coordinate plane is by 2's, not 1's.

Answer:

There are 2 terms.

Step-by-step explanation:

1st term: m

2nd term: 2n

a^(-x) = 1/(pi^(1/x)) in fractional form.

1/a^x = 1/pi

Next, we can rewrite a^(-x) as 1/a^x and substitute the expression for 1/a^x from the above equation:

a^(-x) = 1/a^x = 1/(pi^(1/x))

The value of [tex]a^{-x}[/tex] when [tex]a^x = \pi \ is\ 1/\pi[/tex]. To find the value of [tex]a^{-x}[/tex] when [tex]a^x = \pi[/tex], we can use the properties of exponents.

First, recall that a^(-x) is the reciprocal of [tex]a^x[/tex]. In other words, [tex]a^{-x} = 1 / a^x[/tex].

Given that [tex]a^x = \pi[/tex], we have:

[tex]a^{-x} = 1 / a^x\\a^{-x} = 1 / \pi[/tex]

So, The value of [tex]a^{-x}[/tex] when [tex]a^x = \pi \ is\ 1/\pi[/tex].

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To expand the square of the binomial `(4x-5y)²`, you can use the FOIL method or the binomial square formula:

Using FOIL:

(4x - 5y)² = (4x - 5y)(4x - 5y) (writing out the square as a multiplication of the binomial by itself)

= 16x² - 20xy - 20xy + 25y² (using the FOIL method)

Simplifying:

= 16x² - 40xy + 25y²

Using the binomial square formula:

(4x - 5y)² = (4x)² - 2(4x)(5y) + (5y)² (formula: (a - b)² = a² - 2ab + b²)

= 16x² - 40xy + 25y²

Thus, the expanded form of the binomial `(4x-5y)²` is `16x² - 40xy + 25y²`.

Answer:

i do not know where the following is but here.

Step-by-step explanation:

To square the binomial (4x-5y)², we can use the formula:

(a - b)² = a² - 2ab + b²

In this case, a = 4x and b = 5y. So, we have:

(4x - 5y)² = (4x)² - 2(4x)(5y) + (5y)²

Simplifying the terms inside the parentheses, we get:

= 16x² - 40xy + 25y²

Therefore, the square of the binomial (4x-5y) is equal to the trinomial 16x² - 40xy + 25y².

Each term in the trinomial is obtained by squaring the corresponding term in the binomial and then applying the formula for the cross-product (-2ab).

So, (4x)² = 16x², (5y)² = 25y², and (-2)(4x)(5y) = -40xy.

Therefore, (4x-5y)² = 16x² - 40xy + 25y².

Answer: A is incorrect

Step-by-step explanation:A. 0 < -4, the value 0 is greater than negative 4. So, this is incorrect.

B. -9 < 1, the value 1 is greater than negative 9. So, this is correct.

C. 2 > -3, the value 2 is greater than negative 3. So, this is correct.

D. -7 < -5, the value negative 5 is greater than negative 7. So, this is correct.

Step-by-step explanation:

the product of Janelle's score and 3 is 39, using the variable J to represent Janelle's score.

which can be expressed mathematically as

[tex]j \times 3 = 39[/tex]

cause product is the same as multiplication ✖️

[tex]3j = 39[/tex]

finally, divide both sides by 3

[tex] \frac{3j}{3} = \frac{39}{3} [/tex]

therefore

[tex]j = 13[/tex]

Answer:

13

Step-by-step explanation:

j x 3= 39

so then you use the fraction thingy

[tex]\frac{3j}{3}= \frac{39}{3}[/tex]

so then its 39 divided by 3 gets 13

so its 13

a. The outlier in the data set is Crater lake with a depth of 1,148 feet.

b. The outlier has a significant effect on the mean and range of the data but no effect on the median and mode.

c. The median and mode are measures of center that are less influenced by outliers, so they best describe the data with or without the outlier.

An outlier is a single data point that deviates significantly from the average value of a set of statistics. Outliers are exceptions that exist outside of individual population samples.

The mean is heavily influenced by outliers, so the outlier in this case increases the mean depth of the lakes. The range is the difference between the highest and lowest values, so the outlier also increases the range.

Without the outlier, the median depth is 33.5 feet, which is closer to the majority of the depths in the data set. Therefore, the median is the best measure of center for this data set without the outlier. With the outlier included, the median depth is still 43 feet, and the mode is also 43 feet, so either measure could be used to describe the center of the data set.

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Answer: It would take her 45 minutes to jog 5 miles because first you have to divide 27 by 3 and you get 9 and then you multiply 9 by 5 and you get 45

Answer:

3821.05

Step-by-step explanation:

To find the volume of a sphere, use the formula [tex]4/3\pi r^3[/tex].

Replace R with 9.7 because the diameter is 19.4 and the radius would be half of that, and the question said to use 3.14 as pi.

So it would be: [tex]4/3*3.14*9.7^3[/tex]

Which would equal: 3821.05

Answer:

2in cubed

Step-by-step explanation:

since one side is 1/3 inches and they're 6 sides in a cube

We can do 1/3 x 6 which gives us 2 inches cubed

Answer:

One pattern that can be observed in the repeated table is that each number is obtained by adding 0.09 to the previous number.

Step-by-step explanation:

For example, to get from 0.09 to 0.18, we add 0.09. To get from 0.18 to 0.27, we add 0.09 again, and so on. This pattern continues throughout the table, with each number being 0.09 greater than the previous number.

Part A - In the given table we can observe that there is a continuous table of 0.09 till 0.63.

Part B - The table is in the ‘Step by step explanation’

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Answer:

x= 2.5 and -3.5

Step-by-step explanation:

To solve the equation Ix+1/2I=3, we can break it down into two cases: one where x+1/2 is positive, and one where x+1/2 is negative.

Case 1: x+1/2 is positive

In this case, the absolute value of x+1/2 is equal to x+1/2 itself. So we can rewrite the equation as x+1/2=3. To solve for x, we subtract 1/2 from both sides: x=3-1/2. Simplifying further, we have x=2.5.

Case 2: x+1/2 is negative

In this case, the absolute value of x+1/2 is equal to -(x+1/2). So we can rewrite the equation as -(x+1/2)=3. To solve for x, we first distribute the negative sign: -x-1/2=3. Then, we add 1/2 to both sides: -x=3+1/2. Simplifying further, we have -x=3.5. To isolate x, we multiply both sides by -1: x=-3.5.

So, the solution to the equation Ix+1/2I=3 is x=2.5 and x=-3.5.

Answer: About 12.843 or 12[tex]\frac{59}{70}[/tex]

Step-by-step explanation:

    We will follow the Order of Operations to solve this question.

   Given:

[tex]\displaystyle (\frac{-3}{5})(-\frac{4}{7} )+12.5[/tex]

   Multiply:

[tex]\displaystyle (\frac{-3*-4}{5*7})+12.5[/tex]

[tex]\displaystyle (\frac{12}{35})+12.5[/tex]

   Add:

12 [tex]\frac{59}{70}[/tex]≈ 12.843

Answer:

12.8428571429

Answer:

Step-by-step explanation:

To divide rational numbers, remember the rules of dividing positive and negative numbers: If the dividend and divisor have the same sign, the quotient is positive

4.9 × 10^( -5 ) + 0.0005 =4.9x10^(-5)+5x10^(-4)=

=5.49x10^(-5)=5.49e-5=5.49E(-5)

Which in scientific notation is written as 5.49e-5, where e-5 is the same as 10^(-5).

This answer can also be written as 5.49E(-5) in scientific notation.

Answer: i think its b

Step-by-step explanation:

The volume of the original box is given as

V = lwh

V = 10(6)(3)

V = 180 in³

Answer:

First option

Step-by-step explanation:

This is because if 6 is added to 8 then it becomes 14 and the other side is also 14 Thus, the object will be stationary.

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Answer: The answer is A. 10 ft, 24 ft, 25 ft

Step-by-step explanation: I used a ruler and did everything in cm and the only one that worked was A.

Answer:

A. 10 ft, 24 ft, 25 ft

Step-by-step explanation:

√50 = 7.071

So the dot will be very close to the right side of 7.

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Answer:

The answer is 4/6, or 2/3 if simplified.

1: Not a multiple of 2 or 3

2: A multiple of 2

3: A multiple of 3

4:A multiple of 2

5: Not a multiple of 2 or 3

6:A multiple of 2 and 3

Answer:-13 is to the left of -10. -10 is to the right of -13.

-13<-10

Step-by-step explanation:

-10 is to the left of -13 bc it is closer to the number 0 than -13. -10 is greater than -13.

Answer: Angle D

Step-by-step explanation: