6. Stewart is making fruit punch for
his birthday party. He is filling a
240-ounce bowl with cans of apple
juice and pineapple juice. Each
can of apple juice holds 10 ounces,
while each can of pineapple juice
holds 18 ounces.
Write an inequality in standard
form representing the maximum
number of cans of apple juice, a,
and cans of pineapple juice, p,
Stewart can use.

Answer:  D.  -1

Step-by-step explanation:

Your equation:

[tex]\sqrt[4]{(\sqrt[3]{64}) ^{2} } =(\frac{1}{2} )^{x}[/tex]       >We are going to work from the inside first then out

                                   The cube root of 64 is 4 because 4*4*4=64

[tex]\sqrt[4]{(4) ^{2} } =(\frac{1}{2} )^{x}[/tex]            > 4² = 4*4=16

[tex]\sqrt[4]{(16) } =(\frac{1}{2} )^{x}[/tex]           > the 4th root of 16 is 2 because 2*2*2*2=16

[tex]2 =(\frac{1}{2} )^{x}[/tex]                   > if you have the same bases you can set the

                                   exponents equal.  They are not the same but we

                                    are going to make them the same.  

[tex]2^{1} =(\frac{1}{2} )^{x}[/tex]                  > 2 is the same as 2^1,  i can make the bases the

                                   same if I can make the 2 a reciprocal.  That

                                   happens when I take the negative exponent of the

                                   number

[tex](\frac{1}{2} )^{-1} =(\frac{1}{2} )^{x}[/tex]             >Now that my bases are the same, I can make the

                                exponents =

-1 = x

Usually, a mixed number is the simplest way to express an improper fraction – but sometimes, the fraction ... Don't express the answer as a decimal. Instead ... So, add the whole number back in to get a final result of 6 1/2. ... Write out the factors for the numerator of your fraction, then write out the factors for the denominator.

Answer:

Step-by-step explanation:

Step-by-step explanation:

You would need a calculator in the degree function I believe, but basically for Number 1,

you would set it up in calculator as Sin ^-1 (6/9) or write it down as Sin(X)=(6/9)

2. would be Cos(45)= (X/4) meaning you'd do Cos(45) times 4.

3. is basically Tan(60) =(x/4) so it's basically Tan(60) times 4.

make sure your calculator is in degree mode ? Sorry, I don't remember if you need to be in radiant or degree mode. I can comment or make an edit when I remember.

Answer:

the surface area of the rectangular prism is 572cm².

Step-by-step explanation:

The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:

2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²

So the surface area of the rectangular prism is 572 square centimeters.

The standard form of the equation of the ellipse is (x - 1)² / 16 + (y + 3) / 9 = 1.

In this problem we find the representation of an ellipse on Cartesian plane, whose center is at (h, k) = (1, - 3), whose major semiaxis length is 4 units and whose minor semiaxis length is 3 units. The standard form of the equation of the ellipse is described below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

If we know that (h, k) = (1, - 3), a = 4 and b = 3, then the standard form of the equation of the ellipse is:

(x - 1)² / 16 + (y + 3) / 9 = 1

To learn more on ellipses: https://brainly.com/question/19507943

#SPJ1

Answer:

Total amount of becomes after 16 year is $93649 .

Answer:

3 and 4 ==> see work below

[tex]5. \quad\quad f^{-1}(x) = x^{1/7}[/tex]

[tex]6. \quad\quad f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

Step-by-step explanation:

Definition of inverse functions

If f and g are inverse functions, then f(x) = y if and only if g(y) = x

Or, in other words
If f(g(x)) = (g(f(x)) = x
then f and g are inverse functions

Q3

We have f(x) = x + 4 and g(x) = x - 4

To find f(g(x)), substitute g(x) = x - 4 wherever there is an x term in f(x)

f(g(x)) = g(x) + 4

= x - 4 + 4 = x

g(f(x)) = f(x) - 4

= x + 4 - 4 =x

Hence f(x) and g(x) are inverse functions

Q4

[tex]f(x) = \dfrac{1}{4}x^3\\\\g(x) = (4x)^{1/3}[/tex]

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\\\\end{aligned}[/tex]

[tex]\begin{aligned}(g(x))^3 &= \left((4x)^{1/3} \right)^3 \\& = (4x)^{\frac{1}{3} \cdot 3}\\& = 4x\end{aligned}[/tex]

Therefore

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\&= \dfrac{1}{4} \cdot 4x\\&= x\\\end{aligned}[/tex]

[tex]\begin{aligned}g\left(f(x)\right) & = \left(4f(x)\right)^{1/3}\\&= \left(4 \cdot \dfrac{1}{4}x^3\right)^{1/3}\\& = \left(x^3\right)^{1/3}\\& =x& \end{aligned}[/tex]

So f(x) and g(x) are inverse functions

Q5

[tex]\text{Given $f(x) = x^7 $ we are asked to find inverse $f^{-1}(x)$}[/tex]

[tex]\rm{Let \: y = f(x) = x^7}\\[/tex]

Interchange x and y:
[tex]x = y^7[/tex]

Solve for y:
[tex]y = x^{1/7}[/tex]

The right hand side is the inverse function of f(x)

[tex]f^{-1}(x) = x^{1/7}[/tex]

Q6
[tex]\rm{Given \;f(x) = -\dfrac{2}{5}x^3 \:find\:the\:inverse,\;f^{-1}(x)}[/tex]

Using the same procedure as for Q5

[tex]y=-\dfrac{2}{5}x^3\\\\x=-\dfrac{2}{5}y^3\\\\\text{Solve for y}\\[/tex]

[tex]y^3=-\dfrac{5x}{2}[/tex]

[tex]y=-\left(\dfrac{5x}{2}\right)^{1/3}\\\\\\\text{Inverse of $f(x)$ is $f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually

When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.

For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960

Then new total amount after one year will be $12,000 + $960 = $12 960 ,

This process will continue for each year of the investment and the  formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n

Learn more about money  at:

https://brainly.com/question/329739

#SPJ1

complete quesation:

You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

a.

3.99% compounded monthly

b.

4% compounded quarterly

c.

4.175% compounded annually

d.

4.2% simple interest

In 1973, the batting average of .350 of Rod Carew is more impressive as it has a higher z-score of 2.81

To establish which batting average was more spectacular, we must compare it to the mean and standard deviation of 1970s hitting averages. The case of Jackie Robinson,

z = (x - μ) / σ

z = (.342 - .261) / .0317

z = 2.56

For Rod Carew,

z = (x - μ) / σ

z = (.350 - .261) / .0317

z = 2.81

A higher z-score indicates a more impressive performance relative to the mean. As a result, Rod Carew's .350 batting average was more spectacular, as it had a higher z-score of 2.81 than Jackie Robinson's z-score of 2.56.

To know more about standard deviation, visit,

https://brainly.com/question/475676

#SPJ1

Working backward, the number that Lara started with in performing the mathematical operations was 15.

We can use mathematical operations to determine the initial number that Lara started with.

Mathematical operations include addition, subtraction, division, multiplication, etc.

Let the number that Lara started with = x

x < 20

x ÷ 2 + 6 = y

y ÷ 3 = 4.5

y = 13.5 (4.5 x 3)

x ÷ 2 + 6 = 13.5

x ÷ 2 = 7.5

x = 15 (7.5 x 2)

Thus, Lara started performing the mathematical operations with 15 and got a final result of 4.5.

Learn more about mathematical operations at https://brainly.com/question/4721701.

#SPJ1

Answer: The answer is false

Answer:

False

Step-by-step explanation:

If you were asking true or false it is false

Answer:

-166/, -0.82,

Step-by-step explanation:

The above fraction, decimal are all evaluated answer for (11/16−(3/4)2)×1

The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

We have to given that;

The model shown below is a perfect cube with a volume of 27 cubic units.

Now, We can formulate;

⇒ V = 27 cubic units.

⇒ V = 3 × 9 cubic units.

⇒ V = 3 × 3² cubic units.

Thus, The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ1

answer is : r=1.6 in since the volume of cylinder is :

[tex]\pi {r}^{2} h[/tex]

Answer:

shape

Step-by-step explanation:

Answer:

366,699

Step-by-step explanation:

to solve this problem, we can use the following formula for exponential growth:

population = initial population x (1 + growth rate)^time

where the initial population is the current population, the growth rate is the rate of increase per year, and the time is the number of years.

Plugging in the given values, we get:

population = 300,000 x (1 + 0.02)^10

Simplifying, we get:

population = 300,000 x 1.02^10

Using a calculator, we get:

population ≈ 366,698.79

Rounding to the nearest whole number, we get:

population ≈ 366,699

The population in 10 years will be approximately 366,699

Answer:

364 cents or $3.64

Step-by-step explanation:

We can first convert $4 into cents. There are a 100 cents in $1, so there are 400 cents in $4. Now we can subtract.

400 - 36 = 364

Difference is 364 cents or $3.64

Answer:

  54

Step-by-step explanation:

You want the approximate test grade of a student with a homework grade of 61, using a linear regression equation for the given homework and test scores.

The linear regression equation can be found using any of a number of calculators, apps, or spreadsheets. The attachment shows the equation is approximately ...

  y ≈ 1.22x -20.01

For a homework score of 61, the expected test grade is ...

  y = 1.22(61) -20.01

  y ≈ 54

The student's projected test grade is 54.

__

Additional comment

If the regression coefficients are used to their full precision, the projected test score is about 54.6, which rounds to 55.

<95141404393>

Answer:

[tex]2x=20\sqrt{10}\; \textsf{ft} \approx 63.25\; \sf ft[/tex]

[tex]6x=60\sqrt{10}\; \textsf{ft} \approx 189.74\; \sf ft[/tex]

Step-by-step explanation:

Assuming the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the value of x and then find the measurers of the side lengths.

[tex]\large{\boxed{a^2+b^2=c^2}[/tex]

where:

From inspection of the given diagram:

Substitute these values into the formula and solve for x.

[tex]\begin{aligned} (2x)^2+(6x)^2&=200^2\\2^2\cdot x^2+6^2\cdot x^2&=40000\\4x^2+36x^2&=40000\\40x^2&=40000\\x^2&=1000\\x&=\sqrt{1000}\\x&=\sqrt{100 \cdot 10}\\x&=\sqrt{100}{\sqrt{10}\\x&=10\sqrt{10}\end{aligned}[/tex]

Substitute the found value of x into the expression for each side length.

[tex]2x=2 \cdot 10\sqrt{10}=20\sqrt{10}[/tex]

[tex]6x=6\cdot 10\sqrt{10}=60\sqrt{10}[/tex]

Therefore, the exact side lengths of the given right triangle are:

[tex]20\sqrt{10}\; \textsf{ft}, \;\;60\sqrt{10}\; \textsf{ft}, \;\; 200\; \textsf{ft}[/tex]

The side lengths to the nearest hundredth are:

Answer:

2x³-5x² - 2x + 1

Step-by-step explanation:

We are given

f(x) = 2x³ - 5x²

g(x) = 2x - 1

and asked to find (f - g)(x)

(f - g)(x) is nothing but f(x) - g(x)

(f- g)(x) = f(x) - g(x) = 2x³-5x² - (2x - 1)

= 2x³-5x² - 2x + 1

The numerical expression that represents the sum of eight squared and thirty two will be 96.

A numerical expression is a mathematical expression that consists of numbers and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

The numerical expression that represents the sum of eight squared and thirty two is

= 8² + 32

= 64 + 32

= 96.

The question is incomplete and the complete question is '' What is the numerical expression that represents the sum of eight squared and thirty two''.

To know more about numerical expression here

https://brainly.com/question/27089337

#SPJ1

For the given question the values,

Given value of the function when the condition for x is less than '0' is =

f(x) = x²   for x < 0

The value of the function when the condition x is equals to '0' is =

f(x) = 0     for x = 0

The value of the function when the condition x is greater than '0' is =

f(x) = 3x + 4    for x > 0

From the above information,

To find f(-1) we have to use the x value as x². So, f(-1) = (-1)² = 1

To find f(0) we have to use x value as 0. So, f(0) = 0

To find f(3) we have to use the x value as 3x + 4. So, f(3) = 3(3) + 4 = 13.

From the above analysis, we find the values of f(-1), f(0), and f(3).

To know more about equations,

https://brainly.com/question/25976025

#SPJ1

A graph that correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r is: C. graph C.

In Mathematics and Geometry, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle can be calculated by using the following equation (formula):

Arc length = 2πr × θ/360

In this context, we can reasonably infer and logically deduce that the arc length is directly proportional to the radian measure of the central angle.

Read more on arc and central angle here: https://brainly.com/question/27673190

#SPJ1

Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.

Step-by-step explanation:   a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:

P = 50,000(1.15)^0 = 50,000

Therefore, the population of the town in 2005 was 50,000.

b) We need to find the value of t when the population P exceeds 100,000:

100,000 = 50,000(1.15)^t

Divide both sides by 50,000:

2 = 1.15^t

Take the natural logarithm of both sides:

ln 2 = ln (1.15^t)

Apply the power rule of logarithms:

ln 2 = t ln 1.15

Divide both sides by ln 1.15:

t = ln 2 / ln 1.15

Using a calculator, we get:

t ≈ 10.73

Answer: The given expression, 2430 + 15√2, cannot be simplified further as it is already in its simplest form. However, you can approximate its value using a calculator or by using a decimal approximation of the square root of 2.

Using a calculator, you can directly evaluate the expression to get:

2430 + 15√2 ≈ 2462.11

Alternatively, you can use a decimal approximation of the square root of 2, which is approximately 1.414:

2430 + 15√2 = 2430 + 15 * 1.414 ≈ 2430 + 21.21 = 2451.21

Therefore, 2430 + 15√2 is approximately equal to 2462.11 or 2451.21, depending on the method used for approximation.

Step-by-step explanation:

The value of arc CD is 110⁰.

The value of arc AD is 120⁰.

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)

angle DEC = ¹/₂ (360 - 200)

angle DEC = 80⁰

The value of arc CD is calculated as follows;

80 = ¹/₂ (CD + 50) (intersecting chord theorem)

2 x 80 = CD + 50

160 = CD + 50

CD = 110⁰

Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)

arc AD = 120⁰

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

Answer:

∠ I = 60°

Step-by-step explanation:

using the tangent ratio in the right triangle

tan I = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{HJ}{IJ}[/tex] = [tex]\frac{3\sqrt{30} }{3\sqrt{10} }[/tex] = [tex]\frac{\sqrt{30} }{\sqrt{10} }[/tex] = [tex]\sqrt{\frac{30}{10} }[/tex] = [tex]\sqrt{3}[/tex] , then

∠ I = [tex]tan^{-1}[/tex] ([tex]\sqrt{3}[/tex] ) = 60°

Answer:

  60°

Step-by-step explanation:

You want the measure of angle I in right triangle HIJ, given that the side opposite is 3√30 and the side adjacent is 3√10.

The tangent relation is ...

  Tan = Opposite/Adjacent

In this triangle, ...

  tan(I) = (3√30)/(3√10) = √(30/10) = √3

Then the angle is ...

  I = arctan(√3) = 60°

The measure of angle I is 60°.

__

Additional comment

The trig functions of 30° and 45° and their relationships to each other are based on the side relationships of the two "special" right triangles:

  30°-60°-90° triangle has side ratios 1 : √3 : 2

  45°-45°-90° triangle has side ratios 1 : 1 : √2

Of course, side lengths are in the same order as their opposite angles.

The mnemonic SOH CAH TOA can help you remember the necessary relationships: