Mr. Jonus ordered a pizza to take home. His children ate 4/8 of the pizza and
Mr. Jonus ate 2/8 of the pizza. The remaining pizza was saved for later. Which
equation could be used to represent the whole pizza?

Answer:

[tex]\dfrac{3^{13}}{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot (3^2)^4}{(2^3)^2 \cdot 3^6}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot 3^8}{2^6 \cdot 3^6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{3^{(5+6+8)} \cdot 2^{(4+1)}}{2^6 \cdot 3^6}[/tex]

[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{2^6 \cdot 3^6}[/tex]

[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{3^6 \cdot 2^6}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 3^{(19-6)} \cdot 2^{(5-6)}[/tex]

[tex]\implies 3^{13} \cdot 2^{-1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{3^{13}}{2^1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]

[tex]\implies \dfrac{3^{13}}{2}[/tex]

Answer:

The result is 3¹³ /2

Step-by-step explanation:

Greetings

Answer: [tex]-3 \leq x < 1[/tex]

Step-by-step explanation:

[tex]\sqrt{x+3} \geq 0 \longrightarrow x \geq -3\\\\\sqrt{1-x} > 0 \longrightarrow 1-x > 0 \longrightarrow x < 1\\\\\therefore -3 \leq x < 1[/tex]

The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.

From the equation of the plane 2 · x + y - 3 · z = - 4 we know that its normal vector is (2, 1, - 3). Hence, we have found two direction vectors and already know a point, which are part of this parametric equation:

(x, y, z) = (- 3, 4, 5) + t · (3, 2, 4) + u · (2, 1, - 3)     (1)

The normal vector of the plane is equal to the cross product of the direction vectors of (1):

[tex]\vec n = (3, 2, 4) \,\times\,(2, 1, -3)[/tex]

[tex]\vec n = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&2&4\\2&1&-3\end{array}\right|[/tex]

[tex]\vec n = (-6-4,8+9, 3-4)[/tex]

[tex]\vec n = (-10, 17, -1)[/tex]

Since the plane contains the point (x, y, z) = (- 3, 4, 5), then we find that the independent constant of the equation of the plane is:

- 10 · x + 17 · y - z = k

- 10 · (- 3) + 17 · 4 - 5 = k

30 + 51 - 5 = k

k = 76

The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.

To learn more on planes: https://brainly.com/question/1962726

#SPJ1

The multiplication of the expression (x² + 3x + 2) (2x² + 3x + 1) is 2x⁴ + 9x³ + 14x² + 9x + 2

(x² + 3x + 2) (2x² + 3x + 1)

= 2x⁴ + 3x³ + x² + 6x³ + 9x² + 3x + 4x² + 6x + 2

= 2x⁴ + 3x³ + 6x³ + x² + 9x² + 4x² + 3x + 6x + 2

= 2x⁴ + 9x³ + 14x² + 9x + 2

Learn more about multiplication:

https://brainly.com/question/10873737

#SPJ1

The value of r If r varies directly with the square of m and inversely with s is 240

Suppose r varies directly with the square of m and inversely with s.

If r varies directly with the square of m and inversely with s, then;

r = km²/s

Given that R = 15 when m = 6 s= 4

15 = k(6)²/4

60 = 36k

k = 60/36

k = 5/3

If the value of m = 24 and s = 4, hence;

r = 5/3*24²/4

r = 240

Hence the value of r If r varies directly with the square of m and inversely with s is 240

Learn more on variation here: https://brainly.com/question/25215474

#SPJ1

Answer:

B

Step-by-step explanation:

because at origin they are both positive and when it rotates about 270 both will change to negative

Using the t-distribution, the 96% confidence interval is given as follows:

(18.96, 21.04).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 96% confidence interval, with 100 - 1 = 99 df, is t = 2.0812.

The parameters are given as follows:

[tex]\overline{x} = 20, s = 5, n = 100[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 20 - 2.0812\frac{5}{\sqrt{100}} = 18.96[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 20 + 2.0812\frac{5}{\sqrt{100}} = 21.04[/tex]

More can be learned about the t-distribution at https://brainly.com/question/16162795

#SPJ1

The test statistic, rounded to 2 decimal places is equal to

For this sample, the hypothesis is given by:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

Assuming this sample has a normal distribution, we would use a pooled z-test to determine the value of the test statistic:

Substituting the given parameters into the formula, we have;

[tex]z = \frac{\frac{96}{150} \;-\;0.63}{\sqrt{0.63\; +\; \frac{1\;-\;0.63}{150}} }\\\\z = \frac{0.64 \;-\;0.63}{\sqrt{0.63\; +\; \frac{0.37}{150}}}\\\\z = \frac{0.01}{\sqrt{0.63\; +\; 0.0025}}\\\\z = \frac{0.01}{\sqrt{0.6325}}\\\\[/tex]

z = 0.01/0.7953

z = 0.013.

Read more on test statistic here: https://brainly.com/question/14839648

#SPJ1

Answer:

Given,

1in= 2.54cm

59.69cm=

[tex] \frac{59.69}{2.45} in[/tex]

=23.5 in

Answer: Scott - 18, Kaitlin - 9, Bill - 54

Step-by-step explanation:

Let's view this as units. There are a total of 81 units. If we solve for Scott's orders:

Kaitlin served 9 fewer orders than Scott. We add 9 to 81 --> 9 + 81 = 90.

Now if we view Scott's orders as one unit:

Scott - 1 unit

Kaitlin (after adding 9) - 1 unit

Bill - 3 units (he served 3 times as many orders as Scott)

In total there are 3 + 1 + 1 = 5 units.

90 / 5 = 18.

Therefore, Scott served 18 orders.

18 - 9 = 9.

Kaitlin served 9 orders.

18 x 3 = 54.

Bill served 54 orders.

And to check our answer, 54 + 18 + 9 is 81.

The length if the upper portion of the stand is 33. 56 inches

The formula for the finding the length is given thus;

Total height = length of upper portion + length of base

Where

Length of base = 257/16

Total height = 591/2

Length of upper portion = total height - length of base

= 118/2 - 407/16

= 59 - 25. 44

= 33. 56 inches

Thus, the length if the upper portion of the stand is 33. 56 inches

Learn more about a rectangle here:

https://brainly.com/question/24571594

#SPJ1

Answer:

The last option, (x+2)(x-3)(x-1)

Step-by-step explanation:

The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,

⇒ f (x) = (x - 1) (x - 2) (x - 3)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

Function is,

⇒ f (x) = x³ - 2x² - 5x + 6

Now, We can factor the function as;

Since, 1 is a root of function as it satisfy the function.

So, One factor is,

⇒ (x - 1)

Find another roots as;

(x - 1) ) x³ - 2x² - 5x + 6 ( x² - x - 6

         x³ - x²

        ----------

             - x² - 5x

            - x² + x

            -------------

                    - 6x + 6

                    - 6x + 6

                    ------------

                           0

Hence,

⇒ f (x) = x³ - 2x² - 5x + 6

⇒ f (x) = (x - 1) ( x² - x - 6 )

⇒ f (x) = (x - 1) ( x² - 3x - 2x - 6)

⇒ f (x) = (x - 1) ( x (x - 3) - 2 (x - 3))

⇒ f (x) = (x - 1) (x - 2) (x - 3)

Hence, The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,

⇒ f (x) = (x - 1) (x - 2) (x - 3)

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ5

The sum of the arithmetic series is 325

The given parameters are

a1 = 45

an = 85

n = 5

The formula for the sum of arithmetic series is:

[tex]S_n = \frac n2 * (a_1 + a_n)[/tex]

Substitute the values of a1, an and n in the above equation

[tex]S_5 = \frac 52 * (45 + 85)[/tex]

Add 45 and 85

[tex]S_5 = \frac 52 * 130[/tex]

Divide 130 by 2

[tex]S_5 = 5 * 65[/tex]

Multiply

[tex]S_5 = 325[/tex]

Hence, the sum of the arithmetic series is 325

Read more about  arithmetic series at:

https://brainly.com/question/16415816

#SPJ1

Answer:

B, -1.7

Step-by-step explanation:

-10.2 divided by 6 is -1.7.

I hope this helps!

350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of magic steel and y represent the amount of alloy #33, hence:

(0 * x) + (y * 0.28) = 700(1 - 0.86)   (1)

Also:

x + (1 - 0.28)y = 0.86(700)    (2)

From both equations:

x = 350, y = 350

350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The reason why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c is because they follow the FOIL Technique

We want to explain why x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c.

Now, using the FOIL Technique we can say that the factors are;

(x + p)(x + q)

Expanding this gives;

x² + px + qx + pq

⇒ x² + (p + q)x + pq

Now, applying that to the trinomial; x² + 6x + 8, we can say that;    

p + q = 6, and pq = 8

Thus, solving simultaneously gives;

p = 2 and q = 6.

Thus;

x² + 6x + 8 = (x + 2)(x + 6)

Read more about Factorization of Quadratic Equations at; https://brainly.com/question/1214333

#SPJ1

28 miles upstream requires 28/7 = 4 hours.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

Apply the distance formula:

d = rt

where

d is distance

r is rate or speed

t is time

21 = t*(r+7)  = rt+ 7t

7 = t *(r-7)   = rt - 7t

            28 = 2rt

             14 = rt

             21 = rt + 7t

             21 = 14 + 7t

               7 = 7t

                 t=1

              21 = (r+7)*1 = r+7

                r = 14

The speed of the boat is 14 mph. With the current (downstream), the speed is 14+7 = 21 mph, so 21 miles are traveled in 1 hour. Against the current (upstream), the speed is 14-7 = 7 mph, which means 7 miles are traveled in the same 1-hour time frame.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

28 miles upstream requires 28/7 = 4 hours.

To learn more about downstream refer to:

https://brainly.com/question/340538

#SPJ9

Answer:

Greetings!

The answer for the first figure is attached but the second diagram is not clear.

Also use the image i attached horizontally.

and also it TD subject not Mathematics.

Answer:

Step-by-step explanation:

Therefore, the values of

a

1

and r are 2 and -1, respectively.

The values of a₁ and r of the geometric series are 2 and -1 respectively.

Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.

We have the series 2, -2, 2, -2, ......

Here, The first term is 2.

and, the Common Ratio = -2 / 2

                                        = 2/(-2)

                                         = -1

So, the first term is 2 and r is -1.

Learn more about Geometric Sequence here:

https://brainly.com/question/4853032

#SPJ5

See below for the response to each question

This is the item that is being surveyed.

The surveyed item is birth weights

Hence, the variable is birth weights

From the question, we have:

Average birth weight is 6 pounds 8 ounces.

Hence, the units of the variable are pounds and ounces

This is the total number of babies in Southeast Asia

Hence, the population of interest is the babies in Southeast Asia

This is the people in the survey

Hence, the individual in the study is the 100 babies that were randomly surveyed

This is the value that gives the required information.

Hence, the parameter of interest is the average birth weight

The statistic is the average

Read more about random surveys at:

https://brainly.com/question/15105321

#SPJ1

Answer:

Step-by-step explanation:

Shift right

f(x)=√x-4.7

f(x)=√x-25

f(x)=√x-11

Shift left

f(x)=√x+0.8

f(x)=√x+6

In Economics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

This ultimately implies that, all producers of any product generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.

Based on the information provided, we can logically deduce that this function has its roots at x = 0 and x = 26 and its vertex is a minimum. Thus, this quadratic function which describes the relationship between the number of products produced and the overall profit margin is an increasing function:

Therefore, once they hit 26 items they break even again. The worst case scenario is that they produce 13 items, as they will have a profit of -50 dollars because the minimum point is at (18, -35). Also, the first root tells us that the profit will be 0 when 0 products are sold.

Read more on profit here: https://brainly.com/question/25712706

#SPJ1

Answer: The largest he can possibly build is x = 14

Step-by-step explanation:

The probability that the ball Deborah picks is green is; 3/5.

Since the bag initially contains; 3 red balls, 4 green balls, and 2 yellow balls, after Deborah pulls out the 4 balls: red, red, green, yellow.

The balls remaining are; 1 red ball, 3 green and 1 yellow.

Hence, the probability that the final ball she picks is green is; 3/(3+1+1) = 3/5.

Read more on probability;

https://brainly.com/question/251701

#SPJ1

The shortest distance from A to B in the diagram is 17 m.

The shortest distance from D to B can be found as follows:

using Pythagoras theorem,

c² = a² + b²

where

Therefore,

DB² = 15² + 8²

DB² = 225 + 64

DB² = 289

DB = √289

DB = 17 m

learn more on distance here: https://brainly.com/question/20516334

#SPJ1

Answer:

B, 17 m

Step-by-step explanation:

Founders 23

Answer:

The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units

The number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways

From the given information, we should use the formula for permutation without repetition.

The formula is given as;

Permutation = [tex]\frac{n!}{n -r !}[/tex]

Where n = number of set = 9

r = 4, this is so because, the sides of a square a four

Permutation = [tex]\frac{9!}{9 - 4!}[/tex]

Permutation = [tex]\frac{9!}{5!}[/tex]

Permutation = [tex]\frac{362, 880}{120}[/tex]

Permutation = 3, 024 ways

Thus, the number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways

Learn more about permutation here:

https://brainly.com/question/12468032

#SPJ1

Answer: [tex]10^4[/tex]

Step-by-step explanation:

Assuming we are using the common log (base 10),

[tex]\log 3ty=6\\\\\log 3y +\log t=6\\\\2+\log t =6\\\\\log t=4\\\\t=10^4[/tex]