The circumference of a circle radius r is give

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

Learn more on maximizing volume here;

https://brainly.com/question/10373132

#SPJ4

For isosceles triangle RST  the measure of angle T is 34 degree

In this question, we have been given a isosceles triangle RST with RS = RT.

So, by isosceles triangle theorem,

angle S = angle T

So, angle T = (3x - 2)°

We know that the sum of all angles of triangle is 180°

∠R + ∠S + ∠T = 180°

9x + 4 + 3x - 2 + 3x - 2 = 180°

15x + 4 - 4 = 180°

15x = 180°

x = 12

So, 3x - 2 = 3(12) - 2

                = 34°

Therefore, for triangle RST  the measure of angle T is 34 degree

Learn more about isosceles triangle here:

https://brainly.com/question/2456591

#SPJ1

If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

Learn more about Trigonometric Rules here :

https://brainly.com/question/30641505

#SPJ1

For given  regression model, the number 59.89 in the table tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

In this question we have been given a summary of regression model.

We need to explain the meaning of the number 59.89 in the table.

For given regression model, to view the results of the model, we can use the summary() function in R programming.

In given summary consider the 'Coefficients' table.

The first row gives the estimates of the y-intercept, and the second row gives the regression coefficient of the model.

The 'Estimate' column is the estimated effect, also called the regression coefficient or r² value.

The number 59.89 in the table is coefficient for IsSandwich.

This number tells us that for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Therefore, the meaning of the number 59.89 in the table: for every food item which is sandwich there is a corresponding 59.89-unit increase in Calories.

Learn more about the regression model here:

https://brainly.com/question/14983410

#SPJ4

The complete question is as shown in the following image

Step-by-step explanation:

hop it help you.......

.....

330

Step-by-step explanation:

100% of 300 = 300

10% of 300 = 30

300 + 30 = 330

PURCHASE REQUEST FORM

Date: [Insert date]

To: [Insert name of procurement officer]

Subject: Purchase of Electrical Materials for Repair of Non-Functional Lights

We would like to request the procurement of the following electrical materials for the repair of the non-functional lights along the hallway of the office:

3 sets of new fluorescent lamp at 40 watts each at Php 250.00 pesos each

20 meters of stranded copper wire number 14 at Php 20.00 pesos per meter

3 new sets of flush type single pole switch at Php 100.00 pesos each

The total cost of the materials is Php [Insert total cost].

Please process the request as soon as possible so that we can proceed with the repair works. Thank you for your attention to this matter.

Sincerely,

[Insert your name]

[Insert your designation]

Answer:

47*

Step-by-step explanation:

Each corner of the square is 90*

angle CBE + angle ABE = 90*

fill in the blanks

43 + x = 90

subtract 43 from both sides

x = 47*

Answer:

a)  initial height = 0 m

b)  8 s

c)  vertex = (4, 32)

    maximum height = 32 m

Step-by-step explanation:

Given equation:

\(h=-2t^2+16t\)

where:

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

\(\implies h=-2(0)^2+16(0)\)

\(\implies h=0\)

Therefore, the initial height of the arrow is 0 m.

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

\(\implies -2t^2+16t=0\)

Factor out -2t:

\(\implies -2t(t-8)=0\)

Therefore:

\(\implies -2t=0 \implies t=0\)

And:

\(\implies t-8=0 \implies t=8\)

Therefore, the arrow will hit the ground at 8 seconds.

The vertex is the turning point of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds.  Therefore, t = 0 and t = 8 are the x-intercepts.  The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

\(\implies h=-2(4)^2+16(4)\)

\(\implies h=-32+64\)

\(\implies h=32\)

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

Answer: 3,348 cubic inches

Step-by-step explanation:

1. Since we know that volume= length x width x height, then we can plug our values into this equation.

2. So, we would do volume= 9 x 12 x 21.

3. 9 x 12 = 108, and 108 x 21 =2,268.

4. Now that we have both of the volumes, we have to add them together.

5. 1,080 + 2,268 = 3,348

6. The combined volume is 3,348 cubic inches.

Answer: the answear is 19

Step-by-step explanation:

first you subtract 30 from the 30 and the 125 which takes out the 30 and makes the 125, 95

second you divide 5 by 5 and cross it out

then you divide 95 by 5 and get 19 which is your answer

1^n 2^n ... (p-1)^n is congruent to 0 or -1 mod p depending on n. This statement is known as Fermat's Little Theorem.

Fermat's little theorem is identical to the assertion that ap 1 1 is an integer multiple of p if an is not divisible by p, that is, if an is coprime to p. If a = 2 and p = 7, For example, if a = 2 and p = 7, then 26 = 64, and 64 − 1 = 63 = 7 × 9 is thus a multiple of 7.

According to Fermat's Little Theorem

It states that if p is a prime and a is an integer not divisible by p, then a^(p-1) is congruent to 1 modulo p.

If n is even, then (p-1)^n is congruent to 1^n (mod p), so the product is congruent to 1 mod p.

If n is odd, then (p-1)^n is congruent to -1 (mod p), so the product is congruent to -1 (mod p).

For more questions on Fermat's Little Theorem

https://brainly.com/question/8978786

#SPJ4

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

The answer is 434 !!

You can also solve this by doing 317-117= ?

Answer:

434

Step-by-step explanation:

Here is one solution to the puzzle:

Squares: 2, 8, 16

Circles: 5, 7, 14

Total: 26

You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.

An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.

Therefore, the correct answer is as given above

learn more about odd and even numbers: https://brainly.com/question/2263958

#SPJ1

A .The canoe left the campsite did the motorboat catch up with it 3 hrs and 40 minutes

B . The motorboat travel at 1 hr 40 minutes

A group of campers and one group leader left a campsite in a canoe.

They traveled at an average rate of 10 km/h.

1st Group DATA:

rate = 10 km/h ; distance = x km ; time = d/r = x/10 hrs

Two hours later, the other group leader left the campsite in a motorboat.

He traveled at an average rate of 22 km/h.

Group Leader DATA:

rate = 22 km/h ; distance = x km ; time = d/r = x/22 hrs

A. How long after the canoe left the campsite did the motorboat catch up with it?

Group time - Leader time = 2 hr

x/10 - x/22 = 2

Multiply thru by 110 to get:

11x - 5x = 220

6x = 220

x = 110/3 = km

canoe total time = x/10 = (110/3)/(10) = 11/3 = 3 hrs and 40 minutes

B. How long did the motorboat travel?

motorboat time = x/22 = (110/3)/22 = 1 hr 40 minutes

Learn more about average rate here:

https://brainly.com/question/8728504

#SPJ4

Answer:

a = 2 , b = - 7 , c = - 8

Step-by-step explanation:

expand and simplify the left side then compare the coefficients of like terms on both sides.

(2x + 3)(x - 5) + 7 ← expand factors using FOIL

= 2x² - 10x + 3x - 15 + 7 ← collect like terms

= 2x² - 7x - 8

compare to ax² + bx + c , then

a = 2, b = - 7 , c = - 8

Step-by-step explanation:

Point slope form:

y - y1 = m(x - x1)

(x1, y1) is a point on the line and m = slope

To solve for point slope form, we can plug in both coordinates into the equation

-5 + 9 = m(3 - 2)

4 = m

Next, use one set of coordinates as (x1, y1)

y + 9 = 4(x - 2) <—- point slope form

slope intercept form is y = mx + b

Since we know the slope is 4 from the previous problem, we only have to find y-intercept b.
plus in a set of given coordinates for c and y and solve for b, then reassemble the equation:

-9 = 4(2) + b

-9 = 8 + b

-17 = b

Thus, slope intercept form is y = 4x - 17

Answer:

t-ratio = 0.362

Step-by-step explanation:

In hypothesis testing,

The t-ratio is given by the formula:

\(\dfrac{X-\mu}{s}\)

where μ is the hypothesized mean, X the sample mean and s the sample standard deviation

The Standard Error of the Mean SEM = \(\large \text{{$\dfrac{s}{\sqrt{n}}$}}\)  where n is the sample size.

We We are given:

X = 46,000
μ= 45,000

SEM = 436.81

n = 40

We can find the sample standard deviation
s = SEM x √n
s = 436.81 x √ 40

s = 2762.3

Therefore

t-ratio = (46000 - 45000)/2762.3 = 0.362

Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.

A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.

Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:

Interest = Principal x Rate x Time

Interest = $2,500 x 0.15 x 1

Interest = $375

Thus, the total sum his friend will be required to pay Darrel is:

Total amount = Principal + Interest

Total amount = $2,500 + $375

Total amount = $2,875

Thus, the total amount his friend owes Darrel is $2,875.

To know more about simple interest, visit:

https://brainly.com/question/25845758

#SPJ1

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

for more such questions on sampling method

https://brainly.com/question/13219833

#SPJ8

Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.

As per the question statement, Hector has shortlisted 11 documentaries and 15 foreign films, from which he wants to rent any 4 movies.

We are required to calculate the total of number of combinations of 4 movies from his above mentioned shortlist.

Total number of movies Hector has shortlisted = (11 + 15) = 26.

That is, we will have to calculate the total of number of combinations of 4 movies, Hector can rent from a lot of 26 movies.

Now, we need to know the formula of combination which goes as \([nCr=\frac{n!}{r!(n-r)!} ]\),

When "r" objects are to be selected from a set of "n" objects, such that order of selection does not matter.

Here, (n = 26) and (r = 4), and using these values in the above mentioned equation of nCr, we get

\(26C4=\frac{26!}{4!(26-4)!} =\frac{26!}{4!*22!}=\frac{22!*23*24*25*26}{24*22!}=(23*25*26)=14950\)

That is, Hector can have a total of 14950 number of combinations of 4 movies, from his shortlist of 11 documentaries and 15 foreign films, that he can rent.

To learn more about Combinations, click on the link below.

https://brainly.com/question/8561440

#SPJ1

Answer:

  $5.59

Step-by-step explanation:

You want the unit price of a pair of socks, given that 5 pairs cost $27.95.

The unit price is found by dividing the price by the number of units.

  $27.95/5 = $5.59

The unit price of a pair of socks is $5.59.

Answer:

4 seconds

Step-by-step explanation:

Answer:

34 crayons per box

Step-by-step explanation:

Let the total number of crayons be x.

Total crayons given = 43 x 7 = 301

Total remaining = 5

Total at beginning = 301 + 5 = 306

Crayons per box = 306/9

= 34 crayons per box

There are many 34 crayons in each box.

Answer:

the train travels 400 miles

Step-by-step explanation:

80x5= 400 (i think???!!)

The  value of this expression when w = -5 in w² +  3w - 11 is -1

Algebraic expressions comprises of at least one variable and one operation, it is an expression built up from integer constants, variables, and the algebraic operations

We need to find the value of this expression when w = -5 in w² +  3w - 11

After substituting the value of x as 5, we get the expression as

5² + 3(-5) - 11

25 - 15 - 11

25 - 26

= -1

Therefore, the value of this expression when w = -5 in w² +  3w - 11 is -1

To learn more about algebra refer here

https://brainly.com/question/4344214

#SPJ4

Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

Since we know the sequence is quadratic, we expect the \(n\)-th term to have the general form

\(x_n = an^2 + bn + c\)

Plug in the first 3 known values of the sequence to form a system of equations.

\(x_1 = 3 = a + b + c\)

\(x_2 = 12 = 4a + 2b + c\)

\(x_3 = 25 = 9a + 3b + c\)

Eliminating \(c\) gives

\((4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9\)

\((9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11\)

Eliminating \(b\) gives

\((4a + b) - (3a + b) = 11 - 9 \implies a = 2\)

Solving for \(b,c\), we get

\(4a + b = 11 \implies b = 11-4\cdot2 = 3\)

\(a+b+c=3 \implies c=3-2-3 = -2\)

So, the \(n\)-th term of the sequence is

\(x_n = \boxed{2n^2 + 3n - 2}\)

Answer:

We know that:

H(x) = |1 - x^3|

and:

We want to write H(x) as  f( g(x) ) , such that for two functions:

So we want to find two functions f(x) and g(x) such that:

f( g(x) ) = |1 - x^3|

Where neither of these functions can be an identity function.

Let's define g(x) as:

g(x) = x^3 + 2

And f(x) as:

f(x) = | A - x|

Where A can be a real number, we need to find the value of A.

Then:

f(g(x)) = |A - g(x)|

and remember that g(x) = x^3 + 2

then:

f(g(x)) = |A - g(x)| = |A - x^3 - 2|

And this must be equal to:

|A - x^3 - 2| =  |1 - x^3|

Then:

A = 3

The functions are then:

f(x) = | 3 - x|

g(x) = x^3 + 2

And H(x) =  f( g(x) )

Answer:

12 girls =)

Step-by-step explanation:

Make a table labeled girls and boys like this

2|3

4|6

6|9

8|12

Multiply until you get to 8 boys