9. Mr. Stevenson is ordering shirts and hats for his Boy
Scout Troop. There are 60 scouts in the troop.
Hats come in packs of 3, and shirts come in packs of
5. What is the least number of packs each he
should order so that each scout will have 1 hat and
1 shirt, and none will be left over?

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

For more such questions on rank

https://brainly.com/question/28839672

#SPJ8

Answer:

\(\huge\boxed{(-19)^{-8}=19^{-8}}\)

Step-by-step explanation:

Use

\(a^n\times a^m=a^{n+m}\)

\((-19)^{-12}\times(-19)^4=(-19)^{-12+4}=(-19)^{-8}\)

Answer:

They r correct lol

Step-by-step explanation:

Answer:

photo is not clear so i can't help u

Answer:

i cant really see the q so sorry but goodluck <3

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

learn more about domain of a function: https://brainly.com/question/1369616

#SPJ9

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

for more search question income

https://brainly.com/question/30157678

#SPJ8

The given problem can be exemplified in the following diagram:

Since we are told that "P" is a mid-point of DE, this means that:

Also, since DE represents the entire segment, this means:

Therefore, we may replace the values of DP and PE as "6x + 4" and we also replace the given values of DE, we get:

Adding like terms we get:

Now we solve for "x" first by subtracting 14x from both sides:

Now we subtract 8 from both sides:

Now we divide both sides by -2:

Therefore, the value of "x" is 9. Now we determine the length of DP using the expression for this segment:

Replacing the value of "x":

Solving the operations we get:

Therefore, the length of DP is 58 units.

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

The object's acceleration is \(108.1 ms^{-2\)

Acceleration is the rate of change of velocity over time

The given parameters are:

The acceleration (a) is then calculated using:

\(v^2 = u^2 + 2as\)

So, we have:

\(105^2 = 0^2 + 2 \times a \times 51\)

Simplify

\(11025 = 102a \)

Make a the subject

\(a= 108.1\)

Hence, the object's acceleration is \(108.1 ms^{-2\)

Read more about acceleration at:

https://brainly.com/question/605631

Complete question is;

Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne’s function?

A) 0, 1, 2, 3, 4, …

B) …, −4, −3, −2, −1, 0

C) …, −3, −2, −1, 0, 1, 2, 3, …

D) …, −3.5, −2.5, −1.5, 0, 1.5, 2.5, 3.5, …

Answer:

Option A: {0,1, 2, 3, 4,....}

Step-by-step explanation:

Domain is simply a set of input while the range is a set of output values.

For example, if we have a function named f(x) = x², the domain will be all possible values of x being inputed while the range will be the value of f(x) for all possible values of x inputed.

Now, from the question, we are told that she wrote the amount of money she spent as a function of the number of bottles sold.

If the number of bottles sold is denoted by "x", it means the function is; f(x).

Now, number of bottles has to be a non-negative whole number or simply a non-negative integer. Thus, the possible values of x are all non-negative whole numbers like, 0,1, 2, 3, 4, 5....

Thus,domain is {0,1, 2, 3, 4,....}

Answer:

A. 0,1,2,3,4,.....

Step-by-step explanation:

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

Know more about Square roots,

https://brainly.com/question/16113248

#SPJ1

Hi my name is Fabian and 69% because 69 is a man which is multi colour hair

A) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%. b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

To solve this problem, we will use the properties of the normal distribution and z-scores. Given that the average completion time for the task is 10 minutes and the standard deviation is 3 minutes, we can proceed with the following calculations:

a) To find the percentage of nurses completing the task in less than 5 minutes, we need to calculate the z-score corresponding to a time of 5 minutes and then determine the area under the normal distribution curve to the left of that z-score.

The z-score formula is given by: z = (x - μ) / σ

where x is the time in question (5 minutes), μ is the mean (10 minutes), and σ is the standard deviation (3 minutes).

z = (5 - 10) / 3 = -5/3 ≈ -1.67

Using a standard normal distribution table or a calculator, we can find that the area to the left of -1.67 is approximately 0.0475 or 4.75%. Therefore, approximately 4.75% of nurses complete the task in less than 5 minutes.

b) To find the percentage of nurses requiring more than 10 minutes to complete the task, we calculate the z-score for a time of 10 minutes and find the area to the right of that z-score.

z = (10 - 10) / 3 = 0

The area to the right of z = 0 is 0.5 or 50%. Therefore, approximately 50% of nurses require more than 10 minutes to complete the task.

c) To find the probability that a nurse will take between 8 and 12 minutes to complete the task, we need to find the area under the curve between the z-scores for 8 and 12 minutes.

z1 = (8 - 10) / 3 = -2/3 ≈ -0.67

z2 = (12 - 10) / 3 = 2/3 ≈ 0.67

Using a standard normal distribution table or a calculator, we find the area to the left of z = -0.67 as approximately 0.2514, and the area to the left of z = 0.67 as approximately 0.7514. Therefore, the probability that a nurse will take between 8 and 12 minutes to complete the task is approximately 0.7514 - 0.2514 = 0.5 or 50%.

d) To find the task times that qualify staff nurses for additional training, we need to determine the z-score corresponding to the slowest 20% of completion times and then convert it back to the original time scale.

The z-score corresponding to the slowest 20% is found by locating the z-score that has an area of 0.2 to its left. Using a standard normal distribution table or a calculator, we find this z-score to be approximately -0.84.

Now, we can convert the z-score back to the original time scale:

z = (x - μ) / σ

-0.84 = (x - 10) / 3

Solving for x, we have:

-0.84 * 3 = x - 10

-2.52 = x - 10

x = 10 - 2.52

x ≈ 7.48

Therefore, the task times that qualify staff nurses for additional training are approximately greater than 7.48 minutes.

In summary:

a) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%.

b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

for more such question on percentage visit

https://brainly.com/question/24877689

#SPJ8

Answer:

21x + 35

Step-by-step explanation:

Answer: The probability of choosing an ace or a club is 16.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Statement                     Reason

PR ≅ TR                        Given

<PQR≅<TSR                 Given

<PRQ≅<TRS                Vertical Angles Theorem

PQR=TSR                      SAS  Theorem   (Side-Angle-Side)

If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.

The rational zero theorem is used to determine the rational roots of a polynomial function.

Rational Zero Theorem statement:-

The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients

f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,

p is a factor of the constant a₀,

q  is a factor of the leading coefficient an,

and p and q are relatively prime.

To know more about rational here

https://brainly.com/question/29155547

#SPJ4

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

Learn more on a Ferris wheel here;

https://brainly.com/question/30524034

#SPJ1

The solution is:

⇒ 6b = 95.94   (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒ 12t = 95.94   (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒     (equation to determine cost of one box)

⇒6b = 95.94

⇒b =15.99

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒ (equation to determine cost of per tile)

⇒12t = 95.94

⇒t = 0.7995.

Thus cost of one tile t = $0.7995.

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

Answer:

4

Step-by-step explanation:

Answer:

$3,289.90

Step-by-step explanation:

65,798 times 5%

Answer: bottom right

The value of (5x2−14x+24)÷(x−4)  is 5x + 6

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given ,

5x2 - 14x - 24

         x - 4    

  5x2 multiplied by 14x, then 24.

The first term is 5x2, and 5 is its coefficient.

The coefficient of the middle term, which is -14x, is -14.

"The constant," the final term, is -24.

Step 1: Multiply the first term's coefficient by the constant 5 • -24 to get a result of -120.

Find two factors of -120 whose combined value is equivalent to the middle term's coefficient, which is -14, in step two.

    -120    +    1    =   -119  

    -60    +    2    =    -58  

    -40    +    3    =    -37  

    -30    +    4    =    -26  

    -24    +    5    =    -19  

    -20    +    6    =    -14    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6  

                   5x2 - 20x + 6x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                  5x • (x-4)

            Add up the last 2 terms, pulling out common factors :

                  6 • (x-4)

Step-5 : Add up the four terms of step 4 :

                 (5x+6)  •  (x-4)

Therefore  The value of (5x2−14x+24)÷(x−4)  is 5x + 6

To learn more about mathematical expression refer to :

https://brainly.com/question/1859113

#SPJ1

Simplified term is 5x + 6. Simplification is the process of reducing an expression/fraction/problem to a simpler form.

A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.

Mathematical expressions are made up of different numbers and operations. To simplify them, we must first understand the rule known as the order of operations. It specifies the order in which operations must be performed when simplifying a mathematical expression.

Factoring  5x2 - 14x - 24

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -14x  its coefficient is  -14 .

The last term, "the constant", is  -24

Multiply the coefficient of the first term by the constant   5 • -24 = -120

Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -14 .

-120    +   1   =   -119

-60    +   2  =   -58

-40    +   3  =   -37

-30    +   4  =   -26

-24    +   5  =   -19

-20    +   6  =  -14  

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6

5x2 - 20x + 6x - 24

Add up the first 2 terms, pulling out like factors :

                   5x • (x-4)

Add up the last 2 terms, pulling out common factors :

                   6 • (x-4)

Add up the four terms of step 4 :

                   (5x+6)  •  (x-4)

Which is the desired factorization

Cancel out  (x-4)  which appears on both sides of the fraction line.

 5x + 6

To learn more about Simplification refer :

https://brainly.com/question/28780542

#SPJ1

Answer:

Area of side faces:

Area of bottom face:

Area of 2 triangular faces:

The height of the remaining triangular faces:

The area of 2 triangular faces:

Paper needed:

Let the perimeter of the base is P.

If the height is increased by 1.5 cm then surface area is increased by:

The surface area of the prism include the following: C. two hundred seventy-five and one-eighth cm².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[(23/4 × 4) + (23/4 × 47/4) + (4× 47/4)]

Surface area of rectangular prism = 2[23 + 1081/16 + 47]

Surface area of rectangular prism = 275 1/8 cm².

Read more on surface area of a rectangular prism here: brainly.com/question/28185251

#SPJ1

Answer:

I believe it’s B.

Step-by-step explanation:

Hope this is rite

Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

Learn more on trigonometric identity here;

https://brainly.com/question/24496175

#SPJ1

The expression for the total amount of sales the store makes will be:25s + 28.8p

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the shoe store stocks x pair of sneakers and y pairs of sandals. During a promotion, a pair of sneakers is priced at $50 and a pair of sandals at $36. The shop manages to sell half the sneakers and 80% of the sandal.

Let sneakers = s

Let sandals = p

An expression for the total amount of sales the store makes will be: 1/2(50s) + 0.8(36p).

= 25s + 28.8p

Learn more about expressions on

brainly.com/question/723406

#SPJ1

Answer:

Below

Step-by-step explanation:

Median = 500    S.D. = 100

A)  Look at + z-score table for  .85

        z-score =  +1.04

          you have to be 1.04 S.D. 's to be at 85 th percentile

                  500   + 1.04 * 100 = 604

B)   500 is in the middle (50%)  you need to go UP 40 % and down 40%

             so look for + z score = .900   and     - z-score = .100

                       z score :           =   1.28                             =  - 1.28

                    500 + 1.28 * 100 = 628                 500 - 1.28 * 100 = 372

     so the range of scores would be   372  -  628