find the flux through the boundary of the rectangle for fluid flowing along the vector field .

The determinant of the given elementary matrices is  20 .

What is a Matrix ?

The matrix is defined as an arrangement of set of numbers arranged in rows and columns to form a rectangular array.

In the matrix the horizontal elements are called as Rows and

the vertical elements are called as Columns .

In the question ,

it is given that ,

the matrix is  [tex]\left[\begin{array}{ccc}8&5\\4&5\end{array}\right][/tex]  ,

the determinant of the matrix is represented as ⇒ (8×5 - 5×4)

Simplifying the given expression further ,

we get ,

= 40 - 20

= 20 .

Therefore , the determinant is 20 .

The given question is incomplete, the complete question is

Compute the determinants of the elementary matrices given as [tex]\left[\begin{array}{ccc}8&5\\4&5\end{array}\right][/tex] .

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Option d is correct, s(x)=|3x-4|-9​ this is not a polynomial.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Monomial. Monomial refers to a polynomial with one non-zero term.

Binomial. A binomial is a type of polynomial that has two non-zero terms.

Quadrinomial polynomial. Trinomial.

a polynomial with five factors.

Quadratic polynomial. Linear polynomial.

polynomial cube.

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Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Step-by-step explanation:

Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.

To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.

Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Bruce can be advised to correct his reasoning as the number divisible by six will also remain divisible to 3.

The factor of a number is any number that divides it completely.

In order to find the factors of a number keep dividing it with the known factors.

Given that,

A number is product of 6.

Then, 6 is the factor of that number.

But the factors of 6 are 2 and 3 which implies that 3 is also a factor of that number.

It implies that Bruce has not applied the correct reasoning to reach the conclusion.

Hence, a number which is a product of 6 can also be a product of 3.

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The value of n is 1.6 if 4.8=3n by using simplest method.

A mathematical equation links the two phrases on either side of the sign. It typically simply has an equal sign and one variable. similar to 2x - 4 = 2. Simple equations are used to demonstrate the relationship between two terms when they are positioned on each side of an equal sign. Simple equations are all used to follow the four mathematical operations of addition, subtraction, multiplication, and division.

By employing the shorthand symbol for "equal to" (=), it ensures that both expressions of the equation are equal. Equations utilize arithmetic operations like addition, subtraction, division, and multiplication to balance the expressions on both sides.

4.8=3n

Dividing on both sides with 3, we get

3n/3=4.8/3

n=1.6

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Solving the expression 35.1 = 12.9 + 10.2x gives x to be 2 3/17

A group of numbers or variables coupled with the operations +, -,, or form an expression.

Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.

The given algebraic expression is 35.1 = 12.9 + 10.2x

solving for x

35.1 - 12.9 = 10.2x

10.2x = 22.2

x = 22.2/ 10.2

x = 2 3/17 as a mixed number in simplest form

the value of x is 2 3/17

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(a) The area of the shaded region is 0.2709.

(b) The area of the shaded region is 0.3520.

(c) The area of the shaded region is 0.5555.

(d) The area of the shaded region is 0.6197

What is standard normal curve?

The horizontal axis is approached but never touched by the standard normal curve as it extends indefinitely in both directions. The center of the bell-shaped standard normal curve, which has a z=0 slope, is. Nearly all of the standard normal curve's area lies between z = 3 and z = 3.

The shaded area under the standard normal curve are,

1) Find,  P[Z > 0.61 ]

= P[Z > 0.50]

= 1 - P[Z < -0.50]

= 1 - 0.7291 ( use z table)

=   0.2709

The area of the shaded region is 0.2709.

2) Find,  P[Z < -0.38 ]

= P[Z < -0.38 ]

= 0.3520 ... ( use z table)

The area of the shaded region is 0.3520.

3) Find,  P( -0.58 < Z < 0.98 )

= P(Z < 0.98 ) - P(Z < -0.58 )

= 0.8365 - 0.2810 ......(using z-table)

= 0.5555

The area of the shaded region is 0.5555.

4) Find ,  P( -0.11 < Z > 0.98 )

= 1 - P(Z < 0.98 ) - P(Z < -0.11 )

= 1 - ( 0.8365 - 0.4562 ) ......(using z-table)

= 1 - 0.3803

= 0.6197

Hence, the area of the shaded region is 0.6197.

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The answers of given statements are

a) option (A) i.e Net income.

b) The funds grow faster in case of compund interest.

c) Establish a theory of probable cause is third step

d) Gas and insurance

e) It is the rate for each day that is worked.

f) The production factors are labour, land etc.

g) Three basic questions related to economy are

What will be produced?how will it be produced?

how will the output society produces be distributed?

We have given some statements,

a) Saving should treated as an another type -->

Net income

After all sales-related expenses have been taken out, the remaining earnings are referred to as net income. Savings is the act of holding money for use in the future; it does not include paying for an item or service up front. The saving reffered as net income, or income after all expenses.

b) Compound interest is usually better than simple interest because it pays -->or allows funds to grow at a faster rate than they would in an account with a simple interest rate.

c) Third step in troubleshooting a computer problem is :

Step 3. Establish a theory of probable cause. Eliminate the simple and obvious possible causes.

d) Gas and insurance is expenditure will be the same whether you lease or buy a new vehicle.

e) Hourly pay is the rate for each day that is worked and is often calculated upon the number of hours the labor has been given to the factory.

f)The factors of production are

g) An economic system is any system of allocating scarce resources. Economic systems answer three basic questions:

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Step-by-step explanation:

3√2 means 3 times the square root of 2.

Enter 2. Press the square root key to get square root of 2.

You should see 1.4142135

Now multiply by 3.

You should get 4.2426405

Answer: $1,184,537.217

Step-by-step explanation:

You just multiply the number by 1.22 every year.

For example: year 1 (60,000 * 1.22)= 73,200

Year 2: (73,200 *1.22) =89,304

and so on until year 15 is reached.

a) An expression for the number of bacteria after t hours - [tex]50e^{0.8t}[/tex]

b) The number of bacteria after 7 hours, P(7)=13521.320

c) The rate of growth (in bacteria per hour) after 7, P(t)=1081.705

d) The population will reach 250,000 after - 4.6hours.

a)The exponential growth model is [tex]P = P_{0} e^{rt}[/tex]

Where,

[tex]P_{0}[/tex] = Initial growth

r = growth rate

t = time period

It is given that initially cells, [tex]P_{0}[/tex] = 50

time period, t = 1.5 hours

Population after t = 1.5 hours is , P =875

Substitute the given values in the growth exponential model:

      875 = [tex]50 e^{r * 1.5}[/tex]

 ⇒  [tex]\frac{875}{50}[/tex] =  [tex]e^{r * 1.5}[/tex]

 ⇒ 17.5 = [tex]e^{r * 1.5}[/tex]

 ⇒ log (17.5 ) = log ([tex]e^{r * 1.5}[/tex] )

 ⇒ log (17.5 ) = 1.5r

 ⇒ 1.24 = 1.5r

 ⇒ r = [tex]\frac{1.24}{1.5}[/tex]

    r = 0.8%

Thus, P(t) = [tex]50e^{0.8t}[/tex]

b) Number of bacteria after 7 hours is calculated as follows:

    P(7) = [tex]50 e^{0.8 * 7}[/tex]

    P(7 ) = 13521.320

c) The rate of growth (in bacteria per hour) after 7 hours:

  P(t) = [tex]50e^{0.8t}[/tex]

Differentiate w.r.t :

  P(t) = 50 × [tex]0.8e^{0.8t}[/tex]

       = 50 × [tex]0.8e^{0.8 * 7}[/tex]

      = 1081.705

d) The population at time t is P(t) = 250000

     250000 = [tex]50e^{0.8t}[/tex]

  ⇒   [tex]\frac{250000}{50}[/tex]  =[tex]e^{0.8t}[/tex]

  ⇒  5000 = [tex]e^{0.8t}[/tex]

 ⇒ 0.8t = 3.7

 ⇒  t = 4.6

a) An expression for the number of bacteria after t hours - [tex]50e^{0.8t}[/tex]

b)The number of bacteria after 7 hours, P(7) = 13521.320

c) The rate of growth (in bacteria per hour) after 7, P(t) =  1081.705

d) The population will reach 250,000 after - 4.6hours.

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The congruency of the right triangles by the Hypotenuse-Leg Congruency Theorem can be made true by the following sides.

1. [tex]\overline{RP}[/tex] ≅ [tex]\overline{MF}[/tex] and   [tex]\overline{DP}[/tex] ≅ [tex]\overline{QF}[/tex]

2. [tex]\overline{CI}[/tex] ≅ [tex]\overline{CE}{}[/tex] and    [tex]\overline{AI}[/tex] ≅ [tex]\overline{GE}[/tex]

3. [tex]\overline{TR}[/tex] ≅  [tex]\overline{RT}[/tex]  and  ;[tex]\overline{TQ}[/tex] ≅ [tex]\overline{RS}[/tex]

4. [tex]\overline{DG}[/tex] ≅  [tex]\overline{KN}[/tex] and  [tex]\overline{AD}[/tex] ≅ [tex]\overline{HK}[/tex]

Two right triangles are congruent if  the hypotenuse side and one leg  of one triangle is congruent to  the hypotenuse side and one leg of the other triangle.

The hypotenuse leg congruency theorem states that two right triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle

The hypotenuse side of ΔDPR = [tex]\overline{RP}[/tex]
The hypotenuse side of ΔQMF = [tex]\overline{MF}[/tex]

The corresponding legs of both triangles are;

[tex]\overline{DP}[/tex] corresponds to [tex]\overline{QF}[/tex]

[tex]\overline{DR}[/tex] corresponds to [tex]\overline{MQ}[/tex]

Therefore, ΔDPR is congruent to ΔQFM if  [tex]\overline{RP}[/tex] ≅ [tex]\overline{MF}[/tex]

And the leg  [tex]\overline{DP}[/tex] ≅ [tex]\overline{QF}[/tex] or  [tex]\overline{DR}[/tex] ≅ [tex]\overline{MQ}[/tex]

2. The sides that makes the congruency statement, ΔACI ≅ ΔGCE are found as follows;

The hypotenuse side of  ΔACI = [tex]\overline{CI}[/tex]

The hypotenuse side of triangle ΔGCE = [tex]\overline{CE}{}[/tex]

Therefore,

ΔACI ≅ ΔGCE ican be proved when    [tex]\overline{CI}[/tex]  is congruent to [tex]\overline{CE}{}[/tex], and

 [tex]\overline{AI}[/tex]  is congruent to [tex]\overline{GE}[/tex] or    [tex]\overline{AC}[/tex]  is congruent to [tex]\overline{CG}[/tex]

3. In the figure the specified information are;

[tex]\overline{TR}[/tex] is congruent to [tex]\overline{RT}[/tex] by reflexive property

The triangles are congruent if either;[tex]\overline{TQ}[/tex] iis congruent to [tex]\overline{RS}[/tex] or;[tex]\overline{TS}[/tex] iis congruent to [tex]\overline{RQ}[/tex]

4. The appropriate sides that can be used to prove that  ΔADG ≅ ΔHKN  are the hypotenuse side of both triangles;[tex]\overline{DG}[/tex] and  [tex]\overline{KN}[/tex]

and either the legs; [tex]\overline{AD}[/tex] and [tex]\overline{HK}[/tex] or  [tex]\overline{AG}[/tex] and  [tex]\overline{HN}[/tex]

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,

The Probability of both Zack and Lucy missing the target will be 0.48

Let the probability of Lucy and Zack missing the target be = P(L) and  P(Z), respectively. So, If the probabilities of Zack and Lucy missing the target are as follows-

P(L) = 0.6 and

P(Z) = 0.8

then, the probability of both Lucy and Zack missing the target will be,

P(L) × P(Z) i.e.

0.6×0.8 = 0.48

Probability is basically a method to find out the possibility of likelihood of a certain outcome. In mathematics, it was introduced by Pierre and Cardano in the seventeenth century.

The complete question is-

The probabilities of Lucy and Zack hitting or missing the target are given in the following image. As per that, what will be the probability of both Lucy and Zack missing the target?

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The confidence interval for the task of organizing the poll for the upcoming elections be,

(222.117 , 257.883)

Given, You have been given the task of organizing a poll regarding an upcoming election.

The object is to estimate the proportion of the country that will vote to keep the current government in power.

You have been told to collect a sample and find a 95% confidence interval for the proportion.

This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74.

We have to find the confidence interval,

Subtract 1 from your sample size. 10 – 1 = 9.

Subtract the confidence level from 1, then divide by two.

(1 – .95) / 2 = .025

For 9 degrees of freedom df and α = 0.025, margin of error is 2.262.

Divide your sample standard deviation by the square root of your sample size.

25 / √(10) = 7.90569415

Now, Multiply 2.262 × 7.90569415 = 17.8826802

For the lower end of the range

240 – 17.8826802 = 222.117

For the upper end of the range

240 + 17.8826802 = 257.883

Hence, the confidence interval be (222.117 , 257.883)

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Answer:

The answer is b!

Step-by-step explanation:

the answer is A .

the open end of the arrow points to the bigger variable. When the variable is included there will be a line under the arrow

The linear speed of a person on this Ferris wheel is about 628.2 ft/min.

As a body travels a circular path, it has both a linear speed and an angular speed. The rate it travels on that path is the linear speed, and the rate it turns around the center of that path is the angular speed. The linear speed (v) and angular speed (ω) are related by the radius (r) or v = rω .

Given that ;

Radius = r = 50 ft

Frequency = f = 2 rev/min

The angular speed is the product of the angular displacement for one complete turn, namely 2π radians per revolution, and the frequency (f). That is, the angular speed is equal to ω = 2πf. Substituting this into the formula for linear speed (v), we get:

                                v = r (2πf)

                                    = (50 ft) ( 2π / rev) ( 2 rev/min)

                                    = 200π ft/min

                                    ≈ 628.2 ft/min

The linear speed of a person on this Ferris wheel is about 628.2 ft/min.

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.

Answer:

you forgot the sentences dude

The margin of error with a confidence interval of 0.17 to 0.97 is 0.4.

An indicator of the extent of random sampling error in survey results is the margin of error. In other words, the percentage point difference between the results and the actual population value is indicated by the margin of error. The confidence interval form is given by Confidence Interval = [lower confidence interval limit, upper confidence interval limit]. The confidence interval's total width divided by two is the margin of error.

Here, 95% confidence interval = [0.17, 0.97]. Then, the margin of error is,

[tex]\begin{aligned}\text{Margin of error (E)}&=\frac{\text{(upper confidence interval limit-lower confidence interval limit)}}{2}\\&=\frac{0.97-0.17}{2}\\&=\frac{0.8}{2}\\&=0.4\end{aligned}[/tex]

The answer is 0.4.

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The restrictions on the variables x and y are given as follows:

x ∈ W, y ∈ W.

The first step in obtaining the restrictions of the variables x and y are identifying them, which is done as follows:

Then we known that we usually hear it in the news things such as this sentence:

"On the last Buffalo Bills game, 60,000 tickets were sold".

The amount of tickets sold varies, but the type of number doesn't, it is always a positive non-decimal number.

The number of ticket sold cannot assume neither negative nor decimal values, thus the variables x and y belong to the whole number set and the first option is correct.

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The degree of freedom value for the A× B intersection is  = 6.72

The F value is the value of the F distribution. Various statistical tests generate F values. You can orrect answer is use this value to determine whether your test is statistically significant.

The F value is used in the analysis of variance (ANOVA). It is calculated by dividing the two mean squares. This calculation determines the ratio of explained to unexplained variance.

The F distribution is a theoretical distribution. There are many types of these distributions, each with different degrees of freedom.

Determines the probability of the F value using the degrees of freedom of the F value and the variance source. The probability is the significance value of the test.

AxB intersection:

Interpreting the output of the general linear model command focuses on two parts: the means table and the ANOVA summary table. The average table is the focus of the analysis, while the summary table draws attention to the interesting or statistically significant parts of the average table.

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The formula for calculating it is perimeter of the rectangle = 2(length + width), meaning that it is equal to twice the sum of its length and width.

Given that,

We have to find which equation perfectly describes the ABCD rectangle's perimeter? How do you determine a rectangle's length and width given its perimeter?

We know that,

The total length of a rectangle's outer boundary is known as its perimeter. The formula for calculating it is perimeter = 2(length + width), meaning that it is equal to twice the sum of its length and width.

The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in metres, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.

A rectangle has four 90° angles.

The diagonals of a rectangle are all of the same length.

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Answer:

18

Step-by-step explanation:

72/12=6

6×3=18

.....

Answer:

-----------------------------------

Simplify the equation by distribution, then substitute the value of d and solve for c:

The equation to solve the width of rectangle created by John from 48 square centimetre tiles is w(w+2) = 48

and the greatest width in centimetres use for mosaic is 6 cm.

We have given that

John wants to create a mosaic of rectangular shape.

total area of tile(A) = 48 square centimetre

let l and w be length and width of rectangle

length of rectangle is 2 cm longer than width then length of rectangle (l) =( w+2) cm

Area oa rectangle (A) = l × w

=> (w+2) × w = 48

=> w²+ 2w = 48

which is quadratic equation , solve it

w² + 2w - 48 = 0

=> w² - 6w + 8w - 48 = 0

=> (w-6) (w+8) = 0

=> w = 6, -8

Hence, the required equation is w(w+2) = 48 and width of rectangle is 6cm.

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According to the provided data, to be one of the top 7% earners a manager needs to earn $48,360.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.

The formulas are given below:

[tex]\mu = \frac {\sum x}{N}[/tex]      (Mean)

[tex]\sigma = \sqrt {\frac {\sum (X- \mu ) ^ {2}} {N}[/tex]    (Standard Deviation)

Mean = $48,000

Standard Deviation = $4,000

According to this data, Max Earning made = $48,000 + $4,000

=$52,000

7% of $52,000 = $3,640

To be top 7% earner, A manager must earn = $52,000 - $3,640

=$48,360

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Answer:$53,903

Step-by-step explanation:

Here, the mean, μ, is 48,000 and the standard deviation, σ, is 4,000. Let x be the cutoff salary for teachers in the top 7%. The area to the right of x is 7%=0.07. So, the area to the left of x is 1−0.07=0.93.

Open Excel. Click on an empty cell. Type =NORM.INV(0.93,48000,4000) and press ENTER.

Round the answer to the nearest dollar, is x≈53,903. Therefore, the cutoff salary for managers in the top 7% is $53,903.

The volume of cylinder is 84.82 cubic feet

In this question, we have been given for a cylinder the diameter equals 3 feet and the length equals 12 feet.

We need to find  the volume of a cylinder.

From given data,

diameter d = 3 feet

So, radius r = d/2

                r = 1.5 ft

length of cylinder (h) = 12 ft

The formula for the  volume of a cylinder is,

V = π * r² * h

V = π * 1.5² * 12

V = π * 2.25 * 12

V = 84.82 cubic feet

Therefore, the volume of cylinder with the diameter equals 3 feet and the length equals 12 feet is 84.82 cubic feet

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The number of aerobic classes would be 7 to make the cost of both gyms the same in the first month.

What are linear equations?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are those in which the linear equation contains two variables.

Let x= number of months, and a=no of aerobic classes.

Let Gym A charge a $10 membership fee plus $20.25 per month plus $5.50 per aerobics class.

So we get the equation:

y= 10+20.25x+5.50a

y=30.25+5.50a ------------ as (x=1)

Next, for Gym B, it charges $46 per month plus $3.25 per aerobics class.

So the equation is:

y=46x+3.25a

y=46+3.25a ------------------as (x=1)

Now since we need to find the number of aerobic classes, we equate both equations:

30.25+5.50a = 46+3.25a

2.25a = 15.75

a = 7

Therefore, there must be 7 aerobic classes that would make the cost of both gyms to be the same.

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Answer:

5:8

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

As we know that the area of triangle is 1/2 × base × height so A.TQ

1) finding the triangle area = 1/2 × base × height

= 6 × 5.

= 30

2) finding the area of rectangle = l×b

= 12 × 6

= 72

Now to find total area is 72 + 30 which will be 102

so the answer is = 102