What is the coefficient a in the factorization: \[ x^{2}+a x y+b y^{2}=(x+5 y)(x-4 y) \] Select one: a. \( -20 \) b. 5 c. \( -1 \) d. \( -4 \) e. 1

Therefore , the solution of the given problem of triangle comes out to be  the shape is 55 square miles.

Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here.

Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.

The following method can be used to determine a triangle's area:

A = (1/2)bh

where A represents area, B represents foundation, and H represents height.

We can calculate each triangle's area using the following formula:

=> Area of 1st triangle

=>  (1/2)(10)(7) = 35 square miles

=> Area of 2nd triangle

=>  (1/2)(10)(4) = 20 square miles

The two triangles' combined regions make up the composite shape's surface area.

55 square miles is the combined shape's area

=>  (35 + 20).

Consequently, the combined size of the two triangles in the shape is 55 square miles.

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The measure of ∠FGH is 28 - 4x.

A three-sided polygon with three angles is known as a triangle. It is a basic geometric shape that can be classified based on its sides and angles.

Since G is the midpoint of DF, we have m∠DGF = m∠FGC (vertical angles are equal), so m∠FGD = m∠CGF = (180 - m∠DGF)/2 = (180 - m∠FGC)/2 = m∠GFC. Similarly, m∠FHE = m∠HEC, so m∠FHE = m∠CGF = m∠GFC.

Using angle sum property, we have:

m∠DEF + m∠FED + m∠FDE = 180

60 - 5x + 2(46 + 2x) + m∠FGH = 180

152 + 4x + m∠FGH = 180

m∠FGH = 180 - 152 - 4x

m∠FGH = 28 - 4x

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So the answer is: it took 35.56 minutes to get home on day one.

To find out how long it took to get home on day one, we need to work backwards from day five. Here's how:

On day five, it took 15 minutes to get home. This was 50% faster than on day four, which means that on day four it took 15 minutes / 0.5 = 30 minutes.

On day four, it took 30 minutes, and this was 2 minutes less than on day three. So on day three it took 30 minutes + 2 minutes = 32 minutes.

On day three, it took 32 minutes, and this was 20% longer than on day two. So on day two it took 32 minutes / 1.2 = 26.67 minutes.

On day two, it took 26.67 minutes, and this was 75% of the time it took on day one. So on day one it took 26.67 minutes / 0.75 = 35.56 minutes.

So the answer is: it took 35.56 minutes to get home on day one.

Here's the answer formatted with HTML:

To find out how long it took to get home on day one, we need to work backwards from day five. Here's how:

So the answer is: it took 35.56 minutes to get home on day one.

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so the rate is per annum, so compounding period is 1 per year, hmmm we could use 1 or 2 years to get "r", hmmm let's use 2.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 5903.13\\ P=\textit{original amount deposited}\dotfill &\pounds 5500\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]5903.13 = 5500\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 2} \implies \cfrac{5903.13}{5500}=\left( 1+\cfrac{r}{100} \right)^2 \\\\\\ \sqrt{\cfrac{5903.13}{5500}}=\cfrac{100+r}{100}\implies 100\sqrt{\cfrac{5903.13}{5500}}=100+r \\\\\\ 100\sqrt{\cfrac{5903.13}{5500}}-100=r\implies \stackrel{ \% ~ ~~ ~ }{\boxed{3.6\approx r}}[/tex]

The probability of rolling a dice less than 3 times is 17/100.

It is a branch of mathematics that deals with the occurrence of a random event.

The total no of times rolling = 200

The probability of rolling 1 = 17 times

And, The probability of rolling 2 = 17 times

So, the probability of rollng a dice less than 3 times is

17+17/200

34/200

17/100

Hence, the probability of rolling a dice less than 3 times is 17/100.

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The probability of the sum of the two numbers being even can be calculated using the formula for the probability of independent events.
The formula for the probability of independent events is: P(A and B) = P(A) x P(B
In this case, A represents the first die and B represents the second die.

To calculate the probability of the sum being even, we need to consider the possible outcomes for each die that would result in an even sum.
For the first die, there are three possible outcomes that would result in an even sum: 1, 3, and 5. The probability of any of these outcomes occurring is 3/6, or 1/2.
For the second die, there are also three possible outcomes that would result in an even sum: 2, 4, and 6. The probability of any of these outcomes occurring is also 3/6, or 1/2.
Using the formula for the probability of independent events, we can calculate the probability of the sum being even:
P(A and B) = P(A) x P(B) = (1/2) x (1/2) = 1/4

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This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

It may contain one or more variables, which are symbols that represent unknown quantities or values that can vary. Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships.

For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".

2.077×10⁻⁴ means "2.077 times 10 to the power of -4", which can be rewritten as 0.0002077. This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

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By following the 6 steps explained, you can find the quotient of a multiple of 10 and any number.

To use place value to find the quotient of a multiple of 10 and a number, you can use the following steps:

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The scores of students were normally distributed.

a)Approximately 68% of the students scored between 40 and 62 .

b) The approximately 95% of the students scored between 29 and 73.

We have a nationwide test taken by high school students, Mean score, μ = 51

Standard deviations, s = 12

The scores were normally distributed, that is

X~ N(M= 51, s = 12)

Lower bound of confidence interval= 40

Upper bound of CI = 62

As we know according to empirical rule the percentage of data falls within one,two and three

standard deviations are 68%,95% and 99.7%

respectively.

a) Mean + standard deviations = 51 + 12 = 63 close to 62

= Upper bound

For 2 standard deviations, 51 + 2×12 = 75

Mean - standard deviations= 51 - 12 = 39 close to 40 = lower bound

For 2 standard deviations, 51 - 2×12 = 27

Thus, data falls within one standard deviation

that is under 68% and so, approximately 68% of students scored between 40 and 62.

b) Similarly, the empirical rule demonstrates that 95% of scores falls within two standard deviation.

mean - 2× standard deviations= 51 - 2× 11

= 51 - 22 = 29

mean + 2× standard deviations= 51 + 2×11

= 51 + 22 = 73

Therefore, approximately 95% of students scored

between 29 and 73.

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Complete question:

On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 11

The scores were normally distributed. Complete the following statements.

(a) Approximately ?% of the students scored between 40 and 62 .

(b) Approximately 95% of the students scored between ? and ?

The area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.

An isosceles trapezoid is a type of trapezoid with two parallel sides that are equal in length, and two non-parallel sides that are also equal in length.  The two legs meet at an angle at the top of the trapezoid, and the bases are parallel to each other.

To find the area of the trapezoid, we use the formula:

Area = (b1 + b2) * h / 2

where b1 and b2 are the lengths of the bases, and h is the height.

In this case, b1 = 9, b2 = 21, and h is the distance between the bases. Since the trapezoid is isosceles, the height is also the length of the two diagonals minus the sum of the two bases, divided by 2:

h = (d1 + d2 - b1 - b2) / 2

we will use the Pythagorean theorem:

d1² = h² + (b2 - b1/2)²

d2² = h² + (b2 + b1/2)²

Plugging in the values we get:

h = (d1 + d2 - 9 - 21) / 2

h = (d1 + d2 - 30) / 2

d1² = h² + (21 - 9/2)²

d2² = h² + (21 + 9/2)²

Simplifying, we get:

h = (d1 + d2 - 30) / 2

d1² = h² + 225/4

d2² = h² + 529/4

Substituting the first equation into the other two, we get a system of two equations in two variables:

d1² = ((d1 + d2 - 30) / 2)² + 225/4

d2² = ((d1 + d2 - 30) / 2)² + 529/4

Simplifying and solving for d1 and d2, we get:

d1 = 13

d2 = 17

To find the area, we plug in the values of the bases and the height:

h = (d1 + d2 - 30) / 2 = (13 + 17 - 30) / 2 = 5

Area = (b1 + b2) * h / 2 = (9 + 21) * 5 / 2 = 75

Therefore, the area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.

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Answer:

$512.17

$286.48

$1,958.40

$1,628.85

$56.37

$324.24

$135.55

Note: These calculations were made assuming simple interest. If the interest is compounded, the final amounts will be slightly different.

Step-by-step explanation:

The algebraic equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch.

Mathematical equations with one or more variables and algebraic operations like addition, subtraction, multiplication, division, exponentiation, and roots are known as algebraic equations. By identifying the values of the unknown variables that fulfill the equation, these equations can be used to illustrate mathematical connections between variables and to solve issues.

Although algebraic equations can take many different forms, they often require utilizing the equal sign (=) to make one expression equal to another. For instance, the algebraic equation x + 2 = 7 shows the connection between the constants 2 and 7 and the unknown variable x.

The equation that could be used to find the price of one tire patch is:

4x = 22.2 - 1.9

This equation represents the total cost of the four tire patches (4x) subtracted from the initial balance on Rhyan's gift card ($22.20) and the remaining balance after the sale ($1.90).

Simplifying the equation, we get:

4x = 20.3

Dividing both sides by 4, we get:

x = 5.075

So the price of one tire patch is $5.075.

Therefore, the equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch. None of the other equations listed would lead to the correct answer.

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Answer:

yo

Step-by-step explanation:

C and E

Answer: None of the statements are true.

The expression has only two terms: 17 and (5)(9 + 14y).

No term in the expression equals 23.

The expression has three factors: 17, 5, and (9 + 14y).

The constant in the factor 9 + 14y is 9.

The factors in the expression are 17, 5, 9, and (9 + 14y).

Step-by-step explanation:

Answer: To find the magnitude and direction of the equilibrant of a system of forces, we first need to find the resultant of the forces, and then find the force that will balance the resultant.

For the given system of forces, we can use the Pythagorean theorem to find the magnitude of the resultant:

R = sqrt(32^2 + 48^2)

 = sqrt(1024 + 2304)

 = sqrt(3328)

 ≈ 57.7 N

The direction of the resultant can be found using trigonometry:

tan(theta) = opposite / adjacent

where theta is the angle between the forces, which is 90° in this case. We can choose either force as the adjacent side, and the other force as the opposite side. Let's choose the 32 N force as the adjacent side:

tan(theta) = 48 / 32

theta = atan(48/32)

     ≈ 56.3°

This means that the resultant has a magnitude of approximately 57.7 N and is directed at an angle of approximately 56.3° to the 32 N force.

To find the equilibrant, we need to find a force that has the same magnitude as the resultant but acts in the opposite direction. We can use the same magnitude and opposite direction to find the equilibrant as:

E = -R

 = -57.7 N

This means that the equilibrant has a magnitude of 57.7 N and acts in the opposite direction to the resultant, which is at an angle of approximately 56.3° to the 32 N force.

Step-by-step explanation:

The Big Ideas or Focal Points in the mathematics curriculum for grade 6 are: 1. Ratios and Proportional Relationships
2. The Number System.  3. Expressions and Equations.  4. Geometry.  5. Statistics and Probability.

1. Ratios and Proportional Relationships: Students should be able to understand and use ratios to describe relationships between quantities, and use proportional reasoning to solve problems.

2. The Number System: Students should be able to understand and use negative numbers, and perform operations with multi-digit numbers and decimals.

3. Expressions and Equations: Students should be able to write and evaluate expressions, and use equations to solve problems.

4. Geometry: Students should be able to understand and use the properties of shapes and the relationships between them.

5. Statistics and Probability: Students should be able to use data to make predictions and understand the concept of probability.

These Big Ideas or Focal Points are the key concepts that students should master in grade 6 mathematics in order to be prepared for higher-level math courses.

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To create a multi-dimensional visualization of (a+b)^5, we can use a Pascal's Triangle, which shows the coefficients of each term in the expansion. Each row of the triangle corresponds to a power of (a+b), and the numbers in each row are the coefficients of the terms in the expansion. Here is a visualization of the first six rows of Pascal's Triangle:

```
           1
         1   1
       1   2   1
     1   3   3   1
   1   4   6   4   1
 1   5  10  10   5   1
```

The sixth row corresponds to the expansion of (a+b)^5, and the numbers in this row are the coefficients of the terms in the expansion: 1, 5, 10, 10, 5, 1. We can use these coefficients to create a multi-dimensional visualization of (a+b)^5:

```
            a^5
         5a^4b
      10a^3b^2
    10a^2b^3
  5ab^4
b^5
```

Each term in the expansion is represented by a different level in the visualization, with the coefficient of each term shown at the beginning of the level. This multi-dimensional visualization allows us to see the relationship between the coefficients and the terms in the expansion of (a+b)^5.

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a) The sum of their times is of 4x + 3.

b) The property used is the combination of like terms, which we use to add the terms with the variable x.

c) If Doug ran the race in 27 minutes, the total time for the team is of 111 minutes.

Doug finished first, and the times of the other two athletes are as function of Doug, hence the variable x represents the time needed for Doug to finish the race, that is:

D = x.

Kim finished 3 minutes after Doug, hence:

K = D + 3

K = x + 3.

Conner finished with a time that was twice Doug’s time, hence:

C = 2x.

Then the total time is given as follows:

T = D + K + C

T = x + x + 3 + 2x

T = 4x + 3.

If Doug ran the race in 27 minutes, the total time for the team is obtained as follows:

T = 4 x 27 + 3

T = 111 minutes.

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Answer:

To find the interest rate when given the principal, time, and simple interest, we can use the formula:

Simple Interest = (Principal * Rate * Time) / 100

where:

Simple Interest is the given value of 4252.50

Principal is 18000

Time is 54 months

Rate is the unknown we want to solve for

Substituting the given values, we get:

4252.50 = (18000 * Rate * 54) / 100

Multiplying both sides by 100 and dividing by 18000 * 54, we get:

Rate = (4252.50 * 100) / (18000 * 54)

Rate = 4.398%

Therefore, the interest rate is 4.398% (rounded to three decimal places).

Step-by-step explanation:

Sure! Here is a step-by-step explanation of how to find the interest rate:

Given:

Principal = 18000

Time = 54 months

Simple Interest = 4252.50

Formula:

Simple Interest = (Principal * Rate * Time) / 100

We want to solve for Rate.

Substitute the given values into the formula:

4252.50 = (18000 * Rate * 54) / 100

Simplify by multiplying both sides by 100:

425250 = 18000 * Rate * 54

Divide both sides by 18000 * 54:

Rate = 425250 / (18000 * 54)

Simplify the expression on the right-hand side:

Rate = 0.04398

Convert the decimal to a percentage:

Rate = 4.398%

Therefore, the interest rate is 4.398%.

Using the formula for simple interest, the value for interest rate is obtained as 5.25%.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

We can use the formula for simple interest -

I = P × r × t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

In this case, the principal is $18,000, the time is 54 months which is 4.5 years, and the simple interest is $4,252.50.

Substituting these values in the formula, we get:

4252.50 = 18000 × r × 4.5

Solving for r, we get -

r = 4252.50 / (18000 × 4.5)

= 0.0525 or 5.25%

Therefore, the interest rate is 5.25%.

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Answer: The answer would be C

Step-by-step explanation:

If we start from 56,60,64,68 and were adding 4 each time the next numbers would be 72,76,80

The correct match of each root word with its meaning are :

(i) Anthropology⇔(d) man

(ii) Psychology⇔(c) mind    

(iii) Economy⇔(e) law  

(iv) Democracy⇔(b) people

(v) Judicious⇔(a) judge

The term (i) Anthropology is related to (d) man because,

The term "Anthropology" is called the study of human-societies and cultures and their development.

The term (ii) Psychology is related to (c) mind ,

The term "Psychology" is defined as the scientific-study of behavior and mental processes of mind;

The term (iii) Economy is related to (e) law,

The Economy can be termed as the social science that deals with the production, distribution, and consumption of goods and services and their management.

The economy and practices of commerce are governed by certain laws or principles. So,  the best option to match economy is law.

The term (iv) Democracy is related to (b) people ,

Democracy is defined as system of government by the whole population or all the eligible members of a state, typically through elected representatives.

The term (v) Judicious is related to (a) judge,

The word "judge" is a derived from the word "judicious", which means, showing and using sound judgement.

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The given question is incomplete, the complete question is

Match the below root of each word to its meaning.

(i) Anthropology       (a) judge

(ii) Psychology          (b) people

(iii) Economy             (c) mind

(iv) Democracy         (d) man

(v) Judicious              (e) law

There were 240 pages in the printer task.

To find the number of pages in the printing task, we can use the relationship between time, rate, and work. The formula for this is:

   time × rate = work.

Let's call the number of pages in the printing task "P" and the rate of printer A "R". We can set up the following equations based on the information given in the question:

   40 minutes × R = P(R + 4) × (40 - 16) = P

We can simplify the second equation to get:

    24R + 96 = P

Now we can set the two equations equal to each other and solve for R:

    40R = 24R + 96

    16R = 96

     R = 6

Now we can plug this value of R back into one of the original equations to find P:

     40 minutes × 6 = P

      P = 240

Therefore, the number of pages in the printing task was 240.

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The absolute maximum value of the function on the interval is approximately 2.28, and the absolute minimum value is approximately 0.37. Both of these values are expressed in terms of the notiral number, e.

The absolute maximum value and the absolute minimum value of a function on a given interval can be found by evaluating the function at the endpoints of the interval and at any critical points within the interval. The critical points are the values of x where the derivative of the function is equal to 0 or does not exist.

First, let's find the derivative of the function:
\( f'(x)=e^{\operatorname{xin}(x)} \cdot \operatorname{xin}'(x) \)

Using the chain rule, the derivative of \( \operatorname{xin}(x) \) is:
\( \operatorname{xin}'(x)=\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x) \)

So, the derivative of the function is:
\( f'(x)=e^{\operatorname{xin}(x)} \cdot (\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x)) \)

To find the critical points, we need to set the derivative equal to 0:
\( e^{\operatorname{xin}(x)} \cdot (\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x))=0 \)

Since \( e^{\operatorname{xin}(x)} \) is never equal to 0, we can focus on the second factor:
\( \operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x)=0 \)

This equation cannot be solved algebraically, so we will use a graphing calculator to find the approximate values of x that make the equation true. The values are approximately 0.86 and 4.71.

Now, we will evaluate the function at the endpoints of the interval and at the critical points:
\( f(0)=e^{\operatorname{xin}(0)}=e^0=1 \)
\( f(2 \pi)=e^{\operatorname{xin}(2 \pi)}=e^0=1 \)
\( f(0.86)=e^{\operatorname{xin}(0.86)} \approx 2.28 \)
\( f(4.71)=e^{\operatorname{xin}(4.71)} \approx 0.37 \)

The absolute maximum value of the function on the interval is approximately 2.28, and the absolute minimum value is approximately 0.37. Both of these values are expressed in terms of the notiral number, e.

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Answer:

The math coach has delivered 4 boxes of books, so the number of boxes she still needs to deliver is b. Each box contains 15 books, so the total number of books she still needs to deliver is 15b. She has 495 books to deliver in total. Therefore, we can write the equation:

15b = 495 - 4(15)

Simplifying the right-hand side:

15b = 495 - 60

15b = 435

Dividing both sides by 15:

b = 29

So the math coach still needs to deliver 29 boxes of books.

Answer:

60

Step-by-step explanation:

Answer:

The area of the triangle is 60 unit²

Step-by-step explanation:

We know that the area of a triangle is :

[tex]A= \frac{1}{2}(Base \times Height)[/tex]

Since Base = 12 unit and Height = 10 unit

So

[tex]A= \frac{1}{2}(12\times 10)=60\\[/tex]

Hence the area of this triangle is = 60 unit²

The value of the painting at t = 4 is $400 (V(4) = $400) and the value of the painting at t = 6 is $800 (V(6) = $800).

To find the value of the painting at t = 4 and t = 6, we can simply plug in these values into the function V(t) = 100 • 2^t/2, for t >= 0 where t is the number of years since the painting was purchased, and V(t) is its value (in dollars) at time t, and simplify.

For t = 4, we have:
V(4) = 100 • 2^4/2
V(4) = 100 • 2^2
V(4) = 100 • 4
V(4) = 400

For t = 6, we have:
V(6) = 100 • 2^6/2
V(6) = 100 • 2^3
V(6) = 100 • 8
V(6) = 800

Therefore, V(4) = $400 and V(6) = $800.

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The value of x in the given figure of parallel lines is x = 0.89.

When two parallel lines are sliced by a transversal, alternating interior angles and alternate exterior angles result in the shape "Z".

From the figure we observe that according to alternate interior angle, the angle adjacent to x + 94 is 95x.

Thus, the two angles form a straight line.

The angle of a straight line is 180 degrees.

Thus,

x + 94 + 95x = 180

96x + 94 = 180

x = 0.89

Hence, the value of x in the given figure of parallel lines is x = 0.89.

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Answer:

Step-by-step explanation:

Since he's applying stain (painting) he must be doing only the surface.

Finding the surface area:

33x18=594

33x15=495

18x15=270

594+495+270=

1359 square inches

We will then x2 1359 since we found the area for 1/2 of the box.

It is: 2718

The total cost at an activity level of 8,000 units is $55,000.

The total cost at an activity level of 8,000 units can be found by plugging in the value of X into the cost formula Y= $15,000 + $5X.

Step 1: Plug in the value of X into the cost formula:
Y= $15,000 + $5(8,000)

Step 2: Simplify the equation by multiplying $5 and 8,000:
Y= $15,000 + $40,000

Step 3: Add $15,000 and $40,000 to get the total cost:
Y= $55,000

Therefore, the total cost at an activity level of 8,000 units is $55,000. The correct answer is $55,000.

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1.

y= -5x + 4

slope intercept form is y = mx + b (m) being the slope and (b) being the y intercept

The area of rectangular field is   [tex]\frac{9}{20} \ \text{miles}^2[/tex].

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Here the given rectangle , length= [tex]\frac{9}{10}[/tex]miles and Breadth = [tex]\frac{1}{2}[/tex]miles

Now using area of rectangle formula,

=> A = length× breadth square unit.

=> A = [tex]\frac{9}{10}\times\frac{1}{2}[/tex]

=> A =   [tex]\frac{9}{20} \ \text{miles}^2[/tex]

Hence the area of rectangular field is  [tex]\frac{9}{20} \ \text{miles}^2[/tex].

To learn more about area of rectangle refer the below link

https://brainly.com/question/2607596

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