How long does it take for a deposit of $1400 to double at 5% compounded continuously?

The line representing the equation 7x1 + 4x2 [tex]\leq[/tex] 28 goes through the following two points: (0,7) and (4,0).

Hence, option (c) is the correct choice.

The constraint equation is g(x,y)=c, and we state that x and y are constrained by g(x,y)=c.

Constrained maximum and constrained minimum points are locations (x,y) that are maxima or minima of f(x,y) with the condition that they meet the constraint equation g(x,y)=c.

As per the data given,

We have,

The equation of the constraint: 7 x_1+4 x_2[tex]\leq[/tex] 28

7 x_1+4 x_2 [tex]\leq[/tex] 28

So, putting the value of x_2=0

We will get the above expression as:

7 x_1=28

=>x_1=4

So, the points will be (4,0)

Now, putting the value of x_1=0

Thus, we will get:

4 x_2=28

=>x_2=7

So, the points will be (0,7)

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The answer of given question is fraction 3/5.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorise its types based on these two terms.

[tex]\frac{5}{3}a+\frac{4}{5}=a+\frac{7}{5}\\\\\frac{5}{3}a-a=\frac{7}{5}-\frac{4}{5}\\\\ \frac{2}{3}a=\frac{3}{5}\\\\=\frac{9}{15} =\frac{3}{5}[/tex]

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The number of adults for 24 students is 6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Mr.Cates, the principal at a local middle school, made a rule that there must be 1 adult for every 4 students attending a field trip.

Let the number of students be y and the number of adults be x.

Now, the equation is y=4x

If y=12

Then, x=3

If y=24

Then, x=6

If y=40

Then, x=10

Therefore, the number of adults for 24 students is 6.

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"Your question is incomplete, probably the complete question/missing part is:"

Mr.Cates, the principal at a local middle school, made a rule that there must be 1 adult for every 4 students attending a field trip

Complete the table to show the number of adults for 12, 24 and 40 students.

Number of Students          Number of Adults

              12                                 _____

              24                                 _____

              40                                 _____

The value is -6

We are given a sequence {an} such that sn = 3n - 9. We can find an by using the formula sn = an + d(n - 1).

Substituting the values for sn and d (which is 1 in this case), we get

an = 3n - 9 - (n - 1)

an = 2n - 10

Therefore, when k = 1, an = 2(1) - 10 = -6.

The answer value is -6.

Expand it to 2 liens

The answer is -6, which can be obtained by using the formula an = 3n - 9 - (n - 1).

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When using the Tare function on a balance, start by placing the glassware on the balance. Then Press the tare/zero button to cancel out the mass. Finally, add your sample to the glassware and record the mass of your sample.

The Tare function on a balance is an important tool for accurately recording the mass of a sample. To use this function, start by placing the glassware on the balance. This will provide a baseline reading of the glassware’s mass.

Then, press the tare/zero button to cancel out the mass of the glassware. This will reset the balance to zero. Finally, add your sample to the glassware. This will give you the mass of your sample alone, without the mass of the glassware included.

It is important to use the Tare function to get the most accurate reading of your sample’s mass. With the Tare function, you can make sure the mass you record is the mass of your sample alone.

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The state of Oregon has an area of 90,000 square kilometers.

1. Take the given area of 9.0 x 10^6 square kilometers

2. Move the decimal point 6 places to the left

3. The new area is now 90,000 square kilometers

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 square kilometers.

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 (nine million) square kilometers. This is an area of around 553,000 square miles, and is roughly equivalent to the size of the United Kingdom. It is the 9th largest state in the United States, and is bordered by the states of Washington, Idaho, California, Nevada, and the Pacific Ocean. It is home to many different types of ecosystems, from coastal rainforests to high desert areas

The complete question is :

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 square kilometers.

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The smaller number of the given sum is 15.

Completed question :

The sum of two numbers is 80. If the larger number exceeds four times the smaller by 5, what is the smaller number?

Given data :

Given, sum of two numbers is 61.

Let the smaller number be x

Thus the larger will be 61 - x

Also given, larger number exceeds four times the smaller number by 4.

Therefore, 61 - x = 4x + 5

5x = 56

x = 15

Thus the smaller number is 15.

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The formula for calculating a square pyramid's surface area is SA = P l / 2, where P l is the product of the base perimeter and the slant height.

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The overall order of the reaction is the sum of the orders of the individual reactants, a + b. Therefore, the overall order of the reaction is 2 (1 + 1 = 2).

A. The order of the reaction in X is 1.

B. The order of the reaction in Y is 1.

C. The overall order of the reaction is 2.

The orders of a reaction can be determined from the initial rates obtained from the different experiments. The reaction rate is proportional to the concentrations of the reactants raised to the powers of the order of each reactant.

In experiment 1, the initial rate (2.83 M/s) is proportional to the concentration of X raised to the power of a (2.83 = k[X]^a). Therefore, a = 1.

In experiment 2, the initial rate (2.83 M/s) is proportional to the concentration of Y raised to the power of b (2.83 = k[Y]^b). Therefore, b = 1.

In experiment 3, the initial rate (25.47 M/s) is proportional to the concentration of X raised to the power of a (25.47 = k[X]^a) and the concentration of Y raised to the power of b (25.47 = k[Y]^b). Therefore, a = 1 and b = 1.

The overall order of the reaction is the sum of the orders of the individual reactants, a + b. Therefore, the overall order of the reaction is 2 (1 + 1 = 2).

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The rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

Let's call the rate of the boat in still water "r" and the rate of the current "c". Then the rate of the boat traveling upstream is "r - c" and the rate of the boat traveling downstream is "r + c".

We can use the following formula to calculate the rate of the boat in still water: r = (distance traveled upstream + distance traveled downstream) / (total time taken)

distance traveled upstream = 96 miles

distance traveled downstream = 96 miles

total time taken = 4 hours + 3 hours = 7 hours

r = (96 + 96) / 7 = 192 / 7 = 27.428571428571427 miles per hour

Next, we can use the formula for the rate of the boat traveling upstream to calculate the rate of the current:

96 = (r - c) * 4

96 = 4r - 4c

4c = 4r - 96

c = r - 24

Substituting the value of r that we found earlier, we get:

c = 27.428571428571427 - 24 = 3.4285714285714284 miles per hour

Therefore, the rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

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The rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

Let's call the rate of the boat in still water "r" and the rate of the current "c". Then the rate of the boat traveling upstream is "r - c" and the rate of the boat traveling downstream is "r + c".

We can use the following formula to calculate the rate of the boat in still water: r = (distance traveled upstream + distance traveled downstream) / (total time taken)

distance traveled upstream = 96 miles

distance traveled downstream = 96 miles

total time taken = 4 hours + 3 hours = 7 hours

r = (96 + 96) / 7 = 192 / 7 = 27.428571428571427 miles per hour

Next, we can use the formula for the rate of the boat traveling upstream to calculate the rate of the current:

96 = (r - c) * 4

96 = 4r - 4c

4c = 4r - 96

c = r - 24

Substituting the value of r that we found earlier, we get:

c = 27.428571428571427 - 24 = 3.4285714285714284 miles per hour

Therefore, the rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

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Answer:

38.88 is what she paid

Step-by-step explanation:

0.28x54=15.12

15.12 = 28% of 54

the remaining percentage is 72%

15.12/28=0.54

0.54=1%

1x72 to get 72 percent so,

0.54*72=38.88

The direction of the force on side 1 is 45° downwards from the positive x-axis. The direction of the force is the opposite of the angle obtained in step 3, which is 45° downwards from the positive x-axis.

1. Draw a right triangle, with the two points of the side as the vertices.

2. Using the Pythagorean theorem, calculate the length of the side.

3. Use the inverse tangent function to calculate the angle between the two points.

4. The direction of the force is the opposite of the angle obtained in step 3, which is 45° downwards from the positive x-axis.

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The linear scan strategy for counting the number of negative values in an array involves sequentially going through each element of the array and checking if it is negative.

If the element is negative, the count is incremented. Once the end of the array is reached, the count is returned.

For example, consider an array A = [-2, 3, -1, 4, -7, 9]. The linear scan strategy would be as follows:

1. Initialize count to 0

2. Check if A[0] = -2 is negative, if yes, increment count. Count = 1

3. Check if A[1] = 3 is negative, if no, continue. Count = 1

4. Check if A[2] = -1 is negative, if yes, increment count. Count = 2

5. Check if A[3] = 4 is negative, if no, continue. Count = 2

6. Check if A[4] = -7 is negative, if yes, increment count. Count = 3

7. Check if A[5] = 9 is negative, if no, continue. Count = 3

8. Return count = 3.

Therefore, the linear scan strategy for counting the number of negative values in array A is 3.

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B. The value of a is negative, so the vertex is a minimum.

Vertex is the math word for angle. Most geometric shapes, whether two or three dimensional, have vertices. For example, a square has four vertices, which are its four corners. Vertex can also refer to a point in an angle or in a graphical representation of an equation.

When two lines meet at a point, they form an angle. For polygons, the angle included at each vertex is the interior angle of the polygon.

A vertex is also sometimes used to indicate the 'top' or high point of something, such as the vertex of an isosceles triangle, which is the 'upper' angle across from its base, but this is not its strict mathematical definition.

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The argument is deductive if the arguer thinks that the truth of the premises unquestionably establishes the validity of the conclusion.

The argument is inductive if the arguer thinks that the truth of the premises offers only solid grounds for thinking the conclusion is probably true.

An argument from a particular example to a general rule is known as induction. Deduction leads to a valid conclusion, whereas inductive reasoning merely leads to a likely result based on experience. This is how induction differs from the deduction.

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Answer: 14

Step-by-step explanation:

The measure of each angles are one is 28 and other is 68.

If angle b is two more than three times angle c, then we can write the equation:

b = 3c + 2

Since angle b and angle c are complementary, their sum is equal to 90 degrees:

b + c = 90

We can substitute the value of b from the first equation into the second equation:

3c + 2 + c = 90

4c + 2 = 90

4c = 88

c = 22

So, angle c is 22 degrees and angle b is equal to 3c + 2 = 3 * 22 + 2 = 68 degrees.

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The rule of translation of LMN to L'M'N is: Shift right by 3 units and shift up by 1 unit.

What is a translation of triangles?

A translation of a triangle is a transformation in which a triangle is moved from one position to another, without changing its shape or size.

From the graph, we can see that LMN is translated to L'M'N'

The coordinates of L is:

L = (-6,-4)

The coordinates of L' is:

L' = (-3, 3)

Subtract L from L'

(x, y) = L'-L

(x, y) = (-3,-3)-(-6, -4)

(x, y) = (-3+6,-3+ 4)

x, y)= (3, 1)

Hence, The rule of translation of LMN to L'M'N is: Shift right by 3 units and shift up by 1 unit.

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The final balance of all transaction is $45,880 both in Total Assets and Total Liabilities and Equities.

Please refer to the attached table below for the completed and balanced table.

We will discuss how each transaction is recorded:

a. When Pamela deposit $42,000 to the business bank, it will be recorded as cash inflow and her capital.

b. The purchase of office supplies will be recorded on account. Then, the supplies will record $2,080 and the same account will be recorded under accounts payable.

c. Record cash inflow of $5,760 and the same amount under fees earned.

d. Paid rent by cash will decrease the amount of cash by $2,550 and the same amount is recorded under Rent Expense account.

e. Cash outflow by $940 and decrease on the accounts payable account by the same amount.

f. Records accounts receivable of $4,720 and fees earned with the same amount.

g. Records cash outflow by $850. Records $570 under automobile expense and $280 for Miscellaneous expense.

h. Cash outflows by $1,790 and salaries expense by the same amount.

i. The amount of supplies decreases by $850 and records under the account of supplies expense by the same amount.

j. Cash outflow by $1,700 and records under Drawings account for the same amount.

Please note that all expenses should be recorded as a negative value.

Finally, we can check and confirm that our records are balance by comparing the total Assets and Total liabililties and Equity we have. The total assets is $45,880 and so the Total Liabilities and Equity.

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Answer:

Step-by-step explanation:

According to the weeklybdays of a Calendar, the weekdays are scheduled as:-

Sunday-Monday -Tuesday-Wednesday-Thursday-Friday-Saturday

So, this shows that Monday comes only after Sunday. du to which the present day scheduled is Monday and the day before today(yesterday) is scheduled to be Sunday.

The area of the rectangle with the coordinates A(-2, 2), B(6, 2), C(6, 3), and D(-2, 3) is therefore 15 units.

A rectangle is a polygon with four right angles within Euclidean plane geometry. Users may also refer to it as an equilateral triangular quadrilateral, meaning that all of its edges are equal. A straight angles could also be present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90º vertices as well as equal parallel sides make up a quadrilateral with the look of a rectangle. As a result, it's also known as a vector graphics rectangle. A square is also refereed to as a parallelogram since its opposite angles are parallel and equal.

given

Rectangle's given coordinates are A(-8, 3), B(-3, 3), C(-3, 6), and D. (-8,6)

d = (((x2 - x1)2+(y2 - y1)2) is the distance between the places.

AB = √[{-3 - (-8)}² + (3 - 3)²] = 5 units

BC = √[{-3 - (-3)}² + (6 - 3)²] = 3 units

CD = √[{-8 - (-3)}² + (6 - 6)²] = 5 units

AD = √[{-8 - (-8)}² + (6 - 3)²] = 3 units

5 units for length and 3 units for width.

region of the rectangle,

A = length times width

5 * 3 Equals 15 units, or a.

The area of the rectangle with the coordinates A(-2, 2), B(6, 2), C(6, 3), and D(-2, 3) is therefore 15 units.

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The parametric equation of the line through a parallel to b is X = [-3, 5] + t[1/4, 1]

An equation is a mathematical statement that shows the equality or balance of two expressions. It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.

The equation of a line can be represented in both point-slope form and in parametric form. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

In this case, we have two points, a and b, on the line. We can use these points to find the slope of the line, which is given by:

m = (y2 - y1) / (x2 - x1) = (b[1] - a[1]) / (b[0] - a[0]) = (3 - 5) / (-5 - (-3)) = (3 - 5) / -8 = -2 / -8 = 1/4

y - a[1] = (1/4)(x - a[0])

To convert this equation to parametric form, we can use t as the parameter and express x and y in terms of t:

x = a[0] + t

y = a[1] + (1/4)t

So the parametric equation of the line through a parallel to b is given by:

X = [-3, 5] + t[1/4, 1]

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While equations 24 and 25 are equivalent, equation 23 is not since the two equations are not the same.

When the solution set for two equations is the same, the equations are said to be equivalent. For instance, the equations x + 2 = 6 and 2x = 8 have the same solution set when we solve them both as follows: x + 2 = 6. Take 2 away from both sides.

For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2. When two items or amounts are exactly the same, such as when 12 is equal to 12, but 12 is equivalent to 2/4 since they symbolise.

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While equations 24 and 25 are equivalent, equation 23 is not since the two equations are not the same.

Answer:0.592

Step-by-step explanation:

16/27 = 0.59259259

round it to 3 decimal points so 0.593

Answer:

0.593

Step-by-step explanation:

16/27 = 0.59259259

round it to 3 decimal points so 0.593

There is a 0.43% chance or probability of correctly guessing the ages of all six children.

The probability of correctly guessing the ages of all six children in a family where each child is at least one year old and the sum of their ages is an integer that is at most 31 can be calculated using combinations.

The total number of possible combinations of ages that meet the criteria can be found by multiplying the number of different outcomes for each child's age, giving us 6 x 6 x 6 x 6 x 6 x 6, or 46,656.

To calculate the probability, we need to divide the number of possible combinations that meet the criteria (46,656) by the total number of possible combinations (1,073,741,824).

This gives us the probability of 0.00433, or 0.43%.

This means that there is a 0.43% chance of correctly guessing the ages of all six children.

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Answer:

1.25 as decimal

5/4 as fraction

1 1/4 as mixed number

Step-by-step explanation:

Hope it helps! =D

The rate of petrol consumption in km per llitre given the distance covered and the capacity of Petrol used is 12.5 km per liter

Total distance covered by the car = 500 km

Total capacity of Petrol used = 40 litres

The rate of petrol consumption in km per llitre = Total distance covered by the car / Total capacity of Petrol used

= 500 km / 40 liters

= 12.5 km per liter

Therefore, the unit rate of Petrol consumption of the car is 12.5 km per liter

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The number of subsets that [n] have which contain exactly one element 1 and 2 is 2⁽ⁿ⁻¹⁾ .

Let us assume that [n] means the set {1, 2, 3, ..., n}.

Now For a subset having n elements ,we have  = 2ⁿ total subsets, including the empty set and the set itself.

If we are looking for subsets that contain exactly one of the elements 1 and 2, there are two possibilities:

⇒ The subset contains element 1 but not element 2,

⇒ The subset contains element 2 but not element 1.

If we remove 1 and 2 from this , then the set [n] contains (n-2) elements,

So , the number of subsets become =  2⁽ⁿ⁻²⁾  subsets.

So , there is two ways to have exactly one of elements 1 or 2: add {1} to the subsets described, or add the subset {2} to subsets just described.

Therefore ,  [n] will contain 2⁽ⁿ⁻²⁾ subsets exactly one of 1 or 2

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The average speed of the family during their walk  over a time period of 1.35 hours is 1.407 km/hr

Let us say that the distance covered by the family is x

so , according to the formula of average speed

Average speed = total distance covered/total time taken

Hence,

average speed = [tex]\frac{0.75+1.15}{1.35} km/hr[/tex]

                          = [tex]\frac{1.9}{1.35} km/hr[/tex]

                          = 1.407 km/hr

therefore, the average speed of the family is 1.407 km/hr

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