Your bank account starts with $1550 and every month $50 is automatically deducted for the cable bill. You want to know how long, x, it would take your account to drop below $0. How many months would it take for your account to drop BELOW $0?

Answer:

\(Mike\ Chewer = 14\frac{1}{2}\ hr\)

\(Jennifer\ Glass = 3\frac{3}{4}\ hr\)

\(Fred\ Carlton = 1\frac{1}{4}\ hr\)

\(Amy\ Amaretto = 12\ hr\)

Step-by-step explanation:

Given

\(Mike\ Chewer = 870\ minutes\)

\(Jennifer\ Glass = 225\ minutes\)

\(Fred\ Carlton = 75\ minutes\\\)

\(Amy\ Amaretto = 720\ minutes\)

Required

Convert to hours (in fraction)

To do this, we simply divide the time by 60

\(Mike\ Chewer = 870\ minutes\)

Divide by 60

\(Mike\ Chewer = \frac{870}{60}\ hr\)

\(Mike\ Chewer = \frac{87}{6}\ hr\)

Express as mixed numbers

\(Mike\ Chewer = 14\frac{3}{6}\ hr\)

Simplify

\(Mike\ Chewer = 14\frac{1}{2}\ hr\)

\(Jennifer\ Glass = 225\ minutes\)

Divide by 60

\(Jennifer\ Glass = \frac{225}{60}\ hr\)

Express as mixed numbers

\(Jennifer\ Glass = 3\frac{45}{60}\ hr\)

Simplify

\(Jennifer\ Glass = 3\frac{3}{4}\ hr\)

\(Fred\ Carlton = 75\ minutes\\\)

Divide by 60

\(Fred\ Carlton = \frac{75}{60}\ hr\)

Express as mixed numbers

\(Fred\ Carlton = 1\frac{15}{60}\ hr\)

Simplify

\(Fred\ Carlton = 1\frac{1}{4}\ hr\)

\(Amy\ Amaretto = 720\ minutes\)

Divide by 60

\(Amy\ Amaretto = \frac{720}{60}\ hr\)

\(Amy\ Amaretto = 12\ hr\)

Answer:

2km

Step-by-step explanation:

The dimensions of the room will be 12m x 6m.

So, now calculate the dimensions of the room as follows:

Solve as shown:

Therefore, 12m x 6m will be the dimensions of the room.

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Answer:

b = 2

Step-by-step explanation:

3b + 2(b - 3) = 4

--distributive property-- 2(b - 3) = 2b - 6

3b + 2b - 6 = 4

(add like terms)

5b - 6 = 4

(add 6 to both sides)

5b = 10

(divide both sides by 5 to get b alone)

b = 2

Answer:

1

Step-by-step explanation:

Any thing to the power 0 will always be 1

x⁰=1

(3^-1=1/3)

(4^-1=1/4)

(5^-1=1/5)

1/3+1/4+1/5=47/60

(47/60)^0=1 (as any thing to the power 0 will always be 1 )

Hope this helps you.

Answer: K= 34, n=20, and p=54

Step-by-step explanation: Because the triangles are parallel, we can kind that K and N equal the same as they do on the other triangle, or, 34 and 20. The exterior angles theorem states that the exterior angle is the symbol of the opposite two interior angles, in this case, 34 and 20. So, P=54.

The volume of a cone using the slicing method is determined by integrating the cross-sectional areas of infinitesimally thin slices along the height of the cone.

To understand the formula for the volume of a cone using the slicing method, we divide the cone into infinitely many thin slices. Each slice can be considered as a circular disc with a certain radius and thickness. By integrating the volumes of all these infinitesimally thin slices along the height of the cone, we obtain the total volume.

The cross-sectional area of each slice is given by the formula for the area of a circle: A = π * r^2, where r is the radius of the slice. The thickness of each slice can be represented as dh, where h is the height of the slice. Thus, the volume of each slice can be expressed as dV = A * dh = π * r^2 * dh.

By integrating the volume of each slice from the base (h = 0) to the top (h = H) of the cone, we get the total volume of the cone: V = ∫[0,H] π * r^2 * dh.

Therefore, the formula for the volume of a cone using the slicing method is V = ∫[0,H] π * r^2 * dh, where r is the radius of the cone and H is the height of the cone. This integration accounts for the variation in the cross-sectional area of the slices as we move along the height of the cone, resulting in an accurate determination of the cone's volume.

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The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data

The answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.

In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.

Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.

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It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.

This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.

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The net income for the firm is $160,150 which has been calculated by using the arithmetic operations.

To calculate the net income, we start with the total sales of $734,000 and subtract the total expenses. The total expenses is sum of costs of $315,000, depreciation expense of $48,000, and interest expense of $35,000, resulting in a total expense of $398,000.

After subtracting the total expenses from the total sales, we have:

Net income = $734,000 - $398,000

Net income = $336,000

However, we need to consider the tax expense. The tax rate is given as 35%, which means the firm is required to pay 35% of its taxable income as taxes. To calculate the tax expense, we multiply the net income by the tax rate:

Tax expense = $336,000 * 0.35

Tax expense = $117,600

Finally, we can calculate the net income by subtracting the tax expense from the calculated net income before taxes:

Net income = $336,000 - $117,600

Net income = $218,400

Therefore, the net income for Burlington Exterminators Inc. is $218,400.

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No, the determinant of a matrix can only be calculated for square matrices. A square matrix has an equal number of rows and columns, while a non-square matrix has a different number of rows and columns.

The determinant is a mathematical property that is defined for square matrices only. It is a scalar value that represents certain characteristics of the matrix. To calculate the determinant of a square matrix, you can use various methods such as expansion by minors, cofactor expansion, or using the properties of determinants.

For example, let's consider a 3x2 non-square matrix:

```

A = [[1, 2],

    [3, 4],

    [5, 6]]

```

Since A is a non-square matrix, we cannot calculate its determinant.

the determinant is a concept applicable only to square matrices. Non-square matrices do not have a determinant.

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Greatest number that divides 300, 560 and 500 is 20 .

Given numbers : 300, 560 and 500

First let’s find prime factors of 300,560 and 500

300 = 2^2 *3^1 *5^2

560= 2^4 * 7^1 *5^1

500 = 2^2 * 5^3

So,

Here highest common power of 2 is 2

Here highest common power of 3 is 0

Here highest common power of 5 is 1

Here highest common power of 7 is 0

Thus HCF (300, 560 and 500) = 2^2 * 5^1 * 3 ^0 * 7 ^0

=4*5*1*1

= 20

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Answer:

0.3 since the 7 is bigger than 4 :)) just round up the tenth is the number after the decimal

Answer:

10 tickets in total                                                                                                                                                                                                                                                                                                                                                                  

Step-by-step explanation:

Fun world:

7.65 = 1

8.30 = 2

8.95 = 3

9.60 = 4

10.25 = 5

Game time:

9.25 = 1

9.50 = 2

9.75 = 3

10.00 = 4

10.25 = 5

I really hope this helped you! And i'm sure you won't go to summer school!

The slope of the function is -1/2. The slope of a function represents the rate of change between two variables.

In this case, we are given that the movement along the graph causes the value on the vertical axis to rise by 5 units and the value on the horizontal axis to fall by 10 units.

The slope is calculated by dividing the change in the vertical axis (rise) by the change in the horizontal axis (run). Therefore, the slope is (rise/run) = 5/(-10) = -1/2.

Hence, the slope of the function is -1/2, indicating that for every 10 units decrease in the horizontal axis, there is a corresponding 5-unit increase in the vertical axis.

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Answer:

BC ≈ 10.2 cm

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

BC² + AC² = AB²

BC² + 8² = 13²

BC² + 64 = 169 ( subtract 64 from both sides )

BC² = 105 ( take square root of both sides )

BC = \(\sqrt{105}\) ≈ 10.2 ( to the nearest tenth )

Answer:

The 4th set only has unique x values as it is not repeated making it a function frm the others

Answer:

 -2xy3 • (18x3 - 27xy2 - y)  

 ——————————————————————————

             3          

Step-by-step explanation:

The simplified form of the given expression is 2x-2y³+5x³.

The given expression is -7x+y³+7x³+6x-3y³-2x³+3x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Like terms are those terms whose variables and their exponent power are the same.

Now, (-7x+3x+6x)+(y³-3y³)+(7x³-2x³)

= 2x-2y³+5x³

Therefore, the simplified form of the given expression is 2x-2y³+5x³.

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Therefore, the SUBSET-SUM problem can be reduced to the PARTITION problem in polynomial time. Since SUBSET-SUM is NP-complete, it follows that PARTITION is also NP-complete.

a. Verifier for PARTITION problem:

Given an input (S, U, V) where S is a set of integers and U, V are partitions of S, we can verify in polynomial time whether the sum of elements in U is equal to the sum of elements in V. Therefore, PARTITION is in NP.

b. Reduction from SUBSET-SUM to PARTITION:

To show that PARTITION is NP-complete, we need to show that it is both in NP and NP-hard. We have already shown that it is in NP. Now we will reduce the SUBSET-SUM problem to PARTITION.

Given an instance of the SUBSET-SUM problem, which is a set of integers S = {a1, a2, ..., an} and a target integer T, we can construct an instance of the PARTITION problem as follows:

Let S' = S U {2T} and let U and V be two partitions of S' such that the sum of elements in U is equal to the sum of elements in V. We can easily verify that such partitions exist if and only if there exists a subset of S whose sum is equal to T.

If there exists a subset of S whose sum is equal to T, then we can add 2T to that subset and obtain two partitions of S' with equal sums. Conversely, if we have two partitions of S' with equal sums, then we can remove 2T from the partition that contains it to obtain a subset of S with sum T.

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Answer: 180

Step-by-step explanation:

Answer: 448 inches, I’m pretty sure hope it helps

The fraction computed shows that 9/32 of the shapes are circles.

Find the equivalent ratio for the total shapes:

Total Black Shapes : Total White Shapes = 5 : 11

Multiply by 2:

Total Black Shapes: Total White Shapes = 10 : 22

Find the ratio for the white shapes:

White circles : White squares = 3 : 7

Sum of the units = 3 + 7

Sum of the units = 10

Find the equivalent ratio for the total shapes:

Black circles : Black squares = 3 : 8

Multiply by 2:

Black circles : Black squares = 6 : 16

Sum of the units = 6 + 16

Sum of the units = 22

Combine the ratios:

white circles : white squares : black circles : black square = 3 : 7 : 6 : 16

Circles = 3 + 6

Circles = 9 units

Total = 3 + 7 + 6 + 16

Total = 32 units

Find the fraction of all the shapes that are circles:

Fraction = 9/32

Therefore, 9/32 of the shapes are circles

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The value of the inequality is a x ≥2 or x ≤ -2.

According to the statement

We have to find that the value in the inequality.

So, For this purpose, we know that the

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

From the given information:

7x-14 ≥0 or 4x+5 ≤ -3​

The value of the inequality is a :

7x-14 ≥0 or 4x+5 ≤ -3​

x ≥14/7 or x ≤ -3​-5/4

x ≥2 or x ≤ -8/4

x ≥2 or x ≤ -2.

So, The value of the inequality is a x ≥2 or x ≤ -2.

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If a function f is periodic with period p, then f(t + p) = f(t) for every t. The trigonometric functions y = sin x and y = cos x are periodic, with period 2π and amplitude 1 .

If a function f is periodic with period p, then f(t + p) = f(t) for every t. This is the definition of a periodic function. Therefore, if a function f is periodic with period p, then f(t + p) = f(t) for every t.

To determine the period and amplitude of the trigonometric functions y = sin x and y = cos x, we need to consider their graphs. Both graphs repeat themselves after an interval of 2π. Hence, their period is 2π. The maximum value of the function is 1, and the minimum value of the function is -1. Therefore, the amplitude of both functions is 1.

The graph of the function y = sin x can be represented as shown below:

Graph of y = sin x

The graph of the function y = cos x can be represented as shown below:

Graph of y = cos x

The interval [0, 2π] represents a complete cycle for both graphs. The amplitude of each function is represented by the distance from the x-axis to the maximum or minimum value of the function, which is equal to 1.

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Answer:

The slope is \(\frac{1}{2}\).

Step-by-step explanation:

The formula for slope is rise over run.

The rise is the difference between 5 and 7, which is 2.

The run is the difference between -4 and -8, which 4.

2 over 4 simplifies to 1 over 2, which is \(\frac{1}{2}\).

Hence, the slope is \(\frac{1}{2}\).

Answer: 1/2 or 0.5

Slope formula: (y1-y2) / (x1-x1)

In this example we can set (-4,7) and (-8,5) as:

(-4,7) —> (x1,y1)

(-8,5) —> (x2,y2)

once we plug in our values for x1,y1,x2 and y2 we get:

slope=(7-5)/(-4-(-8))

(double negatives, so it simplifies to -4 + 8)

slope=2/4

slope=1/2

Hope this helped!

Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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The pivot is 37. The low partition is (21, 31, 16, 33). The high partition is (44, 95, 60, 78, 82). The numbers after Partition(numbers, 0, 5) completes are (21, 31, 16, 33, 37, 44, 95, 60, 78, 82).

To determine the pivot, low partition, high partition, and the resulting numbers after executing the Partition operation on the given numbers, we'll follow the process of the quicksort algorithm with the assumption that the element at the midpoint is always chosen as the pivot.

The given numbers are:

numbers = (21, 31, 37, 16, 44, 33, 95, 60, 78, 82)

Partition(numbers, 0, 5) will be called, where the range is from index 0 to index 5 (inclusive).

1. Finding the pivot:

Since the assumption is that the element at the midpoint is chosen as the pivot, the midpoint of the range 0 to 5 is (0 + 5) / 2 = 2. Therefore, the pivot is the element at index 2, which is 37.

2. Partitioning the numbers:

The partitioning step involves rearranging the numbers such that all elements less than the pivot come before it, and all elements greater than the pivot come after it.

Starting with the given numbers: (21, 31, 37, 16, 44, 33, 95, 60, 78, 82)

Comparing each element to the pivot (37), we can partition the numbers into two parts:

Low partition (elements less than the pivot): (21, 31, 16, 33)

High partition (elements greater than the pivot): (44, 95, 60, 78, 82)

3. Numbers after Partition(numbers, 0, 5) completes:

After the partitioning step, the numbers are rearranged such that the elements less than the pivot come before it, and the elements greater than the pivot come after it.

The resulting numbers after Partition(numbers, 0, 5) completes are:

(21, 31, 16, 33, 37, 44, 95, 60, 78, 82)

In summary:

- The pivot is 37.

- The low partition is (21, 31, 16, 33).

- The high partition is (44, 95, 60, 78, 82).

- The numbers after Partition(numbers, 0, 5) completes are (21, 31, 16, 33, 37, 44, 95, 60, 78, 82).

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Answer:

Options (1) and (5) are the correct options.

Step-by-step explanation:

See attachment for the complete question.

Simon's work,

Area of the base = B =\(\frac{1}{2}bh = \frac{1}{2}(5)(13)\)=32.5 m²

Volume = Bh = 32.5(12) = 390 m³

Let's check the error's he made.

Area of the base of the triangular prism

B =\(\frac{1}{2}bh=\frac{1}{2}(5)(12)\)

B = 30 m²

Volume of the prism = (Area of the triangular base)×(Height)

V = 30 × 4

V = 120 m³

Therefore, Options (1) and (5) are the correct options.

Answer:

RAU47 STAR IS CORRECT ON EDG  ENUITY 2021

Step-by-step explanation:

THE AREA OF THE BASE IS 30^2 NOT 32.5^

AND

THE VOLUM E IS 120^3  N OT 390^3

Answer: 5/9

Step-by-step explanation:

Because you are looking for the ratio of BOYS to GIRLS you put those numbers in that order so it would be 10boys/18girls simplified that is 5/9

Answer:

Haaave youuu ever seen a troll

digging a hole

down by the bay?

Step-by-step explanation:

May I have brainliest please? :)