In 3 months John collected a debt of $70.00. What was the average amount of debt John collected per month?

Answer:

Given equation are 3x+4y=11 and 2x+3y=8

Comparing with a

1

x+b

1

y+c

1

=0 and a

2

x+b

2

y+c

2

=0 we have

a

1

=3,b

1

=4,c

1

=−11 and a

2

=2,b

2

=3,c

2

−8

Now , x=

a

1

b

2

−a

2

b

1

b

1

c

2

−b

2

c

1

and y=

a

1

b

2

−a

2

b

1

c

1

a

2

−c

2

a

1

⇒x=

3×3−2×4

4x(−8)−3×(−11)

and y=

3×3−2×4

−11×2−(−8)×3

⇒x=

9−8

−32+33

and y=

9−8

−22+24

⇒x=1 and y=2

Answer:

4 , 1 and 6

Step-by-step explanation:

now ur not in trouble :)

Answer:

32 cm

Step-by-step explanation:

The volume of the container is:

V= area of the base * the heigth

Since the container has a rectangular base the area of it is:

A = length * width

Let L be the missing length

A = L * 10

V = 10* 25 * L

The container can hold 8 Liters when it's completely full to its brim.

8 liters is 8000 cm^3 ( multiply by 1000)

8000 = 10*25*L

8000 = 250 *L

L = 8000/250

L = 32 cm

v=8litres which is 8 × 1000

l=?

b=10

h=25

since, v=lbh (volume of cuboid)

8000=l × 10 × 25

l=8000/250

l=32

therefore the length is 32cm

True. The 3px, 3py, and 3pz orbitals are similar in shape but differ in their orientation or direction.

The p orbitals are one type of orbital that corresponds to the angular momentum number l = 1. These p orbitals are designated as 3px, 3py, and 3pz to indicate their orientations along the x, y, and z axes, respectively.

The p orbitals have a  shape with a node at the nucleus. They consist of two lobes of electron density, one on either side of the nucleus, separated by a region of zero electron density. The lobes are oriented along the designated axes. The 3px orbital points along the x-axis, the 3py orbital points along the y-axis, and the 3pz orbital points along the z-axis. Although they have different orientations, their shapes and sizes are the same.

So, while the 3px, 3py, and 3pz orbitals differ in their orientation in space, they share the same overall shape and size.

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The price of Mira's breakfast before tip was $1.50. We know that she left a 20% tip on top of the price of the breakfast. This means that the tip she left was 0.20x dollars.

An equation is a mathematical statement that proves the equality of two expressions. It has two sides, one on the left and one on the right, separated by an equal sign (=). The expressions on both sides of the equal sign are called the terms of the equation.

Equations are used to represent and solve mathematical relationships. They can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be simple or complex, and they can have one or more variables.

Let the price of Mira's breakfast before tip be x dollars.

The tip she left was 0.20x dollars.

We also know that the total amount she paid, including the tip, was $1.80 more than the price of the breakfast. As a result, we can construct the following equation:

x + 0.20x + 1.80 = total amount paid

Simplifying the equation, we get:

1.20x + 1.80 = total amount paid

We can now solve for x, which is the price of Mira's breakfast before tip:

1.20x = total amount paid - 1.80

1.20x = total amount paid - 1.80

x = (total amount paid - 1.80) / 1.20

We know that the tip Mira left was $1.80, so the total amount paid was:

total amount paid = x + 0.20x + 1.80 = 1.20x + 1.80

By substituting this value for x in the equation, we get:

x = (1.20x + 1.80 - 1.80) / 1.20

x = 1.50

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Answer:

33 units²

Step-by-step explanation:

Setting up an equation to find the area of given kite:

Area of the kite = \(\mathrm{\frac{(2ft+9ft)\times(3ft+3ft)}2}\)

Area of the kite = \(\mathrm{\frac{11ft\times6ft}{2}}\)

Area of the kite = \(\mathrm{\frac{66ft^2}^2}\)

Area of the kite = \(\mathrm{33\;ft^2}\)

Therefore, the area of our given kite is 33 square feet

Kavinsky

Answer:

33 units square

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

it's the third option

Step-by-step explanation:

I think I'm pretty sure

hope this helped ;)

Answer:

550 sit-ups

Step-by-step explanation:

Given

See attachment for chart

Required

Number of sit-ups on March 11

Represent the number of sit-ups with x and the days with y.

So:

\((x_1, y_1) = (1,50)\) --- May 1

\((x_2, y_2) = (2,100)\) --- May 2

First, we calculate the slope of the line chart.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{100 - 50}{2-1}\)

\(m = \frac{50}{1}\)

\(m = 50\)

Next, we calculate the equation using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = 50(x - 1) + 50\)

\(y = 50x - 50 + 50\)

\(y = 50x\)

So, on May 11.

\(x= 11\)

Substitute 11 for x

\(y = 50 * 11\)

\(y = 550\)

Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Learn more

Answer:

(6,4)

Step-by-step explanation:

First we must cross out the -2x and 2x since they're both opposites of each other and thus they cancel each other out.

Now we have:

3y = 0

2y = 20

So next we add the 3 and 2 to get 5y, and then we add 20 and 0 to get 20.

So now we have:

5y = 20

And so we'll simply divide by 5 on both sides, and the answer is y = 4.

Now normally we would plug 4 back in to one of the equations to solve for x, but since only one of the answer choices has 4 in the y position, we can already tell that (6,4) is the answer.

Hope this helps you. Sorry if it doesn't though.

Answer:

9

Step-by-step explanation:

a0 is the regression term that describes the constant or intercept in the linear regression equation.

In a simple linear regression model, the equation takes the form of y = a0 + a1x + e1, where y is the dependent variable (or response variable), x is the independent variable (or predictor variable), a0 is the intercept or constant term, a1 is the coefficient of the independent variable, and e1 is the error term.

The intercept term, a0, represents the value of the dependent variable when the independent variable is zero. For example, in a linear regression model that predicts salary based on years of experience, the intercept would represent the starting salary for someone with zero years of experience. The intercept is an important component of the regression equation because it allows us to make predictions for values of x that are outside the range of our observed data.

The coefficient, a1, represents the change in the dependent variable for each one-unit increase in the independent variable. In the salary example, the coefficient would represent the average increase in salary for each additional year of experience.

Both the intercept and coefficient are estimated from the data using methods such as least squares regression. Once these values are estimated, we can use them to make predictions for new values of x.

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Answer:

$4.25

Step-by-step explanation:

Simple, 12.50 divided by four is 4.25. Meaning the answer is $4.25.

Answer:

$7.65 million dollars / $7.55 * 10^6

Step-by-step explanation:

30*1.5=45 seconds

5.1*1.5=7.65

for scientific notation just take the number of zeros and use that for exponent, and make a dot so it is a number less than 10

a. The average temperature across the rod is independent of time.

b. The average temperature across the rod will approach 30ℓ - 20ℓ^(2).

c. The average height of the vibrating string remains constant over time.

(a) To show that A'(t) = 0, we differentiate A(t) with respect to t:

A'(t) = d/dt [ ∫₀ˡᵤ u(x,t) dx ]

Using the Leibniz rule for differentiating under the integral sign, we have:

A'(t) = ∫₀ˡᵤ ∂u/∂t dx

Now, let's use the heat equation: uₜ = k uₓₓ

A'(t) = ∫₀ˡᵤ k uₓₓ dx

By applying the boundary conditions, we know that uₓ(0,t) = 0 and uₓ(ℓ,t) = 0. This implies that the derivative of u with respect to x is zero at both endpoints.

Therefore, A'(t) = ∫₀ˡᵤ k uₓₓ dx = k [uₓ]₀ˡᵤ = k [0 - 0] = 0

Hence, the average temperature across the rod is independent of time.

(b) In this case, we are given u_t = 2u_xx with Neumann boundary conditions: u_x(0, t) = u_x(1, t) = 0, and the initial condition u(x, 0) = 120x(1 - x).

Since A'(t) = 0 as shown in part (a), we know that the average temperature A(t) is constant over time.

Therefore, to find the constant value of A(t) at long times, we can evaluate A(t) at t = 0:

A(0) = (1/ℓ) ∫₀ˡᵉ u(x, 0) dx

Substitute the initial condition:

A(0) = (1/ℓ) ∫₀ˡᵉ 120x(1 - x) dx

Evaluate the integral:

A(0) = (1/ℓ) [120 * (x^(2)/2 - x^(3)/3)] | from 0 to ℓ

A(0) = (1/ℓ) [120 * (ℓ^(2)/2 - ℓ^(3/3))]

A(0) = 60[ℓ/2 - ℓ^(2/3)]

A(0) = 30ℓ - 20ℓ^(2)

So, after a long time, the average temperature across the rod will approach 30ℓ - 20ℓ^(2).

(c) In this case, we are dealing with the wave equation u_tt = c^(2)* u_xx for 0 < x < ℓ, and we define A(t) as the average height of the vibrating string at time t:

A(t) = (1/ℓ) ∫₀ˡᵉ u(x, t) dx

To find the boundary conditions at x = 0 and x = ℓ for which A''(t) = 0, we need to differentiate A'(t) with respect to t:

A''(t) = d^(2)/dt^(2)[∫₀ˡᵉ u(x, t) dx]

Using the property of Leibniz integration rule, we can interchange the order of differentiation and integration:

A''(t) = ∫₀ˡᵉ (∂^(2)/∂t^(2)) dx

Now, we apply the wave equation u_tt = c^(2)* u_xx to the integrand:

A''(t) = ∫₀ˡᵉ (c^(2)* u_xx) dx

Now, we use the boundary conditions: u_x(0, t) = u_x(ℓ, t) = 0

Since the derivative of a constant is zero, we can rewrite the integral as:

A''(t) = c^(2)* ∫₀ˡᵉ u_xx dx

Now, using integration by parts on the right-hand side:

A''(t) = c^(2)* [u_x(ℓ, t) - u_x(0, t)]

Since both u_x(0, t) and u_x(ℓ, t) are zero due to the Neumann boundary conditions, we have:

A''(t) = 0

Therefore, A(t) need not be constant, but A''(t) is zero, indicating that the average height of the vibrating string remains constant over time.

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Answer:

points

Step-by-step explanation:

The sample in this study is a subset of 500 randomly selected adult pine trees from a total population of 32,000 adult pine trees in a certain national forest. It is used to estimate the average height of all the trees in the population.

Sampling is a common technique used in research to study a large population by selecting a smaller representative group, known as the sample. In this case, the researchers have randomly chosen 500 adult pine trees from the entire population of 32,000 trees. Random sampling helps ensure that each tree in the population has an equal chance of being selected, reducing bias and increasing the generalizability of the findings.

By measuring and analyzing the heights of the 500 sampled adult pine trees, the researchers aim to estimate the average height of all 32,000 adult pine trees in the national forest. The sample is used to make inferences about the population, providing insights into its characteristics without having to measure every single tree.

To ensure the reliability of the findings, the sampling process must be conducted carefully, using appropriate statistical techniques. The selected sample should be representative of the population to ensure accurate estimates of the average height. Statistical analyses will be performed to determine the sample mean, standard deviation, and confidence intervals, providing insights into the average height and its variability within the population.

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The sum of the first 6 terms of the given sequence is -1350.

What is sum?

In mathematics, the term "sum" refers to the result of adding two or more numbers or quantities together. The sum of two numbers a and b is denoted by a + b. Similarly, the sum of three numbers a, b, and c is denoted by a + b + c.

The given sequence is a finite geometric sequence with a common ratio of -3. To find the sum of the first 6 terms of this sequence, we can use the formula for the sum of a finite geometric series:

\(S_n = a(1 - r^n) / (1 - r)\)

where S_n is the sum of the first n terms of the sequence, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the sequence.

Substituting the given values, we get:

\(S_6 = 18(1 - (-3)^6) / (1 - (-3))\\\\S_6 = 18(1 - 729) / 4\\\\S_6 = -1350\)

Therefore, the sum of the first 6 terms of the given sequence is -1350.

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Answer:

Step-by-step explanation:

-1,092

Answer:

Step-by-step explanation:

Conclusion:

Therefore, 4/5 of a dollar is 80 cents.

Hoped this helped.

\(GeniusUser\)

The value of cents in 4/5 dollars would be 80 cents.

Used the concept of measurement unit that states,

A measurement unit is a standard quality used to express a physical quantity. Also, it refers to the comparison between the unknown quantity with the known quantity.

Since we know that;

1 dollar = 100 cents

Hence we get;

The number of cents in 4/5;

4/5 x 100

4 x 20

80 cents.

Therefore, 4/5 of a dollar is 80 cents.

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The value of the domains is given as:

In order to find the results of (fg)(x) and (f/g)(x), we must begin by multiplying and dividing the two functions, respectively:

(fg)(x) = f(x) * g(x) = \(3x * 3(x + 1)^2 = 9x(x + 1)^2\); its domain containing all real numbers.

Similarly, (f/g)(x) = f(x) / g(x) = in a domain that does not \(3x / 3(x + 1)^2 = x / (x + 1)^2\)include x = -1 (if g(x) ≠ 0).

Let us now evaluate  (fg)(5) and (f/g)(5):

(fg)(5) =\(9(5)(5 + 1)^2 = 9(5)*(6)^2\) = 9(5(36)) = 1620 while  

(f/g)(5) = \(5/(5 + 1)^2 = 5/(6)^2\) = 5/36.

Consequently, (fg)(5) equals 1620 and (f/g)(5) is equivalent to 5/36.

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Answer:

x = 6

Step-by-step explanation:

The perimeter is the sum of the 3 sides

Sum the 3 sides and equate to 53

x + 2x + 1 + 5x + 4 = 53 , simplify left side

8x + 5 = 53 ( subtract 5 from both sides )

8x = 48 ( divide both sides by 8 )

x = 6

The value of equation is 1041 according to the commutative property.

According to the statement

We have to solve the given statement

So, For this purpose, We know that the

Commutative property is a binary operation is commutative if changing the order of the operands does not change the result.

From the given information, the equation is:

(2 x 105) + (3 x 104) + (5 x 103) + 4

Now, multiply this with the help of above written property

(210) + (312) + (515) + 4

522+515+4

Now, add the terms

1037+4

Then the solution is

1041.

Then to the commutative property, the solution become

1041.

So, The value of equation is 1041 according to the commutative property.

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No , as we fail to reject the null hypothesis Mr. Goodman claim that his evaluations are significantly different than the history department's.

What is null hypothesis?

Test statistic  X2 =1.9196

p value =0.5893

No , as we fail to reject the null hypothesis Mr.Goodman claim that his evaluations are significantly different than the history department.

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The perimeter of the figure is 28 units

The perimeter of a figure is the total length of its boundary or outer edge. It is the sum of the lengths of all the sides of the figure. The perimeter is usually measured in units such as centimeters, meters, inches, or feet, depending on the measurement system being used.

The perimeter of this figure is the sum total length of the boundaries.

This can be calculated as;

P = 2 + 4 + 5 + 3 + 7 + 7

P = 28 units

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Answer:

The diagonal has to measure 10 meters

Step-by-step explanation:

The diagonal has to be based on the Pythagorean theorem (for right angle triangles) and that is:

\(diagonal^2=side_1^2+side_2^2\\diagonl^2=6^2+8^2\\diagonal ^2=36+64\\diagonal^2=100\\diagonal = 10 \,\,m\)

Answer:

63.6 feet

Step-by-step explanation:

Step-by-step explanation:

(3,3)====(3,-3)

(3,2)====(2,-3)

(5,2)====(2,-5)