The value of a car is $22,000. It loses 13.9% of its value every year. Find the approximate monthly decrease in value. Round your answer to the nearest tenth.

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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Without specific information about the billing structure and rates of Mr. Morake's municipality, we cannot determine if his statement about the basic charge is correct. Mr. Morake stated that the basic charge was not included on the water bill.

The accuracy of Mr. Morake's statement depends on the specific billing practices of his municipality. Water bills usually include both a fixed or basic charge and a variable charge based on water usage. Since we don't have access to the details of his water bill, we cannot confirm if the basic charge was included or billed separately. To verify the statement, it is recommended to refer to the specific billing information provided by the municipality or contact the municipal water department for clarification.

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Answer: 180 miles

Step-by-step explanation:

From the question, we should note that the distance taken will be calculated by using the formula which will be:

Distance = Rate × Time

where,

Rate = 60 miles per hour

Time = 3 hours

Distance = 60 × 3

Distance = 180 miles

Therefore, the distance travelled is 180 miles.

Answer: (-2^4x3a^6b^10)

Step-by-step explanation:

The amount of distance they saved is 67 feet

From the question, we have the following parameters that can be used in our computation:

Dimensions = 93 ft by 151 ft

Walking from corner to corner, we have

Distance = √(93² + 151²)

Distance = 177.34

Next, we have

Distance saved = 151 + 93 - 177.34

Evaluate

Distance saved = 66.66

Approximate

Distance saved = 67

Hence, the distance they saved is 67 feet

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The amount of yellow paint Curt and Melanie should use is 0.45 quarts so that they can make 1.5 quarts bucket of seafoam green paint.We can use per cent equation.

Given that to make 1.5 quarts bucket of seafoam green paint Curt and Melanie have to mix 70 parts blue paint and 30 parts yellow paint.If 100 percent represent total paint then for 1.5 quarts we have to find the proportion of yellow paint.Let it be x.

30%  / 100% =30 / 100 = x / 1.5 quarts.

We can reduce the equation further,

0.3  = x / 1.5.

0.3 * 1.5 = x

x = 0.45

We can also find blue paint proportion similar by substituting 30 per cent to 70 per cent.

As a result of our calculation, we found the amount of yellow paint to be 0.45 quarts.

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Answer:

x =12

Step-by-step explanation:

combine like terms 32+ = -8 = 24 then divide 2x on each side  24/ 2x  which simipfy to 12

Answer:

Perimeter of ΔLMN = 80 units

Step-by-step explanation:

From the figure attached,

m∠K = m∠N = 58°

m∠J = m∠M = 76°

m∠I = m∠L = 46°

Therefore, ΔKJI and ΔNML are the similar triangles.

By the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

\(\frac{JK}{NM}= \frac{JI}{ML}= \frac{KI}{NL}\)

\(\frac{9}{NM}= \frac{11}{27.5}= \frac{12}{30}\)

\(\frac{9}{NM}= \frac{12}{30}\)

NM = \(\frac{9\times 30}{12}\)

NM = 22.5

Perimeter of the triangle LMN = ML + NM + NL

                                                  =  27.5 + 22.5 + 30

                                                  = 80 units

Let A be a symmetric matrix, which means that A is equal to its own transpose, i.e., A = Aᵀ. We want to prove that if A is invertible, then its inverse A⁻¹ is also symmetric.

To show that A⁻¹ is symmetric, we need to show that (A⁻¹)ᵀ = A⁻¹.

We know that A is invertible, so A⁻¹ exists. Taking the transpose of both sides of the equation A = Aᵀ, we get:

(Aᵀ)ᵀ = A

which simplifies to:

A = Aᵀ

Multiplying both sides of this equation by A⁻¹, we get:

A⁻¹ A = A⁻¹ Aᵀ

Using the property of transpose (i.e., (AB)ᵀ = Bᵀ Aᵀ), we can rewrite the right-hand side of the equation as:

A⁻¹ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

where I is the identity matrix.

Substituting this back into the original equation, we get:

A⁻¹ A = I

Taking the transpose of both sides of this equation, we get:

(A⁻¹ A)ᵀ = Iᵀ

which simplifies to:

Aᵀ (A⁻¹)ᵀ = I

Using the property of transpose again, we can rewrite the left-hand side of the equation as:

(A⁻¹)ᵀ Aᵀ = (A A⁻¹)ᵀ = Iᵀ = I

Substituting this back into the equation, we get:

(A⁻¹)ᵀ Aᵀ = I

which can be rearranged as:

(A⁻¹)ᵀ = (Aᵀ)⁻¹

Since we know that A = Aᵀ, we can substitute this into the equation to get:

(A⁻¹)ᵀ = A⁻¹

which shows that A⁻¹ is symmetric. Therefore, if a symmetric matrix is invertible, then its inverse is symmetric also.

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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Answer:

112

Step-by-step explanation:

so although 8 wouldn't fully trust me here my best bet would be 112 because 68 plus 112 is 180 which is half of 360 and 360 Is the degrees 9f the circle.

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

Answer:

x<1 I believe.

Step-by-step explanation:

Subtract -5 from 5 and do the same with the other side making the other side 1. So you get left with the answer.

Answer:

x=(1, -1)

Step-by-step explanation:

x²-1=0

Add 1 to both sides

x²=1

Take the square root of both sides

x=±1

x=(1, -1)

On solving the provided question, we can say that we excluded example 2 above, a maximum of 3 triangles can be created with those rods.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear.

\(2-inch, 3 inch, 4-inch\)

triangle, because 2+3 > 4, 2+4 > 3, and 3+4 > 2

\(2-inch, 3 inch, 5-inch\)

This is doesn't make  a triangle as  \(2+5 > 3, and 3+5 > 2,\)

2+3 is not more  than 5,, they cannot make triangle.

\(2-inch, 4 inch, 5-inch\)

triangle, because 2+4 > 5, 2+5 > 4, and 4+5 > 2

\(3-inch, 4 inch, 5-inch\)

a triangle, because 3+4 > 5, 3+5 > 4, and 4+5 > 3

Therefore, since we excluded example 2 above, a maximum of 3 triangles can be created with those rods.

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Answer:

D

Step-by-step explanation:

Opposite angles are always the same.

\(\sf \: D)∠ \: 2 \: and \: ∠ \: 4\)

\(\sf \: Vertically \: opposite \: angles \: are \: equal \: to \: each \: other. \\ \sf \: The \: other \: options \: are \: linear \: pairs \: and \: they \\ \sf \: may \: or \: may \: not \: be \: equal \: to \: each \: other.\)

Answer ⟶ \(\boxed{\bf{D)∠ \: 2 \: and \: ∠ \: 4}}\)

The area of the circle with a radius of 12 cm is 144π cm².

Important information:

The area of circle with radius \(r\) is:

\(A=\pi r^2\)

Substitute \(r=12\) in the above formula.

\(A=\pi (12)^2\)

\(A=\pi (144)\)

\(A=144\pi\)

Therefore, the area of the circle is 144π cm².

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The complete table of values of the absolute value equation is

x | y

-3 | [5]

-1 | [3]

0 | [2]

1 | [3]

3 | [5]

The absolute value equation of the function is given as

y = |x| + 2

On the incomplete table of values, we have the following x values

x = -3, -1, 0, 1 and 3

Next, we substitute x = -3, -1, 0, 1 and 3 in the equation y = |x| + 2

So, we have:

y = |-3| + 2 = 5

y = |-1| + 2 = 3

y = |0| + 2 = 2

y = |1| + 2 = 3

y = |3| + 2 = 5

So, the complete table of values of the absolute value equation is

x | y

-3 | [5]

-1 | [3]

0 | [2]

1 | [3]

3 | [5]

See attachment for the graph of the absolute value equation

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Answer:

2561.2785

Step-by-step explanation:

All you gotta do is calculate and times 78.93 x 32.45

Answer:

Village Market

Step-by-step explanation:

3.20÷5=.64

7.30÷10=.73

Step-by-step explanation:

We're going to convert all of these to km/h.

Sapons: 80km/2h => 40kmh

Silvers: 180km/3h => 60kmh

Johns: 50kmh

Cunninghams: (to get the 30 mins to 60 mins, multiply the top and the bottom by 2) 35km/30min => 70kmh

Now that they're all in the same form we can put them from least to greatest.

Answer:

(Least) - Sapons

- Johns

-Silvers

(Greatest) - Cunninghams

Answer:

9

Step-by-step explanation:

We can tackle the individual parts and combine

1/5 of the sum of 9 and 6 means 1/5 * (9 + 6)

The quotient of 18 divided by the sum of 2 and 4 is 18 / (2 + 4)

Combing everything gives us (1/5 * (9 +6)) * (18 / (2 + 4)

(1/5 * 15) * 18/6

3 * 3 = 9

The distance from the base of the stand to the campfire is 285.6 feet.

The angle of depression of 35 degrees.

Let's denote the distance from the base of the stand to the campfire as "x."

Since we know that,

The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

Using the tangent function, we have:

tan(35 degrees) = opposite/adjacent

tan(35 degrees) = 200/x

To find the value of x, we can rearrange the equation:

x = 200 / tan(35 degrees)

x ≈ 200 / 0.7002

x ≈ 285.6 feet

Therefore, the distance from the base of the stand to the campfire is 285.6 feet.

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Answer:

14.5

Step-by-step explanation:

If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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Answer:

rotating ΔEAR 180° inside the right angle parallelogram circumscribed by.

original coordinates:

A (-6, 4)

R (-2, 2)

E (-5, -6)

post rotation coordinates: