Solve and graph by using systems of inequalities.
A 24 hour radio station plays only classical music, jazz music, talk programs, and news. It plays at most 12 hours of music per day, of which at least 4 hours is classical. Jazz music gets 25% as much time as classical. Write and graph a system of inequalities.
PLEASE HELP!!!

For sufficiently large values of n, the function f4(n) = 5000nlog(n) will have the largest values among the given functions. Among the given functions, the function f4(n) = 5000nlog(n) will have the largest values for sufficiently large values of n.

This can be understood by comparing the growth rates of the functions. As n increases, the function f1(n) = n^100 will grow rapidly but still be outpaced by the exponential growth of f2(n) = 1000n^2. However, the function f3(n) = 2n grows even faster than f2(n) because it has a linear growth rate.

In contrast, the function f4(n) = 5000nlog(n) exhibits logarithmic growth, where the growth rate slows down as n increases. However, the logarithmic term ensures that the function will eventually surpass the other functions in terms of value for sufficiently large values of n. This is because logarithmic growth is slower than polynomial growth but still faster than constant growth.

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Your answer: A  −14 × {23 + (−47)} = [−14 × 23] + [−14 × (−47)]  This example demonstrates the distributive property of multiplication over addition for rational numbers, which states that for any rational numbers a, b, and c: a × (b + c) = (a × b) + (a × c).

The correct answer is A: −14 × {23 + (−47)} = [−14 × 23] + [−14 × (−47)]. This is an example of the distributive property of multiplication over addition for rational numbers because we are multiplying −14 by the sum of 23 and −47, and we can distribute the multiplication to each term inside the parentheses by multiplying −14 by 23 and −14 by −47 separately, and then add the two results together. This is the basic definition of the distributive property of multiplication over addition. Option B shows the distributive property of multiplication over subtraction, option C shows the product of multiplication and addition, and option D is not a valid equation.

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Answer:

A

Step-by-step explanation:

Answer:

5 + 2x ≤ 27

Step-by-step explanation:

I think you are asking about something like this:

5 + 2x ≤ 27

The sum of 5

5 +

and twice a

number

2x

is at

most 27

≤

Answer:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v

Step-by-step explanation:

its E and A

Answer:

The solutions to the inequality are B, E, and F: 25, 36, and 9.

Step-by-step explanation:

The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:

√x < 10

x < 10^2 = 100

So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:

A. 100 (not a solution)

B. 25 (solution)

C. -100 (not a solution)

D. 105 (not a solution)

E. 36 (solution)

F. 9 (solution)

The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .

In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .

Cylindric coordinates will be used to calculate this integral  \(\int\limits_e {x^2} \, dx\).

The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.

x = r cos θ

y= r sin θ

With these coordinates, we shall characterize the solid E.

The boundary is then x² + y² = r²

The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )

Again z = 16r²

The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then

\(\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta\)

\(=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta\)

\(=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta\)

= 512/3 π

Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .

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Answer:

$1.80

Step-by-step explanation:

Since angle  is BCD is 36 and ABCD  is also. 36, The measure of ZB is known to be 36 degrees. ​

Angle measurement is known to be the rate or the number of rotation from the start to an endpoint of any given ray.

Note that a triangle is composed of shape that has 3 sides and angles

For the △BCD, based on the fact that the side DB ≅ CD, then the base angles will be said to be  the same or equal. This depict that the triangle is known to be an isosceles triangle.

Therefore, since the given triangle m <C = m < D

Based on the fact that ∠CD= 36 degrees an Since angle  is BCD is 36 and ABCD  is also. 36, The measure of ZB is known to be 36 degrees. ​

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Answer:

\(24200 mm^{2}\)

Step-by-step explanation:

200*50+200*50+70*60

=24200 mm^{2}

Answer:

B

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 4 = \(\frac{1}{3}\) (x - 1) ← is in point- slope form

with m = \(\frac{1}{3}\) and (a, b ) = (1, - 4 ) → B

To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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Answer:

x = 3

Step-by-step explanation:

This is an isosceles triangle.  Two angles (D and F) are equal because the sides opposite them are equal (or vice versa).

Thus, side DE = side EF, or

12x - 8 = 4x + 16

Combining like terms:  8x = 24

Thus, x = 24/8 = 3

x = 3

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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Answer:

A) 5

Step-by-step explanation:

Distance between two points is calculated as:

Step 1: locate the coordinate points:

Point 1- (x₁ , y₂) = (-5, -2)

Point 2-(x₁ , y₂)= (-9, -5)

Formula to find distance between two points = √(x₂−x₁)² + (y₂−y₁)²

Step 2: input the values

√(−9− −5)² + (−5− −2)²

= √(−4)² + (−3)²

=√16 + 9

= √25 ........ square root of 25

= 5

Distance between points (-5, -2) and (-9, -5) is 5

work by Tolaosunrinde

Answer:

The numbers are 36 and 68.

Step-by-step explanation:

Let the smaller number be x.

"The larger number is four less than two times the smaller

number."

The larger number is

2x - 4

The sum of the numbers is x + 2x - 4, or 3x - 4.

"The sum of the numbers is 104."

3x - 4 = 104

3x = 108

x = 36

The smaller number is 36.

The larger number is 2x - 4, or

2x - 4 = 2(36) - 4 = 72 - 4 = 68

The larger number is 68.

Answer: The numbers are 36 and 68.

The party was attended by Karen, her mother, 4 other adults, and 110 of Karen's friends, for a total of $ 555.

Since Karen invited 150 friends to her 15th birthday party, but not everyone can attend, Karen's mother want one adult for every 25 of her friends, and the cost of food is $ 20 for every four of her friends, and the adults eat for free, if a total of 116 people (including Karen and her mother) go to the party, to determine how many are adults and how many are Karen's friends and how much will the food cost, the following calculations must be performed:

Therefore, the party was attended by Karen, her mother, 4 other adults, and 110 of Karen's friends, for a total of $ 555.

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False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.

False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.

The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.

However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.

Therefore, increasing heat exchange area is not a direct advantage of lattice structures.

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Answer:

5.83 ft

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

3² + 5² = c²

9 + 25 = c²

34 = c²

c ≈ 5.8309 ≈ 5.83

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

$1680

Step-by-step explanation:

Principal loan amount x Interest rate x Time

= 12000 × 14% × 1

=12000 × 14/100 × 1

=168000/100 × 1

=1680

Answer:

i hope this helps!

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Step-by-step explanation:

P = $ 12000

r = 14%

t = 1 (for first year)

I = (P X r X t)/100

∴ I = (12000 X 14 X 1)/100

   = 120 X 14

   = $ 1680   <---------- (Interest on loan at the end of first year)

∴ Total amount owing at the end of first year = (P + I)

                                                                          = (12000 + 1680)

                                                                          =  $ 13680

Repayment = $ 7800

Amount still outstanding (at the start of second year) = 13680 - 7800

                                                                                       =  $ 5880

Interest on the outstanding amount at the end of second year,

P (new) = $ 5880

r (same) = 14%

t = 1 (for the current second year)

∴ I = (P X r X t)/100

   = (5880 X 14 X 1)/100

   = 82320 / 100

   = $ 823.2   <-------------------------- (Interest on outstanding amount at the end of second year)

Answer:

\(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).

Step-by-step explanation:

According to the Rational Root Theorem, the potential roots of a polynomial are

\(x=\pm\dfrac{p}{q}\)  

where, p is a factor of constant and q is a factor of leading term.

The given polynomial is

\(f(x)=9x^8+9x^6-12x+7\)

Here, 9 is the leading term and 7 is constant.

Factors of 9 are ±1, ±3, ±9.

Factors of 7 are ±1, ±7.

Using rational root theorem, the rational or potential roots are

\(x=\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\)

Therefore, the potential root of f(x) are \(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).  

Answer:

its D, 3/7.

Step-by-step explanation:

just did it egen2020

Answer:

1. n>=-3

2. s<=65

3. n>=25

4. n/3=n-12

5. 3n-1=n+5

6. 2(n+5)=20

Step-by-step explanation:

For the specified requirements, 97 sample size are required.

Given that,

Confidence Interval = 95

Margin of error (m) =0.099

We know , to find Sample size for  estimating a population proportion

n = (Z*/m)² P(1-P)

where , m is margin of error

             P is estimated proportional value.

If we have no preconceived of the value of the  population proportion

, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.

for a 95% confidence interval ,

Z* = 1.960 , m=0.099

Using equation we get

n = (1.96/0.099)²(0.5)( 1 - 0.5 )

By solving,

n = 97.02≅ 97

The necessary sample size is 97

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A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.

A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.

The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.

On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.

This approach can help to improve the accuracy of forecasts and predictions based on the time series data.

In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.

Therefore, Option C is correct answer.

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The scale factor of the dilation in this problem is given as follows:

4.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Two equivalent segments in this problem are given as follows:

FG and F'G'.

The lengths are given as follows:

As parallelogram F'G' is the dilated parallelogram, the scale factor of the dilation is given as follows:

k = 8/2.

k = 4.

Meaning that the third option is the correct option.

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It is more difficult to establish nonspuriousness in quasi-experiment designs, where do not use randomization to assign subjects to treatment and comparison groups. So, option(c) is right.

The prefix quasi means "resembling". Thus, quasi-experimental research is a type of research which resembles to experimental research but it is not a true experimental research. These designs are similar to true experiments but lack random assignment to experimental and control groups. A true experiment, a quasi-experimental design, aims to establish a cause-and-effect relationship between an independent and a dependent variable. Aim of these experiments is to evaluate interventions but without use of randomization. Subjects are assigned to groups based on non-random criteria. Since the independent variable is measured, not manipulated, they are best thought of as correlational research. Thus, the correct answer is to determine a relationship between two variables that is not caused by variation in a third variable, i.e, Nonspuriousness.

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Complete question :

Because quasi-experimental designs do not use randomization to assign subjects to treatment and comparison groups, it is more difficult to establish:

a. Association

b. Time order

c. Nonspuriousness

d. Causal mechanism

e. Context

Answer:

w= 9

Step-by-step explanation:

\( \sqrt{ - 4w + 61} = w - 4\)

Square both sides:

-4w +61= (w -4)²

\(\boxed{(a - b)^{2} = a^2 -2ab + b^2 }\)

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

Why do we use negative square root?

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

Answer: w=9.

Step-by-step explanation:

\(\sqrt{-4w+61}=w-4\)

Tolerance range:

\(\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].\)

Solution:

\((\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14 \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\ range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.\)

The solution set of the inequality as given in the task content is; x ≥-10.

It follows from the task content that the given inequality is; 5x+13≥−37.

On this note, the inequality can be solved as follows;

5x+13≥−37

5x ≥−37 -13

5x ≥−50

x ≥-10.

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To provide Logical Proofs with line-by-line justifications for the following arguments,

Let's use the first 4 rules of inference.

Given below is the justification for each step of the proof with the applicable rule of Inference.

E > M1. A > (E > ~F) Premise2. H v (~F > M) Premise3. A Premise4. ~H  Premise5. A > E > ~F 1, Hypothetical syllogism6.

E > ~F 5,3 Modus Ponens 7 .

~F > M 2,3 Disjunctive Syllogism 8.

E > M 6,7 Hypothetical SyllogismIf

A is true, then E must be true because A > E > ~F.

Also, if ~H is true, then ~F must be true because H v (~F > M). And if ~F is true,

Then M must be true because ~F > M. Therefore, E > M is a valid  based on the given premises using the first four rules of inference.

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