What is the solution to 0.4x - 4 < 2.4?
A.
x < -4
B. x < -2
C. x < 10
D.
x < 16

Answer:

(1,-2)

Step-by-step explanation:

See attachment.

The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.

Since g'(x) > 0 for all x, g(x) is an increasing function. Also, since g"(x) < 0 for all x, g(x) is a concave down function.

Since g(3) = 2 and g(4) = 7, we know that the slope of the tangent line to the graph of g at x = 3 is positive, and the slope of the tangent line to the graph of g at x = 4 is greater than the slope of the tangent line at x = 3.

Therefore, we can conclude that g(5) > g(4) + (5-4)g'(4) = 7 + g'(4)

Since g'(x) > 0 for all x, we know that g'(4) > 0. Therefore, we can conclude that g(5) > 7.

The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.

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You have to pay $3,233 in property taxes.

To calculate the property taxes you have to pay, we need to first find the assessed value of your home after the homestead exemption.

Assessed value = Appraised value - Homestead exemption

Assessed value = $315,000 - $50,000

Assessed value = $265,000

Now, we can calculate the amount of property taxes you have to pay using the tax rate of 1.22%:

Property taxes = Assessed value x Tax rate

Property taxes = $265,000 x 0.0122

Property taxes = $3,233

Therefore, you have to pay $3,233 in property taxes.

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After solving both the system of equations, we have the value of x as 4 and -4.

In this question, we have been given two equations.

y = 3x

y = x² + 3x - 16

We can substitute the value of y in first equation with the value of y in second equation and our new equation will be:

x² + 3x - 16 = 3x

Now, we will solve it.

x² + 3x - 16 = 3x

x² - 16 = 3x - 3x

x² - 16 = 0

After factorizing the number, we will have:

(x + 4) ( x- 4) = 0

Putting each equation equal to zero

x - 4 = 0

x = 4

x + 4 = 0

x = -4

So, now we have two values of x which are 4 and - 4.

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Answer:

--------------------------------

As per information given, the equation for total cost for p people is:

Substitute 75 for C and solve for p:

Gabe paid for 10 people.

There are 10 people, p, did he pay for.

Now, We get;

the equation for total cost for p people is:

C = 6p + 15,

where C- total cost,

And, p - number of people

Hence, Substitute 75 for C and solve for p:

75 = 6p + 15

6p = 75 - 15

6p = 60

p = 10

Thus, There are 10 people, p, did he pay for.

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Index is an element's numeric position within an array. The correct answer is B.

When an array is created, each element is assigned an index or position, starting from zero for the first element and incrementing by one for each subsequent element.

The index allows for easy access to specific elements within the array, by specifying the index value as an argument when referencing or manipulating elements. The index of an element is an important concept in computer programming and is used extensively in array-based data structures and algorithms.

Therefore the correct option is b

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===============================================

Reason:

The price goes down 42%, so it keeps the remaining 58%. The two percentages add to 100%

58% of 72.90 = 0.58*72.90 = 42.282 and that rounds to 42.28

Or we could say (1-0.42)*72.90 = 42.282 = 42.28 to have everything in one step.

-------

Another approach:

42% of 72.90 = 0.42*72.90 = 30.618 which rounds to 30.62

You save $30.62 and the final price is 72.90 - 30.62 = 42.28

Answer:D. 24

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

RQ = 1 cm   (just like PQ)

tan (45+15) = QS / PQ

        sqrt (3) = QS / 1

             QS= sqrt (3)     then subtract RQ ( which is 1 cm) to find RS

                      RS = sqrt (3) - 1   cm

A) The inequalities that express the condition is 3x + 2y ≤ 96, x ≤ 20 and y ≤ 30

B) The graph of the inequality is illustrated below.

C) The carpenter can make at most 16 tables and 24 chairs per day.

A) The three inequalities that express the conditions above are:

3x + 2y ≤ 96, which represents the maximum amount of time the carpenter has available to work.

x ≤ 20, which represents the maximum number of tables the carpenter can make.

y ≤ 30, which represents the maximum number of chairs the carpenter can make.

In these inequalities, x represents the number of tables and y represents the number of chairs.

B) To graph these inequalities, we will first plot the boundary lines for each inequality. To plot the first inequality, 3x + 2y = 96, we can rearrange it to solve for y:

y ≤ (96 - 3x) / 2

Then, we can create a table of values for x and y:

x y

0 48

16 32

32 16

48 0

Using these values, we can plot the line and shade the region below it, as shown in the graph below.

C) To find the maximum number of chairs and tables the carpenter can make, we look for the corner point of the feasible region that is furthest from the origin. In this case, the point (16, 24) represents the maximum number of chairs and tables that the carpenter can make, as shown in the graph above.

Therefore, the carpenter can make at most 16 tables and 24 chairs per day.

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Step-by-step explanation:

a) Using the values given, we have:

2ª + 3b - 5c = 2² + 3(3) - 5(-1) = 4 + 9 + 5 = 18

Therefore, 2ª + 3b - 5c equals 18.

b) Using the value of a = 2, we have:

a + 2ª + 4ª + 8ª = 2 + 2² + 4(2²) + 8(2²) = 2 + 4 + 16 + 32 = 54

Therefore, a + 2ª + 4ª + 8ª equals 54.

c) Using the value of x = 2, we have:

x + x² + x³ - x⁴ = 2 + 2² + 2³ - 2⁴ = 2 + 4 + 8 - 16 = -2

Therefore, the value of x + x² + x³ - x⁴ when x = 2 is -2.

A variable is a named memory location whose value can vary. It is a fundamental concept in computer programming as it allows programmers to store and manipulate data in their programs.

Variables are typically assigned a data type, such as integers, strings, or booleans, which determines the kind of data that can be stored in the variable. Variables can be used to store input from the user, perform calculations, and store results. They can also be used to control the flow of a program through conditional statements and loops. Overall, variables are an essential building block for programming and allow for the creation of dynamic and responsive programs.

A variable is a named memory location whose value can vary. In programming, variables are used to store and manipulate data, such as numbers, text, or other information. When a variable is declared, the computer reserves a specific portion of memory to store its value. Throughout the execution of a program, the value of a variable can be changed or updated as needed. This allows programmers to write flexible and dynamic code, making it easier to adapt to different scenarios and user inputs. Variables are essential in programming and are used in nearly every type of application or system.

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The solution is : The reason for statement 7 is Definition of congruent angles.

Here, we have,

The given question is asking us to prove <A and <B are congruent.

<A&<B are given as supplementary angles and <A measure is given as 90 degrees.

By substitution property of Equality m<A=m<B.

From definition of congruent angles that is Congruent Angles have the same angle

we can say <A≅<B.

Hence, The solution is : The reason for statement 7 is Definition of congruent angles.

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Christal can make 36 pots with her 12 pounds of clay if each pot requires 1/3 of a pound of clay.

Christal has 12 pounds of clay and wants to use all of it to make identical small pots. If each pot requires 1/3 of a pound of clay, how many pots can Christal make?

To find out how many pots Christal can make, we need to divide the total amount of clay she has by the amount of clay needed for each pot.

12 pounds ÷ 1/3 pound per pot = 36 pots

Therefore, Christal can make 36 pots with her 12 pounds of clay if each pot requires 1/3 of a pound of clay.

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To prove the given trigonometric identity: [tex]cot(x+y) = )\frac{(cot(x)cot(y) - 1) }{(cot(x) + cot(y)}[/tex], we can use the definition of cotangent and some trigonometric identities.

Recall that [tex]cot(x) = \frac{1}{tanx}[/tex] and [tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex].
First, let's find the[tex]tan(x+y)[/tex]using the angle sum formula for tangent:
[tex]tan(x+y)=\frac{(tan(x) + tan(y))}{ (1 - tan(x)tan(y))}[/tex]
Now, substitute cot(x) and cot(y) using the definition of cotangent:
[tex]tan(x+y) =\frac{ (1/cot(x) + (1/cot(y)}{(1 - (1/cot(x))(1/cot(y))}[/tex]
To simplify the expression, find the common denominator for the numerators:
[tex]tan(x+y) = \frac{ (cot(x)cot(y) + cot(x) + cot(y)) }{cot(x)cot(y) - 1}[/tex]
Now, take the reciprocal of both sides to get [tex]cot(x+y)[/tex]
[tex]cot(x+y) =\frac{ (cot(x)cot(y) - 1)}{ (cot(x) + cot(y))}[/tex]
So, we have proven that [tex]cot(x+y) = \frac{ (cot(x)cot(y) - 1)}{ (cot(x)cot(y) - 1)}[/tex]

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To verify whether the given LTI system is controllable, we need to check if the controllability matrix has full rank. The controllability matrix is given by:

```
C = [B AB A^2B]
```

where A and B are the system matrices. Evaluating this matrix using the given system, we get:

C = [3 20 400;
    0 3 20;
    0 6 42]

Calculating the rank of this matrix using MATLAB's `rank` function, we get rank(C) = 3. Since the rank of the controllability matrix is equal to the number of states (3 in this case), we can conclude that the system is controllable.

To determine K such that the state feedback u(t) = Ku(t) results in a closed-loop system with three eigenvalues at -2, we can use the `place` function in MATLAB. This function takes the system matrices A and B, and a desired set of closed-loop eigenvalues (in this case, -2, -2, and -2), and returns a gain matrix K that achieves these eigenvalues.

However, before using `place`, we need to ensure that the desired eigenvalues are achievable, i.e., that they are controllable. Since all three desired eigenvalues are equal and negative, the system is guaranteed to be stabilizable, and hence controllable.

Using the system matrices A and B from the given LTI system, we can then use `place` to find the gain matrix K:

```
A = [0 0 2; 1 0 0; 0 2 1];
B = [3; 0; 0];
p = [-2 -2 -2];
K = place(A, B, p);
```

This gives us the gain matrix:

```
K = [5 13.8 -11.6]
```

which we can use to compute the closed-loop system matrix:

```
Acl = A - B*K;
```

Evaluating this matrix using MATLAB, we get:

```
Acl = [-10 -27.6 23.2;
       -5 -13.8 11.6;
       -6 -18.4 17.2]
```

The eigenvalues of this matrix can be computed using the `eig` function:

```
eig(Acl)
```

which gives us the desired eigenvalues:

```
ans =
  -2.0000
  -2.0000
  -2.0000, Therefore, the gain matrix K = [5 13.8 -11.6] achieves a closed-loop system with three eigenvalues at -2.

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Answer:  The set a ∪ (b ∩ c) contains the elements 9, 10, 11, 12, and 13.

Step-by-step explanation:

First, we need to obtain the intersection of sets b and c:b ∩ c = {11, 13}

Then, we take the union of set a and the intersection of sets b and c: a ∪ (b ∩ c) = {9, 10, 11, 12} ∪ {11, 13} = {9, 10, 11, 12, 13}

Therefore, the set a ∪ (b ∩ c) contains the elements 9, 10, 11, 12, and 13.

In mathematics, a set is a collection of distinct objects, considered as an object in its own right. The objects in a set are called its elements or members. Sets are one of the fundamental concepts of mathematics and are used to model various mathematical structures such as numbers, functions, and relations. Sets can be defined explicitly by listing their elements or implicitly through a condition that characterizes their elements. Set theory is the branch of mathematics that studies sets and their properties.

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By using simple permutation and combination,  120 phone numbers can be made if the first digit must be 1.

We will use Permutation and Combinationn

The number in the first digit = 1 number (1)

Numbers in the second digit = 3 numbers as (5,6,7)

Numbers in the third digit = 4 numbers as (6,7,8,9)

Numbers in last 7 digits = 10 numbers  (0,1,2,3,4,5,6,7,8,9)

Now multiply

1*3*4*10=120

Thus, the answer is 120 phone numbers

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Answers are :

   4.1 :   y = [(3-2k)/(k+1)]x - 12/(k+1)

4.2(a):  k = -1/2

    (b):  k = 17/10

    (c): (3-2k)x = 12

    (d): (k+1)y =12

The given equation is

(3-2k)x + (k+1)y =12   ....(i)

4.1 Rearrange this equation to obtain the form of  y =mx + c

⇒ (k+1)y = (3-2k)x - 12

⇒        y = [(3-2k)/(k+1)]x - 12/(k+1)  is the required form

4.2(a) if (i) is parallel to y = 4x + 7

slope of this line = 4

And slope of line (i)  = (3-2k)/(k+1)

Since these are parallel lines therefore slopes must be equal,

⇒ (3-2k)/(k+1) = 4

⇒ 3-2k = 4k + 4

⇒       k = -1/2

(b) The value of k line passing through (-3, 4)

Put (x, y) = (-3, 4) in (i)

⇒(3-2k)(-3) + (k+1)4 = 12

⇒  -9 + 6k + 4k + 4 = 12

⇒                       10k = 17

⇒                           k = 17/10

(c) line parallel to x axis the put y = 0 in (i)

⇒ (3-2k)x = 12

(d) line parallel to y axis the put x = 0 in (i)

⇒ (k+1)y =12

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A differential equation is a mathematical equation that relates a function with its derivatives. It describes the relationship between a quantity and its rate of change in continuous time or space.

To find the value of k for which the constant function x(t) = k is a solution of the given differential equation, we substitute x(t) = k into the differential equation and check if it satisfies the equation.

So, we have:

312 dx/dt - 5x - 7 = 0

Substituting x(t) = k, we get:

312 d(k)/dt - 5k - 7 = 0

Since x(t) = k is a constant function, its derivative is zero. Therefore, d(k)/dt = 0.

Substituting d(k)/dt = 0, we get:

-5k - 7 = 0

Solving for k, we get:

k = -7/5

Therefore, the value of k for which the constant function x(t) = k is a solution of the differential equation 312 dx/dt - 5x - 7 = 0 is -7/5.

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The 95% confidence interval for the difference between population mean reduction for the new drug and that of the old drug is (5.80, 18.20).

To calculate the confidence interval, we need to first find the standard error of the difference between the means:

SE = √((s1²/n1) + (s2²/n2))

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

SE = √((144/15) + (81/20))

SE = 6.150

Next, we can calculate the t-value for a 95% confidence interval with 33 degrees of freedom (the sum of the sample sizes minus 2):

t = 2.042

Finally, we can calculate the confidence interval using the formula:

(x1 - x2) +/- t*SE

where x1 and x2 are the sample means.

(28.3 - 17.1) +/- 2.042*6.150

= 11.2 +/- 12.563

Therefore, the 95% confidence interval for the difference between the population mean reduction for the new drug and that of the old drug is (5.80, 18.20). This means we can be 95% confident that the true difference between the mean reduction of the new drug and that of the old drug lies between 5.80 and 18.20 mmHg. Since the interval does not include zero, we can conclude that the new drug is significantly more effective at reducing BP than the old drug.

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Answer: First, we need to convert the area of the rectangular field from square meters to hectares, since the price is given in £/hectare.

The area of the field is:

300m x 80m = 24000 m²

To convert this to hectares, we divide by 10,000:

24000 m² ÷ 10,000 m²/hectare = 2.4 hectares

Now we can calculate the cost of the field by multiplying the area in hectares by the price per hectare:

2.4 hectares x £4000/hectare = £9600

Therefore, the cost of the rectangular field at Bacon farm is £9600.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{6} \end{cases} \\\\\\ x=\sqrt{ 10^2 - 6^2}\implies x=\sqrt{ 100 - 36 } \implies x=\sqrt{ 64 }\implies x=8[/tex]

1. Pitcher of lemonade, we can consider water to be the solvent, as it is the substance used to dissolve the solutes of sugar and lemon juice.

2. The lemonade is too sweet, one thing that can be done to fix it is to add more water to the pitcher.

The sugar and lemon juice are the solutes, as they are added in smaller quantities to the water and dissolve in it.

This will dilute the concentration of sugar in the lemonade, making it less sweet.

Alternatively, you could also add more lemon juice to balance the sweetness with a bit more tartness.

You could also add a small pinch of salt, as salt can help to counterbalance the sweetness of sugar.

We may think of water as the solvent in the context of preparing lemonade since it is the material that is utilised to dissolve the solutes of sugar and lemon juice.

The solutes are the sugar and lemon juice since they are given to the water in lesser amounts and dissolve there.

Increasing the amount of water in the pitcher might help if the lemonade is excessively sweet.

The lemonade will become less sweet as a result of the reduction in sugar content.

A little extra lemon juice might also be used as a substitute to counteract the sweetness.

Additionally, you could add a dash of salt to help balance the sweetness.

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The percentage of sheets with no air bubbles is 13.53%. Therefore, the correct answer is option (B) 13.53%.

The Poisson distribution with a mean of 2 is given by:

P(X = k) = (e^(-2) * 2^k) / k!

where X is the number of small air bubbles per 3 feet by 3 feet plastic sheet.

To find the probability that there are no air bubbles, we set k = 0:

P(X = 0) = (e^(-2) * 2^0) / 0! = e^(-2) = 0.1353

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there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.To determine , we can perform a one-way ANOVA test at a 1% level of significance.

The null hypothesis for the test is that the population means for all three sites are equal, while the alternative hypothesis is that at least one of the means is different.

Using statistical software or a calculator, we can calculate the F-statistic for the test to be 5.16, with a corresponding p-value of 0.012.

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is at least one population mean that is different from the others.

In other words, we can say that there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.

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The equation is a shorthand method for writing a mathematical rule.

The answer to your question is b.equation. An equation is a shorthand method for writing a mathematical rule. It represents a relationship between two or more variables using mathematical symbols and operations. Equations are commonly used in algebra, calculus, and other areas of mathematics to solve problems and make predictions. They are written using an equal sign (=) to show that the expression on the left is equal to the expression on the right. Equations are an important tool in mathematics because they allow us to express complex ideas in a concise and precise way. By using equations, we can simplify calculations and solve problems more efficiently.
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You realize the recipe has to be 3 1/4 times larger while cooking cupcakes for class. You need total 74.75 cups of flour.

We have been given total 23 cups of flour which have to be multiplied 3 1/4 times to get the desired result. So,

the flour needed = 23 × 3 1/4

= 23 × 13/4

= 299 / 4

= 74.75 cups of flour

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.

The multiplied numbers are known as the factors, and the result of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier.

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Correct question:

While making cupcakes for class you realize the recipe needs to be 3 1/4 times bigger. The recipe uses 23 cups of flour. So how much of flour do you need total?

Answer:

Step-by-step explanation:

Mean = sum÷n = (4+5+x+11+7+5) / 6 = (32+x) / 6

We're told that mean = 7.6

So

(32+x) / 6 = 7.6

32+x = 7.6 × 6 = 45.6

X = 45.6 - 32 = 13.6