Evaluate the expression for x = 5:
2 (x-2)² +5

[tex] \: \huge \mathfrak{ \underbrace{\overbrace{ \pink{A}{\blue{n}}{\green{s}}{ \purple{w}{ \orange{e}{ \red{r}}}}}}} \\ \\ \rightarrow{\bf{\sf{8.366}}} [/tex]

[tex] \: \large \tt \underline{\green{Solution}} [/tex] :

Given : Numbers = 5 , 14

N = 2

[tex] \sf Geometric \: Mean \: = ( x_{1} \times x_{2} \times x_{3}........ x_{n}) {}^{ \frac{1}{n} } \\ \\ = ( 5 \times 14) {}^{ \frac{1}{2} } \\ \\ = (70) {}^{ \frac{1}{2} } \\ \\ or \: (70) {}^{0.5} \\ \\ \rightarrow\fbox{ \blue{8.366}}[/tex]

Answer:

True

Step-by-step explanation:

A vertical number line is line that runs vertically, or up and down. Starting from 0, it has positive numbers moving up and negative numbers moving down.

Based on what we know, positive numbers move up on a vertical number line and move to the right on a horizontal number line. Negative numbers move down on a vertical number line and to the left on a horizontal number line.

So, because 14 is negative, and it's on a vertical number line, it would be below any positive number such as 7.

In short, the answer is true because negative numbers are below or behind positive numbers.

Answer:

C

Step-by-step explanation:

P and N are a linear pair and sum to 180° , that is

P + 67° = 180° ( subtract 67° from both sides )

P = 113°

The option A is the correct answer if An event manager recorded the number of people in different age groups who attended a music concert:

What is Horizontal axis ?

In a graph or chart, the horizontal axis, also known as the x-axis, is the axis that runs horizontally from left to right.

Based on the histogram, the correct data table is:

A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous data. In this case, the histogram titled "Concert Audience" shows the number of people in different age groups who attended a music concert.

The horizontal axis of the histogram represents the age groups in years, with bins from 18 to 24, 25 to 31, 32 to 38, and 39 to 45. The vertical axis represents the number of people in each bin, with values from 0 to 120 at intervals of 20.

To create a data table that accurately represents the data in the histogram, we need to look at the heights of the bars in each bin and determine the corresponding number of people. From the histogram, we can see that:

The bin for ages 18 to 24 has a height of 40, which means that 40 people in that age group attended the concert.

The bin for ages 25 to 31 has a height of 100, which means that 100 people in that age group attended the concert.

The bin for ages 32 to 38 has a height of 200, which means that 200 people in that age group attended the concert.

The bin for ages 39 to 45 has a height of 20, which means that 20 people in that age group attended the concert.

Age Group Number of People

18–24           40

25–31           100

32–38            200

39–45            20

Therefore, The option A is the correct answer.

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We may conclude after answering the presented question that  Option 3 expression has incorrect numbers for both age groups and the number of people.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

The right data table should include the following information based on the provided histogram:

Age Group Number of People

18–24 40

25–31 60

32–38 100

39–45 20

Therefore, the correct answer is:

Age Group Number of People

18–24 40

25–31 60

32–38 100

39–45 20

Option 2 and Option 4 have inaccurate numbers for the number of persons in each age group, whilst Option 3 has incorrect numbers for both age groups and the number of people.

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V = πr^2h

V1 = π14/2^2•9
V1 = π7^2•9

V1 = π49•9

V1 = 1,385.442360233099

V2 = π6/2^2•9

V2 = π3^2•9

V2 = π9•9

V2 = 254.4690049407733

V = V1 - V2

V = 1,385.442360233099 - 254.4690049407733

V = 1,130.973355292326 or 1,130.97

Thus, the volume of the cylinder is 1,130.97cm^3.

The balance of the account after 17 years, considering simple interest, is given as follows:

$21,240.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

The parameter values for this problem are given as follows:

P = 9000, r = 0.08, t = 17.

Hence the balance of the account is given as follows:

A = 9000 x (1 + 0.08 x 17)

A = $21,240.

The problem asks for the balance of the account after 17 years, considering the principal of $9,000 and the interest rate of 8%.

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The option C represent the correct inequalities.

What is inequality ?

Inequality refers to the condition where there is an unequal distribution of resources, opportunities, and benefits among individuals or groups in a society. This can be based on various factors, such as income, wealth, race, gender, ethnicity, education, and social class.

Inequality can take many forms, ranging from economic inequality where some individuals or groups have much more wealth or income than others, to social inequality where some groups face discrimination or exclusion based on their identity.

Inequality can have negative consequences for individuals and society as a whole, including reduced social mobility, increased poverty, and social unrest. Addressing inequality often involves implementing policies and initiatives that aim to level the playing field and provide equal opportunities for all individuals, regardless of their background or circumstances.

Inequality can be represented using various mathematical symbols and expressions, depending on the type of inequality being discussed. Here are some examples:

For a simple inequality comparing two numbers, we use the following symbols:

Greater than: >

Less than: <

Greater than or equal to: ≥

Less than or equal to: ≤

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The probability that for 37 jets, total taxi and takeoff time will be less than 320 minutes is 0.0001.

To find the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes, we need to standardize the distribution using the z-score formula:

z = (x - μ) / σ

where x is the total taxi and takeoff time for 37 jets, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (320 - 378.9) / (2.9sqrt(37)) = -3.68

Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is less than -3.68, which is approximately 0.0001.

Therefore, the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes is approximately 0.0001.

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The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)

Therefore, Leah and Josh should expect to pay $1,156.78 in prepaid interest at the closing.

An equation is a mathematical statement that shows that two expressions are equal to each other. An equation typically contains one or more variables (represented by letters), which are unknown values that we want to find. Equations are used to solve problems in a wide variety of mathematical and scientific fields, as well as in everyday life.

Here,

To calculate the prepaid interest that Leah and Josh will have to pay at the closing, we need to determine the daily interest rate and the number of days between the closing date and the end of the month. Here are the steps:

1. Calculate the total amount of the down payment:

Down payment = 14% x $550,000

Down payment = $77,000

2. Calculate the loan amount:

Loan amount = $550,000 - $77,000

Loan amount = $473,000

3. Calculate the monthly interest rate:

Monthly interest rate = (APR / 12)

Monthly interest rate = (3.70% / 12)

Monthly interest rate = 0.00308333

4. Calculate the daily interest rate:

Daily interest rate = (monthly interest rate / 30)

Daily interest rate = (0.00308333 / 30)

Daily interest rate = 0.00010278

5. Determine the number of days between the closing date (September 6) and the end of the month (September 30):

Number of days = 30 - 6

Number of days = 24

6. Calculate the prepaid interest:

Prepaid interest = (loan amount x daily interest rate x number of days)

Prepaid interest = ($473,000 x 0.00010278 x 24)

Prepaid interest = $1,156.78

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After answering the prοvided questiοn, we can cοnclude that As a result, equatiοn 0.68 pοunds οf fruit remain after the class cοnsumed 2.4 pοunds.

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

Equatiοns can be simple οr cοmplex, regular οr nοnlinear, and include οne οr mοre factοrs. In the equatiοn "x² + 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in many different areas οf mathematics, such as algebra, calculus, and geοmetry.

Tο calculate hοw much fruit remains after the class has cοnsumed 2.4 pοunds, subtract 2.4 frοm 3.08.

3.08 - 2.4 = 0.68

As a result, 0.68 pοunds οf fruit remain after the class cοnsumed 2.4 pοunds.

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The value os x in the following right triangles and trigonometry are:-

Question 6: x= 13.74

question 7: x= 18.52

question 8: x= 60.12

question 9: x= 3.7

Question 6:

tan θ = opposite/adjacent

tan 58° = 22/x

xtan58° = 22

x = 22/ tan58°

Since tan 58° = 1.6003345

x= 22/ 1.6003345

x ≈ 13.74

question 7:

tan θ = opposite/adjacent

tan 51° = x/15

15tan51° = x

x = 15 * 1.2348971

Since tan 51° = 1.2348971

x ≈ 18.52

question 8:

cosθ = adjacent/hypotenuse

cos 37° = 48/x

xcos37° = 48

x = 48/ cos37°

Since cos 37° = 0.79863551004

x= 48/ 0.79863551004

x ≈ 60.12

question 9:

sinθ = opposite/hypotenuse

sin 24° = x/9

9sin24° = x

Since sin 24° = 0.40673664307

x= 9 * 0.40673664307

x ≈ 3.7

The complete question is:-

Unit 8: Right Triangles & Trigonometry

Homework 3: Trigonometry:

Ratios & Finding Missing Sides

Answers for the remaining four problems?

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The answer is option C: (0, -2.5)

The midpoint is the point located exactly halfway between two other points on a line segment. It is also sometimes referred to as the "halfway point" or the "middle point."

To find the midpoint of a line segment, you can use the midpoint formula,

Midpoint = [tex]\frac{(x_1 + x_2)}{2}, \frac{(y_1 + y_2)}{2}[/tex]

We know that Y is the midpoint of XZ, which means that the coordinates of Y are the average of the coordinates of X and Z.

Therefore; Y = (X+Z)/2

or, Z = 2Y - X

Given that; the coordinates are X = (9, 2) and Y = (3, -1)

Put the values of coordinates;

Z = 2*(3, -1) - (9, 2)

Z = (6, -2) - (9, 2)

Z = (-3, -4)

So the coordinates of Z are (-3, -4).

Now the midpoint of YZ,

Midpoint formula: Midpoint =  [tex]\frac{(x_1 + x_2)}{2}, \frac{(y_1 + y_2)}{2}[/tex]

Y  = (3, -1) = (x₁ , y₁)

Z = (-3, -4) = (x₂ , y₂)

Midpoint = [tex]\frac{(3) + (-3)}{2}, \frac{(-1) + (-4)}{2}[/tex]

Midpoint = (0, -2.5)

So the coordinates of the midpoint of YZ are (0, -2.5)

Therefore, the answer is option C: (0, -2.5)

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The linear equation to represent the cost, correct answer is A) C = 0.04z.

What is equation?

An equation is a mathematical statement that shows the equality of two expressions. It consists of two parts, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).

To find the cost per zinnia plant, we can first find the cost per plant for each order separately, and then take the average.

For the first order of 200 zinnia plants at a cost of $23, the cost per plant is:

$23 ÷ 200 = $0.115

For the second order of 500 zinnia plants at a cost of $35, the cost per plant is:

$35 ÷ 500 = $0.07

To find the average cost per plant, we can take the total cost and divide by the total number of plants:

($23 + $35) ÷ (200 + 500) = $0.067

So the cost per zinnia plant is $0.067.

Now we can write the linear equation to represent the cost, C, to purchase z number of zinnia plants:

C = 0.067z

Therefore, the correct answer is A) C = 0.04z.

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the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

To describe the end behavior of a polynomial function, we need to examine the degree and leading coefficient of the function. In the polynomial function f(x) =[tex]2x^3 + 5x^2 - 2x - 3[/tex], the degree is 3 and the leading coefficient is 2.

The end behavior of the polynomial function f(x) is determined by the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the leading term dominates the behavior of the function. Since the leading coefficient is positive and the degree is odd, the function will increase without bound, or approach positive infinity. In other words, as x becomes very large and positive, the function will also become very large and positive.

As x approaches negative infinity, the leading term also dominates the behavior of the function. However, since the degree is odd, the function will decrease without bound, or approach negative infinity. In other words, as x becomes very large and negative, the function will also become very large and negative.

Therefore, the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

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Answer:

x=5.59cm

Step-by-step explanation:

[tex]\frac{x}{12} =cos62\\x=12cos62\\[/tex]

cos62°≈0.4695

x=12*0.4659

x=5.5908

x=5.59cm

Therefore, the lower and upper bounds of m-n are 41.4 and 41.6.

To determine the lower and upper bounds of m-n, we need to first determine the possible range of values for m and n based on their rounding to one decimal place.

For m, since it was rounded to 1 decimal place, its actual value could be anywhere between 48.15 (if the original value was closer to 48.1) and 48.25 (if the original value was closer to 48.2).

Similarly, for n, its actual value could be anywhere between 6.65 (if the original value was closer to 6.6) and 6.75 (if the original value was closer to 6.7).

Therefore, the lower bound of m-n would be when m is at its minimum value of 48.15 and n is at its maximum value of 6.75. So:

m-n = 48.15 - 6.75 = 41.4

Similarly, the upper bound of m-n would be when m is at its maximum value of 48.25 and n is at its minimum value of 6.65. So:

m-n = 48.25 - 6.65 = 41.6

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Answer:

here ya go, i didnt really feel like tpoing so its in the picture

Step-by-step explanation:

If 3x is the cost of x notebooks, we can find the cost of 24 notebooks by substituting x = 24:

3(24) = 72

Therefore, the cost of 24 notebooks is $72.

Answer: y = x + 6

Step-by-step explanation:

         For every unit moved right, the next point is one unit up. This gives us a slope of 1, which we can simplify to just x in the final equation.

[tex]\frac{rise}{run} =\frac{1}{1}=1[/tex]

         We see that the graph intersects the y-axis at (0, 6), giving us a y-intercept of + 6.

         Lastly, we will write the equation.

y = x + 6

         Try it without the 1. Usually we simplify as anything multiplied by 1 is itself.

There are 7 students who are studying both programming languages in the given class of 55 freshman.

This can be determined using a Venn diagram.

A Venn diagram is a graphical representation of sets or classes. The diagram shows sets, their elements, and the union, intersection, and complement of these sets.

A set is a collection of distinct objects, considered as an object in its own right. The elements of a set are frequently things of a similar nature, and sets are characterized by a distinctive property.

The size of a set is represented by the number of elements it contains. Let's use the following symbols to represent sets:

A={Elements in set A}

B={Elements in set B}

The intersection of sets A and B is the set of elements that are in both sets A and B. This can be expressed in the following way

n(A∪B) = n(A) + n(B) - n(A⋂B) where n(A⋂B) is known as intersection

The number of students studying both programming languages can be calculated by taking the intersection of the two sets.

We can use this formula to calculate the number of students studying both programming languages

:|A∩B|=|A|+|B|-|A∪B|

Where |A| denotes the number of elements in set  A studying C programming

|B| denotes the number of elements in set B studying Java

|A∪B| denotes the number of elements in the union of sets A and B (total students)

Now we can substitute the given values into the formula as follows

|A∩B|=38+24−55=7

Therefore, there are 7 students studying both programming languages.

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An expression for the number of bracelets of n beads, where rotations.

Whats an expression for the bracelets?

In mathematics, the term "bracelets" can refer to a type of combinatorial object, specifically, a set of beads arranged in a circular pattern. An expression for the number of bracelets of n beads, where rotations and reflections are considered identical, can be given as follows:

B(n) = (1/n) * (2raise to the power (n-1) + Σ(d|n, d<n) μ((n/d)) * 2 raise to the power ((n/d)-1))

Here, B(n) represents the number of distinct bracelets of n beads, Σ denotes the summation, d|n denotes "d divides n", and μ is the Möbius function.

The first term in the expression, (1/n) * (2 raise to the power (n-1)), represents the number of bracelets that are invariant under rotation. The second term takes into account the bracelets that are not invariant under rotation, but are invariant under reflection, and involves the Möbius function.

This expression can be used to calculate the number of bracelets for any value of n, by plugging in the value of n and evaluating the expression.

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In the above geometric shape, quadrilateral

13) ∠ABC is 109°

14) If BD = 2.8, then CP is 1.1

13)  note that ∠ABC is 109° because the Opposite angles of a quadrilateral sum up to 180°.

Therefore,

∠ABC = 180 - (37+34)

∠ABC = 109°

14)
given that BD is = AC, and

BD = 2.8 while AP = 1.7

Since PC = AC - AP

PC = 2.8 - 1.7

Thus

PC = 1.1

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Answer:

630 000

Step-by-step explanation:

We have to find 18% of the number 3 500 000:

[tex] \frac{3500000 \times 18\%}{100\%} = 630000[/tex]

Their charges will never be equal since Landon's charge will always be higher due to the additional service fee, regardless of the number of hours they work.

To find the number of hours they must work for their charges to be the same, we can set their charges equal to each other and solve for h, the equation of number of hours

10 = 10 + 5h

Subtracting 10 from both sides, we get

0 = 5h

Dividing both sides by 5, we get:

h = 0

This tells us that their charges will never be equal since no matter how many hours they work, Landon's charge will always be higher due to the additional service fee.

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The independent variable in a study is the one that can be controlled or manipulated, and in this case, it is the number of hours of overtime assigned at the facility.

To better understand the relationship between the two variables, we can use mathematical terms. Let's consider X as the independent variable, which represents the number of overtime hours assigned, and Y as the dependent variable, which represents the number of defects in the product. In this case, we can express the relationship between X and Y as:

Y = f(X)

This means that the value of Y is a function of the value of X. In other words, the number of defects in the product depends on the number of overtime hours assigned.

To determine the nature of the relationship between X and Y, we can plot a graph with X on the horizontal axis and Y on the vertical axis. If the graph shows a positive correlation, it means that an increase in X leads to an increase in Y, and vice versa. On the other hand, if the graph shows a negative correlation, it means that an increase in X leads to a decrease in Y, and vice versa.

Finally, if there is no correlation, it means that there is no relationship between X and Y.

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We would need to deposit approximately $1372.03 into an account with a 7.5% interest rate, compounded continuously, to have $2500 in the account 8 years later.

To calculate this, we can use the continuous compounding formula: [tex]A = Pe^(rt)[/tex]

Data:

We know that we want to end up with $2500 after 8 years and that the interest rate is 7.5%.

We can plug in these values and solve for P:

2500 = P * e^(0.075*8)

Simplifying this equation, we get:

2500 = P * e^0.6

Dividing both sides by e^0.6, we get:

P = 2500 / e^0.6

P = 2500/1.82211880039

P = 1372.02909024

P ≈ $1372.03.

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Answer: -10x^2 - 33x + 1

Step-by-step explanation:

Not sure if it’s correct but that’s what I got.

Answer:

Step-by-step explanation:

[tex]\tt 6x\left(x-4\right)-16x^2-\left(9x-1\right)[/tex]

Apply the distributive property :-

[tex]\tt 6x^2-24x-16x^2-9x+1[/tex]

Combine like terms:-

[tex]\tt 6x^2-16x^2=\bf -10x^2[/tex]

[tex]\tt -24x-9x=\bf -33x[/tex]

[tex]\tt 10x^2-33x+1[/tex]

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

Hope this helps!

Answer:

The System of equations has no solution

Step-by-step explanation:

Graphing both equations will produce 2 lines which are parallel because both of them has the same slope but intersecting with X and Y axis in different points