PLS HELP QUICK! 20 POINTS
Can a triangle be formed with side lengths 5, 6, 12? Explain.

No, because 5 + 6 < 12
Yes, because 5 + 6 > 12
No, because 12 − 6 < 6
Yes, because 12 − 6 < 5

Answer:the general form of a hyperbola is 6x^2-5y^2+12x+50y-149=0 the answer is (x+1)^2/5 -((y-5)^2/6=1

Step-by-step explanation:

For the given monthly salaries of the 7 employees of the firm , then the true statement is : (a) mean = median .

In statistics the Mean is defined as sum of a collection of numbers divided by count of numbers .

the given monthly salaries is 9, 7, 8, 7, 10, 11 and 11.  

arranging the data in ascending order ,

we get ; 7 , 7 , 8 , 9 , 10 , 11 , 11 .

the sum of the salaries is = 63 ;

So , the mean is  = 63/7 = 9 .

median is the middle term of the given data that is = 9 ;

the mode is the most times occurred frequency that is 7 and 11 .

On comparing the mean , mode and median ,

we get ; mean = median .

Therefore , the correct statement is (a) mean = median .

The given question is incomplete , the complete question is

The monthly salaries (in thousands of dollars) for a sample of 7 employees of a firm are: 9, 7, 8, 7, 10, 11 and 11.

Which of the following statements is true about the mean, median and mode ?

(a) mean = median

(b) mode < median < mean

(c) mode < mean < median

(d) mode = median = mode .

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(a) The probability that O1 gets the Volvo is  3/10 .

(b) The probability that O2 or O5 will get the Volvo is 1/2  .

In the question ,

it is given that ,

the five officials : O1, O2, O3 , O4 , O5 are to be assigned five different city cars: a Escort,  Lexus,  Nissan, the Taurus, and the Volvo .

From the given data , the table formed is shown below .

From the table , we can observe that ,

O1 will not drive the Escort or a Nissan . So, he has chance of getting one car among Lexus, Taurus & Volvo = 3 possibilities

O2 will not drive the Taurus​ . So, he has chance of getting one car among Escort , Nissan ,Lexus, & Volvo = 4 possibilities

O3 will not drive the Lexus or Volvo​ . So, he has chance of getting one car among Escort , Nissan ,Taurus = 3 possibilities

O4 will not drive the Lexus so he has chance of getting one car among Escort , Nissan ,Taurus, Volvo = 4 possibilities

O5 will not drive the Escort or a Nissan . So, he has chance of getting one car among Lexus, Taurus & Volvo = 3 possibilities .

The  20 possible arrangements for E,L,N,T,V are :

{ (O2, O1, O3, O4, O5),  (O2, O1, O3, O5, O4),  (O2, O1, O4, O3, O5),  

(O2, O5, O3, O1, O4),  (O2, O5, O3, O4, O1),(O2, O5, O4, O3, O1),  

(O3, O1, O2, O4, O5),  (O3, O1, O2, O5, O4),  (O3, O1, O4, O5, O2),  

(O3, O2, O4, O1, O5), (O3, O2, O4, O5, O1),  (O3, O5, O2, O1, O4),  

(O3, O5, O2, O4, O1),  (O3, O5, O4, O1, O2),  (O4, O1, O2, O3, O5),

(O4, O1, O3, O5, O2),  (O4, O2, O3, O1, O5),  (O4, O2, O3, O5, O1),  

(O4, O5, O2, O3, O1),  (O4, O5, O3, O1, O2)  }

Part(a)  : The probability that O1 gets the Volvo is = 6/20 = 3/10 .

and

Part(b) :

Probability of O2 or O5 gets the Volvo = (Probability of O2 getting Volvo
) + (Probability of O5 getting Volvo) .

= 4/20 + 6/20

= 10/20 = 1/2 .

Therefore , the required probability for (a)  is 3/10 and for (b) is 1/2  .

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The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

According to Midpoint theorem, if the midpoints of two sides of a triangle are joined by the segment, then resultant segment is parallel to the third side of the triangle and is half of the length of the third side. Consider the triangle ABC, as shown in the figure. Let the midpoints of the sides AC and AB be given as E and D. Then the line DE is said to be parallel to the side BC, whereas the side DE is half of the side BC i.e., DE || BC and DE = (1/2 BC).

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You pay the interest of 350 dollar on a $43,000 car loan with a fixed APR of 4.9% if the loan is for 5 years

The term annual percentage rate of charge, sometimes referred to as a nominal APR and sometimes referred to as an effective APR, refers to the interest rate for the entire year, rather than just a monthly fee/rate, as applied to a loan, mortgage loan, credit card, and so on. It is a finance charge calculated on an annual basis.

We are given that it took out a car loan for $43,000 car loan with a fixed APR of 4.9% if the loan is for 5 years

We know that r = 4.9/12/100 = 0.0049

p = 43,000

Putting the values in formula we get;

= (43,000x 0.0049 x 2.767)/1.767

= $350

Therefore, the interest will be 350 dollar.

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A continuous function is the one in which the function is continuous is the interval given for the function.

A continuous function that does not satisfy the conclusion of the mean value theorem on a closed interval is the function f(x) = |x| on the interval [-1, 1].

This function is continuous on the interval [-1, 1], but it does not have a derivative at x = 0. Therefore, the mean value theorem does not apply at this point, and there is no value c in the interval [-1, 1] such that f'(c) = (f(1) - f(-1))/(1 - (-1)).

This is an example of a function that is continuous on a closed interval, but does not satisfy the conclusion of the mean value theorem.

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The number of ways to pick a digit, a lowercase letter, an uppercase letter, or one of eight allowable punctuation marks is 70.

The total number of digits (0-9) = 10.

Thus, the number of ways to pick a digit = 10.

The total number of lowercase letters (a - z) = 26

Thus, the number of ways to pick a lowercase letter = 26.

The total number of uppercase letters (A - Z) = 26

Thus, the number of ways to pick an uppercase letter = 26.

The total number of allowable punctuation marks = 8

Thus, the number of ways to pick a punctuation = 8.

Hence, the total number of ways to pick a digit, a lowercase letter, an uppercase letter, or one of eight allowable punctuation marks is -

10 + 26 + 26 + 8 = 70.

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Answer:

1,150 cubic feet.

Step-by-step explanation:

The volume of a hemisphere with a radius of 6.4 feet can be calculated using the formula 4/3 * pi * r^3, where r is the radius of the hemisphere. Plugging in the values, we get 4/3 * pi * 6.4^3 = approximately 1,153 cubic feet. Rounded to the nearest tenth, the volume of the hemisphere is 1,150 cubic feet.

Answer:

6

Step-by-step explanation:

Divide 4 by [tex]2/3[/tex]

[tex]\frac{4}{2/3}[/tex] =[tex]\frac{4*3}{2}[/tex]

=6

Spotify charges $0.98 for individual song and $10 for entire album

According to the question,

Spotify charges "x" dollars for individual songs and "y" for entire album

Also, Person A pays $14.9 to download 5 individual songs and 1 album

Which can be written as

=> 5x + y = 14.9 --------------(1)

Person B pays $22.95 to download 3 individual songs and 2 albums

=> 3x + 2y = 22.95 ---------(2)

Solving these two linear equations by elimination method

Multiplying equation (1) by 2

=> 10x + 2y = 29.8

Now, subtracting these equation

10x + 2y - 3x - 2y = 29.8 - 22.95

=> 7x = 6.85

=> x = 0.98

Replacing value of x in equation (1),

=> 5(0.98) + y = 14.9

=> 4.9 + y = 14.9

=> y = 10

Hence , Spotify charges $0.98 for individual song and $10 for entire album

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The smallest n is n=9.

What is an integer, and what are some examples of them?

A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).

-5, 1, 5, 8, 97, and 3, 043 are some examples of integers.

-1.43, 1 3/4, 3.14,.09, and 5,643.1 are a few examples of numbers that are not integers.

Formally, the set of integers, designated Z, is defined as follows:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Since b=DigitsRearranged(a)

→ a and b have the same remainder when divided by 9

→ a−b is divisible by 9

→ n≥9

And this is sufficient because there is a solution for this n:

a=812,345,709b=701,234,598a−b=111,111,111

So the smallest n is n=9.

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When x = 9, the inequality - 4 + x ≤ 9 has the necessary value.

In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Mathematics that contains at least two terms with variables or integers that are not equal is referred to as being unequal.

Inequality, two integers or algebraic expressions with a declared order link (greater than, greater than, or equal to, less than, or less than or equal to).

As per option (B),

When substituting the values the equation -4 + 9 is less than or equal to 5.

-4 + 9 is 5 so this equation is true

The required value of inequality - 4 + x ≤ 9  is true when x = 9,

Therefore, the correct answer is option (B) -4 + x ≤ 5.

The complete question is:

Which inequality is true when x = 9?

A) 4 - x ≥ 5

B) -4 + x ≤  5

C) 4 + x ≤ 5  

D) -4 - x ≥ 5

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The five number summary of the data set that is represented in the stem and leaf plot is:

Min: 10.

Q1: 24.

Med: 47

Q3: 56.

Max: 68.

To find the five number summary, we need to write out each of the data points given in the stem and leaf plot from the least to the greatest.

Thus, the data set are:

10, 12, 23, 24, 24, 25, 29, 42, 42, 47, 49, 50, 54, 55, 56, 58, 59, 60, 68

Find the middle (median) of the data:

47 is the center of the data set, therefore it is the median of the data.

The minimum value is the least data point, which is 10.

The lower quartile is the center of the first part of the data that is divided by the median, which is 24.

The upper quartile is the center of the second part of the data that is divided by the median, which is 56.

The maximum data value is the largest data point which is, 68.

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The value of the property at the end of year 7 is 15,324,111$. for a detailed answer read below.

The net operating income (NOI) formula determines a company's revenue after operating costs have been subtracted, but before interest and taxes have been subtracted.

The net operating income of the property is given for years 1 to 8 in the question. Z Corporation wants to own the property for seven years and then sell the property in the 8th year. The growth rate in NOI is 3%, and the expected return on property is 12%.

The "going-in" capitalization rate should be calculated as follows: So, using first-year NOI as the basis, the cap rate is. 8.29%

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Answer:

a was ture

b was wrong

Step-by-step explanation:

a)

[tex]\frac{45}{60} =\frac{3}{4}[/tex]

[tex]\frac{36}{48} =\frac{3}{4}[/tex]

b)

[tex]\frac{450m}{3km} =\frac{450}{3000} =\frac{3}{20} \\[/tex]

[tex]\frac{75cm}{7m}=\frac{75}{700} =\frac{15}{140}[/tex][tex]=\frac{1}{7}[/tex]

Answer:

1. 45:60 = 36:48

(45:60)/15 = (36:48)/12         (divide by their GCF)

3:4 = 3:4

2. 4500:3 = 75:700

(4500:3)/3 = (75:700)/25

1500:1 = 3:28

Step-by-step explanation:

The person that was closest to the state record after the jump is; Alex

We are told that Alex jumped 38 feet 11²/₃ inches or 38.9725 ft and that the eighth-grade record is 40.17 feet.

Let see how closer Alex jumped was;

40.17 feet - 38.9725 ft = 1.2425 ft

We are told that Eric jumped 36.89 feet and the state record of the eighthgrade record is 40.17 feet. Thus;

Let see how closer Eric jumped was;

40.17 feet - 36.89 ft = 3.28 ft

We conclude that 1.2425 ft is less than 3.28 ft and as such Alex was closer.

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The minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value must all be calculated before we can create a box plot for the rating points data.

The median of the lower and upper halves of the data must be determined in order to determine the first and third quartiles, respectively. The numbers from the minimum to the median make up the lower half of the data, while the values from the median to the highest make up the upper half.

We must first organize the numbers in numerical order: 93.5, 96.3, 97.9, 98.9, 99.3, 101.1, 103.9, 104.8, 105.1, 109.5. This will help us determine the median of the lower half of the data. The lower half's mean, which is (99.3 + 101.1) / 2 = 100.2, is then the average of the fifth and sixth values.

Again, the numbers must be arranged in numerical order to determine the median of the upper half of the data: 93.5, 96.3, 97.9, 98.9, 99.3, 101.1, 103.9, 104.8, 105.1, and 109.5. The average of the sixth and seventh numbers, or (101.1 + 103.9) / 2, equals 102.5, which is the median of the top half.

Following that, Q1 = 100 indicates the first and third quartiles.

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24 is represents the entry fee in  the amusement park.

A. The total amount of money Carlos will spend $24 if he goes on o rides.

B. The total amount of money Carlos will spend $26 if he goes on 1 ride

C. The change in the total amount of money he will spend $2 for every additional ride he goes on.

D.  The total amount of money Carlos will spend $224 if he goes on 100 rides.

What is a variable?

Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.

Given equation is  y = 2x + 24

24 is represents the entry fee in  the amusement park.

where y represents the total amount of money, in dollars and cents, and a represents the number of rides Carlos goes on.

Putting x = 0 in the equation to find the total amount of money Carlos will spend if he goes on o rides:

y = (2 × 0) + 24

y = 24

Putting x = 1 in the equation to find the total amount of money Carlos will spend if he goes on 1 rides:

y = (2 × 1) + 24

y = 2 + 24

y = 26

The change in the total amount of money he will spend for every additional ride he goes on is $26 - 24 = $2

Putting x = 100 in the equation to find the total amount of money Carlos will spend if he goes on 100 rides:

y = (2 × 100) + 24

y = 200 + 24

y = 224

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Answer:

5%

Step-by-step explanation:

Interest = deposit * annual rate * years

 1500   = 3000 * rate * 10 yrs

1500/(3000*10)  = rate in decimal form = .05   = 5 %

The following statements are correct,

a.) Is used to determine the fit of a model.

b.) Can be inflated by adding more variables.

c.) Referred to as the coefficient of determination

d.) Represents the percent of variability in y that can be explained by the model.

e.) In simple linear regression, it is equal to the correlation coefficient r².

Define Regression Analysis

Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

R² ≡ 1 - SS(res) / SS(tot)

SS(res) + SS(reg) = SS(tot)

R² = SS(reg) / SS(tot) = (SS(reg)/n) / ( SS(tot)/n )

Where,

    SS(tot) = ∑ (y - y(bar) )₂

     SS(reg) =  ∑ (f(i) - y(bar) )²

      SS(res) =  ∑ (y(i) - f(i) )² = ∑e²(i)

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Answer: 12

Step-by-step explanation:

7(3)-2(4)-1=12

The value of x nearest hundredth of an inch is 18.19 inches.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Given that total area of the window is 463 square inches

We will need to write an equation using area of a square an area of a semi circle to find the approximate value of x and we know the total area of the window.

Area of square = [tex]x^{2}[/tex]

The area of the semicircle = [tex]\frac{1}{2}[/tex]πr²

So the radius squared would be 1/4 X squared

And the total area is 463.

We've got to clean this up two times pi times 1/4 that would be 1/8 times pi .

Combine like terms which would be 1.4 x squared.

Divide both sides by 1.4 and take the positive square root.

182x=18

Round to the nearest 100th which would be 18.19.

So value of x which is diameter of semicircle nearest 100th is = 18.19

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H(t) = [tex]\left \{ {{0 if t < 0} \atop {1 if t \geq 0}} \right.[/tex]

As t→0 from the left, H(t) approaches 0, as t→0 from right H(t) approaches 1.

From Laplace transformation definition:

L{f(t)} = [tex]\int\limits^\alpha _0 {e^{-st} f(t)} \, dt[/tex]

Given, H(t) = [tex]\left \{ {{0 if t < 0} \atop {1 if t \geq 0}} \right.[/tex]

Then

L{H(t)} = [tex]\int\limits^1_0 {e^{-st} H(t) } \, dt+\int\limits^\alpha _1 {e^{-st} H(t) } \, dt[/tex]

[tex]=\int\limits^1_0 {e^{-st} (0) } \, dt+\int\limits^\alpha _1 {e^{-st} (1) } \, dt[/tex]

[tex]=[\frac{e^{-st} }{-s} ]^{\alpha }_{1}[/tex]

[tex]=\frac{e^{-st} }{s}[/tex]

L{H(t)} =[tex]\frac{e^{-st} }{s}[/tex]

As t→0 from the left, H(t) approaches 0, as t→0 from right H(t) approaches 1.

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The time for which the cost is the same for both companies is given as follows:

10 minutes.

As the cost per unit of time is constant for each company, the cost functions are linear functions.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients and their meaning are given as follows:

Then the cost functions are given as follows:

Then the costs will be the same when:

1 + 0.2x = 2 + 0.1x

0.1x = 1

x = 1/0.1

x = 10 minutes.

The graph for the cost for Spin Scooter Rentals is given by the image shown at the end of the answer.

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Answer:

45

Step-by-step explanation:

two negative numbers multiplied equals a positive number

Answer:

False

Step-by-step explanation:

Lines that intersect at 90 degrees are called perpendicular lines.

Skew lines do not intercept.

P(V|B)>P(V|A)

P(V|B)>P(V|A), so Bob is more likely to have virus, however is is still very small probability (only 15%), so in order to confirm illness, he should make one more test.

P(A/V) = 0.95

From the text we can also conclude,  that

P(A| V) = 0.1

P(B|V) = 0.9

P(B| V) = 0.5

P(V)= 0.1

What we need to calculate and compare is P( V |A) and P(V|B)

P(V∩A) = P(A) . P(V|A) => P(V|A)

P(V∩A) / P(A)

P(V∩A) means, that Joe has a virus and its detected so.,

P(V∩A) = P(A) . P(V|A) = 0.01 × 0.95

= 0.0095

P(A) is sum of two options: "Joe has virus and it is detected" and "Joe has no virus, but it was mistakenly detected", therefore:

P(A) = P(A) . P(V|A) + P(≈V)

P(A|≈V) = 0.01 . 0.95 + 0.99 . 0.1

= 0.1085

Dividing those 2 numbers we obtain

P(V|A) = 0.0095 / 0.1085

= 0.0875576036

Analogically,

P(V|B) = P(V∩B) / P(B)

= 0.01 . 0.9 / 0.01 . 0.9 + 0.99 . 0.1

= 0.1538461we observe that P(V|B) > P(V|A) ,  

so Bob is more likely to have virus, however is is still very small probability (only 15%), so in order to confirm illness, he should make one more test.

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The two relations that are also functions are:

A relation is a function if and only if each point in the domain is mapped into a single value of the range.

So for example, the following relation:

{ (a, b), (a, c), (d, f)}

The input a is mapped into two different outputs, thus, this is not a function.

Then from the given options the ones that can be functions are:

S = { (-1, 0), (3, 2), (5, 4), (8, 9), (15, 12)}

R = {(0, -1), (2, 1), (5, 4), (7, 9), (14, 12)}

In all the other relations we can see inputs mapped into more than one output.

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Answer:

The time at which the football reaches its highest point is 0.5 seconds.

Step-by-step explanation:

The height of an object thrown into the air is determined by the formula h(t) = -16t^2 + vt + h, where t represents the time in seconds after the object is thrown, v is the initial velocity with which the object is thrown, and h is the initial height from which the object is thrown. In this case, the initial velocity of the object is 16 feet per second and the initial height is 0 feet.

To find the time at which the football reaches its highest point, we need to find the value of t that makes the value of h(t) maximum. This value of t can be found by taking the derivative of the equation h(t) and setting it equal to 0. The derivative of h(t) is given by h'(t) = -32t + 16. Setting h'(t) equal to 0, we get -32t + 16 = 0, which can be solved to get t = 0.5 seconds.

Therefore, the time at which the football reaches its highest point is 0.5 seconds.

An inequality is a mathematical statement that compares two expressions using an inequality symbol. In this case, we have two inequalities that involve the variables \(x\) and \(y\): \(y > -\frac{1}{2} x 2\) and \(2x y \le 8\).

To find the points that satisfy these two inequalities, we must first solve for both \(x\) and \(y\).

To find the points that satisfy the first inequality, we can solve for \(y\) and substitute it into the second inequality:

\[y > -\frac{1}{2} x 2 \implies y = -\frac{1}{2} x 2 + k \quad \text{where} \quad k > 0\]

\[2x (-\frac{1}{2} x 2 + k) \le 8 \implies x^2 - 4x + 8 \le 0\]

Solving for \(x\) yields two solutions: \(x = 2 \pm \sqrt{2}\). To find the points that satisfy both inequalities, we must test both of these solutions in the original inequalities. For \(x = 2 + \sqrt{2}\), we have:

\[y > -\frac{1}{2} \cdot (2 + \sqrt{2}) \cdot 2 \implies y > 4 - 4\sqrt{2}\]

\[2 \cdot (2 + \sqrt{2}) \cdot y \le 8 \implies 8 + 8\sqrt{2} \le 8 \quad \text{which is true}\]

Therefore, the point \((2 + \sqrt{2}, 4 - 4\sqrt{2})\) satisfies both inequalities. For \(x = 2 - \sqrt{2}\), we have:

\[y > -\frac{1}{2} \cdot (2 - \sqrt{2}) \cdot 2 \implies y > 4 + 4\sqrt{2}\]

\[2 \cdot (2 - \sqrt{2}) \cdot y \le 8 \implies 8 - 8\sqrt{2} \le 8 \quad \text{which is true}\]

Therefore, the point \((2 - \sqrt{2}, 4 + 4\sqrt{2})\) also satisfies both inequalities.

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