An author is doing research on an upcoming book on skyscrapers in America. The author gathers data for 10 skyscrapers throughout America and decides to focus on the height data, given in meters, which are reproduced below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the sample standard deviation and the sample variance. Round your answers to one decimal place.

The length of line segment QS is 17.

To find the length of line segment QS, we need to determine the values of x and then substitute them into the given equations.

Given:

Line segment RS = [tex]3x + 2[/tex]

Line segment SQ = [tex]5x - 8[/tex]

Since line l is the perpendicular bisector of line segment RQ, it means that line segments RS and SQ are equal in length.

Therefore, we can set up an equation:

[tex]3x + 2 = 5x - 8[/tex]

To solve for x, we can start by isolating the variable terms on one side:

[tex]2 + 8 = 5x - 3x[/tex]

[tex]10 = 2x[/tex]

Dividing both sides by 2:

[tex]x = \frac{10}{2}[/tex]

[tex]x = 5[/tex]

Now that we have found the value of x, we can substitute it into the equation for line segment SQ:

[tex]SQ = 5x - 8[/tex]

[tex]SQ = 5(5) - 8[/tex]

[tex]SQ = 25 - 8[/tex]

[tex]SQ = 17[/tex]

Therefore, the length of line segment QS is 17.

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The function with the steepest slope is [tex]y = 7x - 3[/tex].

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

[tex]y = -8x + 5[/tex]

Slope: -8

[tex]y - 9 = -2(x + 1)[/tex]

Simplifying, we get [tex]y - 9 = -2x - 2[/tex]

Rearranging, we have [tex]y = -2x + 7[/tex]

Slope: -2

[tex]y = 7x - 3[/tex]

Slope: 7

[tex]y + 2 = 6(x + 10)[/tex]

Simplifying, we get [tex]y + 2 = 6x + 60[/tex]

Rearranging, we have [tex]y = 6x + 58[/tex]

Slope: 6

Therefore, the steepest slope is the [tex]y = 7x - 3[/tex].

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The problem provides the attendance numbers for four specific days of the Boxerville Carnival: Saturday (800 people), Sunday (650 people), Monday (250 people), and Tuesday (350 people). The question asks for the total number of people who attended the carnival on the weekend.

Given that the information about Saturday and Sunday attendance is provided, we have enough information to determine the total number of people who attended the carnival on the weekend. We can simply add the attendance numbers for Saturday and Sunday:

800 + 650 = 1450 people.

Therefore, the problem has sufficient information to calculate the total attendance on the weekend. It is not excessive or lacking in detail, allowing us to accurately find the desired answer.

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Answer:

Step-by-step explanation

You start by knowing that a triangle has 180 degrees in total and this is a right triangle so your total needs to add up to 90. Using the formula 90 subtract 45 then divided by 4+1 and there is your smaller angle.

The universal set for sets A, B, and C is {0, 1, 2, 3, 4, 5, 6, 8}.

The universal set is the set that contains all the elements under consideration. In this case, we have three sets: A, B, and C. To determine the universal set for all three sets, we need to identify the set that includes all the unique elements from each of the individual sets.

Set A contains the elements {1, 3, 5}, Set B contains the elements {2, 4, 6}, and Set C contains the elements {0, 2, 4, 6, 8}. To form the universal set, we need to combine all these elements without any repetition.

By observing the elements in Sets A, B, and C, we can see that the universal set would be the set that includes all the unique elements from these sets. Therefore, the universal set for all three sets is the set that contains {0, 1, 2, 3, 4, 5, 6, 8}.

This means that any element that is present in at least one of the sets A, B, or C is included in the universal set. It covers all the possible elements that can be found in these sets.

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Question

If set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then write the universal set for all three sets.

The value of x in the rhombus ABCD is determined as 23.

option B.

The value of x is calculated by applying the following formula as shown below.

the diagonals of a rhombus intersects at 90 degrees;

the complementary angle of  (4x - 25) = 90 - (4x - 25)

90 - (4x - 25) = x (alternate angles are equal)

90 - 4x + 25 = x

115 = 4x + x

115 = 5x

divide both sides of the equation by 5 to obtain the value of x;

5x = 115

x = 115 / 5

x = 23

Thus, the value of x in the rhombus ABCD is determined as 23.

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Answer:

The lines are not perpendicular because the product of their slopes is not -1.

Step-by-step explanation:

y = 5x - 1

slope = 5

10x + 2y = 0

2y = -10x

y = -5x

slope = -5

The slopes are 5 and -5.

5 × (-5) = -25

The product of the slopes is -25, not -1, so the lines are not peropendicular.

Answer:

The line are not perpendicular.  Perpendicular lines after opposite reciprocals.

Step-by-step explanation:

Change 10x + 2y = 0 into the slope intercept form of a line.

Subtract 10x from both sides

10x - 10x + 2y = 0 - 10 x

2y = -10x  Divide both sides by 2

y = -10x/2

y = -5x.

The slope of the first equation is 5 ( y = 5x -1 ).

The slope of the second equation is -5 ( y = -5x )

The opposite reciprocal of 5 would be -1/5 not -5.

So these lines are not perpendicular.

Helping in the name of Jesus.

Therefore, it will take approximately 7.67 minutes to fill the wading pool completely.

The round wading pool has a diameter of 115 cm and a depth of 25 cm. To find the volume of the pool, we can use the formula for the volume of a cylinder, which is

V = πr^2h.

Since the pool is round, the radius (r) is half the diameter, which is

115 cm / 2 = 57.5 cm.

Plugging in the values, we have

V = π(57.5 cm)^2 * 25 cm ≈ 260,979 cm^3.

The hose is filling the pool at a rate of 34,000 cm^3 per minute.

To determine how long it will take to fill the pool, we divide the volume of the pool by the rate of filling:

260,979 cm^3 / 34,000 cm^3/min ≈ 7.67 minutes.

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The statement for the function of random variable "The density of Y can be found by differentiating the CDF of Y" is false.

The density of a random variable can be found by differentiating its CDF, but only if the random variable is continuous. The random variable X in this case is discrete, so its density cannot be found by differentiating its CDF.

The CDF of a discrete random variable is a step function, which means that it has a jump discontinuity at each point where the value of the random variable changes.

The derivative of a step function is a Dirac delta function, which is a mathematical object that represents a point mass at a specific value. The density of a discrete random variable is the sum of the Dirac delta functions at each point where the value of the random variable changes.

In this case, the CDF of Y is a step function, so its derivative is a Dirac delta function. The density of Y is the sum of the Dirac delta functions at each point where the value of Y changes. However, the value of Y can only change at integer values, so the density of Y is a discrete function, not a continuous function.

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Answer:

To calculate the future value of your monthly investments after saving your money, i can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future Value

P = Monthly investment amount

r = Monthly interest rate

n = Number of months

Given:

Monthly investment amount (P) = 49,000 VNĐ

Monthly interest rate (r) = 6.3% / 12 = 0.00525

Number of months (n) = 10 years * 12 months/year = 120 months

Plugging in these values, i can calculate the future value:

FV = 49,000 * ((1 + 0.00525)^120 - 1) / 0.00525

Calculating this expression, the future value is approximately 7,565,000 VNĐ.

Therefore, after 10 years of investing 49,000 VNĐ per month and earning an interest rate of 6.3% per year, you would have approximately 7,565,000 VNĐ.

Therefore, the length of the photo after the enlargement is 9 inches.

The initial length of the photo is given as 4 inches. After the enlargement, the length becomes 5 more inches. To find the final length, we can add 5 inches to the initial length.

Initial length of the photo: 4 inches

Additional length after enlargement: 5 inches

Final length = Initial length + Additional length

Final length = 4 inches + 5 inches

Final length = 9 inches

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Answer: Triangle C only

Step-by-step explanation: using the formula to find out if the triangle are right angle (a^2+b^2=c^2) the legs are supposed to equal to the hypotenuse. A and B arentaren't equal to the hypotenuse

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = [tex]\frac{PQ}{AB +BQ}[/tex]

[tex]=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}[/tex]

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

[tex]PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}[/tex]

[tex]= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4[/tex]

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The point of intersection of the ellipse with the x-axis is $(\pm \sqrt{2}, 0)$.

To find the point of intersection of the ellipse with the x-axis, we can start by considering the distance between the foci $F_1$ and $F_2$. Using the distance formula, we find that the distance between $F_1$ and $F_2$ is $\sqrt{(2-0)^2 + (0-2)^2} = \sqrt{8} = 2\sqrt{2}$.

Since the ellipse passes through the origin, the sum of the distances from any point on the ellipse to the foci will be equal to the length of the major axis. In this case, the sum of the distances is $2a$, where $a$ represents the semi-major axis.

Since the foci are located at $(0,2)$ and $(2,0)$, we can see that $2a = 2\sqrt{2}$. Solving for $a$, we find $a = \sqrt{2}$.

Now, we can write the equation of the ellipse centered at the origin as $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Since the ellipse passes through the origin, we know that the y-coordinate of the point of intersection on the x-axis is 0.

Substituting $y = 0$ into the equation, we have $\frac{x^2}{(\sqrt{2})^2} + \frac{0^2}{b^2} = 1$, which simplifies to $\frac{x^2}{2} = 1$.

Solving for $x$, we find $x = \pm \sqrt{2}$.

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Answer:

a) 81

b) 83

c) science

Step-by-step explanation:

a)

f(x) = 0.5x + 80

gn x = 2 tests

⇒ f(2) = 0.5(2) + 80

= 1 + 80

= 81

b)

gn x = 2

g(2) = 83

c)

we have g(x) = mx + b

m = (y₂-y₁)/(x₂-x₁)

= (83 - 81)/(2 - 1)

m = 2

for g(1),

g(1) = m(1) + b

81 = 2(1) + b

b = 81 -2

b = 79

⇒ g(x) = 2x + 79

and f(x) = 0.5x + 80

for 4 tests, we have x = 4

g(4) = 2(4) + 79

= 8 + 79

g(4) = 87

f(4) = 0.5(4) + 80

= 2 + 80

f(4) = 82

g(4) = 87 > f(4) = 82

∴Science class has a higher average

The completely factorized form of the expression q² - 4 is (q + 2)(q - 2).

Given the expression in the question:

q² - 4

To factorize the expression q² - 4 completely, we can use the formula for the difference of squares.

The difference of squares formula states that :

a² - b² can be factored as (a + b)(a - b).

Given that:

q² - 4

Replace 4 with 2²
q² - 2²

From this expression, let a = x and b = 2

a² - b² =  (a + b)(a - b)

q² - 2² = (q + 2)(q - 2)

Therefore, the factored form is (q + 2)(q - 2).

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Answer:74

Step-by-step explanation:

DCB arc's degree is equal to 2*<DAB so,

arc DCB=106*2=212 degrees

cicle is 360 degrees total, so,

360-212=148 degrees

and it is arc DAB which is arc for <DCB and same rule applies here:

arc DAB=2*<DCB

<DCB=DAB/2=148/2=74

The following are the solutions to the given problem:A. Cost of Equity Capital:Given,Beta of the firm = 1.00Risk-Free Rate (Rf) = 3.5%Equity Risk Premium = 6%Cost of Equity (Re) = Rf + Beta*(Equity Risk Premium)Re = 3.5% + 1.00(6%)Re = 9.5%B. After-Tax Cost of Debt:Given,

Pre-tax cost of debt = 4.5%Tax rate = 40%

After-tax cost of debt (Rd) = Pre-tax cost of debt x (1 - Tax Rate)Rd = 4.5% x (1 - 0.40)Rd = 2.7%C. Weighted Average Cost of Capital (WACC):Given,

Weightage of Equity (We) = 100 million shares / 100 million shares + 250 million of debtWe = 28.57%Weightage of Debt (Wd) = 250 million of debt / 100 million shares + 250 million of debt

Wd = 71.43%WACC = (We x Re) + (Wd x Rd)WACC = (28.57% x 9.5%) + (71.43% x 2.7%)WACC = 3.91%D. Cost of Equity after Restructuring:Given,New Default Spread = 3 x Old Default SpreadOld Default Spread = 2.7% - 3.5%Old Default Spread = -0.8%New Default Spread = 3 x -0.8%

New Default Spread = -2.4%New After-tax Cost of Debt (Rd) = 2.7% + (-2.4%)Rd = 0.3%New Weightage of Debt (Wd) = 750 million of debt / 100 million shares + 750 million of debt

Wd = 88.24%New Weightage of Equity (We) = 100 million shares / 100 million shares + 750 million of debtWe = 11.76%New Cost of Equity (Re) = 9.5%Re = 9.5%New WACC

= (We x Re) + (Wd x Rd)New WACC = (11.76% x 9.5%) + (88.24% x 0.3%)New WACC = 0.53%E. After-tax Cost of Debt after Restructuring:Given,

New After-tax Cost of Debt (Rd) = 0.3%F. WACC after Restructuring:New WACC = 0.53%G. Value (Price) per Share for the Remaining Shareholders in the Company:Given,

New Shares = 500 million / $11 per share = 45,454,545 shares New Equity Shares = 100 million shares + 45,454,545 shares = 145,454,545 shares Value of Equity = 145,454,545

shares x $11 per shareValue of Equity = $1,600,000,000Value per Share for the Remaining Shareholders in the Company = $1,600,000,000 / 100 million sharesValue per Share for the Remaining Shareholders in the Company = $16.00 per share.

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Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

The trigonometric functions for the angle with the least possible positive measure and the point (-2, √3) on the terminal side are:

sin(0) = √3/2

cos(0) = -1/2

tan(0) = -√3

csc(0) = 2/√3

sec(0) = -2

cot(0) = -1/√3

To sketch an angle in standard position, we start by placing the initial side along the positive x-axis. Since we want the angle with the least possible positive measure, we choose the smallest positive angle, which is 0 degrees or 0 radians.

Next, we plot the point (-2, √3) on the terminal side of the angle. This point lies in the third quadrant of the coordinate plane. We draw a line segment from the origin to this point, representing the terminal side of the angle.

To find the values of the trigonometric functions, we can use the coordinates of the point (-2, √3) to determine the side lengths of a right triangle. The x-coordinate (-2) represents the length of the adjacent side, and the y-coordinate (√3) represents the length of the opposite side. The hypotenuse can be found using the Pythagorean theorem.

Using the values of the sides, we can calculate the trigonometric functions:

sin(0) = opposite/hypotenuse = √3/2

cos(0) = adjacent/hypotenuse = -1/2

tan(0) = opposite/adjacent = -√3

csc(0) = 1/sin(0) = 2/√3

sec(0) = 1/cos(0) = -2

cot(0) = 1/tan(0) = -1/√3

The trigonometric functions for the angle with the least possible positive measure and the point (-2, √3) on the terminal side are:

sin(0) = √3/2

cos(0) = -1/2

tan(0) = -√3

csc(0) = 2/√3

sec(0) = -2

cot(0) = -1/√3

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The other number is 4, 658

Algebraic expressions are described as expressions that are made up of terms, variables, constants and factors.

These algebraic expressions are also made up of arithmetic operations such as;

From the information given, we have that;

sum of 2 number is 34,678

If one of the number is x and the other is 30, 020

Then, we have that;

x + 30,020 =34, 678

collect the like terms, we have;

x = 34, 678 - 30, 020

x = 4, 658

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Answer:

20. A. 357.8 in³

B. 1231.5 yd³

Step-by-step explanation:

20.

A.

Volume of Pyramid : ⅓*base area * height

here,

Base area = area of rectangle=length*breadth =10*8=80in²

Now

Height can be calculated by using Pythagorous theorem

height =[tex]\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}[/tex]

height =[tex]\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in[/tex]

height =13.4 in

Now

Volume of pyramid = ⅓*base area *height

Volume of Pyramid=⅓*80*13.42

Volume of Pyramid=357.8 in³

B.

Volume of cone = ⅓*area of base* height

Here

slant height=24 yd

height =?

diameter=14yd

radius =14/2=7 yd

Let's find the height:

By using the Pythagorous theorem,

slight height²=radius²+height²

substituting value

25²=7²+height²

height²=25²-7²

height =[tex]\sqrt{576}[/tex]=24 yd

Now

Area of Base= πr²=π*7²=153.94 yd²

Now

Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³

So,

Volume of cone is 1231.52 yd³.

Answer:

19. A. 108 mm²

B. 404.5 in²

Step-by-step explanation:

19:

Area of Big triangle: ½*base*height

=½*(18mm+10mm)+12mm

=168mm²

Area of Small triangle=½*base*height

=½*10mm*12mm

=60mm²

Now

Area of shaded region=Area of Big triangle - Area of Small triangle

=168-60

=108 mm²

Therefore Area is 108mm².

20.

We know that:

Area of Parallelogram=Base*Height

here

Base=26 in

let's find height

Sin 45°=Opposite/Hypotenuse

Sin 45°=Height/22

Height=Sin 45°*22

Height=[tex]\frac{1}{\sqrt{2}}*22=11\sqrt{2}[/tex]=15.56

Now,

Area of parallelogram= base*height=26*15.56=404.5 in²

Therefore, Area of Parallelogram=404.5 in²

Hello!

angle1 = (360° - 2 * 150°)/2 = 30°

angle2 = (360° - 2 * 95°)/2 = 85°

y° = 180° - (30° + 85°) = 65°

Answer:

The answer is,

[tex]\sqrt{3}/2[/tex]

Step-by-step explanation:

Since we have cos10cos20 - sin10sin20,

We can use the formula,

cos(a+b) = (cosa)(cosb) - (sina)(sinb)

So, we have,

cos10cos20 - sin10sin20 = cos(10 + 20)

= cos(30)

cos(30) =  sqrt(3)/2

[tex]cos(30) = \sqrt{3}/2[/tex]

The sketch of the front elevation and the side elevation of the prism are added as an attachment

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

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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Therefore, Moira sold approximately 140% as many jars in the second month compared to the first month. This means the number of jars sold in the second month was 140% of the number sold in the first month.

To find the second month's sales as a percentage of the first month's sales, we need to divide the number of jars sold in the second month by the number sold in the first month and then multiply by 100 to get the percentage.

Number of jars sold in the second month: 203

Number of jars sold in the first month: 145

Percentage of second month's sales = (203 / 145) * 100 ≈ 140%

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Selena and Drake both are correct.

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Answer: 19

Step-by-step explanation:

x^2+4x-15=0. To complete the square, it needs to be (x+2)^2, which is x^2+4x+4. Thus, you need to add 19.