To indirectly measure the distance across a river, Arun stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Arun draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

Answer:

Step-by-step explanation:

1)  The equation of circle  having center at origin:

       x² + y² = r²

Where 'r' is the radius.

diameter = 36

r = 36 ÷ 2 = 18

  Equation of circle :

      x² + y² = 18²

       x² + y² = 324

Option d.

2) Find the discriminant D.

 If  D > 0, then the quadratic equation has two distinct real roots.

  If  D= 0, then the quadratic equation has two identical real roots.

  If  D < 0, then the quadratic equation has no real roots.

  D = b² - 4ac

 x² - 6x + 9 = 0

a = 1  ; b = -6 ; c = 9

D = (-6)² - 4*1*9

  = 36 - 36

D = 0

As D = 0, the quadratic equation has two identical real roots

Option a.

3) The axis of symmetry of a parabola is the vertical line passing through the vertex. It will be middle of the x-intercepts.

X- intercepts are -8 , 2

 ( -8 + 2 ) ÷ 2 = -6 ÷ 2  =  -3

x = - 3

Option d.

Using the surface area formula for rectangular and triangular prism, the surface area of the composite figure is: 444 m².

Total surface area = surface area of the top triangular prism + surface area of the bottom rectangular prism - area of the surface both share together.

Surface area of the top triangular prism = (S1 + S2+ S3)L + bh = (10 + 10 + 16)5 + (16)(6) = 276 m².

Surface area of the bottom rectangular prism = 2(wl + hl + hw) = 2·(5·16+4·16+4·5) = 328 m²

Area of the surface both share together = 2(16)(5) = 160 m²

Total surface area = 276 + 328 - 160 = 444 m².

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Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]

The ratio of distance travelled by walking to distance travelled by bus is 1 : 6.

When two quantities of the same units are compared, the ratio is what shows how much of one quantity is included in the other.

Total no. of Feet in a Mile = 5280

Distance Gary walked to the bus stop = 220 feet

Distance travelled by bus = 1/4 mile = (1 / 4)*5280 = 1320 feet

Ratio of distance walking to distance by bus = 220 / 1320 = 1 : 6

Hence, the ratio of distance travelled by walking to distance travelled by bus is 1 : 6.

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Answer:

Perimeter: 4+[tex]\pi \\[/tex] mm

Area: [tex]\pi[/tex] mm^2

Step-by-step explanation:

Perimeter:

90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]

Area:

90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]

Answer: 7.14 mm and 3.14 mm²

Step-by-step explanation:

The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.

Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is

[tex]\frac{1}{2} \pi*2=\pi[/tex]

However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is

[tex]2+2=4[/tex]

By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.

The  area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.

[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]

Hence, the area is [tex]\pi[/tex], or around 3.14 mm².

Ratio scale of measurement for the following variable, The weight of a group of dieters.

Ratio measurement scale of ratio variables include height, weight, and distance. The ratio scale allows for the addition, subtraction, division, and multiplication of data. Additionally, ratio scales have a "real zero," which sets them apart from interval scales. The ratio scale is used to determine weight. The ratio is identical to the interval scale, with the exception that 0 on the scale denotes the absence of anything. serval scales can depict values lower than zero and do not hold a true zero. For instance, you can gauge temperatures as low as -10 degrees Celsius. Contrarily, ratio variables are always greater than zero. Height and weight are measured starting at 0 and never below it. Because they are numbers as we typically think of them, ratio scales are the simplest to comprehend. On a ratio scale, the distance between consecutive numbers is equal, and a score of zero indicates that there is no presence of the thing being measured. The majority of ratio scales are counts of items.

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Step-by-step explanation:

we use the point-slope approach :

y - y1 = m(x - x1)

m is the slope, and (x1, y1) is a point on the line.

so,

1.

y - 2 = 7(x - 1) = 7x - 7

y = 7x - 5

2.

y - -1 = -1×(x - 3) = -x + 3

y + 1 = -x + 3

y = -x + 2

3.

y - 5 = -4(x - -2) = -4x - 8 (3x a "-" is a "-" for 8)

y = -4x - 3

4.

y - 5 = 5/3 × (x - 3) = 5x/3 - 5

y = 5x/3 or 5/3 × x

Answer:

1. [tex]7x-y=5[/tex]

2. [tex]x+y=2[/tex]

3. [tex]4x+y=-3[/tex]

4. [tex]5x-3y=0[/tex]

Step-by-step explanation:

Since we already know the slope and the coordinates of one point, first use the point-slope form to create an equation.

[tex]y-k=m(x-h)[/tex]

[tex]y-2=7(x-1)[/tex]

[tex]y-2=7x-7[/tex]

[tex]7x-y=5[/tex]

[tex]y+1=-1(x-3)[/tex]

[tex]y+1=-x+3[/tex]

[tex]x+y=2[/tex]

[tex]y-5=-4(x+2)[/tex]

[tex]y-5=-4x-8[/tex]

[tex]4x+y=-3[/tex]

[tex]y-5=\frac{5}{3} (x-3)[/tex]

[tex]y-5=\frac{5}{3}x-5[/tex]

[tex]3y-15=5x-15[/tex]

[tex]5x-3y=0[/tex]

Let X be the number of times you win.

The total number of ways to select 2 balls (order does not matter) =>

The number of ways so that two balls are white:

= 3/55

The number of ways so that two balls are red:

= 3/55

The number of ways so that one ball is red, one is white:

= 9

The number of ways so that two balls are blue:

= 10

i.e. p = 10+9/55 = 19/55

The number of ways so that one ball is blue, one is white:

p = 15/55 = 3/11

The number of ways so that one ball is blue, one is red:

15/55 = 3/11

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Answer:

f-¹(x) = (x + 6)/2

Step-by-step explanation:

Replace f(x) with y.

y = 2x – 6

Interchange x and y.

x = 2y – 6

Solve for y.

y = (x + 6)/2

Replace y with  f-¹(x)

f-¹(x) = (x + 6)/2

Answer:

  (b)  I, III

Step-by-step explanation:

The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).

The leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.

If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.

The answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).

  f(2) = 2² -7·2 +10 = 4 -14 +10 = 0

  f(5) = 5² -7·5 +10 = 25 -35 +10 = 0

This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.

Answer:

15

Step-by-step explanation:

The blue angle and the yellow angle form a linear pair, so they are supplementary (angle measures add up to 180).

180 - 165 = 15

The surface area of the composite figure is 524 square meters

The given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:

Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)

Take the sum

Surface area = 2(80+20+64) + 96 + 100

Surface area = 2(164) +196

Surface area = 328 + 196

Surface area = 524 square meters

Hence the surface area of the composite figure is 524 square meters

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The percentage of great lakes states would we expect the economic impact from fishing to be between $234.5 and $401.5 is 50%.

Given that mean is $318 , standard deviation is $83.5 and confidence interval is $234.5 and $401.5.

We have to calculate the percentage of great  lakes that we would expect the economic impact from fishing to be between $234.5 and $401.5.

Because we have not given the sample size taken so we will use any test.We are using z test.

We know that,

z=X-μ/σ

where μ is population mean and σ is population standard deviation.

We cannot find p value between $234.5 and $401.5. We have to find the p value between $234.5 and $318 and then add the p value between $318 and $401.5 by calculating.

P value between $234.5 and $318:

z=234.5-318/83.5

=-83.5/83.5

=-1

p value of -1 is 0.1587

P value between $318 and $401.5:

z=401.5-318.5/83.5

=83.5/83.5

=1

p value of z=1 is 0.3413

Total p value=0.1587+0.3413

=0.5

Total percentage=0.5*100

=50%

Hence the percentage that we would expect the impact to be between $234.5 and $401.5 is 50%.

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The correct statements about the two-way frequency table are:

Option C, and Option E.

According to the statement

we have to check that the given statement is applicable or not on the given conditions.

So, For this purpose

The two-way frequency table is

In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).

the given options are:

Option A the row categories are "wears glasses"

Option B and "do not wear glasses."

Option C two teachers do not wear glasses.

Option D thirty-six students wear glasses.

Option E a total of 6 teachers were polled.

So, The correct statements about the two-way frequency table are:

Option C, and Option E.

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Answer: the corret answer is A, C and E

The numerator in the fixed asset turnover ratio is sales.

To determine the fixed Asset Turnover ratio, the subsequent components are used: fixed Asset Turnover = sales / common fixed property.

The fixed asset turnover ratio exhibits how green an employer is at generating sales from its current fixed assets. A higher ratio implies that control is the usage of its fixed property extra efficiently.

Within the retail region, an asset turnover ratio of 2.5 or greater can be considered good, even as a business enterprise in the software region is much more likely to intention an asset turnover ratio it is among zero.25 and 0.5.

We can now calculate the constant asset turnover ratio by dividing the internet revenue for the yr through the average constant asset balance, which is equal to the sum of the modern-day and earlier duration balance divided through two.

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Answer:

[tex]3y^{2} -3y-5[/tex]

Answer:

9,240

Step-by-step explanation:

For the first number, there are 22 numbers available to choose from. For the second number, there are 21 numbers available, since the first number cannot be the same as the second number. And for the last number, there are 20 remaining numbers to choose from. So, there are 22*21*20=9240 possible sequences.

Answer:

1

Step-by-step explanation:

[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]

When an spherical balloon volume is increasing at the rate of [tex]3ft^3/min[/tex] then the diameter of the balloon is increasing [tex]\frac{3}{2\pi }ft /min[/tex]

How can we find the rate of change of balloon's diameter ?

The volume of a spherical balloon is [tex]v=\frac{4}{3} \pi r^3[/tex]

In form of diameter we can write as

[tex]v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3[/tex]

Now we will differentiate both sides wrt to [tex]t[/tex] we get

[tex]\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft[/tex]

Given in the question [tex]\frac{dv}{dt} =3ft^3/min[/tex]

thus when we substitute the values we get

[tex]\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min[/tex]

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Answer:

The answers are in the image

Step-by-step explanation:

The solution is in the attached image

The true average strain in a way that conveys information about precision and reliability is 27.314.

Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.

We have to calculate the true average strain in a way that conveys information about precision and reliability.

We have to use t test in our problem because sample size is less than 30.

Weknow that,

t=x bar-μ/s[tex]\sqrt{n}[/tex]

where μ is sample mean,

s is sample standard deviation.

Degree of freedom=n-1

=20-1

=19

T value at 95% confidence interval=1.7281

put the values in the formula of t given above.

1.7291=x bar-26/3.4/[tex]\sqrt{20}[/tex]

1.7291=xbar-26/3.4/4.47

1.7291= x bar-26/0.76

1.7291*0.76=x bar-26

1.314=x bar-26

x bar=26+1.314

x bar=27.314

After rounding it will be 27.31

Hence the true average strain in a way that conveys information about precision and reliability is 27.31%.

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Answer:

See below

Step-by-step explanation:

Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear

The equation of a circle whose centre ([tex]-5,-2[/tex]) and radius [tex]2[/tex] is [tex]x^{2}+y^{2}+10x+4y+25=0[/tex]

What is equation of a circle?

A circle is a closed curve drawn from a fixed point called centre of the circle. The distance between the centre of the circle and the arc of the circle is called the radius of the circle.

The equation of a circle with centre [tex](h, k)[/tex] radius [tex]r[/tex] is

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

Given center = [tex](-5,-2)[/tex]  and Radius = [tex]2[/tex]

Put the Given value in the equation:

= [tex](x-(-5))^{2} +(y-(-2))^{2} = 2^{2}[/tex]

= [tex](x+5)^{2} +(y+2)^{2}=2^{2}[/tex]

= [tex](x^{2} +10x+25)+(y^{2}+4y+4)= 4[/tex]

= [tex]x^{2} +y^{2}+10x+ 4y+ 29 = 4[/tex]

= [tex]x^{2} +y^{2}+10x +4y+ 29-4=0[/tex]

= [tex]x^{2} +y^{2}+10x+4y+25=0[/tex]

So, the equation of the circle whose centre is [tex](-5,-2)[/tex] and Radius [tex]2[/tex] is

[tex]x^{2}+y^{2}+10x+4y+25=0[/tex]

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Answer: x-y

Step-by-step explanation:

If x>y, then [tex]x-y > 0[/tex].

So, [tex]|x-y|=x-y[/tex]

The solution of the expression  |x-y| if x>y without using absolute value notation is  (x - y).

A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression

Example = 4y, 3x+4

The absolute value of any number or expression is always positive.

An expression that is either less than or greater than is called as inequality.

Given expression,  |x-y| and the given inequality is x>y.

When x is greater than y, the difference between x and y is already positive.

So, the expression will be (x-y).

So, if x > y, then |x - y| = (x - y).

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The amount of paint needed to cover the wall is 112 square feet

The given parameters are:

Parallel bases = 8 feet and 20 feet

Height = 8 feet

The area is calculated as:

Area = 0.5 * (Sum of parallel bases) * Height

So, we have;

Area = 0.5 * (8 + 20) * 8

Evaluate

Area = 112

Hence, the amount of paint needed to cover the wall is 112 square feet

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Answer:

B.) The graph of g(x) is shifted 4 units up

Step-by-step explanation:

In a linear function in slope-intercept form, b, or 4 in this case, represents the y-intercept which technically acts as a vertical shift

The expression 3 - 7p² + 11(4 + n) to find an example of each kind of expression is;

3 - 7p² + 11(4 + n)

The expression has 3 parts

3 - 7p² + 11(4 + n)

= 3 - 7p² + 44 + 11n

= 47 + 7p² + 11n

Complete question:

Use the expression 3 — 7p2 + 11(4 + n ) to find an example of each kind of expression

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Answer: 3n+3

Step-by-step explanation:

Adding 1 to an odd number results in an even number.