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
�
�
PR, the distance across the river. Round your answer to the nearest foot.
P
R
O
C
E

Answer:$7.49

Step-by-step explanation:

just subtract 42.50 from 49.99
49.99-42.50=7.49

The volume of the solid is 284π/3 cubic inches.

To find the volume of the solid, we need to break it down into simpler shapes and then calculate their volumes separately.

The solid is made up of a cylinder and a hemispherical hole cut from the top of it. Let's first calculate the volume of the cylinder. The height of the cylinder is given as 12 inches and the radius can be calculated as half of the hypotenuse of the triangle (which is 10 inches). Therefore, the radius of the cylinder is 5 inches.

The formula for the volume of a cylinder is Vcylinder = πr^2h, where r is the radius and h is the height. Substituting the values, we get:

Vcylinder = π(5^2)(12) = 300π cubic inches

Now, let's calculate the volume of the hemispherical hole. The rim of the hole is 3 inches thick, which means the radius of the hole is (5 - 3) = 2 inches. The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3.

Substituting the values, we get:

Vhemisphere = (2/3)π(2^3) = 16π/3 cubic inches

Now, the volume of the solid can be found by subtracting the volume of the hemispherical hole from the volume of the cylinder:

Vsolid = Vcylinder - Vhemisphere

Vsolid = 300π - 16π/3

Vsolid = 284π/3 cubic inches

Therefore, the volume of the solid is 284π/3 cubic inches.

For more such questions on Volume of solids

https://brainly.com/question/26712718

#SPJ4

A double number line means the values of two different quantities are expressed in two separate lines such as corresponding values align. Here 1ml of blue water will need 3 ml of yellow water.

Here double line represents the relation between yellow water and blue water required to produce green water. 5ml of blue water needs 15ml of yellow water.

So the ratio is 5 : 15

3. One division in the line for blue water represents 1ml and 1 division in yellow water line is 3 ml.

We can also solve it using proportions

5 : 15 :: 1: x

5/15 = 1/x

x = (1×15)/5 = 3 ml

4. For 11 ml of blue water, it will require 33 ml of yellow water.

5. For 8 ml of blue water, 24 ml of yellow water is needed.

6. If we know the volume needed with 1ml of blue water, we can multiply that volume with any quantities of blue water to calculate the volume needed. For example 4 ml of blue water needs 4×3 = 12 ml of yellow water.

For more information regarding double number line, kindly refer

https://brainly.com/question/13553589

#SPJ4

The complete question is as below.

The other day, we made green water by mixing 5 ml of blue water with 15 ml of yellow water. We want to make a very small batch of the same shade of green water. We need to know how much yellow water to mix with only 1 ml of blue water.

1. On the number line for blue water, label the four tick marks shown.

2. On the number line for yellow water, draw and label tick marks to show the amount of yellow water needed for each amount of blue water.

3. How much yellow water should be used for 1 ml of blue water? Circle where you can see this on the double number line.

4. How much yellow water should be used for 11 ml of blue water?

5. How much yellow water should be used for 8 ml of blue water?

6. Why is it useful to know how much yellow water should be used with 1 ml of blue water?

Answer:

Elizabeth gave away 216 marbles out of a total of 360 marbles.

To find the percentage of marbles that Elizabeth gave away, we can use the formula:

percentage = (part/whole) x 100%

where "part" is the number of marbles Elizabeth gave away, and "whole" is the total number of marbles.

So, plugging in the values we have:

percentage = (216/360) x 100%

percentage = 0.6 x 100%

percentage = 60%

Therefore, Elizabeth gave away 60% of the marbles.

8×4=32

11-8=3

4×3=12

12÷2=6

32+6=38

=38inch^2

it might b wrong tho?

Answer:

2500

Step-by-step explanation:

Total spectator 9500

Men 6375

Women and children = 9500-6375= 3125

Women X

Children 4X

If women and children = 3125

4x + X = 3125

5x = 3125

Divide both sides by 5

X = 625

Women 625

Children 625x4 = 2500

Answer:

We can express 25 pens out of 51 in ratio form as:

25:51

Answer:

We can start by simplifying each parentheses separately and then adding the resulting expressions:

(2^4 – 5^3 – 7) + (−5^5 − 5^2 + 9 + 17)

= (16 - 125 - 7) + (-3125 - 25 + 9 + 17) (using the fact that 2^4 = 16 and 5^3 = 125)

= (-116) + (-3124) (combining like terms)

= -3240

Therefore, the answer is -3240. To express this number in standard form, we write it as:

-3.24 x 10^3

The negative sign indicates that the number is less than zero, and the 3.24 tells us the value of the number. The "x 10^3" part means that we need to multiply 3.24 by 10^3 (which is 1000) to get the actual value of the number:

-3.24 x 10^3 = -3.24 * 1000 = -3240

So, the answer in standard form is -3.24 x 10^3.

Solving a linear equation we can see that he can afford to pay the monthly fee for 28 months

We know that there is an initial fee of $300 plus $7 per month, so the total cost after x months is:

C = 300 + 7*x

And we know that Julio has $500 set aside, then the equation that we need to solve is:

500 = 300 + 7x

500 - 300 = 7x

200 = 7x

200/7 = x = 28.5

Rounding down we get 28.

Learn more about linear equations at.

https://brainly.com/question/1884491

#SPJ1

Answer:

A. X = -4

Step-by-step explanation:

[tex]-6x-24=3x+12\\-9x=36\\x=-4[/tex]

Answer:

The inequality that would represent the possible values for the number of hours lifeguarding, l, and the number of hours walking dogs, d, that Katherine can work in a given week is:

l + d ≤ 14

This is because the sum of the hours worked in both jobs should not exceed 14 hours.

Answer:

slope = 4 , point on line (- 1, 3 )

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y - 3 = 4(x + 1) ← is in point- slope form

with slope m = 4 and (a, b ) = (- 1, 3 )

The measure of the central angle in the "Punk" section is 72 degrees.

The measure of the central angle in the "Punk" section can be determined by calculating the percentage of punk songs sold in relation to the total number of songs sold, and then converting that percentage to degrees.

To calculate the percentage of punk songs sold, divide the number of punk songs sold by the total number of songs sold, and multiply by 100.

For example, if 200 punk songs were sold and the total number of songs sold was 1000, the percentage of punk songs sold would be:

200/1000 * 100 = 20%

To convert this percentage to degrees, multiply the percentage by 360 (the total number of degrees in a circle).

20% * 360 = 72 degrees

Therefore, the measure of the central angle in the "Punk" section is 72 degrees.

Learn more about central angle at

https://brainly.com/question/15698342

#SPJ11

The product of 4/6-2a x 3-a/2 is equal to 2a-1. To calculate this, the fractions must first be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Next, the two terms should be multiplied together, resulting in 2a-1.

The product of 4/6-2a x 3-a/2 can be found by expanding the terms and then solving the equation. First, the fractions must be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Once the fractions are simplified, the two terms should be multiplied together, resulting in 2a-1. Now that the two terms have been multiplied, the equation can be expanded by using the Distributive Property. The equation should be written as (2/3-2a) x (3-a/2). This can be simplified by distributing the 2/3 and 3 across the parentheses. This results in (2-6a+2a^2) x (3-1/2a). Finally, the equation should be simplified by combining like terms. This results in 2-6a+2a^2+3-1/2a, which simplifies to 2a-1. Therefore, the product of 4/6-2a x 3-a/2 is equal to 2a-1.

Learn more about fraction here

https://brainly.com/question/10354322

#SPJ4

The number is 30.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum

Given that,

The sum of the digits of a certain two-digit number is 3.

Since it is a two digit number, there will be a tens place and a ones place.

Let x be the digit in tens place and y be the digit in ones place.

x + y = 3

The number can also be written as 10x + y, since x is in the tens place.

When the number is reversed, tens place changed to ones place and vice versa.

The reversed number is 10y + x.

Given that the value of the number is decreased by 27 when the digits is reversed.

Original number - 27 = Reversed number

10x + y - 27 = 10y + x

9x - 9y = 27

x - y = 3

Also, we have,

x + y = 3  [Equation 1]

x - y = 3   [Equation 2]

Adding the equations,

2x = 6

x = 6/2 = 3

Substituting in equation 1, y = 0

Hence the number is 30.

Learn more about Addition of numbers here :

https://brainly.com/question/29938698

#SPJ1

The angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

To find the angle between two vectors \( \mathbf{u} \) and \( \mathbf{v} \), we can use the formula:
\[ \cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\| \mathbf{u} \| \| \mathbf{v} \|} \]
where \( \theta \) is the angle between the vectors, \( \mathbf{u} \cdot \mathbf{v} \) is the dot product of the vectors, and \( \| \mathbf{u} \| \) and \( \| \mathbf{v} \| \) are the magnitudes of the vectors.

First, we need to find the dot product of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \mathbf{u} \cdot \mathbf{v} = (-4)(-5) + (-1)(-2) = 20 + 2 = 22 \]

Next, we need to find the magnitudes of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \| \mathbf{u} \| = \sqrt{(-4)^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \]
\[ \| \mathbf{v} \| = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \]

Now we can plug these values into the formula and solve for \( \theta \):
\[ \cos \theta = \frac{22}{\sqrt{17} \sqrt{29}} \]
\[ \theta = \cos^{-1} \left( \frac{22}{\sqrt{17} \sqrt{29}} \right) \]

Using a calculator, we find that \( \theta \approx 12.5 \) degrees.

Therefore, the angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

Learn more about Angle

brainly.com/question/28451077

#SPJ11

The total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

What is meant by surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. A solid object's surface area is a measurement of the overall space that the object's surface takes up. Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces.

1) This figure is a cuboid.

  It has six faces and the opposite faces are of equal dimensions.

The surface area of a cuboid is the sum of the areas of each face.

Length l = 10 ft

Width w = 6 ft

Height h = 8 ft

Surface area = 2lw+2lh+2hw = 2 ( lw+ lh+ hw)

                                     = 2 ( 10*6 + 10*8 + 8*6) = 376 sq. feet

2) This figure has 2 similar right triangle faces.

Sum of area of both triangles = 2 * 1/2 * base * height = 3 * 4 = 12 sq. feet

There are two rectangular faces.

Area of front rectangular face = 10 * 5 = 50 sq. feet

Area of base rectangular face = 10*3 = 30 sq. feet

 Total surface area = 12 + 50 + 30 = 92sq. feet

Therefore the total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

To learn more about the surface area, follow the link.

https://brainly.com/question/16519513

#SPJ1

Subtracting -2y² from -4y² + 5d will give us -2y² + 5d.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

To subtract the two polynomials, we first need to distribute the negative sign to the second polynomial.

So, (-4y² + 5d) - (-2y²) becomes -4y² + 5d + 2y².

Now, combine the like terms, which are the terms that contain y²:

-4y² + 5d + 2y² = (-4 + 2)y² + 5d

So, our final answer is:

-2y² + 5d.

Since our answer is in simplest terms, the final answer is -2y² + 5d.

Learn more about subtracting polynomials here: https://brainly.com/question/29783537.

#SPJ11

The greatest common factor of these three expressions, 28w, 8w⁵, and 20w⁴, is 4w.

The greatest common factor (GCF) of three univariate monomials is the largest factor that divides all three expressions. To find the GCF of 28w, 8w⁵, and 20w⁴, we need to find the largest factor that is common to all three expressions.

First, we need to find the GCF of the coefficients of the three expressions. The GCF of 28, 8, and 20 is 4.

Next, we need to find the GCF of the variables of the three expressions. The GCF of w, w⁵, and w⁴ is w, since it is the lowest power of w that is common to all three expressions.

Therefore, the GCF of 28w, 8w⁵, and 20w⁴ is 4w.

Learn more about greatest common factor here: https://brainly.com/question/219464.

#SPJ11

Answer:

Step-by-step explanation:

18

a) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 is 0.00153. b) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 comes out as 0.00153 percent

To find the monthly payment needed to repay a $40,000 loan over 20 years with a 0.5% interest rate per month, we can use the following formula: Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^-Number of payments)

Plugging in the given values: Monthly payment = ($40,000 * 0.005) / (1 - (1 + 0.005)^-240) Monthly payment = $200 / (1 - 0.334) Monthly payment = $200 / 0.666, Monthly payment = $300.30

Therefore, the monthly payment needed to repay the $40,000 loan over 20 years with a 0.5% interest rate per month is $300.30.To find the monthly interest rate for a $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53, we can use the same formula and rearrange it to solve for the monthly interest rate:

Monthly interest rate = (Monthly payment * (1 - (1 + Monthly interest rate)^-Number of payments)) / Loan amount. Plugging in the given values:

0.005 = ($544.53 * (1 - (1 + 0.005)^-240)) / $40,000

0.005 * $40,000 = $544.53 * (1 - (1 + 0.005)^-240)

$200 = $544.53 * (1 - (1 + 0.005)^-240)

$200 / $544.53 = 1 - (1 + 0.005)^-240

0.367 = 1 - (1 + 0.005)^-240

(1 + 0.005)^-240 = 0.633

1 + 0.005 = 0.633^-240

0.005 = 0.633^-240 - 1

0.005 = -0.367

Monthly interest rate = -0.367 / -240

Monthly interest rate = 0.00153

Know more about interest rate here:

https://brainly.com/question/13324776

#SPJ11

Answer:

Step-by-step explanation:

I just knew now I forgot sorry lol

so since 45000 split on a 7:10:13 ratio, so let's simply divide 45000 by (7+10+13) and distribute accordingly to each daughter.

[tex]\stackrel{Ana}{7}~~ : ~~\stackrel{Betty}{10}~~ : ~~\stackrel{Chandra}{13} \\\\\\ \stackrel{Ana}{7\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Betty}{10\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Chandra}{13\cdot \frac{45000}{7+10+13}} \\\\\\ \stackrel{Ana}{7\cdot 1500}~~ : ~~\stackrel{Betty}{10\cdot 1500}~~ : ~~\stackrel{Chandra}{13\cdot 1500} ~~ \implies~\hfill \stackrel{Ana}{10500}~~ : ~~\stackrel{Betty}{15000}~~ : ~~\stackrel{Chandra}{19500}[/tex]

The value of x for the similar triangles is 8 units.

The value of x is determined by applying the principle of similar triangles as shown below.

In the given diagram, we can assume the following for the similar triangles;

length 10 is congruent to length 10 + (3x + 1 )

length 22 is congruent to length 7x -1  + 22

So we will have the following equation;

(3x + 1  + 10 )/ 10 = (7x - 1 + 22 ) / 22

(3x + 11 ) / 10 = ( 7x + 21 ) / 22

22(3x + 11 ) = 10 (7x + 21 )

66x + 242 = 70x + 210

32 = 4x

x = 32 / 4

x = 8

Learn more about similar triangles here: https://brainly.com/question/14285697

#SPJ1

To simplify the complex fraction ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2))), we can use the common denominator method.

Step 1: Find the common denominator for the numerator and denominator of the complex fraction. The common denominator for the numerator is (f^(3))(a^(3)) and the common denominator for the denominator is (f^(2))(a^(2)).

Step 2: Multiply each term in the numerator and denominator by the common denominator to get rid of the fractions.

Numerator: ((1)(a^(3))-(1)(f^(3)))/(f^(3))(a^(3))

Denominator: ((1)(a^(2))-(1)(f^(2)))/(f^(2))(a^(2))

Step 3: Simplify the numerator and denominator by combining like terms.

Numerator: (a^(3)-f^(3))/(f^(3))(a^(3))

Denominator: (a^(2)-f^(2))/(f^(2))(a^(2))

Step 4: Divide the numerator and denominator by the common factor (f^(2))(a^(2)).

Simplified fraction: (a-f)/(f^(1))(a^(1))

Step 5: Simplify the final fraction by canceling out the common factors.

Final answer: (a-f)/(fa)

Therefore, the simplified complex fraction is (a-f)/(fa).

Learn more about numerator and denominato here https://brainly.com/question/7067665

 #SPJ11

The solution for u is 36.

To solve for u using the multiplicative property of equality, we need to isolate u on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction that is attached to u. The reciprocal of (5/6) is (6/5), so we can multiply both sides of the equation by (6/5) to get:

(6/5) * 30 = (6/5) * (5/6) * u

Simplifying the right side of the equation gives us:

(6/5) * 30 = u

Multiplying the fraction and the whole number gives us:

(180/5) = u

Simplifying the fraction gives us:

36 = u

Therefore, the solution for u is 36.

For more such questions on Multiplicative property of equality.

https://brainly.com/question/9070018#

#SPJ11

The answer in simplest form is 9/2

The division involving a whole number and a fraction can be simplified by multiplying the whole number by the reciprocal of the fraction.

The reciprocal of a fraction is obtained by flipping the numerator and denominator.

In this case, the division is 3 ÷ (2/3). The reciprocal of (2/3) is (3/2).

So, we can multiply 3 by (3/2) to simplify the division:

3 × (3/2) = (3/1) × (3/2) = (3 × 3) / (1 × 2) = 9/2

Therefore, the answer in simplest form is 9/2.

To know more about Division simplest form refer here:

https://brainly.com/question/29184276#

#SPJ11

Answer:

$0.50

Step-by-step explanation:

We know

A package of 8 hot dogs is on sale for $4

What is the price per hot dog?

4 / 8 = $0.50

So, the price per hot dog is $0.50

Answer:

To find the total surface area of a square pyramid, we need to find the sum of the areas of its base and its four triangular faces.

In this case, the base is a square with side length 11.5 inches. Therefore, its area is:

Area of base = 11.5^2 = 132.25 square inches

Each triangular face has a base length equal to the side length of the square base, which is 11.5 inches. To find the height of each triangular face, we can use the Pythagorean theorem. Since the pyramid is a square pyramid, the height of each triangular face is also the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

a^2 + b^2 = c^2

where a = b = 11.5/2 = 5.75 (half the length of a diagonal of the square base) and c is the slant height. Solving for c, we get:

c = sqrt(a^2 + b^2) = sqrt(2*(5.75)^2) = 8.121 inches (rounded to 3 decimal places)

The area of each triangular face can be found using the formula:

Area of triangle = (1/2) * base * height

where the base is 11.5 inches and the height is 8.121 inches.

Area of each triangular face = (1/2) * 11.5 * 8.121 = 46.876 square inches (rounded to 3 decimal places)

So, the total surface area of the square pyramid is:

Total surface area = Area of base + 4 * Area of each triangular face

Total surface area = 132.25 + 4 * 46.876 = 330.124 square inches (rounded to 3 decimal places)

Therefore, the total surface area of the square pyramid is approximately 330.124 square inches.