The scale on a map reads 1/2 inch = 75 miles. If the distance between two cities on the map is 3 and 1/4 inches, find the actual distance between the cities

Please find attached to this answer a well labelled diagram of the triangle

Answer:

Approximately 176.6 feet

Step-by-step explanation:

From the question, we are to find the height at which the baseball fan was sitting.

From the attached diagram the height at which the fan was sitting is equivalent to the opposite side of the triangle.

Hence , the appropriate trigonometric function to use to solve this question is the sine function.

Sine = Opposite / Hypotenuse

Opposite is unknown so we refer to it as Y

Hypotenuse = 200feet

While the Angle of depression = 62°

Therefore,

Sine 62° = Y/ 200 feet

Cross multiply

Sine 62° × 200 feet = Y

Y = 176.58951857 feet

Approximately 176.6 feet

Therefore , the height at which the fan is sitting is 176.6 feet

Answer:

$15

Step-by-step explanation:

Let Sam's Money =s

Let Janet's Money =j

[tex]$\frac13$[/tex] of Sam's money equals [tex]$\frac12$[/tex] of Janet's money.

Let n be the number of dollars held by Sam and Jane respectively

Therefore: [tex]$n=\frac13s=\frac12j$[/tex]

s=3n

j=2n

s+j=3n+2n=5n

Together, they have more than $10

Therefore:

5n>10

n>2

The least sum they could have is at n=3

At n=3

s+j=5n=5X3=$15

The least number of dollars they could have combined is $15.

Answer:

A frequency is the number of times a given datum occurs in a data set.

Step-by-step explanation:

Answer:

23 miles per gallon

Step-by-step explanation:

Take the miles and divide by the gallons

218.5 miles/ 9.5 gallon

23 miles per gallon

Answer:

23m/g

Step-by-step explanation:

If a car travels 218.5 miles on 9.5 gallons, you can find how many miles can be traveled on one gallon.

You can make the equation 9.5g=218.5, let g be gallons of gas.

Divide by 9.5 on both sides.

g= 23

The gas mileage is 23 miles for one gallon of gas.

Answer:

42 Volunteers

Step-by-step explanation:

The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V).

This is written as:

[tex]V \propto \frac{1}{T} \\$Introducing the variation constant k\\V = \frac{k}{T}\\$It takes 20 volunteers to build a house in 63 hours.$\\When V=20, T=63\\V = \frac{k}{T}\\20 = \frac{k}{63}\\k=20*63=1260\\$Therefore, the equation connecting V and T is:$\\V = \frac{1260}{T}\\$When T=30 hours, we want to determine the number of volunteers needed V$\\V = \frac{1260}{30}=42\\$42 Volunteers will be needed.$[/tex]

Answer:

The correct answer is perimeter is given by 2 × ( l + w), where l is the length and w is the width of the rectangle.

Step-by-step explanation:

A rectangle has a length of 6 feet and a width of 4 feet. The perimeter of the rectangle can be found using the equation =2×6+2×4.

Let l be the length and w be the width of a rectangle.

Since there four sides of a rectangle, the perimeter is given by adding all the sides.

Therefore perimeter of the rectangle is given by l + l + b + b = 2×l +2×w = 2 × ( l + w).

The equation given by 2 × ( l + w) can also be used to find the perimeter of any given rectangle.

Answer:

x(1.25)

Step-by-step explanation:

x is the yards.

so for example if you need 2 yards of fabric replace x with 2.

Answer:

x=1.25

Step-by-step explanation:

edgu

Answer:

[tex]95.1\ cm^2[/tex]

Step-by-step explanation:

we know that

A square is a quadrilateral that has four equal sides and four equal interior right angles.

The area of the square is given by the formula

[tex]A=b^2[/tex]

where

b is the length side of the square

In this problem we have

[tex]b=9.75\ cm[/tex]

substitute in the formula

[tex]A=(9.75)^2=95.06\ cm^2[/tex]

Round to the nearest tenth

[tex]A=95.1\ cm^2[/tex]

Answer:

95.06cm​

Step-by-step explanation:

Hope this helps

Answer: 70 times

Step-by-step explanation:

If you were to flip a coin 140 times you would expect it to land on tails 70 since 140 divided by 2 is 70 although coins are normally not evenly weighed meaning that it most likely not going to land evenly on both sides.

The expression

is a polynomial. Its type is cubic and the degree is 3.

The given mathematical expression

is a polynomial. A polynomial is an expression that is made up of variables and coefficients, using only the operations of addition, subtraction, and multiplication and non-negative integer exponents. The type of this polynomial is cubic, because the highest power of the variable (the degree) is 3. In this case, the highest degree is the highest exponent of the variable 'x', which is 3. Hence the given polynomial is cubic, with degree of 3.

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The answer is zero (0), when you add any number to it's opposite you always get zero

Answer:

They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.

Step-by-step explanation:

In order to calculate the amount of each ingredient they need for 6 liters of punch we can first create fractions for each ingredient based on the proportions we were given. This is shown bellow:

2 litters lemonade + 1 litter pineapple juice + 1 litter ginger ale = 4 litters punch

Then we have:

lemonade = 2/4

pineaple juice = 1/4

ginger ale = 1/4

If we want to make 6 liters of punch we can just apply this fractions to know how much of each we need:

lemonade = 6*(2/4) = 12/4 = 3 litters

pineaple juice = 6*(1/4) = 1.5 litters

ginger ale = 6*(1/4)  = 1.5 litters

They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.

Answer:

#1: 11 cm

#2: 16.5 in

#3: 2.5 feet

Step-by-step explanation:

#1

[tex]P=2l+2w[/tex] Solve for width by substracting 2l on both sides to isolate 2w

[tex]P-2l=2w[/tex]

or

[tex]2w=P-2l[/tex]

Replace.

[tex]2w=26-2(2)\\2w=26-4\\2w=22\\w=\frac{22}{2}\\ w=11cm[/tex]

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

#2

[tex]P=2l+2w[/tex]

[tex]P=2(3.5)+2(4.75)\\P =7+9.5\\P=16.5in[/tex]

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

#3

[tex]P=2l+2w[/tex]

Solve for l

[tex]2l=P-2w\\2l=7-2(1)\\2l=7-2\\2l=5\\l=\frac{5}{2}\\ l=2.5feet[/tex]

Answer:

( x - 9 )( x - 3 )

Step-by-step explanation:

plz give brainliest

Answer: The length of the dotted line is 3.75 inches.

Please refer to the picture attached for the missing part of the question

Step-by-step explanation: From the information given we have a regular hexagon, that is a six-sided polygon (all sides equal) with the perimeter given as 7.5 inches. The perimeter is the distance all around the figure, hence to determine the length of one side,

Length = 7.5/6

Length = 1.25

Also, the interior angles of a hexagon can be derived with the formula;

Angles = 180 (n - 2)

Where n is the number of sides of the polygon

Interior Angles = 180 (6 - 2)

Interior Angles = 180 x 4

Interior Angles = 720

If the total of the interior angles equals 720, then each angle can be calculated as;

Each Angle = 720/6

Each Angle = 120

Please refer to attached picture tagged SOLUTION Diagram)

Taking triangle GED as shown in the picture, angle E and angle D measure 60 degrees each. This is because angle E in the entire hexagon ABCDEF measures 120 degrees. The line from point G in the center of the hexagon divides the angle into two equal halves. Same applies to all other five angles in the hexagon. Having angle E and D equal to 120 (that is 60 + 60) angle G would be equal to 180 - 120 {sum of angles in a triangle equals 180) which gives us 60. In effect we have an equilateral triangle, with all angles equal. This also means all sides are equal, hence if line ED equals 1.25, it simply means line GE and line GD equals 1.25 as well.

From this result we can now conclude that the line that runs across the hexagon from point F to point C is 1.25 plus 1.25 which equals 2.50.

The dotted line as indicated in the question runs across one side of the hexagon and all through another hexagon, hence the total length of the dotted line equals;

Dotted line = 1.25 + 2.50

Dotted line = 3.75

Therefore the length of the dotted line is 3.75 inches

Answer:

27 inches

Step-by-step explanation:

you divide 2160 by 80 to get the number of inches

2160/80=27

Answer:

5

Step-by-step explanation:

To find the slope given two points, we use the formula

m= (y2-y1)/(x2-x1)

   = (-13-2)/(-2 -1)

   = -15/-3

   =5

Answer:

The slope is 5

Step-by-step explanation:

Δ means the change in

slope = m = Δy/Δx = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-(-13)}{1-(-2)}[/tex] = 15/3 = 5/1 = 5

Slope = 5

Answer:It would be a decrease of 40 percent

Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%

Answer:

40 % decrease or -40%.

Step-by-step explanation:

The decrease is 10 - 6 = 4 feet.

% decrease = (4/10) * 100

= 0.4 * 100

= 40 % decrease.

The probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.

To find the probability that a student passed the test given that they did not complete the homework, you can use conditional probability.

Let:

- [tex]\( A \)[/tex] be the event that a student passed the test.

- [tex]\( B \)[/tex] be the event that a student did not complete the homework.

You're asked to find [tex]\( P(A|B) \),[/tex] the probability of passing the test given not completing the homework.

From the given information:

- Total number of students [tex](\( N \)) = 27[/tex]

- Number of students who passed the test [tex](\( A \)) = 17[/tex]

- Number of students who did not complete the homework [tex](\( B \)) = \( N - 22 = 5 \)[/tex] (since 22 students completed the assignment)

Also, given that there were 3 students who failed the test and did not complete the assignment, we can infer that out of the 5 students who did not complete the homework, 3 of them failed the test.

So, [tex]\( P(A \cap B) = 3 \)[/tex] (the probability of a student both passing the test and not completing the homework).

Using the definition of conditional probability:

[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]

We have:

- [tex]\( P(A \cap B) = 3 \)[/tex]

- [tex]\( P(B) = 5 \)[/tex]

Now we can calculate [tex]\( P(A|B) \)[/tex]:

[tex]\[ P(A|B) = \frac{3}{5} \][/tex]

So, the probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.

The probability that a student passed the test given they didn't complete the homework is 40%.

To solve this problem, we need to determine the probability that a student passed the test given they did not complete the homework. We'll use the given data:

First, calculate the number of students who did not complete the homework:

5 because 27 total - 22 completed = 5 did not complete.

Next, find the number of students who passed the test and did not complete the homework.

Let’s define variables:

We're given that AB' = 3.

Calculate AB:

The total number of students who didn’t complete the homework is 5 (B + B'). Thus, AB (students who passed the test but did not complete the assignment) can be calculated as:

2 (because 5 - 3 = 2 for AB).

Then, the probability is:

P(A|B) = AB / B = 2 / 5. Therefore, the answer is 0.4 or 40%.

Answer: n=4

Step-by-step explanation: 1:4 = 6:24

Answer:

Last one: 5x - 3√y + 1

Step-by-step explanation:

8x + √1 - √9y - √9x^2

8x + 1 - 3√y - 3x

5x + 1 - 3√y

5x - 3√y + 1

Answer:Answer:

Last One: 5x - 3√y + 1

Step-by-step explanation:

8x + √1 - √9y - √9x^2

8x + 1 - 3√y - 3x

5x + 1 - 3√y

5x - 3√y + 1

Step-by-step explanation:

Answer:

Are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

Answer: i3

Step-by-step explanation:

Answer:13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that the base of a solid is the circle [tex]x^2 + y^2 = 9[/tex] and Cross sections of the solid perpendicular to the x-axis are semi-circles.

We know that the cross sections are semicircles with the diameter in the given circle [tex]x^2 + y^2 = 9[/tex]

That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.

Now the area of a semicircle is

[tex]A=\frac{\pi r^2}{2}[/tex] cubic units

Let r = y  and [tex]y^2=9-x^2[/tex]

Then area of the semicircle crossing the x-axis at x is  given by

[tex]A(x)=\frac{1}{2}\pi y^2[/tex] cubic units

[tex]=\frac{1}{2}\pi(9-x^2)[/tex]    

 Now we can find the definite integral of A(x) from x = -3 to x = 3.

Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.

We have that

[tex]A(x)=2(\int_0^3 \frac{1}{2}\pi(9-x^2))dx[/tex]

[tex]=2(\frac{\pi}{2}[9x-\frac{x^3}{3}]_0^3)[/tex]

[tex]=\pi[9(3)-\frac{3^3}{3}-9(0)-(-\frac{0^3}{3})][/tex]

[tex]=\pi[27-\frac{27}{3}][/tex]

[tex]=\pi[27-9][/tex]

[tex]=\pi[18][/tex]

[tex]=18\pi[/tex]

The volume of the solid is 18π cubic units.

The base of the solid is defined by the circle’s equation x² + y² = 9, indicating that the radius of the circle is 3 units. The cross-sections perpendicular to the x-axis are semi-circles.

To find the volume, we need to integrate the area of these semi-circular cross-sections. For a slice at a given x-coordinate, the diameter of the semi-circle is the length of the chord of the circle at that x-coordinate, which is given by 2√(9 - x²). The radius of the semi-circle is then √(9 - x²), and the area of the semi-circle is (1/2)πr².

The area of each semi-circular slice is: A(x) = (1/2)π(√(9 - x²))² = (1/2)π(9 - x²).

The volume V of the solid is obtained by integrating this area from x = -3 to x = 3:

V = ∫[from x = -3 to x = 3] (1/2)π(9 - x²) dx

This simplifies to:

V = (π/2) ∫[from x = -3 to x = 3] (9 - x²) dx

We solve the integral:

V = (π/2) [9x - (x³ / 3)] (from x = -3 to x = 3)

Evaluating this, we get:

V = (π/2) [(9×3 - (3³ / 3)) - (9×(-3) - ((-3)³ / 3))]

V = (π/2) [(27 - 9) - (-27 + 9)]

V = (π/2) [18 + 18]

V = (π/2) 36

V = 18π

Thus, the volume of the solid is 18π cubic units.

Answer:

504

Step-by-step explanation:

The sum of the odd numbers between 30 and 54 will be 504.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

Given numbers are  30 and 54. The sum of the odd integers will be calculated by using the formula below:-

Sn = ( n / 2 ) [ a1 + a2 ]

The total numbers between 30 and 54 will be 12.

Sn = ( 12 / 2 ) [ 31 + 53 )

Sn = 6 x ( 84 )

Sn = 504

Therefore, the sum of the odd numbers between 30 and 54 will be 504.

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Step-by-step explanation:

diameter=7 inches

Area of the circle= π(7/2)² inches²

=38.465

38.5 inches²

Answer:

38.5 inches

Step-by-step explanation:

r = 1/2d

r = 1/2 × 7

r = 3.5

[tex] \boxed{ \bold{formula = \pi \: {r}^{2} }}[/tex]

= 3.14 × 3.5 × 3.5

= 38.465 inches

Find its area to the nearest tenth

38.465 inches

= 38.5 inches

Answer:

The perimeter is 28 (6 plus 8=14 14x2= 28)

Step-by-step explanation:

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The perimeter of quadrilateral DOBC that forms two right triangles is: 28 units.

Based on the tangent theorem, triangles ODC and OBC are right triangles that are congruent. Therefore, their corresponding side lengths are equal.

Perimeter of quadrilateral DOBC = OB + DO + BC + CD = 6 + 6 + 8 + 8

Perimeter of quadrilateral DOBC = 28 units.

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Answer:

9

Step-by-step explanation:

√16=4

5*1=5

4+5=9

hope this helps

Answer:

10 inches.

Step-by-step explanation:

First we need to find what is the bigger dimension of the box, because the relay baton will occupy the box, and the larger dimension of the relay baton (that is, it's length) need to be less or equal than the larger dimension of the box.

The dimensions of the box are: 4 inches, 6 inches and 10 inches.

The larger dimension of the box is 10 inches. So, If we want the relay baton to fit in the box, the maximum length it can have is 10 inches.