UV is tangent to OT. What is m< V? ​

In Linear equation, 5/8 golf balls per ounce are the number of golf balls per Ounce.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Number of golf balls (n) = 20

Total weight (w) = 32 ounces

total weight = number of balls (n) * weight of 1 golf ball

∴ weight of 1 golf ball = w/n =32/20 ounces

⇒ the weight distribution is 1.6 ounce per golf ball

Now, apply unitary method :

32 ounces is total weight of 20 golf balls

∴ 1 ounce amounts to 20/32 golf balls

⇒ there are 5/8 golf balls per ounce

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We have two possible values for y, we have two possible Coordinates for point A: (-3, 1 + √((units)² - (3 - (-3))²)) and (-3, 1 - √((units)² - (3 - (-3))²)).

Here are the terms and steps we'll use in the solution:

1. Point B coordinates: (3, 1)
2. Point A x-coordinate: -3
3. Distance formula: √((x2 - x1)² + (y2 - y1)²)

Let's find the possible coordinates of point A:

Step 1: We know the x-coordinate of point A is -3, so its coordinates will be in the form (-3, y).

Step 2: Apply the distance formula to find the distance between point A (-3, y) and point B (3, 1):

Distance = √((3 - (-3))² + (1 - y)²)

Step 3: Square the distance equation to eliminate the square root:

Distance² = (3 - (-3))² + (1 - y)²

Step 4: Plug in the given distance value and solve for y:

(units)² = (3 - (-3))² + (1 - y)²

Step 5: Solve for (1 - y)²:

(1 - y)² = (units)² - (3 - (-3))²

Step 6: Take the square root of both sides:

1 - y = ±√((units)² - (3 - (-3))²)

Step 7: Solve for y:

y = 1 ±√((units)² - (3 - (-3))²)

Since we have two possible values for y, we have two possible coordinates for point A: (-3, 1 + √((units)² - (3 - (-3))²)) and (-3, 1 - √((units)² - (3 - (-3))²)).

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The graph that shows the residual plot for the height and weight of the 10 players is B. Graph B.

To find the residual plot, you need to use the data on height and weight of 10 players shown on the table, and compare it to figures you get from the formula given of y = -146.7 + 4.76 x.

Doing this, we find two residuals being:

x = 68

Predicted y = -146.7 + 4.76(68) = 175.88

Actual y = 170

Residual = Actual y - Predicted y = 170 - 175.88 = -5.88

x = 70

Predicted y = -146.7 + 4.76(70) = 185.3

Actual y = 185

Residual = Actual y - Predicted y = 185 - 185.3 = -0.3

These points of (68, - 5.88) and ( 70, - 0.3) tally with Graph B so this is the residual plot.

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The volume of 11 gallons is 50 litres.

The volume of 40 litres is 8.8 litres.

The capacity of the tank in gallons is 26.7 gallons

The graph of a proportional relationship is always a straight line through the origin.

Therefore, the graph is a relationship between the variables volumes in litres and gallons. The litres is on the y axis while the gallons is on the x axis.

Hence, let's use the graph to convert the volumes.

11 gallons = 50 litres

40 litres = 8.8 litres

A tank has a volume of 120, 000 cm cube.

1 litre  = 1000 cm³

The capacity of the tank in gallons can be found as follows:

1000 cm³ = 1 litres

120,000 cm³= ?

volume in litres = 120,000 / 1000

volume in litres = 120 litres

From the graph,

36 litres = 8 gallons

120 litres = ?

cross multiply

volume in gallons = 120 × 8  / 36

volume in gallons = 960 / 36

volume in gallons = 26.6666666667

Therefore, the capacity of the tank in gallons is 26.7 gallons

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Answer:

  a) 50 L

  b) 8.8 gal

  c) 26.4 gal

Step-by-step explanation:

Given a graph showing the relationship between (imperial) gallons and litres, you want equivalents for 11 gallons, 50 litres, and 120000 cm³.

You have correctly read the graph, which tells you 11 gallons is about 50 litres.

You have correctly read the graph, which tells you 40 litres is about 8.8 gallons.

You are told that 1000 cm³ is 1 litre, so 120,000 cm³ will be 120 litres.

You notice this is 3 times the volume of the previous question:

  120 L = 3×(40 L) = 3×(8.8 gal) = 26.4 gal

120000 cm³ is about 26.4 gallons.

__

Additional comment

A more precise conversion of 120000 cm³ is 26.3963097959... gallons. The decimal has a very long repeat.

Rita numbered the circles of the figure from 1 to 8, so that the sum of the three numbers on each of the four sides of the square equals 13. The sum of the four numbers written on the colored circles is 10.

The figure is as shown below:

Now, let's check how the numbers are arranged:The sum of the numbers 1, 6, and 6 is 13, and they are written on the same side of the square as the circle labeled with 1.

Similarly, the numbers 2, 5, and 6 are on the same side of the square as the circle labeled with 2, and the numbers 2, 6, and 5 are on the same side of the square as the circle labeled with 3.

Now, the remaining number that has not been used in any of the sides of the square is 4.

Therefore, it should be placed at the center of the square, as shown below:

The numbers on the colored circles are: 1, 2, 3, and 4. Thus, their sum is:

1 + 2 + 3 + 4 = 10

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Is this selection (A) the best one? a high positive number. The result of multiplying a negative number by a positive number is always negative.

The result of multiplying two numbers, whether they are positive or negative, is always positive. 3 plus 4 equals 12. The result is minus 12 since there is only one optimistic and one negative number.

Why does adding two negative numbers together results in a positive number?

Repeated subtraction equals multiplication by a negative. Negative numbers were reduced in negative value after they have been multiplied together. Students may easily relate both ideas thanks towards this comparison among both multiplication and addition.

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Answer:

C

Step-by-step explanation:

given x = a is a solution of f(x) then (x - a) is a factor

here the solutions, where the graph crosses the x- axis, are

x = - 4 , x = - 2 , x = - 1 , then the corresponding factors are

(x - (- 4)) , (x - (- 2)) , (x - (- 1)) , that is

(x + 4) , (x + 2) , (x + 1)

f(x) is then the product of these factors, that is

f(x) = (x + 2)(x + 1)(x + 4) ← in factored form

Answer:

]]] explanation:

Answer:

5

Step-by-step explanation:

In the given question,

center of the circle C = (1, 2)

let P be the point (-3, -1) on the circle (on circumference)

radius of the circle is equal to the distance between the center and any point on its circumference.

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] (distance between two points)

therefore,

[tex]r = \sqrt{(-3 - 1)^2 + (-1 - 2)^2}[/tex]

[tex]r = 5[/tex]

Hopefully this answer helped you!

67 people can maximize the profit.

Let's aasume that x represent the number of people.

so, the number of people on the tour = x + 50

The cost function would be:

C = 6000 + 32x

and the revenue:

R = (200 - 2x)(50 + x)

R = 10000 - 100x + 200x - 2x^2

R = 10000 + 100x - 2x²

So, the profit would be:

P = R - C

P = 10000 + 100x - 2x² - 6000 - 32x

P = 4000 + 68x - 2x²

Now we take the derivative of profit function:

P' = 68 - 4x

Consider P'(x) = 0

68 - 4x = 0

4x = 68

x = 17

So, the number of people on tour: 50+17 = 67

This means that 67 people can maximize the profit.

and the profit would be:

P = 4000 + (68 × 17) - (2 × 17²)

P = $4578

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a.the two-dimensional shape of the cross-section will be a square.

b. the two-dimensional shape of the cross-section will also be a square.

c .The shapes are the same because regardless of the orientation of the cut, the cross-section will always be a square since all sides of a cube are equal.

A two-dimensional shape is a geometric figure that has only two dimensions, namely length and width, but no thickness or depth. Examples of two-dimensional shapes include circles, squares, triangles, rectangles, and polygons. These shapes are typically represented on a flat surface such as a piece of paper or a computer screen.

a. If the cube is sliced horizontally, the two-dimensional shape of the cross-section will be a square.

b. If the cube is sliced vertically, the two-dimensional shape of the cross-section will also be a square.

c. The shapes are the same because regardless of the orientation of the cut, the cross-section will always be a square since all sides of a cube are equal. The orientation of the cut only affects which faces of the cube are visible in the cross-section, but the shape itself remains the same.

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Answer:

False

Step-by-step explanation:

Answer:

[tex]2 \frac{10}{23} [/tex]

Step-by-step explanation:

[tex] \frac{4u - 7}{ - 7} = \frac{u - 4}{4} [/tex]

Use the property of the proportion:

4 × (4u-7) = -7 × (u-4)

16u -28 = -7u + 28

16u + 7u = 28 + 28

23u = 56 / : 23

u =

[tex] 2\frac{10}{23} [/tex]

bh, where b is the base and h is the height of the parallelogram.

In the case of the circle, the base of the parallelogram is the circumference of the circle, which is equal to 2πr, where r is the radius of the circle. The height of the parallelogram is the distance from the center of the circle to the edge of the circle, which is also the radius r. Therefore, we have:

b = 2πr

h = r

Substituting these values into the formula for the area of a parallelogram, we get:

Area = bh = (2πr)(r) = 2πr^2

So the formula for the area of a circle is derived from the formula for the area of a parallelogram by using the circumference of the circle as the base and the radius of the circle as the height.

Answer:

Step-by-step explanation:

D.

Relief rainfall causes Port Antonio on the windward side of the Blue Mountains to receive an average of 430 mm (17 inches) of rain in November while Kingston, in the rain shadow, receives only 175 mm (7 inches).

The two sides of the triangle are equal the triangle is an isosceles triangle.

Triangles with two equal sides are known as isosceles triangles. Triangles are three-sided polygons that can be categorised as equilateral, isosceles, or scalene depending on how long their sides are.

The uneven side of this triangle is referred to as the base since the other two sides are equal in it. The triangle's two equal sides are always opposing equal angles. An isosceles triangle's height is calculated from its base to its vertex (topmost point). The third angle of a right isosceles triangle is 90 degrees.

The coordinates of the triangle are J(-2, 4), K(8, 4) and L (6, -2).

Using the distance formula we have:

The distance between J and K: √((8 - (-2))² + (4 - 4)²) = 10

The distance between K and L: √((6 - 8)² + (-2 - 4)²) = 6.324

The distance between L and J: √((-2 - 6)² + (4 - (-2))²) = 10

Since two sides of the triangle are equal the triangle is an isosceles triangle.

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The answer of the given question based on Return on Investment is (a) 19.64% , (b) $51,575 , (c)  -28.30% , (d)  $42,000.

Investment is the act of allocating resources, like money, time, or effort, with the expectation of generating a return or profit in the future. Investment can take many forms, including purchasing stocks, bonds, mutual funds, real estate, or other financial assets.

The main goal of investment is to grow wealth over time by generating returns that exceed the rate of inflation. There are several types of investment strategies, such as value investing, growth investing, income investing, and diversification, that investors can use to achieve their financial goals.

a. ROI = (final value - initial value)/initial value * 100%

ROI = (67000 - 56000)/56000 * 100% = 19.64%

b. ROI = (final value - initial value)/initial value * 100%

$24,756 = 48% * initial value

initial value = $24,756 / 0.48 = $51,575

c. ROI = (final value - initial value)/initial value * 100%

ROI = ($62.56 - $87.24)/$87.24 * 100% = -28.30%

The negative ROI indicates a loss in investment.

d. The lowest price is $25 and the highest price is $67, so the total return on investment is:

Total Return = 1000 shares * ($67 - $25) = $42,000.

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Answer:

Saanvi recorded the number of math problems she did for homework each night for 10 days.

Step-by-step explanation:

The number of possible ways you can distribute the balls among the three boxes so that each box contains at least one ball = 21

Here we have 3 empty boxes.

Let us assume that a, b and c be these empty boxes.

and the total number of balls = 8

We need to distribute the balls among the three boxes so that each box contains at least one ball.

This means that a + b + c = 8

By allotting 1 ball to each box so that no box remains empty.

We get an equation a + b + c = 5

So, the possible number of ways to by allotting 1 ball to each box so that no box remains empty would be:

⁷C₂

Using combination formula:

⁷C₂

= 7! / 2!(7 - 2)!

= 21

Therefore,  the required number of ways = 21

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Answer:

10%

Step-by-step explanation:

(517-470)/470x100

=10%

Find the difference after tax and divide by the original price and times 100%

The product of 2 and 1 3/6 can be expressed as either 18/6 or 3

The product of 2 and 1 3/6 can be found by multiplying 2 by the mixed number 1 3/6. To do this, we need to convert the mixed number to an improper fraction, then multiply it by 2. Here are two possible expressions that are equal to the product of 2 and 1 3/6

Improper fractions

2 x 1 3/6 = 2 x (1 + 3/6) = 2 x (6/6 + 3/6) = 2 x 9/6 = 18/6

Therefore, the product of 2 and 1 3/6 is equal to 18/6.

Decimals

We can also convert the mixed number 1 3/6 to a decimal and then multiply it by 2. To convert the mixed number to a decimal, we divide the numerator (3) by the denominator (6), which gives us 0.5. Then we add the whole number (1) to get 1.5.

2 x 1.5 = 3

Therefore, the product of 2 and 1 3/6 is equal to 3.

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The double integral of sin(xy) over the rectangle r equals 1 when a is approximately equal to 0.986, with 0 ≤ a ≤ π.

The iterated integral to compute the double integral over the rectangle r = {(x,y) : 0 ≤ x ≤ π, 0 ≤ y ≤ a} of sin(xy) is given by:

∫∫r sin(xy) dA = ∫₀^a ∫₀^π sin(xy) dx dy

Integrating with respect to x first, we have:

∫₀^a ∫₀^π sin(xy) dx dy = ∫₀^a [-cos(πy) + cos(0)] dy

= ∫₀^a (1 - (-1)^n) dy

= a - (a/π)sin(πa)

For what values of a is ∫∫r sin(xy) dA equal to 1?

We need to solve the equation:

a - (a/π)sin(πa) = 1

Multiplying both sides by π, we get:

aπ - a sin(πa) = π

Now, let f(a) = aπ - a sin(πa) - π. We need to find the values of a such that f(a) = 0.

Using numerical methods, we can find that there is only one solution in the interval [0,π], which is approximately a = 0.986.

Therefore, the double integral of sin(xy) over the rectangle r equals 1 when a is approximately equal to 0.986, with 0 ≤ a ≤ π.

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Answer:

Step-by-step explanation:

17/x = 30/84  1. Set up the proportion

30x = 1428     2. Cross multiply and solve for x

x=47.6            3. There's the solution

You can successfully begin a business that serves the requirements of expression your community by leveraging your existing skills and networks and investing in targeted marketing methods.

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

Offering a service that leverages your existing talents and training is one suggestion for beginning a business with $150.00. For example, if you are a graphic designer, you may offer logo creation or other graphic design services to local small businesses or people. Instead, if you have experience with social media marketing, you might offer to handle small businesses' social media accounts.

Ultimately, launching a firm on a tight budget necessitates ingenuity and resourcefulness. You can successfully begin a business that serves the requirements of your community by leveraging your existing skills and networks and investing in targeted marketing methods.

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The height of the tent is approximately 4.87 feet.

To find the height of the tent, we need to first determine the length of the altitude (perpendicular line) drawn from the apex (top point) of the triangle to the base. Let's call this length "h".

We can use the Pythagorean theorem to find "h". Let's draw a line from the apex of the triangle to the midpoint of the base, which will split the isosceles triangle into two congruent right triangles. Then we have

h^2 + (7/2)^2 = 6^2

h^2 + 49/4 = 36

h^2 = 36 - 49/4

h^2 = 95/4

h = sqrt(95)/2

h ≈ 4.87 ft

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Answer: x = -2

Step-by-step explanation: -2 is the answer because -2 to the 3rd power is -8. Hence, 8 * -8 = -64 as the solution.

Answer:

3.75 and B

Step-by-step explanation:

for the first one if the actual is 48 feet, and the image is 12.8, divide both by the image(12.8). The value you have for the image should then become one centimeter, therefore the value you have for the parking lot is the amount of feet/1cm. For the second image, its the same idea. In this case you want to know how tall the scale is, so divide by the amount of meters(just as 6/2=3 and 6/3=2 the real value/scale value=representation of 1 unit and real value/representation of 1 unit = scale value). You get 12.5, however that is per 1 unit, so multiply by five since(the value you get by simply dividing is the answer IF 30 meters were represented in the scale by 1centimeter, but its represented by 5 so you multiply by five)You get 63.5

Therefore , the solution of the given problem of triangle comes out to be    h/s = h/√(h² - s²)..

If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

Triangle ABC and triangle ACD are both right triangles with a common hypotenuse, as shown by the given diagram.

Let's write the lengths of the sides AB or AD as s and the hypotenuse AC as h. (since both triangles have a common side with length s).

The Pythagorean formula can now be used to determine the length of each triangle's third side:

Triangle ABC's third side's length (BC) can be calculated using this formula:

=> BC = √(h² - s²).

The third side's (CD) length in the triangle ACD is also determined by:

=> CD = √(h² - s²).

By dividing each triangle's hypotenuse's (h) length by one of its sides' (s) lengths, the following result is obtained:

In the triangular ABC,

=> h/s = h/ √(h² - s²).

In the triangular ACD

=>  h/s = h/√(h² - s²).

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