Math Essay on probability of the Ohio lottery

Answer:

To solve a right triangle, we can use the Pythagorean theorem, which states that the sum of the squares of the two smaller sides equals the square of the largest side. In this triangle, we have:

a^2 + b^2 = c^2

Plugging in the values we have:

18.7^2 + b^2 = 46.4^2

Solving for b, we have:

b = √(46.4^2 - 18.7^2)

b = √(2159.36 - 349.69)

b = √1809.67

b = 42.6 cm (rounded to the nearest tenth)

Next, we can use the tangent function to find angles A and B:

tan(A) = a/b = 18.7/42.6 = 0.439

A = tan^-1(0.439) = 24° 26' (rounded to the nearest minute)

And, using the Pythagorean theorem:

c^2 = a^2 + b^2 = 18.7^2 + 42.6^2 = 346.69 + 1809.67

B = 90° - A = 90° - 24° 26' = 65° 34' (rounded to the nearest minute)

So the solution is:

a = 18.7 cm

b = 42.6 cm

c = 46.4 cm

A = 24° 26'

B = 65° 34'

C = 90°

Step-by-step explanation:

The required measure of the angle x in the given right triangle is 12.38°.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
Since the question seems to be incomplete the complete question has been attached after the solution.

We have given a triangle where x° is the angle of the right triangle where the hypotenuse is 54 and one legs is 12. With the help of trig ratios
sin x = 12 / 54
x = sin⁻¹(12/54)
x = 12.38°

Thus, the required measure of the angle x in the given right triangle is 12.38°.

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Answer:

He sold 32 pounds of apples, 14 pounds of plums and 23 pounds of peaches.

Step-by-step explanation:

Let:

x = Mass of Apples (pounds)

y = Mass of plums (pounds)

z = Mass of peaches (pounds)

He sold 18 more pounds of apple than pounds of plums:         [tex]x = 18 + y[/tex]

He sold 9 less pounds of peaches than pounds of plums:         [tex]z - 9 = y[/tex]

He sold a total of 69 pounds of fruit:                                       [tex]x + y + z = 69[/tex]

We have 3 unknown variables, therefore a system of 3 linear simultaneous equations:

                                                [tex]x = 18 + y[/tex] ——- (equation i)

                                          [tex]z - 9 = y[/tex]

                                         ∴     [tex]z = 9 + y[/tex] ——— (equation ii)

                                   [tex]x + y + z = 69[/tex] ——- (equation iii)
The above linear simultaneous equations can be solved by Substitution Method:

Substitute (equation i) and (equation ii) into (equation iii) to solve for y. Expand the parenthesis and bring all the like terms together. y has to be made the subject of the equation:

[tex](18 + y) + y + (y + 9) = 69[/tex]

= [tex]18 + y + y + y + 9 = 69[/tex]

= [tex]y + y + y = 69 - 18 - 9[/tex]

= [tex]3y = 42[/tex]

= [tex]y = \frac{42}{3}[/tex]

∴ y = Mass of plums = 14 pounds

Substitute the calculated value of y into the other two equations to solve for x and for z:

                 [tex]x = 18 + (14)[/tex]

              ∴ x = Mass of apples = 32 pounds

                 [tex]z = 9 + (14)[/tex]

              ∴z = Mass of peaches = 23 pounds

Answer: the first box is does not the 2st box does  i hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-2, 3) (2, -1)

(-1 - 3)/(2 + 2)= -4/4 = -1

m = -1

does

does not

y - 3 = -1(x + 2)

y - 3 = -x - 2

y = -x + 1

Option 1

Answer is B. 
y= 2x -3 y= -2x + 1

step by step

First I found the y intercepts at (red line) -3 and (green line) +1.

There is only one answer that shows these two y intercept values.

 To double check this answer, I checked the slope of each line. The red line has a slope of 2 and the green line has a slope of -2.

Slope was found on the graph finding rise over run and compared to the number next to x in the equations.

See attached graph.

Answer:

x = -4°

Step-by-step explanation:

We know that,

→ Sum of angles of straight line is 180°.

Now we have to,

→ Find the required value of x.

Forming the equation,

→ (54°) + (7x + 154°) = 180°

Then the value of x will be,

→ 7x + 154° + 54° = 180°

→ 7x + 208° = 180°

→ 7x = 180° - 208°

→ 7x = -28°

→ x = -28° ÷ 7

→ [ x = -4° ]

Hence, the value of x is -4°.

Answer: I think x = -4

Step-by-step explanation: I used a calculator.

we get two possible solutions: L = 6 and W = 4. Therefore, the length of the land could be 6 meters.

If the rectangular plot has length L and width W, then we know that 2L + 2W = 20 since 20 meters of wire mesh were used. We also know that L × W = 24 since the area of the plot is 24 square meters. Solving these two equations simultaneously, We have the equations:

2L + 2W = 20

L × W = 24

From the first equation, we can solve for L in terms of W:

2L = 20 - 2W

L = 10 - W

Substituting this into the second equation, we get:

(10 - W) × W = 24

Expanding the brackets, we get: 10W - W² = 24

Rearranging and setting equal to zero, we get: W² - 10W + 24 = 0

We can solve this quadratic equation by factoring: (W - 6) × (W - 4) = 0

So the possible solutions for W are: W = 6 or W = 4

If W = 6, then L = 10 - W = 4, so the rectangular plot has dimensions 4 meters by 6 meters. If W = 4, then L = 10 - W = 6, so the rectangular plot has dimensions 6 meters by 4 meters. Therefore, the length of the land is 6 meters. because the length is assumed as the longer side of a shape or an object.

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Complete Question

To enclose a rectangular plot of 24 m², 20 m of wire mesh were used, what is the length of the land?

Answer:

yes

Step-by-step explanation:

Answer:

324

Step-by-step explanation:

To evaluate (a) f(f(2)), we first evaluate f(2) which is 52-4 = 6. Then, we evaluate f(6) which is 56-4 = 26. So, f(f(2)) = 26.

To evaluate (b) g(g(3)), we first evaluate g(3) which is 23^2 = 18. Then, we evaluate g(18) which is 218^2 = 324. So, g(g(3)) = 324

The values of p for which the equation (p+1)x² + 4px +9=0 has equal roots:

p =  (36 ± 59.8)/32

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

The quadratic equation,

(p+1)x² + 4px +9=0

So, for equal roots, we have:

(4p)² - 4 x (p + 1) x 9 = 0

Solving for p, we get:

16p² - 36 p -36 = 0

This is a quadratic equation, and we can find the roots using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a = 16, b = -36, and c = -36.

Plugging in the values into the formula, we get:

p = (36 ± 59.8)/32

Thus, the values of p for which the equation (p + 1)x² + 4px + 9 = 0 have equal roots are  (36 ± 59.8)/32.

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The equation Distance = Speed × Time can be used to calculate the time spent in both city and highway. The sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

Distance is a numerical measurement of the distance between two objects in physical space. It is commonly measured in meters, kilometers, or miles. Angles, such as degrees of longitude and latitude, can also be used to calculate distance.

Distance may be estimated mathematically using methods such as the Pythagorean theorem. When studying the movement of things, such as in physics and engineering, and estimating the speed of objects in motion, distance is a significant component.

Since you know the total distance traveled and the average speed of the vehicle in both city and highway, you can use the equation

Distance = Speed × Time

to solve for the time spent in both city and highway.

For time spent in city:

35 mph × C = 995 miles

C = 995 miles/35 mph = 28.43 hours

For time spent in highway:

60 mph × H = 995 miles

H = 995 miles/60 mph = 16.58 hours

Therefore, the sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

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The required graph has been attached below which represents the given linear equation y = (2/5)x - 4.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To plot the graph of y = (2/5)x - 4, you can follow these steps:

Choose a range of values for x that you want to plot. For example, you can choose x values from -10 to 10.

Substitute the x values into the equation to find the corresponding y values. For example, if x = -10, then y = (2/5)(-10) - 4 = -8.

Plot the ordered pairs (x, y) on a coordinate plane. For example, if x = -10 and y = -8, plot the point (-10, -8) on the plane.

Repeat this process for several x values to plot additional points.

Connect the points with a straight line to obtain the graph of the equation y = (2/5)x - 4.

Note that the graph should be a straight line with a slope of 2/5 and a y-intercept of -4.

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The question seems incomplete, the correct question would be as:

How to plot the graph of y = (2/5)x — 4?

Answer: I believe that the answer is 8x.

Step-by-step explanation:

My explanation is that since x equals a random value, we can still add 5 and 3 to get 8.

I hope this helps!

Step-by-step explanation:

we need to remember 2 things for right-angled triangles (which we need to use to find the sides of the rectangle, so that we then can calculate the area) :

1. Pythagoras

a² + b² = c²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.

2. geometric mean theorem

height = sqrt(p×q)

with p and q being the segments of the baseline the height is splitting it into. in our case MA and AL.

so, to get the length of the rectangle (PL) we use Pythagoras :

PL² = 6² + 8² = 36 + 64 = 100

PL = 10 units

to get PM we first need to get ML. and for that we need to get MA.

6 = sqrt(MA × 8)

36 = MA × 8

MA = 36/8 = 4.5 units

that means ML = 8 + 4.5 = 12.5 units

and again Pythagoras

ML² = PL² + PM²

12.5² = 10² + PM²

156.25 = 100 + PM²

56.25 = PM²

PM = 7.5 = 7.5 units

so, the area of the rectangle is

10 × 7.5 = 75 = 75.00 units²

to "round" to the nearest hundredth.

The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units

The radius of the base = 4 units

The length of the side of the square = 2x

The area of the square = a^2

Where a is side of the square

The area of the square = (2x)^2

= 4x^2

The equation of the circle is

x^2 + y^2 = 16

x^2 = 16 - y^2

The area = 4(16 - y^2 )

= 64 - 4y^2

The volume of the square

V = [tex]\int\limits^a_b {A(y)} \, dy[/tex]

= [tex]\int\limits^4_0 {64-4y^{2} } \, dy[/tex]

= 64×4 - 4×(4^3/3)

= 256 - 256/3

= 512/3 cubic units

Therefore, the volume of the solid is 512/3 cubic units

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Answer:

option (A).

Step-by-step explanation:

The equivalent expression to the given radical expression, when the denominator has been rationalized and x > 5, is 2(√x + √x - 5), or option (A).

The answer is B. 18

When solving similar triangles, you must set up a proportion. We do not know what the other two lengths are for side AB, but we can still solve another way. For side AC, we can set up a proportion of 33/44. We're going to take AM and put that over the total. The total length of side AB is 24, and we're going to use x for AL.

33/44 = x/24

Once finished solving the proportion, you are left with 18

The missing length of triangle is 18.

What exactly is a triangle?

Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorised into three categories based on its sides, namely:

A triangle is categorised into three categories based on its angles, namely:

Now,

As these triangles are similar that means

we can find the proportion of sides from given sides and

from that find x.

So, here  AC/AM=AL/AB

44/33=24/x

AL=24*33/44

AL=18

Hence,

            The missing length AL of triangle is 18.

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Answer:

Therefore, z = 1 + i.

Step-by-step explanation:

Given that the argument of z + 1 is pi/6 and the argument of z - 1 is 2*pi/3, we can use the fact that the argument of a complex number is equal to the angle between the positive x-axis and the line connecting the origin to the complex number in the complex plane.

Let's call the complex number z = a + bi. Then, z + 1 = a + (b + 1), and z - 1 = a - (b - 1).

Using the argument values given, we have:

arg(z + 1) = pi/6, so the line connecting the origin to z + 1 makes an angle of pi/6 with the positive x-axis.

arg(z - 1) = 2pi/3, so the line connecting the origin to z - 1 makes an angle of 2pi/3 with the positive x-axis.

From the above information, we can sketch the complex plane and find the location of the complex number z. We then have two equations for a and b in terms of the argument of the complex numbers:

a = (z + 1 + z - 1)/2 = 1

b = (z + 1 - z - 1)/2 = 1

Therefore, z = 1 + i.

Answer:

y = 18 + b

Step-by-step explanation:

Add 18 to both sides

y = 18 + b

Since the triangles are congruent. Then The size of angle Q is 47°

Congruent Angle:

Congruent angles are often used in architecture, construction, design, and art. Isometrics have the same angular measurements. For example, a regular pentagon has 5 sides and 5 angles, each measuring 108 degrees. Regardless of the size or scale of a regular polygon, the angles are always congruent.

Here is a list of rules for the congruence of angles.

1. The only condition for two angles to be congruent is if the measurements of the angles agree.

2. The lengths and orientations of the two sides of this congruent angle are not important.

According to the Question:

It is given that :

B = 6 cm, 12 cm and 9 cm

A = 47°

R' = 29°

If the triangle is congruent, then all the three sides and angles will be same.

Therefore,

Angle Q = Angle A

Therefore, Angle Q = 47°

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Answer:

(a) To determine the mean and standard deviation of Y, we need to find the expected value and standard deviation of the number of defects that can be sold by Company F. Since the number of defects that can be sold is equal to X if X is less than or equal to 2, and equal to 2 if X is greater than 2, we can use the following formula to find the expected value of Y:

E(Y) = P(X = 0) × 0 + P(X = 1) × 1 + P(X = 2) × 2 + P(X > 2) × 2

E(Y) = 0.58 × 0 + 0.23 × 1 + 0.11 × 2 + 0.03 × 2

E(Y) = 0.23 + 0.22 + 0.03

E(Y) = 0.48

To find the standard deviation of Y, we can use the following formula:

Var(Y) = P(X = 0) × (0 - E(Y))^2 + P(X = 1) × (1 - E(Y))^2 + P(X = 2) × (2 - E(Y))^2 + P(X > 2) × (2 - E(Y))^2

Var(Y) = 0.58 × (0 - 0.48)^2 + 0.23 × (1 - 0.48)^2 + 0.11 × (2 - 0.48)^2 + 0.03 × (2 - 0.48)^2

Var(Y) = 0.58 × 0.2304 + 0.23 × 0.1024 + 0.11 × 0.0304 + 0.03 × 0.0304

Var(Y) = 0.1333

The standard deviation of Y is the square root of the variance:

StdDev(Y) = √Var(Y)

StdDev(Y) = √0.1333

StdDev(Y) = 0.3663

So, the mean and standard deviation of Y are 0.48 and 0.3663, respectively.

(c) To find the mean and standard deviation of the selling price for the fat quarters sold by Company G, we need to find the expected value and standard deviation of the price, taking into account the discount for each defect. We can use the following formula to find the expected value of the price:

E(Price) = $5.00 - $1.50 × E(Defects)

E(Price) = $5.00 - $1.50 × 0.40

E(Price) = $5.00 - $0.60

E(Price) = $4.40

To find the standard deviation of the price, we can use the following formula:

StdDev(Price) = $1.50 × StdDev(Defects)

StdDev(Price) = $1.50 × 0.66

StdDev(Price) = $0.99

So, the mean and standard deviation of the selling price for the fat quarters sold by Company G are $4.40 and $0.99, respectively.

The option B is a linear function. The solution has been obtained by using the properties of a linear function.

What is a linear function?

A function is referred to as linear if it can be represented on a graph as a straight line. Typically, the highest degree of this polynomial function is 1 or 0. Despite the fact that linear functions can be expressed in both calculus and linear algebra.

We are given four functions.

It is clearly visible that option A is not a linear function because the degree of the function is 2.

Option B is a linear function because we obtain a straight line on the graph.

Also, option C is not a linear function because the degree of the function is greater than 1.

Similarly, option D is also not a linear function because it's graph is not a straight line.

Hence, option B is a linear function.

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The value of sin B rounded to the nearest hundredth is 0.80.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

The right triangle represented in the question is given below.

We know that sine of an angle in a right angled triangle is the ratio of it's opposite side to hypotenuse.

In the triangle ABC, AB is the hypotenuse and AC is the opposite side of B.

Sin B = AC / AB

Sin B = b / c

Sin B = 20 / 25

Sin B = 0.8

Hence the value of sine of B is 0.8.

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Example: Add 1/4 + 2/4

Solution: Let us add these fractions using the following steps.

Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)

Step 2: Add the numerators and place the sum over the common denominator. This means (1 + 2)/4 = 3/4

Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4

Any line of the form:

y = (3/2)x + b

Is perpendicular to the given line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is -1.

Here we want to find a line perpendicular to:

2x + 3y = 10

We can rewrite this as:

3y = 10 - 2x

y = (10/3) - (2/3)*x

Then the slope of the perpendicular line must be such that:

a*(-2/3) = -1

a = 3/2

Then any line of the form:

y = (3/2)*x + b

Is perpendicular to the given line.

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Answer:

x=4

Step-by-step explanation:

-6x = -6-18

-6x = -24

-6x/-6 = -24/-6

x =4

The proportional relationship used to find the distance that the train will travel after m minutes is given as follows:

d = 0.12m.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Considering that when the input is of 5, the output is of 0.6, the constant of the relationship in this problem is given as follows:

k = 0.6/5

k = 0.12.

Hence the equation is given as follows:

d = 0.12m.

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Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then  R(t) = 20 + 1.6sin(2πt/5.2).

The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.

In this case, the amplitude is 1.6.

Since the radius changes by a maximum of 1.6 million miles.

The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)

The phase shift is 0, since when t = 0 the radius is increasing.

The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)

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