plot 1 2/5 - 1/2 - 2 1/10 on a number line

In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy  the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).

Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.

From the question, p = number of pounds Juan will buy.

candy=costs $8 per pound

$20/$4 = 5 pounds

p>5

at least 5 pounds

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We need to first determine how many totally odd counting numbers there are between 1 and 9. The answer is 250.

It is an integer that is not divisible by two and therefore has a remainder of 1 when divided by two. It is also referred to as an odd number, an odd integer, or an uneven number.

For this, let us consider all the digits from 1 to 9, and their respective sums.

Digit: 1 Sum: 1 (odd)

Digit: 3 Sum: 3 (odd)

Digit: 5 Sum: 5 (odd)

Digit: 7 Sum: 7 (odd)

Digit: 9 Sum: 9 (odd)

Since all the digits between 1 and 9 and their respective sums are all odd, it means that any counting number less than 10 that is composed of only these digits would be totally odd. This means that there are 5 totally odd counting numbers less than 10, i.e., 1, 3, 5, 7 and 9.

Now, since any counting number less than 1000 can be composed of any combination of these 5 digits, the total number of totally odd counting numbers less than 1000 can be calculated by multiplying the number of digits (5) by the number of combinations of those digits (999). The result of this calculation is 250, which is the answer to the question.

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Here is an example of how to create an object model, UML diagrams, and contract obligations in general.

Let's have a look at a basic "Bank Account" system, where a customer may deposit money, withdraw it, and see the amount of their account. The following classes would be represented in the UML class diagram for this system:

Bank Account Client

The following characteristics would be included in the Bank Account class:

string Account Number

stability: float

and the subsequent techniques:

deposit(float amount) = None

withdrawal(float :amount) = None

float: check Balance()

The following characteristics would apply to the Customer class:

string name

list of accounts[Bank Account]

and the subsequent techniques:

account: Bank Account; add account(account) -> None

account: Bank Account; remove  Account(account: None)

Bank Account: get  Account(Account number: string)

For the Bank Account class, the design by contract obligations would be:

Pre-conditions:

amount > 0

withdraw(amount): amount > 0 and balance >= amount

Check Balance(): None

Post-conditions:

deposit(amount): balance += amount

withdraw(amount): balance -= amount

Check Balance(): return balance

The design by contract responsibilities for the Customer class would be:

Pre-conditions:

Add account(account): account not in accounts

Post-conditions:

Add account(account): accounts. append(account)

remove (account): accounts.

get account (account number): return the Bank Account object with the given account Number.

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The coordinates of the figure after translation & dilation are A''(1,3) ,R''(-1/2,1) , G''(-1,-3/2), Y''(5/2,5/2).

A quadrilateral is a polygon with four sides and four vertices. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Scale factor refers to the ratio of the length or size of an object in one dimension to the length or size of a corresponding object in another dimension. It is commonly used in mathematics and geometry to describe the relationship between two similar figures. For example, if one square has a side length of 4 cm and another square is similar to it with a side length of 8 cm, the scale factor between the two squares is 2:1.

A(2,8) R(3,4) G(2,-1) Y(9,7)

Translate it to 4 units left gives the result:

A'(-2,6) ,R'(-1,2) ,G'(-2,-3), Y'(5,5)

Now dilate it:

A''=(-1,3), R''(-1/2,1), G''(-1,-3/2), Y''(5/2,5/2)

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The length of the arc with a central angle of 285 degrees and radius 16 inches is 79.6 inches

From the question, we have the following parameters that can be used in our computation:

central angle = 285 degrees

Radius = 16 inches

Using the above as a guide, we have the following:

Length of arc = central angle/360 * 2 * 3.14 * Radius

Substitute the known values in the above equation, so, we have the following representation

Length of arc = 285/360 * 2 * 3.14 * 16

Evaluate

Length of arc = 79.6

Hence, the length of the arc is 79.6 inches

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2. The solution to the integral is: -2cot(x) - 4ln|sin(x)| - 3x + C

6. The integral converges and its value is 0.

2. To solve this integral using partial fractions, we need to rewrite the integrand as a sum of simpler fractions. We first rewrite the integrand as follows:

(2cos(x)/sin²(x) - 4 sin(x) - 5) = 2/sin(x)² - 4sin(x) - 5

Now we need to express the first term 2/sin(x)² as a sum of two fractions with different denominators. To do this, we let:

2/sin(x)² = A/sin(x) + B/sin(x)²

Multiplying both sides by sin(x)², we have:

2 = A sin(x) + B

Next, we need to determine the values of A and B. To do this, we can substitute two different values for x that make sin(x) ≠ 0, such as x = 0 and x = π/2.

Substituting x = 0, we get:

2 = A(0) + B

2 = B

Substituting x = π/2, we get:

2 = A(1) + B

2 = A + B

2 = A + 2

Therefore, A = 0.

So we have:

2/sin(x)² = B/sin(x)²

B = 2

Substituting these values back into our original expression, we get:

(2cos(x)/sin²(x) - 4 sin(x) - 5) = 2/sin(x)² - 4sin(x) - 5

= 2/sin(x)² - 4sin(x)/sin(x) + 2sin(x)/sin(x) - 5

= 2/sin(x)² - 4cot(x) + 2 - 5

= 2/sin(x)² - 4cot(x) - 3

Now we can integrate each term separately:

∫2/sin(x)² dx = -2cot(x) + C1

∫-4cot(x) dx = -4ln|sin(x)| + C2

∫-3 dx = -3x + C3

So the solution to the integral is:

∫(2cos(x)/sin²(x) - 4 sin(x) - 5) dx = -2cot(x) - 4ln|sin(x)| - 3x + C

where C = C1 + C2 + C3 is the constant of integration.

6. We can solve this integral by using the substitution u = x - 2, which gives us du = dx. We can then rewrite the integral as:

∞

∫₁ (1/(x-2)²) dx = ∞

∫-∞ (1/u²) du

Now, we can evaluate this integral as:

∞

∫-∞ (1/u²) du = [-1/u]∞

= [0 - (-1/(-∞))]

= 0 - 0

= 0

Therefore, the integral converges and its value is 0.

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The text format of the questions:

2. Use the method of partial fractions to find the integral:

∫(2cos(x)/sin²(x) - 4 sin(x) - 5) dx

6. State whether the integral converges or diverges. If it converges give the value it converges to.

∞

∫₁ (1/(x-2)²) dx

The number of fewer students to get to school by skateboard than by car and bus combined would be 60 fewer students.

To find how many fewer students get to school by skateboard than by car and bus combined, we need to add the number of students who use car and bus and then subtract the number of students who use skateboard.

Car: 30 students

Bus: 40 students

Car + Bus = 30 + 40 = 70 students

Skateboard: 10 students

Difference = (Car + Bus) - Skateboard

Difference = 70 - 10 = 60 students

So, 60 fewer students get to school by skateboard than by car and bus combined.

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Answer:

the volume of the cylinder is 904.32 m³

Step-by-step explanation:

The rate at which the college student is earning credits, given the semesters taken, would be E. 14 credits per Semester.

The formula to find the number of credits the student takes per semester, would be :

( total credits after 3 semesters - total credits at the start ) / number of semesters = credits per semester

total credits after 3 semesters = 54 credits

total credits at the start = 12 credits

The credits per semester is therefore;

= ( 54 - 12 ) / 3

= 42 / 3

= 14 credits per semester

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The complete question is:

Which of these expresses the rate at which she is earning credits? Select the correct answer below:

3 credits per semester

42 credits per semester

14 semesters per credit

12 credits per semester

14 credits per Semester

7 semesters per credit

The given function h(x) is h(-5) = -2, h(-2) = -1 and h(5) = -2.

The set of all possible inputs is the domain of a function. For instance, all real integers other than x=0 are in the domain of f(x)=x2 and g(x)=1/x, respectively. Additionally, custom functions with more restricted domains can be defined.

The definition of the function h(x) is as follows:

h(x) =

-2 if x < 2

-1 if x = -2

Using this definition, we can find the values of h(-5), h(-2), and h(5) as follows:

h(-5): Since -5 < 2, we use the first part of the definition and set h(-5) = -2.

h(-2): Since -2 = -2, we use the second part of the definition and set h(-2) = -1.

h(5): Since 5 > 2, we use the first part of the definition and set h(5) = -2.

Therefore, we have:

h(-5) = -2

h(-2) = -1

h(5) = -2

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Recall the general equation for a line in slope-intercept form:

[tex]y=mx+b[/tex]

where:

[tex]\text{y = y-coordinate}[/tex]

[tex]\text{m}=\bold{slope}[/tex]

[tex]\text{x = x-coordinate}[/tex]

[tex]\text{b = y-intercept}[/tex]

In this equation, if you isolate for [tex]y[/tex], you end up with an equation that looks like this:

[tex]-4x+y=0[/tex]

[tex]-4x +4x+y=0+4x[/tex]

[tex]\implies y=4x+0[/tex]

Recall that in direct variation, the graph goes through the origin, (0,0). Since the y-intercept of this equation is 0, this means the graph intersects the origin. Thus, this graph represents direct variation.

If you were to graph the line, you would see the intersection at (0,0):

graph[tex]\{y=4x [-12.66, 12.65, -6.33, 6.33]\}[/tex]

The one to one functions in the options includes

A one-to-one function, also known as an injective function, is a type of function in mathematics where every element in the domain maps to a unique element in the range.

So we can say that, each input value corresponds to exactly one output value, and no two distinct input values have the same output value.

Graphically, one-to-one functions pass the horizontal line test, meaning that no horizontal line intersects the graph of the function more than once.

Applying the horizontal line test shows that the one-to-one function are: Graph 1, 4 and 6

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Answer:

(a) The total ratio is 1 + 3 = 4, so Jill's share is (3/4) of £60:

Jill's share = (3/4) × £60 = £45.

(b) The ratio of their ages remains the same, so if Jack is one year older, Jill is also one year older. Therefore, Jill's age is 4 and Jack's age is 2, and Jack's share is (2/4) of £60:

Jack's share = (1/2) × £60 = £30.

(c) Let x be the age of Jack when he receives £25 from Uncle Fred. According to the problem, Jill is always two years older than Jack. Therefore, when Jack is x years old, Jill is x + 2 years old. The ratio of their ages is x : (x + 2), and this ratio is equal to 5/7 (25 pounds is 5/7 of 35 pounds, which is the total amount that they will receive). We can write an equation to solve for x:

x/(x+2) = 5/7

7x = 5(x + 2)

7x = 5x + 10

2x = 10

x = 5

Therefore, Jack will be 5 years old when he receives £25 from Uncle Fred at Christmas.

A) £45 because Jill will get 3/4 and Jack will get 1/4. To check our work, 60 divided by 4 is 15. 15 times 3 is 45 and 15 times one is 15.

B) £30 because it is a new year, both nephews will increase by one year. Now Jill is 4 and Jack is 2. So each kid will get half the share. 2 divided by 4 is 0.5 which is half of one. Half of 60 is 30.

C) 5 years Jill will always be 2 years older than Jack; this shows us that if some more years pass, Jill will be 7 and Jack will be 5 —> 1/4 x £60 = £25 Multiplying both sides by 4/60, we get:x = 5/4. This means Jack will be 5.

—————

Please remember to revise this and make it in your own words if you want! I am unsure about question C so comment!! I hope this helps you. -Doodle

—————

For the given right angled triangle cosine of angle B is 5√89/89.(option A).

What is right angled triangle?

It is a particular type of triangle having one angle is 90° or right angle. The adjacent sides of the right angle are called base and the perpendicular and the opposite side of 90° is called hypotenuse.

The given triangle is the right angled triangle. The three sides of a right angled triangle are called base, perpendicular and hypotenuse.

In the given figure base=  5 inches and perpendicular = 8 inches

By Pythagoras theorem at first we will find out the hypotenuse. Let the hypotenuse= c inches

For any right angled triangle,

(perpendicular)² +(base)²= (hypotenuse)²

⇒ (8)² + (5)² = (c)²

⇒ 64+ 25 = c²

⇒ c² =89

⇒ c= ±√89

As hypotenuse cannot be negative

So hypotenuse = √89 inches.

Now to find cosine of angle B that is cos B we will use the trigonometric function.

cos B= Adjacent side/ hypotenuse

         = 5/√89

        = 5√89/89 [ Multiplying the numerator and the denominator by √89 ]

Hence, cosine of angle B is 5√89/89.

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The calculated degrees of freedom for the t-test is 18

The degrees of freedom (df) for an independent t-test with two samples can be calculated using the following formula:

df = (n1 + n2) - 2

Where n1 is the sample size of the first group and n2 is the sample size of the second group.

In this case, the first sample has N = 8 and the second sample has N = 12.

Therefore, the degrees of freedom for the t-test will be:

df = (8 + 12) - 2

df = 18

So the t-test for this experiment will have 18 degrees of freedom.

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The requried, quadratic equation that models the path of the golf ball, is 16.0850t² - 110.560t - 190 = 0 and the angle the ball takes off is 64.4⁰.

The motion of the golf ball can be modeled using two equations, one for the vertical motion and another for the horizontal motion.

The equation for the vertical motion of the ball is given by:

h = V₀t - ¹/₂gt²,

Using the given values, we find that,
V₀ = √(2 x 32.17 x 190) = 110.56 ft/s.

Substituting this value and the value of g into the equation of motion for the vertical direction, we get -190 = 110.56t - ¹/₂(32.17)t², which simplifies to 16.0850t² - 110.560t - 190 = 0.

The equation for the horizontal motion of the ball is given by [tex]x = V_xt[/tex], where x is the horizontal distance traveled, Vx is the initial horizontal velocity, and t is the time. Using the given value of x, we can find Vx as [tex]V_x = 440/t.[/tex]

We can then solve the quadratic equation 16.0850t² - 110.560t - 190 = 0 to find the time t of flight.
Using the formula method, we get t = 8.3 s. Substituting this value into the equation for the horizontal motion, we get [tex]V_x = 440/8.3 = 53.01 ft/s.[/tex]

Finally, we can find the angle of projection θ using the formula tan θ = [tex](V_y) / (V_x)[/tex],

tan θ = (110.56)/(53.01),

which simplifies to tan θ = 2.086. Taking the inverse tangent of both sides, we get θ = tan⁻¹(2.086) = 64.4⁰.

Therefore, the angle at which the ball takes off is 64.4⁰.

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Answer:

The odds that are less generous are 19:1, 14:1, and 15:1.

Step-by-step explanation:

You have to see which numbers are greater than 11.

The correct statements describing the area and perimeter of the patio are:

The area of a rectangle is given by the product of its length and width. So, the area of the patio is:

Area = length x width

Area = (1 + 2x)(2 - 3x)

Therefore, the area of the patio is (1 + 2x)(2 - 3x) square yards.

The perimeter of a rectangle is given by the sum of the lengths of all four sides.

So, the perimeter of the patio is:

Perimeter = 2(length + width)

Perimeter = 2(1 + 2x + 2 - 3x)

Perimeter = 2(3 - x)

Therefore, the perimeter of the patio is 2(3 - x) yards.

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Therefore, The dilated image's vertices are as follows:B'(2 , 3)   C'(3 , 3)     D'(1 , 3)

It is not necessary for the dilation's center to be inside the form. It might be the polygon's vertices. The preimage is still a square in this case, but the center of the dilatation is at the top-left vertex, which is shared by both of the dilated pictures (one smaller and one larger).

To get the vertices of the dilated image, multiply each vertex's coordinate by a factor of three.

B(6,9)⇒B'(1/3×6,1/3×9) = B'(2 , 3)

C(9,9)⇒C'(1/3×9 , 1/3×9) = C'(3 , 3)

D(3,9)⇒D'(1/3×3 ,1/3×9) = D'(1 , 3)

The dilated image's vertices are as follows:

B'(2 , 3)   C'(3 , 3)     D'(1 , 3)

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Answer:

1600

Step-by-step explanation:

The answer you tried is equivalent.

Answer:

The answer for Probability is 1/2

Step-by-step explanation:

7,6,8,1,54,23

Probability of spinning an odd number greater than 3=1,7,23

P=3/6

P=1/2

A circle-based model is highly suitable for the design and construction of roundabouts, which present themselves as practical solutions to tackle traffic-related issues.

Roundabout intersections involve vehicles circulating around a central island in a counterclockwise direction. The circular form guarantees fluidity in traffic movements and significantly reduces the requirement for traffic lights and stops signs while enhancing security.

This model entails using a circle, ascertaining that the diameter corresponds with the width of the roadway, with its center accommodating the location of the island at equidistant distances from all contact points on the circle's periphery, thus ensuring optimal functionality.

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The preimage of the quadrilateral is in the second quadrant. The quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

A quadrilateral is a geometric shape that consists of four straight sides and four angles. It is a two-dimensional shape, also known as a 2D polygon, and can be defined as any closed shape that has four sides. There are many different types of quadrilaterals, each with its own unique set of characteristics.

The second quadrant is characterized by negative x-coordinates and positive y-coordinates, while the fourth quadrant has positive x-coordinates and negative y-coordinates.

If the preimage of the quadrilateral is in the second quadrant, then its x-coordinates are negative and its y-coordinates are positive.

When the quadrilateral is reflected across the x-axis, its x-coordinates will remain the same but its y-coordinates will become negative. Therefore, if the preimage is in the second quadrant and the quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

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Answer:

range = 22

Step-by-step explanation:

the range is the difference between the largest and smallest values in the data set.

largest value = 25 , smallest value = 3

range = 25 - 3 = 22

The requried  [tex]\int_a^{oo} g(x) dx[/tex] must be convergent. Option C is correct.

Since f(x) is greater than or equal to g(x) for all x, we know that:

[tex]\int_a^{oo} f(x) dx\geq\int_a^{oo} g(x) dx[/tex]

If [tex]\int_a^{oo} f(x)[/tex]dx is convergent, then by comparison test, [tex]\int_a^{oo} g(x) dx[/tex] must also be convergent. Therefore, the correct answer is (C) g(x)dx is convergent.

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The amplitude and period of each function are calculated and listed below

The amplitude and period of each function can be determined using their standard form:

y = A sin (Bx + C) or y = A cos (Bx + C)

where |A| is the amplitude, B is the frequency (or angular frequency), and 2π/B is the period.

Let's apply this formula to each function:

y = cos(2x)

Amplitude = 1

Period = 2π/2 = π

y = -sin(2x)

Amplitude = 1

Period = 2π/2 = π

y = -3sin(3x)

Amplitude = 3

Period = 2π/3

y = (1/2)cos(4x)

Amplitude = 1/2

Period = 2π/4 = π/2

y = 10sin(1/2x)

Amplitude = 10

Period = 2π/(1/2) = 4π

y = 5cos(1/4x)

Amplitude = 5

Period = 2π/(1/4) = 8π

y = (-1/3)cos(1/3x)

Amplitude = 1/3

Period = 2π/(1/3) = 6π

y = 4sin(-2x)

Amplitude = 4

Period = 2π/(-2) = -π

y = -2sin(2πx)

Amplitude = 2

Period = 2π/(1) = 2π

y = -3sin(πx)

Amplitude = 3

Period = 2π/π = 2

y = 1 + (1/2)cos(πx)

Amplitude = 1/2

Period = 2π/π = 2

y = -2 + cos(4πx)

Amplitude = 1

Period = 2π/(4π) = 1/2

The graphs of the functions are added as attachment

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The solutions are explained in the solution below.

1) t³ = 216

t = ∛216

t = ∛6×6×6

t = 6

2) a² = 15

a = √15

a = 3.87

3) m³ = 8

m = ∛8

m = ∛2×2×2

m = 2

4) c³ = 343

c = ∛343

c = ∛7×7×7

c = 7

e) f³ = 181

f = ∛181

f = 5.65

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