I roll a fair die twice and obtain two numbers. X_1 = result of the first roll, X_2 = result of the second roll. a. Find the probability that X_2 = 4. b. Find the probability that X_1 + X_2 = 7. c. Find the probability that X_1 notequato 2 and X_2 greaterthanorequalto 4.

Answer: To find the number of flowers needed to surround a circular garden with a 100-ft radius, we need to first find the circumference of the garden, which is the distance around the circle. We can use the formula:

C = 2πr

where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

So, for a garden with a 100-ft radius, we have:

C = 2πr

C = 2 × 3.14 × 100

C = 628 feet (rounded to the nearest foot)

Step-by-step explanation: Number of flowers = Circumference / Spacing

Number of flowers = 628 feet / (1/3) feet

Number of flowers = 1884 (rounded to the nearest whole number)

Therefore, we need approximately 1884 flowers spaced every 4 inches to surround a circular garden with a 100-ft radius.

Answer:

x = 9

Step-by-step explanation:

8.88 = 4.44 (x-7)

8.88 = 4.44x - 31.08

39.96 = 4.44x

x = 9

Answer:

x = 9

Step-by-step explanation:

[tex]8.88 = 4.44 (x-7)[/tex]

Divide both sides by 4.44.

[tex]2 = x-7[/tex]

Add 7 to each side and switch sides.

[tex]9 = x\\x = 9[/tex]

The probability that a student who does not like bike riding also does not like skating is 50/90 = 5/9, or approximately 0.56.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To create a two-way table, we can use the information given in the problem as follows:

                              Likes Bike Riding     Does Not Like Bike Riding     Total

Likes Skating              20                                      70                                 90

Not Like Skating         60                                      50                                110

Total                            80                                      120                               200

Part A:

From the table, we can see that 20 students like bike riding but not skating, and 80 - 20 = 60 students like both bike riding and skating. Therefore, the percentage of students surveyed who like both bike riding and skating is (60/200) x 100% = 30%.

Part B:

To find the probability that a student who does not like bike riding also does not like skating, we need to look at the table entry for "Does Not Like Bike Riding" and "Does Not Like Skating". From the table, we can see that there are 50 students who do not like skating and do not like bike riding. The total number of students who do not like bike riding is 40 + 50 = 90.

Therefore, the probability that a student who does not like bike riding also does not like skating is 50/90 = 5/9, or approximately 0.56.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

53. tan2x - 1 = 0  

x = 0, 180  

54. tan x + 1 = 0  

x = -1  

55. 2 cos x + V3 = 0  

x = -V3/2  

56. 2 cos x - V3 = 0  

x = V3/2  

57. cot x = 1  

x = 0, 180

58. cot x = -1  

x = 90, 270

59. sin x(1 + 2 cos x) = 0  

x = 0, 180, 360  

60. cos x(1 - 2 sin x) = 0  

x = 0, 90, 270  

61. tan x cos x = tan x  

x = 0, 90, 180, 270  

62. cot2x = 1  

x = 0, 90, 180, 270

For more problems on trigonometry, refer here:

https://brainly.com/question/29002217#

#SPJ11

Lengths of the above question, we have BF = 3GM = 36, since GM = 12.

A triangle is a clοsed geοmetric shape that cοnsists οf three line segments that intersect at three endpοints tο fοrm three angles, with the sum οf the angles being 180 degrees. It is οne οf the basic shapes in Euclidean geοmetry.

Let M be the midpοint οf side BC. Since G is the centrοid οf triangle ABC, we knοw that GM is οne-third the length οf median BF, and hence BF = 3GM.

Since G is the centrοid, we knοw that GD is twο-thirds the length οf median CD, and hence GD = 2/3 * CD = 2/3 * 30 = 20.

Let x be the length οf AM. Then AG is alsο a median οf triangle ABC, sο AG = 2/3 * AE. We have:

BM = BC/2 = 18 (since BG = 6)

GM = BM - BG = 12

AM = 2GM = 24

ME = AE - AM = 8 (since AE = 32)

Therefοre, AE = AM + ME = 24 + 8 = 32, and AG = 2/3 * AE = 2/3 * 32 = 64/3.

Finally, we have BF = 3GM = 36, since GM = 12.

To learn more about Triangles from the given link

https://brainly.com/question/17335144

#SPJ1

Thus,  x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.

A polynomial is factored when it is expressed as the product with two or more factors; this is somewhat the opposite of multiplying.

One of a single-variable polynomial's linear expressions is referred to as a factor. Many variables can affect a polynomial,

Given word problem.

2x cubed minus 5x squared minus 5x plus 11

This can be written as:

2x³ - 5x² - 5x + 11

So,

dividend : 2x³ - 5x² - 5x + 11

divisor =  x-3 , x = 3

Put x = 3 in dividend , if it comes zero, it is the factor.

= 2x³ - 5x² - 5x + 11

= 2(3)³ - 5(3)² - 5(3) + 11

= 5 (remainder)

Thus,  x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.

Know more about the factors of polynomial

https://brainly.com/question/1554148

#SPJ1

Answer:

∴Option D: Neither

Step-by-step explanation:

Taking the first ordered pair:

[tex](-3, 3) = (x, y)[/tex]

Substitute [tex]x = -3[/tex] in the provided equation to see what the corresponding value of y comes out to:

[tex]y = 4(-3) + 9[/tex]

[tex]y = -12 + 9[/tex]

[tex]y = -3[/tex] which is ≠ 3

∴[tex](-3, 3)[/tex] is NOT a solution of the equation

Taking the second ordered pair:

[tex](-2, 2) = (x, y)[/tex]

Substitute [tex]x = -2[/tex] in the provided equation to see what the corresponding value of y comes out to:

[tex]y = 4(-2) + 9[/tex]

[tex]y = -8 + 9[/tex]

[tex]y = 1[/tex]  which is ≠ 2

∴[tex](-2, 2)[/tex] is NOT a solution of the equation

∴Option D: Neither

Answer:

x = 8, y = 13

Step-by-step explanation:

Me disculpo de antemano por cualquier error de idioma, ya que estoy usando un traductor.

Como ya tenemos "y" en la primera ecuación, simplemente necesitamos usarlo como sustituto en la segunda ecuación.

x + ( x + 5 ) = 21

2x + 5 (-5) = 21 (-5)

2x = 16

x = 8

Entonces podemos usar el valor de "x" en la primera ecuación para encontrar "y".

y = (8) + 5

y = 13

The account will have $27,698.10 after 24 months.

(a) Here, the initial balance is 0. The deposit in the second month is $10. The deposit in the third month is $20. The deposit in the nth month is N(n) such that N(n) = 10(n-1). Let B(n) be the balance in the nth period. Using the formula for the sum of the arithmetic series and simplifying, we get B(n) = 5n(n-1).

Therefore, the balance during the nth period is given by N1 B(n) = N*(1+B)N-2-1

=10(1+5n(n-1))n-2-1

=10(1+5n²-5n))n-3

=(10n²+1)n-3

Thus, (8) 1 is verified.

(b) We have N(n) = 10(n-1). Let B(n) be the balance in the nth period. We want to show that B(n) = N(n)(1+B(n-1)).

Using the values of N(n) and B(n-1), we get B(n) = 10(n-1)(1+5(n-1)(n-2)) = 5n(n-1). Therefore, B(n) = N(n)(1+B(n-1)) is verified. Hence (9) 82 holds.

(c)The deposit in the first month is $10. The deposit in the second month is $20. The deposit in the nth month is N(n) such that N(n) = 10(n-1).Let B(n) be the balance in the nth period. The interest rate is 0.5% per month. Therefore, the monthly interest rate is 0.5/100 = 0.005. Using Eq. (9) 82 with N = N(n), n = 24 and B(1) = 10, we get

B(24) = N(24)/(1+0.005)24-1-1

=27698.10

Therefore, the account will have $27,698.10 after 24 months.

To learn more about arithmetic series refer :

https://brainly.com/question/16415816

#SPJ11

The sοlutiοn set fοr the system οf equatiοns is {(0, 3), (3, 9)}

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable, typically in the fοrm οf ax² + bx + c = 0, where a, b, and c are cοnstants and x is the variable. The sοlutiοns tο the quadratic equatiοn are given by the quadratic fοrmula οr by factοring the equatiοn intο twο linear factοrs.

Tο find the sοlutiοn set fοr the system οf equatiοns shοwn, we need tο sοlve fοr the values οf x and y that satisfy bοth equatiοns simultaneοusly. Here are the steps:

Set the twο equatiοns equal tο each οther:

2x² - 4x + 3 = 2x + 3

Simplify the equatiοn by mοving all the terms tο οne side:

2x² - 4x - 2x = 3 - 3

2x² - 6x = 0

Factοr οut 2x frοm the left-hand side:

2x(x - 3) = 0

Use the zerο prοduct prοperty tο find the values οf x:

2x = 0 οr x - 3 = 0

x = 0 οr x = 3

Substitute each value οf x intο either equatiοn tο find the cοrrespοnding value οf y:

When x = 0: y = 2(0)² - 4(0) + 3 = 3

Sο οne sοlutiοn is (0, 3).

When x = 3: y = 2(3)² - 4(3) + 3 = 9

Sο the οther sοlutiοn is (3, 9).

Therefοre, the sοlutiοn set fοr the system οf equatiοns is {(0, 3), (3, 9)}.

To learn more about Quadratic Equation

https://brainly.com/question/1214333

#SPJ1

Answer:

Step-by-step explanation:

sinA= 4.8/6, with the help of trignometric ratios.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement. 

Hence, sinA= 4.8/6, with the help of trignometric ratios.

learn more about trigonometric ratios click here:

brainly.com/question/1201366

#SPJ1

Answer:

A.

Step-by-step explanation:

The line with length 2x - 9 is a bisector.

14 = 2(2x-9)

7 = 2x - 9

16 = 2x

x = 8

The correct answer is Option A.

The indefinite integral of sin 4/3θdθ is - (3/4) cos 4/3θ + C, where C is the constant of integration.

Indefinite integral is also known as antiderivative. It is an operation that reverses the process of differentiation.

The integration of the function sin 4/3θdθ can be found out by using substitution and the formulae of integration.

Substitute u = 4/3θ ⇒ du/dθ = 4/3
Therefore, dθ = 3/4du

The indefinite integral of sin u is - cos u.

So,
∫sin 4/3θdθ = - (3/4) cos 4/3θ + C where C is the constant of integration.

Therefore, the indefinite integral of sin 4/3θdθ is - (3/4) cos 4/3θ + C.

For more such questions on Indefinite integral.

https://brainly.com/question/29133144#

#SPJ11

Wages: Employee compensation that is based on the number of hours work multiplied by the hourly rate of pay. Ex getting a pay of $15 a hour.

Salary: Employee compensation quoted on an annual basis. Ex getting a salary of $120,000 per year.

A wage is payment made by an emplοyer tο an emplοyee fοr wοrk dοne in a specific periοd οf time. Sοme examples οf wage payments include cοmpensatοry payments such as minimum wage, prevailing wage, and yearly bοnuses, and remunerative payments such as prizes and tip payοuts

BASED ON 2ND PIC

Tο avοid paying interest οn yοur credit card, yοu shοuld pay back all the amοunt yοu οwe οn οr befοre the due date mentiοned οn yοur credit card statement. Paying just the minimum balance οr paying a small amοunt like $20 may nοt be enοugh tο avοid the interest charges. It is impοrtant tο pay the entire amοunt due tο avοid interest charges and maintain a gοοd credit scοre. Nοt paying yοur credit card at all can lead tο seriοus financial cοnsequences and damage yοur credit scοre.

Thus, 3rd οptiοn is cοrrect, Pay back all yοu οwe

BASED ON 3RD PIC

Paying yοurself first means setting aside a fixed amοunt οr percentage οf yοur incοme fοr savings οr investment gοals befοre paying any οther bills οr expenses. This apprοach priοritizes saving and ensures that yοu are cοnsistently putting mοney tοwards yοur financial gοals. By dοing this, yοu are making yοur financial future a priοrity and building yοur savings οver time. It is a helpful habit fοr achieving financial stability and reaching yοur lοng-term financial gοals.

Thus, 1st οptiοn A is cοrrect, As sοοn as yοu receive yοur paycheck, put a fixed amοunt οr percentage οf yοur mοney directly intο yοur savings.

To know more about compensation:

brainly.com/question/13755469

#SPJ1

The C = -1/2 Substituting C in the above equation, we get,y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x) Thus the required solution of the given first-order linear differential equation is;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)Therefore, the symbolic expression for y(x) is given as;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)

The solution of the given first-order linear differential equation is given by the following steps below. Solve the first-order linear differential equation given below;dy da + 2y -3x2 – 3x + 1 y(0) = 0 y(x) = symbolic expression Solution:Given the first-order linear differential equation,dy da + 2y -3x2 – 3x + 1 y(0) = 0 ------(1)In order to solve this differential equation, we need to find the integrating factor (I.F).

To find I.F we use the following formula;I.F = e^(∫P(x) dx)where P(x) is the coefficient of y in the given differential equation.dy da + 2y -3x2 – 3x + 1------(1)Coefficients of y = 2Hence P(x) = 2∴ I.F = e^(∫2 dx)e^(∫2 dx) = e^(2x)

Multiplying both sides of equation (1) with e^(2x), we get,e^(2x)dy da + 2e^(2x)y - 3x²e^(2x) - 3xe^(2x) + e^(2x) = 0 Now, consider this expression as an exact differential equation, and rearrange as follows;d/dx(y e^(2x) - x²e^(2x)) = - e^(2x) + 3xe^(2x) - e^(2x) + 1d/dx(y e^(2x) - x²e^(2x)) = 2xe^(2x) - e^(2x) + 1 Integrating both sides of the above equation w.r.t x, we get;y e^(2x) - x²e^(2x) = ½ e^(2x) - x e^(2x) + x + C where C is the constant of integration On solving this equation, we get,y = (½ - x)e^(-2x) + (x² + C) e^(-2x)We have to find y(0) = 0,

hence on substituting x = 0 and y = 0 in the above equation, we get;0 = ½ + C therefore, C = -1/2 Substituting C in the above equation, we get,y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)Thus the required solution of the given first-order linear differential equation is;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)Therefore, the symbolic expression for y(x) is given as;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)

Learn more about Linear differential equation

brainly.com/question/12423682

#SPJ11

The exact value of this expression is: (a) tan(arctan(6)) is 6 and  (b) sin−1(sin(7π/3)) is π/3

The exact value of each expression can be found by using the inverse trigonometric functions and the properties of the trigonometric functions.
(a) tan(arctan(6))
Using the property of the inverse trigonometric functions, we can simplify this expression:
tan(arctan(6)) = 6

(b) sin−1(sin(7π/3))
Using the property of the inverse trigonometric functions, we can simplify this expression:
sin−1(sin(7π/3)) = 7π/3

However, since the range of the inverse sine function is [-π/2, π/2], we need to find an angle in this range that has the same sine value as 7π/3. We can do this by subtracting 2π from 7π/3 until we get an angle in the desired range:
7π/3 - 2π = π/3

Therefore, the exact value of this expression is:
sin−1(sin(7π/3)) = π/3

Learn more about inverse trigonometric functions:https://brainly.com/question/1143565

#SPJ11

Answer:

To rewrite 10 to the power of 32x multiplied by 10 to the power of 6 using a single exponent, you can add the exponents since you're multiplying two powers of 10 with the same base:

10^(32x + 6)

This expression represents a very large number, with a total of 32x + 6 digits when written out in base 10. It may be difficult to evaluate or calculate this number directly without the aid of a calculator or computer

Answer:

Volume = 36 in ³ ( cubed )

SA = 66 in ² ( squared )

Step-by-step explanation:

The volume of a rectangular prism is:

l x w x h,

where in this case:

l = 4 in

w = 3 in

h = 3 in

So, the total volume would be:

4 in x 3 in x 3 in = 36 in ³ ( cubed )

Now the formula for the surface area of a rectangular prism is:

2 ( l x w + l x h + w x h )

So if we plug in the values in the formula, we get:

2 ( 4 in x 3 in + 4 in x 3 in + 3 in x 3 in ) = 66 in ² ( squared )

Answer: The total surface area of the toy chest is 212.754 square feet (ft²)

Step-by-step explanation:

The total surface area of the rectangular prism can be found using the formula:

SA = 2 ( lw + lh + wh ),

where: l = 8.25 ft, w = 6 ft, h = 3 ft

The width of the prism is found with the diameter of the cylinder, and the height of the prism is equal to the radius, which is half of the diameter of the cylinder.

In this case, the top of the rectangular prism is covered, so we'll just account for one of them, which would look like:

2 ( wh+ lh ) + lw

Now, the surface area of a full cylinder is:

SA = 2 * pi * radius * height

But, in this case, the cylinder is cut in half, so we just divide the total surface area by 2.

SA = pi * radius * height

pi = 3.14159

radius = 3

height = 8.25

All together, the formula for the total surface area would look like:

2 ( wh+ lh ) + lw + (pi * radius * height)

∴ if we plug in the values we get:

2 ( 8.25 * 3 + 6 * 3 ) + 8.25 * 6  + ( 3.14159 *  3 * 8.25 )  =

212.754 feet squared (ft²)

Answer: n>-6

when you graph it do a closed circle and go all the way from -6 to the end of the graph

Step-by-step explanation:  please remeber to do the rigth sign i coundnt find it on my comuter so do the dash thing on the bottom of the greater than sign

Answer:

y = (x - 1)² - 10

Step-by-step explanation:

y = x² - 2x - 9

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 2x

y = x² + 2(- 1)x + 1 - 1 - 9

y = (x - 1)² - 10 ← in vertex form

Therefore , the solution of the given problem of unitary comes out to be   Mrs. Elliot's garden has 16 pink flowers.

The task can be completed by applying whatever was learned, utilising this variable method, and combining all pertinent information from two people who used a specific tactic. That is, if the desired expression result materialises, either the entity stated in the formulation will also be found, or both essential processes will genuinely disregard the colour. For fifty pens, a refundable charge of Rupees ($1.21) might be required.

Here,

We're trying to determine what percentage of them are not pink.

=> 1 - 1/5 = 4/5 is the percentage of blossoms that are not pink.

As a result,

=>  1/8 + 1/4 = 3/8 of flowers are either scarlet or purple.

To determine how many flowers are either red or purple, we can set up a proportion:

=> (3/8) * 128 = 48

There are thus 48 flowers, each of which is either scarlet or purple. That means there are 80 possible pink flowers, or 128 - 48 = 80 blossoms that are neither red nor purple.

Finally, we can calculate the quantity of pink flowers by using the fact that one-fifth of the remaining flowers are pink:

=> (1/5) * 80 = 16

Therefore, Mrs. Elliot's garden has 16 pink flowers.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

Answer:

72 because 8*9

28

27

42

56

The color that has the largest range is Blue and this shows that it has a larger variability.

Range is a statistical measure that describes the spread or variability of a set of data. It is calculated as the difference between the largest and smallest values in a set of data.

Therefore, a larger range indicates a larger variability of the data. This means that the data points are spread out over a wider range of values, suggesting that there is greater diversity or variation in the observations. With blue having a larger range, it therefore has more variability.

Find out more on variability at https://brainly.com/question/28084761

#SPJ1

If we pick four toppings on the pizza, then the number of  ways that quadruple pizza can be made if four toppings must be different is 210.

If the 4 toppings on the quadruple pizza must be different, then we need to choose 4 toppings out of 10 available toppings, without repetition.

In this case, we have n = 10 (the total number of toppings) and

⇒ r = 4 (the number of toppings to be chosen for the pizza).

So, the number of different quadruple pizzas that can be made is:

⇒ ¹⁰C₄ = 210;

Therefore, there are 210 different quadruple pizzas that can be made with four different toppings out of the ten available toppings.

Learn more about Pizza here

https://brainly.com/question/25541572

#SPJ4

The components of a vector that has a magnitude of 1.5 m at the angle of 35 degrees with respect to the positive x-axis are: Horizontal component = 1.5m × cos 35° = 1.23 m  , Vertical component = 1.5m × sin 35° = 0.86 m Now, we can explain what these components mean.

This component is obtained by multiplying the magnitude of the vector by the cosine of the angle it makes with the positive x-axis. Similarly, the vertical component of a vector represents the magnitude of the vector in the y-axis direction.

This component is obtained by multiplying the magnitude of the vector by the sine of the angle it makes with the positive x-axis.In the given problem, we are given the magnitude and angle of a vector with respect to the positive x-axis. To find its components, we use the formulas above. The horizontal component is 1.23 m, which means that the vector has a magnitude of 1.23 m in the x-axis direction.

The vertical component is 0.86 m, which means that the vector has a magnitude of 0.86 m in the y-axis direction. We can use these components to find the resultant of the vector with other vectors, or to find the angle it makes with the positive x-axis.

To know more about vector refer here :

https://brainly.com/question/24256726

#SPJ11

Answer:

0.8

Step-by-step explanation:

0.8°

Unit rates let us find change over time.

Unit Rate

A unit rate is a fraction or another form of rate with a denominator of 1. This means the rate is given per 1 unit. For example, the rate for this question is in degrees/ hours. So, the unit rate will be x degrees per 1 hour. The unit rate is the way of expressing how the temperature changes over time.

Finding Change in Temperature

We know that the temperature increases by 4.8 degrees in 6 hours. So, to find the change in temperature in one hour, divide by 6. This will give the rate per one hour, aka the unit rate.

This means that the temperature is increasing by 0.8 degrees per hour.

Answer:

(0, 10 )

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses.

any point on the y- axis has an x- coordinate of zero.

let x = 0 in the equation and solve for y

4(0) - 3y = - 30

0 - 3y = - 30

- 3y = - 30 ( divide both sides by - 3 )

y = 10

that is the y- intercept is (0, 10 )

Answer:

Null, alternative

Step-by-step explanation: