amaya nash myOpenMath Home My Classes User Settingsi Log Out Course Messages Calendar Gradebook Home Math1703.01 Sp22 Assessment 5mins x Progress saved Submit and End vo Unit 1: Chapter 6 Quiz 10 points possible 0/6 answered Question 3 2 pts 1 Details Let X represent the full height of a certain species of tree. Assume that X has a normal distribution with a mean of 56.6 ft and a standard deviation of 9.9 ft. A tree of this type grows in my backyard, and it stands 44.7 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers standa 74.4 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers, Enter your answers as decimals accurate to 4 decimal places. Question Help: Message instructor > Next Question

The value of 8 cos(2x) accurate to 4 decimal places is -3.6009.

We can start by drawing a right triangle in Quadrant 1 with an angle x, where the opposite side is 13 and the adjacent side is 8.

Using the Pythagorean theorem, we can find the hypotenuse of the triangle:

 [tex]c^2 = a^2 + b^2\\ c^2 = 13^2 + 8^2\\ c^2 = 169 + 64\\ c^2 = 233\\ c = \sqrt{(233)}[/tex]

Now we can use trigonometric identities to find cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)[/tex]

We can find sin(x) using the triangle we drew earlier:

sin(x) = opposite / hypotenuse

sin(x) = 13 / [tex]\sqrt{(233)}[/tex]

And we can find cos(x) using the triangle as well:

cos(x) = adjacent / hypotenuse

cos(x) = 8 / [tex]\sqrt{(233)}[/tex]

Plugging these values into the identity for cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (8 / \sqrt{(233))^2} - (13 /\sqrt{(233))^2} \\cos(2x) = (64 / 233) - (169 / 233)\\cos(2x) = -105 / 233[/tex]

Finally, we can find 8 cos(2x):

8 cos(2x) = 8 * (-105 / 233)

8 cos(2x) = -3.6009 (rounded to 4 decimal places)

Learn more about Trigonometry: https://brainly.com/question/29002217

#SPJ11

The Quick Meals Diner served 131 child plates and 157 adult plates.

Let's use a system of two equations to represent the given information:

c + a = 288     (1)   // The number of child and adult plates served add up to 288

2.5c + 8.2a = 1614.9   (2)   // The total amount collected is the sum of the prices of all plates served

where c represents the number of child plates served and a represents the number of adult plates served.

We can use equation (1) to solve for c in terms of a:

c = 288 - a

Substituting this expression for c into equation (2), we get:

2.5(288 - a) + 8.2a = 1614.9

720 - 2.5a + 8.2a = 1614.9

5.7a = 894.9

a = 157

So, 157 adult plates were served. Substituting this value into equation (1), we get:

So, 157 adult plates were served. Substituting this value into equation (1), we get:

So, 131 child plates were served.

Therefore, The result is 131 child plates and 157 adult plates.

Learn more about Equation: https://brainly.com/question/10413253

#SPJ11

Step-by-step explanation:

Using the formula V = Pe^(rt), we have:

P = $741

r = 0.058 (since the interest rate is 5.8%)

t = 13

So, V = 741e^(0.05813) = $1613.87 (rounded to the nearest cent)

Therefore, the amount of money in the account after 13 years is $1613.87.

Answer:

Step-by-step explanation:

Answer: x=6, y=8

Using elimination means that we eliminate one of the variables in both equations which help find out the other variable, which we then substitute to find the whole equation.

    3x-4y=-14

+   3x+2y=-2

=>-4y=-14

+   2y=-2

=>-2y=-16

=>y=8

So to find x,

3x-4(8)=-14

=3x=-14+32

=x=18/3 so x=6

PLEASE MARK BRAINLIEST IF THIS HELPED!

No, 5x^2+y=0 is not a direct variation.

Direct variation is a relationship between two variables, x and y, where y is directly proportional to x, meaning that as x increases, y increases in proportion to x, and as x decreases, y decreases in proportion to x.

The equation 5x^2+y=0 does not satisfy this relationship since y is not directly proportional to x. As x increases or decreases, y may change in a non-proportional manner due to the presence of the constant term.

An example of a direct variation equation is y = kx, where k is a constant. In this equation, y is directly proportional to x, with a constant of proportionality k.

Learn more on direct variation here: https://brainly.com/question/6499629

#SPJ1

Answer:

Exact form: 121π

Decimal form: 380.1327111...

Step-by-step explanation:

The area of the circle is given by the formula A = πr², where A is the area of the circle and r is the radius.

Given the diameter of 22cm, we know that the radius is 11cm, as the radius is half the diameter.

We can then put this into the formula to find the area of the circle:

A = πr²

A = π * 11²

A = 121π

Note that the answer here is given in terms of π so it can be expressed in its exact form, as 121π is an irrational number roughly equivalent to 380.1327111... The answer you need to provide will depend on whether the question asks for the exact form, or to a certain number of decimal places / significant figures. If it the latter, you can round off the decimal answer as appropriate.

Answer:

12

Step-by-step explanation:

Its easy and right

Answer:

2

Step-by-step explanation:

For 4 and 6, the common factors are 1 and 2. Since 2 is the highest among the given factors, HCF will be 2 for 4 and 6.

156 customers are expected to wear a black shoe.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

As per the given data:

Customers with black shoes = 13 out of 30

Customers with brown shoes = 17 out of 30

Total customers in the mall = 360

Probability that a customer wears black shoes:

P(B) = 13/30 = 0.433

Number of customers out of 360 expected to wear black shoes:

= P(B) × 360

= 0.433 × 360

= 156 customers.

Hence, 156 customers are expected to wear a black shoe.

To learn more about the probability, visit:

brainly.com/question/11234923.

#SPJ9

The value of x is 7

The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°

Therefore ;

50+28+15x-3 = 180

78-3 +15x = 180

75 +15x = 180

collect like terms

15x = 180-75

15x = 105

divide both sides by 15

x = 105/15

x = 7

therefore the value of the missing variable (x) is 7

learn more about angle on a straight line from

https://brainly.com/question/24024505

#SPJ1

Answer:

We can use the given formula to solve for the cost C:

P = R - C

We know that P = $49.32 and R = $81.18, so we can substitute these values into the formula:

$49.32 = $81.18 - C

Next, we can solve for C by isolating it on one side of the equation:

C = $81.18 - $49.32

C = $31.86

Therefore, it cost Zach $31.86 to make the jewelry he sold at the fair.

An ellipse has an equation equal to 9x^2-144x+16y^2+96y+495=0, the eccentricity of the curve is √7/4.

To compute the eccentricity of the curve of an ellipse, we must first complete the square for both x and y terms to put the equation in standard form.

Complete the square for x terms:
9x²- 144x + 495 = -16y² - 96y
9(x² - 16x) + 495 = -16(y² + 6y)
9(x²- 16x + 64) + 495 - 9(64) = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y)

Complete the square for y terms:
9(x - 8)² + 39 = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y + 9) + 16(9)
9(x - 8)² + 39 - 16(9) = -16(y + 3)²
9(x - 8)² - 105 = -16(y + 3)²

Move constant term to the right side of the equation and divide by -105:
9(x - 8)² - 16(y + 3)² = 105
-9(x - 8)²/105 + 16(y + 3)²/105 = 1
(x - 8)²/(105/9) + (y + 3)²/(105/16) = 1

Identify the values of a^2 and b^2:
a² = 105/9
b² = 105/16

Compute the eccentricity using the formula e = √(1 - (b²/a²)):
e = √(1 - ((105/16)/(105/9)))
e = √(1 - (9/16))
e = √(7/16)
e = √7/4

Therefore, the eccentricity of the curve is √7/4.

Learn more about eccentricity at https://brainly.com/question/13054654

#SPJ11

F = Fran's income

W = Winston's income

[tex]F+W=80000\hspace{5em}\stackrel{ \textit{one quarter} }{\cfrac{W}{4}}=\stackrel{ \textit{one sixth} }{\cfrac{F}{6}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{F+W=80000}\implies F=80000-W \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{W}{4}=\cfrac{F}{6}}\implies \stackrel{\textit{substituting from above}}{\cfrac{W}{4}=\cfrac{80000-W}{6}}\implies 6W=320000-4W \\\\\\ 10W=320000\implies W=\cfrac{320000}{10}\implies \boxed{W=32000}~\hfill \stackrel{ 80000~~ - ~~32000 }{\boxed{F=48000}}[/tex]

The formula holds for k + 1.

What is mathematical induction?

Mathematical induction is a method of mathematical proof used to establish the truth of a statement for an infinite set of values.

To prove the formula for every positive integer n:

3 + 11 + 19 + 27 + ... + (8n - 5) = n(4n - 1)

using mathematical induction, we need to show two things:

Step 1: Base Case

When n = 1, we have:

3 = 1(4(1) - 1)

Simplifying the right-hand side gives:

3 = 3

So the formula holds for n = 1.

Step 2: Inductive Step

Now assume that the formula holds for some positive integer k, which means:

3 + 11 + 19 + 27 + ... + (8k - 5) = k(4k - 1)

We need to show that the formula also holds for k + 1. That is, we need to show that:

3 + 11 + 19 + 27 + ... + (8(k+1) - 5) = (k+1)(4(k+1) - 1)

Starting with the left-hand side of this equation:

3 + 11 + 19 + 27 + ... + (8(k+1) - 5)

= (3 + 11 + 19 + 27 + ... + (8k - 5)) + (8(k+1) - 5) (by adding the next term)

= k(4k - 1) + (8k + 3) (by substituting the formula for k)

[tex]= 4k^2 - k + 8k + 3[/tex]

[tex]= 4k^2 + 7k + 3[/tex]

Now, we simplify the right-hand side of the equation:

(k+1)(4(k+1) - 1)

= (k+1)(4k + 3)

[tex]= 4k^2 + 7k + 3[/tex]

We can see that the left-hand side and the right-hand side are equal.

Hence, the formula holds for k + 1.

To learn more about mathematical induction, Visit

https://brainly.com/question/24672369

#SPJ1

Answer:

34

Step-by-step explanation:

3dds

Answer:

The surface area of a right circular cylinder consists of three parts: the top and bottom circular faces, and the curved lateral surface.

The area of each circular face is given by the formula A = πr^2, where r is the radius. Therefore, the total area of the two circular faces is:

2A = 2πr^2

The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Therefore, the lateral surface area of the cylinder is:

A = 2πrh

Substituting the given values, we get:

A = 2π(5 cm)(9 cm)

Simplifying, we get:

A = 90π cm^2

Adding the areas of the circular faces and the lateral surface, we get the total surface area:

Total surface area = 2A + A = 3A

Substituting the value of A, we get:

Total surface area = 3(90π cm^2) = 270π cm^2

Therefore, the exact surface area of the cylinder is 270π square centimeters.

Answer:

Well question is not clear rewrite

The point where the two lines come together (1,1). Hence, x = 1 and y = 1 are the answers to the system of equations.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

The technique of solving a system of equations involves calculating the unknown variables while maintaining the equations balanced on both sides. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true.

To know more about equations visit:-

https://brainly.com/question/29657983

#SPJ1

The matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]

To find a \( 2 \times 2 \) matrix \( A \) such that \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \], we can solve for A by multiplying both sides of the equation by the inverse of the left matrix. The inverse of \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] \] is \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right]. \] Multiplying both sides of the equation by this inverse gives \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right]A= \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right], \] which simplifies to \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \] Thus, the matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]

Learn more about matrix

brainly.com/question/28180105

#SPJ11

Answer: Y=6/5

Step-by-step explanation:

Y=1/4X+6/5

(set X to zero 1/4(0) = 0)

Y=0+6/5

Y=6/5

The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

To express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form, we need to multiply the two expressions together and then simplify. Here are the steps:

1. Distribute the first term of the first expression to the second expression: (4/3)x * (5/6)x + (4/3)x * (5/3) = (20/18)x^2 + (20/9)x
2. Distribute the second term of the first expression to the second expression: -6 * (5/6)x + -6 * (5/3) = (-30/6)x + (-30/3)
3. Combine the like terms: (20/18)x^2 + (20/9)x + (-30/6)x + (-30/3) = (20/18)x^2 + (-10/9)x + (-30/3)
4. Simplify the fractions: (10/9)x^2 + (-10/9)x + (-10)

So the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

Learn more about trinomial

brainly.com/question/16347049

#SPJ11

Answer:

Step-by-step explanation:

4-5 would be less than 1 so it would be -1

Throughout the hour, 70 percentage of customers add chocolate creamer to their coffee.

Find the proportion of consumers who selected chocolate creamer and add up all of the customers who visited throughout the hour to determine the appropriate percentage.

The number of clients who selected chocolate creamer is calculated by dividing the total number of customers by 100.

Here it is,

For one hour, the manager of a coffee shop counted the number of patrons who added vanilla or chocolate creamer to their coffee.

The question given is:

                         Vanilla      Chocolate    

Age 18 - 30            2               6

Age 30 +                4               8      

2 + 4 + 6 + 8 Equals 20 clients in this instance.

6 + 8 = 14 is the number of clients who select chocolate creamer.

Customers that used chocolate creamer made up: [14/20] / 100 = 70%

As a result, 70% of consumers at that time add chocolate creamer to their coffee.

To know more about Percentage, visit:

https://brainly.com/question/11361491

#SPJ1

The complete question is:

The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?

Answer:

70%

Step-by-step explanation:

i did the quiz lol

Answer:

Step-by-step explanation:

you have 22 bucks and your mom took 2

22-2=20

My Answer:

22-2= 20, right? She can't drink anymore wine if you (shown as "i") used the remaining 20$. Tell me if this makes sense. No wine (none) is consumed if you have no money left.

Answer from Artificial Intellegence (to get another view on the question so you can figure out the best answer):

If you had 22 bucks and your mom took 2 dollars for her weekly wine tasting, you would have 20 dollars left. If you have 0 dollars left, this means your mom spent all of the remaining 20 dollars on wine. Assuming each wine bottle costs the same, we can divide the remaining 20 dollars by the cost of one wine bottle to find how many wine bottles your mom bought for her weekly wine tasting. Without knowing the exact cost of one wine bottle, we can't determine the exact number of wine bottles your mom drank.

The approximate area of Central Park is about 450 square blocks.

The given dimensions of the park stated in the question are

Length of Central Park = 50 blocks

Width of Central Park = 9 blocks

The approximate area of Central Park is the product of its length and width:

So, we have

Area of Central Park = Length x Width

When the given values are substituted into the the equation mentioned above, we obtain the subsequent expression

Area = 50 * 9

Evaluate

Area = 450

Hence, the approximate area is about 450 square blocks.

Read more about areas at

https://brainly.com/question/22972014

#SPJ1

Answer:

it’s 159 sorry

Step-by-step explanation:

10 to the second power is 10x10 which is 100 then 8 to the second power is 8x8 which is 64. 164-5 is 159, I apologize.

In order for a number to be divisible by 12, it must be divisible by both 3 and 4.
To be divisible by 3, the sum of the digits must be divisible by 3.
7 + 7 + 3 + 1 + 8 + 6 + 2 + d + e = 34 + d + e

Since 34 is not divisible by 3, we need d + e to be a multiple of 3 in order for the sum to be divisible by 3.
Possible values for d + e are 3, 6, and 9.

To be divisible by 4, the last two digits of the number must be divisible by 4.
Therefore, we need de to be a multiple of 4.

Possible values for de are 12, 16, 32, 36, 52, 56, 72, 76, and 92.
Out of these, only 12, 36, 52, and 76 have a sum of digits that is a multiple of 3.

So the possible values for de are 12, 36, 52, and 76.
Therefore, the choices of the two-digit numbers de for which n is divisible by 12 are 12, 36, 52, and 76.

To know more about divisible click here:

https://brainly.com/question/21416852

#SPJ11

The requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

Given the functions f(x)=3x+5 and g(x)=1/(x−3), we can find the requested functions by applying the corresponding operations to the functions.

a. (f+g)(x) = f(x) + g(x) = (3x+5) + (1/(x−3)) = (3x(x−3)+5(x−3)+1)/(x−3) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = f(x) ∙ g(x) = (3x+5) ∙ (1/(x−3)) = (3x+5)/(x−3)

c. (2f+3g)(x) = 2f(x) + 3g(x) = 2(3x+5) + 3(1/(x−3)) = (6x+10+3/(x−3)) = (6x(x−3)+10(x−3)+3)/(x−3) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = 3g(x) - 4f(x) = 3(1/(x−3)) - 4(3x+5) = (3-4(3x+5)(x−3))/(x−3) = (-12x^2+8x+57)/(x−3)

Therefore, the requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

Learn more about function

brainly.com/question/12431044

#SPJ11

We can conclude that -

The exponential function is of the form -

f(x) = eˣ

Given is to write the exponential growth and exponential decay equation.

{ 1 } -

The general exponential growth equation is -

[tex]$f(x)=a(1+r)^{x}[/tex]

{ 2 } -

The general exponential decay equation is -

[tex]$\frac {dN}{dt}= -\lambda N[/tex]

Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.

Therefore, we can conclude that -

To solve more questions on functions, visit the link-

https://brainly.com/question/29131910

#SPJ1