1. In a game, if you roll a 6 on a 6-sided number cube, you lose a turn. (a) What is the probability that you roll a 6? Explain your reasoning. (b) What is the probability that you don’t roll a 6? Explain your reasoning. (c) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning. (d) Suppose you rolled the 6-sided number cube 120 times, how many times would you expect to roll a 6? Explain and show all of your work.

Answer:

67.0 cm^3

Step-by-step explanation:

The volume of the cylinder is given by the formula ...

V = πr^2·h

The volume of the hemisphere is given by the formula ...

V = (2/3)πr^3

The volume of the two figures together will be ...

V = πr^2·h + (2/3)πr^3 = πr^2(h +2/3r)

V = π(2 cm)^2·(4 cm + 2/3·2 cm) = 64π/3 cm^3

V ≈ 67.0 cm^3

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

Answer:

165 ways  to choose the paintings

Step-by-step explanation:

This is clearly a Combination problem since we are selecting a few items from a group of items and the order in which we chosen the items does not matter.

The number of possible ways to choose the paintings is;

11C3 = C(11,3) = 165

C denotes the combination function. The above can be read as 11 choose 3 . The above can simply be evaluated using any modern calculator.

Answer:

165 ways

Step-by-step explanation:

Total number of painting, n = 11

Now, three of them are chosen randomly to display in the gallery window.

Hence, r = 3

Since, order doesn't matter, hence we apply the combination.

Therefore, number of ways in which 3 paintings are chosen from 11 paintings is given by

[tex]^{11}C_3[/tex]

Formula for combination is [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Using this formula, we have

[tex]^{11}C_3\\\\=\frac{11!}{3!8!}\\\\=\frac{8!\times9\times10\times11}{3!8!}\\\\=\frac{9\times10\times11}{6}\\\\=165[/tex]

Therefore, total number of ways = 165

Hello there!

Answer:

$24

Step-by-step explanation:

In order to find the answer to your problem, we're going to need to find out how much ONE liter of paint costs.

Lets gather the information of what we know:

2 1/2 liters of paint

↑ Cost $60.

With the information we know, we can solve to find the answer.

In order to get the answer, we would need to divide 60 by 2 1/2 (or 2.5). We would need to do this because when we divide it, it would allow us to get the cost for 1 liter.

Lets solve:

[tex]60 \div 2.5=24[/tex]

When you divide, you should get the answer of 24.

This means that one liter of paint cost $24.

$24 should be your FINAL answer.

Answer:

$24/liter

Step-by-step explanation:

Write the the dollar amount first and the paint volume second in this ratio:

 $60.00

--------------- = $24/liter

2.5 liters

Answer:

The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

Step-by-step explanation:

* Lets explain how to solve the problem

- We need to find the product of the monomials (8x 6y)² and

   [tex]x^{3}y^{4}[/tex]

- At first lets solve the power of the first monomial

- Because the power 2 is on the bracket then each element inside the

  bracket will take power 2

∵ (8x 6y)² = (8)²(x)²(6)²(y)²

∵ (8)² = 64

∵ (x)² = x²

∵ (6)² = 36

∵ (y)² = y²

∴ (8x 6y)² = [64x² × 36y²]

∵ 64 × 36 = 2304 x²y²

∴ The first monomial is 2304 x²y²

∵ The first monomial is 2304 x²y²

∵ The second monomial is [tex]x^{3}y^{4}[/tex]

- Lets find their product

- Remember in multiplication if two terms have same bases then we

  will add their powers

∵ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] =

   2304 [ [tex]x^{2}*x^{3}[/tex] ] [ [tex]y^{2}*y^{4}[/tex] ]

∵ [tex]x^{2}*x^{3}[/tex] = [tex]x^{2+3}[/tex] = [tex]x^{5}[/tex]

∵ [tex]y^{2}*y^{4}[/tex] = [tex]y^{2+4}[/tex] = [tex]y^{6}[/tex]

∴ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] = 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

[tex]\bf \textit{Pythagorean Identities}\\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(\theta )cos^2(\theta )+tan^2(\theta )\implies \cfrac{1}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} +tan^2(\theta ) \\\\\\ 1+tan^2(\theta )\implies sec^2(\theta )[/tex]

Answer:

Step-by-step explanation:

When an angle is bisected the opposite sides and the sides of the bisected angle are in a set ratio.

That translates into

(x + 8)/10 = (2x - 5)/14            Cross multiply

14* (x + 8) = 10* (2x - 5)          Remove the brackets on both sides.

14x + 112 = 20x - 50               Subtract 14x from both sides.

112 = 20x - 14x - 50                Combine

112 = 6x - 50                           Add 50 to both sides.

112+50 = 6x - 50 + 50             Combine

162 = 6x                                   Switch

6x = 162                                   Divide by 6

x = 27

Answer:

a)  333,135,504 different plates

b) 230,315,904 different plates

c) 180,835,200 different plates

Step-by-step explanation:

Pattern: Digit(1-9)-Letter-Letter-Letter-Letter-Digit(1-9)-Digit (1-9)

We will calculate the number of possibilities for the digits part, then for the letters part, then we'll multiply them together.

For the digits, we have 3 numbers, first and last 2 positions. We can consider this is a single 3-digit number, where n = 9 (since they are non-zero digits) and r = 3.  

For the letters part, it's basically a 4-letter word, where n = 26 (A through Z) and r = 4.

(a) How many different license plate numbers are possible?

No limitation on repeats for this question:

For the digits, we have 9 * 9 * 9 = 729 (since repetition is allowed, and we can pick any digit from 0 to 9 for each position)

For the letters we have: 26 * 26 * 26 * 26 = 456,976

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 729 * 456976 = 333,135,504 different plates, when there's no repeat limitation.

(b) How man license plate numbers are possible if no digit appears more than once?

Repeats limitation on digits:

For the digits, we have 9 * 8 * 7 = 504 (since repetition is NOT allowed, we can pick any of 9 digits for first position, then any 8 remaining and finally any 7 remaining at the end)

For the letters we still have: 26 * 26 * 26 * 26 = 456,976

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 504 * 456976 = 230,315,904 different plates, when there's no repeat on the digits.

(c) How man license plate numbers are possible if no digit or letter appears more than once?

Repeats limitation on both digits and letters:

For the digits, we have 9 * 8 * 7 = 504 (

For the letters we still have: 26 * 25 * 24 * 23 = 358,800

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 504 * 358800 = 180,835,200 different plates, when there's no repeat on the digits AND on the letters.

Answer:

[tex]f(-1)=5[/tex]

Step-by-step explanation:

We know that the equation is

[tex]f(x)=-4x^3+2x^2-1[/tex]

We can then plug -1 in for x

[tex]f(-1)=-4(-1)^3+2(-1)^2-1\\\\f(-1)=-4(-1)+2(1)-1\\\\f(-1)=4+2-1\\\\f(-1)=5[/tex]

ANSWER

[tex]f( - 1) = 5[/tex]

EXPLANATION

The given function is

[tex]f(x) = - 4 {x}^{3} + 2 {x}^{2} - 1[/tex]

We substitute x=-1 to obtain:

[tex]f( - 1) = - 4 {( - 1)}^{3} + 2 {( - 1)}^{2} - 1[/tex]

We simplify to obtain;

[tex]f( - 1) = 4 + 2 - 1[/tex]

.

This evaluates to

[tex]f( - 1) = 5[/tex]

Answer:

[tex]\large\boxed{(2x+3)(4x^2-6x+9)}[/tex]

Step-by-step explanation:

[tex]8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)[/tex]

1. 10^5

2. z^5*x^3*y^2

3. 1

Answer:

24 cm², 44 cm², and 66 cm²

Step-by-step explanation:

The rectangular prism has six faces.  The opposite faces have the same area, so we can say there are three faces with unique areas.

The face on the bottom of the rectangular prism has an area of:

A = 11 cm * 4 cm = 44 cm²

The face on the side of the rectangular prism has an area of:

A = 4 cm * 6 cm = 24 cm²

And the face on the front of the rectangular prism has an area of:

A = 11 cm * 6 cm = 66 cm²

So 24 cm², 44 cm², and 66 cm² are all answers that apply.

[tex]5 \div 100 \times 399 \times 1 = 19.95 \: and \: 4 \div 100 \times 399 \times 1 = 15.96[/tex]

Answer:  The correct option is

(A) [tex]c+(c+2)=12,[/tex] where c is the number of dimes.

Step-by-step explanation:  Given that Alice has a total of 12 dimes and nickels and she has 2 more nickels than dimes.

We are to select the correct equation that represents the given problem situation.

Let c represents the number of dimes. Then, the number of nickels will be (c + 2).

Since there are total 12 coins, so the required equation is given by

[tex]c+(c+2)=12.[/tex]

Thus, the required equation is

[tex]c+(c+2)=12,[/tex] where c is the number of dimes.

Option (A) is CORRECT.

The expression for the total number of dimes and nickels is  c+(c+2)=12. Option A is the correct answer.

Given that Alice has a total of 12 dimes and nickels.

Also given that she has 2 more nickels than dimes.

Let us consider that c is the number of dimes. Then the number of nickels is given as,

Number of nickels = c+2

The total sum of dimes and nickels is 12, then,

Number of dimes + Number of nickels = 12

c + (c+2) = 12

Hence the expression for the total number of dimes and nickels is  c+(c+2)=12. Option A is the correct answer.

To know more about the sum, follow the link given below.

https://brainly.com/question/24412452.

Answer:

The determinant of A (the main matrix) is -3; the determinant of y is 30; the determinant of x is 18; the solution to the system is (-6, -10)

Step-by-step explanation:

Set up the matrix to find the determinant of the main matrix.  Find the determinant by multiplying the numbers on the major axis and subtract from that the multiplication of the numbers on the minor axis:

[tex]\left[\begin{array}{ccc}2&-1&\\1&-2\\\end{array}\right][/tex]

Find the determinant by multiplication:

(2×-2)-(1×-1)= -3

To find the determinant of y, replace the second column with the solutions to have a matrix that looks like this:

[tex]\left[\begin{array}{ccc}2&-2\\1&14\\\end{array}\right][/tex]

To find the determinant of that matrix by multiplication:

(2×14)- (1× -2) = 30

Lastly, find the determinant of x by replacing the first column with the solutions.  That matrix will look like this:

[tex]\left[\begin{array}{ccc}-2&-1\\14&-2\\\end{array}\right][/tex]

Find the determinant of x by multiplication:

(-2 × -2) - (14 × -1) = 18

Now we want Cramer's Rule that tells us if we divide the determinant of [tex]A_{x}[/tex]

by the determinant of A, we will find the value of x:

[tex]\frac{A_{x} }{A}=\frac{18}{-3}  =-6[/tex]

and the same for y:

[tex]\frac{A_{y} }{A}=\frac{30}{-3}=-10[/tex]

So the solution to the system is (-6, -10)

2x - y = -2

x = 14 + 2y

2x - y = -2

x - 2y = 14

The system determinant = -3

2 (-2) - 1 (-1)

-4 + 1

-3

The y-determinant = 30

(14) - 1 (-2)

28 + 2

30

The x-determinant = 18

-2 (-2) - 14 (-1)

4 + 14

18

The solution is x = -6 and y = -10 or (-6,-10)

x = 18/-3

x = -6

y = 30/-3

y = -10

Answer:

[tex]\large\boxed{(4x^2 + 8x - 2) - (2x^2 - 4x + 3)=2x^2+12x-5}[/tex]

Step-by-step explanation:

[tex](4x^2 + 8x - 2) - (2x^2 - 4x + 3)\\\\=4x^2 + 8x - 2 -2x^2 -(- 4x)- 3\\\\=4x^2+8x-2-2x^2+4x-3\qquad\text{combine like terms}\\\\=(4x^2-2x^2)+(8x+4x)+(-2-3)\\\\=2x^2+12x-5[/tex]

Answer:

Step-by-step explanation:

This is a negative x^2 quadratic.  I'm not sure if there's anything else you need.

Answer:

To the nearest tenth, the height of the balloon is 2.9 miles

Step-by-step explanation:

The nearer point takes the greater angle of elevation.

The diagram is shown in the attachment.

The height of the balloon above the ground is c unit.

From triangle ABD,

[tex]\tan 42\degree=\frac{c}{x}[/tex]

[tex]\implies x=\frac{c}{\tan 42\degree}[/tex]...eqn1

From triangle ABC,

[tex]\tan 20\degree=\frac{c}{x+4.8}[/tex]

[tex]\implies x+4.8=\frac{c}{\tan 20\degree}[/tex]

[tex]\implies x=\frac{c}{\tan 20\degree}-4.8[/tex]..eqn2

We equate both equations and solve for c.

[tex]\frac{c}{\tan 42\degree}=\frac{c}{\tan 20\degree}-4.8[/tex]

[tex]\frac{c}{\tan 42\degree}-\frac{c}{\tan 20\degree}=-4.8[/tex]

[tex]\implies (\frac{1}{\tan 42\degree}-\frac{1}{\tan 20\degree})c=-4.8[/tex]

[tex]\implies -1.636864905c=-4.8[/tex]

[tex]\implies c=\frac{-4.8}{-1.636864905}[/tex]

[tex]c=2.932435039[/tex]

To the nearest tenth, the height of the balloon is 2.9 miles

Answer:

on usatestprep its 1.2

Step-by-step explanation:

Answer:

X=-4

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

-8x+4=36

          -4

-8x     =32

/-8       /-8

  x      = -4

Answer:

x = 20

Step-by-step explanation:

Formula

x1/x2 = x3/x4

Givens

x = 11

x2 = 11 + 121 = 132

x3 = 10

x4 = 10 + 5x + 10

Solution

11/132 = 10 / (5x + 10 + 10)        Combine

11/132 = 10/(5x + 20)                Cross multiply

11*(5x + 20) = 132 * 10              Combine on the right.

11(5x + 20 ) = 1320                   Divide by 11. (You could remove the brackets, but this is easier.

11(5x + 20)/11 = 1320/11            Do the division

5x + 20 = 120                          Subtract 20 from both sides

5x + 20-20 = 120 - 20             Combine

5x = 100                                   Divide by 5

5x/5 = 100/5

x = 20

Answer:

The maximum height that the ball will reach is 81 ft

Step-by-step explanation:

Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.

For an equation of the form

[tex]at ^ 2 + bt + c[/tex]

So

the t coordinate of the vertice is:

[tex]t =-\frac{b}{2a}[/tex]

In this case the equation is:

[tex]h(t)=72t-16t^2[/tex]

So

[tex]a=-16\\b=72\\c=0[/tex]

Therefore

[tex]t =-\frac{72}{2(-16)}[/tex]

[tex]t=2.25\ s[/tex]

Finally the maximum height that the ball will reach is

[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex]

[tex]h=81\ ft[/tex]

The ball thrown vertically upwards will reach the maximum height of 81 feet after 2.25 seconds.

To find the maximum height the ball will reach, first, we need to recognize that the equation 'h(t)=72t-16t^2' is a quadratic function in the form of 'f(t)=at^2+bt+c'. The maximum point of a quadratic function, also known as the vertex, happens at 't=-b/2a'. In this case, 'a' is -16 and 'b' is 72.

So the maximum height is achieved at 't=-72/(2*-16)' or 't=72/32 = 2.25' seconds.

To find out the maximum height, we just need to substitute this value of t into the equation for h(t):

h(2.25)=72*2.25-16*2.25^2

The above calculation gives a maximum height of 81 feet.

https://brainly.com/question/29081143

#SPJ3

Answer:

b. all real numbers

Step-by-step explanation:

The graphs of positive and negative x^2 parabolas will always have a domain of all real numbers.  Even though you only have a portion of the graph and see a "restriction" on your domain values, it is incorrect to assume that the domain is limited to what you can see.  As the branches of the parabola keep going up and up and up, the values of x keep getting bigger and bigger and bigger.  Again, this is true for all + or - parabolas.

Answer:

The error is C and the solution is B

Step-by-step explanation:

C is because she didn't look left to right to see that is goes on forever

B because you look left and right to see

11) Factors of 55 are 1,5,11,55 Factors of 75 are 1,3,5,15,25,75

The greatest common factor is 5.

12) With algebraic expressions you just simplify and multiplier in the simplification is the greatest common factor.

66yx + 30x^2y --) 6yx( 11 + 5x ) so the greatest common factor is 6yx.

13) 60y + 56x^2 --) 4( 15y + 14x^2 ) so the greatest common factor is 4.

14) 36xy^3 + 24y^2 --) 12y^2( 3xy + 2 ) so the greatest common factor is 12y^2.

15) 18y^2 + 54y^2 --) 18y^2( 1 + 3 ) so the greatest common factor is 18y^2.

16) 80x^3 + 30yx^2 --) 10x^2( 8x + 3y ) so the greatest common factor is 10x^2.

17) 105x + 30yx + 75x --) 15x( 7 + 2y + 5 ) so the greatest common factor is 15x.

18) 140n + 140m^2 + 80m --) 20( 7n + 7m^2 + 4m ) so the greatest common factor is 20.

If you want a further explanation step by step just ask :)

Answer:

1 5/12 inches.

Step-by-step explanation:

That is 3 1/6 - 1 3/4

= 19/6 - 7/4

The lowest common denominator of 4 and 6 is 12, so we have:

38/12 - 21/12

= 17 /12

= 1 5/12 inches (answer).

The remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.

The correct option is (a).

find out how much string is left when [tex]\(1 \frac{3}{4}\)[/tex] inches are cut from a piece initially measuring[tex]\(3 \frac{1}{16}\)[/tex]inches.

1. Convert the mixed numbers to improper fractions:

[tex]- \(1 \frac{3}{4}\) inches = \(\frac{7}{4}\) inches[/tex]

[tex]- \(3 \frac{1}{16}\) inches = \(\frac{49}{16}\) inches[/tex]

2. Make the denominators equal:

  - Multiply the numerator and denominator of [tex]\(\frac{7}{4}\)[/tex]by 16 to make the denominators equal:

[tex]\(\frac{7}{4} = \frac{112}{64}\)[/tex]

  - Now we have:

    - Initial length = [tex]\(\frac{49}{16}\)[/tex] inches

    - Cut length = [tex]\(\frac{112}{64}\)[/tex] inches

3. Subtract the two fractions:

  - Subtract the cut length from the initial length:

[tex]\(\frac{49}{16} - \frac{112}{64}\)[/tex]

  - To subtract, we need a common denominator. The least common multiple (LCM) of 16 and 64 is 64.

 - Convert both fractions to have a denominator of 64:

[tex]\(\frac{49}{16} = \frac{196}{64}\)[/tex]

[tex]\(\frac{112}{64}\) remains the same.[/tex]

- Subtract the numerators:

   [tex]\(\frac{196}{64} - \frac{112}{64} = \frac{84}{64}\)[/tex]

4. Simplify the result:

  - Divide both the numerator and denominator by their greatest common factor (GCF), which is 4:

[tex]\(\frac{84}{64} = \frac{21}{16}\)[/tex]

5. Convert back to a mixed number:

  - Divide the numerator by the denominator:

[tex]\(\frac{21}{16} = 1 \frac{5}{16}\)[/tex]

Therefore, the remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.

ANSWER

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

EXPLANATION

The recursive formula is given as:

[tex]a_n= \frac{1}{3} a_{n-1}[/tex]

where

[tex]a_1=2[/tex]

The explicit rule is given by:

[tex]a_n=a_1 {r}^{n-1}[/tex]

From the recursive rule , we have

[tex]r = \frac{1}{3} [/tex]

We substitute the known values into the formula to get;

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Therefore, the explicit rule is:

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Answer:

[tex]6\frac{7}{9}[/tex]

Step-by-step explanation:

[tex]6\frac{2}{3}+\frac{1}{9} = 6\frac{6}{9}+\frac{1}{9}=6 \frac{7}{9}[/tex]

Answer:

Step-by-step explanation:

its D

Answer:

C: 48 straws

Step-by-step explanation:

First, find the perimeter of one picture frame: (2 x length) + (2 x width).  Convert 20 centimeters to millimeters so that you are working in the same units; there are 10 millimeters in 1 centimeter, so 20 centimeters = 200 millimeters.  

(2 x 200) + (2 x 120) = 400 + 240 = 640

Each picture frame has a perimeter of 640 millimeters.

Next, figure out how many straws are needed for one picture frame:

640/80 = 8

Jana uses 8 straws for each picture frame.  Since she is decorating 6 picture frames, solve 6 x 8 = 48.  

Jana needs 48 straws to complete her project.

Answer:

The son's age is 10 and the daughter's age is 5 now

Step-by-step explanation:

Let

x-----> the son's age now

y----> the daughter's age now

we know that

x=2y ----> equation A

(x+15)+(y+15)+(40+15)=100

x+y+85=100

x+y=15 -----> equation B

Substitute equation A in equation B and solve for y

2y+y=15

3y=15

y=5 years

Find the value of x

x=2(5)=10 years

therefore

The son's age is 10.

The daughter's age is 5

Answer:

Probability of the sticks weight being 2.44 oz or greater is 0.01017 .

Step-by-step explanation:

We are given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz.

Also, it is given that the weight of the drumsticks is normally distributed.

Let X = weight of the drumsticks, so X ~ N([tex]\mu = 2,\sigma^{2} = 0.19^{2}[/tex])

The standard normal z distribution is given by;

               Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

Now, probability of the sticks weight being 2.44 oz or greater = P(X >= 2.44)

P(X >= 2.44) = P( [tex]\frac{X-\mu}{\sigma}[/tex] >= [tex]\frac{2.44-2}{0.19}[/tex] ) = P(Z >= 2.32) = 1 - P(Z < 2.32)

                                                     = 1 - 0.98983 = 0.01017

Therefore, the probability of the sticks weight being 2.44 oz or greater is 0.01017 .

Final answer:

The probability of the sticks weighing 2.44 oz or more is approximately 0.01017.

Explanation:

Given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz, we know the weight of the drumsticks is normally distributed.

Let X represent the weight of the drumsticks, with X being normally distributed with a mean (μ) of 2 and a variance  [tex](\sigma^2) \ of \ 0.19^2[/tex]

To find the probability of the sticks weighing 2.44 oz or more, we need to calculate P(X ≥ 2.44).

We can standardize X using the formula Z = (X - μ) / σ, which results in a standard normal distribution with mean 0 and standard deviation 1.

So, to find P(X ≥ 2.44), we compute P((X - μ) / σ ≥ (2.44 - 2) / 0.19), which simplifies to P(Z ≥ 2.32).

From the standard normal distribution table or a calculator, we find that P(Z < 2.32) is approximately 0.98983.

Therefore, P(Z ≥ 2.32) = 1 - P(Z < 2.32) = 1 - 0.98983 = 0.01017.

Hence, the probability of the sticks weighing 2.44 oz or more is approximately 0.01017.

Answer:

(0,3) and (3,0)

Step-by-step explanation:

The first thing to do is graph the two equations to see where they intersect. Then you know what answer to look for. The graph is below. It was done on desmos.

I take it the first equation is a typo and should be y = x^2 - 4x + 3

Equate the two equations.

-x + 3 = x^2 -4x + 3    Subtract 3 from both sides

-x = x^2 - 4x + 3-3

-x = x^2 - 4x                Add x to both sides.

0 = x^2 - 4x + x

0 = x^2 - 3x                Factor

0 = x(x - 3)

So x can equal 0

or x can equal 3

In either case the right side will reduce to 0.

Case 1. x = 0

y= - x + 3

y = 0 + 3

y = 3

So the point is (0,3)

Case 2. x = 3

y = - x + 3

y = - 3 + 3

y = 0

So the point is (3,0)