*need fast answer please * What are some numbers of pushups that Bucky will never do in any game ?
Answers
Answer:
{1, 2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 64, 68, 72, 74, 76, 78, 80, 82, 86, 90, 94, 98}
Step-by-step explanation:
The total number of pushups Bucky does is the sum sequence of scores in the game. The values in that sequence depend on the order of the goal types.
For example, consider a 2-goal game. Possible sequences of scores are ...
3, 6 (9 pushups)
3, 10 (13 pushups)
7, 10 (17 pushups)
7, 14 (21 pushups)
You can see that for a 1- or 2-goal game, the number of pushups cannot be any of ... 1, 2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16.
The list above is all of the numbers less than 100 that are numbers of pushups Bucky will never do in any game in which the goal values are either 3 or 7.
__
Any game with 8 goals or more will have numbers of pushups more than 100.
Related Questions
Solve for x...
Z = 8(x-h)
X = ????
Please state what X is...
Answers
This is equivalent to x = z/8 + h or x = (1/8)z + h
=================================================
Work Shown:
z = 8(x-h)
z = 8x-8h ... distribute
8x-8h = z
8x = z+8h .... adding 8h to both sides
x = (z+8h)/8 .... dividing both sides by 8
x = z/8 + 8h/8
x = z/8 + h
x = (1/8)z + h
What is the value of x? A. 36 B. 12 C. 32 D. 28
Answers
Answer:
the answer is D I hope this helps
George has a triangle-shaped garden in his backyard. He drew a model of this garden on a coordinate grid with vertices A(4, 2), B(2, 4), and C(6, 4). He wants to create another, similar-shaped garden, A′B′C′, by dilating triangle ABC by a scale factor of 0.5. What are the coordinates of triangle A′B′C′?
Answers
Answer:
A' (2, 1)
B' (1, 2)
C' (3, 2)
Step-by-step explanation:
Scale factor = 0.5
A(⁴₂ ) → A'([tex]\frac{1}{2} * 4\\\frac{1}{2} * 2[/tex]) = (²₁ ) ∴ A'(2, 1)
B(²₄ ) → B'([tex]\frac{1}{2} * 2\\\frac{1}{2} * 4[/tex]) = (¹₂ ) ∴ B'(1, 2)
C(⁶₄ ) → C'([tex]\frac{1}{2} * 6\\\frac{1}{2} * 4[/tex]) = (³₂ ) ∴ C'(3, 2)
Which of the following is the correct equation for the Pythagorean Theorem, where a and b are the side lengths and c is the length of the hypotenuse?
A. a^2-b^2=c^2
B. (a+b)^2=c^2
C.(a-b)^2=c^2
D. a^2+b^2=c^2
Answers
Answer:
[tex]\huge \boxed{ \mathrm{D.} \ \ a^2 +b^2 =c^2}}[/tex]
Step-by-step explanation:
The correct equation for the Pythagorean theorem is:
[tex]\Rightarrow \ \ a^2 +b^2 =c^2[/tex]
c is the length of the hypotenuse of the right triangle
a and b are the side lengths of the right triangle
If one chip is randomly selected from each bag, what is the probability that a chip with a B on it and a chip with a 2 on it will be selected?
Answers
Answer:
it has a 1% chance.
Step-by-step explanation:
Because of the whole there is one chip in it that has a 2 on it so it has a 1% chance out of 100%
choose all the equations for which x=2 is a solution
a. x+3=5
b. x+2=8
c. x+1=1
d. x-2=4
e. x-7=-5
Answers
Answer:
Option A and Option E
Step-by-step explanation:
Option A.
x + 3 = 5
(x + 3) - 3 = 5 - 3
x = 2
Option B.
x + 2 = 8
(x + 2) - 2 = 8 - 2
x = 6
Option C.
x + 1 = 1
(x + 1) - 1 = 1 - 1
x = 0
Option D.
x - 2 = 4
(x - 2) + 2 = 4 - 2
x = 2
Option E.
x - 7 = -5
(x - 7) + 7 = -5 + 7
x = 2
Therefore, Option (A) and Option (E) are the correct options.
Find the surface area of the composite figure. need help asap. Thank You
Answers
Answer: A=276.52 cm²
Step-by-step explanation:
To find the surface area of the figure, we can find the surface area of the rectangular prism and hemisphere. Then we would add them together.
Rectangular Prism
A=2(lw+hl+hw)
Since we are given the length, width, and height, we can directly plug them into the equation and solve.
[tex]A=2((10*5)+(4*10)+(4*5))[/tex]
[tex]A=2(50+40+20)[/tex]
[tex]A=2(110)[/tex]
[tex]A=220 cm^2[/tex]
The surface area for the rectangular prism is 220 cm².
----------------------------------------------------------------------------------------------------------------
Hemisphere
A=2πr²
This formula above is derived from the formula for surface area of a sphere.
The surface area of a sphere is A=4πr². Since the picture displays half of a sphere, we divide that by 2. This gives us A=2πr².
Since we have the radius, all we have to do is plug it in.
[tex]A=2\pi (3)^2[/tex]
[tex]A=2\pi (9)[/tex]
[tex]A=18\pi[/tex]
[tex]A=56.52 cm^2[/tex] *Note I used 3.14 instead of π.
----------------------------------------------------------------------------------------------------------------
Now that we have the surface area of the hemisphere and rectangular prism, we add them together to find the surface area of the entire prism.
A=220+56.52=276.52 cm²
The fourth term of an arithmetic
progression is one less than twice the
second term - If the sixth term is 7
find the first term
Answers
[tex] \huge{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]
Let the first term of the AP be a and the common difference of the AP be d
We know the formula for finding the nth term,
[tex] \large{ \boxed{ \rm{a_n = a + (n - 1)d}}}[/tex]
Here,
an = nth term of the APn = number of terms of APBy using formula,
a4 = a + 3da2 = a + da6 = a + 5dAccording to given condition,
⇛ a4 = 2a2 - 1
⇛ a + 3d = 2(a + d) - 1
⇛ a + 3d = 2a + 2d - 1
⇛ a - 2a + 3d - 2d = -1
⇛ -a + d = -1
⇛ a - d = 1
Then,
⇛ a = d + 1-----------(1)
It is given that, a6 = 7
⇛ a + 5d = 7
Putting a from eq.(1),
⇛ d + 1 + 5d = 7
⇛ 6d + 1 = 7
⇛ 6d = 6
⇛ d = 6/6 = 1
Putting value of d in eq.(1),
⇛ a = 1 + 1 = 2
⛈ First term of the AP(a) = 2
━━━━━━━━━━━━━━━━━━━━
Someone plz help.The temperature started at 35°F. If the temperature went down 4°F and then up 2°F, whats is the temperature difference relative to the high temperature? A) -2°F B) -1°F C) 1°F D) 2°F
Answers
Answer:
The temperature difference relative to the high temperature is -2°F.
Step-by-step explanation:
We are given that the temperature started at 35°F. The temperature went down 4°F and then up 2°F.
Firstly, the original temperature = 35°F
Now, it is stated that the temperature went down 4°F, this means that the temperature decreases by this amount.
So, the new temperature = 35°F - 4°F = 31°F
Now, the temperature went up by 2°F, this means that the temperature increases by this amount.
So, the final temperature = 31°F + 2°F = 33°F
Now, the final temperature difference relative to the high temperature is given by = 33°F - 35°F = -2°F.
{Here, the maximum temperature is 35°F}
Inequalities with > or < symbols are graphed with a dashed line. Inequalities with an ≥or ≤ symbol line are graphed with a solid line. When graphing the inequalities in the example above. Which inequality would you graph using a dashed line? Select all that apply A B C D
Answers
Answer:
b and c
Step-by-step explanation:
both are just greater than or less than
What is an equation of the line that passes through the point (-2, -3) and is
parallel to the line 5x + 2y = 14?
Answers
Answer: 2y + 5x + 16 = 0
Step-by-step explanation:
To solve this you need to understand the principle/ conditions for parallelism and perpendicularity.
for two lines to be parallel to each other, their gradients or slopes (m) must be equal, that is m₁ = m₂
Now from the given equation,
5x + 2y = 14 , we need to rearrange it to conform to the equation of a straight line so that the gradient could be established. ie
y = mx + c where m is the gradient
2y = -5x + 14
y = -5x/2 + 14/2
y = ⁻⁵ˣ/₂ + 7 , therefore , m₁ = ⁻⁵/₂ and m₂ = ⁻⁵/₂ ( parallelism Rule )
The next step is to find the value of C using the coordinate ( -2, -3 )
-3 = ⁻⁵/₂ ˣ ⁻² + C,
-3 = ¹⁰/₂ + C
-3 = 5 + C
C = -8.
Now to find the equation of the line that passed through the coordinate
y = mx + c
y = ⁻⁵ˣ/₂ - 8
2y = -5x - 16
2y + 5x + 16 = 0.
M is the midpoint of line segment AB
Answers
Answer:
The coordinates of A would be (-1, 2)
Step-by-step explanation:
In order to find this, use the mid-point formula.
(xA + xB)/2 = xM
In this, the xA is the x value of point A, xB is the x value of point B, and xM is the x value of M. Now we plug in the known information and solve for xA.
(xA + 5)/2 = 2
xA + 5 = 4
xA = -1
Now we can do the same using the midpoint formula and the y values.
(yA + yB)/2 = yM
(yA + 10)/2 = 6
yA + 10 = 12
yA = 2
This gives us the midpoint of (-1, 2)
[tex] {2}^{x + 2} = 9 \times ( {2}^{x} ) - 2[/tex]
How is this solved pls
Answers
Answer:
[tex]x = 1 - log_{2}(5) [/tex]Step-by-step explanation:
[tex] {2}^{x + 2} = 9 ( {2}^{x} ) - 2[/tex]Using the rules of indices
That's
[tex] {x}^{a + b} = {x}^{a} \times {x}^{b} [/tex]So we have
[tex] {2}^{x + 2} = {2}^{x} \times {2}^{2} = 4( {2}^{x} )[/tex]So we have
[tex]4( {2}^{x}) = 9( {2}^{x} ) - 2[/tex]Let
[tex] {2}^{x} = y[/tex]We have
4y = 9y - 2
4y - 9y = - 2
- 5y = - 2
Divide both sides by - 5
[tex]y = \frac{2}{5} [/tex]But
[tex] {2}^{x} = \frac{2}{5} [/tex]Take logarithm to base 2 to both sides
That's
[tex] log_{2}( {2}^{x} ) = log_{2}( \frac{2}{5} ) [/tex][tex] log_{2}(2) ^{x} = x log_{2}(2) [/tex][tex] log_{2}(2) = 1[/tex]So we have
[tex]x = log_{2}( \frac{2}{5} ) [/tex]Using the rules of logarithms
That's
[tex] log( \frac{x}{y} ) = log(x) - log(y) [/tex]Rewrite the expression
That's
[tex]x = log_{2}(2) - log_{2}(5) [/tex]But
[tex] log_{2}(2) = 1[/tex]So we have the final answer as
[tex]x = 1 - log_{2}(5) [/tex]Hope this helps you
The Jammers basketball team had a
win to loss ratio of 5:1 during their
Season. They won 25 games. How many
games did they lose?
Answers
Answer:
5 Games
Step-by-step explanation:
Step 1: State what is known
We know for every 5 games the win they lose 1 game
They won 5 games
Step 2: Define your variables
Let x represent how many games the Basketball team lost
Step 3: Create equation
[tex]\frac{5}{1}=\frac{25}{x}[/tex]
Step 4: Solve for 'x'
Cross multiply to solve for 'x'
[tex]5x=25[/tex]
[tex]x=\frac{25}{5}[/tex]
x = 5
Therefore the will have lost 5 games
PORFAVOR ALLUDENME :( El estanque de combustible de un automóvil contiene x litros de gasolina, se consumen 25 litros en un primer viaje y 4/19 del resto en un segundo viaje, conservando finalmente 3 litros de gasolina. ¿Qué ecuación modela la situación planteada? a. 25 menos x menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo 25 menos x paréntesis derecho igual 3 b. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo por 25 igual 3 c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3 d. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x más 25 paréntesis derecho igual 3
Answers
Responder:
c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3
Explicación paso a paso:
Dado lo siguiente:
Cantidad original de gasolina en el tanque de combustible = x
Gasolina consumida en el primer viaje = 25 litros
Gasolina restante después del primer viaje = (x - 25) litros
Gasolina consumida en el segundo viaje = 4/19 de lo que queda, es decir;
(4/19) * (x - 25)
Gasolina restante después del segundo viaje = 3 litros
Cantidad inicial - cantidad consumida en el primer viaje - 4/19 de la cantidad restante después del primer viaje = 3
La gasolina que queda después del segundo viaje se puede modelar mediante la ecuación:
x - 25 - 4/19 (x - 25) = 3
Evaluate the expression x+43x when x = 2
a.316
b.34
c.1
d.2
Answers
Answer:
88
Step-by-step explanation:
We are given the expression:
x+43x
and asked to evaluate when x=2. Therefore, we must substitute 2 in for x.
x + 43 x (plug 2 in for each x )
2+43(2)
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Multiply 43 and 2 first.
2+ (43*2)
2+ 86
Add 2 and 86.
88
The expression x+43x when evaluated for x=2 is 88.
Answer:
1
Step-by-step explanation:
Identify the careers that match the descriptions:
Makes sure products meet safety regulations:
Operates equipment to cook meat for packaging in soup cans
Classifies eggs based on size and quality
Operates a large oven in a factory to bake bread before packaging
Operates equipment that mixes ingredients together to make candy
Options:
Agricultural Inspector
Food Baking Machine Operator
Food Batchmaker
Grader or sorter
Food cooking machine operator
Answers
Answer:
1. agricultural inspecter
2. food-cooking machine operator
3. grader or sorter
4. food-baking machine operator
5. food batchmaker
Step-by-step explanation:
i got this correct on ED2021
The correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.
What is food processing?The process of turning agricultural materials into food or transforming one type of food into the next is referred to as transformation.
It is given that:
For the descriptions:
Makes sure products meet safety regulations - agricultural inspector.
Operates equipment to cook meat for packaging in soup cans - food-cooking machine operator.
Classifies eggs based on size and quality - grader or sorter.
Operates a large oven in a factory to bake bread before packaging - food-baking machine operator.
Operates equipment that mixes ingredients together to make candy - food matchmaker.
Thus, the correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.
Learn more about food processing here:
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A lender will make an 80% loan-to-value loan on a property that is appraised for $72,250 and sells for $73,500. If the buyer has saved $14,450 for a down payment, how much more (if any) will he need in order to make the down payment required under the terms of this loan?
Answers
Answer:
$1,250
Step-by-step explanation:
We are given;
Loan to value ratio;LTV = 80% = 0.8
Appraised value of property = $72,250
Selling value of property = $73,500
Now, the formula for Loan to value ratio is;
LTV = Loan amount/Appraised value of property
0.8 = loan amount/72250
Cross multiply to get;
Loan amount = 0.8 × 72250 = $57,800
Now,we are told that he has saved $14,450.
Thus, total money raised including loan = $57,800 + $14,450 = $72,250
Since the selling value = $73,500, then,
Amount left for him to save in order to make down payment = $73,500 - $72,250 = $1,250
John Maynard Keynes and Karl Marx would agree most about the answer to
which question?
O A. Should governments take total control over economies?
B. Are precious metals a good measure of economic strength?
O C. Do free market economies create problems for workers?
D. Is it right for strong countries to control weaker colonies?
Answers
Answer:
Option C: Do free market economies create problems for workers?
Step-by-step explanation:
There was a law called Say's law which states that capitalist production generates its own markets, and therefore, there can't possibly be any gluts or overproduction of goods in relation to market demand.
Now, keynes and marx rejected this say's law because they both believed that gluts or overproduction may likely occur.
They believed that this law would make capitalists own nothing but the right to sell their labor in exchange for wages.
That due to the capitalists competition with themselves for profits, it would squeeze as much work as possible out of the working class people at the lowest possible price and that this competition would cause some capitalist firms to fail, and thereby increasing unemployment among the working class.
Thus, it's clear this was an answer to the question on whether free market economies create problems for workers.
Answer:
A.Should government take total control over economies
Step-by-step explanation:
Factor completely:
3x² (x²+6) - 4(x2+6)
Answers
Answer:
(x² + 6)(3x² - 4)
Step-by-step explanation:
factor out (x² + 6)
(x² + 6)(3x² - 4)
The diameter of the inscribed circle in a regular hexagon is 4√3 inches long. What is the perimeter of this regular hexagon?
Answers
Answer:
12√3 inches or 20.785 inches.
Step-by-step explanation:
A regular hexagon can be defined as a polygon with 6 sides.
The formula for the perimeter of a regular hexagon =
6 × the length of the sides of the hexagon.
From the above question, we are told that there is an inscribed circle I'm the hexagon with a diameter of 4√3 inches long
Step 1
Find the radius of the circle
Radius of the circle = 4√3/2 = 2√3 inches
Step 2
The radius of the inscribed circle = Length of one of the sides of a regular hexagon.
Hence, the perimeter of the regular hexagon = 6 × 2√3
= 12√3 inches
= 20.784609691 inches.
Approximately 20.785 inches
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find x! Round to the nearest tenth!!
Answers
Greetings from Brasil...
Using sine, we will be able to find the value of X
SEN 17 = X/47
X = 47 · SEN 17
X = 47 · 0,29237
X = 13,741
X ≈ 13.7write the desimales 3.17 in word form
Answers
Answer:
Three point one seven is your answer.
Step-by-step explanation:
Hope it will help you:)
There’s other ways you can say it like “Three point seventeen hundredths” and stuff. I personally like saying it like this. (Ik nobody asked but whatever) :)
A man drove 8 miles directly east from his home, made a left turn at an intersection, and then traveled 8 miles due north to his place of work. If a road was made directly from his home to his place of work, what would its distance be? ______ miles
Answers
Answer:
11.3 miles
Step-by-step explanation:
We can use the pythagorean theorem to find the distance from his home to work, since the 3 roads form a right triangle where the new road is the hypotenuse.
a² + b² = c²
8² + 8² = c²
128 = c²
= approx. 11.3 miles
The distance between his home and his work of place is 11.31 miles.
Given,
A man drove 8 miles directly east from his home, made a left turn at an intersection, and then traveled 8 miles due north to his place of work.
A road was made directly from his home to his place of work.
We need to find what would its distance be in miles,
How to construct direction?We have,
North
West <----- ⇅ -------> East
South
What is the Pythagorean theorem?In a right triangle,
The square of the hypotenuse is equal to the sum of the square of the other two sides.
Find the direction of the given statement.
A man drove 8 miles directly east from his home:
8 miles
Home ------------------->East
Made a left turn at an intersection, and then traveled 8 miles due north to his place of work:
North Work
⇅ Left
⇅ 8 miles
Home ------------------->East
⇅
Right
If a road was made directly from his home to his place of work:
Work
Home North
West <------------------⇅ --------------->East
South
A (Work)
/ ║
/ ║
/ ║ 8 miles
/ ║
(Home) B /___________║C
8 miles
Find the distance between home and place of work.
AB = distance between home from work
Applying the Pythagorean theorem.
AB² = BC² + AC²
AB² = 8² + 8²
AB² = 64 + 64
AB² = 128
AB = ±√128
The distance can never be negative here so,
√128 = 11.31
AB = 11.31 miles.
Thus the distance between his home and his work of place is 11.31 miles.
Learn more about justifying the distance Formula using the Pythagorean Theorem here:
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Can someone please help me with these questions! Please explain to me how to do it as well!
Thank You!
Answers
Answer:
(2) (-2, 4), (3, 9)
(3) (-2, 4), (1, 1)
Step-by-step explanation:
My favorite way to answer questions like this is to use a graphing calculator to find the points of intersection. The attached shows the points of interest.
If you want to solve this by hand, equate the expressions for y, then solve the resulting quadratic using any of the methods you know. Once you find the x-values, put those in either equation to find the y-value.
__
(2) x^2 = y = x+6
x^2 -x -6 = 0 . . . . put in standard form
(x -3)(x +2) = 0 . . . . factor
x = 3 or -2 . . . . . find the x-values that make the factors zero
y = x^2 = 9 or 4
The points are (3, 9) and (-2, 4).
__
(3) x^2 = -x +2
x^2 +x -2 = 0 . . . . standard form
(x +2)(x -1) = 0 . . . factored
x = -2 or 1 . . . . . . .zeros
y = x^2 = 4 or 1
The points are (-2, 4) and (1, 1).
_____
Comment on factoring
When you consider the factored form and its expanded equivalent, ...
(x +a)(x +b) = x^2 +(a+b)x +ab
you see that the coefficient of the linear term (a+b) is the sum of factors of the constant term (ab). Your knowledge of multiplication tables will often help you factor equations easily. You need to pay attention to signs.
In problem 2, we want factors of -6 that have a sum of -1:
-6 = (-1)(6) = (-2)(3) = (-3)(2) = (-6)(1)
These factor pairs have sums of 5, 1, -1, -5. The pair whose sum is -1 is the one we're looking for: -3 and 2. So, the factors in problem 2 are (x-3)(x+2).
__
In problem 3, we want factors of -2 that have a sum of +1:
-2 = (-1)(2) = (-2)(1)
These factor pairs have sums of 1, -1. So, the second pair is the one of interest: -2 and 1. That makes the factors be (x-2)(x+1).
Square root of -72 in the form of a+bi
Answers
Answer:
[tex]0+6\sqrt{2}i[/tex]
or just [tex]6\sqrt{2}i[/tex]
Step-by-step explanation:
[tex]\sqrt{-72}[/tex] does not have a real part, it is a pure imaginary number.
Let's simplify.
First step:
[tex]\sqrt{-1}=i[/tex] is the imaginary unit.
So we have that we can write [tex]\sqrt{-72}=i \sqrt{72}[/tex].
Second step:
Let's simplify the factor [tex]\sqrt{72}[/tex] by looking for perfect squares of [tex]72[/tex].
[tex]72=2(36)=2(6^2)[/tex]
So [tex]36[/tex] is a perfect square because it can be written as [tex]6^2[/tex].
[tex]\sqrt{-72}[/tex]
[tex]i \sqrt{72}[/tex]
[tex]i \sqrt{2 \cdot 6^2}[/tex]
[tex]i \sqrt{2} \sqrt{6^2}[/tex]
[tex]i \sqrt{2} 6[/tex]
[tex]6 \sqrt{2}i[/tex]
We could write this as [tex]0+6\sqrt{2}i[/tex].
Casey and David both ride all-terrain vehicles on trails every weekend for fun each month KC rides for a total of 2x hours at an average speed of x miles per hour David rides for more hours a month in KC but at an average speed that is 3 miles per hour less than Casey's average speed write the standard form of the function which describes the total distance of miles that David rides each month
Answers
Answer:
(x - 3)mph * > 2x
Step-by-step explanation:
KC's total rides in hours = 2x
KC's average speed = x
David's average speed :
3 mph less than KC's average speed = (x - 3)mph
David's total ride in hours in a month is more than KC's, that is ( >2x)
From the equation:
Speed = distance / time
Distance = speed * time
Total distance of miles David rides each month:
(x - 3)mph * > 2x
What is the value of the y-coordinate of point A
Answers
Answer: [tex]-\dfrac{1}{2}[/tex]
Step-by-step explanation:
The coordinate at -30° (-30° = 330°) = [tex]\bigg(\dfrac{\sqrt3}{2},-\dfrac{1}{2}\bigg)\\[/tex]
the x-value is [tex]\dfrac{\sqrt3}{2}[/tex]
the y-value is [tex]-\dfrac{1}{2}\\[/tex]
Answer:
-0.5
Step-by-step explanation:
Dean has a piece of wood that is 3/4 of a foot long, He
needs to cut pieces of the wood into 1/16 of a foot long, How
many pieces can Dean cut? How do you know?
Answers
Answer:
1. 12 pieces of wood
2. How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood
Step-by-step explanation:
Total length of wood=3/4 of a foot
He needs to cut pieces of the wood into 1/16 of a foot long
How many pieces can Dean cut
Let x= number of pieces of wood Dean needs to cut
x=Total length of wood / length of each piece
=3/4 ÷ 1/16
=3/4 × 16/1
=48/4
=12 pieces
Number of pieces of the wood Dean can cut =12 pieces
How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood
That is,
3/4 ÷ 1/6
Then follow the procedures in question 1
In the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts (a) through (c).
(a) Determine the sample space. Choose the correct answer below.
A. The sample space is {00, 0, 1, 2, . . . , 30}.
B. The sample space is {00}.
C. The sample space is {00, 0}.
D. The sample space is {1, 2, . . . , 30}.
(b) Determine the probability that the metal ball falls into the slot marked 3 and Interpret this probability by choosing the correct answer below.
A. If the wheel is spun 100 times, it is expected about 31 of those times to result in the ball landing in slot 3.
B. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing not in slot 3.
C. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.
(c) Determine the probability that the metal ball lands in an odd slot and Interpret this probability by choosing the correct answer below.
A. If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.
B. If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in an odd number.
C. If the wheel is spun 1,000 times, it
Answers
Answer:
(a) The sample space is {00, 0, 1, 2, . . . , 30}.
(b) If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.
(c) If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.
Step-by-step explanation:
We are given that in the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30.
To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.
(a) The sample space is {00, 0, 1, 2, . . . , 30} which means the metal ball can land on any of these numbers.
(b) As we know that there is an equal probability of the metal ball landing on any of the slots marked in the sample space.
Total number of slots = 32
Number of slots marked with 3 = 1
So, the probability that the metal ball falls into the slot marked 3 is given by = [tex]\frac{1}{32}[/tex] = 0.031 or 3.1%
This means that if the wheel is spun 100 times, it is expected about 3.1 of those times to result in the ball landing in slot 3.
So, if the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3 because (0.031 [tex]\times[/tex] 1000) = 31.
(c) As we know that the odd slot in the given sample space is {1, 3, 5,......, 29}.
Total number of slots = 32
Number of odd slots = 15
So, the probability that the metal ball lands in an odd slot is given by = [tex]\frac{15}{32}[/tex] = 0.47 or 47%.
This means that if the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.