When the number of times you roll an odd number increases, the theoretical probability that you roll an even number would decrease.
How is the probability of rolling an even number affected ?As the number of times you roll an odd number increases, the theoretical probability that you roll an even number decreases. This is because the probability of rolling an even number is inversely proportional to the number of times you roll an odd number.
If you are rolling a fair die, the probability of rolling an even number is 3/6 or 1/2, and the probability of rolling an odd number is also 3/6 or 1/2.
As the number of times you roll an odd number increases, the number of rolls that are left for an even number decreases, thus the probability of rolling an even number decreases as well.
For example, if you roll the die 10 times and 6 of them are odd numbers, the probability of rolling an even number in the remaining 4 rolls is 4/4 or 1 (100%) because you are guaranteed to roll an even number.
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9. (-12,-62) and (-22, -62) help
In how many years a sum of money doubles at the rate of 8%?
Answer:
about 9 years
Step-by-step explanation:
You want to know the doubling time for money earning an interest rate of 8%.
Rule of 72The rule of 72 tells you the doubling time is about ...
72/(interest rate %) = 72/8 = 9 . . . . years
The sum will double in about 9 years.
__
Additional comment
The actual period will depend on the way interest is compounded. When compounded annually, the time is ...
log(2)/log(1.08) ≈ 9.01 . . . years
Compounded monthly, the time is ...
log(2)/(12·log(1 +.08/12)) ≈ 8.69 . . . years
Solve the equation 5/12 + (-2 11/12) =
Answer: -2 1/2
Step-by-step explanation
if the equation is + but a number is negative, remember that +- = - which means 5/12 + (-2 11/12) = 5/12 - 2 11/12
2 11/12 is bigger than 5/12, so we'll switch it around and it'll become
2 11/12 - 5/12
2 11/12 - 5/12 = 2 6/12
Because 2 11/12 is originally a negative number, +- = -
which means the answer will be negative, so it is -2 6/12.
but we're not done yet, we need to simplify it by dividing it with 6
so the final answer is -2 1/2
if it didn't make any sense at all heres an equation version :
5/12 + (-2 11/12)
= 5/12 - 2 11/12
= 2 11/12 - 5/12
= 2 6/12 (2 11/12 is originally negative so the ans will be negative)
= - 2 6/12 (divide by 6 to simplify)
= - 2 1/2
What is the equation of the line that passes through the point (5, 5) and has a slope of -1?
Help please I am really struggling with my geometry
Answer:
A) [tex]108^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle 1+m\angle 2=180^{\circ} \\ \\ 72^{\circ}+m\angle 2=180^{\circ} \\ \\ m\angle 2=108^{\circ}[/tex]
Triangle Theorems.
What is the Value of X?
Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.
How to find the value of x in a triangle? Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown".The triangle in question is an equilateral triangle.The unknown is called a variable. In order to solve for a variable (like x), you need to isolate the variable. You can isolate the variable by using inverse operations to manipulate the equation. Addition is the inverse of subtraction, and multiplication is the inverse of division.If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle.Alternatively, multiply the hypotenuse by cos(θ) to get the side adjacent to the angle.Thus, all angles are equivalent to 60 degrees.
So, for a triangle, we know that Interior angle + neighbouring outside angle = 180°, 60° + x = 180°, and x = 180° - 60° = 120°.
Thus, a triangle's x value is 120°.
The side x of the right triangle can be found using trigonometric ratios.Therefore,sin 30° = opposite / hypotenusesin 30 = x / 81 / 2 = x /8cross multiply8 = 2xdivide both sides by 28 / 2 = 2x / 2x = 4To learn more about Triangle refer to:
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The equation 3x62x10x4 is true for all real numbers. The equation 6x22x4x1 has no solution. When do you think an equation has all real numbers as its solutions?
When an equation simplifies to 0=0 then it has true for all real numbers or else it does not have solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
3x +6 = 2x +10 +x -4
Subtract (3x+6) from both sides:
(3x +6) -(3x +6) = (2x +10 +x -4) -(3x +6)
0 = x(2 +1 -3) +(10 -4 -6)
0 = 0
0 = 0 . . . . has "all real numbers" as a solution set
6x +2 -2x = 4x +1
Subtract (4x+1) from both sides:
(6x +2 -2x) -(4x +1) = (4x +1) -(4x +1)
x(6 -2 -4) +(2 -1) = 0
0x +1 = 0
1 = 0
Does not have "all real numbers" as a solution set. There is no solution
Hence, when an equation simplifies to 0=0 then it has true for all real numbers or else it does not have solution.
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The perimeter of a rectangular painting is 308 cm. If the length of the painting is 93 cm, what is its width?
Answer: 61 cm.
Step-by-step explanation: The perimeter of any shape is the total distance of the exterior. This means that the sum of all side lengths of a shape is the perimeter. For a rectangle, the sum of both lengths and widths is the perimeter.
You can use the formula 2L+2W=P to solve this problem. 308 is P or the perimeter and 93 is L or the length. We can substitute these values and we get 2(93)+2(w)=308. We then subtract 2(93) or 186 from both sides to get 2W= 122. We then divide by two to get W or the width is equal to 61 cm.
Find the value of 7u +6 given that 3u-8=4.
simplify your answer as much as possible.
Answer:
34.
Step-by-step explanation:
The value of 7u + 6
=3u - 8 = 4
=3u = 4 + 8
=3u = 12
=3u/3 = 12/3
u = 4.
therefore u = 4
=7u + 6
=7(4) + 6
=28 + 6
=34.
At a run festival, 5/7 of the runners are women. If there are 1050 runners, how many are women?
Answer: 750
Step-by-step explanation:
5/7 = women
2/7 = men (to get 2/7, 7/7 - 5/7 and you get 2/7)
5/7 x 1050
= 5 x 1050/7
= 5250/7
=750
The / means divide
I have some extra points so I'm going to give them away BUT you have to answer this question
Make sure to add a drawing on how you answered this
If you get it right ill make you brainly,
Thank caliaquinton for the idea. =D
A graph of triangle ABC after a translation of 1 unit left and 7 units down is shown in the image attached below.
What is a translation?In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of triangle ABC vertically down by 7 units and horizontally left by 1 unit, the coordinates of the image of triangle A'B'C' include the following:
(x, y) → (x - 1, y - 7)
Coordinate A = (-6, 7) → Coordinate A' (-6 - 1, 7 - 7) = (-7, 0)
Coordinate B = (-8, 1) → Coordinate B' = (-8 - 1, 1 - 7) = (-9, -6)
Coordinate C = (-1, 2) → Coordinate C' = (-1 - 1, 2 - 7) = (0, -5)
Next, we would use an online graphing calculator to construct (plot) triangle A'B'C' on a cartesian coordinate based on its vertices after a translation.
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Solve the given initial-value problem. 2y'' + 3y' − 2y = 10x2 − 8x − 13, y(0) = 0, y'(0) = 0
y(x)=
Refer to the images attached. Please let me know if you have any questions regarding how I did things or why.
please need help asap 25 points
Question 17
Opposite angles of a parallelogram are congruent, so [tex]3y+2=62 \implies y=20[/tex].
Adjacent angles of a parallelogram are supplementary, so [tex]62+5x+3=180 \implies x=23[/tex].
Question 18
Diagonals of a parallelogram bisect each other.
[tex]3y+9=2y+16 \implies y=7\\\\10x-24=5x-4 \implies x=4[/tex]
Which graph represent the function?
Answer:
c
Step-by-step explanation:
For the data in the table does y vary directly with x? if it does, write an equation for the direct variation pleaseee!!
Yes, because it is a graph of a straight line with y = 1.625x, y changes for every value of x.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Value set for x and y.
Since it asked if the given equation is linear or not
The general formula for the line:
y = mx +c
where,
m is slope
and c is constant
m = (y₂ - y₁)/(x₂ - x₁)
in our case
m = 26 - 13 / 16 -8
m = 13/8
Thus the equation of a line:
y = 13/8x + c
putting any of the given coordinates in the given equation:
c = 0
Thus, the equation of a line
y = 1.625x
Therefore, yes, y varies for every value of x since it is a graph of a straight line y = 1.625x
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Solve for u.
U/4 = 3
U = ?
x is a whole number such that -4 < x < 2
Answer:
x = [-3, 1]
Step-by-step explanation:
I wrote it in interval notation but if x can be any whole number between those two it can literally be -3, -2, 1, 0 or 1. Unless there are further restrictions or some sort of equation, there is no one number answer. Pick your poison, write it like x = {-3, -2, 1, 0, 1} if you'd like or the way I wrote it.
What is the answer to this
find all three-digit numbers that meet these criteria: all digits are distinct, one digit is odd, and the sum of the digits is five.
Answer:
203, 230, 320, 302, 140, 410, 104, 401
Step-by-step explanation:
To meet the criteria, we have to think of all the ways we can use three distinct numbers, with one of the numbers being odd, which adds up to 5:
1 + 4 + 0 = 5
2 + 3 + 0 = 5
Subsequently, use the numbers we found and rearrange them to form three-digit numbers.
there are 2 sections to this question: a group of teenagers are asked about their favourite hobbies. 9 males and 7 females like sports, a total of 16 people; 2 males and 3 females like video games, a total of 5 people; 3 males and 8 females like watching films, a total of 11 people, a total of 14 males and 18 females participated. question 1 - in fractions what is the probability that a teenager selected at random is female and their favourite hobby is watching films? you can simplify this fraction if you wish. question 2 - the teenager from the question above rejoins the group and another teenager is picked at random what is the probability that the teenager picked at random is male and their favourite hobby is playing video games? you can simplify this fraction if you wish
a) In fractions the probability that a teenager selected at random is female and their favorite hobby is watching films is given as: 1/4, while
b) if the teenager from the question above rejoins the group and another teenager is picked at random, the probability that the teenager picked at random is male and their favorite hobby is playing video games is 1/6.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
With regard to problem (a),
There is a total of 32 teenagers.
Of those, 8 are female with a favorite hobby of watching films.
Thus,
Related Probability = 8/32; divide both numerator and denominator by 8 to get;
= 1/4
With regard to problem (b), the probability that the teenager picked at random is male and their favorite hobby is playing video games is:
P = (14/32) x (2/14)
P = 2/32; thus
P = 1/16.
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Full Question:
A group of teenagers are asked about their favourite hobbies. The results are shown in the following table: Sports Playing video games Watching films Total
Male 9 2 3 14
Female 7 3 8 18
Total 16 5 11 32
Q6a. In fractions, what is the probability that a teenager selected at random is female and their favorite hobby is watching films? You can simplify this fraction if you wish.
Q6b. the teenager from the question above rejoins the group and another teenager is picked at random what is the probability that the teenager picked at random is male and their favourite hobby is playing video games? you can simplify this fraction if you wish
Count the number of different functions with the given domain, target and additional properties
(a) f(0,1}{0,1).
(b) f: (0,1}{0,1). The function f is one-to-one
(c) f. (0,1)5(0,1)
(d) f (0,135 (0,1). The function f is one-to-one
The number of different functions with the given domain, target and additional properties is as follows:
(a) There are infinitely many different functions, as there is no additional property given that could have the domain (0,1) and the target {0,1}.
(b) The only one-to-one function with the domain (0,1) and the target {0,1} is the identity function, f(x) = x. The additional property is that the function is one-to-one.
(c) The function f has a target of and a domain of (0,1) and (0,1). There are an infinite number of possible functions that could have this domain and target because no additional property is provided.
(d) There are infinitely many different one-to-one functions that could have the domain (0,1) and the target (0,1).
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Makin Bread Bakery used 300 kg of flour for bread orders last month. This month, they
had less orders and used 20% less flour. How much flour did they use this month?
Using the percentage method the amount of flour used this month in the bakery for bread orders is 240 kg.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The amount of flour used last month is, a = 300 kg
The percentage of flour less used is = 20%
Calculate the 20 percent of 300 kg flour -
b = 20% × 300
b = 20/100 × 300
b = 60 kg
The amount of flour used this month = a - b
The amount of flour used this month = 300 - 60
The amount of flour used this month = 240 kg.
Therefore, this month 240 kg of flour was used.
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2. When the students at Castle Hill Middle School are separated into 6 equal groups, there are 18 students in each group. How many students are at the school?
Answer:
108 students
Step-by-step explanation:
Just multiply the amount of students in each group by the number of groups (6)(18)=108
so there are 108 students
1) Which of the following relations are functions?
The relation which is a function among the given answer choices are Choices A and D.
Which among the given answer choices represent a function?It follows from the task content that the answer choices which represent a function be identified as required.
By definition, a function is a relation in which case, no one input value is assigned more than one output.
On this note, for Choice A; all input values have only one output value assigned to them and for Choice D; the graph represents a quadratic function in which case, each input value, x is assigned only one output value, y.
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x+2=8-x what is the answer to this
Answer:
[tex]x + 2 = 8 - x \\ \\ \dashrightarrow \: x + x = 8 - 2 \\ \\ \dashrightarrow \: 2x = 6 \\ \\ \dashrightarrow \: x = 3[/tex]
hope helpful ;-;
Answer:
x = 3
Step-by-step explanation:
x+2=8-x what is the answer to this?
x + 2 = 8 - x
move the x to the left and the 2 on the right and change the signx + x = 8 - 2
solve on both sides2x = 6
divide the two parts by 2x = 3
----------------------------
check
3 + 2 = 8 - 3
5 = 5
the answer is goodWhich answers describe the shape below? Check all that apply.
0
A. Rectangle
B. Rhombus
C. Parallelogram
D. Trapezoid
E. Quadrilateral
F. Square
Answer:
Step-by-step explanation:
it do be a quadrilateral parallelogram and rhombus cause it do
Answer:
Step-by-step explanation:
What is the value of x
Answer: 104
Step-by-step explanation:
Angles at a line are equal to 180 degrees so:
180 = 72 + (x + 4)
180 = x + 76
180 -76 = x + 76 -76
104 = x
What is the area of a hexagon 10m by 5m
The area of the hexagon is approximate, Area = (150 √3) m².
What is a formula of a hexagon?
A Regular hexagon has six sides and angles that are congruent and is made up of six equilateral triangles. The formula to find out the area of a regular hexagon is as given:
Area = (3√3 s²)/ 2
where 's' represents the length of a side of the regular hexagon.
A hexagon is a six-sided polygon. The area of a hexagon can be calculated using the formula:
Area = (3 * √3 * (side length)^2) / 2
In this case, the hexagon is 10m by 5m, so the side length of the hexagon is 10m. Plugging this into the formula, we get:
Area = (3 * √3 * (10m)^2) / 2
Area = (3 * √3 * 100m^2) / 2
Hence, the area of the hexagon is approximate:
Area = (150 √3) m².
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Calculate the integral of ze2x + y over the surface of the box in the figure below.
0<= x <= 2
0<= y <= 3
_____________
We will use the triple integral in cylindrical coordinates to calculate the integral across the surface of the box in the illustration.
The integral is given by:
[tex]∫∫∫ {ze}^{2x} + y dzdydx[/tex]
Where x, y, and z are the coordinates and the limits of integration are
[tex]0 <= x <= 2, 0 <= y <= 3, and 0 <= z <= {ze}^{2x} + y[/tex]
We can change the integral into cylindrical coordinates by using the following change of variables:
x = rcosθ
y = rsinθ
z = z
The integral becomes:
[tex]∫(0 to 2)∫(0 to 3)∫(0 to ze^(2r cosθ) + r sinθ) rze^(2r cosθ) + r^2sinθ dzdrdθ[/tex]
Although the integral is challenging to calculate, this method will assess it. The region of integration can be determined by knowing the bounds of z, which would be beneficial given that the box is in rectangular coordinates.
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Below you are given a partial Excel output based on a sample of 25 observations. Coefficients Standard Error Intercept 145 29 x1 20 5 x2 –18 6 x3 4 4 The estimated regression equation is _____. a. y = β0 + β1x1 + β2x2 + β3x3 + ε b. E(y) = β0 + β1x1 + β2x2 + β3x3 c. ŷ = 29 + 5x1 + 6x2 + 4x3 d. ŷ = 145 + 20x1 – 18x2 + 4x3
The estimated regression equation is d. ŷ = 145 + 20x₁ – 18x₂ + 4x₃
This equation is obtained from the coefficients given in the table. It is the equation that best predicts the value of the dependent variable (y) based on the values of the independent variables (x₁, x₂, and x₃).
The equation is in the form of y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε, where β₀, β₁, β₂, and β₃ are the coefficients of the independent variables and ε is the error term. These coefficients represent the change in the dependent variable for a unit change in the independent variable, holding all other independent variables constant.
From the table, we can see that the value of β₀ = 145, which represents the predicted value of y when all independent variables (x₁, x₂, and x₃) are equal to zero.
The value of β₁ = 20 represents the change in the predicted value of y for a unit change in x₁, holding x₂ and x₃ constant. Similarly, the value of β₂ = -18 represents the change in the predicted value of y for a unit change in x₂, holding x₁ and x₃ constant, and the value of β₃ = 4 represents the change in the predicted value of y for a unit change in x₃, holding x₁ and x₂ constant.
So, the estimated regression equation is: ŷ = 145 + 20x₁ – 18x₂ + 4x₃.
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