School band sold 30 raffle tickets each ticket is labeled with a number 1 to 31 winning ticket will be drawn what is the probability that the number of the winning ticket will be of four or the number 19 enter your answer as a fraction in the simplest form in the Box
Answers
Answer:
0.27
Step-by-step explanation:
To solve this problem, we will use Set Theory Approach to Probability.
Let U = the Sample Space which consists of all possible tests.
Of course U = {1,2,3 .... ,30}
So, no elements in that.
U = n = 30
Let Q = the event bearing a multiple of 4 No winning ticket, and,
R = the case that has the No. 19 winning ticket
∴
Q = { 4, 8, 12 , 16 , 20, 24 , 28} , and
R = {19} , so that
Q ∩ R = ϕ
P(Q ∩R ) = 0
As, n(Q) = 7 , n(R) = 1 , we have,
P (Q) = \(\frac{n (A)}{n(U)}\) = \(\frac{7}{30}\), and P (R) = \(\frac{1}{30\\}\)
P (Q∪R) = P(Q ) + P(R) − P(A∩B) = \(\frac{7}{30}\) + \(\frac{1}{30\\}\) − 0 = \(\frac{8\\}{30\\}\)
≅ 0.27 .
Related Questions
What is an equation of the line that passes through the points (5, 8) and (5, 3)?
Answers
Answer:
x = 5
Step-by-step explanation:
Use the slope formula and slope-intercept form y = m x + b to find the equation.
Hope this helps:)
jake finishes piano practice at 2:45 p.m. after practicing for 37 minutes. What time does Natalie’s practice start? Natalie’s practice starts at __________ p.m.
Answers
Answer:
3:22
Step-by-step explanation:
Find the value of X round to the nearest tenth. I need help.
Answers
Answer:
x ≈ 22.1°
Step-by-step explanation:
Using the law of cosines, then
cosC = \(\frac{a^2+b^2-c^2}{2bc}\)
with a = 19, b = 14, c = 8 and C = x, thus
cos x = \(\frac{19^2+14^2-8^2}{2(19)(14)}\)
= \(\frac{361+196-64}{532}\)
= \(\frac{493}{532}\), thus
x = \(cos^{-1}\) (\(\frac{493}{532}\) ) ≈ 22.1° ( to the nearest tenth )
will mark brainliest helpppp
Answers
Answer is B. The base of the pyramid is 16 square inches and the other sides add up to 40. 40+16=56
find the equation of the line. y=?x+? lol helppp please
Answers
Answer:
y=3/4x+(-2) aka the first blank is 3/4 the second blank is -2
Step-by-step explanation:
The first blank is the slope, the second one shows the y-intercept. You are welcome
For the equation, find dy/dx evaluated at the given values
y2 - x5 = -7 at x = 2, y = 5
dy
Answers
The equation y² - x⁵ = -7 at x = 2 and y = 5, the value of dy/dx is 8.
To find dy/dx for the equation y² - x⁵ = -7 at x = 2, y = 5, follow these steps:
1. Differentiate both sides of the equation with respect to x using implicit differentiation.
Differentiating y² with respect to x, we get 2y(dy/dx).
Differentiating -x⁵ with respect to x, we get -5x⁴.
So, we have: 2y(dy/dx) - 5x⁴ = 0.
2. Plug in the given values of x and y into the differentiated equation.
Substitute x = 2 and y = 5: 2(5)(dy/dx) - 5(2⁴) = 0.
3. Solve for dy/dx.
First, simplify the equation: 10(dy/dx) - 80 = 0.
Next, add 80 to both sides: 10(dy/dx) = 80.
Finally, divide both sides by 10 to get: dy/dx = 8.
So, for the equation y² - x⁵ = -7 at x = 2 and y = 5, the value of dy/dx is 8.
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can someone answer page 3 question 3, page 5 question 3, all of page 6
Answers
The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7
What is trigonometrical ratios?Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle. There are three common trigonometric ratios: sine, cosine, and tangent
For page 3 question 3,
a) <A + <B = 90 since <C = right angle
b) SinA = BC/AB and CosB = BC/AB
The ratio of the two angles BC/AB ÷ BC/AB = 1
I notice that the ratio of sinA and cosB gives 1
b) The ratio of CosA and SinB will give
BC/AB ÷ BC/AB
= BC/AB * AB/BC = 1
For page 5 number 3
Tan28 = g/i
g/12.2 = tan28
cross multiplying to have
g = 12.2*tan28
g = 12.2 * 0.5317
g = 6.5
b) the angle I is given as 90-28 degrees
<I = 62 degrees
To find the side h we use the Pythagoras theorem
h² = (12.2)² + (6.5)²
h² = 148.84 +42.25
h²= 191.09
h=√191.09
h= 13.8
For page 6
1) Sin42 = x/18
x=18*sin42
x = 18*0.6691
x = 12.0
2) cos28 = 6/x
xcos28 = 6
x = 6/cos28
x [= 6/0.8829
x = 6.8
3) Tan63 = x/34
x = 34*tan63
x= 34*1.9526
x = 66.4
4) Sin50 123/x
xsin50 = 123
x = 123/sin50
x = 123/0.7660
x =160.6
5) Sin57 = P/8
Pole = 8sin57
the pole = 8*0.8387
The pole = 6.7
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What is the simplified expression for Negative 3 c d minus d (2 c minus 4) minus 4 d?
Answers
Answer:
- 3cd - d (2c - 4) - 4d
Step-by-step explanation:
hope it helps .
Which of the following are the sines for the angles of this triangle? Select all that apply.
Answers
Answer:
Answer attached
Step-by-step explanation:
PLEASE HELP *URRRRGGEEEENTTTTTT*
Identify the meaning of the following word in the sentence below:
The dog’s temperament was perfect for my son.
a.
height
c.
physical and mental character;mood
b.
weight
d.
color; contrast
Answers
Answer:
c
Step-by-step explanation:
Temperament is to do with the personality of someone.
Thus the dog's temperament would relate to its physical and mental character.
c
Temperament is to do with the personality of someone.
Thus the dog's temperament would relate to its physical and mental character.
"Month 1 2 3 4 5 6 7
Value 23 15 20 12 18 22 15
What type of pattern exists in the data?
(a) positive trend pattern
(b) horizontal pattern
(c) vertical pattern
(d) negative trend pattern
Answers
The negative trend pattern exists in the given data.
The Given information is as follows: Month 1 2 3 4 5 6 7
Value 23 15 20 12 18 22 15
To find: What type of pattern exists in the data
The pattern that exists in the given data can be determined by creating a graph between month and value. So, the graph will be as follows: Type of pattern: From the above graph, it is evident that there is a Negative trend pattern in the data. Answer: (d) Negative trend pattern.
Conclusion: Thus, the negative trend pattern exists in the given data.
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Kenny plotted the following pairs of points and said they made a symmetric figure about a line with the rule: y is always 4. Is his figure symmetrical about the line? How do you know? Explain
Answers
Kenny claims that the figure formed by the given pairs of points is symmetric about a line where y is always 4. To determine if the figure is truly symmetrical, we need to analyze the coordinates of the points and check if they exhibit symmetry with respect to the line y = 4.
To determine if the figure is symmetrical about the line y = 4, we need to check if the corresponding points on opposite sides of the line have the same distance from the line. If they do, then the figure is symmetric.
For example, let's say one of the plotted points is (x, y) = (2, 4). If the figure is symmetric, there should be another point on the opposite side of the line y = 4 that is equidistant from the line. However, since y is always 4 according to Kenny's rule, all the points will lie on the line y = 4. Therefore, there won't be any points on the opposite side of the line to exhibit symmetry.
Based on this reasoning, we can conclude that Kenny's figure is not symmetrical about the line y = 4 because all the points lie on the line itself and do not have corresponding points on the opposite side.
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AABC has vertices A(-4,6), B(-6,-4), and C(2,-2).
The following transformation defines A A'B'C':
AA'B'C' =Ds (A ABC)
Choose each correct coordinate for the vertices of A A'B'C'.
Choose 1 point from Point A', 1 point from B', and 1 point from C
Point A'
A' (10, 15)
A' (-10, 15)
A' (-20, 30)
A' (30, 20)
Point B'
OB' (-30, -20)
OB' (10, 15)
OB' (-15, -10)
B' (-6,-4)
Point C'
C' (2,-2)
C' (10, 10)
C' (5,-5)
OC' (4,-4)
C²
Answers
The correct coordinates for the vertices of Δ A'B'C' are A' (10, 15), B' (-3, -3), and C' (8, -8). The transformation Ds is a dilation with center (0,0) and scale factor 5.
The transformation Ds reflects the triangle ΔABC over the line y = x. To find the coordinates of A', we need to switch the x and y-coordinates of A, which gives us A' (6, -4). To find the coordinates of B', we need to switch the x and y-coordinates of B, which gives us B' (-4, 6), and then reflect it over the line y = x by negating both coordinates, which gives us OB' (-(-4), -6) = (-4, -6+(-6)) = (-4,-12). To find the coordinates of C', we do the same as for A', which gives us C' (-2, 2).
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Please Help me Its A Math Problem * Determine if the table below is best modeled by a linear, quadratic or exponential function.
x -1 0 1 2 3 4
y 0.5 1 2 4 8 16
Question options:
Exponential
Quadratic
Linear
Answers
The table below is best modeled by an exponential function. The exponential function that models the table is y = (1)(2)^x or y = 2^x.
This means that the y-values increase by a constant factor as the x-values increase by a constant amount.
To see why this is the case, we can look at the ratio of consecutive y-values in the table. For example, when x increases from -1 to 0, y increases from 0.5 to 1. The ratio of these y-values is 1/0.5 = 2. Similarly, when x increases from 0 to 1, y increases from 1 to 2. The ratio of these y-values is also 2. In fact, for any pair of consecutive y-values in the table, the ratio is always 2. This shows that the y-values increase by a factor of 2 every time the x-values increase by 1.
An exponential function has the form y = ab^x, where a and b are constants. In this case, we can see that b = 2, since that is the factor by which the y-values increase. To find a, we can use any point in the table. For example, when x = 0, y = 1. Substituting these values into the equation, we get:
1 = a(2)^0
1 = a(1)
a = 1
Therefore, the exponential function that models the table is y = (1)(2)^x or y = 2^x.
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r ÷ 8 + q× 3
Please I need your help now please
Answers
Answer:
r/8+3q
Explanation:
There is no value given to this equation so out final answer is a simplified version of the equation
Y = 3 + 2 x +5 for x
Answers
Answer:
\(x=\frac{y-8}{2}\)
Step-by-step explanation:
\(y=3+2x+5 \\ \\ =8+2x \\ \\ y-8=2x \\ \\ x=\frac{y-8}{2}\)
the population of a town increased from 3600 in 2005 to 5650 in 2011. find the absolute and relative (percent) increase.
Answers
Absolute increase in population will be 2050
And percentage increase will be 56.94 %
We have given population in 2005 is 3600
And population in 2011 is 5650
So absolute increase in population = 5650-3600 = 2050
We have to find the percentage increase in population
So relative percentage increase in population will be 2050/3600 *100 = 56.94 %
So population will increase by 60 %
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what is the measure of each angle of a regular 14-gon? if neccessary, round to the nearest tenth.
Answers
Step-by-step explanation:
Side measuring formula is 180(n-2). ---[ n= side]
Question: 14-gon
>by using formula 180(14-2)
> 180×12
> 2160÷ 14. --[divided by 14 side in order to find one side's degree]
> 154.28°
how long will it take $100 to reach $500 when it grows at 10 percent per year?
Answers
It will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.
To find out how long it will take, we can use the formula for compound interest:
A = P(1 + r)^t
Where A is the final amount, P is the principal amount, r is the interest rate, and t is the number of years.
In this case, we want to find out how long it will take for $100 to reach $500 when it grows at 10 percent per year. So we can plug in the values and solve for t:
500 = 100(1 + 0.10)^t
5 = (1.10)^t
Taking the natural logarithm of both sides:
ln(5) = t ln(1.10)
t = ln(5) / ln(1.10)
t = 14.87 years
So it will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.
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two students wish to investigate how the amount of pollution and number of fish in a stream are related. identify the dependent and independent variables.
Answers
In this investigation, the dependent variable is the number of fish in the stream and the independent variable is the amount of pollution.
Variables are symbols or names that are used to represent values in a mathematical or scientific investigation. They allow us to describe and analyze patterns and relationships in data.
There are two main types of variables:
1. Independent variables are variables that are manipulated or controlled in an experiment to determine their effect on the dependent variable. The independent variable is also referred to as the predictor variable or the explanatory variable.
2. Dependent variables are variables that are being measured in an experiment and are dependent on the independent variable. The dependent variable is also referred to as the response variable or the outcome variable. It is the variable that is being affected by the independent variable.
The dependent variable is dependent on the independent variable, as changes in the amount of pollution are expected to affect the number of fish in the stream. The goal of the investigation is to determine the relationship between the two variables and see how changes in the amount of pollution affect the number of fish in the stream.
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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.y = 49 − x2y = 0
Answers
By using the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis, given the functions y = 49 - x^2 and y = 0.The volume of the solid generated by revolving the plane region about the y-axis is 0.
shell method :
To find the volume of the solid,
we'll use the shell method formula:
V = 2 * pi * ∫[a, b] x * h(x) dx
In this case, a = -7, b = 7 (because x = ±√(49 - y)), and h(x) = 49 - x^2. So the integral becomes:
V = 2 * pi * ∫[-7, 7] x * (49 - x^2) dx
Now, let's evaluate the integral:
1. Expand the integrand:
x * (49 - x^2) = 49x - x^3
2. Find the antiderivative:
∫(49x - x^3) dx = 49x^2/2 - x^4/4 + C
3. Plug in the limits of integration and subtract:
[(49(7)^2)/2 - (7)^4/4] - [(49(-7)^2)/2 - (-7)^4/4] = [49(49) - 2401/4] - [49(49) - 2401/4] = 0
4. Multiply by the constant
(2 * pi): 2 * pi * 0 = 0
The volume of the solid generated by revolving the plane region about the y-axis is 0.
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A ___ is a system of basic rules and principles by which a government is organized.
Answers
Answer:
A Constitution is a system of basic rules and principles by which a government is organized.
This is for middle school 8th grade please help me :) DIDNT FORGET IMAGE
Answers
Answer:
Slope: -3/4
y-intercept: ( 0,5)
Step-by-step explanation:
Resource managers need to determine the number of years after which purple loosestrife will cover more than 850 acres of the wetland.
Fill in the values of A, b, and c to write an inequality modeling the number of years, t, for which purple loosestrife will cover more than 850 acres of the wetland.
A(b)^t>c
Answers
Answer:500(1.2)^t> 850
Step-by-step explanation:
got it right on the test
The missing values in the expression are t > log(850/A)/logb if Resource managers need to determine the number of years.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Resource managers need to determine the number of years after which purple loosestrife will cover more than 850 acres of the wetland.
c = 850
\(\rm A(b)^t > 850\)
\(\rm (b)^t > \dfrac{850}{A}\)
Taking log and solving for t:
t > log(850/A)/logb
Thus, the missing values in the expression are t > log(850/A)/logb if Resource managers need to determine the number of years.
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PLEASE HELP!!!!! please? :D
Answers
Answer:
9
Step-by-step explanation:
→ Substitute in the values
2³ +√64 ÷ 8
→ Simplify
8 + 8 ÷ 8
→ Calculate
8 + 1 = 9
Answer:
9
Step-by-step explanation:
2 to the power of 3 is 8
8 + 64 = 72
72 ÷ 8 = 9
find the missing side of each triangle. i need help!!!
Answers
Answer:
√161 yd
Step-by-step explanation:
Hi there!
We're given a right triangle (notice the right angle), the measure of one of the legs (one of the sides that make up the right angle) as 8 yd, and the hypotenuse (the side opposite to the right angle) as 15 yd.
We need to find x, which is the other leg in the triangle
If we are given 2 sides and need to find a third, we can use Pythagorean Theorem, which states that a²+b²=c² if a and b are legs and c is the hypotenuse
In this case, a=8, b=x, and c=15
So let's substitute those values into the formula
(8)²+x²=(15)²
raise everything to the second power
64+x²=225
subtract 64 from both sides
x²=161
take the square root of both x and 161
x=√161, x=-√161
-√161 cannot work in this case, as distance cannot be negative.
The question asks for the answer to be in simplified radical form, but √161 cannot be simplified down further
so the answer is √161 yd
Hope this helps! :)
537,699 in word form
Answers
Answer: five hundred thirty seven thousand six hundred ninety nine
Step-by-step explanation:
what is 28/10 as a proper fraction
Answers
Answer:
Step-by-step explanation:
28/10 as a proper fraction.
28/10 is an improper fraction so you have to turn it into a proper fraction.
To do this divide the numerator (top figure) by 10 (the denominator) which equals 2.8 so to put it as a proper fraction you look at the whole number in 2.8 which is the 2 and keep the number after the decimal point as a fraction over the 10.
The answer would be 2 8/10
true/false if y is a differentiable function of u and u is a differentaible function of u and u is a differentaible function of x, then y is a differentiable function of x
Answers
True. If y is a differentiable function of u and u is a differentiable function of x, then the chain rule states that y is a differentiable function of x.
The chain rule states that if y is a function of u and u is a function of x, then the derivative of y with respect to x is equal to the derivative of y with respect to u multiplied by the derivative of u with respect to x. This means that if y is a differentiable function of u and u is a differentiable function of x, then y is also a differentiable function of x.
In mathematics, a function is said to be differentiable at a point if it is possible to define the derivative of the function at that point. The derivative of a function is a measure of how the function changes as its input (or independent variable) changes. It is defined as the limit of the difference quotient, which is a measure of the rate of change of the function over a small interval around the point of interest.
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What is the third term of the sequence 20 - n²
Answers
A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
As per the given sequence, 20 - n²
The 20 - n² represents the nth term of the sequence.
Thus a(n) = 20 - n²
For the third term n = 3
a(3) = 20 - (3)²
a(3) = 20 - 9 = 11
Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".
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