The number of outcomes, using the Fundamental Counting Theorem, is given as follows:
A. Red exactly 3 times and Purple exactly 2: 10.
B. Red at least ounce in 4 spins: 175.
C. Red at least ounce in 5 spins: 781.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Item a is used with the combination formula, as it is an arrangement of five elements with 3 and 2 repetitions, hence the number of outcomes is:
[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]
What is the Fundamental Counting Theorem?The Fundamental Counting Principle states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item b, in four spins, each with four outcomes, the parameters are given as follows:
[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex]
Hence the number of outcomes is:
N = 4^4 = 256.
For no red results, the parameters are as follows:
[tex]n_1 = n_2 = n_3 = n_4 = 3[/tex]
Hence:
N = 3^4 = 81.
Hence the number of outcomes with at least one red is:
256 - 81 = 175.
For item 3, the lone difference is that there are five trials, hence:
Total outcomes: 4^5 = 1024.None red: 3^5 = 243.At least one red: 1024 - 243 = 781.More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
#SPJ1
Help please: 12+6x<24
Answer:
12+6x<24First by using inverse operations, subtract 12 on both sides.
12-12+6x<24-12Now it will become
6x<12Now divide 6 to isolate x
6x÷6<12÷6Hence, the answer is
X<225 x 10 to the power of 6 in a standard form
4 Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0 Reset Next
The equation of the circle is x² + y² - 41 =0.
What is a circle?A circle is a round-shaped 2-dimensional geometrical figure in which the points on the boundary are equidistant from a fixed point called a center.
Given, a circle centered at O(0,0)and has a point B (4,5) on its circumference.
The radius of the circle is the distance between the points O(0,0) and B (4,5), therefore,
r = √((4-0)² + (5-0)²)
r = √(16+25)
r = √41
The equation of a circle, centered at the origin with a radius of r =√41 units, is given by,
x² + y² = √41²
x² + y² = 41
x² + y² - 41 =0
Hence, the equation of the circle is x² + y² - 41 =0.
Learn more about circles:
https://brainly.com/question/11833983
#SPJ1
the net of a prism is shown
a)how many faces
b)what is the mathmatical name
Answer:
????? you did not show the net of the prism
Step-by-step explanation:
Answer:
b) it's a polyhedron
I don't know what else to say
A rectangle has side links of 3X +6 inches and 2X -4 inches right in expression to represent perimeter of the rectangle then find the perimeter if X equals 9
Answer:
ez hi
Step-by-step explanation:
ez
iply Mixed Numbers What is the product of 1 and 12
Answer: 12
Step-by-step explanation: When multiplying (in this case finding a product,) by one, the number you are multiplying will always be the answer.
Write the equation of the line that passes through the points (2,-8)(2,−8) and (-1,4)(−1,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The simplified point-slope form is y = 2x -12
A simple definition of point-slope form is a line equation written with only one point on the line and the slope of the line. (x, y) is the point form, and the slope is the rise over run or the ratio of the change in y values to the change in x values.
Given points (2,-8) and (-1,4)
We have to determine the answer in point-slope form
The slope formula provides the slope of the line:
m = (y2 -y1)/(x2 -x1)
m = (4 -(-8))/(-1-2) = 12/-3 = -4
the point-slope formula is given by
y-y1 = m(x-x1)
In terms of this formula:
m = 2
y1 = -8
x1 = 2
Let's simplify by plugging these values into the point-slope formula:
y - y1 = m (x - x1)
y - (-8) = (2)(x - 2)
y + 8 = 2(x - 2)
y + 8 = 2x -4
y = 2x -12
Therefore the simplified point-slope form is y = 2x -12
To learn more about point slope form visit
https://brainly.com/question/21605900
#SPJ1
A bacteria culture initially contains 3000 bacteria and doubles every half hour.
1) Find the size of the baterial population after 80 minutes.
2) Find the size of the baterial population after 7 hours.
The size of the bacterial population after 80 minutes is 19048.81
The size of the bacterial population after 7 hours is 49152000.
Given,
A bacterial culture initially contains 3000 bacteria and doubles every half hour.
we are asked to determine the size of the bacterial population after 80 minutes.
The exponential growth law for this problem is
p(t) = 3000 (2)^t/30
where t is the time in minutes. To find the population after 80 minutes, plug in t=80 and evaluate P(80).
p(80) = 3000 (2)^80/30
p(80) = 3000(2)^8/3
p(80) = 19048.81
now, we are asked to determine the size of the bacterial population after 7 hours.
To find it after hours, plug in t=420 minutes (since 7 hrs equals 420 minutes) and evaluate p(420).
p(420) = 3000(2)^420/30
p(420) = 3000(2)^14
p(420) = 49152000
hence we get the required size of the population.
learn more about Population size here:
brainly.com/question/25896797
#SPJ1
Ms. McCool asked Zina to write 5 numbers whose average is 85. Zina immediately wrote
83, 84, 85, 86, and 87. How did she know what to write?
To find the set of numbers with a given mean we can assume them as consecutive terms, Zina did the same thing.
Mean of data:Mean or Arithmetic mean is the average of the given set of numbers. It is also denoted as the equal distribution of values for a given data. To calculate the mean of data, we can use the following formula
Mean/Average = Sum of observations ÷ Number of observations
Here we have
The average of 5 numbers is 85
Let's assume that the 5 numbers are 5 consecutive numbers and the five numbers are x, x+1, x+2, x+3, x+4, and x+5 [ for simple calculations ]
Average of 5 numbers = Sum of numbers / 5
⇒ 85 = (x+ x+ 1 + x+2 + x+3 + x+4 ) /5
⇒ 425 = 5x + 10
⇒ 5x = 415
⇒ x = 83
Then the 5 numbers are 83, 84, 85, 86, and 87
Therefore,
To find the set of numbers with a given mean we can assume them as consecutive terms and we can calculate the mean, Zina did the same thing.
Learn more about the Mean of data at
https://brainly.com/question/12019147
#SPJ1
Simplify the expression (x)(6+x)−2x. Write products as powers when possible.
(x)(6+x)−2x=
Simplifying the expression (x)(6 + x)−2x gives x^2 + 4x
How to simplify the expressionInformation given in the question
the expression (x)(6 + x)−2x
The expression is simplified by first expanding
(x) (6 + x) − 2x
6x + x^2 - 2x
x^2 + 4x (products as powers when possible)
The result here is a quadratic equation without the constant variable. it can be simplified further to give
x(x + 4)
Learn more about quadratic equations:
https://brainly.com/question/29339843
#SPJ1
Convert each mixed number to a fraction greater than one, or each fraction greater than one to a mixed number 5 3/11
A quadratic function
y
=
f
(
x
)
y=f(x) is plotted on a graph and the vertex of the resulting parabola is
(
−
4
,
6
)
(−4,6). What is the vertex of the function defined as
g
(
x
)
=
f
(
x
)
−
4
g(x)=f(x)−4?
g(x) is a vertical dilation of f(x), then the x-value of the vertex does not change, using that we will see that the vertex of g(x) is (-4, 24)
What is the vertex of g(x)?
We know that there is a parabola graphed called f(x), such that the vertex of f(x) is at (-4, 6).
We also have a vertical dilation of this function defined as:
g(x) = 4*f(x)
Notice that because this is a vertical dilation, the x-value of the vertex does not change, then the vertex is at x = -4, like on f(x).
Evaluating there we get:
g(-4) = 4*f(-4)
And because the vertex of f(x) is (-4, 6), then we know that:
f(-4) =6
Replacing that we get:
g(-4) = 4*f(-4) = 4*6 = 24
Then the vertex of g(x) is at (-4, 24)
Learn more about dilations:
https://brainly.com/question/3457976
#SPJ1
A small startup skateboard coMpany projects that the cost per month of manufacturing x skateboards will be C(x)= 10x +500 and the revenue per month from selling x skateboards will be r(x)= -x2+70x. Given that the profit is revenue minus cost for what values of x will the company break even or make a profit
The startup company needs to sell 68 skateboards in order to break even
Profit FunctionTo solve this problem, we have to find the profit of the company and what is required to break-even from total sales.
C(x) = 10x + 500
r(x) = -x² + 70x
Profit = revenue - cost
profit = (-x² + 70x) - 10x + 500
profit = -x² + 70x - 10x + 500
profit = -x² + 60x + 500
Solving the quadratic equation
x = 67.4 ≅68
For the startup to break even, they need to sell at least 68 skateboard.
Learn more on profit function here;
https://brainly.com/question/16866047
#SPJ1
Help pls pls shsjsjsjsjs
Answer:
The answer would be the first one because when you factor -3 out, inside of the parentheses should be all positive because negative times negative is positive.
Tickets for movie admission for adults are
$4.00 each, but half-price is charged for
children. If 265 adult tickets were sold and
he box office collected $1,200, how many
children's tickets were sold?
A) 70
B) 35
C) 280
[D) 140
Answer:
[ D ] 140
Step-by-step explanation
4 x 265 = 1060
1060 - 1200 = -140
the answer is 140 i hope this helped <3
Use point-slope form to write the equation of a line that passes through the point (−7,−4) with slope 10/7
The equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6
The coordinates of the point = (-7, -4)
The slope of the line = 10/7
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Where [tex](x_1,y_1)[/tex] is the coordinates of the point
Substitute the values in the equation
y -(-4) = 10/7(x - (-7))
y + 4 = (10/7)(x + 7)
Convert to slope intercept form
y +4 = (10/7)x + 10
y = (10/7)x + 10 - 4
y = (10/7)x + 6
Hence, the equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6
Learn more about slope intercept form here
brainly.com/question/9682526
#SPJ9
Consider the following scenario.
the three-number bet
(a) Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)
dollars
(b) Interpret it. (Round your answer to one decimal place.)
Over time, you should expect to lose about
cents for every dollar you bet.
a) The expected value of each $1 bet in roulette is of: -$0.988.
b) The interpretation is given as follows: Over time, you should expect to lose about 999 cents for every dollar you bet.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is obtained as the sum of each outcome multiplied by it's respective probability.
The three-number bet is when one sequence of three numbers has to be correctly chosen, hence the probability of winning is of:
p = 1/(10³) = 1/1000.
(as there is only one correct sequence, and for each number, there are 10 outcomes).
The payout is given as follows:
11:1.
That is, if you win, you earn 11 times the amount you bet.
Considering a bet of $1, the distribution of earnings is given as follows:
P(X = 11) = 1/1000.P(X = -1) = 999/1000.Hence the expected value of the bet is:
E(X) = 11/1000 - 999/1000 = -$0.988.
Which is the amount you are expected to lose for every dollar you bet.
More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
#SPJ1
Find the sum of the first n terms of the geometric sequence. n=5, a₁ =4, r = 3
The sum of n terms of geometric sequence with n=5, a₁ =4, r=3 is given by = 484.
Given that the sequence is geometric.
First term is = a₁ = 4
Common ratio is = r = 3
The number of terms for which the sum to be determined = n = 5
So the required sum of n terms of given geometric sequence is given by,
S [tex]=a_1\times\frac{r^n-1}{r-1}[/tex]
S [tex]=4\times\frac{3^5-1}{3-1}[/tex]
S = 4*((243-1)/2)
S = (4*242)/2
S = 484
Hence the sum of the given geometric sequence is 484.
To know more about Geometric Sequence refer to:
https://brainly.com/question/24643676
#SPJ9
The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer 28 62 90
Mobile device 46 64 110
Column totals 74 126 200
PLEASE What is the joint relative frequency of students who use a mobile device in an online class?
64%
55%
32%
23%
The joint relative frequency of students who use a mobile device in an online class is approximately 32%.
The joint relative frequency of students who use a mobile device in an online class, we need to divide the frequency of the intersection of the "Mobile device" and "Online" categories by the total number of students (200 in this case) and express it as a percentage.
From the given two-way frequency table, we can see that the frequency for the intersection of "Mobile device" and "Online" is 64.
The joint relative frequency can be calculated as:
Joint Relative Frequency = (Frequency of intersection / Total number of students) × 100
Joint Relative Frequency = (64 / 200) × 100
Joint Relative Frequency ≈ 32%
For similar questions on frequency
https://brainly.com/question/28821602
#SPJ8
Nick bikes 39 miles in 2 hours while Jane bikes 34 miles in 5 hours. Who bikes faster Nick or Jane?
Answer:
Nick
Step-by-step explanation:
Nick: 39 miles / 2 hours = 19.5 miles per hour
Jane: 34 miles / 5 hours = 6.8 miles per hour
Nick is biking faster!
pediatricians work an average of 40 h per week. The standard deviation is 15 hours. What percentage of pediatricians work more than 70 h per week?
The percentage of pediatricians that work more than 70 h per week is; 2.275%
How to find the percentage from z-score?The formula for z-score of a normal distribution is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
sample mean; x' = 70 hours
population mean; μ = 40 hours
standard deviation; σ = 15 hours
Thus;
z = (70 - 40)/15
z = 2
From online p-value from z-score calculator, we have;
p-value = 0.02275 = 2.275%
Read more about percentage from z-score at; https://brainly.com/question/25638875
#SPJ1
True or False
1 The total number of outcomes in tossing 3 fair coins is 6.
2 The totality of all outcomes is called an event.
3 Empty set of events is considered an event.
4 Sample Space is considered an event.
5 Empirical probability uses frequency to determine the probability.
6 The total number of outcomes in tossing a fair coin and rolling a die at the same time is 12
7 Weather forecasting is considered a subjective probability.
8 The probability of getting odd numbers in rolling a fair die is ⅓
9 If there are 18 students in a room. Where 5 of them are male then the probability of selecting male in a class is 5/18.
10 The probability of the sample space is always 1.
Answer:false
Step-by-step explanation:
see photo for question
1. The hypothesis are given as follows:
Null: [tex]H_0: \mu \leq 178258[/tex]Alternative: [tex]H_1: \mu > 178258[/tex]2. The critical value is of: t = 2.3974.
3. The test statistic is of: t = 2.35.
4. The decision is: Reject the null hypothesis.
5. The conclusion is: There is enough evidence to conclude that the mean is greater.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean in Los Angeles is greater, that is:
[tex]H_0: \mu \leq 178258[/tex]
At the alternative hypothesis, it is tested if there is enough evidence, hence:
[tex]H_1: \mu > 178258[/tex]
The t-distribution is used, as we have the standard deviation for the sample but not for the population. Using a t-distribution calculator, with 55 - 1 = 54 df, a right-tailed test, as we are testing if the mean is greater than a value and a significance level of 0.01, the critical value is:
t = 2.3974.
Hence the decision rule is defined as follows:
t < 2.3974: Do not reject the null hypothesis.t > 2.3974: Reject the null hypothesis.What is the test statistic and the conclusion?The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 191790, \mu = 178258, s = 42627, n = 55[/tex]
Hence the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{191790 - 178258}{\frac{42627}{\sqrt{55}}}[/tex]
t = 2.35.
The test statistic is greater than the critical value, hence:
The null hypothesis is reject.There is enough evidence to conclude that the mean is greater.More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
#SPJ1
i will give brainly if someone helps with thisIf △ABC is translated 3 units left and 2 units up, what would be the translated coordinates of Point C?
Answer: (-2, -2)
Step-by-step explanation:
Right now, the coordinates of point C are (1, -3).
It is first moved 3 units to the left, so the point C would change to (1 - 3, -3) = (-2, -3)
It is then moved 2 units up, so point C would change to (-2, -3 + 2) = (-2, -1)
[10 POINTS] OMGGGGGGG!!!!!!!!!!!!! GUYS I NEED HELP ASAP!!!!!!!! I HAVE TO TURN THIS IN 5 MINUTES!!!!!!!! HELP ME PLEASE!!!!! I'LL GIVE 10 POINTS!!!
2+2= ?
Help please
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions
The values of [tex]D, D_x, D_y[/tex] are, [tex]D = 13, D_x = 8, D_y = 19[/tex].
What is Cramer's rule?
One of the key techniques used to solve an equation system is Cramer's rule. The determinants of matrices are used in this method to derive the values of the system's variables. Thus, the determinant technique is another name for Cramer's rule.
Consider, the given system of equations
-3x + 4y = 4 ...(1)
2x = 7y - 9 ...(2)
equation (2) can be written as,
2x - 7y = -9 ..(3)
Using Cramer's rule, we have to find the determinant of the coefficient matrix
matrix,
D= [tex]\left[\begin{array}{ccc}-3&4\\2&-7\end{array}\right][/tex] = (-3)(-7) - 8 = 21 - 8 = 13
Secondly, find the determinant of x coefficient matrix,
[tex]D_x[/tex] = [tex]\left[\begin{array}{ccc}4&4\\-9&-7\end{array}\right][/tex] = (4)(-7) - (4)(-9) = -28 + 36 = 8
Similarly, find the determinant of y coefficient matrix,
[tex]D_y[/tex] = [tex]\left[\begin{array}{ccc}-3&4\\2&-9\\\end{array}\right][/tex] = (-3)(-9) - (4)(2) = 27 - 8 = 19
Hence, values of the determinants are, [tex]D = 13, D_x = 8, D_y = 19[/tex].
To know more about the Cramer's rule, click on the link
https://brainly.com/question/20354529
#SPJ1
Make w the subject of the formula y - aw = 2w - 1
Answer:
[tex]w=\frac{y+1}{a+2}[/tex]
Step-by-step explanation:
[tex]y-aw=2w-1 \\ \\ y+1=2w+aw \\ \\ y+1=w(a+2) \\ \\ w=\frac{y+1}{a+2}[/tex]
6. Which shows the decimals in the
correct order?
A. 5.271> 5.217 > 5.38
B. 5.38 5.217 > 5.271
C.
5.271
5.38 > 5.217
D. 5.38
5.271 > 5.217
Answer: D. 5.38 > 5.271 > 5.217
IXL Please Help Fast!
Equation of line c parallel to line d and passing through points (2, -6) is
How to equation of line dThe equation of line d will be written in the slope intercept form of the form just like line c,
the slope intercept form is as below
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
y = -5x + 3
slope
m = -5
slope of parallel lines are equal hence slope of line d = -5
using the formula for the slope intercept the equation is written
(y - y₁) = m (x - x₁)
point (2, -6) and m = -5
(y - -6) = -5 (x - 2)
y + 6 = -5x + 10
y = -5x + 4
Learn more about slope intercept:
https://brainly.com/question/29334541
#SPJ1
31-62=152+2-6(3+21) i need the answer to this please help