0.0515 is probability of exactly six successes .
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events. The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Binomial probability with
Number of trials (n) = 8
probability of success ( ρ ) = 0.95
ρ = 0.95
p + q = 1
q = 1 - p
= 1 - 0.95
q = 0.05
x ~ bin( n , ρ )
ρ( X = x ) = ⁿCₓ Pˣ . qⁿ⁻ˣ
the probability of exactly six success .
ρ ( X = 6 ) = ⁸C₆ ( 0.95)⁶ ( 0.05 )⁸ ⁻⁶
= 28 ( 0.7351 ) ( 0.05)²
= 28 ( 0.7351 ) ( 0.0025 )
= 0.051457
ρ( X = 6 ) = 0.0515
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Given the following information about the arithmetic sequence an, find a10. A5=24 a8=39
The 10th term of an arithmetic sequence is found as the 49.
Define the term arithmetic sequence?An ordered group of numbers with a shared difference with each consecutive word is referred as an arithmetic sequence. For particular, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression would be another name for an arithmetic sequence.As per the stated values in question.
Fifth term a5 = 24
8th term a8 = 39.
Let the first term be 'a' and the common difference be 'd'.
Then,
a5 = a + 4d
24 = a + 4d .....eq 1
a8 = a + 7d
39 = a + 7d .....eq 2
Solving eq 1 and 2.
3d = 15
d = 5
a = 4
Now,
a10 = a + 9d
a10 = 4 + (9 x 5)
a10 = 4 + 45
a10 = 49
Thus, the 10th term of an arithmetic sequence is found as the 49.
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PLS ANSWER THIS Solve the following system of equations for all three variables.
The values of x, y and z are 4, 1 and - 6 respectively.
What is the general equation of a Straight line? What is a system of equations in two or three variable.The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied
We have the following equations -
8x + y + 4z = 9
4x - 3y + z = 7
8x - 4y + 5z = - 2
We have -
4x - 3y + z = 7
z = 7 - 4x + 3y
We can write -
8x + y + 4z = 9
as -
8x + y + 4(7 - 4x + 3y) = 9
8x + y + 28 - 16x + 12y = 9 ...Eq[1]
and we can write -
8x - 4y + 5z = - 2
8x - 4y + 5(7 - 4x + 3y) = -2
8x - 4y + 35 - 20x + 15y = - 2 ...Eq[2]
Plot the graph of equation [1] and [2]. We will will get -
x = 4
y = 1
Now -
z = 7 - 4x + 3y
z = 7 - 16 + 3
z = - 6
Therefore, the values of x, y and z are 4, 1 and - 6 respectively.
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If Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
The time taken to label 750 books if Clare labels books at 15 books per minute is 50 minutes.
How to calculate the time used?In this situation, Clare volunteers at a library during the summer and has to label 750 books and she labels books at 15 books per minute and she takes no breaks.
Let the time taken to label the 750 books be represented by x.
This will be illustrated as:
1/x = 15/750
Cross multiply
(15 × x) = (750 × 1)
15x = 750
Divide
x = 750 / 15
x = 50
The time is 50 minutes.
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Complete question
Clare volunteers at a library during the summer and has to label 750 books. Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
which contours are usually drawn darker than the other contours? group of answer choices index contours largest (max) value contour contour interval smallest (min) value contour
Index contours are usually drawn darker than the other contours.
Index Contours are darker and wider than the other regular contour lines for ease of identification. They are labeled with elevation and also have their altitude value mentioned on the dark lines and these values represent the altitudes of the particular contours. Index contours appears after every fifth contours. If the number with contours will increase then its elevation will also increase and similarly if the number associated with contours starts to decrease then its elevation also decreases.
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given that 3p = 2m - 5q, express m in terms of p and q
Answer:
Step-by-step explanation:
3p. = 2m - 5q
-2m. = -3p - 5q
Divide through by -2
m. = (3p + 5q) \2
The equation can be rearranged and expressed in terms of p and q is m = (3p+5q)/2.
Given equation 3p = 2m - 5q
3p + 5q = 2m
(3p + 5q) / 2 =m
Hence, m = (3p+5q) / 2
To express the equation in terms of p and q we need to put all the p and q terms to one side of the equation and m terms to another side of the equation. It can be easily seen that 3p is already on one side and we just need to bring a q term to this side which can be done by shifting 5q from the right-hand side to left-hand side. The equation is now 3p+5q. Now to get the equation in terms of m we need to divide the whole equation by 2 which will give m = (3p+5q) / 2.
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Write a unit rate for the situation.
Situation: 87 students in 3 classrooms
Unit rate:
students per classroom
The unit rate for the given situation is 29 students per classroom.
What is the unit rate?
A unit rate is described as a ratio comparing the first quantity to one unit of the second quantity.
Given situation is 87 students in 3 classrooms.
So, the unit rate [tex]= \frac{87}{3}[/tex] students/classroom
[tex]= 29[/tex] students per classroom
Hence, the unit rate for the given situation is 29 students per classroom.
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PLEASE HELP
In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems. In March's Math Meet, they solved $\frac23$ of the problems. (There might be different numbers of problems asked in November and March.)
In total, the Little Monsters solved $13$ of $30$ problems over both Math Meets. How many problems were asked at March's Math Meet?
The number problems solved by the little Monsters of Beast Academy in March's meet is 15.
How to determine the number of problems solved in March meetThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
let the number of questions solved by little Monsters of Beast Academy in
March's meet be xNovember's meet be yIn November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5
In March's Math Meet, they solved $\frac23$ of the problems = 2x/3
Hence:
y/5 + 2x/3 = 12
x + y = 30
solving the equation gives
x = y = 15
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Help with this please (ASAP)
Pls pls pls help it has to be turned in today!
Using the compound amount formula, the amount after 40 years is 2000(107/100)^40.
In the given question,
Esther got a summer job and decided to set aside $2000 to prepare for retirement without making monthly contribution.
She invests in the US stock market through as index fund that averages a 7% return compounded annually over this 40 year period.
We have to find the total balance in the account after 40 years.
We have to find total balance compounded annually.
The formula of the compound amount is
A = P(1+r/100)^n
where A = Amount
P = Principal Amount
r = interest rate
n = time
From the question we know that
P = $2000, r = 7%, n = 40
Now putting the value in formula
A = 2000(1+7/100)^40
Simplifying
A = 2000(1×100/100+7/100)^40
A = 2000(100/100+7/100)^40
A = 2000((100+7)/100)^40
A = 2000(107/100)^40
You can find the amount after simplifying the amount.
Hence, the amount after 40 years is 2000(107/100)^40.
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the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds. the heaviest 2.5% of the bags packaged by the flour company are labeled as overweight. what is the probability that of 10 randomly chosen bags of flour at least 2 are overweight?
The probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68.
Given, that the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds.
As, we know that
P(X) = (1/s√2π)exp(-1/2((X-m)/s)^2)
where, m is the expected value
and s is the standard deviation.
Now, we have Expected value 10 pounds
and Standard Deviation 0.2 pounds
So, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be
P(X=0) + P(X=1) = (1/0.2√2π)exp(-1/2((0-10)/0.2)^2) + (1/0.2√2π)exp(-1/2((1-10)/0.2)^2)
P(X=0) + P(X=1) = 0.32
So, Required Probability be 0.68.
Now, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68
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what is 56/60 as a percentage
Answer:
93.33%
Step-by-step explanation:
56/60 as a percentage:
56/60 = 0.93333
0.93333 as a percent:
0.93333 * 100 = 93.33%
The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
We have to given that,
To change a number 56/60 into a percentage.
Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Hence, We can write as,
⇒ 56/60 × 100%
⇒ 5600/60
⇒ 93.33%
Therefore, The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of function is positive so the function have maximum value at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value at x=3.
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Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. How many ways can this be done, if the order of the choices is not taken into consideration
Thus, the number of ways in which to choose 4 letters, without replacement, from 17 distinct letters is 57,120.
Define the term permutation?The term permutation applies to a mathematical computation of a number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something can be organized or arranged.Total distinct letters are 17.
There are 17 alternatives for the initial letter if there are 17 letters.
There are just 16 alternatives left once you remove the letter.
Each time you remove a letter, the bag contains one fewer letter.
Number of ways = 17 x 16 x 15 x 14
Number of ways = 57,120
Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.
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Jane was asked to solve the equation `2-4=2(-5+1)`. she believes the solution to the equation is `x=\frac{1}{2}` . explain how jane could confirm that her solution is correct
the solution for the given equation is x= 1/2
an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors
since the given expression is :
`(2-4)=2(-5+1)x²
so solving for the simple arithmetic expression on both sides :
=>-2 =2(-4)x²
=> -2 = -8x²
=>2/8=x²
=>1/4= x²
=>x= 1/2
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X (3x + 5)°
(4x)
Y
(8x - 14)°
B
N
Answer:2
Step-by-step explanation:
1+1 es 2
How many dogs could Roscoe groom if he worked for 40 hours?
90
120
220
200
There are 200 dogs Roscoe groom if he worked for 40 hours.
What is working time?
A person's working time is the time they are engaged in paid work. Personal housework, childcare, and pet care are examples of unpaid work that is not included in the definition of the working week.
In most cases, when someone inquires about your working hours, you should first provide the start time before providing the time you leave for home.
From the given graph we can see that for each three hours the number of dogs are increased by 15.
So, for each one hour the number of dogs increased by 5.
For 18 hours the the number of dogs are 90.
After 18 hours to complete 40 hours we need 22 hours.
So, for 22 hours the number of dogs are
22 x 5 = 110.
Therefore, the total number of dogs worked for 40 hours are,
90 + 110 = 220.
Hence, there are 200 dogs Roscoe groom if he worked for 40 hours.
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To paint a house, a painting company charges
a flat rate of $500 for
supplies, plus $50 for each hour of labor.
a.
How much would the painting company charge to paint
a house that
needs 20 hours of labor? A house that needs 50 hours?
Call the number of hours of labor x.
A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)
Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.
We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000
Write the slope-Intercept form of the given line. Include your work in your final answer.
Type your answer in the box provided to submit your solution.
The slope-Intercept form of the given line is y=x-1.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The given line passes through (0,-1) and (1,0). Therefore, the slope of the given line can be written as,
Slope of the line, m = [0 - (-1)]/(1 - 0)
= 1 / 1
= 1
Now, the equation of the line passing through (0,-1) can be written as,
y = mx + c
(-1) = 1(0) + C
-1 = 0 + C
C = -1
Substitute all the value in the equation of the line,
y = m(x) + c
y = 1(x) + -1
y = x - 1
Hence, the equation of the given line is y=x-1.
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The equation of the line from the given graph can be written as y = x + 1.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
From the given graph the points on the straight line can be determined as (1, 0) and (2, 1).
The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is given as slope = (y₂ - y₁) / (x₂ - x₁).
Then, the slope of the line is (2 - 1) / (1 - 0) = 1
Now, the equation of the line can be written as,
(y - 1) / (x - 0) = 1
⇒ y - 1 = x
⇒ y = x + 1
Hence, the equation of the line in slope-intercept form is given as y = x + 1.
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Jerome invested 260000 for 2 years at a rate of 8%p.a. 1)calculate the simple interest 2)calculate the investment at compound interim interest 3)amount at the end of the simple interest 4)amount at the end of compound 5)difference between the amount at simple interest and compound interest
1) Simple interest is $41600, 2) compound interest is $ 43264, 3) Amount at the end of Simple interest is $301600, 4) Amount at the end of Compound interest is $303264, 5) Difference in the amount of simple and compound interest is $ 1664.
Here it is given:
Principle (P) =$ 260000
Time(t) = 2 years
Rate (R) = 8%
1) We have to find the simple interest:
Simple interest(SI) = P× t × R/ 100
= 260000× 2× 8/ 100
= $41600
2) We have to find Compound Interest
Compound interest(CI) =P( 1 + R/100[tex])^{t}[/tex]- P
= 260000( 1 + 8/100[tex])^{2}[/tex]- 260000
= 260000( 27/25[tex])^{2}[/tex] - 260000
= 303264 - 260000
= $43264
3) Amount at the end of simple interest
Amount = P + SI
= 260000 + 41600
=$301600
4) Amount at the end of compound interest
Amount = P + CI
= 260000+ 43264
= $303264
5) Difference between the amount at simple interest and compound interest
Difference = 303264 - 301600
= $1664
Therefore the simple interest is $41600, the compound interest is $43264, the Amount at the end of simple interest is $ 301600, the amount at the end of the compound interest is $303264, and the difference in the amount of simple interest and compound interest is $1664.
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Solve for a side in right triangles
Really need help with this one!!
The value of side AC is AC = 3.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
The given triangle ΔABC is a right angled triangle.
So, to find the side AC we can use the cosine ratio,
[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]
AC ≈ 3.
Hence, the length of side AC is 3.
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Match each type of transformations with an example and a description of how it affects the graph of a function.
1. Translation; y= f(x) + 2
2. Reflection; y= -f(x)
3. Stretch; y= 2f(x)
4. Shrink; y= 1/2 f(x)
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
What is Reflection?A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
Given:
When f(x) shifts 2 units up, we have
y= f(x) + 2; Translation
When the graph of f(x) to a symmetric position on the opposite side of the x-axis
y= -f(x); Reflection
When it stretches f(x) by a factor of 2
y= 2f(x); Stretch
When it reduces f(x) by a factor of 1/2
y= 1/2f(x); Shrink
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Find the total area for the shape!!
Answer:
56cm²
Step-by-step explanation:
Because this is an irregular shape, you have to split it into two shapes and find the area of each one. Then you can add those two areas together to find the total area of the figure. There are many ways you can split it but the way I did it left me with the equation (12·3)+(4·5). Then all you have to do is multiply and add which will give you a total of 56cm².
I need examples of surds
at intel, the sizes of processor chips have a mean of 1 cm with a standard deviation of 0.2 cm. multiple random samples, each consisting of 35 processor chips, are taken. the sample mean and standard deviation for each sample are recorded to form a sampling distribution. what is the mean and standard deviation of this sampling distribution?
The mean and standard deviation of this sampling distribution is 1 cm and 0.033 cm, respectively.
The sample mean is the arithmetic mean of all the samples of processor chips. The mean of the sample group is known as the sample mean.
Let X denote the multiple random samples of 35 processor chips and each of which represents the size of the processor chips.
Let 'x' be the sample mean of all the random samples X which represents the size of the processor chips.
The mean of the size of processor chips= μ =1 cm
The mean of the sampling distribution x of sample means is equal to the mean of the sizes of the processor chips μ
Mean of sampling distribution x = mean of the size of the processor chips μ
⇒ x = μ
x = 1 cm
The mean of this sampling distribution is 1 cm.
The standard deviation is the amount of variation among the set of values. It is the measure of the dispersion of values in the data set.
The size of the processor chips has a standard deviation of 0.2 cm so σ = 0.2 cm
Let 'x' be the standard deviation of random samples X of the size of processor chips.
Number of random multiple samples of processor chips, n =35
The standard deviation of this sampling distribution can be calculated by using the below formula;
x = σ/[tex]\sqrt{n}[/tex]
Substituting the value of \sigma as "0.2" cm and the value of "n" as 35 in the above formula, we get;
x = 0.2/√35
x = 0.033 cm
The standard deviation of this sampling distribution is 0.033 cm.
The mean of this sampling distribution is 1cm and the standard deviation of this sampling distribution is 0.033 cm.
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I really need help on this one.The amount of milk needed for each of 5 recipes is shown on the line plot.What is the total amount of milk needed for the recipes?
The total amount of milk needed for the recipes, considering the line plot, is of:
5.25 cups.
How to obtain the total amount of milk needed for the recipes?The total amount of milk needed for the recipes is obtained adding all the measures of the line plots.
The measures of the line plot given by the image at the end of the answer are given as follows:
Two measures of 1/4 cups = 0.25 cups, which is half the distance between 0 and 1/2.One measure of 1.25 cups, which is the value at the midpoint between 1 and 1.5.One measure of 1.5 cups.One measure of 2 cups.The total amount is given by the sum of all these measures, hence:
2 x 0.25 + 1.25 + 1.5 + 2 = 5.25 cups.
Missing InformationThe line plot is given by the image at the end of the answer.
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In a candy box, there are 3 times as many candies with nuts as candies without nuts. There are 12 candies in the box. How many candies with nuts are in the box?
Step-by-step explanation:
In a candy box, there are 3 times as many candies with nuts as candies without nuts. There are 12 candies in the box. How many candies with nuts are in the box?
let:
without nuts = x
with nuts = 3x
so:
x + 3x = 12
4x = 12
x = 3, so there are 3 candies without nuts.
Because there are three times more candies with nuts than without:
3 * 3 = 9 candies with nuts
Answer:
9 candies with nuts
Step-by-step explanation:
Suppose the number of candies is x
there three times as many candies with nuts as candies without nuts, so 3x
there are 12 candies in total
3x+x=12
4x=12
x=3
3x=9
2x + 3x equals to 20x find the value of x.
Answer:
Here,
2x+3x=20x
or,5x=20x
or,5x-20x=0
or,15x=0(divide both sides by -15)
hence,x=0
Patricia has $3425.82 in her checking account. How much does she have in her account after
she makes a deposit (puts in )of $9120.75 and a withdrawal (takes out) of $185.90
We're given :
Patricia originally has $3425.82 in her account.
After that, she deposits $9120.75, meaning her amount in her account goes up by $9120.75
Lastly, she withdraws $185.90, meaning her amount in her account goes down by $185.90.
Therefore, after the transactions, she has a total of : 3425.82 + 9120.75 - 185.90 = $12360.67
Rhino poaching is a serious problem and has resulted in rhinos, particularly the black rhino, becoming an endangered species. Statistics suggest that there were 60 500 black rhinos at the beginning of 1970, but only 4 000 remained at the end of 2011. Determine the annual rate of depreciation that these statistics represent.
The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %
What is a rate of depreciation?The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.
The initial number of black rhinos in 1970 = 60,500
The number of black rhinos remaining in 2011 = 4,000
The annual rate of depreciation can be found using the formula;
[tex]FV = PV \cdot \left(1+\dfrac{r}{100} \right)^n[/tex]Where;
FV = The future value = 4,000
PV = The present value = 60,500
r = The annual depreciation rate
n = The number of years
[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]
[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]
[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]
The annual rate of depreciation is approximately 6.41%
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Seamus buys £600 of shares in a new Company. One week later the value of the shares has Increased by 15%. find the value of the shares one week after Seamus bought them. 600/100x 15 =90 90+600=690 Is this a righ answer ?cause i am not so sure if i did it right
Answer:
yes, you did it right!
Step-by-step explanation:
You firsth calculate how much 15% of £600 are.
You did it exactly right. It's £90.
And to work out rhe value of the shares one week later, you add the £90 to the £600.