a) It is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.
b)It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05) ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.
Now, According to the question:
Part (a) Step 1: Given Information
Given, p = 0.097
Formula used:
The expected value
μ = 1/p
Part (a) Step 2: Simplification
The number of independent trials required until first success is distributed geometrically.
A geometric distribution's expected value is
μ = 1/p = 1/0.097 = 10.3039
Hence, it is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.
Part (b) Step 1: Given Information
Given, p = 0.097
Formulae to be used
Geometric probability:
P(X = k) = [tex]q^k^-^1p = (1-p)^k^-^1p[/tex]
Addition rule:
P(A ∪ B) = P(A) + P(B)
Complement rule:
P(A°) = P(not A) = 1 - P(A)
Part (b) Step 2: Simplification
Consider, p = 0.097
Compute the binomial probability definition at k = 1, 2,and3....40 :
P(X = 1) = [tex](1 - 0.097)^1^-^1(0.097)[/tex] = 0.097
Using the complement rule:
P(X ≥ 40) = 1 - P(X ≤ 39) = 1 - 0.9813 = 0.0187 = 1.87%
It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05) ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.
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The given question is incomplete, The complete question is:
Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .
a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?
b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.
A line passes through the points (–1, –5) and (4, 5). the point (a, 1) is also on the line. a coordinate plane. what is the value of a? –2 –1 1 2
The value of a is 2
We can use the slope-intercept form of a line, y = MX + b, to find the equation of the line.
The slope (m) of the line can be found using the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
So, m = (5 - (-5)) / (4 - (-1)) = 10/5 = 2
Now, we can use the point-slope form of a line, y-y1 = m(x-x1)
where (x1,y1) is any point on the line and m is the slope of the line.
In this case, we will use the point (x1, y1) = (–1, –5)
so, y-y1 = m(x-x1) = -5 - 2(-1-x) = -5-2+2x
Now we know that the point (a,1) is also on the line, we can substitute the value of x and y in the equation
so, 1 - (-5) = 2(a - (-1))
1 +5 = 2a+2
6 = 2a+2
4 = 2a
a = 2
Therefore, the value of a is 2.
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Hi, I'm having a little bit of confusion answering this. What I did was:
Tan(20) = 9/x
9 x Tan(20) = x
But my answer was wrong, can someone tell me what I did wrong?
Thanks :)
Answer:
Step-by-step explanation:c
please help me find this answer!
Answer:
[tex]k { { { {y6444396}^{46446?} }^342{?} }^66 {6 { { {6636163 \\ }^{2} }^{2} }^{2} }^{2} {?} }^{?} \times \4166441frac{?}{?} [/tex]
Step-by-step explanation:
djdkkwkwnsjididjfjrje
describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 15 inches, 37 inches
The possible length of the third side of the triangle is x>52 inches.
What is the sum of the first side and second side of any triangle?The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. If the sum of the two sides is equal to the third side, then the two sides will coincide with the third side so a triangle cannot be formed. Hence, the sum of the two sides must be greater than the third side for the triangle to be formed.
Given: Sides of two sides of a triangle as 15 and 37 inches.
let the third side of the triangle be x.
then x>15+37
x>52 inches.
Hence, The possible length of the third side of the triangle is x>52 inches.
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a telephone company charges $0.50 for the first 5 minutes of a call and $0.09 for each additional minute. which interval below represents how a person can talk for $3 (assume that a person cannot talk for a fraction of a minute)?
On solving the provided question, we can say that by equation 15+4 = total minutes, they can talk 19 minute
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x= total minutes -4 the 1st 4 minutes are included in the .30
total cost = .3 + .18 x
[tex]3 = .3 +.18 x\\2.7 = .18x\\2.7/.18 = x\\15 = x[/tex]
x = total minutes -4
15+4 = total minutes
they can talk 19 minute
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After its second bounce, a ball reached a height of 80 cm. The rebound factor for the ball was 0.7. From approximately what height, in cm, was the ball dropped?
A) 34
B) 49
C) 115
D) 163
Answer: The answer is C hope this helps :)
Step-by-step explanation:
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The height of a ball after its second bounce was 80 cm. The ball had a rebound factor of 0.7. Then the height of the ball from where it is dropped is given as,
0.7h = 80
h = 80 / 0.7
h = 14.3 cm
h ≈ 115 cm
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
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if you ate 2.5 cups of this particular cereal, how many calories and grams of fiber would you be consuming?
On solving the provided question, we can say that by linear equation we have 2.5x * cereals = y
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.
2.5 cups of this particular cereal,
the following linear equation, you could calculate how many calories and grams of fiber you were eating.
let x = cereals we eat y = calories
so, equation - 2.5x * cereals = y
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The top of a square table is covered with four equal square tiles. If the side length of each tile is decreased by 75% , how many tiles of the new size would be needed to cover the same table?
Answer:
16
Step-by-step explanation:
The side lengths of the original square was 2. 2 x 2 = 4
.25 x 2 = .5
The squares are now 1/2 x 1/2. One of the 4 original squares will now need 4 new smaller size squares to cover the one square.
4 x 4 = 16
a store manager wants to mix 20 lb of nuts worth $3 per pound with some nuts worth $10 per pound to make a mixture worth $5 per pound. how many pounds of $10 nuts must be used?
you have been told to reduce your department by 15%. your department has 220 workers. there are 512 workers in the whole company. how many workers must be let go (round to the nearest worker)?
To reduce your department by 15%, you would need to let go of 33 workers.
Reducing a department by 15% means that 15% of the current workforce in that department will be let go. To calculate this, you first need to determine the percentage of the total workforce that your department represents. In this case, your department has 220 workers out of 512 workers in the whole company, which represents 43% of the total workforce.
Then, you can calculate the number of workers that need to be let go by multiplying the total number of workers in your department by the percentage that needs to be cut. In this case, that would be
220 x 0.15 = 33 workers
This means that 33 out of the 220 workers in your department would need to be let go in order to achieve a 15% reduction.
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Coins are placed into a treasure chest, and each coin has a radius of 1.6 inches and a height of 0.0625 inches. If there are 170 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
341.63 in3
106.76 in3
85.41 in3
0.50 in3
85.41 cubic inches of the treasure chest is taken up by the coins
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Remember that the volume of a cylinder is given by:
volume = (height)×pi×(radius)²
Where pi = 3.14
Then here the volume of each coin is:
V = (0.0625)(3.14)(1.6)²
= 0.5024 in³
And there are 170 coins, so the total volume is:
170×0.5024
85.408 in³
85.41 in³
Hence, 85.41 cubic inches of the treasure chest is taken up by the coins
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Answer:
c or 85.41
Step-by-step explanation: its simple
four horizontal lines and four vertical lines are drawn in a plane. in how many ways can four lines be chosen such that a rectangular region is enclosed?
Four lines be chosen from four horizontal lines and four vertical lines in a plane such that a rectangular region is enclosed in 36 ways.
The four horizontal lines can be chosen in 4 choose 2 = 6 ways because we have to pick 2 out of 4, and the four vertical lines can be chosen in 4 choose 2 = 6 ways as well as
4C2 = 4!/ (2!×2!)
4C2 = 6
The total number of ways to pick four lines that enclose a rectangular region is 6×6 = 36, where each combination of two horizontal lines and two vertical lines forms a rectangle.
It's important to notice that the order of choosing the lines doesn't matter, so we use the combination formula (nCr) instead of permutation formula (nPr).
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If the points (2, 5), (1, 1) and (a, 3) are collinear, find the value of a.
Answer:
a = 0
(0,3)
Step-by-step explanation:
a food delivery service manager would like to estimate the mean amount of time it takes employees of his company to deliver food to the customers. to do so, he selects a random sample of 10 deliveries from the large number of deliveries made and records the amount of time each of those deliveries took. are the conditions for constructing a t confidence interval met?
Answer: C
Step-by-step explanation:
Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.
1. Constructing a t confidence interval requires that the sample size is greater than 30, so the first condition that must be met is that the sample size is greater than 30.
2. The second condition that must be met is that the sample is a random sample of the population of interest. In this case, the sample is a random sample of 10 deliveries from a large number of deliveries made.
Since both conditions are met, the conditions for constructing a t confidence interval are met.
Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.
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What is the solution to the equation StartFraction y Over y minus 4 EndFraction minus StartFraction 4 Over y + 4 EndFraction = StartFraction 32 Over y
The solutions to the equation y/ (y- 4) - 4/ (y + 4) = 32/ y are approximately 30.948, 4.627 and -3.575.
The given equation is y/ (y- 4) - 4/ (y + 4) = 32/ y
Let us simplify the left hand side (LHS) :
Make the denominator same to (y - 4)(y + 4)
y/ (y- 4) - 4/ (y + 4) = (y/ (y- 4))×((y + 4)/(y + 4)) - (4/ (y + 4))×((y - 4)/(y - 4))
y/ (y- 4) - 4/ (y + 4) = ( y(y + 4) - 4(y - 4))/ (y - 4)(y + 4)
y/ (y- 4) - 4/ (y + 4) = (y² + 4y - 4y + 16)/ (y² - 16)
y/ (y- 4) - 4/ (y + 4) = (y² + 16)/ (y² - 16)
Now plugging this simplified version in LHS
(y² + 16)/ (y² - 16) = 32/ y
y(y² + 16) = 32(y² - 16)
y³ - 32y² + 16y + 32×16 = 0
The solutions are approximately 30.948, 4.627 and -3.575.
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the three sides of a triangular lot are represented by x, 2x, and 3x 2. what are the lengths of each side if the perimeter of the triangular lot is 362 feet? 60 ft, 120 ft, 182 ft 100 ft, 122 ft, 140 ft 60 ft, 60 ft, 242 ft 80 ft, 100 ft, 182 ft
On solving the provided question we can say that any triangle's perimeter is the sum of its three sides' lengths = [tex]\x = 360/6 = > x = 60[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Triangle's sides are x, 2x, and 3x Plus 2 ft. Respectively.
Radius is 362 feet.
Any triangle's perimeter is the sum of its three sides' lengths.
[tex]362 = x + 2 x + 3x +2\\6 x +2=362\\6 x= 362-2\\6 x=360\\x = 360/6\\x = 60[/tex]
Triangle's shortest side measures 60 feet.
Middle side = 2 x 2 x 60 ft = second side
Third side equals 3 x + 2 and is measured as 360+2=180+2=182 ft.
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A region satisfies the inequalities 2 ≤ x ≤ 6 and 3 ≤ y ≤a. What value of a would give the region an area of 24 square units?
Answer: a = 9
Step-by-step explanation:
The given figure formed is a rectangle.
Area of given region (Yellow region) = 24 [tex]unit^{2}[/tex]
Length (l) = 6-2 = 4 units
Breadth (b) = a-3 units
Area = l×b
24 = 4 x (a-3)
6 = a-3
a = 9 units
What is the name of the segment inside the large triangle?
perpendicular bisector
altitude
median
angle bisector
Answer:
Perpendicular Bisector
Given the polynomial Q(x)=4x^3-3x+1, find the polynomial P(x) such that P(x)=2*(Q(x)+P(x)) for any real number x
Given the polynomial Q(x)=4x^3-3x+1,
P(x) = 8x^3 - 6x + 2
What is the polynomial?Generally, To find P(x), we can start by substituting
P(x) = 2*(Q(x) + P(x)) into the equation:
P(x) = 2*(Q(x) + P(x))
This simplifies to:
P(x) = 2*(4x^3 - 3x + 1 + P(x))
Expanding and rearranging the equation gives:
P(x) = 8x^3 - 6x + 2 + 2P(x)
Subtracting 2P(x) from both sides of the equation gives:
P(x) - 2P(x) = 8x^3 - 6x + 2
This simplifies to:
-P(x) = 8x^3 - 6x + 2
Adding P(x) to both sides of the equation gives:
0 = 8x^3 - 6x + 2 + P(x)
Therefore, the polynomial P(x) that satisfies the equation
P(x) = 2*(Q(x) + P(x)) is:
P(x) = 8x^3 - 6x + 2
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How do I do this please
Answer:
Step-by-step explanation:
substitute p for 8, because p=8
question 1 : 8+4=12 ----Yes
question 2: 8x8 =64-------Yes
question 3 5x8=35, not 8----No
question 4 2+8=10, not 12----No
brainly The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points) Source StylesFormatFontSize
Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
What is transformation ?
A transformation is a function that changes the position, size, or shape of an object or a graph. In mathematics, transformations are often used to map a function from one coordinate space to another. There are several types of transformations, including translations, rotations, reflections, and scalings.
Part A: Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
Part B:
Horizontal stretching/shrinking: k is the horizontal scale factor.
Vertical stretching/shrinking: k is the vertical scale factor.
Part C:
Horizontal stretching/shrinking: g(x) = f(kx)
Vertical stretching/shrinking: g(x) = kf(x)
Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.
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[(1/15−2/5)⋅(−3/4)³]÷(−9)
Answer:
[tex]-\frac{1}{64}[/tex]
Step-by-step explanation:
We have:
[tex][( \frac{1}{15} - \frac{2}{5}) * (-\frac{3}{4})^{3}] / (-9)[/tex]
Now, we will multiply the second fraction in the first parentheses by [tex]\frac{3}{3}[/tex] so we can subtract it from the [tex]\frac{1}{15}[/tex]. Then, we will multiply all of the [tex]\frac{3}{4}[/tex]'s. This gives us:
[tex][( \frac{1}{15} - \frac{2}{5} * \frac{3}{3} ) * (-\frac{3}{4} * -\frac{3}{4} * -\frac{3}{4})] / (-9)[/tex]
Which simplifies to:
[tex][( \frac{1}{15} - \frac{6}{15} ) * (-\frac{27}{64})] / (-9)[/tex]
Simplifying:
[tex][(-\frac{5}{15} ) * (-\frac{27}{64})] / (-9)[/tex]
Multiplying in our brackets gives us:
[tex]\frac{9}{64} / (-9)[/tex]
Now, using the rule of KCF (Keep, Change, Flip), we will keep our first fraction, change our division sign to a multiplication sign, and make the last number its reciprocal. This gives us:
[tex]\frac{9}{64} * -\frac{1}{9} = -\frac{1}{64}[/tex]
So, the equation simplified is [tex]-\frac{1}{64}[/tex].
Hope this helped!
a rectangular room is 2 times as long as it is wide, and its perimeter is 36 meters. find the dimension of the room
The dimension of the room is width = 6 meters and length = 12 meters.
What is rectangle ?
A rectangle is a four-sided polygon with opposite sides that are parallel and of equal length. It has four right angles. The two parallel sides are called the length and the width. The length is the longer of the two sides, while the width is the shorter of the two sides.
Let's assume the width of the rectangular room is "w" and the length of the rectangular room is "l"
We know that the perimeter of a rectangle is the sum of twice the length and twice the width: P = 2l + 2w
Given that the perimeter is 36 meters, we can substitute that into the equation ,
36 = 2l + 2w
We also know that the length is 2 times the width, so we can substitute that into the equation: I = 2w
Now we have two equations ,
36 = 2(2w) + 2w
36 = 6w
So the width of the room is 6 meters. To find the length, we can use the information that the length is 2 times the width ,
l = 2w = 2*6 = 12 meters
So the dimension of the room is width = 6 meters and length= 12 meters.
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Casey wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs %60 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?
Select 2 points in the solution of the inequality graphed below.
654-
21
3
x
k
An Isoceles right triangle whose legs measure 6 is continously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a what?
Assuming an isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object, the three-dimensional object is a: D. cone with a diameter of 12.
What are the types of triangle?In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleWhat is a right angle?In Mathematics, a right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees (90°).
Generally speaking, the resulting three-dimensional (3-D) geometric object that is formed when a right-angled triangle is continuously rotated about a leg would be a cone. Additionally, the radius of this cone would be equal to 6 because the base of the right-angled triangle is 6.
Therefore, the diameter of this cone can be calculated as follows;
Diameter of cone = 2 × radius of cone
Diameter of cone = 2 × 6
Diameter of cone = 12 units.
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Complete Question:
An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a
answer choices
cylinder with a diameter of 6
cylinder with a diameter of 12
cone with a diameter of 6
cone with a diameter of 12
An earthworm was in the soil 9 inches below the surface. To find moister soil, it moved down 7 inches.
What is the position of the earthworm now relative to the surface?
inches
Using the addition operation, the position of the earthworm relative to the surface is 16 inches below the surface.
What is the addition operation?One of the four basic mathematical operations, including subtraction, division, and multiplication, is the addition operation.
Using the addition operation involves adding two or more addends to determine the sum. It also involves using the addition operand (+) and the equal symbol (=).
The initial position of the earthworm below the surface = 9 inches
The depth it moved down to find moister soil = 7 inches
The current position = 16 inches (9 + 7) below the surface.
Thus, based on the addition operation, the earthworm is 16 inches below the surface in its endless search for moister soil.
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Select the parallel lines from the given pairs of lines :
Select one:
a.
y = x / 3 + 11, y = x / 2 + 15
b.
y = 3x + 11, y = 3x + 15
c.
y = 3x + 11, y = − 3x + 15
d.
y = 3x + 11, y = x / 2 + 15
Answer:
b.
y = 3x + 11, y = 3x + 15
Step-by-step explanation:
Both lines have the same slope, so they are parallel.
Can anyone please help me?
Answer: C. 3
Step-by-step explanation:
Using the trapezoid midsegment theorem,
[tex]\frac{4x+8x+3}{2}=4x+7.5\\\\\frac{12x+3}{2}=4x+7.5\\\\12x+3=8x+15\\\\4x+3=15\\\\4x=12\\\\x=3[/tex]
What transformation(s) have been applied to function f(x) to get g(x)? Check all that apply.translationreflectiondilationrotation
Transformations that have been applied to function f(x) to get g(x) are translation, reflection, and dilation.
The process of transforming the existing graph or graphed equation, to create a variation of the following chart is called graph conversion. Transformations such as translation, reflection, and dilation have been applied to function f(x) to produce g(x).
Whenever the function is "translated" it is moved in such a very way that it will not alter the shape or rotate in any way.The reflection is a modification of the function's graph all along the x or y-axis (or both).Dilation is defined as a stretch or shortening about in an axis caused by multiplying or subdivisions.Therefore, the answer is "translation , reflection , and dilation".
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Answer:
A) Translation
B) Reflection
C) Dilation
Step-by-step explanation:
