Answer:
A) 6.0
Step-by-step explanation:
First, total amount of hours, since average is sum of the numbers by how many numbers there is.
Day 1=8x2 hr
Day 2=6x1 hr
Day 3=4x2 hr
which is, 16+6+8=30
then divide 30 by how many days there is, which is 5 days.
30/5=6
A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 4 or more customers at this bank in one hour.
Using the Poisson distribution, there is a 0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.A bank gets an average of 12 customers per hour, hence the mean is [tex]\mu = 12[/tex].
The probability that there will be 4 or more customers at this bank in one hour is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-12}12^{0}}{(0)!} \approx 0[/tex]
[tex]P(X = 1) = \frac{e^{-12}12^{1}}{(1)!} \approx 0[/tex]
[tex]P(X = 2) = \frac{e^{-12}12^{2}}{(2)!} = 0.0004[/tex]
[tex]P(X = 3) = \frac{e^{-12}12^{3}}{(3)!} = 0.0018[/tex]
Then:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0.0004 + 0.0018 = 0.0022.
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0022 = 0.9978[/tex]
0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.
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Christine has scored 73, 85, 70, and 63 on her previous four tests. What score does she need on her next test so that her average (mean) is 73?
Answer:
74
Step-by-step explanation:
(73 + 85 + 70 + 63 + x)/5 = 73.
You find the average by adding all of the test scores and dividing that number by the number of tests. We had four test, so will will take that total, plus some mystery number (let's call it x), we divide that total by 5 because now there are 5 tests and not 4. We already know what we want the average to be, we want the average to be 73. We now have:
(291 + x)/5 = 73 Multiply both sides by 5
291 + x =365 Subtract 291 from both sides to get
x = 74
Answer: 74
Step-by-step explanation:
The mean is the average of all the values, which we find by finding the sum of each value and dividing by the total number of data points.
With 5 data points, we can use this equation to find, x, or the data point needed to obtain a mean of 73:
[tex]\frac{73+85+70+63+x}{5}=73\\ 291+x=365\\x=74[/tex]
Find the decimal. _. _ _ _ Clues: (a) The digits 0, 1 and 2 are not used in the decimal. (b) The digit in the ones place is the greatest 1-digit number. The hundredths digit is smaller than 5. The difference between the tenths digit and the ones digit is the hundredths digit. (c) (d) (e) (f) The thousandths digit is greater than 5 and is an odd number. All the digits are different.
Answer:
Step-by-step explanation:
143
or
121
We are accepting
does any of this help
Consider a situation that you might need to use your understanding of probability to make an informed
decision.
• What sorts of information would you collect?
How might you use what you have learned about probability to determine a course of action?
What are the possible benefits and limitations of this approach?
The information that can be collected to make an insurance policy will be information regarding the drivers.
How to illustrate the information?It should be noted that the probability simply means the likelihood of the occurence of an event.
In this case, when choosing a car insurance policy, we can use the probability to determine the likelihood for the need to file a claim.
The course of action is to survey a number of drivers to get information from them.
Also, the benefit of this approach is that the food drivers can pay less premium while the disadvantage can be the cost that's involved.
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1. A situation that can use probability to make an informed decision is when deciding on an insurance policy to take.
2. The information that you would collect for an insurance policy decision includes insurance:
PremiumPolicy coveragePolicy limitsDeductiblesDiscounts.3. An understanding of probability helps the policyholder to:
Analyze different insurance policies to determine the best plan to choose amid uncertainty.Measure the likelihood of an event occurring and its consequences.Determine the level of risk involved.4. Possible Benefits and Limitations of Probability:Using probability, the insurance policyholder enjoys these benefits:
Measure outcomesReduce uncertaintyOptimize policiesSpread risk coveragePredict future losses and events.However, the limitations of probability in measuring insurance risks become prominent under the following situations:
Presence of an infinite number of possible outcomes. Where the outcomes are not equally likely.Thus, probability analyzes insurance policies to determine the best plans and their deductible amounts.
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Check the box labeled Show Segment Parallel to BC. Notice that intersects two sides of creating a smaller triangle, . How is related to ? How do you know?
Find the area of the figure.
Find the area. This is a trapezoid, with bases that measure 5 feet and 10 feet, and a height of 4 feet.
Answer:
A = 30 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases , then
A = [tex]\frac{1}{2}[/tex] × 4 × (5 + 10) = 2 × 15 = 30 ft²
In general, in y=asjn[k(x-d)]+c the equation of the axis of the curve is determined by
the value of
a) d
b) k
c) c
d) a
The equation of the axis of the curve is determined by (c) c
How to determine the equation of the axis?The equation is given as:
y= a sin[k(x - d)] + c
In the above equation, the midline is
y = c
This represents the equation of the curve axis
Hence, the equation of the axis of the curve is determined by (c) c
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Robin can make 8 puppets with the material she already has. For each additional sheet of felt she buys, she can make 5 more puppets. What is an equation that shows how the total number of puppets she can make, y, depends on the number of sheets of felt she buys?
The Rangers won five of the first six games. how many of the next 30 games must the rangers wins have twice as many wins as losses?
Using proportions, it is found that they must win 19 of their next 30 games.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
We want a win-to-loss proportion of 2:1, which is equivalent to a win-to-total proportion of 2:3. We have that:
The team will have won 5 + x games.The team will have played 36 games.Hence:
[tex]\frac{5 + x}{36} = \frac{2}{3}[/tex]
3(5 + x) = 72
15 + 3x = 72
3x = 57
x = 19.
The Rangers must win 19 of their next 30 games.
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Can someone please explain the steps to get too the second answer also please answer too thank you
16. Describe the type of solution for the linear system of
equations given below.
2x + 3y = 15
6y=-4x + 12
F.
no solution
G. infinite solutions
H.
one solution
J. two solutions
Answer:
Step-by-step explanation:
2x+3y=15
multiply by 2
4x+6y=30 ...(1)
6y=-4x+12
4x+6y=12 ...(2)
(1) and (2) represent parallel lines.
Hence no solution.
if x+4/4= y+3/3 then y/3=
The value of y / 3 in the equation is x / 4.
How to use equation to find y / 3 ?Therefore,
x + 4 / 4 = y + 3 / 3
then y / 3 can be found as follows,
x + 4 / 4 = x / 4 + 4 / 4 = x / 4 + 1
y + 3 / 3 = y / 3 + 3 / 3 = y / 3 + 1
x / 4 + 1 = y / 3 + 1
subtract 1 from both sides of the equation
x / 4 + 1 - 1 = y / 3 + 1 - 1
x / 4 = y / 3
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A motorboat travels 132 km in 4 hours going upstream. It travels 196 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer:
Step-by-step explanation:
x = speed of the boat
y = speed of the current
x + y = 162/3 = 54 mph
x - y = 132/3 = 44 mph
Add the two equations to get
2x = 98
x = 49 mph
y = 54 - x = 54 - 49 = 5 mph or something
Write the recursive rule for the 5th term of the sequence: -7, -3, 1, 5, 9
Answer:
Step-by-step explanation:
Let [tex]x_{n}[/tex] represent the nth term in the sequence. Then [tex]x_{n-1}[/tex] represents the previous term
The first term, [tex]x_{1}[/tex] = -7
Each consecutive term is obtained by adding 4 to the previous term.
So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]
How do you classify the following polynomial?
-4x³ + 2x² - 5x+3x²
(I need de classification, no the result)
How large an equilateral triangle can you fit inside a 2-by-2 square?
Answer:
An equilateral triangle with a length of 2
Step-by-step explanation:
A 2-by-2 square implies that the square has a length and width of 2. Since equilateral triangles have the same length for all sides, it tells you that if one side is a certain length, all the other sides must have the same length. The largest length we can fit into this square would be 2 because any larger, the sides of the triangles would not fit into the square. Under the assumption that the length needs to be a whole number, the answer would be 2.
Someone help me with this question!
Answer: [tex]160^{\circ}[/tex]
Step-by-step explanation:
By the exterior angle theorem,
[tex]4x-14+5x-182=5x-100\\\\9x-196=5x-100\\\\4x=96\\\\x=24\\\\\implies m\angle BCD=20^{\circ}\\\\\implies m\angle BCA=160^{\circ}[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Angle BCA = 160°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
By Exterior angle property :
[tex]\qquad❖ \: \sf \:4x - 114 + 5x - 182 = 5x - 100[/tex]
[tex]\qquad❖ \: \sf \:9x -29 6 = 5x - 100[/tex]
[tex]\qquad❖ \: \sf \:9x - 5x = - 100 + 296[/tex]
[tex]\qquad❖ \: \sf \:4x = 96[/tex]
[tex]\qquad❖ \: \sf \:x = 24 \degree[/tex]
Next, Angle BCA = 180° - Angle BCD
( linear pair )
[ let angle BCA = y ]
[tex]\qquad❖ \: \sf \:y = 180 - (5x- 100)[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - (5(24) - 100)[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - (120 - 100)[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - 20[/tex]
[tex]\qquad❖ \: \sf \:y = 160 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Angle BCA = 160°17. The Bricklayer needs 100 pieces of angle, each to be cut 54 3/16" long. 1 point
How many can be cut from a 20% length (do not include waste or thickness of
cut)? How many pieces of 20' angle are needed in order to have the 100
pieces?
The number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5
How to determine the number
From the information given;
The bricklayer needs = 100 pieces of angle
The number of cuts = 54
Length of cuts = 3/ 16'' Inches
a. To determine the number of cuts form a 20% length, we have to multiply the length by the percentage and by the initial number of cuts
= 20/ 100 × 3/ 16 × 54
= 0. 2 × 0. 1875 × 54
= 2. 0
The number of cuts would be 2
b. To determine the number of pieces of 20' angle to have 100 pieces we would divide the initial number of pieces by the angle
= 100/ 20
= 5 pieces
The number of pieces of 20' angle is 5
Thus, the number of cuts from a 20% length is 2 and the number of 20' angle are needed in order to have the 100 pieces is 5
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The slope of the line is 8. Write the point-slope equation for the line using
the coordinates of the labeled point.
The point-slope equation of the line is: y - 2 = 8(x - 2).
How to Write the Point-Slope Equation of a Line?The point-slope equation is: y - b = m(x - a), where:
m = slope(a, b) is a point.Using the coordinates of the point shown in the graph, substitute (a, b) = (2, 2) and m = 8 into y - b = m(x - a):
y - 2 = 8(x - 2)
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How many three-digit multiples of 5 have three different digits?
There are 180 numbers which are three-digit multiples of 5.
According to the statement
we have to find the three digit numbers which are multiples of 5.
we know that three digit numbers are start from 100 to 999 and in 1 line of counting means 100 to 110 there are 2 numbers are multiples of 5.
Here we use Multiplication method to find the number of digit which are a multiple of 5.
It means there are two numbers which are multiples of 5 in the one line of counting and there are 90 lines of counting from 100 to 999.
So, it means the answer will become
2*90 = 180.
So, There are 180 numbers which are three-digit multiples of 5.
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A rectangle has corners E, F, G, D, starting from top left and going clockwise. Point H is halfway between E and F. 2 lines are inscribed in the rectangle. One line goes from D to H and another goes from H to G. Angle E D H is (5 x) degrees and angle H D G is (4 x) degrees. Angles E D G and F G D are right angles. What is the measure of Angle EDH? 10° 40° 50° 90°
The measure of Angle EDH = 50°.
How to estimate the measure of Angle EDH?The angle EDH exists given as 5x° and the angle HDG exists given as 4x°. The angles EDG and FGD exist at right angles. That signifies both angles exist equivalent to 90°.
Angle EDH = 5x°
Angle HDG = 4x°
Angle EDG = 90°
5x + 4x = 90
9x = 90
Divide both sides by 9
x = 90/9
x = 10°
Angle EDH = 5x = 5 × 10 = 50°
The measure of Angle EDH = 50°.
Therefore, the correct answer is option c) 50°.
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What is the product?
Sr-203r-40
O 157-8
0157-8
O 15/+14-8
0152²-140-8
A box contains 5 red marbles and 2 yellow marbles. Consider the two–stage experiment of randomly selecting a marble from a box, NOT replacing it, and then selecting a second marble. Determine the probabilities of the following events:
a. Selecting 2 red marbles.
P (red) =
b. Selecting a red marble on the first draw and a yellow marble on the second.
P (red then yellow) =
c. Selecting at least 1 yellow marble.
P (at least 1 yellow) =
Answer:
a) 10/21 b) 5/21 c)1/21
Step-by-step explanation:
a) your have 7 choice and 5 or them or red, 5/7. You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3. We multiple these two numbers together:
5/7(2/3) = 10/21
b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7. The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified). We multiply these together.
5/7(1/3) =5/21
c) I am assuming that you are still selecting 2 marbles. The first draw would be 2/7. This time I am selecting yellow and there are only 2 choices for yellow. My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6. We multiply these together
2/7(1/6) = 2/42 or 1/21
There are 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class. The students need to be placed on teams of equal size with students from only their own class. What's the largest size of a team?
The largest size of a team according to the task content is; 20 kids.
What is the largest size of a team?It follows from the task content that the population is; 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class.
However, since, the team forming condition states that students be placed on teams of equal size with students from only their own class.
It therefore follows that the largest size of a team is 20 as only 20 students are in Mrs. Tanya's class hence leaving 4 kids in Mrs. Olga's class without a team.
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Represent the following situation using Venn diagrams and answer the questions that follow. In a survey of 100 students in the institute language studies at oxford university, the number of students studying various languages in last four years were found to be : Italian 28, German 30,French 42,Italian and French 10, Italian and German 8, German and French 5, all the three languages 3. (1 point each) a. Venn diagram. b. How many students are studying none of the languages? c. How many students had French as their only language? d. How many students are studying at least one of the languages?
There are 80 students studying at least one language
The Venn DiagramThe given parameters are:
Italian = 28German = 30French = 42Italian and French = 10Italian and German = 8German and French = 5Three languages = 3Using the above parameters, we have:
German and French only = 5 - 3 = 2
Italian and French only = 10 - 3 = 7
Italian and German only = 8 - 3 = 5
French only = 42 - 7 - 2 - 3 = 30
German only = 30 - 2 - 5 - 3 = 20
Italian only = 28 - 7 - 5 - 3 = 13
See attachment for the Venn diagram
Students studying none of the languagesThis is calculated as:
None + At least one = Total
Using the Venn diagram, we have:
None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100
This gives
None + 80 = 100
Subtract 80 from both sides
None = 20
Hence, there are 20 students studying none of the languages
Students studying French onlyThis is calculated as
French only = French - French and Italian - French and German + All three
So, we have:
French only = 42 - 10 - 5 + 3
Evaluate
French only = 30
Hence, there are 30 students studying French only
Students studying at least oneIn (b), we have:
None + At least one = Total ⇒ None + (3 + 2 + 5 + 7 + 13 + 20 + 30) = 100
By comparing both equations, we have
At least one = 3 + 2 + 5 + 7 + 13 + 20 + 30
This gives
At least one = 80
Hence, there are 80 students studying at least one language
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What is the complete factorization of the polynomial below?
x³ + 2x² + 4x+8
A. (x-2)(x+ 2i)(x+2i)
B. (x-2)(x+2i)(x-2i)
C. (x+2)(x + 2i)(x+2i)
D. (x+2)(x+2i)(x-2i)
The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).
What is the complete factorisation of the given polynomial; x³ + 2x² + 4x+8?It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.
It follows from observation that one of the zeros of the polynomial expression is at; x = -2.
Consequently, one of the factors of the polynomial in discuss is; (x+2).
x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)
= (x+2)(x+2i)(x-2i)
Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).
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Hey can someone tell me the steps to solving a system of equations with graphing
Answer:
Let's go through the following example to show how to solve a system of equations by graphing. I won't solve this system, I will just show how to.
[tex]8x-3y = 17\\4x+y=21[/tex]
If you can use an online graphing calculator...
If you have an online grapher (like Desmos) at your disposal, then you can put each equation in it as it is.
Lines intersect -> Put your cursor over the point of intersection to get the solution.Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines are the same and have infinite solutionsIf you have a physical graphing calculator (like TI-84)
1. Get both equations in the form [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
2. Put both equations in the graphing calculator
Lines intersect -> Find the intersection point using your graphing calculator's mechanics (each one is a little different)Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines have the same equation and have infinite solutionsIf you just have graphing paper...
1. Get both equations into the form [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
2. Plug in a few different points for x and calculate their y-values.
3. Plot those points on the graph paper
Lines intersect -> Find the intersection point's coordinates to get the solution for x and y.Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines have the same equation and have infinite solutions.4. (a)(i)Show that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix.
that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix
I need some help with this question for a self-taught course
The support pole must be approximately 7.8 meters long.
What is the length of the support pole?
Based on all the information given in the statement, we prepare a geometric diagram that describes the system formed by the high-security fence and the support pole. The representation is attached below. Lastly, the length of the pole is found by using the law of sines:
l/sin 84° = 6 m /sin 50°
l = 6 m × (sin 84°/sin 50°)
l ≈ 7.790 m
The support pole must be approximately 7.8 meters long.
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