There is a .90 probability that the project will be completed before approximately day 118.
The given information can be solved by using the formula of z-score as follows:
Z = (X - μ)/σ
Where: Z = z-score
X = the time for project completion
μ = the mean time for the critical path
σ = standard deviation for the critical path
σ² = variance of the critical pathσ = √64
σ = 8
Given that the mean time for the critical path is μ = 108 days and σ = 8 days,
Therefore, the z-score of the completion of the project before 108 days is given by:
Z = (X - μ)/σ0.90
= P(Z < z)
= P(Z < (X - 108)/8)P(Z < (X - 108)/8)
= 0.90
Using a z-table or calculator, we find the z-value to be 1.28.
Then,1.28 = (X - 108)/8
Multiplying both sides by 8, we get:10.24 = X - 108
Adding 108 to both sides, we get: X = 118.24
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Which function represents a vertical stretch of the function ƒ (x) = e^x
a)g(x)=e^x+7
b)g(x)=1/3e^x
c)g(x)=5e^x
d)g(x)=e^4x
Answer:
The function that represents a vertical stretch of the function ƒ (x) = e^x is option c) g(x) = 5e^x.
To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.
Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.
Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.
Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.
Find the slope of the line that passes through (2,1) and (0,-2) with explanation please
Answer: 3/2
Step-by-step explanation:
To find the slope of the line that passes through the points (2, 1) and (0, -2), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where:
m = slope of the line
(x1, y1) = coordinates of the first point
(x2, y2) = coordinates of the second point
Plugging in the values we have, we get:
m = (-2 - 1) / (0 - 2)
m = -3 / -2
m = 3/2
Therefore, the slope of the line that passes through the points (2, 1) and (0, -2) is 3/2.
There is an amoeba (a single-celled animal) on a dish.
After one hour, the amoeba divides to form two amoebas.
One hour later, each amoeba divides to form two more.
Every hour, each amoeba divides to form two more.
Write an expression for the number of amoebas after `24` hours.
An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216
How do amoebas develop?Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.
Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.
a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.
b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.
c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.
d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.
Expression = 1 × 2²⁴ = 16,777,216
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how long will it take for $500 to amount to $850 at 10% simple interest? question 37 options: 7 years 5 years 3.5 years 10 years none of these
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 850\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years \end{cases} \\\\\\ 850 = 500[1+(0.1)(t)] \implies \cfrac{850}{500}=1+0.10t\implies \cfrac{17}{10}=1+0.10t \\\\\\ \cfrac{17}{10}-1=0.10t\implies \cfrac{7}{10}=0.10t\implies \cfrac{7}{(10)(0.10)}=t\implies 7=t[/tex]
to avoid a near midair collision (nmac) with a manned airplane, you estimate that your small ua climbed to an altitude greater than 400 feet agl. to whom must you submit a written report of the deviation?
you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).
If you are operating a small unmanned aircraft (UA) and have had a near mid-air collision (NMAC) with a manned airplane, and you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).
According to the FAA regulations, any UAS operator involved in an NMAC with a manned aircraft must submit a report to the FAA within ten days of the incident. This report must include the date, time, and location of the incident, as well as a detailed description of the events leading up to the NMAC.
You can submit the report online via the FAA's Aviation Safety Reporting System (ASRS) website. The ASRS is a voluntary reporting system that allows pilots and UAS operators to report incidents without fear of enforcement action, provided that the incident was not a result of reckless or intentional behavior.
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Angela is using a game piece with faces labeled A, B, C, and D. What is the sample space for rolling the game piece?
The sample space for rolling the game piece is S = {A, B, C, D}
Describe Sets?In mathematics, a set is a well-defined collection of distinct objects, which can be anything like numbers, letters, people, or even other sets. A set is usually denoted by curly braces {} enclosing its elements separated by commas. For example, the set of natural numbers less than or equal to 5 can be denoted as {1, 2, 3, 4, 5}.
Sets can also be described by various methods such as by listing its elements, by set-builder notation, or by using a Venn diagram to visualize relationships between sets. A set can have any number of elements, including none (empty set), and can also have infinite number of elements.
Sets can be combined through set operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements that belong to either A or B (or both). The intersection of two sets A and B is a set that contains all the elements that belong to both A and B. The complement of a set A is the set of all elements that are not in A.
The sample space for rolling the game piece can be represented by the set of possible outcomes, which are the labels on the faces of the game piece. Therefore, the sample space is:
S = {A, B, C, D}
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Sasha had 30 minutes to do a three-problem quiz. She spent 8 3/4
minutes on questions A and 5 1/2
minutes on question B. How much time did she have left for question C?
Which of the contexts below represents exponential growth?
A town's population shrinks at a rate of 8.1% every year.
A taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile.
A town's population grows at a rate of 4% every year.
A radioactive compound decays at a rate of 5% per hour.
The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The context that represents exponential growth is "A town's population grows at a rate of 4% every year."
Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.
As the population grows, the growth rate also increases, resulting in an exponential increase over time.
Let P(t) be the population of the town after t years, where t is a positive integer.
The exponential function that models the population growth is -
[tex]P(t) = P0 \times (1 + r)^t[/tex]
where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.
In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.
Therefore, the exponential function for the town's population growth is -
[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]
Simplifying the expression, we get -
[tex]P(t) = P0 \times 1.04^t[/tex]
This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.
In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).
Therefore, the exponential growth is displayed by town's population growing 4% every year.
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Jane contributes 12% of the total cost of her individual health care. This is a $95.50 deduction from each of her biweekly paychecks.
A) Find Jane's share.
b) Total value of the insurance.
b) Calculate the employer's share.
A) Jane's share is 12% of X, which is equal to 0.12X.
B) the total cost of the insurance is $20,691.67
C) the employer's share is $18,208.67.
The total expense is what?Total cost is the collective term for the cost of production as a whole, which encompasses both fixed and variable costs. The expense necessary to produce a good is referred to in economics as the total cost. There are two parts that make up the total cost: a set price The expense is what never changes.
According to the given information:Let X be the total cost of Jane's individual health care, then:
A) Jane's share is 12% of X, which is equal to 0.12X.
B) We know that Jane's deduction from each biweekly paycheck is $95.50, so she pays a total of:
$95.50 * 26 = $2,483
This amount is equal to 0.12X, so we can set up an equation:
0.12X = $2,483
Solving for X, we get:
X = $20,691.67
Therefore, the total value of the insurance is $20,691.67.
C) The employer's share is the difference between the total cost of the insurance and Jane's share:
Employer's share = Total cost - Jane's share
Employer's share = $20,691.67 - $2,483
Employer's share = $18,208.67
Therefore, the employer's share is $18,208.67.
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Jane's share of the total cost of her individual health care is $795.83, The total value of the insurance is $795.83 + 0.88x and the employer's share is 0.88x.
What is cost?
In mathematics, cost refers to the amount of resources (such as money, time, effort, or materials) that are required to produce or obtain something.
A) To find Jane's share of the total cost of her individual health care, we can use the information that she contributes 12% of the cost, and that this is a $95.50 deduction from each of her biweekly paychecks.
Let x be the total cost of Jane's individual health care. Then:
12% of x = $95.50
0.12x = $95.50
x = $95.50 / 0.12
x = $795.83
Therefore, Jane's share of the total cost of her individual health care is $795.83.
B) To find the total value of the insurance, we can add up both Jane's share and the employer's share.
If Jane is contributing 12% of the total cost, then the employer is contributing the remaining 88% of the cost. So the employer's share can be calculated as:
88% of x = 0.88x
The total value of the insurance is then:
Total value = Jane's share + Employer's share
Total value = $795.83 + 0.88x
C) To calculate the employer's share, we can use the same information as above. The employer is contributing 88% of the total cost, so:
88% of x = 0.88x
Therefore, the employer's share of the total cost of Jane's individual health care is $0.88x, or approximately $700.33 (if we use the value of x that we found in part A).
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if a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective.
The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.
In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:
P(x=0) = (p^5)*(q^0) = p^5
In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.
For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.
To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.
The correct question is:
A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective
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Name 2 figures for which all cross sections taken at a particular orientation
are congruent.
Answer: Rectangular prism & Cylinder
Step-by-step explanation: In geometry, a rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.
A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The line segment joining the two centers is the axis, that denotes the height of the cylinder.
Mrs. Garcia is ordering pizza for students in the Homework Club. A large two-topping pizza is 20% off the regular price of $15. Mrs. Garcia wants to know the sale price. Which equation can be used to find the sale price, s, of the pizza
s = 0.8(15) s = 0.1(15) S = 0.115 S=0.8 15
Regular Price 100% $15
Sale Price 80% $ ?
Discount 20%
The equation that can be used to find the sale price, s, of the pizza is S = 0.8(15).
What is sale price?It is the final amount paid for a product or service and is often lower than the original asking price.
This equation uses the percentage discount of 20%, which can be represented as 0.8, to find the sale price.
To calculate the sale price, the equation multiplies the regular price of $15 by the discount, 0.8.
0.8*15 =12
Therefore, the sale price of the pizza is $12.
The other equations are not correct because they do not take into account the percentage discount of 20%.
S = 0.1(15) does not consider the discount of 20%, as it is multiplying the regular price of $15 by 0.1, which is equivalent to 10%, not 20%.
Similarly, S = 0.115 is incorrect because it is multiplying the regular price of $15 by 1.15, which is equivalent to 115%, not 20%.
Lastly, S=0.8 15 is incorrect because it is not multiplying the regular price of $15 by the discount of 20%, which is 0.8.
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how many ways are there to put 23 identical objects into 7 distinct containers so that no container is empty?
This problem is a classic example of applying the stars and bars combinatorial method.
To solve this problem, we need to distribute 23 identical objects into 7 distinct containers so that none of the containers is empty. Let's start by assuming that each container has at least one object. This means we have distributed 7 objects, leaving 16 objects to be distributed.
We can now use the stars and bars method to distribute these 16 objects. Imagine placing all 16 objects in a line, and placing 6 dividers between them to separate them into 7 groups (one for each container). Each group will then receive the objects that are to the left of the divider.
For example, if we have the sequence OO|OOO|O|OOO|OO|OO|O, this corresponds to 2 objects in the first container, 3 objects in the second container, 1 object in the third container, and so on.
The number of ways to place the 6 dividers in the sequence of 16 objects is the same as the number of ways to choose 6 positions out of 16 to place the dividers. This can be computed using the formula for combinations:
$${16 \choose 6} = \frac{16!}{6!(16-6)!} = 8008$$
Therefore, there are 8008 ways to distribute 23 identical objects into 7 distinct containers so that no container is empty.
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The area of the patio is enter your response here , so the cost of concrete is $ enter your response here. The area of the garden is enter your response here , so the cost of soil is $ enter your response here. The total area of the deck is enter your response here , so the cost of wood is $ enter your response here. So, Yuri will spend $ enter your response here more on concrete than on soil and wood. (Type integers or decimals. )
Yuri will spend $ X more on concrete than on soil and wood.
When answering questions on Brainly, it is important to be factually accurate, concise, and professional.
It is also important to provide a step-by-step explanation of how you arrived at your answer.
The question is asking about the cost of materials for a patio, garden, and deck.
Let's break down the information we have.
Area of the patio = enter your response
Here
Cost of concrete = $ enter your response
Here
Area of the garden = enter your response
here
Cost of soil = $ enter your response
here
Total area of the deck = enter your response
here
Cost of wood = $ enter your response
here
Yuri will spend $ enter your response here more on concrete than on soil and wood.
To find the cost of each material, we need to multiply the area by the cost per unit area.
For example, the cost of concrete would be the area of the patio multiplied by the cost of concrete per unit area.
Let's call the cost per unit area for concrete C, the cost per unit area for soil S, and the cost per unit area for wood W.
Area of patio = P
Cost of concrete = C
Area of garden = G
Cost of soil = S
Total area of deck = D
Cost of wood = W
Yuri will spend X more on concrete than on soil and wood.
To find the values of P, C, G, S, D, and W, we need to use the information given in the question.
However, some values are missing.
We can use the given information to create equations that will help us find these values.
For example, we know that the total area of the deck is the sum of the area of the patio and the area of the garden, so we can write:
D = P + G
Similarly, we can write an equation for the cost of each material.
For example, the cost of concrete is the area of the patio multiplied by the cost per unit area for concrete, so we can write:
C = P * C
Similarly, we can write equations for the cost of soil and wood:
S = G * W, W = D * W
Now we have three equations and three unknowns: P, G, and D. We can solve this system of equations to find these values.
Let's solve for P and G first.
We'll use the equation
D = P + G
to eliminate G from the equations.
C = P * CS = G * WP = D - G
Substitute P = D - G into the first two equations.
C = (D - G) * CW = D * W - G * W
Now we have two equations and two unknowns: D and G.
We can solve for these values.
We'll use the equation
W = D * W - G * W
to eliminate W from the equations.
C = (D - G) * CS = G * SD = P + G = 2G - (W / C)
Substitute D = P + G into the first two equations.
C = P * C + G * CS = G * SW = P + G - DC = P * C + (D - P) * C + (W / C) * C = 2P * C + W
We can now solve for P, G, and D.
P = (C + S + W / C) / 2G = (S + W / C) / 2D = P + G = (C + S + W / C) / 2 + (S + W / C) / 2P = enter your response
here
C = enter your response
here
S = enter your response
here
W = enter your response
here
G = enter your response
here
D = enter your response
here
Now we can find the value of X, which is the difference between the cost of concrete and the combined cost of soil and wood.
X = C - (S + W)X = enter your response.
The area of the patio is enter your response here , so the cost of concrete is $ enter your response here. The area of the garden is enter your response here , so the cost of soil is $ enter your response here. The total area of the deck is enter your response here , so the cost of wood is $ enter your response here.
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Question:
Yuri bought a new house. The diagram shows the layout of his backyard. Yuri is designing improvements that he wants to make. Yuri plans to fill the patio with concrete, the garden with a special soil mixture, and the remaining areas that surround the hot tub with a wood deck. The table shows the costs associated with each project. How much more will Yuri spend on concrete than on soil and wood?
In ΔEFG, m ∠ � = ( 5 � + 6 ) ∘ m∠E=(5x+6) ∘ , m ∠ � = ( 4 � − 6 ) ∘ m∠F=(4x−6) ∘ , and m ∠ � = ( 5 � − 2 ) ∘ m∠G=(5x−2) ∘ . Find m ∠ � . m∠G.
Therefore , the solution of the given problem of angles comes out to be m∠G= 63° is the response to the second component of the query.
What does an angle mean?The curved lines which make up the ends of a skew are divided by its highest and bottom walls using Cartesian measurements. There is a possibility who two poles will collide at an intersection. Another result of two objects interacting is an angle. They most closely mimic dihedral shapes. Two line beams can be arranged in different ways between their extremities to form a two-dimensional curve.
Here,
m∠E + m∠F + m∠G = 180°
Additionally, we are aware that mE = (5x + 6)°, mF = (4x - 6)°, and mG = (5x - 2)°. When we enter these numbers into the formula above, we obtain:
=> (5x + 6)° + (4x - 6)° + (5x - 2)° = 180°
When we simplify and find x, we obtain:
=> 14x - 2 = 180
=> 14x = 182
=> x = 13
Now that we know the three vectors' values:
=> m∠E = (5x + 6)° = (5(13) + 6)° = 71°
=> m∠F = (4x - 6)° = (4(13) - 6)° = 46°
=> m∠G = (5x - 2)° = (5(13) - 2)° = 63°
In light of this, mE = 71°, mF = 46°, and mG = 63°.
The first portion of the question has the following solution:
=> m∠EFG = m∠E + m∠F + m∠G = 71° + 46° + 63° = 180°.
m∠G= 63° is the response to the second component of the query.
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Find m∠AZJ using the figure below
In Linear pair, 52° is the value ∠AZJ .
What is Linear pairs?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.
A pair of adjacent angles is said to be a linear pair if the total of the two angles' (measured) angles is 180°. This means that a linear pair of angles always adds up to 180°. The linear pair of 30°, for instance, is 150°; the linear pair of 70°, 110°; etc.
∠JZF or ∠HZG
Linear pairs form supplementary angles.
∠AZJ = ∠AZH - ∠HZA
= 90° - 38°
∠AZJ = 52°
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Given:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
[tex] \tt \: \: x = \cancel{ \frac{12}{3} }[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \green{ \: x = 4 \: }}}[/tex][tex] \: [/tex]
__________________
hope it helps ⸙
An automobile manufacturer of a certain model of car wants to estimate the mileage this model car gets in highway driving. The population standard deviation is known to be 5.7 mpg. How many cars does the manufacturer need to sample so that a 90% confidence interval for the mean mileage of all cars of this model will have a margin of error of 1.5
mpg?
Please show your work! I would really like to understand this :)
If an automobile manufacturer of a certain model of car wants to estimate the mileage this model car gets in highway driving. The manufacturer needs to sample at least 39 cars.
How to find the sample?We can use the formula for the margin of error in a confidence interval for a mean:
Margin of Error = z* (σ/√n)
Where:
z* is the critical value of the standard normal distribution for the desired level of confidence, which is 90% in this case.
σ is the known population standard deviation, which is 5.7 mpg.
n is the sample size we want to determine.
We want the margin of error to be 1.5 mpg, so we can set up the equation:
1.5 = 1.645 * (5.7 / √n)
where 1.645 is the z-score for 90% confidence level.
Simplifying this equation, we get:
√n = 1.645 * (5.7 / 1.5)
√n = 6.251
Squaring both sides, we get:
n = 39.07
Rounding up to the nearest integer, we get:
n = 39
Therefore, the manufacturer needs to sample at least 39 cars to estimate the highway mileage with a 90% confidence interval and a margin of error of 1.5 mpg.
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The perimeter of a rectangular garden is 43. 8 feet. Its length is 12. 4 feet what is its width
The width of the rectangular garden is 9.5 feet.
Given that the perimeter of a rectangular garden is 43.8 feet and its length is 12.4 feet.
Let's assume the width of the rectangular garden be "w".
Now we need to find the width of the garden.
Solution: Perimeter of a rectangular garden is given by the formula: P = 2(l + w)
where l = length and w = width.
Substituting the given values in the above formula,
we get43.8 = 2(12.4 + w)
We can solve for "w" by simplifying the above equation.
43.8 = 24.8 + 2w43.8 - 24.8 = 2w19 = 2w
Dividing both sides by 2,we get
w = 9.5 feet.
Therefore, the width of the rectangular garden is 9.5 feet.
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bill has a collection of 40 nickels and dimes. together, they add up to $3.50. how many does bill have of each coin?
The number of nickels Bill has is 10.
Therefore, Bill has 10 nickels and 30 dimes.
The given question is as follows.
Bill has a collection of 40 nickels and dimes.
Together, they add up to $3.50.
Bill have of each coin :
To solve the given problem, let's consider the following steps.
Step 1: Let x be the number of nickels and y be the number of dimes.
Based on the given data, we can form the following two equations:
x + y = 40 ... (1) (because Bill has 40 nickels and dimes)
0.05x + 0.10y = 3.50 ... (2) (because the sum of 40 nickels and dimes is $3.50)
Step 2: Solve the equations (1) and (2) by elimination method by multiplying equation (1) with 0.05 and subtracting it from equation (2).
0.05x + 0.05y = 2 ... (3)0.05x + 0.10y = 3.50 ... (4)
Subtracting equation (3) from equation (4),
we get0.05y = 1.50
Dividing both sides by 0.05, we get
y = 30
Therefore, the number of dimes Bill has is 30.
Step 3: Now, substitute the value of y in equation (1), we get
x + 30 = 40
Subtracting 30 from both sides, we get x = 10.
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deduce that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the slim. in particular, the sum cannot be uniformly distributed on the numbers from 2 to 12. g
We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.
Explanation:
When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur
For example:
if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:
P(2) = P(1, 1) = (1/6)² = 1/36
P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1
2) = P(6, 6) = (1/6)² = 1/36
So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.
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a new product is being tested by zed electronics to determine if it will continue to operate in a stable fashion under a variety of conditions. a sample of 400 items were tested, and 60 failed the test. determine a 90 percent confidence interval for the population proportion.
The 90% confidence interval for the population proportion is (0.1171, 0.1829).
To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:
p-bar = x/n = 60/400 = 0.15
where x is the number of items that failed the test and n is the sample size.
Next, we need to find the margin of error, which is given by:
ME = z*√(p_bar(1-p_bar)/n)
where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.
For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:
ME = 1.645*√(0.15(1-0.15)/400) = 0.0329
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:
CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)
Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.
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What is the weight of a 48 kg girl on Earth? Round the answer to the nearest whole number.
___N
Answer:
remember, in order to calculate the weight on earth, we need to multiply the mass of the object with the force of Gravity (9.8 m/s^2 on earth)
so, her weight would be:
48 x 9.8 = 470.4 >>>>>>> Will be 470 if we round it to the nearest whole number.
Step-by-step explanation: Hope this helps. Mark me brainliest!! :)))
Answer: 470
Step-by-step explanation:
Jordan is saving to buy a pair of shoes. He already has saved $30. If the shoes cost $75, write an inequality to determine how much more money he needs to save so he can buy the shoes
The inequality to determine how much more money he needs to save so he can buy the shoes is x ≥ $45
Let x be the amount of money Jordan still needs to save to buy the shoes.
The total cost of the shoes is $75, and Jordan has already saved $30. Therefore, the amount of money he still needs to save is:
x = $75 - $30
Simplifying the right side:
x = $45
So, the inequality that represents how much more money Jordan needs to save is:
x ≥ $45
This means that Jordan needs to save at least $45 more to be able to buy the shoes.
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olympic gold medal has a gram of 586 grams. what is the mass of a 2018 olympic gold medal in hectograms
The mass of a 2018 Olympic gold medal in hectograms is 58.6 hg.
First, we need to know the mass of the Olympic gold medal in grams. According to the question, the mass of an Olympic gold medal is 586 grams.
To convert grams to hectograms, we need to divide the mass in grams by 100. This is because there are 100 grams in 1 hectogram.
To do the division, we can use a calculator. Dividing 586 by 100 gives us 5.86.
The answer we get is in hectograms, so we can write it as 5.86 hg. This means that the mass of a 2018 Olympic gold medal is 5.86 hectograms.
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This is for algebra 1 in grade 9. Can anyone help?
The repair costs $90 for parts, plus $70 per hour for labor describes the situation. The solution has been obtained by using the equation.
What is an equation?
An equation is an assertion that two expressions containing variables and/or numbers are equivalent. The basic driving factors behind the growth of mathematics have been the attempts to rationally answer equations, which are essentially questions.
We are given an equation of the function as C(x) = 90 + 70x.
This depicts that $90 is fixed cost whereas $70 is variable cost and is dependent on the value of x.
So, the statement that describes the given situation is that the he repair costs $90 for parts, plus $70 per hour for labor.
Hence, the fourth option is the correct option.
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a jar contains 21 brown and 19 blue marbles. a marble is drawn at random. what is the theoretical probability of drawing a blue marble?
The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.
To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.
The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).
In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.
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each letter of the alphabet is written on a piece of paper and put in a hat. if a piece of paper is chosen at random, what is the probability that it will be a vowel? the number of favorable outcomes is . the number of possible outcomes is . so p(vowel)
The probability of selecting a vowel from a hat with letters of the alphabet is 5/26 or approximately 0.1923. There are 5 vowels and 26 total letters.
There are 5 vowels in the English alphabet: A, E, I, O, and U. Therefore, the number of favorable outcomes (i.e., the number of vowels in the hat) is 5.
There are a total of 26 letters in the English alphabet. Therefore, the number of possible outcomes (i.e., the number of letters in the hat) is 26.
The probability of selecting a vowel is the ratio of the number of favorable outcomes to the number of possible outcomes:
P(vowel) = number of favorable outcomes / number of possible outcomes
P(vowel) = 5 / 26
Therefore, the probability of selecting a vowel is 5/26 or approximately 0.1923 (rounded to four decimal places).
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Answer:
5
26
5/26
19
Step-by-step explanation:
A publisher reports that 75% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 250 found that 69% of the readers owned a particular make of Car. Find the value of the test statistic. Round your answer to two decimal places
Rounded to two decimal places, the value of the test statistic is 0.41.
The value of the test statistic to compare the publisher's reported percentage of 75% and the marketing executive's claim that the actual percentage is different can be found by using the formula z = (p1 - p2)/(sqrt[p*(1-p)*((1/n1)+(1/n2))]), where p is the pooled proportion, p1 is the proportion of the publisher's readers owning the particular make of car, p2 is the proportion of the random sample owning the particular make of car, n1 is the total number of the publisher's readers, and n2 is the total number of the random sample.
In this case, p = [tex](75% + 69%)/2 = 72%, p1 = 75%, p2 = 69%, n1[/tex]is unknown, n2 = 250. Thus, the test statistic is z =[tex](75%-69%)/(sqrt[72%(1-72%)((1/n1)+(1/250))]) = 0.41.[/tex]
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WILL MAKE U BRAINLIST! HELPS PLS AND SHOW ALL STEPS
Answer:
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Step-by-step explanation:
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