Solution:
Given that,
[tex]A(w) = -w^2 + 100w[/tex]
Where, "w" is the width
Given area is in quadratic form
To find maximum area, we need to find the vertex
[tex]w = \frac{-b}{2a}[/tex]
From given quadratic,
[tex]-w^2 + 100w[/tex]
a = - 1
b = 100
Therefore,
[tex]w = \frac{-100}{2 \times -1}\\\\w = 50[/tex]
We will get maximum area when width w = 50 meters
To find maximum are we plug in 50 for w and find A(50)
[tex]A(50) = -(50)^2 + 100(50)\\\\A(50) = -2500 + 5000\\\\A(50) = 2500[/tex]
So maximum area is 2500 square meter
Answer:50
Step-by-step explanation:
The expression 475 * 1.076 ^ t the average annual per capita health care costs, in dollars, in the US as a function of the number of years since 1970. What does 1.076 represent in this expression?
Answer:
[tex] Y(t)= 475 (1.076)^t [/tex]
Where Y(t) represent the average annual per capita health care costs
475 represent the initial amount for the average annual per capita health care costs
t represent the number of years since 1970
And 1.076 represent the growth factor given by:
[tex] 1+r = 1.076[/tex]
And solving for r we got:
[tex] r = 1.076-1 =0.076[/tex]
So for this case we can say that the value 1.076 represent the growth factor.
Step-by-step explanation:
For this case we have the following model given:
[tex] Y(t)= 475 (1.076)^t [/tex]
Where Y(t) represent the average annual per capita health care costs
475 represent the initial amount for the average annual per capita health care costs
t represent the number of years since 1970
And 1.076 represent the growth factor given by:
[tex] 1+r = 1.076[/tex]
And solving for r we got:
[tex] r = 1.076-1 =0.076[/tex]
So for this case we can say that the value 1.076 represent the growth factor.
Final answer:
In the provided expression, 1.076 represents the annual growth factor of US health care costs, indicating an annual increase of 7.6% since 1970.
Explanation:
The expression 475 * 1.076 ^ t represents the average annual per capita health care costs in the US as a function of the number of years since 1970. Here, 1.076 signifies the annual growth factor of the costs, which means health care costs have been increasing by 7.6% each year since 1970. This exponential function captures the trend of increasing health care expenditure, which plays a significant role in the nation's economy, consuming a larger share of the Gross Domestic Product (GDP) over time.
#7 HELP ! WILL GIVE BRANLIEST
Answer:
x = 8, y = 4√3, z = 8√3
Step-by-step explanation:
Assuming that y is the altitude of the triangle (perpendicular to the hypotenuse), the triangles are similar. So we can write proportions:
x / 4 = 16 / x
x² = 64
x = 8
4 / y = y / 12
y² = 48
y = 4√3
z / 12 = 16 / z
z² = 192
z = 8√3
Note: after finding one side, you can also use Pythagorean theorem to find the other two sides.
Ken and Leah are trying to solve a science homework question. They need to find out how much a rock that weighs 4 pounds on Earth would weigh on Venus. They know they can multiply the number of pounds the rock weighs on Earth by 0.91 to find its weight on Venus. Select the partial products Ken and Leah would need to add to find the product of 4 and 0.91. Mark all that apply.
Answer:
The answer is b and d.
Step-by-step explanation:
An engineer designs a new cargo ship to transport 12,000 standard shipping containers. The ship's cargo hold and a shipping container are similar rectangular prisms. A standard shipping container is 6 meters long, 2.5 m wide, and 2.5 m tall.
What is the volume of the cargo hold of the ship?
Answer:
Vol=[tex]450,000m^3[/tex]
Step-by-step explanation:
Volume of rectangular prism is obtained using the formula:
[tex]V=whl\\w-width\\h-height\\l-length[/tex]
Dimensions of shipping containers is given as:
[tex]w=2.5m\\h=2.5m\\l=6m\\[/tex]
To obtain the volume of the cargo ship, we need to calculate the volume of 1 unit of a shipping container then multiply it by the number of containers the ship can carry.
let n be the number of containers ship can carry.
[tex]V_c=whl\\V_c=2.5m\times2.5m\times6m\\V_c=37.5m^3\\[/tex]
Volume of ship,[tex]V_s[/tex]
[tex]V_s=nV_c[/tex]
But n=12000
[tex]V_s=12000\times37.5m^3\\=450,000m^3[/tex]
#3 only Fractions help
Answer:
7
Step-by-step explanation:
24/1/3 -8/5/6- 8/1/2 (accorin to fractions la)
improper fraction make it into proper fraction
73/3- 53/6- 17/2 (change the base of 3 and 2 into 6)
146/6-53/6-51/6= (146-53-51)/6
= 7
Answer:
Step-by-step explanation:
you got to try your hardest
Twenty people get into an elevator in a hotel with seven floors, and all of them get off at some point. How many different possibilities exist for how the people could get off the elevator?
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
Xavier and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. He bought a total of 11 apples and bananas altogether. Determine the number of apples, x,x, and the number of bananas, y,y, that Xavier bought.
Answer: Xavier bought 2 apples and 9 bananas.
Step-by-step explanation:
Let x represent the number of apples that Javier bought.
Let y represent the number of bananas that Javier bought.
At the store, he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. This is expressed as
0.75x + 0.5y = 6 - - - - - - - - - - - - 1
He bought a total of 11 apples and bananas altogether. This means that
x + y = 11
Substituting x = 11 - y into equation 1, it becomes
0.75(11 - y) + 0.5y = 6
8.25 - 0.75y + 0.5y = 6
- 0.75y + 0.5y = 6 - 8.25
- 0.25y = - 2.25
y = - 2.25/ - 0.25
y = 9
x = 11 - y = 11 - 9
x = 2
At which angle will the hexagon rotate onto itself?
O 60°
90°
120°
180°
Answer: 60°
Step-by-step explanation:
When a figure has a rotational symmetry, it maps onto itself under rotation about a point at the centre.
When an hexagon rotate onto itself,
the vertices must cover to vertices and from sides to sides. There are six angles in a hexagon and the sum of the angles is 360°. Therefore, each angle has a measure of 360°/6 is equal to 60°.
Rotating subsequently by 60 degree will rotate a hexagon onto itself. A hexagon has 6 rotations, that is, a hexagon has a rotational symmetry of 6 and at angle 60°, the hexagon will rotate onto itself.
In research essays, brackets [ ] are used by writers to demonstrate when:__________.a. small changes have been made within exact quotations. b. outside resources have been cited. c. original sources have been paraphrased. d. parts of a quotation were already within quotation marks.
Answer:
A. small changes have been made within exact quotations.
Step-by-step explanation:
Brackets are pair of marks which enclose words or figures in order to separate them from the context. Thus, the use of brackets indicate that the quotation's exact punctuation has been adapted to the punctuation or grammar structure of the essay.
GIVING BRAINLIEST A medical team has found that the blood concentration of a particular medicine has a decay rate of 40% in 24 hours. How much of an initial dose of 1,000 mg of the medicine will be detected after 48 hours? Round to the nearest mg
920 mg
200 mg
449 mg
360 mg
600 mg
Answer:
360 mg.
Step-by-step explanation:
The medicine has a decay rate of 40% in 25 hours, which means after 24 hours its amount will be 100% - 40% = 60% it's original value.
Let us call [tex]t[/tex] the number of hours passed and [tex]d[/tex] the number of 24-hours passed, then we know that
[tex]t = 24d[/tex].
Now, the amount [tex]c[/tex] of medicine left after time [tex]d[/tex] (dth 24-hour) will be
[tex]c = 1000(0.6)^d[/tex]
and since [tex]t =24d[/tex], we have
[tex]$\boxed{c = 1000(0.6)^{\frac{t}{24} }}$[/tex]
We now use this equation to find the final amount after [tex]t =48 hours[/tex]:
[tex]c = 1000(0.6)^{\frac{48}{24} }[/tex]
[tex]c = 1000(0.6)^2 }[/tex]
[tex]\boxed{c =360mg}[/tex]
A department store has a policy of charging a 15% service change on all returned checks. If a check for $725 is returned, how much will the service charge be?
Answer:
Step-by-step explanation:
Altogether there were 72 slices of pizza. Twice as many slices had pepperoni compared to the the slices with just cheese. How many slice had just cheese?
Answer:24
Step-by-step explanation:
By setting up an equation c + 2c = 72, where 'c' represents cheese slices and '2c' represents pepperoni slices, and solving for 'c', we find there were 24 slices of pizza with just cheese.
To solve the problem about the number of pizza slices with different toppings, we can set up an equation based on the information given.
If 'c' represents the number of slices with just cheese, then 2c would represent the number of slices with pepperoni, because there are twice as many pepperoni slices as there are cheese slices. Since the total number of slices is 72, we can form the following equation:
c + 2c = 72
Combining like terms (c + 2c), we get 3c = 72. To find the value of 'c', we divide both sides of the equation by 3:
3c / 3 = 72 / 3
c = 24
Therefore, there were 24 slices of pizza with just cheese.
Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. A researcher wishes to compare academic aptitudes of married lawyers and their spouses. She obtains a random sample of 517 such couples who take an academic aptitude test and determines each spouse's academic aptitude.
Answer:
a) Independent
b) Quantitative
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 517
Sample:
Married lawyers and their spouses.
Response variable:
Comparison of academic aptitudes of married lawyers and their spouses.
a) The given sampling is an example of independent sampling.
This is an independent sample because an individual of sample does not effect any other individual of the sample.
b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.
It is a quantitative measure because the scores can be expressed in numerical.
Answer:
The sampling is independent and the response variable is quantitative.
Explanation:
Given a random sample of [tex]517[/tex] couples
The researcher wishes to compare academic aptitudes of married lawyers and their spouses. Then, she obtains a random sample of [tex]517[/tex] such couples who take an academic aptitude test and determines each spouse's academic aptitudeAn individual of the sample will not affect any other individual of the sample.Therefore, the sampling is independent.Here, the response variable is the aptitude test.The scores of the academic test are represented in numerical form.Thus, the response variable is quantitative.Learn more about Random sample, refer:
https://brainly.com/question/16786843PLLLZ HELP Write a recursive formula for finding the nth term of each geometric sequence.
5, 20, 80, ...
a1 = 20, an = 4an − 1
a1 = 80, an = 4an − 1
a1 = 5, an = 4an − 2
a1 = 5, an = 4an − 1
Answer:
[tex]a_1 = 5,\\a_n =4 a_{n-1}[/tex]
Step-by-step explanation:
The first term of the geometric sequence is
[tex]a_1 =5[/tex].
The common ratio between the consecutive terms is
[tex]\dfrac{20}{5} = 4,[/tex]
[tex]\dfrac{80}{20} = 4;[/tex]
therefore, we see that the nth term is found by
[tex]a_n =4 a_{n-1}[/tex]
Thus, the recursive formula for the geometric sequence is
[tex]a_1 = 5,\\a_n =4 a_{n-1}.[/tex]
The recursive formula for finding the nth term of a geometric sequence is a_n = a_1 * r^(n-1), where a_n represents the nth term, a_1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80. The recursive formula for this sequence is a_1 = 5 and a_n = 4 * a_(n-1).
Explanation:The recursive formula for finding the nth term of a geometric sequence is given by: an = a1 * r(n-1) where an represents the nth term, a1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80, ...
Since the first term is 5, and the common ratio between terms is 4, the recursive formula for this sequence is: a1 = 5 and an = 4 * an-1.
The number of customers waiting for gift-wrap service at a department store is an rv X with possible values 0, 1, 2, 3, 4 and corresponding probabilities 0.1, 0.2, 0.3, 0.25, 0.15. A randomly selected customer will have 1, 2, or 3 packages for wrapping with probabilities 0.55, 0.25, and 0.2, respectively. Let Y = the total number of packages to be wrapped for the customers waiting in line (assume that the number of packages submitted by one customer is independent of the number submitted by any other customer). (a) Determine P(X = 3, Y = 3), i.e., p(3,3).
Answer:
P[X=3,Y=3] = 0.0416
Step-by-step explanation:
Solution:
- X is the RV denoting the no. of customers in line.
- Y is the sum of Customers C.
- Where no. of Customers C's to be summed is equal to the X value.
- Since both events are independent we have:
P[X=3,Y=3] = P[X=3]*P[Y=3/X=3]
P[X=3].P[Y=3/X=3] = P[X=3]*P[C1+C2+C3=3/X=3]
P[X=3]*P[C1+C2+C3=3/X=3] = P[X=3]*P[C1=1,C2=1,C3=1]
P[X=3]*P[C1=1,C2=1,C3=1] = P[X=3]*(P[C=1]^3)
- Thus, we have:
P[X=3,Y=3] = P[X=3]*(P[C=1]^3) = 0.25*(0.55)^3
P[X=3,Y=3] = 0.0416
A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. What is the probability that a customer must open three or more bottles before winning a prize
Answer:
The probability that the customer must open 3 or more bottles before finding a prize is 0.64
Step-by-step explanation:
In order for a customer to have to open at least 3 bottles before winning a prize, then the first two bottles shouldnt have a price. The probability that a bottle doesnt have a price is 1-0.2 = 0.8. Since the bottles are independent from each other, then the probability that 2 bottles dont have a prize is 0.8² = 0.64. Therefore, the probability that the customer must open 3 or more bottles before finding a prize is 0.64
Answer:
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
Step-by-step explanation:
We know that the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next.
Therefore, we get p=0.2 and q=1-p=1-0.2=0.8.
So we will calculate the probability that the buyer will not win the prize in the first and second bottles. We get:
[tex]P=0.8\cdot0.8=0.64[/tex]
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
It is known that a certain function is an inverse proportion. Find the formula for this function if it is known that the function is equal to 12 when the independent variable is equal to 2.
Answer:
[tex]y=\frac{24}{x}[/tex]
Step-by-step explanation:
We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of variation.
Upon substituting [tex]y=12[/tex] and [tex]x=2[/tex] in above equation, we will get:
[tex]12=\frac{k}{2}[/tex]
Let us solve for constant of variation.
[tex]12\cdot 2=\frac{k}{2}\cdot 2[/tex]
[tex]24=k[/tex]
Now, we will substitute [tex]k=12[/tex] in inversely proportion equation as:
[tex]y=\frac{24}{x}[/tex]
Therefore, the formula for the given scenario would be [tex]y=\frac{24}{x}[/tex].
Please help!!! Idk what the answer is, I’m not ver good at graphing
Answer:
see below
Step-by-step explanation:
When a line goes through the origin, it expresses a proportional relationship such that for every point on the line ...
y/x = constant
The graph shows points (-5, 4) and (5, -4) as being on the line. So, we can determine the constant to be ...
constant = (y-value)/(x-value) = -4/5 . . . . . using point K
Then the proportion can be written as ...
y/x = -4/5
Multiplying both sides of this equation by -1 lets us also write the same relation as ...
-y/x = 4/5 . . . . matches the 2nd answer choice
The average lethal blood concentration of morphine is estimated to be 2.5 µg/mL with a standard deviation of 0.95 µg/mL. The data is normally distributed. Examine the range of values 0.05 to 4.95 µg/mL. Answer the following questions and provide the appropriate calculations (13 points):
a. What is the probability associated with the range lethal morphine blood levels?
Answer:
The probability associated with the range lethal morphine blood levels is 0.9902.
Step-by-step explanation:
Let X = lethal blood concentration of morphine.
The random variable X is normally distributed with parameter μ = 2.5 μg/ mL and σ = 0.95 μg/ mL.
Compute the probability of X within the range 0.05 to 4.95 μg/ mL as follows:
[tex]P(0.05<X<4.95)=P(\frac{0.05-2.5}{0.95}<\frac{X-\mu}{\sigma}<\frac{4.95-2.5}{0.95})\\=P(-2.58<Z<2.58)\\=P(Z<2.58)-P(Z<-2.58)\\=P(Z<2.58)-[1-P(Z<2.58)]\\=2P(Z<2.58)-1\\=(2\times0.9951)-1\\=0.9902[/tex]
*Use a z-table for the probability.
Thus, the probability associated with the range lethal morphine blood levels is 0.9902.
Using the properties of the normal distribution, we calculate the probability associated with the lethal morphine blood levels range of 0.05 to 4.95 µg/mL is essentially 1.0 (100%), meaning a lethal concentration is almost certain to fall within this range.
Explanation:To calculate the probability associated with the range of lethal morphine blood levels, we need to use the properties of the normal distribution. The mean (μ) lethal concentration is 2.5 µg/mL and the standard deviation (σ) is 0.95 µg/mL. We are examining the range 0.05 to 4.95 µg/mL.
First, we calculate the z-scores for both the lower limit (0.05 µg/mL) and the upper limit (4.95 µg/mL) of the range using the formula:
Z = (X - μ) / σ
For the lower limit:
Zlower = (0.05 - 2.5) / 0.95 ≈ -2.58
For the upper limit:
Zupper = (4.95 - 2.5) / 0.95 ≈ 2.58
Using a standard normal distribution table, we find the corresponding probabilities for both z-scores. Since the z-scores are symmetrical about the mean, the probability for both is the same. Thus, the probability up to Zlower is about 0.495 (adjusted from table values), and the probability up to Zupper is also about 0.495.
To find the probability within the range, we subtract the probability of the lower limit from the upper limit:
P(0.05 µg/mL < X < 4.95 µg/mL) = P(Zupper) - P(Zlower)
P(0.05 µg/mL < X < 4.95 µg/mL) ≈ 0.495 - (1 - 0.495) = 0.495 - 0.505 = -0.01
The negligible negative value suggests an error, likely due to rounding issues when looking up z-scores in the standard normal distribution table. Correctly, the total area under the curve, which corresponds to the probability of the range, should be virtually 1.0 (or 100%) since both z-scores are quite extreme (far in the tails of the distribution).
Therefore, practically, the probability associated with the given range of lethal morphine blood levels is essentially 1.0 (or 100%), meaning it is almost certain that a lethal concentration falls within this range.
Which statement describes the system of equations? It has infinitely many solutions. It has no solution. It has one solution . It has one solution (8, 2).
A system of equations can have no solution, one unique solution, or infinitely many solutions. A single solution indicates that the equations intersect at a point, no solution suggests parallel lines, and infinitely many solutions mean the equations are the same line expressed differently.
Explanation:When discussing a system of equations, the possible solutions include having no solution, one unique solution, or infinitely many solutions. If a system has no solution, this typically means the equations represent parallel lines that never intersect. In contrast, if there is one solution, the equations represent two lines that intersect at a single point, such as the given solution (8, 2). The presence of infinitely many solutions indicates that the equations are the same line, represented in different forms, and thus they intersect at every point along the line.
To determine which of these scenarios applies to a particular system of equations, one should begin by determining the number of unknowns and the number of equations given. A single linear equation in two variables, such as those given in Practice Test 4 Solutions 12.1 Linear Equations, represents a line. A system composed of two linear equations can be solved using algebraic methods such as substitution or elimination.
If the system consists of the same equation expressed differently, such as y = 2x + 3 and 2y = 4x + 6, then they are essentially the same line, and the system would have infinitely many solutions.
At an IMAX theater, the giant rectangular movie screen has a width 26 feet less than its length. If its perimeter is 332 feet, find the length and the width of the screen.
Answer:
Length=96 feet
Width=70 feet
Step-by-step explanation:
Let the length = l
The width 26 feet less than its length=l-26
Perimeter of the giant rectangular movie screen= 332 feet
Perimeter of a rectangle = 2(L+W)
332=2(l+l-26)
332=2(2l-26)
Expanding the brackets
332=4l-52
4l=332+52
4l=384
l=384/4=96
The Length of the giant rectangular movie screen is 96 feet.
The Width, W=l-26=96-26=70 feet
The dimensions of the screen are: [tex]Length: 96\ feet[/tex] and [tex]Width: 70\ feet[/tex]
To find the dimensions of the IMAX screen, we need to set up a system of equations based on the given information. Let's denote the length of the screen by [tex]\( L \)[/tex] and the width by [tex]\( W \)[/tex].
Given:
1. The width is [tex]26 \ feet[/tex] less than the length: [tex]\( W = L - 26 \)[/tex]
2. The perimeter of the rectangle is [tex]332\ feet: \( 2L + 2W = 332 \)[/tex]
First, we can simplify the perimeter equation:
[tex]\[2L + 2W = 332\][/tex]
Divide both sides by [tex]2[/tex]
[tex]\[L + W = 166\][/tex]
Now, substitute the expression for [tex]\( W \)[/tex] from the first equation into the simplified perimeter equation:
[tex]\[L + (L - 26) = 166\][/tex]
Combine like terms:
[tex]\[2L - 26 = 166\][/tex]
Add 26 to both sides:
[tex]\[2L = 192\][/tex]
Divide both sides by [tex]2[/tex]
[tex]\[L = 96\][/tex]
Now that we have the length, we can find the width using the equation [tex]W = L - 26 \)[/tex]
[tex]\[W = 96 - 26 = 70\][/tex]
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 15 of the 50 boxes on the shelf have the secret decoder ring. The other 35 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/35
Step-by-step explanation:
(15/50)×(14/49)
= 3/35 or 0.0857
Answer:
3/35.
Step-by-step explanation:
Probability (the first one selected has the decoder ring) = 15/50 = 3/10.
Probability (the second one selected has the decoder ring) = 14/49 = 2/7.
Therefore the probability that both have the ring =
3/10 * 2/7
= 6/70
= 3/35.
Note: The probabilities are multiplied because the 2 events are independent.
How many solutions does the system have?
x+y=3
5x+5y=15
A. Exactly one solution
B. No solutions
C. Infinity many solutions
The system has infinitely many solutions because both equations represent the same line in the coordinate plane. So C. Infinity many solutions will be the answer.
To determine the number of solutions for this system of equations, let's analyze it:
[tex]\[\left\{\begin{array}{l}x + y = 3 \\5x + 5y = 15\end{array}\right.\][/tex]
We can simplify the second equation by dividing both sides by 5:
[tex]\[x + y = 3\][/tex]
This equation is identical to the first equation in the system. So, the two equations represent the same line in the coordinate plane.
When two equations represent the same line, they have infinitely many solutions, because every point on the line satisfies both equations.
Therefore, the correct answer is:
(C) Infinitely many solutions
Complete Question:
ixl geometry help pls !
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{small}{large}\qquad \qquad \stackrel{sides}{\cfrac{3}{7}} ~~ = ~~ \stackrel{areas}{\sqrt{\cfrac{A_1}{98}}}\implies \left( \cfrac{3}{7} \right)^2 = \cfrac{A_1}{98}\implies \cfrac{3^2}{7^2}= \cfrac{A_1}{98} \\\\\\ \cfrac{9}{49}= \cfrac{A_1}{98}\implies 882 = 49A_1\implies \cfrac{882}{49}=A_1\implies 18=A_1[/tex]
Answer:
The answer to your question is 18 in²
Step-by-step explanation:
Data
Big rectangle Small rectangle
Area = 98 in² Area = ?
Height = 7 in Height = 3 in
Process
1.- Calculate the base of the big rectangle
Area = base x height
solve for base
base = Area / height
substitution
base = 98 / 7
base = 14 ni
2.- Use proportions to find the base of the small rectangle
x / 3 = 14 / 7
Simplify
x = (14)(3) / 7
result
x = 6 in
3.- Calculate the area of the small rectangle
Area = 6 x 3
= 18 in²
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed with standard deviation 0.25 volt, and the manufacturer wishes to test
H0:μ=5
volts against
H1:μ≠5
, using n = 8 units. a. The acceptance region is 4.85 ≤
x¯¯¯≤5.15
. Find the value of α. b. Find the power of the test for detecting a true mean output voltage of 5.1 volts.
Answer:
a= 0.0897
b= 0.71186
Power of the test for detecting a true mean output voltage of 5.1 volts is 0.28814.
Step-by-step explanation:
See attached pictures.
The value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.
Probability
It is the ratio of favorable events to the total events.
Given
Standard deviation ([tex]\sigma[/tex]) = 0.25
[tex]\mu[/tex] = 5
n = 8
How to calculate ?The acceptance region as
4.85 ≤ [tex]\rm \bar{x}[/tex] ≤5.15
a. Then type I error of probability,
[tex]\alpha = P(4.85> \bar{x}\ when\ \mu =5) + P(\bar{x}\ > 5.15\ when\ \mu =5)\\\alpha = P(\dfrac{4.85-5}{0.25\sqrt{8} } > \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } ) + (\dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } > \dfrac{4.85-5}{0.25\sqrt{8} })\\\alpha = 2P ( z <-1.697)= 0.0897[/tex]
Where, [tex]z = \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} }[/tex]
b. type II error
[tex]\beta = P(4.85 \leq \bar{x} \leq 5.15\ when\ \mu = 5.1)\\\beta = (\dfrac{4.85 - \mu}{0.25/\sqrt{8} }\leq \dfrac{\bar{x} - \mu}{0.25/\sqrt{8} }\leq \dfrac{5.15 - \mu}{0.25/\sqrt{8} }\ when\ \mu=5.1 )\\\beta = P(-2.8284\leq z\leq 0.5657)\\\beta = P(z\leq 0.5657)- P(z\leq -2.8284)\\[/tex]
therefore, the power of the test for detecting a true mean output voltage of 5.1 volt is
[tex]\begin{aligned} 1 - \beta &= 0.28281 \\\beta &= 0.71186\\\end{aligned}[/tex]
Thus, the value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.
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A boeing-747 is flying from New York City to Los Angeles. It leaves La Guardia Airport in NYC at 9:20am with an expectred arrival time at LA of 1:38pm. However, when it reaches Springfield (Illinois) which is 920 miles away from NYC, the piolets are informed that there is a storm in their path which they must avoid. In order to do so they turn 38 degrees to the right. Eventually they cleared to turn back left and return to their original flight path. They rejoin the path when they reach the four corners which is still 650 miles from LA at which point the piolets make one last turn 52 degrees to the right in order to head directly to los angeles. They arrive without futer incidents. How many minutes was the flight delayed
Answer:
I do not know sorry
Step-by-step explanation:
Kim is a medical supplies salesperson. Each month she receives a 5% commission on all her sales of medical supplies up to $20,000 and 8.5% on her total sales over $20,000. Her total commission for May was $3,975. What were her sales for the month of May?
Answer: her sales for the month of May is $55000
Step-by-step explanation:
Let x represent her total sales for the month of May.
Each month she receives a 5% commission on all her sales of medical supplies up to $20,000. This means that for her first sales worth $20000, she earns a commission of
5/100 × 20000 = 1000
She also earns 8.5% on her total sales over $20,000. This means that for sales over $20000, she earns
8.5/100(x - 20000) = 0.085x - 1700
Her total commission for May was $3,975. The expression becomes
1000 + 0.085x - 1700 = 3975
0.085x = 3975 + 1700 - 1000
0.085x = 4675
x = 4675/0.085
x = 55000
Kim's total sales for the month of May were $55,000. The first $1,000 of her commission came from the 5% commission on her first $20,000 in sales. The remaining $2,975 of her commission came from the 8.5% commission on her additional $35,000 in sales.
Explanation:To find out Kim's sales for the month of May, let's first understand her commission structure. She earns a 5% commission on all her sales of medical supplies up to $20,000, and 8.5% on any of her total sales over $20,000. Her total commission for the month of May is given as $3,975.
If her sales were $20,000 or below, her commission would be 5% of that, which would be $1,000 at most. Her commision is definitely more than that, we can infer that her sales were more than $20,000.
To figure out her actual sales, we need to subtract $1,000 from her total commission of $3,975, which gives us $2,975. This amount is the commission she earned at the rate of 8.5% for sales over $20,000. To find out the sales corresponding to this commission, we should divide $2,975 by 8.5% (or 0.085). That gives us the sales amount over $20,000 as $35000.
Therefore, Kim's total sales for the month are the $20,000 she sold to make the first $1,000 of her commission, plus the additional $35,000. So Kim's total sales for the month of May were $55,000.
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113, 183, 479, 120, 117 What is the mean, median and mode? Make sure to label each answer. Round any decimals to the tenths place. Would mean, median or mode be the best measure to describe the data?
Find the area of the shaded region. With steps
Answer: the area of the shaded region is 72.96 ft²
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Diameter of circle = 16 feet
Radius = diameter/2 = 16/2 = 8 feet
Area of circle = 3.14 × 8² = 200.96ft²
The sides of the square are equal. To determine the length of each side of the square, L, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
16² = L² + L²
256 = 2L²
L² = 256/2 = 128
L = √128 ft
Area of the square is
L² = (√128)²
Area = 128 ft²
Area of shaded region is
200.96 - 128 = 72.96 ft²
What are the coordinates of the vertex of the function f(x) = x2 - 12x + 5?
(6,31)
(-6, 31)
(6,-31)
(-6, -31)
Answer:
The vertex is the point (6,-31)
Step-by-step explanation:
we have
[tex]f(x)=x^2-12x+5[/tex]
This is a vertical parabola open upward
The vertex represent a minimum
Convert to vertex form
Complete the square
[tex]f(x)=(x^2-12x+6^2)+5-6^2[/tex]
[tex]f(x)=(x^2-12x+36)-31[/tex]
Rewrite as perfect squares
[tex]f(x)=(x-6)^2-31[/tex] -----> equation in vertex form
therefore
The vertex is the point (6,-31)