The largest area is found to be 8702.5 [tex]ft^{2}[/tex].
We know that area of rectangle
A = xy ........ (1)
Perimeter of rectangle (given) = 590 ft
Using x and y as two variables ;
5x + 2y = 590
solve yb in term of x
y = -5/2 x + 295......(2)
Now we will get area only in one variable from (1) and (2)
A = x ((-5/2)x + 295)
A = -5/2 [tex]x^{2}[/tex] + 295x
differentiate it with respect gto x
A' = -5x + 295........ (3)
find the critical point to get your minima and maxima value.
Put A' = 0, x = 295/5 = 59
x = 59
then , from (2)
y= (-5/2 × 59) + 295 = 147.5
y = 147.5
again differentiate (3)
A'' = -5 < 0. i.e critical point x = 59 is point of maxima.
So, maximum area = 59 × 147.5
Largest area = 8702.5 [tex]ft^{2}[/tex]
Learn more about area here ;
https://brainly.com/question/25292087
#SPJ4
the strong law of large numbers states that, with probability 1, the successive arithmetic averages of a sequence of iid random variables converge to their common mean . what do the successive geometric averages converge to? t
The successive geometric averages of a sequence of iid random variables converge to the common geometric mean.
the strong law of large numbers states that, with probability 1, the successive arithmetic averages of a sequence of iid random variables converge to their common mean . The successive geometric averages of a sequence of iid random variables converge to the common geometric mean. The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of a collection of numbers, denotes the central tendency of that set of numbers. In essence, we multiply the numbers collectively and take the nth root of the multiplied numbers, where n is the total number of data values.
Learn more about mean here
https://brainly.com/question/15323584
#SPJ4
The replacement set for an equation is {10, 24, 25, 36}.
The equation is represented by the sentence, "56 of a number is 30."
What is the solution set of the equation?
Responses
{10}
open curly bracket 10 close curly bracket,
{24}
open curly bracket 24 close curly bracket
{25}
open curly bracket 25 close curly bracket
{36}
The solution set of the equation is {26}
What is Set?Set is a collection of well defined objects.
Given,
The equation is represented by the sentence, "56 of a number is 30."
Replacement set for an equation is {10, 24, 25, 36}.
We need to find the solution set of the equation
"56 of a number is 30"
Fifty six of a number is thirty
56-30
26
Hence, the solution set of the equation is {26}
To learn more on Sets click:
https://brainly.com/question/8053622
#SPJ1
Find x: 2x=1
X=1/2
X=1
X=2
X=-1
Answer: x = 1/2
Step-by-step explanation:
2(1/2)=1
1=1
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If y = -4 when x = 2, find y when x = 3 .
ur answer should have ,-6
When X = 3 then Y = -6
Here is the explanation:
If Y1 = -4 when X1 = 2
and if X2 = 3 when Y2 = ?
The formula is
[tex]\frac{Y2}{X2} =\frac{Y1}{X1}\\\\Y2 = \frac{Y1}{X1} x X2\\\\Y2=\frac{-4}{2}x3\\\\Y2=-6[/tex]
Hence if X = 3 then Y = -6
Read more about direct variation here
https://brainly.com/question/13977805
#SPJ1
You are sent to the store to buy sliced meat for a party. You are told to get
roast beef and turkey, and you are given $30. Roast beef is $4.29/lb and
turkey is $3.99/lb. Write an equation in standard form to relate the pounds
of each kind of meat you could buy at the store with $30.
Write an expression for how much money is spent on roast beef?
Answer:
The Answer is 4.29x + 3.99y = 30
On a coordinate plane, a line goes through (negative 1, 1) and (0, negative 3). a point is at (negative 4, negative 3) and (0, negative 3). what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)? y 3 = −4(x 4) y 3 = –one-fourth(x 4) y 3 = one-fourth(x 4) y 3 = 4(x 4)
The equation of the required line would be x - 4y = 8.
What is the slope-point form of the line?
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
A line goes through the point (-1, 1) and (0,-3)
so the slope of the given line would be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-1}{0-(-1)}\\\\m=-4[/tex]
And we have to find the line which passes through the point (-4, -3) and the required line is perpendicular to the given line.
As we know the product of slopes of perpendicular lines is -1.
So the slope of the required line would be = 1/4
By using a slope-point form of the line, we get
[tex]y - y_1=m(x-x_1)\\\\y-(-3)=\frac{1}{4}(x-(-4))\\\\4(y+3)=x+4\\\\4y+12=x+4\\\\x-4y=8[/tex]
Hence, the equation of the required line would be x - 4y = 8.
To learn more about the slope-point form of the line, visit:
https://brainly.com/question/24907633
#SPJ4
Answer:
C
Step-by-step explanation:
Drag and drop the answer into the box to match each point to its coordinates.
The required Co-ordinates are A(-0.5, -0.25), B(-2.5, 1.5) and C(0.25, 0.5).
How to calculate points on the graph?To diagram a point, first find its situation on the x-axis, then track down its area on the y-hub, lastly plot where these meet. The middle place of the chart is known as the origin and is composed as the point (0, 0) since it's situated at the no point on the x-axis and the no point on the y-axis.
What are Co-ordinates ?The distance of a point from y-hub scaled with the x-hub is called abscissa or x direction of the point. The distance of a point from x-pivot scaled with the y-hub is called ordinate. The abscissa and ordinate all together are called organizes.
According to question:Now we find the co-ordinates of points on the graph,
Point A(-0.5, -0.25)
Point B(-2.5, 1.5)
And
Point C(0.25, 0.5)
Thus, required points are A(-0.5, -0.25), B(-2.5, 1.5) andC(0.25, 0.5).
To know more about Co-ordinates visit:
brainly.com/question/29329368
#SPJ1
what is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? express your answer as a common fraction.
Ratio of the area of a square inscribed in a semicircle with radius 'r' to the area of a square inscribed in a circle with radius 'r' is equal to 2: 5.
As given in the question,
Let ABCD be the square with side 'a' inscribed in a semicircle with radius 'r'.
'O' be the center of the semicircle.
'M' be the midpoint of AB such that MB = a/2
Join OM, OB and OM ⊥ AB
OB = r
OM = BC = a
In ΔOMB.
OB² = OM² + MB²
⇒ r² = a² + (a/2)²
⇒r² = 5a²/4
⇒a² = 4r²/5
Area of the square inscribed in a semicircle = a²
= 4r²/5
Let PQRS be the inscribed in a circle with side 'x'
Diagonal of the square inscribed in a circle = 2r
In ΔPQR,
PR = diagonal
= 2r
PQ = QR = x
PR² = PQ² + QR²
⇒(2r)² = x² + x²
⇒x² = 4r² /2
⇒x² = 2r²
Area of the square inscribed in a circle = x²
= 2r²
Ratio of the area of the square inscribed in ( semicircle to the : circle )
= 4r²/5 / 2r²
= 2 / 5
= 2 : 5
Therefore, ratio of the area of the squares inscribed in a semicircle to the circle is 2 : 5.
Learn more about squares inscribed in a semicircle here
brainly.com/question/3206065
#SPJ4
Independent random samples taken at two companies provided the following information regarding annual salaries of the employees. The population standard deviations are also given below. Company A Company B Sample Size 72 50 Sample Mean (in $1000) 48 43 Population Standard Deviation (in $1000) 12 10 a. We want to determine whether or not there is a significant difference between the average salaries of the employees at the two companies. Compute the test statistic. b. Compute the p-value; and at a=.05, test the hypotheses. c. Which company, if either, appears to have the higher salary? Provide a 95% confidence interval for the difference between the population mean salary of employees for the two companies.
a 95% confidence interval for the variation in the average employee salary for the two companies.
a. The test statistic is calculated by subtracting the sample mean of Company A from the sample mean of Company B, and then dividing the result by the square root of the variance, which is calculated by summing the population standard deviations of Company A and Company B, and then dividing by the sum of the sample sizes of Company A and Company B.
Test statistic = (48 - 43) / √(12^2 + 10^2) / (72 + 50) = 0.766
b. The p-value is calculated by using the test statistic to look up the value in a t-distribution table with degrees of freedom equal to the sum of the sample sizes minus two. The p-value is 0.239.
At a=.05, the null hypothesis that there is no difference between the average salaries of the employees at the two companies cannot be rejected.
c. Company A appears to have the higher salary. The 95% confidence interval for the difference between the population mean salary of employees for the two companies is (3.073, 5.927).
Learn more about confidence interval here
https://brainly.com/question/24131141
#SPJ4
a quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions. how many questions should the student expect to answer correctly?'
According to the binomial distribution, there are 13 questions should the student expect to answer correctly.
Binomial distribution:
in statistics, binomial distribution refers the probability of getting a success must remain the same for the trials we are investigating.
Given,
A quiz consists of 24 questions. each question has 4 answer choices with exactly one correct answer. a student is completely unprepared for the quiz, so he guesses on all 24 questions.
Here we need to find how many questions should the student expect to answer correctly.
While we looking into the given question, we have identified that the total number of questions is 24.
Number of options = 4
So, the probability of getting correct answer = 1/4 = 0.25
The probability of getting incorrect answer is,
=> 1 - 1/4 = 3/4 = 0.75
So, based on the binomial distribution,
X ~ Binomial Distribution (m=25, p=0.25, q=0.75)
Then in probability it can be written as,
=> P (X=13) = (25C13)x ((0.25)¹³) x ((0.75)¹²)
=> P (X=13) = 0.00245461663
Therefore, the number of correct answers is 13.
To know more about Binomial distribution here.
https://brainly.com/question/14565246
#SPJ4
the ____ of a triangle is a segment that connects the midpoints of two side of the triangle called
Answer:
midsegment
Step-by-step explanation:
hope it helps!
A construction company is considering submitting bids for two contracts. The company estimates that it has a 20\%20%20, percent chance of winning any given bid. Here is the probability distribution of x=x=x, equals the number of bids the company wins:.
Where the variance is 0.32, the mean is 0.40, and there are provided sets of probabilities, the standard deviation will be 0.566.
What is standard deviation?The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a high standard deviation are spread out from the mean, whereas those with a low standard deviation are grouped together close to the mean.
Here,
mean=0.4
variance=(Xn-mean)².P(x)n
=(0-0.4)²*(0.64)+(1-0.4)²*(0.32)+(2-0.4)²*0.04
variance=0.32
Standard deviation=√(variance)
=√0.32
=0.566
The standard deviation will be 0.566 where variance in 0.32 and mean is 0.40 and given sets of probability.
To know more about standard deviation,
https://brainly.com/question/13905583
#SPJ4
please help thank you very much
Answer:
x = 1, y = 20
Step-by-step explanation:
The question is asking the length of two wires, so instead of area, we are looking at the perimeter.
For the triangle, the equation looks like this:
(2-x) + 15 + y
For the rectangle, the equation looks like this:
(5-x) + (y-6) × 2
Let's say that x = 2, and y = 12.
The triangles new equation would look like this:
(2-2) + 15 + 12 = 27
The rectangles new equation would look like this:
(5-2) + (12-6) × 2 = 18
The wires are the same length, so these numbers can't be correct.
Let's say that x = 1 and y = 20.
The triangles new equation would look like this:
(2-1) + 15 + 20 = 36
The rectangles new equation would look like this:
(5-1) + (20-6) × 2 = 36
These numbers are the same, so therefore the answer is
x = 1 and y = 20.
Study the sequences (0, 6, 12, 18, 24, . . .) and (1, 6, 36, 216, 1,296, . . .), and answer these questions:
Which of the two sequences is an arithmetic sequence?
What is the common difference of the arithmetic sequence?
Can you think of any other mathematical relationship that exhibits a common difference between numbers?
Answer:
Step-by-step explanation:
In the first sequence, subtracting the previous term from each term starting from the second one gives these values: (0, 6, 12, 18, 24, . . .) is an arithmetic sequence.
How to find the common difference in the arithmetic sequence?
Common difference = second term - first term
The difference between the terms is constant. This sequence is an arithmetic one, with the common difference being 6.
Common difference = 6.
Just by looking at the terms in the second sequence,
(1, 6, 36, 216, 1,296, . . .), the difference between the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.
Like arithmetic sequences, linear equations show a common difference between numbers.
Answer: In the first sequence, subtracting the previous term from each term starting from the second one gives these values:
6 – 0 = 6, 12 – 6 = 6, 18 – 12 = 6, and 24 – 18 = 6.
The difference of the terms is constant. This sequence is an arithmetic one, with the common difference being 6.
Just by looking at the terms in the second sequence, (1, 6, 36, 216, 1,296, . . .), it’s clear that the difference of the consecutive terms is not common. This sequence is not an arithmetic sequence because it is based on the multiply by 6 rule.
Like arithmetic sequences, linear equations show a common difference between numbers.
Step-by-step explanation: Edmentum Answer
Determine the smallest integer value of x in the solution of the following inequality.
5x7-1
The smallest integer value of x in the solution of the following inequality x is strictly less than 2 or x ∈ (-∞, 2)
What are inequalities?Inequalities are statements that are represented as comparison between two or more numbers or algebraic expressions.(strictly less, strictly great, greater, lesser)
Given that the inequality 5x - 7 < 2x - 1
Solving the given equation:
5x - 7 < 2x - 1
5x - 7 - 2x < 2x - 1 - 2x
3x - 7 < -1
3x - 7 + 7 < -1 + 7
3x < 6
x < 2
Therefore, We conclude that x is strictly less than 2.
Hence x ∈ (-∞, 2)
Know more about "inequalities" here:
brainly.com/question/20383699
#SPJ1
If y varies inversely as x and x is 6 when y is 13, what is x when y is 8? a. 9.75 b. 3.69 c. 0.27 d. 6.5
If y fluctuates inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.
Define the term inverse proportion?When one variable declines, the others also decline in the same ratio. When two variables move in opposite directions, one variable reduces as another increases and the other increases as another variable lowers, the variables are said to be inversely proportional. Direct proportion is in opposition to it.Inverse variation is demonstrated by the following equation when two quantities, x and y, are in inverse proportion:-
x y = x1 y1
Now, if x is 6 when y is 13 and y varies inversely with x, then at y =8,
Thus,
x × 8 = 6× 13
x = (6×13)/8
x = 9.75
As a result, if y varies inversely as x as well as x is 6 if y is 13 then x is 9.75 when y is 8.
To know more about the inverse proportion, here
https://brainly.com/question/1266676
#SPJ4
The length of a hadow of a building i 15 m. The ditance from the top of the building to the tip of the hadow i 25 m. Find the height of the building. If neceary, round your anwer to the nearet tenth
Answer:
The height of the building is 20 meters
Step-by-step explanation:
What is Pythagoras theorem ?The Pythagoras Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
[tex]c^{2}=a^{2}+b^{2}[/tex]
Where c is the hypotenuse , a is perpendicular length , b is base
Length of the shadow of a building b = 15 m.
The distance from the top of the building to the tip of shadow c = 25 m
Let us assume the Height of the building to be = a
According to the pythagoras theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
[tex]25^{2}=a^{2}+15^{2}[/tex]
[tex]a^{2} = 25^{2}-15^{2}[/tex]
[tex]a^{2}[/tex] = 625-225
[tex]a^{2}[/tex] = 400
a = 20 meters
The height of the building is 20 meters
To know more about pythagoras theorem
https://brainly.ph/question/14449009
#SPJ4
What is the solution to this equation?
3(4x + 3) = 2x-5(3-X) + 2
Answer: The answer to this question is x= -22/5
on january 1 electro incorporated issued $740,000 of 7.5%, four-year bonds that pay interest semiannually on june 30 and december 31. they are issued at $680,186 and their market rate is 10% at the issue date. after recording the entry for the issuance of the bonds, bonds payable had a balance of $740,000 and discount on bonds payable had a balance of $59,814. electro uses the effective interest bond amortization method. the first semiannual interest payment was made on june 30. complete the necessary journal entry for the interest payment date of june 30 by selecting the account names from the drop-down menus and entering the dollar amounts in the debit or credit columns.
The interest payments is $27,750 and the Bond payable discount is $6,259
The electro incorporated issued $740,000 of 7.5%, four-year bonds that pay interest semiannually on june 30 and december 31.
They are issued at $680,186 and their market rate is 10% at the issue date
Interest payments = $740,000 x 7.5% x 1/2 = $27,750 (the credit to Cash).
bond interest expense = carrying value at 1/1/13 (the beginning of the period) of $680,186 x market rate of 10% x 1/2 = $34,009 (the debit to Bond interest expense).
Bond payable discount
The discount amortization $34,009 - $27,750 = $6,259
Therefore, the interest payments is $27,750 and the Bond payable discount is $6,259
To learn more about discount refer here
https://brainly.com/question/7459025
#SPJ4
Directions: Find the interior angle sum for each regular polygon. Round your answer to the nearest tenth if necessary.
This polygon's angles measure
???
degrees.
Answer:
below
Step-by-step explanation:
The SUM of a n-gon 's interior angles formula is :
SUM = ( n-2) * 180 n = 7 for this figure ( 7 angles)
(7-2) * 180 = 900 degrees
EACH angle in this REGULAR polygon is then 900 / 7 = 128.57°
What are the products 4/9 X 6 and 6 X 4/9
HELP NOW PLEASE
Answer: Both products are 2.6 repeating
The equation c = 10.75p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store.
Which description is true based on the equation of the proportional relationship?
For $0.09, you can buy 1 pound of shrimp.
For $1, you can buy 10.75 pounds of shrimp.
For $10.75, you can buy 10.75 pounds of shrimp.
For $10.75, you can buy 1 pound of shrimp.
Answer: For $1, you can buy 10.75 pounds of shrimp.
Step-by-step explanation: Because p represents pounds and there are 10.75 lbs, and c represents cost. Therefore the answer is: For $1, you can buy 10.75 pounds of shrimp.
in math, a statement that shows that two expressions are equal.
Answer:
= this is that two expression two equal numbers
At 1,000 units of output, the fixed cost of production is $12,500 per week. Total cost of producing 1,000 units per week is $28,500 per week. The variable cost of producing 1,000 units of output per week is equal to _____.
The variable cost of producing 1000 units per week is equal to $16000.
Variable costs are those that change with volume. Raw materials, piece-rate labour, production supplies, commissions, shipping costs, packing costs, and credit card fees are examples of variable costs. The variable costs of production are referred to as "Cost of Goods Sold" in some accounting accounts.
Given,
Fixed cost of production per week =$12500
Total cost of producing 1000 units per week =$28500
then,
variable cost of producing 1000 units per week = 28500-12500=$16000
Thus, the variable cost of producing 1000 units per week is equal to $16000.
To learn more about variable cost refer here
https://brainly.com/question/28652728?referrer=searchResults
#SPJ4
Suppose we observe an unending sequence of days on which the umbrella appears. show that, as the days go by, the probability of rain on the current day increases monotonically toward a fixed point. calculate this fixed point.
The probability computed is <0.8967,0.1033> which roughly shows that, as 90 days pass by, the probability that it will rain on a given day will be increasing monotonically towards a fixed point.
The chance that an event will occur ranges between 0 and 1. Where 0 shows that the event is impossible to occur and 1 shows that the event is bound to occur. If the chance of occurring an event is more than the chance of its not occurring then, it is more likely that the event will occur.
If we take the example of tossing a coin, we can say that the probability that a head will occur or a tail will occur will remain the same, i.e., 50%. The occurrence of heads or tails is equally likely.
These mathematical standards are used in varied fields of gambling, technology, finance, architecture, philosophy, science, etc.
To learn more about probability:
https://brainly.com/question/29583325
#SPJ4
Does anyone know the answer or how to solve this please?
Answer: Choice (E) [tex]\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]
=========================================================
Explanation:
The goal is to find what xz is equal to (in terms of x, y, and z)
We are given [tex]\text{z}= \frac{\text{x}^2}{\text{zy}^2}[/tex]
The only thing we're missing on the left hand side is x.
Let's multiply both sides by x.
[tex]\text{z} = \frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \text{x}*\frac{\text{x}^2}{\text{zy}^2}\\\\\text{xz} = \frac{\text{x}*\text{x}^2}{\text{zy}^2}\\\\\displaystyle \text{xz} = \boldsymbol{\frac{\text{x}^3}{\text{zy}^2}}[/tex]
This points us to choice (E) as the final answer.
Functions h and k are inverse functions, and both are defined for all real numbers. Using this relationship, what is the value of each function composition?.
The value of each function composition is
koh(3) = 3 and hok(-4b) = -4b
Given, Functions h and k are inverse functions, and both are defined for all real numbers.
The functions h and k are inverse functions
A function is said to have an inverse function when it is one-one and onto both.
Also, the composition of function f and function g is defined as fog i.e. f is defined on the range of g and vice-versa.
Then, foh(x) = x for all the real numbers and also,
hof(x) = x for all the real numbers.
Therefore, the value of each function composition foh at x = 3 and hof at x = -4b is 3 and -4b respectively.
Hence, the value of each function composition foh at x = 3 and hof at x = -4b is
foh(3) = 3 and hof(-4b) = -4b.
Learn more about Composite Function here https://brainly.com/question/28404324
#SPJ4
10+\frac{3}{4}y=
10+
4
3
y=
\,\,43
43
Um, is there a possibility that you could clean this question up a bit? It is a little scrambled and hard to make out of the equation given. Thanks!
What is the equation of the line that passes through the point (−3,4) and has a slope of −2?
Answer:
y=−2x−2
Step-by-step explanation:
you are interested in measuring the effects of a computer-assisted instruction program on the math scores of elementary school students; experimental and control students are matched on iq. group of answer choices within-subjects anova independent samples t test related samples t test between-subjects anova
you are interested in measuring the effects of a computer-assisted instruction program on the math scores of elementary school students within-subjects anova.
What is an ANOVA with within-subjects?
When there are identical participants in each group, a one-way repeated measures ANOVA, sometimes referred to as a within-subjects ANOVA, is used to assess whether three or more group means are different. The groups are sometimes referred to as "related" groups as a result.ANOVA within-subjects. Comparisons of the same individuals under various circumstances are included in within-subjects variables. For instance, each child's performance in the "ADHD Treatment" research was assessed four times, once after taking each of the four treatment doses for a week.A repeated measures ANOVA is another name for a within-subjects ANOVA. This kind of test is not just confined to two time periods; it is widely utilised when utilizing a pretest and posttest design.To know more about anova check the below link:
https://brainly.com/question/25800044
#SPJ4