A ballroom has a square dance floor. The area of the floor is 400 square feet. If the length of each side of the square increase by one foot, would its answer be a rational number?
The area of the square dance floor when each side is increased by one foot becomes 441 square feet. Since 441 is an integer, the new area is a rational number because it can be expressed as a fraction with a non-zero denominator.
The question pertains to the change in area of a square dance floor when each side of the square is increased by one foot. Given that the initial area is 400 square feet, we understand that the dimensions of the dance floor are 20 feet by 20 feet, since 20 * 20 = 400. If each side of the square increases by one foot, the new dimensions of the square will be 21 feet by 21 feet, resulting in a new area of 441 square feet.
To answer the question as to whether the new area is a rational number, we need to understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction of two integers, with a denominator that is not zero. Given that 441 is an integer, and the area can be written as 441/1, the new area of the dance floor is indeed a rational number.
What effect does increasing the sample size have on a distribution of sample means?
If the number of samples is increased, this actually leads to a reduction in error of the distribution. This is because of the relationship between variation and sample size which has the formula of:
σx = σ / sqrt (n)
So from the formula we can actually see that the variation and sample size is inversely proportional.
Which means that increasing the sample size results in a reduction of variation.
Answer:
It will have less variation
Increasing the sample size causes the confidence interval to narrow, decreases the standard deviation, and makes the sample mean distribution more normal. This leads to more accurate and reliable estimates of the population parameters.
Explanation:The effect of increasing the sample size in a distribution of sample means primarily involves the confidence interval, the standard deviation, and the progress towards a normal distribution.
Firstly, increasing the sample size reduces the error bound, leading to a narrower confidence interval. This means that the calculated mean is likely to be more accurate representation of the true population mean.
Secondly, as the sample size increases, the standard deviation, which is a measure of spread or dispersion in the data, decreases. So, larger sample sizes result in lesser variability.
Finally, per the central limit theorem, an increased sample size makes the distribution of sample means get closer to a normal distribution, regardless of the population's initial distribution. This property is valid as long as the sample size is large enough (generally taken as 30 or more).
Thus, larger sample sizes tend to provide more accurate and reliable estimates of the population parameters.
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write three different equivalent expressions for the following expression:
16x^8
Three different equivalent expressions for 16x^8 are [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex].
Expressing [tex]\(16x^8\)[/tex] in three different equivalent forms:
1. Expanded Form:
[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex]
2. Factored Form:
[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex]
3. Exponential Form with a Common Base:
[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex]
These expressions show the flexibility in representing the original expression using different algebraic manipulations. The key is to recognize patterns, use properties of exponents, and factor out common terms.
What happens to the arrangement of water molecules as ice melts?
A. Molecules gain enough energy to escape as vapor.
B. Molecules release enough energy to escape as vapor.
C. Molecules release enough energy to move from their fixed positions.
D. Molecules gain enough energy to move from their fixed positions.
An athletic director pays $90 for 12 sun visors for the softball team. a. How much will the athletic director pay to buy 15 more sun visors?
What are the solutions of 2x2 + 8x = −26
In this problem, y = 1/(x2 +
c.is a one-parameter family of solutions of the first-order de y' + 2xy2 = 0. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y(4) = 1/15
How many 1/4 teaspoon doses are im 7/8 teaspoon of medicine
which one of the following items is an example of software
solve for x:
4/x-3 + 2/x^2-9 = 1/x+3
a. -17/3
b.13/3
c.19/3
d.-5
solve each inequality. Justify each step (y-) - 4 + 2y > 11
192 beads to make a necklace and bracelet. 5 times as many beads to make a necklace than a bracelet. How many beads are used to make a the necklace?
Give the angle measure represented by 2 rotations clockwise
the answer to Give the angle measure represented by 2 rotations clockwise. it's A. -720 on edge
f(x)=x^4+7x^3+13x^2-3x-18
Determine the intercepts of the line. 7x-5=4y-6/7x−5=4y−6
Answer:
x.(-1/7,0)
y.(0,1/4)
Step-by-step explanation:
What is 43,000 rounded to the nearest thousand
The Boardman family walked 2/5 of a mile in 2/7 of an hour. What is their unit rate in miles per hour? 20 points
The Boardman family's walking speed is 1.4 miles per hour, which is calculated by dividing the distance walked (2/5 mile) by the time it took (2/7 hour).
A unit rate defines how many units of the first type of quantity correspond to one unit of the second type of quantity. In this case, we need to find out how many miles they walk in one hour.
To calculate the unit rate, we divide the distance by the time. They walked 2/5 of a mile in 2/7 of an hour. Setting up the division, we have:
(2/5) miles / (2/7) hours = (2/5) × (7/2) miles per hour = 7/5 miles per hour
After simplifying, we get that the Boardman family's walking speed is 1.4 miles per hour.
Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 256 ft^3 of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?
To solve the problem we must know about the volume and the surface area of cuboids.
The length of the aquarium is 4, and the width of the aquarium is 8.
Given to us
The aquarium must hold 256 ft^3 of water.We know that the base of the aquarium should be a square, therefore, the length and the breadth of the aquarium will be the same.
Volume of the AquariumLength x breadth x height = 256 ft³
Length x Length x height = 256 ft³
Length ² x height = 256 ft³
[tex]L^2\times H = 256\\\\H = \dfrac{256}{L^2}[/tex]
Surface Area of the AquariumSurface Area of the Aquarium
= Area of the base + (4 x Area of the 4 sides)
[tex]= L^2 + 4(L\times H)[/tex]
Substituting the value of H,
[tex]= L^2 + 4L(\dfrac{256}{L^2})[/tex]
Length of the AquariumLet the surface area be a function of L, therefore,
[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})[/tex]
Differentiating the function to get the minimum,
[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})\\\\f(L) = L^2 + (\dfrac{1024}{L})\\\\f'(L) = 2L - (\dfrac{1024}{L^2})[/tex]
Equating against zero,
[tex]2L - (\dfrac{1024}{L^2}) = 0\\\\\dfrac{2L^3-1024}{L^2} = 0\\\\2L^3-1024 = 0\\\\L = 8[/tex]
Substituting the value of L,
[tex]H = \dfrac{256}{L^2}\\\\H = \dfrac{256}{8^2}\\\\H = 4[/tex]
But this way the area will be more, therefore, replace the value of L with 8,
L = 4
H = 8
Hence, the length of the aquarium is 4, and the width of the aquarium is 8.
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Using the heaviside function write down the piecewise function that is 0 for t < 0 , t2 for t in [0,1] and t for t > 1 .
Final answer:
The piecewise function, using the Heaviside function, is defined as 0 for t < 0, t^2 for t in [0, 1], and t for t > 1.
Explanation:
The piecewise function can be defined using the Heaviside function.
We know that the Heaviside function, H(x), is defined as:
H(x) = 0 for x < 0
H(x) = 1 for x ≥ 0
Using the Heaviside function, the piecewise function can be written as:
f(t) = 0 for t < 0
f(t) = t2 for t ∈ [0, 1]
f(t) = t for t ≥ 1
The table shows the amount that each person spend on snacks, games, and souvenirs the las time they went to the carnival.
Sinea- snacks $5/ games $8/ souvenirs $12
Ren- snacks $10/ games $8/ souvenirs $20
Suppose Sinea and Ren each spend $40 on snacks, and each person spends money using the same ratios as on their last trip. Who spends more on souvenirs? Explain
Exercise 26 proposes modeling iq scores with n(100, 16). what iq would you consider to be unusually high? explain.
how much smaller is the value of the 5 in 57,800 than the value of the 5 in 526,300
Find the equation of the ellipse with the following properties. The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4).
Course hero from a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. in how many ways can it be done?
The perimeter of a rectangle is 42 cm. The longer side has length of 7 cm more than the shorter side. Find the length of longer side
We have found the least squares line for predicting coral growth y from mean sea surface temperature x to be y = 11.6921 − 0.30305x. (a) use the equation to obtain the seven residuals step by step. that is, find the prediction y for each observation and then find the residual y − y. (round your answers to three decimal places.)
From the above equation putting the value of x. we get yhat and reducing it from actual value of y we will get residual
Therefore, as shown on the image below,
What is the mean of the following set of numbers?
{-7, 23, -5, 4}
A. 3.75
B. 9.75
C. -9.75
D. -3.75
the mean is the average
-7+23 -5 +4 = 15
15 / 4 = 3.75
Answer is A
The base of a skyscraper is a triangle bordered by three streets: Main Street, Elm Street, and Maple Street. The Elm Street side is 1 ft shorter than twice the Maple Street side. The Maple Street side is 8 ft shorter than half the Main Street side. The Main Street side is 206 ft. The base of a skyscraper is a triangle bordered by three streets: Main Street, Elm Street, and Maple Street. The Elm Street side is 1 ft shorter than twice the Maple Street side. The Maple Street side is 8 ft shorter than half the Main Street side. The Main Street side is 206 ft.
Part 1 out of 2
(a) Find the two unknown side lengths.
Maple Street is
ft.
Elm Street is
ft.
Translate the following problem to an equation. Do not solve.
55 times what number is 1265?
Choose the correct equation.
A) 55 dot x=1265
B) 23
C) 55/ x=1265
D) 55 dot 1265= x
The translation of the statement '55 times what number is 1265?' into an equation is '55 * x = 1265', which, with 'dot' finding use as multiplication, matches with the provided option A) 55 dot x = 1265.
Explanation:The question asks for the translation of the problem statement into an equation. The phrase '55 times what number is 1265?' implies multiplication. Specifically, 55 is being multiplied by an unknown number (which we can denote by 'x'), and the result of this multiplication is 1265. Therefore, the correct translation of this problem into an equation would be 55 * x = 1265 or in the provided options A) 55 dot x = 1265 where 'dot' indicates multiplication.
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A sequence is defined by the recursive formula f(n+1)=f(n)-2. If f(1)=18,what is f(5)?
The answer is for this problem is 10