Answer:
D
Step-by-step explanation:
The larger standard deviation, the greater the variability. So even before looking at the data, we can eliminate a) and c).
The standard deviations of men's preference of shortest and tallest acceptable height (3.7 and 2.7, respectively) were more than the standard deviations of women's preference of shortest and tallest acceptable height (2.6 and 2.2, respectively).
So men showed greater variability overall because the standard deviations for men were larger than for women. Answer D.
Final answer:
Men showed greater variability in their height preferences for dating partners than women, as indicated by the larger standard deviations in men's responses.
Explanation:
The question asks whether men or women showed greater variability in their height preferences among dating partners based on a study by Salska and colleagues (2008). In the given study, variability is indicated by the standard deviation (SD) values. A larger standard deviation signifies greater variability in the responses. For the shortest acceptable height, men had an SD of 3.7 inches, while women had an SD of 2.6 inches. Likewise, for the tallest acceptable height, men had an SD of 2.7 inches versus women's 2.2 inches. These SD values clearly show that men displayed greater variability in their height preferences compared to women.
PLEASE HELP HELPPPPPPO HELPPPPPPO
Step-by-step explanation:
Remember that in a linear function of the form [tex]f(x)=mx+b[/tex], [tex]m[/tex] is the slope and [tex]b[/tex] is the why intercept.
Part A. Since [tex]g(x)=2x+6[/tex], its slope is 2 and its y-intercept is 6
Now, to find the slope of [tex]f(x)[/tex] we are using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
[tex](x_2,y_2)[/tex] are the coordinates of the second point
From the table the first point is (-1, -12) and the second point is (0, -6)
Replacing values:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-6--(12)}{0-(-1)}[/tex]
[tex]m=\frac{-6+12}{0+1}[/tex]
[tex]m=6[/tex]
The slope of f(x) is bigger than the slope of g(x), which means the line represented by f(x) is stepper than the line represented by g(x).
Part B. To find the y-intercept of f(x) we are taking advantage of the fact that the y-intercept of a linear function occurs when x = 0, so we just need to look in the table for the value of f(x) when x = 0. From the table [tex]f(x)=-6[/tex] when [tex]x=0[/tex]; therefore the y-intercept of [tex]f(x)[/tex] is -6.
We already know that the y-intercept of g(x) is 2. Since 2 is bigger than -6, function g(x) has a greater y-intercept.
Find the limit of the function algebraically. limit as x approaches zero of quantity x cubed plus one divided by x to the fifth power.
Answer:
[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = \text{und} \text{efined}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big)[/tex]
Step 2: Evaluate
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = 0^3 + \frac{1}{0^5}[/tex]Simplify: [tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = \text{und} \text{efined}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
A storage box with a square base must have a volume of 80 cubic centimeters. The top and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Find the dimensions that will minimize cost.
Answer:
The dimensions that will minimize cost are 3.42 cm and 6.84 cm
Step-by-step explanation:
* Lets explain how to solve this problem
- We have a storage box with a square base
- The volume of the box is 80 cm³
* From the information above we can find relation between the two
dimensions of the box
∵ The base of the box is a square with side length L cm
∵ The height of the box is H cm
∵ The volume of the box = area of its base × its height
- The base is a square and area the square = L² cm²
∴ The volume of the box = L² × H
∵ The volume of the box = 80 cm³
∴ L² × H = 80
- Lets find H in terms of L by divide both sides by L²
∴ H = 80/L² ⇒ (1)
- The cost of the top and bottom is $0.20 per cm²
- We can find the cost of top and bottom by multiplying the area of
them by the cost per cm²
∵ The top and the bottom are squares with side length L cm
∴ The area of them = 2 × L² = 2L² cm²
∵ The cost per cm² is $0.20
∴ The cost of top and bottom = 2L² × 0.20 = 0.40L² ⇒ (2)
- Now we can find the cost of the lateral area (area of the 4 side faces)
by multiplying the area of them by the cost per cm²
∵ The lateral area = the perimeter of its base × its height
∵ The base is a square with side length L cm
∴ The perimeter of the base = 4 × L = 4L cm
∵ The height of the box is H cm
∴ The lateral area = 4L × H
- Now lets replace H by L using equation (1)
∴ The lateral area = 4L × 80/L²
- To simplify it : 4 × 80 = 320 and L/L² = 1/L
∴ The lateral area = 320/L cm²
∵ The cost of the sides is $0.10 per cm²
∴ The cost of the lateral area = 320/L × 0.10 = 32/L ⇒ (3)
- Now lets find the total cost of the box by adding (2) and (3)
∴ The total cost (C) = 0.40L² + 32/L
* For the minimize cost we will differentiate the equation of the
cost C with respect to the dimension L (dC/dL) and equate it
by 0 to find the value of L which makes the cost minimum
- In differentiation we multiply the coefficient of L by its power and
subtract 1 from the power
∵ C = 0.40L² + 32/L
- Lets change 32/L to 32L^(-1) ⇒ (we change the sign of the power by
reciprocal it)
∴ C = 0.40L² + 32L^(-1)
- Lets differentiate
∴ dC/dL = (0.40 × 2)L^(2 - 1) + (32 × -1)L^(-1 - 1)
∴ dC/dL = 0.80L - 32L^(-2)
- For the minimum cost put dC/dL = 0
∴ 0.80L - 32L^(-2) = 0 ⇒ add 32L^(-1) to both sides
∴ 0.80L = 32L^(-2)
- Change 32L^(-2) to 32/L² (we change the sign of the power by
reciprocal it)
∴ 0.80L = 32/L² ⇒ use cross multiplication to solve it
∴ L³ = 32/0.80 = 40 ⇒ take ∛ for both sides
∴ L = ∛40 = 3.41995 ≅ 3.42 cm ⇒ to the nearest 2 decimal place
- Substitute this value of L in equation (1) to find H
∵ H = 80/L²
∴ H = 80/(∛40)² = 6.8399 ≅ 6.84 cm ⇒ to the nearest 2 decimal place
* The dimensions that will minimize cost are 3.42 cm and 6.84 cm
Heeeeeelp
Find the z score that corresponds to P99, the 99th percentile of a standard normal distribution curve.
Answer:
about 2.33
Step-by-step explanation:
The value can be found from a probability table, any of several web sites, your graphing calculator, most spreadsheet programs, or any of several phone or tablet apps.
A web site result is shown below. (I have had trouble in the past reconciling its results with other sources.) One of my phone apps gives the z-value as about ...
2.26347874
which is in agreement with my graphing calculator.
Answer:
[tex]Z = 2.325[/tex].
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Find the z score that corresponds to P99, the 99th percentile of a standard normal distribution curve.
This is the value of Z when X has a pvalue of 0.99. This is between 2.32 and 2.33, so the answer is [tex]Z = 2.325[/tex].
A medical equipment industry manufactures X-ray machines. The unit cost c
(the cost in dollars to make each X-ray machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function
c(x)=0.6x^2-108x+19,222. What is the minimum unit cost?
Do not round your answer
Answer:
Minimum Unit Cost = $14,362
Step-by-step explanation:
The standard form of a quadratic is given by:
ax^2 + bx + c
So for our function, we can say,
a = 0.6
b = -108
c = 19,222
We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a
So,
-(-108)/2(0.6) = 108/1.2 = 90
Plugging this value into original function would give us the minimum (unit cost):
[tex]c(x)=0.6x^2-108x+19,222\\c(90)=0.6(90)^2-108(90)+19,222\\=14,362[/tex]
Answer:
The minimum unit cost is 14,362
Step-by-step explanation:
The minimum unit cost is given by a quadratic equation. Therefore the minimum value is at its vertex
For a quadratic function of the form
[tex]ax ^ 2 + bx + c[/tex]
the x coordinate of the vertex is
[tex]x=-\frac{b}{2a}[/tex]
In this case the equation is: [tex]c(x) = 0.6x^2-108x+19,222[/tex]
Then
[tex]a= 0.6\\b=-108\\c=19,222[/tex]
Therefore the x coordinate of the vertex is:
[tex]x=-\frac{(-108)}{2(0.6)}[/tex]
[tex]x=90[/tex]
Finally the minimum unit cost is:
[tex]c(90)=0.6(90)^2-108(90)+19,222\\\\c(90)=14,362[/tex]
New York City covers an area of 302.6 square miles. There are 8.54 million people living in New York City. Los Angeles has an area of 503 square miles and has a population of 3.98 million people. How many more people, per square mile, live in New York City verses Los Angeles? Round to the nearest person per square mile.
Answer:
20,309 people more people per sq mile.
Step-by-step explanation:
First step is to calculate the population density of both cities, then we'll be able to answer the question.
We're looking for a number of people per sq mile... so we'll divide the population by the area.
New York City: 8.54 million people on 302.6 sq miles
DensityNYC = 8,540,000 / 302.6 = 28,222 persons/sq mile
Los Angeles: 3.98 million people on 503 sq miles
DensityLA = 3,980,000 / 503 = 7,913 persons/sq mile
Then we do the difference... 28,222 - 7,913 = 20,309 people more people per sq mile.
If we were to make the ratio, we'd get 3.57, 3.57 more people in NYC per sq mile compare to LA.
Final answer:
New York City has approximately 20,309 more people per square mile than Los Angeles when rounded to the nearest person, based on their population densities.
Explanation:
To calculate how many more people per square mile live in New York City versus Los Angeles, we need to find the population density for each city and then subtract Los Angeles's density from New York City's density.
New York City's population density: 8.54 million people ÷ 302.6 square miles = approximately 28,220 people per square mile.
Los Angeles's population density: 3.98 million people ÷ 503 square miles = approximately 7,911 people per square mile.
The difference in population density: 28,220 people per square mile (NYC) - 7,911 people per square mile (LA) = approximately 20,309 people per square mile.Therefore, about 20,309 more people per square mile live in New York City than in Los Angeles, when rounded to the nearest person.
5. Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
Answer:
6t+3
Step-by-step explanation:
If t represents the number of tens, then 6t is six times the number of tens. 3 more than that is ...
6t+3
Answer:
6t + 3
Step-by-step explanation:
Given: Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens
To Find: Let t represent the number of tens. Write an expression for the number of fives.
Solution:
Total number of ten bills are = [tex]\text{t}[/tex]
As given in question,
The number of fives is three more than six times the number of tens
therefore
total number of fives are
=[tex]6\text{t}+3[/tex]
here, t represents total number of $5 and $10 bills Jeannette has in her wallet
Final expression for total number of [tex]\$5[/tex] bills is [tex]6\text{t}+3[/tex]
f(x) = x2 – 3x – 2 is shifted 4 units right. The result is g(x). What is g(x)?
Answer:
g(x) = x^2 - 11x + 26
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 3x - 2
a shift 4 units to the right implies that we shall be subtracting the constant 4 from the x values of the function;
g(x) = f(x-4)
g(x) = (x - 4)^2 - 3(x - 4) -2
g(x) = x^2 - 8x + 16 - 3x + 12 - 2
g(x) = x^2 - 11x + 26
Which function results after applying the sequence of transformations to f(x)=x^5?
. Reflection over the x-axis
. Vertically Stretch by a factor of 2
. Shift down 1 unit
ANSWERS
---------------
A. g(x)=-2x^5-1
B. g(x)=-(2x)^5-1
C. g(x)=-2x^5+1
D. g(x)=-2(x-1)^5
Need this solved urgently! This is for apex. Also please explain how you got the answer, not just the answer itself.
Answer: Option A
Step-by-step explanation:
Given the parent function [tex]f(x)=x^5[/tex], it can be transformated:
If [tex]f(x)=x^5-k[/tex], then the function is shifted k units down.
If [tex]f(x)=a(x^5)[/tex] and [tex]a > 1[/tex] it is vertically stretched it, but if [tex]0 < a < 1[/tex] it is vertically compressesd.
If [tex]f(x)=-(x^5)[/tex], then the function is reflected over the x-axis.
Then, if the function given is reflected over the x-axis, it is vertically streteched by a factor o 2 and it is shifted down 1 units, the function that results after this transformations is:
[tex]g(x)=-2(x^5)-1[/tex]
[tex]g(x)=-2x^5-1[/tex]
The Roman cubitus is an ancient unit of measure equivalent to about 0.445 m. Convert the 1.95-m height of a basketball forward to cubiti. HINT Use the conversion factor 1 cubitus = 0.445 m. In the conversion factor 1 cubitus = 0.445 m, the term "1 cubitus" is considered to be exact so that it never limits the number of significant figures reported in the answer. cubiti
Answer:
4.382 cubiti
Step-by-step explanation:
That's a simple exercise of cross-multiplication:
[tex]\frac{x}{1.95} = \frac{1}{0.445}[/tex]
x being the measure in cubitus we're looking for. We can isolate it:
x = (1.95 m * 1 ) / (0.445 m/cubitus) = 4.382 cubiti
1.95 m = 4.382 cubiti
Which totally makes sense... since a cubitus is roughly half a meter long... and the basketball is 2 meters high... so there are roughly 4 cubiti in 2 meters.
The height of the basketball forward in cubiti is approximately 4.38.
To convert the height from meters to cubiti, we use the conversion factor provided in the question:
1 cubitus = 0.445 m
Given the height of the basketball forward is 1.95 m, we divide this value by the conversion factor to find the height in cubiti:
Height in cubiti = Height in meters / Conversion factor
Height in cubiti = 1.95 m / 0.445 m/cubitus
Now, we perform the division:
Height in cubiti ≈ 4.38 cubiti
Since the value of 1 cubitus is considered to be exact, the number of significant figures in the answer is determined by the height in meters, which is 1.95 m (three significant figures). Therefore, the answer is rounded to three significant figures as well.
PLEASE HURRY!!! TIMED!!! Will give brainliest!! 70 POINTS!!!
Rashid bought a piece of wood with a length less than 5 feet. The variable w represents the length. The inequality w<5 describes the length of the piece of wood. Which number could be a length of the piece of wood?
4.5
6
11.3
13
Answer: First option.
Step-by-step explanation:
You know that the meaning of the symbol of the inequality "<" is: Less than.
So, you can check each option to find the number that could be a length of this piece of wood.
Given [tex]w<5[/tex], you can substitute each number given in the options into this inequality. Then:
[tex]1)\ w<5\\\\4.5<5\ (This\ is\ true)[/tex]
[tex]2)\ w<5\\\\6<5 (This\ is\ not\ true)[/tex]
[tex]3)\ w<5\\\\11.3<5\ (This\ is\ not\ true)[/tex]
[tex]4)\ w<5\\\\13<5\ (This\ is\ not\ true)[/tex]
Therefore, a lenght of the piece of wood could be 4.5
based on the pattern table what is the value of a?
A. -64
B. -12
C. 1/16
D. 1/64
Based on the pattern table, the value of a is 1/64.
What is the value of a?Given:
[tex]2^{-1} =\frac{1}{2}[/tex][tex]2^{-2} =\frac{1}{4}[/tex][tex]2^{-3} =\frac{1}{8}[/tex][tex]2^{-4} =\frac{1}{16}[/tex][tex]2^{-5} =\frac{1}{32}[/tex]Find:
The value of [tex]2^{-6}[/tex] which is represented by a.Solution:
The negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.
So, [tex]2^{-6} = \frac{1}{2^{6} } = \frac{1}{64}[/tex]
As, [tex]2^{6} = 64[/tex].
So, a = 1/64
Hence, the value of a is 1/64
To learn more about patterns, refer to:
https://brainly.com/question/854376
#SPJ2
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Explain too please.
Taking the cubic root of a number is the same as raising that number to the power of 1/3.
Moreover, we have
[tex]64 = 2^6[/tex]
So, we have
[tex]\sqrt[3]{64} = \sqrt[3]{2^6} = (2^6)^{\frac{1}{3}} = 2^{6\cdot\frac{1}{3}} = 2^2 = 4 [/tex]
Answer:
4
Step-by-step explanation:
Since we see a cube root, we will attempt to rewrite 64 as a number with an exponent of 3.
[tex]\sqrt[3]{64}[/tex]
[tex]= \sqrt[3]{4^3}[/tex]
[tex]= 4 [/tex]
What is the greatest common factor of 24s3, 12s4, and 18s?
3
6
3s
6s
Answer:
=> 6s
Step-by-step explanation:
Given terms
24s^3 ,12s^4 and 18s
GCF consists of the common factors from all the terms whose GCF has to be found.
In order to find GCF, factors of each term has to be made:
The factors of 24s^3:
24s^3=2*2*2*3*s*s*s
The factors of 12s^4:
12s^4=2*2*3*s*s*s*s
The factors of 18s:
18s=2*3*3*s
The common factors are(written in bold):
GCF=2*3*s
=6s
So the GCF is 6s ..
Answer:
6s
Step-by-step explanation:
Plz help ASAP!! Explain your answer! I will mark at brainliest!!!
Part A
Yes, triangle ABC and triangle APQ are similar because of Angle-Angle similarity.
Angle BAC is congruent to Angle PAQ because of reflexive property (they share the same angle).
It is given that Segment BC is parallel to Segment PQ, so Angle ABC is congruent to Angle APQ because the corresponding angles postulate.
Part B
Segment PQ corresponds to Segment BC because they are parallel to each other.
Part C
Angle APQ corresponds to Angle B because of the corresponding angles postulate.
Lines a and b are parallel Line cis perpendicular to both line a and line b. Which
statement about lines a, b, and is NOT true?
CLEARCH
Line a and line b have the same slope.
The sum of the slopes of line b and line cis 0.
The product of the slopes of line cand line bis -1.
The product of the slopes of line a and line cis -1.
Answer:
see below
Step-by-step explanation:
The slopes of parallel lines are the same. The slopes of perpendicular lines are negative reciprocals of each other, hence their product is -1.
___
For the most part, the concept of adding slopes of lines does not relate to parallel or perpendicular lines in any way.
Answer:
c
Step-by-step explanation:
If Joe drives 186.83 miles on a business trip, and the reimbursement from his company is $13.08. At what rate is Joe's employer reimbursing travel miles? (round to the nearest cent)
Please show work
Answer:
7 cents/mile
Step-by-step explanation:
You are looking for a unit rate of cents per mile.
Change the dollar amount to cents, and divide by the number of miles.
$13.08 * (100 cents)/$ = 1308 cents
(1308 cents)/(183 miles) = 7.001 cents/mile
The area of a playground is 64 square yards. The length of the playground is 4 times longer than its width. How can I solve this?
Answer:
If you are looking for the dimensions of the playground, they are that the width is 4 yards and the length is 16 yards
Step-by-step explanation:
We need to know 2 things here: first, the area of a rectangle which is A = l×w,
and then we need to know how to express one dimension in terms of the other, since we have way too many unknowns right now to solve for anything!
We are told that the length is 4 times the width, so if the width is "w", then the length is "4w". We know the area is 64, so let's sub in those values where they belong in the area formula:
64 = 4w(w). Multiplying to simplify we get
[tex]64=4w^2[/tex]
The easiest way to do this is to divide both sides by 4 to get
[tex]16=w^2[/tex]
and when you take the square root of 16 you get 4 and -4. However, the two things in math that will never ever be negative are distance measurements and time. So the -4 won't do. That means that w = 4. If that be the case, and the length is 4 times the width, then the length is 16. And there you go!
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = cos(θ) + sin(10θ) y = sin(θ) + cos(10θ) θ = 0 y(x) =
The equation of the tangent to the curve at the point corresponding to the given values of the parametric equations given is;
y - 1 = ¹/₁₀(x - 1)
We are given;
x = cos θ + sin(10θ)
y = sin θ + cos(10θ)
Since we want to find equation of tangent, let us first differentiate with respect to θ. Thus;
dx/dθ = -sin θ + 10cos (10θ)
Similarly;
dy/dθ = cos θ - 10sin(10θ)
To get the tangent dy/dx, we will divide dy/dθ by dx/dθ to get;
(dy/dθ)/(dx/dθ) = dy/dx = (cos θ - 10sin(10θ))/(-sin θ + 10cos(10θ))
To get the tangent, we will put the angle to be equal to zero.
Thus, at θ = 0, we have;
dy/dx = (cos 0 - 10sin 0)/(-sin 0 + 10cos 0)
dy/dx = 1/10
Also, at θ = 0, we can get the x-value and y-value of the parametric functions.
Thus;
x = cos 0 + sin 0
x = 1 + 0
x = 1
y = sin 0 + cos 0
y = 0 + 1
y = 1
Thus, the equation of the tangent line to the curve in point slope form gives us;
y - 1 = ¹/₁₀(x - 1)
Read more at; https://brainly.com/question/13388803
Final answer:
To find the tangent line to the curve defined by the parametric equations at θ = 0, we compute the derivatives of both x and y with respect to θ, leading to a slope of 1/10. By evaluating the original parametric equations at θ = 0, we find that the tangent passes through (1, 1), resulting in the equation y - 1 = 1/10(x - 1).
Explanation:
To find an equation of the tangent to the given parametric curve at θ = 0, we first need the parametric equations given by x = cos(θ) + sin(10θ) and y = sin(θ) + cos(10θ). To find the slope of the tangent, we compute the derivatives δy/δx = (δy/δθ)/(δx/δθ) at θ = 0.
Computing the derivatives, δx/δθ = -sin(θ) + 10cos(10θ) and δy/δθ = cos(θ) - 10sin(10θ), and plugging in θ = 0, we get δx/δθ = 10 and δy/δθ = 1. Hence, the slope is 1/10. Evaluating the functions at θ = 0 gives x = 1 and y = 1. Thus, the tangent line equation at θ = 0 is y - y_0 = m(x - x_0), which simplifies to y - 1 = 1/10(x - 1).
Show all work to identify the discontinuity and zero of this function. 3x/x^2-9
ANSWER
Zero(s)
[tex]x = 0[/tex]
The function is discontinuous at
[tex]x = - 3 \:and \: x = 3[/tex]
EXPLANATION
The given rational function is
[tex] y = \frac{3x}{ {x}^{2} - 9 } [/tex]
For this function to be equal to zero, then the numerator must be zero.
Equate the numerator to zero and solve for x.
[tex]3x = 0[/tex]
This implies that
[tex]x = \frac{0}{3} = 0[/tex]
The rational function is discontinuous when the denominator is equal to zero.
[tex] {x}^{2} - 9 = 0[/tex]
Solve this quadratic equation using the square root method or otherwise.
[tex] {x}^{2} = \pm \sqrt{9} [/tex]
[tex]{x} = \pm 3[/tex]
There is discontinuity at
[tex]x = - 3 \:and \: x = 3[/tex]
Select the correct answer. Find the slope and the y-intercept of the equation y − 3(x − 1) = 0. A. slope = -3 and y-intercept = -3 B. slope = 3 and y-intercept = 3 C. slope = -3 and y-intercept = 3 D. slope = 3 and y-intercept = -3
Answer:
D. slope = 3 and y-intercept = -3
Step-by-step explanation:
The equation can be rearranged by adding the opposite of the term with parentheses:
y = 3(x -1)
Expanding this to slope-intercept form gives ...
y = 3x -3 . . . . . . . . slope = 3, y-intercept = -3
_____
Slope-intercept form is ...
y = mx +b . . . . . . . . slope = m, y-intercept = b
The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet. What are the dimensions of the flower bed? A. 2 ft by 12 ft B. 3 ft by 8 ft C. 3 ft by 6 ft D. 4 ft by 6 ft
ANSWER
B. 3 ft by 8 ft
EXPLANATION
The area is given as 24 square feet.
This implies that,
[tex]l \times w = 24[/tex]
The perimeter of the rectangular field is given as 22 feet.
This implies that,
[tex]2(l + w) = 22[/tex]
Or
[tex]l + w = 11[/tex]
We make w the subject in this last equation and put it inside the first equation.
[tex]w = 11 - l[/tex]
When we substitute into the first equation we get;
[tex]l(11 - l) = 24[/tex]
[tex]11l - {l}^{2} = 24[/tex]
This implies that,
[tex] {l}^{2} - 11l + 24 = 0[/tex]
[tex](l - 3)(l - 8) = 24[/tex]
[tex]l = 3 \: or \: 8[/tex]
When l=3, w=24
Therefore the dimension is 3 ft by 8 ft
Answer:
The correct answer is option B. 3 ft by 8 ft
Step-by-step explanation:
Points to remember
Area of rectangle = length * breadth
Perimeter of rectangle = 2(Length + Breadth)
It is given that, The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet
To find the correct option
1). Check option A
Area = 2 * 12 = 24
Perimeter = 2( 2 + 12 ) = 28
False
2) Check option B
Area = 3 * 8 = 24
Perimeter = 2(3 + 8 ) = 22
True
3). Check option C
Area = 3 * 6 = 18
Perimeter = 2( 3 + 6 ) = 18
False
4). Check option D
Area = 4 * 6 = 24
Perimeter = 2( 4 +6 ) = 20
False
The correct answer is option B. 3 ft by 8 ft
Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 16x2 + 9y2 = 144. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
In the [tex]x[/tex]-[tex]y[/tex] plane, the base has equation(s)
[tex]16x^2+9y^2=144\implies y=\pm\dfrac43\sqrt{9-x^2}[/tex]
which is to say, the distance (parallel to the [tex]y[/tex]-axis) between the top and the bottom of the ellipse is
[tex]\dfrac43\sqrt{9-x^2}-\left(-\dfrac43\sqrt{9-x^2}\right)=\dfrac83\sqrt{9-x^2}[/tex]
so that at any given [tex]x[/tex], the cross-section has a hypotenuse whose length is [tex]\dfrac83\sqrt{9-x^2}[/tex].
The cross-section is an isosceles right triangle, which means the legs occur with the hypotenuse in a ratio of 1 to [tex]\sqrt2[/tex], so that the legs have length [tex]\dfrac8{3\sqrt2}\sqrt{9-x^2}[/tex]. Then the area of each cross-section is
[tex]\dfrac12\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)=\dfrac{16}9(9-x^2)[/tex]
Then the volume of this solid is
[tex]\displaystyle\frac{16}9\int_{-3}^39-x^2\,\mathrm dx=\boxed{64}[/tex]
Solid [tex]\( S \)[/tex] has elliptical base[tex]\( 16x^2 + 9y^2 = 144 \)[/tex]. Triangular cross-sections yield volume [tex]\( 128 \)[/tex] cubic units.
let's break it down step by step.
1. Understanding the Solid: The solid [tex]\( S \)[/tex] has a base in the shape of an ellipse given by the equation [tex]\( 16x^2 + 9y^2 = 144 \).[/tex] The cross-sections perpendicular to the x-axis are isosceles right triangles with their hypotenuse lying on the base ellipse.
2. **Equation of the Ellipse**: To understand the shape of the base, let's rearrange the equation of the ellipse to find [tex]\( y \)[/tex] in terms of [tex]\( x \):[/tex]
[tex]\[ 16x^2 + 9y^2 = 144 \] \[ y^2 = \frac{144 - 16x^2}{9} \] \[ y = \pm \frac{4}{3} \sqrt{9 - x^2} \][/tex]
3. Finding the Length of the Hypotenuse: The length of the hypotenuse of each triangle is twice the value of [tex]\( y \)[/tex] at any given point on the ellipse. So, the length [tex]\( h \)[/tex] of the hypotenuse is given by:
[tex]\[ h = \frac{8}{3} \sqrt{9 - x^2} \][/tex]
4. Area of Each Cross-Section Triangle: The area of each cross-section triangle is [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \),[/tex] where the base is the same as the height. So, the area is:
[tex]\[ \text{Area} = \frac{1}{2} \times \frac{8}{3} \sqrt{9 - x^2} \times \frac{8}{3} \sqrt{9 - x^2} = \frac{32}{9} (9 - x^2) \][/tex]
5. Integrating to Find Volume: To find the volume of the solid, we integrate the area function over the interval that covers the base ellipse, which is [tex]\([-3, 3]\)[/tex] in this case.
[tex]\[ V = \int_{-3}^{3} \frac{32}{9} (9 - x^2) \, dx \][/tex]
6. Solving the Integral: Integrating [tex]\( (9 - x^2) \)[/tex] with respect to[tex]\( x \)[/tex] yields:
[tex]\[ = \frac{32}{9} \int_{-3}^{3} (9 - x^2) \, dx \] \[ = \frac{32}{9} \left[ 9x - \frac{x^3}{3} \right]_{-3}^{3} \] \[ = \frac{32}{9} \left[ (27 - 9) - (-27 + 9) \right] \] \[ = \frac{32}{9} \times 36 \] \[ = \frac{1152}{9} \] \[ = 128 \][/tex]
7. Final Result: So, the volume of the solid [tex]\( S \)[/tex] is [tex]\( 128 \)[/tex] cubic units.
solve -5/3x+7=9/2 by graphing
Answer:
x = 1.5
Step-by-step explanation:
The left side of the equation is graphed as a straight line with a slope of -5/3 and a y-intercept of +7. The right side of the equation is graphed as a horizontal line at y = 4.5. The point of intersection of these lines has the x-coordinate of the solution: x = 1.5.
I start with 5 oz. of 18-karat gold. It's 75% pure gold, 25% other metals. I need to make it 22-karat, which is 91.7% pure gold. How much pure gold do I need to add to make it 22-karat?
Answer:
about 10.06 oz.
Step-by-step explanation:
Let x represent the number of ounces of pure gold you need to add. Then the amount of gold in the mix is ...
100%·x + 75%·5 = 91.7%·(x+5)
8.3%·x = 5·16.7% . . . . . . subtract 91.7%·x +75%·5
x = 5 · 16.7/8.3 . . . . . . . . divide by the coefficient of x
x ≈ 10.06 . . . . oz
_____
Alternate solution
The amount of non-gold in the given material is 25%·5 oz = 1.25 oz. That is allowed to be 8.3% of the final mix, so the weight of the final mix will be ...
(1.25 oz)/0.083 ≈ 15.06 oz
Since that weight will include the 5 oz you already have, the amount of pure gold added must be ...
15.06 oz - 5 oz = 10.06 oz
_____
Comment on these answers
If you work directly with carats instead of percentages, you find the amount of pure gold you need to add is 10.00 ounces, double the amount you have.
The null and alternate hypotheses are: H0: π1 ≤ π2 H1: π1 > π2 A sample of 100 observations from the first population indicated that X1 is 70. A sample of 150 observations from the second population revealed X2 to be 90. Use the .05 significance level to test the hypothesis. a. State the decision rule. (Round your answer to 2 decimal places.) H0 is rejected if z > b. Compute the pooled proportion. (Round your answer to 2 decimal places.) Pooled proportion c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding the null hypothesis? H0 is
Answer:
365
Step-by-step explanation:
By United States cultural standards, it has been determined that 6 people live comfortably in 1500 square feet of living space. Based on this standard, how many people could be comfortably accommodated with 27,000 square feet of living space? Enter the number only.
I'm unsure about this answer, but I got 108 people. I just did a simple proportion of 6/1500 = x/27000 and solved for x.
Answer:
108 people
Step-by-step explanation:
We can write a proportion to solve this problem. Take the number of people over the living space
6 people x people
------------ = ------------------
1500 ft^2 27000 ft^2
Using cross products
6 * 27000 = 1500 x
Divide each side by 1500
6 * 27000/1500 = 1500x/1500
108 = x
108 people can be reasonably accommodated
Assume that you are provided with the score matrix S, detections can only be matched to a single track, and that tracks cannot be assigned more than once. (a) [5 points] What do the variables in this problem represent? How many are there? (b) [10 points] Define the objective for this 0-1 integer linear program. (c) [15 points] Define the entire 0-1 integer linear program, including constraints, in standard form. How many constraints are there in the program, total?
Final answer:
The variables in this problem represent the scores in the score matrix S. The objective for this 0-1 integer linear program is to maximize the overall score. The entire 0-1 integer linear program in standard form includes constraints to ensure that each detection is assigned to a single track and each track is assigned only once, and there are N + M constraints in total.
Explanation:
(a) In this problem, the variables represent the scores in the score matrix S. There are N detections and M tracks, so we have N rows and M columns in the score matrix.
(b) The objective for this 0-1 integer linear program is to maximize the overall score, which is the sum of the selected detections' scores.
(c) The entire 0-1 integer linear program in standard form can be defined as:
Maximize the objective function: maximize ∑i,j xi,j * Si,j, where xi,j is a binary variable representing whether detection i is assigned to track j.Subject to the constraints:There are N + M constraints in total.
please respond asap!!!
The answer is:
The difference between the circle and the square is:
[tex]Difference=4\pi -8[/tex]
Why?To solve the problem, we need to find the area of the circle and the area of the square, and then, subtract them.
For the square we have:
[tex]side=2\sqrt{2}[/tex]
We can calculate the diagonal of a square using the following formula:
[tex]diagonal=side*\sqrt{2}[/tex]
So,
[tex]diagonal=2\sqrt{2}*\sqrt{2}=2*(\sqrt{2})^{2}=2*2=4units[/tex]
The area will be:
[tex]Area_{square}=side^{2}= (2\sqrt{2})^{2} =4*2=8units^{2}[/tex]
For the circle we have:
[tex]radius=\frac{4units}{2}=2units[/tex]
The area will be:
[tex]Area_{Circle}=\pi *radius^{2}=\pi *2^{2}=\pi *4=4\pi units^{2}[/tex]
[tex]Area_{Circle}=4\pi units^{2}[/tex]
Then, the difference will be:
[tex]Difference=Area_{Circle}-Area{Square}=4\pi -8[/tex]
Have a nice day!
ANSWER
[tex]4\pi - 8[/tex]
EXPLANATION
The diagonal of the square can be found
using Pythagoras Theorem.
[tex] {d}^{2} = {(2 \sqrt{2} )}^{2} + {(2 \sqrt{2} )}^{2} [/tex]
[tex]{d}^{2} = 4 \times 2+ 4 \times 2[/tex]
[tex]{d}^{2} = 8+ 8[/tex]
[tex]{d}^{2} = 16[/tex]
Take positive square root
[tex]d = \sqrt{16} = 4[/tex]
The radius is half the diagonal because the diagonal formed the diameter of the circle.
Hence r=2 units.
Area of circle is
[tex]\pi {r}^{2} =\pi \times {2}^{2} = 4\pi[/tex]
The area of the square is
[tex] {l}^{2} = {(2 \sqrt{2)} }^{2} = 4 \times 2 = 8[/tex]
The difference in area is
[tex]4\pi - 8[/tex]
The perimeter of a rectangular field is 328 yards. If the length of the field is 89 yards, what is its width?
Set up an equation based on the information given
[tex]89 + 89 + x + x = 328[/tex]
Combine like terms
[tex]89 + 89 = 178[/tex]
[tex]x + x = 2x[/tex]
[tex]2x + 178 = 328[/tex]
Solve
[tex]2x + 178 = 328[/tex]
[tex]328 - 178 = 150[/tex]
[tex]2x = 150[/tex]
[tex]x = 75[/tex]
Answer
The width of the rectangular field is 75 yards.