The volume of a box(V) varies directly with its length(l). If a box in the group has a length of 30 inches, and the girth of 20 inches (perimeter of the side formed by the width and height), what is its height? Use k = 24. (Hint: Volume = length • width • height. Solve for length, and substitute into the equation for constant of proportionality.)?

Answers

Answer 1

[tex]\bf \textit{V varies directly with l}\implies V=kl\qquad k=24\implies V=24l \\\\\\ \textit{volume of the box, or a rectangular prism}\\\\ V=lwh\qquad \begin{cases} l=length\\ w=width\\ h=height\\ ----------\\ k=24 \end{cases}\implies \boxed{lwh=24l} \\\\\\ \textit{girth of the box }\\\\ w+w+h+h=20\implies 2w+2h=20\implies 2(w+h)=20 \\\\\\ thus\qquad w+h=\cfrac{20}{2}\implies \boxed{w=10-h}[/tex]

[tex]\bf \\\\ -------------------------------\\\\ lwh=24l\implies wh=24\implies (10-h)h=24\implies 10h-h^2=24 \\\\\\ 0=h^2-10+24\implies 0=(h-6)(h-4)\implies h= \begin{cases} 6\\ 4 \end{cases}[/tex]

now, notice, we didn't use the length of 30inches.... since the "l"'s cancel each other anyway, so it doesn't weight much on what the value for "h" is, by simply doing the substution of "w" from the Girth.

Related Questions

Please I'm stuck in this problem

Answers

The answer is 2wx^5(the root is 3) square root of 9w. I hope this makes sense.

An earthquake with a rating of 3.2 is not usually felt. What is the value of x when the Richter scale rating is 3.2? Round your answer to the nearest hundredth.

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10^3.2=1584.893≈1584.89

Pediatric asthma survey, n = 50. suppose that asthma affects 1 in 20 children in a population. you take an srs of 50 children from this population. can the normal approximation to the binomial be applied under these conditions? if not, what probability model can be used to describe the sampling variability of the number of asthmatics?

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In this situation,
n=50, p=1/20, q=(1-p)=19/20, and npq=19/8=2.4

We would like np and npq to be a large number, at least greater than 10.
The normal approximation can always be applied, but the result will be very approximate, depending on the values of np and npq.

Situations are favourable for the normal approximation when p is around 0.5, say between 0.3 and 0.7, and n>30.

"Normal approximation" is using normal probability distribution to approximate the binomial distribution, when n is large (greater than 70) or exceeds the capacity of most hand-held calculators. The binomial distribution can be used if the following conditions are met:
1. Bernoulli trials, i.e. exactly two possible outcomes.2. Number of trials is known before and constant throughout the experiment, i.e. independent of outcomes.3. All trials are independent of each other.4. Probability of success is known, and remain constant throughout trials.
If all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given byP(x)=C(N,x)(p^x)(1-p)^(N-x)and,C(N,x) is number of combinations of selecting x objects out of N.
The mean is np, and variance is npq.

For the given situation, np=2.5, npq=2.375, so standard deviation=sqrt(2.375)=1.54.

n=50, p=1/20, q=(1-p)=19/20, and npq=19/eight=2.4

We would like np and npq to be a huge range, at least extra than 10.

The ordinary approximation can usually be carried out, but the result might be very approximate, relying on the values of np and npq.

conditions are favorable for the normal approximation when p is around 0.5, say among 0.3 and 0.7, and n>30.

For the given scenario, np=2.five, npq=2.375, so widespread deviation=sqrt(2.375)=1.54.

underneath what conditions binomial distribution tends to be everyday distribution?

the theory states that any distribution becomes normally allotted whilst the variety of variables is satisfactorily massive. for example, the binomial distribution has a tendency to alternate into the regular distribution with suggest and variance.

Learn more about binomial distribution here: https://brainly.com/question/15246027

#SPJ2

simplify the expression I-30I

Answers

it would be only 30

Steve can complete the 100m dash in 10 seconds while Paul can run it in 12 seconds. How does Steve's time compare to Paul's?

Answers

Steve is faster than Paul by 2 seconds after 100m

5 times the difference of 29 and a number is 215. Which equation below can be used to find the unknown number?

Answers

Is it multiple choice? If not I would say 215=5(x)-29

Answer:

The required equation is [tex]5(29-n)=215[/tex]

Step-by-step explanation:

Given : 5 times the difference of 29 and a number is 215.

To find : Which equation can be used to find the unknown number?

Solution :

Let the number be 'n'.

The difference of 29 and a number i.e. [tex]29-n[/tex]

5 times the difference of 29 and a number i.e. [tex]5(29-n)[/tex]

5 times the difference of 29 and a number is 215 i.e. [tex]5(29-n)=215[/tex]

Therefore, the required equation is [tex]5(29-n)=215[/tex]

simplify the expression below. show your work. -(-7y+12)

Answers

[tex]-(-7y+12) = 7y -12[/tex]

Quadrilateral ABCD is similar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 4th side on quadrilateral ABCD?

Answers

Final answer:

The length of the fourth side on quadrilateral ABCD is 120 feet.

Explanation:

Given that quadrilateral ABCD is similar to quadrilateral EFGH, we can use the property of similar figures to find the length of the fourth side on quadrilateral ABCD.

If the two shortest sides of quadrilateral EFGH are 6 feet and 12 feet long, we can set up a proportion using the corresponding sides of the two quadrilaterals.

Let x be the length of the fourth side on quadrilateral ABCD.

Using the property of similar figures, we have:

(60/6) = (x/12)

Cross multiplying, we get:

6x = 720

Dividing both sides by 6, we find:

x = 120

Therefore, the length of the fourth side on quadrilateral ABCD is 120 feet.

A geometry class has a total of 34 students. The number of males is 14 more than the number of females. How many males and how many females are in the class?

Answers

m=14+f, m+f=34. Solve for the equations simultaneously.

one way is to substitute teh first into the second to get, 14+2f=34, or 7+f=17, or f=10. Since f is 10 and m+f=34, m=34-10=24.

Good luck!

Can someone please help me solve this triangle problem, picture is shown.

Answers

(4t + 4t + 4t) (addition form)

3(4t) (multiplication form)

these are two forms you can use to get your answer

answer: 12t

hope this helps

perimeter = 4t + 4t + 4t

and

perimeter = 4t * 3

The principal $3000 is accumulated with 3% interest, compounded semiannually for 6 years.

Answers

The formula is
A=p (1+r/k)^kt
A accumulated amount?
P principle 3000
R interest rate 0.03
K compounded semiannually 2
T time 6 years
A=3,000×(1+0.03÷2)^(2×6)
A=3,586.85

What is the distance between (–6, 2) and (8, 10) on a coordinate grid?

Answers

Distance Formula: d = √(x₂ - x₁)² + (y₂ - y₁)²

(-6 , 2) and (8 , 10)
x₁ y₁ x₂ y₂

d = √(8 - (-6))² + (10 - 2)²
d = √(8+6)² + (10 - 2)²
d = √(14)² + (8)²
d = √(196) + (64)
d = √ 260
d = 2√65

I think this is right, but I am not sure.

Answer:

D. √260

Step-by-step explanation:

Use the distance formula then input the points (–6, 2) and (8, 10) into it to get √(-6 −2)^2 + (2 −10)^2. Finaly simplify/solve and you get √260.

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.[-5, 5] by [-5, 5] (1 point)

Answers

The general form for this curve is:
[tex]r = Acos \theta + B[/tex]
Now find A,B given 2 points:
[tex]r(0) = 5, r(\pi) = 1[/tex]
[tex]A +B = 5 \\ \\ -A+B = 1[/tex]
Solving this system yields:
[tex]A = 2, B = 3 \\ \\ r = 2cos \theta + 3[/tex]

Answer:

r = 2 - 3 cos θ

Step-by-step explanation:

This is the best I could come up with.

Find the value of x in 4000(1.5x) = 25,000. show all work

Answers

4000(1.5)x = 25,000
25000/4000 = 1.5x
6.25 = 1.5x
25/6 = x

4000(1.5x)=25000 divide both sides by 4000

1.5x=6.25 divide both sides by 1.5

x=25/6

x=4 1/6

But that is pretty simplistic, I suspect that you actually meant this was an exponential function of the form:

4000(1.5^x)=25000 divide both sides by 4000

1.5^x=6.25 take the natural log of both sides

xln(1.5)=ln(6.25) divide both sides by ln(1.5)

x=ln(6.25)/ln(1.5)

x≈4.52 (to nearest hundredth)

value for X^2 left for 95% confidence interval when n=18

Answers

Given that n = 18, then the degree of freedom is n - 1 = 17.

From the table of Chi Square [tex](X^2)[/tex]

The value of [tex](X^2)[/tex] to the left for 95% confidence interval given a degree of freedom of 17 is 8.672

Which figure has the correct lines of symmetry drawn in?

Answers

The figure which has the correct lines of symmetry drawn is figure D.

What is line of symmetry?

A line of symmetry refers to the line that divides a shape or an object into two equal and symmetrical parts.

The figure given is a five sided shape referred to as a pentagon.

A pentagon has five lines of symmetry.

Therefore, the correct line of symmetry is 5 lines drawn from each angle respectively.

Answers

I would use substitution. The value of t in terms of s is already given so you can just plug that into the equation like this.
4s-3(-2s-1)=8

A bag of fruit contains 3 apples and 2 oranges and 1 banana and 4 pears.Gerald will randomly selected two pieces of fruit one at a time from the bag and not put is back. What is the probability that the first piece of fruit Gerald selects will be a banana and the second piece of fruit will be a pear??

Answers

Final answer:

The probability that Gerald will first select a banana and then a pear from the bag without replacement is 2/45.

Explanation:

To determine the probability that Gerald selects a banana first and then a pear without replacement, we have to consider the total number of possible outcomes for each draw and the favorable outcomes for the event.

For the first draw, the total number of fruits is 10 (3 apples + 2 oranges + 1 banana + 4 pears). The favorable outcome of drawing a banana is 1 since there's only one banana.

The probability of drawing a banana on the first draw is therefore 1/10. After drawing the banana, there are 9 fruits left in the bag with 4 pears among them.

The probability of then drawing a pear is 4/9. To find the total probability of both events happening in sequence (a banana first and then a pear), multiply the two probabilities:

P(banana first and pear second) = P(banana first) × P(pear second)
= (1/10) × (4/9)
= 4/90
= 2/45.

The simplification process shows that the probability Gerald will first select a banana and then a pear is 2/45.

Triple my number add six and subtract twice my number my number plus three

Answers

3N + 6 - 2N = N + 3
N + 6 = N + 3
N cancels out.
Therefore it is a false statement.

Which expression is equivalent to (7^3)−2
A- 1 over 7 times 7 times 7 times 7 times 7 times 7
B- 7
C- 1 over 7
D-negative 1 over 7 times 7 times 7 times 7 times 7 times 7

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}} \\\\ -------------------------------\\\\ (7^3)^{-2}\implies 7^{-2\cdot 3}\implies 7^{-6}\implies \cfrac{1}{7^6}\implies \cfrac{1}{7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7}[/tex]

What is the value of k in the equation below? 5k - 2k = 12? 1 1/5, 1 5/7, 3, 4

Answers

Hi there!

5k - 2k = 12
Solve for K
3k = 12
Divide both sides by 3
3k/3 = 12/3
k = 4
The correct answer is : 4

I hope that helps!
Brainliest answer :)

Answer:4

Step-by-step explanation:

Sidney made $26 more than seven times Casey's weekly salary. If x represents Casey's weekly salary, write an expression for sidney's weekly salary

Answers

7x+26 becase it is 7 times and then you add 26

hey can you just please help me solve these two problems
1- according to the bipartisan policy center (BPC), 57.5% of all eligible voted in the 20112 presidential elections. while there are over 350 million Americans, the BPC estimates that only 219 million are eligible to vote. how many eligible voters in 2012 election?

2-sarah's sandwich shop sells a specialty sandwich for $4.95 that contains a quarter of a pound of turkey. if sarah buys 12 pounds of turkey meat but eats a tenth of a pound on the way to her sandwich shop, what is the maximum number of sandwiches she can make?

Answers

2)

well, she needs 1/4lb to make a sandwich, well, she bought 12lbs and then she couldn't resist, because she got some ketchup also I gather, she couldn't resist giving it a nibble and ate 1/10lb

so.. is 12 - 1/10, and how many times 1/4 goes into that difference

[tex]\bf 12-\cfrac{1}{10}\implies \cfrac{120-1}{10}\implies \cfrac{119}{10} \\\\\\ \textit{how many times }\frac{1}{4}\textit{ goes in to }\frac{119}{10}? \\\\\\ \cfrac{\frac{119}{10}}{\frac{1}{4}}\implies \cfrac{119}{10}\cdot \cfrac{4}{1}\implies \cfrac{238}{5}\implies \boxed{47\frac{3}{5}} \\\\\\ \cfrac{47\cdot 5+3}{5}\implies \cfrac{238}{5}[/tex]

well, noone is going to buy a half-eaten sandwich or 3/5 of a sandwich, so, she can only make 47 whole sandwiches, hmmmm I'm thinking she can just give the 3/5 to the dogs.

A taxi cab charges $0.55 per mile in addition to a $1.75 flat rate fee. Susie has $10 to spend on a taxi cab ride. The taxi driver will not give anyone a ride unless they are going somewhere that is more than 2 miles away. Model Susie’s situation with a system of inequalities.

Answers

The taxi driver doesn't give anyone a ride unless it's 2 miles away, as such you need to add at least $0.55x2 in addition to the $1.75 at the start
1.75+(0.55x2)=2.85
As Susie only has 10 dollars to spend, she can't exceed that. So Susie must spend more than $2.85(minimum from the taxi) and less than $10(her money)
so,
$2.85<Susie<$10

A ship traveled for 4 hours heading east and for 3 hours heading north. If the total distance traveled was 149 miles, and the ship traveled 3 miles per hour faster heading north, at what speed was the ship traveling east?

Answers

just like the previous one

if the ship travelled a total of 149 miles, then let's say it travelled East "d" miles and thus it travelled North the slack of 149 and "d", thus " 149 - d".

now, if the rate travelling East is say "r", then the faster rate going North is " r + 3".

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ East&d&r&4\\ North&149-d&r+3&3 \end{array} \\\\\\ \begin{cases} \boxed{d}=4r\\ 149-d=(r+3)3\\ ----------\\ 149-\boxed{4r}=3(r+3) \end{cases}[/tex]

solve for "r".

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

Answers

At first, she was grading papers at 10 papers per hour. To meet her time limit, she would have to begin grading them at 12 papers per hour, or 20% faster than her previous rate

so, she has 3hrs to grade all papers, for 35 students.. alrite.

the first 5, she does them in 30minutes.. what's the speed rate? well, 5/30 or 1/6

now, she has still 2 hours and a half, or 150 minutes, to do the remaining 30 papers... she has to work at a rate of 30/150 then... which is 1/5 simplified.

now if we take 1/6 as the 100%, what is 1/5 in percentage then?

[tex]\bf \begin{array}{ccllll} rate&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{6}&100\\\\ \frac{1}{5}&x \end{array}\implies \cfrac{\frac{1}{6}}{\frac{1}{5}}=\cfrac{100}{x}\implies \cfrac{1}{6}\cdot \cfrac{5}{1}=\cfrac{100}{x}\implies \cfrac{5}{6}=\cfrac{100}{x} \\\\\\ x=\cfrac{6\cdot 100}{5}\implies x=120[/tex]

so 1/5 is 120% in relation to 1/6... meaning the rate of 1/5 she needs to move through, namely 1 paper every 5 minutes, is 20% faster than 1/6.

How many inches are in a foot?

Answers

there are 12 inches in a foot

There are 12 inches in a foot.

How do you find a vector that is orthogonal to 5i + 12j ?

Answers

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\ slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \boxed{5i+12j}\implies \begin{array}{rllll} \ \textless \ 5&,&12\ \textgreater \ \\ x&&y \end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5} \\\\\\ slope=\cfrac{12}{{{ 5}}}\qquad negative\implies -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12} \\\\\\ \ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}[/tex]

if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.

so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.

so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.

or using a unit vector for those above, then

[tex]\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}} \\\\\\ \cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}} \\\\\\ \cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}[/tex]

To find a vector orthogonal to 5i + 12j, we can use the property that orthogonal vectors have a dot product of 0. By setting up equations and solving them accordingly, you can find a vector that is perpendicular to 5i + 12j.

Orthogonal vectors: To find a vector orthogonal to 5i + 12j, we need to find a vector with a dot product of 0 with 5i + 12j. Since the dot product of orthogonal vectors is zero, we can set up equations and solve them to find a vector that is perpendicular to 5i + 12j.

Find the rectangular coordinates of the point with the polar coordinates. ordered pair negative 5 comma 5 pi divided by 3

Answers

[tex]\bf \begin{array}{rllll} (-5&,&\frac{5\pi }{3})\\ \uparrow &&\uparrow \\ r&&\theta \end{array}\qquad \begin{cases} x=rcos(\theta )\\ y=rsin(\theta )\\ ----------\\ x=(-5)cos\left( \frac{5\pi }{3} \right)\\ \qquad -5\cdot \frac{1}{2}\\ \qquad -\frac{5}{2}\\ y=(-5)sin\left( \frac{5\pi }{3} \right)\\ \qquad -5\cdot -\frac{\sqrt{3}}{2}\\ \qquad \frac{5\sqrt{3}}{2} \end{cases}\implies \left(-\frac{5}{2}\ ,\ \frac{5\sqrt{3}}{2} \right)[/tex]

find two consecutive even integers such that the smaller added to five times the larger give you a sum of 46.

Answers

First consecutive integer: n
Second consecutive integer: n + 2 (next even integer)
n + 5(n + 2) = 46
n + 5n + 10 = 46

6n + 10 = 46
6n = 36
n = 6
n + 2 = 8
Your answer is 6 and 8

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