A packing box is 4 ft deep. One side of the box is 1.5 times longer than the other. The volume of the box is 24 ft3 . What are the dimensions of the box?

Answers

Answer 1

The dimensions of the packing box are 2 × 3 × 4 feet.

How to calculate the volume of a geometric figure?

Based on the information provided, we can reasonably infer and logically deduce that the shape of this packing box is a cuboid.

Mathematically, the volume of a cuboid can be calculated by using this following formula:

Volume = L × W × H

Where:

L represents the length of a cuboid.W represents the width of a cuboid.H represents the height of a cuboid.

Substituting the given parameters into the volume of a cuboid formula, we have;

24 = L × (1.5L) × 4

24 = 6L²

L² = 24/6

L = √4

Length, L = 2 feet.

Width, = 1.5L = 1.5(2) = 3 feet.

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Related Questions

y= 2x + 3

y= -3x + 3

Answers

Answer:

Below

Step-by-step explanation:

I suppose you are looking for a solution to the system of equations

  since both equations are equal to 'y' they are equal:

 2x+3  = -3x+3       add 2x to both sides of the equation

 5x + 3 = 3              subtract 3 from both sides

 5x = 0            so x = 0

  if x =0 then find y    y = 2(0) + 3 = 3

       the solution is (0,3)

for a certain type of soil the number of wireworms per cubic foot has a mean of 100 . assuming a poisson distribution of wireworms, give an interval that will include at least 5 / 9 of the sample values of wireworm counts obtained from a large number of 1 -cubic-foot samples.

Answers

An interval that will include at least 5/9 of the sample values of wireworm counts obtained is (85,115).

Let us consider a random variable Y which follows the Poisson distribution with parameter λ=100

The Mean of the Poisson distribution of λ(μ)=100

The variance of the Poisson distribution σ²=100

We need to find an interval that will include at least 5/9 of the sample values.

We have the Mean of the Poisson distribution λ=100

The variance of the Poisson distribution is σ²=100

The standard deviation of the Poisson distribution is σ =√100=10

Now, consider Tchebysheff’s rule:

Let X be a random variable with finite expected value and finite non-zero variance then for any real number k > 0,

Pr(|X-μ|≥kσ)=≤1/k².

1-1/k²=5/9

1-5/9=1/k²

4/9=1/k²

k²=9/4

k=1.5

So the interval contains all the values within 1.5 standard deviations from the mean:

μ±1.5(σ)

100±1.5(10)

100±10

(85,115).

Hence, The interval is (85, 115).

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Pls help

I will give 65 points for the first person to answer my question.

Thank you!

Answers

first off let's check how much is 5% of hmmm say "x"

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of x}}{\left( \cfrac{5}{100} \right)x}\implies 0.05x[/tex]

so if we increase "x" by that much, that's just "x + 0.05x" = 1.05x.  Now, let's find how much is 5% of that

[tex]\stackrel{\textit{5\% of 1.05x}}{\left( \cfrac{5}{100} \right)1.05x}\implies (0.05)(1.05x)\implies 0.0525x \\\\\\ \stackrel{\textit{now let's add that, to 1.05x}}{1.05x~~ + ~~0.0525x}\implies 1.1025x[/tex]

so our "x" went up by 0.1025x, now let's conver that to a percent, 0.1025 * 100 = 10.25%.

Can somebody help me please

Answers

93,101,109,117,125,133,141,149,157,165

93,101,109,117,125,133,141,149,157,165. The ratio is +8 (:

can someone tell me how i find answer for this problem?

Answers

Answer:

  P(x) = x²(x +1)(x -2)²

Step-by-step explanation:

You want the 5th degree polynomial with leading coefficient 1 that has roots of 0 and 3, each with multiplicity 2, and a root of -1.

Factors

You recall that a polynomial with root p has (x -p) as a factor. A root that is repeated m times has multiplicity m.

You recall that an exponent is used to signify the number of times a factor is repeated.

The factored form of P(x) is then ...

  P(x) = (x -2)²(x -0)²(x -(-1)) . . . . . roots 2 and 0 repeated twice, root -1

  P(x) = x²(x +1)(x -2)²

__

Additional comment

If you like, you can multiply it out and collect terms. The result will be ...

  P(x) = x⁵ -3x⁴ +4x²

after five years of owning a roth individual retirement account (ira), a person wants to buy his first home, the person can withdraw money from the roth ira

Answers

A person who has owned a Roth IRA for five years may withdraw money from the account to buy their first home. The individual has to meet certain requirements and can't withdraw more than $10,000 per person.

A Roth IRA is a type of individual retirement account that allows for tax-free withdrawals of contributions at any time, without penalty or taxes. After five years of ownership, a person who has a Roth IRA may withdraw money from the account to buy their first home. This withdrawal is known as a "first-time homebuyer distribution."

However, there are certain rules and limitations to be aware of when withdrawing money from a Roth IRA for a first home purchase. The individual must be a first-time homebuyer, defined as someone who has not owned a home in the past two years. Additionally, the maximum amount that can be withdrawn for a first home purchase is $10,000 per person.

It's important to note that while contributions to a Roth IRA can be withdrawn tax-free and without penalty, earnings on those contributions may be subject to taxes and penalties if withdrawn before age 59 and a half.

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Write the correct domain and range of the relation. {(-4,-4),(-1,3),(0,5),(3,9)}

Answers

Answer:

domain: {-4, -1, 0, 3}range: {-4, 3, 5, 9}

Step-by-step explanation:

You want the domain and range of the relation {(-4,-4),(-1,3),(0,5),(3,9)}.

Domain

The domain is the set of first numbers of the ordered pairs:

  {-4, -1, 0, 3}

Range

The range is the set of second numbers of the ordered pairs:

  {-4, 3, 5, 9}

Answer:

Domain: {-4, -1, 0, 3}

Range: {-4, 3, 5, 9}

Step-by-step explanation:

The Domain is the number that is on the x-axis.

The Range is the number on the y-axis.

Its quite simple. Hope this HELPED! HAVE A GOOD DAY AND NIGHT!!!!!!!!!!

what is 8 1/6-3 7/12​

Answers

Answer: 4 7/12

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{8\dfrac{1}{6} - 3 \dfrac{7}{12}}[/tex]

[tex]\mathsf{= \dfrac{8\times6 + 1}{6} - \dfrac{3\times12 + 7}{12}}[/tex]

[tex]\mathsf{= \dfrac{48 + 1}{6} - \dfrac{36 + 7}{12}}[/tex]

[tex]\mathsf{= \dfrac{49}{6} - \dfrac{43}{12}}[/tex]

[tex]\mathsf{= \dfrac{49}{6}\times\dfrac{2}{2} - \dfrac{43}{12}\times\dfrac{1}{1}}[/tex]

[tex]\mathsf{= \dfrac{49\times2}{6\times2} - \dfrac{43\times1}{12\times1}}[/tex]

[tex]\mathsf{= \dfrac{98}{12} - \dfrac{43}{12}}[/tex]

[tex]\mathsf{= \dfrac{98 - 43}{12 - 0}}[/tex]

[tex]\mathsf{= \dfrac{55}{12}\rightarrow 4\dfrac{7}{12}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{4\dfrac{7}{12}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

find p if (p, 2p+1) is solution of 11x-2y=5​

Answers

Answer:

p = 1

Step-by-step explanation:

since (p, 2p + 1) is a solution then it makes the equation true.

substitute x = p and y = 2p + 1 into the equation and solve for p

11p - 2(2p + 1) = 5 ← distribute parenthesis and simplify left side

11p - 4p - 2 = 5

7p - 2 = 5 ( add 2 to both sides )

7p = 7 ( divide both sides by 7 )

p = 1

At a music store, Rita got a $12 discount on an item originally priced at $48. What percent discount did she get?

Answers

Answer:

a $12 discount like what is it soupoust to be

Urgent!! Not sure what the right answer is, I know it’s not B. Or C.

Answers

Option C) The given set of data is distributed as 3,3,5,4,3,2, 5,6,5 ther are 2 peeks showing that the data si bimodally distributed.

What is distribution ?

A function called data distribution identifies all potential values for a variable and assesses its relative frequency (probability of how often they occur). Any population with dispersed data is referred to as a distribution.

Being monomodal refers to having a one mode. In mathematics, unimodality more broadly refers to the existence of only one greatest value that is somehow specified.

Two modes comprise a bimodal distribution. In other words, two processes with distinct distributions' results are combined into a single collection of data. The distribution sometimes goes by the name "double-peaked." For instance, consider the distribution of data for two production shifts in a manufacturing facility.

The given set of data is distributed as 3,3,5,4,3,2, 5,6,5 ther are 2 peeks showing that the data si bimodally distributed.

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determine each length in right triangle . right triangle abc with right angle at vertex b. point d lies on side ac. dashed segment bd is drawn. angles

Answers

Using the Pythagorean theorem and the Law of Cosines, we can solve for the lengths of each side in right triangle ABC.

The right triangle ABC with right angle at vertex B can be solved using the Pythagorean theorem. The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.

We can determine the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can determine that side BC is equal to the length of side AB. This means that the length of side AB is equal to the square root of the square of side AC. The length of side AC can be determined by finding the length of the dashed segment BD.

To find the length of dashed segment BD, we can use the Law of Cosines. The Law of Cosines states that in any triangle, the square of the length of a side is equal to the sum of the squares of the other two sides minus twice the product of the other two sides multiplied by the cosine of the angle opposite the side. In this case, we are finding the length of side BD. We can use the angle ABC and side AC to solve for the length of side BD.

Therefore, using the Pythagorean theorem and the Law of Cosines, we can solve for the lengths of each side in right triangle ABC.

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b2 = 3, h = 3, and A = 12 b1= 7.2 5 9

Answers

The length of b1 is given as follows:

b1 = 5 units.

How to obtain the area of a trapezoid?

The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.

For the trapezoid in this problem, the parameters are given as follows:

Bases 3 and b1.Height of 3.Area of 12.

Hence the length of b1 is obtained as follows:

3(3 + b1)/2 = 12

9 + 3b1 = 24

3b1 = 15

b1 = 15/3

b1 = 5 units.

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You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $85.00, two for $83.00 each, and in general the group rate per room is found by taking $2 off the base of $85 for each extra room rented.

(c) Find a formula for a function R = R(n) that gives the total revenue from renting rooms to a convention host.
(d) Use functional notation to show the total revenue from renting a block of 9 rooms to a group. Calculate the value.

Answers

The formula for a function R = R(n) is R(n) = n(85 - 2n) and the total revenue for 9 room is $603

How to determine the formula for a function R = R(n)

From the question, we have the following parameters that can be used in our computation:

Base fee = $85.00

Rate = $2 off

Using the above as a guide, we have the following:

R(n) = n(85 - 2n)

Where n is the number of rooms

The value of block of 9 rooms

This means that

n = 9

So, the notation is

R(9)

The value is

R(9) = 9 *(85 - 2 * 9)\

R(9) = 603

Hence, the value is $603

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The graph below is the function f(x)

Answers

The required answers are:

lim f(x) = -1

1-2-

lim f(x) = -1

1+2+

lim f(x) = -3

r2

f(2) = -3

How to solve this

Given image has a graph of the function f(x)

To find [tex]\lim_{x\rightarrow 2^-}f(x), lim f(2) 12+, lim f(x) 12 and f(2)[/tex]

We have from the image of the graph the function f(x) is a discontinuous function with x=2 is the point of discontinuity.

Now from the graph the value of f(x) at x=2 i.e. f(2) = -3 as the graph has a bold dot at y=-3.

Next [tex]\lim_{x\rightarrow 2^-}f(x)=\lim_{x\rightarrow 2^+}f(x)=-1[/tex] as in the graph of f(x) it has a small circle at y = -1.

As f(2) = -3 so [tex]\lim_{x\rightarrow 2}f(x)=f(2)=-3[/tex]

Thus the required answers are

lim f(x) = -1

1-2-

lim f(x) = -1

1+2+

lim f(x) = -3

r2

f(2) = -3

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4 divided by 2 left square brackets 2 plus 2 right square brackets equals?

Answers

The given expression "4 divided by 2 left square brackets 2 plus 2 right square brackets equals" gives the solution one divided by 2.

How to solve expressions?

4 divided by 2 left square brackets 2 plus 2 right square brackets equals?

4 ÷ 2(2 + 2)

based on the concept of PEMDAS

P = parenthesis

E = Exponent

M = Multiplication

D = Division

A = Addition

S = Subtraction

= 4 ÷ 2(4)

= 4 ÷ 8

= 4/8

= 1/2

Therefore, the correct answer is 1/2(one divided by two

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Which elements listed below are required for an inverse trig problem to find a missing angle?
*check all that apply
A right triangle
The length of at least one side
The measure of at least one angle
The length of at least 2 sides

Answers

The elements listed above that are required for an inverse trig problem to find a missing angle include the following:

A. A right triangle.

D. The length of at least 2 sides.

What is a right angle?

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Generally speaking, the length of at least two (2) sides is an element that is required for an inverse trig problem in order to find a missing angle in a right angled triangle.

In conclusion, both a right triangle and the length of at least two (2) sides must be provided in order to find a missing angle in a right angled triangle.

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If 80% of a number is 560, what will be 70% of that number?

Answers

Answer:

490

Step-by-step explanation:

80/100×the total number= 560

solved for the total number Which is equal 700

700×70% = 490

ax-b=4 if a≠0
please help immeditatlyl
jfasjflsajdflskadjfsadfsadf

Answers

Answer:

Graphical form: Ax-b=4 simplifies to Ax-b-4=0

Text form: Ax-b=4 simplifies to Ax-b-4=0

Cartoon (animation) form: simplify_cartoon%28+Ax-b=4+%29

For tutors: simplify_cartoon( Ax-b=4 )

Step-by-step explanation:

The population growth rate due to the difference in births and deaths in the U.S. is estimated to
be 0.5% per year. Given a 2001 population size of about 285 million, calculate the projected
population size in 2025. Use the exponential growth equation (N= No e"), to calculate the
population. In the equation, No is the initial population (285,000,000), r is the growth rate expressed as a
decimal (0.005), t is the number of years (25), e is a constant (defined as the base of the natural
logarithm), and N, is the population after t years.

Answers

In 2025, we would have  321 million people Since we do have an exponential growth function here.

What is exponential growth?

Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current value. In mathematical terms, it can be expressed as y = ab^x.

We then have that;

P = Poe^rt

P = population at time t

Po = Initial population

r = rate of growth

t = time taken

Then;

t = 24 years

r = 0.005

Thus;

P = 285 * 10^6e^24 * 0.005

P = 321 million people

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I’m a lil bit confused please help

Answers

Answer:

5000

Step-by-step explanation:

10×16=160

160 Btu?

is 5000

because the closesd value in the graph is 5000

for 160

A mapping diagram represents a relationship that contains three different input values and four different output values. Is the relationship a function

Answers

The relationship is not a function.

What is Function?

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given that,

A mapping diagram represents a relationship that contains three different input values and four different output values.

Let A be the set of input values and B be the set of output values.

Number of elements in A = 3

Number of elements in B = 4

This means that 3 elements in A has four elements as image in B.

Thus, an element in A must have two different images in B.

But by the definition of functions, there can't be more than one image for an element in set A.

Hence the given relationship is not a function.

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Zachary purchased a computer for $1,300 on a payment plan. Two months after he purchased the computer, his balance was $1,090. Seven months after he purchased the computer, his balance was $565. What is an equation that models the balance y after x months?
The equation ______ models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)

Answers

Answer:

[tex]y=-105x+1300[/tex]

Step-by-step explanation:

Define the variables:

Let x be the number of months after Zachary purchased a computer.Let y be the balance of the payment plan (in dollars).

Given information:

Purchase price of the computer = $1,300Balance = $1,090 after 2 months.Balance = $565 after 7 months.

Therefore:

x = 0, y = 1300x = 2, y = 1090x = 7, y = 565

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Determine if the equation is linear by calculating the slope between each pair of (x, y) points:

[tex]\implies \text{Slope}\;(m)=\dfrac{565-1090}{7-2}=-105[/tex]

[tex]\implies \text{Slope}\;(m)=\dfrac{1090-1300}{2-0}=-105[/tex]

As the slope is the same, the equation is linear.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The initial purchase price of the computer was $1,300. So when x = 0, y = 1300.  Therefore, the y-intercept is 1300.  

We have already calculated the slope as -105.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:

[tex]y=-105x+1300[/tex]

64. Use a graph to estimate the critical numbers of f(x)=| x^3-3x^2+2| correct to one decimal place.

Answers

The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = | x³ -3x² + 2|

Now, We know that;

⇒ All the critical points are find as;

⇒ f '(x) = 0

⇒ 3x² - 6x = 0

⇒ 3x(x - 2) = 0

⇒ x = 0

⇒ x = 2

Thus, The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.

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The table represents a linear function. What is the slope of the function?
-2 8
-1 2
0 -4
1 -10
2 -16

Answers

The answer is -6.,  is the slope of the function.

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

In order to determine the slope of the function, we have to know about linear function.

In any linear function, we can get its slope using two pairs of coordinates that belong to the linear function.

m=Slope of the linear function.

P1=(x1,y1)=First pair of coordinate.

P2=(x2,y2)=Second pair of coordinate.

In this case, we have many pairs of coordinates, so we choose two of them:

P_1=(-2,8)

P_2=(0,-4)

Then, we replace them in the slope formula:

m = y2-y1/x2-x1

   = -6

Finally, the slope of the function is -6.

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Which three criteria do binomial experiments meet? There are only two trials. The trials are independent. There are only two outcomes per trial. Each outcome is repeatable. The probability of success is the same for each trial.

Answers

The three criteria that binomial experiments meet are :

The trials are independent. There are only two outcomes per trial. The probability of success is the same for each trial.

What criteria should binomial experiments meet ?

The experiment is referred to as a binomial experiment since there are only two possible output values in a binomial experiment. In the case of binomial experiments, the number of independence variables is fixed.

In the case of binomial experiments, the number of independence variables is fixed. The total number of output values for the binomial experiment is 2. For the binomial experiment, each of the two outputs has a 50% chance of happening—50% for success and 50% for failure.

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Answer:

B. The trials are independent.

C. There are only two outcomes per trial.

E. The probability of success is the same for each trial.

Step-by-step explanation:

and then

B. a survey asking 50 people if they like pizza

C. a survey measuring 50 people to see if they are over 6 feet tall

On the defense of a football team,there are three types of players on the field.What is the probability of picking each type of player at random out of the 11 players

Answers

Answer: The probability of picking each type of player at random depends on the number of players of each type on the field. If the number of players of each type is not specified, it is not possible to determine the probability of picking each type of player at random.

Step-by-step explanation:

What is the sum of the measures of the exterior angles of any convex polygon?
A.90
B.180
C.360
D.720

Answers

Answer:

360

Step-by-step explanation:

If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360°

hope dis helpsssssss

Find the amount of tax and the tax rate. Round to two decimal places
Cost of item: $126
Selling price: $133.36
Tax amount: $
Tax rate:

Answers

Answer:

Tax amount: $7.36

Tax rate: 5.84%

Step-by-step explanation:

First, we have to find the tax amount by taking

$133.36 - $126 = $7.36

Tax amount: $7.36

To find the tax rate, we take

7.36 divided by 126, times 100 = 5.84%

Tax rate: 5.84%

So,

Tax amount: $7.36

Tax rate: 5.84%

What is the equation of the function that is graphed as line a?



y = 4 x - 3
y = - 1/4 x + 3
y = 1/4x + 3
y = -4 x - 3

Answers

Answer:

y = 4x - 3

Step-by-step explanation:

y = mx + b

The m is the slope and the b is the y-intercept.

The slope is 4.  If you start at the point (0,-3) and go up 4 units and then 1 unit to the right, you will be back on the line at point (2,4) The slope is the rise over the run.  The rise is 4 and the run is 1.  4/1 = 4.

The slope (m) is 4.

The y-intercept is where the line crosses the y axis.  It crosses at (0,-3)

The y-intercept (b) is -3

Plug 4 in for m and -3 in for b

y = mx + b

y = 4x -3

Answer:

[tex]y = 4x - 3[/tex]

Step-by-step explanation:

we need to find out the equation of the function that is graphed. From the given graph we can see that the line passes through points (0,-3) and (2,5) . So we can find out the slope of the line as ,

[tex]\implies m =\dfrac{y_2-y_2}{x_2-x_1}=\tan\theta\\[/tex]

[tex]\implies m =\dfrac{-3-5}{0-2} \\[/tex]

[tex]\implies m =\dfrac{-8}{-2} \\[/tex]

[tex]\implies \mathfrak{ m = 4 }\\[/tex]

Now we may use point slope form of the line to find out the equation of the line as,

[tex]\implies y - y_1 = m(x-x_1) \\[/tex]

[tex]\implies y -(-3) = 4(x-0) \\[/tex]

[tex]\implies y +3 = 4x\\[/tex]

[tex]\implies \underline{\underline{ y = 4x -3}} \\[/tex]

And we are done!

-TσηγSтαяκ

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