Use complete sentences to explain the process you would use to find the volume of the shipping box.(Trying to help my son with this)
Answers
Part A)
The given shipping box is a cuboid.
Recall that the longest length of the cuboid is diagonal.
The length of the longest item that fits inside the shipping box is the measure of the diagonal of the given box.
Given that measure breadth=16 inches and measure height = 12 inches.
Recall the formula for the diagonal d of the cuboid is
[tex]d=\sqrt[]{l^2+b^2+h^2}[/tex]We need to find the measure of the length of the cuboid.
Consider the base of the cuboid which is in rectangle shape.
Here breadth of the rectangle is 16 inches and diagonal of the rectangle is 24 inches.
Recall the formula for the diagonal of the rectangle is
[tex]diagonal_{}=\sqrt[]{l^2+b^2}[/tex]Substitute diagonal =24 inches and breath =16 inches, we get
[tex]24_{}=\sqrt[]{l^2+16^2}[/tex][tex]24_{}=\sqrt[]{l^2+256}[/tex]Taking square on both sides, we get
[tex]24^2_{}=l^2+256[/tex][tex]576-256=l^2[/tex][tex]320=l^2[/tex]Taking square root on both sides, we get
[tex]\sqrt[]{320}=l[/tex][tex]l=17.89\text{ inches}[/tex]Now, substitute l=17.89, b=16, and h=12 in the diagonal of the cuboid equation to find the diagonal of the cuboid.
[tex]d^{}=\sqrt[]{17.89^2+16^2+12^2}[/tex][tex]d^{}=\sqrt[]{320+256+144}=\sqrt[]{720}=26.83\text{ inches}[/tex]Hence the length of the longest item that fits inside the shipping box is 26.8 inches.
Part B)
Consider the length l=17.89 inches, b=16 inches, and height h=12 inches.
Recall the formula for the volume of the cuboid is
[tex]V=l\times w\times h[/tex]Substitute the length l=17.89 inches, b=16 inches, and height h=12 inches, we get
[tex]V=17.89\times16\times12[/tex][tex]V=3434.88inches^3[/tex]Hence the volume of the given shipping box is 3434.88 cubic inches.
Related Questions
Multiplying Polynomials 5y[tex] ({5y}^{2} + y + 3)(x - 2)[/tex]
Answers
Let's distribute those factors, and expand this:
[tex]\begin{gathered} (5y^2+y+3)\mleft(x-2\mright) \\ 5xy^2-10y^2+xy-2y+3x-6 \\ \end{gathered}[/tex]There's no further way beyond that. Either we pick the factored form or the expanded version of that polynomial. As this is not an equation we stop it here.
what is the x intercepts or zeros for y = x^2 - 6x + 5
Answers
Solution:
Given;
[tex]y=x^2-6x+5[/tex]The x-intercepts are the points where y=0.
Thus;
[tex]x^2-6x+5=0[/tex]Thus;
[tex]\begin{gathered} x^2-x-5x+5=0 \\ \\ x(x-1)-5(x-1)=0 \\ \\ x-1=0,x-5=0 \\ \\ x=1,x=5 \end{gathered}[/tex]ANSWER:
[tex]x=1,x=5[/tex]For which equation would x = 12 be a solution?x - 12 = 12x - 24 = 12x - 14 = 2x - 5 = 7
Answers
Explanation
We are required to solve each equation till we arrive at the one that satisfies the "x=12" question.
First equation:
[tex]\begin{gathered} x-12=12 \\ Collect\text{ like terms} \\ x=12+12 \\ x=24 \end{gathered}[/tex]Second equation:
[tex]\begin{gathered} x-24=12 \\ Collect\text{ like terms} \\ x=12+24 \\ x=36 \end{gathered}[/tex]Third equation:
[tex]\begin{gathered} x-14=2 \\ Collect\text{ like terms} \\ x=2+14 \\ x=16 \end{gathered}[/tex]Last equation:
[tex]\begin{gathered} x-5=7 \\ Collect\text{ like terms} \\ x=7+5 \\ x=12 \end{gathered}[/tex]Hence, the last equation is the solution.
Given a polyhedron with 6 vertices and 12 edges, how many faces does it have?
Answers
SOLUTION
GIVEN
A polyhedron has 6 vertices and 12 edges.
TO DETERMINE
The number of faces
CONCEPT TO BE IMPLEMENTED
Euler’s formula for Polyhedron :
For polyhedron F + V = E + 2
Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .
EVALUATION
Here it is given that a polyhedron has 6 vertices and 12 edges
V = Number of vertices = 6
E = Number of edges = 12
F = Number of faces = ?
By Euler’s formula
F + V = E + 2
⇒ F + 6 = 12 + 2
⇒ F + 6 = 14
⇒ F = 8
FINAL ANSWER
The number of faces = 8
Slope The first two sets of points are 9,-24 and 13,-21
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We need to find the slope using the points (9, -24) and (13 , -21)
so, the slope = 3/4
Do the data in the table you made support the notion the arch is not a parabola? Explain why.
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The parabola that has the height and width similar to the Gateway arc, gives;
(a) The quadratic equation of the parabola is presented as follows;
[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]
(b) The completed table is presented as follows;
Width. Height
567. 63.12
478. 225.67
308. 459.2
What is the shape of the graph of a quadratic function?The shape of a quadratic function is a parabola, which is either upward facing or downward facing
(a) The given dimensions of the arc are;
Height = 625
Width at the base = 598
The points on the parabola are therefore;
(0, 0), (598÷2, 625) = (299, 625), (598, 0)
The equation of the parabola is of the form;
f(x) = a•x² + b•x + c, which gives;
f(0) = 0 = a×0² + b×0 + c = c
c = 0
f(299) = 625 = a×299² + b×299 + 0...(1)
f(598) = 0 = a×598² + b×598...(2
(a×598² + b×598) - 2×(a×299² + b×299) = 0 - 2×625
a•178802 = -2×625
a = -2×625 ÷ 178802
a ≈ -6.991 × 10^(-3)
b ≈ 4.181.
The equation is therefore;
[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]
(b)
The table of values is completed as follows;
When the width is 567 feet, x = 299 - 567÷2 = 15.5
[tex] \displaystyle{f(15.5) = -6.991 × 10^{-3} \times 15.5² + 4.181 \times 15.5 approx 63.12} [/tex]
When the width is 478 feet, x = 299 - 478÷2 = 60
[tex] \displaystyle{f(60) = -6.991 × 10^{-3} \times 60² + 4.181 \times 60 approx 225.67} [/tex]
When the width is 308 feet, x = 299 - 308÷2 = 145
[tex] \displaystyle{f(145) = -6.991 × 10^{-3} \times 145² + 4.181 \times 145 approx 459.2} [/tex]
The table is therefore presented as follows;
Width. Height
567. 63.12
478. 225.67
308. 459.2
Learn more about the equation of a parabola in mathematics here;
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Please help me solve this using six grade math (easy formulas)
Answers
We will break the surface area of the tent up into its sides, the front and the back and the bottom.
Area of the sides: 2(5*7) = 70
Area of the front and the back: 2( 1/2 (6*4)) = 24
Area of the bottom: 7*6 = 42
Least amount of fabric required = 136ft
Floyd is an aspiring music artist. He has arecord contract that pays him a base rate of$200 a month and an additional $12 for eachalbum that he sells. Last month he earned atotal of $644.Write an equation to determine the numberof albums (a) Floyd sold last month.Find the number of albums Floyd sold lastmonth.albums
Answers
Explanation:
Equate the given data to solve for x.
$200 + $12x = $644.
To determine the number of albums sold, Let x be the number of album sold by Floyd last month.
200 + 12x = 644
12x =644-200
12x = 444
x = 444/12
x= 37.
Floyd has sold 37 albums last month.
Answer:
The equation to determine the number of albums Floyd sold last month is 200+12x = 644.
and the number of album Floyd sold last month is 37.
First drop down menu A. 2 B. 4 C. 8 Second drop down main choices A.30 B. 120 C. 60
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the question, it takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box that holds 15 cups of sugar.
If we double the dimensions of the box,
it means that the scale factor will be 2.
Hence, the area factor will be:
[tex]2^2=\text{ 2 x 2 = 4}[/tex]Part A:
The new box would require 4 oz -- ( OPTION B)
of paint to cover with the paint.
Part B:
Given the scale factor is 2,
Then the area factor is 2 x 2 = 4,
Then the volume factor is 2 x 2 x 2 = 8 times
Recall that:
The rectangular prism box holds 15 cups of sugar,
Then the new box would hold ( 15 x 8 = 120 cups of sugar ) --OPTION B
Find the cube roots of 4−6i4−6iShow all your work.Include an explanation and diagram showing how DeMoivre's Theorem helps to solve this problem.
Answers
Given the following complex number
[tex]z=4-6i[/tex]We will find the cube root of the complex number using the following formula:
[tex]^3\sqrt{z}=\sqrt[3]{|z|}*(cos\text{ }\frac{\theta+2\pi k}{3}+i*sin\text{ }\frac{\theta+2\pi k}{3})[/tex]The formula is called De Moivre's theorem of the nth root
We have substituted n = 3
So, first, we will convert the given number from the rectangular form to the polar form
[tex]\begin{gathered} |z|=\sqrt{4^2+6^2}\approx7.211 \\ \theta=tan^{-1}\frac{-6}{4}=303.7\degree \end{gathered}[/tex]Substitute the magnitude and the angle and k = 0, 1, 2
So, there are 3 cubic roots of the given number as follows:
[tex]\begin{gathered} k=0\rightarrow z_1=\sqrt[3]{7.211}(cos\frac{303.7}{3}+i*sin\frac{303.7}{3})=1.932(cos101.23+i*sin101.23) \\ \\ k=1\rightarrow z_2=\sqrt[3]{7.211}(cos\frac{303.7+2\pi}{3}+i*sin\frac{303.7+2\pi}{3})=1.932(cos221.23+i*sin221.23) \\ \\ k=2\rightarrow z_3=\sqrt[3]{7.211}(cos\frac{303.7+4\pi}{3}+i*sin\frac{303.7+4\pi}{3})=1.932(cos341.23+i*sin341.23) \end{gathered}[/tex]Solve the system of two inequalities.y<6y≥-4Same format as the question below. Only the inequality is changed.
Answers
Given the system of inequalities:
[tex]\begin{cases}y<6 \\ y\ge-4\end{cases}[/tex]First Inequality: y<6
• The inequality sign is <, therefore, the ,type of boundary line is Dashed.
The equation of the boundary line is y=6. Therefore:
• Two points on the boundary line are: (0, 6) and (2, 6)
The region below the line will be shaded.
Second Inequality: y≥-4
• The inequality sign is ≥, therefore, the ,type of boundary line is Solid.
The equation of the boundary line is y=-4. Therefore:
• Two points on the boundary line are: (0, -4) and (2, -4)
The region above the line will be shaded.
The graph is attached below:
7-Which beans are the better deal? Kidney Beans $1.18 per lb O Lima Beans $213 for 2 lbs 76-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
Answers
Given :
Two kinds of Beans :
1. Kidney Beans $1.18 per lb
The unit price = $1.18
2. O Lima Beans $213 for 2 lbs
The unit price = 2.13/2 = 1.065
Rounding to the nearest hundredth
So,
The unit
1) A submarine is 84 feet below the surface of the water and descends 10 feet deeper every minute. How many minutes will it take for the submarine to be located 219 feet below the surface? Write and solve an equation.
Answers
Answer
The equation for this question is
84 + 10x = 219
The number of minutes it'll take the submarine to reach 219 feet is 13.5 minutes
Explanation
Let the number of minutes it will take the submarine to reach 219 feet below the surface be x minutes.
The number of feet the submarine reaches in x minutes = (10x) feet
Since the submarine started from 84 feet, in x minutes, it would have reached a depth of
(84 + 10x) feet
This is equal to 219 feet
84 + 10x = 219
Subtract 84 from both sides
84 + 10x - 84 = 219 - 84
10x = 135
Divide both sides by 10
(10x/10) = (135/10)
x = 13.5 minutes
Hope this Helps!!!
If 40% of the selling price of eight $65 sweater is profit then how much money profit does the store make when the sweater is sold
Answers
Remember that 40%=0.4.
Per sweater, the profit is
[tex]65\cdot0.4=26[/tex]$26 of profit per sweater.
Finally, for the eight sweaters, the total profit is
[tex]26\cdot8=208[/tex]$208 is the profit for 8 sweaters
suppose that the time required to complete a 1040r tax form is normally distributed with a mean of 100 minutes and a standard deviation of 15 minutes. what proportion of 1040r tax forms will be completed in less than 77 minutes? round your answer to at least four decimal places.
Answers
The proportion of 1040r tax forms completed in less than 77 minutes = 0.06301
How to find the proportion of the tax forms?
The time required to complete a 1040r tax form = normally distributed
Mean = [tex]\mu[/tex] = 100 minutes
Standard deviation = [tex]\sigma[/tex] = 15 minutes
The proportion of 1040r tax forms completed in less than 77 minutes is given by ,
P( X< 77 ) = P ( Z < [tex]\frac{77-100}{15}[/tex] )
= P( Z < - 1.53 )
=0.06301
Cumulative probability in the normal distribution =0.06301 or 6.301%
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.The natural and social sciences frequently utilize normal distributions to describe real-valued random variables whose distributions are unknown, which is why normal distributions are essential in statistics. Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the normal distribution.A bell curve is another name for a normal distribution.To learn more about normal distribution, refer:
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A tennis racket cost 12$ more than a hockey stick , if the price of the two is 31$ find the cost of a tennis racket
Answers
So $31 - 12 = 19
19 / 2 = 9.5
So 9.5 is the cost of the hockey stick, now lets find the cost of the racket
$9.5 + 12 = 21.5
Therefore the cost of the tennis racket is $21.5
Use the triangle to answer the question.Find the sine of angle Y.
Answers
In a right triangle, given an angle, the ratio between the opposite side of this angle by the hypotenuse is equal to the sine of the angle. Using this relation in our triangle, we have
[tex]\sin Y=\frac{6}{10}=\frac{3}{5}[/tex]Michael and his sister Mel share the job of mowing the grass in their yard. Michael mows ⅓ of the yard, and Mel mows the rest. Mel can mow ¾ of the entire yard in an hour.How long will it take Mel to finish mowing the yard?? Also after Michael mows 1/3 of the yard what fraction of the yard does mel need to mow?
Answers
Michael Mows = 1/3 of the yard
Mel mows the rest = 1-1/3 = 2/3 of the yard
Mel mows = 3/4 of the yard in an hour
After Michael mows 1/3 of the yard what fraction of the yard does Mel need to mow?
1- 1/3 = 2/3 of the yard
How long will it take Mel to finish mowing the yard??
2/3 / (3/4) = 8/9 hours = 0.89 hours
Which is an equivalent expression for 4 times d raised
to the negative third power all over quantity 18 times d
raised to the ninth power end quantity?
Answers
Answer:
2d⁻³/9d⁻⁹
Step-by-step explanation:
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
18 times d raised to the ninth power = (18 × d)⁻⁹ = 18d⁻⁹
the equation as a quotient:
Expression = 4d⁻³/18d⁻⁹
Expression = 2d⁻³/9d⁻⁹
Kacie is constructing the inscribed circle for △MNP. She constructed the angle bisectors of angle M and angle N and labeled the intersection of the bisectors as point A.Which construction is a correct next step for Kacie?Open the compass to the width of AM¯¯¯¯¯¯ and draw a circle centered at point A.Open the compass to the width of , A M ¯ , and draw a circle centered at point , A, .Construct the perpendicular bisector of AM¯¯¯¯¯¯ .Construct the perpendicular bisector of , A M ¯ , .Open the compass to the width of AP¯¯¯¯¯ and draw a circle centered at point A.Open the compass to the width of , A P ¯ , and draw a circle centered at point , A, .Construct the line that passes through point A and is perpendicular to NP¯¯¯¯¯¯ .
Answers
From the statement, we know that:
• Kacie is constructing the inscribed circle for △MNP,
,• she constructed the angle bisectors of angle M and angle N,
• and labelled the intersection of the bisectors as point A.
(1) Now, Kacy must construct a perpendicular from the centre point to one side of the triangle.
(2) After this, she must place the compass on the centre point while adjusting its length to the point where the perpendicular crosses the triangle.
(3) Finally, she must draw the inscribed circle.
So the answer is that Kacy must construct the perpendicular bisector of AM.
AnswerConstruct the perpendicular bisector of AM
Subtract these polynomials.
(3x + 2x + 4) (x + 2x+ 1) =
Answers
=(3x2 + 2x + 4) - (x2 + 2x + 1)
Combine like terms
=(3x2-x2)+(2x-2x)+(4-1)
=2x2+0+3
The 2x terms cancel each other to 0
=2x2+3
C) 2x2+3 is the answer.
Hope this helps!
Answer:
15x^2+17x+4
Step-by-step explanation:
(3x+2x+4)(x+2x+1)
Combine 3x and 2x to get 5x.
(5x+4)(x+2x+1)
Combine x and 2x to get 3x.
(5x+4)(3x+1)
Apply the distributive property by multiplying each term of 5x+4 by each term of 3x+1.
15x ^2+5x+12x+4
Combine 5x and 12x to get 17x.
15x^2+17x+4
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Find the length of arc CD. Use 3.14for tt. Round to the nearest tenth.h 7.9 cm66.40D[? ]cm
Answers
For this problem we know that the radius is 7.9cm and the angle between C and D is 66.4ª. We also want to find the arclenght so we can use the following formula:
[tex]AL=\frac{x}{360}\cdot2\pi r[/tex]Where x is the angle and r the radius r=7.9cm. So then replacing into the function we got:
[tex]AL=\frac{66.4}{360}\cdot2\pi(7.9cm)=9.16\operatorname{cm}[/tex]And if we round to the nearest tenth we got 9.2 cm
Evaluate 4w - 3y if w = 7 and y = 6
Answers
Answer:
10
Explanation:
Given the expression:
[tex]4w-3y[/tex]If w=7 and y=6
[tex]\begin{gathered} 4w-3y=4(7)-3(6) \\ =28-18 \\ =10 \end{gathered}[/tex]The value of the expression is 10.
Im in algebra 2 but we are also learning geometry the question asks to find the length of each arc
Answers
The length of the arc = 8π/3 mi
Explanation:The length of an arc is given by the fomula:
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]The radius, r = 8 ml
[tex]\theta=60^0[/tex][tex]\begin{gathered} L=\frac{60}{360}\times2\pi\times8 \\ \\ L=\frac{16\pi}{6} \\ \\ L=\frac{8\pi}{3} \end{gathered}[/tex]The length of the arc = 8π/3 mi
50% of $277 is $144True or False
Answers
Answer:
FALSE
Explanation:
Given the expression
50% of $277
This can also be written as;
= 50/100 * 277
= 1/2 * 277
= 277/2
= 138.5
Therefore 50% of $277 is $138.5 not $144 rendering the question FALSE
Translate the description below as an algebraic expression:The product of v and the difference of c and 10
Answers
We have to translate the expression "The product of v and the difference of c and 10".
We know that the expression is a product of two factors: v and a difference. The difference is between the terms c and 10, so it can be written as (c-10).
Then, the product can be written as:
[tex]v\cdot(c-10)[/tex]Answer: the expression is v*(c-10)
(CO 6) Find the regression equation for the following data setx 245 187 198 189 176 266 210 255y 50 54 55 78 44 41 51 60cannot be determinedŷ = 74.17x – 0.09ŷ = -0.09x + 74.17ŷ = 0.09x – 74.17
Answers
Answer
ŷ = -0.09x + 74.17
Explanation
For the given data set:
x 245 187 198 189 176 266 210 255
y 50 54 55 78 44 41 51 60
The sum of x = 245 + 187 + 198 + 189 + 176 + 266 + 210 + 255 = 1726
The sum of y = 50 + 54 + 55 + 78 + 44 + 41 + 51 + 60 = 433
Mean x = 1726/8 = 215.75
Mean y = 433/8 = 54.125
Sum of squares (SSx) = 8391.5
Sum of products (SP) = -779.75
(Check the table below of the data for a better understanding).
The regression Equation is given by ŷ = bX + a
b = SP/SSx = -779.75/8391.5 = -0.09292
a = My - bMx = 54.13 - (-0.09 x 215.75) = 74.17279
Therefore, the regression equation for the data set is: ŷ = -0.09292x + 74.17279
The correct answer is ŷ = -0.09x + 74.17
while exploring a volcano zane heard somerumbling, so he decided to climb up out of there as quicklyas he could zane's elevation relative to the edge of the inside of the volcano (in meter) as a function time (in seconds) is graphed. PLEASE HELP ME WITH THIS How long did it take Zane to reach the edge of the volcano?
Answers
We have to find the time it took for Zane to be in the same elevation as the edge of the Volcano, that is, when his relative elevation is 0 on the graphic.
This happens at a time of 35 seconds. So:
It took Zane 35 seconds to reach the edge of the volcano.
Solve pls. I neeeeeeeeed your help.
Answers
Answer:
70 over 39
Step-by-step explanation:
here's the solution first multiple the numbers with the fraction then calculate after that simply the fractions and the answer is
[tex] \frac{70}{39} [/tex]
Find the volume of the top of the prism, volume of the bottom prism, and total volume of figure.
Answers
Volume of the top of the prism: 460 cm^3
Volume of the bottom of the prism: 1 768 cm^3
Total volume of the figure: 2 228 cm^3
Explanation:
Volume of the top of the prism:
. Since it is a prism from trapezoid
. . Volume = Area of the trapezium base * heights between trapezium ends
[tex]\begin{gathered} Area\text{ of a trapezium base}=\frac{top\text{ base+bottom base}}{2}*height \\ ...\text{ =}\frac{6+17}{2}*(22-17) \\ ...=\frac{23}{2}*5 \\ Area\text{ = 57.5 cm}^2 \end{gathered}[/tex][tex]Volume=57.5*8=460\text{ }cm^3[/tex]Volume of the bottom prism:
. Since the price has a rectangular base:
Volume = Area of one base * height between reactangular bases
Area of one base :
[tex]17*13=221\text{ }cm^2[/tex]Volume:
[tex]221*8=1\text{ }768\text{ }cm^3[/tex]Total volume of the figure:
Volume of the top + Volume of the bottom = Total volume
[tex]221+1\text{ }768=2\text{ }228\text{ }cm^3[/tex]NB:
To find any volume of a given prism, start with finding the area of one base, then multiply that area by the height (in other words the sides that link the two bases)