A theater wants to build movable steps that they can use to go on and off the stage. The dimesions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props. How much space is inside the steps?
Answers
Answer:
The total volume of the space inside the steps is 2880 cubic inches.
Step-by-step explanation:
Given : A theater wants to build movable steps that they can use to go on and off the stage. The dimensions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props.
To find : How much space is inside the steps?
Solution :
According to question,
The image form of store props is a prism split into two rectangular prism.
Refer the attached figure below.
The bottom portion of the steps having dimension [tex]16\times 20\times 6 in[/tex]
The volume of the bottom portion is
[tex]V=l\times b\times h\\V=16\times 20\times 6\\V=1920 in^3[/tex]
The top part have a width of 8 inches as entire width of bottom is 16 inches.
Length is 20 inches.
Height of the steps is 6 inches as total height is 12 inches.
The volume of the top part is
[tex]V=l\times b\times h\\V=20\times 8\times 6\\V=960 in^3[/tex]
So, the total volume of the space inside the steps is
1920+960 = 2880 cubic inches.
Therefore, The total volume of the space inside the steps is 2880 cubic inches.
Related Questions
Just need help finding X and Y
Answers
Answer:
x = 8 and y= 12Step-by-step explanation:
For x use the Pythagorean theorem:
[tex]x^2+6^2=10^2[/tex]
[tex]x^2+36=100[/tex] subtract 36 from both sides
[tex]x^2=64\to x=\sqrt{64}\\\\x=8[/tex]
We know: x + y = 20. Substitute:
[tex]8+y=20[/tex] subtract 8 from both sides
[tex]y=12[/tex]
Write the slope-intercept form of the equation that passes through the point (2, 3) and is parallel to the line y = 5/8x - 7
Answers
Answer: [tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]
Step-by-step explanation:
The slope-intercept form of a equation of the line is:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept-
If the lines are parallel then they have the same slope:
[tex]m=\frac{5}{8}[/tex]
You can find the value of b by substituting the point given and the slope into the equation and solving for b:
[tex]3=\frac{5}{8}*2+b\\b=\frac{7}{4}[[/tex]
Then the equation is:
[tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]
Answer:
[tex]y = \frac{5}{8} x+\frac{7}{4}[/tex]
Step-by-step explanation:
We are to write the slope intercept form of the equation which passes through the point (2, 3) and is parallel to the line [tex]y = \frac{5}{8} x-7[/tex].
We know that the standard (slope-intercept) form of an equation of a line is given by: [tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept.
Since we are to find the equation of the line parallel to the given equation so its slope will be same as of [tex]y = \frac{5}{8} x-7[/tex].
Finding the y-intercept:
[tex]y=mx+c[/tex]
[tex]3=\frac{5}{8}(2)+c[/tex]
[tex]c=\frac{7}{4}[/tex]
Therefore, the equation will be [tex]y = \frac{5}{8} x+\frac{7}{4}[/tex].
What is the graph of the function x^2-9x+20 over x-4
Answers
Answer:
a straight line: y = x -5, with a hole at (4, -1)
Step-by-step explanation:
The rational function can be simplified to ...
[tex]f(x)=\dfrac{x^2-9x+20}{x-4}=\dfrac{(x-5)(x-4)}{(x-4)}\\\\f(x)=x-5\qquad\text{$x\ne 4$}[/tex]
The graph of this is a straight line, with a hole at x=4, where the function is not defined.
Subtract 8 y^2 − 5 y + 7 from 2 y^2 + 7 y + 1 1
The answer is: −6y ^2 +12y+4
Answers
Answer:
[tex]\large\boxed{-6y^2+12y+4}[/tex]
Step-by-step explanation:
[tex](2y^2+7y+11)-(8y^2-5y+7)\\\\=2y^2+7y+11-8y^2-(-5y)-7\\\\=2y^2+7y+11-8y^2+5y-7\qquad\text{combine like terms}\\\\=(2y^2-8y^2)+(7y+5y)+(11-7)\\\\=-6y^2+12y+4[/tex]
Which statements describe one of the transformations performed on f(x)=x^2 to create g(x)=2(x+5)^2+5
Answers
Answer:
Translated to the left 5 units and up 5 units and compressed horizontally by 2 units.
Step-by-step explanation:
The parent function given is [tex]f(x)=x^2[/tex]
This function has its vertex at the origin.
If we move this function 5 units to the left and 5 units up, then its vertex will now be at [tex](-5,5)[/tex].
If the parent function is then compressed horizontal by a factor of 2, then the transformed function will now have equation.
[tex]g(x)=2(x+5)^2+5[/tex]
Choose the function whose graph is given by:
Answers
Answer:
y = tan(x -π) -1
Step-by-step explanation:
It looks like a straight tangent function shifted down one unit. Since the tangent function has a period of π, ...
tan(x -π) = tan(x)
so you're only looking for the function that has a translation downward of 1 unit. Of course that translation is accomplished by adding -1 to the original function.
The appearance of the graph is of ...
y = tan(x) -1
The choice that is equivalent to this is ...
y = tan(x -π) -1
Answer:
y = tan (x-pi)-1
Step-by-step explanation:
The function in the graph is a periodic function with intervals of pi and having discontinuities at regular intervals.
Hence this must be a transformation of the original trignometric funciton
tan x. y intercept is at -1 which shows that there is a vertical shift of 1 unit down.
Hence the funciton is y = tanx-1
But tan x is not given in any of the options.
Let us check which is equivalent to tan x-1
We find that tan(x-pi) = -tan (pi-x) = -(-tanx) = tanx
Hence the option 3 is the right answer
Kendall is buying a home for $119,000. She is making a 12% down payment and financing the rest with a 20-year loan at a 4.5% interest. What is her monthly mortgage payment?
Answers
Answer:
$455.97
Step-by-step explanation:
119000 × 0.12 = 14280
119000 - 14280 = 104720
104720 × 1.045 = 109432.4
109432.4/(20×12)
109432.4/240
455.97 a month
Answer:
$662.46
Step-by-step explanation:
PLEASE HELP !!ASAP
Write this equation in Standard Form:
y space equals space 6 over 5 x space plus space 2
6x + 5y = -10
6x + 5y = 2
6x – 5y = 2
6x – 5y = -10
which one is it???
Answers
Answer:
6x-5y=-10
Step-by-step explanation:
We are given an equation in words and we are to translate it and then re-write its standard form:
'y space equals space 6 over 5 x space plus space 2 '
[tex] y = \frac { 6 } { 5 } x + 2 [/tex]
Re-arranging this given equation to get:
[tex] y - 2 = \frac { 6 } { 5 } x [/tex]
[tex]5(y-2)=6x[/tex]
[tex]5y-10=6x[/tex]
[tex]6x-5y=-10[/tex]
So the correct answer option is 6x-5y=-10.
rational exponents: quotient rule
u^2/5 / u^1/2
Answers
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{u^{\frac{2}{5}}}{r^{\frac{1}{2}}}\implies \cfrac{1}{u^{\frac{1}{2}}\cdot u^{-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{1}{2}-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{5-4}{10}}}\implies \cfrac{1}{u^{\frac{1}{10}}}\implies u^{-\frac{1}{10}}[/tex]
What is the value of y? 3y^2 − 6 = 42
Answers
Hey there!
Let's start by adding 6 to both sides of the equation to eliminate the -6.
3y^2 = 48
Next, let's divide both sides by 3 to eliminate the 3.
y^2 = 16
Find the square root of both sides.
y = ±4
It can be both positive or negative 4 because -4 x -4 and 4 x 4 both equal 16.
The value of y is ±4.
Hope this helps!
Is (–2n)^4 = –8n^4? Choose the best explanation for why or why not.
A. Yes; –2 times 4 makes –8, and the n becomes n^4.
B. Yes; for n = 1, (-2n)^4 = -8 x 1 not equal to -8n^4
C. No; for values other than 0, (–2n)^4 = 16n^4 not equal to –8n^4.
D. No; the negative in front of the 2 means –2n^4 needs to become 1/2n^4
Answers
Answer:
The answer would be C
Final answer:
No, (-2n)⁴ is not equal to -8n⁴ because when -2 is raised to the fourth power, it results in a positive 16, making the correct evaluation of the expression 16n⁴. The correct answer is option (C).
Explanation:
The question is whether (-2n)⁴ is equal to -8n⁴. To evaluate the expression (-2n)⁴, you must raise both -2 and n to the fourth power. Since the exponent is even, the negative sign in front of 2 will become positive after being raised to the fourth power: (-2n)⁴ = (-2)⁴ × n⁴ = 16n⁴
So, the correct statement is No; for values other than 0, (–2n)⁴ = 16n⁴ not equal to –8n⁴. When raising a negative number to an even power, the result is positive, and (-2)⁴ equates to 16, not -8. Therefore, the option C is correct.
As a result, the misconception that -2 times 4 makes -8 is incorrect when dealing with exponents, as the negative sign is squared, turning it positive.
Which of these points does not change its location when it is reflected across the y-axis? A (2, 0) b (0, 6) c (3, 3) d (5, 5)
Answers
Answer:
B. (0,6)
Step-by-step explanation:
To solve this question, you'll need to figure out what the final point is after reflecting each point. A quick way to figure this out is by multiplying (-1) to the x-coordinate.
When you reflect A. (2,0) over the y-axis, the point becomes (-2,0).
When you reflect C. (3,3) over the y-axis, the point becomes (-3,3).
When you reflect D. (5,5) over the y-axis, the point becomes (-5,5).
The only answer that does not change location is B. (0,6) as it stays at (0,6). If you multiply 0 by any number, it will always stay 0.
Multiplying the x-coordinate by (-1) to find the reflection point only works if you are reflecting it over the y-axis. You would multiple the y-coordinate by (-1) if you were reflecting over the x-axis.
B because it has the point 0 which can not be negative when reflected across the y axis like 2, 3, and 5 can.
in the circle below, f is the center, gi is the diameter and m
Answers
Answer:
Part a) [tex]m<HIG=40\°[/tex]
Part b) IHG is a semicircle and GJI is a semicircle
Part c) HIJ is a major arc and HIJG is a major arc
Part d) [tex]arc\ GH=80\°[/tex]
Part e) [tex]arc\ GJI=180\°[/tex]
Step-by-step explanation:
Part a) Give an inscribed angle
we know that
The inscribed angle measures half that of the arc comprising
so
in this problem m<HIG is an inscribed angle
[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex]
[tex]arc\ HG=80\°[/tex] ----> by central angle
substitute
[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]
Part b) Give a semicircle
we know that
The diameter divide the circle into two semicircles
so
GI is a diameter
therefore
IHG is a semicircle
GJI is a semicircle
Part c) Give a major arc
we know that
The measure of a major arc is greater than 180 degrees
therefore
HIJ is a major arc
HIJG is a major arc
Part d) Measure of arc GH
we know that
[tex]arc\ GH=m<HFG[/tex] ----> by central angle
so
[tex]arc\ GH=80\°[/tex]
Part e) Measure of arc GJI
we know that
[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle
What is the greatest common factor of 35b^2,15b^3 and 5b?
Answers
The greatest common factor is 5b.
EXPLANATION
The first expression can be rewritten as
[tex]35 {b}^{2} = 5 \times 7 \times {b}^{2} [/tex]
The second expression is rewritten as
[tex]15 {b}^{3} = 3 \times 5 {b}^{3} [/tex]
The third expression is
[tex]5b = 5 \times b[/tex]
The greatest common factor is the product of the least powers of the common factors.
[tex]GCF=5 \times b = 5b[/tex]
HELP PLEASE 23 POINTS ASAP Hanna arranged financing for her bachelor’s degree. She borrowed $5,000 as a student loan backed by the federal government, and she also received a grant of $3,000 for books and supplies. Hanna is also in the top 3% of her high school class and was awarded a $15,000 scholarship for her academic achievements. Lastly, Hanna took out a private loan for $6,000.
Not counting any interest Hanna may have to pay, how much of her financing is she required to pay back?
Answers
Scholarships and grants do not need to be paid back.
Government loans and private loans do need to be paid back.
She has 2 loans. $5,000 and $6,000.
She needs to pay back $11,000
In quadrilateral ABCD, diagonals AC and BD bisect one another:
Quadrilateral ABCD is shown with diagonals AC and BD intersecting at point P.
What statement is used to prove that quadrilateral ABCD is a parallelogram? (5 points)
Angles BAD and ADC are congruent.
Corresponding angles BCD and CDA are supplementary.
Sides CD and DA are congruent.
Triangles BPA and DPC are congruent.
Answers
Answer:
Triangles BPA and DPC are congruent.
Step-by-step explanation:
The statement above is the only one of the bunch that is true, so is the best selection.
You don't even need to worry too much about how you might make the proof. You just need to be concerned with which are plausible answers. There's only one.
An experiment consists of rolling a die, flipping a coin, and spinning a spinner divided into 4 equal regions. The number of elements in the sample space of this experiment is
12
3
6
48
Answers
Answer:
48
Step-by-step explanation:
The sample space of the experiment contains all the possible outcomes of all events.
There are 3 events that are taking place.
Rolling a die which has 6 possible outcomes.
Flipping a coin which has 2 possible outcomes.
Spinning a spinner which has 4 possible outcomes.
Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.
i.e.
Total outcomes = 6 x 2 x 4 = 48
The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48
Answer:
48
Step-by-step explanation:
In the given experiment, three events take place which include rolling a die, flipping a coin and spinning a spinner.
The possible outcomes of each of these events are as follows:
Rolling a die - 6
Flipping a coin - 2
Spinning a spinner - 4
Therefore, by multiplying their possible outcomes, we can find the number of elements in the sample space of this environment.
Number of elements = 6 × 2 × 4 = 48
Tony plans to run a 5,000-meter fun run at a constant rate of 250 meters per minute. He uses function f to model his distance from the finish line x minutes after the start of the race.
x f(x)
0 5,000
1 4,750
2 4,500
3 4,250
4 4,000
5 3,750
6 3,500
A.
Tony's function is always decreasing.
B.
Tony's function is always negative.
C.
Tony's function is exponential.
D.
The domain of Tony's function is [0 , 5,000].
Answers
Answer:
Option A.
Step-by-step explanation:
Based on the information provided on the question
the function used to model Tony's run is:
f(x) = -250*x + 5000
This means that after x = 20 minutes, Tony will arrive to the finish line
f(20) = -250*(20) + 5000 = -5000 + 5000 = 0
The function is always decreasing, because we are dealing with a line with negative slope.
Option A.
A 6 ounce package of fruit snacks contains 45 pieces how many pieceswould would you expect in a10 ounce package
Answers
Answer:
75 pieces
Step-by-step explanation:
1. determine how many pieces per ounce by dividing 45 by 6 (# of pieces in a 6 oz bag)
45/6= 7.5 pieces per ounce
2. multiply 7.5 (for one ounce) by 10
7.5*10 = 75
Answer:
75
Step-by-step explanation:
just answer it
HELPPPPP!! The formula gives the volume V of a right cylinder with radius r and height h.
V=πr²h Solve for r.
Explain your answer. Should either answer be discarded? Why or why not?
Answers
Answer:
see explanation
Step-by-step explanation:
Isolate r² by dividing both sides by πh
r² = [tex]\frac{V}{h\pi }[/tex]
Take the square root of both sides
r = ± [tex]\sqrt{\frac{V}{h\pi } }[/tex]
The negative part can be discarded as r > 0, hence
r = [tex]\sqrt{\frac{V}{h\pi } }[/tex]
Using the diagram, to what height can the crane raise building material? Round to the nearest foot.
A) 62 ft
B) 75 ft
C) 78 ft
D) 80 ft
Answers
Answer:
C) 78 ft
Step-by-step explanation:
The side opposite the angle has the ratio to the hypotenuse:
Sin = Opposite/Hypotenuse
Then the solution to this problem is found by substituting the given information and solving for the height.
sin(45°) = height/(110 ft)
(110 ft)·sin(45°) = height ≈ 77.7817 ft
Rounded to the nearest foot, the crane can raise material to a height of 78 ft.
Cabrera bought 4 baseballs for him and his friends to use during practice. Each baseball cost 3.42. What was the total cost of the 4 baseballs?
Answers
Answer:
$13.68
Step-by-step explanation:
3.42 x 4
Final answer:
To find the total cost of 4 baseballs, each costing $3.42, we multiply the cost of one baseball by the number of baseballs, resulting in a total cost of $13.68.
Explanation:
The question asks to calculate the total cost of 4 baseballs, provided that each costs $3.42. To find the total cost, we need to multiply the cost of one baseball by the number of baseballs that were purchased. Hence, the calculation of the total cost of baseball is given by $3.42 (cost of one baseball) × 4 (number of baseballs) = $13.68. Therefore, the total cost of the 4 baseballs is $13.68.
One geometry question need this as soon as possible please!
Answers
simplify :7x + 3x - 5 + 8x + 5 = 180
x = 10
A company offers you a job with an annual salary of $60 000 for the first year and a 5% raise every year after. Approximately how much money in total would you earn in 5 years of working there?
$76577
$331538
$315000
$75000
Answers
Answer:
$75000
Step-by-step explanation:
5% of $60000 is $3000 and $3000 x 5 is $15000 and $15000 + $60000 is $75000
To calculate the total salary over 5 years with an initial salary of $60,000 and a 5% annual raise, you add the salary of each year considering the raise. The salaries over 5 years will be $60,000; $63,000; $66,150; $69,457.50; $72,930.38 respectively, amounting to a total of $331,537.88, which is approximately $331,538.
The question asks how much money you would earn total after 5 years of working at a company starting with a $60,000 salary and receiving a 5% raise each year. This is a problem of geometric progression in mathematics. To calculate the total amount earned over 5 years, we have to apply the formula for the sum of a geometric series because the salary increases by a fixed percentage each year. The salary each year is as follows: Year 1 - $60,000, Year 2 - $60,000*1.05, Year 3 - $60,000*(1.05)^2, Year 4 - $60,000*(1.05)^3, and Year 5 - $60,000*(1.05)^4.
Here is the calculation step-by-step:
Year 1: $60,000Year 2: $60,000 * 1.05Year 3: $60,000 * (1.05)²Year 4: $60,000 * (1.05)³Year 5: $60,000 * (1.05)⁴Now, add up the salaries for each year to find the total earnings:
Year 1: $60,000Year 2: $63,000 (5% of $60,000 is $3,000, so $60,000 + $3,000)Year 3: $66,150Year 4: $69,457.50Year 5: $72,930.38Add up these amounts to get the total earnings after 5 years:
Total = $60,000 + $63,000 + $66,150 + $69,457.50 + $72,930.38 = $331,537.88, which can be rounded to approximately $331,538.
Therefore, the correct answer is: $331,538.
The side of a square is 12 feet. What is the area of the square? A) 12 sq. Ft. B) 24 sq. Ft. Eliminate C) 48 sq. Ft. D) 144 sq. Ft.
Answers
Answer:D) 144
Step-by-step explanation:12*12=144
Answer:
the answer is 144
Step-by-step explanation:
New refrigerator costs $3,250 and it was on sale 20% off. How much would you save if you buy it on sale?
Answers
Answer:
(3250/100)*80 = $ 2600 - 3250 = $650
Step-by-step explanation:
HELPPPPPPPPPPPPPPP ONNNNNNNNNNN MATHHHHHHHH
Answers
One of the roots of the equation 10x2?33x+c=0 is 5.3. Find the other root and the coefficient c.
Answers
The other root of the quadratic equation is -2, and the coefficient c is -106, found using the sum and product of roots formulas.
The other root and the coefficient c of the quadratic equation 10x²- 33x + c = 0, given that one of the roots is 5.3. Using the fact that the sum of the roots of a quadratic equation ax² + bx + c = 0 is equal to -b/a, we can find the other root. With one root known to be 5.3 and a = 10, b = -33, the sum of the roots must be 3.3. Therefore, the other root is 3.3 - 5.3 = -2. To find the coefficient c, we use the fact that the product of the roots of a quadratic equation is equal to c/a. Thus, c = 5.3 * (-2) * 10 = -106. The other root of the equation is -2, and the coefficient c is -106.
Given that DE = 75 inches what is the length of EF ?
Answers
Answer:
61.19 inchesStep-by-step explanation:
Use the sine law:
[tex]\dfrac{DE}{\sin(\angle F)}=\dfrac{EF}{\sin(\angle D)}[/tex]
We have:
[tex]DE=75\ in\\\\m\angle F=75^o\to\sin75^o\approx0.9659\\\\m\angle D=52^o\to\sin52^o\approx0.788[/tex]
Substitute:
[tex]\dfrac{75}{0.9659}=\dfrac{EF}{0.788}[/tex] cross multiply
[tex]0.9659EF=(75)(0.788)[/tex]
[tex]0.9659EF=59.1[/tex] divide both sides by 0.9659
[tex]EF\approx61.19[/tex]
The length of the EF is 61.19 inches if the DE = 75 inches option fourth is correct.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have:
DE = 75 inches
By using the sin law:
sin52/EF = sin75/DE
sin52/EF = sin75/75
sin52/EF = 0.0128
EF = 61.185 ≈ 61.19 inches
Thus, the length of the EF is 61.19 inches if the DE = 75 inches option fourth is correct.
Learn more about the triangle here:
brainly.com/question/25813512
#SPJ2
Marvin says that all rhombuses are squares are Athena says that all squares are rhombuses who is correct explain
Answers
Answer:
Athena
Step-by-step explanation:
Squares are rhombuses but rhombuses are not squares