The volume of the box is 216 ft cube.
How to find volume of a box?He filled a box with 4 layers of cubes that measured one foot on each side
The bottom of the box fit 6 cubes,
1 cube length = 1 ft.
Therefore,
volume of the box = 6³
Therefore,
volume of the box = 216 ft³
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How many outfits can be made with 40 shirts and 15 pairs of pants
Answer:
600
Step-by-step explanation:
So I'm assuming an outfit is considered one shirt, and one pair of pants... But anyways, this can be expressed in a graph. So for each shirt, there are going to be 15 possible pants you can chose. And this goes for each shirt. So in other words you're simply adding up 15, 40 amount of times. Or 15 * 40, which is 600. I attached an image that illustrates this graph. You can also think of it in terms of choosing one of 15 pants and then for each pant, there are 40 possible shirts to choose from. This is essentially adding up 40, 15 times, or in other words 40 * 15, which is going to get you the same result. But in my diagram I used it in terms of choosing a shirt first.
Answer:
600
Step-by-step explanation:
Pair 1 of pants goes with 40 shirts
Pair 2 of pants goes with 40 shirts
Pair 3 of pants goes with 40 shirts
Pair 4 of pants goes with 40 shirts
Pair 5 of pants goes with 40 shirts
Pair 6 of pants goes with 40 shirts
Pair 7 of pants goes with 40 shirts
Pair 8 of pants goes with 40 shirts
Pair 9 of pants goes with 40 shirts
Pair 10 of pants goes with 40 shirts
Pair 11 of pants goes with 40 shirts
Pair 12 of pants goes with 40 shirts
Pair 13 of pants goes with 40 shirts
Pair 14 of pants goes with 40 shirts
Pair 15 of pants goes with 40 shirts
Add up everything (not including the 1,2,3,4,5,...14,15 pairs of pants because each pair of pants goes with 40 different shirts so u just add up all the 40's) and you would get 600 outfits.
Another simple way of doing this would just be multiplying 40x15
jacqueline works on math 7/12 hours everyday . how many hours did she work on math after 24 day
Answer:
14
Step-by-step explanation:
24/12=2
(2)7=14 hours
can someone help me with this? I’ll mark you brainliest
The point (0, 0) lies in the shaded region and satisfies the solution for the inequality y ≥ 3x - 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequality y ≥ 3x - 2, since the point (0, 0) lies on the shaded region, hence:
0 ≥ 3(0) - 2
0 ≥ -2
The point (0, 0) satisfies the solution for the inequality y ≥ 3x - 2
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Find the length of the hypotenuse on the following right triangle.
Answer:
Step-by-step explanation:
HELPPPPP!!
Sarai loves music and decides to paint a music staff on her bedroom wall. She knows that it is important to make the lines parallel, or the end result will not look correct. She pencils in the image below, but before she uses paint, she wants to make sure the lines are parallel. Remembering what she has learned in Geometry class, she uses a piece of tape to make a transversal and decides to measure some angles.
Using Sarai’s measurements, Line 1 must be parallel to Line 3 according to which postulate or theorem?
Can you also please explain how you got the answer? thank you <3
Using Sarai's measurements, Line 3 must be parallel to Line 5 by option (A) Converse of Alternate Exterior Angles Theorem.
What is the Alternate Exterior Angles theorem?The alternate Exterior Angles theorem states, "If two lines are parallel and they are intersected by the same straight line then the alternative exterior angles formed by the figure are equal to each other."
The converse of this theorem states that "If two lines intersected by one transverse and formed alternate exterior angles, and if they are equal to each other then that two lines are parallel to each other."
Here in Sarai's measurement, we can conclude that Line 3 and Line 5 are intersected by one straight line, and the formed alternate exterior angles both are 65, which shows they are equal to each other.
Hence by Converse of the Alternate Exterior Theorem, we can say that both lines are parallel to each other.
So, Line 3 must be parallel to Line 5 according to the Converse of Alternate Exterior Angles Theorem.
Hence Option (A) is correct.
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2x - 5y = 2
3x + 2y = -16
Answer:
(-4,-2)
Step-by-step explanation:
Isolate x:
2x - 5y = 2
2x = 5y + 2
x = 5/2y + 1
Substitute and solve for y:
3(5/2y + 1) + 2y = -16
15/2y + 3 + 2y = -16
7.5y + 2y = -16 - 3
9.5y = -19
y = -2
Substitute and solve for x:
2x - 5y = 2
2x - 5(-2) = 2
2x + 10 = 2
2x = -8
x = -4
help me please i dont understand
20 points
Answer:
50 [tex]cm^{2}[/tex]
Step-by-step explanation:
Area of a trapezoid: [tex]\frac{a+b}{2} h[/tex]
[tex]\frac{a+b}{2} h[/tex]
= [tex]\frac{14+6}{2} (5)[/tex]
= [tex]\frac{20}{2} (5)[/tex]
= [tex]10(5)[/tex]
= 50 sq. cm
(Round answers to
the nearest hundredth.)
Answer:
28.31
Step-by-step explanation:
So in this case you're going to need to use the law of sines which essentially states that: [tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex] which should apply to any of the sides. the lowercase a and b are the opposite sides of the angles A and B. In this example the angle A is given and C is given, but not in the text. Since you have the right angle thing in the diagram, angle C is a right angle (90 degrees).
Given information:
[tex]\angle A = 32\\a=15\\\angle C = 90 \text{(the right angle symbol in the diagram of the triangle)}[/tex]
Law of sines equation:
[tex]\frac{a}{sinA}=\frac{b}{sinB} \text{ can be applied to any two sides }[/tex]
Plug in known information:
[tex]\frac{15}{sin(32)}=\frac{c}{sin (90)}[/tex]
since sin(90) = 1, simplify the fraction
[tex]\frac{15}{sin(32)} = c[/tex]
Calculate sin(32)
[tex]\frac{15}{0.530}\approx c[/tex]
Divide
[tex]28.306\approx c[/tex]
If you haven't learned law of sines yet and don't quite understand why it works you can also use the definition of tan to find what b equals and then use the Pythagorean Theorem to solve for c
tan is defined as: [tex]\frac{opposite}{adjacent}[/tex]
[tex]tan(32)=\frac{15}{b}[/tex]
now multiply both sides by b
[tex]b * tan(32)=15[/tex]
Divide both sides by tan 32
[tex]b = \frac{15}{tan(32)}[/tex]
[tex]b\approx 24.005[/tex]
Now use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
[tex](24.005)^2+15^2=c^2\\[/tex]
Square known values
[tex]576.241+225=c^2[/tex]
Add the values
[tex]801.241 = c^2[/tex]
take the square root of both sides
[tex]28.306\approx c[/tex]
Rounding to the nearest hundredth gives you 28.31
Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?
9.6, –4.8, 2.4, –1.2, 0.6, ...
f(n + 1) = (–0.5)f(n)
f(n + 1) = (0.5)f(n)
f(n + 1) = f(0.5n)
f(n + 1) = f(–0.5n)
Answer: f(n + 1) = (–0.5)f(n)
Step-by-step explanation:
This is a geometric series with common ratio -0.5.
How are evidence and counterexamples used in proofs . In a direct proof evidence is used to blank .on the other hand a counterexample is a single example that blank
Evidence is used in proofs to support a claim.
What is an evidence?It should be noted that evidence simply means a claim that's is used to support a proposition that's it's true.
In this case, evidence is used in proofs to support a claim. On the other hand, counterexample is used to disprove a theory.
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Miguel plans on retiring in 16 years, and he wants to double his money by that time. He's contacted various banks, looking for a CD that compounds interest monthly, and to calculate what annual interest rate he needs, he is using the rule of 72. (3 points: Part I – 1 point; Part II – 1 point; Part III – 1 point)
Part I: What is the rule of 72? To represent the annual interest rate, use r.
Part II: What equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires?
Part III: What annual interest rate does Miguel need to double his money by the time he retires?
The rule of 72 is a rule of thumb that is used to determine the doubling time for an investment given the annual interest rate.
The equation Miguel needs to set up is r = 72/16.
The interest rate is 4.5%.
What is the rule of 72?
The rule of 72 is used to determine the time it would take an investment to double in value. The doubling time is determined by dividing 72 by the interest rate.
Number of years it would take an investment to double = 72 / interest rate
n = 72 / r
r = 72 / n
72 / 16 = 4.5%
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what is the answer?
please help
Answer:
Slope = 1/3
Step-by-step explanation:
Slope:Pick any two points. (-1,-2) ; (2,-1)[tex]\sf \ x_1=-1 ; \ y_1=-2\\\\ x_2 = 2 ; \ y_2=-1[/tex]
Find the slope using the formula.[tex]\sf \boxed{\bf \ Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-1-[-2]}{2-[-1]}\\\\ =\dfrac{-1+2}{2+1}\\\\= \dfrac{1}{3}[/tex]
Analyze the diagram below.
Which statements regarding the diagram are correct? Check all that apply.
ST ≅ ST by the reflexive property.
∠RWS ≅ ∠UWT because they are vertical angles.
△RWS ≅ △UWT by AAS.
△RST ≅ △UST by SAS.
∠WTU ≅ ∠WSR because CPCTC.
Based on the relevant congruent theorems, all of the statements are correct except: D. △RST ≅ △UST by SAS.
What is the AAS Congruence Theorem?Two triangles that have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles are proven to be congruent by the AAS congruence theorem.
Thus, △RWS ≅ △UWT by AAS because they have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles.
△RST cannot be proven to be congruent to △UST by SAS because there is no sufficient information.
Based on the reflexive property, ST ≅ ST. Also, using the CPCTC, all parts of the two congruent triangles are equal, therefore, ∠WTU ≅ ∠WSR.
The only statement that is incorrect is: D. △RST ≅ △UST by SAS.
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Answer:
A, B, C and E
Step-by-step explanation:
A telegraph pole stands on a line joining two points P and Q on the ground.
The telegraph pole is 9 m tall. The angle of depression of the top of the pole to point P
is 4°. The angle of depression of the top of the pole to point Q is 7º. What is the
horizontal distance between P and Q.
Step-by-step explanation:
let's call the top of the pole T, and the ground point of the pole G.
so, the situation gives us 2 right-angled triangles:
PTG and QTB.
from both triangles we know one leg (TG, the pole = 9 m), the inner angles at G (90° in both cases), and actually the inner angles at T, because we know the angles of depression there.
the inner triangle angles at T are just the complementary angles of the angles of depression (that means they add up together to 90°).
the inner angle at PTG = 90 - 4 = 86°
the inner angle at QTG = 90 - 7 = 83°
and because the sum of all angles in a triangle is always 180°, we even know the third angles at P and Q :
angle P = 180 - 90 - 86 = 4°
angle Q = 180 - 90 - 83 = 7°
yes, they are the same as the angles of depression (must be the same).
so, we know from both triangles 1 side and all 3 angles.
with the law of sine we can get every missing side.
particularly we need the second legs (sides in the ground) to get the distance between both points.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides always opposite of their related angles.
TG/sin(4) = PG/sin(86)
PG = 9×sin(86)/sin(4) = 128.7059963... m
TG/sin(7) = QG/sin(83)
QG = 9×sin(83)/sin(7) = 73.29911785... m
the distance between P and Q can have now 2 solutions :
if P and Q are on different sides of the pole, then
PQ = 128.7059963... + 73.29911785... = 202.0051142... m
but if they are on the same side of the pole, then their distance is
PQ = 128.7059963... - 73.29911785... = 55.40687846... m
due to the phrasing of the first sentence I suspect the first solution to be right.
but just in case, I gave you also the second possible solution.
What is the answer to this pythagoras question?
The length of the segment AB will be equal to 9.848 units.
What is the Pythagorean theorem?It states that in the right-angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The length of segment AB will be calculated as:-
Points are A(1,7) and B(10,3)
AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
AB = [tex]\sqrt{(10-1)^2+(3-7)^2}[/tex]
AB = √(81+16)
AB = √97
AB = 9.848
Therefore the length of the segment AB will be equal to 9.848 units.
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Which rectangular equation represents the parametric equations x = t²-4 and y = 2t?
Oy = 2(x² + 4)
* y = 2(x² - 4)
Oy = 2√x+4
O y = 2√√x-4
Answer:
[tex]\displaystyle{y=2\sqrt{x+4}}[/tex]
Step-by-step explanation:
We are given parametric equations of:
[tex]\displaystyle{x=t^2-4}[/tex] and [tex]\displaystyle{y=2t}[/tex]
Isolate t-variable in [tex]\displaystyle{x=t^2-4}[/tex] first by adding both sides by 4:
[tex]\displaystyle{x+4=t^2-4+4}\\\\\displaystyle{x+4=t^2}[/tex]
Square root both sides then write plus-minus:
[tex]\displaystyle{\sqrt{x+4}=\sqrt{t^2}}\\\\\displaystyle{t=\pm \sqrt{x+4}}[/tex]
Since the choice determines y-term as a function and only positive t-value exists, substitute only [tex]\displaystyle{t=\sqrt{x+4}}[/tex] in [tex]\displaystyle{y=2t}[/tex].
Therefore, the answer is [tex]\displaystyle{y=2\sqrt{x+4}}[/tex]
Answer:
c
Step-by-step explanation:
What is the least amount of integers you must pick in order to be sure that at least two of them have the same remainder when divided by 15
There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.
It is given that at least two of them should have the same remainder when divided by 15.
Division algorithm.
Let aa be an integer and d a positive integer. Then there are unique integers q and r with [tex]0\leq r < d[/tex] such that [tex]a=dq+r[/tex]
q is called the quotient and r is called the remainder
q=a div d
r=a mod d
Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.
Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.
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A cube shaped suitcase has a length of 3x + 2 units. What is an expression for its area of the
base?
Answer:
[tex]\huge\boxed{\sf 9x^2+12x+4 \ units^2}[/tex]
Step-by-step explanation:
Given that,
Length of cube = l = 3x + 2 units
Base Area:[tex]= l \times l\\\\= (3x+2)(3x+2)\\\\= 3x(3x+2)+2(3x+2)\\\\= 9x^2+6x+6x+4\\\\= 9x^2+12x+4 \ units^2\\\\\rule[225]{225}{2}[/tex]
answer pleaseeeeeeeeeeeeeee
Answer:
A. Square
Step-by-step explanation:
Hope this helps!
Please mark brainliest! Thanks!
Can someone help me with this please?
Answer: 14.79
Step-by-step explanation:
[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]
The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y.
x=2, y=5
The equation that relates x and y is y = 2.5x.
How to solve variation?
The values of x and y vary directly. Therefore,
y α x
where
x and y are the variable.Hence,
y = kx
where
k = constant of proportionality.Therefore,
x = 2
y = 5
5 = 2k
k = 5 / 2
k = 2.5
Hence, the equation that relates x and y are as follows;
y = 2.5x
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What is the value of this subject when a =2 and b= -3?
a^3-b^3/5
Answer:
7
Step-by-step explanation:
a^3 = 2^3 = 8
b^3 = -3^3 = -27
(8 - (-27))/5= (8+27)/5 =35/5=7
Jon, Dave, and Kevin collected rocks at the beach. Each boy collected 25 rocks. How many rocks did the boys collect in all?
By taking the product between the number of boys and the number of rocks that each gets, we conclude that they collected 75 rocks.
How many rocks did the boys collect in all?
We know that there are 3 boys, and each boy collected 25 rocks.
If we take the product between the number of boys and the number of rocks that each boy collected, we get:
R = 3*25 rocks = 75 rocks.
We conclude that the boys collected 75 rocks in total.
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Find the length of line segments (4,6) and (5,2)
Answer: [tex]\displaystyle d=\sqrt{1 7}\;\text{or about 4.123 units}[/tex]
Step-by-step explanation:
We can use the distance formula to solve. Let (4, 6) be point one and (5, 2) be point two.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(5-4)^2 +(2-6)^2}[/tex]
[tex]\displaystyle d=\sqrt{(1)^2 +(-4)^2}[/tex]
[tex]\displaystyle d=\sqrt{1 +16}[/tex]
[tex]\displaystyle d=\sqrt{1 7}[/tex]
For the regular hexagon below, if BC = 9 m and AP = 8 m, find it's area.
what is the following product?
√10 10
A)10
B) 10/10
C) 10√10
D) 100
Answer: C
Step-by-step explanation:
[tex]\sqrt10 10=10\sqrt{10}[/tex]
Need asap pls correct answer
Answer: B. G(x) = (x-5)^2
Step-by-step explanation:
This will shift the graph 5 units right
Find ST. Help me please. Thank you :)
The value of ST is 3
How to solve for ST?The given parameters are:
RT = 8
RS = 5
To calculate ST, we make use of the following straight line theorem
RT = RS + ST
This gives
8 = 5 + ST
Subtract 5 from both sides
ST = 3
Hence, the value of ST is 3
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30 mi / h = ____ ft / min
a.
2640
c.
880
b.
264
d.
2112
Answer:
A. 2640
Step-by-step explanation:
44 feet per second 30 miles per hour is 2640 feet per minute
Determine the equation, in vertex form, of a parabola that has been:
(a) reflected in the x-axis and horizontally shifted right 4 units.
(b) vertically compressed by a factor of 1/4 and vertically translated 5 units down
(c) vertically stretched by a factor of 4, translated 3 units left and 2 units up
Answer:
[tex]a)\ y=-(x-5)^2;\\b)\ y=4x^2-5;\\c)\ (y-2)^2=4*(x+3).[/tex]
Good luck!