The cuboid can hold 27.2 cubic inches of popcorn
What is a right rectangular prism?A right rectangular prism is also called the cuboid. it is a solid three dimensional shape with 6 faces, 12 edges and 8 vertices.
Analysis:
Volume of cuboid = length x width x height
= 5 x 3 x 29/4 = 108.75 cubic inches
When it is quarter full, volume = 1/4 x 108.75 = 27.2 cubic inches
In conclusion, the volume of the cuboid is 27.2 cubic inches.
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12. The sum of two consecutive integers is 59. Write an
equation that models this situation and find the
values of the two integers.
Step-by-step explanation:
Equation=>x+x+1=59
2x=58
x=29
the numbers are 29 and 30
Farmer Bob has pigs and chickens. He has 37 animals, and there are 124 legs among them altogether. How
many chickens does Bob have?
Yolanda invests $30,000 in an account that offers a compound interest rate of 7.9% per year. Which of the following is the correct equation for how much Yolanda will have in year 10? O A. A(10) = 30,000 • (1 + 0.079) 10 O B. A(10) = 30,000 - (1 + 0.79)10 - 1 O C. A(10) = 30,000 - (1 + 0.079)10 - 1 O D. A(10) = 30,000 - (1 + 0.079) 10 + 1
Find the distance between the two points. (-1, 6). (2.8)
Round to the nearest hundredth
The distance between the two points. (-1, 6). (2.8) is 3.61 units
How to determine the distance?The points are given as: (-1,6) and (2,8)
The distance is calculated using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
This gives
[tex]d = \sqrt{(-1 -2)^2 + (6 -8)^2}[/tex]
Evaluate the sum of squares
[tex]d = \sqrt{13}[/tex]
Evaluate the exponent
d = 3.61
Hence, the distance between the two points. (-1, 6). (2.8) is 3.61 units
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The measure of an angle is 153°. What is the measure of its supplementary angle?
Answer:
27
Step-by-step explanation:
Supplementary angles add up to 180 degrees
So to find the measure of an angle supplementary to a given angle, we simply subtract the given angle from 180
The given angle here has a measure of 153 degrees
So the angle's supplement has a measure of 180 - 153 = 27 degrees.
Pls help asap and show your work I’ll give brainliest
Answer: 3360 ft squared
Step-by-step explanation:
Short side : 30 x 14 = 420
Long side 30 x 3 x 14 = 1260
420 + 420 + 1260 + 1260 = 3360
pls give brainliest
have a nice day
Area of shorter side
BH30(14)420ft²Area of longer sides
420(3)1260ft²Total Lateral surface area
2(1260+420)2(1680)3380ft²Renark:-
The general LSA formula of cuboid can also be used to solve
LSA=2×H(L+B)Find the volume of this object.
Use 3 for π.
Volume of a Cylinder
V= πr²h
Volume of a Sphere
3 cm.
V= / Tr³
4 cm
V≈ [?]cm³
Enter
10 cm.
Answer:
408 cm^3
Step-by-step explanation:
You have to find the volume of each object individually. You first find the volume of the sphere, so you input the radius, which is 3, into the equation which comes out to be 108 cm^3. You then have to find the volume of the cylinder, and since you have the diameter of the cylinder, and you need the radius, and the radius is half of the diameter, you would input 5 into the equation as the radius, since half of 10 is 5. That comes out to be 300 cm^3, so then you add the two volumes together, which is 408 cm^3
5/x+3=4/x simplify please
Answer:
12
Step-by-step explanation:
cross multiply. 5*x=(x+3)4 5x=4x+12, therefore x=12
How do I answer this question
Answer:
9³
Step-by-step explanation:
We know that,
[tex]a^b[/tex] ÷ [tex]a^c[/tex] = [tex]a^b^-^c[/tex]
By following the above, let us solve the given question.
Let us solve now.
⇒ 9⁵ ÷ 9²
⇒ 9⁵⁻²
⇒ 9³
I don't know the answer help me please
write as a power function. The energy, e, produced in a nuclear reaction is proportional to the mass, m, with a constant of variation being c^2, the square of the speed of light
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The power function of the energy is e=mc².
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The power function is a polynomial. Given the energy, e, produced in a nuclear reaction is proportional to the mass, m. Therefore, we can write,
e ∝ m
To remove proportionality we need to add a constant of variation which is c², the square of the speed of light
e = m c²
Hence, the power function of the energy is e=mc².
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3 1/7 as an improper fraction
Answer:
Its is already an impoper fraction.
1 soda + 1 cupcake+1popsicle=$22.00
1 soda +3cupcakes+3popsicle=$40.00
if a cupcake cost,$2:00 more than a popsicle,find the cost of the following
a)1 cupcake
b)1 popsicle
Answer:
a) 1 cupcake = $5.50
b) 1 Popsicle = $3.50
Step-by-step explanation:
Let s = cost of one soda
Let c = cost of one cupcake
Let p = cost of one Popsicle
From the given information we can create 3 equations:
Equation 1: s + c + p = 22Equation 2: s + 3c + 3p = 40Equation 3: c = p + 2Subtract Equation 1 from Equation 2 to eliminate the variable s:
s + 3c + 3p = 40
- s + c + p = 22
2c + 2p = 18
Substitute Equation 3 into this new equation and solve for p:
⇒ 2c + 2p = 18
⇒ 2(p + 2) + 2p = 18
⇒ 2p + 4 + 2p = 18
⇒ 4p = 14
⇒ p = 3.5
Substitute the found value of p into Equation 3 and solve for c:
⇒ c = p + 2
⇒ c = 3.5 + 2
⇒ c = 5.5
To find the cost of a soda (s), substitute the found values of p and c into Equation 1:
⇒ s + c + p = 22
⇒ s + 5.5 + 3.5 = 22
⇒ s = 13
Therefore,
1 soda costs $131 cupcake costs $5.501 Popsicle costs $3.50Simplify the following expression: 4-3 x 4-8.
Answer: -3x^4-4
Step-by-step explanation: -3x^4+4-8 > =-3x^4-4
A nuclear power plant has two independent safety systems. The probability the first will not operate properly in an emergency P (A) is 0.01, and the probability the second will not operate P (B) in an emergency is 0.03. What is the probability that in an emergency both of the safety systems will not operate?
Step-by-step explanation:
they are independent systems, so in case of an emergency both systems will activate.
this is like rolling 2 dice and asking for the probability that both will show 1.
the probability that both will fail is the product of the individual probabilities for failure :
0.01 × 0.03 = 0.0003
so, the third answer option is correct.
FYI - the probability for 2 dice to both roll 1 is
1/6 × 1/6 = 1/36
Three of these fractions are equivalent:
A.30/70
B.12/30
C.9/21
D.6/14
Which one is the odd one out?
A.
D.
B
C
Answer:
b is the odd one out
Step-by-step explanation:
30/70= .428
12/30= .4
9/21= .428
6/14= .428
all are equal except 12/30
hope this helped!
After completing a fraction division problem, Clarice used multiplication to check her answer.
Division: 7 and one-half divided by 1 and one-half = 5. Check: 5 times 1 and one-half = 5 and one-half.
Could Clarice verify her answer?
Answer:
Step-by-step explanation:
After completing a fraction division problem, Clarice used multiplication to check her answer. Division: 7 and one-half divided by 1 and one-half = 5. Check: 5 times 1 and one-half = 5 and one-half. Could Clarice verify her answer? Explain.After completing a fraction division problem, Clarice used multiplication to check her answer. Division: 7 and one-half divided by 1 and one-half = 5. Check: 5 times 1 and one-half = 5 and one-half. Could Clarice verify her answer? Explain.Why can you use fraction multiplication to check the answer to a fraction division problem? How do you use multiplication to check a division problem?
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If the measure of arc AB = 58 and the measure of arc CD = 18, what is the value of x? The figure is not drawn to scale.
The correct answer is option D. which is the angle x will be 38 degrees.
What is the angle of arc theorem?The measure of the angle created when two chords collide inside a circle is one-half the sum of the arcs intercepted by the angle and its vertical angle.
Here we have a measure of arc AB = 58 and the measure of arc CD = 18, So what is the value of x?
The value of x will be calculated by using the angle of arc theorem.
x = Sum of the arcs / 2
x = ( 58 + 18 ) / 2
x = ( 38 degrees )
Therefore the correct answer is option D. which is the angle x will be 38 degrees.
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A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate School Business Engineering Others Total Yes 70 84 126 280 No 182 208 130 520 Total 252 292 256 800 Of those students who are majoring in business, what percentage plans to go to graduate school?a. 40.4.b. 10.5.c. 28.8.d. 30.0.
Using the percentage concept, it is found that of those students who are majoring in business, the percentage plans to go to graduate school is given by:
c. 28.8.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, there are 252 students majoring is business, and of those, 70 plan to go to graduate school, hence the percentage is given by:
[tex]P = \frac{70}{252} \times 100\% = 28.8\%[/tex]
Hence option C is correct.
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prove that 6(n+6)-(2n+3) is odd number for all n£N
Answer:
[tex]\begin{aligned}6(n+6)-(2n+3) & = 6n+36-2n-3\\& = 4n+33\\& = 4n + 32 + 1\\& = 2(2n+16) + 1\end{aligned}[/tex]
Any number multiplied by 2 is even, therefore 2(2n + 16) is even.
If 2(2n + 16) is even, then adding 1 to this makes it odd.
Thus proving that the given expression is an odd number for all [tex]n \in \mathbb{N}[/tex]
I need this problem solved
Answer:
5
Step-by-step explanation:
geometry please help
Answer: 31
Step-by-step explanation:
Assuming this is a rhombus, then the diagonals are perpendicular, meaning angle MQN measures 90 degrees.
Now, if we consider triangle MNQ, we know that angles in a triangle add to 180 degrees, meaning NMQ measures 31 degrees.
PLEAASSE HELP! DUE TODAY
Answer:
1/4
Step-by-step explanation:
1 hour 15 minutes = 75 minutes
25 mins + 75mins = 100 minutes
25/100 minutes x 100 = 25%
25% = 1/4 of the time was spent reading.
Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south. He is not sure where to point his broomstick, considering that the wind is pretty strong at 21 km/h [S 55° E]. His broomstick has an airspeed of 18 m/s. Determine the heading he should have and the velocity of the broom with respect to the ground.
Harry Potter decides it’s too cold for him to stay in Hogwarts and wants to fly straight south, the heading he should have and the velocity of the broom with respect to the ground are mathematically given as
VR = 20, 699 m/s South
What is the heading he should have and the velocity of the broom with respect to the ground?Divide horizontal and vertical components of Vs and Vw vectors
For Vs
Vs = Vs cos∅ [s] + Vs Sin∅ [w]
Vs = 18 Co58 [s] + 18 sin∅ [w]
For Vw
Vw = Vw Cos 55' [s] + Vw Sin 55 [E]
5.8333 x Cos 55 (s) + 5-8333 Sin 55 [E]
Vw = 3.3458 [s] + 4.7783 [E]
Resultant velocity VR = Vs + Vw
VR= 18 Coso (s) + 18 sine [w] +3.3458 (5) +42783 (E)
VR = (186030 +3.3458) [5] + (18sing - 4.7183)6]
(Harry Potter) flies south
18sin∅ - 4.7783 18=0
Hence
Sin∅ = 4.7783 18/18
∅ =sin{-1}(4.7783 18/18)
∅ = 15.3943
Harry Potter flies in the direction south to ∅ = $15.3943w]
Hence velocity
VR = (18 cos∅ + 35452) s + 0
VR = (17.3541 +3-3458) s
VR = 20, 69999 m/s South
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Question 1
1 pts
You are going to buy a new car. There are two body styles(sedan or hatchback), 5 colors
and 3 models.
How many total choices can you choose from?
O 20
O 30
O 15
O 10
The function f(x) is shown below.
x
f(x)
–6
1
–3
2
2
5
5
3
8
0
If g(x) is the inverse of f(x), what is the value of f(g(2))?
–6
The value of f(g(2)) is 2.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given table is
x f(x)
–6 1
–3 2
2 5
5 3
8 0
If the coordinates of a function f(x) is defined as (x,y)
then, the coordinates of inverse of f(x) is defined as (y,x).
f(g(y))= f(x) [ g(x)= (y,x)]
f(g(y))= y
So, If g(x) is the inverse of f(x), the f(g(y)) = y.
Also, we know g(x) is the inverse of f(x), then f(g(2)) = 2.
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Leigh plans to estimate the area of the figure on the grid by identifying the full and partial squares that make up the figure.
On a coordinate plane, a figure contains 3 full squares and 12 partial squares.
If Leigh uses the strategy, which statement best describes the figure?
3 full squares and 12 partial squares
3 full squares and 15 partial squares
4 full squares and 7 partial squares
4 full squares and 13 partial squares
If Leigh uses the strategy, the statement that describes the figure is A. 3 full squares and 12 partial squares.
How to depict the information?From the information, Leigh plans to estimate the area of the figure on the grid by identifying the full and partial squares that make up the figure.
It was stated that on a coordinate plane, a figure contains 3 full squares and 12 partial squares.
Therefore, the correct option is A.
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Which of the following best describes the histogram?
The histogram is evenly distributed.
The histogram is symmetrical.
The left side of the histogram has a cluster.
The left side of the histogram is the mirror image of the right side.
histor Grammer
Step-by-step explanation:
lol bhsg HD tcvh by by by g
In a class test(3+) marks are given for every correct answer and (-2) marks are given for every incorrect answer (-2) marks are given for every incorrect answer and no marks for not attempting any question. (i) radhika scored 20 marks. if she got 12 correct answers, how many questions has she attempted incorrectly? (ii) mohini scores -5 marks in this test, though she has got 7 correct answers. how many questions has she attempted incorrectly?
The number of incorrect answers made by Radhika is 8; the number of incorrect answers made by Mohini = 13
How to solve algebra word problems?
We are given;
Marks obtained for 1 right answer = +3
Marks obtained for 1 wrong answer = −2
(i) Marks scored by Radhika = 20
Marks obtained for 12 correct answers = 12 × 3 = 36
Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers = 20 − 36 = −16
Marks obtained for 1 wrong answer = −2
Thus, number of incorrect answers = (−16) ÷(−2) = 8
Therefore, the number of incorrect answers made by Radhika = 8
(ii) Marks scored by Mohini = −5
Marks obtained for 7 correct answers = 7 × 3 = 21
Marks obtained for incorrect answers = Total score − Marks obtained for 12 correct answers = − 5 − 21 = −26
Marks obtained for 1 wrong answer = −2
Thus, number of incorrect answers = (−26) ÷ (−2) = 13
So, the number of incorrect answers made by Mohini = 13
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A line has a slope of -3 and passes through the point
passes through the point (-2, -3/2)
By substituting into the equation y = mx + b, find the value of b for this line
Answer:
If I am not mistaking it should be -7.5
Step-by-step explanation:
Answer:
b = -15/2
y = -3x -15/2
Step-by-step explanation:
The value of the y-intercept can be found from a point and the slope of the line by solving the slope-intercept equation for the intercept.
__
intercepty = mx + b . . . . . . . equation of a line with slope m and y-intercept b
y -mx = b . . . . . . . . subtract mx from both sides
For the point (x, y) = (-2, -3/2) and slope m = -3, the value of b is ...
b = -3/2 -(-3)(-2) = -3/2 -6
b = -15/2 . . . . . the value of b for this line
__
equation of the lineThen the equation for the line is ...
y = mx +b
y = -3x -15/2