The missing number using Euler's formula is: Option A. 17
The maximum volume of a square pyramid is: Option B. 4,608
What is Euler's formula?"It is a geometrical formula. V − E + F = 2, where V represents number of vertices, E represents number of edges and F represents number of faces."
What is square pyramid?"Square pyramid is a three dimensional geometrical figure where four triangular sides are associated to square base."
What is cube?"A cube is a three-dimensional geometric structure with six congruent square face."
Formula for volume of a square pyramid:[tex]V=\frac{1}{3}a^{2}h[/tex]
where [tex]a[/tex] represents the length of square base and [tex]h[/tex] represents the height of the pyramid.
Consider the first question,
number of vertices (V) = 13
number of edges (E) = 28
So, using Euler's formula:
[tex]13-28+F=2[/tex]
⇒ [tex]-15+F=2[/tex]
⇒ [tex]F=2+15[/tex]
⇒ [tex]F=17[/tex]
So, the number of faces are 17.
Hence, the correct answer is option A. 17
Consider last question,
the side length of a cube = 24 cm
As the square pyramid fit inside a cube.
⇒ the length of the square base of a pyramid [tex]b[/tex] = 24 cm
and the height of a square pyramid [tex]h[/tex] = 24 cm
So, the volume of a square pyramid is,
[tex]V=\frac{1}{3} a^{2} h[/tex]
⇒ [tex]V=\frac{1}{3}[/tex] × [tex]24^{2}[/tex] × [tex]24[/tex]
⇒ [tex]V= 4608[/tex] [tex]cm^{3}[/tex]
Therefore, the maximum volume of a square pyramid that can fit inside a cube with a side length of 24 cm is [tex]4608[/tex] [tex]cm^{3}[/tex].
And the correct answer is option B. 4,608
Learn more about Euler's formula here,
https://brainly.com/question/22069428
Learn more about volume of a square pyramid here:
https://brainly.com/question/2501401
#SPJ2
They traveled 200 kilometers in total, and they biked 40 kilometers more than they were bussed. how many kilometers did they travele by bike
Make a box and whisker plot of the data.
24, 18, 29, 21, 16, 23, 13, 11
PLLLLLLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Find the value of n.
Multiply. 0.35 × 0.003 =
Answer:
0.00105
Step-by-step explanation:
Sharon wants to know the difference between the average amount she stacked and the average amount Diane stacked. Which operation would she use to find the difference?
The mean of a set of five numbers is 4.8. Given that the sixth number is x and the mean of these six numbers is 5.5, find the value of x.
The point (-1.3, -1.7) is located in which quadrant?
katy buys ‘x’ cakes.
Gugu buys 3 times as many cakes as katy.
Deanna buys 2 more cakes than Katy.
Each cake costs 85p
The total of the cakes is £52.70
How many cakes did each girl buy?
Answer:
Katy bought 12 cakes
Gugu bought 36 cakes
Deanna bought 14 cakes
Step-by-step explanation:
A line has a slope of -5 and passes through (1,-1). Which is the equation of the line in point-slope form?
I WILL GIVE BRAINLIEST The area of the surface of the trampoline (square) is equal to twice its perimeter. Find the dimensions. length= 4x ft., width= (x+6) ft.
FACTORING POLYNOMIALS/SOLVE THE EQUATION BY FACTORING HOMEWORK
How can you prove a triangle is a right triangle? select one:a. use the distance formula to see if at least two sides are congruent.b. use the slope formula to see if any sides are perpendicular.c. use the distance formula to see if all three sides are congruent.d. use the slope formula to see if any sides are parallel?
5/8 ≠ (3/4 + 1/16) because 5/8 < 3/4 EXPLAIN THIS PROBLEM AND WHAT IT MEANS
Given that f(x) = x2 − 4x − 3 and g(x) = the quantity of x plus three, over four, solve for f(g(x)) when x = 9.
−6
3
6
9
Final answer:
The solution to f(g(x)) when x = 9 is -6.
Explanation:
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain), where each input is related to exactly one output.
Given:
f(x) = x2 - 4x - 3, g(x) = (x + 3) / 4
To find f(g(x)) when x = 9:
Calculate g(9): Substitute x = 9 into g(x) to get (9 + 3) / 4 = 12 / 4 = 3Substitute g(9) into f(x): Substitute g(9) = 3 into f(x) to get f(3) = 32 - 4(3) - 3 = 9 - 12 - 3 = -6Therefore, f(g(x)) when x = 9 is -6.
Haley sings for $1,000 an hour. Her rate increases by 50% after midnight. If she sings one
night from 8:30 pm until 1:00 am, how much should she be paid?
a) $4500 b) $5000 c) $5500 d) $6000
Algebra question ( Matrices and Determinants ) 20 points
How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?
A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h
What is the length of an arc cut off by an angle of 3 radians on a circle of radius 8 inches?
I need step by step instructions on how to get the y-intercept for the following function:
f(x)=x^3-18x^2+107x-210.
PLS HELP ME ASAP WITH 1!
BRAINLIEST WILL BE GIVEN HOPEFULLY
Do question 2 if u can, if u can’t it’s fine
(Random answers gets moderated)
Which is the correct form of the quadratic formula? A) x = b ± b2 - 4ac a B) x = b ± b2 - 4ac 2a C) x = - b ± b2 - 4ac a D) x = - b ± b2 - 4ac 2a
The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).
Hence, option D) is the correct answer.
What is a Quadratic Equation?Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x using the quadratic formula;
x = (-b±√(b² - 4ac)) / (2a)
The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).
Hence, option D) is the correct answer.
Learn more about quadratic equations here: brainly.com/question/1863222
#SPJ2
Divide 2y2 + 8 by 2y + 4. Which expression represents the quotient and remainder?
Final answer:
To divide 2y² + 8 by 2y + 4, use long division to find the quotient and remainder.
Explanation:
To divide 2y² + 8 by 2y + 4, we can use long division. Here are the steps:
Divide the first term of the dividend by the first term of the divisor, which gives us y.
Multiply the entire divisor by y to get 2y² + 4y.
Subtract 2y² + 4y from the dividend 2y² + 8 to get 4.
Next, divide 4 by 2y + 4, which gives us 2.
Finally, we have a remainder of 0.
Therefore, the quotient is y + 2 and the remainder is 0.
WILL VOTE BRAINIEST IF CORRECT(must be next few minutes): The formula for the area of circle A is Area=πr2 . Sector CAB is a fraction of circle A. In degrees, the fraction is θ/360∘ . In radians, the fraction is _____. Inserting this fraction into the formula for the area of a circle, and then simplifying, results in the formula _____.
(image attached)
choices: 2pi0, 0pi, 0/2pi, area=0r^2, area= 2pi0r^2, area= 0/2r^2
The fraction of the sector of a circle in radians is (θπ/180). Substituting this fraction into the formula for the area of a circle, and simplifying, results in the formula for the area of the sector being A = (θπ/360) * r^2.
Explanation:In a circle, the angle in degrees is often converted to radians for calculations. A full circle is equivalent to 360 degrees or 2π radians. Therefore, if the sector angle is θ degrees, then in radians, the equivalent is (θ/360) * 2π = θπ/180.
Inserting this into the formula for the area of a circle, which is A = πr2, the area A of the sector becomes a fraction of the full circle's area, which is calculated as follows: (θ/360) * A = (θ/360) * πr2 = (θπ/180) * r2. Simplifying this results in the formula A = (θπ/360) * r2.
Learn more about Circle Sector Area here:https://brainly.com/question/15849991
#SPJ12
For a sector in a circle, the fraction is θ/2π in radians. After substituting this into the formula for circle's area, we get the area of sector as Area = (θr²)/2.
Explanation:The fraction in radians for a sector in a circle is θ/2π, because there are 2π radians in a whole circle. As the formula for the area of circle A is Area=πr², when we insert this fraction, which represents the proportion of the circle that Sector CAB occupies, we get the formula for the area of a sector: Area= (θ/2π) * πr². This simplifies to Area= (θr²)/2, as the π's cancel out. This formula says that the area of a sector is proportionate to its central angle and the square of the radius of the circle.
Learn more about Circle Sector Area here:https://brainly.com/question/15849991
#SPJ12
6. Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is experimental probability of winning a free gallon of milk?
A. 11/156
B. 49/52
C. 2/39
D. 3/52*****?
The experimental probability of winning a free gallon of milk will be calculated as under -
It is given that, total number of outcomes = 156
Non-winning customers = 147 (it is given in the question)
Thus, the winning customers will be = Total outcomes - Non-winning customers
Expected winning customers = 156 - 147 = 9
The probability is calculated as -
Probability (Winning customer) = [tex] \frac{Winning Customers}{Total Customers} [/tex]
Probability (Winning customer) = [tex] \frac{9}{156} [/tex] = [tex] \frac{3}{52} [/tex]
How much of a 14% iodine solution should be added to 89 ounces of a 47% iodine solution to get a 29% solution
A company spent 32% of its annual budget developing a new machine. What fraction of the company's budget was spent developing the new machine?
We have been given that the company spent 32% of its annual budget developing a new machine.
Let us convert the percentage to fraction.
[tex]32 \%=\frac{32}{100} \\ \\ 32 \%=\frac{4\times 8}{4\times 25}\\ \\ \text{Cancel 4 from numerator and denominator}\\ \\ 32 \%=\frac{8}{25}[/tex]
Thus, when we convert 32% to fraction that will be equal to 8/25.
Hence, [tex]\frac{8}{25}[/tex] company's budget was spent developing the new machine.
For which angle is secant undefined?
30°
45°
180°
270°
Answer:
the answer is 180 degrees
Step-by-step explanation:
i used my head and my google maths
Rewrite the expression log(3x) as an equivalent logarithmic expression using only addition.
What is the 12th term of the sequence? 3, −9, 27, −81, 243, ...
531441
−531441
177147
−177147
Choose an example of a fixed expense and an example of a variable expense, and explain why they are classified that way.
Fixed costs, such as rent, remain constant regardless of production levels, while variable costs, like raw material expenses, will fluctuate based on the level of production.
Explanation:Firms classify their costs into two categories: fixed costs and variable costs. Fixed costs are expenses that do not change regardless of the level of production. For instance, a lease on a retail space would be considered a fixed cost as it remains the same whether you sell a lot or a little. On the other hand, variable costs are directly tied to the level of production. For example, the cost of buying materials to produce a product tends to rise as the level of production increases. It's variable because the more you produce, the more materials you would need, and therefore the cost varies with the level of output.
Learn more about Fixed and Variable Costs here:https://brainly.com/question/31543052
#SPJ2
3(−4x) + 3(5) = 12
−12x + 15 = 12
−12x + 15 − 15 = 12 − 15
−12x = −3
x =
Answer: 1/4
don't forget to rate and thank plz.