Answer:
148:370
Step-by-step explanation:
2+5=7 parts
518÷7=74
1 part =74
2×74=148
5×74=370
A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids.
A hexagon is shown. The hexagon is comprised of 2 congruent isosceles trapezoids. The bases of the trapezoid have lengths of 5 and 8. The height of the trapezoid is 3.
The volume of the prism is 234 cubic units. What is the height of the prism?
3 units
4 units
6 units
8 units
Answer:
the answer is 4 units im pretty sure
Step-by-step explanation:
The height of the prism is 6 units.
The correct option is C.
What is a prism?A prism is a polyhedron in three dimensions with two identical ends.
To find the height of the prism, we need to use the formula for the volume of a prism, which is:
Volume = Base area x Height
Since the prism has two congruent hexagonal bases, we can find the base area by adding the areas of the two congruent isosceles trapezoids.
The area of an isosceles trapezoid is given by the formula:
Area = ((b1 + b2) / 2) x h
where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.
In this case, the two parallel bases have lengths of 5 and 8, and the height of each trapezoid is 3, so the area of one trapezoid is:
Area = ((5 + 8) / 2) x 3 = 19.5 square units
The base area of the prism is then:
Base area = 2 x 19.5 = 39 square units
We are given that the volume of the prism is 234 cubic units, so we can use the formula for the volume of a prism to find the height:
Volume = Base area x Height
234 = 39 x Height
Height = 6 units
Therefore, the height of the prism is 6 units.
To learn more about the prism;
https://brainly.com/question/12649592
#SPJ7
Which expression is equivalent to (startfraction 4 m n over m superscript negative 2 baseline n superscript 6 baseline endfraction) superscript negative 2? assume m not-equals 0, n not-equals 0.
The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].
From the principle of indices we get,
Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]
Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]
Multiplication, [tex]a^{mn}=(a^m)^n[/tex]
negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]
Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
Calculating we get,
[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae
[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]
[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices
[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula
Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].
Learn more about Indices here -
https://brainly.com/question/170984
#SPJ10
Answer:
b
Step-by-step explanation:
edge 23
The distance between points A and B is 15. The coordinates of point A are (1, 18) and the
coordinates of B are (13, z). Solve for the two values of z. Show your work to prove your
answer.
Answer:
9 and 27
Step-by-step explanation:
let me know if you want an explanation
Help me with steps please!
Answer:
18, 36, 54
Step-by-step explanation:
Find the least common multiple of 6 and 9:
Multiples of 6: 6, 12, 18, ......
Multiples of 9: 9, 18, 27, ......
We see that 18 is the least common multiple of 6 and 9.
Additional multiples of 18 are 36 and 54.
If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.
How to estimate an integer which is divisible by 6 and by 9?Consider the statement as a contradiction.
The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.
Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product [tex]$2 \times 3 \times 3=18$[/tex] exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of [tex]$2 \times 2 \times 3 \times 3=36$[/tex] which exists also not divisible by 54.
Therefore, the correct answer is option e) 54.
To learn more about integers
https://brainly.com/question/96523
#SPJ2
The area of a rectangle, A = l • w is represented by the expression 24x^6y^15. Which could be the dimensions of the rectangle?
After calculating the value, l & w could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
Calculation:The inquiry relates to the laws of indices
where, [tex]x^{a} * x^{b}=x^{a+b}[/tex]
Provided the query, A= [tex]24x^{6}y^{15}[/tex]
[tex]2* 12[/tex] might be used to calculate the length and width of 24.
Hence,
[tex]x^{6}=x^{5} * x^{1} =x^{5+1}[/tex]
& [tex]y^{15}= y^{8} * y^{7} =y^{8+7}[/tex]
So, it can be written as,
A=l * w
⇒ [tex]24x^{6}y^{15}[/tex] = [tex]2x^{5}y^{8}[/tex] * [tex]12xy^{7}[/tex]
Therefore, it is concluded that the dimensions of the rectangle could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
Learn more about rectangles:
https://brainly.com/question/15019502?referrer=searchResults
#SPJ10
if 9^x=25, what does 3^x equal?
Answer:
[tex]3^x=5[/tex]
Step-by-step explanation:
Given:
[tex]9^x=25[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^x=25[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2x}=25[/tex]
Apply the same exponent rule:
[tex]\implies (3^x)^2=25[/tex]
Square root both sides:
[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]
[tex]\implies 3^x=5[/tex]
Five hundred ten of 650 high school students said that pizza was their favorite food in the school cafeteria.
what is the margin of error? round to four decimal places.
0.0005
0.0003
0.0161
0.0322
If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.
Margin of errorGiven:
Sample proportion=Five hundred ten=510
Sample size=650
Hence:
Margin of error=z×√p×(1-p)/n
Margin of error=2√510/650× (1-510/650)÷650
Margin of error=2√0.78461538×(1-0.78461538)÷650
Margin of error=2√0.78461538×0.21538462÷650
Margin of error=2√0.168994085÷650
Margin of error=2√0.0002599909
Margin of error=0.0322
Therefore the correct option is D.
Learn more about margin of error here:https://brainly.com/question/24289590
#SPJ1
Reposting this question since no one helped last time
Answer:
450 N
Step-by-step explanation:
Since you have the VOLUME and the HEIGHT of the prism, you can calculate the AREA of the prism base :
18 m^3 / 3 m = 6 m^2 area
Now you are given pressure = force / area
75 n/m^2 = force / 6 m^2
6 *75 = force = 450 N
Answer:
450 newtons
Step-by-step explanation:
To solve for the force, we first need to find the area. (Force = Pressure × Area)
[tex]Area = \frac{volume}{height} = \frac{18m^{3} }{3m} = 6m^{2}[/tex]
Now we just substitute this number into [tex]Force = Pressure * Area[/tex] and get that [tex]Force = 75newtons/m^{2} * 6m^{2} = 450 newtons[/tex]
(p.s. Units are very important! This question doesn't require any unit
conversions, but others might.)
Two open cylinders have the same radius but one is twice as long as the other.
a) Calculate the volume of the two cylinders and compare them using a final statement (sentence).
b) Calculate the surface area of the two cylinders and compare them using a final statement (sentence). If you notice a relationship between volume and surface area,add it to your final
statement. (God bless anyone who can help me ).
Answer:
shown below
Step-by-step explanation:
a) V = h(pi)r²
let x = height
and c = the constant radius
V1 = 2x(pi)c²
V2 = x(pi)c²
let c = random number, such as 2
let x = 3
2x(pi)4
x(pi)4
pi(4) = 12.57
3 x 12.57 = 37.7
6 x 12.57 = 75.4
We can compare these ans realise that the cylinder with double the height will also have double the volume.
b) SA = h(pi)2c
SA1 = 2x(pi)2c
SA2 = x(pi)2c
let c = 2
let x = 3
2(3)(pi)(2(2))
6(pi)4
24(pi)
3(pi)(2)(2)
3(pi)(4)
12(pi)
I don't need to finish the calulation to see that this is also halved. So the surface area of the one with the double length is twice the surface area of the one with a smaller height.
Comparatively, both the volume and surface area are doubled when the height is doubled.
QED.
Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
The measure of angle ABC is
°.
The measure of angle BAC is
°.
The measure of angle ACB is
°.
The measure of angle ∠ACB is 70°. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
∠ABC + ∠BCA + ∠CAB = 180°
60° + ∠BCA + 50° = 180°
∠BCA = 180° – 110°
∠BCA = 70°
Then the correct option is C.
The complete question is given below.
Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
The measure of ABC is 60
The measure of BAC is 50
The measure of ACB will be
a. 50
b. 60
c. 70
d. 120
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
Answer:
Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
The measure of angle ABC is
✔ 60
°.
The measure of angle BAC is
✔ 50
°.
The measure of angle ACB is
✔ 70
°.
Step-by-step explanation:
2
Select the correct answer.
What is the solution to the equation?
3+√3x5 = x
O A.
-2 and -7
OB.
2 and 7
O C.
-2
OD. 7
The solution to the equation is x = 7 , -2 , Option C and D is the right answer.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.
It is given that the equation is
[tex]\rm 3 +\sqrt{3x - 5}= x[/tex]
Taking square on both sides
3x-5 = (x-3)²
3x-5 = x² +9 -6x
x² -9x -14 = 0
x² -7x +2x -14 = 0
x(x-7) +2(x-7) = 0
(x-7)(x+2) = 0
x =7 , x = -2
Therefore the solution to the equation is x = 7 , -2 , Option C and D is the right answer.
To know more about Equation
https://brainly.com/question/10413253
#SPJ1
Find the range for the given domain: {-2, -1, and 0} and the function is y = 3x2.
The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.
What is range?
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that:-
The range for the given domain: {-2, -1, and 0} and the function is y = 3x².
The range will be the value of y at each given value of the domain.
Domain: { -2, -1, 0 }
y = 3x²
At x = -2 → y = 3 ( -2)² = 12
At x = -1 → y = 3 (-1)² = 3
At x = 0 → y = 3 (0) = 0
Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.
To know more about Range follow
brainly.com/question/26098895
#SPJ1
If 1:w is equivalent to 1⅔: 5, find w.
Answer:
w = 3
Step-by-step explanation:
1/w = 1 2/3 / 5 cross multiply
1 2/3 (w) = 5
w = 5 / ( 1 2/3 ) = 5 / ( 5/3) = 15/5 = 3
Which pair of ratios makes a proportion?
A. 1/4 and 5/25
B. 1/4 and 7/24
C. 1/4 and 10/48
D. 1/4 and 9/36
Answer:
D. 1/4 and 9/36Step-by-step explanation:
If two ratios make a proportion then it can be shown as:
a/b = c/d ⇒ ad = bcLet's verify the answer choices with this method
A. 1/4 and 5/25
1*25 = 4*525 = 20, incorrect, not a proportionB. 1/4 and 7/24
1*24 = 4*7 24 = 28, incorrect, not a proportionC. 1/4 and 10/48
1*48 = 4*1048 = 40, incorrect, not a proportionD. 1/4 and 9/36
1*36 = 4*936 = 36, correct, this is a proportionhe tables represent the functions f(x) and g(x). A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, f(x), has the entries, negative 5, negative 3, negative 1, 1, 3, 5. A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, g(x), has the entries, negative 13, negative 9, negative 5, negative 1, 3, 7. Which input value produces the same output value for the two functions?
A function assigns the values. The input value that produces the same output value for the two functions is 1.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given tables the x is the input while f(x) and g(x) are the outputs of the respective functions. Therefore, the input for which the two given functions will return the same output is 1.
Hence, the input value that produces the same output value for the two functions is 1.
Learn more about Function:
https://brainly.com/question/5245372
#SPJ1
y = x - 1/2, (-5, -2)
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = x - 1/2, (-5, -2)
we can plug in the point (-5, -2)
-2 = (-5) - 1/2
-2 = -5.5
-2 does not equal -5.5 so this point is not on the line
Learn more about slope and y-intercept here: brainly.com/question/12763756
Given: f(a)= a³ +a and g(a) = a -1 Find: (fog)(a)
Answer:
(fog)(a) = a³ - 3a² + 4a - 2
= (a - 1)×(a² - 2a + 2)
Step-by-step explanation:
Given :
g(a) = a -1
f(a)= a³ +a
…………………………
(fog)(a) = f(g(a)))
= g(a)³ + g(a)
= (a - 1)³ + (a - 1)
= (a³ - 3a² + 3a - 1) + (a - 1)
= a³ - 3a² + 3a - 1 + a - 1
= a³ - 3a² + 3a + a - 1 - 1
= a³ - 3a² + 4a - 2
Second method :
(fog)(a) = f(g(a)))
= f(a - 1)
= (a - 1)³ + (a - 1)
= (a - 1)×[(a - 1)² + 1]
= (a - 1)×[a² - 2a + 1 + 1]
= (a - 1)×(a² - 2a + 2)
Complete the statements about the cross sections of cylinders and cones.
The cross section parallel to the base of a cone is a
The cross section parallel to the base of a cylinder is a
The cross section perpendicular to the base of a cone is a
The cross section perpendicular to the base of a cylinder is a
The cross-section parallel to the base of a cone is a circle
The cross-section parallel to the base of a cylinder is a circle
The cross-section perpendicular to the base of a cone is a triangle
The cross-section perpendicular to the base of a cylinder is a rectangle
Make "t" subject by algebra:-
s=ut+at2
Find the y-intercept and the slope of the line.
6x-2y=5
Answer:
m=3
b=(0,5)
Step-by-step explanation:
ST
6
9
10
Which phrase best describes the translation from the graph y = 2x² to the graph of y = 2x² + 5?
O 5 units up
O 5 units down
O 5 units right
O 5 units left
The answer to the question is 5 units up.
A sequence of numbers begins with 12 and progresses
geometrically. Each number is the previous number
divided by 2.
Which value can be used as the common ratio in an
explicit formula that represents the sequence?
N/H
02
06
O 12
Answer:
1/2
Step-by-step explanation:
since every time you divide by 2, the common ratio is 1/2
Find the general solution of the given differential equation. cos^2(x)sin(x)dy/dx+(cos^3(x))y=1 g
If the given differential equation is
[tex]\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1[/tex]
then multiply both sides by [tex]\frac1{\cos^2(x)}[/tex] :
[tex]\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)[/tex]
The left side is the derivative of a product,
[tex]\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)[/tex]
Integrate both sides with respect to [tex]x[/tex], recalling that [tex]\frac{d}{dx}\tan(x) = \sec^2(x)[/tex] :
[tex]\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx[/tex]
[tex]\sin(x) y = \tan(x) + C[/tex]
Solve for [tex]y[/tex] :
[tex]\boxed{y = \sec(x) + C \csc(x)}
which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex].
Help me please I need this for tomorrow please please
Fraction
4 5/6 -2 2/7 - 1 3/14
Answer:
1.3 or 1.333333
Step-by-step explanation:
Just do it!
What is the solution set for Ix+3| =5?
S-8 and s-8
s=-2 and s=2
s=-8 and s=2
s = 2 and s= 8
What value of a make the equation 14-a=19-12
[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]
Answer:
7
Step-by-step explanation:
14-a=19-12
14-a=7
14-7=a
7=a
Combine like terms
Choose the end behavior of the graph of each polynomial function.
Options
Falls to the left and rises to the right
Rises to the left and falls to the right
Rises to the left and rises to the right
Falls to the left and falls to the right
Using limits, the end behavior of the functions are given as follows:
a. Rises to the left and falls to the right.
b. Rises to the left and rises to the right.
c. Falls to the left and rises to the right.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In item a, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty[/tex]
Hence it rises to the left and falls to the right.
In item b, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty[/tex]
Rises to the left and rises to the right.
In item c, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty[/tex]
Falls to the left and rises to the right.
More can be learned about limits and end behavior at https://brainly.com/question/22026723
#SPJ1
8. How do outliers affect the mean of a data set?
OIt does not change.
It depends whether the outlier is a high outlier or a low outlier.
It decreases.
It increases.
Answer:
it depends on whether the outlier is a high outlier or a low outlier
Step-by-step explanation:
The mean of a data set is the average of the data set. So if I had the data set {5, 2, 10} the average would be (5+2+10)/3 = 5.667. Now if I added an outlier like 10,000 it would increase the mean significantly. It changes it significantly but I cannot say whether it increases or decreases it without knowing the value of the outlier, since if I had the outlier -10,000 that would decrease the mean, but I had the outlier 10,000 it would increase it. So it depends on whether the outlier is a high outlier or a low outlier
A trash can is in the shape of a cylinder. It has a radius of 2 feet and a height of 5 feet. What is the volume of the trash can? Round to the nearest tenth. Use 3.14 for pi
Answer: 62.8 cubic feet
Step-by-step explanation:
R is radius
H is height
R=2ft
H=5ft
V=(3.14)(2)^2(5)
V=62.8 cubic feet