Answers
Area of the base of the prism: Ab=Area of the equilateral triangle
Height of the prism: h=6
Ab=A triangle= sqrt(3)/4*s^2
Ab=sqrt(3)/4*3^2
Ab=sqrt(3)/4*9
Ab=9 sqrt(3)/4
V=Ab*h
V=[9 sqrt(3)/4](6)
V=54 sqrt(3) /4
V=27 sqrt(3) / 2
V=27/2 sqrt(3)
Related Questions
Due tomorrow. Please help!!!!
Answers
[tex]d=\dfrac{a_{17}-a_{7}}{17-7}=\dfrac{81-41}{17-7}=\dfrac{40}{10}=4[/tex]
The first term of the sequence can be found from either of the given terms.
[tex]a_{7}=41=a_{1}+(7-1)d=a_{1}+24\\a_{1}=41-24=17[/tex]
The sum of 40 terms is
[tex]S_{40}=\dfrac{40}{2}(a_{1}+a_{40})=20(17+(17+39\cdot 4)=20\cdot 190=3800[/tex]
The sum of the first 40 terms is 3800.
A school play cost $1,200 to produce. if tickets sold for $5 each, the profit, p, made on the play by selling x tickets is given by the equation shown. p=5x−1,200 what is the slope of the line representing this equation?
Answers
Slope is always the number attached to x.
The slope of the line representing this equation will be;
⇒ $5
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The tickets sold for $5 each, the profit, p, made on the play by selling x tickets is given by the equation shown,
⇒ p = 5x - 1,200
Now,
We know that;
The slope - intercept form of an equation is,
y = mx + c
Where, 'm' is slope of the line and 'c' is y - intercept.
Here, The equation is,
⇒ p = 5x - 1200
By comparing, we get;
⇒ Slope (m) = 5
Thus, The slope of the line representing this equation = 5
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Before a renovation, a movie theater had 111 seats. After the renovation, the theater has 154 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
A. 28.1% B. 38.7% C. 43.3% D. 24.8%
Answers
(New number-Old number)/(Old number)×100
new number=154 seats
old number =111 seats
thus
Percentage increase is:
(154-111)/111×100
=38.7%
Answer: B. 38.7%
Which of the following have been used to measure wealth in early societies?
Cows
Dogs
Grain
Land
Metals
Answers
The answer is cows, metals, land, and grains.
how do I solve this?
Answers
[2² * (√(3x⁵))² - 2² * (√y)²]
Now simplify. Placing a square root to the power of 2 just cancels each other out so you're left with:
[4(3x⁵) - 4y]
Simplify again for your answer:
12x⁵ - 4y
the number of mosquito at the beginning of the summer was 4,000. the population of mosquito is expected to grow at a rate of 25% a month . how many mosquitoes will there be after 4 months
Answers
Using the formula for exponential growth and given an initial population of 4,000 mosquitoes with a 25% monthly growth rate, the mosquito population is expected to grow to approximately 9,766 after 4 months.
Explanation:The question involves calculating the growth of a mosquito population over a period, specifically after 4 months, given an initial population of 4,000 mosquitoes and a monthly growth rate of 25%. To find the population after 4 months, we use the formula for exponential growth:
P = P0 × (1 + r)n
where P is the population at the end, P0 is the initial population, r is the growth rate (expressed as a decimal), and n is the number of time periods.
Substituting the values, we get:
P = 4000 × (1 + 0.25)4
P = 4000 × (1.25)4
After calculating, we find that P = 9765.63. Thus, the population of mosquitoes after 4 months is expected to be approximately 9,766.
The mosquito population grows from 4,000 to approximately 9,766 over 4 months with a 25% monthly increase.
The initial number of mosquitoes is 4,000, and the population increases at a rate of 25% per month. To find the population after 4 months, we use the formula for compound interest:
P = P0 [tex](1 + r)^{t[/tex]
where:
P0 is the initial populationr is the growth ratet is the time in monthsGiven:
P0 = 4,000r = 25% or 0.25t = 4Substitute these values into the formula:
P = 4000 × (1 + 0.25)⁴
First, calculate (1 + 0.25):
1 + 0.25 = 1.25
Then, raise this to the power of 4:
(1.25)⁴ = 2.4414
Finally, multiply by the initial population:
P = 4000 × 2.4414 = 9765.6
Thus, the mosquito population after 4 months is approximately 9,766.
An item is priced at $13.04. If the sales tax is 5%, what does the item cost including sales tax? If necessary, round to the nearest cent.
A.
$13.56
B.
$13.24
C.
$12.39
D.
$13.69
Answers
13.04 * 0.05 = 0.652
When you round it to the nearest cent you get 69 cents
so the answer is D) 13.69
WHO LIKES PARABOLAS 3 MULTIPLE CHOICE
1. What is the vertex of the parabola? y−3=12(x+5)^2
2. The equation of a parabola is y=12x2+6x+23 .
What is the equation of the directrix?
y = 5.5
y = 4.5
y = 2
y = 0.5
3.The equation of a parabola is 132(y−2)2=x−1 .
What are the coordinates of the focus?
(−7, 2)
(1, 10)
(1, −6)
(9, 2)
Answers
[tex]y-3=12(x+5)^{2} \\ \\ y= 12(x+5)^{2}+3[/tex]
The vertex of the general parabolic equation:
[tex]y=a(x-h)^{2}+k [/tex]
lies at (h,k)
Comparing the given equation to general equation, we can write:
h = - 5
k = 3
So, the vertex of the given parabola will be (-5, 3)
Question 2) Equation of Directrix
The correct equation of the parabola is:
[tex]y= \frac{1}{2} x^{2} +6x+23 \\ \\ [/tex]
First we need to convert the equation to standard form as shown below:
[tex]y= \frac{1}{2}( x^{2} +12x)+23 \\ \\ y= \frac{1}{2}( x^{2} +12x+36)+23- \frac{1}{2}(36) \\ \\ y= \frac{1}{2}(x+6)^{2}+5 \\ \\ y-5= \frac{1}{2}(x+6)^{2} \\ \\ 2(y-5)=(x+6)^{2} \\ \\ 4( \frac{1}{2})(y-5)= (x+6)^{2}[/tex]
The directrix of the general parabola of the form:
[tex]4p(y-k)=(x-h)^{2} [/tex]
is y = k - p
Comparing equation of given parabola with general parabolic equation, we can write:
p =1/2
k = 5
So, equation of directirx will be:
y = 5 - 1/2 = 4.5
So, option B gives the correct answer.
Question 3) Focus of the parabola
The correct equation of the parabola is:
[tex] \frac{1}{32}(y-2)^{2}=x-1 \\ \\ (y-2)^{2}=32(x-1) \\ \\ (y-2)^{2}=4*8(x-1)[/tex]
Comparing this equation to the general parabolic equation, we can write:
p=8
h =1
k = 2
The focus of the parabola will be at (h+p,k) = (9,2)
So the focus of the parabola is at (9,2)
Thus, option D gives the correct answer.
Complete the solution of the equation. Find the value of Y when X equals 2. 2x - 2y = 22
Answers
substitute 2 as the value of x.
we get;
2*2 -22 = 2y
4 - 22 = -18 = 2y
y = -9
The value of Y when x = 2 is y = -9
If prices increase at a monthly rate of 1.1%, by what percentage do they increase in a year, What is the annual inflation rate
Answers
P0=$1
A=P(1+r)^(td)
A=1(1+0.011)^12
A=1(1.011)^12
A=$1.1403
Yearly increase will therefore be 14.03%. Hence the inflation per year is 14.03%
Final answer:
To find the annual inflation rate when prices increase at a monthly rate of 1.1%, you use the formula for compounding interest, resulting in an approximate annual rate of 13.97%.
Explanation:
If prices increase at a monthly rate of 1.1%, to calculate the annual inflation rate, you should consider the compounding effect over the year. The general formula for finding the total percentage increase over multiple periods when compounded at each period is:
(1 + rate)^number of periods - 1.
In this case, the monthly rate is 1.1%, or 0.011 when expressed as a decimal. The number of periods (months) in a year is 12. Plugging these values into the formula gives:
(1 + 0.011)^12 - 1,
which calculates to:
1.011^12 - 1 = 0.1397 or 13.97%.
So, the annual inflation rate when prices increase at a monthly rate of 1.1% is approximately 13.97%.
The perimeter of a rectangle is 30 centimeters. The width of the rectangle is 6 centimeters. How long is the rectangle?
Answers
Anyone know this geometry question? Will give brainiest
Answers
Someone please help me?
Answers
AP = BP
3x-4 = 2x +12
subtract 2x from each side:
x-4 = 12
add 4 to each side:
x = 16
now we know x, replace x with 16 in the equation for AP:
AP = 3(16) -4
AP = 48 -4
AP = 44 meters
{3, 4, 7} list all the subsets.
Answers
Subsets that have 3 items: {3, 4, 7} which is the original set. Any set is a subset of itself.
---------------------------------------------------------------------------------------
Subsets that have 2 items
{3, 4}, {3, 7}, {4, 7}
---------------------------------------------------------------------------------------
Subsets that have 1 item
{3}, {4}, {7}
---------------------------------------------------------------------------------------
Subsets that have 0 items: the empty set which we write { } or using the symbol [tex]\varnothing[/tex]
---------------------------------------------------------------------------------------
So all together we have 8 subsets
{3, 4, 7}
{3, 4}, {3, 7}, {4, 7}
{3}, {4}, {7}
{ }
Side Note: There are n = 3 items in the original set so there are 2^n = 2^3 = 8 subsets possible. The collection of all subsets is known as a power set.
The subsets of {3, 4, 7} are {}, {3}, {4}, {7}, {3, 4}, {3, 7}, {4, 7}, {3, 4, 7}
Explanation:
When listing all the subsets of {3, 4, 7}, we include the empty set {}, as well as all the subsets that can be formed by selecting one or more elements from the original set. In this case, the subsets are:
{}{3}{4}{7}{3, 4}{3, 7}{4, 7}{3, 4, 7}Learn more about Mathematics here:https://brainly.com/question/26854035
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The chord AB is a diameter of O. True or false.
Answers
Answer:
False.
Step-by-step explanation:
We have been given a graph and a statement. We are asked to determine whether the given statement is true or false.
Statement: The chord AB is a diameter of O.
We know that diameter of a circle is a chord that passes through the center of the circle.
Upon looking at our given graph, we can see that chord AB doesn't pass through the center at point 'o', therefore, AB is not a diameter of circle O.
Therefore, the given statement is false.
Answer: False
Step-by-step explanation:
I just got it right on the quiz
A professor wants to arrange his books on a shelf. he has 30 books and only space on the shelf for 20 of them. how many different 20-book arrangements can he make using the 30 books? this is an example of a problem that can be solved using which method?
Answers
The number of possible arrangements is
[tex]P\left(30,20\right)=\frac{30!}{\left(30-20\right)!\times 20!}=30,045,015[/tex]
There are 30,045,015 possible 20-book arrangements.
Answer: Total arrangement are 30045015
Given problem will be solved with help of combination.
Step-by-step explanation:
When we find the arrangement in which the order does not matter then we use combination,
Here, we have to find the possible arrangement in which order does not matter,
Thus, we will use combination to find the answer.
Here the total number of books = 30
A self contains, the number of book = 20,
Hence, the total arrangement of 20 books out of 30 books
[tex]=^{30}C_{20}[/tex]
[tex]=\frac{30!}{20!(30-20)!}[/tex]
[tex]=\frac{30\times 29\times 28\times 27\times 26\times 25\times 24\times 23\times 22\times 21}{10!}[/tex]
[tex]=\frac{4.9557887\times 10^{12} }{3628800 }=30045015 [/tex]
Peaches varied directly as apples. when there were 40 peaches, there were 120 apples. how many apples went with 500 peaches?
Answers
let the number of peaches be p and that of apples be a
hence
p=ka
where
k is constant of proportionality given by:
k=p/a
when:
p=40, a=120
thus
k=40/120=1/3
thus the equation will be:
p=1/3a
thus the number of apples where there are 500 peaches will be:
500=1/3a
multiplying both sides by 3 we get:
500×3=1/3a×3
a=1500
Select the statement that is true. Answer Choices The sum of 0.12x2+0.3⎯⎯⎯ and 1.5x2−0.75 is 1.62x2+0.416 . -0.45x2+0.9 subtracted from 2.5x2−7.32 is -2.95x2+8.22 . The difference of 18.94x−0.4⎯⎯⎯ and -10.2x+4.5 is 8.74x−4.94⎯⎯⎯ . The product of 0.6⎯⎯⎯x+3.4 and -6x+5.7 is -4x2−16.6x+19.38 .
Answers
1]
(0.12x^2+0.3)+(1.5x^2-0.75)
=(0.12x^2+1.5x^2)+(0.3+0.75)
=1.62x+1.05
2]
(2.5x^2-7.32)-(-0.45x^2+0.9)
(2.5x^2+0.45x^2)+(-7.32-0.9)
2.95x^2-8.22
3](18.94x-0.4)-(-10.2x+4.5)
=(18.94x+10.2x)+(-0.4-4.5)
=29.14x-4.9
4] (x+3.4)(-6x+5.7)
=x(-6x+5.7)+3.4(-6x+5.7)
=-6x^2+5.7x-20.4x+19.38
=-6x^2-14.7x+19.38
Which of the following segments is a radius of O?
Please help
Answers
The segment that is a radius is
[tex]\bar{RO} [/tex]
EXPLANATION
A radius is any line segment from the center of a circle to the circumference.
From the above diagram, the center of the circle is O.
The points on the circumference are A, R S and T.
The only line from the circumference to the centre in the options above is the line segment RO.
The correct answer is B.
Note however that
[tex]\bar{AS}[/tex]
is a diameter, which is a special chord.
[tex]\bar{RA}[/tex]
is a chord.
[tex]
\bar{ST}[/tex]
is also a chord.
answer these questions. Number 1 and number 2.
Answers
2) A cone, the top right one, is being formed by the rotation.
In the data set below, what is the mean absolute deviation?4461526If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD):
Answers
If so, then the MAD is 1.43
To find the MAD, you first find the mean of the list. It is 4.
Then find the absolute difference of each number from the mean.
Those values are: 0,0,2,3,1,2,2
Now find the mean of those numbers and you have about: 1.43
What is the inverse of the function f(x)= 19/x^3 ?
Answers
Answer: [tex]f^{-1}(x)=\sqrt[3]{\dfrac{19}{x}}[/tex]
A function has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}. Which set of ordered pairs represents this function?
A.{(1, 2), (3, 4), (5, 6), (7, 2)}
B.{(1, 2), (3, 6), (5, 4), (5, 2)}
C.{(1, 2), (3, 2), (5, 2), (7, 2)}
D.{(1, 4), (3, 4), (5, 6), (7, 6)}
Answers
{1, 3, 5, 7}
We have the following range:
{2, 4, 6}
A value of the range belongs to each value of the domain.
Therefore, the ordered pairs are:
(1, 2)
(3. 4)
(5, 6)
Answer:
A. {(1, 2), (3, 4), (5, 6), (7, 2)}
A barn is an atomic unit of area equal to 10–28 m2. what is the surface area of the earth expressed in units of barn? assume the earth is a sphere with a radius of km. (the surface area of a sphere is 4πr2.)
Answers
we know that
surface area of a sphere=4*pi*r²
for r=6380 km------->r=6380 x 10^3 m
surface area of of the earth=4*pi*(6380 x 10^3)²-----> 511506576035121,52 m²
if 1 barn is equal to-------------> 10^(-28) m²
x barn----------------------> 511506576035121,52 m²
x=511506576035121,5/(10^(-28))------> x=5.12 x 10^42 barn
the answer is5.12 x 10^42 barn
Chauncey has 42 coins, all dimes and quarters. the total value of all these coins is $5.70. how many dimes does he have?
Answers
32 dimes = $3.20
$3.20 + $2.50 = $5.70
To determine the number of dimes Chauncey has, you can use the system of equations stemming from the total number of coins and their total value. Following through with the calculations, it turns out that Chauncey has 32 dimes.
Explanation:The subject at hand revolves around the concept of linear equations. Given that Chauncey has 42 coins (all dimes and quarters) worth $5.70, you can use a system of equations to figure out the number of each type of coin.
First, let d be the number of dimes and q be the number of quarters. The total number of coins is 42, so the first equation is d + q = 42.Second, a dime is worth $0.10 and a quarter is worth $0.25. Since the total value of coins is $5.70, another equation you can form is 0.10d + 0.25q = 5.70.Having formed this system of two equations, you can solve it by multiplying the first equation by 0.10, which gives 0.10d + 0.10q = 4.2.Subtract this new equation from the second equation: 0.10d + 0.25q - 0.10d - 0.10q = 5.70 - 4.2. Simplify this to 0.15q = 1.5.Divide each side by 0.15, then q = 10. Substitute q = 10 into the first equation to solve for d. This gives d = 42 - 10 = 32.So, Chauncey has 32 dimes.
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Rectangle ABCD is shown below with line EF passing through the center:
If rectangle ABCD is dilated by a scale factor of five about the center of the rectangle to create rectangle A'B'C'D', dilated line E'F' will
A: be parallel to the original line
B: shift five units to the right
C: be perpendicular to the original line
D: lie on the same line as the original
Answers
D: lie on the same line as the original
Answer:
D lie on thesame line as the original
Step-by-step explanation:
I took the test and hurray! It was correct
The population of a town increased from 5,400 to 6,000 people. What was the percent of the increase?
Answers
percentage increase = 600/5400 x 100 = 11.11%
Answer: 11.11%
two negative integers have a sum of -18 and a product of 80. what are the integers?
Answers
-8*-10=80
Please rate brainliest if this helped you.
The most reasonable answer would -8 and -10.
-8 * -10 = 80
-8 + -10 = 18
Hope I helped!
You are painting a ceiling in a room. The room measures 30 feet by 40 feet. One gallon of paint costs $25 and covers 200 square feet. How much will it cost to paint the ceiling?
A. $6
B. $17.50
C. $150
D. $1,200
Answers
the area of the room=30*40------> 1200 ft²
1 gallon of paint cover----------------> 200 ft²
x---------------------------> 1200 ft²
x=1200/200------> x=6 gallons
1 gallon cost------------> $25
6 gallons-----------> x
x=6*25-----> x=$150
the answer is
the option C. $150
Answer:
C. $150
Step-by-step explanation:
we know that
the area of the room=30*40------> 1200 ft²
1 gallon of paint cover----------------> 200 ft²
x---------------------------> 1200 ft²
x=1200/200------> x=6 gallons
1 gallon cost------------> $25
6 gallons-----------> x
x=6*25-----> x=$150
the answer is
the option C. $150
What is the equation for a line that passes through the points (-3,-3) and (6,21)?
Answers
[tex]\bf \cfrac{24}{9}\implies \cfrac{8}{3} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=\cfrac{8}{3}[x-(-3)] \\\\\\ y+3=\cfrac{8}{3}(x+3)\implies y+3=\cfrac{8}{3}x+8\implies y=\cfrac{8}{3}x+5[/tex]