Answer:
the largest number that is less than (2+√3)^6 is 2701
Step-by-step explanation:
[tex]\bigstar \ (2+\sqrt{3})^6= \\\\C{}^{0}_{6}2^{6}+C{}^{1}_{6}2^{5}\sqrt{3}^1+C{}^{2}_{6}2^{4}\sqrt{3}^2+C{}^{3}_{6}2^{3}\sqrt{3}^3+C{}^{4}_{6}2^{2}\sqrt{3}^4+C{}^{5}_{6}2^{1}\sqrt{3}^5+C{}^{6}_{6}\sqrt{3}^6[/tex]
[tex]=64+192\sqrt{3}+720 +480\sqrt{3} +540+108\sqrt{3} +27\\=1351+780\sqrt{3}[/tex]
[tex]\bigstar\ (2-\sqrt{3} )^6 =\\\\1351-780\sqrt{3}[/tex]
[tex]\bigstar\ \bigstar\ (2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =\\\\1351+780\sqrt{3}+1351-780\sqrt{3}[/tex]
[tex]\Longrightarrow(2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =2702[/tex]
[tex]\Longrightarrow(2+\sqrt{3} )^6 =2702-(2-\sqrt{3} )^6[/tex]
[tex]0 < \left( 2-\sqrt{3} \right) < 1 \Longrightarrow 0 < \left( 2-\sqrt{3} \right)^{6} < 1 \Longrightarrow-1 < \left( 2-\sqrt{3} \right)^{6} < 0[/tex]
[tex]\Longrightarrow2702-1 < 2702-\left( 2-\sqrt{3} \right)^{6} < 2702+0[/tex]
[tex]\Longrightarrow 2701 < \left( 2+\sqrt{3} \right)^{6} < 2702[/tex]
Find the slope easy giving brainlest
Answer:
Problem 20: [tex]m[/tex] = [tex]2[/tex]
Problem 21: [tex]m[/tex] = [tex]-2[/tex]
Problem 22: [tex]m[/tex] = [tex]1[/tex]
Problem 23: [tex]m[/tex] = [tex]3[/tex]
Step-by-step explanation:
The formula to find the slope of a line: [tex]m = \frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex].
Problem 20:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{3-7}{2-4}[/tex]
[tex]m[/tex] = [tex]\frac{-4}{-2}[/tex]
[tex]m[/tex] = [tex]2[/tex]
Problem 21:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{-5-1}{2--1}[/tex]
[tex]m[/tex] = [tex]\frac{-6}{3}[/tex]
[tex]m[/tex] = [tex]-2[/tex]
Problem 22:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{3-7}{-6--2}[/tex]
[tex]m[/tex] = [tex]\frac{-4}{-4}[/tex]
[tex]m[/tex] = [tex]1[/tex]
Problem 23:
1) Substitute the values into the formula and solve it.
[tex]m[/tex] = [tex]\frac{-4-2}{-4--2}[/tex]
[tex]m[/tex] = [tex]\frac{-6}{-2}[/tex]
[tex]m[/tex] = [tex]3[/tex]
*Extra*: The equation of a line is written in this form: [tex]y = mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is [tex]y[/tex]-intercept
I need some help with this question.
Answer:
I believe it would be C
Step-by-step explanation:
71+36=107
180-107=73
it don't make sense for it to be right because none of the angles are 90°
If EH = w and GH = 4w - 51, what is GH?
Answer:
Step-by-step explanation:
EH=w
then it is as simple as pluggin in
gh=4(eh)-51
Sarah makes home-made jewelry sets. Each jewelry set includes a necklace, a bracelet and two earrings. Given below are the number of beads Sarah adds to each type of jewelry.
Necklace: 48
Bracelet: 19
Earrings: 6 (both earrings combined)
What is the largest number of jewelry sets she can make with 7100 beads?
Based on the number of beads that are needed to make a jewelry set, the largest number of jewelry sets that Sarah can make with 7,100 beads is 97 jewelry sets.
What amount of jewelry sets can Sarah make?First find the total number of beads used per jewelry set:
= Necklace + Bracelet + Earrings
= 48 + 19 + 6
= 73 beads
If she had 7,100 beads, the sets she could make would be:
= Total number of beads / Beads per set
= 7,100 / 73
= 97 jewelry sets
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Find the Interquartile Range for the following test scores: 98, 93, 75, 86, 79, 82, 77 (Remember to put in order)
Please help so lost, it is not making any sense
????????
Step-by-step explanation:
1,1,1
Can someone help please?
See attached. The box-and-whisker plot gives us all the information we need to solve.
Minimum: 13
Maximum: 35
Range: 22
-> 35 - 13 = 22
Median: 20.5
A car's speed is 80 2/3 miles in one hour. Going at the same speed, how far (in miles) will it travel in 2 1/4 hours?
Answer:
181.5 miles
Step-by-step explanation:
80 2/3 m/hr * 2 1/4 hr = 181. 5 miles
The graph of Fx), shown below, resembles the graph of G(x) = x, but it has
been changed somewhat. Which of the following could be the equation of
Fx)?
5
GO) = x2
5
FOO = ?
+
O A. F(x) = -x2 - 4
O B. FX) = x2 - 4
O C. Fx) = -(x - 4)2
O D. Fx) = -(x+4)2
Using translation concepts, it is found that the equation of F(x) could be given by:
A. F(x) = -x² - 4.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function g(x) = x² was reflected over the x-axis and shifted 4 units down, hence f(x) is given by:
A. F(x) = -x² - 4.
More can be learned about translation concepts at https://brainly.com/question/4521517
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In a random sample of 2500 sports fans, 61% prefer basketball over soccer.
What is the Margin of error in this survey?
Margin of error = [m]%
The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The Margin of error in this survey is 1%.
What is the margin of error?The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.
The random sample of 2500 sports fans, out of which 61% prefer basketball over soccer, therefore, we can write n=2500 and p=0.61. Thus, the margin of error can be written as,
[tex]MOE=\sqrt{\dfrac{\hat p(1-\hat p)}{n}} = \sqrt{\dfrac{0.61(1-0.61)}{2500}} = 0.00975 = 0.975\% \approx 1\%[/tex]
Hence, the Margin of error in this survey is 1%.
Learn more about Margin of Error:
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Which of the triangles shown are obtuse triangles?
A group of triangles. Triangle A has three equal angles. Triangle B has two acute angles and one obtuse angle. Triangle C has two acute angles and one ninety degree angle. Triangle d has two acute angles and one obtuse angle.
Group of answer choices
Triangle A and Triangle B
Triangle B and Triangle D
Answer:
BD
Step-by-step explanation:
Write the standard form of the equation of a circle with radius 3 and center (11, 3)
Answer:
x² - 22x + y² - 6y + 121 = 0
Step-by-step explanation:
General Form of Equation
(x - h)² + (y - k)² = r²Solving
(x - 11)² + (y - 3)² = (3)²x² - 22x + 121 + y² - 6y + 9 = 9x² - 22x + y² - 6y + 121 = 0Answer:
(x+11)2+(y−3)2=81
mark me brainliest
Step-by-step explanation:
which graph represents y=3x-5
Answer:
(it won't let me paste a graph here)
(but it a / line on the graph.)
Step-by-step explanation:
Use Desmos Graphic Calculator, plot this equation in and it should show up a graph of that. : )
Juan has 22 balloons and each balloon can hold up to 8.23 ounces of water. How much water would he use if he filled all the balloons completely?
Answer:
181.06
Step-by-step explanation:
Which scale you would use on the coordinate plane to plot each set of points? A Select . (1.-6).(-7,-8), (-3, 7), (0.9) • (-20, -30).(-40, 10), (20, -10), 5. -20) Select] Select) •,( (-3,-1), (§. -13), 3, 3), (1,0
Answer:qjs
Step-by-step explanation:
A
X= -7 to 1
Y= -8 to 9
B
X= -40 to 20
Y= -30 to 10
Find the missing angle
Answer:
36 degrees
Step-by-step explanation:
We do bottom triangle first:
33+90=123. 180-123=57
Go to upper tri: 90-57=33
111+33=144. 180-144=36.
?=36 degrees
Hope it helps
could i have some quick quick help?
Turn over into vertex form
y=-30t²+450t-790y=-30(t²-15x+79/3)Solving
y=-30[(t-15/2)²-359/12]Open brackets
y=-30(t-15/2)²+1795/2Accurating
y=-30(t-7.5)²+897..5Compare to Vertex form y=a(x-h)²+k
Vertex
(h,k)=7.5,897.5Max profit is $897.5
ticket price should be $7.5Answer:
$7.50
Step-by-step explanation:
Completing the square formula
[tex]\begin{aligned}y & =ax^2+bx+c\\& =a\left(x^2+\dfrac{b}{a}x\right)+c\\\\& =a\left(x^2+\dfrac{b}{a}x+\left(\dfrac{b}{2a}\right)^2\right)+c-a\left(\dfrac{b}{2a}\right)^2\\\\& =a\left(x-\left(-\dfrac{b}{2a}\right)\right)^2+c-\dfrac{b^2}{4a}\end{aligned}[/tex]
[tex]\begin{aligned}P & =-30t^2+450t-790\\& =-30\left(t^2+\dfrac{450}{-30}t\right)-790\\\\& =-30\left(t^2+\dfrac{450}{-30}t+\left(\dfrac{450}{2(-30)}\right)^2\right)-790-(-30)\left(\dfrac{450}{2(-30)}\right)^2\\\\& =-30\left(t-\left(-\dfrac{450}{2(-30)}\right)\right)^2-790-\dfrac{450^2}{4(-30)}\\\\& =-30(t-7.5)^2+897.5\end{aligned}[/tex]
Therefore, the vertex is (7.5, 897.5)
So the ticket price that maximizes daily profit is the x-value of the vertex: $7.50
3. Seth uses a bowl to fill a container with soil. The
bowl holds 3/4 cup of soil. How many cups of soil
does the container hold if it takes 13 full bowls of soil
to fill it?
how many solutions does the following have? 3 (2x-4) = 2 (3x-6)
Answer: There are infinite solutions.
Step-by-step explanation:
3(2x-4) = 2(3x-6)
6x - 12 = 6x - 12
-12 = -12
0 = 0
In how many ways can a teacher arrange 5 students in the front row of a classroom if there are 20 students in the class
Answer:
4 times
Step-by-step explanation:
because there's only enough space for that many in each row.
Which sport is required to have both male and female competitors ?
A. Hockey
B. Water polo
C. Mixed doubles tennis
D. Swimming
Answer:
Mixed Doubles Tennis
Step-by-step explanation:
The key word is "mixed." In this case it means a male and female competitor
b) f(x) = 3 |x – 41| + 5
Domain:
Range:
Where does the energy stored in coal originally come from?
A. The Earth's Core
B. Minerals
C. The Sun
D. Radioactive material in the crust
Answer: The Sun
Step-by-step explanation:
Energy has existed from the beginning of time. The sun was the initial source of energy, providing heat and light during the day. People used light to wake up and sleep, depended on wood and dung for heat, and water power to run primitive mills.
Select all the correct answers.
Which four inequalities can be used to find the solution to this absolute value inequality?
Answer:Which four inequalities can be used to find the solution to this absolute value inequality?3+2|x-11 <9
2(x - 1) <-3
x-1 <9
X-1 >-9
-2(x - 1) > 3
x-1-3
X-1 <3
Step-by-step explanation:
There is no document, so nobody could answer.
If x + 1 and x-1 ghe factors of f (x) = x ^ 3 + 2ax + b calculate the valves of a and b. using theses values of and by factorise f(x) completely.
Since both x + 1 and x - 1 are factors of f(x), we have the factorization
x³ + 2ax + b = (x + 1) (x - 1) (x - b)
where the last root must be x = b in order that b is the constant term in the cubic.
Expanding the right side and equating coefficients gives
x³ + 2ax + b = x³ - bx² - x + b
which tells us
-b = 0 ⇒ b = 0
2a = -1 ⇒ a = -1/2
Then we have
f(x) = x³ + 2 (-1/2) x + b = x³ - x
or
f(x) = x (x + 1) (x - 1)
answer these questions and show working out.
(extra points for all)
Answer:
See below
Step-by-step explanation:
We can find the Highest Common Factor (HCF) by the prime factorization of the terms.
===============================================================
a) 4 and 5
⇒ 4 = 4 x 1
⇒ 5 = 5 x 1
⇒ HCF (4, 5) = 1
=============================================================
b) 8 and 13
⇒ 8 = 2 x 2 x 2 x 1
⇒ 13 = 13 x 1
⇒ HCF (8, 13) = 1
=============================================================
i) 80 and 120
⇒ 80 = 40 x 2
⇒ 120 = 40 x 3
⇒ HCF (80, 120) = 40
the student council at mountain view high school plans to conduct a survey to determine the student body's opinion of the new lunch menu. which of the following sampling methods would be most likely to result in self-selection bias?
A. obtaining an alphabetical list of all students and surveying every 10th student
B. setting up a booth in the lunchroom where students can give theirthoughts
C. handing out a questionnaire to students leaving campus at lunchtime
D. handing out a questionnaire to seniors only
The sampling method that would be most likely to result in self-selection bias is given by:
D. handing out a questionnaire to seniors only
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, in option D, only seniors are involved, that is, it does not involve all segements, hence it would be most likely to result in self-selection bias.
More can be learned about sampling concepts at https://brainly.com/question/25122507
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Answer: C. handing out a questionnaire to students leaving campus at lunchtime
Step-by-step explanation:
Find the surface area and volume of the figure.
Step-by-step explanation:
this is again a combined object.
at the bottom there is a cylinder.
and on top there is half of a sphere (I assume it is a sphere, because there is no additional information about its height, and we could therefore not solve this otherwise).
for the total volume we need to calculate both volumes and add these results.
for the total surface area we need to calculate both surface areas, but remove the top surface area of the cylinder, because the half-sphere is covering it.
so, let's start with the volume :
the volume is a cylinder is
ground area × height = pi×r² × height
the radius is half of the diameter, so, r = 18/2 = 9 ft.
in our case that gives us
pi×9² × 10 = pi×81 × 10 = 810×pi = 2,544.690049... ft³ ≈
≈ 2,544.7 ft³
the volume of a sphere is
pi×r³ × 4/3
and of a half-sphere therefore
pi×r³ × 4/3 / 2 = pi×r³ × 2/3 = pi×9³ × 2/3 = pi×9² × 2 =
= pi×81 × 2 = 162×pi = 508.9380099... ft³
≈ 508.9 ft³
the total volume is then
3,053.628059... ft³ ≈ 3,053.6 ft³
the surface area :
the surface area of a cylinder is
the areas of the circles on the top and the bottom (but here we need only the bottom) plus the area of the lateral side area, the "mantle", which is the circumference of the basic circle times height.
so, in our case we get
pi×r² + 2×pi×r×height
pi×9² + 2×pi×9×10 = 81pi + 180pi = 261pi =
= 819.9556826... ft² ≈ 820 ft²
the surface area of a sphere is
4×pi×r²
and therefore if a half-sphere
4×pi×r² / 2 = 2×pi×r²
in our case
2×pi×9² = 2×pi×81 = 162pi = 508.9380099... ft²
≈ 508.9 ft²
the total surface area is then
1,328.893692... ft² ≈ 1,328.9 ft²
The histogram below represents the high tempatures recorded each day over a one month period. How many days had a tempature below 60
Answer: 22
Step-by-step explanation:
write a event that has a probability of 1
A probability of 1 means that the event will happen. If the probability of a road traffic accident was 1 there would be nothing you could do to stop it.
that's my answer