Answers
Related Questions
This exercise involves the formula for the area of a circular sector. The area of a circle is 700 m2. Find the area of a sector of this circle that subtends a central angle of 3 rad.
Answers
Answer:
334.4 m²
Step-by-step explanation:
The formula for the area of a sector is given as:
1/2 × r² × θ
Where θ = Central angle
Area of a Circle = 700 m²
The formula for the area of a circle = πr²
r = Radius of a circle
r² = Area / π
r = √Area / π
r = √700/π
r = 14.927053304 m
Approximately, r = 14.93 m
Therefore, the area of the sector
= 1/2 × r² × θ
= 1/2 × 14.93² × 3 rad
= 334.35735 m²
Approximately, Area of the sector = 334.4 m²
Find value a when the angle between vectors U=(2,a) and V = (-6;8) is pie/4
Answers
Answer:
Step-by-step explanation:
The formula to find the angle between 2 vectors is
[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is
u·v = (2×(-6)) + (a×8) so
u·v = -12 + 8a. Then we need the magnitudes of both u and v:
[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and
[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]
Putting all of together looks like this:
[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get
[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is
[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:
100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get
800 + 200a² = 256a² -768a + 576. Combine like terms to come up with
0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.
Therefore, the value for a is 14. I checked it...it works
Answer:
a = 14, U = (2, 14)
Step-by-step explanation:
the other answer is correct.
just to add the solution path for the quadratic equation
0 = 56a² - 768a - 224
in general, a quadratic equation usually expressed in x
0 = ax² + bx + c
has its solution as
x = (-b ± sqrt(b² - 4ac))/(2a)
for us here this looks like this then
a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =
= (768 ± sqrt(589824 + 4×56×224))/112 =
= (768 ± sqrt(589824 + 50176))/112 =
= (768 ± sqrt(640000))/112 = (768 ± 800)/112
a1 = (768 + 800)/112 = 1568/112 = 14
a2 = (768 - 800)/112 = -32/112 = -0.29
and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.
so, 14 is the solution for U.
A square dancing contest has 245 teams of 4 pairs each. How many dancers are participating in the contest?
Answers
Answer:
1960 dancers
Step-by-step explanation:
your are on "ace" level and need help here ?
a pair is 2 people
4 pairs is therefore 4×2 people = 8
245 teams of 4 pairs or 8 people each means
245×8 = 1960 people
write 0.824 as a fraction in the simplest form
Answers
A high school has 32 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 233 pounds
Answers
Answer:
[tex]\% = 11.96\%[/tex]
Step-by-step explanation:
Given
See attachment for box plot
Required
Percentage greater than or equal to 233
From the box plot, the maximum is:
[tex]Max = 244[/tex]
The minimum is:
[tex]Min = 152[/tex]
Percentage greater than 233 is calculated as:
[tex]\% = \frac{Max - 233}{Max - Min}[/tex]
[tex]\% = \frac{244 - 233}{244-152}[/tex]
[tex]\% = \frac{11}{92}[/tex]
Express as percentage
[tex]\% = \frac{11}{92}*100\%[/tex]
[tex]\% = \frac{1100}{92}\%[/tex]
[tex]\% = 11.96\%[/tex]
Answer this guys please
Answers
[tex]\longrightarrow{\green{A.\:-8}}[/tex] ✔
Step-by-step explanation:
[tex]f(x )= - {x}^{2} + 1[/tex]
Plugging in the value "[tex]x\:=\:-3[/tex]" in the above expression, we have
[tex]f( - 3) = - ({ - 3})^{2} + 1 \\ \\ = - ( - 3 \times - 3) + 1 \\ \\ = - (9) + 1 \\ \\ = - 9 + 1 \\ \\ = - 8[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
[tex] \quad \quad \quad \quad \tt{f(x) = { - x}^{2} + 1} \: \: when \: \: x = - 3[/tex]
Let's try![tex] \quad \quad \quad \quad \tt{ ⟶f(x) = { - x}^{2} + 1}[/tex]
[tex] \quad \quad \quad \quad \tt{⟶f(-3) = {- (-3)}^{2} + 1}[/tex]
[tex] \quad \quad \quad \quad \tt{⟶ f( - 3) = { - (9) + 1}}[/tex]
[tex]\quad \quad \quad \quad \tt{⟶ f( - 3) = { - 9 + 1}}[/tex]
[tex]\quad \quad \quad \quad \tt{ ⟶f( - 3) = { -8}}[/tex]
Hence, The answer is:[tex]\quad \quad \quad \quad \boxed{\tt{ \color{green}f( - 3) = { - 8}}}[/tex]
_________
#LetsStudy
El opuesto y el semejante de 8xy
Answers
Answer:
No entiendo
Step-by-step explanation:
4) A piece of hematite contains 70%
iron. If the hematite weighed 60g,
how much iron would there be?
6) A survey of 250 trees in a small
Answers
Answer:
42g
Step-by-step explanation:
70% of 60 = 42
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Answers
Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] ...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
[tex]\pm a=\pm 4[/tex]
[tex]a=4[/tex]
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
[tex]\pm c=\pm 2\sqrt{5}[/tex]
[tex]c=2\sqrt{5}[/tex]
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]
[tex]16+b^2=20[/tex]
[tex]b^2=20-16[/tex]
[tex]b^2=4[/tex]
Taking square root on both sides, we get
[tex]b=\sqrt{4}[/tex] [b>0]
[tex]b=2[/tex]
Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get
[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]
[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]
Therefore, the correct option is (d).
Find the value of x. Round to the nearest 10th
Answers
Answer:
44.94
Step-by-step explanation:
Any help to solve this one?
Answers
Answer:
Step-by-step explanation:
[tex]81^{1/2}[/tex]
[tex]3^4*{1/2}[/tex]
[tex]3^{4/2}[/tex]
[tex]3^{2}[/tex]
9
[tex]-16^{3/4}[/tex]
[tex](-2)^{4 *3/4}[/tex]
[tex](-2)^{12/4}[/tex]
[tex](-2)^{3}[/tex]
-8
Element X is a radioactive isotope such that its mass decreases by 73% every
hour. If an experiment starts out with 680 grams of Element X, write a
function to represent the mass of the sample after t hours, where the rate of
change per minute can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the
percentage rate of change per minute, to the nearest hundredth of a percent.
Mi
Answers
Answer:
Step-by-step explanation:
The element decay percentage rate of change 2.22% per minute.
What is radioactive isotope?
Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.
Here, mass decreases by 73% every hour.
Weight of element X is 680 grams.
According to question,
f(t) = 680 (1 - 73%)ⁿ
f(t) = 680 (1 - 0.73)ⁿ
f(t) = 680 X 0.27ⁿ
f(t) = 680 X 0.9778ⁿ
f(t) = 680 X (1 - 0.02322)ⁿ
Thus, the element decay percentage rate of change 2.22% per minute.
Learn more about radioactive isotope from:
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What is the slope of the line shown below?
10
O A. 2
5
(3,6)
OB. 4
O c. -4
-5
10
15
5
(1,-2)
-5
O D. 2
-10
Answers
Answer:
B
Step-by-step explanation:
Slope Formula
6 - (-2) / 3 - 1
8 / 2 = 4
The slope of the graph is 4.
Option B is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The coordinates from the graph are:
(1, -2), and (3, 6)
Now,
Slope.
= (6 -(-2)) / (3 - 1)
= (6 + 2) / 2
= 8/2
= 4
Thus,
The slope of the graph is 4.
Learn more about equation of a line here:
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Leila buys candy that costs 8 dollars per pound. She will spend more than 40 dollars on candy. What are the possible numbers of pounds she will buy?
Answers
Answer:
She must buy more than 5 lbs
Step-by-step explanation:
First write the inequality
cost per pound * number of pounds > total cost
8 * lbs > 40
Divide each side by 8
8 lbs /8 > 40/8
lbs > 5
She must buy more than 5 lbs
In a certain year, 86% of all Caucasians in the U.S., 77% of all African-Americans, 77% of all Hispanics, and 84% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 11% African-American, and 10% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic
Answers
Answer:
Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%
Step-by-step explanation:
We are given that
Population was Caucasian=64%
Population was African-American=11%
Population was Hispanic=10%
Let the population of U.S=10000
Now,
Population was Caucasian=[tex]\frac{64}{100}\times10000=6400[/tex]
Population was African-American=[tex]\frac{11}{100}\times 10000=1100[/tex]
Population was Hispanic=[tex]\frac{10}{100}\times 10000=1000[/tex]
Population of others=10000-(6400+1100+1000)=1500
Population of Caucasians used the Internet for e-mail=86% of 6400
Population of Caucasians used the Internet for e-mail=[tex]\frac{86}{100}\times 6400[/tex]
Population of Caucasians used the Internet for e-mail=5504
Population of African-American used the Internet for e-mail=77% of 1100
Population of African-American used the Internet for e-mail=[tex]\frac{77}{100}\times 1100=847[/tex]
Population of Hispanics used the Internet for e-mail=77% of 1000
Population of Hispanics used the Internet for e-mail=[tex]\frac{77}{100}\times 1000=770[/tex]
Population of others used the Internet for e-mail=84% of 1500
Population of others used the Internet for e-mail=[tex]\frac{84}{100}\times 1500=1260[/tex]
Total population used the Internet for e-mail=5504+847+770+1260
Total population used the Internet for e-mail=8381
Percentage of U.S resident who used the Internet for e-mail were Hispanic
=[tex]\frac{Population \;of \;Hispanics \;used \;the \;Internet \;for \;e-mail}{total\;population\; used \;the \;Internet \;for\; e-mail}\times 100[/tex]
Percentage of U.S resident who used the Internet for e-mail were Hispanic=[tex]\frac{770}{8381}\times 100[/tex]
Percentage of U.S resident who used the Internet for e-mail were Hispanic=9.19%
Name this triangle by its sides and angles. This is a(n) ____________________ triangle.
a triangle with one right angle and three non-congruent sides
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right triangle
Hope this helps! :)
If the number of orders at a production center this month is a Geom(0.7) random variable, find the probability that we'll have at most 3 orders.
Answers
Answer: 0.973
Step-by-step explanation:
The probability mass function of geometric distribution is
[tex]f(x)=(1-p)^{x-1}p,\ \ \ x=1,2,3,...[/tex], p= probability of success on a trial.
As per given, we have
p=0.7
The probability that we'll have at most 3 orders [tex]P(X\leq3)=P(x=1)+P(x=2)+P(x=3)[/tex]
[tex]=(1-0.7)^{1-1}(0.7)+(1-0.7)^{2-1}(0.7)+(1-0.7)^{3-1}(0.7)\\\\=0.7+0.21+0.063\\\\=0.973[/tex]
hence, the required probability = 0.973
The probability that we'll have at most 3 orders will be "0.973".
According to the question,
→ [tex]x \sim Geometric (p)[/tex]
here,
p = 0.7
then,
→ [tex]P(X=x) = (1-p)^{x-1}\times p[/tex]
By putting the given values, we get
[tex]= (1-0.7)^{x-1}\times 0.7[/tex]
hence,
The probability that we'll have at most 3 orders will be:
→ [tex]P(X \leq 3)=P(X=1)+P(X=2)+P(X=3)[/tex]
[tex]=0.7+0.21+0.063[/tex]
[tex]=0.973[/tex]
Thus the above response is correct.
Learn more about probability here:
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Use the grouping method to factor this polynomial.
x^3 + 2x^2 + 12x +24
A. (x^2+6)(x+2)
B. (x^2 +2)(x+6)
C. (x^2 +2)(x+12)
D. (x^2 +12)(x+2)
Answers
Answer:
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Step-by-step explanation:
[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]
[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]
[tex] {x}^{2} (x+2)+12(x+2)[/tex]
[tex]( {x}^{2} + 12)(x + 2)[/tex]
Hope it is helpful...Dan has an old lawn mower! It takes him 1 hour to mow the whole lawn. How many square yards does Dan cut in one minute? Hints: There are 60 minutes in 1 hour. To find the unit rate divide the area of the lawn by the amount of time it takes Dan to mow the whole lawn.
40 square yards per minute
400 square yards per minute
2400 square yards per minute
240 square yards per minute
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Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60
Step-by-step explanation:
the number 3.14063 written correct to 3 decimal places is
Answers
Answer:
3.141
Step-by-step explanation:
3 decimals is .xxx, and you round the last digit up, so it becomes 3.141
Answer:
3.141
Step-by-step explanation:
since the forth number behind the decimal place is bigger than 5 we round up the third number.
I hope this helps in anyway.
GIVING OUT BRAINLIEST HELP ME PLSS !!
Answers
Answer:
C) 5.66
Step-by-step explanation:
For a 45-45-90 triangle, the length of each leg length (not including the hypotenuse) is congruent to each other. If 8=y√2, then y=8/√2=4√2=5.66
Answer:
5.66
Step-by-step explanation:
take 45 degree as reference angle
using cos rule
cos 45 =adjacent /hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] =y/8
[tex]\frac{1}{\sqrt{2} } *8=y[/tex]
[tex]\frac{8}{\sqrt{2} }=y[/tex]
[tex]4\sqrt{2} =y[/tex]
5.66=y
The manager of a local car dealership wants to conduct a customer satisfaction survey. Which group of people should make up a sample of the population?
A. sales people in the dealership
B. mechanics who work at the dealership
C. people who bought cars from the dealership
D. prospective buyers who visit the dealership
Answers
Answer:
Step-by-step explanation:
A customer satisfaction survey refers to a questionnaire that's designed by a company in order for businesses to know what customers think about their products.
Since the manager of a local car dealership wants to conduct a customer satisfaction survey, then the group of people should make up a sample of the population will be the people who bought cars from the dealership
Answer:
c
Step-by-step explanation:
Plz help me solve this
Answers
PLEASE HELP!!!
WILL MARK BRAINLIEST!!!
Solve for X and Y in the rectangle.
Thank you!m
Answers
Y = 20
X = 70
We know Y is 20 because both triangles are the same size. 20 is in the opposite corner to Y. The right corner is 90 degrees. There are 180 degrees in a triangle. To get your answer you are going to add 20 and 90 to get 110 then you will subtract 110 from 180.
The volume of a sphere is 904.32 mm3. What is the approximate volume of a cone that has the same height and a circular base with the same diameter? Use 3.14 for π and round to the nearest hundredth.
Answers
Answer:
[tex]V_c=452.16\ mm^3[/tex]
Step-by-step explanation:
Given that,
The volume of a sphere is 904.32 mm³.
The volume of a cone that has the same height and circular base with the same diameter is:
[tex]V_c=\dfrac{1}{3}\pi r^2 \times 2r=\dfrac{2}{3}\pi r^3[/tex]
The volume of a sphere with the same radius is:
[tex]V_s=\dfrac{4}{3}\pi r^3=2\times \dfrac{2}{3}\pi r^3[/tex]
So, the volume of sphere is :
[tex]V_c=\dfrac{V_s}{2}\\\\V_c=\dfrac{904.32 }{2}\\\\V_c=452.16\ mm^3[/tex]
So, the volume of the cone is [tex]452.16\ mm^3[/tex].
There are 6 chef assistants and 2 servers. How many staff are working there?
Answers
Answer: 8
Step-by-step explanation:
are you in elementary school
Answer:
8 staff
Step-by-step explanation:
6 +2 = 8 There are 8 staff working there.
If this is done a different way explain or lmk? Hope you are having a wonderful day!! Of not it'll get better I promisee! <33 :))
An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 8 novels and 6 plays.
a. How many different ways can he choose the books to put on the list if he wants to include at least two plays?
b. Find the standard deviation.
Answers
Answer:
A) 3 ways
B) sorry don't know.
Step-by-step explanation:
2 P and 2 N
3P and 1 N
4P
So 3 ways.
The total cost of a truck rental, y, for x days, can be modeled by y=24x+39. What is the rate of change for this function?
Answers
Answer:
24 per day
Step-by-step explanation:
'x' = days, so since 24 is with x, the rate of change is 24
Determine if each proportion on the left is True or False. Answer options on the right side may be used more than once.
True
False
28/16=14/8
3/5=9/15
4/32=10/78
3/4=12/16
Answers
Answer:
28/16=14/8 true
3/5=9/15 true
4/32=10/78 false
3/4=12/16 true
Step-by-step explanation:
DID IT ON BRIDGE
its my final, please help!!!!!!!!!!
Answers
Answer:
both apply
Step-by-step explanation:
i guessed just do it
