Answer:
C, B, A
Step-by-step explanation:
From smallest to largest, the side lengths are ...
AB = c = m -2AC = b = mBC = a = m +4The shortest side is opposite the smallest angle, so the angles, smallest to largest, are C, B, A.
___
Comment on side naming
Side c is opposite vertex (and angle) C, so is between vertices A and B. Thus the names AB and c are both names for the side of the triangle opposite angle C.
Answer:
C, B, A
Step-by-step explanation:
A customer's stock value seems to be rising exponentially. The equation for
the linearized regression line that models this situation is log(y) = 0.30X +0.296
where x represents number of weeks. Which of the following is the best
approximation of the number of weeks that will pass before the value of the
stock reaches $600?
The answer is:
The correct option is A. 8.3.
Why?To calculate the number of weeks that will pass, we need to use the given information.From the statement we know that we need to use the value of $600 substituting it as "y", and then, isolate "x", so, calculating we have:
[tex]log(y)=0.30x+0.296\\\\log(600)=0.30x+0.296\\\\2.78=0.30x+0.296\\\\2.78-0.296=0.30x\\\\x=\frac{2.78-0.296}{0.30}=8.28=8.3[/tex]
Hence, the correct option is A. 8.3.
Have a nice day!
Morena, a scuba diver, used the expression below to describe her position in relation to sea level. 0 + (–15) + 6 Which statement could describe the diver's movements? Morena started at 15 feet below sea level, then dove down 6 more feet. Morena started at 15 feet above sea level, then dove down 6 more feet. Morena started at sea level, dove down 15 feet, then dove down 6 more feet. Morena started at sea level, dove down 15 feet, then rose up 6 feet.
Answer:
mirena started at sea level, dove down 15 feet then rose up 6 feet
Step-by-step explanation:
she starts at zero the goes up -15 feef and then up 6 feet
Answer:
Morena started at sea level, dove down 15 feet, then rose up 6 feet.
Step-by-step explanation:
The expression is composed by three values. The first value indicates the starting point; which is 0, meaning sea level. The second component is -15, this indicates that Morena dove 15 feet below sea level, so she dove down. The third component is 6, this indicate that she drove up 6 feet, so she rose up. The position of Morena should be at 9 feet below sea level. The equation should be:
X = 0 + (-15) + 6
X = 0 - 15 + 6
X = -15 + 6
X = -9 down sea level
X means the Morena's postion
You have reason to believe that there are actually
more raisins in each box than the company
claims. What is Your alternative hypothesis?
Answer:
The answer is A.) u < 200
next one is B.) u > 200
The alternative hypothesis in your testing would be: u < 20; u > 200.
What is Alternative Hypothesis?An alternative hypothesis can be defined as a statement in statistical inference which is used in contradictory form against what is stated in the null hypothesis.
Alternative hypothesis is the alternative t a null hypothesis in hypothesis testing.
Therefore, the alternative hypothesis in your testing would be: u < 20; u > 200.
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the values in the table represent an exponential function.what is the common ratio of the associated geometric sequence
x y
1 8
2 32
3 128
4 512
5 2048
A.4 B.24 C.40 D.8
Answer:
A. 4
Step-by-step explanation:
Pick two terms with consecutive x-values and find their ratio. That is the common ratio.
for x = 2 and x = 1,
r = 32/8 = 4
The common ratio is 4.
_____
You can check other pairs of terms if you want to confirm.
r = 2048/512 = 4 . . . . for x=5 and 4.
Answer:
Hi!
The correct answer is A. 4.
Step-by-step explanation:
To find the common ratio of an geometric sequence of set A = {a₁, a₂, a₃, ..., aₙ} you can use the formula:
[tex]r=\frac{a_{i+1}}{a_i}[/tex]
If you pick x = 4 to find the ratio, you have to replace in the formula:
[tex]r=\frac{a_{4+1}}{a_4} =\frac{a_{5}}{a_4}[/tex] // replace the values
[tex]r= \frac{2048}{512} = 4[/tex]
The common ratio of this geometric sequence is 4.
5. A raffle prize of 14x^2 /15 dollars is to be divided among 7x people. Write an expression for the amount of money that each person will receive
Given that the raffle prize is to be divided equally, the amount of money each person will receive will be equal to the total raffle prize (14x^(2)/15) divided by the number of people (7x). Thus, we get:
(14x^(2)/15) / 7x
= (14x^(2)/15) * (1/7x)
= 14x^(2)/15*7x
= 14x^(2)/105x
= 2x/15 (Divide both the numerator and denominator by 7x)
Therefor, each person would receive 2x/15 dollars.
If you know how to cancel when dealing with fractions, you can get to this step much easier, however this way also works. The idea with cancelling would be that when you had (14x^(2)/15) / 7x, you would recognise that 14x^2 may be divided by 7x straight away to get 2x. Then you would have 2x/15 as your answer.
!!!!!!PLEASE HELP!!!!!What is the minimum value for the function f(x)=1/2(x+3)(x-5)
Answer:
the minimum value is 1/2x^2+4x+15/2 (write down the work below)
Step-by-step explanation:
f(x)=1/2*(x+3)*(x+5)=0
multiply the parenthesis by 1/2
(1/2x+3/2)*(x+5)
multiply the parenthesis
1/2x^2+5/2x+3/2x+15/2
calculate the equation
1/2x^2+4x+15/2 is you're answer
A poll is given, showing 65% are in favor of a new building project. If 4 people are chosen at random, what is the probability that exactly 3 of them favor the new building project? Preview
Answer:
0.38Explanation:
When 4 people are chosen at random, the probability that exactly 3 of them favor the new building project may be thought as four cases:
- the first one is against and the other three are in favor
- the second one is against and the other three are in favor
- the third one is against and the other three are in favor
- the fourth one is against and the other three are in favor.
Each one of those probabilities are equal to:
(0.35) × (0.65)³ = 0.09611875↑ ↑
one against three in favor
Since, there are four equal results: 4 × 0.09611875 = 0.384475
Rounded to 2 significant digits that is 0.38.
The probability that exactly 3 out of 4 people randomly selected from a poll, where 65% of people are in favor of a certain building project, are also in favor of it is approximately 0.3835 or 38.35%.
Explanation:This question is about the calculation of probability related to a poll result. To calculate the probability that exactly 3 of 4 randomly chosen people favor the new building project, we should consider this as a binomial probability problem, because each person either supports the project or not, and each person is independent of the others. Accordingly, the probability that exactly 3 out of 4 people are in favor is given by the formula:
P(X=3)=C(4,3)*(0.65)^3*(1-0.65)^(4-3)=4*(0.65)^3*(0.35)=(4*0.2746*0.35)=0.3835
So, the probability that exactly 3 of them favor the new building project is approximately 0.3835 or 38.35%.
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PLEASE HELP ME WITH THIS MATH QUESTION
Answer: 24%
Step-by-step explanation:
2610+8120 = The undergraduates and graduates combined.
That is 10730. You are figuring out the probability the student is a graduate when those two graduates are combined, because that is all the data given. So you would do 2610/10730 in your calculator, resulting in 24.324324324%. As it says rounded to the nearest percent in parentheses, it has to round to the whole number, 24%, and .3 rounds down.
What is the surface area of a cube that has a side length of 8 mm? Use the formula is SA=6^2, where SA is the surface area of the cube and s is the length of each side.
48mm^2
96mm^2
384mm^2
2,304mm^2
Answer:
The surface area is [tex]SA=384\ mm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the cube is equal to
[tex]SA=6s^{2}[/tex]
we have
[tex]s=8\ mm[/tex]
substitute
[tex]SA=6(8)^{2}[/tex]
[tex]SA=384\ mm^{2}[/tex]
Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}. What is A ∩ B?
[tex]A=\{1,3,5,\ldots,99\}\\B=\{50,55,\ldots,150\}\\\\A\cap B=\{55,65,75,85,95\}[/tex]
Answer:
[tex]A\bigcap B=\left \{ 55,65,75,85,95 \right \}[/tex]
Step-by-step explanation:
Set A contains odd numbers between 0 and 100.
So, the elements in set A are as, Set A[tex]=\left \{ 1,3,5,7,9,11,13,15,...99 \right \}[/tex]
Set B contains the numbers between 50 and 150, that are evenly divisible by 5.
So, the elements in set B are are as, Set B
[tex]=\left \{ 55,60,65,70,75,80,85,90,... 145\right \}[/tex]
Now, we need to find [tex]A\bigcap B[/tex]
To find [tex]A\bigcap B[/tex] , we need to find the common elements in Set A and Set B.
The common elements in Set A and Set B is [tex]\left \{ 55,65,75,85,95 \right \}[/tex]
So, [tex]A\bigcap B=\left \{ 55,65,75,85,95 \right \}[/tex]
What is the solution for the system of equations {9x+8y=3 6x−12y=−11?
Answer:
( - [tex]\frac{1}{3}[/tex], [tex]\frac{3}{4}[/tex] )
Step-by-step explanation:
Given the 2 equations
9x + 8y = 3 → (1)
6x - 12y = - 11 → (2)
To eliminate the y- term multiply (1) by 1.5
13.5x + 12y = 4.5 → (3)
Add (2) and (3) term by term
(6x + 13.5x) + (- 12y + 12y) = (- 11 + 4.5)
19.5x = - 6.5 ( divide both sides by 19.5 )
x = [tex]\frac{-6.5}{19.5}[/tex] = - [tex]\frac{1}{3}[/tex]
Substitute this value into either of the 2 equations and solve for y
Using (1), then
- 3 + 8y = 3 ( add 3 to both sides )
8y = 6 ( divide both sides by 8 )
y = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
Solution is (- [tex]\frac{1}{3}[/tex], [tex]\frac{3}{4}[/tex] )
Geometry PEOPLE COME HELP
Answer:
The answer should be. ( 7,2 )
Answer: second option.
Step-by-step explanation:
Given the transformation [tex]T:(x,y)[/tex]→[tex](x+3,y+1)[/tex]
You must substitute the x-coordinate of the point B [tex]x=4[/tex]) and the y-coordinate of the point B [tex]y=1[/tex]) into [tex](x+3,y+1)[/tex] to find the x-coordinate and the y-coordinate of the image of the point B.
Therefore, the image of B(4,1) is the following:
[tex](x+3,y+1)=(4+3,1+1)=(7,2)[/tex]
You can observe that this matches with the second option.
15x – 24 > 3(4x – 10)Solve using the addition and multiplication principle. One of these is the answer. {x | x ? -2} {x | x ? -2} {x | x < -2} {x | x > -2
Answer:
bsqaure +csqaure =bsqaure
Step-by-step explanation:
Two 6-sided dice are rolled at the same time. How many outcomes correspond to the event that the sum of the numbers is 5? A. 2 B. 3 C. 4 D. 5
A - the sum of the numbers is 5
[tex]A=\{(1,4),(4,1),(2,3),(3,2)\}\\|A|=4\Rightarrow \text{C}[/tex]
Given the following linear function, sketch the graph of the function and find the domain and range.
f(x) = 2/3x - 3
1. To sketch the function f(x) = (2/3)x - 3, we first need to find two points that we can later join to sketch the line, for example the x- and y-intercepts.
a) The x-intercept occurs when f(x) = 0, so if f(x) = 0, then:
f(x) = (2/3)x - 3
0 = (2/3)x - 3
3 = (2/3)x (Add three to both sides)
3*(3/2) = x (Multiply both sides by 3/2)
9/2 = x
We have now found the x-intercept at (9/2, 0)
b) The y-intercept occurs when x = 0, so:
f(x) = (2/3)x - 3
f(0) = (2/3)*0 - 3
f(0) = -3
Now we know that the y-intercept is at (0, -3)
c) All that's left is to sketch the graph axes and label them, plot the two points, join them together using a ruler and label their coordinates.
2. The Domain is the range of x-values for which the function exists, and the Range is the range of y-values for which the function exists.
Since there haven't been any constraints specified, we can say that both the Domain and Range are (-∞, ∞), since the graph continues forever both along the x- and y-axis.
(Note that this isn't always the case and would change if, for example, the question stipulated that there was a domain of [0, 5] and you had to find the range. Then, you would calculate the value of y at each end of the domain (if x = 0, y = -3 and if x = 5, y = 1/3) - in my example, the range would thus be [-3, 1/3].)
The quadratic model f(x) = –5x2 + 200 represents the approximate height, in meters, of a ball x seconds after being dropped. The ball is 50 meters from the ground after about how many seconds? 2.45 3.16 5.48 7.07
Answer:
t = 5.48
Step-by-step explanation:
f(x) = -5x² + 200
given f(t) = 50 when x = time(t)
Hence,
50 = -5t² + 200
5t² = 200 - 50
5t² = 150
t² = 30
t = √30 = 5.48
The number of seconds are 5.48, the correct option is C.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given that;
f(x) = –5x2 + 200
Now,
To find the time when the ball is 50 meters from the ground, we need to solve the equation:
f(x) = 50
Substituting f(x) with -5x^2 + 200 and simplifying, we get:
-5x^2 + 200 = 50
-5x^2 = -150
x^2 = 30
x = ±√30
Since x represents time, we only consider the positive value of x. Therefore,
x ≈ 5.48
Therefore, by the quadratic equations the answer will be 5.48
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What is the circumference of circle P?
Express your answer in terms of Pi
PB= 29 m
Answer:
The formula for circumference: 2rpi
PB = r = 29m
The circumference of circle P is:
2(29)pi
=58pi
Answer:
The circumference of circle =58π m
Step-by-step explanation:
Points to remember
Circumference of circle = 2πr
Where r is the radius of the circle
From the figure we can see a circle with radius PB = 29 m
To find the circumference of circle
Here r = 29 m
Circumference = 2πr
= 2 * π * 29
= 58π m
Therefore the circumference of circle =58π m
Which mathematicians first used the symbol pi Why?
William Jones
Step-by-step explanation:The number pi (π) is a platonic concept and has been used for 4000 years. The number pi can be approached but never reached. In general, this number means the constant ratio of the circumference to the diameter of any circle. Ancient Babylonians, Egyptians, and even Archimedes, one of the greatest mathematicians of the ancient world tried to approximate the value of pi, but in the 1700s, mathematicians began using the Greek letter π that was introduced by William Jones, in his second book Synopsis Palmariorum Matheseos or A New Introduction to the Mathematics base. Then, this symbol was popularized and adopted in 1737 by the greatest mathematician Leonhard Euler.
Which account has the highest effective annual interest rate? Not necessary but please show how you got your answer.
A. Account 1: Interest is compounded quarterly at an annual rate of 4.20%.
B. Account 2: Interest is compounded monthly at an annual rate of 4.15%.
C. Account 3: Interest is compounded semiannually at an annual rate of 4.10%
D. Account 4: Interest is compounded annually at a rate of 4.25%.
Answer:
A. 4.20% compounded quarterly
Step-by-step explanation:
The effective annual multiplier on an account with annual interest rate r compounded n times per year is ...
(1 +r/n)^n
When doing multiple evaluations of the same expression, it is convenient to let a spreadsheet or calculator do them from a list of inputs. In the attached, we round the result to 4 decimal places to make comparison easier.
The highest effective rate is 4.2% compounded 4 times per year.
____
Example calculation
(1 +0.042/4)^4 = 1.0105^4 = 1.0426661426550625 ≈ 1.0427
Answer:
A) Account 1: Interest is compounded quarterly at an annual rate of 4.20%
Find the distance between the points (– 4, 7, – 3) and (4, – 1, – 2).
Answer:
√129
Step-by-step explanation:
The distance formula between two points is:
d² = (x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²
Plugging in:
d² = (4 − (-4))² + (-1 − 7)² + (-2 − (-3))²
d² = 8² + 8² + 1²
d² = 129
d = √129
please help lolol
Name the following segment or point.
Given:
L, M, N are midpoints
centroid of triangle ABC
P
Q
R
Answer:
Q
Step-by-step explanation:
Each line from a vertex to the midpoint of the opposite side is called a median. The point where the medians intersect, point Q, is the centroid.
The centroid of ΔABC is point Q.
Answer:
Q
Step-by-step explanation:
We are given that L,M and N are midpoints of sides AC,AB and BC of a triangle.
We have to find the centroid of triangle ABC.
Centroid of triangle : It is defined as the intersection point of medians of triangle.
Medians of triangle ABC are BL,CN and AM.
Medians BL, CN and AM are intersect at point Q.
Therefore, centroid of triangle ABC is Q by definition of centroid of triangle.
Answer:Q
Explain your answer.
Thanks-Aparri
Answer:
2 raisins
Step-by-step explanation:
The mean is calculated in the usual way: the sum divided by the number of numbers.
mean = (5 +9 +5 +5 +7 +11)/6 = 7
The deviations are the differences from the mean:
deviation = {5, 9, 5, 5, 7, 11} -7 = {-2, 2, -2, -2, 0, 4}
and the absolute deviation is the absolute value of these numbers:
absolute deviation = {2, 2, 2, 2, 0, 4}
The mean absolute deviation (MAD) is the average of these values:
(2 +2 +2 +2 +0 +4)/6 = 2
The mean absolute deviation is 2.
_____
It is generally convenient to let technology do the computation. A spreadsheet or graphing calculator can do this easily.
Tara is planning a baby shower for her sister. The restaurant charges $450 for the first 25 people plus $15 for each additional guest If Tara can spend at most $700, find the greatest number of people who can attend the shower.
Answer with Step-by-step explanation:
Tara can spend at most $700
Restaurant charges $450 for the first 25 people and $15 for each additional guest
Let x be the number of additional guest
⇒ 450+15x<700
⇒ 15x<250
⇒ x<250/15
⇒ x<16.67
Hence, Maximum additional guest can be 16
25+16=41
Hence, the greatest number of people who can attend the shower is:
41
WILL GIVE BRAINIEST TO THE BEST ANSWER (multiple choice question)
Addison mows three lawn(s) per day and earns $35.00 per lawn. If Addison spends three days mowing, how much money will he earn? Identify the input and output.
A- Input: $315.00 days Output: 9 lawns
B- Input: 3 days Output: $315.00
C- Input: 9 lawns Output: $315.00
D- Input: $315.00 Output: 3 days
Answer:
im going to say c is the answer to this question
Answer: C
Step-by-step explanation:
What is the missing constant term in the perfect square that starts with x^2+2x
Answer:
1
Step-by-step explanation:
The constant term in a perfect square trinomial with leading coefficient 1 is the square of half the coefficient of the linear term.
(2/2)² = 1
The missing constant term is 1.
Answer: The correct answer is: " 1 " .
_____________________________________________________
→ " x² + 2x + 1 = (x + 1)² " .
_____________________________________________________
_____________________________________________________
Step-by-step explanation:
_____________________________________________________
Let us assume that the question asks us to solve for the "missing constant term in the following equation:
→ " x² + 2x + b = 0 " ;
→ in which: " b " is the "missing constant term" for which we shall solve.
_____________________________________________________
The form of an equation in the perfect square would be:
→ (x + b) ² = x² + 2bx + b² ;
→ In our case, "b" ; refer to the "missing constant term" for which we shall solve.
_____________________________________________________
→ " x² + 2x + b = 0 " ;
Note that the term in the equation with the highest degree (highest exponent) is:
→ " x² " ; with an "implied coefficient" of: " 1 " (one) ;
→ {since "any value" , multiplied by " 1 " , results in that same initial value.}.
→ Since the term with the highest degree has a "co-efficient" of " 1 " ;
we can solve the problem; i.e. "Solve for "b" ; accordingly:
_____________________________________________________
→ " x² + 2x + b = 0 " ;
Subtract "b" from each side of the equation:
→ " x² + 2x + b - b = 0 - b " ;
→ to get:
→ x² + 2x = - b
Now we want to complete x² + 2x into a perfect square.
To do so, we take the: "2" (from the: "+2x" );
→ and we divide that value {in our case, "2"}; by "2" ;
to get: "[2/2]" ; and then we "square" that value;
→ to get: " [2/2]² " .
_____________________________________________________
Now, we add this "squared value" to: " x² + 2x " ; as follows:
→ " x² + 2x + [2/2]² " ; and simply: " [2/2]² = [1]² = 1 ."
_____________________________________________________
x² + 2x + (2/2)² = x² + 2x + 1 ;
= (x + 1)² ;
_____________________________________________________
Now: " x² + 2x = - b " ;
We add "(2/2)² " ; to each side of the equation;
→ In our case, " [2/2]² = [1]² = 1 " ;
→ As such, we add: " 1 " ; to each side of the equation:
→ x² + 2x + (2/2)² = - b + (2/2)² ;
→ Rewrite; substituting " 1 " [for: " (2/2)² "] :
→ x² + 2x + 1 = 1 - b ;
→ x² + 2x + 1 = 1 - b ;
_____________________________________________________
And assume "b" would equal "1" ;
since assuming the question refers to the equation:
"x² + 2x ± b = 0 " ; solve for "b" ;
And: "b = 1 " ;
Then: " x² + 2x + 1 = ? 1 - b ??
→ then: " 1 - b = 0 " ; Solve for "b" ;
→ Add "b" to each side of the equation:
" 1 - b + b = 0 + b " ;
→ to get: " 1 = b " ; ↔ " b = 1 " ; Yes!
___________________________________________________
Also, to check our work:
_____________________________________________________
Remember, from above:
_____________________________________________________
" The form of an equation in the perfect square would be:
→ (x + b)² = x² + 2bx + b² " ; _____________________________________________________
→ Let us substitute "1" for all values of "b" :
→ " (x + 1) ² = x² + 2*(b)*(1) + 1² " ;
→ " (x + 1)² = x² + (2*1*1) + (1*1) " ;
→ " (x + 1)² = ? x² + 2 + 1 " ?? ; Yes!
→ However, let us check for sure!
_____________________________________________________
→ Expand: " (x + 1)² " ;
→ " (x + 1)² = (x + 1)(x + 1) " ;
_____________________________________________________
→ " (x + 1)(x + 1) " ;
_____________________________________________________
Note the following property of multiplication:
_____________________________________________________
→ " (a + b)(c + d) = ac + ad + bc + bd " ;
_____________________________________________________
As such:
_____________________________________________________
→ " (x + 1)(x + 1) " ;
= (x*x) + (1x) + (1x) + (1*1) ;
= x² + 1x + 1x + 1 ;
→ Combine the "like terms" :
+ 1x + 1x = + 2x ;
And rewrite:
= x² + 2x + 1 .
_____________________________________________________
" (x + 1)² = ? x² + 2 + 1 " ?? ; Yes!
_____________________________________________________
→ So: The answer is: " 1 " .
_____________________________________________________
→ " x² + 2x + 1 = (x + 1)² " .
_____________________________________________________
Hope this answer helped!
Best wishes to you in your academic endeavors
— and within the "Brainly" community!
_____________________________________________________
If varies directly with y and x = 6 m when y = 15, find x when y = 20
If x varies directly with y, then :
● Increase in x results in increase of y
● Decrease in x results in decrease of y
● It is represented by : x ∝ y
[tex]\mathsf{\bigstar\;\;If\;x\;varies\;directly\;with\;y\;then : \large\boxed{\mathsf{\dfrac{x_1}{x_2} = \dfrac{y_1}{y_2}}}}[/tex]
Here : x₁ = 6 and y₁ = 15 and x₂ = x₂ and y₂ = 20
Substituting the values we get :
[tex]\mathsf{\implies \dfrac{6}{x_2} = \dfrac{15}{20}}[/tex]
[tex]\mathsf{\implies x_2 = \dfrac{20 \times 6}{15}}[/tex]
[tex]\mathsf{\implies x_2 = 8}[/tex]
Answer : x = 8 when y = 20
Answer:
x = 8
Step-by-step explanation:
Given that x varies directly as y then the equation relating them is
x = ky ← k is the constant of variation
To find k use the condition x = 6 when y = 15
k = [tex]\frac{x}{y}[/tex] = [tex]\frac{6}{15}[/tex] = 0.4
x = 0.4y ← equation of variation
When y = 20, then
x = 0.4 × 20 = 8
CAN SOMEONE CHECK MY WORK GEOMETRY PEOPLE ONLY PLS
Answer:
Is the graph shown the initial triangle, or the translated one?
Step-by-step explanation:
PLEAS HELP ME FIND THE AREA OF THE SHADED SECTOR
ANSWER
461.7 yd²
EXPLANATION
The shaded region represents a sector.
The area of the sector is a fraction of the area of the whole circle.
Area of sector
[tex] = \frac{angle \: \: of \:sector }{360 \degree} \times \pi {r}^{2} [/tex]
We substitute the angle of the sector and the radius of the circle to obtain:
[tex] = \frac{167 \degree}{360 \degree} \times \pi \times {17.8}^{2} [/tex]
[tex] = 461.7 {yd}^{2} [/tex]
Therefore the area of the shaded region to the nearest tenth is 461.7 square yards.
Answer:
Area of shaded sector = 461.5 yd²
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where 'r' is the radius of circle
To find the area of given circle
Here r = 17.8 yd
Area = πr²
= 3.14 * 17.8²
= 3.14 * 316.84
= 994.8776 yd²
To find the area of shaded region
Central angle of sector = 167°
Area of sector = (167/360) * area of circle
= (167/360) *994.8776
= 461.52 ≈ 461.5 yd²
There are 8 movies that you would like to see currently showing in theatres. In how many different ways can you choose a movie to see this Saturday and one to see this Sunday?
Answer:
56
Step-by-step explanation:
Assumption: You don't watch the same movie twice
I will explain in 2 ways
METHOD 1: Multiplication Rule
On Saturday, you have 8 choices. On Sunday, you have 7 choices because u have already watched 1 movie on Saturday
8×7 = 56
METHOD 2: Permutation
Since 'order' is important, i.e. watching movie A on Saturday & B on Sunday is different from watching B on Saturday & A on Sunday, so it's
8P2 = 56
Using the permutation formula, it is found that you can choose a movie to see this Saturday and one to see this Sunday in 56 ways.
The order in which the movies are chosen is important, as they are respective to different days, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 2 movies will be chosen from a set of 8, hence:
[tex]P_{(8,2)} = \frac{8!}{6!} = 8 \times 7 = 56[/tex]
Hence, you can choose a movie to see this Saturday and one to see this Sunday in 56 ways.
More can be learned about the permutation formula at https://brainly.com/question/25925367
What is the shape of the cross section of the cylinder in each situation?
Drag and drop the answer into the box to match each situation.
Answer: The first box is circle and second box is rectangle.
Step-by-step explanation:
If you are asking about the shape of the cross section for a right circular cylinder, that is the case. A parabola or triangle can't be sliced so the cross section is parallel or perpendicular to the base.
If the cross section is parallel to the base, it is a circle.
If the cross section is perpendicular to the base, it is a rectangle.