Answers
Answer:
D
Step-by-step explanation:
The arc AB is calculated as
AB = circumference of circle × fraction of circle
= 2πr × [tex]\frac{120}{360}[/tex]
= 2π × 24 × [tex]\frac{1}{3}[/tex] = [tex]\frac{48\pi }{3}[/tex] = 16π → D
Related Questions
Gold-192 is a radioactive isotope with a half-life of 4.95 hours. How long would it take for a 25 gram sample of Gold-192 to decay until only 2 grams remain? a. about 9.1 hours b. about 31 hours c. about 18 hours d. about 61.9 hours
Answers
Answer:
Step-by-step explanation:
The formula you will need for this is:
[tex]A=A_0(\frac{1}{2})^{\frac{t}{H}[/tex] where A is the amount after some decay has happened, A₀ is the intial amount, t is the time in hours, and H is the half-life in hours. Those values for us are:
A = 2 g
A₀ = 25 g
H = 4.95 hrs and
t = ?
Filling in:
[tex]2=25(\frac{1}{2})^{\frac{t}{4.95}[/tex] Keep in mind that, because of the nature of the exponential form of this equation, you CANNOT simply multiply the 25 by the 1/2. Exponential equations don't work that way. Begin instead by dividing both sides by 25 to get
[tex].08=(\frac{1}{2})^{\frac{t}{4.95}[/tex] The goal is to get that t out from its exponential position. Do that by taking the natural log of both sides:
[tex]ln(.08)=ln(.5)^{\frac{t}{4.95}[/tex]
After you take the natural log of the right side, the property allows you to bring the exponent down out front:
[tex]ln(.08)=\frac{t}{4.95}ln(.5)[/tex]
Now divide both sides by ln(.5) to get
[tex]\frac{ln(.08)}{ln(.5)}=\frac{t}{4.95}[/tex]
Simplify the left side out on your calculator to get
[tex]\frac{-2.525728644}{-.6931471806}=\frac{t}{4.95}[/tex] and then divide:
[tex]3.643856=\frac{t}{4.95}[/tex]
Finally, multiply both sides by 4.95 to get
3.643856(4.95) = t so
t = 18.0 hours which is choice C
Which of the following options have the same value as 25, percent of 64
Answers
ANSWER:
16
Answer:
a
Step-by-step explanation:
if -1 and-2 are the zeroes of the cubic polynomial x³-2x²+ax+b, then find the value of a and b
Answers
Answer:
a = - 13, b = - 10
Step-by-step explanation:
Given that x = - 1 and x = - 2 are zeros then
f(- 1) = 0 and f(- 2) = 0, that is substituting value into the polynomial
f(- 1) = (- 1)³ - 2(- 1)² - a + b = 0 , that is
- 1 - 2 - a + b = 0
- a + b = 3 → (1)
f(- 2) = (- 2)³ - 2(- 2)² - 2a + b = 0, that is
- 8 - 8 - 2a + b = 0
- 2a + b = 16 → (2)
Multiply (1) by - 2
2a - 2b = - 6 → (3)
Add (2) and (3) term by term to eliminate a
- b = 10 ( multiply both sides by - 1 )
b = - 10
Substitute b = - 10 into (1) and evaluate for a
- a - 10 = 3 ( add 10 to both sides )
- a = 13 ( multiply both sides by - 1 )
a = - 13
what is estimation? can we estimte sum,difference,product and quotient?
Answers
Answer:
Yes
Step-by-step explanation:
Estimated difference > Actual difference. Hence, 1000 is the approximate answer. 2. We can estimate the product and quotient of numbers by rounding off the numbers to the greatest place.
Please answer it in two minutes
Answers
Answer:
8√3
Step-by-step explanation:
Sin 30 =4√3/DE
DE = 4√3/Sin30 = 8√3
(05.03 MC)
An observer (O) spots a plane (P) taking off from a local airport and flying at a 23° angle horizontal to her line of sight and located directly above a tower (T). The observer also notices a bird (B) circling directly above her. If the distance from the plane (P) to the tower (T) is 5,000 feet, how far is the bird (B) from the plane (P)? Round to the nearest whole number.
Answers
Step-by-step explanation:
let x be the distance between B and P
tan(67)=x/5000
x=2.3558 . 5000
x=11779feet
Answer:
11,779 feet
Step-by-step explanation:
Is the answer
Consider the quadratic function that has x-intercepts of -1 and 7 and passes through the point (-2,-20). What is the
value of a in the factored form of this function?
Answers
Answer:
a = -20/9.
Step-by-step explanation:
We can write it as
f(x) = a(x - 7)(x + 1)
When x = -2 and y = -20 (at the point(-2, -20):
-20 = a(-2 -7)(-2 + 1)
-20 = -9*-1 a
9a = -20
a = -20/9.
Determine the number of terms in the sequence: 5240,4365, 3490, 2615, ..., -2635
Answers
Answer:
I believe the number of terms are 10
Step-by-step explanation:
The number of terms in the given sequence(5240,4365, 3490, 2615, ..., -2635) is 10.
What is a sequence?In mathematics, a sequence is an enumerated group of elements in which repetitions are allowed and order is significant.
How to solve this problem?The 1st term in the given sequence is 5240
The 2nd term is 4365 = 5240 - 875
The 3rd term is 3490 = 4365 - 875
The 4th term is 2615 = 3490 - 875
Then the 5th term is 2615 - 875 = 1740
The 6th term is 1740 - 875 = 865
The 7th term is 865 - 875 = - 10
The 8th term is - 10 - 875 = - 885
The 9th term is - 885 - 875 = - 1760
The 10 the term is - 1760 - 875 = - 2635.
Therefore the number of terms in the given sequence(5240,4365, 3490, 2615, ..., -2635) is 10.
Know more about sequences here -
https://brainly.com/question/22241938
#SPJ2
The Guzman family lives 240 miles from Mexico City. If the Guzmans travel in
their car at 60 miles per hour, how long does it take for them to get to Mexico
Answers
Answer:
4 hours
Step-by-step explanation:
To find the time it takes to travel the distance, divide the distance by the speed they are going.
(240 miles)/(60 miles per hour) = 4 hours
It will take them 4 hours.
Answer:Answer:
4 hours
Step-by-step explanation:
To find the time it takes to travel the distance, divide the distance by the speed they are going.
(240 miles)/(60 miles per hour) = 4 hours
It will take them 4 hours.
Step-by-step explanation:
Tim is investigating the relationship between the number of years since a tree was planted and the height of the tree in feet. His data are shown in the table.
Years Since Tree was Planted vs. Height of Tree
Years since tree was planted, x
Height of tree in feet, y
2
17
3
25
5
42
6
47
7
54
9
69
Using a regression calculator, what is a good prediction for the height of the tree when it is 100 years old?
A calculator screen. A 2-column table with 6 rows titled Data. Column 1 is labeled x with entries 2, 3, 5, 6, 7, 9. Column 2 is labeled y with entries 17, 25, 42, 47, 54, 69. The regression equation is y almost-equals 7.36 x + 3.08; r almost-equals 0.998.
A good prediction for the height of the tree when it is 100 years old is about 315 feet because that is what the trend line, y almost-equals 3.08 x + 7.36, produced by the regression calculator predicts.
A good prediction for the height of the tree when it is 100 years old is about 739 feet because that is what the trend line, y almost-equals 7.36 x + 3.08, produced by the regression calculator predicts.
There is not a good prediction for the height of the tree when it is 100 years old because the trend line produced by the regression calculator does not give a prediction.
There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.
Answers
Answer: There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.
Step-by-step explanation:
Years since tree was planted (x) - - - - height (y)
2 - - - - 17
3 - - - - 25
5 - - - 42
6 - - - - 47
7 - - - 54
9 - - - 69
Using a regression calculator :
The height of tree can be modeled by the equation : ŷ = 7.36X + 3.08
With y being the predicted variable; 7.36 being the slope and 3.08 as the intercept.
X is the independent variable which is used in calculating the value of y.
Predicted height when years since tree was planted(x) = 100
ŷ = 7.36X + 3.08
ŷ = 7.36(100) + 3.08
y = 736 + 3.08
y = 739.08
Forward prediction of 100 years produced by the trendline would probably give an invalid value because the trendline only models a range of 9 years prediction. However, a linear regression equation isn't the best for making prediction that far in into the future.
Answer:
D
Step-by-step explanation:
There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.
Which of the following equations have no real solution but have two complex solutions?
Answers
Explanation:
Because there discriminant are less than 0
Discriminant = b^2 - 4ac
We use this formula to determine the if the equation has real roots or not
I’m really not sure what the answer to this question is, can anyone help?
Answers
Answer:
25(sqrt(2)+1)
Some explanation:
The exact form is 25*sqrt(2) + 25.
If we divide by 25, we are left with sqrt(2) + 1.
So 25(sqrt(2) + 1) is the correct answer.
Hope that helps a little!
What is the sign of 123 1/23 + (-123 1/23) A) positive B) negative C) zero
Answers
Answer:
Positive
Step-by-step explanation:
123 1/23 + (-123 1/23)
Opening the bracket, we have ;
123 1/23 - 123 1/23 = 0
Kindly note that 0 is not a sign, so we cannot select it as an option.
0 is a positive number and not negative.
Thus the sign we have is the positive sign and that gives our answer
Monica bought a car for $x 3 years ago. Due to an inflation rate of 6% p.a. this car is now worth Mexican peso 50,000. Calculate the cat's original purchase price
Answers
Answer:
its 60198.6
Step-by-step explanation:
use the formula present price=orginal price(1-rate/100)^years
Please someone help a girl in need :)
Answers
Hey there! :)
Answer:
We can use the Pythagorean theorem to show that both triangles contain equivalent shorter legs:
Triangle A:
13² = 12² + b²
169 = 144 + b²
25 = b²
b, or the other leg, = 5 cm.
--------------------------------------
Triangle B:
c² = 12² + 5²
c² = 144 + 25
c² = 169
c = 13 cm.
---------------
Both triangles contain legs with side-lengths 5, 12, and 13 cm. The triangles are congruent because the lengths of the corresponding sides between triangle A and B are equivalent, which was proved using the Pythagorean Theorem.
y
10
1
B(7,9)
Create a rectangle around the parallelogram. The
dimensions of this rectangle are
Find the area of the four right triangles surrounding the
parallelogram. The total area of the triangles is
square units
Subtract the triangle areas from the area of the
rectangle to obtain the area of the parallelogram. The
area of parallelogram ABCD is square units.
6
2
-10
6
-6
A-3,-1)
-2
10
C(8, -1)
D(-2,-11)
Answers
Answer:
rectangle: 11 × 20triangle area: 110 u²parallelogram area: 110 u²Step-by-step explanation:
See below for a graph showing the parallelogram and the rectangle.
The dimensions of the rectangle are 11 by 20. The rectangle area is ...
rectangle area = bh = (11)(20) = 220 . . . square units
There are 2 right triangles with a base of 10 and a height of 1. There are 2 right triangles with a base of 10 and a height of 10. The total area of the triangles is ...
triangle area = 2(1/2)(10)(1) +2(1/2)(10)(10) = 10(1 +10) = 110 . . . square units
The area of the parallelogram is the difference of these, ...
parallelogram area = rectangle area - triangle area
= (220 units²) -(110 units²) = 110 units²
The area of parallelogram ABCD is 110 square units.
_____
Check
The parallelogram has a base of 10√2 and a height of 5.5√2, so an area of (10√2)(5.5√2) = 110 square units. This matches the above result.
Answer:
1) 11 by 20 2) 110 3) 110 correct on edg
Step-by-step explanation:
Create a rectangle around the parallelogram. The dimensions of this rectangle are
11 by 20
Find the area of the four right triangles surrounding the parallelogram. The total area of the triangles is
110 square units.
Subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. The area of parallelogram ABCD is
110 square units.
Which of the following is a set in correct set notation?(1,2,3){4,5,6} the letters of the alphabet 7,8,9
Answers
Answer: {4,5,6}
Step-by-step explanation: Sets could be explained as a representation of elements which could be numbers, alphabets or a collection of items which are wrapped inside a curly bracket {}. Generally in mathematical or statistical parlance, once elements are wrapped around curly braces, the collection of those emmts is called a set. And therefore, set arithmetic such as union, intersection, complement e.t.c can be performed on elements of the given set. Elements wrapped in curly braces signifies that the elements reperesents an entire entity.
In the question given above, {7,8,9} reperesents a set containing three elements : 7, 8,9.
Solve for x 4x−2=3x+4
Answers
Answer:
x=6
Step-by-step explanation:
Answer:
x = 6
hope this helps!
The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) Estimate how long it takes the population to double. (Round your answer to two decimal places.)
Answers
Answer:
90.91 years
Step-by-step explanation:
If the rate of population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year, increase in yearly population = 1.1/100 × 7,100,000,000
= 1.1 × 71,000,000
= 78,100,000
The amount increases by 78.1million every year.
To know how long it will take the population to double.
double of the initial population = 2×7,100,000,000 = 14,200,000,000
Increment per year = 78,100,000
Time it will take for the population to double = 7,100,000,000/78,100,000
= 90.91
≈ 91
This means it will take about 90.91years for the population to double
Multiply. 2 3/4* 4/5 Choose 1 answer: (a) 2 7/20 (b) 2 1/5 (c) 1 3/5 (d) 11/20
Answers
Answer:
[tex]\boxed{\red{ \frac{11}{5} = 2 \frac{1}{5} }}[/tex]
Answer B is correct.
Step-by-step explanation:
[tex]2 \frac{3}{4} \times \frac{4}{5} \\ \frac{11}{4} \times \frac{4}{5} \\ \frac{44}{20} \\ = \frac{11}{5} = 2 \frac{1}{5} [/tex]
Answer:
Hello!
_____________________
Exact Form: [tex]\frac{11}{5}[/tex]
Decimal Form: 2.2
Mixed Number Form: [tex]2\frac{1}{5}[/tex]
Step-by-step explanation: Simplify the expression.
So your anwser woould be ( B ) 2 1/5
Hope this helped you!
:D
Can someone help me pls
Answers
Answer:
H. $12.50
Step-by-step explanation:
Misha wants 1 1/4 yards for each of two straps, for a total of 2 1/2 yards. The ribbon costs $5 per yard, so the total cost for the two straps is ...
(2 1/2 yards)($5 /yard) = $12.50
Forest fires are most likely to occur when the air temperature (t) is greater than 60°F.
Write an inequality for the situation.
please help me asap!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The temperature (t) needs to be greater than 60
So you would have t > 60
Answer:
t > 60
Explanation:
In order to answer this question we must determine two things: what two terms will be compared in the inequality and what symbol we will use to compare them. Let's start by finding, 'what two terms will be compared.'
Read the following quote from the problem...
"Forest fires are most likely to occur when the air temperature (t) is greater than 60°F."
Since the temperature (t) must be greater than sixty degrees to start a forest fire, these are the two terms that we will be comparing in the inequality.
Now, let's find out what symbol we will use to compare the terms.
Because the problem uses the phrase "greater than" to represent the comparison between the temperature of the air and an average of sixty degrees, the symbol we will be using in the inequality is the greater than sign, >.
Finally, use all the facts we have established to write the inequality.
· t = air temperature
· > = greater than
· 60 = max temp. before forest fire occurs
Therefore, the inequality for the solution is t > 60.
An archeologist in Turkey discovers a spear head that contains 27% of its original amount of C-14
Answers
Answer:
it is 13093 i got it correct
5x + y = 2
2x-3y = 62
Answers
Hey there! :)
Answer:
x = 4, y = -18 or (4, -18).
Step-by-step explanation:
Given:
5x + y = 2
2x - 3y = 62
We can use substitution to solve this problem. Rearrange the first equation in terms of y:
5x + y = 2 ---> y = -5x + 2
Substitute in this equation for y into the second equation:
2x - 3(-5x + 2) = 62
Distribute -3:
2x + 15x - 6 = 62
Combine like terms:
17x - 6 = 62
Add 6 to both sides:
17x = 68
Divide both sides by 17:
x = 4.
Plug in this value for x into an equation to solve for y:
5(4) + y = 2
20 + y = 2
y = -18.
Therefore, the solutions to this system of equations are:
x = 4, y = -18 or (4, -18).
help i need help quick I will mark u brainllest
Answers
Answer:
C
∠L and∠Q
Step-by-step explanation:
in the congruence statementit shows
A. JL and PR
JKL≅PQR
THEY MATCH-not this one
B. ∠K and ∠Q
JKL≅ PQR
THEY MATCH-not this one
C.∠L and ∠Q
JKL≅PQR
THEY DO NOT MATCH
D. ∠J and ∠P
JKL≅PQR
THEY MATCH-not this one
Hello i need some help
Answers
Answer:
y = 2x - 1
Step-by-step explanation:
(3, 5) (5, 9)
slope = (9-5)/(5-3) = 4/2 = 2
y = mx + b
5 = 2(3) + b
-1 = b
y = 2x -1
Answer:
f(x)=2x-1; y=2x-1
Step-by-step explanation:
First we need to find the slope and to do so you use the equation [tex]\frac{y_{1} -y_{2}}{x_{1}-x_{2}}[/tex] .
Plugging in for the values we get (9-5)/(5-3)=4/2=2, which means we have a slope of 2.
Now we just have to find the y-intercept, and to do this we multiply the x-value by the slope (2) and see what we have to add to that to get the y-value.
For example, 5*2=10, 10-1=9, so -1 is our y-intercept.
This means our equation in slope-intercept form is y=2x-1 and in function form is f(x)=2x-1
true or false:
If ab>0 then a>0 and b>0.
Answers
Answer:
false
Step-by-step explanation:
because a<0 and b<0 then ab>0
Answer:
False
Step-by-step explanation:
You don't know what a or b is for example it could be a=-3 b=-4. In that case ab= 12 but a and b indavidually are less than zero making this statment false
You Identify the ratio of the average number of bass to the averg
Answers
Answer:
Step-by-step explanation:
Using six random samples, the average number of catfish in the samples was 5.7
Answer:
Uhhhh......Hi??
What is the additive inverse of x if x equals -32
Answers
Answer:
32
Step-by-step explanation:
The additive inverse means, the opposite sign,
for example the additive inverse means -2 turns into 2.
So -32 would be 32.
Answer:
[tex]\boxed{x=32}[/tex]
Step-by-step explanation:
The additive inverse of a number is the opposite of that number.
-32 opposite is 32.
Khairul agrees to lay a road 3000m long in 30 days. He employs 50 men,who works for 8 hours a day .After 20 working days, he finds that only 1200 m of the road is completed. Each man now works for 10 hours a day and they have to finish the project in 10 days' time. So , Khairul decides to employ more men to work on the project. How many more men are to be employed to finish the work on time?
Answers
Answer:
10 more men
Step-by-step explanation:
1.5 road made per man