Answers
The function rule that relates y (circumference) to x (diameter) is y = π x [pi × x]
Explanation:Since x represents the diameter of the circle and y represents the circumference.
For a circle with radius r, circumference of the circle (y)equals,
y = 2πr ................................(1)
Diameter of a circle is twice the radius of the circle.
Assuming x as the diameter
[tex]x = 2\times r = 2r[/tex] ...........................(2)
Substituting (2) in (1), we get
y = π(2r) = πx ..............................................(3)
A function rule is an equation that determines the relation between a dependent variable and an independent variable. The relation between diameter of a circle and its circumference can be given as
Circumference = Pi × Diameter of circle
y = π × x
where π = 3.142
Related Questions
Which function is not linear?
tof
Select one:
O a. f(x)=5/x
O b. f(x)=3x4
O c. f(x)=-7x
O d. f(x)=5
Answers
Answer:
f(x)=-7x is the only one linear
Step-by-step explanation:
I'm wondering if this is mistake or not with your question, but if you graph each function, all but one graph is linear.
Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runners’ locations starting at 9:00 a.m.
who runs fastest?
Answers
Caedin runs fastest (he has the highest speed)
Step-by-step explanation:
The question in this problem is "who runs fastest": this means that the problem is asking us "which runner has the greatest speed?"
The speed of a body is a scalar quantity defined as
[tex]v=\frac{d}{t}[/tex]
where
d is the distance covered by the body
t is the time elapsed
In order to calculate the distance covered by each runner, we have to sum the length of all the pieces of motion, regardless of their direction.
From the graph, we observe that:
- Andy moves from x = 0 to x = 1.25 miles, so the distance covered is d = 1.25 miles. Since the time taken is 10 minutes, his speed is
[tex]v=\frac{1.25}{10}=0.125 mi/min[/tex]
- Berta moves from x = 0.5 miles to x = 1.15 miles, so the distance covered is
d = 1.15 - 0.5 = 0.65 miles
The time taken is 10 minutes, so her speed is
[tex]v=\frac{0.65}{10}=0.065 mi/min[/tex]
- Finally, Caeding moves first from x = 1.5 miles to x = 0, so he covers a distance of
[tex]d_1 = 1.5 mi[/tex]
Then he also moves from x = 0 to x = 1.0 miles, so he covers an additional distance of
[tex]d_2=1.0 mi[/tex]
So the total distance is
[tex]d=d_1+d_2=1.5+1.0=2.5 mi[/tex]
And since the time taken is 10 minutes, the speed is
[tex]v=\frac{2.5}{10}=0.25 mi/min[/tex]
Therefore, Caedin has the highest speed.
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How many integers between 10 and 50 (inclusive) meet the following conditions? 1. The sum of the digits is odd. 2. The number is a perfect square.
a) 3
b) 4
c) 5
d) 6
Answers
There are only a handful of perfect squares in the given range: 16, 25, 36, and 49
The sum of their digits wil be odd if one digit is odd and the other is even, which is the case for 16, 25, and 49. So the answer is A.
You deposit $7500 in an account that pays 5.2% interest compounded continuously. Find the balance after 10 years.
Answers
Answer:$3900
Step-by-step explanation:
A sports team is throwing an end-of-season party at the fitness club. The costs associated with the party include a $150 flat fee for the room rental and a $14 per person charge for the Italian buffet. An 18% tip must be added to the cost of the food. Express the total cost for the party as a function of the number of people attending
Answers
Answer:
[tex]c(x)=150+16.52x[/tex]
With x being the number of people attending the party, and c(x) the cost in dollars.Explanation:
The total cost is comprised of three costs, namely the flat fee for the room rental ($150), the charge person for the Italian buffet ($14 per person), and the tip (18% added to the cost of the food). With this you can build your equation:
[tex]Total\text{ }cost=$150+$14x+18\%\times (14x)[/tex]
Where x respresents the number of people attending the party.
Convert 18% to its decimal form, which is 0.18 and simplify the equation:
[tex]Total\text{ }cost=$150+$14x+0.18\times (14x)=150+14x+2.52x\\ \\ Total\text{ }cost=150+16.52x[/tex]
Hence, calling the function c(x), it is:
[tex]c(x)=150+16.52x[/tex], with x being the number of people attending the party, and c(x) the cost in dollars.
The function which representing the total cost of party is [tex]150+16.52x[/tex]
Total cost :Let us consider that number of people who attending part be x.
The room rental amount is $150.
The charge of the Italian buffet for per person = $14
For x number of people [tex]=14x[/tex]
Since, 18% tip added to the cost of the food.
Tip cost [tex]=14x*\frac{18}{100} =2.52x[/tex]
Total cost of the party [tex]=150+14x+2.52x=150+16.52x[/tex]
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Consider the line segment shown on the coordinate plane. What are the coordinates of midpoint AB?
A- (-1, 1/2)
B- (1, 1/2)
C - (1, -1)
D-(1,2)
Answers
What number 0.2% of 50?
Answers
Answer:
0.2% of 50 = [tex]0.1[/tex]
Step-by-step explanation:
0.2% of 50
We have to find 0.2% of 50
[tex]50*0.2*\frac{1}{100}[/tex]
[tex]50*\frac{2}{10}* \frac{1}{100}[/tex]
=[tex]\frac{5*2}{100}[/tex]
=[tex]\frac{10}{100}\\\\ \frac{1}{10}\\\\0.1[/tex]
The 0.2% of 50 is 0.1
Answer:
0.1
Step-by-step explanation:
The equation of a straight line is y+10=5x
Answers
Answer:
y=5x-10
Step-by-step explanation:
y+10=5x
y=5x-10
one fifth ÷ 4 = ⬜
Luis said the solution is 20.
Matt said the solution is .1/20
Who is correct? Explain your reasoning.
Answers
Matt said the solution 1/20 is the correct answer.
Step-by-step explanation:
step 1 :
one fifth ÷ 4 = one part in five equal parts / 4
= (1/5) / 4
The expression can be written as (1/5) / (4/1)
step 2 :
To solve the division of fractions, take reciprocal of the denominator and do multiplication.
The reciprocal of denominator (4/1) is 1/4.
step 3 :
(1/5) / (4/1) = (1/5) [tex]\times[/tex] (1/4)
= 1/20
∴ Matt said the solution is 1/20 is correct.
91.8% of 648 toy robots on an assembly line will be approved by the quality control inspector. Write and
solve a proportion to find how many robots will be approved.
Answers
Answer:
595 will be approved.
Step-by-step explanation:
Multiply 648 by 0.918: the result is 594.9, which should be rounded up to 595.
A metal worker makes a box from a 15inch by 20inch piece of tin by cutting a square with a side length x out of each corner and folding up the sides
a) write expressions for length width and height of the box
b) write a polynomial for the volume of the box
Answers
Answer:
a) Length = (20 - 2x) inches
Width = (15 - 2x) inches
b) Volume = (20 - 2x)(15 - 2x)x cubic inches.
Step-by-step explanation:
A metalworker makes a box from 15 inches by 20 inches piece of tin by cutting a square with a side length x out of each corner and folding up the sides.
a) So, the length of the box will become (20 - 2x) inches.
And, the width of the box will become (15 - 2x) inches.
b) The volume of the box will be = (Length × Width × Height)
= (20 - 2x)(15 - 2x)x cubic inches. (Answer)
If 2d÷4=5, does 2d÷4+6=5+4
Answers
Answer:
3/2d
Step-by-step explanation:
ad 5 and 4 then subtracts 6 from both sides then divide 2 from 3 and get 3/2
A right triangle has a base of 12 yards and a height of 7 yards. If you were to construct a similar but not congruent right triangle with a base of 26 yards, what would be the height of your new triangle rounded to the nearest tenth?
Answers
To find the height of a new right triangle similar to the original with a base of 26 yards, use the ratio of sides from the original triangle (7/12) to set a proportion. Solve the proportion to get the new height as 15.2 yards (or 45.5 feet).
Since the triangles are similar, the ratio of their corresponding sides must be the same. To find the height of the new triangle with a base of 26 yards, we set up a proportion using the corresponding sides of the original triangle:
7 yards / 12 yards = height / 26 yards
By cross-multiplying and solving for the unknown height, we get:
7 yards * 26 yards = height * 12 yards
182 y = height * 12 yards
height = 182 / 12 yards
height = 15.1666667 yards
Since 1 yard = 3 feet, we convert the height to feet:
15.1666667 yards * 3 feet/yard = 45.5 feet
Therefore, the height of the new right triangle is approximately 15.2 yards or 45.5 feet when rounded to the nearest tenth of a foot.
Summer exercises for 0.5 hour on Monday Wednesday and Friday each week. How many hours will she exercise in four weeks
Answers
Answer:
She will exercise for 6 hours in four weeks.
Step-by-step explanation:
Summer exercises for 0.5 hour on Monday, 0.5 hour on Wednesday, and 0.5 hour on Friday. There are 3 days where she exercises for 0.5 hour.
3 days X 0.5h = 1.5h each week
For four weeks, multiply the hours each week by 4.
1.5h X 4 weeks = 6h
Therefore Summer will exercise for 6 hours over the course of 4 weeks.
Answer:
6 hours
Step-by-step explanation:
We know that Summer exercises for 0.5 (Or a half) hour every day, three days a week (Monday, Wednesday, Friday). We need to found out how many hours she exercises in 4 weeks.
To solve this we first find out how many hours she exercises in one week. To do so, we set up an equation like this:
(Time exercising) x (# of days exercising) = (Hours spent exercising in one week)
Plug in the given numbers:
0.5 x 3 = 1.5 hours
If we know she exercises 1.5 (Or one and a half) hours in 1 week, we multiply this number by 4 to find out how many hours she exercises in 4 weeks. This can be shown in an equation like this:
1.5 x 4 = 6
So Summer will exercise for 6 hours in 4 weeks.
You have two fair, six-sides dice. However, the dice have been modified so that instead or 1,2,3,4,5,6 the sides are numbered 1,2,2,2,3,4.
What is the probability the total of the two dice is an even number?
Answers
Answer:
.
Step-by-step explanation:
Answer:
5/9.
Step-by-step explanation:
Prob ( first dice = 2 and second = 2) = 1/2 * 1/2 = 1/4
Prob ( first = 2 , second = 4) = 1/2 * 1/6 = 1/12
Prob ( first = 4 and second = 2) = 1/12.
Prob ( first = 3 and second = 1 ) = 1/36
Prob ( first = 1 and second = 3) = 1/36.
Prob ( first = 3 and second = 3) = 1/6 *1/6 = 1/36.
Prob (first = 1 and second = 1 = 1/36.
Prob (first = 4 and second = 4 = 1/36.
Required probability is the sum of these which is:
5/9.
I hope I've thought of all the possible outcomes.
find the equation of the line that passes through the point (2,6) and with a slope of 3
using yinterstep form
Answers
slope intercept form: y=mx+b
y=3x+6
y=3(2)+6
y=6+6
y=12
15 POINTS!
IMAGE ATACHED
Answers
Answer:
Step-by-step explanation:
T think its the 3rd option down
Answer:
b
Step-by-step explanation:
Normal Distribution
Using the graph as a reference, select all
statements that are true about a normal distribution
of data.
Normal distributions are symmetrical about
the mean, m.
The total area under the curve is 100.
Ninety-five percent of the data lies within 1
standard deviation of the mean.
The probability that an event is within 1
standard deviation above the mean is 34%.
All data sets are normally distributed
Answers
Answer:
1 and 4.
Step-by-step explanation:
i just did it
Amy has a collection of marbles in three sizes, small, medium, and large. She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles.
Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Write an algebraic expression to represent the number of large marbles she has.
If Amy has a total of 560 marbles, how many of each size does she have? Show your work.
Answers
Answer:
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
i) Let the number of small marbles be x
ii) let the number of medium marbles be y
iii) let the number of large marbles be z
iv) Amy has 5 times as many small marbles as medium marbles therefore we can write 5y = x
v) the number of large marbles is two more than than three times the number of medium marbles therefore we can write
z = 3y + 2
vi) Amy has a total of 560 marbles therefore we can write x + y + z = 560
vii) Therefore from i) we can write x = 5y
viii) using vii) and v) in vi) we can write
x + y + z = 5y + y + 3y + 2 = 560
ix) Therefore 9y = 558 .... therefore y = [tex]\frac{558}{9}[/tex] = 62
x) Therefore from i) we get x = y [tex]\times[/tex] 5 = 62 [tex]\times[/tex] 5 = 310
xi) Therefore z = (3 [tex]\times[/tex] 62) + 2 = 188
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Which number is farther from 0: -7 or 5
Answers
Answer is : -7
Answer:
-7
Step-by-step explanation
There are 5 pennies for every 6 quarters in Ahmed's pocket. Could Ahmed have a total of 30 coins in his pocket? Explain
Answers
Ahmed cannot have total of 30 coins in his pocket
Solution:
Given that,
There are 5 pennies for every 6 quarters in Ahmed's pocket
We are asked if Ahmed can have a total of 30 coins in his pocket
From given,
5 pennies for every 6 quarters
Therefore, ratio is:
penny : quarter = 5 : 6
Total = 5 + 6 = 11
Then the total number of coins must be multiple of 11
But 30 is not a multiple of 11
Therefore, Ahmed cannot have total of 30 coins in his pocket
No, Ahmed cannot have a total of 30 coins in his pocket.
Explanation:Yes, Ahmed could have a total of 30 coins in his pocket.
To determine how many quarters and pennies Ahmed could have, we can set up a ratio.
The ratio of pennies to quarters is 5:6.
Let the number of quarters be represented by 6x, where x is a positive integer. Then, the number of pennies would be 5x.
To find out if Ahmed could have a total of 30 coins, we need to solve the equation 6x + 5x = 30.
Combining like terms, we obtain 11x = 30. By dividing both sides of the equation by 11, we find that x = 2.7272 (repeating).
Since x must be a positive integer, we can conclude that Ahmed cannot have a total of 30 coins in his pocket.
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From 45 ft to 92 ft?
Answers
Answer:47
Step-by-step explanation:
Answer:
47 feet
Step-by-step explanation:
92 feet-45 feet= 47 feet
Answer is 47 feet
ILL MARK YOU BRAINLIEST IF YOU ANSWER CORRECTLY
Write in scientific notation: 0.0042
A) 42 x 10^-2
B) 4.2 x 10^-4
C)4.2 x 10^-3
D).42 x 10^-4
---------------------------------------------------
write in standard notation:6.12 x 10^3
A)6120
B)612
C) 61,200
D)61.2
Answers
Answer:
Scientific Notation:
4.2 × 10^-3
E-Notation:
4.2e-3
Engineering Notation:
4.2 × 10^-3
Real Number:
0.0042
Step-by-step explanation:
15 inches increased by 20%
Answers
Answer:
18
Step-by-step explanation:
15 + Percentage increase =
15 + (20% × 15) =
15 + 20% × 15 =
(1 + 20%) × 15 =
(100% + 20%) × 15 =
120% × 15 =
120 ÷ 100 × 15 =
120 × 15 ÷ 100 =
1,800 ÷ 100 =
18
a:b=5:3 find the value of 3a+4b:5a+2b
Answers
Yo sup??
a:b=5:3
a/b=5/3
a=5x
b=3x
3a+4b:5a+2b
=15x+12x:25x+6x
=27x:31x
=27:31
Hope this helps.
Answer:
Step-by-step explanation:
a:b=5:3 the value of 3a+4b:5a+2b
(3*5)+(4*3):(5*5)+(2*3)
15+12:25+6
=27:31
What's the common denominator for 3/8 and 3/10?
Answers
Amy drove to her mothers house, which is 204 miles away. If it took her 3 hours, what was her average speed?
Answers
68 m/s was her average speed
Amy's average speed was 68 mph (miles per hour)
Calculating average speedFrom the question, we are to determine what Amy's average speed was
Average speed can be calculated by using the formula,
[tex]Average\ speed =\frac{Distance}{Time}[/tex]
From the given information,
Distance covered = 204 miles
Time = 3 hours
Then
Average speed = [tex]\frac{204}{3}[/tex]
Average speed = 68 mph (miles per hour)
Hence, Amy's average speed was 68 mph (miles per hour)
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A post it note has an area of A square inches. The width of the post it note is 4 inches.which equation represents X the length of the post it note in inches A X=4/A. B. X=A+2(4) C. X=A/4. D. X=A-2(4)
Answers
Answer:
Option C. X=A/4
Step-by-step explanation:
we know that
The area of the rectangular post it note is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
In this problem we have
[tex]W=4\ in\\L=X\ in[/tex]
substitute
[tex]A=4X[/tex]
solve for x
That means ----> isolate the variable x
Divide by 4 both sides
[tex]X=\frac{A}{4}[/tex]
An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.What is the explicit rule for this situation, and how many marbles will be in the 10th row?Drag and drop the answers into the boxes to match the situation.Explicit ruleNumber of marbles in the 10th rowAn = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,
Answers
The explicit rule for the number of marbles in 10th row is An= 12+ n-1.
Step-by-step explanation:
Total number of rows = 10 rowsThe number of marbles in the 1st row = 12 marblesOne marble is added to each successive rowTherefore, for the remaining 9 rows out 10 rows ⇒ 9 marbles are added.
The number of marbles in the 10th row = 12+9 = 21 marbles.The explicit rule is An = 12 + n-1For n= 10, then
⇒ A10 = 12 + (10-1)
⇒ A10 =12+9 = 21
Answer:
A(n)=11+n
Step-by-step explanation: took test
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x-3)?
Answers
Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x - 3)? THE ANSWER IS D.