John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for pi , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%
Answers
Answer: A. 51%
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex] , where r = radius of the circle.
In the figure below, we have the complete question.
According to that,
Radius of outer circle = 7ft
Radius of inner circle = 5ft
The probability that the thumbtack will be placed on the inner circle
[tex]=\dfrac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=\dfrac{\pi (5)^2}{\pi (7)^2}\\\\=\dfrac{25}{49}[/tex][π is canceled from numerator and denominator
in percent, [tex]\dfrac{25}{49}\times100=51.0204081633\%\approx51\%[/tex]
So, the probability that the thumbtack will be placed on the inner circle = 51%
Hence, the correct option is A. 51%.
Related Questions
Rewrite y=x^2-8x+15 in vertex form. Then state whether the vertex is a maximum or a minimum and give it´s coordinates.
Answers
Answer:
[tex]\large \boxed{\sf \ \ y=(x-4)^2-1 \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]y = x^2-8x+15\\ \\\text{*** we need to complete the square ***} \\ \\y=(x-4)^2-4^2+15=(x-4)^2-16+15=(x-4)^2-1[/tex]
And then the vertex is (4, -1) and as a > 0 the vertex is a minimum.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
11. John has a life insurance policy that will pay his family $32,000 per year if he dies. If interest rates are at 2.5% when the insurance company has to pay, what is the amount of the lump sum that the insurance company must put into a bank account?
Answers
Answer:
$1280000
Step-by-step explanation:
Given that :
John has a life insurance policy that will pay his family $32,000 per year if he dies
If interest rates are at 2.5% when the insurance company has to pay
The amount of the lump sum that the insurance company must out into a bank account can be determined by the division of the amount to be paid by the interest rate.
i.e
the amount of the lump sum = $32000/2.5%
the amount of the lump sum = $32000/0.025
the amount of the lump sum = $1280000
Find SP when CP=Rs.400 and proft%=4%
Answers
Answer:
[tex]\boxed{Selling\ Price = Rs.\ 424}[/tex]
Step-by-step explanation:
Cost Price = Rs. 400
Profit = 4 % of Cost Price
=> [tex]\frac{4}{100} * 600[/tex]
=> 4 * 6
=> Profit = Rs. 24
Now, Selling Price = Cost Price + Profit
Selling Price = 400+24
Selling Price = Rs. 424
Answer:
Selling price = ₹ 416
Step-by-step explanation:
Cost Price = ₹ 400
Profit% = 4 %
Profit = 4 % of cost price
= [tex]\frac{4}{100}*400\\\\[/tex]
= 4 * 4
= ₹ 16
Selling price = Cost price + profit
= 400 + 16
= ₹ 416
Determine whether the data set is a population or a sample. Explain your reasoning. The temperature in four state capitals out of 50 Choose the correct answer below. A. Population, because it is a collection of temperatures for all of the state nbspcapitals. B. Sample, because it is a collection of temperatures for all of the state nbspcapitals comma but there are other countries. C. Sample, because the collection of temperatures for four state capitals is a subset of all state capitals. D. Population, because it is a subset of all state capitals.
Answers
Answer:
The correct answer is C. Sample, because the collection of temperatures for four state capitals is a subset of all state capitals.
Step-by-step explanation:
we cannot fully understand this answer without first defining the parameters that are involved in the questions, the two key terms are; Population or sample.
Population: a population contains all the set of data which is in consideration and
Sample: Sample is the range of values in an experiment.
The main difference between a population :A population basically includes all the elements from a set of data while a sample only consists of one or more observations drawn from the population.
we can say safely that a sample is a subset of a population.
Since we it have been stated that the temperatures of from four states capitals out of 50 states then our explanation supports our answer.
Paige launched a ball using a catapult she built. The height of the ball (in meters above the ground) ttt seconds after launch is modeled by h(t)=-5t^2+40th(t)=−5t 2 +40th, left parenthesis, t, right parenthesis, equals, minus, 5, t, squared, plus, 40, t Paige wants to know when the ball will hit the ground. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=h(t)=h, left parenthesis, t, right parenthesis, equals 2) How many seconds after launch does the ball hit the ground? seconds
Answers
Answer:
1) Factor form : [tex]h(t)=-5t(t-8)[/tex]
2) 8 second after launch.
Step-by-step explanation:
The height of the ball (in meters above the ground) t seconds after launch is modeled by
[tex]h(t)=-5t^2+40t[/tex]
To find the time when ball hit the ground, we need to find the factor form of the given function.
[tex]h(t)=-5t(t-8)[/tex]
When ball hi the ground, then height of the ball from the ground is 0.
[tex]h(t)=0[/tex]
[tex]-5t(t-8)=0[/tex]
Using zero product property, we get
[tex]-5t=0\Rightarrow t=0[/tex]
[tex]t-8=0\Rightarrow t=8[/tex]
Ball hit the ground at t=0 and t=8. It means ball hit the ground in starting and 8 second after launch.
Answer:
-5t(t - 8) and it hit 8 seconds after launch.
HELP MEEEEEEE please
Answers
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Consider the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{T'V'}{TV}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
need help A S A P NOWWWWW
Answers
Answer:
x = 73
Step-by-step explanation:
The measure of the sum of the arcs in a circle = 360°.
Sum the given arc measures and equate to 360, that is
95 + 52 + 67 + 2x = 360
214 + 2x = 360 ( subtract 214 from both sides )
2x = 146 ( divide both sides by 2 )
x = 73
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
the trig function you would use to find x would be cosine becuase its adjacent/ hypotenuse.
solving it would give you 49 becuase its cosine(x)=13/20 and you have to multiply by the inverse of cosine
to solve for y you would use sine of y which would be opposite/ hypotenuse = 13/20
Oscar says to Vanesa: "I am five times the age you were when I was the age you are; and when you are the age I am, our ages will add up to 72 years." How old is Vanessa? Please
Answers
Answer:
Vanessa is 60 and the other person is 12
Step-by-step explanation:
X + 5x = 72
6x = 72
x = 12
12 x 5 = 60
vanessa is 60
the other person is 12
60 + 12 = 72
Answer:
18
Step-by-step explanation:
Let's say x is Oscar's age, and y is Vanessa's age.
When Oscar was Vanessa's age, Vanessa was y−(x−y) = 2y−x years old. Oscar is five times older than this:
x = 5 (2y − x)
x = 10y − 5x
6x = 10y
3x = 5y
When Vanessa is Oscar's age, Oscar will be x+(x−y) = 2x−y years old. The sum of their ages will by 72.
2x−y + x = 72
3x − y = 72
Substituting:
5y − y = 72
4y = 72
y = 18
Vanessa is 18. Which means Oscar is 30.
Let's check our answer. When Oscar was 18, Vanessa was 6. Oscar is 5 times older than that (30). When Vanessa is 30, Oscar will be 42, and their ages will add up to 72.
Please help ill rate 5 stars and give brainlyest
Answers
Answer:
Option C.
Step-by-step explanation:
It is given that, a menu at a local diner has
Appetizers = 12
Entrees = 8
Choice of desserts = 4
We need to find the different meal combinations which are possible if you select one appetizer, one entree and one dessert form the menu.
Total ways to select an Appetizers = 12
Total ways to select an entrees = 8
Total ways to select a desserts = 4
Now,
Total combinations for different meal [tex]=12\times 8\times 4=384[/tex]
Therefore, the correct option is C.
Answer:
see below
Step-by-step explanation:
the answer is c
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased
Answers
Answer:
[tex]\large \boxed{87.5 \, \%}[/tex]
Step-by-step explanation:
Let x = the original number of books
Then 0.375x = the total number of biographies
and 0.20 x = the original number of biographies
[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]
PLEASE help me...! I am really stuck on this question.
Answers
Answer:
D
Step-by-step explanation:
the domain of 3^x is (-∞,∞) and the range is (0,∞)
the domain of 3^x-5 is (-∞,∞) and the range is (-5,∞)
the domain doesn't change, the range (-5,∞)
The table below shows the students in an Algebra 1 class. What is the probability that a randomly chosen student will be a girl? (Note: If your fraction will reduce, you need to reduce it.)
Answers
This means there is a 3/5 chance that a randomly chosen student is a girl.
Two different sizes of square metal duct are joined by a piece that is a frustum of a pyramid. Find the lateral surface area, if the small end is square with one side of length 17 in. and the larger square end is of length 19 in. on one side with a slant height of 2 in.
Answers
Answer:
288 in²
Step-by-step explanation:
The formula used to solve this question is :
Lateral Surface Area = s( P1 + P2)
Where s = slant height = 2 inches
P1 and P2 = Perimeter of the bases
Perimeter of base 1 = 4 × length of the end of the small square
4 × 17 inches = 68 inches
Perimeter of base 2 = 4 × length of the end of the large square
4 × 19 inches = 76 inches
Lateral Surface Area = 2 × (68 + 76)
= 2 × 144
= 288 in²
I dont know how to solve this question using proportions:
212.7 = 16.8% of
Answers
Answer:
17,725/14.
Step-by-step explanation:
Let's say that the blank is represented by x.
Since the question asks what is 16.8% of x, we can set up a proportion where 16.8 out of 100 is equivalent to 212.7 out of x. The 100 represents the "whole" number, which corresponds to x. The 212.7 IS the 16.8 of x.
[tex]\frac{16.8}{100} =\frac{212.7}{x}[/tex]
16.8 * x = 212.7 * 100
16.8x = 21,270
x = 21,270 / 16.8
x = 212,700 / 168
x = 17,725 / 14 = 1,266.071429
To check our work, 1,266.071429 * 0.168 = 212.7.
Hope this helps!
What is the solution to the system of equations?
2/3x - 1/3y = -2
-2x + y = -6
There is no solution.
There are infinitely many solutions.
There is only one solution, (2, –2).
There is only one solution, (–2, –10).
Answers
Answer:
There is no solution.
Rewrite -2x + y = -6 so it starts with y =...
y = 2x - 6
Substitute that in 2/3x - 1/3y = -2 gives:
2/3x - 1/3*(2x -6) = -2
2/3x - 2/3x + 2 = -2
0 + 2 = -2
This statement is not true, and that means there is no solution.
what is 35 - (0.35 x 100)
Answers
Answer:
0
Step-by-step explanation:
First let's solve for the value in the parentheses.
[tex]0.35 \cdot 100 = 35[/tex]
We know this is correct because if we multiply a value by 100, the decimal point is moved 2 places to the left.
35 - 35 = 0, so the value of this expression equals out to be 0.
Hope this helped!
Help me with this please. I typed it on my iPad
Answers
Rearrange this formula Α= πr2 for the area of a circle to solve for r in-terms of A.
What is the new formula?
Answers
Answer:
sqrt( A / pi ) =r
Step-by-step explanation:
Α= pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt( A / pi ) = sqrt(r^2)
sqrt( A / pi ) =r
Answer: A/2pi = r
all you have to do is single out the r to get the new equation
One standard size for the United States flag is 19 feet by 10 feet. On a flag of this size, the union (the blue rectangle in the top-left corner) is 7 5 8 feet by 5 3 8 feet. Astronauts on the Apollo missions had a flag on a shoulder patch, use the scale factor 1/60 and find the union dimensions for the patch
Answers
Answer: 0.127 feet by 0.090 feet
Step-by-step explanation:
Given that :
The USA's flag dimension = 19feet by 10feet
Union's (blue rectangle in the top left corner) dimension = 7 5/8 feet by 5 3/8 feet.
Union dimension for the shoulder patch of the USA flag used by astronauts for the Apollo mission has a scale factor of 1/60
Therefore, dimension of the union patch ;
1/60 * ( 7 5/8 feet by 5 3/8 feet)
1/60 * (61 / 8 feet by 43/8 feet)
61/480 feet by 43/480 feet
0.127 feet by 0.0895 feet
0.127 feet by 0.090 feet
Bianca has a piece of rope that is 22 feet long. She cuts the rope into 3 pieces of equal length. Explain how to determine the length, in feet , of each piece of rope. What is the length, in feet, of each piece of rope written as a mixed numbers? Explain how to use a multiplication equation to check your answer.
Answers
Answer:
Hey there!
To solve this problem, you want to divide 22 by 3, which is about 7.33 feet.
We can check this by seeing 7.33 times 3=22
Hope this helps :)
Text: these two triangles are similar
Values from left to right: 10, 12, 9
What is the area of the shaded area
Answers
Answer:
26.25 cm²
Step-by-step explanation:
The area of the shaded part is the area of the shaded triangle subtract the area of the white triangle.
Since the triangles are similar then the ratios of corresponding sides are equal.
let the height of the white triangle be h, then
[tex]\frac{12}{9}[/tex] = [tex]\frac{10}{h}[/tex] ( cross- multiply )
12h = 90 ( divide both sides by 12 )
h = 7.5
shaded area = [tex]\frac{1}{2}[/tex] × 12 × 10 - [tex]\frac{1}{2}[/tex] × 9 × 7.5 = 60 - 33.75 = 26.25 cm²
The measure of one base angle is an isosceles triangle is 20 degree. the measure of the largest angle in the triangle is
Answers
Answer:
140°
Step-by-step explanation:
Every triangles angles when combined equals 180°
In an isosceles triangle there are 2 acute angles and one obtuse angles.
It was given that the base angle/acute angle is 20°
This brings us to our equation. 20° + 20° + x = 180°
20 + 20 = 40
40 + x = 180
Now we solve algebraically:
180-40= 140
Therefore the answer is x = 140°
I hope this helps!
Water drips from a faucet at a rate of 41 drops/minute. Assuming there are 15,000 drops in a gallon, how many minutes would it take for the dripping faucet to fill a 1‑gallon bucket? Round your answer to the nearest whole number.
Answers
Answer:
366 minutes
Step-by-step explanation:
divide 15000 by 41
Issac surveyed the employees at the law firm each employee was asked to record their highest level of education completed. Two hundred sixty six woolens completed the survey . How many of those people completed graduate school?
Answers
Complete Question :
Isaac surveyed the employees at a law firm. Each employee was asked to record their highest level of education completed. The
results are shown in the table below.
Highest Level of Education Completed
Education Level
Percentage
High School
5%
Community College
10%
Four-Year College
60%
Graduate School
25%
Two-hundred sixty people completed the survey. How many of those people completed graduate school?
Answer:
65 people
Step-by-step explanation:
Given the following :
Number of survey participants = 260
Percentage that completed graduate school = 25%
Number of participants who completed graduate school ;
Total Number of participants × percentage that completed graduate school
260 participants × 25%
260 × 0.25
= 65
Answer:
65 people
Step-by-step explanation:
I took the test and that was the correct answer
if an article is sold with 20% discount,there will be a profit of 15%.If it is sold at 10% discount, there will be a profit of Rs.200.Calculate the market price of an article
Answers
Answer:
The market price of the article is Rs. 978.72
Step-by-step explanation:
Let x represents the market price.
Let y represents the selling price.
Let z represents the cost price.
if an article is sold with 20% discount then there will be a profit of 15%.
SP = CP+Profit =z+0.15z=1.15z
ATQ
[tex]0.80x = 1.15z\\0.80x- 1.15z = 0[/tex]
If it is sold at 10% discount then there will be a profit of Rs.200
ATQ
[tex]0.9x - z = 200[/tex]
Now we are supposed to find the market price of an article.
[tex]0.9x - z= 200[/tex]
Multiplying 1.15 both sides
[tex]0.9x \times 1.15 - 1.15z = 200 \times 1.15\\1.035x - 1.15z = 230[/tex]
We know that[tex]1.15z = 0.80x[/tex]
[tex]1.035x - 0.80z = 230\\0.235x = 230\\x = \frac{230}{0.235}\\x= Rs. 978.72[/tex]
Hence The market price of the article is Rs. 978.72
What translation is made from f(x) = f(x) + 6?
Answers
Answer:
moves it up 6 units
Step-by-step explanation:
y = f(x) + C C > 0 moves it up
f(x) = f(x) + 6 moves it up 6 units
Answer:
Vertical shift, 6 up.
Step-by-step explanation:
The entire function f(x) has a value of six added to it. That means that regardless of where f(x) was plotted on the coordinate plane, after the translation f(x) + 6, every single point would increase its value by six. Since all points would increase their values by six, the entire function would shift 6 up.
The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table. A 2-column table has 4 rows. The first column is labeled Eye Color with entries brown, green, blue, hazel. The second column is labeled Number of People with entries 20, 6, 17, 7. What is the probability that a person chosen at random from this group has brown or green eyes? StartFraction 3 Over 25 EndFraction StartFraction 7 Over 25 EndFraction StartFraction 13 Over 25 EndFraction StartFraction 17 Over 25 EndFraction
Answers
Answer:
[tex]P(Brown\ or\ Green) = \frac{13}{25}[/tex]
Step-by-step explanation:
Given
[tex]n(Brown) = 20[/tex]
[tex]n(Green) = 6[/tex]
[tex]n(Blue) = 17[/tex]
[tex]n(Hazel) = 7[/tex]
Required
Determine the probability of Brown or Green eyes
First, the total number of respondents have to be calculated;
[tex]Total = 20 + 6 + 7 + 17[/tex]
[tex]Total = 50[/tex]
The events described above is a mutually exclusive event and as such, the required probability will be calculated by;
[tex]P(Brown\ or\ Green) = P(Brown) + P(Green)[/tex]
Calculating P(Brown)
[tex]P(Brown) = \frac{n(Brown)}{Total}[/tex]
Substitute 20 for n(Brown) and 50 for Total
[tex]P(Brown) = \frac{20}{50}[/tex]
Calculating P(Green)
[tex]P(Green) = \frac{n(Green)}{Total}[/tex]
Substitute 6 for n(Green) and 50 for Total
[tex]P(Green) = \frac{6}{50}[/tex]
So;
[tex]P(Brown\ or\ Green) = P(Brown) + P(Green)[/tex]
[tex]P(Brown\ or\ Green) = \frac{20}{50} + \frac{6}{20}[/tex]
Take LCM
[tex]P(Brown\ or\ Green) = \frac{20+6}{50}[/tex]
[tex]P(Brown\ or\ Green) = \frac{26}{50}[/tex]
Divide the numerator and denominator by 2
[tex]P(Brown\ or\ Green) = \frac{13}{25}[/tex]
Answer:
13/25
Step-by-step explanation:
Total number of people = 50
Probability of choosing a person with brown eyes [P(A)] = 20/50
Probability of choosing a person with green eyes [P(B)] = 6/50
Using the addition rule of mutual exclusive events (since they have specified brown OR blue, we use this formula):
P(A U B) = P(A) + P(B)
=> P(A U B) = 20/50 + 6/50 = 26/50 = 13/25
Therefore the probability of a person choosing a group that has brown or green eyes = 13/25
Also I got it right on edge haha, if you're still worried!!!!!!!!
Hope this helps :))))))))))))))
What number is 16% of 80?
Write and solve an equation to answer the question.
Answers
Answer:
The answer is 12
Step-by-step explanation:
Trust me, kay? Please mark Brainliest!!!!
Answer:
12.8
Step-by-step explanation:
16% of 80
[tex]\frac{16}{100}[/tex] × 80
[tex]\frac{16}{10}[/tex] × 8
[tex]\frac{16}{5}[/tex] × [tex]\frac{4}{1}[/tex]
16 × 4
5
12[tex]\frac{4}{5}[/tex] = 12.8
What is the 52nd term of -11,-2,7,16,25,34
Answers
Answer:
448
Step-by-step explanation:
Formula
tn = a + (n - 1)d
Givens
a = - 11
n = 52
d = 9
Solution
t52 = -11 + (51)*9
t52 = - 11 + 459
t52 = 448