Answers
Answer: Area of Fountain = 147/147.58
Area of Circular path = 28.26
Step-by-step explanation:
formula for area of circle = pi x r^2
radius of fountain - [tex]\\ \sqrt{47} \\[/tex]
area= 22/7 x 47 (as [tex]\sqrt{47}[/tex] is squared)
=147
radius of circular path - [tex]\sqrt{56}[/tex]
area= 22/7 x 9 ( [tex]\sqrt{56}[/tex] is radius and [tex]\sqrt{47}[/tex] is of the fountain subtract them you'll get 9 )
=28.26
Related Questions
Mr. Wilson invested money in two accounts his total investment was $8000. If one account pays 6% and interest and the other pays 12% interest how much did he invest in each account if he earned a total of $600 in an interest in one year
Answers
Answer:
Mr. Wilson invested $ 2,000 in the 12% simple interest account and $ 6,000 in the 6% simple interest account.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of the investment = $ 8,000
Interest rate of the first account= 6% simple
Interest rate of the second account= 12% simple
Interest of the accounts in a year = $ 600
2. How much did he invest in each account?
For answering the question, we will use the following equation:
x = Amount invested in the first account
8,000 - x = Amount invested in the second account
0.06x + 0.12 * (8,000 - x) = 600
0.06x + 960 - 0.12x = 600
-0.06x = 600 - 960 (Subtracting 960 at both sides)
-0.06x = -360
x = -360/-0.06
x = 6,000 ⇒ 8,000 - x = 2,000
Mr. Wilson invested $ 2,000 in the 12% simple interest account and $ 6,000 in the 6% simple interest account.
In Mr. Rojo’s art class, students are asked to create an orange background for their new painting. They mixed red paint and yellow paint to create a shade of orange. The table shows the number of pints of red paint, y, and yellow paint, x, different students used to create the orange color. Pints of Yellow (x) Pints of Red (y) 2 3 3 4.5 4 6 6 9 Identify the equation that relates the number of pints of red and yellow paint used. x=1.5y y=1.5x y=4.5x x=4.5y
Answers
Answer:
y = 1.5x.
Step-by-step explanation:
2 yellow (x) 3 red (y) (3 /2 = 1.5)
3 yellow 4.5 red (1.5)
4 yellow 6 red (1.5)
6 yellow 9 red (1.5)
So the equation is
y = 1.5x
A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12% vinegar. The chef wants to make 320 milliliters of a mixture that contains 23%vinegar. How much vinegar and how much Italian dressing should she use?
Answers
Answer:
40 mL of vinegar,
280 mL of dressing
Step-by-step explanation:
Let v = the milliliters ( mL ) of 100% vinegar,
Then it should be that 320 - v = mL of dressing.
v + .12( 320 - v ) = .23( 320 ) - So in this case the mL of vinegar is associated with the percent of vinegar composed. 100 percent is, in other words, 1, and is multiplied by " v " the mL of 100% vinegar. 1 [tex]*[/tex] v is also v, and so is written as such in our equation. 0.12 is the decimal form of the 12% vinegar, associated with the mL of dressing - as the italian dressing is composed of 12% vinegar. 23% is 0.23 in decimal form, multiplied by the mL of of vinegar in the mixture, 320 mL.
Let's solve for the mL of 100% vinegar, subtracting from 320 to receive the mL of dressing,
v + .12( 320 - v ) = .23( 320 ) - Distribute " .12 "
v + 38.4 - 0.12v = .23( 320 ) - Multiply " 0.32 " by " 320 "
v + 38.4 - 0.12v = 73.6 - Combine like terms and add / subtract
0.88v = 35.2 - Divide 0.88 on either side
v = 40 mL of vinegar,
320 - v = 320 - 40 = 280 mL of dressing
What is the solution of sqrtx^2+49 = x+5?
Answers
Answer:
x = 12/5Step-by-step explanation:
√x² + 49 = x + 5
Square both sides
(√x² + 49)² = ( x + 5)²
x² + 49 = x² + 10x + 25
Simplify
10x = 49 - 25
10x = 24
Divide both sides by 10
x = 12/5Hope this helps you
Which of the following is true about a point? It is a location. It is infinitely long. It has an endpoint. It has width.
Answers
Answer:it is a location
Step-by-step explanation:
The others are simply wrong
The statement that can be said to be through about point is that a point is a location.
A point is a location in a geometry space used in demarcating an area or region with a dot representation. It does not have any long line or an endpoint. It does not also have a length or width. It is usually used to make a notion about a specified region.
For example: If I want to measure a distance of 6 cm. I can place my divider from the mathematical set on the meter-rule and measure out 6 cm.
Then, place 6 cm on the plain sheet to show two different dots indicating the distance of 6cm before I draw the distance of 6cm with my drawing pencil.
Learn more about a point here:
https://brainly.com/question/22932149?referrer=searchResults
Match the number with its opposite.
Answers
Answer:
3.2 matches with (A) -3.3
-2.3 matches with (C) 2.3
-1.5 matches with (B) 1.5
5.1 matches with (D) -5.1
What is the measure of a?
Answers
Answer:
a=129
Step-by-step explanation:
the angles are complementary which is is 180
51+a=180
a=180-51
a=129
4) Jacqueline, Hanry, and Stanley bought a pizza pie to share for dinner. Harry ate
1/2 of the pie, and then Jacqueline ate 1/2 of what was left. After Jacqueline
finished, Stanley ate 1/2 of what was left of the pie. What fractional part of the
pizza pie was left after Stanley finished eating? Help please
Answers
Answer:
1/8
Step-by-step explanation:
ok so before i start i wanna say that this is gonna get confusing.....
Since the pizza is a whole quantity let us take it as 1.
Harry ate half of the pizza therefore the fraction that Harry ate = 1/2 of 1
= 1/2 × 1 = 1/2
Therefore fraction Harry ate = 1/2
Fraction of pizza left = 1 - 1/2 (LCM = 2)
= 1/2
Jacqueline ate 1/2 of what was left.
So, Fraction of pizza Jacqueline ate = 1/2 × 1/2 = 1/4
Therefore fraction of pizza left after both Harry and Jacqueline ate =
1 - (1/2 +1/4) = 1 - 3/4 (LCM = 4) = 1/4
Therfore fraction of pizza left = 1/4
Stanley ate 1/2 of what was left.
So, fraction of pizza Stanley ate = 1/2 × 1/4 = 1/8
Therefore, fraction of pizza left after all three of them ate =
1 - (1/2 + 1/4 + 1/8) = 1 - 7/8 (LCM = 8) = 1/8
I hope this helps .......i know this is rlly confusing but i dont know how else to put it : )
Have a nice day!
Name four fractions whose
values are between 1/7 and 1/5
Answers
Answer:
21/140, 22/140, 23/140, 24/140
Step-by-step explanation
7 and 5 have a common multiple of 140.
140/7 = 20 , 20/140
140/5 = 28, 28/140
21, 22, 23, 24, 25, 26, and 27 are all numbers between 20 and 28.
Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number solutions does the equation have? Discriminant = b2-4ac
Answers
Greetings from Brasil...
The equation:
X² + 4X + 1 = - 3
X² + 4X + 1 + 3 = 0
X² + 4X + 4 = 0
Δ = b² - 4.a.c
Δ = 4² - 4.1.4
Δ = 0
so we have just 1 solution
X = (- b ± √Δ)2a
X = (- 4 ± √0)2.1
X = - 4/2
X = - 2Answer:
X=-2
Step-by-step explanation:
Use more than one equation.
X=-2
X=2
minus the four from the left over.
answer X=-2
If the public debt in 2006 was $6,783,231,062,743.62 and the budget
for 2007 was in deficit by $595,821,633,586.70, what was the public
debt in 2007? (Include commas.)
Answers
Answer:
677,727,284,640,775 ?
Please help me with this problem from my geometry:((
Answers
The histogram represents the distributions of boiling
temperatures, in degrees Celsius, of tap water and a
mixture of salt water.
Boiling Temperatures
10
9
8
7
6
Number
of
Trials
5
-Tap Water
Salt Water
4 3
N
1
0
98°C
99 C 100C 101 102 103 104°C
Temperature (°C)
Answers
Answer:
The mean boiling temperature of the tap water is 2°C less than hat of the mixture of salt water.
Step-by-step explanation:
The complete question is attached below.
From the provided data it can be seen that the distributions of boiling temperatures, in degrees Celsius, of both tap water and a mixture of salt water are approximately symmetric.
It is known that, for a symmetric distribution,
Mean = Median = Mode
The median for the two distributions are:
Median (Tap water) = 100°C
Median (Mixture of salt water) = 102°C
Then the mean for the two distributions would be:
Mean (Tap water) = 100°C
Mean (Mixture of salt water) = 102°C
So, the mean boiling temperature of the tap water is 2°C less than hat of the mixture of salt water.
Answer: It's B :)
Step-by-step explanation:
Is 31/50 greater than 1/2
Answers
Answer:
Yes
Step-by-step explanation:
You can take 1/2 and find a common denominator if this helps you.
We will multiply 1/2 by 25/25 because 25/25 equals 1 so you get the same amount just with a different numerator and denominator. So you get 25/50 and then you compare. 31/50 > 25/50
Which of the following exponential functions is represented by the graph? Question 7 options: A) ƒ(x) = (1∕5)x B) ƒ(x) = (1∕5)–x C) ƒ(x) = –5x D) ƒ(x) = 5–x
Answers
Answer:
[tex]f(x) = (\frac{1}{5})^{-x}[/tex]
Step-by-step explanation:
Given
The graph above
Required
Determine from the list of options, the function of the graph
To determine the function, we have to test each of the options
But first, we nees to write out the points on the graph
(1,5), (0,1), (-1,1/5) and (-2, 1/25)
A. [tex]f(x) = (\frac{1}{5})^x[/tex]
Point 1: When x = 1, f(x) = 5
[tex]f(x) = (\frac{1}{5})^x[/tex]
[tex]f(1) = (\frac{1}{5})^1[/tex]
[tex]f(1) = (\frac{1}{5})[/tex]
There's no need to check further as the first point doesn't lie on the graph
B. [tex]f(x) = (\frac{1}{5})^{-x}[/tex]
Point 1: When x = 1, f(x) = 5
[tex]f(x) = (\frac{1}{5})^{-x}[/tex]
[tex]f(1) = (\frac{1}{5})^{-1}[/tex]
[tex]f(1) = 1/(\frac{1}{5})[/tex] --- Law of indices
[tex]f(1) = 1*(\frac{5}{1})[/tex]
[tex]f(1) = 1*5[/tex]
[tex]f(1) = 5[/tex]
Point 2: When x = 0, f(x) = 1
[tex]f(0) = (\frac{1}{5})^{-0}[/tex]
[tex]f(0) = (\frac{1}{5})^{0}[/tex]
[tex]f(0) = 1[/tex] --- The expression raise to power 0 is 1
Point 3: When x = -1, x = 1/5
[tex]f(x) = (\frac{1}{5})^{-x}[/tex]
[tex]f(-1) = (\frac{1}{5})^{-(-1)}[/tex]
[tex]f(-1) = (\frac{1}{5})^{1}[/tex] ----- Law of indices
[tex]f(-1) = (\frac{1}{5})[/tex]
Point 4: When x = -2, x = 1/25
[tex]f(x) = (\frac{1}{5})^{-x}[/tex]
[tex]f(-2) = (\frac{1}{5})^{-(-2)}[/tex]
[tex]f(-2) = (\frac{1}{5})^{2}[/tex] ----- Law of indices
[tex]f(-2) = \frac{1}{5} * \frac{1}{5}[/tex]
[tex]f(-2) = \frac{1}{25}[/tex]
There's no need to check other options as this function satisfy the 4 points on the graph;
Hence;
[tex]f(x) = (\frac{1}{5})^{-x}[/tex] is the exponential function represented on the graph
Help ASAP in this picture
Answers
Answer:
the first choice
Step-by-step explanation:
0.25= 0.25
2/3= 0.3333333
56%= 0.56
0.25<0.33<0.56
0.25=0.25
2/3= 0.333
%56= 0.56
What is the expectation for a binomial distribution with p = 0.5 and n = 8?
Answers
Answer: 4
Step-by-step explanation:
Given the following :
P = probability of success = 0.5
n = number of trials = 8
The expected value of a binomial distribution with probability of success P and number of trials n is defined by:
E(n, p) = n * p
Therefore, expected value when P = 0.5 and n = 8
E(8, 0.5) = 8 × 0.5
= 4
The expected value of the binomial distribution is 4
Fill in the missing numbers to complete the factorization. Some of the numbers could be negative. Type the numbers in
increasing order.
x3 + 2x2 - x - 2 = (x +
p(x+
Answers
Answer:
(x-1)(x+1)(x+2)
Step-by-step explanation:
X³+2x²-x-2
(X-1)(x²+3x+2)
(x-1)(x+1)(x+2)
You have linear functions p(x) and q(x). You know p(2)=3, and p(q(x))=4x+7 for all x. Find q(-1).
Answers
Answer:
q(-1)=-2
Step-by-step explanation:
1) flip the equation:
4x+7=-1
2) subtract 7 from both sides:
4x=-8
3) divide both sides by 4:
x=-2
HOPE THIS HELPS!!!! :)
Which of the following sequences is not an arithmetic sequence? 0, -2, -4, -6, ... 1, 5, 9, 13, ... 15, 12, 9, 6, ... -1, -2, -4, -8, ...
Answers
Answer:
D. -1,-2,-4,-8
Step-by-step explanation:
An arithmetic sequence means that there is a pattern between the numbers that is constant, that deals with either adding or subtracting.
The last sequence here, is not arithmetic because it is being multiplied by 2 every time.
Please help me on this question
Answers
Answer:
x = [tex]\frac{k(a+r)}{7}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{7x}{k}[/tex] - r ( add r to both sides )
a + r = [tex]\frac{7x}{k}[/tex] ( multiply both sides by k to clear the fraction )
k(a + r) = 7x ( divide both sides by 7 )
[tex]\frac{k(a+r)}{7}[/tex] = x
Answer:
ak - kr k(a - r)
x = -------------- or x = ------------
7 7
Step-by-step explanation:
1. Multiply all three terms by k to eliminate the fraction:
ak = 7x - kr
2. Subtract kr from both sides:
7x = ak - kr
3. Divide both sides by 7:
ak - kr k(a - r)
x = -------------- or x = ------------
7 7
If a b and c are three different numbers which of the following equations has infinitely many solutions
a. ax=bx+c
b. ax+b=ax+c
c. ax+b=ax+b
Answers
Answer: c ax + b = ax+ b
Step-by-step explanation: Seems like a trick question, especially since Answer c has no c in the equation. But once you put in numbers for a,b,and c, there cannot be infinite solutions for x in the first two examples.
Set up two or three equations and test them as proof.
Hurry !!!!!
The data Ilst shows the cost, In dollars, of different brands of sneakers at a shoe store.
44.99, 59.99, 32.30, 65.00, 52.59
What is the standard deviation, to the nearest tenth, of the data If the scores represent only a sample of data on sneaker
prices at the store?
ao
Answers
Answer:
12.895
Step-by-step explanation:
Standard deviation is a statistic that measures the dispersion of a sample. The sample standard deviation measures the spread of data distribution of the sample. It is usually used to estimate the population standard deviation.
Box A contains 5 dark chocolates and
10 milk chocolates. Box B contains 12
dark chocolates and 12 milk chocolates.
Craig picks a box at random and then
takes out one chocolate at random.
What is the probability that he gets a dark
chocolate?
% (1 d.p.)
Answers
Explanation:
Chances of getting box A or B = 1/2
Chances of getting dark choco in Box A:
P = 5/15 = 1/3
Chances of getting dark choco in Box B:
P = 12/24 = 1/2
The probability of getting a dark choco from a random box is:
P = 1/2(1/3 + 1/2) = 1/2(2/6 + 3/6) = 1/2(5/6) = 5/12
Look at the triangle:
What is the value of cos xº? (1 point)
A. 8÷17
B. 17 = 8
C. 15 = 17
D. 8 = 15
Answers
Answer:
15/17
Step-by-step explanation:
You can calculate cosine by doing adjacent / hypotenuse so cos x° = 15/17.
Which of the following coordinates represents a point that is collinear with the given points.
(-8, 0) and (4,-3)
O (-4,-1)
O (2,-3)
O (4,-4)
O (-4,1)
Answers
Answer:
A) (-4,-1)
Step-by-step explanation:
a line graphed with those coordinates would have a slope of -3/12, or -1/4.
Following that slope, you would go through (-4,-1). So that is the point collinear with the given points.
Felix drew two box-and-whisker plots to compare the same sets of data: In the form of a paragraph, use complete sentences to describe some of the differences in the prices of the two sets of books. Refer to the box and whisker plots to justify your answer.
Answers
The first set of data shows that the difference in the prices is very small while the second set of data shows a larger variety of prices. The first set represents its prices in equally divided groups making it easier to read and determine than the second set of data.
If x2 + 6x + 8 = 0 , then x could equal which of the following?
Answers
Answer:
x = -4 , -2
Step-by-step explanation:
I am assuming "x2" is x^2. If the equation is x^2 + 6x + 8 = 0, then you first have to factor the equation x^2 + 6 + 8.
In order to do that, you would have to find the multiples of 1 (from x) and 8.
We can see that 1 * 1 is 1, so that is the only pair that would work for the problem. 4 * 2 is 8, but 8 * 1 is also 8. So, which set of numbers do we have to choose? It's actually really simple. You multiply the first set of numbers (1 and 1) with one of the sets from 8 ( 4 and 2 or 8 and 1). Then when you are finished multiplying them together, you add them together to see if they equal to the number in the middle (6x). So 1(x) * 4 is 4x, and 1(x) * 2 is 2x, and when we add the numbers together, we get 6x, which is the middle number, so therefore, 4 and 2 is the correct set of numbers, not 8 and 1, because if we multiply and add those together, we get 7x, not 6x.
After doing that, you have to put them like this:
(x + 4)(x + 2)
This is so when you multiply them together, you get the starting equation. But we have to solve for x. In order to do that, we have to plug that into the equation we started off with.
(x + 4)(x + 2)=0
Now we have to make x + 4 and x + 2 equal to 0, so x is -4 and -2. There are two correct answers. Hope this helps :)
Answer:
x is -2 and -4
Alice is building a caterpillar habitat for some caterpillars she found in her back yard. She plans to cover all sides of the habitat with screen so the caterpillars get plenty of fresh air. What is the total amount of screen that Alice will need for her habitat?
Answers
Answer:
perimeter of a cuboid is 4(L+B+H).
so, L=1m, B=0.4m,H=0.8m
substituting by formula,
4(1+0.4+0.8)
= 4(2.2)
=8.8
AMOUNT OF SCREEN THAT ALICE REQUIRES FOR HER HABITAT IS 8.8m
Step-by-step explanation:
HOPE IT HELPS. PLEASE MARK IT AS BRAINLIEST
Answer:
3.04 m^2
Step-by-step explanation:
FIRST GETS BRAINLLESTIf you spin the spinner below 80 times, which of the following outcomes are reasonable? Select all that apply. A) Lands on blue 43 times B) Lands on yellow 8 times C) Lands on red 33 times D) Lands on red 62 times
Answers
Answer:
A, B, C
Step-by-step explanation:
Answer:
A) Lands on blue 43 times
B) Lands on yellow 8 times
C) Lands on red 33 times
Step-by-step explanation:
Blue is 1/2 of the spinner so theoretically is should be landed on 1/2 of the time which is 40/80 but experimentally, it can differ slightly. Using this same logic, it can be applied to yellow and red. Yellow is 1/8 of the spinner so it should be landed on about 10 out of the 80 times. Red is 3/8 of the spinner so it should be landed on approximately 30 out of 80 times.