Answer:
Step-by-step explanation:
Not near enough information to know.
I ASSUME that the pool is surrounded by a walkway of constant width (w = 2 ft, from comments)
The pool shape is important as well. No mention of the shape
If the pool is circular and the walkway is 3 ft wide
the fence encloses a diameter of 110/π = 35 ft
so the diameter of the pool would be 35 - 2(3) = 29 ft.
POOL IS RECTANGULAR from comments
If the pool is square and the walkway is 2 ft wide, each side of the fence is
110 / 4 = 27.5 ft and the pool would be 27.5 - 2(2) = 23.5 ft on a side.
There are an infinite number of rectangular width and length dimensions and walkway dimensions which would result in a fence length of 110 ft.
Edit from comments
Still an infinite number of rectangular length an width dimensions for a pool with a 2 ft wide walkway around it.
Let's say that we are told the pool is 12 ft wide with 2 ft walkway.
Let L be the pool length
110 = 2(12 + 2(2)) + 2(L + 2(2))
110 = 32 + 2L + 8
70 = 2L
L = 35 ft
Line y=2x+3 is tangent to a circle with center (2,-3). Which of the length of the radius of the circle?
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:
y+3=-1/2(x-2)
We can simplify this to
y= -1/2x-2
We can then check the point of intersection:
-1/2x-2=2x+3
-5=2.5x
x=-2
we can plug this in to the first equation to get y=2(-2)+3=-1
So the point of intersection of the circle and the tangent line is (-2,-1)
Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.
[tex]\sqrt{(-2-2)^{2}+(-1-(-3))^{2} } =\sqrt{(-4)^{2}+2^{2} } =\sqrt{20} =2\sqrt{5}[/tex]
The radius of the circle is [tex]2\sqrt{5}[/tex]
For Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The line y=2x+3 is tangent to the circle with center (2,-3)
The distance from the center of the circle to the line is equal to the radius of the circle.
The distance from a point (x₁, y₁) to a line Ax + By + C = 0 is given by the formula:
d = |Ax₁+ By₁ + C| /√A² + B²
The equation of the line is y = 2x + 3, which can be written in the form Ax + By + C = 0 as (-2)x + y - 3 = 0.
d = |-2(2) + (-3) - 3| / √(-2)² + 1²
d=10/√5
The radius of the circle is equal to the distance from the center to the tangent line, which is:
radius = 10/√5
Hence, for Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5
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danny is offering 36$ for 4 hours of swimming lessons. Martin in offering 54$ for 3 hours of swimming lessons. whose offer is better
Answer:
Danny's offer is cheaper
Step-by-step explanation:
Danny is offering 36$ for 4 hours meaning you would do 36÷4=9 (9$ per hour)
Martin is offering 54$ for 3 hours so 54÷3=18 (18$ per hour)
Or the faster way of finding why is Danny is offering more hours for cheaper
Hope this helps
Help me please i really need it
=======================================================
Explanation:
The ratio we want is in the format green:red:total which means we list the number of green first, then the number of red next, then the number total last. The order is very important. This is because we'll simply list the numbers without saying the color name or "total". So the reader will imply what the numbers refer to, based on this order mentioned.
We have:
50 red70 green42 yellow50+70+42 = 120+42 = 162 totalThe ratio of green to red to total is 70:50:162
To reduce the ratio, we divide all three parts of that ratio by the GCF 2
70/2 = 3550/2 = 25162/2 = 81The ratio 70:50:162 fully reduces to 35:25:81 which is the final answer.
This says that for every 35 green marbles, we have 25 red marbles and 81 total marbles.
An online survey asked a sample of high school students their favorite type of music, and the results were tabulated above. Find the probability that a person chosen at random did not choose pop music, given that the student is a sophomore or a junior.
Answer:
87/103
Step-by-step explanation:
A group of 8 people are sharing gummy bears each person wants 5 gummy bears each bag has 9 gummy bears
At least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.
The given parameters;
total number of people sharing the gummy bears, n = 8 peoplenumber of gummy bears in each bag, = 9 gummy bearsnumber of gummy bears needed by each person = 5 gummy bearsThe number of gummy bear bags needed to share 5 gummy bears to each person is calculated as follows;
let the number of gummy bears bag = x
[tex]\frac{9x}{8} = 5\\\\9x = 40\\\\x = \frac{40}{9} \\\\x = 4.4[/tex]
Thus, at least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.
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what is 2 3/15 roumded to the nearest half
Answer:
It is 7 whole
Step-by-step explanation:
3/15 is 5 without anything left plus the 3 is 7
6-3y+(-7y)+5.6 i really need answers
Answer:
+2 • (25y + 29)/5
Step-by-step explanation:
When Abrams born his parent put $2000 in account that you did 1.2% interest compounded semi annually when he turns 16 in Spain to give him the money to buy a car how much will Abrams you receive on his 16th birthday
Answer:
$2421.95
Step-by-step explanation:
To calculate the final value from compound interest, we can use the formula
A = P(1+r/n)^(nt), where A represents the final amount, P is the initial amount, r is the rate, n is the number of times compounded per time period, and t is the amount of time.
Here, P is 2000, 1.2% is the rate (to convert to a decimal, we can divide by 100 to get 0.012), n = 2 because it is compounded semi-annually, and 16 is the number of years, or t. Plugging these in, we get
2000(1+0.012/2)^(2*16) = 2421.95
John made 357$ for 17 hours of work.
At the same rate, how many hours would he have to work to make $237???
Answer: 14 hours
Step-by-step explanation: First I found the unit rate of how much money per hour. So, 357 divided by 17 = 21. So know I know that she earns 21$ per hour. Then, I did 237 divided by 17 which would be 13 remainder 16. Since he only get paid if he works for a full hour, I think the answer would be 14.
[tex]\begin{array}{ccll} \$&hrs\\ \cline{1-2} 357&17\\ 237&x \end{array}\implies \cfrac{357}{237}=\cfrac{17}{x}\implies \implies \cfrac{119}{79}=\cfrac{17}{x}\implies 119x=1343 \\\\\\ x = \cfrac{1343}{119}\implies x = \cfrac{79}{7}\implies x = 11\frac{2}{7}\leftarrow \textit{11 hours, 17 minutes and 8 seconds}[/tex]
Suppose that 100,000 men were screened for prostate cancer for the first time. Of these, 4,000 men had a positive result on the screening blood test; of those who tested positive, 800 had a biopsy indicating a diagnosis of prostate cancer. Among the remaining 96,000 men who screened negative, 100 developed prostate cancer within the following year and were assumed to be false negatives to the screen. a) set-up the two-by-two table for this data. (please provide an actual table) b) what is the prevalence of prostate cancer in this population? c) calculate and interpret the sensitivity of this screening test d) calculate and interpret the specificity of this screening test. e) Calculate and interpret the positive predictive value of this screening test.
An actual two-by-two table is a tabular representation containing two rows and two columns.
The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancerThe rows consist of the predicted positive screening and predicted negative values a)Mathematically, the set-up of the two-by-two table for this data can be computed as:
Tested True Positive for cancer True Negative Total
Predicted Positive 800 3200 4000
Predicted Negative 100 95900 96000
Total 900 99100 100000
b)The prevalence rate of prostate cancer in this population is:
[tex]\mathbf{ =\dfrac{900}{100000}}[/tex]
[tex]\mathbf{ =\dfrac{9}{1000}}[/tex]
= 9 per thousand.
c)
The calculation of the sensitivity of this screening is as follows:
[tex]\mathbf{=\dfrac{TP}{TP+PN_1}}[/tex]
where;
TP = True positive for cancerPN₁ = Predicted Negative for true positive cancer∴
[tex]\mathbf{=\dfrac{800}{800+100}}[/tex]
= 0.889
= 88.9%
The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.
d)The calculation of the specificity of this screening is as follows:
[tex]\mathbf{=\dfrac{PN_2}{PN_2+TN}}[/tex]
where;
TN = True positive for cancerPN₂ = Predicted Negative for true negative cancer∴
[tex]\mathbf{=\dfrac{95900}{95900+3200}}[/tex]
= 0.9677
= 96.77%
The interpretation shows that 96.7% of an actual negative is correctly identified as such.
e)
The positive predicted value of the screening test is computed as:
[tex]\mathbf{= \dfrac{TP}{TP + TN}}[/tex]
[tex]\mathbf{= \dfrac{800}{800 + 3200}}[/tex]
= 0.2
= 20%
The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.
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Identify the function as a power function, a polynomial function, or neither.
[tex]fx=\frac{x^2}{x^2-1}[/tex]
Answer:
I think this is neither. As you can see the value of x reaches infinity and negative infinity, the value gets infinetly closer to 1.
pls help wiht this question ill give you 69 points whoever awnsers
Answer:
what's thequestion?
Step-by-step explanation:
write clearly please
Answer: this is 4
Step-by-step explanation: A+b=2+2=4
261,256,251,...
Find the 50th term.
Find the 50th term.
Answer:
16
Step-by-step explanation:
261 - 256 - 251
-5 by step
to 50th term there is 49 -5's from 261.
261 + 49.(-5) = 261 - 245 = 16
Answer:
16
Step-by-step explanation:
The sequence appears to be an arithmetic sequence. To find the 50th term we should create a general formula for the sequence.
General formula of an arithmetic sequence: [tex]a_n=a_1+(n-1)d[/tex]
where An = nth term, a1 = first term , n = number of terms and d = common difference.
The first term is 261 so a1 = 261
The common difference appears to be -5
( 256 - 261 = -5 ) and ( 251 - 256 = -5 )
so d = -5
We want to find the 50th term so n = 50
We then plug all of this in to get the 50th terms
Formula : [tex]a_n=a_1+(n-1)d[/tex]
a1 = 261 , n = 50 and d = -5
[tex]a_n=261 + (50-1)-5[/tex]
subtract 1 from 50
[tex]a_n=261+(49)(-5)[/tex]
multiply 49 and -5
[tex]a_n=261-245[/tex]
subtract 245 from 261
[tex]a_n=16[/tex]
The 50th term is 16
A total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rate if the annual interest is $430?
3,400 at 10%
600 at 15%
This is the answer.
Please help me will give brainliest
Answer:
f(x) = 8.917x³ + 2x² + 0.083x - 7
Step-by-step explanation:
f(x)= y
Let the coefficients of x³, x², x be a, b, c and the constant be d
y= ax³ + bx² + cx + d
When y = -65, x = -2
-65= a(-2)³ + b(-2)² + c(-2) + d
-65= -8a + 4b - 2c + d ...eq. 1
When y = -14, x = -1
-14= a(-1)³ + b(-1)² + c(-1) + d
-14= -a + b - c + d ...eq. 2
When y = -7, x = 0
-7= a(0)³ + b(0)² + c(0) + d
-7 = d ...eq.3
When y = 4, x = 1
4= a(1)³ + b(1)² + c(1) + d
4= a + b + c + d ...eq. 4
when y = 78, x = 2
78 = a(2)³ + b(2)² + c(2) + d
78= 8a + 4b + 2c + d ...eq. 5
From eq. 3, d is - 7
putting d as - 7 in equations 1, 2, 4 and 5
In eq. 1,
-65= -8a + 4b - 2c - 7
-58= -8a + 4b - 2c ...eq. 6
In eq. 2
-14= -a + b - c - 7
-7= -a + b - c ...eq. 7
In eq. 4,
4= a + b + c - 7
11= a + b + c ...eq. 8
In eq. 5
78= 8a + 4b + 2c - 7
85= 8a + 4b + 2c ...eq.9
Subtracting eq. 9 from eq. 6
-143 = -16a - 4c... eq 10
subtracting eq. 8 from eq 7
-18= -2a - 2c
9= a + c
a = 9 - c ...eq 11
putting a as 9 - c in eq. 10
-143 = -16(9 - c) - 4c
-143 = -144 + 16c - 4c
1= 12c
c = 1/12 or 0.083
putting c as 1/12 in eq. 11
a = 9 - 1/12
a = 107/12 or 8.917
Putting a as 107/12 and c as 1/12 in eq. 8
11= 107/12 + b + 1/12
multiplying through by 13
132 = 107 + 12b + 1
132 - 108 = 12b
24= 12b
b = 24/12
= 2
Therefore, a= 8.917, b= 2, c= 0.083 and d = -7
f(x) = 8.917x³ + 2x² + 0.083x - 7
I need help with this
I need help on this question pls
Answer:
t = 17.5 f = 12
Step-by-step explanation:
If MNOP is a square, you know that each angle is going to be 90°. To solve, let's first set each equation equal to 90°:
[tex]90 = 4t + 20[/tex]
and
[tex]90 = 7f + 6[/tex]
Then solve both equations:
[tex]90 = 4t + 20 \\ 70 = 4t \\ 17.5 = t[/tex]
and
[tex]90 = 7f + 6 \\ 84 = 7f \\ 12 = f[/tex]
I hope that helps!
[tex]3^{2x+1} -4.9^{x} =-9[/tex]
Which expression shows a way to find 20% of 950
1/20 / 950
1/20 • 950
1/5 • 950
1/5 / 950
Answer:
C
Step-by-step explanation:
20% x 950
Calculate 20% x 950 = 190
Match the options one by one and there
Answer:
C: 1/5 · 950Step-by-step explanation:
I got it correct on I-ready.
Hope this helps!!
math problem need help give 5 stars and good rating if do
Answer:
The answer is A, 20%.
Step-by-step explanation:
If you find 30 out of 150, it is 20%. A simple way to do it is add 30 up until you get 150. So in this case it is 5 times. Then you do 100% divided by 5 which is 20%. Hope this helps!
A number increased from 3,631 to 8,140. Find the amount of increase.
Answer: 4509
8,140-3,631
= 4509
What is the value of 40 1/2÷3 1/2
Answer:
81/7 (11.57, 11 4/7)
Step-by-step explanation:
Lets rewrite these mixed fractions
[tex]40\frac{1}{2}=\frac{81}{2}[/tex]
[tex]3\frac{1}{2} =\frac{7}{2}[/tex]
Here we can do divide these two numbers:
[tex]\frac{\frac{81}{2} }{\frac{7}{2} }=\frac{81}{7}[/tex]
The answer therefore is 81/7, or 11.571 (11 4/7)
Find the domain of the graphed function.
Answer:
A
Step-by-step explanation:
the domain is all the possible numbers that the x can be, so to find this from the graph you find the x-value of the leftmost point, which is -1 in this case, and the x-value of the rightmost point, which is 3. this means the range of values would be -1 <= x <= 3
How many cups of cream would you need for 7 cups of sugar
Answer:
sugar is bad so just use cream
Step-by-step explanation:
sugar can increase the risk of weight gain, diabetes, tooth cavities, and more.
hope this helps
Which expression has a value of −8?
Answer:
-4+-3+2-3
Step-by-step explanation:
harold bought 3 pounds of red apples
Answer:
what's your question?
Ray had $50. he bought two shirts that cost $19 each. how much money did Ray have after buying the shirts? Alex's answer to the word problem is $29. Is Alex's answer reasonable? explain.
no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes? on average a shirt cost 15 bucks but 19? yeah no
Answer:
Step-by-step explanation:
no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes? on average a shirt cost 15 bucks but 19? yeah no
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Hep help help help help math math
Answer:
5(37)+10
10(17.5)+5
Step-by-step explanation:
5x+10=180
-10 -10
5x=170
divide by 5
x=37
---------------------
10x+5=180
-5 -5
10x=175
divide by 10
x=17.5