The largest section of the pool is 11307.2 square feet and it seems feasible to add a water slide based on this area. In order to fill the pool, considering that the average depth is 4 feet, approximately 338511.6 gallons of water would be needed.
Explanation:We will first find the area of the circular pool, keeping in mind that the hypotenuse of the triangle serves as the diameter. We will use the formula for the area of a circle, A = πr², where r is the radius of the circle. Here, the radius is half of the hypotenuse so it's 120 feet / 2 = 60 feet.
This makes the area of the circle A = π * 60² = 3600π square feet. This, minus the area of the triangle which can be calculated by (1/2) * base * height = (1/2) * 60 * 103.92 = 3117.6 square feet. So, the largest section of the pool is 3600π - 3117.6 = 11307.2 square feet.
Additional structures such as a water slide could be considered based on the remaining area. Due to size of the pool, it seems feasible to add a water slide without significantly disrupting the swimming space. However, additional calculations considering the base area of the slide would be required for a definitive answer.
The amount of water needed to fill the pool is calculated by multiplying the volume of the pool by the weight of the water. If the average depth of the pool is 4 feet, the volume of the pool (ignoring the central triangle) is 11307.2*4 = 45228.8 cubic feet. As 1 cubic foot of water equals roughly translates to 7.48 gallons, the pool would require approximately 45228.8 * 7.48 = 338511.6 gallons of water.
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A box has dimensions of 17 inches long.1.3 feet wide, and 8 inches high. What is the valine of the box? The formula for the volume is V = l• w •h.
convert the feet to inches so all 3 dimensions are in the same measurement
1.3 x 12 = 15.6 inches
now multiply them all
17 x 15.6 x 8 = 2121.6 cubic inches
round the answer if you need to
The estimated measurements of the objects are shown below.
-length of a grain of salt: 0.0002 centimeters
-width of a key ring: 0.02 centimeters
Find the measurements written in standard notation to the estimated measurements in scientific notation.
The standard notation 0.0002 cm becomes 2 × 10^-4 and 0.02 cm becomes 2 × 10^-2, both in scientific notation.
Explanation:The standard notation for 0.0002 centimeters is 2 × 10^-4 in scientific notation. Meanwhile, the standard notation for 0.02 centimeters is 2 × 10^-2 in scientific notation.
You arrive at these translations by recognizing that the number 0.0002 means you've moved the decimal point four units to the right from 2 (thus raising 10, the base, to -4), and 0.02 represents moving the decimal point two units to the right from 2 (thus raising 10 to the -2).
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2. Richmond Appliance repairs washing machines. The revenue that the company earns is given by the function R(h) = 20 + 45h dollars for every h hours spent repairing washing machines. The company’s overhead cost is given by the function C(h) = 5h2 – 30 dollars. For what number of hours does the company break even? Show your work.
Answer:
The number of hours needed for the company to break even happens when
, rearranging to make the equation 'zero' on LHS
, divide each term by 5
, factorise
, equate each factor to zero
and
We choose the positive value of
Hence, the number of hours needed to break even is
Step-by-step explanation:
Name the binomial you can multiply by (x + 9) to get the product x 2 + 5x – 36. A. 4 – x B. x + 6 C. x – 4 D. x – 6
Q and R are independent events. If P(Q)= 1/8 and P(R)=2/5 find P(Q and R).
The probability of independent events Q and R both occurring is calculated by multiplying the individual probabilities of each event. Thus in this case, P(Q and R) = (1/8) * (2/5) = 1/20.
Explanation:The question posed asks for the probability of events Q and R both occurring. Given that Q and R are independent events, the likelihood of both happening is calculated by multiplying the probabilities of each event.
That is, P(Q and R) = P(Q)P(R). From the question, we know that P(Q) is 1/8 and P(R) is 2/5.
Therefore, the probability of both Q and R occurring would be (1/8) * (2/5) = 1/20.
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If the area of a rectangle is 16 then the length is 4 and the width is 4 what is the counterexample
7x7-9exponent x 7 7exponent
Answer:
1/7
Step-by-step explanation:
Suppose A and B are independent events if P(A) = 0.4 And P(B) = 0.1, what is P(A'uB)? APEX
Answer:0.6
Step-by-step explanation:
Find the zeros of the function. f(x) = 4x3 - 12x2 - 40x
Someone pls help me!! and thank you if you do !
Use allfour operations only once without parentheses to write an expression that has a value of 100 only using 3's
There are a lot of ways to write an expression using only 3 to get an answer of 100. Some examples are:
1st example:
3 / 3 + 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
= 1 + 99
= 100
2nd example:
3 / 3 + 3 * 3 * 3 * 3 + 3 * 3 * 3 – 3 * 3
1 + 81 + 27 – 9 = 100
the line of best fit drawn on a scatter plot ____
A. is a line that goes through each data plot.
B. always has a positive slope.
C. is a line drawn through the first and last points.
D. approximates the linear relationship of the data.
Lana Powell has cumulative earnings of $110,000 at the end of September. In the first week in October she earns $2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on $110,100 and Medicare of 1.45%):
Answer:
Lana Powell has cumulative earnings of $110,000 at the end of September. In the first week in October she earns $2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on $110,100 and Medicare of 1.45%):
Step-by-step explanation:
In the first week of October on the $ 2,000, we must deduct the two expenses, that of 6.2% and 1.45%, and then add them between them and subtract them from the $ 2000.
It would be the following: 2000 x 6.2% = $ 124; 2000 x 1.45% = 29; 124 + 29 = $ 153 is the amount to be deducted from the $ 2,000; $ 2000 - $ 153 = $ 1847.
Lana Powell's paycheck for the first week in October would have $124 deducted for Social Security and $29 for Medicare, resulting in a total deduction of $153. Her cumulative earnings are not considered here as she has exceeded the earnings threshold of $110,100 for Social Security tax.
Explanation:Lana Powell's earnings for the first week in October are subject to deductions for Social Security at a rate of 6.2% and Medicare at a rate of 1.45%. To calculate these deductions, you multiply her weekly earnings by the respective rates:
Social Security deduction = $[tex]2000*6.2/100 = $124[/tex]Medicare deduction = $[tex]2000*1.45/100 = $29[/tex]Therefore, the total amount deducted from Lana Powell's paycheck for Social Security and Medicare is $124 + $29 = $153.
Note that you do not consider her cumulative earnings in this case. The Social Security tax is applicable only up to a wage base limit of $110,100 and since her cumulative earnings have already exceeded this limit, she would not be paying any additional Social Security tax beyond this earnings threshold.
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The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = 1/2 (x – 1). What is the slope-intercept form of the equation for this line?
Answer:
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]
Step-by-step explanation:
Hello
thanks for asking this question, I think I can help you with this
if you have the point-slope form of the equation of a line, just isolate "y" to find the slope-intercept form
Step 1
[tex]y-3=\frac{1}{2} (x-1)\\\\y-3=\frac{x}{2}-\frac{1}{2} \\Add\ 3\ in\ both sides\\\\y-3+3=\frac{x}{2}-\frac{1}{2} +3\\y=\frac{x}{2}-\frac{1}{2}+3\\y=\frac{x}{2}+\frac{5}{2}[/tex]
so the answer is
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]
where 1/2 is the slope, and 5/2 is the intercept with y-axis
I really hope it helps , Have a great day.
In which one of the above figures is AB = AC?
A. Figure B
B. Figure C
C. Figure A
D. Figure D
Answer: The answer is (D). the image is attached.
Step-by-step explanation: We are given four figures from which we are to select the one with AB = AC.
In figure (A), AB and AC are two chords of the circle with common point A. Since the lengths of two chords of a circle may not be equal, so AB may not be equal to AC. This option is not correct.
In figure (B), AB is a tangent at point B and AC is the extension of a chord which meets the tangent AB at point A. Since the lengths of AB and AC may not be equal, so this option is also incorrect.
In figure (C), AB and AC are extensions of two chords which meets at point A outside the circle, so they may not be congruent. So, this option will also not work.
In figure (D), AB and AC are two tangents from a common point A to the circle at B and C respectively.
We have the Two-Tangent Theorem which states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.
So, we have AB ≅ AC.
Thus, (D) is the correct option.
Which of the following is a solution to the inequality y < –2x + 3?
A. (1,1)
B. (3,0)
C. (-3,10)
D. (0,0)
Please select the best answer from the choices provided
y < -2x +3
A. (1, 1) → x = 1, y = 1
substitute:
1 < -2(1) + 3
1 < 1 FALSE
B. (3, 0) → x = 3, y = 0
substitute
0 < -2(3) +3
0 < -3 FALSE
C. (-3, 10) → x = -3, y = 10
substitute
10 < -2(-3) +3
10 < 9 FALSE
D. (0, 0) → x = 0, y = 0
substitute
0 < -2(0) + 3
0 < 3 CORRECT
Answer: D. (0, 0)
Grace is half her father joseph's age. in 10 years grace will be three-fifths joseph's age. ten years ago, grace was one third joseph's age. how old are grace and joseph now
After setting up a system of equations based on the given age relationships and solving for both Grace and Joseph, we deduce that Grace is 20 years old and Joseph is 40 years old currently.
Let's denote Grace's current age as G and Joseph's current age as J. According to the problem, Grace is half of Joseph's age, so we have the first equation:
G = 0.5 * J
In 10 years, Grace will be three-fifths of Joseph's age, giving us the second equation:
G + 10 = (3/5) * (J + 10)
Ten years ago, Grace was one-third of Joseph's age, which gives us the third equation:
G - 10 = (1/3) * (J - 10)
We now have a system of three equations with two variables. We can solve this system to find the current ages of Grace and Joseph. After solving for G and J, we find that Grace is 20 years old and Joseph is 40 years old.
A game spinner is divided into 5 equal sections numbered 1 to 5. How many outcomes are in the sample space for 4 spins of this spinner? a. 625 b. 125 c. 20 d. 500
The correct option is a. 625.
The total number of outcomes in 4 spins of the spinner can be found by multiplying the number of outcomes in one spin by itself 4 times, resulting in 625 outcomes.
The sample space for 4 spins of the spinner can be calculated by raising the number of outcomes in one spin to the power of the number of spins.
In this case, as there are 5 outcomes on the spinner, the total number of outcomes in 4 spins would be 5^4 = 625.
Therefore, the correct option is a. 625.
(3x/4)>51 ( line underneath >)
A file that is 256 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
What is the number of degrees in the measure of each exterior angle of a regular polygon of 18 sides?
A city's current population is 1,000,000 people. It is growing at a rate of 3.5% per year. The equation P=1,000,000(1.035)^x models the city's population growth where x is the number of years from the current year. In approximately how many years will the pooulation be 1,400,000? Round to nearest tenth
Using the Degree minute second method to describe an angle, one degree of angle measurement can be divided into how many minutes?
How do you simplify the square root of 27?
A runner is running 5 miles per hour. how many feet is the runner running per second.
Evaluate the function rule for the given value. Y=12×3^x for x=-2
Answer:
The value of function at x = -2 is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Given : Function [tex]Y=12\times 3^x[/tex]
We have to evaluate the given function at x = - 2
Consider the given function [tex]Y=12\times 3^x[/tex]
Since, y is a function in terms of x.
So, put x = - 2 in given function.
We get,
[tex]Y=12\times 3^{-2}[/tex]
Since, [tex]3^{-2}=\frac{1}{3^2}=\frac{1}{9}[/tex]
[tex]Y=12\times \frac{1}{9}[/tex]
Simplify, we have,
[tex]Y=\frac{4}{3}[/tex]
Thus, The value of function at x = 2 is [tex]\frac{4}{3}[/tex].
The scatter plot shows the test scores of a group of students who surfed the Internet for different amounts of time in a day.
What will most likely happen to the test scores of students if the number of hours they surf the Internet increases?
Test scores will decrease because the graph shows a negative association.
Test scores will increase because the graph shows a positive association.
Test scores will increase because the graph shows a negative association.
Test scores will decrease because the graph shows a positive association.
Answer: The correct answer is "Test scores will increase because the graph shows a negative association."
Step-by-step explanation: Negative association is decreasing and positive is increasing but in this case we flip it to get our answer.
The impact of time spent surfing the internet on students' test scores depends on whether the association represented on the scatter plot is positive or negative. In a positive association, scores increase with increased internet time, while in a negative association, scores decrease.
Explanation:Based on the question, it seems there is a relationship between the time spent surfing the Internet and students' test scores which is represented by a scatter plot. The association between these variables can be either positive, negative, or no association. A positive association means as the hours of surfing the internet increase, the test scores also increase. A negative association implies that as the hours of surfing the internet increase, the test scores decrease.
However, the question didn't provide the information about whether the scatter plot shows a positive or a negative association between these two variables, which is crucial to determine what happens to the test scores as internet surfing time increases.
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Use a translation rule to describe the translation of X that is 1 units to the left and 6 units up.
A.
T < -1, 6> (x)
B.
T < -1, -6> (x)
C.
T < 1, 6> (x)
D.
T < 1, -6> (x)
Answer:
C. < 1,6 > (x)
Step-by-step explanation:
We know that,
Translation is the transformation that shifts the image in any direction.
The general form of horizontal translation of f(x) to f(x±k) and vertical translation of f(x) to f(x)±k where k is any constant.
Now, as the given function 'X' is translated 1 unit to the left i.e. translated horizontally by 1 unit i.e. X+1.
Also, the function is translated 6 units up i.e. translated vertically by 6 units i.e. X+6.
Hence, the solution is < 1,6 >(x).
If 4 less than a number is less than 4 and greater than -3, find the number.
In ΔABC shown below, point A is at (0, 0), point B is at (x2, 0), point C is at (x1, y1), point D is at x sub 1 over 2, y sub 1 over 2, and point E is at the quantity of x sub 1 plus x sub 2 over 2, y sub 1 over 2: Triangle ABC is shown. Point D lies on segment AC and point E lies on segment BC. A segment is drawn between points D and E. Point A is at the origin. Prove that segment DE is parallel to segment AB.
Segment AB has slope 0. Segment DE, with midpoints of AC and BC, also has slope 0. Thus, DE is parallel to AB.
To prove that segment DE is parallel to segment AB, we need to show that the slopes of both segments are equal.
The slope of segment AB, denoted as [tex]\( m_{AB} \)[/tex], can be calculated using the coordinates of points A and B:
[tex]\[ m_{AB} = \frac{{y_B - y_A}}{{x_B - x_A}} \][/tex]
Given that point A is at (0, 0) and point B is at [tex]\((x_2, 0)\)[/tex], the slope [tex]\( m_{AB} \)[/tex] is:
[tex]\[ m_{AB} = \frac{{0 - 0}}{{x_2 - 0}} = 0 \][/tex]
Now, let's find the coordinates of points D and E.
Point D lies on segment AC, so it is at the midpoint of segment AC. Therefore, the coordinates of point D, denoted as [tex]\((x_{D}, y_{D})\)[/tex], are the average of the coordinates of points A and C:
[tex]\[ x_{D} = \frac{{x_1 + 0}}{2} = \frac{{x_1}}{2} \][/tex]
[tex]\[ y_{D} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Similarly, point E lies on segment BC, so it is at the midpoint of segment BC. Therefore, the coordinates of point E, denoted as [tex]\((x_{E}, y_{E})\)[/tex], are the average of the coordinates of points B and C:
[tex]\[ x_{E} = \frac{{x_1 + x_2}}{2} \][/tex]
[tex]\[ y_{E} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Now, let's calculate the slope of segment DE, denoted as [tex]\( m_{DE} \)[/tex]:
[tex]\[ m_{DE} = \frac{{y_{E} - y_{D}}}{{x_{E} - x_{D}}} \][/tex]
Substituting the coordinates of points D and E:
[tex]\[ m_{DE} = \frac{{\frac{{y_1}}{2} - \frac{{y_1}}{2}}}{{\frac{{x_1 + x_2}}{2} - \frac{{x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = \frac{0}{{\frac{{x_1 + x_2 - x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = 0 \][/tex]
Since the slopes of segments AB and DE are both equal to 0, we can conclude that segment DE is parallel to segment AB.