The faster pipe can fill and drain the pool at a rate of 640.34 cubic feet per hour.
Reese is installing a rectangular pool in her backyard that is 30 feet long, 14 feet wide, and has an average depth of 8 feet. To fill and drain the pool, she is using two pipes. Let's call the slower pipe's rate of filling and draining the pool "r" (in units of volume per hour). Then, according to the problem, the faster pipe's rate is 2r+1 (since it is "1 more than 2 times faster" than the slower pipe).
If both pipes are open and working properly, we know it will take 3.5 hours to fill the pool. That means the total volume of the pool is:
V = length x width x depth
V = 30 ft x 14 ft x 8 ft
V = 3,360 cubic feet
We also know that when both pipes are open, they can fill the pool in 3.5 hours. That means the combined rate of filling the pool is:
V / t = (r + 2r+1)
3360 / 3.5 = 3r+1
960 = 3r+1
959 = 3r
r = 319.67 cubic feet per hour
So the slower pipe can fill and drain the pool at a rate of 319.67 cubic feet per hour. To find the rate of the faster pipe, we just need to substitute this value into our equation for the faster pipe's rate:
2r+1 = 2(319.67) + 1
2r+1 = 640.34
Therefore, the faster pipe can fill and drain the pool at a rate of 640.34 cubic feet per hour.
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The polynomial â 2x2 + 700x represents the budget surplus of the town of Alphaville.
Betaville's surplus is represented by x2 - 100x + 80,000. If x represents the tax revenue in
thousands from both towns, enter the expression that represents the total surplus of both
towns together.
The expression that represents the total surplus of both towns together is ?
The total surplus of both towns together is represented by the polynomial [tex]3x^2 + 600x + 80,000.[/tex]
The expression that represents the total surplus of both towns together is (â 2x2 + 700x) + (x2 - 100x + 80,000).?To find the total surplus of both towns together, we need to add the budget surplus of Alphaville and Betaville.
The budget surplus of Alphaville is represented by the polynomial [tex]2x^2 + 700x.[/tex]
The budget surplus of Betaville is represented by the polynomial x^2 - 100x + 80,000.
Therefore, the expression that represents the total surplus of both towns together is:
[tex](2x^2 + 700x) + (x^2 - 100x + 80,000)[/tex]
Simplifying this expression, we get:
[tex]3x^2 + 600x + 80,000[/tex]
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A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid m. What is the shape of the cross section?
A. Trapezoid
B. Rectangle
C. Triangle
D. Cylinder
The shape of the cross section of a right rectangular pyramid sliced vertically (down) by a plane not passing through the vertex of the pyramid m is a trapezoid. (A)
This is because when a pyramid is sliced vertically, the resulting cross section is always a two-dimensional representation of the pyramid's base.
Since the base of a right rectangular pyramid is a rectangle, slicing it vertically will result in a trapezoid-shaped cross section. The top and bottom sides of the trapezoid will be parallel, and the other two sides will be slanted.
In a right rectangular pyramid, the vertex m is located directly above the center of the rectangle base. When a plane is passed through this vertex, it will result in a triangular cross section. However, when a plane is passed through a different point, as described in the question, it will result in a trapezoidal cross section.(A)
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Calcula dos numeros cuya suma sea 191 y su diferencia 67
The two numbers are 129 and 62, which satisfy the given conditions: their sum is 191 and their difference is 67 .
You are asked to find two numbers whose sum is 191 and whose difference is 67. Let's use the variables x and y to represent these two numbers.
We can establish the following two equations under the given conditions: 1) x + y = 191 2) x - y = 67
Now we can solve this system of linear equations to find the values of x and y.
We can start by adding both equations:
(x + y) + (x - y) = 191 + 67
2x = 258
Then we'll divide by 2 to find the value of x:
x = 129
Now, we can plug x into Equation 1 to find the value of y:
129 + y = 191
y = 191 - 129
y = 62
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which of the following becomes key indicator of whether or not a hypothesis can be supported? a. chi-square b. degrees of freedom c. significance level d. critical value
The significance level is the key indicator of whether or not a hypothesis can be supported. (option c)
In statistical analysis, there are several key indicators that are used to determine whether a hypothesis can be supported. One of these indicators is the significance level, which is denoted by the symbol alpha (α).
Another key indicator is the critical value, which is a value that is determined from a statistical distribution and is used to determine whether the observed data is statistically significant.
The test compares the observed frequencies of the categories to the expected frequencies, assuming that there is no association between the variables. The degrees of freedom refer to the number of categories minus one.
Therefore, to answer the original question, option (c)
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Bob and Anna are planning to meet for lunch at Sally's Restaurant, but they forgot to schedule a time. Bob and Anna are each going to randomly choose from either 1\text{ p. M. }1 p. M. 1, start text, space, p, point, m, point, end text, 2\text{ p. M. }2 p. M. 2, start text, space, p, point, m, point, end text, 3\text{ p. M. }3 p. M. 3, start text, space, p, point, m, point, end text, or 4\text{ p. M. }4 p. M. 4, start text, space, p, point, m, point, end text to show up at Sally's Restaurant. They must both choose exactly the same time in order to meet. Bob has a "buy one entree, get one entree free" coupon that he can only use if he meets up with Anna. If he successfully meets with Anna, Bob's lunch will cost him \$5$5dollar sign, 5. If they do not meet, Bob's lunch will cost him \$10$10dollar sign, 10. What is the expected cost of Bob's lunch?
The expected cost of Bob's lunch is $8.75.
To find the expected cost of Bob's lunch, we need to determine the probability that Bob and Anna will meet at Sally's Restaurant at the same time.
There are 4 possible times for Bob and Anna to choose from: 1 PM, 2 PM, 3 PM, and 4 PM. Since they are choosing randomly, the probability of them both choosing the same time is 1/4 (one out of four choices).
Now we can calculate the expected cost of Bob's lunch. If they meet successfully, Bob's lunch will cost $5. If they do not meet, Bob's lunch will cost $10. We can find the expected cost by multiplying the probability of each outcome by its corresponding cost, and then adding these products together.
Expected cost = (Probability of meeting) * (Cost if they meet) + (Probability of not meeting) * (Cost if they don't meet)
Expected cost = (1/4) * $5 + (3/4) * $10
Expected cost = $1.25 + $7.50
Expected cost = $8.75
The expected cost of Bob's lunch is $8.75.
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find cif a = 2.74 mi, b = 3.18 mi and ZC = 41.9°. Enter c rounded to 2 decimal places. C= mi Assume LA is opposite side a, ZB is opposite side b, and ZC is opposite side c.
Cif a = 2.74 mi, b = 3.18 mi and ZC = 41.9° and c^2 = a^2 + b^2 - 2ab*cos(C)where C is the angle opposite to side c, c comes to be ≈ 4.26 mi.
The Law of Cosines is a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them. To get side c, we can use the law of cosines, which states that c² = a² + b² - 2ab cos(C).
Plugging in the given values, we get:
c² = (2.74)² + (3.18)² - 2(2.74)(3.18)cos(41.9°)
c² ≈ 18.126
Taking the square root of both sides, we get:
c ≈ 4.26 mi
Rounding to 2 decimal places, c ≈ 4.26 mi.
Therefore, the answer is: c ≈ 4.26 mi.
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In 2003 the social security tax rate was 6. 2% and the maximum taxable income was $87,000. 0. If Linda earned $54,122, how much did she contribute to social security?
Linda contributed $3,355.56 to social security in 2003.
The Social Security tax is a payroll tax that is deducted from employees' paychecks to help fund the Social Security program, which provides retirement, disability, and survivor benefits to eligible individuals.
The Social Security tax rate is typically 6.2% for employees and employers, and the maximum amount of taxable earnings is determined each year by the Social Security Administration (SSA).
In 2003, the maximum taxable earnings was $87,000. This means that any earnings above $87,000 were not subject to Social Security taxes.
To calculate Linda's contribution to social security in 2003, we will use the given social security tax rate of 6.2% and her income of $54,122.
Convert the tax rate percentage to a decimal by dividing by 100.
6.2% / 100 = 0.062
Multiply Linda's income by the decimal tax rate.
$54,122 * 0.062 = $3,355.56
Linda contributed $3,355.56 to social security in 2003.
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Mario traced this trapezoid. Then he cut it out and arranged the trapezoids to form a rectangle.
Pls give me a good explanation!
The calculated area of the rectangle is 70 + 7x
From the question, we have the following parameters that can be used in our computation:
Mario cuts out and arranged the trapezoids to form a rectangle.
Using the above as a guide, we have the following:
Area of rectangle = base * height
In this case, we have
base = 10 + x
Where x is the length of the missing side
Next, we have
height = 7
Substitute the known values in the above equation, so, we have the following representation
Area = 7 * (10 + x)
Evaluate
Area = 70 + 7x
Hence, the area of the rectangle is 70 + 7x
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Mark invests $5,000 and earns $375 in simple interest over a 3 year period. What was the interest rate on the investment? answer is 2.5%
Ifj is inversely related to the cube of k, and j = 3 when k is 6, which of the following is another possible value for j and K?
(A) j = 18, k = 2
(B) j=6, k = 3
(C) j=81, k = 2
(D) j = 2, k = 81
(E) j = 3, k=2
Another possible value for j and K is (A) j = 18, k = 2
How to determine the valuesNote that in inverse variation, one of the variables increases while the other decreases.
From the information given, we have that;
j is inversely related to the cube of k,
This is represented as;
j ∝ 1/k³
Now, find the constant of variation
K = jk³
Substitute the vales
K = 3 × 6³
find the cube value
K = 648
Then, we have that;
j = 648 / 2³ = 81
For option B:
j = 648 / 3³ = 24
For option C:
j = 648 / 2³ = 81
For option D:
j = 648 / 81³ = 0.0008
For option E:
j = 648 / 2³ = 81
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The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In ( - x3 + 9x2 +21x + 1) (0 sxs 10). a) Find the number of units that should be sold in order to maximize the total profit. b) What is the maximum profit? a) The number of units that should be sold in order to maximize the total profit is (Simplify your answer.) b) The maximum profit is approximately $. (Do not round until the final answer. Then round to the nearest dollar as needed.)
Final Answer: a. The number of units that should be sold in order to maximize the profit is 7 thousand units.
b. The maximum profit is approximately $5.51
Conceptual part: a. In order to find maximum profit we need to differentiate the profit function
so, p(x)= [tex]ln(-x^3+9x^2+21x+1)[/tex][tex]dp/dx = (-3x^2+18x+21)/-x^3+9x^2+21x+1[/tex] = 0
[tex]-3x^2+18x+21=0[/tex]
[tex](x-7) (x+1) = 0[/tex]
as profit can't be negative.
hence x=7.
b. We can determine the maximum profit by substituting x=7 in profit function.
[tex]p(7) = ln(-7^3+9*7+21*7+1)[/tex]
[tex]p(7) = ln(246)[/tex]
p(7) = 5.51
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12 less than the product of 3 and a number, x, is at most -18
The given inequality is 3x - 12 ≤ -18. To solve for x, we can add 12 to both sides of the inequality to obtain 3x ≤ -6. Then, dividing both sides of the inequality by 3 gives x ≤ -2. Therefore, any value of x less than or equal to -2 will satisfy the inequality.
In solving the inequality, we first used the addition property of inequalities to add 12 to both sides of the inequality. This property states that if a < b, then a + c < b + c, where c is any real number. By adding 12 to both sides, we were able to isolate the variable term on one side of the inequality.
Next, we used the division property of inequalities to divide both sides of the inequality by 3. This property states that if a < b and c > 0, then a/c < b/c. By dividing both sides of the inequality by 3, we were able to solve for x.
Finally, we found that any value of x less than or equal to -2 will satisfy the inequality. This means that the solution set for the inequality is {x | x ≤ -2}. We also verified that x = -2 is a valid solution to the inequality, which confirms our solution.
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Evaluate the limit using L'Hospital's rule
lim (e^x + 2x - 1)/2x
To evaluate the limit using L'Hospital's rule, we need to take the derivative of both the numerator and denominator separately until we get a determinate form. We have:
lim (e^x + 2x - 1) / (2x)
Taking the derivative of the numerator:
lim (e^x + 2) / 2
Taking the derivative of the denominator:
lim 2
Since we now have a determinate form, we can evaluate the limit by plugging in the value of x. We get:
(e^x + 2) / 2
As x approaches infinity, e^x also approaches infinity, so the limit diverges to positive infinity. Therefore, the limit does not exist.
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Question 5
Not yet answered
An ice-cream parlor used a scatterplot to record their total sales, in dollars, each day (s) and
the corresponding average temperature, in ºf, on that day (t). They then found a trend line of
this data to be s = 12. 75t + 32. What is the predicted total sales the ice-cream parlor makes
if the average temperature of the day is 72°f?
Marked out of
1. 00
P Flag question
O a.
$950. 00
O b. $820. 00
O c. $1,275. 00
O d. $740. 00
The predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00.
You are asked to find the predicted total sales (s) for the ice-cream parlor when the average temperature (t) is 72°F, using the trend line equation s = 12.75t + 32.
Step 1: Plug the given temperature (72°F) into the trend line equation:
s = 12.75(72) + 32
Step 2: Calculate the value of 12.75(72):
12.75 * 72 = 918
Step 3: Add 32 to the result from Step 2:
918 + 32 = 950
So, the predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00. Therefore, the correct answer is (a) $950.00.
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About 8 out of 10 people entering a community college need to take a refresher mathematics course. if there
are 850 entering students, how many will probably need a refresher mathematics course?
Approximately 680 out of the 850 entering students will probably need to take a refresher mathematics course which is calculated using simplified fraction.
We are given that about 8 out of 10 people entering a community college need to take a refresher mathematics course. We need to find out how many of the 850 entering students will probably need this course.
Step 1: Determine the proportion of students who need the refresher course.
The proportion is 8 out of 10, which can be written as a fraction: 8/10.
Step 2: Simplify the fraction.
Divide both the numerator (8) and the denominator (10) by their greatest common divisor, which is 2:
8 ÷ 2 = 4
10 ÷ 2 = 5
So, the simplified fraction is 4/5.
Step 3: Calculate the number of students who need the refresher course.
To find the number of students who probably need the course, multiply the total number of entering students (850) by the simplified fraction (4/5):
850 * (4/5) = (850 * 4) / 5 = 3400 / 5 = 680
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D is the centroid of PQR PA= equals 17 BD equals nine and DQ equals 14 find each missing measure
The centroid of the triangle is D and the measures of sides are solved
Given data ,
Let the triangle be represented as ΔPQR
Now , the centroid of the triangle is D
where the measure of PA = 17 units
The measure of BD = 9 units
And , the measure of side DQ = 14 units
Now , centroid of a triangle is formed when three medians of a triangle intersect
And , from the properties of centroid of triangle , we get
PA = AR
DR = DQ
AD = BD
On simplifying , we get
The measure of side AR = 17 units
PR = PA + AR = 34 units
The measure of side DR = 14 units
BR = BD + DR = 23 units
The measure of side AD = 9 units
AQ = AD + DQ = 23 units
Hence , the centroid is solved
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Will mark brainliest if correct
Step-by-step explanation:
See image for calculations:
(Note that interior angle + exterior angle = 180 degrees)
AND sum of exterior angles = 360 that is where the first formula comes from.
A bicycle mechanic wants to put a strip of plastic between the tube and tire of a 26-in. diameter bicycle tire. to the nearest inch, how long should the strip of plastic be?
The bicycle mechanic should cut a strip of plastic approximately 82 inches long to place between the tube and tire of the 26-inch diameter bicycle tire.
To calculate the length of the strip of plastic needed, we first need to determine the circumference of the tire. The formula for the circumference of a circle is C=2πr, where C is the circumference, π is approximately 3.14, and r is the radius of the circle.
In this case, the tire diameter is 26 inches, so the radius is 13 inches (half of the diameter). Therefore, the circumference of the tire is: C = 2πr = 2π(13) = 81.64 inches (rounded to two decimal places)
To ensure that the strip of plastic fits snugly between the tube and tire, it should be the same length as the circumference of the tire. Therefore, the strip of plastic should be 82 inches long (rounded to the nearest inch).
In summary, the bicycle mechanic should cut a strip of plastic that is 82 inches long to fit between the tube and tire of the 26-inch diameter bicycle tire.
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Kaylie put $900 in a savings account, earning 11% interest for 7 years. she did not make any additional deposits or withdrawals. what is the amount of interest kaylie earned?
Kaylie earned $693 in interest on her savings account.
What was the total amount of money Kaylie had in her savings account after 7 years of depositing $900 and earning 11% interest on it?Kaylie deposited $900 in a savings account and earned 11% interest on it for 7 years. After the 7-year period, Kaylie earned $693 in interest, which was compounded annually.
This brought the total amount of money in her savings account to $1,593. The power of compounding interest in savings accounts can help grow your money significantly over time.
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 the measures of the angles of a triangle are shown in the figure below solve for X
Answer:
x = 13
Step-by-step explanation:
We Know
The sum of angles of a triangle must add up to 180°
We know 2 angles, one is 60° and the other is 90°
Solve for x.
Let's solve
3x - 9 + 60 + 90 = 180
3x + 141 = 180
3x = 39
x = 13
The table shows the
average rainfall, in inches, in Miami for each
of the first six months of 2020. Write ordered
pairs for the data in the table
The ordered pairs for the data in the table include the following:
(1, 2.09)(2, 2.42)(3, 3.00)(4, 3.20)(5, 4.98)(6, 8.27)What is an ordered pair?In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Based on the table shown in the image attached below, we can reasonably infer and logically deduce that all of the coordinate points or ordered pairs would be located in quadrant 1.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A random number generator picks a number from 12 to 41 in a uniform manner. Round answers to 4 decimal places when possible.
a. The mean of this distribution is
b. The standard deviation is
c. The probability that the number will be exactly 36 is P(x = 36) =
d. The probability that the number will be between 21 and 23 is P(21 < x < 23) =
e. The probability that the number will be larger than 26 is P(x > 26) =
f. P(x > 16 | x < 18) =
g. Find the 49th percentile.
h. Find the minimum for the lower quartile
The mean of this distribution is 26.5. The standard deviation is 8.0623. The probability that the number will be exactly 36 is P (x = 36) = 0.0286. The probability that the number will be between 21 and 23 is P (21 < x < 23) = 0.0400. The probability that the number will be larger than 26 is P (x > 26) = 0.2857. P (x > 16 | x < 18) = undefined. The 49th percentile is 29.3700. The minimum for the lower quartile is 19.75.
a. The mean of a uniform distribution is the average of the maximum and minimum values, so in this case, the mean is:
mean = (12 + 41) / 2 = 26.5
Therefore, the mean of this distribution is 26.5.
b. The standard deviation of a uniform distribution is given by the formula:
sd = (b - a) / sqrt(12)
where a and b are the minimum and maximum values of the distribution, respectively. So in this case, the standard deviation is:
sd = (41 - 12) / sqrt(12) = 8.0623
Therefore, the standard deviation of this distribution is 8.0623.
c. Since the distribution is uniform, the probability of getting any specific value between 12 and 41 is the same. Therefore, the probability of getting exactly 36 is:
P(x = 36) = 1 / (41 - 12 + 1) = 0.0286
Rounded to four decimal places, the probability is 0.0286.
d. The probability of getting a number between 21 and 23 is:
P(21 < x < 23) = (23 - 21) / (41 - 12 + 1) = 0.0400
Rounded to four decimal places, the probability is 0.0400.
e. The probability of getting a number larger than 26 is:
P(x > 26) = (41 - 26) / (41 - 12 + 1) = 0.2857
Rounded to four decimal places, the probability is 0.2857.
f. The probability that x is greater than 16, given that it is less than 18, can be calculated using Bayes' theorem:
P(x > 16 | x < 18) = P(x > 16 and x < 18) / P(x < 18)
Since the distribution is uniform, the probability of getting a number between 16 and 18 is:
P(16 < x < 18) = (18 - 16) / (41 - 12 + 1) = 0.0400
The probability of getting a number greater than 16 and less than 18 is zero, so:
P(x > 16 and x < 18) = 0
Therefore:
P(x > 16 | x < 18) = 0 / 0.0400 = undefined
There is no valid answer for this question.
g. To find the 49th percentile, we need to find the number that 49% of the distribution falls below. Since the distribution is uniform, we can calculate this directly as:
49th percentile = 12 + 0.49 * (41 - 12) = 29.37
Rounded to four decimal places, the 49th percentile is 29.3700.
h. The lower quartile (Q1) is the 25th percentile, so we can calculate it as:
Q1 = 12 + 0.25 * (41 - 12) = 19.75
Therefore, the minimum for the lower quartile is 19.75.
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In ΔEFG, g = 5. 2 cm, e = 5. 1 cm and ∠F=42°. Find the area of ΔEFG, to the nearest 10th of a square centimeter
The area of ΔEFG is approximately 6.7 square centimeters.
To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:
Area = (1/2)ab * sin(C)
In this case, a = g, b = e, and C = ∠F. Plug in the values:
Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)
Area ≈ 6.675 square centimeters
So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.
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70% of a class is at lunch what percentage is still studying?
Answer:
30%
Step-by-step explanation:
If there are only 2 categories:
Students at lunch and students studying, then the whole is 100%
100% - 70% = 30%
Helping in the name of Jesus.
The mean of the data set below is 11. What is the value of x? Explain.
12, 9, 12.5, 13, x, 10, 11, 11, 7, 9
From the given data 11 is the mean of the data set.
What is Mean ?
In statistics, the mean (also called the average) is a measure of central tendency that represents the typical value in a data set. It is calculated by adding up all the values in the data set and dividing by the number of values.
To find the value of x in the data set, we can use the formula for the mean (also called the average). The mean is calculated by adding up all the values in the data set and dividing by the number of values. In other words:
mean = (sum of all values) : (number of values)
We are given that the mean of the data set is 11, so we can write:
11 = (12 + 9 + 12.5 + 13 + x + 10 + 11 + 11 + 7 + 9) : 10
Here, we have 10 values in the data set (including the unknown value x), so we divide the sum of all the values by 10 to find the mean.
To solve for x, we can start by simplifying the right-hand side of the equation:
110 = 75.5 + x
Next, we can isolate x by subtracting 75.5 from both sides:
x = 34.5
Therefore, the value of x that makes the mean of the data set equal to 11 is x = 34.5.
In other words, if we replace the unknown value x with 34.5, the resulting data set will have a mean of 11. This means that the sum of all the values in the data set will be 110, since:
12 + 9 + 12.5 + 13 + 34.5 + 10 + 11 + 11 + 7 + 9 = 110
And when we divide this sum by 10, we get:
110 : 10 = 11
Therefore, From the given data 11 is the mean of the data set.
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Hydrologists sometimes use Manning's equation to calculate the velocity v, in feet per second, of water flowing through a pipe. The velocity depends on the hydraulic radius R in feet, which is one-quarter of the diameter of the pipe when the pipe a flowing full; the slope S of the pipe, which gives the vertical drop in foot for each horizontal foot; and the roughness coefficient n, which depends on the material of which the pipe is made. The relationship is given by the following. v = 1.486/n R^2/3 S^1/2 For a certain brass pipe, the roughness coefficient has been measured to be n = 0.014. The pipe has a diameter of 3 feet and a slope of 0.4 foot per foot. (That is, the pipe drops 0.4 foot for each horizontal foot.) If the pipe is flowing full, find the hydraulic radius of the pipe. () Find the velocity of the water flowing through the pipe. ()
The velocity of the water flowing through the pipe is approximately 7.83 feet per second. The hydraulic radius of the pipe can be calculated as follows:
R = d/4
where d is the diameter of the pipe. In this case, the diameter is 3 feet, so the hydraulic radius is:
R = 3/4 = 0.75 feet
Now, we can use the given formula to calculate the velocity of the water:
[tex]v =[/tex][tex]1.486/n[/tex] [tex]R^(2/3) S^(1/2)[/tex]
Substituting the given values, we get:
v = 1.486/0.014 (0.75[tex])^(2/3)[/tex] (0.4[tex])^(1/2)[/tex] ≈ 7.83 feet per second
Therefore, the velocity of the water flowing through the pipe is approximately 7.83 feet per second.
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The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is 35 meters wide at the base and 20. 6 meters tall, what was the minimum amount of glass needed to construct the pyramid?
The minimum amount of glass needed to construct the Louvre pyramid is approximately 3133 square meters.
What is the minimum amount of glass needed to construct the glass pyramid in front of the Louvre museum in Paris, if the pyramid is 35 meters wide at the base and 20.6 meters tall?
The surface area of a square base pyramid can be calculated by adding the area of the base to the sum of the areas of the four triangular faces.
The area of the square base is simply the width of the base squared:
Area_base = (35 m)^2 = 1225 square meters
The area of each triangular face can be calculated using the formula:
Area_triangle = (1/2) * base * height
For the Louvre pyramid, the base of each triangular face is equal to the width of the base of the pyramid, which is 35 meters. The height of each triangular face can be found using the Pythagorean theorem:
[tex]height^2 = (1/2 * width)^2 + height^2[/tex]
[tex]height = sqrt((1/2 * 35 m)^2 + (20.6 m)^2)[/tex]
height = 29.2 m
Therefore, the area of each triangular face is:
Area_triangle = (1/2) * (35 m) * (29.2 m) = 508.5 square meters
The total surface area of the pyramid is:
Surface_area = Area_base + 4 * Area_triangle
Surface_area = 1225 + 4 * 508.5
Surface_area = 3133 square meters
Since the pyramid is made of glass, we need to calculate the minimum amount of glass needed to construct it. Assuming the glass is thin and flat, we can simply use the surface area of the pyramid to estimate the amount of glass needed.
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4. What is the difference in the radii of the circles? (3 points) (this is for the ana circle question
The difference between the radii of the two circular tracks is 15ft
How do we calculate?The total length of track 1 is 220ft, which means that the circumference of the circle is 220ft
we find the diameter of each track.
The circumference of a circle can be found using the formula
P = πd
d = P /π
track 1, we have
d1 = P1 / π
d1 = 220 / π
d1 = 70.03 ft.
track 2, we have
d2 = P2 / π
d2 = 126 / π
d2 = 40.11 ft.
radius of tract 1 = 35.01 ft
radius of track 2 = 20.05 ft
The difference between the two track radius is
∆r = r1 - r2
∆r = 110 / π - 63 / π
∆r = (110 - 63) / π
∆r = 47 / π
∆r = 14.96 ft.
∆r = 15 ft
In conclusion, difference between the radii of the two circular tracks is 15ft
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#complete question:
What is the difference between the radii of the two circular tracks? Answer the questions to find out.
1. Are the distances of 220 feet and 126 feet the radii, diameters, or circumferences of the two circles?
given the expression, (n⁵)⁶ what will exponent be in the simplified exponential form?
The expression given in a simplified form is n³⁰
What are index forms?Index forms are described as those mathematical forms that are used to write numbers that are too large or small in more convenient forms.
They are also expressed as a number or variable that is raised to an exponents.
Index forms are also referred to as standard forms or scientific notations.
Following the rules of index forms, we have that;
Add the exponent with like bases and are being multipliedIn expanding the bracket, also multiply the exponentsFrom the information given, we have that;
(n⁵)⁶
Multiply the exponents
n³⁰
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9. the square footage and monthly rental of 15 similar one-bedroom apartments yield the linear
regression formula y = 1.3485x + 840.51, where x represents the square footage and y represents
the monthly rental price. round answers to the nearest whole number.
Based on the linear regression formula y = 1.3485x + 840.51, you can calculate the monthly rental price (y) for a one-bedroom apartment by plugging in the square footage (x) of the apartment.
The linear regression formula for the 15 similar one-bedroom apartments is y = 1.3485x + 840.51, where x represents the square footage and y represents the monthly rental price. This means that for every square foot increase in the apartment size, the monthly rental price is predicted to increase by $1.35.
The y-intercept of the formula is $840.51, which represents the predicted monthly rental price for an apartment with 0 square footage (this is not possible in reality, but is used in the formula for mathematical purposes). To get the rental price, round your answer to the nearest whole number. For example, if an apartment has 500 square feet, you'd calculate: y = 1.3485(500) + 840.51 ≈ 1344.76, which rounds to $1,345 as the monthly rental price.
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