Therefore, the lower and upper bounds of m-n are 41.4 and 41.6.
upper boundTo determine the lower and upper bounds of m-n, we need to first determine the possible range of values for m and n based on their rounding to one decimal place.
For m, since it was rounded to 1 decimal place, its actual value could be anywhere between 48.15 (if the original value was closer to 48.1) and 48.25 (if the original value was closer to 48.2).
Similarly, for n, its actual value could be anywhere between 6.65 (if the original value was closer to 6.6) and 6.75 (if the original value was closer to 6.7).
Therefore, the lower bound of m-n would be when m is at its minimum value of 48.15 and n is at its maximum value of 6.75. So:
m-n = 48.15 - 6.75 = 41.4
Similarly, the upper bound of m-n would be when m is at its maximum value of 48.25 and n is at its minimum value of 6.65. So:
m-n = 48.25 - 6.65 = 41.6
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Harry buys a TV priced at £1200 plus 20% VAT. He pays £300 deposit and the balance in ten equal monthly payments. Calculate each monthly payment.
Answer:
Step-by-step explanation:
Step 1: Find the TV price:
£1200×(100%+20%)= £1440
Step 2: Find the final price Harry have to pay:
since he deposited £300 so the ammout he have to pay is:
£1440 - £300 = £1140
Step 3: Find the monthly payment
in this case he pays equally every month so we take the ammount he has to pay devided by 10 months
£1140÷10=£114
Conclusion: He has to pay £114 every month
Find an equation following defining the following function and state the domain of the function.
The value of the addition of the two composite function is (x - 6) + √(x + 7).
What are functions?A function in mathematics is a relationship between a set of possible outputs (the range) and a set of inputs (the domain), with the assets that each input is connected to exactly one output. By carrying out operations like addition, subtraction, multiplication, division, and composition with other functions, functions can be changed. By summing the results of the two functions f(x) and g(x), we may add them. In a similar manner, we may combine two functions, f(x) and g(x), by inserting the output of g(x) into f(x).
Given that f(x) = x - 6 and g(x) = √(x + 7).
The composite function (f + g)(x) is given as:
(f + g)(x) = f(x) + g(x)
= (x - 6) + √(x + 7)
Hence, the value of the addition of the two composite function is (x - 6) + √(x + 7).
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Find the value of the discriminant for the quadratic:
x²- 7 + 6 = 0
Value of the discriminant?
How many zeros?
What type?
(a) The discriminant is positive (25)
(b) The quadratic equation has two zeros.
(c) The type of the zeros is real and distinct.
What is the discriminant of the quadratic equation?The given quadratic equation is: x² - 7x + 6 = 0
To find the discriminant, we use the formula:
Discriminant = b² - 4ac
Here, a = 1, b = -7, and c = 6.
So, the discriminant is:
b² - 4ac = (-7)² - 4(1)(6) = 49 - 24 = 25
Therefore, the discriminant is 25.
To determine the number of zeros, we use the discriminant as follows:
If the discriminant is positive (greater than zero), then the quadratic equation has two real and distinct roots.If the discriminant is zero, then the quadratic equation has one real and repeated root.If the discriminant is negative (less than zero), then the quadratic equation has two complex conjugate roots.Here, the discriminant is positive (25), so the quadratic equation has two real and distinct roots.
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PLEASE HELP!!!
1.) Circle A has been transformed to Circle B. What is the translation rule for these circles?
A.) (x-2),(y+3)
B.) (x+2),(y+3)
C.) (x-1),(y+4)
D.) (x+4),(y+3)
*Please Show All Work***
2.) Circle A has been transformed to Circle B. What is the scale factor of Circle A to Circle B?
The translation of circle A to circle B is achieved using the translation rule
B.) (x + 2),(y + 3)The scale factor of Circle A to Circle B is 2
What is translation in geometry?In geometry, translation refers to a transformation that moves an object in a straight line without changing its size, shape, or orientation.
This movement is done by sliding the object along a line, which is called the axis of the translation.
The scale factor is solved by comparing the diameter
Circle A has diameter of 2 units
Circle B has diameter of 4 units
let the scale factor be k
diameter of circle A * k = diameter of circle B
2 * k = 4
k = 4 / 2
k = 2
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The length of a classroom is 7 meters. How many centimeters long is the classroom?
Answer:
700 cm
Step-by-step explanation:
Mutiply the value by 100.
Consider a scenario in which Romeo responds positively to Juliet's feelings, and Juliet responds equally to her own feelings, but responds negatively to Romeo's feelings. The corresponding system is: R = 1 j = -R+J (a) Use the (A,T) chart to classify the behavior of the system. (b) Calculate the eigenvalues and eigenvectors of the system. Sketch the behavior of the system in the phase plane. (c) Sketch in particular the solution curb that starts at R(0) = 1, J0) = 1. (d) Predict what will happen to the couple in the long term, if starting at this initial point.
The solution curve represents a spiral that converges towards the origin.
(a) To classify the behavior of the system, we can use the (A,T) chart. Here, A is the sum of the elements in each row of the system matrix and T is the sum of the absolute values of the off-diagonal elements.
The system matrix for this scenario is:
[ 0 1 ]
[-1 1 ]
So, A = 1 for both rows, and T = 1 (absolute value of the off-diagonal element).
Using the (A,T) chart, we can see that the system is a focus.
(b) To find the eigenvalues and eigenvectors of the system, we need to solve the characteristic equation:
| 0-lambda 1 | |u| |0|
| -1 1-lambda| [tex]\times[/tex] |v| = |0|
Expanding the determinant, we get:[tex]\lambda^2[/tex] -[tex]\lambda[/tex] + 1 = 0
Solving for lambda using the quadratic formula, we get:[tex]\lambda[/tex] = (1 +/- sqrt(3)i) / 2
So, the eigenvalues are complex conjugates with a real part of 1/2. The eigenvectors can be found by solving the system of linear equations:(0 - lambda)u + v = 0
(-1)u + (1 - lambda)v = 0
For lambda = (1 + sqrt(3)i) / 2, we get:u = [1, -1 + sqrt(3)i]
For lambda = (1 - sqrt(3)i) / 2, we get:u = [1, -1 - sqrt(3)i]
(c) To sketch the solution curve that starts at R(0) = 1, J(0) = 1, we can use the eigenvectors and eigenvalues. The general solution for the system can be written as:[x(t), y(t)] = [tex]c_1 \times u_1 \times e^(l \ambda1 \times t) + c2 \times u2 \times e^(\lambda2 \times t)[/tex]
where c1 and c2 are constants determined by the initial conditions, u1 and u2 are the eigenvectors, and lambda1 and lambda2 are the eigenvalues.
Plugging in the values, we get:
[tex][x(t), y(t)] = c_1 \times [1, -1 +\ sqrt(3)i] \times e^{((1 + \sqrt(3)i)t} / 2) + c_2\times [1, -1 - \sqrt(3)i] \times e^{((1 - \sqrt(3)i)t} / 2)[/tex]
Using the initial condition R(0) = 1, J(0) = 1, we get:
[tex]c_1 + c_2 = 1[/tex]
(-1 + sqrt(3)i)c1 + (-1 - sqrt(3)i)c2 = 1
Solving for [tex]c_1[/tex] and [tex]c_2[/tex], we get:
[tex]c_1[/tex] = (1 + sqrt(3)i) / (2[tex]\times[/tex] sqrt(3)i)
[tex]c_2[/tex]= (1 - sqrt(3)i) / (2 [tex]\times[/tex] sqrt(3)i)
Plugging in these values, we get:
[x(t), y(t)] = [1, 0] [tex]\times[/tex] e^((1 + sqrt(3)i)t / 2) + [0, 1] [tex]\times[/tex] e^((1 - sqrt(3)i)t / 2)
This solution curve represents a spiral that converges towards the origin.
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A carton of milk is supposed to contain 16 fluid ounces but it only contain 15 fluid ounces. What is the percent error?
Answer:
Step-by-step explanation:
error = 16 - 15 = 1 fluid ounce
percent error [tex]=\frac{1}{16} \times 100=\frac{100}{16}=6.25 \%[/tex]
This time, make a simple coaster that "bumps" the axis at x = 500. remember to make sure that the track rises before it falls! y = ax(x – 1000 )
The coaster starts at a height of 250, then drops down to 0 at x=500, and then rises back up to a height of 250. The bump is located at x=500 and is the highest point on the coaster.
y = -0.0005(x-500)² + 250
The coaster starts at the highest point (y=250) when x=0 and then drops down to x=500 by following the equation y=ax(x-1000). To create the bump, we need to make the coaster rise before it falls, so we use a quadratic equation that has a vertex at x=500 and y=250 (the initial height).
The equation y = -0.0005(x-500)² + 250 is a downward-facing quadratic equation with a maximum value of y=250 at x=500. This means that as the coaster approaches x=500, it starts to rise, and then falls down again. The coefficient -0.0005 controls the steepness of the coaster's drop and the height of the bump.
Here's a graph of the coaster:
^
260| *
| *
| *
| *
| *
height | *
| *
| *
0 +--------------->
0 500 1000 x-axis
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what is the area of an equilateral triangle whose side length is 8 cm? leave your answer in simplest radical form.
The area of the equilateral triangle with a side length of 8 cm is 16√(3) cm².
To find the altitude of an equilateral triangle with a side length of 8 cm, we can use the Pythagorean theorem.
The Pythagorean theorem is states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In these triangles, the side opposite the 60-degree angle is half the length of the hypotenuse, which is 8 cm. Using the Pythagorean theorem, we can find that the length of the altitude is:
Altitude = √(8² - (4²)) = √(48) = 4√(3)
Now that we know the altitude, we can plug it into the formula for the area of a triangle:
Area = (base x height) / 2 = (8 x 4√(3)) / 2 = 16√(3) cm²
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5/18 + 2/12
A) 1/2
B) 4/9
C) 8/18
D)7/30
Answer:
B. 4/9
Step-by-step explanation:
We can simplify the given expression by finding a common denominator for 18 and 12. The least common multiple of 18 and 12 is 36.
Multiplying the first fraction 5/18 by 2/2 (which equals 1) to get a denominator of 36:
5/18 = 5/18 x 2/2 = 10/36
Multiplying the second fraction 2/12 by 3/3 (which equals 1) to get a denominator of 36:
2/12 = 2/12 x 3/3 = 6/36
Now we can add the two fractions with the same denominator:
10/36 + 6/36 = 16/36
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 4:
16/36 = 4/9
Therefore, the solution is B) 4/9.
Answer:
the answer for the question is b) 4/9
QUESTION 2 2.1 Determine the following products: 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9)
The products of 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9) is -3x² - 9x - 27
How to find the products: 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9)2.1.1 x(x-1) can be simplified using the distributive property of multiplication:
x(x-1) = xx - x1 = x^2 - x
2.1.1 x(x-1):
Expanding the expression x(x-1) using the distributive property:
x(x-1) = x^2 - x
Therefore, the product of 2.1.1 is:
x(x-1) = x^2 - x
2.1.2 (-3)(x² + 3x + 9):
Expanding the expression (-3)(x² + 3x + 9) using the distributive property:
(-3)(x² + 3x + 9) = -3x² - 9x - 27
Therefore, the product of 2.1.2 is:
(-3)(x² + 3x + 9) = -3x² - 9x - 27
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Help please ! I’ll mark brainliest <333
Answer:
A) 6; B) 29∘; C) 29∘; D) 151∘
Step-by-step explanation:
A) Since ∠3 = ∠5 (opposite angles), we can make an equation:
5x - 1 = 3x + 11
5x - 3x = 11 + 1
2x = 12 / : 2
x = 6
B) ∠3 = 5x - 1 (x = 6)
∠3 = 5 × 6 - 1 = 29∘
C) ∠3 = ∠1 = 29∘ (cross angles)
D) ∠2 = 180∘ - ∠1 = 180∘ - 29∘ = 151∘
40.7 x 19.3 whats the product and explain how
Answer:
Step-by-step explanation:
the answer is 785.51
Given ab and be are diameter of circle P. Diameter whether the arc is a minor arc, a major arc or a semi-circle of circle P. The find the measure of the arc. A. CD b. AE c. BC d. AC e. ADC f.AED g.CE H. BAD
Answer:
a. m(arc) CD = 65°
b. m(arc) AE = 120°
c. m(arc) BC = 55°
d. m(arc) AC = 115°
e. m(arc) ADC = 245°
f. m(arc) AED = 180°
g. m(arc) CE = 125°
h. m(arc) BAD = 240°
Step-by-step explanation:
a.
m<CPD = 180 - 55 - 60 = 65
m(arc) CD = 65°
b.
m<APB = 60°
m<APE = 180° - 60° = 120°
m(arc) AE = 120°
c.
m(arc) BC = 55°
d.
m(arc) AC = 60° + 55° = 115°
e.
m(arc) ADC = 120° + 60° + 65 = 245°
f.
m(arc) AED = 180°
g.
m(arc) CE = 60° + 65° = 125°
h.
m(arc) BAD = 60° + 120° + 60° = 240°
Graph the given function to determine the zeros and the locations of the x-intercepts. f(x)=3x2−21x+18
The x-intercepts of the function are x₁ = 1, x₂ = 6.
What is a quadratic equation?Any equation of the form [tex]\rm ax\²+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
To find the zeros, we need to solve the equation f(x) = 0. We can use the quadratic formula for this, which is given by:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c.
[tex]x = (-(-21) \pm \sqrt{((-21)^2 - 4(3)(18))) / 2(3)}\\\\x = (21 \pm\sqrt{(441 - 216)) / 6}\\\\x = (21 \pm\sqrt{(225)) / 6}\\\\x_1 = 1 \ \rm and \ x_2 = 6[/tex]
Therefore, the zeros of the function f(x) are x₁ = 1 and x₂ = 6.
To find the x-intercepts, we need to plot the graph of the function and look for the points where the graph intersects the x-axis. We can start by plotting a few points to get a rough idea of the shape of the graph:
When x = 0, f(x) = 1
When x = 1, f(x) = 0
When x = 2, f(x) = 0
When x = 3, f(x) = 0
When x = 4, f(x) = 6
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the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
The probability of a person being randomly choosing having waiting time greater than 4.25 is 0.2917 or 29.17%.
To answer this question we need to know about-
Probability is the measure of the likelihood of an event to happen. The probability value ranges between 0 and 1.
When the probability value is 0, it means that the event is impossible to happen.
When the probability value is 1, it means that the event is certain to happen.
Uniform distribution is when the values of a probability distribution are spread uniformly across the interval, it is called a Uniform distribution
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes.
The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is found as follows:
Let X = Waiting time of a randomly selected passenger P(X > 4.25) = ?
Now we have to use the uniform distribution formula to find the probability:
P(C< X >D)=C-D/B-A
where C = lower value of the selected interval
D= upper value of the selected interval
B= highest value of the selected interval
A= lowest value of the selected interval
putting above values in the formula -
P(X > 4.25) = 6 - 4.25/6-0= 0.2917
Hence the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.2917.
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in an experiment, once the independent and dependent variables are determined, we have a choice to make about the other variables. if we hold everything else constant, we are reducing what kinds of variables? a. intervening b. confounding c. random d. control
The correct option - d. control. After identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.
Explain about the control variables?Something kept constant or constrained in a research study is referred to as a control variable. Although not being relevant to the study's goals, this variable is controlled since it could have an impact on the results.
Variables can be controlled either directly by maintaining their value throughout a study (for example, by maintaining a constant room temperature in such an experiment) or indirectly by using techniques like randomization as well as statistical control . Research biases including omitted variable bias can be avoided by including control variables in your analysis.Thus, after identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.
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a distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. find p81, which is the score separating the bottom 81% from the top 19%.
If the distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. the score separating the bottom 81% from the top 19% is 168.24.
The value of p81, which is the score separating the bottom 81% from the top 19%, can be calculated as follows:
The given, Mean = μ = 93.2
Standard deviation = σ = 87.4
We are supposed to find the score separating the bottom 81% from the top 19% which is nothing but the 81st percentile.
Let X be a random variable with a normal distribution, then the z-score of the 81st percentile is calculated as follows:
z = InvNorm(0.81)
z ≈ 0.8 (by standard normal distribution tables)
The 81st percentile in terms of X is given by:
p81 = μ + zσp81
= 93.2 + 0.8(87.4)p81
p81 = 168.24
Thus, the score separating the bottom 81% from the top 19% is 168.24.
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HELP 25 points
For Number 3 fill in the blanks of the process.
(9 points total: 0.5 points for each blank!)
(3x3)(8x + 1)
= (24x^2)(8x) + (3x+3)(1)-8x+ (8x) - 3(192x^)
= (192x^)x² + 3x - (3x-2)x - 3
= (192x^)x² - (192x^)x - 3
3.
Answer:
(3x^3)(8x + 1)
= (3x^3)(8x) + (3x^3)(1)
= 24x^4 + 3x^3
= 3x^3(8x + 1) + 24x^2 - 24x^2 + 3x^3
= 3x^3(8x + 1) - 24x^2 + 3x^3
= 24x^4 - 24x^2 + 3x^3
= 3x^3 + (-24x^2 + 24x^4)
Step-by-step explanation:
1-3x less than or equal to -2x< 3x+5
Answer:
x∈ [1; +∞)
Step-by-step explanation:
First write down the whole inequality:
1 - 3x ≤ -2 ﹤ 3x + 5
Then it can be seen that there are two separate inequalities here, so we have a system of inequalities:
{1 - 3x ≤ -2,
{3x + 5 ﹥ -2;
we express x from both inequalities:
From the first one:
-3x ≤ -2 - 1
-3x ≤ -3 / : (-3)
x ≥ 1
From the second one:
3x ﹥ -2 - 5
3x ﹥ -7 / : 3
[tex]x﹥ - \frac{7}{3} [/tex]
[tex]x﹥ - 2 \frac{1}{3} [/tex]
So, now that we have expressed x from both inequalities, we can write down the general range of x values for them (as you can see in the picture, the answer is the common values of x for both inequalities, both red and green colors):
x∈ [1; +∞)
Julian has 10 apples and he gives 2 apples to his friends about how many apples he has left.
A manufacturer of graphing calculators has determined that 11,000 calculators per week will be sold at a price of $98. At a price of $93, it is estimated that 13,150 calculators would be sold.
(a) Determine a linear function that will predict the number of calculators y that would be sold at a given price x.
(b) Use this model to predict the number of calculators that would be sold each week at a price of $73.
a: ______ b:______
Answer:
(a) To determine the linear function that predicts the number of calculators sold at a given price, we need to find the equation of the line that passes through the points (98, 11,000) and (93, 13,150).First, we can find the slope of the line using the formula:slope = (change in y) / (change in x)slope = (13,150 - 11,000) / (93 - 98)slope = -430 per 1 dollar decrease in price(Note that we can interpret the negative slope as an inverse relationship between price and quantity demanded. As price decreases, the quantity demanded increases.)Next, we can use the point-slope form of a line to find the equation of the line:y - y1 = m(x - x1)where y1 = 11,000, x1 = 98, and m = -430.y - 11,000 = -430(x - 98)Simplifying and solving for y, we get:y = -430x + 51,340Therefore, the linear function that predicts the number of calculators sold at a given price is:y = -430x + 51,340(b) To predict the number of calculators that would be sold each week at a price of $73, we can substitute x = 73 into the linear function we found in part (a):y = -430(73) + 51,340y = 18,140Therefore, we predict that 18,140 calculators would be sold each week at a price of $73.
What is 1. 2 x 10 ^5 in standard form?
Answer: 0.000012
Step-by-step explanation: The exponent is -5, making it 10 to the power of negative 5. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 5 times
1.2 -> 0.000012
Use regrouping to solve. Make sure your answer is not an
improper fraction.
10-1-1-6-²-2--
69
Noitoont insloviups no son datin
-1
To use regrouping to solve, we need to add and subtract the numbers in the expression, taking care to keep track of any negative signs.
10 - 1 - 1 - 6 - ² - 2
= 10 - (1 + 1) - 6 - ² - 2 [Group the first two numbers together and add them]
= 10 - 2 - 6 - ² - 2 [Simplify the first three terms]
= (10 - 2) - 6 - ² - 2 [Group the first two terms together and subtract them]
= 8 - 6 - ² - 2 [Simplify the first two terms]
= 2 - ² - 2 [Simplify the first two terms]
= -1 [Simplify the expression by subtracting ² and 2 from -1]
Therefore, the final answer is -1.
In winter, the price of apples suddenly went up by $0. 75 per pound. Sam bought 3 pounds of apples at the new price for a total of of $5. 88. Write an equation to determine the original price per pound
The equation to determine the original price per pound is 3(x + 0.75) = 5.88, where x is original price per pound. so, the original price is $1.21.
Let x be the original price per pound of apples.
When the price increased, the new price became x + 0.75.
Sam bought 3 pounds of apples at the new price for a total of $5.88. This can be expressed as:
3(x + 0.75) = 5.88
Expanding the left side of the equation, we get:
3x + 2.25 = 5.88
Subtracting 2.25 from both sides, we get:
3x = 3.63
Dividing by 3, we get:
x = 1.21
Therefore, the original price per pound of apples was $1.21.
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Show all work to receive credit.
1. A pyramid has a height of 18 in. and a base with area 256 in2. What is the volume of the pyramid?
Answer:
1536 in^3.
Step-by-step explanation:
Volume = 1/3 * area of base * height
= 1/3 * 256 * 18
= 1536 in^3.
midpoint of -34 and -37
Answer:
Step-by-step explanation:
35.5
A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0. 40 cubic foot per minute. At this rate how many hours will it take for the water level to drop 2 feet?
It will take 32 hours for the water level to drop 2 feet.The rate of leaking is 0.40 cubic feet per minute.
To calculate how many hours it will take for the water level to drop 2 feet, we can use the following formula:Time (in hours) = Volume of water (in cubic feet) ÷ Rate of leaking (in cubic feet per minute)In this case, the volume of water is equal to the volume of the pool, which can be calculated using the formula V = l × w × h, where l is the length of the pool, w is the width of the pool, and h is the height of the pool. In this case, l = 24, w = 8, and h = 4, so the volume of the pool is V = (24)(8)(4) = 768 cubic feet.The rate of leaking is 0.40 cubic feet per minute.Therefore, the time (in hours) it will take for the water level to drop 2 feet is equal toTime (in hours) = 768 cubic feet ÷ 0.40 cubic feet per minute Time (in hours) = 1920 minutes Time (in hours) = 32 hoursTherefore, it will take 32 hours for the water level to drop 2 feet.
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nelly has 250 discs. this is 14 less than 8 times the number of discs valerie has.
Find the area of the rectangle below:
What is the area?
Step-by-step explanation:
Find length b by using the Pythagorean theorem for right triangles
17^2 = 8^2 + b^2
b = 15
the area = L x W = 15 X 8 = 120 cm^2
Answer:
120
Step-by-step explanation:
Find out B- 17 squared- 8 squared ( square root) = 15
b = 15
8 X 15 = 120
we used the method of pythagoros - a squared + b squared = c squared
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