36 bags of soil are required to spread a 6 feet layer over a garden bed that is 4 feet by 3 feet.
How many bags of soil are required to spread a 4 feet layer over the garden bed?Given information:
The garden bed has a length of 4 feet.
The garden bed has a width of 3 feet.
The layer of soil to be spread over the garden bed is 6 feet.
One bag of soil contains 2 cubic feet of soil.
To find the number of bags of soil required to spread a 6 feet layer over the garden bed, we need to calculate the volume of soil needed and then divide it by the volume of each bag of soil.
The volume of soil needed can be calculated by multiplying the length, width, and height (depth) of the soil:
Volume = length x width x depth
Volume = 4 feet x 3 feet x 6 feet
Volume = 72 cubic feet
This means we need a total of 72 cubic feet of soil to spread a 6 feet layer over the garden bed.
Next, we need to determine the number of bags of soil required. Since each bag contains 2 cubic feet of soil, we can divide the total volume of soil needed by the volume of each bag to get the number of bags required:
Number of bags = Volume of soil needed / Volume of each bag
Number of bags = 72 cubic feet / 2 cubic feet per bag
Number of bags = 36 bags
Therefore, 36 bags of soil are required to spread a 6 feet layer over a garden bed that is 4 feet by 3 feet.
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The dean of students at a large college is interested in learning about their opinions regarding the percentage of
first-year students who should be given parking privileges in the main lot. he sends out an email survey to all
students about this issue. a large number of first-year students reply but very few sophomores, juniors, and seniors
reply. based on the responses he receives, he constructs a 90% confidence interval for the true proportion of
students who believe first-year students should be given parking privileges in the main lot to be (0.71, 0.79). which
of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?
o response bias
o nonresponse bias
o sampling variation
o undercoverage bias
mark this and retum
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The potential factor that may have an impact on the confidence interval, but is not accounted for by the margin of error, is nonresponse bias.
The dean of students received a large number of responses from first-year students but very few from sophomores, juniors, and seniors. Nonresponse bias occurs when some individuals chosen for a sample do not respond to a survey or study. In this case, the dean of students may not have received a representative sample of the opinions of all students, which could lead to an overestimation or underestimation of the true proportion of students who believe first-year students should be given parking privileges in the main lot.
The margin of error is the amount of random sampling error in a survey's results. It reflects the level of precision in the survey's results and decreases as the sample size increases. However, nonresponse bias is a systematic error that is not accounted for by the margin of error, as it may lead to a biased sample and inaccurate results. To minimize nonresponse bias, the dean of students could have used techniques such as follow-up emails or incentives to encourage a higher response rate from all student groups.
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Use this scenario on this and the next problem.
Tobias received an inheritance from his grandfather of $20,000. When he gets out of
college in 4 years he wants to use it as a down payment on a piece of lakeside property.
If he puts all the money in a savings account paying 6. 5% interest compounded daily,
how much money will be in the account at the end of the four years to use as the down
payment on the property?
The amount of money that will be in the account at the end of the four years to use as the down payment on the property is $26,102.47.
What is the compound interest?In the above question, we need to use the formula for compound interest and it is:
A = P(1 + r/n)^(nt)
Note that:
A = the amount of money at the end of the investment
P = the principal amount
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the number of years of the investment
Since:
P = $20,000
r = 6.5% = 0.065
n = 365 (note the interest is compounded everyday)
t = 4
We shall put the values into the formula:
A = $20,000(1 + 0.065/365)^(365*4)
A = $20,000(1.0178)¹⁴⁶⁰
A = $20,000 x 1.305124
A = $26,102.47
Therefore, at the end of the four years, there will be $26,102.47.
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7. The table shows the linear relationship between the total amount Mrs. Jacobs will be
charged for a skating party and the number of children attending.
Which equation best represents y, the total amount in dollars Mrs. Jacobs will be
charged for
x number of children attending the skating party?
The equation that best represents the linear relationship between the total amount Mrs. Jacobs will be charged and the number of children attending the skating party is y = mx + b.
In this case, y represents the total amount in dollars that Mrs. Jacobs will be charged, x represents the number of children attending the party, m represents the slope of the line, and b represents the y-intercept.
To find the equation, we need to determine the slope and y-intercept from the table given. From the table, we can see that for every additional child attending the party, the total amount charged increases by $10. This means that the slope (m) of the line is 10.
To find the y-intercept (b), we can look at the table and see that when there are zero children attending the party, the total amount charged is $50. This means that the y-intercept is 50.
Putting it all together, the equation that best represents the linear relationship is y = 10x + 50.
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A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly. How much will the homeowner owe after 8 years? Group of answer choices $78,090 $65,023 $78,117 $67,300
A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly.
So we have to find 2.3% of 65,000 which is 1495
Now we have to multiply 1,495 by 8 because it is 8 years which is 11960. Now we add 11,960 to 65,000 and our answer is
Answer : 76960
(Choice 1)
Jaoan reads that themass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. How many kilograms is an average elephant's brain?
Answer:
Step-by-step explanation:
Let's call the mass of an average man's brain "m."
According to the problem, the mass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. We can write this as:
mass of elephant's brain = m + 3 4/10
To find out how many kilograms an average elephant's brain weighs, we need to know the value of "m." However, this information is not given in the problem.
Therefore, we cannot determine the exact mass of an average elephant's brain.
Jerome wants to buy grass seed to cover his whole lawn, except for the pool. the pool is 4 5/6 m by 2 1/3 m. find the area the grass seed needs to cover.
Jerome will need approximately 138.72 square meters of grass seed to cover his lawn.
To find the area that the grass seed needs to cover, we first need to find the area of the entire lawn. Let's assume that the lawn is rectangular in shape.
Jerome hasn't given us the dimensions of the lawn, so let's say that it measures 10 meters by 15 meters. Therefore, the area of the entire lawn would be:
10 meters x 15 meters = 150 square meters
Now we need to subtract the area of the pool from the area of the entire lawn.
The pool measures 4 5/6 meters by 2 1/3 meters, which we can convert to improper fractions:
4 5/6 = (4 x 6 + 5) / 6 = 29 / 6
2 1/3 = (2 x 3 + 1) / 3 = 7 / 3
So the area of the pool would be:
29/6 meters x 7/3 meters = 203/18 square meters
To find the area that the grass seed needs to cover, we subtract the area of the pool from the area of the entire lawn:
150 square meters - 203/18 square meters
To subtract these two values, we need to get a common denominator:
150 square meters = (150 x 18) / 18 = 2700/18 square meters
203/18 square meters = 203/18 square meters
So the area that the grass seed needs to cover would be:
2700/18 square meters - 203/18 square meters = 2497/18 square meters
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 1:
2497/18 square meters ≈ 138.72 square meters
Therefore, Jerome will need approximately 138.72 square meters of grass seed to cover his lawn, excluding the area around the pool.
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For Items 6-10, the height of an object, in centimeters, is modeled by the function y = 42sin (π/10 (x-h)+ 55. Determine whether each statement is always, sometimes, or never true.
6. The period of the function is 20.
7. The maximum height of the object is 55 centimeters
8. The minimum height of the object occurs when x=0
9. The graph of the function has the midline y= 55
10. The amplitude of the function is 84.
Answer:
It's fascinating to observe how the volume of different shapes can vary based on their measurements. For instance, a cylinder with a height of 6 centimeters and radius r1 has a volume of 302 cubic centimeters. Do you require further assistance?
As for the new set of instructions, please consider the following statements:
6. Sometimes true. The period of the function is determined by the formula T= 2π/b, where b is the coefficient of x in the argument of the sine function. In this case, b = π/5, so T= 10.
7. Always true. The maximum height of the object is equal to the amplitude of the function plus the vertical shift, which is 55 centimeters.
8. Sometimes true. The minimum height of the function occurs when the sine function has a value of -1, which happens at x= h-5. So, if h= 0, then x= -5, which means the statement is sometimes true depending on the value of h.
9. Always true. The midline of the function is determined by the vertical shift, which is 55 in this case.
10. Always true. The amplitude of the function is given by A= |b|, where b is the coefficient of x in the argument of the sine function. In this case, A= 42π/5, which simplifies to 84.
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23. The function is defined by f:x → x + 2. Another function g is such that fg: x → 1/x-1 , x ≠ 1
Find g.
What is the volume of a right rectangular prism with a length of 4. 8 meters, a width of 2. 3 meters, and a height
of 0. 9 meters?
O4. 968 m3
O9. 936 m3
O 11. 94 m3
O 34. 86 m3
PLS ANSWER FAST I WILL GIVE BRAINIEST!!!!!
Answer:
Step-by-step explanation:
The volume of the given prism is 9.936 cubic meters, To calculate the volume of a right rectangular prism, we need to multiply its length, width, and height together.
Given that the length of the prism is 4.8 meters, the width is 2.3 meters, and the height is 0.9 meters, we can calculate the volume using the formula:
Volume = length x width x height
Volume = 4.8 m x 2.3 m x 0.9 m
Volume = 9.936 m^3
Therefore, the volume of the right rectangular prism is 9.936 cubic meters.
It is important to note that when we calculate volume, we are dealing with a three-dimensional space, and the units we use must be cubed (m^3 in this case). This is because we are measuring the amount of space occupied by the object in all three dimensions.
In summary, to find the volume of a right rectangular prism, we simply multiply its length, width, and height together. In this case, the volume of the given prism is 9.936 cubic meters.
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Hallar la altura de una asta bandera, si un estudiante la observa desde un punto a, con un ángulo de 30° y entre el estudiante y la asta hay una distancia de 10m.
Answer:
The height of the flagpole is approximately 5.774 meters.
Step-by-step explanation:
Let's call the height of the flagpole h. We can use trigonometry to set up the following equation:
tan(30°) = h/10
Simplifying this equation, we get:
h = 10 tan(30°)
Using a calculator, we find that tan(30°) ≈ 0.5774, so:
h ≈ 5.774 meters
Therefore, the height of the flagpole is approximately 5.774 meters.
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Find the area of this irregular shape hint area of a triangle a = bh÷2
Answer:
The area of the irregular shape is 62 feetExplanation :
We are given with two shapes triangle and a rectangle.
From the above diagram
We can see that Breadth of the rectangle is 5 ft and length of 10 ft.
As we know that area of Rectangle is length × Breadth
Area(rectangle) = l × b
Area (rectangle) = 10 × 5
Area (rectangle) = 50 ft².
Now,
Area (triangle) = bh ÷ 2where
b is base (10 - 6 = 4 ft)h = Height (11 - 5 =6 ft)Area (triangle) = 4 × 6 ÷ 2
Area (triangle) = 24 ÷ 2
Area (triangle) = 12 ft².
Total area = Area of rectangle + Area of triangle
Total area = 50 + 12
Total area = 62 feet
Therefore, The area of the irregular shape is 62 feet.
In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept. Explain what each represents.
Use first two points and the slope equation to find the slope:
m = (4225 - 1990)/(5 - 2) = 745The slope is 745.
Use the first point and point-slope equation to find the y-intercept:
y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the given pointy - 1990 = 745(x - 2)y - 1990 = 745x - 1490y = 745x - 1490 + 1990y = 745x + 500The y-intercept is 500.
The slope of 745 represents the profit per month and the y-intercept of 500 represents the initial profit.
Find the surface area of the regular pyramid shown to the nearest whole number. The figure is not drawn to scale.
*
Captionless Image
1209 m^2
790 m^2
1125 m^2
898 m^2
The surface area of the regular pyramid is 1209 m².
How to find the surface area of the regular pyramid?A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles and are called lateral faces.
A pyramid is called by the shape of its base.
The surface area of the regular hexagonal pyramid is given by the formula:
SA = 3b(a + s)
Where a is the apothem, b is the base and s is the slant height of the pyramid.
In this case:
a = 8.5√3 m
b = 17 m
s = 9 m
SA = 3 * 17 * (8.5√3 + 9)
SA = 1209 m²
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answer please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9/7
explain:
(36-27) 7
9/7
Scott has a rectangular garage that has a length of 234 inches. The width is 1. 5 times shorter than the length. What is the area of his garage?
The area of garage is 36,504 square inches.
The width of Scott's garage is 156 inches (since it is 1.5 times shorter than the length of 234 inches).
so width = 234/1.5
=> 156
To find the area, we multiply the length by the width:
=> 234 inches x 156 inches
=> 36,504 square inches.
To explain, the formula for finding the area of a rectangle is length x width. In this problem, we are given the length of the garage as 234 inches and are told that the width is 1.5 times shorter than the length.
To find the width, we can multiply the length by 1.5 to get 351 inches (which is longer than the length, so we know it must be incorrect). Instead, we need to divide the length by 1.5 to find the width, which gives us 156 inches. Then, we can multiply the length by the width to find the area of the garage, which is 36,504 square inches.
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David’s net worth is 45,765. 78 and his assets have a value of 62,784,24 if his assets increase by 2,784. 89 and his liabilities decrease y 3,742. 36 what is his net worth
David's net worth: 86,329.95
To calculate David's new net worth, we need to add the increase in assets and subtract the decrease in liabilities from his current net worth.
New assets value = 62,784.24 + 2,784.89 = 65,569.13
New liabilities value = David's current net worth - his current assets value
New liabilities value = 45,765.78 - 62,784.24 = -17,018.46
Since his liabilities have decreased by 3,742.36, we need to subtract this value from the new liabilities value:
New liabilities value = -17,018.46 - 3,742.36 = -20,760.82
Now we can calculate his new net worth by subtracting his new liabilities value from his new assets value:
New net worth = 65,569.13 - (-20,760.82) = 86,329.95
Therefore, David's new net worth is 86,329.95.
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At the beginning of the summer, the water level in an underground well was -3 feet. During the hot summer months, the water level fell 4 feet. The expression -3 -4 gives the water level in feet at the end of the summer.
What was the water level at the end of the summer?
Answer:
-7 feet
Step-by-step explanation:
-3-4 = -7, so it is -7 feet
In a laboratory experiment, the population of bacteria in a petri dish started off at 380 and is growing exponentially at 3% per day. Write a function to represent the population of bacteria after tt days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent
The function is P(t) = 380 x [tex]1.0300^{t}[/tex], which is an exponential function, and the rate of change is 1.24% each hour.
The equation P(t) = 380 x [tex](1 + 0.03)^{t}[/tex] represents the population of bacteria after t days.
Rounding to four decimal digits and simplifying:
P(t) = 380 x [tex]0.0300^t[/tex]
We can use the following formula to determine the percentage rate of change each hour:
r = [tex]100 \times e^{(ln(1 + 0.03)/24) - 1)}[/tex]
where e is the Euler's number, ln is the natural logarithm, and r is the percentage rate of change per hour.
Rounding to the nearest tenth of a percent and simplifying:
r = 1.24%
This exponential function simulates the population of bacteria multiplying exponentially at a rate of 3% each day in a petri dish.
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Consider the variable coefficient linear second order non-homogeneous ODE
x^2y^n - 2xy' + (x^2 +2)y =. 3x^3, for x > 0
Write down the associated homogeneous equation.
x²y' - 2xy' + (x² + 2)y = 0 is the associated homogeneous equation with non-homogeneous ODE x²yⁿ - 2xy' + (x² +2)y = 3x³.
It should be noted that the equation is same as the variable coefficient linear second order non-homogeneous ODE but just the right side zero.
The complementary solutions or homogeneous solutions to this homogeneous equation serve as the foundation for the space of all solutions to the non-homogeneous equation.
By assuming that y has the form y(x) = xr and substituting this into the homogeneous equation to create a characteristic equation, we can determine the complementary solutions. We may find the values of r that correspond to solutions of the type y(x) = xr by looking at the characteristic equation's roots.
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When calculating the price (p) of an item that has been marked down by 25%, Denise states that the expression
p - 0. 25p will calculate the
sale price. Kristal says that a shorter way to calculate the sale price would be to use the expression 0. 75p. Who is correct
A Denise is correct.
B Kristal is correct. .
C Both Denise and Kristal are correct.
D Neither Denise nor Kristal are correct.

Both Denise and Kristal are correct. The expression "p - 0.25p" is equivalent to "0.75p," which represents the sale price after a 25% markdown. Therefore, option C is the correct answer.
Denise's expression, "p - 0.25p," represents the original price (p) minus the 25% markdown (0.25p). This simplifies to 0.75p, which is indeed the sale price.
On the other hand, Kristal's expression, "0.75p," directly represents the sale price after applying a 25% discount. This expression skips the intermediate step of subtracting the markdown from the original price.
Both expressions, "p - 0.25p" and "0.75p," yield the same result, which is the sale price after a 25% markdown. Therefore, both Denise and Kristal are correct in their calculations.
The choice between the two expressions comes down to personal preference or convenience. Some individuals may find it easier to directly calculate the sale price using a percentage of the original price, while others may prefer subtracting the markdown amount from the original price.
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You are buying fabric to make a patio umbrella in the shape of a regular hexagon. The res fabric costs $s. 75 per square yard and the white fabric costs $2i50 per square yard. You can only order whole numbers of square yards of fabric. What will be the cost of the fabric
The cost of the fabric will be $55.63.
To find the cost of the fabric, you need to first determine the total area of the fabric needed to make the patio umbrella. Since the patio umbrella is in the shape of a regular hexagon, it can be divided into six congruent equilateral triangles. The formula for the area of an equilateral triangle is A = (sqrt(3)/4)*s^2, where s is the length of one side of the hexagon.
Let's assume the length of one side of the hexagon is x. Then the area of one of the equilateral triangles is A = (sqrt(3)/4)x^2. Since there are six of these triangles in the hexagon, the total area of the hexagon is 6A = 6(sqrt(3)/4)*x^2 = (3sqrt(3)/2)*x^2.
To determine the amount of orange fabric needed, you can multiply the area of the hexagon by the number of square yards in one square foot and round up to the nearest whole number of square yards. Similarly, you can do the same for the white fabric.
Let's say the hexagon has a side length of 6 feet, so x=6ft. Then the area of the hexagon is (3sqrt(3)/2)*(6ft)^2 = 93.53 square feet. Converting square feet to square yards gives 10.39 square yards. Therefore, you need to order at least 11 square yards of each fabric.
The cost of the orange fabric is $s. 75 per square yard, so 11 square yards will cost 11 * $s. 75 = $28.13. The cost of the white fabric is $2.50 per square yard, so 11 square yards will cost 11 * $2.50 = $27.50. Therefore, the total cost of the fabric will be $28.13 + $27.50 = $55.63.
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Can you help me with this question step by step.
Answer:
32
Step-by-step explanation:
There are 28 full shaded squares
There are 8 half squares
2 half squares make up 1 full square
So 28 + 4 = 32
Area is 32 units
A large apartment complex has 1,500 units, which are filling up at a rate of 10% per month. If the
apartment complex starts with 15 occupied units, what logistic function represents the number of
units occupied over time?
ON(t)
1500
1+114e-0. 101
ON(t)
800
1+114e-0. 101
N(t)
800
1+99e-0. 100
N(t)
1500
1+99e-0. 101
The logistic function that represents the number of units occupied over time is given by:
[tex]N(t) = (K / (1 + A * e^(-r*t))),[/tex]
where N(t) is the number of units occupied at time t, K is the carrying capacity (maximum number of units that can be occupied),
A is the initial amount of units occupied, r is the growth rate, and e is the base of the natural logarithm.
In this case, the carrying capacity K is 1500 units, and the initial amount of occupied units A is 15 units. The growth rate r can be calculated as follows:
[tex]r = ln((10%)/(100% - 10%)) = ln(0.1/0.9) ≈ -0.101[/tex]
Substituting the given values into the logistic function, we get:
[tex]N(t) = (1500 / (1 + 15 * e^(-0.101*t)))[/tex]
Simplifying further, we get:
[tex]N(t) = (100 / (1 + e^(-0.101*t))) + 15[/tex]
Therefore, the logistic function that represents the number of units occupied over time is:
[tex]N(t) = (100 / (1 + e^(-0.101*t))) + 15[/tex], where t is measured in months.
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Michelle has four credit cards with the balances and interest rates listed below. She wants to pay off her credit
cards one at a time, based on the interest rate. In which order should Michelle pay off her credit cards?
>>>>>a. 3,2,1,4<<<<
b. 1,2,3,4
c. 2,4,3,1
d. 4,1,3,2
Answer:
a) 3, 2, 1, 4
Step-by-step explanation:
If you have multiple credit cards with different APRs, it is best to pay off the card with the highest APR first. This is because you will save the most money in interest by paying off the highest-rate debt first.
Therefore, as Michelle has four credit cards, each with different APRs, she should pay them off in order of the highest to lowest interest rate.
Since the highest APR is 23%, credit card #3 should be paid off first.
The next highest APR is 19%, so credit card #2 should be paid off second.
Credit card #1 should be paid off next as it has an APR of 17%.
Finally, credit card #4 should be paid off last, as it has the lowest APR of 15%.
So the order in which Michelle should pay off her credit cards is:
3, 2, 1, 4A scale model of a statue has a height of 10 cm. The real statue has a height of 2 m. The model and statue are both made of the same stone which has a density of 2 g/cm(3). The mass of the real statue is 1632 kg. Find the volume of the model in cm(3)
Answer:
102 cm³
Step-by-step explanation:
density = m/v
1 g = 0.001 kg
Volume of real statue = v = m/d = 1632 kg / 0.002 kg/cm³ = 816,000 cm³
scale factor for height: 200 cm : 10 cm = 20 : 1
scale factor for volume: 20³ : 1³ = 8,000 : 1
Volume of model = 816,000 cm³ / 8,000 = 102 cm³
54/g - 8 when g = 6 and h=3
The value of the simplified expression is -15.
What is the simplification of the expression?
The simplification of the expression is determined by substituting the appropriate values of the variables into the equation.
The given expression; = 54/g - 8h
The value of g = 6 and the value of h = 3,
The value of the expression is calculated as follows;
= 54/g - 8h
= 54/6 - 8(3)
= 9 - 24
= - 15
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The complete question is below:
54/g - 8h, when g = 6 and h=3
Piscine is replacing the paving stones around her inground pool. Her pool is 10 m
by 5 m, and is surrounded by a 1. 5 m border of paving stones.
a) How many square metres of paving stones will she need in total?
b) If each paving stone is 25 cm by 40 cm, in theory, how many paving stones
will she need?
c) Will your answer in part b) actually be enough? Try fitting the stones in the
space to see whether Piscine can complete the border with exactly that
number of stones, or whether there will be waste, requiring some extras.
If Her pool is 10 m by 5 m and is surrounded by a 1. 5 m border of paving stones. Therefore, Piscine will need a total of 104 square meters of paving stones.
a) The area of the pool plus the surrounding border of paving stones can be calculated as follows:
Total area = (length + 2 x border width) x (width + 2 x border width)
Total area = (10 + 2 x 1.5) x (5 + 2 x 1.5)
Total area = 13 x 8
Total area = 104 square meters
Therefore, Piscine will need a total of 104 square meters of paving stones.
b) We need to convert the dimensions of each paving stone to meters:
25 cm = 0.25 m
40 cm = 0.4 m
The area of each paving stone is:
0.25 m x 0.4 m = 0.1 square metres
The number of paving stones required can be calculated by dividing the total area by the area of each paving stone:
Number of paving stones = Total area / Area of each paving stone
Number of paving stones = 104 / 0.1
Number of paving stones = 1040
In theory, Piscine will need 1040 paving stones.
c) To determine whether the answer in part b) will be enough, we need to see if we can fit the paving stones into the available space without any gaps. We can arrange the paving stones in rows, with each row containing 10 stones (since the width of the pool is 5 m and the width of each paving stone is 0.4 m).
There will be 26 rows of paving stones around the pool (since the length of the pool plus the two borders is 13 m and the length of each paving stone is 0.25 m). Therefore, the total number of paving stones required is: 26 rows x 10 stones per row = 260 stones
Since the number of paving stones required is less than the number calculated in part b), Piscine will have enough paving stones to complete the border around her pool without any waste.
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The time it takes Susan to drive to work each day is normally distributed with a mean of 42 minutes and a standard deviation of 4 minutes.
Approximately what percent of workdays does it take Susan between 38 and 46 minutes to drive to work?
50%
68%
95%
99. 7%
We can use the empirical rule to estimate the percentage of workdays it takes Susan between 38 and 46 minutes to drive to work. According to the empirical rule, for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean
- About 95% of the data falls within two standard deviations of the mean
- About 99.7% of the data falls within three standard deviations of the mean
Since the mean is 42 minutes and the standard deviation is 4 minutes, one standard deviation below the mean is 38 minutes, and one standard deviation above the mean is 46 minutes. So, about 68% of the time it takes Susan between 38 and 46 minutes to drive to work.
Therefore, the answer is (B) 68%.
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Which ordered pair is a solution to the following system of inequalities?
y < –x2 + x
y > x2 – 4
(0, –1)
(1, 1)
(2, –3)
(3, –6)
(0, -1) is the solution to the given system of inequalities.
Option A is the correct answer.
We have,
To determine which ordered pair is a solution to the system of inequalities, we need to check if each ordered pair satisfies both inequalities simultaneously.
Let's evaluate each option:
(0, -1):
For this option, we have:
y < -x² + x
-1 < -(0)² + 0
-1 < 0
y > x² - 4
-1 > (0)² - 4
-1 > -4
Since both inequalities are satisfied simultaneously, (0, -1) is a solution to the system.
(1, 1):
For this option, we have:
y < -x² + x
1 < -(1)² + 1
1 < 0
y > x² - 4
1 > (1)² - 4
1 > -3
Since both inequalities are not satisfied simultaneously, (1, 1) is not a solution to the system.
(2, -3):
For this option, we have:
y < -x² + x
-3 < -(2)² + 2
-3 < -2
y > x² - 4
-3 > (2)² - 4
-3 > 0
Since both inequalities are not satisfied simultaneously, (2, -3) is not a solution to the system.
(3, -6):
For this option, we have:
y < -x² + x
-6 < -(3)² + 3
-6 < -6
y > x² - 4
-6 > (3)² - 4
-6 > 5
Since both inequalities are not satisfied simultaneously, (3, -6) is not a solution to the system.
Thus,
(0, -1) is the only solution to the given system of inequalities.
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40 points!!!
Peyton's photo album has 6 1/2 pages of family photos and f pages of
photos of friends. Write an expression that shows the total number
of pages in Peyton's album. Then evaluate the expression if there are
3 1/2 pages of photos of friends.
The expression that shows the total number of pages in Peyton's album is 6 1/2 + f.
We are given that;
Number of pages= 6 1/2
Now,
To write an expression that shows the total number of pages in Peyton’s album, you need to add the number of pages of family photos and the number of pages of friends photos. The expression is:
6 1/2 + f
To evaluate the expression if there are 3 1/2 pages of photos of friends, you need to substitute f with 3 1/2 and then add the fractions. The answer is
6 1/2 + 3 1/2 = 10
Therefore, by the expression the answer will be 6 1/2 + f.
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