Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall.
To determine how many gallons of paint Ms. Paquette used for one coat on the rectangular wall, we first need to calculate the total area of the wall.
Area of the wall = length x width
= 25.5 feet x 10 feet
= 255 square feet
Now, to find out how many gallons of paint are needed for one coat, we need to know the coverage rate of the paint. This information is usually provided on the paint can label. Let's assume that the coverage rate for the paint Ms. Paquette used is 350 square feet per gallon.
To calculate how many gallons of paint are needed, we can divide the total area of the wall by the coverage rate of the paint:
255 square feet ÷ 350 square feet per gallon = 0.7286 gallons
This means that Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall. Since paint is typically sold in 1-gallon containers, she would need to purchase at least one gallon of paint to complete one coat on this wall.
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If the value of a in the quadratic function f(x) = ax2 + bx + c is -8, the function will_______.
(I would give Brainliest, but I don't know how to do that ;-;)
Many thanks!
Answer:
Step-by-step explanation:
f(x) = ax² + bx + c a= -8
f(x) = -8x² + bx + c that a controls the direction and the stretch.
So the function will be stretched by 8. The negative represents the direction because, it's negative, it will be facing down.
Not sure how your class describes it but it could be facing down, concaved down, or expands downward.
The ratios of successive numbers in the Fibonacci sequence eventually get closer to which number?
a.
1. 61
c.
2. 3
b.
1. 46
d.
1
The ratios of successive numbers in the Fibonacci sequence eventually get closer to a. 1.61
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1 (0, 1, 1, 2, 3, 5, 8, 13, ...). When you take the ratio of successive numbers in the sequence (e.g., 5/3 or 8/5), it converges to approximately 1.618, also known as the Golden Ratio or Phi.
The closest option in your list is 1.61, which is option (a).
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ratios of sin y and cos x share?
Answer:
sin (y) = oppoaite / hypotenus
sin (y) = oppoaite / hypotenus sin (y) = opp/hyp
And for geting cos
cos(x) = adjecent / hypotenus
cos(x) = adjecent / hypotenus cos(x) = adj/hyp
On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set.
The solution to the system of equations shown above is the ordered pairs [-2, -9] and [3, -4].
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = -x² + 2x - 1 ......equation 1.
2x - 2y = 14 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pairs (-2, -9) and (3, -4).
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Marcus charges 130$ per week to pet sit. Next week he is offering an 18% discount. What is the amount of the discount?
Answer:23.4
Step-by-step explanation: 18 divided by 130
The amount of the discount is $23.40.
The problem asks us to find the amount of the discount given a percentage discount on a known price. To do this, we use the formula for calculating a percentage of a number.
To calculate the discount amount, we need to find 18% of the original price, which is $130 per week.
We can start by calculating 18% of $130:
Discount = 0.18 * $130 = $23.40
Therefore, the amount of the discount is $23.40.
What is the recursive formula for the sequence -1, -3, -9, -33 ...
The recursive formula for an, the nth term of the sequence is a(n) = a(n - 1) * 2 where a(1) = -1
How to determine the recursive formula of the sequenceFrom the question, we have the following parameters that can be used in our computation:
-1, -3, -9, -3³ ...
The above definitions imply that we simply multiply 3 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a(n) = a(n - 1) * 3
Where
a(1) = -1
Hence, the sequence is a(n) = a(n - 1) * 2 where a(1) = -1
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You pick a card at random. (1234)
What is P(greater than 1 or divisor of 2)?
The probability of picking a number greater than 1 or a divisor of 2 is 3/4.
Calculating the probability P(greater than 1 or divisor of 2)?The numbers greater than 1 or divisor of 2 in the set {1, 2, 3, 4} are {2, 3, 4}.
Therefore, the probability of picking a number greater than 1 or a divisor of 2 is:
P(greater than 1 or divisor of 2) = P(2 or 3 or 4) = P(2) + P(3) + P(4)
Since there are four equally likely outcomes, the probability of each individual outcome is 1/4. Thus, we have:
P(greater than 1 or divisor of 2) = 1/4 + 1/4 + 1/4 = 3/4
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(65 points) ASAP!!! Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.
Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)
Part B: Explain how you know the equation from Part A is correct. (1 point)
Part C: Solve the equation from Part A. Show every step of your work. (2 points)
Answer:
Total wood = 4.5 Left over wood = 0.7 let 1 piece of wood = x
hence we have 5x+0.7=4.5
5x=4.5 - 0.7
5x = 3.8 x= 3.8/5 = 0.76 ft
Step-by-step explanation:
Answer:
A: 5x + 0.7 = 4.5
B: You know the equation is correct because it takes into account that Warren cut five pieces of wood that are equal in length from a 4.5 feet long piece of wood. The total length of the five pieces of wood should equal the length of the original piece of wood, minus the leftover wood he has. In other words, 5x represents the total length of the five pieces of wood cut, and 0.7 represents the amount of wood left over after the cutting.
C: 0.76 feet
Step-by-step explanation:
Part A:
Let x be the length of each of the five pieces of wood cut from the 4.5 feet long piece of wood. The equation that could be used to determine the length of each piece is:
5x + 0.7 = 4.5
Part B:
You know the equation is correct because it takes into account that Warren cut five pieces of wood that are equal in length from a 4.5 feet long piece of wood. The total length of the five pieces of wood should equal the length of the original piece of wood, minus the leftover wood he has. In other words, 5x represents the total length of the five pieces of wood cut, and 0.7 represents the amount of wood left over after the cutting.
Part C:
5x + 0.7 = 4.5
5x = 4.5 - 0.7
5x = 3.8
x = 3.8/5
x = 0.76
Therefore, each of the five pieces of wood that Warren cut is 0.76 feet long.
What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter
your answer as a decimal to the ten thousandths place.
Student
0.25
0.10
0.35
0.30
Chemistry
000
Physics
Env Sci
Biology
0.45
1st choice
Not 1st
0.55
0.55 1st choice
0.45
0.20
0.80
0.30
0.70
Not 1st
1st choice
Not 1st
1st choice
Not 1st
P(Chem and 1st choice) = (0 25)(0.45) = 0.1125
P(Chem and Not 1st) = (0.25)(0.55) = 0.1375
P(Phys and 1st choice) = (0.35)(0.55) = 0.1925
P(Phys and Not 1st) = (0.35)(0.45) = 0.1575
P(ES and 1st Choice) = (0.30)(0.20) = 0.0600
P(ES and Not 1st) = (0.30)(0.80) = 0.2400
P(Bio and 1st choice) = (0.10)(0.30) = 0.0300
P(Bio and Not 1st) = (0.10)(0.70) = 0.0700
The probability that a student took AP Chemistry given they did not get into their first-choice college is 0.0566.
What is the probability?The probability that a student took AP Chemistry given they did not get into their first-choice college is calculated using the formula below:
P(Chem | Not 1st) = P(Not 1st | Chem) * P(Chem) / P(Not 1st)P(Not 1st | Chem) =0.1375
P(Chem) = 0.25
P(Not 1st) = P(Chem and Not 1st) + P(Phys and Not 1st) + P(ES and Not 1st) + P(Bio and Not 1st)
P(Not 1st)= 0.1375 + 0.1575 + 0.2400 + 0.0700
P(Not 1st)= 0.6050
Substituting the values in the formula above:
P(Chem | Not 1st) = 0.1375 * 0.25 / 0.6050
P(Chem | Not 1st) = 0.0566
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Luis created a spreadsheet of his expenses for three months. Which of Luis's expenses are variable expenses
utility bill
Expenses Jan Feb Mar
rent
$1,250,00 $1,250,00 $1,250,00
$124. 11 $108. 72 $121. 69
car loan payment $384. 00 3384,00 $384. 00
Insurance payment 397. 18 597. 18 $97. 18
groceries
$315,43 $367. 25 $341. 04
clothing
$72. 18 $152. 74 $0. 00
fuel
$108. 71 $117. 46 $127. 34
Variable expenses are expenses that fluctuate from month to month, and are typically not a fixed amount. Examples of variable expenses include groceries, fuel, clothing, and entertainment. These expenses can be influenced by various factors such as personal choices, seasonality, and external events.
In Luis's expenses, the following expenses are variable expenses:
Groceries: The amount spent on groceries changes from month to month depending on the types of food Luis purchases and the quantity he buys.Clothing: This expense is variable because Luis only spent money on clothing in January and February, and did not spend anything on clothing in March.Fuel: The amount spent on fuel changes from month to month depending on how often Luis drives and the price of gasoline.On the other hand, the following expenses are fixed expenses:
Rent: This expense is fixed because Luis pays the same amount for rent every month.Car loan payment: This expense is fixed because Luis is required to pay the same amount for his car loan every month.Insurance payment: This expense is fixed because Luis is required to pay the same amount for his insurance every month.Utility bill: The utility bill could be either a variable or fixed expense, depending on the type of utility. For example, if the utility bill is for electricity, it may be a variable expense because the amount of electricity used can fluctuate from month to month. However, if the utility bill is for a fixed service such as internet, it would be a fixed expense.To learn more about “utility” refer to the https://brainly.com/question/14729557
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Answer:
groccieries is the answer for plato 2023
A piece of wire of length 50 is out, and the resulting two pieces are formed to make a corde and a square. Where should the wre be cut to day minance and provimine the continet water who? (e) To minimize the combined area, the wire should be cut so that a length of 25.964 used for the circle and a longen er 3.04 es lo quem (Round to the nearest thousandth as needed) (1) To maximize the combined uros, there should be cut so that a length of used for the circle and we canned tere dere (Round to the nearest thousandth as needed) Evaluate the following limit. Use Thôpitals Rule when it is convenient and applicable Iim cox How should the given timt be evaluated? Select the correct choice below and, if necessary, in the answer box to complete your choice A. U topitals Rule more than once to rewrite the imtin ta final fomas tim 9. Multiply the expension by a una traction to obtain im (1) OG UTHopitals Rule exactly once to rewrite the imit im OD. Vse direction Evaluate the limit imetype an exact answer
To minimize the combined area of a circle and a square made from a wire of length 50, you should cut the wire so that 25.964 units are used for the circle (as the circumference) and 24.036 units are used for the square (as the perimeter).
To maximize the combined areas, the optimal cutting point cannot be determined due to the lack of information provided in the question. For the limit evaluation, it's not clear which limit should be evaluated, as the question has some typos and irrelevant parts. If you can provide the correct limit expression, I will be happy to help you evaluate it using the appropriate method, such as Hsopital's Rule or other techniques.
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Find an angle in each quadrant with a common reference angle with 306°, from 0°≤θ<360°
The angle in each quadrant with a common reference angle with 306° are
Quadrant 1 is 126°Quadrant 2 is 54°Quadrant 3 is 306°Quadrant 4 is 234°To find angles in each quadrant with a common reference angle with 306°, we first need to determine the reference angle for 306°.
Reference angle is the acute angle between the terminal side of an angle and the x-axis. We can find the reference angle for any angle θ by subtracting the nearest multiple of 180° from θ and taking the absolute value of the result. In this case:
|306° - 180°| = 126°
So, the reference angle for 306° is 126°.
Now, we can find an angle in each quadrant with a common reference angle of 126°:
1st quadrant: The angle with a reference angle of 126° in the 1st quadrant is simply 126°.
2nd quadrant: To find the angle with a reference angle of 126° in the 2nd quadrant, we need to subtract the reference angle from 180° (since all angles in the 2nd quadrant are between 90° and 180°).
180° - 126° = 54°
So, an angle with a reference angle of 126° in the 2nd quadrant is 54°.
3rd quadrant: To find the angle with a reference angle of 126° in the 3rd quadrant, we need to subtract the reference angle from 180° and then add 180° (since all angles in the 3rd quadrant are between 180° and 270°).
180° + 126° = 306°
So, an angle with a reference angle of 126° in the 3rd quadrant is 306°.
4th quadrant: To find the angle with a reference angle of 126° in the 4th quadrant, we need to subtract the reference angle from 360° (since all angles in the 4th quadrant are between 270° and 360°).
360° - 126° = 234°
So, an angle with a reference angle of 126° in the 4th quadrant is 234°.
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Paige walks to the park 2/3 mile away it takes her 16 minutes to get there how many miles per minutes
The Paige walks at a speed of approximately 0.04167 miles per minute to get to the park.
How we find the miles per minutes?To calculate Paige's speed, we used the formula:
Speed = Distance / Time
Given that Paige walks to the park 2/3 mile away, we substitute Distance with 2/3 mile and Time with 16 minutes. We get:
Speed = 2/3 mile / 16 minutes
Simplifying the expression by converting minutes to hours, we get:
Speed = 2/3 mile / (16/60) hours
Simplifying further by multiplying both the numerator and denominator by 60, we get:
Speed = [tex](2/3) * (60/1)[/tex] mile/hour / (16/1) minutes
Speed = 0.04167 mile/minute (rounded to 5 decimal places)
"Paige walks to the park 2/3 mile away it takes her 16 minutes to get there how many miles per minutes" is that Paige walks at a speed of approximately 0.04167 miles per minute.
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how much soda do you need if you buy 20 bags of 4 bags of hot chips and 3 bottles of soda.
If each bag of hot chips requires around 500 ml of soda to drink with, then 46,000 ml of soda would be needed to buy 20 bags of 4 bags of hot chips and 3 bottles of soda.
To determine how much soda is needed if you buy 20 bags of 4 bags of hot chips and 3 bottles of soda, we need to know the volume of each bottle of soda.
Assuming each bottle of soda contains 2 liters of soda, the total volume of soda needed can be calculated as follows:
One bag of hot chips contains 4 bags of chips.So, 20 bags of hot chips contain 20 x 4 = 80 bags of chips.Each bag of chips may require around 500 ml of soda to drink with.Therefore, the total soda needed for all bags of chips is 80 x 500 ml = 40,000 ml.Three bottles of soda are also purchased, which contain a total of 3 x 2000 ml = 6000 ml.The total soda needed is the sum of the soda needed for the chips and the soda purchased, which is 40,000 ml + 6000 ml = 46,000 ml.To know more about volume, refer to the link below:
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The value of y varies directly with x. When y = 75, x=1/2. What is the value of y, when x is 2 1/2
Answer:
y=60
Step-by-step explanation:
y=kx75=k×1/275=1/2k75÷1/2=1/2k÷1/2k=150y=kxy=150×2 1/2y= 60Ms. Griffin has 0. 8 liters of hot tea and 4 teacups. She will divide the tea evenly among the cups. Which model represents 0. 8 divide by 4
The model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.
To find the amount of tea in each teacup, you need to divide the total amount of tea (0.8 liters) by the number of teacups (4). The model for this is 0.8 ÷ 4. Follow these steps:
1. Divide 0.8 by 4:
0.8 ÷ 4 = 0.2
2. Interpret the result:
Each teacup will have 0.2 liters of hot tea.
So, the model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.
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write a math sequence for this problem! lilah and her little brother max went to the beach they dug 290 seashells and 645 rocks how many rocks and seashells did max and lilah collect in all?
Answer:
935 Rocks and shells
Step-by-step explanation:
To find the total number of rocks and seashells collected by Max and Lilah, we can use the addition operation. Let S be the number of seashells and R be the number of rocks. Then, the math sequence for this problem is:
S + R = Total
Substituting the given values, we get: 290 + 645 = Total
Simplifying the right-hand side, we get:
935 = TotalTherefore, Max and Lilah collected a total of 935 rocks and seashells in all.
To find the total number of rocks and seashells collected by Lilah and Max, we simply need to add the number of seashells and rocks they each collected. Let S represent the number of seashells and R represent the number of rocks. Then, the equation is:
S + R = 290 + 645
Simplifying this expression, we get:
S + R = 935
935 rocks and seashells.
What is the perimeter of the triangle?
?? units.
Answer:
36 units
Step-by-step explanation:
You want to know the perimeter of the right triangle with leg lengths 9 units and 12 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides. We can count squares to find the lengths of the horizontal and vertical legs. The length of the hypotenuse can be found using the Pythagorean theorem:
c² = a² +b²
c² = 9² +12² = 81 +144 = 225
c = √225 = 15 . . . . length of the hypotenuse
Then the perimeter is ...
P = a +b +c = 9 +12 +15 = 36 . . . units
The perimeter of the triangle is 36 units.
__
Additional comment
The leg lengths have the ratio 9:12 = 3:4, telling you this is a 3:4:5 right triangle. This means you know the side lengths are 3:4:5 = 9:12:15, and their sum is 9+12+15 = 36.
It is handy to memorize a few of the Pythagorean triples that often show up in algebra, trig, and geometry problems: {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.
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A taho vendor having lost control of his cart down a slight hill runs after it in an attempt to keep it from running into a concrete wall however he did not get there in time and the 100 kg cart crashes assuming that in its downhill run the cart got a final velocity of 2m/s and that the impact stopped the cart in 0.15s, (a) determine the change in the cart's momentum (b) estimate the average force that the wall exerts on the cart (neglecting the angle of the hill) (c) determine the direction of the impulse that acted on the cart
(a) The change in the cart's momentum is -200 kg m/s.
(b) The average force that the wall exerts on the cart is 1333.33 N.
(c) The impulse that acted on the cart is in the opposite direction to the cart's initial momentum.
(a) The change in momentum can be calculated as the final momentum minus the initial momentum. The initial momentum of the cart is zero since it was at rest, and the final momentum is calculated as (mass of cart) x (final velocity) = 100 kg x 2 m/s = 200 kg m/s. Therefore, the change in momentum is -200 kg m/s.
(b) The average force can be calculated using the impulse-momentum theorem, which states that the impulse acting on an object is equal to the change in its momentum. The impulse is calculated as (mass of cart) x (final velocity - initial velocity) = 100 kg x (2 m/s - 0 m/s) = 200 kg m/s.
The time taken for the cart to come to a stop is given as 0.15 s. Therefore, the average force exerted by the wall is 1333.33 N.
(c) The direction of the impulse is opposite to the initial momentum of the cart, which was in the direction of the hill. Since the cart was moving downhill, the impulse that acted on it was in the upward direction.
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 Part C
The rectangular sides of the treasure box will be cut from wooden planks
5
9 feet long and foot wide. How many planks will Mr. Penny need so
9
16
that his 18 students can each construct one treasure box?
Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.
To determine the number of planks required, we need to calculate the total amount of wood needed for all 18 students' treasure boxes.
Each treasure box has two identical rectangular sides.
Each side is cut from a wooden plank that is 5/9 feet long and 1 foot wide.
Therefore, the area of each side is [tex](5/9) \times 1 = 5/9[/tex] square feet.
Since there are two identical sides for each treasure box, the total area of wood needed for one treasure box is [tex](5/9) \times 2 = 10/9[/tex] square feet.
To find the total wood needed for 18 students' treasure boxes, we multiply the area per treasure box by the number of treasure boxes:
Total wood needed [tex]= (10/9) \times 18 = 20[/tex] square feet.
So, Mr. Penny will require a total of 20 square feet of wooden planks for all 18 students to construct their treasure boxes.
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Question: What is the number of planks required for Mr. Penny's 18 students to each construct one treasure box if the rectangular sides of the treasure box will be cut from wooden planks that are 5/9 feet long and 1 foot wide?
under a time crunch, you only have time to take a sample of 15 water bottles and measure their contents. the sample had a mean of 20.05 ounces with a sample standard deviation of 0.3 ounces. what would be the 90% confidence interval, when we assumed these measurements are normally distributed? g
The 90 % confidence interval is ( 19.92 , 20.18 )
What is confidence interval?A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the number of samples n = 15
Let the mean of the sample be μ = 20.05
Let the standard deviation σ = 0.3
Now , the z score of 90 % confidence interval is z = 1.645
The 90% confidence interval is calculated by the equation
A = μ ± z ( σ / √n )
Substituting the values in the equation , we get
P = μ + z ( σ / √n )
Q = μ - z ( σ / √n )
Now , the value of P is
P = 20.05 + 1.645 ( 0.3/√15 )
P = 20.05 + ( 0.4935 / 3.873 )
P = 20.05 + 0.12742
P = 20.18
Now , the value of Q is
Q = μ - z ( σ / √n )
Q = 20.05 - 1.645 ( 0.3/√15 )
Q = 20.05 - ( 0.4935 / 3.873 )
Q = 20.05 - 0.12742
Q = 19.92
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solve this problem:
Suppose that you are headed toward a plateau 50 m high. If the angle of elevation to the top of the plateau is 20 , how far are you from the base of the plateau?
Answer:
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's call the distance from the base of the plateau to our position "x". We can then use the tangent function to find x:
tan(20°) = opposite / adjacent
In this case, the opposite side is the height of the plateau (50 m) and the adjacent side is x. So we can write:
tan(20°) = 50 / x
To solve for x, we can rearrange this equation:
x = 50 / tan(20°)
Using a calculator, we get:
x = 143.45 meters (rounded to two decimal places)
Therefore, if the angle of elevation to the top of the plateau is 20 degrees, and the plateau is 50 meters high, we are approximately 143.45 meters away from the base of the plateau.
Answer:
The distance is 137.3739 feet.
Step-by-step explanation:
I hope this answer is right.
Suppose a friend or family asked you how it could be possible that an annual interest rate is higher than 100%. write out an explanation of what you might say to them
If someone asked me how it could be possible for an annual interest rate to be higher than 100%, I would explain that it is actually quite common in certain situations, particularly in the case of loans with very short terms or loans with high fees.
For example, let's say you borrowed $100 from a lender and agreed to pay back $110 in one week. The lender is essentially charging you 10% interest for the one-week loan period, but if you annualize that rate, it comes out to over 520%. This is because the lender is charging you a very high interest rate for a very short period of time.
Another example would be if you took out a payday loan, which typically have very high fees attached to them. For instance, you might borrow $500 and have to pay back $575 in two weeks. The interest rate on this loan might be calculated as the $75 fee divided by the $500 borrowed, which comes out to 15%. However, if you annualize that rate, it comes out to over 390%.
In both of these examples, the interest rate is very high because the loan term is very short and/or the fees are very high. It's important to note that borrowing at such high interest rates can be extremely costly and can lead to a cycle of debt, so it's generally recommended to avoid loans with high interest rates whenever possible.
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x+y=112
y=x-58
using elimination
PLEASE HELP ME!!!!
Answer:
x=85
y=27
;)
Step-by-step explanation:
x+y=112
y=x-58
add 58 to the other side
58+y=x
Subtract y
x-y=58
x+y=112
Now if we add these we get
2x=170
x=85
Then if we substitute 85 in x+y=112
85+y=112
112
-85
____
27
Check your Answer on
y=x-58
27=85-58
27=27
This is the Answer
Please DM me if I should reexplain THANK YOU!
Hope this helps!
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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find the missing side length
Answer:
Step-by-step explanation:
[tex]x^{2}[/tex]=a²+b²
x²=6²+2.5²
x²=36+6.25
x²=42.25
√x=√42.25
x=6.5
Answer:
6.5
Step-by-step explanation:
6^2 + 2.5^2 = c^2
•36 + 6.25 = c^2
•42.25 = c^2
• find square root of 42.25 = 6.5
• 6.5 = C
In a circle, an angle measuring 2.2radians intercepts an are of length 11.9.Find the radius of the circle to the nearest
10th.
The radius of the circle to the nearest 10th is 5.4
Showing how to calculate radiusThe formula for calculating the length of an arc of a circle is:
length of arc = radius x angle in radians
l = rθ
where
r = radius of the circle
l = length of arc
θ = angle in radians
From the question, we are given:
length of arc = 11.9
angle in radians (θ) = 2.2radians
The we can plug in the values
11.9 = r x 2.2
make r the subject of the formula
r = 11.9/2.2
r = 5.41 (to 2 decimal places)
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Need help on the stretch part URGENT
The equation of the quadratic function in the stretch part is f(x) = x² + 4x - 11
Calculating the equation of the function (the stretch part)From the question, we have the following parameters that can be used in our computation:
Zeros: -2 ± √15
This means that
Zeros: -2 - √15 and -2 + √15
The equation of the function is calculated as
f(x) = product of (x - zeros)
So, we have
f(x) = (x - (-2 -√15)) * (x - (-2 + √15))
When expanded, we have
f(x) = (x + 2 + √15)) * (x + 2 - √15))
Evaluate the products
f(x) = x² + 4x - 11
Hence, the function is f(x) = x² + 4x - 11
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Payton bought a 15-year treasury bond for a face amount of $700. The 2. 5% interest will be
compounded quarterly. What will the future value of Patrick's investment be when he goes to
cash it in on the maturity date 15 years from now?
The future value of Payton's investment will be $1,048.29 when he cashes in the bond on the maturity date 15 years from now.
To calculate the future value of Payton's 15-year treasury bond, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
where FV is the future value, PV is the present value (or face amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, the present value is $700, the interest rate is 2.5% or 0.025, the interest is compounded quarterly, so n = 4, and the time period is 15 years.
Plugging in the values, we get:
FV = $700 * (1 + 0.025/4)^(4*15)
FV = $700 * (1 + 0.00625)^60
FV = $700 * 1.49756
FV = $1,048.29
Therefore, the future value of Payton's investment will be $1,048.29 when he cashes in the bond on the maturity date 15 years from now.
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Help guys asap i need correct answers only!! find the volume of the cylinder. find the volume of a cylinder with the same radius and double the height.
the volume of the cylinder in^3?
the volume of with the same radius and double the height is
To find the volume of the cylinder, we need to use the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
If we have a cylinder with radius r and height h, and another cylinder with the same radius r but double the height (2h), the volume of the second cylinder is:
V' = πr^2(2h) = 2πr^2h
So, to answer the questions:
The volume of the cylinder is V = π(5 cm)^2(8 cm) = 100π cubic cm, which is approximately 314.16 cubic cm rounded to two decimal places.
The volume of the cylinder with the same radius and double the height is V' = 2π(5 cm)^2(8 cm) = 200π cubic cm, which is approximately 628.32 cubic cm rounded to two decimal place
