The dimensions of a rectangular playground are 50 times the dimensions of a scale drawing of the playground the area of the scale drawing is 6 feet what is the area of the actual playground
The area of the actual playground is [tex]\( 15000 \)[/tex] square feet. To solve this problem, we need to understand the relationship between the scale drawing and the actual playground dimensions.
Let's denote:
- [tex]\( l \)[/tex] as the length of the scale drawing,
- [tex]\( w \)[/tex] as the width of the scale drawing,
- [tex]\( L \)[/tex] as the length of the actual playground, and
- [tex]\( W \)[/tex] as the width of the actual playground.
Given that the dimensions of the actual playground are 50 times the dimensions of the scale drawing, we have the following relationships:
[tex]\[ L = 50l \][/tex]
[tex]\[ W = 50w \][/tex]
We are given that the area of the scale drawing is 6 square feet. The area of a rectangle is given by the formula [tex]\( \text{Area} = \text{length} \times \text{width} \).[/tex] So, for the scale drawing:
[tex]\[ \text{Area of scale drawing} = l \times w = 6 \][/tex]
Now, we need to find the length and width of the actual playground and then calculate its area.
From the relationship between the actual playground and the scale drawing, we have:
[tex]\[ L = 50l \][/tex]
[tex]\[ W = 50w \][/tex]
So, we can express [tex]\( l \) and \( w \)[/tex] in terms of [tex]\( L \) and \( W \)[/tex]:
[tex]\[ l = \frac{L}{50} \][/tex]
[tex]\[ w = \frac{W}{50} \][/tex]
Now, let's substitute these expressions into the equation for the area of the scale drawing:
[tex]\[ \text{Area of scale drawing} = \left(\frac{L}{50}\right) \times \left(\frac{W}{50}\right) = 6 \][/tex]
[tex]\[ \frac{L \times W}{2500} = 6 \][/tex]
To find the area of the actual playground, we need to solve for [tex]\( L \times W \):[/tex]
[tex]\[ L \times W = 6 \times 2500 = 15000 \][/tex]
Therefore, the area of the actual playground is [tex]\( 15000 \)[/tex] square feet.
please help
given center of m below you can conclude that ml is congruent to
A. center of m
B. ma
C. jr
D. el
Answer:
B. ma
Step-by-step explanation:
In a circle, equal chords are equidistant from the centre.
In the given circle, OE = JR = 3.8.
Therefore, chords OE and JR are equal.
Hence, they should be equidistant from the center.
Their distances from the center are:
ML and MA
So, ML is congruent to MA.
A coin is tossed 100 times resulting in 46 heads and 54 tails. The same coin is tossed 1000 times resulting in 495 heads and 505 tails. What is the theoretical probability of getting heads with this coin?
You ask randomly chosen students which candidate they will vote for in the upcoming election. A total of 50 students in the sample said they will vote for Candidate A. There are 2500 students in the school. Find the number of students in the sample who said they will vote for Candidate C. Then predict the number of students in the school who will vote for Candidate C.
You ask randomly chosen students which candidate they will vote for in the upcoming election. A total of 50 students in the sample said they will vote for Candidate A. There are 2500 students in the school. Find the number of students in the sample who said they will vote for Candidate C. Then predict the number of students in the school who will vote for Candidate C.
Final answer:
The sample size is calculated to be 200 based on the percentage for Candidate A. From the sample, 120 students said they will vote for Candidate C. Predicting based on this sample, 1,500 students in the school will vote for Candidate C.
Explanation:
To find the number of students in the sample who said they will vote for Candidate C, we need to use the percentages given for each candidate. If Candidate A is 25%, Candidate B is 15%, and Candidate C is 60%, and knowing that 50 students in the sample voted for Candidate A, we can determine the total sample size. Since Candidate A represents 25% of the sample, we can calculate the total sample size using the equation 50 = 0.25 × (total sample size). Solving for total sample size gives us 200.
With the sample size known, we can calculate the number of students who said they will vote for Candidate C by taking 60% of 200, which is 120 students in the sample. To predict the number of students in the school who will vote for Candidate C, we use the proportion of the sample who choose Candidate C to estimate the proportion for the entire school population. Since there are 2,500 students in the school, we predict that 60% of 2,500 will vote for Candidate C, which amounts to 1,500 students.
Help I don’t know the answer (only answer if you know what it truly is)
(This question has 4 parts)
1. Use an appropriate technology to simulate 25 tosses of a coin. Report your results
2.What experimental probability is indicated by this data?
3. What is the theoretical probability that a coin toss will yield a result of heads? Or tails?
4. Explain any differences between the theoretical probability and the experimental probability.
(Sorry for so much but I honestly have no idea how to do this)
(Please make a good answer with details and include how you did it)
Heads - 9
Tails - 16
----
Probability of heads = 9/25 = 0.36 = 36%
Probability of tails = 16/25 = 0.64 = 64%
----
Heads = 36%
Tails = 64%
----
The experimental probability basically says the answer but the theoretical probability clears out the answer.
NEED HELP ASAP!!! Susan makes $5 per hour babysitting and $7 per hour as a life guard. Her goal is to make at least $140. which of the following represents three possible solutions to the problem?
The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube?
The volume of a cube is found with the following formula:
[tex] l \times w \times h [/tex]
The length, width, and height must all be the same value in a cube. This means that you can replace variables l, w, and h with one variable, s:
[tex] \boxed{s} \times s \times s = s^3 [/tex]
The expression s can represent the length of a side of the cube.
The expression represents s, the length of a side of the cube is [tex]\rm s^3=64[/tex].
What is the volume of the cube?The volume of the cube formula is:
The volume of a Cube = Length × Width × Height
The volume of a cube is 64 cubic inches.
where s is the length of a side of the cube.
The side of the cube is;
[tex]\rm The \ volume \ of\ a\ Cube = Length \times Width \times Height \\\\ The \ volume \ of\ a\ Cube =s \times s \times s\\\\The \ volume \ of\ a\ Cube =s^3\\\\s^3=64[/tex]
Hence, the expression represents s, the length of a side of the cube is [tex]\rm s^3=64[/tex].
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What is the square root of 2290
The area of a circle of radius 12 units is equal to the surface area of a sphere of radius 6 units. True or false
The area of a 2D form is the amount of space within its perimeter. The given statement is true.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given that radius of the circle is 12 units, and the radius of the sphere is 6 units.
The area of the circle = π(12)² = 144π units²
The surface area of the sphere = 4π(6)² = 144π units²
As it can be observed that the area of a circle of radius 12 units is equal to the surface area of a sphere of radius 6 units.
Hence, the given statement is true.
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find the total volume of each figure shown measured in cm (not to scale)
Answer:
Step-by-step explanation:
Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?
Choose all that give the correct expression.
A) Steven lost four $10 bills, and now he has −$40. −4 × 10
B) If I lose 8 pounds per month for 3 months, my weight will change −24 pounds total. 3 × (−8)
C) Sarah spends $2 for each fare on the commuter train. She rides the train 10 times during a week. 2 × (−10)
D) Pat and Amy were on a diet for 4 months. Pat lost an average of 3 pounds a month, and Amy lost an average of 4 pounds a month. 4((−3) + (−4))
Answer:
the answer would be A B and D
Step-by-step explanation:
had to figure it out myself -.-
you toss two dice one time what is the probability of getting an even number on the first die or a sum of 6
A sphere and a cylinder have the same diameter. The height of the cylinder is equal to its diameter. Which shape has a greater volume?
The cylinder has a greater volume than the sphere when both have the same diameter and the cylinder's height is equal to its diameter, as the formulas for their volumes show that V_cylinder > V_sphere.
The question asks which shape has a greater volume: a sphere with the same diameter as a cylinder or a cylinder where the height is equal to the diameter. To solve this, we need to compare their volumes using mathematical formulas.
The volume of a sphere with radius r is given by V_sphere = (4/3) * π * r^3. Since the diameter of the cylinder is the same as the diameter of the sphere, we can use the same value for r, where r is half of the diameter.
The volume of a cylinder with radius r and height h (which, in this case, is also 2r) is calculated as V_cylinder = π * r^2 * h. For the cylinder, since h = 2r, we substitute to get V_cylinder = π * r^2 * (2r) = 2 * π * r^3.
Comparing the two volumes, it is clear that the volume of the cylinder (2 * π * r^3) is greater than that of the sphere ((4/3) * π * r^3). Therefore, the cylinder has a greater volume than the sphere when both shapes have the same diameter and the cylinder's height is equal to its diameter.
Dexter has a gift card for $20.00 to an electronics store. He also has a coupon for 25% off his entire purchase, so he will be paying 75% of the total cost. He plans to buy a video game for $10.00 and batteries for $2.00. Select the equation that represents how much money will be left on his gift card after his purchases if x represents his remaining balance.
Answer:
The linear equation that represent the situation is [tex]x=20-0.75(10+2)[/tex]
The remaining balance on his gift card is [tex]\$11[/tex]
Step-by-step explanation:
Let
x------> represents the remaining balance
we know that
The linear equation that represent the situation is equal to
[tex]x=20-0.75(10+2)[/tex]
Solve
[tex]x=20-0.75(12)[/tex]
[tex]x=20-9[/tex]
[tex]x=\$11[/tex]
Answer:
its B
Step-by-step explanation:
Please Answer if you can!
I have 5 questions.
1. Ron is seeking a loan with a simple interest rate of 7% per year. He wants to borrow $4,500.
How much will he be charged in interest after 36 months?
A. $9,450
B. $945
C. $11,340
D. $5,445
2. In Texas the state sales tax rate is 6%. Beth purchases a washing machine at $420.00 and a dryer for $360.00.
How much will Beth's total be including state sales tax?
A. $445.20
B. $826.80
C. $780.00
D. $46.80
3. Mrs. Garland bought x number of shirts for the new members of her chorus. The cost for x number of shirts, including $3.99 shipping, was $77.49. Each shirt costs $12.25. There was no sales tax on the purchase. Which equation can be used to find x, total number of shirts purchased?
A. 3.99x + 2.25 = 77.49
B. 3.99(x + 12.25) = 77.49
C. 12.25x + 3.99 = 77.49
D. 12.25(x + 3.99) =77.49
4. Efua and Ngozi go to McDonalds. They each order 1 item off the $1 menu. How much will they pay with 8% tax?
A. $0.16
B. $2.08
C. $54
D. $2.16
5. Hanane eats at a restaurant. The service is poor, so she only leaves a 5% tip on a $50 bill. What was the total bill including tip?
A. $52.50
B. $25
C. $2.50
D. $55
Thanks!
for 1 i got $945.
For 2 i got $826.80.
For 3 i got c.
For 4 i got $2.16.
For 5 i got $52.50
A company’s profit is modeled by the function p(x) = -2x2 + 60x − 2, where p is the profit in thousands of dollars and x is the number of units sold in hundreds.
Based on the profit function, the company has to make ___ hundred units to make a maximum profit
To find the number of units the company needs to sell to make maximum profit, we need to find the vertex of the parabola represented by the profit function. The vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, the company needs to sell 1500 units to make a maximum profit.
Explanation:The profit function is given as p(x) = -2[tex]x^2[/tex] + 60x - 2, where p is the profit in thousands of dollars and x is the number of units sold in hundreds. To find the quantity that yields the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, a = -2 and b = 60. Plugging these values into the formula, we get x = -60 / (2*(-2)) = 15. Since x represents the number of units sold in hundreds, the company needs to sell 1500 units to make a maximum profit.
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20 PTS HURRY
A blackboard has an area of 28ft2 and a perimeter of 22 ft. What are the dimensions of the board?
2[L + W] =22
L*W = 28
W = 28/L sub this in the first equation
Solve for L:
2 (L + 28/L) = 22
Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
L + 28/L = 11
Write the left hand side as a single fraction.
Bring L + 28/L together using the common denominator L:
(L^2 + 28)/L = 11
Multiply both sides by a polynomial to clear fractions.
Multiply both sides by L:
L^2 + 28 = 11 L
Move everything to the left hand side.
Subtract 11 L from both sides:
L^2 - 11 L + 28 = 0
Factor the left hand side.
The left hand side factors into a product with two terms:
(L - 7) (L - 4) = 0
Find the roots of each term in the product separately.
Split into two equations:
L - 7 = 0 or L - 4 = 0
Look at the first equation: Solve for L.
Add 7 to both sides:
L = 7 or L - 4 = 0
Look at the second equation: Solve for L.
Add 4 to both sides:
L = 7 or L = 4 and W=4 or W = 7
How do you find the area of a triangle?
Lamar buys $75 worth of clothes. He pays $81,including sales tax. What is the tax rate?
Hence, the tax rate is [tex]8[/tex]%.
What is the tax rate?
A tax rate is a percentage at which an individual or corporation is taxed.
The United States, both the federal government and many of the states, uses a progressive tax rate system, in which the percentage of tax charged increases as the amount of the person's or entity's taxable income increases.
Here given that,
Lamar buys $[tex]75[/tex] worth of clothes. He pays $[tex]81[/tex],including sales tax.
So,
Sales Tax = $[tex]81[/tex] - $[tex]75[/tex]
= $[tex]6[/tex]
Then the Sales Tax Rate
= [tex]\frac{6}{75}[/tex] × [tex]100=8[/tex] %
Hence, the tax rate is [tex]8[/tex]%.
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Solve for x.
80
22
40
12
What is the value of the expression 24 – (7 + 5) ÷ 6 + 8?
The value of the expression 24 – (7 + 5) ÷ 6 + 8 is: 30
What is BODMAS rule?
The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to the BODMAS rule. Any phrase can only be solved correctly if the BODMAS rule or the PEDMAS rule is used.
In the question, The given expression is 24 – (7 + 5) ÷ 6 + 8.
we will solve this expression using the BODMAS rule
which states the order of the operator in which we should use them in an expression.
That is:
B for brackets;
O: for of
D: for Division
M: for Multiplication
A: for Addition
S: for Subtraction
So, using the same in the given expression:
24 – (7 + 5) ÷ 6 + 8
Removing the bracket by solving it first:
⇒24 – 12 ÷ 6 + 8
After that: Divide :
⇒24-2+8
Then Addition:
⇒32-2:
At last: by subtraction, we get:
⇒30
Hence, the value of the expression 24 – (7 + 5) ÷ 6 + 8
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Subtract a-4 from 4a+16 and simplify your answer. The variable a should appear only once in your answer.
Subtracting a-4 from 4a+16 and then simplifying the expression will be 3a + 20.
This is a simple expression and we have to subtract a-4 from 4a+16 and then simplify the answer. This will be:
(4a + 16) - (a - 4)
= 4a - a + 16 + 4
= 3a + 20
In conclusion, based on the calculation above, the answer is 3a + 20.
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The Newbridge Spartans are painting their gymnasium. They need to paint 2,224 square feet. If they have already painted 922 square feet, how many more square feet do they have left?
Answer:
1,302 square feet
Step-by-step explanation:
Be
A = 2,224 total square feet to paint
B = 922 square feet already painted
C =? square feet left to paint
According to the description given,
A = B + C
Isolating C,
C = A - B
C = 2,224 - 922
C = 1,302 square feet left to paint
Hope this helps!
The radius of circle O is 24,and OC = 11. What is the length of AB?
Answer: The correct option is (A) 42.7 units.
Step-by-step explanation: Given that the radius of the circle center at O is 24 units and OC is 11 units.
We are to find the length of chord AB.
We have,
in the right-angled triangle OCB (m∠OCB = 90°),
OB = 24 units and OC = 11 units.
Using Pythagoras theorem in ΔOCB, we have
[tex]OB^2=OC^2+BC^2\\\\\Rightarrow BC=\sqrt{OB^2-OC^2}\\\\\Rightarrow BC=\sqrt{24^2-11^2}\\\\\Rightarrow BC=\sqrt{576-121}\\\\\Rightarrow BC=\sqrt{455}\\\\\Rightarrow BC=21.33.[/tex]
Since OC is perpendicular to chord AB, so AC = BC.
Therefore, we get
[tex]AB=AC+BC=2\times BC=2\times 21.33=42.66=42.7.[/tex]
Thus, the required length of AB is 42.7 units.
Option (A) is CORRECT.
Is there a direct proportion in 2y-5=x? If there is one, what is the constant of proportionality?
Thomas ordered 2 Japanese comic books and twice that number of American comic books. He also ordered 4 Spanish comic books. Thomas told his mom he ordered 8 comic books.
Was Thomas's calculation reasonable?
A.
Yes, it is reasonable because 2 + 2 + 4 = 8.
B.
No, it is not reasonable because 2 + 4 = 6.
C.
No, it is not reasonable because 2 + 4 + 4 = 10.
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This system has one solution.
{y=−2x+4y
{=x2+4x+13
What is the y-coordinate of the solution?
Enter your answer in the box. y =[]
Answer:
The y-coordinate of the solution is, 10
Step-by-step explanation:
Given the system of equation:
[tex]y = -2x+4[/tex] ....[1]
[tex]y=x^2+4x+13[/tex] ....[2]
Equate the equation [1] and [2] we have;
[tex]-2x+4 = x^2+4x+13[/tex]
Add 2x to both sides of an equation:
[tex]4 = x^2+6x+13[/tex]
Subtract 4 from both sides we have;
[tex]0= x^2+6x+9[/tex]
or
[tex]x^2+6x+9=0[/tex]
Using perfect square:
[tex](x+a)^2 = x^2+2ax+a^2[/tex]
⇒We can write the equation as:
[tex]x^2+2 \cdot 3x+3^2=0[/tex]
then;
[tex](x+3)^2 = 0[/tex]
⇒[tex]x+3 = 0[/tex]
Subtract 3 from both sides we have;
x = -3
Substitute value of x in [1] we have;
[tex]y = -2(-3)+4[/tex]
⇒[tex]y =6+4=10[/tex]
Solution for the given system of equation = (-3, 10)
Therefore, the y-coordinate of the solution is, 10