Answer:
[tex]10 ft^2[/tex]
Step-by-step explanation:
We are given that
Length of soccer field=336 feet
Width of soccer field=210 ft
Width of soccer table=2.5 feet
We have to find the area of soccer table which is similar to soccer field in size.
Let x be the length of soccer table.
We know that when two figures are similar then ratio of their corresponding sides are equal.
[tex]\frac{336}{x}=\frac{210}{2.5}[/tex]
[tex]x=\frac{336\times 2.5}{210}=4[/tex]
Length of soccer table=4 ft
Area of soccer table=[tex]length\times breadth[/tex]
Area of soccer table=[tex]4\times 2.5=10 ft^2[/tex]
Hence , the area of soccer table=[tex]10 ft^2[/tex]
What is 2x + 11y when x = 4 and y = 2?
A. 30
B. 38
C. 48
D. 136
Solve the given differential equation dN/dt=kN, (k=constant) ...?
Work for 8554 divided by 94
the rainfalls 2 years ago was 10.2 inches.last year total was 20 percent greater. what was last years rainfalls total
write 2.18 as a mixed number in simplest form
The decimal number 2.18 can be written as the mixed number 2 9/50, considering that .18 is equivalent to the fraction 18/100, which simplifies to 9/50.
Explanation:The number 2.18 is not technically a mixed number, but it can be written in a format similar to a mixed number. A mixed number is defined as a number that includes both a whole number and a proper fraction. In this case, the whole number is 2 and the decimal .18 could be viewed as a type of fraction. If we want to express .18 as a fraction, we can convert it to 18/100. This fraction, however, can be further simplified to 9/50 by dividing both the numerator and the denominator by 2. Therefore, we could write 2.18 as the mixed number 2 9/50.
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how would you write 2.04 in words
The graph of f(x) = 6(0.25)x and its reflection across the y-axis, g(x), are shown.
What is the domain of g(x)?
all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers greater than or equal to 0
The correct answer is:
a. all real numbers
When we reflect a function across the y-axis, the x-values change their signs. For the function [tex]\( f(x) = 6(0.25)^x \)[/tex], the domain consists of all real numbers since the function is defined for all real values of x.
When we reflect this function across the y-axis to get g(x), the domain of g(x) remains the same as the original function f(x). This is because reflecting across the y-axis does not affect the x-values for which the function is defined.
So, the correct answer is:
a. all real numbers
What is the common difference d of the sequence?
9, −8, −25, −42, −59, ...
d =
Factor completely 4x2 – 8x – 60
Answer
(4x – 20)(x + 3)
4(x – 1)(x + 15)
4(x – 5)(x + 3)
(4x – 4)(x + 15) ...?
Final answer:
To factor the expression 4x² − 8x − 60 completely, factor out the greatest common factor of 4, then factor the resulting quadratic expression, which results in C. 4(x − 5)(x + 3).
Explanation:
The question asks you to factor completely the quadratic expression [tex]4x^2 - 8x - 60[/tex]To factor this expression, first, look for any common factors among the terms. Here, the common factor is 4. Factoring out the 4 gives you [tex]4(x^2 - 2x - 15).[/tex]Next, we factor the quadratic expression within the parentheses.
We look for two numbers that multiply to give − 15 (the constant term) and add to give − 2 (the coefficient of x). These numbers are − 5 and + 3, so the expression factors further into 4(x − 5)(x + 3).
The completely factored form of the quadratic expression [tex]4x^2 - 8x - 60[/tex] is C. 4(x − 5)(x + 3).
Write 6% as a decimal.
List the integers between the square root of 15 and the square root of 48 ?
What third congruence do you need to prove that ΔADB ΔCDB by AAS?
AB (that equal sign with the ~ above it) BC
AD (that equal sign with the ~ above it) DC
∠ ABD ∠ CBD
∠ DBA ∠ CDB
Solve the systems of equations 6x+3y=9 2x+3y=1
To solve the given system of linear equations, subtract one equation from the other to eliminate the y-variable, then solve for x and substitute back to find y. The solution is x = 2, y = -1.
Explanation:To solve the system of equations 6x + 3y = 9 and 2x + 3y = 1, we can use the subtraction method. We want to find the values of x and y that satisfy both equations simultaneously. Observing that both equations have the term 3y, we can subtract the second equation from the first to eliminate the y-terms:
Subtract the second equation from the first: (6x + 3y) - (2x + 3y) = 9 - 1.Simplify the subtraction: 4x = 8.Divide both sides by 4 to solve for x: x = 2.Substitute x back into one of the original equations to solve for y: 2(2) + 3y = 1.Solve for y: 4 + 3y = 1 --> 3y = -3 --> y = -1.The solution to the system of equations is x = 2, y = -1.
algebra help?
write a function rule for the area of a triangle with a base of 3 cm greater than 5 times its height. what is the area of a triangle when its height is 6 cm?
Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30.
Let x represent Mary's age.
Which inequality represents Mary’s possible age?
A. 0 < x < / = 9
B. 0 < x < / = 18
C. 0 < x < 18
D. 0 < x < 9
2x+3+x<30
3x<27
x<9
The answer would be D.
Nadia wants to fill her rectangular fish tank with water. The fish tank measures 2 ft x 1 ft x 1.5 ft. The water level in her fish tank needs to be at least 0.25 ft from the top. She uses a bucket that hold 1.25 ft^3 of water. How many buckets of water does Nadia need to fill the fish tank?
Nadia needs 2 buckets of water to fill the fish tank.
Explanation:To calculate the volume of water needed to fill the fish tank, we need to find the volume of the tank and subtract the volume of the empty space. The volume of the tank is 2 ft x 1 ft x 1.5 ft = 3 ft³. The volume of the empty space is 2 ft x 1 ft x 0.25 ft = 0.5 ft³. Therefore, the volume of water needed is 3 ft³ - 0.5 ft³ = 2.5 ft³.
Next, we divide the volume of water needed by the volume of water in each bucket to find the number of buckets needed. 2.5 ft³ divided by 1.25 ft³/bucket = 2 buckets. Therefore, Nadia needs 2 buckets of water to fill the fish tank.
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Which of the following represents the graph of f(x) = 2x + 2?
Answer with explanation:
The given function is :
[tex]y= f(x)=2^x+2[/tex]
To plot the graph of this function , we find x, for different integral values of y and x for different integral values of y and plot these points in x y plane.
x 0 1 2 3
y 3 4 6 10
Join these points to get required curve.
A new drug has been found to be effective in treating 75% of the people afflicted by a certain disease. If the drug is administered to 400 people who have this disease, what are the mean and the standard deviation of the number of people for whom the drug can be expected to be effective? (Round your standard deviation to two decimal places.)
Answer:
The mean is 300 and the standard deviation is 8.67.
Step-by-step explanation:
It has been given that the drug has been found to be effective in treating 75% of the people afflicted by a certain disease.
Therefore, probability of success is given by p = 0.75
Now, total number of people affecting from the disease, n = 400
We know the formula for mean, which is given by
[tex]\mu=np\\\mu=400\times 0.75\\\mu=300[/tex]
And the standard deviation is
[tex]\sigma=\sqrt{np(1-p)}\\\sigma=\sqrt{400\cdot0.75(1-0.75)}\\\sigma=8.67[/tex]
Therefore, the mean is 300 and the standard deviation is 8.67.
A quiz consists of 4 true-false questions. What is the probability of getting 100% on the quiz by randomly guessing the answer to all 4 questions?
Answer: The probability of getting 100 % on the quiz is 0.0625.
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Step-by-step explanation:
Since we have given that
Number of true-false questions = 4
Number of chances of answer = 2
1) True,
2) False
Probability of getting correct answer is given by
[tex]\frac{1}{2}[/tex]
Probability of getting 100% on the quiz by randomly guessing the answer to all 4 questions is given by
[tex]\frac{1}{2}^4\\\\=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\\\=\frac{1}{16}\\\\=0.0625[/tex]
Hence, The probability of getting 100 % on the quiz is 0.0625.
Find the Nth term of the following sequence...
7, 27, 47, 67, .....
The price of an item has been reduced by 70% . The original price was $60 . What is the price of the item now?
Final answer:
The original price of the item was $60, and after a 70% reduction, the new price is $18.
Explanation:
The original price of an item was $60. After being reduced by 70%, we need to calculate what the new price will be. We can calculate the amount of discount by multiplying 70% with the original price, which is $60.
To find the discount amount: $60 × 0.70 = $42
Now, subtract the discount amount from the original price to find the new price: $60 - $42 = $18.
Therefore, after a 70% reduction, the new price of the item is $18.
The latest demand equation for your Yoda vs. Alien T-shirts is given by: q = −40x + 800 where q is the number of shirts you can sell in one week if you charge $x per shirt. The Student Council charges you $400 per week for use of their facilities, and the T-shirts cost you $4 each. Find the weekly cost as a function of the unit price x. ...?
The weekly cost as a function of the unit price x can be calculated by subtracting the revenue from the total cost. The revenue is given by the demand equation q = -40x + 800, and the total cost is the sum of the fixed cost and the variable cost. Therefore, the weekly cost as a function of the unit price x is -160x + 3600.
The weekly cost as a function of the unit price x can be calculated by subtracting the revenue from the total cost.
Revenue is given by the demand equation q = -40x + 800, where q is the number of shirts sold at price x.
Total cost is the sum of the fixed cost and the variable cost. The fixed cost is $400 per week for use of the facilities, and the variable cost is $4 per shirt.
Therefore, the weekly cost as a function of the unit price x is given by:
Cost(x) = 400 + 4q = 400 + 4(-40x + 800) = 400 - 160x + 3200 = -160x + 3600
So, the weekly cost as a function of the unit price x is -160x + 3600.
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The are of a rectangle is 525 square centimeters. The ratio of the length to the width is 7: 3. Find the length and the width.
To solve for the rectangle's dimensions, the area 525 cm² is divided by the ratio of length to width (7:3), revealing a width of 15 cm and a length of 35 cm.
To find the length and width of a rectangle with an area of 525 square centimeters and a length-to-width ratio of 7:3, we can use proportions. Let's define the width as w centimeters. Then, since the ratio of the length to the width is 7:3, the length can be represented as (7/3)w centimeters.
The area of a rectangle is given by length imes width. Therefore, we can set up the equation (7/3)w × w = 525 to represent the area. To find w, we solve for w² = (525 × 3) / 7, which gives us w² = 225.
By taking the square root of both sides, we see that w = 15 centimeters. Now to find the length, we use the ratio: length = (7/3) × 15 = 35 centimeters.
A train needs 4 hours to go from the first station to the second. If the third station is 120 miles away and the total travel time must be no more than 7 hours, write an inequality that would let you find the slowest average speed, v, the train could have.
If you invest 1,700$ at an annual interest rate of 8.9% compounded continuously. How much will you have in the account after 10 years have passed?
A: $1, 858.24
B: $20,698.60
C:$41,397.20
D$4, 139.72
Mark can make 42 birdays cakes in 7 days how many birthday cakes can mark make in 5 days?
Answer:
30
Step-by-step explanation:
a landscaper estimates that a set of plants can be installed in six hours by 12 workers the landscaper wants to finish a set of plants in 4 hours assuming that the variables are inversely related how many workers should the landscaper bring to the job
justin has 6 bags of dog food his dogs eat 3/4 bag each day. how long will his dog food last
Solve the inequality. 2>8−43h
Final answer:
To solve the inequality 2 > 8 - 43h, subtract 8 from both sides and divide by -43, then flip the inequality sign. The solution is h > 6/43.
Explanation:
To solve the inequality 2 > 8 - 43h, we need to isolate the variable h. Let's start by subtracting 8 from both sides:
2 - 8 > 8 - 8 - 43h
-6 > -43h
Next, we divide both sides of the inequality by -43, but since we are dividing by a negative number, the inequality sign flips:
-6/-43 < -43h/-43
Simplifying the expression:
6/43 < h
The solution to the inequality is h > 6/43.
The two triangles below are similar. What is the similarity ratio of ΔABC to ΔXYZ?
1:2
2:1
3:2
2:3
To find the similarity ratio of ΔABC to ΔXYZ, compare the corresponding sides of the triangles. The ratio will be one of the named proportions based on the specific measurements of the triangles, which are not provided in the question.
Explanation:The question pertains to finding the similarity ratio of two similar triangles. The similarity ratio of triangles is the ratio of any two corresponding lengths in the triangles. This question specifically asks for the ratio of triangle ΔABC to triangle ΔXYZ. Without the specific lengths provided, a general solution is to compare the corresponding sides of the triangles. For instance, if the length of side AB in ΔABC is twice the length of side XY in ΔXYZ, then the similarity ratio would be 2:1. If it was the other way around, the ratio would be 1:2. Similarly, if AB was three halves the length of XY, the ratio would be 3:2, and if AB was two thirds the length of XY, the ratio would be 2:3. The correct ratio would be one of the options given based on the specific lengths provided in the problem, which are not included in the question as stated.
Final answer:
Without specific side lengths, it's impossible to provide the similarity ratio of ΔABC to ΔXYZ. Additional measures of corresponding sides are needed for such a calculation.
Explanation:
To determine the similarity ratio of two similar triangles, you need to compare the lengths of corresponding sides. However, in the provided question, no specific measurements for the triangles are given, so it is not possible to calculate the exact similarity ratio of ΔABC to ΔXYZ. We would need additional information, such as the lengths of corresponding sides from both triangles, to be able to determine the correct ratio.
The process would involve dividing the length of a side from ΔABC by the length of the corresponding side from ΔXYZ. For instance, if side AB of ΔABC measures 6 cm and the corresponding side XY of ΔXYZ measures 3 cm, then the similarity ratio is 6:3 or simplified as 2:1.