The area of each of the patios is 1600 m².
The mason builds two patios with the same area. One of the patios is square, and the other is rectangular. The rectangular patio is 10 m longer but 8 m less wide than the square patio. We need to find the area of each patio.
Let the side length of the square patio be denoted by the variable "x". The area of the square can be calculated as follows.
A1 = x²
The length and breadth of the rectangular patio is "x + 10" and "x - 8", respectively. The area of the rectangular patio is calculated below.
A2 = (x + 10)*(x - 8)
A2 = x² + 2x - 80
We know that the areas of both patios are equal.
A1 = A2
x² = x² + 2x - 80
2x = 80
x = 40
Hence, the area of each patio is A = x² = 40² = 1600 m².
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Nick’s youth group has 20 regular students that attend weekly get togethers. They saved up enough money for each person to go swimming 15 times each with the daily pay plan. After they saved that amount, they found out they can use the early pay plan and save money. They plan to donate their savings to the church since it’s in need of a new sound system. How much money will they be able to donate with the savings from all 20 youth? (Please show all your work for full credit)
The money that the group will be able to donate with the savings from all 20 youth is $1400.
What is the amount?Let the daily pay plan for each youth = y.
Daily pay plan for 20 youths = 20y
Weekly pay plan = 7 × 20y = 140y
Assuming each youth saves $10 daily
Daily savings for 20 youth:
= 20 × $10
= $200
Weekly savings for 20 youth:
= 7 × $200
= $1400
If they used the early pay plan 140y to go swimming, they saved $1400 which they donated to the church.
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a) Factorise 3x²+ 13x10
Answer:
(3x+10)(x+1)
Step-by-step explanation:
This is the answer for 3x^2+13x+10.
I think you made an error while typing.
Hope this helps!
The diameter of holes for a cable harness is known to have a normal distribution with a standard deviation of 0. 01 inch. A random sample of size 10 yields an average diameter of 1. 5045 inch. Find the 99% and 95% two-tailed/two-sided confidence intervals on the mean diameter and explain the difference of the interval between the two confidence levels.
For the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.
As given in the question,
Confidence interval for population mean is given by:
[tex]\bar{x}[/tex] ± z × ( σ / √n)
Where,
σ = population standard deviation.
n= sample size
[tex]\bar{x}[/tex] = Sample mean
Given values from the random sample size are :
σ = 0.01 inches
n= 10
[tex]\bar{x}[/tex] = 1.5045
Critical value confidence interval (using x-value table)
z for 99% = 2.576 and Significance level = 0.01
z for 95% = 1.960 and Significance level = 0.05
99% two-sided confidence interval on the mean hole diameter is equal to :
[tex]\bar{x}[/tex] ± z × ( σ / √n)
= 1.5045 ± 2.576 × ( 0.01 / √10)
= 1.5045 ± 0.00815 (approximately)
= 1.5045 - 0.00815 , 1.5045 + 0.00815
= ( 1.49635 , 1.51265 )
95% two-sided confidence interval on the mean hole diameter is equal to :
[tex]\bar{x}[/tex] ± z × ( σ / √n)
= 1.5045 ± 1.960 × ( 0.01 / √10)
= 1.5045 ± 0.00620 (approximately)
= 1.5045 - 0.00620 , 1.5045 + 0.00620
= ( 1.4983 , 1.5107 )
Therefore, for the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.
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Find the value of X that makes lines u and v parallel 7-12
The value of x that makes lines u and v parallel is 6. Option A is correct.
First, let us understand the angles formed by parallel and transversal lines:
The different types of angles are alternate exterior angles, alternate interior angles, corresponding angles, consecutive angles, etc.
From the picture attached,
If the lines u and v are parallel and a third line (transversal) is intersecting these lines at two distinct points,
Both the angles given in the picture will be equal in measure as these angles are alternate exterior angles if u and v are parallel.
20x + 10 = 130 degrees
20x = 130 - 10 degrees
x = 120 / 20 = 6
So, the value of x is 6.
Thus, the value of x that makes lines u and v parallel is 6. Option A is correct.
For question please check the below figure:
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Here are the first six terms of an arithmetic sequence.
1
7 13 19 25 31
a) Find an expression, in terms of n, for the nth term of this sequence.
The nth term of a different sequence is 5n²
b) Work out the 4th term of this sequence. 4th term =
(a) The expression of nth term of arithmetic sequence is [tex]a_n=1+(n-1)6[/tex] and (b) 4th term of the series [tex]a_n=5n^2\\[/tex] is 80.
What is arithmetic sequence?
It is a sequence of numbers which have same difference between two consecutive numbers. The common difference can be any positive number or negative number or even it can be 0.
The six terms of the arithmetic sequence are as follows:
1,7,13,19,25,31
Calculate the common difference as follows:
7-1=6
13-7=6
19-13=6
Since it is an arithmetic sequence hence common difference is 6.
Hence, [tex]d=6[/tex].
Now, substitute value of the first term and the common difference in the following expression of the nth term.
[tex]a_n=a+(n-1)d\\a_n=1+(n-1)6[/tex]
Now, the nth term of another sequence is as follows:
[tex]a_n=5n^2\\[/tex]
Substitute n=4 in the above equation.
[tex]a_4=5(4)^2\\=80[/tex]
Hence, (a) the expression of nth term is [tex]a_n=1+(n-1)6[/tex] and 4th term of the series [tex]a_n=5n^2\\[/tex] is 80.
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which of the following is a heuristic commonly used in problem solving? group of answer choices regression analysis local minimization means-end analysis local maximization functional fixedness
The commonly used technique in problem solving is means-end analysis
One typical heuristic is to define subproblems or subgoals. Means-ends analysis, which entails determining how to close the gap between a goal and the actual situation, is another frequently employed heuristic. You can divide a problem into smaller problems and deal with each one separately by using means-ends analysis.
Heuristic problem-solving entails what?
A problem-solving heuristic is a non-formal, speculative process that, in certain circumstances, produces a solution but not in others. The strategy can be either more or less successful than employing an algorithm because the results of applying a heuristic are unpredictable.
So,therefore the means-end analysis is commonly used technique in problem solving
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Find the value of *p* using Cos. Answer with explanation and I will give brainlist.
Answer:
The angle is approximately 111.199 degrees.
Step-by-step explanation:
Cosine is adjacent over hypotenuse.
The hypotenuse is the longest side of the triangle.
In this cos the hypoteneuse is a. However, we can only use cos on right triangles and on the angles that are not 90 degrees. In this case, p would be the 90 degree angle if we could use cosine.
In this case, you need the law of cosines, not cosine. The law of cosine says [tex]c=\sqrt{a^2+b^2-2 a b cosp}[/tex] where c is the side opposite to the angle, a and b are the sides adjacent to the angle, and p is the angle. The law of cosine works for all the triangles.
Plugging in the numbers:
[tex]5.3=\sqrt{3.6^2+2.8^2-2*3.6*2.8* cosp}\\5.3^2=20.8-20.16* cosp}\\7.29=-20.16*cosp\\cos^{-1}\frac{7.29}{ -20.16}=p\\p=111.198929[/tex]
What is the solution to the system of equations graphed below?
the answer for your question above is (-1,-1) or you could say option no.3
johnny the gambler tosses 6 fair six-sided dice numbered 1 through 6. in order to win the jackpot, he needs a 5 or 6 on exactly 3 of the dice. what are johnny's chances to win?
The probability of Johnny winning is [tex]20 *(\frac{2^3}{3^6} )[/tex].
Given data;
Johnny throws six equal dice with six sides and the numbers 1 through 6 on them. He needs a 5 or 6 on precisely 3 of the dice to take home the prize. What are Johnny's odds of winning?
The probability of 5 or 6 = 2/6
= 1/3
The probability of not 5 or 6 = 4/6
= 2/3
The total probability of getting in exactly 3 chances;
⇒ ⁶C₃ * (1/3)³ * (2/3)³
⇒ [tex]20 *(\frac{2^3}{3^6} )[/tex]
Hence, the chances for Johnny to win are [tex]20 *(\frac{2^3}{3^6} )[/tex].
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What is the slope of the line on this graph? Please help me.
Answer:
2/3
Step-by-step explanation:
the slope is rise over run so y/x
A family buys a studio apartment for $200,000. They pay a down payment of $20,000. a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would an $80,000 down payment be?
Answer:A. 20% B.45%
A= 40,000/40,000/200000=.2 Or 20%b. 90,000/200000=.45
Step-by-step explanation:
hope i helped!
A train journey started at 17 50 and finished at 02 25 the next day.
How long did the train journey take?
Give your answer in hours and minutes
Answer:
8 hours and 35 minutes. (8:35)
Step-by-step explanation:
8 hours and 35 minutes.
515 minutes.
Linear Equation Word Problems
The Bike Rental Shop charges $12 plus $9 an hour for renting a bike. Darnell paid $57 to rent a bike. How many hours did he pay to have the bike checked out?
Answer: 5 hours.
Step-by-step explanation: First you need to subtract the $12 fee from the total to find out how many hours he paid for. 57-12=45. So if he paid $45 at $9 per hour, 45 divided by 9 equals 5.
Which function includes all the ordered pairs in the table
The function that includes all the ordered pairs in the given table is y = -x - 4
First choose two points
First point = (0, -4)
Second point = (2, -6)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (-6 - (-4) / (2 - 0)
= -6 + 4 / 2
= -2 / 2
= -1
Here at X = 0, the value of Y = -4
Therefore the y intercept of the line = -4
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Substitute the values in the slope intercept form
y = -1x - 4
y = -x - 4
Hence, The function that includes all the ordered pairs in the given table is y = -x - 4
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A line passes through the points (2,20) and (9,27) Write a linear function rule in terms of x and y for this line.
The linear function rule of the equation is y = x + 18
How to determine the linear function rule?From the question, the points on the line are given as
(2, 20) and (9, 27).
So, we have the following ordered pairs
(x, y) = (2, 20) and (9, 27).
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (2, 20) and (9, 27).
Substitute the known values in the above equation
So, we have the following equation
Slope = (27 - 20)/(9 - 2)
Evaluate the above quotient
Slope = 1
The equation is then calculated as
y = Slope(x - X) + Y
Substitute the known values in the above equation
So, we have the following equation
y = 1 * (x - 2) + 20
So, we have
y = x + 18
Hence, the equation of the line is y = x + 18
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Brianna and Gavin used partial quotients to show 552 divided by 23
willing to give extra points ( 50 more!)
Briannas work:
Step 1: Subtract (20×23) from 552 to get 92.
Step 2: Subtract (4×23) from 92 to get 0.
Step 3: Add partial quotients.
Gavins work:
Step 1: Subtract (10×23) from 552 to get 322.
Step 2: Subtract (10×23) from 322 to get 92.
Step 3: Subtract (2×23) from 92 to get 46.
Step 4: Subtract (2×23) from 46 to get 0.
Step 5: Add the partial quotients.
Which student(s) correctly calculated the quotient? Explain your answer
The student that correctly used partial quotients to show 552 divided by 23 was Gavin.
What is the purpose of partial quotients?The purpose of partial quotients is to facilitate division as by using partial quotients students can easily divide big numbers by using easy multiples first and then adding the multiplers to find the final divisiors. The recommended numbers to use are 5 or 10.
Which student used this method correctly?Based on the information provided, it can be conclude Gavin was better at applying this method because he used only easy multiples (10, 2) to make the number easier to divide, while Brianna completed the process only through to steps, which is not recommended when applying this method.
In conclusion, Gavin was the one who correctly used the method and calculated the result.
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10x+5y=5x+20 solve for y
The value of y in the expression is y= - (x + 4) or, y= (x -4)
ExpressionAlgebraic expression in mathematics is a phrase that include coefficients, unknown variables operations, and constants
To solve for y in the equation 10x+5y=5x+20 we apply algebraic rule;
Step 1: Collect the like terms by moving the unknown 'ý' to the left side of the equation
5y =5x -10x+20
Step 2: Evaluate the the expression 5y =5x -10x+20
5y = -5x + 20
Step 3: Divide both sides by 5
[tex]\frac{5y }{5}[/tex] = [tex]\frac{-5x +20}{5}[/tex]
y = -5x/5 + 20/5
y = - (x + 4) or, y= (x -4)
Therefore, the value of y in the expression is y= - (x + 4) or, y= (x -4)
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factorise fully 7x^3-35
Answer: 7(x^3-5)
Step-by-step explanation:
the common number between 7 and 35 is seven( 7*1=7, 7*5=35)
so with the 7 outside the parenthesis we end up having inside the parenthesis x^3 and 5 because x=1 and 7*1=7 and the 5 because 7*5=35 so if we distribute the seven we would get the original answer
Answer:
[tex]7(x^3-5)[/tex]
Step-by-step explanation:
Given expression:
[tex]7x^3-35[/tex]
To factor the given expression, begin by rewriting 35 as 7 · 5:
[tex]\implies 7x^3-7 \cdot 5[/tex]
Now factor out the common term 7:
[tex]\implies 7(x^3-5)[/tex]
What is the equation of the line in slope-intercept form?
Answer:
y= [tex]\frac{5}{2}[/tex]X +5
Step-by-step explanation:
2
Determine the volume of the rectangular
prism, if each cube represents 1 unit.
The volume of the rectangular prism is 12 cubic inches
It is given that Each cube represent 1 unit
The base length of the rectangular prism = 4 inches
The base width of the rectangular prism = 3 inches
The height of the rectangular prism = 1 inches
The volume of the rectangular prism = The base length of the rectangular prism × The base width of the rectangular prism × The height of the rectangular prism
Substitute the values in the equation
The volume of the rectangular prism = 4 × 3 × 1
= 12 cubic inches
Hence, the volume of the rectangular prism is 12 cubic inches
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Write the expression without brackets and then simplify.
a) 6 + 5(3x – 2)
The expression when the brackets are removed is 15x - 4
How to rewrite the expression without the brackets?From the question, we have the following expression that can be used in our computation:
6 + 5(3x - 2)
The above expression has brackets
So, we start by expanding the brackets
Solving further, we have
6 + 5(3x - 2) = 6 + 15x - 10
Collect the like terms
This gives
6 + 5(3x - 2) = 15x - 10 + 6
Evaluate the like terms
So, we have
6 + 5(3x - 2) = 15x - 4
Hence, the expression is 15x - 4
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Given N(-6,-8), O(5, 3), P(0, 9), and Q(x, 1). Find a such that NO || PQ.
The value of x is -8.
1).
N(-6,-8), O(5, 3), P(0, 9), and Q(x, 1).
slope between NO = y2 - y1 / x2 - x1
= 3 - (-8) / 5 - (-6)
= 3+8 / 5+6
= 11/11
= 1
slope between PQ = 1-9 / x-0
= -8/x.
Given lines are parallel so there slopes are equal
1 = -8/x
x = -8.
Therefore the value of x is -8.
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Which expressions are equivalent to g16? Check all that apply.
The equivalent expressions are (6^(-4) )^(-4), (6^(-2) )^(-8) and (6^8 )^2
Using exponent property, we have
[tex](a^{m})^{n} = a^{m*n}[/tex]
The given expressions is 6^16
From the question, we have
(6^0 )^16=6^(0×16)
⇒6^0 ≠ 6^16
(6^8 )^8=6^(8×8)
⇒6^64 ≠ 6^16
(6^(-4) )^(-4)=6^(-4x-4)
⇒6^16
(6^(-2) )^(-8)=6^(-2×-8)
⇒6^16
(6^(-1) )^16=6^(-1×16)
⇒6^(-16)≠6^16
(6^8 )^2=6^(8×2)
⇒6^16
Multiplication:
In mathematics, multiplying the numbers is used to find the product of two or more numbers. We frequently perform one of the basic mathematical operations. The simplest basic application is to use multiplication tables. Mathematicians multiply two integers to express the repetitive addition of one number to another. It is possible to contain natural numbers, fractions, integers, whole numbers, and other forms of numbers. M would either be added to itself 'n' times or subtracted from itself when M is multiplied by n.
Complete question:
Which expressions are equivalent to 6^16?
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Can someone please help me
From the given data
a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks
b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km
In the graph,
The x axis represents the Time since start in minutes and the y axis represents the distance from the start in kilometers.
In x axis each block represents 5 minutes
The maximum value of time taken in table = 35 minutes
Then the number of squares wide does the grid need to be so that the data fits on the graph = 35 / 5
= 7 blocks
Part b
If the grid is 20 squares tall
The maximum value of distance = 1.8 km
Then the value of A will be
1.8 / 20 = 0.09 km
Hence, from the given data
a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks
b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km
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Simplify: (3x+4) - (x+2)
Answer:
[tex] \sf \: 2x + 2[/tex]
Step-by-step explanation:
Given expression,
→ (3x + 4) - (x + 2)
Let's simplify the expression,
→ (3x + 4) - (x + 2)
→ 3x + 4 - x - 2
→ (3x - x) + (4 - 2)
→ (2x) + (2)
→ 2x + 2
Hence, the answer is 2x + 2.
The product of -8 and -4 is -32 it is false hope you like it and please give me a five star rating thank you very much hope this helps
Answer:
The answer is false.
Step-by-step explanation:
If you do not already know this, a negative and a negative equals a positive. Therefore, instead of –8 • –4 = –32, the correct answer would be –8 • –4 = 32.
Hope that helps! Have an amazing rest of your day! Brainliest welcome! :)
Answer: is false.
hope this helps
have a good day
Step-by-step explanation:
Mark is reading a new book for his Literature class. The book has a total of 160 pages. Mark’s goal is to complete of the book by the end of the week. If Mark has read 24 pages so far, what fraction of the 1/4 book does Mark have left to read by the end of the week in order to reach his goal?
The fraction left for Mark to read is 17/20.
How to calculate the fraction?From the information illustrated, he wants to complete of the 160 pages book by the end of the week and Mark has read 24 pages so far.
The number of pages left will be:
= 160 - 24
= 136 pages
Therefore, the fraction of pages left will be:
= Number of pages left / Total pages
= 136 / 160
= 17/20
The fraction is 17/20.
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A child's height is 59.3 inches, what is the height of the child in feet? Round your answer to the nearest tenth.
1 ft = 12 in
three boys and three boys are lined up in a row. what is the probability of all three girls being together
The probability that all three girls are together is 0.03
Here we will use the string method
Consider 3 girls as a single element, and consider the other 3 boys as 3 separate elements
So total we have 4 element
So the arrangement of 4 elements is given by 4!
Arrangement of girls inside a single element given by 3!
So the way of getting all girls together is given by 4! × 3! = 24 × 6 =144
Total way of arranging 7 people given by 7! = 5040
Probability = Required cases / Total cases
= 144 / 5040
= 0.03
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reyshel has to carry 20 pounds of clothes everyday 1 pound is about 453.6 grams about how many grams does reyshel have to carry in a day
Answer:9072
Step-by-step explanation:
453.6 x 20 = 9072