A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.
One possible set could be 3 cm, 4 cm, and 5 cm.
To verify if this set forms a right triangle, we can apply the Pythagorean theorem.
Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.
Adding these two values together gives us 25.
Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.
It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.
There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.
These sets are known as Pythagorean triples.
Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.
In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
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Does (0, 0) make the equation y = 8x true?
Hence, (0, 0) makes the Equation Y = 8x TRUE
0 = 8 * 0
0 = 0
TRUE
Step-by-step explanation:
Identify the X-Intercept:X = 0
Identify the Y-Intercept:Y = 0
Substitute the indicated values:Y = 8 * 0
Substitute the indicated values:0 = 8 * 0
Judge Whether the Equation is TRUE:0 = 8 * 0 is: TRUE
Determine the point:Hence, (0, 0) makes the Equation Y = 8x TRUE0 = 8 * 0
0 = 0
TRUE
Cheers to the person who also gave the (HINT) in the Comment Sections: Which makes the EQUATION (true).Hope it helps!
What are all ordered triples of positive integers (x,y,z) whose products is 4 times their sum, If x < y < z
Answer:
You can factor xz+1−yz+1
by dividing out x−y
Step-by-step explanation:
This shows that x−y
is a power of 2.
But they must only have the same parity-they can both be even. In particular, there are many solutions with z=0
If z=1
you can factor it as (x−y)(x+y)=2100
and you can find a finite number of solutions here. I think, but have not proved, that you will not find any with larger z
steven earns extra money babysitting. He charges $28.75 for 5 hours and $46.00 for 8 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
The equation representing the relationship is: y = $5.75x
This equation shows that Steven charges $5.75 per hour for babysitting.
To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can create an equation based on the given information. We have two data points: $28.75 for 5 hours and $46.00 for 8 hours.
We can assume that the relationship between the hours and the charges is linear, meaning that the rate of charge per hour is constant. Let's calculate this rate:
Rate of charge per hour = (Total charge for 8 hours - Total charge for 5 hours) / (8 hours - 5 hours)
= ($46.00 - $28.75) / (8 hours - 5 hours)
= $17.25 / 3 hours
= $5.75 per hour
Now, we can write the equation to represent the relationship:
y = mx + b
Where:
y is the amount charged
x is the number of hours
m is the rate of charge per hour ($5.75 per hour)
b is the y-intercept (the amount charged when x = 0)
Substituting the values, we have:
y = $5.75x + b
To find the value of b, we can use one of the data points. Let's use the data point of $28.75 for 5 hours:
28.75 = $5.75 * 5 + b
28.75 = 28.75 + b
b = 28.75 - 28.75
b = 0
Therefore, the equation representing the relationship is:
y = $5.75x
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The ages of dogs and cats at an animal shelter are shown. Make a Venn diagram to show the number of animals that are dogs and are over 8 years old. The answer choices are in the pictures below.
The Venn diagram which shows the number of animals that are dogs and are over 8 years old is diagram option D.
What is a Venn diagram?A venn diagram is a diagram representing some sets by contours of closed shapes, such as circles or ellipses and indicating the relationships between the sets by overlapping the shapes to show that the corresponding sets have a non-empty intersection, and by possibly enclosing all of the sets within a universal set represented typically by a rectangle such that the total number of simply connected regions is 2n, where n is the number of depicted sets which are proper subsets of the universal set.
Animals that are dogs and are over 8 years old = 2
Over 8 = 4
Intersection = 3
Complete question?
The ages of dogs and cats at an animal shelter are shown. Make a Venn diagram to show the number of animals that are dogs and are more than 8 years old.
Species Dog Cat Dog Cat Dog Cat
Age 12 9 9 2 2 13
Species Dog Cat Dog Cat Dog Cat
Age 8 12 5 11 10 3
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42. Arun and Vijay are partners in a firm sharing profit & loss in the ratio of 3: 2.
BALANCE SHEET (Extract)
Liabilities = ₹ 0
Assets = Machinery ₹ 2,00,000
If the value of machinery in the Balance Sheet is excess by 100/3%, find the value of machinery to be shown in the New Balance Sheet.
[Ans.: 1,50,000.)
Answer:
₹ 1,50,000
Step-by-step explanation:
You want to know the value of machinery to be shown if the value ₹ 2,00,000 is (100/3)% too high.
ValueThe value shown (₹ 2,00,000) is (100/3)% more than the actual value, so the relation is ...
₹ 2,00,000 = actual value + (100/3)% × actual value
₹ 2,00,000 = actual value · (1 +1/3)
Multiplying by 1/(1 +1/3), we have ...
actual value = (3/4)·(₹ 2,00,000) = ₹ 1,50,000
The value of machinery to be shown in the New Balance Sheet is ₹1,50,000.
__
Additional comment
(100/3)% = (100/3)/100 = 1/3
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in economics functions that involve revenue cost and profit are used. For example suppose that R(x) and C(x) denote the total revenue and total cost, respectively of the producing a new grocery cart for wholesaler. Then the difference P(x) =R(x)-C(x) represents the total profit for producing x carts. Given R(x)=60x- o.4x^2 and
a)P(x)
b) R(70),C,(70),and P(70)
c) using the graphing calculator,graph the three functions in the viewing window[0,160,0,3200]
a) P(x) = 60x - 0.4x^2 - C(x)
b) R(70) = 60(70) - 0.4(70)^2, C(70) is missing. P(70) = R(70) - C(70), incomplete without C(70).
c) Graph R(x) = 60x - 0.4x^2, C(x) not given, P(x) = R(x) - C(x), incomplete without C(x) equation.
a) To find P(x), we need to subtract C(x) from R(x):
P(x) = R(x) - C(x)
= (60x - 0.4x^2) - C(x)
b) To find R(70), C(70), and P(70), we substitute x = 70 into the respective functions:
R(70) = 60(70) - 0.4(70)^2
= 4200 - 0.4(4900)
= 4200 - 1960
= 2240
C(70) = ??? (The equation for total cost, C(x), is not provided. Please provide the equation for C(x) to calculate C(70).)
P(70) = R(70) - C(70)
= 2240 - C(70) (We need the value of C(70) to calculate P(70).)
c) To graph the functions R(x), C(x), and P(x) in the given viewing window [0, 160] for x and [0, 3200] for y, we can use a graphing calculator or software. However, since the equation for C(x) is not provided, we are unable to graph the complete functions.
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solve for w in the equation
Answer:
w = 5
Step-by-step explanation:
[tex] log_{2}(32) = w \\ 32 = {2}^{w} \\ {2}^{w} = {2}^{5} \\ w = 5[/tex]
ABM B students claims that more than 10% of their section wears glasses. A survey among 35 students pose that 8 of them are wearing glasses. Does this provide sufficient evidence that more than 10% of ABM B students wear glasses?
Use a=0.01 and p-value approach.
The p-value (0.036) is less than the significance level (α = 0.01), we reject the null hypothesis.
To determine if there is sufficient evidence to support the claim that more than 10% of ABM B students wear glasses, we can conduct a hypothesis test using the p-value approach.
Null hypothesis (H0): The proportion of ABM B students wearing glasses is equal to or less than 10%.
Alternative hypothesis (Ha): The proportion of ABM B students wearing glasses is greater than 10%.
Let p be the true proportion of ABM B students wearing glasses. We want to test if p > 0.10.
Given that we have conducted a survey of 35 students and found that 8 of them are wearing glasses, we can calculate the sample proportion, denoted by [tex]\bar p[/tex], as 8/35 ≈ 0.229.
Next, we calculate the test statistic, which follows an approximate standard normal distribution under the null hypothesis.
Test statistic: z = ([tex]\bar p[/tex] - p) / sqrt(p * (1 - p) / n)
= (0.229 - 0.10) / sqrt(0.10 * (1 - 0.10) / 35)
≈ 1.798
To determine the p-value, we find the probability of observing a test statistic greater than or equal to 1.798 assuming the null hypothesis is true.
Using a standard normal distribution table or a calculator, we find that the probability of observing a test statistic as extreme as 1.798 is approximately 0.036.
Since the p-value (0.036) is less than the significance level (α = 0.01), we reject the null hypothesis.
Therefore, we have sufficient evidence to support the claim that more than 10% of ABM B students wear glasses based on the survey results.
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How do I solve for this?
A mass suspended from a spring oscillates in simple harmonic motion. The mass completes 5 cycles every second, and the distance between the highest point and the lowest point of the oscillation is 12 cm. Find an equation of the form y = a sin
To find the equation for the simple harmonic motion of a mass suspended from a spring, you need to determine the amplitude (a) and the sine function. The equation is y = a sin (2π/T) t, where T is the period.
Explanation:To find the equation of the form y = a sin for the simple harmonic motion of a mass suspended from a spring, we need to determine the values of a and sin.
The given information states that the mass completes 5 cycles every second and the distance between the highest point and the lowest point of the oscillation is 12 cm. The period (T) of one cycle can be calculated by dividing 1 second by the number of cycles per second. In this case, T = 1/5 = 0.2 seconds. The amplitude (a) is half of the total distance between the highest and lowest points, which is 12 cm. Therefore, a = 12/2 = 6 cm.Now we can plug these values into the equation
y = a sin (2π/T) t,
where
T is the period t is the time.So, the equation for the simple harmonic motion is y = 6 sin (2π/0.2) t.
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Convert each of the given equations from polar to rectangular form.
r=tanθ
r=2/(1-sinθ)
Step-by-step explanation:
To convert equations from polar form to rectangular form, we can use the following conversions:
1. For the equation r = tan(θ):
In rectangular form, we can express r in terms of x and y using the relationships:
r = √(x² + y²)
tan(θ) = y / x
Substituting these values into the equation r = tan(θ), we get:
√(x² + y²) = y / x
Squaring both sides of the equation, we have:
x² + y² = y² / x²
Multiplying both sides by x², we get:
x⁴ + x²y² = y²
Therefore, the rectangular form of the equation r = tan(θ) is:
x⁴ + x²y² - y² = 0
2. For the equation r = 2 / (1 - sin(θ)):
Using the same conversions as above, we have:
r = √(x² + y²)
1 - sin(θ) = 1 - y / r
Substituting these values into the equation r = 2 / (1 - sin(θ)), we get:
√(x² + y²) = 2 / (1 - y / √(x² + y²))
Squaring both sides of the equation, we have:
x² + y² = 4 / (1 - y / √(x² + y²))
Multiplying both sides by (1 - y / √(x² + y²)), we get:
(x² + y²)(1 - y / √(x² + y²)) = 4
Expanding and simplifying the equation, we have:
x² + y² - y = 4 - 4y / √(x² + y²)
Multiplying both sides by √(x² + y²), we get:
(x² + y² - y)√(x² + y²) = 4√(x² + y²) - 4y
Therefore, the rectangular form of the equation r = 2 / (1 - sin(θ)) is:
(x² + y² - y)√(x² + y²) = 4√(x² + y²) - 4y
Gabe Amedeo, a nuclear physicist, needs 60 liters of a 40% acid solution. He currently has a 20% solution and a 50% solution. How many liters of each does he need to make the needed 60 liters of 40% acid solution
Gabe Amedeo needs 20 liters of the 20% solution and 40 liters of the 50% solution to make the 60 liters of 40% acid solution.
To make a 60-liter solution of 40% acid concentration, Gabe Amedeo needs to determine the amount of the 20% and 50% solutions required. Let's assume he needs x liters of the 20% solution and (60 - x) liters of the 50% solution.
To find the amount of acid in each solution, we multiply the volume by the acid concentration. For the 20% solution, the amount of acid is 0.20x liters, and for the 50% solution, it is 0.50(60 - x) liters.
To achieve a 40% concentration in the final solution, the total amount of acid should be 0.40(60) liters, which is 24 liters.
Setting up an equation based on the acid quantities:
0.20x + 0.50(60 - x) = 24
Solving this equation, we find that x = 20. Therefore, Gabe needs 20 liters of the 20% solution and (60 - 20) = 40 liters of the 50% solution to obtain the desired 60 liters of a 40% acid solution.
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What is the slope of a line that is perpendicular to the line whose equation is
3x +5y = 4?
=================================================
Explanation:
The standard form equation Ax+By = C has the slope m = -A/B.
Flip the fraction to get -B/A and flip the sign to get B/A.
Original slope = -A/BPerpendicular slope = B/AMultiplying these fractions together gets us -1. Note: A and B must be nonzero.
-----------
In the case of 3x+5y = 4, the slope is -A/B = -3/5
The negative reciprocal is -(-5/3) = 5/3 which is the perpendicular slope
(-3/5)*(5/3) = -1
Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents. Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.
Based on the scatterplot, the form of the relationshipbetween fire spread rate and wind speed can be described as a positive correlation.
How is this so?As wind speed increases,the fire spread rate also tends to increase.
b. Direction -
Based on the given scatterplot,the direction of the relationship between fire spread rate and wind speed appears to be positive.
As the wind speed increases,the fire spread rate generally tends to increase as well.
c. Strength -
The scatterplot suggests a moderate to strong relationship between fire spread rate and wind speed.
The data points exhibit a somewhat linear pattern, indicating that there is a noticeable association between these variables.
The firespread rate tends to increase consistently as the wind speed increases, suggesting a relatively strong positive correlation between the two factors.
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Full Question:
Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents.
Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.
Wind Speed (miles/hour) Fire Spread Rate (feet/minute)
0.76 0
1.78 2
3.34 4
5.38 6
8.10 8
11.75 10
16.70 12
A scatterplot of these data is shown here -
1. Based on the scatterplot, how would you describe the following with regard to the relationship between fire spread rate and wind speed?
a. Form:
b. Direction:
c. Strength:
a complement of another good
Question 10
10 p
Until recently, Cynthia's Cycles rented bicycles for $8 and they rented 320 bicycles per month. They just
raised the price to $12 and as a result, they only rent 280 bicycles per month.
Using the midpoint rule, find the price elasticity of demand for Cynthia's Cycles. [a]
The price elasticity of demand is calculated using the midpoint formula:
Price Elasticity of Demand = (Percentage Change in Quantity Demanded / Percentage Change in Price) * 100
To find the percentage change in quantity demanded, we use the formula:
Percentage Change in Quantity Demanded = (New Quantity Demanded - Original Quantity Demanded) / ((New Quantity Demanded + Original Quantity Demanded) / 2) * 100
And for the percentage change in price, we use the formula:
Percentage Change in Price = (New Price - Original Price) / ((New Price + Original Price) / 2) * 100
Given the information provided:
Original price (P1) = $8
Original quantity demanded (Q1) = 320 bicycles
New price (P2) = $12
New quantity demanded (Q2) = 280 bicycles
Let's calculate the percentage changes:
Percentage Change in Quantity Demanded:
Percentage Change in Quantity Demanded = (280 - 320) / ((280 + 320) / 2) * 100
Percentage Change in Price:
Percentage Change in Price = (12 - 8) / ((12 + 8) / 2) * 100
Now we can calculate the price elasticity of demand using the midpoint formula:
Price Elasticity of Demand = (Percentage Change in Quantity Demanded / Percentage Change in Price) * 100
Substituting the calculated values, we have:
Price Elasticity of Demand = ((280 - 320) / ((280 + 320) / 2) * 100) / ((12 - 8) / ((12 + 8) / 2) * 100)
Simplifying further:
Price Elasticity of Demand = (-40) / (20 / 10)
Price Elasticity of Demand = -2
Therefore, the price elasticity of demand for Cynthia's Cycles is -2.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
Please look at my photo. Thank you.
The minimum unit cost for this problem is given as follows:
$340.
How to obtain the minimum unit cost?The quadratic function defining the cost for this problem is given as follows:
C(x) = 0.1x² - 68x + 19017.
The coefficients are given as follows:
a = 0.1, b = -68, c = 19017.
As a > 0, the minimum unit cost is the x-coordinate of the vertex, obtained as follows:
x = -b/2a
x = 68/0.2
x = $340.
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Link went into two different houses and broke some clay pots to collect some rupees. In the first house he collected 15 green rupees and 5 red rupees for a total value of 115. The second house he collected 7 green rupees and 4 red rupees for a total value of 87. What System of Equations represents this if x represents the value of a green rupee and y represents the value of a red rupee.
The system of equations that represents Link's rupee collection would be in the form of: 15x + 5y = 1157x + 4y = 87
Let x represent the value of a green rupee and y represent the value of a red rupee. Link went into two different houses and broke some clay pots to collect some rupees. He collected 15 green rupees and 5 red rupees in the first house, and 7 green rupees and 4 red rupees in the second house.
Link's collection of green and red rupees can be represented in the form of a system of equations. Let's use x and y as variables for green and red rupees, respectively. In the first house, Link collected 15 green rupees and 5 red rupees, with a total value of 115.
This can be expressed as: 15x + 5y = 115. Simplifying this equation: 3x + y = 23--- Equation (1) In the second house, Link collected 7 green rupees and 4 red rupees, with a total value of 87. This can be expressed as: 7x + 4y = 87.
Simplifying this equation: 7x/7 + 4y/7 = 87/7x + (4/7)y = 12.43x + y = 12.43 (multiplying both sides by 3)--- Equation (2)Thus, the system of equations that represents Link's rupee collection would be in the form of: 15x + 5y = 115 (Equation 1) 7x + 4y = 87 (Equation 2)
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For a function f(z) and a particular input value z = a, then we may write the difference
quotient as
f(a+h)-f(a)
h
where h 0.
Now, let f(z)=z³-14z and consider the input value a = 3. We could now write the
difference quotient as
f(3+h)-f(3)
h
where h / 0.
Use this difference quotient to calculate the average rate of change of f(z) from z = 3 to
z=3+h for the following particular values of h.
When h = 0.2, the average rate of change of f(z) is
When h= 0.1, the average rate of change of f(z) is
When h= 0.01, the average rate of change of f(a) is
When h= -0.01, the average rate of change of f(z) is
When h-0.1, the average rate of change of f(z) is
When h=-0.2, the average rate of change of f(z) is
A class of 33 children were asked to name their favourite colour.
All the results are shown in the bar chart below.
Put the correct numbers on the vertical axis of the bar chart.
Step-by-step explanation:
There are ELEVEN colored boxes for the 33 children .....so each box represents THREE
the numbers on the L from the bottom up should then be
3 6 9 12 15
An investor wants to save money to purchase real estate. She buys an annuity with monthly payments that earn 5% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 15 years if each monthly payment is $68.
Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the
list of financial formulas.
The total value of the annuity in 15 years, with monthly payments of $68 and an interest rate of 5% compounded monthly, would be approximately $30,063.89.
To determine the total value of the annuity in 15 years if each monthly payment is $68 and payments will be made at the end of each month, we have to make use of the concept of future value of an annuity. This will help us in finding out the total value of annuity.
The future value of an annuity is the accumulated total value of all the payments or deposits made, including the interest earned over the specified period. It represents the amount of money that will be available at a future date, considering the compounding effect of interest.
The formula to calculate the future value of an annuity is:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
Where:
FV is the future value of the annuity,
P is the amount of each payment or deposit,
r is the interest rate per period,
n is the number of payment periods.
In this case, we have been given monthly payment as $68, 5% as the interest rate per year, and number of payment period as 15 years.
So, by substituting all the given data in the equation to find future value of an annuity, we get:
[tex]FV = 68 * [(1 + 0.05/12)^{180} - 1] / (0.05/12)[/tex]
[tex]FV = 68 * [(1.00416667)^{180} - 1] / (0.00416667)[/tex]
[tex]FV = 68 * [2.8696931 - 1] / 0.00416667[/tex]
[tex]FV = 68 * 1.8696931 / 0.00416667[/tex]
FV ≈ $30,063.89
Therefore, the total value of the annuity in 15 years, with monthly payments of $68 and an interest rate of 5% compounded monthly, would be approximately $30,063.89.
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In the addition of two four-digit numbers below, each different letter represents a different digit. Compute the value of the sum. AABB + BACC = CCBA Show the steps involved
Answer:
The sum is 9954----------------------------------------
Write the sum as:
AABB
+ BACC
---------
CCBA
First, in order all three numbers be 4-digit, all A, B and C should be ≠ 0.
Next, from units and tens columns we conclude that:
C = 9 and B = A + 1.Now, from hundreds column, A + A = 9, it means:
A = 4 and 1 was carried over from the sum on the tens column.Finally,
B = A + 1 = 4 + 1 = 5.Testing what we have:
4455 + 5499 = 9954All look good!
To compute the value of the sum, we could add up the figures 4455 and 5499 to arrive at the result 9954.
How to compute the figuresTo compute the figures, we are given a set of letters that represent the arrangement of the figures. If we give the value of A to equal 4, B = 5, and C = 9, we can obtain a sum of the figures in the following way:
4455
+ 5499
= 9954
So, the summation of the figures with figures corresponding to the letter arrangement gives us the sum of 9954.
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The perimeter of a rectangular swimming pool is 154m.its lengh is 2m more than twice its breadth.what is the length and breadth of the pool (also find the equation and use transpose method)
Let's denote the length of the pool as L and the breadth as B.
According to the given information, the perimeter of the rectangular swimming pool is 154m. The formula for the perimeter of a rectangle is given by:
[tex]\displaystyle\sf P = 2(L + B)[/tex]
Substituting the given value of the perimeter, we have:
[tex]\displaystyle\sf 154 = 2(L + B)[/tex]
Dividing both sides of the equation by 2, we get:
[tex]\displaystyle\sf 77 = L + B[/tex]
We are also given that the length of the pool is 2m more than twice its breadth. Mathematically, we can express this as:
[tex]\displaystyle\sf L = 2B + 2[/tex]
Now we can substitute this value of L in terms of B into the equation we obtained earlier:
[tex]\displaystyle\sf 77 = (2B + 2) + B[/tex]
Simplifying the equation, we have:
[tex]\displaystyle\sf 77 = 3B + 2[/tex]
Subtracting 2 from both sides of the equation, we get:
[tex]\displaystyle\sf 75 = 3B[/tex]
Dividing both sides of the equation by 3, we obtain:
[tex]\displaystyle\sf B = 25[/tex]
Now we can substitute this value of B into the equation for L:
[tex]\displaystyle\sf L = 2(25) + 2[/tex]
Simplifying the equation, we have:
[tex]\displaystyle\sf L = 52[/tex]
Therefore, the length of the pool is 52m and the breadth is 25m.
Using the transpose method, we can rearrange the equation [tex]\displaystyle\sf 77 = L + B[/tex] to solve for L:
[tex]\displaystyle\sf L = 77 - B[/tex]
Then, substituting this expression for L in the equation [tex]\displaystyle\sf L = 2B + 2[/tex], we have:
[tex]\displaystyle\sf 77 - B = 2B + 2[/tex]
Adding B to both sides of the equation, we get:
[tex]\displaystyle\sf 77 = 3B + 2[/tex]
Subtracting 2 from both sides of the equation, we obtain:
[tex]\displaystyle\sf 75 = 3B[/tex]
Finally, dividing both sides of the equation by 3, we find:
[tex]\displaystyle\sf B = 25[/tex]
By substituting this value of B back into the equation [tex]\displaystyle\sf L = 77 - B[/tex], we get:
[tex]\displaystyle\sf L = 77 - 25 = 52[/tex]
Hence, the length of the pool is 52m and the breadth is 25m.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
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first 5 terms in the sequence
Answer:
To find the first five terms in the recursive sequence defined by the given formula, we start with the initial term a₁ and use the recursion formula An = 5 * An-1.
Given that the first term a₁ is not specified, I will assume it to be 1 for this example. Using this assumption, we can calculate the first five terms of the sequence:
a₁ = 1 (assumed)
a₂ = 5 * a₁ = 5 * 1 = 5
a₃ = 5 * a₂ = 5 * 5 = 25
a₄ = 5 * a₃ = 5 * 25 = 125
a₅ = 5 * a₄ = 5 * 125 = 625
So, the first five terms in the recursive sequence are:
(1, 5, 25, 125, 625)
None of the options you provided (such as {1, 풀, 29, 20, 734}, {23 38 {,,,,} 101 10 10}, or {17,4,523}) match the calculated terms.
Step-by-step explanation:
Order the square root of 40, negative 6.2 repeating, twenty-five fourths, and negative six and five eighths from least to greatest.
Step-by-step explanation:
first, let's convert our numbers into common forms to make them easier to work with;
√40 = 6.325 (3dp)-6.2 recurring remains the same --> - 6.222...25/4: four can go into 25 six times with one left over, so therefore 25/4 =6.25 (because 1 lot of 1/4 = 0.25)-6 and 5/8s: 1/8 is half of 1/4 so therefore 1/8 must equal 0.125, making 5/8s equal to 0.625 (5 x 0.125), and so 6 and 5/8s equals -6.625Ordered From least to greatest: -6.625, -6.2 repeating, 25/4s, and √40
DON'T FORGET THAT IT IS NEGATIVE 6.2222 AND NEGATIVE -6 AND 5/8s
A company that manufactures machine parts determines that q units of a part will be sold when the price is p = 110 – q dollars per unit. The total cost to produce those q units is C(g) dollars, where C(q) = q³ - 25q² + 2q +3,000
a. For what value of q is the profit maximized?
b. Find the consumer surplus at the level of production that corresponds to maximum profit.
Step-by-step explanation:
a. To find the value of q that maximizes profit, we need to find the value of q that maximizes revenue and then subtract the cost to produce that quantity. Revenue is equal to the price per unit multiplied by the quantity sold, or R(q) = q(110 - q). Thus, profit is given by P(q) = R(q) - C(q) = q(110 - q) - (q³ - 25q² + 2q + 3,000). Simplifying this expression, we get P(q) = -q³ + 85q² - 108q - 3,000. To find the value of q that maximizes profit, we need to take the derivative of P(q) with respect to q and set it equal to zero. This gives us -3q² + 170q - 108 = 0. Solving for q using the quadratic formula, we get q = 4.89 or q = 23.44. Since the company cannot produce a fractional quantity of parts, the value of q that maximizes profit is 23.
b. Consumer surplus is the difference between the maximum price that a consumer is willing to pay for a good and the actual price that they pay. In this case, the maximum price that a consumer is willing to pay is given by the demand function, p = 110 - q. At the level of production that corresponds to maximum profit, q = 23, so the price per unit is p = 110 - 23 = 87 dollars. The consumer surplus is then given by the integral of the demand function from q = 0 to q = 23, or ∫[0,23] (110 - q) dq = 23(110) - (23²/2) = 1,955 dollars.
Malik visits an ice cream parlor four times a week. On Monday he orders a scoop of pistachio ice
cream, on Tuesday he orders a scoop of mango ice cream, and on Wednesday and Thursday, he orders
a scoop of chocolate.
In one year (52 weeks), Malik will order..........
scoops of pistachio ice cream,..............
scoops of mango ice cream, and..................
scoops of
chocolate ice cream.
One year, Malik will order:
52 scoops of pistachio ice cream
52 scoops of mango ice cream
104 scoops of chocolate ice cream.
In one year (52 weeks), Malik visits the ice cream parlor four times a week. Let's calculate the total number of scoops of each flavor he will order:
Scoops of pistachio ice cream: Since he orders a scoop of pistachio ice cream only on Mondays, and there are 52 weeks in a year, Malik will order 52 scoops of pistachio ice cream.
Scoops of mango ice cream: Since he orders a scoop of mango ice cream only on Tuesdays, and there are 52 weeks in a year, Malik will order 52 scoops of mango ice cream.
Scoops of chocolate ice cream: Malik orders a scoop of chocolate ice cream on both Wednesdays and Thursdays. Since there are two days (Wednesday and Thursday) each week when he orders chocolate ice cream, Malik will order 2 scoops of chocolate ice cream per week. In 52 weeks, he will order a total of 2 x 52 = 104 scoops of chocolate ice cream.
So, in one year, Malik will order:
52 scoops of pistachio ice cream
52 scoops of mango ice cream
104 scoops of chocolate ice cream.
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Reason Consider the function f(x) = 2|x|.
a. Graph fover the domain -4 ≤x≤ 4.
b. What is the rate of change over the interval 0≤x≤4?
c. How is the rate of change over this interval related to the form of the function? .
a. To graph the function f(x) = 2|x| over the domain -4 ≤ x ≤ 4, we consider the absolute value function |x|. The absolute value of a number gives us its distance from zero on the number line. Since we are taking the absolute value of x, the function will always be positive or zero.
For x < 0, the expression inside the absolute value brackets, -x, will be positive. Therefore, f(x) = 2(-x) = -2x.
For x ≥ 0, the expression inside the absolute value brackets, x, will be positive. Therefore, f(x) = 2x.
We can plot the points for both cases and obtain the graph as follows:
For x < 0:
When x = -4, f(x) = 2(-4) = -8.
When x = -3, f(x) = 2(-3) = -6.
When x = -2, f(x) = 2(-2) = -4.
When x = -1, f(x) = 2(-1) = -2.
For x ≥ 0:
When x = 0, f(x) = 2(0) = 0.
When x = 1, f(x) = 2(1) = 2.
When x = 2, f(x) = 2(2) = 4.
When x = 3, f(x) = 2(3) = 6.
When x = 4, f(x) = 2(4) = 8.
Plotting these points, we get a V-shaped graph with the vertex at (0, 0) and the arms extending upwards and downwards.
b. The rate of change over the interval 0 ≤ x ≤ 4 can be determined by calculating the slope of the line connecting two points on the graph. Taking any two points on the interval, for example, (0, 0) and (4, 8), we can calculate the slope as (change in y) / (change in x):
Slope = (8 - 0) / (4 - 0) = 8 / 4 = 2.
Therefore, the rate of change over the interval 0 ≤ x ≤ 4 is 2.
c. The rate of change over this interval, which is 2, is constant. It means that for every unit increase in x, the value of f(x) increases by 2. This is consistent with the linear relationship between x and f(x) within this interval. The graph of the function f(x) = 2|x| has a constant slope because the absolute value function changes linearly, resulting in a consistent rate of change for the function f(x).
Find the exact value of the area of the shaded region. The length of the side of the grid squares is 1 unit.
RSM problem
The area of the shaded part is
81.963 square unitsHow to find the area of the shaded regionThe region comprises of 6 quarter circles with different radius
Area of the quarter circles are as follows
1.
= 3.142 * 8² / 4
= 50.272
2.
= 3.142 * 5² / 4
= 19.638
3.
= 3.142 * 3² / 4
= 7.07
4.
= 3.142 * 2² / 4
= 3.142
5 and 6.
= (3.142 * 1² / 4) * 2
= 1.571
Area of the shaded part
= 50.272 + 19.638 + 7.07 + 3.142 + 1.571
= 81.963 square units
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The following table shows the salary of 7 people in an office last year.
Name Income
Andy £13500
Bevan £27500
Cheryl £13750
Deva £79000
Elliott £19250
Frankie £29000
Grace £15000
a) Work out the mean income to 2 DP.
b) Deva was given a large bonus for 30 years service.
Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?
Answer:
a) The mean income to 2 DP is £28142.86
b) The mean income excluding Deva's income is £19666.67
Step-by-step explanation:
The formula for mean is,
m = sum of terms/number of terms
Now n = number of terms = number of people = 7
And in the sum, we will input their salaries, so we get,
a) m = (13500 + 27500 + 13750 + 79000 + 19250 + 29000 + 15000)/7
m = 197000/7
m = 28142.85714
to 2 DP, we get,
m = £28142.86
b) Excluding Deva's income, i.e. excluding 79000, and then, the number of people becomes 6, so we get the mean,
Mean without Deva's Income = (13500 + 27500 + 13750 + 19250 + 29000 + 15000)/6
Mean without Deva's Income = 118000/6
Mean without Deva's Income = 19666.66667
to 2 DP, we get,
Mean without Deva's Income = 19666.67
or,
Mean without Deva's Income = £19666.67
At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $78 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.20. Over the first 40 days she was employed at the restaurant, the mean daily amount of her tips was $79.24. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $78?
If the test statistic is greater than the critical value, we can conclude that Ms. Brigden's daily tips average more than $78 at the 0.02 significance level.b
To determine if Ms. Brigden can conclude that her daily tips average more than $78, we can conduct a hypothesis test. The null hypothesis (H0) states that the mean daily tips is $78, while the alternative hypothesis (Ha) states that the mean daily tips is greater than $78.
Let's set up the hypotheses:
H0: μ = $78 (Mean daily tips is $78)
Ha: μ > $78 (Mean daily tips is greater than $78)
Given that the population standard deviation is $4.20, the sample mean over the first 40 days is $79.24.
Next, we perform a one-sample t-test, using the sample mean, population standard deviation, sample size, and significance level.
Using the provided information, we calculate the test statistic:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
= ($79.24 - $78) / ($4.20 / sqrt(40))
After calculating the test statistic, we compare it to the critical value from the t-distribution table at the 0.02 significance level with (40-1) degrees of freedom.
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that Ms. Brigden's daily tips average more than $78.
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A person leaves home and walks 6 miles west, then 3 miles southwest.
How far from home is she?
miles
In what direction must she walk to head directly home?
degrees North of East
The person is approximately 6.36 miles from home and must walk approximately 19.11 degrees North of East to head directly home.
To determine the distance, we can use Pythagorean theorem, because the person has moved horizontally as well as vertically. The person walks 6 miles west making a horizontal displacement and 3 miles southwest making both horizontal and vertical displacement.
Since, the vertical displacement is 3 miles southwest which is equal to 3 miles * cos(45 degrees) as southwest is 45 degrees from west. So, the horizontal diplacement is 6 miles and the vertical displacement is 3 miles * cos(45 degrees) which is equivalent to 2.121 miles.
To find the distance, we can use Pythagorean theorem:
[tex]Distance = \sqrt{(horizontal-displacement)^2 + (vertical-displacement)^2}[/tex]
[tex]Distance = \sqrt{(6 miles)^2 + (2.121 miles)^2}[/tex]
[tex]Distance = \sqrt{36 + 4.5}[/tex]
[tex]Distance = \sqrt{40.5}[/tex]
Distance = 6.36 miles (rounded to two decimal places)
Now, to determine the direction, she must walk directly to home, we can calculate the angle between home and her current position.
[tex]Angle = tan^{-1}(\frac{vertical-displacement}{horizontal-displacement} )[/tex]
[tex]Angle = tan^{-1}(\frac{2.121}{6} )[/tex]
Angle = 19.11 degrees
Therefore, she must walk approximately 19.11 degrees North of East and is approximately 6.36 miles far away from home.
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