answer quick please!!
Match the following reasons with the statements given.
Prove:
The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
Given:
RAS is isosceles
AM is median
Prove:
RAM SAM
1. Triangle RAS is isosceles, AM is a median
Reflexive
2. AR = AS
Definition of median
3. AM = AM
Given
4. MR = MS
Definition of isosceles triangle.
5. Triangle RAM congruent to Triangle SAM
SSS
Answers
The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
What is median ?The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Each triangle has three medians, one from each vertex, and they are concurrent at a point called the centroid. The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
According to given information :Triangle RAS is isosceles, AM is a median --> Definition of isosceles triangleAR = AS --> Definition of medianAM = AM --> ReflexiveMR = MS --> Median divides the base into two congruent segmentsTriangle RAM congruent to Triangle SAM --> SASTherefore, the median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
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Related Questions
Please help, Progress reports for the semester coming out soon!!
(Look at screenshot) <33
Answers
Answer:
The graph will be parallel with x-axis and intersects y at -8
Step-by-step explanation:
For the function y = -8, whatever the x is, y is always -8.
x y
-10 8
-9 8
-3 8
-2 8
2 8
The graph will be parallel with x-axis and intersects y at -8
Find all the zeros. Write the answer in exact form. c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24
Answers
The exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.
To find all the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24, we need to find the values of x that make c(x)=0. One way to do this is by using the Rational Root Theorem, which states that if a polynomial has rational zeros, then they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The factors of the constant term, 24, are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. The factors of the leading coefficient, 3, are ±1 and ±3. Therefore, the possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24.
Using synthetic division, we can test these possible zeros to see if they are actually zeros of the polynomial. After testing, we find that the zeros are -4, -3/2, 2, and 1.
So, the exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.
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Jane wants to buy 15 tomatoes. She asks for 1 kg of tomatoes at a shop. Jane assumes that each tomato has a weight of 75 g. (b) (i) If Jane's assumption is correct, will she get 15 tomatoes? You must show how you get your answer. (ii) If Jane's assumption is not correct, could she get 15 tomatoes? Justify your answer.
Answers
(i) If Jane's assumption is correct, she will not get 15 tomatoes.
(ii) If Jane's supposition about the body mass of the each tomato is wrong, she could not obtain 15 tomatoes to 1 kg of tomatoes.
What types of things are assumptions?
An presumption is something you believe to be true despite the lack of evidence. People might presume, for instance, that you are a geek if you wear spectacles, even though that is untrue.
(b) (i) If Jane's assumption is correct, then the weight of 15 tomatoes would be:
15 tomatoes × 75 g/tomato = 1125 g
Since 1 kg is equal to 1000 g, Jane would need to buy at least:
1125 g / 1000 g/kg = 1.125 kg of tomatoes
Therefore, Jane would need to ask for at least 1.125 kg of tomatoes to get 15 tomatoes if her assumption about the weight of each tomato is correct.
(b) (ii) If Jane's assumption about the weight of each tomato is not correct, it is possible that she could get 15 tomatoes with 1 kg of tomatoes, depending on the actual weight of each tomato.
For example, if each tomato actually weighs 67 g, then 15 tomatoes would weigh:
15 tomatoes × 67 g/tomato = 1005 g
This is less than 1 kg, so Jane would get 15 tomatoes with 1 kg of tomatoes.
On the other hand, if each tomato actually weighs 100 g, then 15 tomatoes would weigh:
15 tomatoes × 100 g/tomato = 1500 g
This is more than 1 kg, so Jane would not get 15 tomatoes with 1 kg of tomatoes if her assumption about the weight of each tomato is incorrect.
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
The area of the triangle is approximately 6.696 square feet.
What is Area of Triangle?
The area of a triangle is the amount of space enclosed by the three sides of the triangle
To find the area of a triangle with two sides and the included angle, we can use the following formula:
Area = (1/2) x a x b x sin(C)
where "a" and "b" are the lengths of the two sides and "C" is the angle between them.
Substituting the given values, we get:
Area = (1/2) x 3.2 ft x 4.7 ft x sin(62 degrees)
Using a calculator, we can evaluate sin(62 degrees) to be approximately 0.88.
So, Area = (1/2) x 3.2 ft x 4.7 ft x 0.88
= 6.696 ft²
Therefore, the area of the triangle is approximately 6.696 square feet.
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Answer:
The answer is 6.64 ft^2
Step-by-step explanation:
Graph Y=2x on this chart thanks
Answers
Answer:
Step-by-step explanation:
The slope is 2 so rise / run = 2 / 1, or up two right one.
How does lowering interest rates by a government’s central bank affect the economy?
Answers
Lowering interest rate by a government's central bank can have a significant impact on the economy, as it affects the cost of borrowing money for businesses and individuals, as well as the return on savings and investments.
Lowering interest rate reduces the cost of borrowing money, making it easier for businesses and individuals to access credit. It can also encourage consumers to spend more money, as they may have more disposable income due to lower borrowing costs or higher investment returns.
It can also lead to increased inflation, as businesses and individuals have more money to spend and demand for goods and services increases and reduced returns on savings and investments, which can discourage people from saving and lead to more spending
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Determine whether the following trinomial is a perfect square trinomial. 16a^(2)-40ab+25b^(2)
Answers
Yes, the given trinomial is a perfect square trinomial.
To determine whether a trinomial is a perfect square trinomial, we can use the formula:
(a-b)^(2) = a^(2) - 2ab + b^(2)
In this case, we can compare the given trinomial with the formula and see if it matches.
16a^(2)-40ab+25b^(2) = (4a)^(2) - 2(4a)(5b) + (5b)^(2)
This matches the formula, so we can conclude that the given trinomial is a perfect square trinomial.
Another way to determine whether a trinomial is a perfect square trinomial is to factor it and see if it can be written as a binomial squared.
In this case, we can factor the given trinomial as follows:
16a^(2)-40ab+25b^(2) = (4a-5b)(4a-5b) = (4a-5b)^(2)
Since the trinomial can be written as a binomial squared, we can conclude that it is a perfect square trinomial.
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Can somebody help with this problemo
Answers
Answer: end balance: $8,496.95
total interest: $1,496.95
Step-by-step explanation: total interest = $7000 × 8.554% × 30 ÷ 12 = $1,496.95
end balance = $7000 + $1,496.95 = $8,496.95
Find a basis of the subspace ofR4defined by the equation3x1−9x2+2x3−3x4=0
Answers
The basis of the subspace of R4 defined by the equation3x1−9x2+2x3−3x4=0 is {(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}
A basis of the subspace of R4 defined by the equation 3x1−9x2+2x3−3x4=0 can be found by solving the equation for one of the variables in terms of the others and then writing the general solution as a linear combination of vectors.
First, solve the equation for x1 in terms of the other variables:
3x1 = 9x2 - 2x3 + 3x4
x1 = 3x2 - (2/3)x3 + x4
Next, write the general solution as a linear combination of vectors:
(x1, x2, x3, x4) = (3x2 - (2/3)x3 + x4, x2, x3, x4)
= x2(3, 1, 0, 0) + x3(-2/3, 0, 1, 0) + x4(1, 0, 0, 1)
Finally, the basis of the subspace is the set of vectors that make up the linear combination:
{(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}
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Three clocks ring once at the same time. After that, the first clock rings after every 90 minutes,
the second after every 30 minutes, and third after every 60 minutes. After how many minutes will they again ring together?
Answers
Answer:
me no habla ingles?
Step-by-step explanation:
in ABC m
jjj k
kkkkkkk
kkk
Answers
can some one please help me with this
Answers
We can rewrite the inequality as:
95 ≤ u ≤ 155
How to solve the inequality?Here we have the absolute value inequality:
|125 - u| ≤ 30
Where the variable is u.
The absolute value can be decomposed into two inequalities:
(125 - u) ≤ 30
(125 - u) ≥ -30
Solving these two we will get:
125 - 30 ≤ u
125 + 30 ≥ u
Then the compound inequality is:
95 ≤ u ≤ 155
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p(x)=7x^(3)-10x^(2)+8x-5 According to the rational zero theorem, the possible zeros for p(x) are +-((1,5)/(1,7))
Answers
Yes, according to the Rational Zero Theorem, the possible zeros of the polynomial p(x) are +-(1,5/1,7). The only factorization that works in this case is p/q = 1.5/1.7, which yields the zeros +-(1,5/1,7).
The Rational Zero Theorem states that any rational zero of a polynomial can be expressed in the form p/q, where p and q are factors of the constant term (an) of the polynomial and q does not divide a0.
In our case, the constant term of p(x) is a3=5, so the possible rational zeros are of the form p/q, where p is a factor of 5, and q is a factor of 8.
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Find the minimum and maximum values of z=7x+3y , if possible, for the following set of constraints.
4x + 6y ≥ 24
x + 6y ≥ 12
x ≥ 0, y ≥ 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is (Round to the nearest tenth as needed.) B. There is no minimum value.
Answers
The minimum value is 24
To find the minimum value of z=7x+3y, we must use the given constraints to determine the values of x and y.
First, solve 4x + 6y ≥ 24. Rearrange the equation to solve for x: x ≥ (24 - 6y) / 4.
Next, solve x + 6y ≥ 12. Rearrange the equation to solve for y: y ≥ (12 - x) / 6.
Using the two equations, determine the possible values of x and y:
If y = 0, then x = 6
If x = 0, then y = 2
Substitute the possible values of x and y into the equation z = 7x + 3y and find the minimum value:
z = 7(6) + 3(0) = 42
z = 7(0) + 3(2) = 24
Therefore, the minimum value of z is 24.
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To get from Boone to Charlotte, you would have to drive about 156.6 km on the shortest route. To get from Boone to Anchorage, AK, you would have to drive 4,212.7 miles. How many orders of magnitude larger is the distance from Boone to Anchorage than Boone to Charlotte? (1 mi = 1.61 km).
Answers
Answer: 1.64. To find the difference in orders of magnitude between the two distances, we first need to convert both distances to the same unit of measurement. We'll convert both distances to kilometers.
The distance from Boone to Charlotte is already in kilometers, so we don't need to do any conversion for that distance.
The distance from Boone to Anchorage is in miles, so we'll need to convert that distance to kilometers. To do this, we'll multiply the number of miles by the conversion factor 1.61 km/mi:
4,212.7 mi × 1.61 km/mi = 6,782.45 km
Now that both distances are in kilometers, we can compare them to find the difference in orders of magnitude. An order of magnitude is a factor of 10, so we'll divide the larger distance by the smaller distance and then take the base 10 logarithm of the result:
log10(6,782.45 km / 156.6 km) = log10(43.3) ≈ 1.64
So the distance from Boone to Anchorage is about 1.64 orders of magnitude larger than the distance from Boone to Charlotte.
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For a function f(x)f(x) and a particular input value x=ax=a, then we may write the difference quotient as
f(a+h)−f(a)/h
where h≠0
Now, let f(x)=x^3−15x 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(x) from x=3 to x=3+h for the following particular values of h.
When h=0.2 the average rate of change of f(x) is __________ .
When h=0.1, the average rate of change of f(x) is ____________ .
When h=0.01, the average rate of change of f(x) is ____________ .
When h=−0.01, the average rate of change of f(x) is _____________ .
When h=−0.1, the average rate of change of f(x) is ______________ .
When h=−0.2, the average rate of change of f(x) is ______________ .
Answers
The average rate of change of f(x) for the given values of h are:
When h=0.2, the average rate of change of f(x) is 112.84.
When h=0.1, the average rate of change of f(x) is 206.41.
When h=0.01, the average rate of change of f(x) is 1850.5601.
When h=−0.01, the average rate of change of f(x) is -1807.5399.
When h=−0.1, the average rate of change of f(x) is -171.39.
When h=−0.2, the average rate of change of f(x) is -80.76.
To calculate the average rate of change of f(x) for the given values of h, we need to substitute the values of h into the difference quotient and simplify.
When h=0.2:
f(3+0.2)−f(3)/0.2 = [(3.2^3−15(3.2)) - (3^3−15(3))]/0.2 = (32.768 - 10.2) - (27 - 45)/0.2 = 22.568/0.2 = 112.84
When h=0.1:
f(3+0.1)−f(3)/0.1 = [(3.1^3−15(3.1)) - (3^3−15(3))]/0.1 = (29.791 - 9.15) - (27 - 45)/0.1 = 20.641/0.1 = 206.41
When h=0.01:
f(3+0.01)−f(3)/0.01 = [(3.01^3−15(3.01)) - (3^3−15(3))]/0.01 = (27.270601 - 8.765) - (27 - 45)/0.01 = 18.505601/0.01 = 1850.5601
When h=−0.01:
f(3+(-0.01))−f(3)/(-0.01) = [(2.99^3−15(2.99)) - (3^3−15(3))]/(-0.01) = (26.730399 - 8.655) - (27 - 45)/(-0.01) = 18.075399/(-0.01) = -1807.5399
When h=−0.1:
f(3+(-0.1))−f(3)/(-0.1) = [(2.9^3−15(2.9)) - (3^3−15(3))]/(-0.1) = (24.389 - 8.25) - (27 - 45)/(-0.1) = 17.139/(-0.1) = -171.39
When h=−0.2:
f(3+(-0.2))−f(3)/(-0.2) = [(2.8^3−15(2.8)) - (3^3−15(3))]/(-0.2) = (21.952 - 7.8) - (27 - 45)/(-0.2) = 16.152/(-0.2) = -80.76
Therefore, the average rate of change of f(x) for the given values of h are:
When h=0.2, value is 112.84.
When h=0.1, value is 206.41.
When h=0.01, value is 1850.5601.
When h=−0.01, value is -1807.5399.
When h=−0.1, value is -171.39.
When h=−0.2, value is -80.76.
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A boat traveled downstream a distance of
38
mi and then came right back. If the speed of the current was
6
mph and the total trip took
4
hours and 45 minutes, find
the average speed of the boat relati
Answers
The average speed of the boat relative to the water is approximately 17.08 mph.
The average speed of the boat relative to the water can be found by using the formula for distance, speed, and time:
distance = speed × time
We can use this formula to set up two equations, one for the downstream trip and one for the upstream trip:
38 = (s + 6) × t₁
38 = (s - 6) × t₂
We can then use the given information about the total time of the trip to find the values of t₁ and t₂:
4.75 = t₁ + t₂
We can rearrange the first two equations to solve for t₁ and t₂ in terms of s:
t1 = 38/(s + 6)
t2 = 38/(s - 6)
Substituting these values into the third equation and simplifying gives us:
4.75 = 38/(s + 6) + 38/(s - 6)
4.75s² - 57s - 114 = 0
Using the quadratic formula, we can solve for s:
s = (57 ± √(57₂ - 4(4.75)(-114)))/(2(4.75))
s ≈ 17.08 or s ≈ -3.01
Since the speed of the boat cannot be negative, t
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help me complete this and i will mark brainlirst
Answers
Answer:
Step-by-step explanation:
The method to find the midpoint of two points is (a + b)/2 a and b both being x+x and y+y for the differentiating coordinates respectively.
here, it would be x = (-2 + 4)/2 and y = (5-5)/2
giving you the coordinate [ 1 , 0 ]
The value of y varies directly with x. When y = 1.5, x = 5. What is the value of y when x is 30?
Answers
variables y = 1.5, x = 5, hence, the value of y is 9 when x is 30
How are linear equations solved?Two variables, such as x and y, are proportional to one another and their ratio is constant when they vary directly. In other words, if y and x vary directly, their relationship can be written as y = kx, where k is the proportionality constant. With the knowledge that y = 1.5 when x = 5 as provided, we can utilise this information to find the value of y when x equals 30:
1.5 = k(5) \sk = 1.5/5 \sk = 0.3
We can use the equation y = kx to get the value of y for x = 30 now that we know the value of k:
y = 0.3(30) \sy = 9
Hence, the value of y is 9 when x is 30.
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Alex has a pile of two pence coins. She swapped exactly half of them for the same number of 10p coins. Now she has £4.20. How much money did Alex have initially?"
Answers
Alex initially had 60 two pence coins.
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is used to solve problems and represent mathematical relationships and formulas. In algebra, letters and other symbols are used to represent numbers and quantities, allowing us to express mathematical relationships and patterns in a more general and abstract way.
What is Simplification?In mathematics, simplification refers to the process of reducing an expression or equation to a simpler form. This is typically done by applying mathematical operations or rules to the expression or equation to eliminate unnecessary terms, factors, or operations.
For example, if we have the expression (x^2 + 4x + 4)/(x + 2), we can simplify it by factoring the numerator and canceling out the common factor with the denominator. This gives us (x + 2), which is a simplified form of the original expression.
In the given question,
Let's start by using some algebra to solve the problem.
Let's say that Alex initially had x two pence coins. After swapping half of them for 10p coins, she would have x/2 ten pence coins. We can use this information to set up an equation relating the value of her coins to the total amount of money she ended up with:
0.02x + 0.10(x/2) = 4.20
Simplifying this equation, we get:
0.02x + 0.05x = 4.20
0.07x = 4.20
x = 60
So Alex initially had 60 two pence coins. Checking our answer, we can see that she swapped half of them for 30 ten pence coins. The value of her 60 two pence coins is 0.02 x 60 = £1.20, and the value of her 30 ten pence coins is 0.10 x 30 = £3.00. Together, these add up to £4.20, as required.
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given an "Armfield pump rig" to find the characteristics and efficiency of a pump experimentally. In this context, the pump is an energy converter that converts electrical power into hydraulic power.
the sample points are logged with a constant setting of rotational speed (angular velocity). power data is registered along the way - electric power into the electric motor, pressure from the pump and volume flow during throttling of the water flow out of the pump.
given data from EXCELbelow:
use EXCEL to solve the questions below, and explain step by step procedure
a) Calculate effects and efficiencies for all operating points.
b) Create a graph showing the delivery pressure (Pa) ("Pump 1") as a function of volume flow (Flow Rate Q) in (m3 / s)
c) Create a graph showing motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s) on an axis and efficiency (Pump 1 (%) on a secondary axis
Answers
To calculate the effect of the pump, use the formula: P = Q * ΔP / η and To calculate the efficiency of the pump, use the formula: η = P / P_e. Use the data provided in the EXCEL file.
To solve the questions, follow these steps:
a) Calculate effects and efficiencies for all operating points:
1. To calculate the effect of the pump, use the formula: P = Q * ΔP / η, where P is the power of the pump, Q is the volume flow rate, ΔP is the pressure difference across the pump, and η is the efficiency of the pump.
2. To calculate the efficiency of the pump, use the formula: η = P / P_e, where P is the power of the pump, and P_e is the electrical power input to the pump.
3. Use the data provided in the EXCEL file to calculate the effects and efficiencies for all operating points.
b) Create a graph showing the delivery pressure (Pa) ("Pump 1") as a function of volume flow (Flow Rate Q) in (m3 / s):
1. Select the data for the delivery pressure (Pa) and volume flow (Flow Rate Q) in the EXCEL file.
2. Click on the "Insert" tab in EXCEL and select the "Scatter" chart option.
3. Choose the "Scatter with Straight Lines" option to create a graph showing the delivery pressure (Pa) as a function of volume flow (Flow Rate Q).
c) Create a graph showing motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s) on an axis and efficiency (Pump 1 (%) on a secondary axis:
1. Select the data for the motor power (Pump 1) (W) and volume flow (Flow Rate) Q (l / s) in the EXCEL file.
2. Click on the "Insert" tab in EXCEL and select the "Scatter" chart option.
3. Choose the "Scatter with Straight Lines" option to create a graph showing the motor power (Pump 1) (W) as a function of volume flow (Flow Rate) Q (l / s).
4. Add a secondary axis to the graph by clicking on the "Format" tab in EXCEL and selecting the "Secondary Axis" option.
5. Select the data for the efficiency (Pump 1 (%) and add it to the secondary axis of the graph.
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75. Linear Speed at the Equator. The earth has a 4000-mi radius and rotates one revolution every 24 hr. What is the linear speed of a point on the equator, in miles per hour? 76. Linear Speed of the Earth. The earth is about 93,000,000 mi from the sun and traverses its orbit, which is nearly circular, every 365.25 days. What is the linear velocity of the earth in its orbit, in miles per hour?
Answers
75. To find the linear speed of a point on the equator, we need to use the formula for the circumference of a circle: C = 2πr. The radius of the earth is 4000 mi, so the circumference of the earth at the equator is C = 2π(4000) = 8000π mi. The earth rotates one revolution every 24 hours, so the linear speed of a point on the equator is 8000π/24 = 333.33π mi/hr ≈ 1047.2 mi/hr.
76. To find the linear speed of the earth in its orbit, we need to use the same formula for the circumference of a circle, but this time the radius is the distance from the earth to the sun, which is 93,000,000 mi. The circumference of the earth's orbit is C = 2π(93,000,000) = 186,000,000π mi. The earth traverses its orbit every 365.25 days, or 8766 hours. So the linear speed of the earth in its orbit is 186,000,000π/8766 = 21,174.6π mi/hr ≈ 66,555.8 mi/hr.
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use the body temperatures, in degrees in fahrenheit, listed in the accompanying table. the range of the data is 3.5 degrees F. use the range rule of thumb to estimate the value of the standard deviation. compare the result to the actual standard deviation of the data rounded to two decimal places, 0.72 degrees F, assuming the goal is to approximate the standard deviation within 0.2 degrees F.
Answers
The estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F
The range rule of thumb is used to estimate the standard deviation of a data set using the range of the data. In this case, the range of the data is 3.5 degrees F. Using the range rule of thumb, the standard deviation of the data can be estimated by taking the range (3.5) and dividing it by 4, which gives us an estimated standard deviation of 0.875 degrees F.
This estimated value is within 0.2 degrees F of the actual standard deviation of the data (0.72 degrees F).
To compare this result to the actual standard deviation of the data, we subtract the estimated value from the actual value and take the absolute value of the result. This gives us the difference between the two values:
|0.72 - 0.875| = 0.155
Since the difference between the estimated and actual standard deviations is less than 0.2 degrees F, we can say that the range rule of thumb provides a reasonable approximation of the standard deviation for this data set.
In conclusion, the estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F, and this value is within 0.2 degrees F of the actual standard deviation of 0.72 degrees F.
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A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 49° and AB = 8. 9. Calculate the length of AC rounded to 3 SF
Answers
Answer:
/AC/=10.2
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(a) (9 points) Find the minima and maxima of the following functions at a given interval:y=sin(x)in the interval[2π,4π]. (b) (4 points) Furthermore, determine thexvalues at which maxima and minima occurs. Hints: Please refer to the solveset (equation, variable, Interval (numn1, num2)) function to obtain the value within the given interval. However, solveset() does not return the values as an array. Therefore, it may require further processing. Additionally,πis accessed in SymPy as "sp.pi"
Answers
maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)
For part (a), to find the minima and maxima of the function y=sin(x) in the interval [2π, 4π], you can use the SymPy solves
et() function, which takes an equation, a variable and an interval (numn1, num2) as inputs. To do this, you can use the following code:
minima, maxima = sp.solveset(sp.Eq(sp.sin(x), 0), x, (sp.pi*2, sp.pi*4))
For part (b), to determine the x-values at which the maxima and minima occurs, you can use the minima and maxima values from the previous solveset() function and evaluate the sin(x) at those points. For example:
maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)
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The question is in the screenshot:
Answers
The value of the trigonometric function sin A, tan A, and sec A will be 3/5, 3/4, and 5/4.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Use the triangle to evaluate each function.
Hypotenuse AB has a length of 5, BC has a length of 4, and side AC has a length of 3.
Then the value of the trigonometric function will be
sin A = BC / AB
sin A = 3 / 5
tan A = BC / AC
tan A = 3 / 4
sec A = AB / AC
sec A = 5 / 4
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Find the missing dimension in the figure below if the surface area is given as 216.18 m2
Answers
Answer:
x=4.3m
Step-by-step explanation:
It is made up by six graphics.
Two triangles=1/2*x*5.6*2=5.6x
Base rectangular: 11.3x
Back rectangular: 11.3*5.6=63.28
Front rectangular:11.3*7.1=80.23
Add together: 5.6x+11.3x+63.28+80.23=216.18
16.9x=72.67
x=4.3m
6.
Erin and Christa were working on cubing
binomials for math homework. Erin believed they
could save time with a shortcut. She wrote down
the rule below for Christa to follow.
(a + b)³ = a³ + b³
Does Erin's shortcut always work? Justify your
result algebraically.
PLEASE SHOW WORK
Answers
If Erin and Christa were working on cubing binomials for math homework. Erin's shortcut does not always work and should not be used.
Does Erin's shortcut always work?Erin's shortcut is not correct. To see why, let's expand (a+b)³ using the binomial theorem: :
(a+b)³ = (a+b)(a+b)(a+b)
= (a+b)(a²+2ab+b²)
= a³ + 2a²b + ab² + a²b + 2ab² + b³
= a³ + 3a²b + 3ab² + b³
So the correct expansion of (a+b)³ has four terms, not two as Erin's shortcut suggests. Therefore, Erin's shortcut does not always work and should not be used.
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Suppose z varies inversely with t and that z=6 when t=8. What is the value of z when t=2 ?
Answers
The value of z when t=2 is 24
The value of z varies inversely with t, which means that the product of z and t is a constant. We can write this relationship as:
zt = k
Where k is the constant. We are given that z=6 when t=8, so we can plug these values into the equation to find k:
6*8 = k
k = 48
Now we can use this value of k to find the value of z when t=2. Plugging in these values gives us:
z*2 = 48
Solving for z gives us:
z = 48/2
z = 24
Therefore, the value of z when t=2 is 24.
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Find the median of the solutions to the equation 3x^3+5x^2−6x−10=0. (A) −√2 (B) √2 (C) −5/9 (D) −3/5 (E) None of these
Answers
The median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0 is -√2. The correct answer is A.
To find the median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0, first find the solutions of the equation and then find the middle value of those solutions.
Group the terms and factor out (3x + 5).
(3x³ + 5x²) + (-6x − 10) = 0
(3x + 5)(x²) + (3x + 5)(-2) = 0
(3x + 5)(x² - 2) = 0
Factor (x² - 2).
(3x + 5)(x + √2)(x - √2) = 0
So the solutions of the equation are x = -5/3, x = -√2, and x = √2.
To find the median of these solutions, we need to order them from least to greatest:
-5/3 < -√2 < √2
The median of these solutions is -√2.
Therefore, the correct answer is (A) -√2.
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