find the dimensions (radius r and height h) of the cone of maximum volume that can be inscribed in a sphere of radius 2.
Answers
The dimensions of the radius is 4/3[tex]\sqrt{2}[/tex] and that of height is 8/3.
Let r be the radius of the cone, be the radius of the sphere and h be the height of the cone.
Let's put DˆOB=x with limitations 0≤x≤π.
In the right-angled triangle DOB:
r=DB=Rsinx, OD=Rcosx, than
h=CD=OC+OD=R+Rcosx=R(1+cosx).
So the volume of the cone is:
V=1/3πr²h ⇒V=1/3π(Rsinx)²⋅R(1+cosx)
V=1/3πR³sin²x(1+cosx)
V'=1/3πR³⋅[2sinx⋅cosx⋅(1+cosx)+sin2x(−sinx)]
=1/3πR³sinx[2cosx(1+cosx)−sin2x]
=1/3πR³sinx(2cosx+2cos2x−sin2x)
=1/3πR³sinx(2cosx+2cos2x−1+cos2x)
=1/3πR³sinx(3cos2x+2cosx−1)
Now let's find the signum of the derivative, since sinx≥0 for every x in the limitations, then:
V'≥0⇒3cos²x+2cosx−1≥0
⇒Δ/4=(b/2)²−ac =1+3=4
cosx=(−b/2)±√Δ/4 / a
=−1±2/3,
So:
cosx≤−1∨cosx≥1/3
The first one has only the solution:
x=π
the second:
−arccos(1/3)≤x≤arccos(1/3), but for the limitations:
0≤x≤arccos(1/3).
The function gros from zero to arccos(1/3), and then it decreases.
So x=arccos(1/3) is the maximum requested.
Let's find now r and h:
r=Rsinx
=R√1−cos2x
= 2√1−(1/3)²
= 2√1−1/9
=2√9−1/9
=2√8/9
=2⋅2√2/3
=4/3√2
h=R(1+cosx)=2(1+1/3)
=2(3+1/3)
=8/3.
Therefore the radius is 4/3√2 and the height is 8/3.
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Related Questions
On December 31 Retail company’s estimated taxes for the first quarter total $50,000. The entry to record this payment is:
Complete the necessary journal entry by selecting the account names from the pull-down menus and entering dollar amounts in the debit and credit columns.
Transaction List
On December 31 Retail company’s estimated taxes for the first quarter total $50,000. The entry to record this payment is:
Answers
The entry to record this payment when the company’s estimated taxes for the first quarter total $50,000 will be:
Debit Income taxes payable $50000
Credit Cash $50000.
What is a journal?A journal is a book in which all of a company's transactions are recorded for the first time. Journaling is the process of recording transactions in a journal. Every transaction has two effects: one is debited and the other is credited.
The act of keeping or making records of any transaction, economic or non-economic, is referred to as a journal entry. An accounting journal, which shows a company's debit and credit balances, records transactions. The journal entry may include multiple recordings, each of which is either a debit or a credit. A journal entry's purpose is to physically or digitally record every business transaction properly and accurately.
The journal entry based on the information is illustrated.
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what are the solutions to this system of equations 2x y 3 y 3 2 x 2 2
Answers
The solutions to the system of equations 2x + y = 3 and y - 3 = 2x - 2 are (1,5) and (-2,-1).
What formulae are used?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.
What is an equation example?The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.
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convert y + 4 = 2(x-3) into slope intercept form (also explain how you got to this answer)
Answers
Answer:
Step-by-step explanation:
slope intercept is y=mx+b
y+4=2(x-3)
y=2(x-3)-4
y=2x-6-4
y=2x-10
In parallelogram hijk the measure of angle H is 45 what is K
Answers
On solving the provided question, we got to know that ∠ H + ∠ K = 45°.
K therefore has a 135° measure.
What is a Parallelogram?A unique kind of quadrilateral created by parallel lines is a parallelogram. A parallelogram might have different angles between its neighboring sides, but it must have parallel opposite sides in order to be considered one. If a quadrilateral's opposite sides are parallel and congruent, it is a parallelogram. As a result, a parallelogram is a quadrilateral with both pairs of opposite sides being parallel and equal.
the K-value of the angle.
First of all, we should be aware that the sum of the adjacent angles in the parallelogram ABCD, which has the angles A, B, C, and D, is 180°.
[tex]angle A + angle B = 180\\ angle B + angle C = 180\\ angle C + angle D = 180\\ angle A + angle D = 180[/tex]
They're considered to be a linear pair.
As a result, the parallelogram HIJK, whose angle H = 45°, is what we have.
Therefore, ∠ H +∠K = 180° (linear pair),
∠ K = 180° - 45°
∠ K = 135°,
and
∠ H + ∠ K = 45°.
K therefore has a 135° measure.
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gail is a student in a class that has been asked to conduct a hypothesis test for a population proportion. the null and alternative hypotheses are: h0: p
Answers
Gail's friends does not reject the null hypothesis.
What is null and alternate hypothesis?
Statisticians test hypotheses using null and alternate hypotheses. The alternative hypothesis of a test states your research's prediction of an effect or relationship, whereas the null hypothesis of a test consistently predicts no effect or no relationship between variables.
Given:
H0: p = 0.4
Ha: p ≠ 0.4
Gail uses a level of significance of α = 0.05, she does not reject the null hypothesis.
Therefore the p-value she obtained is greater than 0.05
Andrew uses a level of significance of α = 0.1
Since from given information we can not say if p value is > 0.1 or less, hence
it is impossible to tell from the information given.
Ben uses α = 0.01
Since p-value is greater than 0.05 hence definitely greater than 0.01
Hence, Gail's friends does not reject the null hypothesis.
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Complete question:
Gail is a student in a class that has been asked to conduct a hypothesis test for a population proportion. The null and alternative hypotheses are: H0: p = 0.4 Ha: p ≠ 0.4 Gail is given a sample and calculates the test statistic. Using a level of significance of α = 0.05, she does not reject the null hypothesis. Gail's friends, Andrew and Ben, also use the sample to calculate a test statistic. However, they differ in the level of significance they use. Andrew uses a level of significance of α = 0.1, while Ben uses α = 0.01. All three students perform their calculations correctly. For each of Gail's friends, select whether or not they reject the null hypothesis, or whether it is impossible to tell from the information given.
I need this please help me
Answers
Answer: m∠A = 72°, m∠C = 56°
Step-by-step explanation: All triangles interior angles add up to 180, This is an isosceles triangle which by rule mean that angles m∠A and m∠B and the same value of 72°. Now it becomes an equation to find m∠C, of
72 + 72 + x = 180.
144 + x = 180
x = 56
Could someone please help me?
Answers
Answer:
Option B
Step-by-step explanation:
Use the formula
[tex]x = \frac{-b\±\sqrt{b^{2}-4ac } }{2a}[/tex]
now input the values. In equation [tex]x^{2} - 5x + 7 = 0[/tex], a = 1, b = -5 & c = 7
By taking positive sign we get,
[tex]x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
⇒[tex]x = \frac{-(-5)+\sqrt{(-5)^{2}-4.1.7 } }{2.1}[/tex]
⇒[tex]x = \frac{5+\sqrt{25-28 } }{2}[/tex]
⇒[tex]x = \frac{5+\sqrt{-3 } }{2}[/tex]
In the same way, by taking minus sign, we get [tex]x = \frac{5-\sqrt{-3 } }{2}[/tex]
An angle measures 1.2 radians and the initial ray of the angle points in the 3-o'clock direction. A circle is centered at the angle's vertex. 1. rad a. The terminal point is how many radii to the right of the circle's center? radii b. The terminal point is how many radii above the circle's center? radii
Answers
The terminal point is 0.36 radii to the right of the circle's center.
The terminal point is 0.93 radii above the circle's center.
Here, the 3 O'clock line is OA and the terminal point is on the line OP.
The angle θ = 1.2 radians
Let the radius = r
The distance of the terminal point to the right of the center = OQ
= r × cos θ
= r × cos 1.2
= r × 0.36
So, it is equal to 0.36 radii
The distance of the terminal point above the center = PQ
= r × sin θ
= r × sin 1.2
= r × 0.93
So, it is equal to 0.93 radii.
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a jet plane can carry up to 200,000 liters of fuel. it used 130,000 liters of fuel during a flight. what percentage of the fuel capacity did it not use on this flight?
Answers
35% of the fuel Capacity did not use on this flight.
How to calculate percent change of any quantity?Step 1: Calculate the change i.e., subtract old value from the new value
Step 2: Divide that change by the old value.
Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)
Percentage change = ((final value - initial value) ÷final value) ×100
Given: Total capacity in a fuel tank of a jet = 200000 liters
Used fuel =130000 liters
% Of fuel which is not used = ((total capacity of fuel tank - used fuel) ÷total capacity of fuel tank) ×100
[tex]=\frac{200000-130000}{200000}*100\\=\frac{70000}{2000}[/tex]
=35%
Therefore, 35% of the fuel capacity did not used in this flight.
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You and your friends order a meal for $149.58. How much should you leave (including tip) if you want to leave an 18% tip?
Answers
The total amount that should be left including 18% tip is $176.5
What is percentage?
A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the percent sign, "%". A % is a number without dimensions and without a standard measurement.
We are given that you and your friend ordered a meal worth of $149.58
Now also we want to leave a tip of 18% of the total amount.
Hence the total amount that should be left is needed to be calculated
To do that we first calculate the 18% of the total amount then add it to the original amount
18% of the total value is
[tex]149.58*\frac{18}{100}\\ =26.92[/tex]
This is the value of tip that needed to be given
Now we add this to the original price
We get
149.58+26.92
=176.50
The total amount that needs to be paid with tip is $176.5
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eight times times a number decreased by four times a number is equal to 36 find the number.
Answers
Answer:
9
Step-by-step explanation:
8x - 4x = 36
4x = 36
x = 36/4 = 9
Answer:
9
Step-by-step explanation:
8n-4n=36
n=9
8(9)-4(9)=36
Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually.
Multiple Choice
$1,085.82
$1,463.13
$164,313.82
$163,313
Answers
The amount must be $164,313.82 deposited in her local bank. which is the correct answer would be an option (C).
For yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually.
Let's assume that the amount would be P deposited in her local bank
As per the given question, the required solution would be as:
P = 18000[1 - (1 + 9/100)⁻²⁰]/0.09
P = 18000[1 - (1 + 0.09)⁻²⁰]/0.09
P = $164,313.82
Therefore, the required amount must be $164,313.82 deposited in her local bank.
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Zahra has a bag that contains apple chews, strawberry chews, and lime chews. She performs an experiment. Zahra randomly removes a chew from the bag, records the result, and returns the chew to the bag. Zahra performs the experiment 41 times. The results are shown below:
An apple chew was selected 34 times.
A strawberry chew was selected 5 times.
A lime chew was selected 2 times.
Based on these results, express the probability that the next chew Zahra removes from the bag will be lime chew as a percent to the nearest whole number.
Answers
The probability that the next chew would be a lime chew is 5%.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the next chew would be a lime chew = number of lime chews / total number of chews
Total number of chews = 34 + 5 + 2 = 41
The probability that the next chew would be a lime chew = (2 / 41) x 100 = 5%
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a machine is used to fill bags with a popular brand of trail mix. the machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. of the following, which is the least weight of a bag in the top 5 percent of the distribution? responses
Answers
The top five percent of the distribution's lowest weight as calculated from the given data for a bag is 246.
Average population = 240
Standard deviation for the population; 3
Z-score can be calculated as ,
z = (x' - μ)/σ
Now, in order to determine which of the top 5 values in the distribution has the least weight, we will use the significance threshold of 1 - 0.05/2 = 0.025.
Z-score is 1.96 at significance level 0.025.
Thus;
1.96 = (x' - 240)/3
3 × 1.96 = x' - 240
x' = 240 + 5.88
x' = 245.88
Getting close to a whole number results ,
x' = 246
The two z-score tables are as follows:
Positive Z Score Table: The observed value is greater than the average of all values.
An observed value that is below the mean of all values is shown by a negative Z score table.
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pls help !
Solve the system using inverse
matrices.
(9x - 2y = 12
3x + 4y = 18
([? ],[ ])
Answers
The solved inverse matrices.
(9x - 2y = 12
3x + 4y = 18
([2],[3 ])
How to solve the system using inverse matrices?To solve a system of linear equations using inverse matrices, we can express the system in matrix form as follows:
[9 -2] [x] = [12]
[3 4] [y] [18]
Then we can find the inverse of the coefficient matrix, which is the matrix containing the coefficients of the variables in the system:
[9 -2]^⁻¹ = 1/((9)(4) - (-2)(3)) * [ 4 2]
[3 4] [ -3 9]
= 1/14 * [ 4 2] = [2/7 1/7]
[ -3 9] [-3/7 2/7]
We can then multiply both sides of the equation by the inverse matrix to obtain the solution:
[2/7 1/7] [9 -2] [x] = [2/7 1/7] [12]
[-3/7 2/7] [3 4] [y] [-3/7 2/7] [18]
[x] = [2/7 1/7]^-1 [2/7 1/7] [9 -2] [x]
[y] [-3/7 2/7] [-3/7 2/7] [3 4] [y]
[x] = [1 0] [9 -2] [x]
[y] [0 1] [3 4] [y]
This simplifies to the following system of equations:
9x - 2y = 12
3x + 4y = 18
Therefore in solving this system, we find that x = 2 and y = 3. So, the solution to the original system is (x, y) = (2, 3).
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3. The quilt is made of squares with diagonals. (Lesson 3-12)
The length of BD is 4.
a. Find the length of AE.
Answers
Answer:2
Step-by-step explanation:took a test
Milo has a collection of DVDs. Out of 45
DVDs, 40% are comedies and the remaining
are action-adventures. How many action-
adventure DVDs does Milo own?
Answers
Answer:
27 vidoe are actions adventure.
Step-by-step explanation:
1005 would we all of the vidoes. 100% - 40 % = 60%
60% is the same as .6
.6 x 45 = 27
Answer:
Milo has 27 action-adventure DVDs--------------------------------------
40% of 45 DVD's are comedies.
It is in number:
45*40/100 = 18The rest are action-adventures:
45 - 18 = 27Raquel is playing a game where she throws a ball that paper called a trash ball into her trashcan the diameter of the top of the trashcan is 20 inches Raquel once the trash ball to have a diameter that is 1/4 the diameter of the top of the trashcan what should the timing of Raquel trash Be?
Answers
The diameter of the top of the trash ball is 5 inch.
What is a diameter?A straight line that runs through the middle of a body or figure from the sideways particularly a circle or sphere is called as a diameter of a circle or sphere.
Given that the diameter of top of the trash can is 20 inch.
And the diameter of trash ball is 1/4th of the diameter of trash can.
The diameter of trash ball = 1/4 ( the diameter of trash can )
The diameter of trash ball = 1/4 (20 inch)
The diameter of trash ball = 20/4
The diameter of trash ball = 5 inch.
Therefore, the diameter of the top of the trash ball is 5 inch.
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The complete question is;
Raquel is playing a game where she throws balled-up paper called a “trash ball” into her trash can. The diameter of the top of the trash can is 20 inch . Raquel wants the “trash ball” to have a diameter that is 1/4 the diameter of the top of the trash can. What should the diameter of Raquel's “trash ball” be? .
6. Solve 8(12-4x) ≥ 82 and graph the solution set.
Answers
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The solution set is x ≤ 0.4.
The graph of the solution is
<-----__-1.5__-1__-0.5__0__0.5__1__1.5------>
<------------------o
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
8(12 - 4x) ≥ 82
96 - 32x ≥ 82
96 - 82 ≥ 32x
14 ≥ 32x
x ≤ 14/32
x ≤ 7/16
x ≤ 0.4
This can be graphed using a number line.
<-----__-1.5__-1__-0.5__0__0.5__1__1.5------>
<------------------o
Thus,
The solution set is x ≤ 0.4.
The graph of the solution is given above.
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Aaron and Gene have a total of 758 baseball cards. 437 of the cards are from Aaron. How many cards are from Gene? Identify the equation that represents how to find the amount of baseball cards that come from Gene.
Answers
1. The number of baseball cards from Gene is 321.
2. An equation that represents finding the number of baseball cards that come from Gene is g = 758 - a.
What is an equation?An equation is a mathematical statement that shows the equality of two or more mathematical expressions.
Equations are solved to solve mathematical problems with unknown variables, combining numbers and variables with mathematical operands.
We depict equations using the equation symbol (=).
The total number of baseball cards with Aaron and Gene = 758
The number of cards from Aaron, a = 437
The number of cards from Gene = g
g = 758 - a.
= 758 - 437
= 321
Thus, using the above equation, we can use the subtraction operation to find that Gene brought 321 baseball cards.
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Which of the following is NOT a geometric sequence?A. 3, 6, 9, B. 3, 9, 27,... C. 4, 8, 16, D. 7, -7, 7, -7...
Answers
Of the following, a sequence which is not a geometric sequence is 3, 6, 9, ... (Option A)
A geometric sequence refers to a sequence in which each term is determined by multiplying the preceding term by the same value which is called the common ratio (r). Hence, the common ratio determined by dividing a term by preceding term is constant in a geometric sequence.
In the given options,
A) r = 6/3 ≠ 9/6
B) r = 9/3 = 27/9 = 3
C) r = 8/4 = 16/8 = 2
D) r = -7/7 =7/-7 = -7/7 = -1
As the common ratio r is constant for option B, C and D, they are geometric sequences. The ratio between consecutive terms is not the same for option A, it is not a geometric sequence.
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T/F state in predicate calculus that an array of int, say a, is sorted. you may use the java expression syntax (e.g., a.length, a[i],
Answers
For instance, we might simply show the following conditional statement:
1. Return true if the array's size is zero or one.
2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.
In the given question, we have to state true or false for the given statement.
In our programs, we frequently want to be able to "conditionally" execute certain actions, i.e., "if this is true, then do X, but if this other thing is true, then do Y." It's similar to how we dress when we get out of bed: "If it's sunny, I wear sunglasses, but if it's raining, I take an umbrella." In our programs, we can use if statements, if/else statements, and conditional expressions to do things conditionally.
If a condition is true, an if statement instructs the computer to run a certain piece of code. Only if x is bigger than 0 do we output a message in the following code:
We would be able to see the message on the canvas since x is 5, which is bigger than 0. If we modified x to -1, the message wouldn't appear at all because x wouldn't be greater than 0.
A conditional expression is one that can only be evaluated as either true or false, and the x > 0 qualifies as one. A boolean value is one that can only be either true or false (as opposed to a number or a string). For instance, we might simply show the following conditional statement:
1. Return true if the array's size is zero or one.
2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.
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The right question is:
State in predicate calculus that an array of int, say a, is sorted. You may use the Java expression syntax (e.g., a.length, a[i], ==, and <) and logical operators (&&).
Use the drop-down menus to complete each statement about the functions f and g
Note: Exponential functions are of the form f(x) = ab^x
-linear/exponential/neither
-differences/quotients
-constant/non-constant
Answers
A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
Hence, in this problem, the function g(x) is exponential, as when the input x is increased by one, the output g(x) is multiplied by two.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
Hence, in this problem, the function f(x) is linear, as when the input x is increased by one, the output f(x) is increased by a constant of six.
Missing InformationThe problem is given by the image shown at the end of the answer.
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In the figure below, a II b, and O is the center of the circle.
Answers
The measure of the central angles of the circle are, respectively:
m ∠ BOC = 60°
m ∠ COD = 120°
m ∠ AOD = 60°
m ∠ AOB = 120°
m ∠ DOB = 180°
How to determine the measure of the central angles within the circle
In this problem we find a geometric system formed by a circle, two parallel lines and two additional lines that intersect each other at the center of the circle. Then, the angles DOC, COB, AOB and DOB are central angles of the circle such that:
m ∠ DOC + m ∠ COB + m ∠ AOB + m ∠ DOB = 360°
Then, by direct inspection, we find that the measures of the central angles are, respectively:
m ∠ BOC = 60°
m ∠ COD = 120°
m ∠ AOD = 60°
m ∠ AOB = 120°
m ∠ DOB = m ∠ COD + m ∠ BOC = 120° + 60° = 180°
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You purchased a share of stock for $29. One year later you received $2.25 as dividend and sold the share for $28. Your holding-period return was _________.(SHOW CALCULATION)
Answers
"F(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i"
Answers
Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.
What is function?Function is a relation or expression involving one or more variables.
The zeros are:
x = 3/2
x = -3/2
x = (3/2)*i
x = (-3/2)*i
First, for a given function f(x), we define the zeros as the values of x such that:
f(x) = 0.
Then we must solve:
f(x) = 16*x^4 - 81 = 0
Solving this for x leads to:
16*x^4 = 81
x^4 = 81/16
x^2 = ±√(81/16) = 9/4
x = ±√±(9/4) = ±3/2 and ±(3/2)*i
So there are 4 zeros, and these are:
x = 3/2
x = -3/2
x = (3/2)*i
x = (-3/2)*i
Where the two complex zeros come from evaluating the second square root on
-9/4.
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two equilateral triangles are contained in a square whose side length is $2\sqrt{3}$. the bases of these triangles are opposite sides of the square, and their intersection is a rhombus. the area of the rhombus can be expressed in the from $a b\sqrt{c}$ for integers $a,b,$ and $c$ such that $c$ square-free. determine $-a b c$.
Answers
The area of the rhombus inside a square formed by two equilateral triangles is 1.856 cm².
Here we have to find the area of the rhombus.
Data given:
sides of a square = 2√3 cm
Let ABCD be a square whose sides are 2√3 cm.
As two triangles are inscribed in a square so ABE and CDG be equilateral triangles in square ABCD.
The altitude of the equilateral triangle ABE and CDE = 2√3 sin 60°
= 2√3 × √3/2
= 3cm
The diagonal EG of the rhombus EFGH = 2√3 - 2(2√3 - 3)
= 2.535 cm
The diagonal FH of the rhombus, EFGH = 2√3 - 2(√3tan 30°)
= 1.464 cm
The formula for the area of the rhombus = d1 × d2 / 2
where d1 and d2= diagonal of a rhombus
Now the area of the rhombus EFGH = EG × FH / 2
= 2.535 × 1.464 / 2
= 1.856 cm².
Therefore the area of the rhombus is 1.856 cm².
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Arandomsampleof5weeksshowedthatacruise agency received the following number of weekly specials to the Caribbean: 20, 73, 75, 80, 82. a. Compute the mean, median, and mode. b. Which measure of central tendency best describes the data? c. Comment on the distribution of the data.
Answers
The mean is 66, the median is 75 and the mode is None.
The center or typical value of a dataset is represented by summary statistics known as measures of central tendency. These metrics, such as the mean, median, and mode, are examples. These statistics, often known as the central location of a distribution, show where the majority of values in a distribution fall.
Given,
No. of observations = 5
Mean = Total observations/ no. of observations = 20+73+75+80+82/5 = 66
Median = Middle most observation arranged from smallest to largest = 75
Mode = Observation which occurs at least twice = None
Mean describes the data the best because it takes the average of all the given data.
The distribution of the data set is scattered and the shape of the frequency graph is going upwards.
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Choose one point on the graph of the proportional relationship and explain what this point means in terms of the situation
Answers
A point on the graph is (30, 4) and the meaning is that the cost of 30 units of electricity is £4
How to interpret the point on the graph of the proportional relationshipFrom the question, we have the graph that can be used in our computation:
From the graph, we have the following ordered pairs
(0, 0) and (30, 4)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (30, 4)
The gradient of the line is then calculated using the following slope equation
gradient = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (30, 4)
Substitute the known values in the above equation
So, we have the following equation
gradient = (4 - 0)/(30 - 0)
Evaluate
gradient = 4/30
So, the gradient of the line is 4/30
As a general rule:
Generally, slope or gradient means rate
This means that the gradient of this line represent the rate
i.e. the amount for each unit is 4/30
So, we can conclude that the point (30, 4) on the graph means that the cost of 30 units is £4
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Complete question
An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.
See attachment for graph
You are running a fuel economy study. One of the cars you find is blue. It can travel
45 1/2 miles on 1 1/4 gallons
of gasoline. Another car is red. It can travel
24 4/5 on 4/5 gallons
of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
Answers
The unit rate for miles per gallon for each car will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of gasoline.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
You are running an efficiency study. One of the vehicles you find is blue. It can travel 45 ¹/₂ miles on 1 ¹/₄ gallon of fuel. Another vehicle is red. It can travel 24 ⁴/₅ on ⁴/₅ gallons of fuel.
The rate of blue cars is given as,
⇒ (45 ¹/₂) / (1 ¹/₄)
⇒ 45.5 / 1.25
⇒ 36.4 miles per gallon
The rate of red cars is given as,
⇒ (24 ⁴/₅) / (⁴/₅)
⇒ 24.8 / 0.8
⇒ 31 miles per hour
The unit rate for miles per gallon for each car will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of gasoline.
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