Answer: Option "a" is the only expression that represents a function.
Step-by-step explanation:
A function f(x) = y is a "operator" that takes an input element, x, and assigns it to only one output element, y.
So, if we have that for a given value of x.
f(x) = y and f(x) = h
where y and h are different values, then this is not a function, because is assigning the input value x to two different output values.
Let's see the different options:
a) {(1, 2), (4, −2), (8, 3), (9, −3)}
This points are of the form (x, y)
We can see that each value of x is assigned to only one value of y, so this can represent a function.
b) y^2 = 16 − x^2
Ok, suppose that x = 0, then:
y^2 = 16 - 0 = 16
then we have that y*y = 16.
So y can take two different values:
y = 4 ---> 4*4 = 16
y = -4 ---> -4*-4 = 16.
So this is not a function.
c) 2x^2 + y^2 = 5
First, we want to isolate y in one side:
y^2 = 5 - 2*x^2
Here we have a similar case to the option b, and we can use a similar argument to prove that this is not a function, so we can discard this.
d) x = 7.
Ok, this is not a relation between two variables, so this is not a function, as if x is the input value, we have only one value of x that solves the equation.
A class with n kids lines up for recess. The order in which the kids line up is random with eachordering being equally likely. There are three kids in the class named John, Betty, and Mary. The useof the word "or" in the description of the events, should be interpreted as the inclusive or. That is"A or B" means thatAis true,Bis true, or bothAandBare true.Give an expression for each of the probabilities below as a function ofn. Simplify your final expressionas much as possible so that your answer does not include any expressions of the form (a/b).Requried:a. What is the probability that Betty is first in line or Mary is last in line? b. Explain the method used to calculate probability.
Answer:
A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
B) The method used is Relative frequency approach.
Step-by-step explanation:
From the question, we are told a sample of n kids line up for recess.
Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).
Since we are being asked about 3 kids from the class, let's assign a letter to each kid:
J: John
B: Betty
M: Mary
A) Now, we want to find the probability that Betty is first in line or Mary is last in line.
In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;
P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
Where;
The suffix 1 refers to the first position while the suffix n refers to the last position.
Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)
This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.
B) The method used is Relative frequency approach.
In this method, the probabilities are usually assigned on the basis of experimentation or historical data.
For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.
Also, let n_A be the number of times that A did occur.
Now, the relative frequency would be written as (n_A)/n.
Thus, in this method, we will define P(A) as:
P(A) = lim:n→∞[(n_A)/n]
Given this pair of probabilities, the probability that Mary is the first is n(A) = n-1!, while the probability that Betty is last is n(A) = n-1!
There are n! ways of making this arrangement
We have probability of A: Betty is the first person in this line
Probability of B: Mary is the last person
A U B = p(A) + p(B) - p(A ∩ B)
n(A) = n-1 that is given that Betty is the first person on the line.
then n(A) = n-1!
As the last person on the line P(B) = n-1!
Probability of (A∩B) =( n-2)! this has Mary as the first and Betty as the last person.
Remaining students that would have to be on this line are n-2
Prob(A∪B) = n(A ∪ B)/n!
= 2(n-2)/n(n-1)
What is the probability theory in Mathematics?This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.
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A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x-2)=48 What is the length, x, of the garden?
Answer:
[tex]x {}^{2} - 2x = 48[/tex]
[tex]x { }^{2} - 2x - 48 = 0[/tex]
using quadratic formula,
[tex] - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac} \div 2a[/tex]
[tex]2 + \sqrt{196} \div 2[/tex]
[tex]2 + 14 \div 2[/tex]
[tex]x = 8[/tex]
or
[tex]x = - 6[/tex]
hello, if someone can give me a hand with this upper and lower bound excercise please? l get 3 marks of 5 but l cant find what l am missing please thanks
Answer: maximum "safe" Force = 415.58 N
Step-by-step explanation:
Length = 1.2 m
lower bound is 1.15 (because it rounds up to 1.2)
upper bound is 1.24 (because it rounds down to 1.2)
Note: 1.25 would round up to 1.3
width = 2.5 m
lower bound is 2.45 (because it rounds up to 2.5)
upper bound is 2.54 (because it rounds down to 2.5)
Note: 2.55 would round up to 2.6
Pressure = 150 N/m²
lower bound is 147.5 (because it rounds up to 150)
upper bound is 152.4 (because it rounds down to 150)
Note: 152.5 would round up to 155
Max "safe" Force means minimum Area and minimum Pressure (lower bounds)
Force = Area x Pressure
= length x width x Pressure
= 1.15 x 2.45 x 147.5
= 415.58
The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP
Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............
Step-by-step explanation:
From the first statement,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6 -----------------------------------1
second statement
sum of the next 4 terms inclusive
T₉ = ⁹/₂(2a + 8d ) = 69
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
divide through by 18 to reduce to lowest time
a + 4d = 11 ------------------------------------------2
Now solve the two equation simultaneously to find a and d
a + 2d = 6
a + 4d = 11
-2d = -5
d = ⁵/₂.
Now substitute for d to get a
a + 2(⁵/₂) = 6
a + 5 = 6
a = 6 - 5
a = 1.
Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............
The AP if, The sum of the first 5 terms of an AP is 30 and the sum of the four terms from T6 to T9 is 69, is 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
What is sequence?
An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given:
The sum of the first 5 terms of an AP is 30,
Write the equations as shown below,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6
T₉ = ⁹/₂(2a + 8d ) = 69 (sum of the next 4 terms inclusive)
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
a + 4d = 11
Solve the equation as shown below,
d = ⁵/₂, and a = 1.
Therefore, the AP = 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
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Simply this question and get marked branlist
Answer:
72/n^5r
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
13)
● 2d^3 × c^6 × 8d^5 × c^2
Isolate the similar terms
● (2×8)× (d^3 × d^5)×(c^6×c^2)
● 16 × d^(3+5) × c^(6+2)
● 16 × d^8 × c^8
● 16 × (dc)^8
● 16(dc)^8
■■■■■■■■■■■■■■■■■■■■■■■■■■
● 8n×r^(-4) ×9×n^(-6)×r^3
Isolate the similar terms
● (8×9)× (r^(-4)×r^3) × (n×n^(-6))
● 72 × r^(-4+3) × n^(1-6)
● 72 × r^-1 × n^(-5)
● 72 ×(1/r) × (1/n^5)
● 72/(r×n^5)
How many different sets of polar coordinates can be given for a point, within one rotation? I thought it was infinite, but the given options are 1, 2, 3, and 4.
Answer:
the answer is 4
Step-by-step explanation:
so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get
Answer:
Solution : 4
Step-by-step explanation:
The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,
( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )
Respectively if theta was q say,
( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )
Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.
Please help me so confused
Answer:
m = 15
Step-by-step explanation:
m/9 + 2/3 = 7/3
Subtract 2/3 from each side
m/9 + 2/3 -2/3= 7/3 -2/3
m/9 = 5/3
Multiply each side by 9
m/9 *9 = 5/3 *9
m = 15
i need help quick!!!
Answer: A,C, and D
Step-by-step explanation:
Answer:
the answer to this question may be option B, C and D
help asap!! will get branliest.
Answer:
5/2
Step-by-step explanation:
5^(-3). 2^2.5^6 / (2^3.5^2)
By the law of indices,
=5^(-3+6-2).2^(2-3)
=5^1.2^(-1)
=5. 2^-1
=5/2
in the diagram EF and GH are straight lines. Find the values of a,b,c and d
a data set includes 110 body temperatures of healthy adult humans having a mean of 98.1F and a standard deviation of 0.64F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans
Answer:
The 99% confidence interval is [tex]97.94 < \mu < 98.26[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 110
The sample mean is [tex]\= x = 98.1 \ F[/tex]
The standard deviation is [tex]\sigma = 0.64 \ F[/tex]
Given that the confidence level is 99% the level of significance i mathematically evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution, the values is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]
[tex]E = 0.1574[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]
[tex]97.94 < \mu < 98.26[/tex]
Answer:
Step-by-step explanation:
How should a musician effectively convey emotions or ideas in a performance?
Answer:
Within the factors hindering expression in music, tempo is the most important number of factors such as your mood.
Step-by-step explanation:
If one wants to convey a message, they should try these:
a) Use real life
b) introduce symbolism
c) convey sensory disruption, e.t.c.
Hope these helps.
A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by performing yoga exercises. A treatment group and a control group are selected. The sample statistics are given below. Construct a 90% confidence interval for the difference between the two population means, Would you recommend using yoga exercises? Treatment Group Control Group n1 = 100 n2 = 100 1 = 178 2 = 193 s1 = 35 s2 = 37
Answer:
90% confidence interval for the difference between the two population means
( -23.4166 , -6.5834)
Step-by-step explanation:
Step(i):-
Given first sample size n₁ = 100
Given mean of the first sample x₁⁻ = 178
Standard deviation of the sample S₁ = 35
Given second sample size n₂= 100
Given mean of the second sample x₂⁻ = 193
Standard deviation of the sample S₂ = 37
Step(ii):-
Standard error of two population means
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]
Degrees of freedom
ν = n₁ +n₂ -2 = 100 +100 -2 = 198
t₀.₁₀ = 1.6526
Step(iii):-
90% confidence interval for the difference between the two population means
[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]
(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)
(-15-8.4166 , -15 + 8.4166)
( -23.4166 , -6.5834)
Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below: Write the number shown on the calculator display in standard form. A. 60,466,176 B. 600,000,000 C. 6,000,000,000 D. 60,000,000,000
Answer:
d. 60000000000
Step-by-step explanation:
Answer:
The answer is D. 60,000,000,000
Step-by-step explanation:
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?
Answer:
eddfdgdccggģdffcdrrfxddxcvgfx
A technician is testing light bulbs to determine the number of defective bulbs. The technician records the table below to show the results. Result of Light Bulb Test Number of Bulbs Tested 14 28 84 336 Number of Defective Bulbs Found 1 2 6 ? The technician expects to find 24 defective bulbs when 336 are tested. Which statement explains whether the technician’s reasoning is correct, based on the information in the table?
Answer:
He should find 24 defective lightbulbs.
Step-by-step explanation:
1. Divide the number of defective bulbs by the total number of bulbs for each section.
2. Make sure the number you get is the same each time.
3. Divide the guessed number of bulbs (24) by the total number of bulbs (336)
4. If the number you got for step 4 matches the number you got for step 3, then he is right
Answer:
The answer is A
Step-by-step explanation:
on NCCA
a collection of quantitative or numerical data that describes a property of an object or event.
metric system
1.base unit
2.number
3.units
4.measure
5.SI system
Answer:
measure
Step-by-step explanation:
The collection of quantitative or numerical data that describes a property of an object or event is called a measured/measurement.
The SI Unit is a metric system. An example of an SI Unit is the kilogram, centimeter, second, etc.
Measurements are made by comparing a particular quantity with an SI unit or assigning numbers to certain objects in a way that reflects its value.
A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5
questions if you guess randomly on each question?
The answer is 1/2 because there are total 10 questions. So, the probability of getting 5 correct answers is 5/10 that is 1/2.
Mark me as brainleist
Look at the figure below. which ratio represents tan 0?
A -5/4, B -4/5, C -3/4, D 3/5.
The required value of the tanФ is given as -3/4. C option is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.
here,
Tan(180 - Ф) = -tanФ = perpendicular / base
From figure, perpendicular= 12 and base = 16
-tanФ = 12 / 16
tanФ = -3/4
Thus, the required value of the tanФ is given as -3/4. C option is correct.
Learn more about trigonometry equations here:
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A classroom has 35 students. If the ratio of boys to girls was 5:2, , how many girls were in the class
Answer:
35/14
Step-by-step explanation: 35/14
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
35/14 is your answer.
Answer:
10 girls.
Step-by-step explanation:
Boys: 5x
Girls: 2x
next... 5x + 2x = 35
7x= 35
x=5
Answer. 10 girls.
Hello again. if someone gives me a hand with this book thickness excercise please thanks
Answer:
Known:
• a book have front, back and 200 pages
• front= 0.7 mm
• back= 0.7 mm
• each page= 0,14 mm
ask:
calculate the minimum thickness...?
answer:
a. 200 p × 0,14 = 28 mm
b. front + back = 0.7+0.7= 1.4 mm
Thickness= 28+1,4 = 29,4 mm
I hope this helps
if u have question let me know in comments^_^
Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043 Keith reads that the mean nap is 22 minutes. The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. 1.39 or 1.43 or 2.88 or 0.70
Answer:
The t-statistic is [tex]t = 0.6956[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 22 \ minutes[/tex]
The standard deviation is [tex]s = 7.043[/tex]
The given data is 23, 35, 17, 30, 20, and 19.
Generally the sample mean is mathematically evaluated as
[tex]\= x = \frac{23+ 35+17+ 30+ 20+ 19 }{6}[/tex]
[tex]\= x =24[/tex]
The t-statistic is mathematically evaluated as
[tex]t = \frac{ \= x - \mu }{\frac{s}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 24 - 22 }{\frac{ 7.043}{ \sqrt{6} } }[/tex]
=> [tex]t = 0.6956[/tex]
Answer: 0.70
Step-by-step explanation:
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 3%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that
Answer:
The probability that none of the LED light bulbs are defective is 0.7374.
Step-by-step explanation:
The complete question is:
What is the probability that none of the LED light bulbs are defective?
Solution:
Let the random variable X represent the number of defective LED light bulbs.
The probability of a LED light bulb being defective is, P (X) = p = 0.03.
A random sample of n = 10 LED light bulbs is selected.
The event of a specific LED light bulb being defective is independent of the other bulbs.
The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.
The probability mass function of X is:
[tex]P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...[/tex]
Compute the probability that none of the LED light bulbs are defective as follows:
[tex]P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}[/tex]
[tex]=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374[/tex]
Thus, the probability that none of the LED light bulbs are defective is 0.7374.
1f 12% of x is equal to 6% of y, then 18% of x will be equal to how much percent ofy?
Answer:
9%
Step-by-step explanation:
12x=6y eq 1
18x=9y eq 2
A baseball is hit 3 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the maximum height. Round your answer to the nearest integer.
Answer:
53
Step-by-step explanation:
i used an angle of 45 degrees.
Distance from ground = 3feets
Angle = 45⁰
U is the initial velocity = 80ft/sec
g = 32
The question wants us to vfind maximum height
We have
r(t) = (80cos45⁰)ti + [3 + 80sin45⁰]t - 0.5(32)t²
We know cos 45 is also sin45 = 1/√2
r(t) = (40√2)ti + [3+40√2]t - 16t²
When we differentiate with respect to t:
r'(t) = (40√2)i + (40√2 - 32t)
= 40√2 =32t
t = 40√2/32
t= 20√2/16
We put the value of t into (3 + 40√2)t -16t²
When we substitute and simplify this we have
3 + 56.57 + 1.77 -16 +8
= 53.34
Which is approximately 53.
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen and bedroom)?
Answer:
The area of the house is A. 1,108
area please it's easy plzzzzzzzzzz
a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.
Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²
The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²
b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.
Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,
Area of Striped Region : 40 - 22 = 18 m²
write 32 1/2 in radical form
Answer:
Nothing further, the simplest answer is 32 1/2
Step-by-step explanation:
Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a confidence level of 98%, and use the results from a prior Harris poll that gave a confidence interval of (0.44, 0.51) for the proportion of Democrats who have a sibling.
Answer:
The minimum sample size is [tex]n =135[/tex]
Step-by-step explanation:
From the question we are told that
The confidence interval is [tex]( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)[/tex]
The margin of error is [tex]E = 0.1[/tex]
Generally the sample proportion can be mathematically evaluated as
[tex]\r p = \frac{ upper \ limit + lower \ limit }{2}[/tex]
[tex]\r p = \frac{ 0.51 + 0.44}{2}[/tex]
[tex]\r p = 0.475[/tex]
Given that the confidence level is 98% then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 98[/tex]
[tex]\alpha = 2\%[/tex]
[tex]\alpha =0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
Generally the minimum sample size is evaluated as
[tex]n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )[/tex]
[tex]n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )[/tex]
[tex]n =135[/tex]
The mean temperature for the first 4 days in January was 8°C. The mean temperature for the first 5 days in January was 7°C. What was the temperature on the 5th day? SOMEONE HELP FIRST ANSWER BRAINLIEST THIS TIME I PROMISE LOL
Answer:
The temperature of the 5th day was 3°C
Step-by-step explanation:
Mean temperature of the first 4 days = 8°C
Note that:
Mean = Sum of temperatures ÷ number of days
∴ 8 = sum of temperature ÷ 4
[tex]= 8 = \frac{sum\ of\ temperatures}{4}[/tex]
[tex]= sum\ of\ temperatures\ = 8\ \times\ 4 = 32[/tex]
Therefore the sum of the first 4 days = 32
Let the temperature of the next day (the fifth day) be m
Hence,
sum of the temperatures of first 5 days = 32 + m - - - - (1)
Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:
Mean temperature of the first 5 days = 7
[tex]Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)[/tex]
Now, you will notice that equation (1) = equation (2)
∴ 32 + m = 35
m = 35 - 32 = 3
therefore, the temperature of the 5th day was 3°C
