The probability of winning at least one prize is 0.40951.
What is probability?Probability is the likelihood that an event will occur.
The following information can be deduced:
P = probability of winning = 1/10
q = probability of not winning = 1- (1/10) = 9/10
x = no. of winning
then, p (x ≥ 1) = 1 - p (x < 1)
= 1 - p (x=0)
= 1 - ⁵C₀ (1/10)^⁰ (9/10)^(5-0)
= 1 - (1) (1) (9/10)^5
= 1 - (9/10)^5
= 1 - 0.59049
= 0.40951
Therefore, the probability is 0.40951.
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Levi makes the minimum salary for actuary. Andres maybe the median salary for cpa. Who makes more money
Answer:
Andres
why?
Because he is median salary for cpa
Please help !! Only answer if 100% it is correct :)
Answer:
F(x) moved right 2 units to become G(X).
According to graph transformations, that means G(X) = F(X - 2) = [tex](X-2)^{3}[/tex].
I think that's how you do it :\
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams
Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]
Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.
Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:
[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:
[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]
Divide both sides by 9:
[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]
By logarithm properties:
[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]
Solve for t:
[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]
So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
On Friday Evelyn sold 9 dresses and 20 pairs of pants. On Saturday she sold twice as many dresses and 10 more pants than Friday. How many dresses did Evelyn sell on Friday and Saturday?
Answer: 27 Dresses and 50 Pants
Step-by-step explanation:
If she sold 9 pairs of pants and
9 x 2 = 18
18 + 9 = 27
20 + 10 = 30
30 + 20 = 50
Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.
Evelyn's sales of dresses and pants over two days, Friday and Saturday. We'll use some mathematical expressions and reasoning to find out how many dresses Evelyn sold on each day.
Let's start by assigning some variables to represent the number of dresses and pants Evelyn sold on Friday and Saturday. We'll use "F" for Friday and "S" for Saturday. So, let [tex]D_F[/tex] be the number of dresses sold on Friday, [tex]D_S[/tex] be the number of dresses sold on Saturday, [tex]P_F[/tex] be the number of pants sold on Friday, and [tex]P_S[/tex] be the number of pants sold on Saturday.
According to the problem, on Friday, Evelyn sold 9 dresses, which can be expressed as:
[tex]D_F[/tex] = 9
She also sold 20 pairs of pants on Friday:
[tex]P_F[/tex] = 20
Now, let's move on to Saturday's sales. It says she sold twice as many dresses as Friday, which means the number of dresses on Saturday is double that of Friday's sales:
[tex]D_S = 2 * D_F[/tex]
Additionally, she sold 10 more pairs of pants on Saturday compared to Friday:
[tex]P_S = P_F + 10[/tex]
We already know that [tex]D_F = 9[/tex], so we can find the number of dresses sold on Saturday by substituting this value into the equation for [tex]D_S[/tex]:
[tex]D_S = 2 * 9 = 18[/tex]
Next, we'll calculate the number of pants sold on Saturday using the given information. Since [tex]P_F = 20[/tex], we can find [tex]P_S[/tex]:
[tex]P_S = 20 + 10 = 30[/tex]
So, to summarize, Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.
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What is the gradient of the blue line?
5
4
3
2
1
-5 -4 -3 -2 - 1 0 1. 2. 3. 4. 5
- 1
- 2
- 3
- 4
- 5
The line starts at (-5,3) and finishes (5,0.5)
Answer:
The gradient is -0.25
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-5,3)[/tex]
[tex](x_2,y_2) = (5,0.5)[/tex]
Required
The gradient (m)
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{0.5-3}{5--5}[/tex]
[tex]m = \frac{-2.5}{10}[/tex]
[tex]m = -0.25[/tex]
PRACTICE
Find and circle the verb to be in the text about
Sean Canty.
2 a Practice the verb to be.
5 b
2. We are
1.1
.... at home.
in the classroom.
3. My father ............. at work now.
4. My grandmother ....... alive.
5. It ............. Saturday today.
1. What
2
-
3. Whe
4. How
5. Wha
2h
jvdhvfggvvvbbbbbbbbb
If you select a random sample of 6 people, what is the probability that all but one of them are using Chrome as their browser? (show all work - use data below)
Use the data provided below:
Chrome: 52.57%
Safari: 31.17%
Firefox: 4.29%
Edge: 2.91%
IE: 2.47%
Samsung: 2.36%
Answer:
0.1143 = 11.43% probability that all but one of them are using Chrome as their browser
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they use Chrome, or they do not. The probability of a person using Chrome is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Chrome: 52.57%
This means that [tex]p = 0.5257[/tex]
Sample of 6 people
This means that [tex]n = 6[/tex]
What is the probability that all but one of them are using Chrome as their browser?
5 using Chrome, so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{6,5}.(0.5257)^{5}.(1-0.5257)^{1} = 0.1143[/tex]
0.1143 = 11.43% probability that all but one of them are using Chrome as their browser
If s(x)= 2 -x^2 and f(x)=3x, which value is equivalent to (s°f)(-7)
please help On a coordinate plane, a point is 4 units to the left and 1 unit down.
For the point shown:
The x-coordinate is
The y-coordinate is
.
g The point is in quadrant
.
Answer:
assuming that you start at the origin (0,0)
(-4,-1) would be the poiny
x coord = -4
y coord = -1
the point is in the 3 quadrant
Step-by-step explanation:
8. The point in a distribution below which 75% of the cases lie in the?
A 3rd decile
B. 7th percentile C. 3rd quartile D. 1st quartile
Answer:
C. 3rd quartile
Step-by-step explanation:
Percentile:
A data belonging to the xth percentile means that the data is greater than x% of the values of the data-set, and smaller than (100 - x)%.
Point below 75% of the cases lie:
This is the 75th percentile, which is the 3rd quartile, as 75 = 3*100/4. Thus, the correct answer is given by option c.
With the information that you gather from the summary tables, test the following (you can use excel when appropriate): Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance. Determine if there is sufficient evidence to conclude the average amount of deaths is equal to 6000 in the United States and territories at the 0.10 level of significance. Determine if there is sufficient evidence to conclude the average amount of marriages is greater or equal to 2500 in the United States and territories at the .05 level of significance. Determine if there is sufficient evidence to conclude the average amount of divorces is less than or equal to 4000 in the United States and territories at the 0.10 level of significance.
Answer:
Kindly check explanation
Step-by-step explanation:
A.)
H0 : μ = 5000
H0 : μ > 5000
xbar = 6671 ; s = 8185.21 ; n = 52 ; α = 0.05
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (6671 - 5000) ÷ (8185.21/√52)
T = 3.814
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at 3.814; 51 = 0.000185
Pvalue < α ; Reject H0 and conclude that average birth is greater than 5000
B)
H0 : μ = 6000
H0 : μ < 6000
xbar = 4187 ; s = 4386 ; n = 52 ; α = 0.01
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (4187 - 6000) ÷ (4386/√52)
T = - 2.981
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at - 2.981; 51 = 0.0022
Pvalue < α ; Reject H0 and conclude that average death is less than 6000
C.)
H0 : μ < 2500
H0 : μ ≥ 2500
xbar = 2744 ; s = 3134.41 ; n = 52 ; α = 0.05
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (2744 - 2500) ÷ (3134.41/√52)
T = 0.561
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at 0.561; 51 = 0.289
Pvalue > α ; Fail to Reject H0 and conclude that average marriage is not greater Tha or equal to 2500
D.)
H0 : μ = 4000
H0 : μ ≤ 4000
xbar = 1451 ; s = 1217 ; n = 52 ; α = 0.01
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (1451 - 4000) ÷ (1217/√52)
T = - 15.10
Pvalue from Test statistic : ; df = n - 1 = 52-1= 51
Pvalue at - 15.10; 51 = 0.000001
Pvalue < α ; Reject H0 and conclude that average divorce is less eqaul to 4000
Which statement is true about the equations
-3x + 4y = 12 and 1/4x-1/3y = 1
O The system of the equations has exactly one solution at (-8, 3).
O The system of the equations has exactly one solution at (-4, 3).
O The system of the equations has no solution; the two lines are parallel.
O The system of the equations has an infinite number of solutions represented by either equation.
To test for the significance of a regression model involving 3 independent variables and 51 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.
Answer:
numerator degree of freedom = 3
Denominator degree of freedom = 47
Step-by-step explanation:
The numerator degree of freedom is given by :
p - 1 ; where p = number of predictors ;
p = number of independent variables + 1
Number of independent variables = 3
p = 3 + 1 = 4
Numerator degree of freedom = p - 1 = 4 - 1 = 3
The denominator degree of freedom = n - p ; where n = number of observations
Number of observations, n = 51
Denominator degree of freedom = n - p = 51 - 4 = 47
2.According to www.city-data, the mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000. Check the three assumptions associated with the Central Limit Theorem. What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009
Answer:
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.
This means that [tex]\mu = 192723, \sigma = 42000[/tex]
Sample of 75:
This means that [tex]n = 75, s = \frac{42000}{\sqrt{75}}[/tex]
What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?
1 subtracted by the p-value of Z when X = 190000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}[/tex]
[tex]Z = -0.56[/tex]
[tex]Z = -0.56[/tex] has a p-value of 0.2877
1 - 0.2877 = 0.7123
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.
if a plane can travel 500 miles per hour with wind and 400 miles per hour against the wind find the speed of the plane with out a wind and speed of the wind.
Answer: hello there here is your answer:
Still air speed:450 mph.
Step-by-step explanation:
500-450=450-400=50 mph
Still air speed:450 mph. Wind speed:50 mph..
hope this help have a good day
If U= {1,2,3,......8} , A={1,4,6,7} , B= {2,4,5,7} & C= {3,5,6,7} prove that 1) An( BUC ) = ( AnB) U ( AnC ). 2) AU (BnC)= (AUB) n ( AUC )
Step-by-step explanation:
BUC={2,3,4,5,6,7}
An(BUC)={4,6,7}
AnB={4,7},AnC={6,7}
(AnB)U(AnC)={4,6,7}
Au(BnC)={1,4,5,6,7}
(AUB)n(AUC)= {1,4,5,6,7}
If three sandwiches and two bags of chips cost
$22.00, and two sandwiches and one bag of chips
cost $14.25, how much does a bag of chips cost?
Answer:
Chips: 1.25 and Sandwiches: 6.5
Step-by-step explanation:
3s+2c=22
2s+c=14.25
The cost of bag and chips should be 1.25 and 6.5.
The calculation is as follows:3s+2c=22
2s+c=14.25
Here we need to multiply by 2 in equation 2
3s + 2c = 22
2s + 2c = 28.25
s = 6.5
Now
c should be
2(6.5) + c = 14.25
13 + c = 14.25
c = 1.25
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In a right triangle, the lengths of the two legs are 8 cm and 10 cm respectively. Find the hypotenuse of the triangle.
9 cm
10.5 cm
12 cm
12.8 cm
12.8, pythagorean theorem.
Can someone answer? Please I tried everything I don’t know how to do this.
Step-by-step explanation:
-7.2(x-15.6)= -9-7.2x+112.32= -9-7.2x= -9-112.32-7.2x= -121.32x= -121.32/ -7.2x=16.85hope it helps.stay safe healthy and happy.2.
The height of a kicked football can be represented by the polynomial - 16+ + 22t+
3, where tis the time in seconds. Find the factored form of the polynomial.
-
5
A) (8t + 3)(-2t + 1)
OB) (-8t+ 3)(2t+ 1)
8
OC) (8t+ 1)(-2t + 3)
OD) (-8t + 1)(2t+ 3)
Pls answer this last question in full method
Answer:
if the sum of two angles is 90° they are said to be complementary
If one angle is x
the other should be (90 - x)°
so the complementary angle of x is (90 - x)
You have some money to invest in one of two accounts. The first account pays
5% simple interest, and the second pays 4% compound interest. How would
you decide which account to use? Discuss your answer.
Answer:
compound interest
Step-by-step explanation:
compound interest yields higher profit than simple interest
Answer:
the simple interest function will be greater in the beginning, but the
compound interest equation will overtake the simple after a while.
it appears that the 4% compound equation will overtake the simple at about 10 years
Step-by-step explanation:
[tex]1 + .05t = 1(1.04)^t[/tex]
6. Calculate the area of the octagon in the
figure below.
Answer:
[tex]41\text{ [units squared]}[/tex]
Step-by-step explanation:
The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.
The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:
4 triangles (corners)3 rectangles (one in the middle, two on top after you remove triangles)Formulas:
Area of rectangle with length [tex]l[/tex] and width [tex]w[/tex]: [tex]A=lw[/tex] Area of triangle with base [tex]b[/tex] and height [tex]h[/tex]: [tex]A=\frac{1}{2}bh[/tex]Area of triangles:
All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.
Thus, the total area of one is [tex]A=\frac{1}{2}\cdot 2\cdot 2=2\text{ square units}[/tex]
The area of all four is then [tex]2\cdot 4=8[/tex] units squared.
Area of rectangles:
The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of [tex]3\cdot 2=6[/tex] units squared, and the both of them have a total area of [tex]6\cdot 2=12[/tex] units squared.
The last rectangle has a width of 7 and a height of 3 for a total area of [tex]7\cdot 3=21[/tex] units squared.
Therefore, the area of the entire octagon is [tex]8+12+21=\boxed{41\text{ [units squared]}}[/tex]
A survey was held to find the time taken by students to reach school from
their homes. Each student was asked to choose from 5, 10, 15, 20, or 25
minutes.
Number of
Minutes 5 10 15 20 25
Number of
Students
11
8
2
3
6
What is the mode for the data set?
A. 5 min b. 10 min c. 20 min d. 25 min
Hello,
in France, the mode is the value having the greater repetition
mode= 5 (repetition=11)
How do I solve this?
The answer for the first line segment : (-3,-7) (-4,0)
The answer for 2nd line segment is :(-3,8) (-9,-5)
Step-by-step explanation:
Let do line segment QR and ST. first.
Step 1: Find a line that contains a points that is perpendicular to the line of reflection
"A reflection of a pre image and new image is perpendicular to the line of reflection.
This means for points Q,S,T and R, there is a line that. contains one point that is perpendicular to the line of reflection.
A line that is perpendicular to the line of reflection is the negative reciprocal of the slope so this means all 4 lines must be on a different slopes but the slopes must be 1/2.
To simplify, things, here are the lines that will all 4 points be on
Point R will be on line y=1/2x-11/2Point Q will be on line y=1/2x+2Point S will be on line y=1/2x+19/2Point T will be on line y=1/2x-1/2Step 2: Find a point where both the line and line of reflection intersect at.
Now we need to find a line where both the line of reflections and the 4 lines will intersect at separately.
The line with Point R will intersect with the line of reflection at point (1,-5)The line with Point Q will intersect with line of reflection at Point (-2,1)The line with Point S will intersect at point (-5,7)The line worth Point T will intersect at Point(-1,-1).Step 3: Find the endpoints given the midpoint and the originally endpoint.
A reflection per and new image is equidistant from the point of reflection. So we. an say that the point where the line intersect is the midpoint of the pre and new image.
Using this info,
The endpoint for R prime is (-3, -7).The endpoint for Q prime is (-4,0). The endpoint of S prime is (-3,8).The endpoint of T prime is (-9,-5).Connect R prime and Q prime. And that the new line segments
Connects S prime and T prime and that the new line segments.
Which of the following is equivalent to the expression log2a=r? 2a = r logr2 = a 2r = a log2r = a
9514 1404 393
Answer:
(c) 2^r = a
Step-by-step explanation:
The relationship between log forms and exponential forms is ...
[tex]\log_2(a)=r\ \Leftrightarrow\ 2^r=a[/tex]
__
Additional comment
I find this easier to remember if I think of a logarithm as being an exponent.
Here, the log is r, so that is the exponent of the base, 2.
This equivalence can also help you remember that the rules of logarithms are very similar to the rules of exponents.
Answer: Choice C) [tex]2^r = a[/tex]
This is the same as writing 2^r = a
==========================================================
Explanation:
Assuming that '2' is the base of the log, then we'd go from [tex]\log_2(a) = r[/tex] to [tex]2^r = a[/tex]
In either equation, the 2 is a base of some kind. It's the base of the log and it's the base of the exponent.
The purpose of logs is to invert exponential operations and help isolate the exponent. A useful phrase to help remember this may be: "if the exponent is in the trees, then we need to log it down".
The general rule is that [tex]\log_b(y) = x[/tex] converts to [tex]y = b^x[/tex] and vice versa.
Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.
Answer:
[tex]\bar x = 107.11[/tex]
[tex]\sigma_x = 31.07[/tex]
Step-by-step explanation:
See comment for complete question
Given
[tex]x: 97\ 178\ 129\ 90\ 75\ 94\ 116\ 100\ 85[/tex]
Solving (a): The sample mean
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{97+ 178+ 129+ 90+ 75+ 94+ 116+ 100+ 85}{9}[/tex]
[tex]\bar x = \frac{964}{9}[/tex]
[tex]\bar x = 107.11[/tex]
Solving (b): The sample standard deviation
This is calculated as:
[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{(97 - 107.11)^2 +.............+ (85- 107.11)^2 }{9-1}}[/tex]
[tex]\sigma_x = \sqrt{\frac{7720.8889}{8}}[/tex]
[tex]\sigma_x = \sqrt{965.1111125}[/tex]
[tex]\sigma_x = 31.07[/tex]
Know idea how to get an answer to this
Step-by-step explanation:
k=8.6
i think it is the right answer
Select the correct answer.
Which is the simplified form of the expression ?
Answer:
a) b^5/12
Step-by-step explanation:
b^2/3 ÷ b^1/4 [if bases are the same then subtract the exponents]
2/3 - 1/4 = 5/12
A test taker gets 70 on 1st exam, 80 on 2nd exam, 2/3 of 4/5 of his 2nd exam on his 3rd test. If the professor gives 5 points extra credit on his 4th exam and his average score is 80, what was his score on the 4th exam
=================================================
Explanation:
The phrasing "2/3 of 4/5 of his 2nd exam on his 3rd test" is a bit clunky in my opinion. It seems more complicated than it has to be.
The student got 80 on the second exam. 4/5 of this is (4/5)*80 = 0.8*80 = 64. Then we take 2/3 of this to get (2/3)*64 = 42.667 approximately. If we assume only whole number scores are given, then this would round to 43.
Let x be the score on the fourth exam. Since 5 points of extra credit are given, the student actually got x+5 points on this exam.
So we have these scores
first exam = 70second exam = 80third exam = 43fourth exam = x+5Adding up these scores and dividing by 4 will get us the average
(sum of scores)/(number of scores) = average
(70+80+43+x+5)/4 = 80
(x+198)/4 = 80
x+198 = 4*80
x+198 = 320
x = 320 - 198
x = 122
So the student got a score of x+5 = 122+5 = 127 on the fourth exam.